Optimal. Leaf size=27 \[ e^{e^{e^x}+\frac {1}{3} x \left (7-e^{4+\frac {12}{x}}+x\right )} \]
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Rubi [A] time = 1.11, antiderivative size = 33, normalized size of antiderivative = 1.22, number of steps used = 2, number of rules used = 2, integrand size = 77, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.026, Rules used = {12, 6706} \begin {gather*} \exp \left (\frac {1}{3} \left (x^2-e^{\frac {4 (x+3)}{x}} x+7 x+3 e^{e^x}\right )\right ) \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6706
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{3} \int \frac {e^{\frac {1}{3} \left (3 e^{e^x}+7 x-e^{\frac {12+4 x}{x}} x+x^2\right )} \left (e^{\frac {12+4 x}{x}} (12-x)+7 x+3 e^{e^x+x} x+2 x^2\right )}{x} \, dx\\ &=\exp \left (\frac {1}{3} \left (3 e^{e^x}+7 x-e^{\frac {4 (3+x)}{x}} x+x^2\right )\right )\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 1.66, size = 30, normalized size = 1.11 \begin {gather*} e^{e^{e^x}-\frac {1}{3} e^{4+\frac {12}{x}} x+\frac {1}{3} x (7+x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 37, normalized size = 1.37 \begin {gather*} e^{\left (\frac {1}{3} \, {\left ({\left (x^{2} - x e^{\left (\frac {4 \, {\left (x + 3\right )}}{x}\right )} + 7 \, x\right )} e^{x} + 3 \, e^{\left (x + e^{x}\right )}\right )} e^{\left (-x\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 \frac {{\left (2 \, x^{2} + 3 \, x e^{\left (x + e^{x}\right )} - {\left (x - 12\right )} e^{\left (\frac {4 \, {\left (x + 3\right )}}{x}\right )} + 7 \, x\right )} e^{\left (\frac {1}{3} \, x^{2} - \frac {1}{3} \, x e^{\left (\frac {4 \, {\left (x + 3\right )}}{x}\right )} + \frac {7}{3} \, x + e^{\left (e^{x}\right )}\right )}}{3 \, x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.28, size = 26, normalized size = 0.96
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{{\mathrm e}^{x}}-\frac {x \,{\mathrm e}^{\frac {4 x +12}{x}}}{3}+\frac {x^{2}}{3}+\frac {7 x}{3}}\) | \(26\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [F] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \frac {1}{3} \, \int \frac {{\left (2 \, x^{2} + 3 \, x e^{\left (x + e^{x}\right )} - {\left (x - 12\right )} e^{\left (\frac {4 \, {\left (x + 3\right )}}{x}\right )} + 7 \, x\right )} e^{\left (\frac {1}{3} \, x^{2} - \frac {1}{3} \, x e^{\left (\frac {4 \, {\left (x + 3\right )}}{x}\right )} + \frac {7}{3} \, x + e^{\left (e^{x}\right )}\right )}}{x}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 5.70, size = 27, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{\frac {7\,x}{3}}\,{\mathrm {e}}^{-\frac {x\,{\mathrm {e}}^4\,{\mathrm {e}}^{12/x}}{3}}\,{\mathrm {e}}^{\frac {x^2}{3}}\,{\mathrm {e}}^{{\mathrm {e}}^{{\mathrm {e}}^x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.89, size = 27, normalized size = 1.00 \begin {gather*} e^{\frac {x^{2}}{3} - \frac {x e^{\frac {4 x + 12}{x}}}{3} + \frac {7 x}{3} + e^{e^{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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