What is the integral of x^8ln(3x) ?

The integral of x^8ln(3x) is 1/9 x^9ln(3x)-(x^9)/(81)+C

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integral of x^8ln(3x)

\int x^{8} ln (3 x) d x

\frac{1}{9} x^{9} ln (3 x) - \frac{x ^{9}}{81} + C

Solution steps

\int x^{8} ln (3 x) d x

Apply Integration By Parts

: \frac{1}{9} x^{9} ln (3 x) - \int \frac{x ^{8}}{9} d x

= \frac{1}{9} x^{9} ln (3 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 (3 x) - \frac{x ^{9}}{81}

Add a constant to the solution

= \frac{1}{9} x^{9} ln (3 x) - \frac{x ^{9}}{81} + C

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What is the integral of x^8ln(3x) ?
The integral of x^8ln(3x) is 1/9 x^9ln(3x)-(x^9)/(81)+C