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

The integral from-1 to 1 of (x-3+1/(x-2)) is -ln(3)-6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from-1 to 1 of (x-3+1/(x-2))

\int_{- 1}^{1} (x - 3 + \frac{1}{x - 2}) d x

- ln (3) - 6

Decimal

- 7.09861 \dots

Solution steps

\int_{- 1}^{1} x - 3 + \frac{1}{x - 2} 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}^{1} x d x - \int_{- 1}^{1} 3 d x + \int_{- 1}^{1} \frac{1}{x - 2} d x

\int_{- 1}^{1} x d x = 0

\int_{- 1}^{1} 3 d x = 6

\int_{- 1}^{1} \frac{1}{x - 2} d x = - ln (3)

= 0 - 6 - ln (3)

Simplify

= - ln (3) - 6

What is the integral from-1 to 1 of (x-3+1/(x-2)) ?
The integral from-1 to 1 of (x-3+1/(x-2)) is -ln(3)-6