** 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 $\frac{3x-5}{\left(x-1\right)\left(x^2-1\right)}$ inside the integral in factored form

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

$\int\frac{3x-5}{\left(x-1\right)^2\left(x+1\right)}dx$

Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((3x-5)/((x-1)(x^2-1)))dx. Rewrite the expression \frac{3x-5}{\left(x-1\right)\left(x^2-1\right)} inside the integral in factored form. Rewrite the fraction \frac{3x-5}{\left(x-1\right)^2\left(x+1\right)} in 3 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{\left(x-1\right)^2}+\frac{-2}{x+1}+\frac{2}{x-1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{\left(x-1\right)^2}dx results in: \frac{1}{x-1}.

** Final answer to the problem ** **

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