int(d theta)/(sin theta cos^(3)theta)=

int(d theta)/((sin theta-2cos theta)(2sin theta+cos theta))=

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

int (d theta)/((sin theta - 2 cos theta)(2 sin theta + cos theta))

Let the be an integrable function defined on [0,a] if I_(1)=int_(pi//2)^(pi//2) cos theta f(sin theta cos ^(2) theta)d theta and I_(2)=int_(0)^(pi//2)sin 2 theta f(sin theta cos ^(2) theta)d theta then

int_(0)^((pi)/(2))(sin^(3)theta)/(sin^(3)theta+cos^(3)theta)d theta

int(sin^(6)theta+cos^(6)theta)/(sin^(2)theta cos^(2)theta)d theta=

I=int_(0)^( pi/4)(sin2 theta)/(sin^(2)theta+cos^(4)theta)d theta

int _(0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) theta )=

int _(0)^(pi//4) ( 4 sin 2 theta d theta )/(sin^(4) theta +cos^(4) theta )=

Evaluate int _(0)^(pi//2) (cos^(4) theta)/(sin^(4) theta + cos^(4) theta)d theta