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- Integrate by partial fractions
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- Weierstrass Substitution
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- Product of Binomials with Common Term
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Rewrite the fraction $\frac{x^3+4x^2+x}{\left(x^2+4\right)\left(x^2+1\right)}$ in $2$ simpler fractions using partial fraction decomposition
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$\frac{x+\frac{16}{3}}{x^2+4}+\frac{-4}{3\left(x^2+1\right)}$
Learn how to solve problems step by step online. Integrate the function (x^3+4x^2x)/((x^2+4)(x^2+1)) from -infinity to infinity. Rewrite the fraction \frac{x^3+4x^2+x}{\left(x^2+4\right)\left(x^2+1\right)} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{x+\frac{16}{3}}{x^2+4}+\frac{-4}{3\left(x^2+1\right)}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{x+\frac{16}{3}}{x^2+4}dx results in: -\ln\left(\frac{2}{\sqrt{x^2+4}}\right)+\frac{8}{3}\arctan\left(\frac{x}{2}\right). Gather the results of all integrals.
