What is the integral of 3-4/(2x+1) ?

The integral of 3-4/(2x+1) is 3x-2ln|2x+1|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3-4/(2x+1)

\int 3 - \frac{4}{2 x + 1} d x

3 x - 2 ln ∣ 2 x + 1 ∣ + C

Solution steps

\int 3 - \frac{4}{2 x + 1} 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 3 d x - \int \frac{4}{2 x + 1} d x

\int 3 d x = 3 x

\int \frac{4}{2 x + 1} d x = 2 ln ∣ 2 x + 1 ∣

= 3 x - 2 ln ∣ 2 x + 1 ∣

Add a constant to the solution

= 3 x - 2 ln ∣ 2 x + 1 ∣ + C

f (x) = 3 x^{5} - 4 x^{4} + 9 x - 6

\int_{0}^{1} 2 π (8 - x) (x^{2}) d x

\int_{- 2}^{2} 2 - x^{2} d x

(x^{2} + 1)^{x + 1}

\frac{d}{d x} (x^{3} + 4 x - 15)

What is the integral of 3-4/(2x+1) ?
The integral of 3-4/(2x+1) is 3x-2ln|2x+1|+C