Integrand size = 347, antiderivative size = 35 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\frac {\left (-e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}}+x+\log (3+x)\right )^2}{-1-x} \]
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Timed out. \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Leaf count is larger than twice the leaf count of optimal. \(77\) vs. \(2(35)=70\).
Time = 0.37 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.20 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=-\frac {1+e^{\frac {6}{x^2 \log ^2((-1+x) x)}}+x-2 e^{\frac {3}{x^2 \log ^2((-1+x) x)}} x+x^2-2 \left (e^{\frac {3}{x^2 \log ^2((-1+x) x)}}-x\right ) \log (3+x)+\log ^2(3+x)}{1+x} \]
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Result contains higher order function than in optimal. Order 9 vs. order 3.
Time = 0.04 (sec) , antiderivative size = 266, normalized size of antiderivative = 7.60
\[-\frac {\ln \left (3+x \right )^{2}}{1+x}+\frac {2 \ln \left (3+x \right )}{1+x}-\frac {2 x \ln \left (3+x \right )+x^{2}+2 \ln \left (3+x \right )+x +1}{1+x}-\frac {{\mathrm e}^{\frac {24}{x^{2} \left (-i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{3}+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i x \right )+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right )-i \pi \,\operatorname {csgn}\left (i x \left (-1+x \right )\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right )+2 \ln \left (x \right )+2 \ln \left (-1+x \right )\right )^{2}}}}{1+x}+\frac {2 \left (x +\ln \left (3+x \right )\right ) {\mathrm e}^{\frac {12}{x^{2} \left (-i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{3}+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i x \right )+i \pi \operatorname {csgn}\left (i x \left (-1+x \right )\right )^{2} \operatorname {csgn}\left (i \left (-1+x \right )\right )-i \pi \,\operatorname {csgn}\left (i x \left (-1+x \right )\right ) \operatorname {csgn}\left (i x \right ) \operatorname {csgn}\left (i \left (-1+x \right )\right )+2 \ln \left (x \right )+2 \ln \left (-1+x \right )\right )^{2}}}}{1+x}\]
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Time = 0.27 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.89 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=-\frac {x^{2} - 2 \, {\left (x + \log \left (x + 3\right )\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, x \log \left (x + 3\right ) + \log \left (x + 3\right )^{2} + x + e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 1}{x + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (27) = 54\).
Time = 0.66 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.86 \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=- x + \frac {\left (- x - 1\right ) e^{\frac {6}{x^{2} \log {\left (x^{2} - x \right )}^{2}}} + \left (2 x^{2} + 2 x \log {\left (x + 3 \right )} + 2 x + 2 \log {\left (x + 3 \right )}\right ) e^{\frac {3}{x^{2} \log {\left (x^{2} - x \right )}^{2}}}}{x^{2} + 2 x + 1} - 2 \log {\left (x + 3 \right )} - \frac {\log {\left (x + 3 \right )}^{2}}{x + 1} + \frac {2 \log {\left (x + 3 \right )}}{x + 1} - \frac {1}{x + 1} \]
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\[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\int { -\frac {{\left (x^{7} + 6 \, x^{6} + x^{5} - 8 \, x^{4} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )^{2} + 4 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} - {\left ({\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3} + 24 \, x^{3} + 84 \, x^{2} + 12 \, {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x^{2} - x\right ) + 24 \, x - 36\right )} e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, {\left (12 \, x^{4} - {\left (2 \, x^{5} + 2 \, x^{4} - 4 \, x^{3} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} + 42 \, x^{3} + 12 \, x^{2} + 6 \, {\left (x^{4} + 3 \, x^{3} - x^{2} + {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x + 3\right ) - 3 \, x\right )} \log \left (x^{2} - x\right ) + 6 \, {\left (2 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right )} \log \left (x + 3\right ) - 18 \, x\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )}}{{\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3}} \,d x } \]
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\[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\int { -\frac {{\left (x^{7} + 6 \, x^{6} + x^{5} - 8 \, x^{4} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )^{2} + 4 \, {\left (x^{5} + x^{4} - 2 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} - {\left ({\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3} + 24 \, x^{3} + 84 \, x^{2} + 12 \, {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x^{2} - x\right ) + 24 \, x - 36\right )} e^{\left (\frac {6}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )} + 2 \, {\left (12 \, x^{4} - {\left (2 \, x^{5} + 2 \, x^{4} - 4 \, x^{3} - {\left (x^{5} + 2 \, x^{4} - 3 \, x^{3}\right )} \log \left (x + 3\right )\right )} \log \left (x^{2} - x\right )^{3} + 42 \, x^{3} + 12 \, x^{2} + 6 \, {\left (x^{4} + 3 \, x^{3} - x^{2} + {\left (x^{3} + 3 \, x^{2} - x - 3\right )} \log \left (x + 3\right ) - 3 \, x\right )} \log \left (x^{2} - x\right ) + 6 \, {\left (2 \, x^{3} + 7 \, x^{2} + 2 \, x - 3\right )} \log \left (x + 3\right ) - 18 \, x\right )} e^{\left (\frac {3}{x^{2} \log \left (x^{2} - x\right )^{2}}\right )}}{{\left (x^{7} + 4 \, x^{6} + 2 \, x^{5} - 4 \, x^{4} - 3 \, x^{3}\right )} \log \left (x^{2} - x\right )^{3}} \,d x } \]
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Timed out. \[ \int \frac {\left (8 x^4-x^5-6 x^6-x^7+\left (8 x^3-4 x^4-4 x^5\right ) \log (3+x)+\left (-3 x^3+2 x^4+x^5\right ) \log ^2(3+x)\right ) \log ^3\left (-x+x^2\right )+e^{\frac {6}{x^2 \log ^2\left (-x+x^2\right )}} \left (-36+24 x+84 x^2+24 x^3+\left (-36-12 x+36 x^2+12 x^3\right ) \log \left (-x+x^2\right )+\left (-3 x^3+2 x^4+x^5\right ) \log ^3\left (-x+x^2\right )\right )+e^{\frac {3}{x^2 \log ^2\left (-x+x^2\right )}} \left (36 x-24 x^2-84 x^3-24 x^4+\left (36-24 x-84 x^2-24 x^3\right ) \log (3+x)+\left (36 x+12 x^2-36 x^3-12 x^4+\left (36+12 x-36 x^2-12 x^3\right ) \log (3+x)\right ) \log \left (-x+x^2\right )+\left (-8 x^3+4 x^4+4 x^5+\left (6 x^3-4 x^4-2 x^5\right ) \log (3+x)\right ) \log ^3\left (-x+x^2\right )\right )}{\left (-3 x^3-4 x^4+2 x^5+4 x^6+x^7\right ) \log ^3\left (-x+x^2\right )} \, dx=\int -\frac {{\ln \left (x^2-x\right )}^3\,\left (\ln \left (x+3\right )\,\left (4\,x^5+4\,x^4-8\,x^3\right )-{\ln \left (x+3\right )}^2\,\left (x^5+2\,x^4-3\,x^3\right )-8\,x^4+x^5+6\,x^6+x^7\right )-{\mathrm {e}}^{\frac {6}{x^2\,{\ln \left (x^2-x\right )}^2}}\,\left (24\,x-\ln \left (x^2-x\right )\,\left (-12\,x^3-36\,x^2+12\,x+36\right )+84\,x^2+24\,x^3+{\ln \left (x^2-x\right )}^3\,\left (x^5+2\,x^4-3\,x^3\right )-36\right )+{\mathrm {e}}^{\frac {3}{x^2\,{\ln \left (x^2-x\right )}^2}}\,\left (\ln \left (x+3\right )\,\left (24\,x^3+84\,x^2+24\,x-36\right )-36\,x+24\,x^2+84\,x^3+24\,x^4+{\ln \left (x^2-x\right )}^3\,\left (\ln \left (x+3\right )\,\left (2\,x^5+4\,x^4-6\,x^3\right )+8\,x^3-4\,x^4-4\,x^5\right )-\ln \left (x^2-x\right )\,\left (36\,x+\ln \left (x+3\right )\,\left (-12\,x^3-36\,x^2+12\,x+36\right )+12\,x^2-36\,x^3-12\,x^4\right )\right )}{{\ln \left (x^2-x\right )}^3\,\left (x^7+4\,x^6+2\,x^5-4\,x^4-3\,x^3\right )} \,d x \]
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