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

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

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integral of 1/((x+a))

integral

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

ln ∣ x + a ∣ + C

Solution steps

\int \frac{1}{x + a} 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 = x + a

= ln ∣ x + a ∣

Add a constant to the solution

= ln ∣ x + a ∣ + C