What is the integral from 2 to 6 of ln(x) ?

The integral from 2 to 6 of ln(x) is 2ln(108)-4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2 to 6 of ln(x)

\int_{2}^{6} ln (x) d x

2 ln (108) - 4

Decimal

5.36426 \dots

Solution steps

\int_{2}^{6} ln (x) d x

Apply Integration By Parts

= [x ln (x) - \int 1 d x]_{2}^{6}

\int 1 d x = x

= [x ln (x) - x]_{2}^{6}

Compute the boundaries:

6 ln (6) - 4 - 2 ln (2)

= 6 ln (6) - 4 - 2 ln (2)

Simplify

= 2 ln (108) - 4

What is the integral from 2 to 6 of ln(x) ?
The integral from 2 to 6 of ln(x) is 2ln(108)-4