Optimal. Leaf size=21 \[ 2 e^{-4+e^x-x-e^x x} x^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(46\) vs. \(2(21)=42\).
time = 0.04, antiderivative size = 46, normalized size of antiderivative = 2.19, 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 {2 e^{e^x (1-x)-x-4} \left (e^x x^3+x^2\right )}{-e^x (1-x)+e^x+1} \end {gather*}
Antiderivative was successfully verified.
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Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {2 e^{-4+e^x (1-x)-x} \left (x^2+e^x x^3\right )}{1+e^x-e^x (1-x)}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.05, size = 20, normalized size = 0.95 \begin {gather*} 2 e^{-4-e^x (-1+x)-x} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.34, size = 19, normalized size = 0.90
method | result | size |
risch | \(2 x^{2} {\mathrm e}^{-{\mathrm e}^{x} x +{\mathrm e}^{x}-x -4}\) | \(19\) |
norman | \(2 x^{2} {\mathrm e}^{-4} {\mathrm e}^{-\left (x -1\right ) {\mathrm e}^{x}-x}\) | \(21\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.33, size = 18, normalized size = 0.86 \begin {gather*} 2 \, x^{2} e^{\left (-x e^{x} - x + e^{x} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.37, size = 18, normalized size = 0.86 \begin {gather*} 2 \, x^{2} e^{\left (-{\left (x - 1\right )} e^{x} - x - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.09, size = 19, normalized size = 0.90 \begin {gather*} \frac {2 x^{2} e^{- x - \left (x - 1\right ) e^{x}}}{e^{4}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 18, normalized size = 0.86 \begin {gather*} 2 \, x^{2} e^{\left (-x e^{x} - x + e^{x} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 6.74, size = 20, normalized size = 0.95 \begin {gather*} 2\,x^2\,{\mathrm {e}}^{-x\,{\mathrm {e}}^x}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-4} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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