The function `f(theta)=d/(d(theta))int_0^theta(dx)/(1-costhetacosx)` satisfies the differential equation

The function (d)/(d theta)int_(0)^( theta)(dx)/(1-cos theta cos x) satisfies

The function f(theta)=(d)/(d theta)int_(0)^( theta)(d theta)/((1-cos2 theta)(1+cos2 theta)) satisfies the differential equation.

f(theta)=int_0^1 (x+sin theta)^2 dx

int tan^(5)theta d theta=

int (tan theta d theta) / (1-sin theta)

int(costheta-cos2theta)/(1-cos theta)d theta=

int sin^4 theta d theta

int sin ^ (3) theta d theta

Solve int(cos^(3)theta)/(1-sin theta)d theta