Integrand size = 259, antiderivative size = 31 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 x^2 \left (e^{\log ^2(x)}-\frac {x}{x-\frac {(1+x)^2}{x^2}}\right )^2 \]
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Leaf count is larger than twice the leaf count of optimal. \(85\) vs. \(2(31)=62\).
Time = 1.15 (sec) , antiderivative size = 85, normalized size of antiderivative = 2.74, number of steps used = 7, number of rules used = 5, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.019, Rules used = {6820, 12, 6874, 1602, 2326} \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 x^2 e^{2 \log ^2(x)}+\frac {75 x^8}{\left (-x^3+x^2+2 x+1\right )^2}+\frac {150 x^5 e^{\log ^2(x)} \left (x^3 (-\log (x))+x^2 \log (x)+2 x \log (x)+\log (x)\right )}{\left (-x^3+x^2+2 x+1\right )^2 \log (x)} \]
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Rule 12
Rule 1602
Rule 2326
Rule 6820
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {150 x \left (x^3-e^{\log ^2(x)} \left (-1-2 x-x^2+x^3\right )\right ) \left (e^{\log ^2(x)} \left (1+2 x+x^2-x^3\right )^2+x^3 \left (4+6 x+2 x^2-x^3\right )+2 e^{\log ^2(x)} \left (1+2 x+x^2-x^3\right )^2 \log (x)\right )}{\left (1+2 x+x^2-x^3\right )^3} \, dx \\ & = 150 \int \frac {x \left (x^3-e^{\log ^2(x)} \left (-1-2 x-x^2+x^3\right )\right ) \left (e^{\log ^2(x)} \left (1+2 x+x^2-x^3\right )^2+x^3 \left (4+6 x+2 x^2-x^3\right )+2 e^{\log ^2(x)} \left (1+2 x+x^2-x^3\right )^2 \log (x)\right )}{\left (1+2 x+x^2-x^3\right )^3} \, dx \\ & = 150 \int \left (\frac {x^7 \left (-4-6 x-2 x^2+x^3\right )}{\left (-1-2 x-x^2+x^3\right )^3}+e^{2 \log ^2(x)} x (1+2 \log (x))-\frac {e^{\log ^2(x)} x^4 \left (-5-8 x-3 x^2+2 x^3-2 \log (x)-4 x \log (x)-2 x^2 \log (x)+2 x^3 \log (x)\right )}{\left (-1-2 x-x^2+x^3\right )^2}\right ) \, dx \\ & = 150 \int \frac {x^7 \left (-4-6 x-2 x^2+x^3\right )}{\left (-1-2 x-x^2+x^3\right )^3} \, dx+150 \int e^{2 \log ^2(x)} x (1+2 \log (x)) \, dx-150 \int \frac {e^{\log ^2(x)} x^4 \left (-5-8 x-3 x^2+2 x^3-2 \log (x)-4 x \log (x)-2 x^2 \log (x)+2 x^3 \log (x)\right )}{\left (-1-2 x-x^2+x^3\right )^2} \, dx \\ & = 75 e^{2 \log ^2(x)} x^2+\frac {75 x^8}{\left (1+2 x+x^2-x^3\right )^2}+\frac {150 e^{\log ^2(x)} x^5 \left (\log (x)+2 x \log (x)+x^2 \log (x)-x^3 \log (x)\right )}{\left (1+2 x+x^2-x^3\right )^2 \log (x)} \\ \end{align*}
Leaf count is larger than twice the leaf count of optimal. \(100\) vs. \(2(31)=62\).
Time = 0.22 (sec) , antiderivative size = 100, normalized size of antiderivative = 3.23 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 \left (2 x+x^2+e^{2 \log ^2(x)} x^2+\frac {28+69 x+60 x^2}{\left (1+2 x+x^2-x^3\right )^2}+\frac {2 e^{\log ^2(x)} x^5}{1+2 x+x^2-x^3}-\frac {35+29 x+18 x^2}{1+2 x+x^2-x^3}\right ) \]
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Leaf count of result is larger than twice the leaf count of optimal. \(102\) vs. \(2(30)=60\).
Time = 26.50 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32
method | result | size |
risch | \(75 x^{2}+150 x +\frac {1350 x^{5}+825 x^{4}-2250 x^{3}-3825 x^{2}-2250 x -525}{x^{6}-2 x^{5}-3 x^{4}+2 x^{3}+6 x^{2}+4 x +1}+75 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{2}-\frac {150 x^{5} {\mathrm e}^{\ln \left (x \right )^{2}}}{x^{3}-x^{2}-2 x -1}\) | \(103\) |
parallelrisch | \(\frac {2700 x^{4} {\mathrm e}^{2 \ln \left (x \right )^{2}}+450 x^{8}+450 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{2}+900 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{5}-1350 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{6}-900 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{7}+450 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{8}+900 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{5}+1800 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{6}+900 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{7}-900 \,{\mathrm e}^{\ln \left (x \right )^{2}} x^{8}+1800 \,{\mathrm e}^{2 \ln \left (x \right )^{2}} x^{3}}{6 x^{6}-12 x^{5}-18 x^{4}+12 x^{3}+36 x^{2}+24 x +6}\) | \(163\) |
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Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (31) = 62\).
Time = 0.27 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.23 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\frac {75 \, {\left (x^{8} - 7 \, x^{6} + 14 \, x^{5} + 21 \, x^{4} - 14 \, x^{3} - 42 \, x^{2} + {\left (x^{8} - 2 \, x^{7} - 3 \, x^{6} + 2 \, x^{5} + 6 \, x^{4} + 4 \, x^{3} + x^{2}\right )} e^{\left (2 \, \log \left (x\right )^{2}\right )} - 2 \, {\left (x^{8} - x^{7} - 2 \, x^{6} - x^{5}\right )} e^{\left (\log \left (x\right )^{2}\right )} - 28 \, x - 7\right )}}{x^{6} - 2 \, x^{5} - 3 \, x^{4} + 2 \, x^{3} + 6 \, x^{2} + 4 \, x + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (24) = 48\).
Time = 0.22 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.68 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=75 x^{2} + 150 x + \frac {- 150 x^{5} e^{\log {\left (x \right )}^{2}} + \left (75 x^{5} - 75 x^{4} - 150 x^{3} - 75 x^{2}\right ) e^{2 \log {\left (x \right )}^{2}}}{x^{3} - x^{2} - 2 x - 1} + \frac {1350 x^{5} + 825 x^{4} - 2250 x^{3} - 3825 x^{2} - 2250 x - 525}{x^{6} - 2 x^{5} - 3 x^{4} + 2 x^{3} + 6 x^{2} + 4 x + 1} \]
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Leaf count of result is larger than twice the leaf count of optimal. 131 vs. \(2 (31) = 62\).
Time = 0.20 (sec) , antiderivative size = 131, normalized size of antiderivative = 4.23 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\frac {75 \, {\left (x^{8} - 7 \, x^{6} + 14 \, x^{5} + 21 \, x^{4} - 14 \, x^{3} - 42 \, x^{2} + {\left (x^{8} - 2 \, x^{7} - 3 \, x^{6} + 2 \, x^{5} + 6 \, x^{4} + 4 \, x^{3} + x^{2}\right )} e^{\left (2 \, \log \left (x\right )^{2}\right )} - 2 \, {\left (x^{8} - x^{7} - 2 \, x^{6} - x^{5}\right )} e^{\left (\log \left (x\right )^{2}\right )} - 28 \, x - 7\right )}}{x^{6} - 2 \, x^{5} - 3 \, x^{4} + 2 \, x^{3} + 6 \, x^{2} + 4 \, x + 1} \]
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\[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=\int { \frac {150 \, {\left (x^{10} - 2 \, x^{9} - 6 \, x^{8} - 4 \, x^{7} + {\left (x^{10} - 3 \, x^{9} - 3 \, x^{8} + 8 \, x^{7} + 12 \, x^{6} - 3 \, x^{5} - 17 \, x^{4} - 15 \, x^{3} - 6 \, x^{2} + 2 \, {\left (x^{10} - 3 \, x^{9} - 3 \, x^{8} + 8 \, x^{7} + 12 \, x^{6} - 3 \, x^{5} - 17 \, x^{4} - 15 \, x^{3} - 6 \, x^{2} - x\right )} \log \left (x\right ) - x\right )} e^{\left (2 \, \log \left (x\right )^{2}\right )} - {\left (2 \, x^{10} - 5 \, x^{9} - 9 \, x^{8} + 7 \, x^{7} + 24 \, x^{6} + 18 \, x^{5} + 5 \, x^{4} + 2 \, {\left (x^{10} - 2 \, x^{9} - 3 \, x^{8} + 2 \, x^{7} + 6 \, x^{6} + 4 \, x^{5} + x^{4}\right )} \log \left (x\right )\right )} e^{\left (\log \left (x\right )^{2}\right )}\right )}}{x^{9} - 3 \, x^{8} - 3 \, x^{7} + 8 \, x^{6} + 12 \, x^{5} - 3 \, x^{4} - 17 \, x^{3} - 15 \, x^{2} - 6 \, x - 1} \,d x } \]
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Time = 13.48 (sec) , antiderivative size = 103, normalized size of antiderivative = 3.32 \[ \int \frac {-600 x^7-900 x^8-300 x^9+150 x^{10}+e^{\log ^2(x)} \left (-750 x^4-2700 x^5-3600 x^6-1050 x^7+1350 x^8+750 x^9-300 x^{10}+\left (-300 x^4-1200 x^5-1800 x^6-600 x^7+900 x^8+600 x^9-300 x^{10}\right ) \log (x)\right )+e^{2 \log ^2(x)} \left (-150 x-900 x^2-2250 x^3-2550 x^4-450 x^5+1800 x^6+1200 x^7-450 x^8-450 x^9+150 x^{10}+\left (-300 x-1800 x^2-4500 x^3-5100 x^4-900 x^5+3600 x^6+2400 x^7-900 x^8-900 x^9+300 x^{10}\right ) \log (x)\right )}{-1-6 x-15 x^2-17 x^3-3 x^4+12 x^5+8 x^6-3 x^7-3 x^8+x^9} \, dx=150\,x+75\,x^2\,{\mathrm {e}}^{2\,{\ln \left (x\right )}^2}-\frac {-1350\,x^5-825\,x^4+2250\,x^3+3825\,x^2+2250\,x+525}{x^6-2\,x^5-3\,x^4+2\,x^3+6\,x^2+4\,x+1}+75\,x^2+\frac {150\,x^5\,{\mathrm {e}}^{{\ln \left (x\right )}^2}}{-x^3+x^2+2\,x+1} \]
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