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

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

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integral of 2/(x+2)

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

2 ln ∣ x + 2 ∣ + C

Solution steps

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

Take the constant out:

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

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

Apply u-substitution

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

= 2 \cdot \int \frac{1}{u} d u

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= 2 ln ∣ u ∣

Substitute back

u = x + 2

= 2 ln ∣ x + 2 ∣

Add a constant to the solution

= 2 ln ∣ x + 2 ∣ + C

f (x) = 2 x + 1 + \frac{6}{x}, at x = 2

sin (4 x)

x \to 0 + lim (\frac{2}{x ^{2} - x})

y = cos (5 x + 1)

\frac{6 x}{x + 3}