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 $\frac{2x-1}{x\left(x^2+1\right)^2}$ in $3$ simpler fractions using partial fraction decomposition
Learn how to solve integrals of rational functions problems step by step online.
$\frac{-1}{x}+\frac{x+2}{\left(x^2+1\right)^2}+\frac{x}{x^2+1}$
Learn how to solve integrals of rational functions problems step by step online. Find the integral int((2x-1)/(x(x^2+1)^2))dx. Rewrite the fraction \frac{2x-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+2}{\left(x^2+1\right)^2}+\frac{x}{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+2}{\left(x^2+1\right)^2}dx results in: \frac{1}{-2\left(x^2+1\right)}+\arctan\left(x\right)+\frac{x}{\left(x^2+1\right)^{\left(\frac{1}{2}+\frac{1}{2}\right)}}.
