What is the integral of t^{2/5}ln(t) ?

The integral of t^{2/5}ln(t) is 5/7 t^{7/5}ln(t)-25/49 t^{7/5}+C

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integral of t^{2/5}ln(t)

\int t^{\frac{2}{5}} ln (t) d t

\frac{5}{7} t^{\frac{7}{5}} ln (t) - \frac{25}{49} t^{\frac{7}{5}} + C

Solution steps

\int t^{\frac{2}{5}} ln (t) d t

Apply Integration By Parts

: \frac{5}{7} t^{\frac{7}{5}} ln (t) - \int \frac{5}{7} t^{\frac{2}{5}} d t

= \frac{5}{7} t^{\frac{7}{5}} ln (t) - \int \frac{5}{7} t^{\frac{2}{5}} d t

\int \frac{5}{7} t^{\frac{2}{5}} d t = \frac{25}{49} t^{\frac{7}{5}}

= \frac{5}{7} t^{\frac{7}{5}} ln (t) - \frac{25}{49} t^{\frac{7}{5}}

Add a constant to the solution

= \frac{5}{7} t^{\frac{7}{5}} ln (t) - \frac{25}{49} t^{\frac{7}{5}} + C

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What is the integral of t^{2/5}ln(t) ?
The integral of t^{2/5}ln(t) is 5/7 t^{7/5}ln(t)-25/49 t^{7/5}+C