What is the integral from 1 to 2 of x*ln(x) ?

The integral from 1 to 2 of x*ln(x) is 2ln(2)-3/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of x*ln(x)

\int_{1}^{2} x \cdot ln (x) d x

2 ln (2) - \frac{3}{4}

Decimal Notation

0.63629 \dots

Solution steps

\int_{1}^{2} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

2 ln (2) - \frac{3}{4}

= 2 ln (2) - \frac{3}{4}

n = 0 \sum \infty \frac{1}{( n ^{2} + 1 )}

y = \frac{2}{x - 6}, (8, 1)

5 x - 6 y (x^{2} + 1) \frac{d y}{d x} = 0

2 y y^{^{'}} + 2 = y^{2} + 2 x, y (0) = 7

\int 16 arctan (x) d x

What is the integral from 1 to 2 of x*ln(x) ?
The integral from 1 to 2 of x*ln(x) is 2ln(2)-3/4