integration of cot x cosec^2x/1-cot^2x dx

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A beautiful result in calculus: Solution using complex analysis ( Integral cos(x)/(x^2+1) )

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integration of cot x cosec^2x/1-cot^2x dx

Asked by Balbir | 05 Aug, 2017, 09:40: PM

$begin mathsize 16px style integral fraction numerator cotx space cosec squared straight x over denominator 1 minus cot squared straight x end fraction dx 1 minus cot squared straight x equals straight t minus 2 cotx space cross times open parentheses negative cosec squared straight x close parentheses dx equals dt cotx space cross times cosec squared straight x dx equals fraction numerator begin display style dt end style over denominator 2 end fraction integral fraction numerator begin display style dt over 2 end style over denominator straight t end fraction 1 half log open vertical bar straight t close vertical bar plus straight c fraction numerator begin display style 1 end style over denominator begin display style 2 end style end fraction log open vertical bar 1 minus cot squared straight x close vertical bar plus straight c end style$

Answered by Sneha shidid | 07 Aug, 2017, 08:50: AM

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