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" (2) "int(0)^( pi/2)(sin x cos n)/(1+si...

" (2) "int_(0)^( pi/2)(sin x cos n)/(1+sin^(4)x)

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int_(0)^(pi//2)(sin x.cos x)/(1+sin^(4)x)dx=

int_(0)^((pi)/(2))(sin x cos x)/(1+sin^(4)x)dx

int_(0)^( pi/2)((sin x cos x) /(1+sin 4x ))dx

Prove that : int_(0)^(pi//2) (x sin x cos x)/(sin^(4) x+ cos^(4)x)dx =(pi)/(16)

int_(0)^( pi/2)(sin x-cos x)/(1+sin x*cos x)*dx

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int_(0)^(pi//2) (16sin x. cos x)/(sin^(4) x + cos^(4)x)dx=

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int_(0)^(pi//2) (sin x cos x) / ((1 + 2 sin x ) ( 1+ sin x))dx =