Optimal. Leaf size=29 \[ e^{4 e^x+e^5 x^2} \left (e^5-\log ^2(1+\log (4))\right ) \]
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Rubi [A] time = 0.14, antiderivative size = 29, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6706} \begin {gather*} e^{e^5 x^2+4 e^x} \left (e^5-\log ^2(1+\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{4 e^x+e^5 x^2} \left (e^5-\log ^2(1+\log (4))\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.07, size = 29, normalized size = 1.00 \begin {gather*} e^{4 e^x+e^5 x^2} \left (e^5-\log ^2(1+\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.26, size = 33, normalized size = 1.14 \begin {gather*} -{\left (\log \left (2 \, \log \relax (2) + 1\right )^{2} - e^{5}\right )} e^{\left ({\left (x^{2} e^{10} + 4 \, e^{\left (x + 5\right )}\right )} e^{\left (-5\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.29, size = 37, normalized size = 1.28 \begin {gather*} -e^{\left (x^{2} e^{5} + 4 \, e^{x}\right )} \log \left (2 \, \log \relax (2) + 1\right )^{2} + e^{\left (x^{2} e^{5} + 4 \, e^{x} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 28, normalized size = 0.97
method | result | size |
norman | \(\left ({\mathrm e}^{5}-\ln \left (1+2 \ln \relax (2)\right )^{2}\right ) {\mathrm e}^{4 \,{\mathrm e}^{x}+x^{2} {\mathrm e}^{5}}\) | \(28\) |
risch | \(-\ln \left (1+2 \ln \relax (2)\right )^{2} {\mathrm e}^{4 \,{\mathrm e}^{x}+x^{2} {\mathrm e}^{5}}+{\mathrm e}^{5} {\mathrm e}^{4 \,{\mathrm e}^{x}+x^{2} {\mathrm e}^{5}}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.75, size = 28, normalized size = 0.97 \begin {gather*} -{\left (\log \left (2 \, \log \relax (2) + 1\right )^{2} - e^{5}\right )} e^{\left (x^{2} e^{5} + 4 \, e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.10, size = 25, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{4\,{\mathrm {e}}^x+x^2\,{\mathrm {e}}^5}\,\left ({\mathrm {e}}^5-{\ln \left (\ln \relax (4)+1\right )}^2\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 26, normalized size = 0.90 \begin {gather*} \left (- \log {\left (1 + 2 \log {\relax (2 )} \right )}^{2} + e^{5}\right ) e^{x^{2} e^{5} + 4 e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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