What is the integral from 2 to 4 of (ln(x))^3 ?

The integral from 2 to 4 of (ln(x))^3 is 30ln^3(2)-42ln^2(2)+36ln(2)-12

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 2 to 4 of (ln(x))^3

\int_{2}^{4} (ln (x))^{3} d x

30 ln^{3} (2) - 42 ln^{2} (2) + 36 ln (2) - 12

Decimal

2.76501 \dots

Solution steps

\int_{2}^{4} (ln (x))^{3} d x

Apply Integration By Parts

= [x ln^{3} (x) - \int 3 ln^{2} (x) d x]_{2}^{4}

\int 3 ln^{2} (x) d x = 3 (x ln^{2} (x) - 2 (x ln (x) - x))

= [x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x))]_{2}^{4}

Compute the boundaries:

30 ln^{3} (2) - 42 ln^{2} (2) + 36 ln (2) - 12

= 30 ln^{3} (2) - 42 ln^{2} (2) + 36 ln (2) - 12

What is the integral from 2 to 4 of (ln(x))^3 ?
The integral from 2 to 4 of (ln(x))^3 is 30ln^3(2)-42ln^2(2)+36ln(2)-12