** Final answer to the problem

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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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Rewrite the expression $\frac{x}{1-x^2}$ inside the integral in factored form

Learn how to solve integrals by partial fraction expansion problems step by step online.

$\int\frac{x}{\left(1+x\right)\left(1-x\right)}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int(x/(1-x^2))dx. Rewrite the expression \frac{x}{1-x^2} inside the integral in factored form. Rewrite the fraction \frac{x}{\left(1+x\right)\left(1-x\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{2\left(1+x\right)}+\frac{1}{2\left(1-x\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{2\left(1+x\right)}dx results in: -\frac{1}{2}\ln\left(x+1\right).

** Final answer to the problem ** **

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