1. The problem statement, all variables and given/known data ∫(x^3)/(x^2 + 9) dx 2. Relevant equations 3. The attempt at a solution This question can be solved using long division, but I just wanted to know why I can't do it this other way. So I start with one substitution, t = x^2, dt = 2xdx. By taking out 1/2 from the integrand, I can make the integral: ∫(t dt)/(t + 9) Then, using another substitution, u = t + 9, t = u - 9, du = dt I make the equation into: ∫(u - 9)du / (u) Separating the integrand into two separate integrals, I can solve it, and it becomes: 1/2 [(x^2 + 9) - 9ln(x^2 + 9)] + C However, this isn't the right answer because the right answer does't contain a 9/2 constant inside. Why can't I solve this integral this way? Thanks for any help in advance.