What is the integral of x*ln(x) ?

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

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integral of x*ln(x)

\int x \cdot ln (x) d x

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

Solution steps

\int x ln (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{\partial}{\partial x} (x \cdot y)

\int_{0}^{π} (sin (x))^{2} d x

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

\frac{d}{d x} (8^{x} - 5^{x})

x \to 0 + lim ((4 x)^{\frac{4}{x}})

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