Optimal. Leaf size=25 \[ e^{-4+e^x-x+\frac {\left (x+\frac {x^2}{5}\right )^2}{x}} \]
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Rubi [A] time = 0.10, antiderivative size = 20, normalized size of antiderivative = 0.80, number of steps used = 2, number of rules used = 2, integrand size = 38, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.053, Rules used = {12, 6706} \begin {gather*} e^{\frac {1}{25} \left (x^3+10 x^2-100\right )+e^x} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{25} \int e^{e^x+\frac {1}{25} \left (-100+10 x^2+x^3\right )} \left (25 e^x+20 x+3 x^2\right ) \, dx\\ &=e^{e^x+\frac {1}{25} \left (-100+10 x^2+x^3\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.18, size = 21, normalized size = 0.84 \begin {gather*} e^{-4+e^x+\frac {2 x^2}{5}+\frac {x^3}{25}} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.51, size = 15, normalized size = 0.60 \begin {gather*} e^{\left (\frac {1}{25} \, x^{3} + \frac {2}{5} \, x^{2} + e^{x} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.30, size = 15, normalized size = 0.60 \begin {gather*} e^{\left (\frac {1}{25} \, x^{3} + \frac {2}{5} \, x^{2} + e^{x} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.05, size = 16, normalized size = 0.64
method | result | size |
risch | \({\mathrm e}^{\frac {x^{3}}{25}+\frac {2 x^{2}}{5}-4+{\mathrm e}^{x}}\) | \(16\) |
norman | \({\mathrm e}^{\frac {1}{25} x^{3}+\frac {2}{5} x^{2}-4} {\mathrm e}^{{\mathrm e}^{x}}\) | \(18\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.44, size = 15, normalized size = 0.60 \begin {gather*} e^{\left (\frac {1}{25} \, x^{3} + \frac {2}{5} \, x^{2} + e^{x} - 4\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.08, size = 18, normalized size = 0.72 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^x}\,{\mathrm {e}}^{-4}\,{\mathrm {e}}^{\frac {2\,x^2}{5}}\,{\mathrm {e}}^{\frac {x^3}{25}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 22.73, size = 19, normalized size = 0.76 \begin {gather*} e^{\frac {x^{3}}{25} + \frac {2 x^{2}}{5} - 4} e^{e^{x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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