To evaluate the integral \(\int \tan^3(2x) \sec(2x) \, dx\), we can use a substitution method to simplify the expression and then integrate. Here's how to solve it:

### Step 1: Substitution

Let's use the substitution method. We know that the derivative of \(\tan(2x)\) is related to \(\sec^2(2x)\), which can help us in the integration process.

1. **Substitute**: Let \( u = \tan(2x) \). Then, the derivative \( du = 2 \sec^2(2x) \, dx \) or \( \frac{du}{2} = \sec^2(2x) \, dx \).

2. **Rewrite the integral**:

Learn how to evaluate the integral ∫ tan^3(2x) sec(2x) dx using substitution method. This problem involves trigonometric functions and integration techniques. Suitable for college-level students studying calculus.

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