What is the integral of ln(x)x^5 ?

The integral of ln(x)x^5 is 1/6 x^6ln(x)-(x^6)/(36)+C

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integral of ln(x)x^5

\int ln (x) x^{5} d x

\frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36} + C

Solution steps

\int ln (x) x^{5} d x

Apply Integration By Parts

: \frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x

= \frac{1}{6} x^{6} ln (x) - \int \frac{x ^{5}}{6} d x

\int \frac{x ^{5}}{6} d x = \frac{x ^{6}}{36}

= \frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36}

Add a constant to the solution

= \frac{1}{6} x^{6} ln (x) - \frac{x ^{6}}{36} + C

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What is the integral of ln(x)x^5 ?
The integral of ln(x)x^5 is 1/6 x^6ln(x)-(x^6)/(36)+C