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Integral Calculus

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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

Cool goIITian

Joined: 30 Nov 2008
Posts: 49
6 Jan 2009 23:16:32 IST
1 people liked this

(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.

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