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

= \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

\frac{2}{x ^{2}}

\frac{d}{d x} (ln ((x^{2})^{2}))

(- π, 0), (- \frac{π}{2}, 4)

\frac{2}{y}

\int \frac{x ^{2} - 2}{2 x} d x

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