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int(0)^(2 pi)(x sin^(2n)x)/(sin^(2n)x+co...

int_(0)^(2 pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2)x)dx,(n in N)/(x)

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

For n gt 0 int_(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

For n gt 0 int_(0)^(2pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx= ….

Prove that, int_(0)^(2pi)(xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx=pi^(2) .

int_(0)^(2pi) (xsin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx,n gt 0 , is equal to

For n in N, int_(0)^(2pi) (x sin^(2n)x)/(sin^(2n) x + cos^(2n) x) dx=

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

The value of the integral int_0^pi (x sin^(2n) x)/(sin^(2n) x + cos^(2n) x)dx is :