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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 calcul intégral 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 calcul intégral problems step by step online. int(1/((x+1)(x^2+1)))dx&0&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}.
