Optimal. Leaf size=23 \[ e^{e^{\left (-1+\frac {e^4}{4 x^2}+x\right ) \left (x+x^2\right )}} \]
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Rubi [F] time = 2.77, 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 \frac {\exp \left (e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right ) \left (-e^4-4 x^2+12 x^4\right )}{4 x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {1}{4} \int \frac {\exp \left (e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right ) \left (-e^4-4 x^2+12 x^4\right )}{x^2} \, dx\\ &=\frac {1}{4} \int \left (-4 \exp \left (e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right )-\frac {\exp \left (4+e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right )}{x^2}+12 \exp \left (e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right ) x^2\right ) \, dx\\ &=-\left (\frac {1}{4} \int \frac {\exp \left (4+e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right )}{x^2} \, dx\right )+3 \int \exp \left (e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right ) x^2 \, dx-\int \exp \left (e^{\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}}+\frac {-4 x^2+4 x^4+e^4 (1+x)}{4 x}\right ) \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.75, size = 28, normalized size = 1.22 \begin {gather*} e^{e^{\frac {e^4}{4}+\frac {e^4}{4 x}-x+x^3}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.79, size = 72, normalized size = 3.13 \begin {gather*} e^{\left (\frac {4 \, x^{4} - 4 \, x^{2} + {\left (x + 1\right )} e^{4} + 4 \, x e^{\left (\frac {4 \, x^{4} - 4 \, x^{2} + {\left (x + 1\right )} e^{4}}{4 \, x}\right )}}{4 \, x} - \frac {4 \, x^{4} - 4 \, x^{2} + {\left (x + 1\right )} e^{4}}{4 \, 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 \frac {{\left (12 \, x^{4} - 4 \, x^{2} - e^{4}\right )} e^{\left (\frac {4 \, x^{4} - 4 \, x^{2} + {\left (x + 1\right )} e^{4}}{4 \, x} + e^{\left (\frac {4 \, x^{4} - 4 \, x^{2} + {\left (x + 1\right )} e^{4}}{4 \, x}\right )}\right )}}{4 \, x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.30, size = 24, normalized size = 1.04
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {\left (x +1\right ) \left (4 x^{3}-4 x^{2}+{\mathrm e}^{4}\right )}{4 x}}}\) | \(24\) |
norman | \({\mathrm e}^{{\mathrm e}^{\frac {\left (x +1\right ) {\mathrm e}^{4}+4 x^{4}-4 x^{2}}{4 x}}}\) | \(25\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 1.28, size = 20, normalized size = 0.87 \begin {gather*} e^{\left (e^{\left (x^{3} - x + \frac {e^{4}}{4 \, x} + \frac {1}{4} \, e^{4}\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.81, size = 23, normalized size = 1.00 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{4\,x}}\,{\mathrm {e}}^{\frac {{\mathrm {e}}^4}{4}}\,{\mathrm {e}}^{-x}\,{\mathrm {e}}^{x^3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.40, size = 19, normalized size = 0.83 \begin {gather*} e^{e^{\frac {x^{4} - x^{2} + \frac {\left (x + 1\right ) e^{4}}{4}}{x}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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