Integrand size = 120, antiderivative size = 24 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=e^x+x^2-\frac {75}{x \left (-7-x-x^2\right )^2} \]
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Leaf count is larger than twice the leaf count of optimal. \(354\) vs. \(2(24)=48\).
Time = 0.97 (sec) , antiderivative size = 354, normalized size of antiderivative = 14.75, number of steps used = 63, number of rules used = 17, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.142, Rules used = {6873, 6874, 2225, 628, 632, 210, 754, 836, 814, 648, 642, 652, 752, 742, 736, 832, 787} \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=\frac {50 x^3}{243}-\frac {8 (23 x+259) x^2}{81 \left (x^2+x+7\right )}+\frac {818 x^2}{243}-\frac {434 (x+14) x}{243 \left (x^2+x+7\right )}-\frac {49 (x+14) x}{9 \left (x^2+x+7\right )^2}+\frac {25 (227-32 x)}{2646 \left (x^2+x+7\right )}+\frac {32 (2 x+1)}{243 \left (x^2+x+7\right )}+\frac {98 (5 x+7)}{81 \left (x^2+x+7\right )}+\frac {25 (13-x)}{42 \left (x^2+x+7\right )^2}-\frac {343 (x+14)}{27 \left (x^2+x+7\right )^2}+\frac {125 (2 x+1)}{18 \left (x^2+x+7\right )^2}+\frac {25 (281-41 x)}{1134 \left (x^2+x+7\right ) x}+\frac {25 (13-x)}{18 \left (x^2+x+7\right )^2 x}-\frac {(x+14) x^6}{27 \left (x^2+x+7\right )^2}-\frac {(x+14) x^5}{9 \left (x^2+x+7\right )^2}-\frac {(41 x+385) x^4}{243 \left (x^2+x+7\right )}-\frac {8 (x+14) x^4}{9 \left (x^2+x+7\right )^2}-\frac {2 (16 x+161) x^3}{81 \left (x^2+x+7\right )}-\frac {43 (x+14) x^3}{27 \left (x^2+x+7\right )^2}+\frac {56 (2 x+1) x^3}{9 \left (x^2+x+7\right )^2}+\frac {980 x}{243}+e^x-\frac {11050}{3969 x} \]
[In]
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Rule 210
Rule 628
Rule 632
Rule 642
Rule 648
Rule 652
Rule 736
Rule 742
Rule 752
Rule 754
Rule 787
Rule 814
Rule 832
Rule 836
Rule 2225
Rule 6873
Rule 6874
Rubi steps \begin{align*} \text {integral}& = \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{x^2 \left (7+x+x^2\right )^3} \, dx \\ & = \int \left (e^x+\frac {375}{\left (7+x+x^2\right )^3}+\frac {525}{x^2 \left (7+x+x^2\right )^3}+\frac {225}{x \left (7+x+x^2\right )^3}+\frac {686 x}{\left (7+x+x^2\right )^3}+\frac {294 x^2}{\left (7+x+x^2\right )^3}+\frac {336 x^3}{\left (7+x+x^2\right )^3}+\frac {86 x^4}{\left (7+x+x^2\right )^3}+\frac {48 x^5}{\left (7+x+x^2\right )^3}+\frac {6 x^6}{\left (7+x+x^2\right )^3}+\frac {2 x^7}{\left (7+x+x^2\right )^3}\right ) \, dx \\ & = 2 \int \frac {x^7}{\left (7+x+x^2\right )^3} \, dx+6 \int \frac {x^6}{\left (7+x+x^2\right )^3} \, dx+48 \int \frac {x^5}{\left (7+x+x^2\right )^3} \, dx+86 \int \frac {x^4}{\left (7+x+x^2\right )^3} \, dx+225 \int \frac {1}{x \left (7+x+x^2\right )^3} \, dx+294 \int \frac {x^2}{\left (7+x+x^2\right )^3} \, dx+336 \int \frac {x^3}{\left (7+x+x^2\right )^3} \, dx+375 \int \frac {1}{\left (7+x+x^2\right )^3} \, dx+525 \int \frac {1}{x^2 \left (7+x+x^2\right )^3} \, dx+686 \int \frac {x}{\left (7+x+x^2\right )^3} \, dx+\int e^x \, dx \\ & = e^x+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {1}{27} \int \frac {x^5 (84+3 x)}{\left (7+x+x^2\right )^2} \, dx+\frac {1}{9} \int \frac {x^4 (70+2 x)}{\left (7+x+x^2\right )^2} \, dx+\frac {25}{42} \int \frac {54-3 x}{x \left (7+x+x^2\right )^2} \, dx+\frac {8}{9} \int \frac {x^3 (56+x)}{\left (7+x+x^2\right )^2} \, dx+\frac {25}{18} \int \frac {67-4 x}{x^2 \left (7+x+x^2\right )^2} \, dx+\frac {49}{9} \int \frac {14-2 x}{\left (7+x+x^2\right )^2} \, dx-\frac {56}{3} \int \frac {x^2}{\left (7+x+x^2\right )^2} \, dx-\frac {343}{9} \int \frac {1}{\left (7+x+x^2\right )^2} \, dx+\frac {125}{3} \int \frac {1}{\left (7+x+x^2\right )^2} \, dx+\frac {602}{9} \int \frac {x^2}{\left (7+x+x^2\right )^2} \, dx \\ & = e^x+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {25 (227-32 x)}{2646 \left (7+x+x^2\right )}+\frac {25 (281-41 x)}{1134 x \left (7+x+x^2\right )}-\frac {434 x (14+x)}{243 \left (7+x+x^2\right )}+\frac {32 (1+2 x)}{243 \left (7+x+x^2\right )}+\frac {98 (7+5 x)}{81 \left (7+x+x^2\right )}-\frac {2 x^3 (161+16 x)}{81 \left (7+x+x^2\right )}-\frac {8 x^2 (259+23 x)}{81 \left (7+x+x^2\right )}-\frac {x^4 (385+41 x)}{243 \left (7+x+x^2\right )}-\frac {1}{729} \int \frac {(-4620-450 x) x^3}{7+x+x^2} \, dx+\frac {25 \int \frac {1458-96 x}{x \left (7+x+x^2\right )} \, dx}{7938}-\frac {1}{243} \int \frac {(-2898-246 x) x^2}{7+x+x^2} \, dx+\frac {25 \int \frac {2652-246 x}{x^2 \left (7+x+x^2\right )} \, dx}{3402}-\frac {8}{243} \int \frac {(-1554-96 x) x}{7+x+x^2} \, dx-\frac {686}{243} \int \frac {1}{7+x+x^2} \, dx+\frac {250}{81} \int \frac {1}{7+x+x^2} \, dx+\frac {490}{81} \int \frac {1}{7+x+x^2} \, dx-\frac {784}{81} \int \frac {1}{7+x+x^2} \, dx+\frac {8428}{243} \int \frac {1}{7+x+x^2} \, dx \\ & = e^x+\frac {256 x}{81}+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {25 (227-32 x)}{2646 \left (7+x+x^2\right )}+\frac {25 (281-41 x)}{1134 x \left (7+x+x^2\right )}-\frac {434 x (14+x)}{243 \left (7+x+x^2\right )}+\frac {32 (1+2 x)}{243 \left (7+x+x^2\right )}+\frac {98 (7+5 x)}{81 \left (7+x+x^2\right )}-\frac {2 x^3 (161+16 x)}{81 \left (7+x+x^2\right )}-\frac {8 x^2 (259+23 x)}{81 \left (7+x+x^2\right )}-\frac {x^4 (385+41 x)}{243 \left (7+x+x^2\right )}-\frac {1}{729} \int \left (7320-4170 x-450 x^2-\frac {30 (1708-729 x)}{7+x+x^2}\right ) \, dx+\frac {25 \int \left (\frac {1458}{7 x}-\frac {6 (355+243 x)}{7 \left (7+x+x^2\right )}\right ) \, dx}{7938}-\frac {1}{243} \int \left (-2652-246 x+\frac {6 (3094+729 x)}{7+x+x^2}\right ) \, dx+\frac {25 \int \left (\frac {2652}{7 x^2}-\frac {4374}{49 x}+\frac {6 (-2365+729 x)}{49 \left (7+x+x^2\right )}\right ) \, dx}{3402}-\frac {8}{243} \int \frac {672-1458 x}{7+x+x^2} \, dx+\frac {1372}{243} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )-\frac {500}{81} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )-\frac {980}{81} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )+\frac {1568}{81} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )-\frac {16856}{243} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right ) \\ & = e^x-\frac {11050}{3969 x}+\frac {980 x}{243}+\frac {818 x^2}{243}+\frac {50 x^3}{243}+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {25 (227-32 x)}{2646 \left (7+x+x^2\right )}+\frac {25 (281-41 x)}{1134 x \left (7+x+x^2\right )}-\frac {434 x (14+x)}{243 \left (7+x+x^2\right )}+\frac {32 (1+2 x)}{243 \left (7+x+x^2\right )}+\frac {98 (7+5 x)}{81 \left (7+x+x^2\right )}-\frac {2 x^3 (161+16 x)}{81 \left (7+x+x^2\right )}-\frac {8 x^2 (259+23 x)}{81 \left (7+x+x^2\right )}-\frac {x^4 (385+41 x)}{243 \left (7+x+x^2\right )}+\frac {15220 \arctan \left (\frac {1+2 x}{3 \sqrt {3}}\right )}{729 \sqrt {3}}+\frac {25 \int \frac {-2365+729 x}{7+x+x^2} \, dx}{27783}-\frac {25 \int \frac {355+243 x}{7+x+x^2} \, dx}{9261}-\frac {2}{81} \int \frac {3094+729 x}{7+x+x^2} \, dx+\frac {10}{243} \int \frac {1708-729 x}{7+x+x^2} \, dx+24 \int \frac {1+2 x}{7+x+x^2} \, dx-\frac {3736}{81} \int \frac {1}{7+x+x^2} \, dx \\ & = e^x-\frac {11050}{3969 x}+\frac {980 x}{243}+\frac {818 x^2}{243}+\frac {50 x^3}{243}+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {25 (227-32 x)}{2646 \left (7+x+x^2\right )}+\frac {25 (281-41 x)}{1134 x \left (7+x+x^2\right )}-\frac {434 x (14+x)}{243 \left (7+x+x^2\right )}+\frac {32 (1+2 x)}{243 \left (7+x+x^2\right )}+\frac {98 (7+5 x)}{81 \left (7+x+x^2\right )}-\frac {2 x^3 (161+16 x)}{81 \left (7+x+x^2\right )}-\frac {8 x^2 (259+23 x)}{81 \left (7+x+x^2\right )}-\frac {x^4 (385+41 x)}{243 \left (7+x+x^2\right )}+\frac {15220 \arctan \left (\frac {1+2 x}{3 \sqrt {3}}\right )}{729 \sqrt {3}}+24 \log \left (7+x+x^2\right )-\frac {11675 \int \frac {1}{7+x+x^2} \, dx}{18522}-\frac {136475 \int \frac {1}{7+x+x^2} \, dx}{55566}-9 \int \frac {1+2 x}{7+x+x^2} \, dx-15 \int \frac {1+2 x}{7+x+x^2} \, dx-\frac {5459}{81} \int \frac {1}{7+x+x^2} \, dx+\frac {20725}{243} \int \frac {1}{7+x+x^2} \, dx+\frac {7472}{81} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right ) \\ & = e^x-\frac {11050}{3969 x}+\frac {980 x}{243}+\frac {818 x^2}{243}+\frac {50 x^3}{243}+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {25 (227-32 x)}{2646 \left (7+x+x^2\right )}+\frac {25 (281-41 x)}{1134 x \left (7+x+x^2\right )}-\frac {434 x (14+x)}{243 \left (7+x+x^2\right )}+\frac {32 (1+2 x)}{243 \left (7+x+x^2\right )}+\frac {98 (7+5 x)}{81 \left (7+x+x^2\right )}-\frac {2 x^3 (161+16 x)}{81 \left (7+x+x^2\right )}-\frac {8 x^2 (259+23 x)}{81 \left (7+x+x^2\right )}-\frac {x^4 (385+41 x)}{243 \left (7+x+x^2\right )}-\frac {7196 \arctan \left (\frac {1+2 x}{3 \sqrt {3}}\right )}{729 \sqrt {3}}+\frac {11675 \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )}{9261}+\frac {136475 \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )}{27783}+\frac {10918}{81} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right )-\frac {41450}{243} \text {Subst}\left (\int \frac {1}{-27-x^2} \, dx,x,1+2 x\right ) \\ & = e^x-\frac {11050}{3969 x}+\frac {980 x}{243}+\frac {818 x^2}{243}+\frac {50 x^3}{243}+\frac {25 (13-x)}{42 \left (7+x+x^2\right )^2}+\frac {25 (13-x)}{18 x \left (7+x+x^2\right )^2}-\frac {343 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {49 x (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {43 x^3 (14+x)}{27 \left (7+x+x^2\right )^2}-\frac {8 x^4 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^5 (14+x)}{9 \left (7+x+x^2\right )^2}-\frac {x^6 (14+x)}{27 \left (7+x+x^2\right )^2}+\frac {125 (1+2 x)}{18 \left (7+x+x^2\right )^2}+\frac {56 x^3 (1+2 x)}{9 \left (7+x+x^2\right )^2}+\frac {25 (227-32 x)}{2646 \left (7+x+x^2\right )}+\frac {25 (281-41 x)}{1134 x \left (7+x+x^2\right )}-\frac {434 x (14+x)}{243 \left (7+x+x^2\right )}+\frac {32 (1+2 x)}{243 \left (7+x+x^2\right )}+\frac {98 (7+5 x)}{81 \left (7+x+x^2\right )}-\frac {2 x^3 (161+16 x)}{81 \left (7+x+x^2\right )}-\frac {8 x^2 (259+23 x)}{81 \left (7+x+x^2\right )}-\frac {x^4 (385+41 x)}{243 \left (7+x+x^2\right )} \\ \end{align*}
Time = 3.22 (sec) , antiderivative size = 41, normalized size of antiderivative = 1.71 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=e^x+\frac {-75+49 x^3+14 x^4+15 x^5+2 x^6+x^7}{x \left (7+x+x^2\right )^2} \]
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[Out]
Time = 0.15 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33
method | result | size |
risch | \(x^{2}-\frac {75}{x \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}+{\mathrm e}^{x}\) | \(32\) |
parts | \(x^{2}-\frac {75}{49 x}-\frac {75 \left (-x^{3}-2 x^{2}-15 x -14\right )}{49 \left (x^{2}+x +7\right )^{2}}+{\mathrm e}^{x}\) | \(37\) |
norman | \(\frac {-75+x^{7}+x^{5} {\mathrm e}^{x}-735 x -210 x^{2}-176 x^{3}-16 x^{4}+2 x^{6}+49 \,{\mathrm e}^{x} x +14 \,{\mathrm e}^{x} x^{2}+15 \,{\mathrm e}^{x} x^{3}+2 \,{\mathrm e}^{x} x^{4}}{x \left (x^{2}+x +7\right )^{2}}\) | \(73\) |
parallelrisch | \(\frac {-75+x^{7}+x^{5} {\mathrm e}^{x}-735 x -210 x^{2}-176 x^{3}-16 x^{4}+2 x^{6}+49 \,{\mathrm e}^{x} x +14 \,{\mathrm e}^{x} x^{2}+15 \,{\mathrm e}^{x} x^{3}+2 \,{\mathrm e}^{x} x^{4}}{x \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}\) | \(85\) |
default | \(\frac {\frac {125}{18}+\frac {125 x}{9}}{\left (x^{2}+x +7\right )^{2}}+\frac {\frac {32}{243}+\frac {64 x}{243}}{x^{2}+x +7}-\frac {75}{49 x}+x^{2}+{\mathrm e}^{x}-\frac {4 \,{\mathrm e}^{x} \left (173 x^{3}-546 x^{2}-147 x -3773\right )}{81 \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}-\frac {43 \,{\mathrm e}^{x} \left (68 x^{3}+255 x^{2}+483 x +490\right )}{486 \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}-\frac {225 \left (\frac {112}{243} x^{3}-\frac {455}{162} x^{2}+\frac {70}{81} x -\frac {8428}{243}\right )}{343 \left (x^{2}+x +7\right )^{2}}+\frac {28 \,{\mathrm e}^{x} \left (x^{3}-57 x^{2}-168 x -343\right )}{81 \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}+\frac {-\frac {343 x}{27}-\frac {4802}{27}}{\left (x^{2}+x +7\right )^{2}}+\frac {49 \,{\mathrm e}^{x} \left (7 x^{3}+6 x^{2}+39 x -133\right )}{162 \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}+\frac {\frac {490}{81} x^{3}+\frac {245}{27} x^{2}-\frac {686}{27} x +\frac {4802}{81}}{\left (x^{2}+x +7\right )^{2}}+\frac {-\frac {12470}{243} x^{3}+\frac {731}{81} x^{2}-\frac {15050}{81} x +\frac {48461}{243}}{\left (x^{2}+x +7\right )^{2}}+\frac {343 \,{\mathrm e}^{x} \left (4 x^{3}+15 x^{2}+57 x +86\right )}{486 \left (x^{4}+2 x^{3}+15 x^{2}+14 x +49\right )}+\frac {\frac {5984}{81} x^{3}+\frac {10120}{27} x^{2}+\frac {17024}{27} x +\frac {134848}{81}}{\left (x^{2}+x +7\right )^{2}}+\frac {{\mathrm e}^{x} \left (1009 x^{3}+3237 x^{2}+7392 x +11123\right )}{162 x^{4}+324 x^{3}+2430 x^{2}+2268 x +7938}-\frac {2 \left (\frac {5797}{243} x^{3}+\frac {11305}{162} x^{2}+\frac {14602}{81} x +\frac {138229}{486}\right )}{\left (x^{2}+x +7\right )^{2}}+\frac {{\mathrm e}^{x} \left (1480 x^{3}-8301 x^{2}-1995 x -55174\right )}{486 x^{4}+972 x^{3}+7290 x^{2}+6804 x +23814}-\frac {6 \left (-\frac {1280}{243} x^{3}+\frac {899}{81} x^{2}-\frac {1232}{81} x +\frac {42385}{486}\right )}{\left (x^{2}+x +7\right )^{2}}+\frac {-\frac {784}{81} x^{3}-\frac {4928}{27} x^{2}-\frac {3136}{27} x -\frac {52136}{81}}{\left (x^{2}+x +7\right )^{2}}+\frac {-\frac {4975}{3969} x^{3}-\frac {9025}{2646} x^{2}-\frac {17875}{1323} x -\frac {21625}{1134}}{\left (x^{2}+x +7\right )^{2}}\) | \(528\) |
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Leaf count of result is larger than twice the leaf count of optimal. 75 vs. \(2 (19) = 38\).
Time = 0.28 (sec) , antiderivative size = 75, normalized size of antiderivative = 3.12 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=\frac {x^{7} + 2 \, x^{6} + 15 \, x^{5} + 14 \, x^{4} + 49 \, x^{3} + {\left (x^{5} + 2 \, x^{4} + 15 \, x^{3} + 14 \, x^{2} + 49 \, x\right )} e^{x} - 75}{x^{5} + 2 \, x^{4} + 15 \, x^{3} + 14 \, x^{2} + 49 \, x} \]
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Time = 0.11 (sec) , antiderivative size = 29, normalized size of antiderivative = 1.21 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=x^{2} + e^{x} - \frac {75}{x^{5} + 2 x^{4} + 15 x^{3} + 14 x^{2} + 49 x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 385 vs. \(2 (19) = 38\).
Time = 0.31 (sec) , antiderivative size = 385, normalized size of antiderivative = 16.04 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=x^{2} - \frac {25 \, {\left (884 \, x^{4} + 2055 \, x^{3} + 11580 \, x^{2} + 12859 \, x + 23814\right )}}{7938 \, {\left (x^{5} + 2 \, x^{4} + 15 \, x^{3} + 14 \, x^{2} + 49 \, x\right )}} - \frac {11594 \, x^{3} + 33915 \, x^{2} + 87612 \, x + 138229}{243 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} + \frac {2560 \, x^{3} - 5394 \, x^{2} + 7392 \, x - 42385}{81 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} + \frac {8 \, {\left (748 \, x^{3} + 3795 \, x^{2} + 6384 \, x + 16856\right )}}{81 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} - \frac {43 \, {\left (290 \, x^{3} - 51 \, x^{2} + 1050 \, x - 1127\right )}}{243 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} - \frac {25 \, {\left (32 \, x^{3} - 195 \, x^{2} + 60 \, x - 2408\right )}}{2646 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} - \frac {56 \, {\left (14 \, x^{3} + 264 \, x^{2} + 168 \, x + 931\right )}}{81 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} + \frac {49 \, {\left (10 \, x^{3} + 15 \, x^{2} - 42 \, x + 98\right )}}{81 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} + \frac {125 \, {\left (4 \, x^{3} + 6 \, x^{2} + 48 \, x + 23\right )}}{162 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} - \frac {343 \, {\left (2 \, x^{3} + 3 \, x^{2} + 24 \, x + 133\right )}}{243 \, {\left (x^{4} + 2 \, x^{3} + 15 \, x^{2} + 14 \, x + 49\right )}} + e^{x} \]
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Leaf count of result is larger than twice the leaf count of optimal. 82 vs. \(2 (19) = 38\).
Time = 0.27 (sec) , antiderivative size = 82, normalized size of antiderivative = 3.42 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx=\frac {x^{7} + 2 \, x^{6} + x^{5} e^{x} + 15 \, x^{5} + 2 \, x^{4} e^{x} + 14 \, x^{4} + 15 \, x^{3} e^{x} + 49 \, x^{3} + 14 \, x^{2} e^{x} + 49 \, x e^{x} - 75}{x^{5} + 2 \, x^{4} + 15 \, x^{3} + 14 \, x^{2} + 49 \, x} \]
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Time = 8.64 (sec) , antiderivative size = 32, normalized size of antiderivative = 1.33 \[ \int \frac {525+225 x+375 x^2+686 x^3+294 x^4+336 x^5+86 x^6+48 x^7+6 x^8+2 x^9+e^x \left (343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8\right )}{343 x^2+147 x^3+168 x^4+43 x^5+24 x^6+3 x^7+x^8} \, dx={\mathrm {e}}^x-\frac {75}{x^5+2\,x^4+15\,x^3+14\,x^2+49\,x}+x^2 \]
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