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

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

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integral of 1/((a+x))

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

ln ∣ a + x ∣ + C

Solution steps

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

= ln ∣ a + x ∣

Add a constant to the solution

= ln ∣ a + x ∣ + C