What is the integral from 0 to 1 of 3ln(6x) ?

The integral from 0 to 1 of 3ln(6x) is 3(ln(6)-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 0 to 1 of 3ln(6x)

\int_{0}^{1} 3 ln (6 x) d x

3 (ln (6) - 1)

Decimal

2.37527 \dots

Solution steps

\int_{0}^{1} 3 ln (6 x) d x

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= 3 \cdot \int_{0}^{1} ln (6 x) d x

Apply Integration By Parts

= 3 [x ln (6 x) - \int 1 d x]_{0}^{1}

\int 1 d x = x

= 3 [x ln (6 x) - x]_{0}^{1}

Compute the boundaries:

ln (6) - 1

= 3 (ln (6) - 1)

What is the integral from 0 to 1 of 3ln(6x) ?
The integral from 0 to 1 of 3ln(6x) is 3(ln(6)-1)