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

The integral of-2/(x-1) is -2ln|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-2/(x-1)

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

- 2 ln ∣ x - 1 ∣ + C

Solution steps

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

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= - 2 \cdot \int \frac{1}{x - 1} d x

Apply u-substitution

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

= - 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= - 2 ln ∣ u ∣

Substitute back

u = x - 1

= - 2 ln ∣ x - 1 ∣

Add a constant to the solution

= - 2 ln ∣ x - 1 ∣ + C

\int \frac{x + 1}{x ^{2} - 2 x - 8} d x

\int sin (7 π) t d t

\int \frac{1}{cos ^{4} ( 9 x )} d x

\int \frac{4 x + 6}{( x ^{2} + 3 x + 7 ) ^{4}} d x

\int (6 sec (x) tan (x) - 7 sec^{2} (x)) d x