What is the integral of 1/((x-2)(x-5)) ?

The integral of 1/((x-2)(x-5)) is -1/3 ln|x-2|+1/3 ln|x-5|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 1/((x-2)(x-5))

\int \frac{1}{( x - 2 ) ( x - 5 )} d x

- \frac{1}{3} ln ∣ x - 2 ∣ + \frac{1}{3} ln ∣ x - 5 ∣ + C

Solution steps

\int \frac{1}{( x - 2 ) ( x - 5 )} d x

Take the partial fraction of

\frac{1}{( x - 2 ) ( x - 5 )} : - \frac{1}{3 ( x - 2 )} + \frac{1}{3 ( x - 5 )}

= \int - \frac{1}{3 ( x - 2 )} + \frac{1}{3 ( x - 5 )} 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}{3 ( x - 2 )} d x + \int \frac{1}{3 ( x - 5 )} d x

\int \frac{1}{3 ( x - 2 )} d x = \frac{1}{3} ln ∣ x - 2 ∣

\int \frac{1}{3 ( x - 5 )} d x = \frac{1}{3} ln ∣ x - 5 ∣

= - \frac{1}{3} ln ∣ x - 2 ∣ + \frac{1}{3} ln ∣ x - 5 ∣

Add a constant to the solution

= - \frac{1}{3} ln ∣ x - 2 ∣ + \frac{1}{3} ln ∣ x - 5 ∣ + C

\int 6 x (4 x^{2} - 9)^{2} d x

f (x) = 3 x - 0.6 x ln (x)

x \to 2 lim (x^{2} - 8 x - 2)

\frac{\partial}{\partial x} (3 x^{2} + 2 x y - 7 y^{2})

f (x) = 3 - 5 x^{2}

What is the integral of 1/((x-2)(x-5)) ?
The integral of 1/((x-2)(x-5)) is -1/3 ln|x-2|+1/3 ln|x-5|+C