Optimal. Leaf size=19 \[ 26 e^{e^{\frac {e^{e^4 x}}{2}+x}} \]
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Rubi [F] time = 0.46, 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 \exp \left (e^{\frac {1}{2} \left (e^{e^4 x}+2 x\right )}+\frac {1}{2} \left (e^{e^4 x}+2 x\right )\right ) \left (26+13 e^{4+e^4 x}\right ) \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int 13 e^{\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )} \left (2+e^{4+e^4 x}\right ) \, dx\\ &=13 \int e^{\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )} \left (2+e^{4+e^4 x}\right ) \, dx\\ &=13 \int \left (2 e^{\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )}+\exp \left (4+e^4 x+\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )\right )\right ) \, dx\\ &=13 \int \exp \left (4+e^4 x+\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )\right ) \, dx+26 \int e^{\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )} \, dx\\ &=13 \int \exp \left (\frac {1}{2} \left (8+e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 \left (1+e^4\right ) x\right )\right ) \, dx+26 \int e^{\frac {1}{2} \left (e^{e^4 x}+2 e^{\frac {e^{e^4 x}}{2}+x}+2 x\right )} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.15, size = 19, normalized size = 1.00 \begin {gather*} 26 e^{e^{\frac {e^{e^4 x}}{2}+x}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.70, size = 60, normalized size = 3.16 \begin {gather*} 26 \, e^{\left (\frac {1}{2} \, {\left (2 \, x e^{4} + e^{\left (x e^{4} + 4\right )} + 2 \, e^{\left (\frac {1}{2} \, {\left (2 \, x e^{4} + e^{\left (x e^{4} + 4\right )}\right )} e^{\left (-4\right )} + 4\right )}\right )} e^{\left (-4\right )} - \frac {1}{2} \, {\left (2 \, x e^{4} + e^{\left (x e^{4} + 4\right )}\right )} e^{\left (-4\right )}\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 13 \, {\left (e^{\left (x e^{4} + 4\right )} + 2\right )} e^{\left (x + \frac {1}{2} \, e^{\left (x e^{4}\right )} + e^{\left (x + \frac {1}{2} \, e^{\left (x e^{4}\right )}\right )}\right )}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.11, size = 14, normalized size = 0.74
method | result | size |
norman | \(26 \,{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x \,{\mathrm e}^{4}}}{2}+x}}\) | \(14\) |
risch | \(26 \,{\mathrm e}^{{\mathrm e}^{\frac {{\mathrm e}^{x \,{\mathrm e}^{4}}}{2}+x}}\) | \(14\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.48, size = 13, normalized size = 0.68 \begin {gather*} 26 \, e^{\left (e^{\left (x + \frac {1}{2} \, e^{\left (x e^{4}\right )}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.20, size = 14, normalized size = 0.74 \begin {gather*} 26\,{\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^{x\,{\mathrm {e}}^4}}{2}}\,{\mathrm {e}}^x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 14, normalized size = 0.74 \begin {gather*} 26 e^{e^{x + \frac {e^{x e^{4}}}{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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