What is the integral of (xln(x)) ?

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

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integral of (xln(x))

\int (x 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

\int (x + 1) y^{2} \cdot sin (\frac{x y}{3}) d x

x \to 0 - lim (g (t))

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

y^{^{''}} + 4 y = 2 sin (2 x)

\int \frac{1}{4 x ^{2} + 9} d x

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