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