a*int_(0)^( pi/4)(sin2 theta)/(sin^(4)theta^(4)+cos^(4)theta)d theta

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

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

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

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

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

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

int_(0)^(pi)(sin4theta)/(sintheta)d theta=0

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)) (sin2 theta) / (sin ^ (4) theta + cos (4) theta) d theta

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