What is the integral of ((x+5))/(x^2+10x) ?

The integral of ((x+5))/(x^2+10x) is 1/2 ln|x|+1/2 ln|x+10|+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+10x)

\int \frac{( x + 5 )}{x ^{2} + 10 x} d x

\frac{1}{2} ln ∣ x ∣ + \frac{1}{2} ln ∣ x + 10 ∣ + C

Solution steps

\int \frac{x + 5}{x ^{2} + 10 x} d x

Take the partial fraction of

\frac{x + 5}{x ^{2} + 10 x} : \frac{1}{2 x} + \frac{1}{2 ( x + 10 )}

= \int \frac{1}{2 x} + \frac{1}{2 ( x + 10 )} 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 \frac{1}{2 x} d x + \int \frac{1}{2 ( x + 10 )} d x

\int \frac{1}{2 x} d x = \frac{1}{2} ln ∣ x ∣

\int \frac{1}{2 ( x + 10 )} d x = \frac{1}{2} ln ∣ x + 10 ∣

= \frac{1}{2} ln ∣ x ∣ + \frac{1}{2} ln ∣ x + 10 ∣

Add a constant to the solution

= \frac{1}{2} ln ∣ x ∣ + \frac{1}{2} ln ∣ x + 10 ∣ + C

\int (x^{2} + 3 x) sin (x) d x

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

\int \frac{1 - x}{- x ^{2}} d x

\int \frac{1}{2 y + 5} d y

\int \frac{9}{1 - x ^{2}} d x

What is the integral of ((x+5))/(x^2+10x) ?
The integral of ((x+5))/(x^2+10x) is 1/2 ln|x|+1/2 ln|x+10|+C