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

The integral of (3x)/(x-1) is 3(x-1+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)/(x-1)

\int \frac{3 x}{x - 1} d x

3 (x - 1 + ln ∣ x - 1 ∣) + C

Solution steps

\int \frac{3 x}{x - 1} d x

Take the constant out:

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

= 3 \cdot \int \frac{x}{x - 1} d x

Apply u-substitution

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

= 3 \cdot \int \frac{u + 1}{u} d u

Expand

\frac{u + 1}{u} : 1 + \frac{1}{u}

= 3 \cdot \int 1 + \frac{1}{u} d u

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= 3 (\int 1 d u + \int \frac{1}{u} d u)

\int 1 d u = u

\int \frac{1}{u} d u = ln ∣ u ∣

= 3 (u + ln ∣ u ∣)

Substitute back

u = x - 1

= 3 (x - 1 + ln ∣ x - 1 ∣)

Add a constant to the solution

= 3 (x - 1 + ln ∣ x - 1 ∣) + C

\int 4 cos (\frac{1}{4} π x) d x

\int cos^{2 x} (d) x d x

\int x^{2} sin (x^{3} + 2) d x

\int e^{5 - 3 x} d x

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

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