Optimal. Leaf size=11 \[ -\frac{1}{2 \left (x^2+1\right )} \]
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Rubi [A] time = 0.0021301, antiderivative size = 11, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 2, integrand size = 14, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.143, Rules used = {28, 261} \[ -\frac{1}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
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Rule 28
Rule 261
Rubi steps
\begin{align*} \int \frac{x}{1+2 x^2+x^4} \, dx &=\int \frac{x}{\left (1+x^2\right )^2} \, dx\\ &=-\frac{1}{2 \left (1+x^2\right )}\\ \end{align*}
Mathematica [A] time = 0.0011637, size = 11, normalized size = 1. \[ -\frac{1}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
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Maple [A] time = 0.043, size = 10, normalized size = 0.9 \begin{align*} -{\frac{1}{2\,{x}^{2}+2}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A] time = 0.991789, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{2 \,{\left (x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A] time = 1.45597, size = 22, normalized size = 2. \begin{align*} -\frac{1}{2 \,{\left (x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A] time = 0.080482, size = 8, normalized size = 0.73 \begin{align*} - \frac{1}{2 x^{2} + 2} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A] time = 1.14512, size = 12, normalized size = 1.09 \begin{align*} -\frac{1}{2 \,{\left (x^{2} + 1\right )}} \end{align*}
Verification of antiderivative is not currently implemented for this CAS.
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