7.1 Integration By Parts/12

Evaluate the integral

${\begin{aligned}\int p^{5}ln(p)dp\\[2ex]\end{aligned}}$

${\begin{aligned}u=ln(p)\quad \quad dv=p^{5}dp\\[2ex]du={\frac {1}{p}}\quad \quad \quad v={\frac {1}{6}}p^{6}\\[2ex]\end{aligned}}$

Failed to parse (unknown function "\begin{align}"): {\displaystyle \begin{align} \int p^5 ln (p)dp \quad = \quad \frac{1}{6}p^6 ln(p) - \int p^6 \frac{1}{p} dp \quad = <pre style="color: red"> \quad \frac{1}{6}p^6 ln(p)-\frac{1}{36}p^6+C </pre> \end{align} }