What is the integral from 2 to 5 of x/(x-1) ?

The integral from 2 to 5 of x/(x-1) is 3+2ln(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral from 2 to 5 of x/(x-1)

\int_{2}^{5} \frac{x}{x - 1} d x

3 + 2 ln (2)

Decimal

4.38629 \dots

Solution steps

\int_{2}^{5} \frac{x}{x - 1} d x

Apply u-substitution

: \int_{1}^{4} \frac{u + 1}{u} d u

= \int_{1}^{4} \frac{u + 1}{u} d u

Expand

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

= \int_{1}^{4} 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}^{4} 1 d u + \int_{1}^{4} \frac{1}{u} d u

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

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

= 3 + 2 ln (2)

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

\int_{0}^{1} (4 x + 3 x^{2}) d x

\int_{0}^{x} t cos (t) d t

\int_{0}^{1} x^{17} + 1 7^{x} d x

\int_{1}^{2} v d v

What is the integral from 2 to 5 of x/(x-1) ?
The integral from 2 to 5 of x/(x-1) is 3+2ln(2)