What is the integral of (1/(x+5)) ?

The integral of (1/(x+5)) is ln|x+5|+C

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integral of (1/(x+5))

\int (\frac{1}{x + 5}) d x

ln ∣ x + 5 ∣ + C

Solution steps

\int \frac{1}{x + 5} 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 + 5

= ln ∣ x + 5 ∣

Add a constant to the solution

= ln ∣ x + 5 ∣ + C

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