What is the integral from 1 to 3 of (x+1/x) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 1 to 3 of (x+1/x)

\int_{1}^{3} (x + \frac{1}{x}) d x

4 + ln (3)

Decimal Notation

5.09861 \dots

Solution steps

\int_{1}^{3} x + \frac{1}{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}^{3} x d x + \int_{1}^{3} \frac{1}{x} d x

\int_{1}^{3} x d x = 4

\int_{1}^{3} \frac{1}{x} d x = ln (3)

= 4 + ln (3)

\int_{50}^{100} \frac{x}{17 + 6 x ^{2}} d x

\int_{0}^{1} x^{3} x^{2} + 1 d x

\int_{1}^{5} 8 x - 16 d x

\int_{0}^{1} x^{\frac{8}{9}} d x

\int_{1}^{5} (x + 1) d x

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