Problem

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

Solution

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: \(\boxed{\frac{1}{k} \ln |kx+g| + C}\)

From Solvely APP
Source: https://solvelyapp.com/problems/8527/

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