Optimal. Leaf size=17 \[ e^{5-e^{\frac {1}{x}}+x-x^2} \]
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Rubi [A] time = 0.33, antiderivative size = 17, normalized size of antiderivative = 1.00, number of steps used = 1, number of rules used = 1, integrand size = 35, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.029, Rules used = {6706} \begin {gather*} e^{-x^2+x-e^{\frac {1}{x}}+5} \end {gather*}
Antiderivative was successfully verified.
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Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=e^{5-e^{\frac {1}{x}}+x-x^2}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.16, size = 17, normalized size = 1.00 \begin {gather*} e^{5-e^{\frac {1}{x}}+x-x^2} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 3.00, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (-x^{2} + x - e^{\frac {1}{x}} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.16, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (-x^{2} + x - e^{\frac {1}{x}} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.17, size = 16, normalized size = 0.94
method | result | size |
norman | \({\mathrm e}^{-{\mathrm e}^{\frac {1}{x}}-x^{2}+x +5}\) | \(16\) |
risch | \({\mathrm e}^{-{\mathrm e}^{\frac {1}{x}}-x^{2}+x +5}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.49, size = 15, normalized size = 0.88 \begin {gather*} e^{\left (-x^{2} + x - e^{\frac {1}{x}} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.79, size = 18, normalized size = 1.06 \begin {gather*} {\mathrm {e}}^{-{\mathrm {e}}^{1/x}}\,{\mathrm {e}}^5\,{\mathrm {e}}^{-x^2}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.28, size = 12, normalized size = 0.71 \begin {gather*} e^{- x^{2} + x - e^{\frac {1}{x}} + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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