{"id":8186,"date":"2021-11-16T17:59:37","date_gmt":"2021-11-16T12:29:37","guid":{"rendered":"https:\/\/mathemerize.com\/?p=8186"},"modified":"2021-11-16T18:22:20","modified_gmt":"2021-11-16T12:52:20","slug":"integrate-x2-x-1over-x2-1-with-respect-to-x","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/integrate-x2-x-1over-x2-1-with-respect-to-x\/","title":{"rendered":"Integrate \\(x^2 + x – 1\\over x^2 – 1\\) with respect to x."},"content":{"rendered":"

Solution :<\/h2>\n

\\(\\int\\) \\(x^2 + x – 1\\over x^2 – 1\\) dx = \\(\\int\\) (\\(x^2 – 1\\over x^2 – 1\\) + \\(x\\over x^2 – 1\\))dx<\/p>\n

= \\(\\int\\) 1 dx + \\(\\int\\) \\(x\\over x^2 – 1\\)) dx<\/p>\n

Let \\(x^2 – 1\\) = t\u00a0 \\(\\implies\\) 2x dx = dt<\/p>\n

= x + \\(\\int\\) \\(dt\\over 2t\\)<\/p>\n

= x + \\(1\\over 2\\) \\(\\int\\) \\(1\\over t\\) dt<\/p>\n

since, integration of \\(1\\over x\\) = log x<\/p>\n

= x + \\(1\\over 2\\) log t + C<\/p>\n

Substituing the value of t here, we get<\/p>\n

= x + \\(log(x^2 – 1)\\over 2\\) + C<\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : \\(\\int\\) \\(x^2 + x – 1\\over x^2 – 1\\) dx = \\(\\int\\) (\\(x^2 – 1\\over x^2 – 1\\) + \\(x\\over x^2 – 1\\))dx = \\(\\int\\) 1 dx + \\(\\int\\) \\(x\\over x^2 – 1\\)) dx Let \\(x^2 – 1\\) = t\u00a0 \\(\\implies\\) 2x dx = dt = x + \\(\\int\\) \\(dt\\over 2t\\) = x …<\/p>\n

Integrate \\(x^2 + x – 1\\over x^2 – 1\\) with respect to 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":"\nIntegrate \\(x^2 + x - 1\\over x^2 - 1\\) with respect to x. - Mathemerize<\/title>\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\/integrate-x2-x-1over-x2-1-with-respect-to-x\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Integrate \\(x^2 + x - 1\\over x^2 - 1\\) with respect to x. - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"Solution : (int) (x^2 + x – 1over x^2 – 1) dx = (int) ((x^2 – 1over x^2 – 1) + (xover x^2 – 1))dx = (int) 1 dx + (int) (xover x^2 – 1)) dx Let (x^2 – 1) = t\u00a0 (implies) 2x dx = dt = x + (int) (dtover 2t) = x … Integrate (x^2 + x – 1over x^2 – 1) with respect to x. 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