Đặt \(\left\{\begin{array}{l} {u=x} \\ {{\rm d}v={\rm e}^{3x} } \end{array}\right. \Rightarrow \left\{\begin{array}{l} {{\rm d}u={\rm d}x} \\ {v=\frac{1}{3} {\rm e}^{3x} } \end{array}\right. .\)
Khi đó: \(\int x{\rm e}^{3x} {\rm d}x=\frac{1}{3} x{\rm e}^{3x} -\frac{1}{3} \int {\rm e}^{3x} {\rm d}x =\frac{1}{3} x{\rm e}^{3x} -\frac{1}{9} {\rm e}^{3x} +C.\)