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

The integral from 3 to 5 of ((x+2)^2)/(x-2) is 16ln(3)+20

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral from 3 to 5 of ((x+2)^2)/(x-2)

\int_{3}^{5} \frac{( x + 2 ) ^{2}}{x - 2} d x

16 ln (3) + 20

Decimal

37.57779 \dots

Solution steps

\int_{3}^{5} \frac{( x + 2 ) ^{2}}{x - 2} d x

Long division

\frac{( x + 2 ) ^{2}}{x - 2} : x + 6 + \frac{16}{x - 2}

= \int_{3}^{5} x + 6 + \frac{16}{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_{3}^{5} x d x + \int_{3}^{5} 6 d x + \int_{3}^{5} \frac{16}{x - 2} d x

\int_{3}^{5} x d x = 8

\int_{3}^{5} 6 d x = 12

\int_{3}^{5} \frac{16}{x - 2} d x = 16 ln (3)

= 8 + 12 + 16 ln (3)

Simplify

= 16 ln (3) + 20

What is the integral from 3 to 5 of ((x+2)^2)/(x-2) ?
The integral from 3 to 5 of ((x+2)^2)/(x-2) is 16ln(3)+20