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Chapter 4: Problem 2

Find the indefinite integral. $$ \int \frac{1}{x-5} d x $$

Short Answer

Expert verified
The integral of \(\frac{1}{x-5}\) dx is \(ln |x - 5| + C.

Step by step solution

01

Identify integral form

Notice the integral is in the form \(\int \frac{1}{u} du\), where \(u = x - 5\)
02

Apply logarithmic integral rule

By applying the logarithmic integral rule \(\int \frac{1}{u} du = ln |u| + C\), the integral becomes: \(ln |x - 5| + C\), where \(C\) is the constant of integration.

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