{"id":6809,"date":"2021-10-21T17:54:14","date_gmt":"2021-10-21T12:24:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6809"},"modified":"2021-11-01T19:32:30","modified_gmt":"2021-11-01T14:02:30","slug":"evaluate-int-cos4xdxover-sin3xsin5x-cos5x3over-5","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/evaluate-int-cos4xdxover-sin3xsin5x-cos5x3over-5\/","title":{"rendered":"Evaluate : \\(\\int\\) \\(cos^4xdx\\over {sin^3x{(sin^5x + cos^5x)^{3\\over 5}}}\\)"},"content":{"rendered":"

Solution :<\/h2>\n

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

= \\(\\int\\) \\(cos^4xdx\\over {sin^6x{(1 + cot^5x)^{3\\over 5}}}\\) = \\(\\int\\) \\(cot^4xcosec^2xdx\\over {{(1 + cot^5x)^{3\\over 5}}}\\)<\/p>\n

Put \\(1+cot^5x\\) = t<\/p>\n

\\(5cot^4xcosec^2x\\)dx = -dt<\/p>\n

= -\\(1\\over 5\\) \\(\\int\\) \\(dt\\over {t^{3\/5}}\\) = -\\(1\\over 2\\) \\(t^{2\/5}\\) + C<\/p>\n

= -\\(1\\over 2\\) \\({(1+cot^5x)}^{2\/5}\\) + 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

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

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

Solution : I = \\(\\int\\) \\(cos^4xdx\\over {sin^3x{(sin^5x + cos^5x)^{3\\over 5}}}\\) = \\(\\int\\) \\(cos^4xdx\\over {sin^6x{(1 + cot^5x)^{3\\over 5}}}\\) = \\(\\int\\) \\(cot^4xcosec^2xdx\\over {{(1 + cot^5x)^{3\\over 5}}}\\) Put \\(1+cot^5x\\) = t \\(5cot^4xcosec^2x\\)dx = -dt = -\\(1\\over 5\\) \\(\\int\\) \\(dt\\over {t^{3\/5}}\\) = -\\(1\\over 2\\) \\(t^{2\/5}\\) + C = -\\(1\\over 2\\) \\({(1+cot^5x)}^{2\/5}\\) + C Similar Questions What is the integration …<\/p>\n

Evaluate : \\(\\int\\) \\(cos^4xdx\\over {sin^3x{(sin^5x + cos^5x)^{3\\over 5}}}\\)<\/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":"default","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":"\nEvaluate : \\(\\int\\) \\(cos^4xdx\\over {sin^3x{(sin^5x + cos^5x)^{3\\over 5}}}\\)<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, 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