What is the integral of xln(2x) ?

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

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integral of xln(2x)

\int x ln (2 x) d x

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

Solution steps

\int x ln (2 x) d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

\frac{sec ( x )}{x}

\frac{d y}{d x} = e^{x + y}

\frac{d}{d x} (ln (6 x - 5))

\frac{d}{d x} (ln (x^{3} - 27 x - 5))

\frac{d y}{d x} = x - 2

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