Optimal. Leaf size=28 \[ e^{-\frac {8}{x}-x+\left (\frac {4}{x}+x^2+\log \left (\frac {16 x}{3}\right )\right )^2} \]
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Rubi [F] time = 11.71, 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 (\frac {16-8 x+7 x^3+x^6+\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )+x^2 \log ^2\left (\frac {16 x}{3}\right )}{x^2}\right ) \left (-32+16 x+7 x^3+2 x^4+4 x^6+\left (-8 x+2 x^2+4 x^4\right ) \log \left (\frac {16 x}{3}\right )\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 \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \left (-32+16 x+7 x^3+2 x^4+4 x^6+\left (-8 x+2 x^2+4 x^4\right ) \log \left (\frac {16 x}{3}\right )\right )}{x^3} \, dx\\ &=\int \left (\frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \left (-32+16 x+7 x^3+2 x^4+4 x^6\right )}{x^3}+\frac {2 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \left (-4+x+2 x^3\right ) \log \left (\frac {16 x}{3}\right )}{x^2}\right ) \, dx\\ &=2 \int \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \left (-4+x+2 x^3\right ) \log \left (\frac {16 x}{3}\right )}{x^2} \, dx+\int \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \left (-32+16 x+7 x^3+2 x^4+4 x^6\right )}{x^3} \, dx\\ &=2 \int \left (-\frac {4 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \log \left (\frac {16 x}{3}\right )}{x}+2 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) x \log \left (\frac {16 x}{3}\right )\right ) \, dx+\int \left (7 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right )-\frac {32 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right )}{x^3}+\frac {16 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right )}{x^2}+2 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) x+4 \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) x^3\right ) \, dx\\ &=2 \int \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) x \, dx+2 \int \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \log \left (\frac {16 x}{3}\right )}{x} \, dx+4 \int \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) x^3 \, dx+4 \int \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) x \log \left (\frac {16 x}{3}\right ) \, dx+7 \int \exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \, dx-8 \int \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right ) \log \left (\frac {16 x}{3}\right )}{x^2} \, dx+16 \int \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right )}{x^2} \, dx-32 \int \frac {\exp \left (\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {\left (8 x+2 x^4\right ) \log \left (\frac {16 x}{3}\right )}{x^2}+\log ^2\left (\frac {16 x}{3}\right )\right )}{x^3} \, dx\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.13, size = 43, normalized size = 1.54 \begin {gather*} e^{\frac {16}{x^2}-\frac {8}{x}+7 x+x^4+\frac {2 \left (4+x^3\right ) \log \left (\frac {16 x}{3}\right )}{x}+\log ^2\left (\frac {16 x}{3}\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.81, size = 41, normalized size = 1.46 \begin {gather*} e^{\left (\frac {x^{6} + x^{2} \log \left (\frac {16}{3} \, x\right )^{2} + 7 \, x^{3} + 2 \, {\left (x^{4} + 4 \, x\right )} \log \left (\frac {16}{3} \, x\right ) - 8 \, x + 16}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 1.15, size = 42, normalized size = 1.50 \begin {gather*} e^{\left (x^{4} + 2 \, x^{2} \log \left (\frac {16}{3} \, x\right ) + \log \left (\frac {16}{3} \, x\right )^{2} + 7 \, x + \frac {8 \, \log \left (\frac {16}{3} \, x\right )}{x} - \frac {8}{x} + \frac {16}{x^{2}}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 48, normalized size = 1.71
method | result | size |
risch | \(\left (\frac {16 x}{3}\right )^{2 x^{2}} \left (\frac {16 x}{3}\right )^{\frac {8}{x}} {\mathrm e}^{\frac {x^{6}+x^{2} \ln \left (\frac {16 x}{3}\right )^{2}+7 x^{3}-8 x +16}{x^{2}}}\) | \(48\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 1.20, size = 95, normalized size = 3.39 \begin {gather*} \frac {e^{\left (x^{4} - 2 \, x^{2} \log \relax (3) + 8 \, x^{2} \log \relax (2) + 2 \, x^{2} \log \relax (x) + \log \relax (3)^{2} + 16 \, \log \relax (2)^{2} - 2 \, \log \relax (3) \log \relax (x) + 8 \, \log \relax (2) \log \relax (x) + \log \relax (x)^{2} + 7 \, x - \frac {8 \, \log \relax (3)}{x} + \frac {32 \, \log \relax (2)}{x} + \frac {8 \, \log \relax (x)}{x} - \frac {8}{x} + \frac {16}{x^{2}}\right )}}{2^{8 \, \log \relax (3)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 0.38, size = 106, normalized size = 3.79 \begin {gather*} \frac {2^{8\,x^2}\,2^{32/x}\,x^{2\,x^2}\,x^{8/x}\,x^{8\,\ln \relax (2)}\,{\mathrm {e}}^{{\ln \relax (3)}^2}\,{\mathrm {e}}^{7\,x}\,{\mathrm {e}}^{x^4}\,{\mathrm {e}}^{16\,{\ln \relax (2)}^2}\,{\mathrm {e}}^{-\frac {8}{x}}\,{\mathrm {e}}^{\frac {16}{x^2}}\,{\mathrm {e}}^{{\ln \relax (x)}^2}}{2^{8\,\ln \relax (3)}\,3^{2\,x^2}\,3^{8/x}\,x^{2\,\ln \relax (3)}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [B] time = 0.64, size = 44, normalized size = 1.57 \begin {gather*} e^{\frac {x^{6} + 7 x^{3} + x^{2} \log {\left (\frac {16 x}{3} \right )}^{2} - 8 x + \left (2 x^{4} + 8 x\right ) \log {\left (\frac {16 x}{3} \right )} + 16}{x^{2}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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