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

The integral of (1/(x-5)) is 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-5))

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

ln ∣ x - 5 ∣ + C

Solution steps

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

Apply u-substitution

: \int \frac{1}{u} d u

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x - 5

= ln ∣ x - 5 ∣

Add a constant to the solution

= ln ∣ x - 5 ∣ + C

\int 2 sec^{6} (10 x) d x

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

\int 4 sin (5 x + 7) d x

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

\int \frac{x - 18}{x ^{2} ( x + 2 )} d x