# How do you use partial fraction decomposition to decompose the fraction to integrate #(x^2-4)^-1#?

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To decompose the fraction ( \frac{1}{x^2 - 4} ) using partial fraction decomposition, you would first factor the denominator ( x^2 - 4 ) as ( (x - 2)(x + 2) ). Then, you express the fraction as the sum of two simpler fractions with undetermined coefficients:

[ \frac{1}{x^2 - 4} = \frac{A}{x - 2} + \frac{B}{x + 2} ]

Where ( A ) and ( B ) are constants to be determined. Then, you solve for ( A ) and ( B ) by finding a common denominator and equating coefficients. Once you have ( A ) and ( B ), you integrate each term separately.

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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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