Optimal. Leaf size=21 \[ 3 e^{e^{\frac {2}{3} e^{e^x} x (1+x)}}+x \]
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Rubi [F] time = 3.80, antiderivative size = 0, normalized size of antiderivative = 0.00, number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used = {} \begin {gather*} \int \left (1+\exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) \left (2+4 x+e^x \left (2 x+2 x^2\right )\right )\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=x+\int \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) \left (2+4 x+e^x \left (2 x+2 x^2\right )\right ) \, dx\\ &=x+\int 2 \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) \left (1+2 x+e^x x+e^x x^2\right ) \, dx\\ &=x+2 \int \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) \left (1+2 x+e^x x+e^x x^2\right ) \, dx\\ &=x+2 \int \left (\exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right )+2 \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) x+\exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+x+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) x+\exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+x+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) x^2\right ) \, dx\\ &=x+2 \int \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) \, dx+2 \int \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+x+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) x \, dx+2 \int \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+x+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) x^2 \, dx+4 \int \exp \left (e^x+e^{\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )}+\frac {1}{3} e^{e^x} \left (2 x+2 x^2\right )\right ) x \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.02, size = 21, normalized size = 1.00 \begin {gather*} 3 e^{e^{\frac {2}{3} e^{e^x} x (1+x)}}+x \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.65, size = 61, normalized size = 2.90 \begin {gather*} {\left (x e^{\left (\frac {2}{3} \, {\left (x^{2} + x\right )} e^{\left (e^{x}\right )} + e^{x}\right )} + 3 \, e^{\left (\frac {2}{3} \, {\left (x^{2} + x\right )} e^{\left (e^{x}\right )} + e^{\left (\frac {2}{3} \, {\left (x^{2} + x\right )} e^{\left (e^{x}\right )}\right )} + e^{x}\right )}\right )} e^{\left (-\frac {2}{3} \, {\left (x^{2} + x\right )} e^{\left (e^{x}\right )} - e^{x}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \int 2 \, {\left ({\left (x^{2} + x\right )} e^{x} + 2 \, x + 1\right )} e^{\left (\frac {2}{3} \, {\left (x^{2} + x\right )} e^{\left (e^{x}\right )} + e^{\left (\frac {2}{3} \, {\left (x^{2} + x\right )} e^{\left (e^{x}\right )}\right )} + e^{x}\right )} + 1\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.15, size = 16, normalized size = 0.76
method | result | size |
risch | \(x +3 \,{\mathrm e}^{{\mathrm e}^{\frac {2 \,{\mathrm e}^{{\mathrm e}^{x}} \left (x +1\right ) x}{3}}}\) | \(16\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.67, size = 21, normalized size = 1.00 \begin {gather*} x + 3 \, e^{\left (e^{\left (\frac {2}{3} \, x^{2} e^{\left (e^{x}\right )} + \frac {2}{3} \, x e^{\left (e^{x}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.59, size = 22, normalized size = 1.05 \begin {gather*} x+3\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {2\,x\,{\mathrm {e}}^{{\mathrm {e}}^x}}{3}}\,{\mathrm {e}}^{\frac {2\,x^2\,{\mathrm {e}}^{{\mathrm {e}}^x}}{3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 2.78, size = 22, normalized size = 1.05 \begin {gather*} x + 3 e^{e^{\left (\frac {2 x^{2}}{3} + \frac {2 x}{3}\right ) e^{e^{x}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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