# How to find the antiderivative of #(5x)/(x^2-1)dx#?

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To find the antiderivative of (5x)/(x^2 - 1)dx, you can use the method of partial fraction decomposition. First, factor the denominator as (x - 1)(x + 1). Then, express the integrand as a sum of partial fractions with undetermined coefficients:

(5x)/(x^2 - 1) = A/(x - 1) + B/(x + 1)

Find the values of A and B by equating the numerators:

5x = A(x + 1) + B(x - 1)

Once you have the values of A and B, integrate each term separately to find the antiderivative. The result will be:

Antiderivative = A ln|x - 1| + B ln|x + 1| + C, where C is the constant of integration.

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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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