# Computing two integrals - per-partes?

I start with integrals and attempting to figure out these two integrals, but can't move from a spot

1. $\int x^2 lnx dx$
2. $\int \frac{lnx}{\sqrt[3]{x}}dx$

The first example - it doesn't look so complicated, but I just can't get the right result. And the second looks pretty complicated, not sure what do to first there.

Thank you

• For the second one, use the "rationalizing substitution" $\ u^3 \ = \ x \$ , then keep in mind that $\ \ln (u^3) \ = \ 3 \ \ln u \$ . – colormegone May 3 '14 at 18:56

$$\int x^2 \ln x dx = \frac{1}{3} \int \ln x d(x^3) = \frac{1}{3} \ln x x^3 - \frac{1}{3} \int x^3 d(\ln x) = \frac{1}{3} \ln x x^3 - \frac{1}{3} \int x^2 dx$$
$$= \frac{1}{3} \ln x \ x^3 - \frac{1}{9}x^3 + C$$