Optimal. Leaf size=22 \[ \left (5+\frac {1}{9} e^{2-2 x} \log ^2(4)\right ) (-3+\log (5)) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 0.95, 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*} -\frac {1}{9} e^{2-2 x} \log ^2(4) (3-\log (5)) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{9} \left (2 \log ^2(4) (3-\log (5))\right ) \int e^{2-2 x} \, dx\\ &=-\frac {1}{9} e^{2-2 x} \log ^2(4) (3-\log (5))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 0.86 \begin {gather*} \frac {1}{9} e^{2-2 x} \log ^2(4) (-3+\log (5)) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.45, size = 26, normalized size = 1.18
method | result | size |
gosper | \(\frac {4 \ln \left (2\right )^{2} \left (\ln \left (5\right )-3\right ) {\mathrm e}^{-2 x +2}}{9}\) | \(19\) |
norman | \(\left (\frac {4 \ln \left (2\right )^{2} \ln \left (5\right )}{9}-\frac {4 \ln \left (2\right )^{2}}{3}\right ) {\mathrm e}^{-2 x +2}\) | \(25\) |
derivativedivides | \(-\frac {\left (-8 \ln \left (2\right )^{2} \ln \left (5\right )+24 \ln \left (2\right )^{2}\right ) {\mathrm e}^{-2 x +2}}{18}\) | \(26\) |
default | \(-\frac {\left (-\frac {8 \ln \left (2\right )^{2} \ln \left (5\right )}{9}+\frac {8 \ln \left (2\right )^{2}}{3}\right ) {\mathrm e}^{-2 x +2}}{2}\) | \(26\) |
risch | \(\frac {4 \,{\mathrm e}^{-2 x +2} \ln \left (2\right )^{2} \ln \left (5\right )}{9}-\frac {4 \,{\mathrm e}^{-2 x +2} \ln \left (2\right )^{2}}{3}\) | \(28\) |
meijerg | \(-\frac {4 \ln \left (2\right )^{2} \ln \left (5\right ) {\mathrm e}^{-2 x +2 \,{\mathrm e}^{2} x} \left (1-{\mathrm e}^{-2 \,{\mathrm e}^{2} x}\right )}{9}+\frac {4 \,{\mathrm e}^{-2 x +2 \,{\mathrm e}^{2} x} \ln \left (2\right )^{2} \left (1-{\mathrm e}^{-2 \,{\mathrm e}^{2} x}\right )}{3}\) | \(56\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 22, normalized size = 1.00 \begin {gather*} \frac {4}{9} \, {\left (\log \left (5\right ) \log \left (2\right )^{2} - 3 \, \log \left (2\right )^{2}\right )} e^{\left (-2 \, x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.43, size = 22, normalized size = 1.00 \begin {gather*} \frac {4}{9} \, {\left (\log \left (5\right ) \log \left (2\right )^{2} - 3 \, \log \left (2\right )^{2}\right )} e^{\left (-2 \, x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.04, size = 24, normalized size = 1.09 \begin {gather*} \frac {\left (- 12 \log {\left (2 \right )}^{2} + 4 \log {\left (2 \right )}^{2} \log {\left (5 \right )}\right ) e^{2 - 2 x}}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 22, normalized size = 1.00 \begin {gather*} \frac {4}{9} \, {\left (\log \left (5\right ) \log \left (2\right )^{2} - 3 \, \log \left (2\right )^{2}\right )} e^{\left (-2 \, x + 2\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 5.16, size = 16, normalized size = 0.73 \begin {gather*} \frac {4\,{\mathrm {e}}^{2-2\,x}\,{\ln \left (2\right )}^2\,\left (\ln \left (5\right )-3\right )}{9} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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