What is the integral of xln(ax) ?

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

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integral of xln(ax)

\int x ln (a x) d x

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

Solution steps

\int x ln (a x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{d}{d x} (cos (x) cos (y))

\int_{1}^{4} \frac{x ^{2} + 2}{5 x - x ^{2}} d x

x (25.5)

\frac{d}{d x} (x^{2} - 4 x - 2)

f (x) = \frac{4 x}{x + 2}, (2, 2)

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