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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 4/(x+2)

\int \frac{4}{x + 2} d x

4 ln ∣ x + 2 ∣ + C

Solution steps

\int \frac{4}{x + 2} d x

Take the constant out:

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

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

Apply u-substitution

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

= 4 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 4 ln ∣ u ∣

Substitute back

u = x + 2

= 4 ln ∣ x + 2 ∣

Add a constant to the solution

= 4 ln ∣ x + 2 ∣ + C

y^{^{''}} - 4 y^{^{'}} - 5 y = 0, y (0) = 3, y^{^{'}} (0) = 9

\int \frac{s}{( s ^{2} + 16 ) ^{2}} d s

\frac{d}{d x} (100 (y - x^{2})^{2} + (1 - x)^{2})

\frac{d}{d x} (\frac{24 x}{2 x + 3})

x \to 0 lim (\frac{x}{- x})