Optimal. Leaf size=17 \[ \frac {e^{x+\frac {\log (3)}{x}}}{2 x^2} \]
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Rubi [A] time = 0.24, antiderivative size = 15, normalized size of antiderivative = 0.88, number of steps used = 3, number of rules used = 3, integrand size = 37, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.081, Rules used = {6688, 12, 2288} \begin {gather*} \frac {3^{\frac {1}{x}} e^x}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2288
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {3^{\frac {1}{x}} e^x \left (-2 x+x^2-\log (3)\right )}{2 x^4} \, dx\\ &=\frac {1}{2} \int \frac {3^{\frac {1}{x}} e^x \left (-2 x+x^2-\log (3)\right )}{x^4} \, dx\\ &=\frac {3^{\frac {1}{x}} e^x}{2 x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 15, normalized size = 0.88 \begin {gather*} \frac {3^{\frac {1}{x}} e^x}{2 x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.55, size = 19, normalized size = 1.12 \begin {gather*} e^{\left (\frac {x^{2} + x \log \left (\frac {1}{2 \, x^{2}}\right ) + \log \relax (3)}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.19, size = 17, normalized size = 1.00 \begin {gather*} e^{\left (x + \frac {\log \relax (3)}{x} - \log \left (2 \, x^{2}\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.18, size = 13, normalized size = 0.76
method | result | size |
risch | \(\frac {3^{\frac {1}{x}} {\mathrm e}^{x}}{2 x^{2}}\) | \(13\) |
gosper | \({\mathrm e}^{\frac {x \ln \left (\frac {1}{2 x^{2}}\right )+\ln \relax (3)+x^{2}}{x}}\) | \(20\) |
default | \({\mathrm e}^{\frac {x \ln \left (\frac {1}{2 x^{2}}\right )+\ln \relax (3)+x^{2}}{x}}\) | \(20\) |
norman | \({\mathrm e}^{\frac {x \ln \left (\frac {1}{2 x^{2}}\right )+\ln \relax (3)+x^{2}}{x}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.53, size = 14, normalized size = 0.82 \begin {gather*} \frac {e^{\left (x + \frac {\log \relax (3)}{x}\right )}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.58, size = 12, normalized size = 0.71 \begin {gather*} \frac {3^{1/x}\,{\mathrm {e}}^x}{2\,x^2} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.33, size = 19, normalized size = 1.12 \begin {gather*} e^{\frac {x^{2} + x \log {\left (\frac {1}{2 x^{2}} \right )} + \log {\relax (3 )}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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