Optimal. Leaf size=33 \[ 3-2 x-\log \left (\frac {1}{2} e^{e^{\frac {2}{x}-5 e^{e^{x^2}} x}} x\right ) \]
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Rubi [F] time = 1.47, 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 {-x-2 x^2+e^{\frac {2-5 e^{e^{x^2}} x^2}{x}} \left (2+e^{e^{x^2}} \left (5 x^2+10 e^{x^2} x^4\right )\right )}{x^2} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (10 e^{e^{x^2}+\frac {2}{x}-5 e^{e^{x^2}} x+x^2} x^2-\frac {e^{-5 e^{e^{x^2}} x} \left (-2 e^{2/x}+e^{5 e^{e^{x^2}} x} x-5 e^{e^{x^2}+\frac {2}{x}} x^2+2 e^{5 e^{e^{x^2}} x} x^2\right )}{x^2}\right ) \, dx\\ &=10 \int e^{e^{x^2}+\frac {2}{x}-5 e^{e^{x^2}} x+x^2} x^2 \, dx-\int \frac {e^{-5 e^{e^{x^2}} x} \left (-2 e^{2/x}+e^{5 e^{e^{x^2}} x} x-5 e^{e^{x^2}+\frac {2}{x}} x^2+2 e^{5 e^{e^{x^2}} x} x^2\right )}{x^2} \, dx\\ &=10 \int e^{e^{x^2}+\frac {2}{x}-5 e^{e^{x^2}} x+x^2} x^2 \, dx-\int \left (2-5 e^{e^{x^2}+\frac {2}{x}-5 e^{e^{x^2}} x}-\frac {2 e^{\frac {2}{x}-5 e^{e^{x^2}} x}}{x^2}+\frac {1}{x}\right ) \, dx\\ &=-2 x-\log (x)+2 \int \frac {e^{\frac {2}{x}-5 e^{e^{x^2}} x}}{x^2} \, dx+5 \int e^{e^{x^2}+\frac {2}{x}-5 e^{e^{x^2}} x} \, dx+10 \int e^{e^{x^2}+\frac {2}{x}-5 e^{e^{x^2}} x+x^2} x^2 \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.37, size = 28, normalized size = 0.85 \begin {gather*} -e^{\frac {2}{x}-5 e^{e^{x^2}} x}-2 x-\log (x) \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.69, size = 28, normalized size = 0.85 \begin {gather*} -2 \, x - e^{\left (-\frac {5 \, x^{2} e^{\left (e^{\left (x^{2}\right )}\right )} - 2}{x}\right )} - \log \relax (x) \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 {2 \, x^{2} - {\left (5 \, {\left (2 \, x^{4} e^{\left (x^{2}\right )} + x^{2}\right )} e^{\left (e^{\left (x^{2}\right )}\right )} + 2\right )} e^{\left (-\frac {5 \, x^{2} e^{\left (e^{\left (x^{2}\right )}\right )} - 2}{x}\right )} + x}{x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.08, size = 29, normalized size = 0.88
method | result | size |
risch | \(-2 x -\ln \relax (x )-{\mathrm e}^{-\frac {5 x^{2} {\mathrm e}^{{\mathrm e}^{x^{2}}}-2}{x}}\) | \(29\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.54, size = 25, normalized size = 0.76 \begin {gather*} -2 \, x - e^{\left (-5 \, x e^{\left (e^{\left (x^{2}\right )}\right )} + \frac {2}{x}\right )} - \log \relax (x) \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 1.42, size = 25, normalized size = 0.76 \begin {gather*} -2\,x-\ln \relax (x)-{\mathrm {e}}^{2/x}\,{\mathrm {e}}^{-5\,x\,{\mathrm {e}}^{{\mathrm {e}}^{x^2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 5.84, size = 24, normalized size = 0.73 \begin {gather*} - 2 x - e^{\frac {- 5 x^{2} e^{e^{x^{2}}} + 2}{x}} - \log {\relax (x )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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