{"id":7905,"date":"2021-11-10T16:18:46","date_gmt":"2021-11-10T10:48:46","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7905"},"modified":"2021-11-10T23:00:00","modified_gmt":"2021-11-10T17:30:00","slug":"what-is-the-integration-of-x-log-x-dx","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-x-log-x-dx\/","title":{"rendered":"What is the integration of x log x dx ?"},"content":{"rendered":"

Solution :<\/h2>\n

We have, I = \\(\\int\\) x log x dx<\/p>\n

By using integration by parts<\/a>,<\/p>\n

And taking log x as first function and x as second function. Then,<\/p>\n

I = log x { \\(\\int\\) x dx } – \\(\\int\\) { \\({d\\over dx}(log x) \\times \\int x dx\\) } dx<\/p>\n

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

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

\\(\\implies\\) I = \\(x^2\\over 2\\) log x – \\(1\\over 2\\) (\\(x^2\\over 2\\)) + C<\/p>\n

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

Hence. the integration of x log x with respect to x is \\(x^2\\over 2\\) log x – \\(x^2\\over 2\\) + C<\/p>\n

\n

Similar Questions<\/h3>\n

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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 \\((log x)^2\\) dx ?<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : We have, I = \\(\\int\\) x log x dx By using integration by parts, And taking log x as first function and x as second function. Then, I = log x { \\(\\int\\) x dx } – \\(\\int\\) { \\({d\\over dx}(log x) \\times \\int x dx\\) } dx I = (log x) \\(x^2\\over …<\/p>\n

What is the integration of x log x 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 x log x dx ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of x log x dx 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-x-log-x-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 x log x dx ? 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