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