Final answer to the problem
$\frac{-3}{2\left(x+1\right)}+\frac{-3}{2\left(x-1\right)}+\frac{3}{2}\ln\left|x+1\right|-\frac{3}{2}\ln\left|x-1\right|+C_0$
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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(6/((x^2-1)^2))dx. Rewrite the expression \frac{6}{\left(x^2-1\right)^2} inside the integral in factored form. Rewrite the fraction \frac{6}{\left(x+1\right)^2\left(x-1\right)^2} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{3}{2\left(x+1\right)^2}+\frac{3}{2\left(x-1\right)^2}+\frac{3}{2\left(x+1\right)}+\frac{-3}{2\left(x-1\right)}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{3}{2\left(x+1\right)^2}dx results in: \frac{-3}{2\left(x+1\right)}.
Final answer to the problem
$\frac{-3}{2\left(x+1\right)}+\frac{-3}{2\left(x-1\right)}+\frac{3}{2}\ln\left|x+1\right|-\frac{3}{2}\ln\left|x-1\right|+C_0$
