Final answer to the problem
$-\frac{1}{4}\ln\left|1+x^2\right|+\frac{1}{4}\ln\left|x+1\right|+\frac{1}{4}\ln\left|-x+1\right|+C_0$
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Step-by-step Solution
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- Integrate by partial fractions
- Integrate by substitution
- Integrate by parts
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
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1
Rewrite the expression $\frac{x}{x^4-1}$ inside the integral in factored form
$\int\frac{x}{-\left(1+x^2\right)\left(1+x\right)\left(1-x\right)}dx$
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\int\frac{x}{-\left(1+x^2\right)\left(1+x\right)\left(1-x\right)}dx$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(x/(x^4-1))dx. Rewrite the expression \frac{x}{x^4-1} inside the integral in factored form. Take the constant \frac{1}{-1} out of the integral. Rewrite the fraction \frac{x}{\left(1+x^2\right)\left(1+x\right)\left(1-x\right)} in 3 simpler fractions using partial fraction decomposition. Simplify the expression.
Final answer to the problem
$-\frac{1}{4}\ln\left|1+x^2\right|+\frac{1}{4}\ln\left|x+1\right|+\frac{1}{4}\ln\left|-x+1\right|+C_0$
