Final answer to the problem
$-x-\frac{1}{2}\ln\left|-x+1\right|+\frac{1}{2}\ln\left|x+1\right|+C_0$
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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
Divide $x^2$ by $1-x^2$
$\begin{array}{l}\phantom{-x^{2}+1;}{-1\phantom{;}\phantom{;}}\\-x^{2}+1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{-x^{2}+1;}\underline{-x^{2}\phantom{-;x^n}+1\phantom{;}\phantom{;}}\\\phantom{-x^{2}+1\phantom{;}\phantom{;};}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2)/(1-x^2))dx. Divide x^2 by 1-x^2. Resulting polynomial. Expand the integral \int\left(-1+\frac{1}{1-x^2}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int-1dx results in: -x.
Final answer to the problem
$-x-\frac{1}{2}\ln\left|-x+1\right|+\frac{1}{2}\ln\left|x+1\right|+C_0$
