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Chapter 6: Problem 7

Identify \(u\) and \(d v\) for finding the integral using integration by parts. (Do not evaluate the integral.) $$ \int x \sec ^{2} x d x $$

Short Answer

Expert verified
The selection for the integration by parts is: \(u = x\) and \(d v = \sec^2x dx\).

Step by step solution

01

Identify \(u\) and \(d v\)

In the integral \(\int x \sec ^{2} x d x\), we want to select \(u\) and \(d v\) in a way that will simplify the integral. It is often best to choose \(u\) to be the algebraic part of the expression. So we take \(u\) to be \(x\). Then, the rest of the integrand \(\sec ^{2} x d x\) is our \(d v\).
02

Write down \(u\)

Based on the above, we write down our selection for \(u\). Thus, \(u=x\).
03

Write down \(d v\)

Based on our selection of \(u\), we write down our selection for \(d v\). Thus, \(d v = \sec ^{2} x d x\).

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