Optimal. Leaf size=26 \[ \frac {e^{5 \sqrt {\frac {8-\log \left (e^x x\right )}{x}}}}{x} \]
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Rubi [B] Leaf count is larger than twice the leaf count of optimal. \(101\) vs. \(2(26)=52\).
time = 0.17, 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 = {2326}
\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 2326
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 = 0.09, 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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Maple [F]
time = 0.10, 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*} \text {Failed to integrate} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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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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Sympy [F(-2)]
time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Exception raised: SystemError} \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*} \text {could not integrate} \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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