`int_0^(pi/2)(sin2theta)/(sin^4theta+cos^4theta) d theta`

if I=int_0^(pi/4) (sin2theta)/(sin^2theta+cos^4theta)d(theta) then I equals

Consider int_0^(pi//2)(sin2thetad theta)/(sin^4theta+cos^4theta) Show that value of the integral is pi/2 .

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

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)(sin4theta)/(sintheta)d theta=0

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