What is the integral from 2 to 4 of xln(x) ?

The integral from 2 to 4 of xln(x) is 14ln(2)-3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 4 of xln(x)

\int_{2}^{4} x ln (x) d x

14 ln (2) - 3

Decimal

6.70406 \dots

Solution steps

\int_{2}^{4} x ln (x) d x

Apply Integration By Parts

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

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

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

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

Compute the boundaries:

14 ln (2) - 3

= 14 ln (2) - 3

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

\int_{0}^{x} 4 e^{- 2 x} d x

\int_{0}^{1} \frac{1}{e ^{- x} + e ^{x}} d x

\int_{0}^{\frac{π}{6}} 8 cos (x) d x

\int_{0}^{\frac{π}{2}} (x + 1) sin (x) d x

What is the integral from 2 to 4 of xln(x) ?
The integral from 2 to 4 of xln(x) is 14ln(2)-3