What is the integral of x^7ln(3x) ?

The integral of x^7ln(3x) is 1/8 x^8ln(3x)-(x^8)/(64)+C

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integral of x^7ln(3x)

\int x^{7} ln (3 x) d x

\frac{1}{8} x^{8} ln (3 x) - \frac{x ^{8}}{64} + C

Solution steps

\int x^{7} ln (3 x) d x

Apply Integration By Parts

= \frac{1}{8} x^{8} ln (3 x) - \int \frac{x ^{7}}{8} d x

\int \frac{x ^{7}}{8} d x = \frac{x ^{8}}{64}

= \frac{1}{8} x^{8} ln (3 x) - \frac{x ^{8}}{64}

Add a constant to the solution

= \frac{1}{8} x^{8} ln (3 x) - \frac{x ^{8}}{64} + C

What is the integral of x^7ln(3x) ?
The integral of x^7ln(3x) is 1/8 x^8ln(3x)-(x^8)/(64)+C