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