What is the integral of p^6ln(p) ?

The integral of p^6ln(p) is 1/7 p^7ln(p)-(p^7)/(49)+C

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integral of p^6ln(p)

\int p^{6} ln (p) d p

\frac{1}{7} p^{7} ln (p) - \frac{p ^{7}}{49} + C

Solution steps

\int p^{6} ln (p) d p

Apply Integration By Parts

= \frac{1}{7} p^{7} ln (p) - \int \frac{p ^{6}}{7} d p

\int \frac{p ^{6}}{7} d p = \frac{p ^{7}}{49}

= \frac{1}{7} p^{7} ln (p) - \frac{p ^{7}}{49}

Add a constant to the solution

= \frac{1}{7} p^{7} ln (p) - \frac{p ^{7}}{49} + C

What is the integral of p^6ln(p) ?
The integral of p^6ln(p) is 1/7 p^7ln(p)-(p^7)/(49)+C