Optimal. Leaf size=20 \[ \frac {e^{-80+8 x-\frac {32}{3+\log (4)}}}{\log ^8(x)} \]
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Rubi [A] time = 0.86, antiderivative size = 35, normalized size of antiderivative = 1.75, number of steps used = 2, number of rules used = 2, integrand size = 46, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.043, Rules used = {2274, 2288} \begin {gather*} \frac {4^{-\frac {8 (10-x)}{3+\log (4)}} e^{-\frac {8 (34-3 x)}{3+\log (4)}}}{\log ^8(x)} \end {gather*}
Antiderivative was successfully verified.
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Rule 2274
Rule 2288
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=\int \frac {\exp \left (\frac {8 (-34+3 x+(-10+x) \log (4))}{3+\log (4)}\right ) \log ^{-1+\frac {8 (-3-\log (4))}{3+\log (4)}}(x) (-8+8 x \log (x))}{x} \, dx\\ &=\frac {4^{-\frac {8 (10-x)}{3+\log (4)}} e^{-\frac {8 (34-3 x)}{3+\log (4)}}}{\log ^8(x)}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.43, size = 25, normalized size = 1.25 \begin {gather*} \frac {e^{8 x-\frac {16 (17+5 \log (4))}{3+\log (4)}}}{\log ^8(x)} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 1.07, size = 34, normalized size = 1.70 \begin {gather*} e^{\left (\frac {8 \, {\left (2 \, {\left (x - 10\right )} \log \relax (2) - {\left (2 \, \log \relax (2) + 3\right )} \log \left (\log \relax (x)\right ) + 3 \, x - 34\right )}}{2 \, \log \relax (2) + 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [B] time = 0.37, size = 76, normalized size = 3.80 \begin {gather*} e^{\left (\frac {16 \, x \log \relax (2)}{2 \, \log \relax (2) + 3} - \frac {16 \, \log \relax (2) \log \left (\log \relax (x)\right )}{2 \, \log \relax (2) + 3} + \frac {24 \, x}{2 \, \log \relax (2) + 3} - \frac {160 \, \log \relax (2)}{2 \, \log \relax (2) + 3} - \frac {24 \, \log \left (\log \relax (x)\right )}{2 \, \log \relax (2) + 3} - \frac {272}{2 \, \log \relax (2) + 3}\right )} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.04, size = 38, normalized size = 1.90
method | result | size |
risch | \({\mathrm e}^{\frac {-16 \ln \relax (2) \ln \left (\ln \relax (x )\right )+16 x \ln \relax (2)-24 \ln \left (\ln \relax (x )\right )-160 \ln \relax (2)+24 x -272}{2 \ln \relax (2)+3}}\) | \(38\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [B] time = 0.60, size = 79, normalized size = 3.95 \begin {gather*} \frac {e^{\left (\frac {16 \, x \log \relax (2)}{2 \, \log \relax (2) + 3} - \frac {16 \, \log \relax (2) \log \left (\log \relax (x)\right )}{2 \, \log \relax (2) + 3} + \frac {24 \, x}{2 \, \log \relax (2) + 3} - \frac {24 \, \log \left (\log \relax (x)\right )}{2 \, \log \relax (2) + 3} - \frac {272}{2 \, \log \relax (2) + 3}\right )}}{2^{\frac {160}{2 \, \log \relax (2) + 3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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mupad [B] time = 7.22, size = 83, normalized size = 4.15 \begin {gather*} \frac {2^{\frac {16\,x}{2\,\ln \relax (2)+3}}\,{\mathrm {e}}^{-\frac {272}{2\,\ln \relax (2)+3}}\,{\mathrm {e}}^{\frac {24\,x}{2\,\ln \relax (2)+3}}}{2^{\frac {160}{2\,\ln \relax (2)+3}}\,{\ln \relax (x)}^{\frac {24}{2\,\ln \relax (2)+3}}\,{\ln \relax (x)}^{\frac {16\,\ln \relax (2)}{2\,\ln \relax (2)+3}}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.51, size = 37, normalized size = 1.85 \begin {gather*} e^{\frac {8 \left (3 x + \left (2 x - 20\right ) \log {\relax (2 )} + \left (-3 - 2 \log {\relax (2 )}\right ) \log {\left (\log {\relax (x )} \right )} - 34\right )}{2 \log {\relax (2 )} + 3}} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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