Optimal. Leaf size=27 \[ e^{5-e (1-x)+2 x}-x-x \left (e^x+x\right ) \]
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Rubi [A] time = 0.03, antiderivative size = 32, normalized size of antiderivative = 1.19, number of steps used = 5, number of rules used = 3, integrand size = 30, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.100, Rules used = {2227, 2194, 2176} \begin {gather*} -x^2-x+e^x+e^{(2+e) x-e+5}-e^x (x+1) \end {gather*}
Antiderivative was successfully verified.
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Rule 2176
Rule 2194
Rule 2227
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-x-x^2+(2+e) \int e^{5+e (-1+x)+2 x} \, dx+\int e^x (-1-x) \, dx\\ &=-x-x^2-e^x (1+x)+(2+e) \int e^{5-e+(2+e) x} \, dx+\int e^x \, dx\\ &=e^x+e^{5-e+(2+e) x}-x-x^2-e^x (1+x)\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 25, normalized size = 0.93 \begin {gather*} e^{5+e (-1+x)+2 x}-e^x x-x (1+x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.45, size = 26, normalized size = 0.96 \begin {gather*} -x^{2} - x e^{x} - x + e^{\left ({\left (x - 1\right )} e + 2 \, x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.14, size = 26, normalized size = 0.96 \begin {gather*} -x^{2} - x e^{x} - x + e^{\left ({\left (x - 1\right )} e + 2 \, x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 27, normalized size = 1.00
method | result | size |
default | \(-{\mathrm e}^{x} x -x +{\mathrm e}^{\left (x -1\right ) {\mathrm e}+5+2 x}-x^{2}\) | \(27\) |
norman | \(-{\mathrm e}^{x} x -x +{\mathrm e}^{\left (x -1\right ) {\mathrm e}+5+2 x}-x^{2}\) | \(27\) |
risch | \(-{\mathrm e}^{x} x -x +{\mathrm e}^{x \,{\mathrm e}-{\mathrm e}+2 x +5}-x^{2}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.36, size = 26, normalized size = 0.96 \begin {gather*} -x^{2} - x e^{x} - x + e^{\left ({\left (x - 1\right )} e + 2 \, x + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.11, size = 28, normalized size = 1.04 \begin {gather*} {\mathrm {e}}^{2\,x-\mathrm {e}+x\,\mathrm {e}+5}-x-x\,{\mathrm {e}}^x-x^2 \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.13, size = 22, normalized size = 0.81 \begin {gather*} - x^{2} - x e^{x} - x + e^{2 x + e \left (x - 1\right ) + 5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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