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

The function f(theta)=(d)/(d(theta))int_(0)^( theta)(dx)/(1-cos theta cos x) 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 theta d theta)/(1-sin theta)

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

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

6) int_0^(pi/4)sec^4theta d theta

6) int_0^(pi/4)sec^4theta d theta