Optimal. Leaf size=19 \[ e^{\frac {256}{\log ^2\left (5-2 x-x^2+\log (x)\right )}} \]
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Rubi [A]
time = 0.35, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 1, number of rules used = 1, integrand size = 65, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.015, Rules used = {6838}
\begin {gather*} e^{\frac {256}{\log ^2\left (-x^2-2 x+\log (x)+5\right )}} \end {gather*}
Antiderivative was successfully verified.
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Rule 6838
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{\frac {256}{\log ^2\left (5-2 x-x^2+\log (x)\right )}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.07, size = 19, normalized size = 1.00 \begin {gather*} e^{\frac {256}{\log ^2\left (5-2 x-x^2+\log (x)\right )}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.02, size = 19, normalized size = 1.00
method | result | size |
risch | \({\mathrm e}^{\frac {256}{\ln \left (\ln \left (x \right )-x^{2}-2 x +5\right )^{2}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [B] Leaf count of result is larger than twice the leaf count of optimal. 101 vs.
\(2 (18) = 36\).
time = 0.30, size = 101, normalized size = 5.32 \begin {gather*} \frac {2 \, x^{2} e^{\left (\frac {256}{\log \left (-x^{2} - 2 \, x + \log \left (x\right ) + 5\right )^{2}}\right )}}{2 \, x^{2} + 2 \, x - 1} + \frac {2 \, x e^{\left (\frac {256}{\log \left (-x^{2} - 2 \, x + \log \left (x\right ) + 5\right )^{2}}\right )}}{2 \, x^{2} + 2 \, x - 1} - \frac {e^{\left (\frac {256}{\log \left (-x^{2} - 2 \, x + \log \left (x\right ) + 5\right )^{2}}\right )}}{2 \, x^{2} + 2 \, x - 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.38, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (\frac {256}{\log \left (-x^{2} - 2 \, x + \log \left (x\right ) + 5\right )^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.88, size = 17, normalized size = 0.89 \begin {gather*} e^{\frac {256}{\log {\left (- x^{2} - 2 x + \log {\left (x \right )} + 5 \right )}^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.42, size = 18, normalized size = 0.95 \begin {gather*} e^{\left (\frac {256}{\log \left (-x^{2} - 2 \, x + \log \left (x\right ) + 5\right )^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.50, size = 18, normalized size = 0.95 \begin {gather*} {\mathrm {e}}^{\frac {256}{{\ln \left (\ln \left (x\right )-2\,x-x^2+5\right )}^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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