Optimal. Leaf size=14 \[ e^x (-1+x-9 (-6+\log (\log (4)))) \]
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Rubi [A]
time = 0.01, antiderivative size = 21, normalized size of antiderivative = 1.50, number of steps
used = 4, number of rules used = 2, integrand size = 16, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.125, Rules used = {2207, 2225}
\begin {gather*} e^x (x+54)-e^x-9 e^x \log (\log (4)) \end {gather*}
Antiderivative was successfully verified.
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Rule 2207
Rule 2225
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left ((9 \log (\log (4))) \int e^x \, dx\right )+\int e^x (54+x) \, dx\\ &=e^x (54+x)-9 e^x \log (\log (4))-\int e^x \, dx\\ &=-e^x+e^x (54+x)-9 e^x \log (\log (4))\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 12, normalized size = 0.86 \begin {gather*} e^x (53+x-9 \log (\log (4))) \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.12, size = 19, normalized size = 1.36
method | result | size |
gosper | \(-{\mathrm e}^{x} \left (-x +9 \ln \left (2 \ln \left (2\right )\right )-53\right )\) | \(17\) |
default | \({\mathrm e}^{x} x +53 \,{\mathrm e}^{x}-9 \,{\mathrm e}^{x} \ln \left (2 \ln \left (2\right )\right )\) | \(19\) |
norman | \(\left (53-9 \ln \left (2\right )-9 \ln \left (\ln \left (2\right )\right )\right ) {\mathrm e}^{x}+{\mathrm e}^{x} x\) | \(20\) |
risch | \(-9 \,{\mathrm e}^{x} \ln \left (2\right )-9 \,{\mathrm e}^{x} \ln \left (\ln \left (2\right )\right )+\left (53+x \right ) {\mathrm e}^{x}\) | \(21\) |
meijerg | \(1-\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}-\left (-9 \ln \left (2 \ln \left (2\right )\right )+54\right ) \left (1-{\mathrm e}^{x}\right )\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.27, size = 20, normalized size = 1.43 \begin {gather*} {\left (x - 1\right )} e^{x} - 9 \, e^{x} \log \left (2 \, \log \left (2\right )\right ) + 54 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.40, size = 16, normalized size = 1.14 \begin {gather*} {\left (x + 53\right )} e^{x} - 9 \, e^{x} \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 = 0.04, size = 17, normalized size = 1.21 \begin {gather*} \left (x - 9 \log {\left (2 \right )} - 9 \log {\left (\log {\left (2 \right )} \right )} + 53\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.40, size = 16, normalized size = 1.14 \begin {gather*} {\left (x + 53\right )} e^{x} - 9 \, e^{x} \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 = 1.67, size = 13, normalized size = 0.93 \begin {gather*} {\mathrm {e}}^x\,\left (x-\ln \left ({\ln \left (4\right )}^9\right )+53\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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