Optimal. Leaf size=14 \[ e^{1-e^x+x} x^2 \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(29\) vs. \(2(14)=28\).
time = 0.07, antiderivative size = 29, normalized size of antiderivative = 2.07, number of steps
used = 2, number of rules used = 2, integrand size = 26, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.077, Rules used = {12, 2326}
\begin {gather*} \frac {e^{x-e^x+1} x \left (x-e^x x\right )}{1-e^x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int e^{1-e^x+x} x \left (8+4 x-4 e^x x\right ) \, dx\\ &=\frac {e^{1-e^x+x} x \left (x-e^x x\right )}{1-e^x}\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.01, size = 14, normalized size = 1.00 \begin {gather*} e^{1-e^x+x} x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.15, size = 17, normalized size = 1.21
method | result | size |
default | \(4 \,{\mathrm e}^{\ln \left (\frac {x^{2}}{4}\right )+1-{\mathrm e}^{x}+x}\) | \(17\) |
norman | \(4 \,{\mathrm e}^{\ln \left (\frac {x^{2}}{4}\right )+1-{\mathrm e}^{x}+x}\) | \(17\) |
risch | \(x^{2} {\mathrm e}^{1-\frac {i \pi \mathrm {csgn}\left (i x^{2}\right )^{3}}{2}+i \pi \,\mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i x^{2}\right )^{2}-\frac {i \pi \,\mathrm {csgn}\left (i x^{2}\right ) \mathrm {csgn}\left (i x \right )^{2}}{2}-{\mathrm e}^{x}+x}\) | \(62\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.31, size = 12, normalized size = 0.86 \begin {gather*} x^{2} e^{\left (x - e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.39, size = 16, normalized size = 1.14 \begin {gather*} 4 \, e^{\left (x - e^{x} + \log \left (\frac {1}{4} \, x^{2}\right ) + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.07, size = 10, normalized size = 0.71 \begin {gather*} x^{2} e^{x - e^{x} + 1} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [A]
time = 0.43, size = 12, normalized size = 0.86 \begin {gather*} x^{2} e^{\left (x - e^{x} + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 8.89, size = 13, normalized size = 0.93 \begin {gather*} x^2\,\mathrm {e}\,{\mathrm {e}}^{-{\mathrm {e}}^x}\,{\mathrm {e}}^x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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