# How do you integrate #intdx/ sqrt(x^2 - a^2)#?

so:

Use now the trigonometric identity:

Then:

Undoing the substitution:

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Then

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To integrate ( \int \frac{dx}{\sqrt{x^2 - a^2}} ), where ( a ) is a constant:

- Make a trigonometric substitution ( x = a \sec(\theta) ).
- Compute ( dx = a \sec(\theta) \tan(\theta) d\theta ).
- Substitute ( x ) and ( dx ) in terms of ( \theta ) into the integral.
- Simplify the integral in terms of ( \theta ).
- Integrate the simplified expression with respect to ( \theta ).
- Substitute back ( \theta ) in terms of ( x ) to get 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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