Question

$\int x^3\log xdx$

Answer 1

$$\begin{gathered} \int x^3\log xdx \\ \mathrm{Taking}\log x\mathrm{as}\mathrm{the}\mathrm{first}\mathrm{function}\mathrm{and}{x}^3\mathrm{as}\mathrm{the}\mathrm{second}\mathrm{function}. \\ =\log x\int x^{3}dx-\int \left(\frac{d}{dx}\log x\int x^{3}dx\right)dx \\ =\left(\log x\right)\frac{x^4}{4}-\int \frac{1}{x}\left(\frac{x^4}{4}\right)dx \\ =\frac{x^4}{x}\log x-\frac{x^4}{16}+C \end{gathered}$$