Optimal. Leaf size=18 \[ e^{2 x} \left (-\frac {2}{e^{12}}-\log (4)\right )^2 \]
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Rubi [A]
time = 0.01, antiderivative size = 18, normalized size of antiderivative = 1.00, number of steps
used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2225}
\begin {gather*} e^{2 x-24} \left (2+e^{12} \log (4)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\left (2 \left (2+e^{12} \log (4)\right )^2\right ) \int e^{-24+2 x} \, dx\\ &=e^{-24+2 x} \left (2+e^{12} \log (4)\right )^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 18, normalized size = 1.00 \begin {gather*} e^{-24+2 x} \left (2+e^{12} \log (4)\right )^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.14, size = 28, normalized size = 1.56
method | result | size |
gosper | \(4 \left ({\mathrm e}^{24} \ln \left (2\right )^{2}+2 \,{\mathrm e}^{12} \ln \left (2\right )+1\right ) {\mathrm e}^{2 x} {\mathrm e}^{-24}\) | \(28\) |
default | \(4 \left ({\mathrm e}^{24} \ln \left (2\right )^{2}+2 \,{\mathrm e}^{12} \ln \left (2\right )+1\right ) {\mathrm e}^{2 x} {\mathrm e}^{-24}\) | \(28\) |
norman | \(4 \left ({\mathrm e}^{24} \ln \left (2\right )^{2}+2 \,{\mathrm e}^{12} \ln \left (2\right )+1\right ) {\mathrm e}^{2 x} {\mathrm e}^{-24}\) | \(28\) |
derivativedivides | \(\frac {\left (8 \,{\mathrm e}^{24} \ln \left (2\right )^{2}+16 \,{\mathrm e}^{12} \ln \left (2\right )+8\right ) {\mathrm e}^{2 x} {\mathrm e}^{-24}}{2}\) | \(29\) |
risch | \(4 \ln \left (2\right )^{2} {\mathrm e}^{24} {\mathrm e}^{2 x -24}+8 \ln \left (2\right ) {\mathrm e}^{12} {\mathrm e}^{2 x -24}+4 \,{\mathrm e}^{2 x -24}\) | \(36\) |
meijerg | \(-4 \ln \left (2\right )^{2} \left (1-{\mathrm e}^{2 x}\right )-8 \,{\mathrm e}^{-12} \ln \left (2\right ) \left (1-{\mathrm e}^{2 x}\right )-4 \,{\mathrm e}^{-24} \left (1-{\mathrm e}^{2 x}\right )\) | \(42\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.30, size = 23, normalized size = 1.28 \begin {gather*} 4 \, {\left (e^{24} \log \left (2\right )^{2} + 2 \, e^{12} \log \left (2\right ) + 1\right )} e^{\left (2 \, x - 24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.34, size = 23, normalized size = 1.28 \begin {gather*} 4 \, {\left (e^{24} \log \left (2\right )^{2} + 2 \, e^{12} \log \left (2\right ) + 1\right )} e^{\left (2 \, x - 24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 27, normalized size = 1.50 \begin {gather*} \frac {\left (4 + 8 e^{12} \log {\left (2 \right )} + 4 e^{24} \log {\left (2 \right )}^{2}\right ) e^{2 x}}{e^{24}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 23, normalized size = 1.28 \begin {gather*} 4 \, {\left (e^{24} \log \left (2\right )^{2} + 2 \, e^{12} \log \left (2\right ) + 1\right )} e^{\left (2 \, x - 24\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 23, normalized size = 1.28 \begin {gather*} {\mathrm {e}}^{2\,x-24}\,\left (8\,{\mathrm {e}}^{12}\,\ln \left (2\right )+4\,{\mathrm {e}}^{24}\,{\ln \left (2\right )}^2+4\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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