Optimal. Leaf size=29 \[ \frac {-3-e^{6-x^2-\frac {\log (3)}{x^2}}+5 \log (3)}{\log (3)} \]
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Rubi [A] time = 0.24, antiderivative size = 30, normalized size of antiderivative = 1.03, number of steps used = 2, number of rules used = 2, integrand size = 39, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.051, Rules used = {12, 6706} \begin {gather*} -\frac {3^{-\frac {1}{x^2}} e^{\frac {6 x^2-x^4}{x^2}}}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {\int \frac {e^{\frac {6 x^2-x^4-\log (3)}{x^2}} \left (2 x^4-2 \log (3)\right )}{x^3} \, dx}{\log (3)}\\ &=-\frac {3^{-\frac {1}{x^2}} e^{\frac {6 x^2-x^4}{x^2}}}{\log (3)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 22, normalized size = 0.76 \begin {gather*} -\frac {3^{-\frac {1}{x^2}} e^{6-x^2}}{\log (3)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.68, size = 23, normalized size = 0.79 \begin {gather*} -\frac {e^{\left (-\frac {x^{4} - 6 \, x^{2} + \log \relax (3)}{x^{2}}\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 21, normalized size = 0.72 \begin {gather*} -\frac {e^{\left (-x^{2} - \frac {\log \relax (3)}{x^{2}} + 6\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 20, normalized size = 0.69
method | result | size |
risch | \(-\frac {\left (\frac {1}{3}\right )^{\frac {1}{x^{2}}} {\mathrm e}^{-x^{2}+6}}{\ln \relax (3)}\) | \(20\) |
gosper | \(-\frac {{\mathrm e}^{-\frac {x^{4}-6 x^{2}+\ln \relax (3)}{x^{2}}}}{\ln \relax (3)}\) | \(24\) |
norman | \(-\frac {{\mathrm e}^{\frac {-\ln \relax (3)-x^{4}+6 x^{2}}{x^{2}}}}{\ln \relax (3)}\) | \(27\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.52, size = 21, normalized size = 0.72 \begin {gather*} -\frac {e^{\left (-x^{2} - \frac {\log \relax (3)}{x^{2}} + 6\right )}}{\log \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 2.43, size = 21, normalized size = 0.72 \begin {gather*} -\frac {{\mathrm {e}}^6\,{\mathrm {e}}^{-x^2}}{3^{\frac {1}{x^2}}\,\ln \relax (3)} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.16, size = 20, normalized size = 0.69 \begin {gather*} - \frac {e^{\frac {- x^{4} + 6 x^{2} - \log {\relax (3 )}}{x^{2}}}}{\log {\relax (3 )}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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