What is the integral from 1 to 5 of 8/x ?

The integral from 1 to 5 of 8/x is 8ln(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 8/x

\int_{1}^{5} \frac{8}{x} d x

8 ln (5)

Decimal Notation

12.87550 \dots

Solution steps

\int_{1}^{5} \frac{8}{x} d x

Take the constant out:

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

= 8 \cdot \int_{1}^{5} \frac{1}{x} d x

Use the common integral:

\int \frac{1}{x} d x = ln (∣ x ∣)

= 8 [ln ∣ x ∣]_{1}^{5}

Compute the boundaries:

ln (5)

= 8 ln (5)

\int_{- 5}^{4} x^{2} + 5 - x d x

\int_{1}^{x} \frac{1}{1 + t ^{2}} d t

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

\int_{0}^{\frac{π}{2}} 8 + 4 cos (x) d x

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

What is the integral from 1 to 5 of 8/x ?
The integral from 1 to 5 of 8/x is 8ln(5)