What is the integral of xln(-6x) ?

The integral of xln(-6x) is 1/2 x^2ln(-6x)-(x^2)/4+C

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integral of xln(-6x)

\int x ln (- 6 x) d x

\frac{1}{2} x^{2} ln (- 6 x) - \frac{x ^{2}}{4} + C

Solution steps

\int x ln (- 6 x) d x

Apply Integration By Parts

= \frac{1}{2} x^{2} ln (- 6 x) - \int \frac{x}{2} d x

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

= \frac{1}{2} x^{2} ln (- 6 x) - \frac{x ^{2}}{4}

Add a constant to the solution

= \frac{1}{2} x^{2} ln (- 6 x) - \frac{x ^{2}}{4} + C

What is the integral of xln(-6x) ?
The integral of xln(-6x) is 1/2 x^2ln(-6x)-(x^2)/4+C