Evaluate: (i) `intsec^4x\ dx`

Explanation

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

### Step 1: Rewrite the integral
We start with the integral:
\[ I = \int \sec^4 x \, dx \]
We can express \(\sec^4 x\) in terms of \(\sec^2 x\) and \(\tan^2 x\):
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