Integrand size = 306, antiderivative size = 36 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=\frac {x}{-4-\frac {3}{x}+x-\left (5-x-\frac {x}{4+\frac {\log ^2(16)}{x^2}}\right )^2} \] Output:
x/(x-(5-x/(16*ln(2)^2/x^2+4)-x)^2-4-3/x)
Leaf count is larger than twice the leaf count of optimal. \(99\) vs. \(2(36)=72\).
Time = 0.25 (sec) , antiderivative size = 99, normalized size of antiderivative = 2.75 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=-\frac {x^2 \left (4 x^2+\log ^2(16)\right )^2}{-216 x^6+25 x^7+3 \log ^4(16)+29 x \log ^4(16)+x^4 \left (48-98 \log ^2(16)\right )+x^3 \log ^2(16) \left (232+\log ^2(16)\right )+2 x^5 \left (232+5 \log ^2(16)\right )+x^2 \left (24 \log ^2(16)-11 \log ^4(16)\right )} \] Input:
Integrate[(-1536*x^9 - 7424*x^10 + 400*x^12 + (-1536*x^7 - 7424*x^8 - 320* x^9 + 440*x^10)*Log[16]^2 + (-576*x^5 - 2784*x^6 - 160*x^7 + 157*x^8)*Log[ 16]^4 + (-96*x^3 - 464*x^4 - 20*x^5 + 22*x^6)*Log[16]^6 + (-6*x - 29*x^2 + x^4)*Log[16]^8)/(2304*x^8 + 44544*x^9 + 194560*x^10 - 198048*x^11 + 69856 *x^12 - 10800*x^13 + 625*x^14 + (2304*x^6 + 44544*x^7 + 195520*x^8 - 18900 8*x^9 + 63216*x^10 - 9220*x^11 + 500*x^12)*Log[16]^2 + (864*x^4 + 16704*x^ 5 + 73680*x^6 - 67482*x^7 + 21374*x^8 - 2942*x^9 + 150*x^10)*Log[16]^4 + ( 144*x^2 + 2784*x^3 + 12340*x^4 - 10680*x^5 + 3200*x^6 - 416*x^7 + 20*x^8)* Log[16]^6 + (9 + 174*x + 775*x^2 - 632*x^3 + 179*x^4 - 22*x^5 + x^6)*Log[1 6]^8),x]
Output:
-((x^2*(4*x^2 + Log[16]^2)^2)/(-216*x^6 + 25*x^7 + 3*Log[16]^4 + 29*x*Log[ 16]^4 + x^4*(48 - 98*Log[16]^2) + x^3*Log[16]^2*(232 + Log[16]^2) + 2*x^5* (232 + 5*Log[16]^2) + x^2*(24*Log[16]^2 - 11*Log[16]^4)))
Below are the steps used by Rubi to obtain the solution. The rule number used for the transformation is given above next to the arrow. The rules definitions used are listed below.
| \(\displaystyle \int \frac {400 x^{12}-7424 x^{10}-1536 x^9+\left (x^4-29 x^2-6 x\right ) \log ^8(16)+\left (440 x^{10}-320 x^9-7424 x^8-1536 x^7\right ) \log ^2(16)+\left (157 x^8-160 x^7-2784 x^6-576 x^5\right ) \log ^4(16)+\left (22 x^6-20 x^5-464 x^4-96 x^3\right ) \log ^6(16)}{625 x^{14}-10800 x^{13}+69856 x^{12}-198048 x^{11}+194560 x^{10}+44544 x^9+2304 x^8+\left (x^6-22 x^5+179 x^4-632 x^3+775 x^2+174 x+9\right ) \log ^8(16)+\left (500 x^{12}-9220 x^{11}+63216 x^{10}-189008 x^9+195520 x^8+44544 x^7+2304 x^6\right ) \log ^2(16)+\left (150 x^{10}-2942 x^9+21374 x^8-67482 x^7+73680 x^6+16704 x^5+864 x^4\right ) \log ^4(16)+\left (20 x^8-416 x^7+3200 x^6-10680 x^5+12340 x^4+2784 x^3+144 x^2\right ) \log ^6(16)} \, dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle \int \left (\frac {-156250000 x^5-1350000000 x^4-5864000000 x^3 \left (1+\frac {875 \log ^2(16)}{46912}\right )-24708960000 x^2 \left (1+\frac {14875 \log ^2(16)}{411816}\right )-102057574400 x \left (1+\frac {125 \log ^2(16) \left (1368832+3625 \log ^2(16)\right )}{4082302976}\right )-411920265216 \left (1+\frac {625 \log ^2(16) \left (4001792+24375 \log ^2(16)\right )}{51490033152}\right )}{9765625 \left (-25 x^7+216 x^6-464 x^5 \left (1+\frac {5 \log ^2(16)}{232}\right )-48 x^4 \left (1-\frac {49 \log ^2(16)}{24}\right )-232 x^3 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right )-24 x^2 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right )-29 x \log ^4(16)-3 \log ^4(16)\right )}+\frac {40434032685056 x^6 \left (1-\frac {125 \log ^2(16) \left (-4604686592+15625 \log ^4(16)-35300000 \log ^2(16)\right )}{10108508171264}\right )-196029766631424 x^5 \left (1-\frac {5 \log ^2(16) \left (-948025732096+671875 \log ^4(16)-5311226000 \log ^2(16)\right )}{98014883315712}\right )-19772172730368 x^4 \left (1+\frac {\log ^2(16) \left (-3784345902592+390625 \log ^6(16)-1788100000 \log ^4(16)-234209966400 \log ^2(16)\right )}{4943043182592}\right )-98014883315712 x^3 \log ^2(16) \left (1-\frac {\log ^2(16) \left (-4768179906816+2734375 \log ^4(16)-28650360000 \log ^2(16)\right )}{98014883315712}\right )-9886086365184 x^2 \log ^2(16) \left (1-\frac {\log ^2(16) \left (508555669888+364453125 \log ^4(16)+45222830000 \log ^2(16)\right )}{4943043182592}\right )-12251860414464 x \log ^4(16) \left (1+\frac {625 \log ^2(16) \left (948948224+5803125 \log ^2(16)\right )}{12251860414464}\right )-1235760795648 \log ^4(16) \left (1+\frac {625 \log ^2(16) \left (4001792+24375 \log ^2(16)\right )}{51490033152}\right )}{9765625 \left (-25 x^7+216 x^6-464 x^5 \left (1+\frac {5 \log ^2(16)}{232}\right )-48 x^4 \left (1-\frac {49 \log ^2(16)}{24}\right )-232 x^3 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right )-24 x^2 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right )-29 x \log ^4(16)-3 \log ^4(16)\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle -\frac {4 \log ^4(16) \left (347211271776256+19318164896000 \log ^2(16)+143958593750 \log ^4(16)-56640625 \log ^6(16)\right ) \int \frac {1}{\left (-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )^2}dx}{1708984375}-\frac {\log ^2(16) \left (1940833568882688+1365039331667968 \log ^2(16)+53986859488000 \log ^4(16)+246041796875 \log ^6(16)+171875000 \log ^8(16)\right ) \int \frac {x}{\left (-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )^2}dx}{1708984375}-\frac {2 \log ^2(16) \left (14936075931353088+772869273805184 \log ^2(16)+1681719694000 \log ^4(16)-40023046875 \log ^6(16)-11718750 \log ^8(16)\right ) \int \frac {x^2}{\left (-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )^2}dx}{1708984375}-\frac {\left (7763334275530752+1744513680539648 \log ^2(16)-64698288339200 \log ^4(16)-1906487000000 \log ^6(16)+2583984375 \log ^8(16)\right ) \int \frac {x^3}{\left (-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )^2}dx}{1708984375}-\frac {4 \left (4863354302857216+235704797457920 \log ^2(16)-394090584000 \log ^4(16)-19364750000 \log ^6(16)-5859375 \log ^8(16)\right ) \int \frac {x^4}{\left (-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )^2}dx}{341796875}+\frac {2 \left (9048648599666688+662395940224000 \log ^2(16)+6789877250000 \log ^4(16)-4474609375 \log ^6(16)\right ) \int \frac {x^5}{\left (-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )^2}dx}{1708984375}-\frac {8 \left (51490033152+2501120000 \log ^2(16)+15234375 \log ^4(16)\right ) \int \frac {1}{-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)}dx}{9765625}-\frac {\left (4082302976+171104000 \log ^2(16)+453125 \log ^4(16)\right ) \int \frac {x}{-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)}dx}{390625}-\frac {96 \left (411816+14875 \log ^2(16)\right ) \int \frac {x^2}{-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)}dx}{15625}-\frac {8}{625} \left (46912+875 \log ^2(16)\right ) \int \frac {x^3}{-25 x^7+216 x^6-464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5-48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4-232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3-24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)}dx+\frac {3456}{25} \int \frac {x^4}{25 x^7-216 x^6+464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5+48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4+232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3+24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2+29 \log ^4(16) x+3 \log ^4(16)}dx+16 \int \frac {x^5}{25 x^7-216 x^6+464 \left (1+\frac {5 \log ^2(16)}{232}\right ) x^5+48 \left (1-\frac {49 \log ^2(16)}{24}\right ) x^4+232 \log ^2(16) \left (1+\frac {\log ^2(16)}{232}\right ) x^3+24 \log ^2(16) \left (1-\frac {11 \log ^2(16)}{24}\right ) x^2+29 \log ^4(16) x+3 \log ^4(16)}dx+\frac {4 \left (10108508171264+575585824000 \log ^2(16)+4412500000 \log ^4(16)-1953125 \log ^6(16)\right )}{1708984375 \left (-25 x^7+216 x^6-2 \left (232+5 \log ^2(16)\right ) x^5-2 \left (24-49 \log ^2(16)\right ) x^4-\log ^2(16) \left (232+\log ^2(16)\right ) x^3-\log ^2(16) \left (24-11 \log ^2(16)\right ) x^2-29 \log ^4(16) x-3 \log ^4(16)\right )}\) |
Input:
Int[(-1536*x^9 - 7424*x^10 + 400*x^12 + (-1536*x^7 - 7424*x^8 - 320*x^9 + 440*x^10)*Log[16]^2 + (-576*x^5 - 2784*x^6 - 160*x^7 + 157*x^8)*Log[16]^4 + (-96*x^3 - 464*x^4 - 20*x^5 + 22*x^6)*Log[16]^6 + (-6*x - 29*x^2 + x^4)* Log[16]^8)/(2304*x^8 + 44544*x^9 + 194560*x^10 - 198048*x^11 + 69856*x^12 - 10800*x^13 + 625*x^14 + (2304*x^6 + 44544*x^7 + 195520*x^8 - 189008*x^9 + 63216*x^10 - 9220*x^11 + 500*x^12)*Log[16]^2 + (864*x^4 + 16704*x^5 + 73 680*x^6 - 67482*x^7 + 21374*x^8 - 2942*x^9 + 150*x^10)*Log[16]^4 + (144*x^ 2 + 2784*x^3 + 12340*x^4 - 10680*x^5 + 3200*x^6 - 416*x^7 + 20*x^8)*Log[16 ]^6 + (9 + 174*x + 775*x^2 - 632*x^3 + 179*x^4 - 22*x^5 + x^6)*Log[16]^8), x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(114\) vs. \(2(37)=74\).
Time = 0.81 (sec) , antiderivative size = 115, normalized size of antiderivative = 3.19
| method | result | size |
| gosper | \(-\frac {16 x^{2} \left (16 \ln \left (2\right )^{4}+8 x^{2} \ln \left (2\right )^{2}+x^{4}\right )}{256 \ln \left (2\right )^{4} x^{3}+160 x^{5} \ln \left (2\right )^{2}+25 x^{7}-2816 x^{2} \ln \left (2\right )^{4}-1568 x^{4} \ln \left (2\right )^{2}-216 x^{6}+7424 \ln \left (2\right )^{4} x +3712 x^{3} \ln \left (2\right )^{2}+464 x^{5}+768 \ln \left (2\right )^{4}+384 x^{2} \ln \left (2\right )^{2}+48 x^{4}}\) | \(115\) |
| risch | \(\frac {-x^{2} \ln \left (2\right )^{4}-\frac {x^{4} \ln \left (2\right )^{2}}{2}-\frac {x^{6}}{16}}{\ln \left (2\right )^{4} x^{3}+\frac {5 x^{5} \ln \left (2\right )^{2}}{8}+\frac {25 x^{7}}{256}-11 x^{2} \ln \left (2\right )^{4}-\frac {49 x^{4} \ln \left (2\right )^{2}}{8}-\frac {27 x^{6}}{32}+29 \ln \left (2\right )^{4} x +\frac {29 x^{3} \ln \left (2\right )^{2}}{2}+\frac {29 x^{5}}{16}+3 \ln \left (2\right )^{4}+\frac {3 x^{2} \ln \left (2\right )^{2}}{2}+\frac {3 x^{4}}{16}}\) | \(115\) |
| default | \(\frac {-x^{2} \ln \left (2\right )^{4}-\frac {x^{4} \ln \left (2\right )^{2}}{2}-\frac {x^{6}}{16}}{\ln \left (2\right )^{4} x^{3}+\frac {5 x^{5} \ln \left (2\right )^{2}}{8}+\frac {25 x^{7}}{256}-11 x^{2} \ln \left (2\right )^{4}-\frac {49 x^{4} \ln \left (2\right )^{2}}{8}-\frac {27 x^{6}}{32}+29 \ln \left (2\right )^{4} x +\frac {29 x^{3} \ln \left (2\right )^{2}}{2}+\frac {29 x^{5}}{16}+3 \ln \left (2\right )^{4}+\frac {3 x^{2} \ln \left (2\right )^{2}}{2}+\frac {3 x^{4}}{16}}\) | \(116\) |
| norman | \(\frac {-16 x^{6}-128 x^{4} \ln \left (2\right )^{2}-256 x^{2} \ln \left (2\right )^{4}}{256 \ln \left (2\right )^{4} x^{3}+160 x^{5} \ln \left (2\right )^{2}+25 x^{7}-2816 x^{2} \ln \left (2\right )^{4}-1568 x^{4} \ln \left (2\right )^{2}-216 x^{6}+7424 \ln \left (2\right )^{4} x +3712 x^{3} \ln \left (2\right )^{2}+464 x^{5}+768 \ln \left (2\right )^{4}+384 x^{2} \ln \left (2\right )^{2}+48 x^{4}}\) | \(116\) |
| parallelrisch | \(\frac {-6400 x^{2} \ln \left (2\right )^{4}-3200 x^{4} \ln \left (2\right )^{2}-400 x^{6}}{6400 \ln \left (2\right )^{4} x^{3}+4000 x^{5} \ln \left (2\right )^{2}+625 x^{7}-70400 x^{2} \ln \left (2\right )^{4}-39200 x^{4} \ln \left (2\right )^{2}-5400 x^{6}+185600 \ln \left (2\right )^{4} x +92800 x^{3} \ln \left (2\right )^{2}+11600 x^{5}+19200 \ln \left (2\right )^{4}+9600 x^{2} \ln \left (2\right )^{2}+1200 x^{4}}\) | \(117\) |
Input:
int((65536*(x^4-29*x^2-6*x)*ln(2)^8+4096*(22*x^6-20*x^5-464*x^4-96*x^3)*ln (2)^6+256*(157*x^8-160*x^7-2784*x^6-576*x^5)*ln(2)^4+16*(440*x^10-320*x^9- 7424*x^8-1536*x^7)*ln(2)^2+400*x^12-7424*x^10-1536*x^9)/(65536*(x^6-22*x^5 +179*x^4-632*x^3+775*x^2+174*x+9)*ln(2)^8+4096*(20*x^8-416*x^7+3200*x^6-10 680*x^5+12340*x^4+2784*x^3+144*x^2)*ln(2)^6+256*(150*x^10-2942*x^9+21374*x ^8-67482*x^7+73680*x^6+16704*x^5+864*x^4)*ln(2)^4+16*(500*x^12-9220*x^11+6 3216*x^10-189008*x^9+195520*x^8+44544*x^7+2304*x^6)*ln(2)^2+625*x^14-10800 *x^13+69856*x^12-198048*x^11+194560*x^10+44544*x^9+2304*x^8),x,method=_RET URNVERBOSE)
Output:
-16*x^2*(16*ln(2)^4+8*x^2*ln(2)^2+x^4)/(256*ln(2)^4*x^3+160*x^5*ln(2)^2+25 *x^7-2816*x^2*ln(2)^4-1568*x^4*ln(2)^2-216*x^6+7424*ln(2)^4*x+3712*x^3*ln( 2)^2+464*x^5+768*ln(2)^4+384*x^2*ln(2)^2+48*x^4)
Leaf count of result is larger than twice the leaf count of optimal. 93 vs. \(2 (37) = 74\).
Time = 0.12 (sec) , antiderivative size = 93, normalized size of antiderivative = 2.58 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=-\frac {16 \, {\left (x^{6} + 8 \, x^{4} \log \left (2\right )^{2} + 16 \, x^{2} \log \left (2\right )^{4}\right )}}{25 \, x^{7} - 216 \, x^{6} + 464 \, x^{5} + 256 \, {\left (x^{3} - 11 \, x^{2} + 29 \, x + 3\right )} \log \left (2\right )^{4} + 48 \, x^{4} + 32 \, {\left (5 \, x^{5} - 49 \, x^{4} + 116 \, x^{3} + 12 \, x^{2}\right )} \log \left (2\right )^{2}} \] Input:
integrate((65536*(x^4-29*x^2-6*x)*log(2)^8+4096*(22*x^6-20*x^5-464*x^4-96* x^3)*log(2)^6+256*(157*x^8-160*x^7-2784*x^6-576*x^5)*log(2)^4+16*(440*x^10 -320*x^9-7424*x^8-1536*x^7)*log(2)^2+400*x^12-7424*x^10-1536*x^9)/(65536*( x^6-22*x^5+179*x^4-632*x^3+775*x^2+174*x+9)*log(2)^8+4096*(20*x^8-416*x^7+ 3200*x^6-10680*x^5+12340*x^4+2784*x^3+144*x^2)*log(2)^6+256*(150*x^10-2942 *x^9+21374*x^8-67482*x^7+73680*x^6+16704*x^5+864*x^4)*log(2)^4+16*(500*x^1 2-9220*x^11+63216*x^10-189008*x^9+195520*x^8+44544*x^7+2304*x^6)*log(2)^2+ 625*x^14-10800*x^13+69856*x^12-198048*x^11+194560*x^10+44544*x^9+2304*x^8) ,x, algorithm="fricas")
Output:
-16*(x^6 + 8*x^4*log(2)^2 + 16*x^2*log(2)^4)/(25*x^7 - 216*x^6 + 464*x^5 + 256*(x^3 - 11*x^2 + 29*x + 3)*log(2)^4 + 48*x^4 + 32*(5*x^5 - 49*x^4 + 11 6*x^3 + 12*x^2)*log(2)^2)
Leaf count of result is larger than twice the leaf count of optimal. 109 vs. \(2 (26) = 52\).
Time = 25.30 (sec) , antiderivative size = 109, normalized size of antiderivative = 3.03 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=\frac {- 16 x^{6} - 128 x^{4} \log {\left (2 \right )}^{2} - 256 x^{2} \log {\left (2 \right )}^{4}}{25 x^{7} - 216 x^{6} + x^{5} \cdot \left (160 \log {\left (2 \right )}^{2} + 464\right ) + x^{4} \cdot \left (48 - 1568 \log {\left (2 \right )}^{2}\right ) + x^{3} \cdot \left (256 \log {\left (2 \right )}^{4} + 3712 \log {\left (2 \right )}^{2}\right ) + x^{2} \left (- 2816 \log {\left (2 \right )}^{4} + 384 \log {\left (2 \right )}^{2}\right ) + 7424 x \log {\left (2 \right )}^{4} + 768 \log {\left (2 \right )}^{4}} \] Input:
integrate((65536*(x**4-29*x**2-6*x)*ln(2)**8+4096*(22*x**6-20*x**5-464*x** 4-96*x**3)*ln(2)**6+256*(157*x**8-160*x**7-2784*x**6-576*x**5)*ln(2)**4+16 *(440*x**10-320*x**9-7424*x**8-1536*x**7)*ln(2)**2+400*x**12-7424*x**10-15 36*x**9)/(65536*(x**6-22*x**5+179*x**4-632*x**3+775*x**2+174*x+9)*ln(2)**8 +4096*(20*x**8-416*x**7+3200*x**6-10680*x**5+12340*x**4+2784*x**3+144*x**2 )*ln(2)**6+256*(150*x**10-2942*x**9+21374*x**8-67482*x**7+73680*x**6+16704 *x**5+864*x**4)*ln(2)**4+16*(500*x**12-9220*x**11+63216*x**10-189008*x**9+ 195520*x**8+44544*x**7+2304*x**6)*ln(2)**2+625*x**14-10800*x**13+69856*x** 12-198048*x**11+194560*x**10+44544*x**9+2304*x**8),x)
Output:
(-16*x**6 - 128*x**4*log(2)**2 - 256*x**2*log(2)**4)/(25*x**7 - 216*x**6 + x**5*(160*log(2)**2 + 464) + x**4*(48 - 1568*log(2)**2) + x**3*(256*log(2 )**4 + 3712*log(2)**2) + x**2*(-2816*log(2)**4 + 384*log(2)**2) + 7424*x*l og(2)**4 + 768*log(2)**4)
Leaf count of result is larger than twice the leaf count of optimal. 112 vs. \(2 (37) = 74\).
Time = 0.06 (sec) , antiderivative size = 112, normalized size of antiderivative = 3.11 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=-\frac {16 \, {\left (x^{6} + 8 \, x^{4} \log \left (2\right )^{2} + 16 \, x^{2} \log \left (2\right )^{4}\right )}}{25 \, x^{7} + 16 \, {\left (10 \, \log \left (2\right )^{2} + 29\right )} x^{5} - 216 \, x^{6} - 16 \, {\left (98 \, \log \left (2\right )^{2} - 3\right )} x^{4} + 7424 \, x \log \left (2\right )^{4} + 128 \, {\left (2 \, \log \left (2\right )^{4} + 29 \, \log \left (2\right )^{2}\right )} x^{3} + 768 \, \log \left (2\right )^{4} - 128 \, {\left (22 \, \log \left (2\right )^{4} - 3 \, \log \left (2\right )^{2}\right )} x^{2}} \] Input:
integrate((65536*(x^4-29*x^2-6*x)*log(2)^8+4096*(22*x^6-20*x^5-464*x^4-96* x^3)*log(2)^6+256*(157*x^8-160*x^7-2784*x^6-576*x^5)*log(2)^4+16*(440*x^10 -320*x^9-7424*x^8-1536*x^7)*log(2)^2+400*x^12-7424*x^10-1536*x^9)/(65536*( x^6-22*x^5+179*x^4-632*x^3+775*x^2+174*x+9)*log(2)^8+4096*(20*x^8-416*x^7+ 3200*x^6-10680*x^5+12340*x^4+2784*x^3+144*x^2)*log(2)^6+256*(150*x^10-2942 *x^9+21374*x^8-67482*x^7+73680*x^6+16704*x^5+864*x^4)*log(2)^4+16*(500*x^1 2-9220*x^11+63216*x^10-189008*x^9+195520*x^8+44544*x^7+2304*x^6)*log(2)^2+ 625*x^14-10800*x^13+69856*x^12-198048*x^11+194560*x^10+44544*x^9+2304*x^8) ,x, algorithm="maxima")
Output:
-16*(x^6 + 8*x^4*log(2)^2 + 16*x^2*log(2)^4)/(25*x^7 + 16*(10*log(2)^2 + 2 9)*x^5 - 216*x^6 - 16*(98*log(2)^2 - 3)*x^4 + 7424*x*log(2)^4 + 128*(2*log (2)^4 + 29*log(2)^2)*x^3 + 768*log(2)^4 - 128*(22*log(2)^4 - 3*log(2)^2)*x ^2)
Leaf count of result is larger than twice the leaf count of optimal. 114 vs. \(2 (37) = 74\).
Time = 0.53 (sec) , antiderivative size = 114, normalized size of antiderivative = 3.17 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=-\frac {16 \, {\left (x^{6} + 8 \, x^{4} \log \left (2\right )^{2} + 16 \, x^{2} \log \left (2\right )^{4}\right )}}{25 \, x^{7} + 160 \, x^{5} \log \left (2\right )^{2} + 256 \, x^{3} \log \left (2\right )^{4} - 216 \, x^{6} - 1568 \, x^{4} \log \left (2\right )^{2} - 2816 \, x^{2} \log \left (2\right )^{4} + 464 \, x^{5} + 3712 \, x^{3} \log \left (2\right )^{2} + 7424 \, x \log \left (2\right )^{4} + 48 \, x^{4} + 384 \, x^{2} \log \left (2\right )^{2} + 768 \, \log \left (2\right )^{4}} \] Input:
integrate((65536*(x^4-29*x^2-6*x)*log(2)^8+4096*(22*x^6-20*x^5-464*x^4-96* x^3)*log(2)^6+256*(157*x^8-160*x^7-2784*x^6-576*x^5)*log(2)^4+16*(440*x^10 -320*x^9-7424*x^8-1536*x^7)*log(2)^2+400*x^12-7424*x^10-1536*x^9)/(65536*( x^6-22*x^5+179*x^4-632*x^3+775*x^2+174*x+9)*log(2)^8+4096*(20*x^8-416*x^7+ 3200*x^6-10680*x^5+12340*x^4+2784*x^3+144*x^2)*log(2)^6+256*(150*x^10-2942 *x^9+21374*x^8-67482*x^7+73680*x^6+16704*x^5+864*x^4)*log(2)^4+16*(500*x^1 2-9220*x^11+63216*x^10-189008*x^9+195520*x^8+44544*x^7+2304*x^6)*log(2)^2+ 625*x^14-10800*x^13+69856*x^12-198048*x^11+194560*x^10+44544*x^9+2304*x^8) ,x, algorithm="giac")
Output:
-16*(x^6 + 8*x^4*log(2)^2 + 16*x^2*log(2)^4)/(25*x^7 + 160*x^5*log(2)^2 + 256*x^3*log(2)^4 - 216*x^6 - 1568*x^4*log(2)^2 - 2816*x^2*log(2)^4 + 464*x ^5 + 3712*x^3*log(2)^2 + 7424*x*log(2)^4 + 48*x^4 + 384*x^2*log(2)^2 + 768 *log(2)^4)
Time = 0.61 (sec) , antiderivative size = 102, normalized size of antiderivative = 2.83 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=-\frac {16\,x^2\,{\left (x^2+4\,{\ln \left (2\right )}^2\right )}^2}{25\,x^7-216\,x^6+\left (160\,{\ln \left (2\right )}^2+464\right )\,x^5+\left (48-1568\,{\ln \left (2\right )}^2\right )\,x^4+\left (3712\,{\ln \left (2\right )}^2+256\,{\ln \left (2\right )}^4\right )\,x^3+\left (384\,{\ln \left (2\right )}^2-2816\,{\ln \left (2\right )}^4\right )\,x^2+7424\,{\ln \left (2\right )}^4\,x+768\,{\ln \left (2\right )}^4} \] Input:
int(-(4096*log(2)^6*(96*x^3 + 464*x^4 + 20*x^5 - 22*x^6) + 256*log(2)^4*(5 76*x^5 + 2784*x^6 + 160*x^7 - 157*x^8) + 16*log(2)^2*(1536*x^7 + 7424*x^8 + 320*x^9 - 440*x^10) + 65536*log(2)^8*(6*x + 29*x^2 - x^4) + 1536*x^9 + 7 424*x^10 - 400*x^12)/(4096*log(2)^6*(144*x^2 + 2784*x^3 + 12340*x^4 - 1068 0*x^5 + 3200*x^6 - 416*x^7 + 20*x^8) + 256*log(2)^4*(864*x^4 + 16704*x^5 + 73680*x^6 - 67482*x^7 + 21374*x^8 - 2942*x^9 + 150*x^10) + 16*log(2)^2*(2 304*x^6 + 44544*x^7 + 195520*x^8 - 189008*x^9 + 63216*x^10 - 9220*x^11 + 5 00*x^12) + 65536*log(2)^8*(174*x + 775*x^2 - 632*x^3 + 179*x^4 - 22*x^5 + x^6 + 9) + 2304*x^8 + 44544*x^9 + 194560*x^10 - 198048*x^11 + 69856*x^12 - 10800*x^13 + 625*x^14),x)
Output:
-(16*x^2*(4*log(2)^2 + x^2)^2)/(7424*x*log(2)^4 + x^5*(160*log(2)^2 + 464) - x^4*(1568*log(2)^2 - 48) + 768*log(2)^4 - 216*x^6 + 25*x^7 + x^2*(384*l og(2)^2 - 2816*log(2)^4) + x^3*(3712*log(2)^2 + 256*log(2)^4))
Time = 0.17 (sec) , antiderivative size = 175, normalized size of antiderivative = 4.86 \[ \int \frac {-1536 x^9-7424 x^{10}+400 x^{12}+\left (-1536 x^7-7424 x^8-320 x^9+440 x^{10}\right ) \log ^2(16)+\left (-576 x^5-2784 x^6-160 x^7+157 x^8\right ) \log ^4(16)+\left (-96 x^3-464 x^4-20 x^5+22 x^6\right ) \log ^6(16)+\left (-6 x-29 x^2+x^4\right ) \log ^8(16)}{2304 x^8+44544 x^9+194560 x^{10}-198048 x^{11}+69856 x^{12}-10800 x^{13}+625 x^{14}+\left (2304 x^6+44544 x^7+195520 x^8-189008 x^9+63216 x^{10}-9220 x^{11}+500 x^{12}\right ) \log ^2(16)+\left (864 x^4+16704 x^5+73680 x^6-67482 x^7+21374 x^8-2942 x^9+150 x^{10}\right ) \log ^4(16)+\left (144 x^2+2784 x^3+12340 x^4-10680 x^5+3200 x^6-416 x^7+20 x^8\right ) \log ^6(16)+\left (9+174 x+775 x^2-632 x^3+179 x^4-22 x^5+x^6\right ) \log ^8(16)} \, dx=\frac {-512 \mathrm {log}\left (2\right )^{4} x^{3}-1280 \mathrm {log}\left (2\right )^{4} x^{2}-14848 \mathrm {log}\left (2\right )^{4} x -1536 \mathrm {log}\left (2\right )^{4}-320 \mathrm {log}\left (2\right )^{2} x^{5}-320 \mathrm {log}\left (2\right )^{2} x^{4}-7424 \mathrm {log}\left (2\right )^{2} x^{3}-768 \mathrm {log}\left (2\right )^{2} x^{2}-50 x^{7}-928 x^{5}-96 x^{4}}{6912 \mathrm {log}\left (2\right )^{4} x^{3}-76032 \mathrm {log}\left (2\right )^{4} x^{2}+200448 \mathrm {log}\left (2\right )^{4} x +20736 \mathrm {log}\left (2\right )^{4}+4320 \mathrm {log}\left (2\right )^{2} x^{5}-42336 \mathrm {log}\left (2\right )^{2} x^{4}+100224 \mathrm {log}\left (2\right )^{2} x^{3}+10368 \mathrm {log}\left (2\right )^{2} x^{2}+675 x^{7}-5832 x^{6}+12528 x^{5}+1296 x^{4}} \] Input:
int((65536*(x^4-29*x^2-6*x)*log(2)^8+4096*(22*x^6-20*x^5-464*x^4-96*x^3)*l og(2)^6+256*(157*x^8-160*x^7-2784*x^6-576*x^5)*log(2)^4+16*(440*x^10-320*x ^9-7424*x^8-1536*x^7)*log(2)^2+400*x^12-7424*x^10-1536*x^9)/(65536*(x^6-22 *x^5+179*x^4-632*x^3+775*x^2+174*x+9)*log(2)^8+4096*(20*x^8-416*x^7+3200*x ^6-10680*x^5+12340*x^4+2784*x^3+144*x^2)*log(2)^6+256*(150*x^10-2942*x^9+2 1374*x^8-67482*x^7+73680*x^6+16704*x^5+864*x^4)*log(2)^4+16*(500*x^12-9220 *x^11+63216*x^10-189008*x^9+195520*x^8+44544*x^7+2304*x^6)*log(2)^2+625*x^ 14-10800*x^13+69856*x^12-198048*x^11+194560*x^10+44544*x^9+2304*x^8),x)
Output:
(2*( - 256*log(2)**4*x**3 - 640*log(2)**4*x**2 - 7424*log(2)**4*x - 768*lo g(2)**4 - 160*log(2)**2*x**5 - 160*log(2)**2*x**4 - 3712*log(2)**2*x**3 - 384*log(2)**2*x**2 - 25*x**7 - 464*x**5 - 48*x**4))/(27*(256*log(2)**4*x** 3 - 2816*log(2)**4*x**2 + 7424*log(2)**4*x + 768*log(2)**4 + 160*log(2)**2 *x**5 - 1568*log(2)**2*x**4 + 3712*log(2)**2*x**3 + 384*log(2)**2*x**2 + 2 5*x**7 - 216*x**6 + 464*x**5 + 48*x**4))