`int_0^(pi/2) sintheta costheta (a^2sin^2 theta+b^2cos^2theta)^(1/2) d theta=(1/3)((a^2+ab+b^2)/(a+b))`

int_(0)^((pi)/(2))sinthetacostheta(a^(2)sin^(2)theta+b^(2)cos^(2)theta)^((1)/(2))d theta=(1)/(3)((a^(2)+ab+b^(2))/(a+b))

int_0^(pi//2)(theta/sintheta)^2d theta=

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

int(cos2theta)/((sintheta+costheta)^2)d theta is equal to

Prove that int_0^(pi/2)(costheta-sintheta)/(1+sintheta.costheta)d theta=0.

int_(pi//4)^(pi//2)(costheta)/((cos\ (theta)/(2)+sin\ (theta)/(2)))\ d theta

int(cos2theta)/((sintheta+costheta)^(2))d""theta is equal to

int(cos2theta)/((sintheta+costheta)^(2))d""theta is equal to