What is the integral from 1 to 5 of (4x-4/x) ?

The integral from 1 to 5 of (4x-4/x) is 48-4ln(5)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 5 of (4x-4/x)

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

48 - 4 ln (5)

Decimal Notation

41.56224 \dots

Solution steps

\int_{1}^{5} 4 x - \frac{4}{x} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{5} 4 x d x - \int_{1}^{5} \frac{4}{x} d x

\int_{1}^{5} 4 x d x = 48

\int_{1}^{5} \frac{4}{x} d x = 4 ln (5)

= 48 - 4 ln (5)

\frac{2}{s ^{2} + 2 s + 3}

\frac{- 1 + 3 s ^{2}}{s \cdot ( s ^{2} - 1 )}

\int \frac{x ^{3}}{( 1 + 5 x ^{2} ) ^{3}} d x

\int 4 x^{2} 3 x^{3} + 2 d x

\frac{d}{d x} (\frac{15 x ^{6}}{3 x})

What is the integral from 1 to 5 of (4x-4/x) ?
The integral from 1 to 5 of (4x-4/x) is 48-4ln(5)