{"id":7914,"date":"2021-11-10T17:14:38","date_gmt":"2021-11-10T11:44:38","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7914"},"modified":"2022-01-04T19:21:11","modified_gmt":"2022-01-04T13:51:11","slug":"what-is-the-integration-of-log-cos-x-dx","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-log-cos-x-dx\/","title":{"rendered":"What is the integration of log cos x dx ?"},"content":{"rendered":"

Solution :<\/h2>\n

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

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

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

Taking log cos x as first function and 1 as second function. Then,<\/p>\n

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

I = x log cos x – \\(\\int\\) { \\({-sinx\\over cos x} x\\) } dx<\/p>\n

I = x log cos x + \\(\\int\\) x tan x dx<\/p>\n

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

I = x log cos x + x log |sec x | – \\(\\int\\) {1.(log sec x)} dx<\/p>\n

I = x log cos x + x log sec x – I<\/p>\n

2I = x log cos x + x log sec x + C<\/p>\n

I = \\(x log cos x\\over 2\\) + \\(x log sec x\\over 2\\) + C<\/p>\n

Hence, the integration of log cos x with respect to x is \\(x log cos x\\over 2\\) + \\(x log sec x\\over 2\\) + C<\/p>\n

\n

Similar Questions<\/h3>\n

What is the integration of \\((log x)^2\\) 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 = \\(\\int\\) log cos x dx By using integraton by parts, I = \\(\\int\\) 1.log cos x dx Taking log cos x as first function and 1 as second function. Then, I = log cos x \\(\\int\\) 1 dx – \\(\\int\\) { \\({d\\over dx}\\) (log cos x) \\(\\int\\) 1 dx …<\/p>\n

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