Optimal. Leaf size=25 \[ \frac {x}{3 x+\frac {1}{2} x \log \left (\log \left (\log \left (9+\frac {4 x}{5}+\log (2)\right )\right )\right )} \]
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Rubi [A] time = 0.19, antiderivative size = 18, normalized size of antiderivative = 0.72, number of steps used = 3, number of rules used = 3, integrand size = 156, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {12, 6688, 6686} \begin {gather*} \frac {2}{\log \left (\log \left (\log \left (\frac {4 x}{5}+9+\log (2)\right )\right )\right )+6} \end {gather*}
Antiderivative was successfully verified.
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Rule 12
Rule 6686
Rule 6688
Rubi steps
\begin {gather*} \begin {aligned} \text {integral} &=-\left (8 \int \frac {1}{(1620+144 x+180 \log (2)) \log \left (\frac {1}{5} (45+4 x+5 \log (2))\right ) \log \left (\log \left (\frac {1}{5} (45+4 x+5 \log (2))\right )\right )+(540+48 x+60 \log (2)) \log \left (\frac {1}{5} (45+4 x+5 \log (2))\right ) \log \left (\log \left (\frac {1}{5} (45+4 x+5 \log (2))\right )\right ) \log \left (\log \left (\log \left (\frac {1}{5} (45+4 x+5 \log (2))\right )\right )\right )+(45+4 x+5 \log (2)) \log \left (\frac {1}{5} (45+4 x+5 \log (2))\right ) \log \left (\log \left (\frac {1}{5} (45+4 x+5 \log (2))\right )\right ) \log ^2\left (\log \left (\log \left (\frac {1}{5} (45+4 x+5 \log (2))\right )\right )\right )} \, dx\right )\\ &=-\left (8 \int \frac {1}{(45+4 x+\log (32)) \log \left (9+\frac {4 x}{5}+\log (2)\right ) \log \left (\log \left (9+\frac {4 x}{5}+\log (2)\right )\right ) \left (6+\log \left (\log \left (\log \left (9+\frac {4 x}{5}+\log (2)\right )\right )\right )\right )^2} \, dx\right )\\ &=\frac {2}{6+\log \left (\log \left (\log \left (9+\frac {4 x}{5}+\log (2)\right )\right )\right )}\\ \end {aligned} \end {gather*}
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Mathematica [A] time = 0.03, size = 18, normalized size = 0.72 \begin {gather*} \frac {2}{6+\log \left (\log \left (\log \left (9+\frac {4 x}{5}+\log (2)\right )\right )\right )} \end {gather*}
Antiderivative was successfully verified.
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fricas [A] time = 0.50, size = 16, normalized size = 0.64 \begin {gather*} \frac {2}{\log \left (\log \left (\log \left (\frac {4}{5} \, x + \log \relax (2) + 9\right )\right )\right ) + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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giac [A] time = 0.46, size = 23, normalized size = 0.92 \begin {gather*} \frac {2}{\log \left (\log \left (-\log \relax (5) + \log \left (4 \, x + 5 \, \log \relax (2) + 45\right )\right )\right ) + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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maple [A] time = 0.03, size = 17, normalized size = 0.68
method | result | size |
risch | \(\frac {2}{\ln \left (\ln \left (\ln \left (\ln \relax (2)+\frac {4 x}{5}+9\right )\right )\right )+6}\) | \(17\) |
Verification of antiderivative is not currently implemented for this CAS.
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maxima [A] time = 0.47, size = 23, normalized size = 0.92 \begin {gather*} \frac {2}{\log \left (\log \left (-\log \relax (5) + \log \left (4 \, x + 5 \, \log \relax (2) + 45\right )\right )\right ) + 6} \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 {8}{\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\,\ln \left (\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\right )\,\left (4\,x+5\,\ln \relax (2)+45\right )\,{\ln \left (\ln \left (\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\right )\right )}^2+\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\,\ln \left (\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\right )\,\left (48\,x+60\,\ln \relax (2)+540\right )\,\ln \left (\ln \left (\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\right )\right )+\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\,\ln \left (\ln \left (\frac {4\,x}{5}+\ln \relax (2)+9\right )\right )\,\left (144\,x+180\,\ln \relax (2)+1620\right )} \,d x \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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sympy [A] time = 0.45, size = 17, normalized size = 0.68 \begin {gather*} \frac {2}{\log {\left (\log {\left (\log {\left (\frac {4 x}{5} + \log {\relax (2 )} + 9 \right )} \right )} \right )} + 6} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
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