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

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

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integral of 1/((2+x))

integral

\frac{1}{( 2 + x )}

ln ∣ 2 + x ∣ + C

Solution steps

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

Apply u-substitution

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = 2 + x

= ln ∣ 2 + x ∣

Add a constant to the solution

= ln ∣ 2 + x ∣ + C