{"id":7661,"date":"2021-11-01T18:10:15","date_gmt":"2021-11-01T12:40:15","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7661"},"modified":"2021-11-01T19:32:51","modified_gmt":"2021-11-01T14:02:51","slug":"what-is-the-integration-of-x-tan-inverse-x-dx","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-x-tan-inverse-x-dx\/","title":{"rendered":"What is the integration of x tan inverse x dx ?"},"content":{"rendered":"

Solution :<\/h2>\n

Let I = \\(\\int\\) x\\(tan^{-1}x\\) dx<\/p>\n

By using Integration by parts rule,<\/p>\n

Taking tan inverse x as first function and x as second function. Then,<\/p>\n

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

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

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

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

\\(\\implies\\) I = \\(x^2\\over 2\\)\\(tan^{-1}x\\) – \\(1\\over 2\\) (\\(x – tan^{-1}x\\)) + C<\/p>\n

\n

Similar Questions<\/h3>\n

What is the integration of tan inverse root x ?<\/a><\/p>\n

Prove that \\(\\int_{0}^{\\pi\/2}\\) log(sinx)dx = \\(\\int_{0}^{\\pi\/2}\\) log(cosx)dx = -\\(\\pi\\over 2\\)log 2.<\/a><\/p>\n

Evaluate : \\(\\int\\) \\(cos^4xdx\\over {sin^3x{(sin^5x + cos^5x)^{3\\over 5}}}\\)<\/a><\/p>\n

Evaluate : \\(\\int\\) \\(dx\\over {3sinx + 4cosx}\\)<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let I = \\(\\int\\) x\\(tan^{-1}x\\) dx By using Integration by parts rule, Taking tan inverse x as first function and x as second function. Then, I = (\\(tan^{-1}x\\)) \\(\\int\\) x dx – \\(\\int\\){\\({d\\over dx}\\)(\\(tan^{-1}x\\) \\(\\int\\) x dx} dx I = (\\(tan^{-1}x\\))\\(x^2\\over 2\\) – \\(\\int\\)\\({1\\over 1 + x^2}\\) \\(\\times\\) \\(x^2\\over 2\\) dx \\(\\implies\\) I …<\/p>\n

What is the integration of x tan inverse 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 tan inverse x dx ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of x tan inverse x dx using integration by parts rule.\" \/>\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-tan-inverse-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 tan inverse x dx ? 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