What is the integral of (ln(x))x ?

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

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integral of (ln(x))x

\int (ln (x)) x d x

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

Solution steps

\int ln (x) x d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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