Optimal. Leaf size=20 \[ 4 e^{-\frac {-2+x+x^2+\log (x)}{x^2}} x^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(84\) vs. \(2(20)=40\).
time = 0.08, antiderivative size = 84, normalized size of antiderivative = 4.20, number of steps
used = 1, number of rules used = 1, integrand size = 45, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.022, Rules used = {2326}
\begin {gather*} \frac {4 e^{\frac {x^3-x^2-x-\log (x)+2}{x^2}-x} (-x-2 \log (x)+5)}{x \left (\frac {-3 x^2+2 x+\frac {1}{x}+1}{x^2}+\frac {2 \left (x^3-x^2-x-\log (x)+2\right )}{x^3}+1\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {4 e^{-x+\frac {2-x-x^2+x^3-\log (x)}{x^2}} (5-x-2 \log (x))}{x \left (1+\frac {1+\frac {1}{x}+2 x-3 x^2}{x^2}+\frac {2 \left (2-x-x^2+x^3-\log (x)\right )}{x^3}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.14, size = 25, normalized size = 1.25 \begin {gather*} 4 e^{-1+\frac {2}{x^2}-\frac {1}{x}} x^{2-\frac {1}{x^2}} \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 20, normalized size = 1.00
method | result | size |
risch | \(4 x^{2} {\mathrm e}^{-\frac {\ln \left (x \right )+x^{2}+x -2}{x^{2}}}\) | \(20\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 25, normalized size = 1.25 \begin {gather*} 4 \, x^{2} e^{\left (-\frac {1}{x} - \frac {\log \left (x\right )}{x^{2}} + \frac {2}{x^{2}} - 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 19, normalized size = 0.95 \begin {gather*} 4 \, x^{2} e^{\left (-\frac {x^{2} + x + \log \left (x\right ) - 2}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 39.44, size = 26, normalized size = 1.30 \begin {gather*} 4 x^{2} e^{- x} e^{\frac {x^{3} - x^{2} - x - \log {\left (x \right )} + 2}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.39, size = 19, normalized size = 0.95 \begin {gather*} 4 \, x^{2} e^{\left (-\frac {x^{2} + x + \log \left (x\right ) - 2}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.08, size = 25, normalized size = 1.25 \begin {gather*} 4\,x^{2-\frac {1}{x^2}}\,{\mathrm {e}}^{-1}\,{\mathrm {e}}^{-\frac {1}{x}}\,{\mathrm {e}}^{\frac {2}{x^2}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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