Final answer to the problem
$-\frac{1}{4}\ln\left|x+2\right|+\frac{1}{4}\ln\left|x-2\right|+C_0$
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Step-by-step Solution
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(1/(x^2-4))dx. Rewrite the expression \frac{1}{x^2-4} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x+2\right)\left(x-2\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{4\left(x+2\right)}+\frac{1}{4\left(x-2\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{4\left(x+2\right)}dx results in: -\frac{1}{4}\ln\left(x+2\right).
Final answer to the problem
$-\frac{1}{4}\ln\left|x+2\right|+\frac{1}{4}\ln\left|x-2\right|+C_0$
