How do I integrate f(x)=(x^3e^(2x))/(x^2 +1)^2 by parts?

$\frac{1}{2} \left[\left(1 + i\right) {e}^{2 i} E i \left(2 x - 2 i\right) + \left(1 - i\right) {e}^{- 2 i} E i \left(2 x + 2 i\right) + \frac{{e}^{2} x}{{x}^{2} + 1}\right] + C$