What is the integral of (3x-4)/((x-5)(x+1)) ?

The integral of (3x-4)/((x-5)(x+1)) is 11/6 ln|x-5|+7/6 ln|x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of (3x-4)/((x-5)(x+1))

\int \frac{3 x - 4}{( x - 5 ) ( x + 1 )} d x

\frac{11}{6} ln ∣ x - 5 ∣ + \frac{7}{6} ln ∣ x + 1 ∣ + C

Solution steps

\int \frac{3 x - 4}{( x - 5 ) ( x + 1 )} d x

Take the partial fraction of

\frac{3 x - 4}{( x - 5 ) ( x + 1 )} : \frac{11}{6 ( x - 5 )} + \frac{7}{6 ( x + 1 )}

= \int \frac{11}{6 ( x - 5 )} + \frac{7}{6 ( x + 1 )} 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{11}{6 ( x - 5 )} d x + \int \frac{7}{6 ( x + 1 )} d x

\int \frac{11}{6 ( x - 5 )} d x = \frac{11}{6} ln ∣ x - 5 ∣

\int \frac{7}{6 ( x + 1 )} d x = \frac{7}{6} ln ∣ x + 1 ∣

= \frac{11}{6} ln ∣ x - 5 ∣ + \frac{7}{6} ln ∣ x + 1 ∣

Add a constant to the solution

= \frac{11}{6} ln ∣ x - 5 ∣ + \frac{7}{6} ln ∣ x + 1 ∣ + C

\int sin (10 x) sin (20 x) sin (30 x) d x

\int \frac{5 - 4 y ^{2}}{3 + 2 y} d y

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

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

\int 9.8 x + 10 d x

What is the integral of (3x-4)/((x-5)(x+1)) ?
The integral of (3x-4)/((x-5)(x+1)) is 11/6 ln|x-5|+7/6 ln|x+1|+C