Optimal. Leaf size=14 \[ -e^{12+\frac {2}{x}-x} \]
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Rubi [A] time = 0.27, antiderivative size = 14, normalized size of antiderivative = 1.00, number of steps used = 2, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {6688, 6706} \begin {gather*} -e^{-x+\frac {2}{x}+12} \end {gather*}
Antiderivative was successfully verified.
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Rule 6688
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {e^{12+\frac {2}{x}-x} \left (2+x^2\right )}{x^2} \, dx\\ &=-e^{12+\frac {2}{x}-x}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 14, normalized size = 1.00 \begin {gather*} -e^{12+\frac {2}{x}-x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 21, normalized size = 1.50 \begin {gather*} -x e^{\left (-\frac {x^{2} + x \log \relax (x) - 12 \, x - 2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.49, size = 16, normalized size = 1.14 \begin {gather*} -e^{\left (-\frac {x^{2} - 12 \, x - 2}{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 17, normalized size = 1.21
method | result | size |
risch | \(-{\mathrm e}^{-\frac {x^{2}-12 x -2}{x}}\) | \(17\) |
gosper | \(-x \,{\mathrm e}^{12} {\mathrm e}^{-\frac {x \ln \relax (x )+x^{2}-2}{x}}\) | \(23\) |
norman | \(-x \,{\mathrm e}^{12} {\mathrm e}^{\frac {-x \ln \relax (x )-x^{2}+2}{x}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.64, size = 13, normalized size = 0.93 \begin {gather*} -e^{\left (-x + \frac {2}{x} + 12\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.86, size = 14, normalized size = 1.00 \begin {gather*} -{\mathrm {e}}^{-x}\,{\mathrm {e}}^{12}\,{\mathrm {e}}^{2/x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.31, size = 19, normalized size = 1.36 \begin {gather*} - x e^{12} e^{\frac {- x^{2} - x \log {\relax (x )} + 2}{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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