Optimal. Leaf size=28 \[ 2 e^{x-\left (3+\log \left (e^{2 e^{4+\frac {x}{\log (4)}}}\right )\right )^2} x \]
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Rubi [B] time = 0.91, antiderivative size = 106, normalized size of antiderivative = 3.79, number of steps used = 4, number of rules used = 3, integrand size = 83, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.036, Rules used = {12, 6741, 2288} \begin {gather*} -\frac {2 e^{x-12 e^{\frac {x}{\log (4)}+4}-4 e^{\frac {2 x}{\log (4)}+8}-9} \left (12 x e^{\frac {x}{\log (4)}+4}+8 x e^{\frac {2 x}{\log (4)}+8}-x \log (4)\right )}{\log (4) \left (-\frac {12 e^{\frac {x}{\log (4)}+4}}{\log (4)}-\frac {8 e^{\frac {2 x}{\log (4)}+8}}{\log (4)}+1\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6741
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \exp \left (-9-12 e^{\frac {x+4 \log (4)}{\log (4)}}-4 e^{\frac {2 (x+4 \log (4))}{\log (4)}}+x\right ) \left (-24 e^{\frac {x+4 \log (4)}{\log (4)}} x-16 e^{\frac {2 (x+4 \log (4))}{\log (4)}} x+(2+2 x) \log (4)\right ) \, dx}{\log (4)}\\ &=\frac {\int 2 \exp \left (-9-12 e^{\frac {x+4 \log (4)}{\log (4)}}-4 e^{\frac {2 (x+4 \log (4))}{\log (4)}}+x\right ) \left (-12 e^{4+\frac {x}{\log (4)}} x-8 e^{8+\frac {2 x}{\log (4)}} x+\log (4)+x \log (4)\right ) \, dx}{\log (4)}\\ &=\frac {2 \int \exp \left (-9-12 e^{\frac {x+4 \log (4)}{\log (4)}}-4 e^{\frac {2 (x+4 \log (4))}{\log (4)}}+x\right ) \left (-12 e^{4+\frac {x}{\log (4)}} x-8 e^{8+\frac {2 x}{\log (4)}} x+\log (4)+x \log (4)\right ) \, dx}{\log (4)}\\ &=-\frac {2 e^{-9-12 e^{4+\frac {x}{\log (4)}}-4 e^{8+\frac {2 x}{\log (4)}}+x} \left (12 e^{4+\frac {x}{\log (4)}} x+8 e^{8+\frac {2 x}{\log (4)}} x-x \log (4)\right )}{\left (1-\frac {12 e^{4+\frac {x}{\log (4)}}}{\log (4)}-\frac {8 e^{8+\frac {2 x}{\log (4)}}}{\log (4)}\right ) \log (4)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.75, size = 33, normalized size = 1.18 \begin {gather*} 2 e^{-9-12 e^{4+\frac {x}{\log (4)}}-4 e^{8+\frac {2 x}{\log (4)}}+x} x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.96, size = 36, normalized size = 1.29 \begin {gather*} 2 \, x e^{\left (x - 4 \, e^{\left (\frac {x + 8 \, \log \relax (2)}{\log \relax (2)}\right )} - 12 \, e^{\left (\frac {x + 8 \, \log \relax (2)}{2 \, \log \relax (2)}\right )} - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int -\frac {2 \, {\left (4 \, x e^{\left (\frac {x + 8 \, \log \relax (2)}{\log \relax (2)}\right )} + 6 \, x e^{\left (\frac {x + 8 \, \log \relax (2)}{2 \, \log \relax (2)}\right )} - {\left (x + 1\right )} \log \relax (2)\right )} e^{\left (x - 4 \, e^{\left (\frac {x + 8 \, \log \relax (2)}{\log \relax (2)}\right )} - 12 \, e^{\left (\frac {x + 8 \, \log \relax (2)}{2 \, \log \relax (2)}\right )} - 9\right )}}{\log \relax (2)}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.09, size = 37, normalized size = 1.32
method | result | size |
risch | \(2 x \,{\mathrm e}^{-4 \,{\mathrm e}^{\frac {8 \ln \relax (2)+x}{\ln \relax (2)}}-12 \,{\mathrm e}^{\frac {8 \ln \relax (2)+x}{2 \ln \relax (2)}}+x -9}\) | \(37\) |
norman | \(2 x \,{\mathrm e}^{-4 \,{\mathrm e}^{\frac {8 \ln \relax (2)+x}{\ln \relax (2)}}-12 \,{\mathrm e}^{\frac {8 \ln \relax (2)+x}{2 \ln \relax (2)}}+x -9}\) | \(40\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.63, size = 30, normalized size = 1.07 \begin {gather*} 2 \, x e^{\left (x - 4 \, e^{\left (\frac {x}{\log \relax (2)} + 8\right )} - 12 \, e^{\left (\frac {x}{2 \, \log \relax (2)} + 4\right )} - 9\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.22, size = 32, normalized size = 1.14 \begin {gather*} 2\,x\,{\mathrm {e}}^{-4\,{\mathrm {e}}^{\frac {x}{\ln \relax (2)}}\,{\mathrm {e}}^8}\,{\mathrm {e}}^{-12\,{\mathrm {e}}^{\frac {x}{2\,\ln \relax (2)}}\,{\mathrm {e}}^4}\,{\mathrm {e}}^{-9}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.29, size = 36, normalized size = 1.29 \begin {gather*} 2 x e^{x - 4 e^{\frac {2 \left (\frac {x}{2} + 4 \log {\relax (2 )}\right )}{\log {\relax (2 )}}} - 12 e^{\frac {\frac {x}{2} + 4 \log {\relax (2 )}}{\log {\relax (2 )}}} - 9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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