Integrand size = 200, antiderivative size = 36 \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=\frac {e^x}{x}-\frac {4-x}{-x+\left (5 \sqrt [5]{e}-x\right )^2 x} \]
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Leaf count is larger than twice the leaf count of optimal. \(482\) vs. \(2(36)=72\).
Time = 1.35 (sec) , antiderivative size = 482, normalized size of antiderivative = 13.39, number of steps used = 25, number of rules used = 11, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.055, Rules used = {6, 6820, 6874, 2228, 628, 630, 31, 754, 814, 646, 652} \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=-\frac {\left (6+5 \sqrt [5]{e}\right ) \left (5 \sqrt [5]{e}-x\right )}{-x^2+10 \sqrt [5]{e} x-25 e^{2/5}+1}-\frac {2 \left (-5 \sqrt [5]{e} x+25 e^{2/5}+1\right )}{x \left (-x^2+10 \sqrt [5]{e} x-25 e^{2/5}+1\right )}-\frac {40 \sqrt [5]{e} \left (-5 \sqrt [5]{e} x+25 e^{2/5}+1\right )}{\left (1-25 e^{2/5}\right ) \left (-x^2+10 \sqrt [5]{e} x-25 e^{2/5}+1\right )}-\frac {5 \sqrt [5]{e} x-25 e^{2/5}+1}{-x^2+10 \sqrt [5]{e} x-25 e^{2/5}+1}+\frac {e^x}{x}+\frac {2 \left (3+25 e^{2/5}\right )}{\left (1-25 e^{2/5}\right ) x}+\frac {20 \left (2+5 \sqrt [5]{e}\right ) \sqrt [5]{e} \log \left (-x+5 \sqrt [5]{e}+1\right )}{\left (1+5 \sqrt [5]{e}\right )^2}+\frac {5}{2} \sqrt [5]{e} \log \left (-x+5 \sqrt [5]{e}+1\right )+\frac {\left (3+5 \sqrt [5]{e}\right ) \left (1-25 e^{2/5}\right ) \log \left (-x+5 \sqrt [5]{e}+1\right )}{\left (1+5 \sqrt [5]{e}\right )^3}-\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (-x+5 \sqrt [5]{e}+1\right )+\frac {20 \left (2-5 \sqrt [5]{e}\right ) \sqrt [5]{e} \log \left (x-5 \sqrt [5]{e}+1\right )}{\left (1-5 \sqrt [5]{e}\right )^2}-\frac {5}{2} \sqrt [5]{e} \log \left (x-5 \sqrt [5]{e}+1\right )+\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (x-5 \sqrt [5]{e}+1\right )-\frac {\left (3-5 \sqrt [5]{e}\right ) \left (1+5 \sqrt [5]{e}\right ) \log \left (x-5 \sqrt [5]{e}+1\right )}{\left (1-5 \sqrt [5]{e}\right )^2} \]
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Rule 6
Rule 31
Rule 628
Rule 630
Rule 646
Rule 652
Rule 754
Rule 814
Rule 2228
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{\left (1+625 e^{4/5}\right ) x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx \\ & = \int \frac {100 e^{2/5}+625 e^{\frac {4}{5}+x} (-1+x)+10 \sqrt [5]{e} (-8+x) x-500 e^{\frac {3}{5}+x} (-1+x) x-20 e^{\frac {1}{5}+x} (-1+x)^2 x (1+x)+e^x (-1+x)^3 (1+x)^2-2 \left (2-6 x^2+x^3\right )+50 e^{\frac {2}{5}+x} \left (1-x-3 x^2+3 x^3\right )}{x^2 \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )^2} \, dx \\ & = \int \left (\frac {e^x (-1+x)}{x^2}+\frac {12 \left (1+\frac {5 \sqrt [5]{e}}{6}\right )}{\left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2}-\frac {4 \left (1-25 e^{2/5}\right )}{x^2 \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2}-\frac {80 \sqrt [5]{e}}{x \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2}-\frac {2 x}{\left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2}\right ) \, dx \\ & = -\left (2 \int \frac {x}{\left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2} \, dx\right )+\left (2 \left (6+5 \sqrt [5]{e}\right )\right ) \int \frac {1}{\left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2} \, dx-\left (4 \left (1-25 e^{2/5}\right )\right ) \int \frac {1}{x^2 \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2} \, dx-\left (80 \sqrt [5]{e}\right ) \int \frac {1}{x \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )^2} \, dx+\int \frac {e^x (-1+x)}{x^2} \, dx \\ & = \frac {e^x}{x}-\frac {\left (6+5 \sqrt [5]{e}\right ) \left (5 \sqrt [5]{e}-x\right )}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {40 \sqrt [5]{e} \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{\left (1-25 e^{2/5}\right ) \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {2 \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{x \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {1-25 e^{2/5}+5 \sqrt [5]{e} x}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}+\left (-6-5 \sqrt [5]{e}\right ) \int \frac {1}{-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2} \, dx+\left (5 \sqrt [5]{e}\right ) \int \frac {1}{-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2} \, dx-\frac {\left (20 \sqrt [5]{e}\right ) \int \frac {-4+10 \sqrt [5]{e} x}{x \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )} \, dx}{1-25 e^{2/5}}-\int \frac {-2 \left (3+25 e^{2/5}\right )+20 \sqrt [5]{e} x}{x^2 \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )} \, dx \\ & = \frac {e^x}{x}-\frac {\left (6+5 \sqrt [5]{e}\right ) \left (5 \sqrt [5]{e}-x\right )}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {40 \sqrt [5]{e} \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{\left (1-25 e^{2/5}\right ) \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {2 \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{x \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {1-25 e^{2/5}+5 \sqrt [5]{e} x}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}+\frac {1}{2} \left (-6-5 \sqrt [5]{e}\right ) \int \frac {1}{-1-5 \sqrt [5]{e}+x} \, dx+\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \int \frac {1}{1-5 \sqrt [5]{e}+x} \, dx+\frac {1}{2} \left (5 \sqrt [5]{e}\right ) \int \frac {1}{-1-5 \sqrt [5]{e}+x} \, dx-\frac {1}{2} \left (5 \sqrt [5]{e}\right ) \int \frac {1}{1-5 \sqrt [5]{e}+x} \, dx-\frac {\left (20 \sqrt [5]{e}\right ) \int \left (-\frac {4}{\left (-1+25 e^{2/5}\right ) x}+\frac {2 \left (-25 \sqrt [5]{e}+125 e^{3/5}+2 x\right )}{\left (-1+25 e^{2/5}\right ) \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )}\right ) \, dx}{1-25 e^{2/5}}-\int \left (-\frac {2 \left (3+25 e^{2/5}\right )}{\left (-1+25 e^{2/5}\right ) x^2}-\frac {80 \sqrt [5]{e}}{\left (-1+25 e^{2/5}\right )^2 x}+\frac {2 \left (-3-350 e^{2/5}+625 e^{4/5}+40 \sqrt [5]{e} x\right )}{\left (-1+25 e^{2/5}\right )^2 \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )}\right ) \, dx \\ & = \frac {2 \left (3+25 e^{2/5}\right )}{\left (1-25 e^{2/5}\right ) x}+\frac {e^x}{x}-\frac {\left (6+5 \sqrt [5]{e}\right ) \left (5 \sqrt [5]{e}-x\right )}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {40 \sqrt [5]{e} \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{\left (1-25 e^{2/5}\right ) \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {2 \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{x \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {1-25 e^{2/5}+5 \sqrt [5]{e} x}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (1+5 \sqrt [5]{e}-x\right )+\frac {5}{2} \sqrt [5]{e} \log \left (1+5 \sqrt [5]{e}-x\right )+\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (1-5 \sqrt [5]{e}+x\right )-\frac {5}{2} \sqrt [5]{e} \log \left (1-5 \sqrt [5]{e}+x\right )-\frac {2 \int \frac {-3-350 e^{2/5}+625 e^{4/5}+40 \sqrt [5]{e} x}{-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2} \, dx}{\left (1-25 e^{2/5}\right )^2}+\frac {\left (40 \sqrt [5]{e}\right ) \int \frac {-25 \sqrt [5]{e}+125 e^{3/5}+2 x}{-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2} \, dx}{\left (1-25 e^{2/5}\right )^2} \\ & = \frac {2 \left (3+25 e^{2/5}\right )}{\left (1-25 e^{2/5}\right ) x}+\frac {e^x}{x}-\frac {\left (6+5 \sqrt [5]{e}\right ) \left (5 \sqrt [5]{e}-x\right )}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {40 \sqrt [5]{e} \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{\left (1-25 e^{2/5}\right ) \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {2 \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{x \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {1-25 e^{2/5}+5 \sqrt [5]{e} x}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (1+5 \sqrt [5]{e}-x\right )+\frac {5}{2} \sqrt [5]{e} \log \left (1+5 \sqrt [5]{e}-x\right )+\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (1-5 \sqrt [5]{e}+x\right )-\frac {5}{2} \sqrt [5]{e} \log \left (1-5 \sqrt [5]{e}+x\right )-\frac {\left (\left (3-5 \sqrt [5]{e}\right ) \left (1+5 \sqrt [5]{e}\right )\right ) \int \frac {1}{1-5 \sqrt [5]{e}+x} \, dx}{\left (1-5 \sqrt [5]{e}\right )^2}+\frac {\left (\left (1-5 \sqrt [5]{e}\right ) \left (3+5 \sqrt [5]{e}\right )\right ) \int \frac {1}{-1-5 \sqrt [5]{e}+x} \, dx}{\left (1+5 \sqrt [5]{e}\right )^2}+\frac {\left (20 \left (2-5 \sqrt [5]{e}\right ) \sqrt [5]{e}\right ) \int \frac {1}{1-5 \sqrt [5]{e}+x} \, dx}{\left (1-5 \sqrt [5]{e}\right )^2}+\frac {\left (20 \left (2+5 \sqrt [5]{e}\right ) \sqrt [5]{e}\right ) \int \frac {1}{-1-5 \sqrt [5]{e}+x} \, dx}{\left (1+5 \sqrt [5]{e}\right )^2} \\ & = \frac {2 \left (3+25 e^{2/5}\right )}{\left (1-25 e^{2/5}\right ) x}+\frac {e^x}{x}-\frac {\left (6+5 \sqrt [5]{e}\right ) \left (5 \sqrt [5]{e}-x\right )}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}-\frac {40 \sqrt [5]{e} \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{\left (1-25 e^{2/5}\right ) \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {2 \left (1+25 e^{2/5}-5 \sqrt [5]{e} x\right )}{x \left (1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2\right )}-\frac {1-25 e^{2/5}+5 \sqrt [5]{e} x}{1-25 e^{2/5}+10 \sqrt [5]{e} x-x^2}+\frac {\left (1-5 \sqrt [5]{e}\right ) \left (3+5 \sqrt [5]{e}\right ) \log \left (1+5 \sqrt [5]{e}-x\right )}{\left (1+5 \sqrt [5]{e}\right )^2}-\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (1+5 \sqrt [5]{e}-x\right )+\frac {5}{2} \sqrt [5]{e} \log \left (1+5 \sqrt [5]{e}-x\right )+\frac {20 \left (2+5 \sqrt [5]{e}\right ) \sqrt [5]{e} \log \left (1+5 \sqrt [5]{e}-x\right )}{\left (1+5 \sqrt [5]{e}\right )^2}-\frac {\left (3-5 \sqrt [5]{e}\right ) \left (1+5 \sqrt [5]{e}\right ) \log \left (1-5 \sqrt [5]{e}+x\right )}{\left (1-5 \sqrt [5]{e}\right )^2}+\frac {1}{2} \left (6+5 \sqrt [5]{e}\right ) \log \left (1-5 \sqrt [5]{e}+x\right )-\frac {5}{2} \sqrt [5]{e} \log \left (1-5 \sqrt [5]{e}+x\right )+\frac {20 \left (2-5 \sqrt [5]{e}\right ) \sqrt [5]{e} \log \left (1-5 \sqrt [5]{e}+x\right )}{\left (1-5 \sqrt [5]{e}\right )^2} \\ \end{align*}
Time = 10.15 (sec) , antiderivative size = 57, normalized size of antiderivative = 1.58 \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=\frac {-4+25 e^{\frac {2}{5}+x}+x-10 e^{\frac {1}{5}+x} x+e^x \left (-1+x^2\right )}{x \left (-1+25 e^{2/5}-10 \sqrt [5]{e} x+x^2\right )} \]
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Time = 0.58 (sec) , antiderivative size = 34, normalized size of antiderivative = 0.94
method | result | size |
risch | \(\frac {x -4}{\left (25 \,{\mathrm e}^{\frac {2}{5}}-10 x \,{\mathrm e}^{\frac {1}{5}}+x^{2}-1\right ) x}+\frac {{\mathrm e}^{x}}{x}\) | \(34\) |
norman | \(\frac {-4+\left (25 \,{\mathrm e}^{\frac {2}{5}}-1\right ) {\mathrm e}^{x}+x +{\mathrm e}^{x} x^{2}-10 \,{\mathrm e}^{x} {\mathrm e}^{\frac {1}{5}} x}{x \left (25 \,{\mathrm e}^{\frac {2}{5}}-10 x \,{\mathrm e}^{\frac {1}{5}}+x^{2}-1\right )}\) | \(50\) |
parallelrisch | \(\frac {-10 \,{\mathrm e}^{x} {\mathrm e}^{\frac {1}{5}} x +{\mathrm e}^{x} x^{2}+25 \,{\mathrm e}^{\frac {2}{5}} {\mathrm e}^{x}-{\mathrm e}^{x}+x -4}{\left (25 \,{\mathrm e}^{\frac {2}{5}}-10 x \,{\mathrm e}^{\frac {1}{5}}+x^{2}-1\right ) x}\) | \(51\) |
parts | \(\frac {{\mathrm e}^{x}}{x}-\frac {2 \left (31250 \,{\mathrm e}^{\frac {6}{5}}-3750 \,{\mathrm e}^{\frac {4}{5}}+150 \,{\mathrm e}^{\frac {2}{5}}-2\right )}{\left (625 \,{\mathrm e}^{\frac {4}{5}}-50 \,{\mathrm e}^{\frac {2}{5}}+1\right )^{2} x}+\frac {\munderset {\textit {\_R} =\operatorname {RootOf}\left (\textit {\_Z}^{4}-20 \,{\mathrm e}^{\frac {1}{5}} \textit {\_Z}^{3}+\left (150 \,{\mathrm e}^{\frac {2}{5}}-2\right ) \textit {\_Z}^{2}+\left (-500 \,{\mathrm e}^{\frac {3}{5}}+20 \,{\mathrm e}^{\frac {1}{5}}\right ) \textit {\_Z} +625 \,{\mathrm e}^{\frac {4}{5}}-50 \,{\mathrm e}^{\frac {2}{5}}+1\right )}{\sum }\frac {\left (2+2 \left (-15625 \,{\mathrm e}^{\frac {6}{5}}+1875 \,{\mathrm e}^{\frac {4}{5}}-75 \,{\mathrm e}^{\frac {2}{5}}+1\right ) \textit {\_R}^{2}+\left (-3750 \,{\mathrm e}^{\frac {4}{5}}+3000 \,{\mathrm e}^{\frac {3}{5}}+100 \,{\mathrm e}^{\frac {2}{5}}-75000 \,{\mathrm e}-40 \,{\mathrm e}^{\frac {1}{5}}-390625 \,{\mathrm e}^{\frac {8}{5}}+62500 \,{\mathrm e}^{\frac {6}{5}}+625000 \,{\mathrm e}^{\frac {7}{5}}-1\right ) \textit {\_R} -7500 \,{\mathrm e}^{\frac {4}{5}}-500 \,{\mathrm e}^{\frac {3}{5}}+18750 \,{\mathrm e}+5 \,{\mathrm e}^{\frac {1}{5}}-2343750 \,{\mathrm e}^{\frac {8}{5}}+250000 \,{\mathrm e}^{\frac {6}{5}}-312500 \,{\mathrm e}^{\frac {7}{5}}+1953125 \,{\mathrm e}^{\frac {9}{5}}\right ) \ln \left (x -\textit {\_R} \right )}{-125 \,{\mathrm e}^{\frac {3}{5}}+75 \textit {\_R} \,{\mathrm e}^{\frac {2}{5}}-15 \,{\mathrm e}^{\frac {1}{5}} \textit {\_R}^{2}+\textit {\_R}^{3}+5 \,{\mathrm e}^{\frac {1}{5}}-\textit {\_R}}}{2 \left (625 \,{\mathrm e}^{\frac {4}{5}}-50 \,{\mathrm e}^{\frac {2}{5}}+1\right )^{2}}\) | \(223\) |
default | \(\text {Expression too large to display}\) | \(15571\) |
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none
Time = 0.26 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.17 \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=\frac {{\left (x^{2} - 10 \, x e^{\frac {1}{5}} + 25 \, e^{\frac {2}{5}} - 1\right )} e^{x} + x - 4}{x^{3} - 10 \, x^{2} e^{\frac {1}{5}} + 25 \, x e^{\frac {2}{5}} - x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 100 vs. \(2 (20) = 40\).
Time = 3.04 (sec) , antiderivative size = 100, normalized size of antiderivative = 2.78 \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=- \frac {x \left (- 625 e^{\frac {4}{5}} - 1 + 50 e^{\frac {2}{5}}\right ) - 200 e^{\frac {2}{5}} + 4 + 2500 e^{\frac {4}{5}}}{x^{3} \left (- 50 e^{\frac {2}{5}} + 1 + 625 e^{\frac {4}{5}}\right ) + x^{2} \left (- 6250 e - 10 e^{\frac {1}{5}} + 500 e^{\frac {3}{5}}\right ) + x \left (- 1875 e^{\frac {4}{5}} - 1 + 75 e^{\frac {2}{5}} + 15625 e^{\frac {6}{5}}\right )} + \frac {e^{x}}{x} \]
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Exception generated. \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=\text {Exception raised: RuntimeError} \]
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Leaf count of result is larger than twice the leaf count of optimal. 1602 vs. \(2 (27) = 54\).
Time = 0.37 (sec) , antiderivative size = 1602, normalized size of antiderivative = 44.50 \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=\text {Too large to display} \]
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Time = 13.78 (sec) , antiderivative size = 32, normalized size of antiderivative = 0.89 \[ \int \frac {-4+100 e^{2/5}+12 x^2-2 x^3+\sqrt [5]{e} \left (-80 x+10 x^2\right )+e^x \left (-1+x+2 x^2-2 x^3-x^4+x^5+e^{4/5} (-625+625 x)+e^{3/5} \left (500 x-500 x^2\right )+e^{2/5} \left (50-50 x-150 x^2+150 x^3\right )+\sqrt [5]{e} \left (-20 x+20 x^2+20 x^3-20 x^4\right )\right )}{x^2+625 e^{4/5} x^2-500 e^{3/5} x^3-2 x^4+x^6+e^{2/5} \left (-50 x^2+150 x^4\right )+\sqrt [5]{e} \left (20 x^3-20 x^5\right )} \, dx=\frac {{\mathrm {e}}^x}{x}+\frac {x-4}{x^3-10\,{\mathrm {e}}^{1/5}\,x^2+\left (25\,{\mathrm {e}}^{2/5}-1\right )\,x} \]
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