Optimal. Leaf size=26 \[ 3+e^{\frac {-x+\frac {x^2}{16}+x \log (3)}{2 x}} \]
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Rubi [A] time = 0.00, antiderivative size = 15, normalized size of antiderivative = 0.58, number of steps used = 2, number of rules used = 2, integrand size = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.118, Rules used = {12, 2194} \begin {gather*} \sqrt {3} e^{\frac {x-16}{32}} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{32} \int e^{\frac {1}{32} (-16+x+16 \log (3))} \, dx\\ &=\sqrt {3} e^{\frac {1}{32} (-16+x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 15, normalized size = 0.58 \begin {gather*} \sqrt {3} e^{\frac {1}{32} (-16+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.54, size = 10, normalized size = 0.38 \begin {gather*} e^{\left (\frac {1}{32} \, x + \frac {1}{2} \, \log \relax (3) - \frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.15, size = 10, normalized size = 0.38 \begin {gather*} e^{\left (\frac {1}{32} \, x + \frac {1}{2} \, \log \relax (3) - \frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 11, normalized size = 0.42
method | result | size |
gosper | \({\mathrm e}^{\frac {\ln \relax (3)}{2}+\frac {x}{32}-\frac {1}{2}}\) | \(11\) |
derivativedivides | \({\mathrm e}^{\frac {\ln \relax (3)}{2}+\frac {x}{32}-\frac {1}{2}}\) | \(11\) |
default | \({\mathrm e}^{\frac {\ln \relax (3)}{2}+\frac {x}{32}-\frac {1}{2}}\) | \(11\) |
norman | \({\mathrm e}^{\frac {\ln \relax (3)}{2}+\frac {x}{32}-\frac {1}{2}}\) | \(11\) |
risch | \(\sqrt {3}\, {\mathrm e}^{-\frac {1}{2}+\frac {x}{32}}\) | \(11\) |
meijerg | \(-{\mathrm e}^{\frac {\ln \relax (3)}{2}-\frac {1}{2}} \left (1-{\mathrm e}^{\frac {x}{32}}\right )\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.37, size = 10, normalized size = 0.38 \begin {gather*} e^{\left (\frac {1}{32} \, x + \frac {1}{2} \, \log \relax (3) - \frac {1}{2}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.04, size = 10, normalized size = 0.38 \begin {gather*} \sqrt {3}\,{\mathrm {e}}^{x/32}\,{\mathrm {e}}^{-\frac {1}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.09, size = 12, normalized size = 0.46 \begin {gather*} \sqrt {3} e^{\frac {x}{32} - \frac {1}{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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