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