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

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

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

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

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

Solution steps

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

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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