What is the integral of x^{1/8}ln(x) ?

The integral of x^{1/8}ln(x) is 8/9 x^{9/8}ln(x)-64/81 x^{9/8}+C

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integral of x^{1/8}ln(x)

\int x^{\frac{1}{8}} ln (x) d x

\frac{8}{9} x^{\frac{9}{8}} ln (x) - \frac{64}{81} x^{\frac{9}{8}} + C

Solution steps

\int x^{\frac{1}{8}} ln (x) d x

Apply Integration By Parts

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

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

\int \frac{8}{9} x^{\frac{1}{8}} d x = \frac{64}{81} x^{\frac{9}{8}}

= \frac{8}{9} x^{\frac{9}{8}} ln (x) - \frac{64}{81} x^{\frac{9}{8}}

Add a constant to the solution

= \frac{8}{9} x^{\frac{9}{8}} ln (x) - \frac{64}{81} x^{\frac{9}{8}} + C

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What is the integral of x^{1/8}ln(x) ?
The integral of x^{1/8}ln(x) is 8/9 x^{9/8}ln(x)-64/81 x^{9/8}+C