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(i) int(0)^(pi//2)(sin^(7)x)/((sin^(7)x+...

`(i) int_(0)^(pi//2)(sin^(7)x)/((sin^(7)x+cos^(7)x))dx=(pi)/(4)`
`(ii) int_(0)^(pi//2)(sin^(5)xdx)/((sin^(5)x+cos^(5)x))dx=(pi)/(4)`

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

int_(0)^(pi/2)(cos^(5)x dx)/(sin^(5)x+cos^(5)x)

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Prove that : int_(0)^(pi//2) (cos^(5))/(sin^(5) x+cos^(5) x)dx= (pi)/(4)

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

int_(0)^(pi//2) (cos^(5)x)/(sin^(5)x+cos^(5)x)dx is equal to

int_(0)^(pi//2)sin^(4)xcos^(5)x dx=