TITLE: Per partes integration: $\int x^2 \ln x dx$
QUESTION [6 upvotes]: Can I asked you guys for help with solving of this integral? Thank you.
It could go well with the per-parted method, but I am not able to finish it.
$$\int x^2 \ln x dx$$

REPLY [2 votes]: $$\int x^{2}\ln(x)\ dx=\left[\frac{1}{3}x^3\ln(x)\right]-\int \frac{1}{3}x^2dx=\frac{1}{3}x^3\ln(x) - \frac{1}{9}x^3 + C.$$