`int _(0)^(pi) (xdx)/(1+cosalphasinx),`0<`alpha`<`pi`.

Evaluate: int_0^pi(x dx)/(1+cosalphasinx),w h e r e0ltalphaltpidot

int_(0)^( pi/4)sec xdx

int_(0)^(pi/4)(sec^6xdx)

int_0^(pi/2) cos^5xdx

int_0^(pi/4) sec^4xdx

int_0^(pi/4) tan^3xdx

int_0^pi xcos^2xdx

int_(0)^( pi)x sin^(-1)xdx

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)sec^(2)xdx