7.1 Integration By Parts/12

Evaluate the integral.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} \int p^5 ln (p)dp \\[2ex] \end{align} }

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://en.wikipedia.org/api/rest_v1/":): {\displaystyle \begin{align} u= ln(p) \quad \quad dv=p^5dp \\[2ex] du = \frac{1}{p} \quad \quad \quad v= \frac{1}{6}p^6 \\[2ex] \end{align} }

Failed to parse (Conversion error. Server ("https://en.wikipedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{aligned}\int p^{5}ln(p)dp\\[2ex]&={\frac {1}{6}}p^{6}ln(p)-\int p^{6}{\frac {1}{p}}dp\\[2ex]&={\frac {1}{6}}p^{6}ln(p)-{\frac {1}{36}}p^{6}+C\end{aligned}}}