Evaluate : `intsec^4 x tan x dx.`

Explanation

To evaluate the integral \( \int \sec^4 x \tan x \, dx \), we can use substitution and integration techniques. Here’s a step-by-step solution:

### Step 1: Identify the substitution
Notice that the derivative of \( \sec x \) is \( \sec x \tan x \). This suggests that we can use \( t = \sec x \) as our substitution.

### Step 2: Differentiate the substitution
Differentiate \( t = \sec x \):
\[
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