# How do I evaluate the integral #intsec^3(x) tan(x) dx#?

I would start by writing your integrand as:

I can write the integral in a new equivalent form:

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To evaluate the integral (\int \sec^3(x) \tan(x) , dx), you can use the substitution method. Let ( u = \sec(x) + \tan(x) ) and ( du = (\sec(x)\tan(x) + \sec^2(x)) , dx ).

Then, the integral becomes (\int u^3 , du), which is straightforward to integrate. After integrating, substitute back ( u = \sec(x) + \tan(x) ) to get the final result.

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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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