Integrand size = 111, antiderivative size = 35 \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=\frac {e^{e^2} (3-x) \left (-e^{-1+x}+x\right ) \log \left (\frac {5}{x}\right )}{4-x^2} \]
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Leaf count is larger than twice the leaf count of optimal. \(97\) vs. \(2(35)=70\).
Time = 3.77 (sec) , antiderivative size = 97, normalized size of antiderivative = 2.77, number of steps used = 81, number of rules used = 22, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.198, Rules used = {1608, 28, 6874, 205, 213, 267, 294, 272, 45, 2360, 2361, 12, 6031, 2373, 266, 2393, 6820, 2208, 2209, 2301, 6857, 2634} \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{x+e^2-1} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{x+e^2-1} \log \left (\frac {5}{x}\right )}{4 (x+2)} \]
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Rule 12
Rule 28
Rule 45
Rule 205
Rule 213
Rule 266
Rule 267
Rule 272
Rule 294
Rule 1608
Rule 2208
Rule 2209
Rule 2301
Rule 2360
Rule 2361
Rule 2373
Rule 2393
Rule 2634
Rule 6031
Rule 6820
Rule 6857
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{x \left (16-8 x^2+x^4\right )} \, dx \\ & = \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{x \left (-4+x^2\right )^2} \, dx \\ & = \int \left (-\frac {12 e^{e^2}}{\left (-4+x^2\right )^2}+\frac {4 e^{e^2} x}{\left (-4+x^2\right )^2}+\frac {3 e^{e^2} x^2}{\left (-4+x^2\right )^2}-\frac {e^{e^2} x^3}{\left (-4+x^2\right )^2}+\frac {12 e^{e^2} \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2}-\frac {8 e^{e^2} x \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2}+\frac {3 e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2}-\frac {e^{-1+e^2+x} \left (-12+4 x+3 x^2-x^3+8 x \log \left (\frac {5}{x}\right )+2 x^2 \log \left (\frac {5}{x}\right )-4 x^3 \log \left (\frac {5}{x}\right )+x^4 \log \left (\frac {5}{x}\right )\right )}{x \left (-4+x^2\right )^2}\right ) \, dx \\ & = -\left (e^{e^2} \int \frac {x^3}{\left (-4+x^2\right )^2} \, dx\right )+\left (3 e^{e^2}\right ) \int \frac {x^2}{\left (-4+x^2\right )^2} \, dx+\left (3 e^{e^2}\right ) \int \frac {x^2 \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2} \, dx+\left (4 e^{e^2}\right ) \int \frac {x}{\left (-4+x^2\right )^2} \, dx-\left (8 e^{e^2}\right ) \int \frac {x \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2} \, dx-\left (12 e^{e^2}\right ) \int \frac {1}{\left (-4+x^2\right )^2} \, dx+\left (12 e^{e^2}\right ) \int \frac {\log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2} \, dx-\int \frac {e^{-1+e^2+x} \left (-12+4 x+3 x^2-x^3+8 x \log \left (\frac {5}{x}\right )+2 x^2 \log \left (\frac {5}{x}\right )-4 x^3 \log \left (\frac {5}{x}\right )+x^4 \log \left (\frac {5}{x}\right )\right )}{x \left (-4+x^2\right )^2} \, dx \\ & = \frac {2 e^{e^2}}{4-x^2}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{2 \left (4-x^2\right )}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {1}{2} e^{e^2} \text {Subst}\left (\int \frac {x}{(-4+x)^2} \, dx,x,x^2\right )+e^{e^2} \int \frac {x}{-4+x^2} \, dx+\frac {1}{2} \left (3 e^{e^2}\right ) \int \frac {1}{-4+x^2} \, dx-\frac {1}{2} \left (3 e^{e^2}\right ) \int \frac {\log \left (\frac {5}{x}\right )}{-4+x^2} \, dx+\left (3 e^{e^2}\right ) \int \left (\frac {4 \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2}+\frac {\log \left (\frac {5}{x}\right )}{-4+x^2}\right ) \, dx-\int \frac {e^{-1+e^2+x} \left (-12+4 x+3 x^2-x^3+x \left (8+2 x-4 x^2+x^3\right ) \log \left (\frac {5}{x}\right )\right )}{x \left (4-x^2\right )^2} \, dx \\ & = \frac {2 e^{e^2}}{4-x^2}-\frac {3}{4} e^{e^2} \text {arctanh}\left (\frac {x}{2}\right )+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{2 \left (4-x^2\right )}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}+\frac {3}{4} e^{e^2} \text {arctanh}\left (\frac {x}{2}\right ) \log \left (\frac {5}{x}\right )+\frac {1}{2} e^{e^2} \log \left (4-x^2\right )-\frac {1}{2} e^{e^2} \text {Subst}\left (\int \left (\frac {4}{(-4+x)^2}+\frac {1}{-4+x}\right ) \, dx,x,x^2\right )-\frac {1}{2} \left (3 e^{e^2}\right ) \int -\frac {\text {arctanh}\left (\frac {x}{2}\right )}{2 x} \, dx+\left (3 e^{e^2}\right ) \int \frac {\log \left (\frac {5}{x}\right )}{-4+x^2} \, dx+\left (12 e^{e^2}\right ) \int \frac {\log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2} \, dx-\int \left (\frac {4 e^{-1+e^2+x}}{\left (-4+x^2\right )^2}-\frac {12 e^{-1+e^2+x}}{x \left (-4+x^2\right )^2}+\frac {3 e^{-1+e^2+x} x}{\left (-4+x^2\right )^2}-\frac {e^{-1+e^2+x} x^2}{\left (-4+x^2\right )^2}+\frac {e^{-1+e^2+x} \left (8+2 x-4 x^2+x^3\right ) \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2}\right ) \, dx \\ & = -\frac {3}{4} e^{e^2} \text {arctanh}\left (\frac {x}{2}\right )+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {3}{4} e^{e^2} \text {arctanh}\left (\frac {x}{2}\right ) \log \left (\frac {5}{x}\right )-3 \int \frac {e^{-1+e^2+x} x}{\left (-4+x^2\right )^2} \, dx-4 \int \frac {e^{-1+e^2+x}}{\left (-4+x^2\right )^2} \, dx+12 \int \frac {e^{-1+e^2+x}}{x \left (-4+x^2\right )^2} \, dx+\frac {1}{4} \left (3 e^{e^2}\right ) \int \frac {\text {arctanh}\left (\frac {x}{2}\right )}{x} \, dx-\frac {1}{2} \left (3 e^{e^2}\right ) \int \frac {1}{-4+x^2} \, dx-\frac {1}{2} \left (3 e^{e^2}\right ) \int \frac {\log \left (\frac {5}{x}\right )}{-4+x^2} \, dx+\left (3 e^{e^2}\right ) \int -\frac {\text {arctanh}\left (\frac {x}{2}\right )}{2 x} \, dx+\int \frac {e^{-1+e^2+x} x^2}{\left (-4+x^2\right )^2} \, dx-\int \frac {e^{-1+e^2+x} \left (8+2 x-4 x^2+x^3\right ) \log \left (\frac {5}{x}\right )}{\left (-4+x^2\right )^2} \, dx \\ & = -\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {3}{8} e^{e^2} \operatorname {PolyLog}\left (2,-\frac {x}{2}\right )+\frac {3}{8} e^{e^2} \operatorname {PolyLog}\left (2,\frac {x}{2}\right )-3 \int \left (\frac {e^{-1+e^2+x}}{8 (-2+x)^2}-\frac {e^{-1+e^2+x}}{8 (2+x)^2}\right ) \, dx-4 \int \left (\frac {e^{-1+e^2+x}}{16 (2-x)^2}+\frac {e^{-1+e^2+x}}{16 (2+x)^2}+\frac {e^{-1+e^2+x}}{8 \left (4-x^2\right )}\right ) \, dx+12 \int \left (\frac {e^{-1+e^2+x}}{32 (-2+x)^2}+\frac {e^{-1+e^2+x}}{16 x}-\frac {e^{-1+e^2+x}}{32 (2+x)^2}-\frac {e^{-1+e^2+x} x}{16 \left (-4+x^2\right )}\right ) \, dx-\frac {1}{2} \left (3 e^{e^2}\right ) \int -\frac {\text {arctanh}\left (\frac {x}{2}\right )}{2 x} \, dx-\frac {1}{2} \left (3 e^{e^2}\right ) \int \frac {\text {arctanh}\left (\frac {x}{2}\right )}{x} \, dx+\int \frac {e^{-1+e^2+x} (-3+x)}{x \left (4-x^2\right )} \, dx+\int \left (\frac {4 e^{-1+e^2+x}}{\left (-4+x^2\right )^2}+\frac {e^{-1+e^2+x}}{-4+x^2}\right ) \, dx \\ & = -\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}+\frac {3}{8} e^{e^2} \operatorname {PolyLog}\left (2,-\frac {x}{2}\right )-\frac {3}{8} e^{e^2} \operatorname {PolyLog}\left (2,\frac {x}{2}\right )-\frac {1}{4} \int \frac {e^{-1+e^2+x}}{(2-x)^2} \, dx-\frac {1}{4} \int \frac {e^{-1+e^2+x}}{(2+x)^2} \, dx-\frac {1}{2} \int \frac {e^{-1+e^2+x}}{4-x^2} \, dx+\frac {3}{4} \int \frac {e^{-1+e^2+x}}{x} \, dx-\frac {3}{4} \int \frac {e^{-1+e^2+x} x}{-4+x^2} \, dx+4 \int \frac {e^{-1+e^2+x}}{\left (-4+x^2\right )^2} \, dx+\frac {1}{4} \left (3 e^{e^2}\right ) \int \frac {\text {arctanh}\left (\frac {x}{2}\right )}{x} \, dx+\int \frac {e^{-1+e^2+x}}{-4+x^2} \, dx+\int \left (\frac {e^{-1+e^2+x}}{8 (-2+x)}-\frac {3 e^{-1+e^2+x}}{4 x}+\frac {5 e^{-1+e^2+x}}{8 (2+x)}\right ) \, dx \\ & = -\frac {e^{-1+e^2+x}}{4 (2-x)}+\frac {e^{-1+e^2+x}}{4 (2+x)}+\frac {3}{4} e^{-1+e^2} \operatorname {ExpIntegralEi}(x)-\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}+\frac {1}{8} \int \frac {e^{-1+e^2+x}}{-2+x} \, dx+\frac {1}{4} \int \frac {e^{-1+e^2+x}}{2-x} \, dx-\frac {1}{4} \int \frac {e^{-1+e^2+x}}{2+x} \, dx-\frac {1}{2} \int \left (\frac {e^{-1+e^2+x}}{4 (2-x)}+\frac {e^{-1+e^2+x}}{4 (2+x)}\right ) \, dx+\frac {5}{8} \int \frac {e^{-1+e^2+x}}{2+x} \, dx-\frac {3}{4} \int \frac {e^{-1+e^2+x}}{x} \, dx-\frac {3}{4} \int \left (\frac {e^{-1+e^2+x}}{2 (-2+x)}+\frac {e^{-1+e^2+x}}{2 (2+x)}\right ) \, dx+4 \int \left (\frac {e^{-1+e^2+x}}{16 (2-x)^2}+\frac {e^{-1+e^2+x}}{16 (2+x)^2}+\frac {e^{-1+e^2+x}}{8 \left (4-x^2\right )}\right ) \, dx+\int \left (-\frac {e^{-1+e^2+x}}{4 (2-x)}-\frac {e^{-1+e^2+x}}{4 (2+x)}\right ) \, dx \\ & = -\frac {e^{-1+e^2+x}}{4 (2-x)}+\frac {e^{-1+e^2+x}}{4 (2+x)}-\frac {1}{8} e^{1+e^2} \operatorname {ExpIntegralEi}(-2+x)+\frac {3}{8} e^{-3+e^2} \operatorname {ExpIntegralEi}(2+x)-\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {1}{8} \int \frac {e^{-1+e^2+x}}{2-x} \, dx-\frac {1}{8} \int \frac {e^{-1+e^2+x}}{2+x} \, dx+\frac {1}{4} \int \frac {e^{-1+e^2+x}}{(2-x)^2} \, dx-\frac {1}{4} \int \frac {e^{-1+e^2+x}}{2-x} \, dx+\frac {1}{4} \int \frac {e^{-1+e^2+x}}{(2+x)^2} \, dx-\frac {1}{4} \int \frac {e^{-1+e^2+x}}{2+x} \, dx-\frac {3}{8} \int \frac {e^{-1+e^2+x}}{-2+x} \, dx-\frac {3}{8} \int \frac {e^{-1+e^2+x}}{2+x} \, dx+\frac {1}{2} \int \frac {e^{-1+e^2+x}}{4-x^2} \, dx \\ & = -\frac {1}{8} e^{1+e^2} \operatorname {ExpIntegralEi}(-2+x)-\frac {3}{8} e^{-3+e^2} \operatorname {ExpIntegralEi}(2+x)-\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {1}{4} \int \frac {e^{-1+e^2+x}}{2-x} \, dx+\frac {1}{4} \int \frac {e^{-1+e^2+x}}{2+x} \, dx+\frac {1}{2} \int \left (\frac {e^{-1+e^2+x}}{4 (2-x)}+\frac {e^{-1+e^2+x}}{4 (2+x)}\right ) \, dx \\ & = \frac {1}{8} e^{1+e^2} \operatorname {ExpIntegralEi}(-2+x)-\frac {1}{8} e^{-3+e^2} \operatorname {ExpIntegralEi}(2+x)-\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2}+\frac {1}{8} \int \frac {e^{-1+e^2+x}}{2-x} \, dx+\frac {1}{8} \int \frac {e^{-1+e^2+x}}{2+x} \, dx \\ & = -\frac {e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2-x)}-\frac {5 e^{-1+e^2+x} \log \left (\frac {5}{x}\right )}{4 (2+x)}+\frac {3 e^{e^2} x \log \left (\frac {5}{x}\right )}{4-x^2}-\frac {e^{e^2} x^2 \log \left (\frac {5}{x}\right )}{4-x^2} \\ \end{align*}
Time = 3.26 (sec) , antiderivative size = 44, normalized size of antiderivative = 1.26 \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=e^{-1+e^2} \left (-\frac {\left (e^x (-3+x)+e (-4+3 x)\right ) \log \left (\frac {5}{x}\right )}{-4+x^2}-e \log (x)\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(65\) vs. \(2(32)=64\).
Time = 0.96 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.89
method | result | size |
parallelrisch | \(\frac {{\mathrm e}^{{\mathrm e}^{2}} \ln \left (\frac {5}{x}\right ) x^{2}-{\mathrm e}^{-1+x} {\mathrm e}^{{\mathrm e}^{2}} \ln \left (\frac {5}{x}\right ) x -3 \,{\mathrm e}^{{\mathrm e}^{2}} \ln \left (\frac {5}{x}\right ) x +3 \,{\mathrm e}^{{\mathrm e}^{2}} {\mathrm e}^{-1+x} \ln \left (\frac {5}{x}\right )}{x^{2}-4}\) | \(66\) |
risch | \(\frac {{\mathrm e}^{{\mathrm e}^{2}} \left (x \,{\mathrm e}^{-1+x}+3 x -3 \,{\mathrm e}^{-1+x}-4\right ) \ln \left (x \right )}{x^{2}-4}-\frac {{\mathrm e}^{{\mathrm e}^{2}} \left (2 x^{2} \ln \left (x \right )+2 \ln \left (5\right ) x \,{\mathrm e}^{-1+x}+6 x \ln \left (5\right )-6 \ln \left (5\right ) {\mathrm e}^{-1+x}-8 \ln \left (x \right )-8 \ln \left (5\right )\right )}{2 \left (x^{2}-4\right )}\) | \(82\) |
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none
Time = 0.30 (sec) , antiderivative size = 33, normalized size of antiderivative = 0.94 \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=\frac {{\left (x^{2} - {\left (x - 3\right )} e^{\left (x - 1\right )} - 3 \, x\right )} e^{\left (e^{2}\right )} \log \left (\frac {5}{x}\right )}{x^{2} - 4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 66 vs. \(2 (24) = 48\).
Time = 0.21 (sec) , antiderivative size = 66, normalized size of antiderivative = 1.89 \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=- e^{e^{2}} \log {\left (x \right )} + \frac {\left (- 3 x e^{e^{2}} + 4 e^{e^{2}}\right ) \log {\left (\frac {5}{x} \right )}}{x^{2} - 4} + \frac {\left (- x e^{e^{2}} \log {\left (\frac {5}{x} \right )} + 3 e^{e^{2}} \log {\left (\frac {5}{x} \right )}\right ) e^{x - 1}}{x^{2} - 4} \]
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Leaf count of result is larger than twice the leaf count of optimal. 140 vs. \(2 (28) = 56\).
Time = 0.34 (sec) , antiderivative size = 140, normalized size of antiderivative = 4.00 \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=\frac {3}{8} \, {\left (\frac {4 \, x}{x^{2} - 4} - \log \left (x + 2\right ) + \log \left (x - 2\right )\right )} e^{\left (e^{2}\right )} + \frac {3}{8} \, e^{\left (e^{2}\right )} \log \left (x + 2\right ) - \frac {3}{8} \, e^{\left (e^{2}\right )} \log \left (x - 2\right ) - \frac {3 \, x {\left (2 \, \log \left (5\right ) + 1\right )} e^{\left (e^{2} + 1\right )} + 2 \, {\left (x e^{\left (e^{2}\right )} \log \left (5\right ) - 3 \, e^{\left (e^{2}\right )} \log \left (5\right ) - {\left (x e^{\left (e^{2}\right )} - 3 \, e^{\left (e^{2}\right )}\right )} \log \left (x\right )\right )} e^{x} - 8 \, e^{\left (e^{2} + 1\right )} \log \left (5\right ) + 2 \, {\left (x^{2} e^{\left (e^{2} + 1\right )} - 3 \, x e^{\left (e^{2} + 1\right )}\right )} \log \left (x\right )}{2 \, {\left (x^{2} e - 4 \, e\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 77 vs. \(2 (28) = 56\).
Time = 0.29 (sec) , antiderivative size = 77, normalized size of antiderivative = 2.20 \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=-\frac {x^{2} e^{\left (e^{2}\right )} \log \left (x\right ) + x e^{\left (x + e^{2} - 1\right )} \log \left (\frac {5}{x}\right ) + 3 \, x e^{\left (e^{2}\right )} \log \left (\frac {5}{x}\right ) - 4 \, e^{\left (e^{2}\right )} \log \left (x\right ) - 3 \, e^{\left (x + e^{2} - 1\right )} \log \left (\frac {5}{x}\right ) - 4 \, e^{\left (e^{2}\right )} \log \left (\frac {5}{x}\right )}{x^{2} - 4} \]
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Timed out. \[ \int \frac {e^{e^2} \left (-12 x+4 x^2+3 x^3-x^4+e^{-1+x} \left (12-4 x-3 x^2+x^3\right )\right )+e^{e^2} \left (12 x-8 x^2+3 x^3+e^{-1+x} \left (-8 x-2 x^2+4 x^3-x^4\right )\right ) \log \left (\frac {5}{x}\right )}{16 x-8 x^3+x^5} \, dx=\int -\frac {{\mathrm {e}}^{{\mathrm {e}}^2}\,\left (12\,x+{\mathrm {e}}^{x-1}\,\left (-x^3+3\,x^2+4\,x-12\right )-4\,x^2-3\,x^3+x^4\right )-{\mathrm {e}}^{{\mathrm {e}}^2}\,\ln \left (\frac {5}{x}\right )\,\left (12\,x-{\mathrm {e}}^{x-1}\,\left (x^4-4\,x^3+2\,x^2+8\,x\right )-8\,x^2+3\,x^3\right )}{x^5-8\,x^3+16\,x} \,d x \]
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