1. The problem statement, all variables and given/known data lim (x→0) of the definite integral (from 1 to 1+x) of (cos(t))/t all over x 2. Relevant equations Integration by parts L'hospital's rule 3. The attempt at a solution I believe that I must first solve the definite integral, and then take this result and use L'hospital's rule in order to solve the equation. However, using integration by parts on the integral has lead me nowhere. I was hoping somebody could point me in the correct direction. Thanks.