Optimal. Leaf size=23 \[ e^{(-5+x) x \left (-x+\frac {1+x-\log (\log (4))}{x}\right )} \]
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Rubi [A] time = 0.21, antiderivative size = 26, normalized size of antiderivative = 1.13, number of steps used = 1, number of rules used = 1, integrand size = 42, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.024, Rules used = {6706} \begin {gather*} e^{-x^3+6 x^2-4 x-5} \log ^{5-x}(4) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{-5-4 x+6 x^2-x^3} \log ^{5-x}(4)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.36, size = 26, normalized size = 1.13 \begin {gather*} e^{-5-4 x+6 x^2-x^3} \log ^{5-x}(4) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.83, size = 26, normalized size = 1.13 \begin {gather*} e^{\left (-x^{3} + 6 \, x^{2} - {\left (x - 5\right )} \log \left (2 \, \log \relax (2)\right ) - 4 \, x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.48, size = 31, normalized size = 1.35 \begin {gather*} e^{\left (-x^{3} + 6 \, x^{2} - x \log \left (2 \, \log \relax (2)\right ) - 4 \, x + 5 \, \log \left (2 \, \log \relax (2)\right ) - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 20, normalized size = 0.87
method | result | size |
risch | \({\mathrm e}^{-\left (x -5\right ) \left (x^{2}+\ln \relax (2)+\ln \left (\ln \relax (2)\right )-x -1\right )}\) | \(20\) |
derivativedivides | \({\mathrm e}^{\left (5-x \right ) \ln \left (2 \ln \relax (2)\right )-x^{3}+6 x^{2}-4 x -5}\) | \(28\) |
default | \({\mathrm e}^{\left (5-x \right ) \ln \left (2 \ln \relax (2)\right )-x^{3}+6 x^{2}-4 x -5}\) | \(28\) |
norman | \({\mathrm e}^{\left (5-x \right ) \ln \left (2 \ln \relax (2)\right )-x^{3}+6 x^{2}-4 x -5}\) | \(28\) |
gosper | \({\mathrm e}^{-x^{3}-x \ln \left (2 \ln \relax (2)\right )+6 x^{2}+5 \ln \left (2 \ln \relax (2)\right )-4 x -5}\) | \(32\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.43, size = 26, normalized size = 1.13 \begin {gather*} e^{\left (-x^{3} + 6 \, x^{2} - {\left (x - 5\right )} \log \left (2 \, \log \relax (2)\right ) - 4 \, x - 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.44, size = 29, normalized size = 1.26 \begin {gather*} {\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{-x^3}\,{\mathrm {e}}^{6\,x^2}\,{\left (2\,\ln \relax (2)\right )}^{5-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.15, size = 24, normalized size = 1.04 \begin {gather*} e^{- x^{3} + 6 x^{2} - 4 x + \left (5 - x\right ) \log {\left (2 \log {\relax (2 )} \right )} - 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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