1. The problem statement, all variables and given/known data ∫((cosX)-1)/x dx 2. Relevant equations Taylor Series 3. The attempt at a solution My approach was basically to to split the integral into two more manageable parts which gave me ∫(cosX/x)dx - ∫(1/x)dx The solutions manual did it completely differently and instead changed the index of the sum to start from n=1 instead of n=0 which "ate up" the 1 on top. I guess my question is, did I do it wrong or is my solution correct, only not as pretty? I got the same sum as they did, except mine starts at 0 and I have an extra natural log.