# How do you integrate #(x^2+3x)/(x^2-4)# using partial fractions?

The answer is

Since the degree of the numerator is not less than the degree of the denominator, perform a long division

Therefore,

By factorising the denominator,

Now, we perform the partial fraction decomposition

So,

Therefore,

So,

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To integrate (x^2 + 3x)/(x^2 - 4) using partial fractions, you first factor the denominator as (x - 2)(x + 2). Then, express the given fraction as the sum of two simpler fractions:

(x^2 + 3x)/(x^2 - 4) = A/(x - 2) + B/(x + 2)

To find A and B, multiply both sides by (x - 2)(x + 2) to clear the denominators. Then, substitute appropriate values of x to solve for A and B. Once you have A and B, integrate each term separately. Finally, combine the integrals to get the result.

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