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[Post New]9 Apr 2008 10:41:52 IST
    Subject: Re:dx/((sin x)^5+(cos x)^5) integrate this
[Up]
ramkumar_november (1270)

Blazing goIITian

Olaaa!! Perrrfect answer. 230  [290 rates]
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here is a more detailed proof.....
 
I  =  int
 
 
x^5+y^5=(x^2+y^2)(x^3+y^3)-x^2y^2(x+y)
 
sin^5x+cos^5x=(sin^2x+cos^2x)(sin^3x+cos^3x)-sin^2xcos^2x(sinx+cosx)
 
sin^5x+cos^5x=sin^3x+cos^3x-sin^2xcos^2x(sinx+cosx)
 
sin^5x+cos^5x=(sinx+cosx)(sin^2x+cos^2x-sinxcosx)-sin^2xcos^2x(sinx+cosx)
 
sin^5x+cos^5x=(sinx+cosx)(1-sinxcosx)-sin^2xcos^2x(sinx+cosx)
 
sin^5x+cos^5x=(sinx+cosx)(1-sinxcosx-sin^2xcos^2x)
 
so
 
I  =  int
 
multiply numerator and denominator by  sinx+cosx
 
I  =  int
 
I  =  int
 
now proceed by substituting , sinx-cosx=t......
 
clear????
 
sorry for typing mistakes....
 
 
 this reply: 5 points  (with 1 Olaaa!! Perrrfect answer.   in 1 votes )   [?]
 
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