# How do you integrate int x^3ln(5x) by integration by parts method?

$\int {x}^{3} \ln \left(5 x\right) \mathrm{dx} = {x}^{4} / 4 \left(\ln \left(5 x\right) - \frac{1}{4}\right)$
$\int {x}^{3} \ln \left(5 x\right) \mathrm{dx} = \int \ln \left(5 x\right) d \left({x}^{4} / 4\right) = {x}^{4} / 4 \ln \left(5 x\right) - \int {x}^{4} / 4 d \left(\ln \left(5 x\right)\right) = {x}^{4} / 4 \ln \left(5 x\right) - \int {x}^{4} / 4 \frac{1}{x} \mathrm{dx} = {x}^{4} / 4 \ln \left(5 x\right) - \int {x}^{3} / 4 \mathrm{dx} = {x}^{4} / 4 \ln \left(5 x\right) - {x}^{4} / 16 \mathrm{dx} = {x}^{4} / 4 \left(\ln \left(5 x\right) - \frac{1}{4}\right)$