What is the integral of \sqrt[5]{x}ln(x) ?

The integral of \sqrt[5]{x}ln(x) is 5/6 x^{6/5}ln(x)-25/36 x^{6/5}+C

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integral of \sqrt[5]{x}ln(x)

\int 5 x ln (x) d x

\frac{5}{6} x^{\frac{6}{5}} ln (x) - \frac{25}{36} x^{\frac{6}{5}} + C

Solution steps

\int 5 x ln (x) d x

Apply Integration By Parts

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

\int \frac{5}{6} x^{\frac{1}{5}} d x = \frac{25}{36} x^{\frac{6}{5}}

= \frac{5}{6} x^{\frac{6}{5}} ln (x) - \frac{25}{36} x^{\frac{6}{5}}

Add a constant to the solution

= \frac{5}{6} x^{\frac{6}{5}} ln (x) - \frac{25}{36} x^{\frac{6}{5}} + C

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What is the integral of \sqrt[5]{x}ln(x) ?
The integral of \sqrt[5]{x}ln(x) is 5/6 x^{6/5}ln(x)-25/36 x^{6/5}+C