Integrand size = 383, antiderivative size = 33 \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=e^{3-\frac {1}{3} x \log \left (-x+\frac {\log (5)}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )} \]
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\[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=\int \frac {\exp \left (\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )\right ) \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx \]
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Rubi steps \begin{align*} \text {integral}& = \int \frac {e^3 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3} \left (-100 x^2+50 x^3+25 x^4-\left (20-12 x-7 x^2\right ) \log (5)+\left (-4+2 x+x^2\right ) \left (10 x^2+\log (5)\right ) \log \left (-4+2 x+x^2\right )+x^2 \left (-4+2 x+x^2\right ) \log ^2\left (-4+2 x+x^2\right )+\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )\right )}{3 \left (4-2 x-x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx \\ & = \frac {1}{3} e^3 \int \frac {\left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3} \left (-100 x^2+50 x^3+25 x^4-\left (20-12 x-7 x^2\right ) \log (5)+\left (-4+2 x+x^2\right ) \left (10 x^2+\log (5)\right ) \log \left (-4+2 x+x^2\right )+x^2 \left (-4+2 x+x^2\right ) \log ^2\left (-4+2 x+x^2\right )+\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )\right )}{\left (4-2 x-x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx \\ & = \frac {1}{3} e^3 \int \left (\frac {100 x^2 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )}-\frac {50 x^3 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )}-\frac {25 x^4 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )}-\frac {\left (-20+12 x+7 x^2\right ) \log (5) \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )}-\frac {\left (10 x^2+\log (5)\right ) \log \left (-4+2 x+x^2\right ) \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )}-\frac {x^2 \log ^2\left (-4+2 x+x^2\right ) \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )}-\left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3} \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )\right ) \, dx \\ & = -\left (\frac {1}{3} e^3 \int \frac {\left (10 x^2+\log (5)\right ) \log \left (-4+2 x+x^2\right ) \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx\right )-\frac {1}{3} e^3 \int \frac {x^2 \log ^2\left (-4+2 x+x^2\right ) \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx-\frac {1}{3} e^3 \int \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3} \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right ) \, dx-\frac {1}{3} \left (25 e^3\right ) \int \frac {x^4 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx-\frac {1}{3} \left (50 e^3\right ) \int \frac {x^3 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx+\frac {1}{3} \left (100 e^3\right ) \int \frac {x^2 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx-\frac {1}{3} \left (e^3 \log (5)\right ) \int \frac {\left (-20+12 x+7 x^2\right ) \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3}}{\left (-4+2 x+x^2\right ) \left (5+\log \left (-4+2 x+x^2\right )\right ) \left (5 x^2-\log (5)+x^2 \log \left (-4+2 x+x^2\right )\right )} \, dx \\ & = \text {Too large to display} \\ \end{align*}
Time = 0.20 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48 \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=e^3 \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{x \left (5+\log \left (-4+2 x+x^2\right )\right )}\right )^{-x/3} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.23 (sec) , antiderivative size = 566, normalized size of antiderivative = 17.15
\[x^{\frac {x}{3}} {\left (\ln \left (x^{2}+2 x -4\right )+5\right )}^{\frac {x}{3}} {\left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}^{-\frac {x}{3}} {\mathrm e}^{3+\frac {i x {\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{\ln \left (x^{2}+2 x -4\right )+5}\right )}^{3} \pi }{6}-\frac {i x {\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{\ln \left (x^{2}+2 x -4\right )+5}\right )}^{2} \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x^{2}+2 x -4\right )+5}\right )}{6}-\frac {i x {\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{\ln \left (x^{2}+2 x -4\right )+5}\right )}^{2} \pi \,\operatorname {csgn}\left (i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )\right )}{6}+\frac {i x \,\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{\ln \left (x^{2}+2 x -4\right )+5}\right ) \pi \,\operatorname {csgn}\left (\frac {i}{\ln \left (x^{2}+2 x -4\right )+5}\right ) \operatorname {csgn}\left (i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )\right )}{6}-\frac {i x \,\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{\ln \left (x^{2}+2 x -4\right )+5}\right ) \pi {\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{x \left (\ln \left (x^{2}+2 x -4\right )+5\right )}\right )}^{2}}{6}+\frac {i x \,\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{\ln \left (x^{2}+2 x -4\right )+5}\right ) \pi \,\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{x \left (\ln \left (x^{2}+2 x -4\right )+5\right )}\right ) \operatorname {csgn}\left (\frac {i}{x}\right )}{6}+\frac {i x \pi {\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{x \left (\ln \left (x^{2}+2 x -4\right )+5\right )}\right )}^{3}}{6}-\frac {i x \pi {\operatorname {csgn}\left (\frac {i \left (-\left (\ln \left (x^{2}+2 x -4\right )+5\right ) x^{2}+\ln \left (5\right )\right )}{x \left (\ln \left (x^{2}+2 x -4\right )+5\right )}\right )}^{2} \operatorname {csgn}\left (\frac {i}{x}\right )}{6}}\]
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Time = 0.28 (sec) , antiderivative size = 49, normalized size of antiderivative = 1.48 \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=e^{\left (-\frac {1}{3} \, x \log \left (-\frac {x^{2} \log \left (x^{2} + 2 \, x - 4\right ) + 5 \, x^{2} - \log \left (5\right )}{x \log \left (x^{2} + 2 \, x - 4\right ) + 5 \, x}\right ) + 3\right )} \]
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Exception generated. \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=\text {Exception raised: PolynomialError} \]
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Time = 0.42 (sec) , antiderivative size = 46, normalized size of antiderivative = 1.39 \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=e^{\left (-\frac {1}{3} \, x \log \left (-x^{2} {\left (\log \left (x^{2} + 2 \, x - 4\right ) + 5\right )} + \log \left (5\right )\right ) + \frac {1}{3} \, x \log \left (x\right ) + \frac {1}{3} \, x \log \left (\log \left (x^{2} + 2 \, x - 4\right ) + 5\right ) + 3\right )} \]
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Leaf count of result is larger than twice the leaf count of optimal. 81 vs. \(2 (30) = 60\).
Time = 7.24 (sec) , antiderivative size = 81, normalized size of antiderivative = 2.45 \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=e^{\left (-\frac {1}{3} \, x \log \left (-\frac {x^{2} \log \left (x^{2} + 2 \, x - 4\right )}{x \log \left (x^{2} + 2 \, x - 4\right ) + 5 \, x} - \frac {5 \, x^{2}}{x \log \left (x^{2} + 2 \, x - 4\right ) + 5 \, x} + \frac {\log \left (5\right )}{x \log \left (x^{2} + 2 \, x - 4\right ) + 5 \, x}\right ) + 3\right )} \]
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Time = 15.82 (sec) , antiderivative size = 51, normalized size of antiderivative = 1.55 \[ \int \frac {e^{\frac {1}{3} \left (9-x \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )} \left (100 x^2-50 x^3-25 x^4+\left (20-12 x-7 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (4-2 x-x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )+\left (100 x^2-50 x^3-25 x^4+\left (-20+10 x+5 x^2\right ) \log (5)+\left (40 x^2-20 x^3-10 x^4+\left (-4+2 x+x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (4 x^2-2 x^3-x^4\right ) \log ^2\left (-4+2 x+x^2\right )\right ) \log \left (\frac {-5 x^2+\log (5)-x^2 \log \left (-4+2 x+x^2\right )}{5 x+x \log \left (-4+2 x+x^2\right )}\right )\right )}{-300 x^2+150 x^3+75 x^4+\left (60-30 x-15 x^2\right ) \log (5)+\left (-120 x^2+60 x^3+30 x^4+\left (12-6 x-3 x^2\right ) \log (5)\right ) \log \left (-4+2 x+x^2\right )+\left (-12 x^2+6 x^3+3 x^4\right ) \log ^2\left (-4+2 x+x^2\right )} \, dx=\frac {{\mathrm {e}}^3}{{\left (-\frac {x^2\,\ln \left (x^2+2\,x-4\right )-\ln \left (5\right )+5\,x^2}{5\,x+x\,\ln \left (x^2+2\,x-4\right )}\right )}^{x/3}} \]
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