{"id":7667,"date":"2021-11-01T19:22:29","date_gmt":"2021-11-01T13:52:29","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7667"},"modified":"2021-11-06T00:55:06","modified_gmt":"2021-11-05T19:25:06","slug":"what-is-the-integration-of-tan-inverse-root-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-tan-inverse-root-x\/","title":{"rendered":"What is the integration of tan inverse root x ?"},"content":{"rendered":"

Solution :<\/h2>\n

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

By Applying integration by parts,<\/p>\n

Taking \\(tan^{-1}\\sqrt{x}\\) as first function and 1 as second function. Then<\/p>\n

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

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

Let \\(\\sqrt{x}\\) = t<\/p>\n

\\(1\\over 2\\sqrt{x}\\) dx = dt \\(\\implies\\) dx = 2t dt<\/p>\n

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

\\(\\implies\\) I = x\\(tan^{-1}\\sqrt{x}\\)\u00a0 – \\(\\int\\) dt + \\(\\int\\) \\(1\\over 1 + t^2\\)<\/p>\n

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

Hence, I = x\\(tan^{-1}\\sqrt{x}\\) – \\(\\sqrt{x}\\) + \\(tan^{-1}\\sqrt{x}\\) + C<\/p>\n

\n

Similar Questions<\/h3>\n

What is the integration of x tan inverse x dx ?<\/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\\) \\(tan^{-1}\\sqrt{x}\\).1 dx By Applying integration by parts, Taking \\(tan^{-1}\\sqrt{x}\\) as first function and 1 as second function. Then I = \\(tan^{-1}\\sqrt{x}\\) \\(\\int\\) 1 dx – \\(\\int\\) {\\(d\\over dx\\)\\(tan^{-1}\\sqrt{x}\\) \\(\\int\\) 1 dx } dx I = x\\(tan^{-1}\\sqrt{x}\\) – \\(\\int\\) \\(1\\over 2(1+x)\\sqrt{x}\\) . x dx Let \\(\\sqrt{x}\\) = t \\(1\\over 2\\sqrt{x}\\) …<\/p>\n

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