1. The problem statement, all variables and given/known data Find the integral of 1/(1+cosx) dx from -pi/2 to pi/2. 2. Relevant equations None. 3. The attempt at a solution Here's my work: 1/(1+cosx)=(1-cosx)/((1+cosx)(1-cosx))=(1-cosx)/(1-cos^2 x)=(1-cosx)/sin^2 x This is what I've got so far. But this doesn't seem to simplify the integrand.