# How do you integrate #sec^3(x)#?

To do this, Integration by Parts is used.

Apply the formula.

May God bless you all. I hope this explanation helps.

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To integrate ( \sec^3(x) ), you can use the method of integration by parts. This involves choosing parts of the integrand to differentiate and integrate separately.

Here's how you can do it:

- Let ( u = \sec(x) ) and ( dv = \sec^2(x) dx ).
- Differentiate ( u ) to get ( du = \sec(x) \tan(x) dx ).
- Integrate ( dv ) to get ( v = \tan(x) ).

Now, use the integration by parts formula:

[ \int u , dv = uv - \int v , du ]

Substitute the values of ( u ), ( dv ), ( du ), and ( v ) into this formula and solve the integral.

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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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