What is the integral of ln(x)x ?

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

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integral of ln(x)x

\int ln (x) x d x

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

Solution steps

\int ln (x) x d x

Apply Integration By Parts

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

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

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

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

Add a constant to the solution

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

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

\frac{\partial}{\partial x} (x^{2} + 2 x y + y^{4})

f (x) = \frac{4}{x}, (- 9, - \frac{4}{9})

\frac{\partial}{\partial y} (x + y - 8)

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