Evaluate `int_(0)^(pi)(xsinx)/(1+cos^(2)x)dx`

Evaluate : int_(0)^(pi)(4xsinx)/(1+cos^(2)x)dx.

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

Evaluate int _(0)^(pi//2)(dx)/(1+ cos x)

Evaluate the integrals by using substitution int_(0)^(pi/2)(sinx)/(1+cos^(2)x)dx

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

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

Evaluate int _(0)^(pi//2) sqrt(1+ cos x ) dx

Prove that int_(0 )^(a) f (x) dx = int_(0)^(a) f (a -x) dx hence evaluate int_(0)^(pi/2) ( cos^5 x)/( cos^2 x+ sinn ^5 x) dx