# How do you integrate int x^2lnx by parts from [1,2]?

${\int}_{1}^{2} {x}^{2} \ln x \mathrm{dx} = \frac{8}{3} \ln 2 - \frac{7}{9}$
${\int}_{1}^{2} {x}^{2} \ln x \mathrm{dx} = {\int}_{1}^{2} \ln x d \left({x}^{3} / 3\right) = {\left[{x}^{3} / 3 \ln x\right]}_{1}^{2} - {\int}_{1}^{2} {x}^{3} / 3 d \left(\ln x\right) = \frac{8}{3} \ln 2 - {\int}_{1}^{2} {x}^{3} / 3 \frac{\mathrm{dx}}{x} = \frac{8}{3} \ln 2 - {\int}_{1}^{2} {x}^{2} / 3 \mathrm{dx} = \frac{8}{3} \ln 2 - {\left[{x}^{3} / 9\right]}_{1}^{2} = \frac{8}{3} \ln 2 - \frac{7}{9}$