{"id":7903,"date":"2021-11-10T16:00:23","date_gmt":"2021-11-10T10:30:23","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7903"},"modified":"2021-11-10T22:20:43","modified_gmt":"2021-11-10T16:50:43","slug":"what-is-the-integration-of-log-x2-dx","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-log-x2-dx\/","title":{"rendered":"What is the integration of \\((log x)^2\\) dx ?"},"content":{"rendered":"

Solution :<\/h2>\n

We have, I = \\((log x)^2\\) . 1 dx, Then ,<\/p>\n

where \\((log x)^2\\) is the first function and 1 is the second function according to ilate rule,<\/p>\n

I = \\((log x)^2\\) { \\(\\int\\) 1 dx} – \\(\\int\\) {\\(d\\over dx\\) \\((log x)^2\\) . \\(\\int\\) 1 dx } dx<\/p>\n

I = \\((log x)^2\\) x – \\(\\int\\) 2 log x . \\(1\\over x\\) . x dx<\/p>\n

I = x \\((log x)^2\\) – 2 \\(\\int\\) log x .1 dx<\/p>\n

\\(\\implies\\) I = x \\((log x)^2\\) – 2[ log x { \\(\\int\\) 1 dx } – \\(\\int\\) { \\(d\\over dx\\) (log x) \\(\\int\\) 1 dx } dx ]<\/p>\n

\\(\\implies\\) I = x \\((log x)^2\\) – 2 { (log x) x – \\(\\int\\) \\(1\\over x\\) x dx }<\/p>\n

Hence, I = x( \\((log x)^2\\) – 2 (x log x – x) + C<\/p>\n

\n

Similar Questions<\/h3>\n

What is the integration of log cos x dx ?<\/a><\/p>\n

What is the integration of log 1\/x ?<\/a><\/p>\n

What is the integration of 1\/x log x ?<\/a><\/p>\n

What is the integration of x log x dx ?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, I = \\((log x)^2\\) . 1 dx, Then , where \\((log x)^2\\) is the first function and 1 is the second function according to ilate rule, I = \\((log x)^2\\) { \\(\\int\\) 1 dx} – \\(\\int\\) {\\(d\\over dx\\) \\((log x)^2\\) . \\(\\int\\) 1 dx } dx I = \\((log x)^2\\) x …<\/p>\n

What is the integration of \\((log x)^2\\) dx ?<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[52,43],"tags":[],"yoast_head":"\nWhat is the integration of \\((log x)^2\\) dx ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of ((log x)^2) with respect to x by using integration by parts.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/what-is-the-integration-of-log-x2-dx\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"What is the integration of \\((log x)^2\\) dx ? 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