Originally Posted by

**arbolis** I'm betting I have to solve it using partial fractions : $\displaystyle \int \frac{2x^3+3x^2+2x+4}{(x^2+1)^2}dx$. So I found $\displaystyle A$, $\displaystyle B$, $\displaystyle C$ and $\displaystyle D$ and I reached to that the solution must be equal to $\displaystyle \int \frac{2x+3}{x^2+1}+\frac{4}{(x^2+1)^2}dx=\ln |x^2+1|+4\int \frac{dx}{(x^2+1)^2}$. And I'm stuck here! This last integral looks quite simple I know, and is very similar to $\displaystyle \arctan (x)$, but I don't know how to solve it. I tried by integration by parts, u-substitution. Should I try for trigonometric substitution? If yes, please start me up making a good choice for the sub. I'm not used to trigo-sub... Thanks.