What is the integral from 2 to 4 of x/(x-1) ?

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

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 x/(x-1)

\int_{2}^{4} \frac{x}{x - 1} d x

2 + ln (3)

Decimal

3.09861 \dots

Solution steps

\int_{2}^{4} \frac{x}{x - 1} d x

Apply u-substitution

= \int_{1}^{3} \frac{u + 1}{u} d u

Expand

\frac{u + 1}{u} : 1 + \frac{1}{u}

= \int_{1}^{3} 1 + \frac{1}{u} d u

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

\int_{1}^{3} 1 d u = 2

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

= 2 + ln (3)

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