What is the integral of uln(u) ?

The integral of uln(u) is 1/2 u^2ln(u)-(u^2)/4+C

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integral of uln(u)

\int u ln (u) d u

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

Solution steps

\int u ln (u) d u

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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