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Note that for sec²(x) - tan²(x) = 1, we have:

-tan²(x) = 1 - sec²(x)

tan²(x) = sec²(x) - 1

Rewrite the expression as:

∫ (sec²(x) - 1) dx

= ∫ sec²(x) dx - ∫ 1 dx

Finally, integrate each expression to get:

tan(x) - x + K where K is the arbitrary constant

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