What is the integral of (x+5)/(x-2) ?

The integral of (x+5)/(x-2) is x-2+7ln|x-2|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (x+5)/(x-2)

\int \frac{x + 5}{x - 2} d x

x - 2 + 7 ln ∣ x - 2 ∣ + C

Solution steps

\int \frac{x + 5}{x - 2} d x

Apply u-substitution

: \int \frac{u + 7}{u} d u

= \int \frac{u + 7}{u} d u

Expand

\frac{u + 7}{u} : 1 + \frac{7}{u}

= \int 1 + \frac{7}{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 d u + \int \frac{7}{u} d u

\int 1 d u = u

\int \frac{7}{u} d u = 7 ln ∣ u ∣

= u + 7 ln ∣ u ∣

Substitute back

u = x - 2

= x - 2 + 7 ln ∣ x - 2 ∣

Add a constant to the solution

= x - 2 + 7 ln ∣ x - 2 ∣ + C

\int 6 θ cos (θ) d θ

\frac{x + 2}{4 x - 3}

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

y^{^{'}} = y^{2} - 3 y

\int x (2 x + 5)^{8} d x

What is the integral of (x+5)/(x-2) ?
The integral of (x+5)/(x-2) is x-2+7ln|x-2|+C