Optimal. Leaf size=24 \[ e^{e^x \log ^2(2)}+\frac {x}{2+i \pi +\log (14)} \]
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Rubi [A] time = 0.03, antiderivative size = 24, normalized size of antiderivative = 1.00, number of steps used = 4, number of rules used = 3, integrand size = 40, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.075, Rules used = {12, 2282, 2194} \begin {gather*} e^{e^x \log ^2(2)}+\frac {x}{2+i \pi +\log (14)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rule 2282
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \left (1+e^{x+e^x \log ^2(2)} \log ^2(2) (2+i \pi +\log (14))\right ) \, dx}{2+i \pi +\log (14)}\\ &=\frac {x}{2+i \pi +\log (14)}+\log ^2(2) \int e^{x+e^x \log ^2(2)} \, dx\\ &=\frac {x}{2+i \pi +\log (14)}+\log ^2(2) \operatorname {Subst}\left (\int e^{x \log ^2(2)} \, dx,x,e^x\right )\\ &=e^{e^x \log ^2(2)}+\frac {x}{2+i \pi +\log (14)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 24, normalized size = 1.00 \begin {gather*} e^{e^x \log ^2(2)}+\frac {x}{2+i \pi +\log (14)} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.84, size = 55, normalized size = 2.29 \begin {gather*} \frac {{\left ({\left (i \, \pi + \log \left (14\right ) + 2\right )} e^{\left (x + e^{\left (x + 2 \, \log \left (\log \relax (2)\right )\right )} + 2 \, \log \left (\log \relax (2)\right )\right )} + x e^{\left (x + 2 \, \log \left (\log \relax (2)\right )\right )}\right )} e^{\left (-x - 2 \, \log \left (\log \relax (2)\right )\right )}}{i \, \pi + \log \left (14\right ) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 28, normalized size = 1.17 \begin {gather*} \frac {{\left (i \, \pi + \log \left (14\right ) + 2\right )} e^{\left (e^{x} \log \relax (2)^{2}\right )} + x}{i \, \pi + \log \left (14\right ) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.07, size = 24, normalized size = 1.00
method | result | size |
risch | \(\frac {x}{\ln \relax (2)+\ln \relax (7)+i \pi +2}+{\mathrm e}^{\ln \relax (2)^{2} {\mathrm e}^{x}}\) | \(24\) |
norman | \(-\frac {\left (i \pi -\ln \left (14\right )-2\right ) x}{\pi ^{2}+\ln \left (14\right )^{2}+4 \ln \left (14\right )+4}+{\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}\) | \(39\) |
default | \(\frac {x +i \pi \,{\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}+\ln \left (14\right ) {\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}+2 \,{\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}}{\ln \left (14\right )+i \pi +2}\) | \(50\) |
derivativedivides | \(\frac {\ln \left ({\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}\right )+\ln \left (14\right ) {\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}+i \pi \,{\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}+2 \,{\mathrm e}^{{\mathrm e}^{2 \ln \left (\ln \relax (2)\right )+x}}}{\ln \left (14\right )+i \pi +2}\) | \(58\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 28, normalized size = 1.17 \begin {gather*} \frac {{\left (i \, \pi + \log \left (14\right ) + 2\right )} e^{\left (e^{x} \log \relax (2)^{2}\right )} + x}{i \, \pi + \log \left (14\right ) + 2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.32, size = 21, normalized size = 0.88 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x\,{\ln \relax (2)}^2}+\frac {x}{\ln \left (14\right )+2+\Pi \,1{}\mathrm {i}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.21, size = 19, normalized size = 0.79 \begin {gather*} \frac {x}{2 + \log {\left (14 \right )} + i \pi } + e^{e^{x} \log {\relax (2 )}^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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