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

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

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

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

The value of int_(0)^(pi//2)ln((sin^(2)theta)/(cos^(3)theta))d theta is

int(d theta)/(sin theta cos^(3)theta) is equal to

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

Show that int_(0)^(pi//2) (cos^(2) theta)/(cos^(2) theta + 4 sin^(2) theta)d theta = (pi)/(6)

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 d theta=

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