{"id":39700,"date":"2026-08-06T15:56:18","date_gmt":"2026-08-06T15:56:18","guid":{"rendered":"https:\/\/mp.moonpreneur.com\/math-corner\/?p=39700"},"modified":"2026-08-06T16:02:19","modified_gmt":"2026-08-06T16:02:19","slug":"integral-of-1-x","status":"publish","type":"post","link":"https:\/\/mp.moonpreneur.com\/math-corner\/integral-of-1-x\/","title":{"rendered":"Integral of 1\/x: Formula, Proof, Examples &#038; Rules"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"39700\" class=\"elementor elementor-39700\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t<div class=\"elementor-inner\">\n\t\t\t\t<div class=\"elementor-section-wrap\">\n\t\t\t\t\t\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-6c8e233 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6c8e233\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a6fa447\" data-id=\"a6fa447\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db2bbcc elementor-widget elementor-widget-text-editor\" data-id=\"db2bbcc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The <\/span><b>integral of 1\/x<\/b><span style=\"font-weight: 400;\"> is one of the most important formulas in calculus. Unlike most algebraic functions, it <\/span><b>cannot be integrated using the standard power rule<\/b><span style=\"font-weight: 400;\">. Instead, it has a unique logarithmic result that every calculus student should know.<\/span><\/p><p><span style=\"font-weight: 400;\">The formula is:<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-81bdfff elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"81bdfff\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-87c0df6\" data-id=\"87c0df6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-be426a9 elementor-widget elementor-widget-html\" data-id=\"be426a9\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:700px;margin:25px auto;padding:25px;border-radius:16px;background:#fffdf3;border-left:8px solid #f4b400;text-align:center;box-shadow:0 8px 18px rgba(0,0,0,.08);\">\r\n\r\n<h3 style=\"margin-top:0;color:#b57a00;\">\ud83d\udcd8 Integral of 1\/x Formula<\/h3>\r\n\r\n<div style=\"font-size:32px;font-weight:bold;color:#222;margin:18px 0;\">\r\n\u222b 1\/x dx = ln|x| + C\r\n<\/div>\r\n\r\n<p style=\"font-size:16px;color:#555;margin:0;\">\r\nThe logarithmic rule used when the exponent is <strong>\u22121<\/strong>.\r\n<\/p>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-5a50ba1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5a50ba1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-571df3d\" data-id=\"571df3d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-aca79e1 elementor-widget elementor-widget-text-editor\" data-id=\"aca79e1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">where:<\/span><\/p><ul><li style=\"font-weight: 400;\" aria-level=\"1\"><b>ln<\/b><span style=\"font-weight: 400;\"> is the natural logarithm.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>|x|<\/b><span style=\"font-weight: 400;\"> is the absolute value of x.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><b>C<\/b><span style=\"font-weight: 400;\"> is the constant of integration.<\/span><\/li><\/ul><p><span style=\"font-weight: 400;\">Understanding why this formula is different\u2014and how it compares with similar integrals like the <\/span><b>integral of 1\/x\u00b2<\/b><span style=\"font-weight: 400;\"> and the <\/span><b>integral of 1\/(1+x\u00b2)<\/b><span style=\"font-weight: 400;\">\u2014helps build a strong foundation in integration.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-1b0c1b5 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1b0c1b5\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-70744e9\" data-id=\"70744e9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6066da4 elementor-widget elementor-widget-text-editor\" data-id=\"6066da4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h2><b>Integral of 1\/x Formula<\/b><\/h2>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-fb86fa3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fb86fa3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-42bd084\" data-id=\"42bd084\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-28cbba0 elementor-widget elementor-widget-text-editor\" data-id=\"28cbba0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">The standard formula is:<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-264707b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"264707b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-16f0289\" data-id=\"16f0289\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-55a842b elementor-widget elementor-widget-html\" data-id=\"55a842b\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"border:2px solid #f4b400;border-radius:12px;padding:20px;background:#fffef8;margin:30px 0;\">\r\n\r\n<h3 style=\"margin-top:0;color:#b57a00;\">\u26a0 Why Doesn't the Power Rule Work?<\/h3>\r\n\r\n<p>The power rule says:<\/p>\r\n\r\n<div style=\"font-size:24px;font-weight:bold;text-align:center;padding:15px 0;\">\r\n\u222b x<sup>n<\/sup> dx = x<sup>n+1<\/sup> \/(n+1) + C\r\n<\/div>\r\n\r\n<p>For <strong>1\/x<\/strong>, the exponent is <strong>\u22121<\/strong>.<\/p>\r\n\r\n<div style=\"background:#fff6d5;padding:14px;border-radius:10px;text-align:center;font-size:22px;font-weight:bold;\">\r\nn + 1 = \u22121 + 1 = 0\r\n<\/div>\r\n\r\n<p style=\"margin-bottom:0;\">\r\nSince dividing by zero is impossible, the power rule cannot be used.\r\nInstead:\r\n<\/p>\r\n\r\n<div style=\"margin-top:15px;font-size:26px;font-weight:bold;text-align:center;color:#b57a00;\">\r\n\u222b1\/x dx = ln|x| + C\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-a16e6fc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a16e6fc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-0268098\" data-id=\"0268098\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-eb49499 elementor-widget elementor-widget-html\" data-id=\"eb49499\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"background:#f9fbff;border-radius:15px;padding:22px;margin:30px 0;border-left:7px solid #3b82f6;\">\r\n\r\n<h3 style=\"margin-top:0;color:#2563eb;\">\u2714 Quick Proof<\/h3>\r\nThe easiest way to verify the formula is by differentiation. <br \/>\r\nSuppose:\r\n\r\n<div style=\"font-size:22px;text-align:center;margin:15px 0;\">\r\nF(x)=ln\u2223x\u2223\r\n<\/div>\r\n\r\n<p style=\"margin-bottom:0;\">\r\nDifferentiate both sides:\r\n<div style=\"font-size:22px;text-align:center;margin:15px 0;\">\r\nd\/dx\u200b(ln\u2223x\u2223)=1\/x\r\n<\/div>\r\nSince differentiating <strong>ln|x|<\/strong> gives back\r\n<strong>1\/x<\/strong>, its antiderivative must be:\r\n<\/p>\r\n\r\n<div style=\"font-size:28px;font-weight:bold;text-align:center;margin-top:18px;\">\r\n\u222b1\/x dx = ln|x| + C\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-ebf818e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ebf818e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-f830711\" data-id=\"f830711\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-22939f0 elementor-widget elementor-widget-text-editor\" data-id=\"22939f0\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h2><b>Solved Examples<\/b><\/h2>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-23503ef elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"23503ef\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-dc909b4\" data-id=\"dc909b4\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f90772b elementor-widget elementor-widget-html\" data-id=\"f90772b\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:750px;margin:30px auto;background:#fff;border:1px solid #eee;border-radius:16px;overflow:hidden;box-shadow:0 8px 20px rgba(0,0,0,.08);\">\r\n\r\n<div style=\"background:#f4b400;color:#fff;padding:15px 20px;\">\r\n<h3 style=\"margin:0;\">Example 1<\/h3>\r\n<\/div>\r\n\r\n<div style=\"padding:22px;\">\r\n\r\n<p><strong>Find<\/strong><\/p>\r\n\r\n<div style=\"background:#fff9dc;padding:18px;border-radius:10px;text-align:center;font-size:28px;font-weight:bold;\">\r\n\u222b 1\/x dx\r\n<\/div>\r\n\r\n<div style=\"margin-top:25px;border-left:5px solid #f4b400;padding-left:18px;\">\r\n\r\n<h4 style=\"margin-top:0;color:#b57a00;\">Solution<\/h4>\r\n\r\n<p>Using the formula directly,<\/p>\r\n\r\n<div style=\"background:#f7f7f7;padding:18px;border-radius:10px;text-align:center;font-size:26px;font-weight:bold;\">\r\n\u222b 1\/x dx = ln|x| + C\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-d3234d1 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"d3234d1\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-f4fd608\" data-id=\"f4fd608\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ea8ca80 elementor-widget elementor-widget-html\" data-id=\"ea8ca80\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:750px;margin:30px auto;background:#fff;border:1px solid #eee;border-radius:16px;overflow:hidden;box-shadow:0 8px 20px rgba(0,0,0,.08);\">\r\n\r\n<div style=\"background:#f4b400;color:#fff;padding:15px 20px;\">\r\n<h3 style=\"margin:0;\">Example 2<\/h3>\r\n<\/div>\r\n\r\n<div style=\"padding:22px;\">\r\n\r\n<p><strong>Find<\/strong><\/p>\r\n\r\n<div style=\"background:#fff9dc;padding:18px;border-radius:10px;text-align:center;font-size:28px;font-weight:bold;\">\r\n\u222b 5\/x dx\r\n<\/div>\r\n\r\n<div style=\"margin-top:25px;border-left:5px solid #f4b400;padding-left:18px;\">\r\n\r\n<h4 style=\"margin-top:0;color:#b57a00;\">Solution<\/h4>\r\n\r\n<p>Take the constant outside:<\/p>\r\n\r\n<div style=\"background:#f7f7f7;padding:15px;border-radius:10px;text-align:center;font-size:24px;\">\r\n5 \u222b 1\/x dx\r\n<\/div>\r\n\r\n<div style=\"text-align:center;font-size:22px;margin:15px 0;\">\r\n\u2193\r\n<\/div>\r\n\r\n<div style=\"background:#fff9dc;padding:15px;border-radius:10px;text-align:center;font-size:24px;\">\r\n= 5 ln|x| + C\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-db83633\" data-id=\"db83633\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ae27efe elementor-widget elementor-widget-html\" data-id=\"ae27efe\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:750px;margin:30px auto;background:#fff;border:1px solid #eee;border-radius:16px;overflow:hidden;box-shadow:0 8px 20px rgba(0,0,0,.08);\">\r\n\r\n<div style=\"background:#f4b400;color:#fff;padding:15px 20px;\">\r\n<h3 style=\"margin:0;\">Example 3<\/h3>\r\n<\/div>\r\n\r\n<div style=\"padding:22px;\">\r\n\r\n<p><strong>Find<\/strong><\/p>\r\n\r\n<div style=\"background:#fff9dc;padding:18px;border-radius:10px;text-align:center;font-size:28px;font-weight:bold;\">\r\n\u222b 3\/x dx\r\n<\/div>\r\n\r\n<div style=\"margin-top:25px;border-left:5px solid #f4b400;padding-left:18px;\">\r\n\r\n<h4 style=\"margin-top:0;color:#b57a00;\">Solution<\/h4>\r\n\r\n<p>Using the constant multiple rule,<\/p>\r\n\r\n<div style=\"background:#f7f7f7;padding:15px;border-radius:10px;text-align:center;font-size:24px;\">\r\n3 \u222b 1\/x dx\r\n<\/div>\r\n\r\n<div style=\"text-align:center;font-size:22px;margin:15px 0;\">\r\n\u2193\r\n<\/div>\r\n\r\n<div style=\"background:#fff9dc;padding:15px;border-radius:10px;text-align:center;font-size:24px;\">\r\n= 3 ln|x| + C\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-4d9ee6f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4d9ee6f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ef0ef7d\" data-id=\"ef0ef7d\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6ddb0de elementor-widget elementor-widget-text-editor\" data-id=\"6ddb0de\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h2><b>Similar Integrals You Should Know<\/b><\/h2>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-52b87e9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"52b87e9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-73d6f4c\" data-id=\"73d6f4c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-400dfab elementor-widget elementor-widget-text-editor\" data-id=\"400dfab\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Many students confuse the <\/span><b>integral of 1\/x<\/b><span style=\"font-weight: 400;\"> with other common integrals. Here&#8217;s how they differ.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-00f0232 elementor-widget elementor-widget-html\" data-id=\"00f0232\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"overflow-x:auto;margin:35px 0;\">\r\n\r\n<table style=\"width:100%;border-collapse:collapse;font-size:16px;\">\r\n\r\n<thead>\r\n\r\n<tr style=\"background:#f4b400;color:#fff;\">\r\n\r\n<th style=\"padding:15px;\">Function<\/th>\r\n\r\n<th style=\"padding:15px;\">Integral<\/th>\r\n\r\n<th style=\"padding:15px;\">Rule Used<\/th>\r\n\r\n<\/tr>\r\n\r\n<\/thead>\r\n\r\n<tbody>\r\n\r\n<tr style=\"background:#fffdf3;\">\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>1\/x<\/strong><\/td>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\">ln|x| + C<\/td>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\">Logarithmic Rule<\/td>\r\n\r\n<\/tr>\r\n\r\n<tr>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>1\/x\u00b2<\/strong><\/td>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\">\u22121\/x + C<\/td>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\">Power Rule<\/td>\r\n\r\n<\/tr>\r\n\r\n<tr style=\"background:#fffdf3;\">\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>1\/(1+x\u00b2)<\/strong><\/td>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\">tan\u207b\u00b9(x) + C<\/td>\r\n\r\n<td style=\"padding:14px;border:1px solid #eee;\">Inverse Trigonometric Rule<\/td>\r\n\r\n<\/tr>\r\n\r\n<\/tbody>\r\n\r\n<\/table>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-5f7b27e elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5f7b27e\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d903a39\" data-id=\"d903a39\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-19ea930 elementor-widget elementor-widget-text-editor\" data-id=\"19ea930\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Integral of 1\/x\u00b2<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-40b5e2c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"40b5e2c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d450d4b\" data-id=\"d450d4b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ce132db elementor-widget elementor-widget-text-editor\" data-id=\"ce132db\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Rewrite it as:<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-e96c78b elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e96c78b\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a26063b\" data-id=\"a26063b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3db8340 elementor-widget elementor-widget-html\" data-id=\"3db8340\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:760px;margin:35px auto;background:#fff;border:1px solid #eee;border-radius:16px;overflow:hidden;box-shadow:0 8px 18px rgba(0,0,0,.08);\">\r\n\r\n<div style=\"background:#f4b400;color:#fff;padding:16px 22px;\">\r\n<h3 style=\"margin:0;\">Integral of 1\/x\u00b2<\/h3>\r\n<\/div>\r\n\r\n<div style=\"padding:25px;\">\r\n<div style=\"background:#fff9dc;padding:16px;border-radius:10px;text-align:center;font-size:28px;font-weight:bold;\">\r\n1\/x\u00b2 = x<sup>\u22122<\/sup>\r\n<\/div>\r\n\r\n<div style=\"margin:25px 0 15px;\">\r\n<strong>Apply the power rule:<\/strong>\r\n<\/div>\r\n\r\n<div style=\"background:#f7f7f7;padding:18px;border-radius:10px;text-align:center;font-size:24px;line-height:1.8;\">\r\n\u222b x<sup>\u22122<\/sup> dx\r\n<\/div>\r\n\r\n<div style=\"text-align:center;font-size:24px;color:#888;margin:15px 0;\">\r\n\u2193\r\n<\/div>\r\n\r\n<div style=\"background:#fff9dc;padding:18px;border-radius:10px;text-align:center;font-size:24px;line-height:1.8;\">\r\n= x<sup>\u22121<\/sup> \/ (\u22121) + C\r\n<\/div>\r\n\r\n<div style=\"text-align:center;font-size:24px;color:#888;margin:15px 0;\">\r\n\u2193\r\n<\/div>\r\n\r\n<div style=\"background:#eef8ff;padding:18px;border-radius:10px;text-align:center;font-size:28px;font-weight:bold;color:#0f4c81;\">\r\n= \u22121\/x + C\r\n<\/div>\r\n\r\n<p style=\"margin-top:25px;margin-bottom:0;line-height:1.8;\">\r\nUnlike the <strong>integral of 1\/x<\/strong>, this one follows the normal power rule.\r\n<\/p>\r\n\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-5ae633c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5ae633c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d1fb732\" data-id=\"d1fb732\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-fa6ef08 elementor-widget elementor-widget-text-editor\" data-id=\"fa6ef08\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Unlike the <\/span><b>integral of 1\/x<\/b><span style=\"font-weight: 400;\">, this one follows the normal power rule.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-7b3ec4f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7b3ec4f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6a3a054\" data-id=\"6a3a054\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e541fc7 elementor-widget elementor-widget-text-editor\" data-id=\"e541fc7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h3><b>Integral of 1\/(1+x\u00b2)<\/b><\/h3>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-28b5baf elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"28b5baf\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2af5053\" data-id=\"2af5053\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-67e7dc2 elementor-widget elementor-widget-text-editor\" data-id=\"67e7dc2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">This is another standard integral.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-0db931a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"0db931a\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-807d12b\" data-id=\"807d12b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-239574f elementor-widget elementor-widget-html\" data-id=\"239574f\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"max-width:760px;margin:35px auto;background:#fff;border:1px solid #eee;border-radius:16px;overflow:hidden;box-shadow:0 8px 18px rgba(0,0,0,.08);\">\r\n\r\n<div style=\"background:#3b82f6;color:#fff;padding:16px 22px;\">\r\n<h3 style=\"margin:0;\">Integral of 1\/(1+x\u00b2)<\/h3>\r\n<\/div>\r\n\r\n<div style=\"padding:25px;\">\r\n\r\n<div style=\"background:#eef6ff;padding:20px;border-radius:10px;text-align:center;font-size:28px;font-weight:bold;\">\r\n\u222b 1\/(1+x\u00b2) dx = tan<sup>\u22121<\/sup>(x) + C\r\n<\/div>\r\n\r\n<div style=\"margin-top:25px;padding:18px;background:#f8fbff;border-left:5px solid #3b82f6;border-radius:10px;line-height:1.8;\">\r\n\r\n<strong>Remember:<\/strong><br \/><br \/>\r\n\r\nWhenever you see the expression <strong>1\/(1+x\u00b2)<\/strong>, you can directly apply this standard integration formula without using the power rule.\r\n\r\n<\/div>\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-b2443e4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"b2443e4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-19e4f3c\" data-id=\"19e4f3c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b299245 elementor-widget elementor-widget-text-editor\" data-id=\"b299245\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">This formula appears frequently in trigonometric substitution and differential equations.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-9d89318 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9d89318\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-68003c8\" data-id=\"68003c8\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b3c0531 elementor-widget elementor-widget-text-editor\" data-id=\"b3c0531\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h2><b>Common Mistakes<\/b><\/h2>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-e7cad37 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e7cad37\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-cb04a9a\" data-id=\"cb04a9a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-50b4290 elementor-widget elementor-widget-html\" data-id=\"50b4290\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(240px,1fr));gap:20px;margin:35px 0;\">\r\n\r\n<div style=\"background:#fff4f4;padding:18px;border-left:6px solid #ef4444;border-radius:12px;\">\r\n<h4>\u274c Using the Power Rule<\/h4>\r\n<p>1\/x is the exception. Do not apply the standard power rule.<\/p>\r\n<\/div>\r\n\r\n<div style=\"background:#fff9e8;padding:18px;border-left:6px solid #f4b400;border-radius:12px;\">\r\n<h4>\u274c Forgetting |x|<\/h4>\r\n<p>Always write <strong>ln|x|<\/strong>, not simply ln(x).<\/p>\r\n<\/div>\r\n\r\n<div style=\"background:#eef7ff;padding:18px;border-left:6px solid #3b82f6;border-radius:12px;\">\r\n<h4>\u274c Missing + C<\/h4>\r\n<p>Every indefinite integral must include the constant of integration.<\/p>\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-52485ec elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"52485ec\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8a7bb54\" data-id=\"8a7bb54\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-cac42ac elementor-widget elementor-widget-html\" data-id=\"cac42ac\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<div style=\"background:#fffdf3;border-radius:16px;padding:25px;margin:35px 0;box-shadow:0 8px 20px rgba(0,0,0,.08);\">\r\n\r\n<h2 style=\"text-align:center;color:#b57a00;margin-top:0;\">\r\n\ud83d\udcda Integration Cheat Sheet\r\n<\/h2>\r\n\r\n<table style=\"width:100%;border-collapse:collapse;\">\r\n\r\n<tr style=\"background:#f4b400;color:#fff;\">\r\n<th style=\"padding:14px;\">Integral<\/th>\r\n<th style=\"padding:14px;\">Answer<\/th>\r\n<\/tr>\r\n\r\n<tr>\r\n<td style=\"padding:14px;border:1px solid #eee;\">\u222b1\/x dx<\/td>\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>ln|x| + C<\/strong><\/td>\r\n<\/tr>\r\n\r\n<tr>\r\n<td style=\"padding:14px;border:1px solid #eee;\">\u222b1\/x\u00b2 dx<\/td>\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>\u22121\/x + C<\/strong><\/td>\r\n<\/tr>\r\n\r\n<tr>\r\n<td style=\"padding:14px;border:1px solid #eee;\">\u222b1\/(1+x\u00b2) dx<\/td>\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>tan\u207b\u00b9(x) + C<\/strong><\/td>\r\n<\/tr>\r\n\r\n<tr>\r\n<td style=\"padding:14px;border:1px solid #eee;\">\u222bk\/x dx<\/td>\r\n<td style=\"padding:14px;border:1px solid #eee;\"><strong>k ln|x| + C<\/strong><\/td>\r\n<\/tr>\r\n\r\n<\/table>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-a228c9f elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a228c9f\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-4c5ce05\" data-id=\"4c5ce05\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-43b11e5 elementor-widget elementor-widget-html\" data-id=\"43b11e5\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<!-- Related Math Guides -->\r\n<div style=\"max-width:760px;margin:25px auto;font-family:Arial,Helvetica,sans-serif;\">\r\n\r\n<h2 style=\"font-size:24px;font-weight:700;color:#2563eb;margin-bottom:15px;\">\r\nExplore Related Math Guides:\r\n<\/h2>\r\n\r\n<div style=\"display:grid;grid-template-columns:repeat(auto-fit,minmax(210px,1fr));gap:12px;\">\r\n\r\n<!-- Card 1 -->\r\n<a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/how-to-subtract-fractions\/\" target=\"_blank\" style=\"text-decoration:none;color:#2563eb;\">\r\n<div style=\"background:#eaf3ff;border-radius:22px;padding:16px 18px;height:115px;display:flex;flex-direction:column;justify-content:space-between;\">\r\n<div style=\"font-size:14px;line-height:1.45;font-weight:500;text-align:left !important;text-align-last:left !important;word-spacing:normal !important;letter-spacing:normal !important;white-space:normal;word-break:normal;overflow-wrap:break-word;\">\r\nHow to Subtract Fractions: A Step-by-Step Guide for Beginners\r\n<\/div>\r\n<div style=\"font-size:20px;line-height:1;color:#2563eb;\">\u21aa<\/div>\r\n<\/div>\r\n<\/a>\r\n\r\n<!-- Card 2 -->\r\n<a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/how-to-divide-fractions\/\" target=\"_blank\" style=\"text-decoration:none;color:#2563eb;\">\r\n<div style=\"background:#eaf3ff;border-radius:22px;padding:16px 18px;height:115px;display:flex;flex-direction:column;justify-content:space-between;\">\r\n<div style=\"font-size:14px;line-height:1.45;font-weight:500;text-align:left !important;text-align-last:left !important;word-spacing:normal !important;letter-spacing:normal !important;white-space:normal;word-break:normal;overflow-wrap:break-word;\">\r\nHow to Divide Fractions: Simple Steps, Examples &amp; Practice Problems\r\n<\/div>\r\n<div style=\"font-size:20px;line-height:1;color:#2563eb;\">\u21aa<\/div>\r\n<\/div>\r\n<\/a>\r\n\r\n<!-- Card 3 -->\r\n<a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/how-to-add-fractions\/\" target=\"_blank\" style=\"text-decoration:none;color:#2563eb;\">\r\n<div style=\"background:#eaf3ff;border-radius:22px;padding:16px 18px;height:115px;display:flex;flex-direction:column;justify-content:space-between;\">\r\n<div style=\"font-size:14px;line-height:1.45;font-weight:500;text-align:left !important;text-align-last:left !important;word-spacing:normal !important;letter-spacing:normal !important;white-space:normal;word-break:normal;overflow-wrap:break-word;\">\r\nHow to Add Fractions \u2013 3 Simple Steps\r\n<\/div>\r\n<div style=\"font-size:20px;line-height:1;color:#2563eb;\">\u21aa<\/div>\r\n<\/div>\r\n<\/a>\r\n\r\n<!-- Card 4 -->\r\n<a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/factors-of-36\/\" target=\"_blank\" style=\"text-decoration:none;color:#2563eb;\">\r\n<div style=\"background:#eaf3ff;border-radius:22px;padding:16px 18px;height:115px;display:flex;flex-direction:column;justify-content:space-between;\">\r\n<div style=\"font-size:14px;line-height:1.45;font-weight:500;text-align:left !important;text-align-last:left !important;word-spacing:normal !important;letter-spacing:normal !important;white-space:normal;word-break:normal;overflow-wrap:break-word;\">\r\nFactors of 36 \u2013 Prime Factorization, Factor Pairs, and Examples\r\n<\/div>\r\n<div style=\"font-size:20px;line-height:1;color:#2563eb;\">\u21aa<\/div>\r\n<\/div>\r\n<\/a>\r\n\r\n<!-- Card 5 -->\r\n<a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/0-375-as-a-fraction\/\" target=\"_blank\" style=\"text-decoration:none;color:#2563eb;\">\r\n<div style=\"background:#eaf3ff;border-radius:22px;padding:16px 18px;height:115px;display:flex;flex-direction:column;justify-content:space-between;\">\r\n<div style=\"font-size:14px;line-height:1.45;font-weight:500;text-align:left !important;text-align-last:left !important;word-spacing:normal !important;letter-spacing:normal !important;white-space:normal;word-break:normal;overflow-wrap:break-word;\">\r\nWhat is 0.375 as a Fraction? Learn to Convert Decimal to Fraction Form\r\n<\/div>\r\n<div style=\"font-size:20px;line-height:1;color:#2563eb;\">\u21aa<\/div>\r\n<\/div>\r\n<\/a>\r\n\r\n<!-- Card 6 -->\r\n<a href=\"https:\/\/mp.moonpreneur.com\/math-corner\/what-is-long-division-method\/\" target=\"_blank\" style=\"text-decoration:none;color:#2563eb;\">\r\n<div style=\"background:#eaf3ff;border-radius:22px;padding:16px 18px;height:115px;display:flex;flex-direction:column;justify-content:space-between;\">\r\n<div style=\"font-size:14px;line-height:1.45;font-weight:500;text-align:left !important;text-align-last:left !important;word-spacing:normal !important;letter-spacing:normal !important;white-space:normal;word-break:normal;overflow-wrap:break-word;\">\r\nWhat is the Long Division Method? Step-by-Step Guide for Kids\r\n<\/div>\r\n<div style=\"font-size:20px;line-height:1;color:#2563eb;\">\u21aa<\/div>\r\n<\/div>\r\n<\/a>\r\n\r\n<\/div>\r\n\r\n<\/div>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-3b075fd elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3b075fd\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-aa73d3f\" data-id=\"aa73d3f\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6d42353 elementor-widget elementor-widget-text-editor\" data-id=\"6d42353\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<h2 style=\"text-align: center;\"><strong>Conclusion<\/strong><\/h2>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-fd50d55 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"fd50d55\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a195ac6\" data-id=\"a195ac6\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2ec9d2f elementor-widget elementor-widget-text-editor\" data-id=\"2ec9d2f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-text-editor elementor-clearfix\">\n\t\t\t\t<p><span style=\"font-weight: 400;\">Want to excite your child about math and sharpen their math skills? Moonpreneur&#8217;s online math curriculum is unique as it helps children understand math skills through hands-on lessons, assists them in building real-life applications, and excites them to learn math.\u00a0<\/span><\/p><p><span style=\"font-weight: 400;\">You can opt for our <\/span><a href=\"https:\/\/moonpreneur.com\/innovator-program\/advanced-math\/\"><span style=\"font-weight: 400;\">Advanced Math<\/span><\/a><span style=\"font-weight: 400;\"> or Vedic Math+Mental Math courses. Our <\/span><a href=\"https:\/\/mp.moonpreneur.com\/math-quiz-for-kids\/\"><span style=\"font-weight: 400;\">Math Quiz<\/span><\/a><span style=\"font-weight: 400;\"> for grades 3rd, 4th, 5th, and 6th helps in further exciting and engaging in mathematics with hands-on lessons.<\/span><\/p>\t\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"has_eae_slider elementor-section elementor-top-section elementor-element elementor-element-cc58627 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cc58627\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t\t\t<div class=\"elementor-row\">\n\t\t\t\t\t<div class=\"has_eae_slider elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-33af559\" data-id=\"33af559\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-column-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-8daff96 elementor-widget elementor-widget-html\" data-id=\"8daff96\" data-element_type=\"widget\" data-widget_type=\"html.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<section class=\"faq-section\" style=\"max-width:900px;margin:40px auto;font-family:Arial,sans-serif;\">\r\n\r\n  <h2 style=\"text-align:center;font-size:32px;color:#1d4ed8;margin-bottom:25px;\">\r\n    Frequently Asked Questions\r\n  <\/h2>\r\n\r\n  <div class=\"faq-item\" style=\"border:1px solid #dbeafe;border-radius:10px;margin-bottom:15px;padding:20px;background:#fff;\">\r\n    <h3 style=\"margin-top:0;color:#0f172a;font-size:22px;\">Q1. What is the integral of 1\/x?<\/h3>\r\n\r\n    <p style=\"font-weight:bold;color:#1d4ed8;margin-bottom:10px;\">Ans.<\/p>\r\n\r\n    <p style=\"line-height:1.8;\">\r\n      The <strong>integral of 1\/x<\/strong> is:\r\n    <\/p>\r\n\r\n    <div style=\"margin-top:15px;padding:15px;background:#f8fbff;border-radius:8px;text-align:center;font-size:24px;font-weight:bold;\">\r\n      \u222b 1\/x dx = ln|x| + C\r\n    <\/div>\r\n  <\/div>\r\n\r\n  <div class=\"faq-item\" style=\"border:1px solid #dbeafe;border-radius:10px;margin-bottom:15px;padding:20px;background:#f8fbff;\">\r\n    <h3 style=\"margin-top:0;color:#0f172a;font-size:22px;\">Q2. Why is the integral of 1\/x not found using the power rule?<\/h3>\r\n\r\n    <p style=\"font-weight:bold;color:#1d4ed8;margin-bottom:10px;\">Ans.<\/p>\r\n\r\n    <p style=\"line-height:1.8;\">\r\n      The power rule fails because the exponent is <strong>\u22121<\/strong>, which makes the denominator equal to <strong>zero<\/strong>. Since division by zero is undefined, the power rule cannot be applied. Instead, the integral is <strong>ln|x| + C<\/strong>.\r\n    <\/p>\r\n  <\/div>\r\n\r\n  <div class=\"faq-item\" style=\"border:1px solid #dbeafe;border-radius:10px;margin-bottom:15px;padding:20px;background:#fff;\">\r\n    <h3 style=\"margin-top:0;color:#0f172a;font-size:22px;\">Q3. What is the integral of 1\/x\u00b2?<\/h3>\r\n\r\n    <p style=\"font-weight:bold;color:#1d4ed8;margin-bottom:10px;\">Ans.<\/p>\r\n\r\n    <p style=\"line-height:1.8;\">\r\n      The <strong>integral of 1\/x\u00b2<\/strong> is:\r\n    <\/p>\r\n\r\n    <div style=\"margin-top:15px;padding:15px;background:#f8fbff;border-radius:8px;text-align:center;font-size:24px;font-weight:bold;\">\r\n      \u222b 1\/x\u00b2 dx = \u22121\/x + C\r\n    <\/div>\r\n  <\/div>\r\n\r\n  <div class=\"faq-item\" style=\"border:1px solid #dbeafe;border-radius:10px;margin-bottom:15px;padding:20px;background:#f8fbff;\">\r\n    <h3 style=\"margin-top:0;color:#0f172a;font-size:22px;\">Q4. What is the integral of 1\/(1+x\u00b2)?<\/h3>\r\n\r\n    <p style=\"font-weight:bold;color:#1d4ed8;margin-bottom:10px;\">Ans.<\/p>\r\n\r\n    <p style=\"line-height:1.8;\">\r\n      The <strong>integral of 1\/(1+x\u00b2)<\/strong> is:\r\n    <\/p>\r\n\r\n    <div style=\"margin-top:15px;padding:15px;background:#f8fbff;border-radius:8px;text-align:center;font-size:24px;font-weight:bold;\">\r\n      \u222b 1\/(1+x\u00b2) dx = tan\u207b\u00b9(x) + C\r\n    <\/div>\r\n  <\/div>\r\n\r\n  <div class=\"faq-item\" style=\"border:1px solid #dbeafe;border-radius:10px;padding:20px;background:#fff;\">\r\n    <h3 style=\"margin-top:0;color:#0f172a;font-size:22px;\">Q5. Why do we write ln|x| instead of ln(x)?<\/h3>\r\n\r\n    <p style=\"font-weight:bold;color:#1d4ed8;margin-bottom:10px;\">Ans.<\/p>\r\n\r\n    <p style=\"line-height:1.8;\">\r\n      The absolute value ensures the logarithm is valid for both positive and negative values of <strong>x<\/strong> (except zero). Writing <strong>ln|x|<\/strong> makes the antiderivative correct over its entire domain.\r\n    <\/p>\r\n  <\/div>\r\n\r\n<\/section>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>The integral of 1\/x is one of the most important formulas in calculus. Unlike most algebraic functions, it cannot be integrated using the standard power rule. Instead, it has a unique logarithmic result that every calculus student should know. The formula is: \ud83d\udcd8 Integral of 1\/x Formula \u222b 1\/x dx = ln|x| + C The [&hellip;]<\/p>\n","protected":false},"author":116,"featured_media":39703,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false},"categories":[969,1035],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/39700"}],"collection":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/users\/116"}],"replies":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/comments?post=39700"}],"version-history":[{"count":5,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/39700\/revisions"}],"predecessor-version":[{"id":39714,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/posts\/39700\/revisions\/39714"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media\/39703"}],"wp:attachment":[{"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/media?parent=39700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/categories?post=39700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mp.moonpreneur.com\/math-corner\/wp-json\/wp\/v2\/tags?post=39700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}