Integrand size = 325, antiderivative size = 25 \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\frac {3+x}{\log \left (\log \left (-\frac {3}{x}+\log (x+\log (5+x (4+x)))\right )\right )} \]
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\[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx \]
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Rubi steps Aborted
Time = 0.27 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=-\frac {-3-x}{\log \left (\log \left (-\frac {3}{x}+\log \left (x+\log \left (5+4 x+x^2\right )\right )\right )\right )} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.15 (sec) , antiderivative size = 136, normalized size of antiderivative = 5.44
\[\frac {3+x}{\ln \left (-\ln \left (x \right )+\ln \left (x \ln \left (\ln \left (x^{2}+4 x +5\right )+x \right )-3\right )-\frac {i \pi \,\operatorname {csgn}\left (\frac {i \left (x \ln \left (\ln \left (x^{2}+4 x +5\right )+x \right )-3\right )}{x}\right ) \left (-\operatorname {csgn}\left (\frac {i \left (x \ln \left (\ln \left (x^{2}+4 x +5\right )+x \right )-3\right )}{x}\right )+\operatorname {csgn}\left (\frac {i}{x}\right )\right ) \left (-\operatorname {csgn}\left (\frac {i \left (x \ln \left (\ln \left (x^{2}+4 x +5\right )+x \right )-3\right )}{x}\right )+\operatorname {csgn}\left (i \left (x \ln \left (\ln \left (x^{2}+4 x +5\right )+x \right )-3\right )\right )\right )}{2}\right )}\]
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Time = 0.26 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\frac {x + 3}{\log \left (\log \left (\frac {x \log \left (x + \log \left (x^{2} + 4 \, x + 5\right )\right ) - 3}{x}\right )\right )} \]
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Timed out. \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\text {Timed out} \]
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Time = 0.44 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\frac {x + 3}{\log \left (\log \left (x \log \left (x + \log \left (x^{2} + 4 \, x + 5\right )\right ) - 3\right ) - \log \left (x\right )\right )} \]
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Time = 5.25 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.16 \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\frac {x + 3}{\log \left (\log \left (x \log \left (x + \log \left (x^{2} + 4 \, x + 5\right )\right ) - 3\right ) - \log \left (x\right )\right )} \]
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Time = 18.14 (sec) , antiderivative size = 28, normalized size of antiderivative = 1.12 \[ \int \frac {-45 x-78 x^2-48 x^3-12 x^4-x^5+\left (-45-51 x-21 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log \left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )}{\left (-15 x^2-12 x^3-3 x^4+\left (-15 x-12 x^2-3 x^3\right ) \log \left (5+4 x+x^2\right )+\left (5 x^3+4 x^4+x^5+\left (5 x^2+4 x^3+x^4\right ) \log \left (5+4 x+x^2\right )\right ) \log \left (x+\log \left (5+4 x+x^2\right )\right )\right ) \log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right ) \log ^2\left (\log \left (\frac {-3+x \log \left (x+\log \left (5+4 x+x^2\right )\right )}{x}\right )\right )} \, dx=\frac {x+3}{\ln \left (\ln \left (\frac {x\,\ln \left (x+\ln \left (x^2+4\,x+5\right )\right )-3}{x}\right )\right )} \]
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