integração p/ partes

[graça]

\(\int \chi \varepsilon \left ( 3x \right )dx\)

[Man Utd]

\(\int \chi \varepsilon \left ( 3x \right )dx\)

olá

está meio confuso,seria \(\int x*e^{3x}dx\) ? se sim confira a resolução:

\(\\\\\\ \int x*e^{3x}dx \\\\ u=x\rightarrow du=dx \\\\ dv=e^{3x}dx\rightarrow v=\frac{e^{3x}}{3} \\\\\\ \int x*e^{3x}dx =x*\frac{e^{3x}}{3}-\int \frac{e^{3x}}{3} dx \\\\\\ \int x*e^{3x}dx =x*\frac{e^{3x}}{3}-\frac{1}{3}\int e^{3x}dx \\\\\\ \int x*e^{3x}dx =x*\frac{e^{3x}}{3}-\frac{1}{3}*(\frac{e^{3x}}{3}) \\\\\\ \int x*e^{3x}dx =x*\frac{e^{3x}}{3}-\frac{e^{3x}}{9}+C\)

att mais