Final answer to the problem
$-\frac{1}{16}\arctan\left(\frac{x}{2}\right)-\frac{1}{32}\ln\left|x+2\right|+\frac{1}{32}\ln\left|-x+2\right|+C_0$
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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^4-16))dx. Rewrite the expression \frac{1}{x^4-16} inside the integral in factored form. Take the constant \frac{1}{-1} out of the integral. Rewrite the fraction \frac{1}{\left(4+x^2\right)\left(2+x\right)\left(2-x\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{8\left(4+x^2\right)}+\frac{1}{32\left(2+x\right)}+\frac{1}{32\left(2-x\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$-\frac{1}{16}\arctan\left(\frac{x}{2}\right)-\frac{1}{32}\ln\left|x+2\right|+\frac{1}{32}\ln\left|-x+2\right|+C_0$
