Final answer to the problem
$\frac{1}{2}x^2+x+\ln\left|x-1\right|+C_0$
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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 $x-1$
$\begin{array}{l}\phantom{\phantom{;}x\phantom{;}-1;}{\phantom{;}x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;}x\phantom{;}-1\overline{\smash{)}\phantom{;}x^{2}\phantom{-;x^n}\phantom{-;x^n}}\\\phantom{\phantom{;}x\phantom{;}-1;}\underline{-x^{2}+x\phantom{;}\phantom{-;x^n}}\\\phantom{-x^{2}+x\phantom{;};}\phantom{;}x\phantom{;}\phantom{-;x^n}\\\phantom{\phantom{;}x\phantom{;}-1-;x^n;}\underline{-x\phantom{;}+1\phantom{;}\phantom{;}}\\\phantom{;-x\phantom{;}+1\phantom{;}\phantom{;}-;x^n;}\phantom{;}1\phantom{;}\phantom{;}\\\end{array}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((x^2)/(x-1))dx. Divide x^2 by x-1. Resulting polynomial. Expand the integral \int\left(x+1+\frac{1}{x-1}\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int xdx results in: \frac{1}{2}x^2.
Final answer to the problem
$\frac{1}{2}x^2+x+\ln\left|x-1\right|+C_0$
