Optimal. Leaf size=23 \[ e^x (1-x)+x^2+x \left (e^{14+e+x}+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 33, normalized size of antiderivative = 1.43, number of steps used = 5, number of rules used = 2, integrand size = 20, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2176, 2194} \begin {gather*} 2 x^2-e^x x+e^x-e^{x+e+14}+e^{x+e+14} (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=2 x^2-\int e^x x \, dx+\int e^{14+e+x} (1+x) \, dx\\ &=-e^x x+2 x^2+e^{14+e+x} (1+x)+\int e^x \, dx-\int e^{14+e+x} \, dx\\ &=e^x-e^{14+e+x}-e^x x+2 x^2+e^{14+e+x} (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.01, size = 22, normalized size = 0.96 \begin {gather*} -e^x (-1+x)+e^{14+e+x} x+2 x^2 \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.64, size = 38, normalized size = 1.65 \begin {gather*} {\left (2 \, x^{2} e^{\left (e + 14\right )} + {\left (x e^{\left (e + 14\right )} - x + 1\right )} e^{\left (x + e + 14\right )}\right )} e^{\left (-e - 14\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.25, size = 21, normalized size = 0.91 \begin {gather*} 2 \, x^{2} + x e^{\left (x + e + 14\right )} - {\left (x - 1\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 21, normalized size = 0.91
method | result | size |
norman | \(\left ({\mathrm e}^{{\mathrm e}} {\mathrm e}^{14}-1\right ) x \,{\mathrm e}^{x}+2 x^{2}+{\mathrm e}^{x}\) | \(21\) |
risch | \({\mathrm e}^{{\mathrm e}+x +14} x -\left (x -1\right ) {\mathrm e}^{x}+2 x^{2}\) | \(22\) |
default | \({\mathrm e}^{{\mathrm e}+x +14} \left ({\mathrm e}+x +14\right )-14 \,{\mathrm e}^{{\mathrm e}+x +14}-{\mathrm e}^{{\mathrm e}+x +14} {\mathrm e}+2 x^{2}-{\mathrm e}^{x} x +{\mathrm e}^{x}\) | \(44\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.79, size = 21, normalized size = 0.91 \begin {gather*} 2 \, x^{2} + x e^{\left (x + e + 14\right )} - {\left (x - 1\right )} e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.32, size = 19, normalized size = 0.83 \begin {gather*} {\mathrm {e}}^x+2\,x^2+x\,{\mathrm {e}}^x\,\left ({\mathrm {e}}^{\mathrm {e}+14}-1\right ) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 20, normalized size = 0.87 \begin {gather*} 2 x^{2} + \left (- x + x e^{14} e^{e} + 1\right ) e^{x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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