Optimal. Leaf size=30 \[ e^{-e^{-5+e^5-x}} x \left (4+4 (4-x)-x^2\right ) \]
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Rubi [A]
time = 0.07, antiderivative size = 29, normalized size of antiderivative = 0.97, number of steps
used = 2, number of rules used = 2, integrand size = 76, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {1600, 2326}
\begin {gather*} e^{-e^{-x+e^5-5}} \left (-x^3-4 x^2+20 x\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 1600
Rule 2326
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\int e^{-e^{-5+e^5-x}} \left (-20+8 x+3 x^2+e^{-5+e^5-x} \left (-20 x+4 x^2+x^3\right )\right ) \, dx\\ &=e^{-e^{-5+e^5-x}} \left (20 x-4 x^2-x^3\right )\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.10, size = 25, normalized size = 0.83 \begin {gather*} -e^{-e^{-5+e^5-x}} x \left (-20+4 x+x^2\right ) \end {gather*}
Antiderivative was successfully verified.
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Maple [C] Result contains higher order function than in optimal. Order 9 vs. order
3.
time = 0.14, size = 151, normalized size = 5.03
method | result | size |
risch | \(-x \left (x^{2}+4 x -20\right ) {\mathrm e}^{\frac {i \pi \mathrm {csgn}\left (i x \left (x^{2}+4 x -20\right )\right )^{3}}{2}+\frac {i \pi \mathrm {csgn}\left (i x \left (x^{2}+4 x -20\right )\right )^{2} \mathrm {csgn}\left (i x \right )}{2}+\frac {i \pi \mathrm {csgn}\left (i x \left (x^{2}+4 x -20\right )\right )^{2} \mathrm {csgn}\left (i \left (x^{2}+4 x -20\right )\right )}{2}-\frac {i \pi \,\mathrm {csgn}\left (i x \left (x^{2}+4 x -20\right )\right ) \mathrm {csgn}\left (i x \right ) \mathrm {csgn}\left (i \left (x^{2}+4 x -20\right )\right )}{2}-i \pi \mathrm {csgn}\left (i x \left (x^{2}+4 x -20\right )\right )^{2}-{\mathrm e}^{{\mathrm e}^{5}-x -5}}\) | \(151\) |
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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.35, size = 27, normalized size = 0.90 \begin {gather*} e^{\left (-e^{\left (-x + e^{5} - 5\right )} + \log \left (-x^{3} - 4 \, x^{2} + 20 \, x\right )\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.10, size = 20, normalized size = 0.67 \begin {gather*} \left (- x^{3} - 4 x^{2} + 20 x\right ) e^{- e^{- x - 5 + e^{5}}} \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*} \text {could not integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 1.43, size = 23, normalized size = 0.77 \begin {gather*} -x\,{\mathrm {e}}^{-{\mathrm {e}}^{-x}\,{\mathrm {e}}^{-5}\,{\mathrm {e}}^{{\mathrm {e}}^5}}\,\left (x^2+4\,x-20\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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