`int_(0)^(pi//2) (sin^(2)theta)/ (1+cos theta)^(2) d theta =`

The value of int_(0)^(pi//2)ln((sin^(2)theta)/(cos^(3)theta))d theta is

int (sin ^ (2) theta) / ((1 + cos theta) ^ (2)) d theta

int_ (0) ^ (pi / 2) ((theta) / (sin theta)) ^ (2) d theta =

int_(0)^( pi/2) sin^(2)theta cos theta d theta

int_(0)^( pi/2)sin^(2)theta d theta=

int_(0)^( pi/2)sin^(2)theta d theta=

If I_(1)=int_(0)^(1)(dx)/(e^(x)(1+x)) and I_(2)=int_(0)^( pi/2)(e^(sin^(2)theta)sin theta cos theta d theta)/((2-sin^(2)theta)) then (where [ .] denotes greatest integer function)

int_(0)^(2pi) (sin 2 theta)/(a-b cos 2 theta )d theta =

int_(0)^((pi)/(2))sin^(2)theta cos^(6)theta d theta equals