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Chapter 6: Problem 6

Identify \(u\) and \(d v\) for finding the integral using integration by parts. (Do not evaluate the integral.) $$ \int \ln 3 x d x $$

Short Answer

Expert verified
In the integral \(\int \ln 3x dx\), the term \(u\) is \(\ln 3x\) and \(dv\) is \(dx\). So, \(du = \frac{1}{x} dx\) and \(v = x\).

Step by step solution

01

Identify the \(u\) term

From the integral \(\int \ln 3x dx\), for easier differentiation, \(u\) is chosen as \(\ln 3x\).
02

Differentiating \(u\)

The derivative of \(u\), denoted as \(du\), would hence be given by \( \frac{1}{x} dx\).
03

Identify the \(dv\) term

The remaining part \(\int dx\) is chosen as \(dv\). It is chosen to be \(dv\) because it is easy to integrate.
04

Integrating \(dv\)

The integral of \(dv\), denoted as \(v\), is simply \(x\).

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