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

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

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

Evaluate: int_0^(pi//2)(sin x)/(1+cos^2x)dx

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

If I_(1) = int_(0)^(pi) (x sin x)/(1+cos^2x) dx , I_(2) = int_(0)^(pi) x sin^(4)xdx then, I_(1) : I_(2) is equal to

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

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

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

int_(0)^(pi) x sin x cos^(2)x\ dx

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