# How do you find the integral of #int 1/(1 + sec(x))#?

Take note of this:

Apply the parametric formula now:

Then:

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To find the integral of ( \int \frac{1}{1 + \sec(x)} ), you can use the substitution method. Let ( u = \tan(\frac{x}{2}) ). Then ( \sec(x) = \frac{1}{\cos(x)} = \frac{1}{\frac{1 - u^2}{1 + u^2}} = \frac{1 + u^2}{1 - u^2} ). Rewrite the integral in terms of ( u ). After simplifying, you will get a form that can be integrated using standard techniques.

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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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