What is the integral of p^7ln(p) ?

The integral of p^7ln(p) is 1/8 p^8ln(p)-(p^8)/(64)+C

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integral of p^7ln(p)

\int p^{7} ln (p) d p

\frac{1}{8} p^{8} ln (p) - \frac{p ^{8}}{64} + C

Solution steps

\int p^{7} ln (p) d p

Apply Integration By Parts

: \frac{1}{8} p^{8} ln (p) - \int \frac{p ^{7}}{8} d p

= \frac{1}{8} p^{8} ln (p) - \int \frac{p ^{7}}{8} d p

\int \frac{p ^{7}}{8} d p = \frac{p ^{8}}{64}

= \frac{1}{8} p^{8} ln (p) - \frac{p ^{8}}{64}

Add a constant to the solution

= \frac{1}{8} p^{8} ln (p) - \frac{p ^{8}}{64} + C

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What is the integral of p^7ln(p) ?
The integral of p^7ln(p) is 1/8 p^8ln(p)-(p^8)/(64)+C