Find `int sin^2 theta cos^4 theta d theta`.

int (sin theta + cos theta) * d theta

int sin^4 theta d theta

int _(0) ^(pi) sin ^(2) theta cos theta d theta

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

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

Find (d (sin ^ (2) theta * cos 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

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

Evaluate: int cos2 theta ln((cos theta+sin theta)/(cos theta-sin theta))d theta