What is the integral of x^9ln(3x) ?

The integral of x^9ln(3x) is 1/10 x^{10}ln(3x)-(x^{10})/(100)+C

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integral of x^9ln(3x)

\int x^{9} ln (3 x) d x

\frac{1}{10} x^{10} ln (3 x) - \frac{x ^{10}}{100} + C

Solution steps

\int x^{9} ln (3 x) d x

Apply Integration By Parts

: \frac{1}{10} x^{10} ln (3 x) - \int \frac{x ^{9}}{10} d x

= \frac{1}{10} x^{10} ln (3 x) - \int \frac{x ^{9}}{10} d x

\int \frac{x ^{9}}{10} d x = \frac{x ^{10}}{100}

= \frac{1}{10} x^{10} ln (3 x) - \frac{x ^{10}}{100}

Add a constant to the solution

= \frac{1}{10} x^{10} ln (3 x) - \frac{x ^{10}}{100} + C

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What is the integral of x^9ln(3x) ?
The integral of x^9ln(3x) is 1/10 x^{10}ln(3x)-(x^{10})/(100)+C