What is the integral of p^8ln(p) ?

The integral of p^8ln(p) is 1/9 p^9ln(p)-(p^9)/(81)+C

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integral of p^8ln(p)

\int p^{8} ln (p) d p

\frac{1}{9} p^{9} ln (p) - \frac{p ^{9}}{81} + C

Solution steps

\int p^{8} ln (p) d p

Apply Integration By Parts

: \frac{1}{9} p^{9} ln (p) - \int \frac{p ^{8}}{9} d p

= \frac{1}{9} p^{9} ln (p) - \int \frac{p ^{8}}{9} d p

\int \frac{p ^{8}}{9} d p = \frac{p ^{9}}{81}

= \frac{1}{9} p^{9} ln (p) - \frac{p ^{9}}{81}

Add a constant to the solution

= \frac{1}{9} p^{9} ln (p) - \frac{p ^{9}}{81} + C

\int cos^{3} (8 x) sin^{- 2} (8 x) d x

y^{^{'}} = \frac{( y ^{2} + 1 )}{2 y}

\int \frac{12 x ^{2} + x + 2}{x ( x ^{2} + 1 )} d x

n = 1 \sum \infty \frac{3}{n + 1}

f (x) = sin (8 x + 4)

What is the integral of p^8ln(p) ?
The integral of p^8ln(p) is 1/9 p^9ln(p)-(p^9)/(81)+C