$\int\frac{2x}{x^2-4}dx$

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$\int\frac{2x}{\left(x+2\right)\left(x-2\right)}dx$

Learn how to solve problems step by step online. int((2x)/(x^2-4))dx. Rewrite the expression \frac{2x}{x^2-4} inside the integral in factored form. Apply the formula: \int\frac{ab}{c}dx=a\int\frac{b}{c}dx, where a=2, b=x and c=\left(x+2\right)\left(x-2\right). Rewrite the fraction \frac{x}{\left(x+2\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{2\left(x+2\right)}+\frac{1}{2\left(x-2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.