What is the integral of 1/((x+3)) ?

The integral of 1/((x+3)) is ln|x+3|+C

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integral of 1/((x+3))

integral

\frac{1}{( x + 3 )}

ln ∣ x + 3 ∣ + C

Solution steps

\int \frac{1}{x + 3} d x

Apply u-substitution

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

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

Use the common integral:

\int \frac{1}{u} d u = ln (∣ u ∣)

= ln ∣ u ∣

Substitute back

u = x + 3

= ln ∣ x + 3 ∣

Add a constant to the solution

= ln ∣ x + 3 ∣ + C

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