Integrand size = 65, antiderivative size = 24 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=\frac {x^2 (-x+\log (9))^2}{e^{32} \left (-3-\frac {11 x}{2}\right )^4} \]
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Leaf count is larger than twice the leaf count of optimal. \(95\) vs. \(2(24)=48\).
Time = 0.08 (sec) , antiderivative size = 95, normalized size of antiderivative = 3.96, number of steps used = 3, number of rules used = 2, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.031, Rules used = {12, 2099} \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=\frac {16 \left (216+121 \log ^2(9)+396 \log (9)\right )}{14641 e^{32} (11 x+6)^2}-\frac {192 \left (72+121 \log ^2(9)+198 \log (9)\right )}{14641 e^{32} (11 x+6)^3}-\frac {32 (12+11 \log (9))}{14641 e^{32} (11 x+6)}+\frac {576 (6+11 \log (9))^2}{14641 e^{32} (11 x+6)^4} \]
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Rule 12
Rule 2099
Rubi steps \begin{align*} \text {integral}& = \frac {\int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5} \, dx}{e^{32}} \\ & = \frac {\int \left (-\frac {2304 (6+11 \log (9))^2}{1331 (6+11 x)^5}+\frac {32 (12+11 \log (9))}{1331 (6+11 x)^2}+\frac {576 \left (72+198 \log (9)+121 \log ^2(9)\right )}{1331 (6+11 x)^4}-\frac {32 \left (216+396 \log (9)+121 \log ^2(9)\right )}{1331 (6+11 x)^3}\right ) \, dx}{e^{32}} \\ & = \frac {576 (6+11 \log (9))^2}{14641 e^{32} (6+11 x)^4}-\frac {32 (12+11 \log (9))}{14641 e^{32} (6+11 x)}-\frac {192 \left (72+198 \log (9)+121 \log ^2(9)\right )}{14641 e^{32} (6+11 x)^3}+\frac {16 \left (216+396 \log (9)+121 \log ^2(9)\right )}{14641 e^{32} (6+11 x)^2} \\ \end{align*}
Time = 0.04 (sec) , antiderivative size = 43, normalized size of antiderivative = 1.79 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=-\frac {16 \left (1296+9504 x+2662 x^3 (12+11 \log (9))-121 x^2 \left (-216+121 \log ^2(9)\right )\right )}{14641 e^{32} (6+11 x)^4} \]
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Time = 0.12 (sec) , antiderivative size = 51, normalized size of antiderivative = 2.12
method | result | size |
risch | \(\frac {{\mathrm e}^{-32} \left (\left (-\frac {384}{161051}-\frac {64 \ln \left (3\right )}{14641}\right ) x^{3}+\left (\frac {64 \ln \left (3\right )^{2}}{14641}-\frac {3456}{1771561}\right ) x^{2}-\frac {13824 x}{19487171}-\frac {20736}{214358881}\right )}{x^{4}+\frac {24}{11} x^{3}+\frac {216}{121} x^{2}+\frac {864}{1331} x +\frac {1296}{14641}}\) | \(51\) |
norman | \(\frac {\left (-\frac {64 \left (11 \ln \left (3\right )+6\right ) {\mathrm e}^{-16} x^{3}}{11}+\frac {64 \left (121 \ln \left (3\right )^{2}-54\right ) {\mathrm e}^{-16} x^{2}}{121}-\frac {13824 x \,{\mathrm e}^{-16}}{1331}-\frac {20736 \,{\mathrm e}^{-16}}{14641}\right ) {\mathrm e}^{-16}}{\left (11 x +6\right )^{4}}\) | \(59\) |
gosper | \(\frac {64 \left (14641 x^{2} \ln \left (3\right )^{2}-14641 x^{3} \ln \left (3\right )-7986 x^{3}-6534 x^{2}-2376 x -324\right ) {\mathrm e}^{-32}}{14641 \left (14641 x^{4}+31944 x^{3}+26136 x^{2}+9504 x +1296\right )}\) | \(60\) |
parallelrisch | \(\frac {{\mathrm e}^{-32} \left (-20736+937024 x^{2} \ln \left (3\right )^{2}-937024 x^{3} \ln \left (3\right )-511104 x^{3}-418176 x^{2}-152064 x \right )}{214358881 x^{4}+467692104 x^{3}+382657176 x^{2}+139148064 x +18974736}\) | \(60\) |
default | \(2 \,{\mathrm e}^{-32} \left (-\frac {8 \left (-\frac {144 \ln \left (3\right )^{2}}{121}-\frac {864 \ln \left (3\right )}{1331}-\frac {1296}{14641}\right )}{\left (11 x +6\right )^{4}}-\frac {32 \left (\frac {\ln \left (3\right )}{1331}+\frac {6}{14641}\right )}{11 x +6}-\frac {32 \left (\frac {36 \ln \left (3\right )^{2}}{121}+\frac {324 \ln \left (3\right )}{1331}+\frac {648}{14641}\right )}{3 \left (11 x +6\right )^{3}}-\frac {16 \left (-\frac {2 \ln \left (3\right )^{2}}{121}-\frac {36 \ln \left (3\right )}{1331}-\frac {108}{14641}\right )}{\left (11 x +6\right )^{2}}\right )\) | \(86\) |
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Leaf count of result is larger than twice the leaf count of optimal. 57 vs. \(2 (22) = 44\).
Time = 0.24 (sec) , antiderivative size = 57, normalized size of antiderivative = 2.38 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=-\frac {64 \, {\left (14641 \, x^{3} \log \left (3\right ) - 14641 \, x^{2} \log \left (3\right )^{2} + 7986 \, x^{3} + 6534 \, x^{2} + 2376 \, x + 324\right )} e^{\left (-32\right )}}{14641 \, {\left (14641 \, x^{4} + 31944 \, x^{3} + 26136 \, x^{2} + 9504 \, x + 1296\right )}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 65 vs. \(2 (24) = 48\).
Time = 0.76 (sec) , antiderivative size = 65, normalized size of antiderivative = 2.71 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=\frac {x^{3} \left (- 937024 \log {\left (3 \right )} - 511104\right ) + x^{2} \left (-418176 + 937024 \log {\left (3 \right )}^{2}\right ) - 152064 x - 20736}{214358881 x^{4} e^{32} + 467692104 x^{3} e^{32} + 382657176 x^{2} e^{32} + 139148064 x e^{32} + 18974736 e^{32}} \]
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Leaf count of result is larger than twice the leaf count of optimal. 55 vs. \(2 (22) = 44\).
Time = 0.19 (sec) , antiderivative size = 55, normalized size of antiderivative = 2.29 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=-\frac {64 \, {\left (1331 \, x^{3} {\left (11 \, \log \left (3\right ) + 6\right )} - 121 \, {\left (121 \, \log \left (3\right )^{2} - 54\right )} x^{2} + 2376 \, x + 324\right )} e^{\left (-32\right )}}{14641 \, {\left (14641 \, x^{4} + 31944 \, x^{3} + 26136 \, x^{2} + 9504 \, x + 1296\right )}} \]
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Time = 0.26 (sec) , antiderivative size = 42, normalized size of antiderivative = 1.75 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=-\frac {64 \, {\left (14641 \, x^{3} \log \left (3\right ) - 14641 \, x^{2} \log \left (3\right )^{2} + 7986 \, x^{3} + 6534 \, x^{2} + 2376 \, x + 324\right )} e^{\left (-32\right )}}{14641 \, {\left (11 \, x + 6\right )}^{4}} \]
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Time = 12.98 (sec) , antiderivative size = 83, normalized size of antiderivative = 3.46 \[ \int \frac {384 x^3+\left (-576 x^2+352 x^3\right ) \log (9)+\left (192 x-352 x^2\right ) \log ^2(9)}{e^{32} \left (7776+71280 x+261360 x^2+479160 x^3+439230 x^4+161051 x^5\right )} \, dx=\frac {64\,{\mathrm {e}}^{-32}\,\left (198\,\ln \left (3\right )+121\,{\ln \left (3\right )}^2+54\right )}{14641\,{\left (11\,x+6\right )}^2}-\frac {768\,{\mathrm {e}}^{-32}\,\left (99\,\ln \left (3\right )+121\,{\ln \left (3\right )}^2+18\right )}{14641\,{\left (11\,x+6\right )}^3}-\frac {64\,{\mathrm {e}}^{-32}\,\left (11\,\ln \left (3\right )+6\right )}{14641\,\left (11\,x+6\right )}+\frac {2304\,{\mathrm {e}}^{-32}\,{\left (11\,\ln \left (3\right )+3\right )}^2}{14641\,{\left (11\,x+6\right )}^4} \]
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