1. The problem statement, all variables and given/known data prove the following reduction formula, n>0 ∫((1+x^2)^n) dx=(x(1+x^2)^n)(1/(2n+1)) +2n/(2n+1)∫(1+x^2)^(n-1) dx 2. Relevant equations none 3. The attempt at a solution one of many attempts, i get close, but no cigar. Huge blow to the calculus ego. Any help would be greatly appreciated. I just need a point in the right direction. ∫((1+x^2)^n) dx=uv-∫vdu u=(1+x^2)^n dv=dx du= n(1+x^2)^(n-1)(2x)dx v=x ∫((1+x^2)^n) dx=x(1+x^2)^n -2n∫(x^2)((1+x^2)^(n-1))dx if i use another iteration of integration by parts (IBP) it just gets worse. i tried to substitute for x^2 but it didnt really help either.