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

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

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integral of ln(x)x^8

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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