Optimal. Leaf size=31 \[ \frac {4 e^{-9+\frac {2}{x}-x-\frac {x+\log (x)}{x}}-x}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(69\) vs. \(2(31)=62\).
time = 0.11, antiderivative size = 69, normalized size of antiderivative = 2.23, number of steps
used = 1, number of rules used = 1, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {2326}
\begin {gather*} \frac {4 e^{\frac {-x^2-10 x+2}{x}} x^{-\frac {1}{x}-3} \left (x^2-\log (x)+3\right )}{\frac {-x^2-10 x-\log (x)+2}{x^2}+\frac {2 x+\frac {1}{x}+10}{x}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{\frac {2-10 x-x^2}{x}} x^{-3-\frac {1}{x}} \left (3+x^2-\log (x)\right )}{\frac {10+\frac {1}{x}+2 x}{x}+\frac {2-10 x-x^2-\log (x)}{x^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 23, normalized size = 0.74 \begin {gather*} 4 e^{-10+\frac {2}{x}-x} x^{-1-\frac {1}{x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.10, size = 22, normalized size = 0.71
method | result | size |
risch | \(\frac {4 \,{\mathrm e}^{-\frac {x^{2}+\ln \left (x \right )+10 x -2}{x}}}{x}\) | \(22\) |
norman | \(\frac {4 \,{\mathrm e}^{\frac {-\ln \left (x \right )-x^{2}-10 x +2}{x}}}{x}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.34, size = 23, normalized size = 0.74 \begin {gather*} \frac {4 \, e^{\left (-x - \frac {\log \left (x\right )}{x} + \frac {2}{x} - 10\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 21, normalized size = 0.68 \begin {gather*} \frac {4 \, e^{\left (-\frac {x^{2} + 10 \, x + \log \left (x\right ) - 2}{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 17, normalized size = 0.55 \begin {gather*} \frac {4 e^{\frac {- x^{2} - 10 x - \log {\left (x \right )} + 2}{x}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 21, normalized size = 0.68 \begin {gather*} \frac {4 \, e^{\left (-\frac {x^{2} + 10 \, x + \log \left (x\right ) - 2}{x}\right )}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 3.54, size = 23, normalized size = 0.74 \begin {gather*} \frac {4\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-10}\,{\mathrm {e}}^{2/x}}{x^{\frac {1}{x}+1}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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