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

The integral of y*ln(y) is 1/2 y^2ln(y)-(y^2)/4+C

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integral of y*ln(y)

\int y \cdot ln (y) d y

\frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4} + C

Solution steps

\int y ln (y) d y

Apply Integration By Parts

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

\int \frac{y}{2} d y = \frac{y ^{2}}{4}

= \frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4}

Add a constant to the solution

= \frac{1}{2} y^{2} ln (y) - \frac{y ^{2}}{4} + C

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What is the integral of y*ln(y) ?
The integral of y*ln(y) is 1/2 y^2ln(y)-(y^2)/4+C