Optimal. Leaf size=11 \[ -\frac {1}{2 \left (x^2+1\right )} \]
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Rubi [A] time = 0.00, antiderivative size = 11, normalized size of antiderivative = 1.00, 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*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 1.00 \[ -\frac {1}{2 \left (x^2+1\right )} \]
Antiderivative was successfully verified.
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fricas [A] time = 0.93, size = 9, normalized size = 0.82 \[ -\frac {1}{2 \, {\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 9, normalized size = 0.82 \[ -\frac {1}{2 \, {\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.91 \[ -\frac {1}{2 \left (x^{2}+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.35, size = 9, normalized size = 0.82 \[ -\frac {1}{2 \, {\left (x^{2} + 1\right )}} \]
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.02, size = 11, normalized size = 1.00 \[ -\frac {1}{2\,\left (x^2+1\right )} \]
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.73 \[ - \frac {1}{2 x^{2} + 2} \]
Verification of antiderivative is not currently implemented for this CAS.
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