Optimal. Leaf size=22 \[ 3 e^{4-x} \left (5+x+2 e^{x^2} \log (\log (4))\right ) \]
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Rubi [A]
time = 0.02, antiderivative size = 37, normalized size of antiderivative = 1.68, number of steps
used = 4, number of rules used = 3, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.091, Rules used = {2207, 2225,
2268} \begin {gather*} 6 e^{x^2-x+4} \log (\log (4))+3 e^{4-x} (x+4)+3 e^{4-x} \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rule 2268
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\log (\log (4)) \int e^{4-x+x^2} (-6+12 x) \, dx+\int e^{4-x} (-12-3 x) \, dx\\ &=3 e^{4-x} (4+x)+6 e^{4-x+x^2} \log (\log (4))-3 \int e^{4-x} \, dx\\ &=3 e^{4-x}+3 e^{4-x} (4+x)+6 e^{4-x+x^2} \log (\log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 22, normalized size = 1.00 \begin {gather*} 3 e^{4-x} \left (5+x+2 e^{x^2} \log (\log (4))\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.36, size = 39, normalized size = 1.77
method | result | size |
default | \(-3 \,{\mathrm e}^{-x +4} \left (-x +4\right )+27 \,{\mathrm e}^{-x +4}+6 \ln \left (2 \ln \left (2\right )\right ) {\mathrm e}^{x^{2}-x +4}\) | \(39\) |
norman | \(\left (6 \ln \left (2\right )+6 \ln \left (\ln \left (2\right )\right )\right ) {\mathrm e}^{x^{2}} {\mathrm e}^{-x +4}+3 x \,{\mathrm e}^{-x +4}+15 \,{\mathrm e}^{-x +4}\) | \(40\) |
risch | \(6 \,{\mathrm e}^{x^{2}-x +4} \ln \left (2\right )+6 \,{\mathrm e}^{x^{2}-x +4} \ln \left (\ln \left (2\right )\right )+\left (15+3 x \right ) {\mathrm e}^{-x +4}\) | \(41\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.29, size = 38, normalized size = 1.73 \begin {gather*} 3 \, {\left (x e^{4} + e^{4}\right )} e^{\left (-x\right )} + 6 \, e^{\left (x^{2} - x + 4\right )} \log \left (2 \, \log \left (2\right )\right ) + 12 \, e^{\left (-x + 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 28, normalized size = 1.27 \begin {gather*} 3 \, {\left (x + 5\right )} e^{\left (-x + 4\right )} + 6 \, e^{\left (x^{2} - x + 4\right )} \log \left (2 \, \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.26, size = 31, normalized size = 1.41 \begin {gather*} \left (3 x + 6 e^{x^{2}} \log {\left (\log {\left (2 \right )} \right )} + 6 e^{x^{2}} \log {\left (2 \right )} + 15\right ) e^{4 - x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 28, normalized size = 1.27 \begin {gather*} 3 \, {\left (x + 5\right )} e^{\left (-x + 4\right )} + 6 \, e^{\left (x^{2} - x + 4\right )} \log \left (2 \, \log \left (2\right )\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.11, size = 33, normalized size = 1.50 \begin {gather*} 15\,{\mathrm {e}}^{4-x}+\ln \left ({\ln \left (4\right )}^6\right )\,{\mathrm {e}}^{x^2-x+4}+3\,x\,{\mathrm {e}}^{4-x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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