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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

\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

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