Optimal. Leaf size=9 \[ \frac{x}{x^2+1} \]
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Rubi [A] time = 0.0039017, antiderivative size = 9, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.1, Rules used = {28, 383} \[ \frac{x}{x^2+1} \]
Antiderivative was successfully verified.
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Rule 28
Rule 383
Rubi steps
\begin{align*} \int \frac{1-x^2}{1+2 x^2+x^4} \, dx &=\int \frac{1-x^2}{\left (1+x^2\right )^2} \, dx\\ &=\frac{x}{1+x^2}\\ \end{align*}
Mathematica [A] time = 0.0041393, size = 9, normalized size = 1. \[ \frac{x}{x^2+1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.045, size = 10, normalized size = 1.1 \begin{align*}{\frac{x}{{x}^{2}+1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.980252, size = 12, normalized size = 1.33 \begin{align*} \frac{x}{x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.33412, size = 18, normalized size = 2. \begin{align*} \frac{x}{x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.079362, size = 5, normalized size = 0.56 \begin{align*} \frac{x}{x^{2} + 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.11334, size = 9, normalized size = 1. \begin{align*} \frac{1}{x + \frac{1}{x}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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