# How do you integrate #(sec(x)^2-1)(sin(x)/cos(x))#?

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To integrate (sec(x)^2-1)(sin(x)/cos(x)), you can use the substitution method. Let u = sec(x), then du = sec(x)tan(x)dx. Rewrite the expression as (u^2 - 1)(1/u), which simplifies to (u^2/u - 1/u), and further simplifies to (u - 1/u). Now, substitute u = sec(x) and du = sec(x)tan(x)dx into the integral. This gives ∫(u - 1/u)du. Integrate term by term to get (1/2)u^2 - ln|u| + C. Finally, substitute u = sec(x) back into the expression to get the final result: (1/2)sec^2(x) - ln|sec(x)| + C.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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