Optimal. Leaf size=26 \[ 2 \left (2+\frac {1}{5} e^{5-e^{10}-x-x^2}+x\right ) \]
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Rubi [A] time = 0.02, antiderivative size = 25, normalized size of antiderivative = 0.96, number of steps used = 3, number of rules used = 2, integrand size = 29, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.069, Rules used = {12, 2236} \begin {gather*} \frac {2}{5} e^{-x^2-x-e^{10}+5}+2 x \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 2236
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{5} \int \left (10+e^{5-e^{10}-x-x^2} (-2-4 x)\right ) \, dx\\ &=2 x+\frac {1}{5} \int e^{5-e^{10}-x-x^2} (-2-4 x) \, dx\\ &=\frac {2}{5} e^{5-e^{10}-x-x^2}+2 x\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.05, size = 25, normalized size = 0.96 \begin {gather*} \frac {2}{5} e^{5-e^{10}-x-x^2}+2 x \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.75, size = 21, normalized size = 0.81 \begin {gather*} 2 \, x + \frac {2}{5} \, e^{\left (-x^{2} - x - e^{10} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.17, size = 21, normalized size = 0.81 \begin {gather*} 2 \, x + \frac {2}{5} \, e^{\left (-x^{2} - x - e^{10} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.02, size = 22, normalized size = 0.85
method | result | size |
risch | \(2 x +\frac {2 \,{\mathrm e}^{-{\mathrm e}^{10}-x^{2}-x +5}}{5}\) | \(22\) |
default | \(2 x +\frac {2 \,{\mathrm e}^{-{\mathrm e}^{10}-x^{2}-x +5}}{5}\) | \(24\) |
norman | \(2 x +\frac {2 \,{\mathrm e}^{-{\mathrm e}^{10}-x^{2}-x +5}}{5}\) | \(24\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.33, size = 21, normalized size = 0.81 \begin {gather*} 2 \, x + \frac {2}{5} \, e^{\left (-x^{2} - x - e^{10} + 5\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.12, size = 23, normalized size = 0.88 \begin {gather*} 2\,x+\frac {2\,{\mathrm {e}}^{-{\mathrm {e}}^{10}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^5\,{\mathrm {e}}^{-x^2}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.11, size = 17, normalized size = 0.65 \begin {gather*} 2 x + \frac {2 e^{- x^{2} - x - e^{10} + 5}}{5} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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