Question

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

Answer 1

$\ln|x+5|+C$

Answer 2

Solution:

Let

$$u = x+5 \quad \Rightarrow \quad du = dx.$$

Then the integral transforms to

$$\int \frac{1}{u}\,du = \ln|u|+C.$$

Substitute back to get:

$$\ln|x+5|+C.$$

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Core Explanation:
Substitute $u=x+5$ then integrate to obtain $\ln|u|+C$ and substitute back.