Optimal. Leaf size=11 \[ \frac{x}{1-2 x^2} \]
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Rubi [A] time = 0.0050256, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 22, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.091, Rules used = {28, 383} \[ \frac{x}{1-2 x^2} \]
Antiderivative was successfully verified.
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Rule 28
Rule 383
Rubi steps
\begin{align*} \int \frac{1+2 x^2}{1-4 x^2+4 x^4} \, dx &=4 \int \frac{1+2 x^2}{\left (-2+4 x^2\right )^2} \, dx\\ &=\frac{x}{1-2 x^2}\\ \end{align*}
Mathematica [A] time = 0.0057191, size = 12, normalized size = 1.09 \[ -\frac{x}{2 x^2-1} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.046, size = 11, normalized size = 1. \begin{align*} -{\frac{x}{2} \left ({x}^{2}-{\frac{1}{2}} \right ) ^{-1}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.956096, size = 16, normalized size = 1.45 \begin{align*} -\frac{x}{2 \, x^{2} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.31542, size = 22, normalized size = 2. \begin{align*} -\frac{x}{2 \, x^{2} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.081402, size = 8, normalized size = 0.73 \begin{align*} - \frac{x}{2 x^{2} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.13147, size = 16, normalized size = 1.45 \begin{align*} -\frac{x}{2 \, x^{2} - 1} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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