{"id":7911,"date":"2021-11-10T16:53:14","date_gmt":"2021-11-10T11:23:14","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7911"},"modified":"2021-11-10T22:59:04","modified_gmt":"2021-11-10T17:29:04","slug":"what-is-the-integration-of-log-1-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/what-is-the-integration-of-log-1-x\/","title":{"rendered":"What is the integration of log 1\/x ?"},"content":{"rendered":"

Solution :\u00a0<\/h2>\n

We have, I = \\(\\int\\) \\(log {1\\over x}\\) dx<\/p>\n

I = \\(\\int\\) \\(log 1 – log x\\) dx = \\(\\int\\) (-log x) dx<\/p>\n

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

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

where log x is the first function and 1 is the second function according to ilate rule.<\/p>\n

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

I = – {(log x) x – \\(\\int\\) \\(1\\over x\\).x }dx\u00a0<\/p>\n

= – x (log x) + \\(\\int\\) 1 dx<\/p>\n

= – x (log x) + x + C = x – x log x + C<\/p>\n

Hence, the integration of\u00a0 log 1\/x with respect to x is x – log x + C<\/p>\n

\n

Similar Questions<\/h3>\n

What is the integration of log cos x dx ?<\/a><\/p>\n

What is the integration of \\((log x)^2\\) dx ?<\/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\n\n

<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution :\u00a0 We have, I = \\(\\int\\) \\(log {1\\over x}\\) dx I = \\(\\int\\) \\(log 1 – log x\\) dx = \\(\\int\\) (-log x) dx By using integration by parts formula, Let I = -(\\(\\int\\) log x .1) dx where log x is the first function and 1 is the second function according to ilate …<\/p>\n

What is the integration of log 1\/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 log 1\/x ? - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post you will learn what is the integration of log 1\/x with respect to x 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-1-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 log 1\/x ? 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