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

The integral of (x*ln(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

Popular >

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{d}{d j} (3 i + 4 j)

f (x) = sec^{2} (x) - 3

\int \frac{4 x ^{2} - 81}{x ^{3}} d x

\frac{d}{d x} (\frac{3}{8 ( x + 1 ) ^{\frac{5}{2}}})

(e^{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