Optimal. Leaf size=21 \[ e^{e^{2-\frac {6 \left (-10-\frac {e^x}{x}\right )}{x}}} \]
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Rubi [F] time = 1.72, 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 {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right ) \left (-60 x+e^x (-12+6 x)\right )}{x^3} \, dx \end {gather*}
Verification is not applicable to the result.
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Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \left (\frac {6 \exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right ) (-2+x)}{x^3}-\frac {60 \exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2}\right ) \, dx\\ &=6 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right ) (-2+x)}{x^3} \, dx-60 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx\\ &=6 \int \left (-\frac {2 \exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^3}+\frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2}\right ) \, dx-60 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx\\ &=6 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx-12 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+x+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^3} \, dx-60 \int \frac {\exp \left (e^{\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}}+\frac {2 \left (3 e^x+30 x+x^2\right )}{x^2}\right )}{x^2} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.58, size = 19, normalized size = 0.90 \begin {gather*} e^{e^{2+\frac {6 e^x}{x^2}+\frac {60}{x}}} \end {gather*}
Antiderivative was successfully verified.
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fricas [B] time = 0.96, size = 56, normalized size = 2.67 \begin {gather*} e^{\left (\frac {x^{2} e^{\left (\frac {2 \, {\left (x^{2} + 30 \, x + 3 \, e^{x}\right )}}{x^{2}}\right )} + 2 \, x^{2} + 60 \, x + 6 \, e^{x}}{x^{2}} - \frac {2 \, {\left (x^{2} + 30 \, x + 3 \, e^{x}\right )}}{x^{2}}\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 {6 \, {\left ({\left (x - 2\right )} e^{x} - 10 \, x\right )} e^{\left (\frac {2 \, {\left (x^{2} + 30 \, x + 3 \, e^{x}\right )}}{x^{2}} + e^{\left (\frac {2 \, {\left (x^{2} + 30 \, x + 3 \, e^{x}\right )}}{x^{2}}\right )}\right )}}{x^{3}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.39, size = 19, normalized size = 0.90
method | result | size |
risch | \({\mathrm e}^{{\mathrm e}^{\frac {6 \,{\mathrm e}^{x}+2 x^{2}+60 x}{x^{2}}}}\) | \(19\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.59, size = 16, normalized size = 0.76 \begin {gather*} e^{\left (e^{\left (\frac {60}{x} + \frac {6 \, e^{x}}{x^{2}} + 2\right )}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 4.35, size = 18, normalized size = 0.86 \begin {gather*} {\mathrm {e}}^{{\mathrm {e}}^2\,{\mathrm {e}}^{\frac {6\,{\mathrm {e}}^x}{x^2}}\,{\mathrm {e}}^{60/x}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.65, size = 19, normalized size = 0.90 \begin {gather*} e^{e^{\frac {4 \left (\frac {x^{2}}{2} + 15 x + \frac {3 e^{x}}{2}\right )}{x^{2}}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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