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

The integral from 1 to 2 of (ln(2x))/(2x) is (3ln^2(2))/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 2 of (ln(2x))/(2x)

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

\frac{3 ln ^{2} ( 2 )}{4}

Decimal

0.36033 \dots

Solution steps

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

Take the constant out:

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

= \frac{1}{2} \cdot \int_{1}^{2} \frac{ln ( 2 x )}{x} d x

Apply u-substitution

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

= \frac{1}{2} \cdot \int_{2}^{4} \frac{ln ( u )}{u} d u

Apply u-substitution

: \int_{l n (2)}^{2 l n (2)} v d v

= \frac{1}{2} \cdot \int_{l n (2)}^{2 l n (2)} v d v

Apply the Power Rule

: [\frac{v ^{2}}{2}]_{l n (2)}^{2 l n (2)}

= \frac{1}{2} [\frac{v ^{2}}{2}]_{l n (2)}^{2 l n (2)}

Compute the boundaries:

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

= \frac{1}{2} (2 ln^{2} (2) - \frac{ln ^{2} ( 2 )}{2})

Simplify

= \frac{3 ln ^{2} ( 2 )}{4}

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

\int_{1}^{s i n (x)} 4 t^{3} d t

\int_{0}^{\frac{1}{4}} sin^{2} (π x) d x

\int_{4}^{e^{x}} (y^{4} sin (y)) d y

\int_{0}^{\frac{π}{2}} 4 x cos (2 x) d x

What is the integral from 1 to 2 of (ln(2x))/(2x) ?
The integral from 1 to 2 of (ln(2x))/(2x) is (3ln^2(2))/4