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

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

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 (2ln(x))/x

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

3 ln^{2} (2)

Decimal

1.44135 \dots

Solution steps

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

Take the constant out:

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

= 2 \cdot \int_{2}^{4} \frac{ln ( x )}{x} d x

Apply u-substitution

= 2 \cdot \int_{l n (2)}^{2 l n (2)} u d u

Apply the Power Rule

= 2 [\frac{u ^{2}}{2}]_{l n (2)}^{2 l n (2)}

Compute the boundaries:

2 ln^{2} (2) - \frac{ln ^{2} ( 2 )}{2}

= 2 (2 ln^{2} (2) - \frac{ln ^{2} ( 2 )}{2})

Simplify

= 3 ln^{2} (2)

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