How To integrate x e^3x

 

$$\begin{array}{l}\int x{\mathrm{e}}^{3x}\mathrm{d}x\\ \\ ByParts\\ Let\Rightarrow u=xdv={\mathrm{e}}^{3\mathrm{x}}\\ du=1v=\frac{{\mathrm{e}}^{3\mathrm{x}}}{3}\\ x\frac{{\mathrm{e}}^{3\mathrm{x}}}{3}-\int \frac{{\mathrm{e}}^{3\mathrm{x}}}{3}dx\\ x\frac{{\mathrm{e}}^{3\mathrm{x}}}{3}-\frac{{\mathrm{e}}^{3\mathrm{x}}}{9}\end{array}$$