Optimal. Leaf size=27 \[ \frac {10 e^{e^{-4-\frac {e^{2+(-4-x) x}}{x}}}}{x} \]
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Rubi [B] time = 0.27, antiderivative size = 97, normalized size of antiderivative = 3.59, number of steps used = 1, number of rules used = 1, integrand size = 79, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.013, Rules used = {2288} \begin {gather*} \frac {10 \left (2 x^2+4 x+1\right ) \exp \left (-x^2+e^{-\frac {e^{-x^2-4 x+2}+4 x}{x}}-4 x+2\right )}{x^3 \left (\frac {e^{-x^2-4 x+2}+4 x}{x^2}-\frac {2 \left (2-e^{-x^2-4 x+2} (x+2)\right )}{x}\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {10 e^{2+e^{-\frac {e^{2-4 x-x^2}+4 x}{x}}-4 x-x^2} \left (1+4 x+2 x^2\right )}{x^3 \left (\frac {e^{2-4 x-x^2}+4 x}{x^2}-\frac {2 \left (2-e^{2-4 x-x^2} (2+x)\right )}{x}\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 28, normalized size = 1.04 \begin {gather*} \frac {10 e^{e^{-4-\frac {e^{2-4 x-x^2}}{x}}}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.60, size = 29, normalized size = 1.07 \begin {gather*} 10 \, e^{\left (e^{\left (-\frac {4 \, x + e^{\left (-x^{2} - 4 \, x + 2\right )}}{x}\right )} - \log \relax (x)\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int \frac {10 \, {\left ({\left (2 \, x^{2} + 4 \, x + 1\right )} e^{\left (-x^{2} - 4 \, x - \frac {4 \, x + e^{\left (-x^{2} - 4 \, x + 2\right )}}{x} + 2\right )} - x\right )} e^{\left (e^{\left (-\frac {4 \, x + e^{\left (-x^{2} - 4 \, x + 2\right )}}{x}\right )} - \log \relax (x)\right )}}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.13, size = 28, normalized size = 1.04
method | result | size |
risch | \(\frac {10 \,{\mathrm e}^{{\mathrm e}^{-\frac {{\mathrm e}^{-x^{2}-4 x +2}+4 x}{x}}}}{x}\) | \(28\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} 10 \, \int \frac {{\left ({\left (2 \, x^{2} + 4 \, x + 1\right )} e^{\left (-x^{2} - 4 \, x - \frac {4 \, x + e^{\left (-x^{2} - 4 \, x + 2\right )}}{x} + 2\right )} - x\right )} e^{\left (e^{\left (-\frac {4 \, x + e^{\left (-x^{2} - 4 \, x + 2\right )}}{x}\right )}\right )}}{x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.32, size = 27, normalized size = 1.00 \begin {gather*} \frac {10\,{\mathrm {e}}^{{\mathrm {e}}^{-4}\,{\mathrm {e}}^{-\frac {{\mathrm {e}}^{-4\,x}\,{\mathrm {e}}^2\,{\mathrm {e}}^{-x^2}}{x}}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.73, size = 22, normalized size = 0.81 \begin {gather*} \frac {10 e^{e^{\frac {- 4 x - e^{- x^{2} - 4 x + 2}}{x}}}}{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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