Optimal. Leaf size=17 \[ \frac {e^{x+\frac {\log (3)}{x}}}{2 x^2} \]
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Rubi [A]
time = 0.16, 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 = {6820, 12, 2326}
\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 2326
Rule 6820
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 = 0.01, 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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Maple [A]
time = 0.76, size = 20, normalized size = 1.18
method | result | size |
risch | \(\frac {3^{\frac {1}{x}} {\mathrm e}^{x}}{2 x^{2}}\) | \(13\) |
gosper | \({\mathrm e}^{\frac {x \ln \left (\frac {1}{2 x^{2}}\right )+\ln \left (3\right )+x^{2}}{x}}\) | \(20\) |
default | \({\mathrm e}^{\frac {x \ln \left (\frac {1}{2 x^{2}}\right )+\ln \left (3\right )+x^{2}}{x}}\) | \(20\) |
norman | \({\mathrm e}^{\frac {x \ln \left (\frac {1}{2 x^{2}}\right )+\ln \left (3\right )+x^{2}}{x}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.69, size = 14, normalized size = 0.82 \begin {gather*} \frac {e^{\left (x + \frac {\log \left (3\right )}{x}\right )}}{2 \, x^{2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.42, size = 19, normalized size = 1.12 \begin {gather*} e^{\left (\frac {x^{2} + x \log \left (\frac {1}{2 \, x^{2}}\right ) + \log \left (3\right )}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.12, size = 19, normalized size = 1.12 \begin {gather*} e^{\frac {x^{2} + x \log {\left (\frac {1}{2 x^{2}} \right )} + \log {\left (3 \right )}}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.38, size = 17, normalized size = 1.00 \begin {gather*} e^{\left (x + \frac {\log \left (3\right )}{x} - \log \left (2 \, x^{2}\right )\right )} \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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