Optimal. Leaf size=16 \[ e^x \left (4-(-6+e)^4-x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 28, normalized size of antiderivative = 1.75, number of steps used = 2, number of rules used = 2, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.074, Rules used = {2176, 2194} \begin {gather*} e^x-e^x \left (x+e^4-24 e^3+216 e^2-864 e+1293\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-e^x \left (1293-864 e+216 e^2-24 e^3+e^4+x\right )+\int e^x \, dx\\ &=e^x-e^x \left (1293-864 e+216 e^2-24 e^3+e^4+x\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.04, size = 24, normalized size = 1.50 \begin {gather*} -e^x \left (1292-864 e+216 e^2-24 e^3+e^4+x\right ) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 21, normalized size = 1.31 \begin {gather*} -{\left (x + e^{4} - 24 \, e^{3} + 216 \, e^{2} - 864 \, e + 1292\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.12, size = 32, normalized size = 2.00 \begin {gather*} -{\left (x + 1292\right )} e^{x} - e^{\left (x + 4\right )} + 24 \, e^{\left (x + 3\right )} - 216 \, e^{\left (x + 2\right )} + 864 \, e^{\left (x + 1\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 25, normalized size = 1.56
method | result | size |
risch | \(\left (-{\mathrm e}^{4}+24 \,{\mathrm e}^{3}-216 \,{\mathrm e}^{2}+864 \,{\mathrm e}-x -1292\right ) {\mathrm e}^{x}\) | \(25\) |
gosper | \(-{\mathrm e}^{x} \left (x +{\mathrm e}^{4}-24 \,{\mathrm e}^{3}+216 \,{\mathrm e}^{2}-864 \,{\mathrm e}+1292\right )\) | \(28\) |
norman | \(\left (-{\mathrm e}^{4}+24 \,{\mathrm e}^{3}-216 \,{\mathrm e}^{2}+864 \,{\mathrm e}-1292\right ) {\mathrm e}^{x}-{\mathrm e}^{x} x\) | \(34\) |
default | \(864 \,{\mathrm e} \,{\mathrm e}^{x}-216 \,{\mathrm e}^{2} {\mathrm e}^{x}-{\mathrm e}^{x} x -1292 \,{\mathrm e}^{x}+24 \,{\mathrm e}^{x} {\mathrm e}^{3}-{\mathrm e}^{4} {\mathrm e}^{x}\) | \(41\) |
meijerg | \({\mathrm e}^{4} \left (1-{\mathrm e}^{x}\right )-24 \,{\mathrm e}^{3} \left (1-{\mathrm e}^{x}\right )+216 \,{\mathrm e}^{2} \left (1-{\mathrm e}^{x}\right )-864 \left (1-{\mathrm e}^{x}\right ) {\mathrm e}+1292+\frac {\left (-2 x +2\right ) {\mathrm e}^{x}}{2}-1293 \,{\mathrm e}^{x}\) | \(55\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.36, size = 36, normalized size = 2.25 \begin {gather*} -{\left (x - 1\right )} e^{x} - e^{\left (x + 4\right )} + 24 \, e^{\left (x + 3\right )} - 216 \, e^{\left (x + 2\right )} + 864 \, e^{\left (x + 1\right )} - 1293 \, e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 3.07, size = 21, normalized size = 1.31 \begin {gather*} -{\mathrm {e}}^x\,\left (x-864\,\mathrm {e}+216\,{\mathrm {e}}^2-24\,{\mathrm {e}}^3+{\mathrm {e}}^4+1292\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 24, normalized size = 1.50 \begin {gather*} \left (- x - 216 e^{2} - 1292 - e^{4} + 24 e^{3} + 864 e\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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