What is the integral of ln^3(x) ?

The integral of ln^3(x) is xln^3(x)-3(xln^2(x)-2(xln(x)-x))+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of ln^3(x)

\int ln^{3} (x) d x

x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

Solution steps

\int ln^{3} (x) d x

Apply Integration By Parts

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

\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))

Add a constant to the solution

= x ln^{3} (x) - 3 (x ln^{2} (x) - 2 (x ln (x) - x)) + C

What is the integral of ln^3(x) ?
The integral of ln^3(x) is xln^3(x)-3(xln^2(x)-2(xln(x)-x))+C