Final answer to the problem
$2x+\ln\left|-1+x\right|-\ln\left|1+x\right|-2\left(\frac{1}{2}x+\left(-\frac{1}{2}\ln\left|x+1\right|+\frac{1}{2}\ln\left|x-1\right|\right)x+\frac{1}{2}\left(-1+\left(x+1\right)\ln\left|x+1\right|\right)-\frac{1}{2}\left(1+\left(x-1\right)\ln\left|x-1\right|\right)\right)+C_0$
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Step-by-step Solution
How should I solve this problem?
- Integrate by parts
- Integrate by partial fractions
- Integrate by substitution
- Integrate using tabular integration
- Integrate by trigonometric substitution
- Weierstrass Substitution
- Integrate using trigonometric identities
- Integrate using basic integrals
- Product of Binomials with Common Term
- FOIL Method
- Load more...
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1
Find the integral
$\int\frac{x^2-2x+1}{x^2-1}dx$
Learn how to solve integral calculus problems step by step online.
$\int\frac{x^2-2x+1}{x^2-1}dx$
Learn how to solve integral calculus problems step by step online. Integrate the function (x^2-2x+1)/(x^2-1). Find the integral. Divide x^2-2x+1 by x^2-1. Resulting polynomial. Expand the integral \int\left(1+\frac{-2x+2}{x^2-1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately.
Final answer to the problem
$2x+\ln\left|-1+x\right|-\ln\left|1+x\right|-2\left(\frac{1}{2}x+\left(-\frac{1}{2}\ln\left|x+1\right|+\frac{1}{2}\ln\left|x-1\right|\right)x+\frac{1}{2}\left(-1+\left(x+1\right)\ln\left|x+1\right|\right)-\frac{1}{2}\left(1+\left(x-1\right)\ln\left|x-1\right|\right)\right)+C_0$
