Final answer to the problem
$-\frac{1}{2}\ln\left|x+1\right|+\frac{1}{x}+\frac{1}{2}\ln\left|x-1\right|+C_0$
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Step-by-step Solution
Learn how to solve integrals of rational functions problems step by step online. Find the integral int(1/((x^2-1)x^2))dx. Rewrite the expression \frac{1}{\left(x^2-1\right)x^2} inside the integral in factored form. Rewrite the fraction \frac{1}{\left(x+1\right)x^2\left(x-1\right)} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{2\left(x+1\right)}+\frac{-1}{x^2}+\frac{1}{2\left(x-1\right)}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{2\left(x+1\right)}dx results in: -\frac{1}{2}\ln\left(x+1\right).
Final answer to the problem
$-\frac{1}{2}\ln\left|x+1\right|+\frac{1}{x}+\frac{1}{2}\ln\left|x-1\right|+C_0$
