What is the integral of 5/(27(x+3)) ?

The integral of 5/(27(x+3)) is 5/27 ln|x+3|+C

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

integral of 5/(27(x+3))

\int \frac{5}{27 ( x + 3 )} d x

\frac{5}{27} ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{5}{27 ( x + 3 )} d x

Take the constant out:

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

= \frac{5}{27} \cdot \int \frac{1}{x + 3} d x

Apply u-substitution

= \frac{5}{27} \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= \frac{5}{27} ln ∣ u ∣

Substitute back

u = x + 3

= \frac{5}{27} ln ∣ x + 3 ∣

Add a constant to the solution

= \frac{5}{27} ln ∣ x + 3 ∣ + C

What is the integral of 5/(27(x+3)) ?
The integral of 5/(27(x+3)) is 5/27 ln|x+3|+C