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

The integral of ln(x)*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 ln(x)*x

\int ln (x) \cdot 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

f (x) = 2 x 3 - 4 x, at x = - 1

\int - 5 x^{- 1} d x

\int_{- \infty}^{4} \frac{1}{x ^{2} + 1} d x

(\frac{3 x ^{2} - 2}{2 x + 3})^{3}

\int (5 x^{2} + 6 x - 8) d x

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