Try multiplying either by (1-sinx)/(1-sinx).
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.