The problem is:

int (1+sinx)/(1-sin)dx

I tried doing this:

Let u=sinx, x=sin^(-1)u, so dx= du/sqrt(1-u^2)

Then I got

integral of (1+u)/(1-u)*(du)/(sqrt(1-u^2))

which is equal to

integral of ((1+u)*sqrt(1-u^2))/((1-u)^2(1+u)) du

I tried to figure it out using partial fractions from there, but that didn't work out. Any suggestions? Thanks!

When I multiply by (1-sinx)/(1-sinx) I just end up with

integral of cosx/(2-2sinx-cos^2x)dx

which I still don't know how to integrate.