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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

\int (3 + \frac{1}{2 x + 2}) d x

3 x + \frac{1}{2} ln ∣ 2 x + 2 ∣ + C

Solution steps

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

\int 3 d x = 3 x

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

= 3 x + \frac{1}{2} ln ∣ 2 x + 2 ∣

Add a constant to the solution

= 3 x + \frac{1}{2} ln ∣ 2 x + 2 ∣ + C

\int sec (x) sec (x) d x

\int 21 x cos (3 x) - 8 sin (3 x) d x

\int sin^{11} (x) cos^{4} (x) d x

\int (2 x ln (x)) d x

\int x csc^{2} (a x) d x

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