Optimal. Leaf size=25 \[ e^{e^3+x-\log ^2\left (\frac {x}{2}+\log (4)\right )}+\log ^2(3) \]
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Rubi [A] time = 0.28, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 1, number of rules used = 1, integrand size = 50, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.020, Rules used = {6706} \begin {gather*} e^{x-\log ^2\left (\frac {1}{2} (x+\log (16))\right )+e^3} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{e^3+x-\log ^2\left (\frac {1}{2} (x+\log (16))\right )}\\ \end {aligned} \end {gather*}
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Mathematica [F] time = 0.45, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {e^{e^3+x-\log ^2\left (\frac {1}{2} (x+2 \log (4))\right )} \left (x+2 \log (4)-2 \log \left (\frac {1}{2} (x+2 \log (4))\right )\right )}{x+2 \log (4)} \, dx \end {gather*}
Verification is not applicable to the result.
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fricas [A] time = 0.46, size = 18, normalized size = 0.72 \begin {gather*} e^{\left (-\log \left (\frac {1}{2} \, x + 2 \, \log \relax (2)\right )^{2} + x + e^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.18, size = 18, normalized size = 0.72 \begin {gather*} e^{\left (-\log \left (\frac {1}{2} \, x + 2 \, \log \relax (2)\right )^{2} + x + e^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 19, normalized size = 0.76
method | result | size |
norman | \({\mathrm e}^{-\ln \left (2 \ln \relax (2)+\frac {x}{2}\right )^{2}+{\mathrm e}^{3}+x}\) | \(19\) |
risch | \({\mathrm e}^{-\ln \left (2 \ln \relax (2)+\frac {x}{2}\right )^{2}+{\mathrm e}^{3}+x}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.55, size = 33, normalized size = 1.32 \begin {gather*} e^{\left (-\log \relax (2)^{2} + 2 \, \log \relax (2) \log \left (x + 4 \, \log \relax (2)\right ) - \log \left (x + 4 \, \log \relax (2)\right )^{2} + x + e^{3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.28, size = 18, normalized size = 0.72 \begin {gather*} {\mathrm {e}}^{-{\ln \left (\frac {x}{2}+\ln \relax (4)\right )}^2}\,{\mathrm {e}}^{{\mathrm {e}}^3}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.32, size = 17, normalized size = 0.68 \begin {gather*} e^{x - \log {\left (\frac {x}{2} + 2 \log {\relax (2 )} \right )}^{2} + e^{3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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