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

Answer

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Answer

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

Steps

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

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

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

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

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