I'm having trouble with an integral involved in deriving the work-energy theorem 1. The problem statement, all variables and given/known data I'm trying to get from ∫mv/√(1-v^2/c^2)dv to -mc^2(1-v^2/c^2). 2. Relevant equations 3. The attempt at a solution I start out by putting gamma on top to yield: ∫mv(1-v^2/c^2)^-1/2, then I square everything to get rid of the square root term and end up with: ∫m^2 v^2 - m^2 v^2 (v^2/c^2)dv, and then to get rid of the fractions I end up with: ∫c^2 m^2 v^2 - m^2 v^4dv, which, when I try to integrate, gets me no where close to the answer. What am I doing wrong? Should I be doing a U-substitution or chain rule?