1. The problem statement, all variables and given/known data Derive a formula for the antiderivative of sec x using the identity that sec x= cos x/ (1-sin^2x). Use a substitution for sin x and then partial fractions. Then multiply the solution by (1+sin x)/ (1+sin x) to obtain the more familiar formula for the antiderivative. 2. Relevant equations Known antiderivative of sec x: ln (tanx+secx)+c 3. The attempt at a solution U= sinx, du =cosxdx intergral of du/1-u^2 integral of A/(1-u) + integral of B/(1+u) = integral of 1/(1-u^2) A+B=1 Au-Bu=0 A= 1/2, B=1/2 plugging back in and integrating I got 1/2(ln(1-sinx)+ln(1+sinx))... can this be simplified more? I am confused about how multiplying my solution by (1+sinx)/(1+sinx) is going to give me the formula I want... perhaps I made a math error? Please help!