What is the integral of sqrt(y)ln(y) ?

The integral of sqrt(y)ln(y) is 2/3 y^{3/2}ln(y)-4/9 y^{3/2}+C

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integral of sqrt(y)ln(y)

\int y ln (y) d y

\frac{2}{3} y^{\frac{3}{2}} ln (y) - \frac{4}{9} y^{\frac{3}{2}} + C

Solution steps

\int y ln (y) d y

Apply Integration By Parts

: \frac{2}{3} y^{\frac{3}{2}} ln (y) - \int \frac{2}{3} y^{\frac{1}{2}} d y

= \frac{2}{3} y^{\frac{3}{2}} ln (y) - \int \frac{2}{3} y^{\frac{1}{2}} d y

\int \frac{2}{3} y^{\frac{1}{2}} d y = \frac{4}{9} y^{\frac{3}{2}}

= \frac{2}{3} y^{\frac{3}{2}} ln (y) - \frac{4}{9} y^{\frac{3}{2}}

Add a constant to the solution

= \frac{2}{3} y^{\frac{3}{2}} ln (y) - \frac{4}{9} y^{\frac{3}{2}} + C

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What is the integral of sqrt(y)ln(y) ?
The integral of sqrt(y)ln(y) is 2/3 y^{3/2}ln(y)-4/9 y^{3/2}+C