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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

integral of 3/(2+x)

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

3 ln ∣ 2 + x ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 3 ln ∣ u ∣

Substitute back

u = 2 + x

= 3 ln ∣ 2 + x ∣

Add a constant to the solution

= 3 ln ∣ 2 + x ∣ + C

\frac{d y}{d x} + 10 tan (10 x) y = 5 cos (10 x)

y^{^{'}} = y^{2} sin (t)

x \to 0 lim (x csc (4 x))

11

\frac{d}{d x} (\frac{2 x}{4 x - 1})