Integration by parts

The idea

$\int u\frac{dv}{dx}\,dx = uv - \int v\frac{du}{dx}\,dx$. Choose $u$ to be the part that gets simpler when differentiated, usually the power of $x$; with $\ln x$, always choose $u = \ln x$.

1. Pick $u$ and $\frac{dv}{dx}$; find $\frac{du}{dx}$ and $v$.
2. Write $uv - \int v\frac{du}{dx}\,dx$.
3. Integrate what is left; use parts again if needed.

Watch out Keep the minus sign in front of the second integral.