So, the integral becomes:
$\int (\sec^2(x) - 1)(1 + \tan^2(x)) dx$
Now, we expand the expression inside the integral:
$\int (\sec^2(x) + \tan^2(x)\sec^2(x) - 1 - \tan^2(x)) dx$
Next, we split the integral into separate terms:
$\int \sec^2(x) dx + \int
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