Evaluate the indefinite integral. (Remember to use absolute values where appropriate. Use $C$ for the constant of integration.)
\[
\int \frac{d x}{k x+g} \quad(k \neq 0)
\]

Answer

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Answer

Final Answer: $\boxed{\frac{1}{k} \ln |kx+g| + C}$

Steps

Step 1 ：The integral is in the form of $\int \frac{1}{ax+b} dx$, which is a standard integral form.

Step 2 ：The integral of $\frac{1}{ax+b}$ with respect to $x$ is $\frac{1}{a} \ln |ax+b| + C$, where $C$ is the constant of integration.

Step 3 ：In this case, $a=k$ and $b=g$.

Step 4 ：So, the integral of $\frac{1}{kx+g}$ with respect to $x$ is $\frac{1}{k} \ln |kx+g| + C$.

Step 5 ：Final Answer: $\boxed{\frac{1}{k} \ln |kx+g| + C}$