" iv."int_(0)^(2 pi)(x sin^(2n)x)/(sin^(2n)x+cos^(2n)x)dx

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

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

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

Len N be set of natural numbers. For n in N defiine I_(n)=int_(0)^(pi) (x sin^(2n)(x))/(sin^(2n)(x)+cos^(2n)(x)) dx . Then for m,n in N