Optimal. Leaf size=13 \[ \frac {1}{2 \left (9-x^2\right )} \]
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Rubi [A] time = 0.00, antiderivative size = 13, 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} \begin {gather*} \frac {1}{2 \left (9-x^2\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 28
Rule 261
Rubi steps
\begin {align*} \int \frac {x}{81-18 x^2+x^4} \, dx &=\int \frac {x}{\left (-9+x^2\right )^2} \, dx\\ &=\frac {1}{2 \left (9-x^2\right )}\\ \end {align*}
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Mathematica [A] time = 0.00, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{2 \left (x^2-9\right )} \end {gather*}
Antiderivative was successfully verified.
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IntegrateAlgebraic [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {x}{81-18 x^2+x^4} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.78, size = 9, normalized size = 0.69 \begin {gather*} -\frac {1}{2 \, {\left (x^{2} - 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 9, normalized size = 0.69 \begin {gather*} -\frac {1}{2 \, {\left (x^{2} - 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.00, size = 10, normalized size = 0.77 \begin {gather*} -\frac {1}{2 \left (x^{2}-9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.33, size = 9, normalized size = 0.69 \begin {gather*} -\frac {1}{2 \, {\left (x^{2} - 9\right )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.05, size = 11, normalized size = 0.85 \begin {gather*} -\frac {1}{2\,\left (x^2-9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 8, normalized size = 0.62 \begin {gather*} - \frac {1}{2 x^{2} - 18} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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