What is the integral of ln(x)sqrt(x^{13)} ?

The integral of ln(x)sqrt(x^{13)} is 2/15 x^{15/2}ln(x)-4/225 x^{15/2}+C

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integral of ln(x)sqrt(x^{13)}

\int ln (x) x^{13} d x

\frac{2}{15} x^{\frac{15}{2}} ln (x) - \frac{4}{225} x^{\frac{15}{2}} + C

Solution steps

\int ln (x) x^{13} d x

Apply Integration By Parts

: \frac{2}{15} x^{\frac{15}{2}} ln (x) - \int \frac{2}{15} x^{\frac{13}{2}} d x

= \frac{2}{15} x^{\frac{15}{2}} ln (x) - \int \frac{2}{15} x^{\frac{13}{2}} d x

\int \frac{2}{15} x^{\frac{13}{2}} d x = \frac{4}{225} x^{\frac{15}{2}}

= \frac{2}{15} x^{\frac{15}{2}} ln (x) - \frac{4}{225} x^{\frac{15}{2}}

Add a constant to the solution

= \frac{2}{15} x^{\frac{15}{2}} ln (x) - \frac{4}{225} x^{\frac{15}{2}} + C

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What is the integral of ln(x)sqrt(x^{13)} ?
The integral of ln(x)sqrt(x^{13)} is 2/15 x^{15/2}ln(x)-4/225 x^{15/2}+C