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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 $\frac{x^2+2x}{x^3-x^2+x-1}$ inside the integral in factored form
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$\int\frac{x^2+2x}{\left(x^{2}+1\right)\left(x-1\right)}dx$
Learn how to solve problems step by step online. Find the integral int((x^2+2x)/(x^3-x^2x+-1))dx. Rewrite the expression \frac{x^2+2x}{x^3-x^2+x-1} inside the integral in factored form. Rewrite the fraction \frac{x^2+2x}{\left(x^{2}+1\right)\left(x-1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-\frac{1}{2}x+\frac{3}{2}}{x^{2}+1}+\frac{3}{2\left(x-1\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-\frac{1}{2}x+\frac{3}{2}}{x^{2}+1}dx results in: -\frac{1}{4}\ln\left(x^{2}+1\right)+\frac{3}{2}\arctan\left(x\right).
