What is the integral of 1/(x(x+35)) ?

The integral of 1/(x(x+35)) is 1/35 ln|x|-1/35 ln|x+35|+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(x+35))

\int \frac{1}{x ( x + 35 )} d x

\frac{1}{35} ln ∣ x ∣ - \frac{1}{35} ln ∣ x + 35 ∣ + C

Solution steps

\int \frac{1}{x ( x + 35 )} d x

Take the partial fraction of

\frac{1}{x ( x + 35 )} : \frac{1}{35 x} - \frac{1}{35 ( x + 35 )}

= \int \frac{1}{35 x} - \frac{1}{35 ( x + 35 )} 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}{35 x} d x - \int \frac{1}{35 ( x + 35 )} d x

\int \frac{1}{35 x} d x = \frac{1}{35} ln ∣ x ∣

\int \frac{1}{35 ( x + 35 )} d x = \frac{1}{35} ln ∣ x + 35 ∣

= \frac{1}{35} ln ∣ x ∣ - \frac{1}{35} ln ∣ x + 35 ∣

Add a constant to the solution

= \frac{1}{35} ln ∣ x ∣ - \frac{1}{35} ln ∣ x + 35 ∣ + C

\int (x y + z) d z

\int x \cdot sin^{3} (3 x) d x

\int \frac{4 x ^{2} + 4 x + 4}{( x ^{2} + 1 ) ^{2}} d x

\int \frac{9 t ^{2} - 2}{3 t + 1} d t

\int \frac{x}{( x - 1 ) ( x ^{2} + 6 x + 11 )} d x

What is the integral of 1/(x(x+35)) ?
The integral of 1/(x(x+35)) is 1/35 ln|x|-1/35 ln|x+35|+C