What is the integral of (ln(x))^2 ?

The integral of (ln(x))^2 is 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

Popular >

integral of (ln(x))^2

\int (ln (x))^{2} d x

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

Solution steps

\int (ln (x))^{2} d x

Apply Integration By Parts

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

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

\int 2 ln (x) d x = 2 (x ln (x) - x)

= x ln^{2} (x) - 2 (x ln (x) - x)

Add a constant to the solution

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

\int_{- 1}^{1} ((1) - (x^{2})) d x

\frac{\partial}{\partial y} ((x + y)^{2} + (x + 1)^{2})

n = 2 \sum \infty \frac{1}{n 4 ^{n}}

6 e^{x} cos (x)

f (x) = - \frac{1}{( 5 x + 1 ) ^{2}}

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