# How do you integrate #int 2/sqrt(x^2-4)dx# using trigonometric substitution?

Use x = 2*sec(u) as a first substitution.

So, we have:

And there we have it, let me know if you need any help with the last bit but it's fairly easy to figure out if you look at a few triangles.

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To integrate ( \int \frac{2}{\sqrt{x^2 - 4}} , dx ) using trigonometric substitution, let ( x = 2\sec\theta ). Then, ( dx = 2\sec\theta \tan\theta , d\theta ). Substitute these into the integral, and simplify to express the integral in terms of ( \theta ). Finally, solve the resulting integral in terms of ( \theta ), and resubstitute ( x ) to obtain the final answer.

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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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