1. The problem statement, all variables and given/known data Find all f(x) satisfying: ∫f dx ∫1/f dx = -1 2. Relevant equations 3. The attempt at a solution I solved for ∫1/f dx and differentiated both sides (using the quotient rule for the right side): ∫1/f dx = -1 / ∫f dx 1/f = f / (∫f dx)2 (∫f dx)2 = f2 ∫fdx = ±f f = ±f' Solving the differential equation for f = f ' I get f = cex But when I try to prove if my solution is correct, I got: ∫cex dx ∫ 1/(cex) dx = -1 (ex + k1)(-e-x + k2) = -1 And I don't know what to do to get -1 on the left side. Could you give me a hint please?