Integrate the functions`tan^3 2xsec2x`

Explanation

To solve the integral of the function \( \tan^3(2x) \sec(2x) \, dx \), we can follow these steps:

### Step 1: Rewrite the integral
We start with the integral:
\[ \int \tan^3(2x) \sec(2x) \, dx \]
We can rewrite \( \tan^3(2x) \) as \( \tan^2(2x) \tan(2x) \) and use the identity \( \tan^2(2x) = \sec^2(2x) - 1 \):
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