Prove that: `int_0^(2pi)(xsin^(2n)x)/(sin^(2n)+cos^(2n)x)dx`= `pi^2`

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

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

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

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

Evaluate int_(0)^(2pi)(xcos^(2n)x)/(cos^(2n)x+sin^(2n)x)dx

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

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

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

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