Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- Choose an option
- 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
- Load more...
Rewrite the fraction $\frac{x^2-2x}{\left(x-1\right)^2\left(x^2+1\right)^2}$ in $4$ simpler fractions using partial fraction decomposition
Learn how to solve problems step by step online.
$\frac{-1}{4\left(x-1\right)^2}+\frac{-\frac{1}{2}x+1}{\left(x^2+1\right)^2}+\frac{1}{2\left(x-1\right)}+\frac{-\frac{1}{2}x-\frac{1}{4}}{x^2+1}$
Learn how to solve problems step by step online. Find the integral int((x^2-2x)/((x-1)^2(x^2+1)^2))dx. Rewrite the fraction \frac{x^2-2x}{\left(x-1\right)^2\left(x^2+1\right)^2} in 4 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{-1}{4\left(x-1\right)^2}+\frac{-\frac{1}{2}x+1}{\left(x^2+1\right)^2}+\frac{1}{2\left(x-1\right)}+\frac{-\frac{1}{2}x-\frac{1}{4}}{x^2+1}\right)dx into 4 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{-1}{4\left(x-1\right)^2}dx results in: \frac{1}{4\left(x-1\right)}. The integral \int\frac{-\frac{1}{2}x+1}{\left(x^2+1\right)^2}dx results in: \frac{1}{4\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)}}.