Can someone help me find the integral of 1/(1+cos(x))dx

Answer 1

Multiply and divide by 1 - cosx to get:

∫ [(1 - cosx) / (1-cos²x)] dx = ∫ [(1 - cosx) / sin²x]dx = ∫ csc²x dx - ∫[cosx / sin²x]dx = -cotx - ∫[cosx / sin²x]dx

Do the remaining integral by u-substitution using u = sinx.