What is the integral from 0 to 1 of ln^2(x) ?

The integral from 0 to 1 of ln^2(x) is 2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 0 to 1 of ln^2(x)

\int_{0}^{1} ln^{2} (x) d x

2

Solution steps

\int_{0}^{1} ln^{2} (x) d x

Apply Integration By Parts

: [x ln^{2} (x) - \int 2 ln (x) d x]_{0}^{1}

= [x ln^{2} (x) - \int 2 ln (x) d x]_{0}^{1}

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

= [x ln^{2} (x) - 2 (x ln (x) - x)]_{0}^{1}

Compute the boundaries:

2

= 2

\int_{0}^{1} \frac{1 - x}{1 + x} d x

\int_{2}^{4} x^{2} - 6 x + 9 d x

\int_{0}^{1} \frac{1}{( 5 - 4 x ) ^{2}} d x

\int_{- 4}^{0} - x^{2} - 4 x d x

\int_{1}^{2} \frac{6}{x} d x

What is the integral from 0 to 1 of ln^2(x) ?
The integral from 0 to 1 of ln^2(x) is 2