Optimal. Leaf size=26 \[ \frac {e^{5 \sqrt {\frac {8-\log \left (e^x x\right )}{x}}}}{x} \]
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Rubi [B] time = 0.26, antiderivative size = 101, normalized size of antiderivative = 3.88, number of steps used = 1, number of rules used = 1, integrand size = 80, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.012, Rules used = {2288} \begin {gather*} \frac {e^{5 \sqrt {\frac {8-\log \left (e^x x\right )}{x}}} \left (8-\log \left (e^x x\right )\right ) \left (x-\log \left (e^x x\right )+9\right )}{x \left (\frac {e^{-x} \left (e^x x+e^x\right )}{x^2}+\frac {8-\log \left (e^x x\right )}{x^2}\right ) \left (8 x^2-x^2 \log \left (e^x x\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\frac {e^{5 \sqrt {\frac {8-\log \left (e^x x\right )}{x}}} \left (8-\log \left (e^x x\right )\right ) \left (9+x-\log \left (e^x x\right )\right )}{x \left (\frac {e^{-x} \left (e^x+e^x x\right )}{x^2}+\frac {8-\log \left (e^x x\right )}{x^2}\right ) \left (8 x^2-x^2 \log \left (e^x x\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.14, size = 26, normalized size = 1.00 \begin {gather*} \frac {e^{5 \sqrt {\frac {8-\log \left (e^x x\right )}{x}}}}{x} \end {gather*}
Antiderivative was successfully verified.
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fricas [F(-2)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: TypeError} \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 (5 \, {\left (x - \log \left (x e^{x}\right ) + 9\right )} \sqrt {-\frac {\log \left (x e^{x}\right ) - 8}{x}} - 2 \, \log \left (x e^{x}\right ) + 16\right )} e^{\left (5 \, \sqrt {-\frac {\log \left (x e^{x}\right ) - 8}{x}}\right )}}{2 \, {\left (x^{2} \log \left (x e^{x}\right ) - 8 \, x^{2}\right )}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [F] time = 0.02, size = 0, normalized size = 0.00 \[\int \frac {\left (\left (-\ln \left ({\mathrm e}^{x} x \right )+x +9\right ) \sqrt {\frac {-25 \ln \left ({\mathrm e}^{x} x \right )+200}{x}}-2 \ln \left ({\mathrm e}^{x} x \right )+16\right ) {\mathrm e}^{\sqrt {\frac {-25 \ln \left ({\mathrm e}^{x} x \right )+200}{x}}}}{2 x^{2} \ln \left ({\mathrm e}^{x} x \right )-16 x^{2}}\, dx\]
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 {{\left ({\left (x - 1\right )} x - x^{2} + {\left (x - 17\right )} \log \relax (x) + \log \relax (x)^{2} - 8 \, x + 72\right )} e^{\left (\frac {5 \, \sqrt {-x - \log \relax (x) + 8}}{\sqrt {x}}\right )}}{{\left ({\left (x - 17\right )} \log \relax (x) + \log \relax (x)^{2} - 9 \, x + 72\right )} x} + \frac {1}{2} \, \int -\frac {2 \, {\left (x \log \relax (x)^{4} - {\left (\log \relax (x)^{2} - x - 19 \, \log \relax (x) + 89\right )} x^{3} + 2 \, {\left (x^{2} - 17 \, x\right )} \log \relax (x)^{3} + {\left (x \log \relax (x)^{2} - x^{2} - 2 \, {\left (9 \, x - 1\right )} \log \relax (x) + 81 \, x - 17\right )} x^{2} + 81 \, x^{3} + {\left (x^{3} - 52 \, x^{2} + 433 \, x\right )} \log \relax (x)^{2} - {\left (2 \, {\left (x - 17\right )} \log \relax (x)^{3} + \log \relax (x)^{4} + {\left (x^{2} - 52 \, x + 433\right )} \log \relax (x)^{2} + 73 \, x^{2} - {\left (17 \, x^{2} - 452 \, x + 2448\right )} \log \relax (x) - 1313 \, x + 5184\right )} x - 1296 \, x^{2} - 18 \, {\left (x^{3} - 25 \, x^{2} + 136 \, x\right )} \log \relax (x) + 5184 \, x\right )} e^{\left (\frac {5 \, \sqrt {-x - \log \relax (x) + 8}}{\sqrt {x}}\right )}}{{\left (x \log \relax (x)^{4} + 2 \, {\left (x^{2} - 17 \, x\right )} \log \relax (x)^{3} + 81 \, x^{3} + {\left (x^{3} - 52 \, x^{2} + 433 \, x\right )} \log \relax (x)^{2} - 1296 \, x^{2} - 18 \, {\left (x^{3} - 25 \, x^{2} + 136 \, x\right )} \log \relax (x) + 5184 \, x\right )} x^{2}}\,{d x} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [F] time = 0.00, size = -1, normalized size = -0.04 \begin {gather*} \int \frac {{\mathrm {e}}^{\sqrt {-\frac {25\,\ln \left (x\,{\mathrm {e}}^x\right )-200}{x}}}\,\left (\sqrt {-\frac {25\,\ln \left (x\,{\mathrm {e}}^x\right )-200}{x}}\,\left (x-\ln \left (x\,{\mathrm {e}}^x\right )+9\right )-2\,\ln \left (x\,{\mathrm {e}}^x\right )+16\right )}{2\,x^2\,\ln \left (x\,{\mathrm {e}}^x\right )-16\,x^2} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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