What is the integral from 0 to 1 of ln(x)x ?

The integral from 0 to 1 of ln(x)x is -1/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of ln(x)x

\int_{0}^{1} ln (x) x d x

- \frac{1}{4}

Decimal

- 0.25

Solution steps

\int_{0}^{1} ln (x) x d x

Apply Integration By Parts

: [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{1}

= [\frac{1}{2} x^{2} ln (x) - \int \frac{x}{2} d x]_{0}^{1}

\int \frac{x}{2} d x = \frac{x ^{2}}{4}

= [\frac{1}{2} x^{2} ln (x) - \frac{x ^{2}}{4}]_{0}^{1}

Compute the boundaries:

- \frac{1}{4}

= - \frac{1}{4}

\int_{2}^{6} 7 d x

\int_{1}^{5} \frac{ln ( r )}{r ^{2}} d r

\int_{x^{3}}^{8} 2 x y d y

\int_{0}^{(4 - x^{2})} y d y

\int_{0}^{6} - 3 x^{2} - 12 x + 180 d x

What is the integral from 0 to 1 of ln(x)x ?
The integral from 0 to 1 of ln(x)x is -1/4