Question

Find three integrals in Exercises 21–66 that can be solved by the application of double-angle formulas.

Short answer

$$\begin{gathered} \int \tan 2xdx \\ \int sec4xdx \\ \int se{c}^{3}2xdx \end{gathered}$$

Step-by-step solution

Step 1. Given information

Double-angle formulas are to be used.

Step 2. Explanation

Double angle formulas are as follows:

$\begin{array}{rcl}\sin 2x& =& 2\sin x\cos x\\ \cos 2x& =& 2{\cos }^{2}x-1\\ \tan 2x& =& \frac{2\tan x}{1-{\tan }^{2}x}\end{array}$

Following integrals can be solved by the application of double-angle formulas:

$$\begin{gathered} \int \tan 2xdx \\ \int sec4xdx \\ \int se{c}^{3}2xdx \end{gathered}$$