`int_0^(pi/4) (2sinthetacostheta)/(sin^4theta+cos^4theta)d theta`

int(2sin theta cos theta)/(sin^(4)theta+cos^(4)theta)d theta

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

The value of the integral int_(0)^(pi//4) (sin theta+cos theta)/(9+16 sin 2theta)d theta , is

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

int(2sin2 theta-cos theta)/(6-cos^(2)theta-4sin theta)d theta

int_(0)^( pi)(sin theta+cos theta)/(sqrt(1+sin2 theta))d theta

sin^2theta+cos^4theta=cos^2theta+sin^4theta

Find :int(cos theta)/((4+sin^(2)theta)(5-4cos^(2)theta))d 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