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Since the integral $\int_{1}^{3}\frac{2x}{x^2-4}dx$ has a discontinuity inside the interval, we have to split it in two integrals
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$\int_{1}^{2}\frac{2x}{x^2-4}dx+\int_{2}^{3}\frac{2x}{x^2-4}dx$
Learn how to solve definite integrals problems step by step online. Integrate the function (2x)/(x^2-4) from 1 to 3. Since the integral \int_{1}^{3}\frac{2x}{x^2-4}dx has a discontinuity inside the interval, we have to split it in two integrals. Factor the difference of squares x^2-4 as the product of two conjugated binomials. Factor the difference of squares x^2-4 as the product of two conjugated binomials. Rewrite the fraction \frac{2x}{\left(x+2\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition.