Solving this the simple way I got the right solution, but I also tried to solve it a different way and got it wrong. I want to know where I went wrong the second way. 1. The problem statement, all variables and given/known data ∫cosh2(x)sinh(x)dx = ? 2. Relevant equations cosh(x)sinh(x) = (1/2)*sinh(2x) 3. The attempt at a solution The solution is simple by guessing and checking with the chain rule: ∫cosh2(x)sinh(x)dx = 1/3*cosh3(x) But then I try to manipulate the expression in the integral I get a different result: cosh2(x)sinh(x) = cosh(x)cosh(x)sinh(x) = cosh(x)*(1/2)*sinh(2x) = (ex+e-x)/2*(1/2)*(e2x-e-2x)/2 = (1/4)*((e3x-e-3x)/2+(ex-e-x)/2 = (1/4)*(sinh(3x)+sinh(x)) Integrating that gives (1/4)*∫(sinh(3x)+sinh(x))dx = (1/4)*(∫sinh(3x)dx+∫sinh(x)dx) = (1/4)*((cosh(3x)/3)+cosh(x)) I'm not sure how to directly compare the two results, but plugging in some number for x and solving each shows that they aren't equal. I'm quite sure the first solution is correct, so where did I go wrong in the second?