Optimal. Leaf size=26 \[ -x^2+\left (1+e^{e^4}\right ) \left (2-e^{-3+x}+2 x\right ) \]
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Rubi [A] time = 0.01, antiderivative size = 34, normalized size of antiderivative = 1.31, number of steps used = 4, number of rules used = 1, integrand size = 27, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.037, Rules used = {2194} \begin {gather*} -x^2+2 e^{e^4} x+2 x-e^{x-3}-e^{x+e^4-3} \end {gather*}
Antiderivative was successfully verified.
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Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x-x^2+e^{e^4} \int \left (2-e^{-3+x}\right ) \, dx-\int e^{-3+x} \, dx\\ &=-e^{-3+x}+2 x+2 e^{e^4} x-x^2-e^{e^4} \int e^{-3+x} \, dx\\ &=-e^{-3+x}-e^{-3+e^4+x}+2 x+2 e^{e^4} x-x^2\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.02, size = 34, normalized size = 1.31 \begin {gather*} -e^{-3+x}-e^{-3+e^4+x}+2 x+2 e^{e^4} x-x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.44, size = 29, normalized size = 1.12 \begin {gather*} -x^{2} + {\left (2 \, x - e^{\left (x - 3\right )}\right )} e^{\left (e^{4}\right )} + 2 \, x - e^{\left (x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.33, size = 29, normalized size = 1.12 \begin {gather*} -x^{2} + {\left (2 \, x - e^{\left (x - 3\right )}\right )} e^{\left (e^{4}\right )} + 2 \, x - e^{\left (x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 28, normalized size = 1.08
method | result | size |
norman | \(\left (-{\mathrm e}^{{\mathrm e}^{4}}-1\right ) {\mathrm e}^{x -3}+\left (2 \,{\mathrm e}^{{\mathrm e}^{4}}+2\right ) x -x^{2}\) | \(28\) |
default | \(2 x +{\mathrm e}^{{\mathrm e}^{4}} \left (2 x -{\mathrm e}^{x -3}\right )-x^{2}-{\mathrm e}^{x -3}\) | \(30\) |
risch | \(2 x \,{\mathrm e}^{{\mathrm e}^{4}}-{\mathrm e}^{x -3+{\mathrm e}^{4}}-{\mathrm e}^{x -3}-x^{2}+2 x\) | \(30\) |
derivativedivides | \(-4 x +12+{\mathrm e}^{{\mathrm e}^{4}} \left (2 x -6-{\mathrm e}^{x -3}\right )-\left (x -3\right )^{2}-{\mathrm e}^{x -3}\) | \(34\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.40, size = 29, normalized size = 1.12 \begin {gather*} -x^{2} + {\left (2 \, x - e^{\left (x - 3\right )}\right )} e^{\left (e^{4}\right )} + 2 \, x - e^{\left (x - 3\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.72, size = 26, normalized size = 1.00 \begin {gather*} x\,\left (2\,{\mathrm {e}}^{{\mathrm {e}}^4}+2\right )-{\mathrm {e}}^{x-3}\,\left ({\mathrm {e}}^{{\mathrm {e}}^4}+1\right )-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.10, size = 26, normalized size = 1.00 \begin {gather*} - x^{2} + x \left (2 + 2 e^{e^{4}}\right ) + \left (- e^{e^{4}} - 1\right ) e^{x - 3} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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