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- Integrate by partial fractions
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Rewrite the fraction $\frac{x^2}{\left(196+x^2\right)^2}$ in $2$ simpler fractions using partial fraction decomposition
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\frac{1}{196+x^2}+\frac{-196}{\left(196+x^2\right)^{2}}$
Learn how to solve integrals by partial fraction expansion problems step by step online. Find the integral int((x^2)/((196+x^2)^2))dx. Rewrite the fraction \frac{x^2}{\left(196+x^2\right)^2} in 2 simpler fractions using partial fraction decomposition. Expand the integral \int\left(\frac{1}{196+x^2}+\frac{-196}{\left(196+x^2\right)^{2}}\right)dx into 2 integrals using the sum rule for integrals, to then solve each integral separately. The integral \int\frac{1}{196+x^2}dx results in: \frac{1}{14}\arctan\left(\frac{x}{14}\right). The integral \int\frac{-196}{\left(196+x^2\right)^{2}}dx results in: -\frac{1}{14}\left(\frac{1}{2}\arctan\left(\frac{x}{14}\right)+\frac{7x}{196+x^2}\right).
