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Integral Calculus
nipun
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Joined: 6 Jan 2009
Post: 20
6 Jan 2009 23:03:06 IST
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integration of (sin^8 x - cos^8 x)/(1-2sin^2 (x) cos^2 (x)). Please give whole solution
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Integral Calculus

integration of (sin^8 x - cos^8 x)/(1-2sin^2 (x) cos^2 (x)). Please give whole solution


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venkat
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Joined: 30 Nov 2008
Posts: 49
6 Jan 2009 23:16:32 IST
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(sin^4x-cos^4x)(sin^4x+cos^4x)/[1-2sin^2xcos^2x]


=(sin^2x+cos^2x)(sin^2x-cos^2x)[(sin^2x+cos^2x)^2-2sin^2xcos^2x]/[1-2sin^2xcos^2x]


=(-cos2x)(1-2sin^2xcos^2x)/[1-2sin^2xcos^2x]


=integral(-cos2x)


-sin2x/2+c


all the best for your exams.


please reply me.
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