What is the integral of xln(4x) ?

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

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integral of xln(4x)

\int x ln (4 x) d x

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

Solution steps

\int x ln (4 x) d x

Apply Integration By Parts

: \frac{1}{2} x^{2} ln (4 x) - \int \frac{x}{2} d x

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

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

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

Add a constant to the solution

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

x \to 2 + lim (\frac{x}{( 2 - x ) ^{3}})

y^{^{'}} + \frac{y}{x} - y = 0

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\frac{d}{d θ} ((1 + 2 sin (θ)) cos (θ))

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