Optimal. Leaf size=19 \[ -e^{3-e-x}+x-x^2 \]
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Rubi [A]
time = 0.06, antiderivative size = 19, normalized size of antiderivative = 1.00, number of steps
used = 3, number of rules used = 2, integrand size = 25, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.080, Rules used = {6820, 2225}
\begin {gather*} -x^2+x-e^{-x-e+3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2225
Rule 6820
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (1+e^{3-e-x}-2 x\right ) \, dx\\ &=x-x^2+\int e^{3-e-x} \, dx\\ &=-e^{3-e-x}+x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A]
time = 0.02, size = 19, normalized size = 1.00 \begin {gather*} -e^{3-e-x}+x-x^2 \end {gather*}
Antiderivative was successfully verified.
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Maple [A]
time = 0.03, size = 33, normalized size = 1.74
method | result | size |
risch | \(-x^{2}+x -{\mathrm e}^{3-{\mathrm e}-x}\) | \(20\) |
norman | \(\left ({\mathrm e}^{x} x -{\mathrm e}^{x} x^{2}-{\mathrm e}^{-{\mathrm e}} {\mathrm e}^{3}\right ) {\mathrm e}^{-x}\) | \(29\) |
default | \({\mathrm e}^{3-{\mathrm e}} \left (-{\mathrm e}^{-x}+{\mathrm e}^{{\mathrm e}} {\mathrm e}^{-3} x -x^{2} {\mathrm e}^{{\mathrm e}} {\mathrm e}^{-3}\right )\) | \(33\) |
Verification of antiderivative is not currently implemented for this CAS.
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Maxima [A]
time = 0.26, size = 19, normalized size = 1.00 \begin {gather*} -x^{2} + x - e^{\left (-x - e + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Fricas [A]
time = 0.36, size = 28, normalized size = 1.47 \begin {gather*} -{\left ({\left (x^{2} - x\right )} e^{\left (x + e - 3\right )} + 1\right )} e^{\left (-x - e + 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Sympy [A]
time = 0.05, size = 15, normalized size = 0.79 \begin {gather*} - x^{2} + x - \frac {e^{3} e^{- x}}{e^{e}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Giac [B] Leaf count of result is larger than twice the leaf count of optimal. 39 vs.
\(2 (19) = 38\).
time = 0.43, size = 39, normalized size = 2.05 \begin {gather*} -{\left (x + e - 3\right )}^{2} + 2 \, {\left (x + e - 3\right )} e - 5 \, x - 5 \, e - e^{\left (-x - e + 3\right )} + 15 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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Mupad [B]
time = 0.08, size = 20, normalized size = 1.05 \begin {gather*} x-x^2-{\mathrm {e}}^{-\mathrm {e}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^3 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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