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 $\frac{1}{\left(x+1\right)\left(x^2+1\right)}$ in $2$ simpler fractions using partial fraction decomposition
Learn how to solve definite integrals problems step by step online.
$\frac{1}{2\left(x+1\right)}+\frac{-\frac{1}{2}x+\frac{1}{2}}{x^2+1}$
Learn how to solve definite integrals problems step by step online. Integrate the function 1/((x+1)(x^2+1)) from 0 to 1. Rewrite the fraction \frac{1}{\left(x+1\right)\left(x^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int_{0}^{1}\left(\frac{1}{2\left(x+1\right)}+\frac{-\frac{1}{2}x+\frac{1}{2}}{x^2+1}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int_{0}^{1}\frac{1}{2\left(x+1\right)}dx results in: \frac{1}{2}\ln\left(2\right). The integral \int_{0}^{1}\frac{-\frac{1}{2}x+\frac{1}{2}}{x^2+1}dx results in: -\frac{1}{4}\ln\left(2\right)+\frac{\pi }{8}.
