`int_(pi/2)^pi e^x ((1-sinx)/(1-cosx))dx`

Evaluate int_(pi/3)^(pi/2) e^x((1+sinx)/(1+cosx))dx

int_(0)^(pi//2)e^(x)((1+sinx)/(1+cosx))dx=?

Evaluate: int_0^(pi//2) e^x (sinx-cosx) dx

Determine the value of int_(-pi)^(pi) (2x(1+sinx))/(1+cos^(2)x)dx .

Evaluate the following integral: int_(-pi)^pi(2x(1+sinx))/(1+cos^2dx)dx

int_0^(pi/2) cosx/(1+sinx)dx

int_(0)^(pi//2)(sinx)/(sqrt(1+cosx))dx

Evaluate int_0^(pi/2) (sinx-cosx)/(1+sinxcosx)dx

int_(-pi//2)^(pi//2)(sinx)/(1+cos^(2)x)e^(-cos^(2)x)dx is equal to

If I_(1)=int_(0)^((pi)/(2))e^(sinx)(1+x cos x)dx and I_(2)=int_(0)^((pi)/(2))e^(cosx)(1-x sin x)dx, then [(I_(1))/(I_(2))] is equal to (where [x] denotes the greatest integer less than or equal to x)