Integrand size = 149, antiderivative size = 29 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=\frac {25 \left (5-\frac {1}{5} x (3+x)\right )}{1-\left (4+e^3-x\right )^2 x} \]
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Timed out. \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=\text {\$Aborted} \]
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Rubi steps Aborted
Time = 0.04 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.24 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=\frac {5 \left (-25+3 x+x^2\right )}{-1+\left (4+e^3\right )^2 x-2 \left (4+e^3\right ) x^2+x^3} \]
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Time = 0.27 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.48
method | result | size |
risch | \(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\) | \(43\) |
gosper | \(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\) | \(44\) |
norman | \(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\) | \(45\) |
parallelrisch | \(\frac {5 x^{2}+15 x -125}{x \,{\mathrm e}^{6}-2 x^{2} {\mathrm e}^{3}+x^{3}+8 x \,{\mathrm e}^{3}-8 x^{2}+16 x -1}\) | \(45\) |
default | \(-\frac {5 \left (\munderset {\textit {\_R} =\operatorname {RootOf}\left (1+\textit {\_Z}^{6}+\left (-4 \,{\mathrm e}^{3}-16\right ) \textit {\_Z}^{5}+\left (48 \,{\mathrm e}^{3}+6 \,{\mathrm e}^{6}+96\right ) \textit {\_Z}^{4}+\left (-192 \,{\mathrm e}^{3}-4 \,{\mathrm e}^{9}-48 \,{\mathrm e}^{6}-258\right ) \textit {\_Z}^{3}+\left (260 \,{\mathrm e}^{3}+{\mathrm e}^{12}+16 \,{\mathrm e}^{9}+96 \,{\mathrm e}^{6}+272\right ) \textit {\_Z}^{2}+\left (-16 \,{\mathrm e}^{3}-2 \,{\mathrm e}^{6}-32\right ) \textit {\_Z} \right )}{\sum }\frac {\left (397-\textit {\_R}^{4}-6 \textit {\_R}^{3}+\left (14 \,{\mathrm e}^{3}+{\mathrm e}^{6}+115\right ) \textit {\_R}^{2}+2 \left (-201-50 \,{\mathrm e}^{3}\right ) \textit {\_R} +25 \,{\mathrm e}^{6}+200 \,{\mathrm e}^{3}\right ) \ln \left (x -\textit {\_R} \right )}{16-\textit {\_R} \,{\mathrm e}^{12}+6 \textit {\_R}^{2} {\mathrm e}^{9}-12 \textit {\_R}^{3} {\mathrm e}^{6}+10 \textit {\_R}^{4} {\mathrm e}^{3}-3 \textit {\_R}^{5}-16 \textit {\_R} \,{\mathrm e}^{9}+72 \textit {\_R}^{2} {\mathrm e}^{6}-96 \textit {\_R}^{3} {\mathrm e}^{3}+40 \textit {\_R}^{4}-96 \textit {\_R} \,{\mathrm e}^{6}+288 \textit {\_R}^{2} {\mathrm e}^{3}-192 \textit {\_R}^{3}+{\mathrm e}^{6}-260 \textit {\_R} \,{\mathrm e}^{3}+387 \textit {\_R}^{2}+8 \,{\mathrm e}^{3}-272 \textit {\_R}}\right )}{2}\) | \(229\) |
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Time = 0.26 (sec) , antiderivative size = 40, normalized size of antiderivative = 1.38 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=\frac {5 \, {\left (x^{2} + 3 \, x - 25\right )}}{x^{3} - 8 \, x^{2} + x e^{6} - 2 \, {\left (x^{2} - 4 \, x\right )} e^{3} + 16 \, x - 1} \]
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Time = 1.36 (sec) , antiderivative size = 39, normalized size of antiderivative = 1.34 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=- \frac {- 5 x^{2} - 15 x + 125}{x^{3} + x^{2} \left (- 2 e^{3} - 8\right ) + x \left (16 + 8 e^{3} + e^{6}\right ) - 1} \]
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Time = 0.19 (sec) , antiderivative size = 36, normalized size of antiderivative = 1.24 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=\frac {5 \, {\left (x^{2} + 3 \, x - 25\right )}}{x^{3} - 2 \, x^{2} {\left (e^{3} + 4\right )} + x {\left (e^{6} + 8 \, e^{3} + 16\right )} - 1} \]
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Time = 0.28 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.41 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=\frac {5 \, {\left (x^{2} + 3 \, x - 25\right )}}{x^{3} - 2 \, x^{2} e^{3} - 8 \, x^{2} + x e^{6} + 8 \, x e^{3} + 16 \, x - 1} \]
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Time = 8.42 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.45 \[ \int \frac {1985-2010 x+575 x^2-30 x^3-5 x^4+e^6 \left (125+5 x^2\right )+e^3 \left (1000-500 x+70 x^2\right )}{1-32 x+272 x^2+e^{12} x^2-258 x^3+96 x^4-16 x^5+x^6+e^9 \left (16 x^2-4 x^3\right )+e^6 \left (-2 x+96 x^2-48 x^3+6 x^4\right )+e^3 \left (-16 x+260 x^2-192 x^3+48 x^4-4 x^5\right )} \, dx=-\frac {5\,x^2+15\,x-125}{-x^3+\left (2\,{\mathrm {e}}^3+8\right )\,x^2+\left (-8\,{\mathrm {e}}^3-{\mathrm {e}}^6-16\right )\,x+1} \]
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