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Integrate cos^9x/sin x with respect to …

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Integrate cos^9x/sin x with respect to x ....please give answer...

Posted by Pooja Bhakar 6 years ago

CBSE > Class 12 > Mathematics

2 answers

Pooja Bhakar 6 years ago

Nice explanation bro

Vishal Kumar 6 years ago

€ - integration I = €cos^9x/sinx dx I = € cos^8x cosx/sinx dx I = € ( cos^2x )^4 cosx/sinx dx I = € ( 1 - sin^2x )^4 cosx/sinx dx let sinx = t Differenciate w.r.t. x Cosx = dt/dx Cosx dx = dt I = € ( 1 - t^2 )^4 /t dt I = € 1 - 4t^2 + 6t^4 - 4t^6 + t^8 /t dt I = € 1/t - 4t + 6t^3 - 4t^5 + t^7 dt I = ln|t| - 2t^2 + 3t^4/2 - 2t^6/3 + t^8/8 + C I = ln|sin| - 2sin^2x + 3sin^4x/2 - 2sin^6x/3 + sin^8x/8 + C

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