Optimal. Leaf size=22 \[ e^{\frac {-2-x-x^2+\log (x)}{x}} x^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(63\) vs. \(2(22)=44\).
time = 0.05, antiderivative size = 63, normalized size of antiderivative = 2.86, number of steps
used = 1, number of rules used = 1, integrand size = 33, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.030, Rules used = {2326}
\begin {gather*} -\frac {e^{-\frac {x^2+x+2}{x}} x^{\frac {1}{x}} \left (-x^2-\log (x)+3\right )}{\frac {2 x-\frac {1}{x}+1}{x}-\frac {x^2+x-\log (x)+2}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\frac {e^{-\frac {2+x+x^2}{x}} x^{\frac {1}{x}} \left (3-x^2-\log (x)\right )}{\frac {1-\frac {1}{x}+2 x}{x}-\frac {2+x+x^2-\log (x)}{x^2}}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.33, size = 20, normalized size = 0.91 \begin {gather*} e^{-1-\frac {2}{x}-x} x^{2+\frac {1}{x}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 22, normalized size = 1.00
method | result | size |
norman | \({\mathrm e}^{\frac {\ln \left (x \right )-x^{2}-x -2}{x}} x^{2}\) | \(22\) |
risch | \({\mathrm e}^{\frac {\ln \left (x \right )-x^{2}-x -2}{x}} x^{2}\) | \(22\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 21, normalized size = 0.95 \begin {gather*} x^{2} e^{\left (-x + \frac {\log \left (x\right )}{x} - \frac {2}{x} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.41, size = 20, normalized size = 0.91 \begin {gather*} x^{2} e^{\left (-\frac {x^{2} + x - \log \left (x\right ) + 2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 15, normalized size = 0.68 \begin {gather*} x^{2} e^{\frac {- x^{2} - x + \log {\left (x \right )} - 2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.41, size = 20, normalized size = 0.91 \begin {gather*} x^{2} e^{\left (-\frac {x^{2} + x - \log \left (x\right ) + 2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 4.35, size = 20, normalized size = 0.91 \begin {gather*} x^{\frac {1}{x}+2}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-\frac {2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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