Integrand size = 168, antiderivative size = 26 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {\log (2)}{-3-x+\left (3+x+\left (\frac {25}{9 x^2}+x\right )^2\right )^2} \] Output:
ln(2)/((3+x+(x+25/9/x^2)^2)^2-3-x)
Leaf count is larger than twice the leaf count of optimal. \(61\) vs. \(2(26)=52\).
Time = 0.02 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561 x^8 \log (2)}{390625+562500 x^3+303750 x^4+101250 x^5+303750 x^6+218700 x^7+112266 x^8+105705 x^9+45927 x^{10}+13122 x^{11}+6561 x^{12}} \] Input:
Integrate[((20503125000*x^7 + 18452812500*x^10 + 7971615000*x^11 + 1992903 750*x^12 + 3985807500*x^13 + 1434890700*x^14 - 693530505*x^16 - 602654094* x^17 - 258280326*x^18 - 172186884*x^19)*Log[2])/(152587890625 + 4394531250 00*x^3 + 237304687500*x^4 + 79101562500*x^5 + 553710937500*x^6 + 512578125 000*x^7 + 293878125000*x^8 + 485810156250*x^9 + 476697656250*x^10 + 330920 437500*x^11 + 328796313750*x^12 + 271477777500*x^13 + 180099450000*x^14 + 137973893400*x^15 + 93382686756*x^16 + 53122842360*x^17 + 31210998489*x^18 + 15525517374*x^19 + 6356565801*x^20 + 2592369198*x^21 + 774840978*x^22 + 172186884*x^23 + 43046721*x^24),x]
Output:
(6561*x^8*Log[2])/(390625 + 562500*x^3 + 303750*x^4 + 101250*x^5 + 303750* x^6 + 218700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 656 1*x^12)
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.
| \(\displaystyle \int \frac {\left (-172186884 x^{19}-258280326 x^{18}-602654094 x^{17}-693530505 x^{16}+1434890700 x^{14}+3985807500 x^{13}+1992903750 x^{12}+7971615000 x^{11}+18452812500 x^{10}+20503125000 x^7\right ) \log (2)}{43046721 x^{24}+172186884 x^{23}+774840978 x^{22}+2592369198 x^{21}+6356565801 x^{20}+15525517374 x^{19}+31210998489 x^{18}+53122842360 x^{17}+93382686756 x^{16}+137973893400 x^{15}+180099450000 x^{14}+271477777500 x^{13}+328796313750 x^{12}+330920437500 x^{11}+476697656250 x^{10}+485810156250 x^9+293878125000 x^8+512578125000 x^7+553710937500 x^6+79101562500 x^5+237304687500 x^4+439453125000 x^3+152587890625} \, dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle \log (2) \int \frac {6561 \left (-26244 x^{19}-39366 x^{18}-91854 x^{17}-105705 x^{16}+218700 x^{14}+607500 x^{13}+303750 x^{12}+1215000 x^{11}+2812500 x^{10}+3125000 x^7\right )}{43046721 x^{24}+172186884 x^{23}+774840978 x^{22}+2592369198 x^{21}+6356565801 x^{20}+15525517374 x^{19}+31210998489 x^{18}+53122842360 x^{17}+93382686756 x^{16}+137973893400 x^{15}+180099450000 x^{14}+271477777500 x^{13}+328796313750 x^{12}+330920437500 x^{11}+476697656250 x^{10}+485810156250 x^9+293878125000 x^8+512578125000 x^7+553710937500 x^6+79101562500 x^5+237304687500 x^4+439453125000 x^3+152587890625}dx\) |
| \(\Big \downarrow \) 27 |
| \(\displaystyle 6561 \log (2) \int \frac {-26244 x^{19}-39366 x^{18}-91854 x^{17}-105705 x^{16}+218700 x^{14}+607500 x^{13}+303750 x^{12}+1215000 x^{11}+2812500 x^{10}+3125000 x^7}{43046721 x^{24}+172186884 x^{23}+774840978 x^{22}+2592369198 x^{21}+6356565801 x^{20}+15525517374 x^{19}+31210998489 x^{18}+53122842360 x^{17}+93382686756 x^{16}+137973893400 x^{15}+180099450000 x^{14}+271477777500 x^{13}+328796313750 x^{12}+330920437500 x^{11}+476697656250 x^{10}+485810156250 x^9+293878125000 x^8+512578125000 x^7+553710937500 x^6+79101562500 x^5+237304687500 x^4+439453125000 x^3+152587890625}dx\) |
| \(\Big \downarrow \) 2462 |
| \(\displaystyle 6561 \log (2) \int \left (\frac {-108 x^7+54 x^6+270 x^5+387 x^4-1686 x^3-111 x^2+6869 x-1003}{27 \left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )}+\frac {-207804366 x^{11}-323436888 x^{10}-280306089 x^9-1454650002 x^8-1434866400 x^7+570172500 x^6-2027936250 x^5-3710323125 x^4+1222781250 x^3+43359375 x^2-2683203125 x+391796875}{27 \left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}\right )dx\) |
| \(\Big \downarrow \) 2009 |
| \(\displaystyle 6561 \log (2) \left (\frac {391796875}{27} \int \frac {1}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx-\frac {2683203125}{27} \int \frac {x}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+\frac {499703125}{3} \int \frac {x^2}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+\frac {1476546250}{9} \int \frac {x^3}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx-\frac {263792500}{3} \int \frac {x^4}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+103050000 \int \frac {x^5}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+170770850 \int \frac {x^6}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+34653432 \int \frac {x^7}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+\frac {78245883}{2} \int \frac {x^8}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+34514298 \int \frac {x^9}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx+2131029 \int \frac {x^{10}}{\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )^2}dx-\frac {1003}{27} \int \frac {1}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx+\frac {6869}{27} \int \frac {x}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx-\frac {37}{9} \int \frac {x^2}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx-\frac {562}{9} \int \frac {x^3}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx+\frac {43}{3} \int \frac {x^4}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx+10 \int \frac {x^5}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx+2 \int \frac {x^6}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx-4 \int \frac {x^7}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625}dx+\frac {47509}{486 \left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^9+112266 x^8+218700 x^7+303750 x^6+101250 x^5+303750 x^4+562500 x^3+390625\right )}\right )\) |
Input:
Int[((20503125000*x^7 + 18452812500*x^10 + 7971615000*x^11 + 1992903750*x^ 12 + 3985807500*x^13 + 1434890700*x^14 - 693530505*x^16 - 602654094*x^17 - 258280326*x^18 - 172186884*x^19)*Log[2])/(152587890625 + 439453125000*x^3 + 237304687500*x^4 + 79101562500*x^5 + 553710937500*x^6 + 512578125000*x^ 7 + 293878125000*x^8 + 485810156250*x^9 + 476697656250*x^10 + 330920437500 *x^11 + 328796313750*x^12 + 271477777500*x^13 + 180099450000*x^14 + 137973 893400*x^15 + 93382686756*x^16 + 53122842360*x^17 + 31210998489*x^18 + 155 25517374*x^19 + 6356565801*x^20 + 2592369198*x^21 + 774840978*x^22 + 17218 6884*x^23 + 43046721*x^24),x]
Output:
$Aborted
Leaf count of result is larger than twice the leaf count of optimal. \(58\) vs. \(2(24)=48\).
Time = 0.15 (sec) , antiderivative size = 59, normalized size of antiderivative = 2.27
| method | result | size |
| default | \(\frac {\ln \left (2\right ) x^{8}}{x^{12}+2 x^{11}+7 x^{10}+\frac {145}{9} x^{9}+\frac {154}{9} x^{8}+\frac {100}{3} x^{7}+\frac {1250}{27} x^{6}+\frac {1250}{81} x^{5}+\frac {1250}{27} x^{4}+\frac {62500}{729} x^{3}+\frac {390625}{6561}}\) | \(59\) |
| risch | \(\frac {\ln \left (2\right ) x^{8}}{x^{12}+2 x^{11}+7 x^{10}+\frac {145}{9} x^{9}+\frac {154}{9} x^{8}+\frac {100}{3} x^{7}+\frac {1250}{27} x^{6}+\frac {1250}{81} x^{5}+\frac {1250}{27} x^{4}+\frac {62500}{729} x^{3}+\frac {390625}{6561}}\) | \(59\) |
| gosper | \(\frac {6561 x^{8} \ln \left (2\right )}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625}\) | \(62\) |
| norman | \(\frac {6561 x^{8} \ln \left (2\right )}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625}\) | \(62\) |
| parallelrisch | \(\frac {6561 x^{8} \ln \left (2\right )}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625}\) | \(62\) |
| orering | \(-\frac {\left (6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625\right ) x \left (-172186884 x^{19}-258280326 x^{18}-602654094 x^{17}-693530505 x^{16}+1434890700 x^{14}+3985807500 x^{13}+1992903750 x^{12}+7971615000 x^{11}+18452812500 x^{10}+20503125000 x^{7}\right ) \ln \left (2\right )}{\left (26244 x^{12}+39366 x^{11}+91854 x^{10}+105705 x^{9}-218700 x^{7}-607500 x^{6}-303750 x^{5}-1215000 x^{4}-2812500 x^{3}-3125000\right ) \left (43046721 x^{24}+172186884 x^{23}+774840978 x^{22}+2592369198 x^{21}+6356565801 x^{20}+15525517374 x^{19}+31210998489 x^{18}+53122842360 x^{17}+93382686756 x^{16}+137973893400 x^{15}+180099450000 x^{14}+271477777500 x^{13}+328796313750 x^{12}+330920437500 x^{11}+476697656250 x^{10}+485810156250 x^{9}+293878125000 x^{8}+512578125000 x^{7}+553710937500 x^{6}+79101562500 x^{5}+237304687500 x^{4}+439453125000 x^{3}+152587890625\right )}\) | \(272\) |
Input:
int((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+14348907 00*x^14+3985807500*x^13+1992903750*x^12+7971615000*x^11+18452812500*x^10+2 0503125000*x^7)*ln(2)/(43046721*x^24+172186884*x^23+774840978*x^22+2592369 198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842360*x^1 7+93382686756*x^16+137973893400*x^15+180099450000*x^14+271477777500*x^13+3 28796313750*x^12+330920437500*x^11+476697656250*x^10+485810156250*x^9+2938 78125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+23730468750 0*x^4+439453125000*x^3+152587890625),x,method=_RETURNVERBOSE)
Output:
ln(2)*x^8/(x^12+2*x^11+7*x^10+145/9*x^9+154/9*x^8+100/3*x^7+1250/27*x^6+12 50/81*x^5+1250/27*x^4+62500/729*x^3+390625/6561)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).
Time = 0.08 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561 \, x^{8} \log \left (2\right )}{6561 \, x^{12} + 13122 \, x^{11} + 45927 \, x^{10} + 105705 \, x^{9} + 112266 \, x^{8} + 218700 \, x^{7} + 303750 \, x^{6} + 101250 \, x^{5} + 303750 \, x^{4} + 562500 \, x^{3} + 390625} \] Input:
integrate((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+14 34890700*x^14+3985807500*x^13+1992903750*x^12+7971615000*x^11+18452812500* x^10+20503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^22+ 2592369198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842 360*x^17+93382686756*x^16+137973893400*x^15+180099450000*x^14+271477777500 *x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+485810156250*x ^9+293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+2373 04687500*x^4+439453125000*x^3+152587890625),x, algorithm="fricas")
Output:
6561*x^8*log(2)/(6561*x^12 + 13122*x^11 + 45927*x^10 + 105705*x^9 + 112266 *x^8 + 218700*x^7 + 303750*x^6 + 101250*x^5 + 303750*x^4 + 562500*x^3 + 39 0625)
Leaf count of result is larger than twice the leaf count of optimal. 60 vs. \(2 (20) = 40\).
Time = 1.80 (sec) , antiderivative size = 60, normalized size of antiderivative = 2.31 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561 x^{8} \log {\left (2 \right )}}{6561 x^{12} + 13122 x^{11} + 45927 x^{10} + 105705 x^{9} + 112266 x^{8} + 218700 x^{7} + 303750 x^{6} + 101250 x^{5} + 303750 x^{4} + 562500 x^{3} + 390625} \] Input:
integrate((-172186884*x**19-258280326*x**18-602654094*x**17-693530505*x**1 6+1434890700*x**14+3985807500*x**13+1992903750*x**12+7971615000*x**11+1845 2812500*x**10+20503125000*x**7)*ln(2)/(43046721*x**24+172186884*x**23+7748 40978*x**22+2592369198*x**21+6356565801*x**20+15525517374*x**19+3121099848 9*x**18+53122842360*x**17+93382686756*x**16+137973893400*x**15+18009945000 0*x**14+271477777500*x**13+328796313750*x**12+330920437500*x**11+476697656 250*x**10+485810156250*x**9+293878125000*x**8+512578125000*x**7+5537109375 00*x**6+79101562500*x**5+237304687500*x**4+439453125000*x**3+152587890625) ,x)
Output:
6561*x**8*log(2)/(6561*x**12 + 13122*x**11 + 45927*x**10 + 105705*x**9 + 1 12266*x**8 + 218700*x**7 + 303750*x**6 + 101250*x**5 + 303750*x**4 + 56250 0*x**3 + 390625)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).
Time = 0.03 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561 \, x^{8} \log \left (2\right )}{6561 \, x^{12} + 13122 \, x^{11} + 45927 \, x^{10} + 105705 \, x^{9} + 112266 \, x^{8} + 218700 \, x^{7} + 303750 \, x^{6} + 101250 \, x^{5} + 303750 \, x^{4} + 562500 \, x^{3} + 390625} \] Input:
integrate((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+14 34890700*x^14+3985807500*x^13+1992903750*x^12+7971615000*x^11+18452812500* x^10+20503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^22+ 2592369198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842 360*x^17+93382686756*x^16+137973893400*x^15+180099450000*x^14+271477777500 *x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+485810156250*x ^9+293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+2373 04687500*x^4+439453125000*x^3+152587890625),x, algorithm="maxima")
Output:
6561*x^8*log(2)/(6561*x^12 + 13122*x^11 + 45927*x^10 + 105705*x^9 + 112266 *x^8 + 218700*x^7 + 303750*x^6 + 101250*x^5 + 303750*x^4 + 562500*x^3 + 39 0625)
Leaf count of result is larger than twice the leaf count of optimal. 61 vs. \(2 (29) = 58\).
Time = 0.14 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561 \, x^{8} \log \left (2\right )}{6561 \, x^{12} + 13122 \, x^{11} + 45927 \, x^{10} + 105705 \, x^{9} + 112266 \, x^{8} + 218700 \, x^{7} + 303750 \, x^{6} + 101250 \, x^{5} + 303750 \, x^{4} + 562500 \, x^{3} + 390625} \] Input:
integrate((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+14 34890700*x^14+3985807500*x^13+1992903750*x^12+7971615000*x^11+18452812500* x^10+20503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^22+ 2592369198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842 360*x^17+93382686756*x^16+137973893400*x^15+180099450000*x^14+271477777500 *x^13+328796313750*x^12+330920437500*x^11+476697656250*x^10+485810156250*x ^9+293878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+2373 04687500*x^4+439453125000*x^3+152587890625),x, algorithm="giac")
Output:
6561*x^8*log(2)/(6561*x^12 + 13122*x^11 + 45927*x^10 + 105705*x^9 + 112266 *x^8 + 218700*x^7 + 303750*x^6 + 101250*x^5 + 303750*x^4 + 562500*x^3 + 39 0625)
Time = 2.29 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561\,x^8\,\ln \left (2\right )}{6561\,x^{12}+13122\,x^{11}+45927\,x^{10}+105705\,x^9+112266\,x^8+218700\,x^7+303750\,x^6+101250\,x^5+303750\,x^4+562500\,x^3+390625} \] Input:
int((log(2)*(20503125000*x^7 + 18452812500*x^10 + 7971615000*x^11 + 199290 3750*x^12 + 3985807500*x^13 + 1434890700*x^14 - 693530505*x^16 - 602654094 *x^17 - 258280326*x^18 - 172186884*x^19))/(439453125000*x^3 + 237304687500 *x^4 + 79101562500*x^5 + 553710937500*x^6 + 512578125000*x^7 + 29387812500 0*x^8 + 485810156250*x^9 + 476697656250*x^10 + 330920437500*x^11 + 3287963 13750*x^12 + 271477777500*x^13 + 180099450000*x^14 + 137973893400*x^15 + 9 3382686756*x^16 + 53122842360*x^17 + 31210998489*x^18 + 15525517374*x^19 + 6356565801*x^20 + 2592369198*x^21 + 774840978*x^22 + 172186884*x^23 + 430 46721*x^24 + 152587890625),x)
Output:
(6561*x^8*log(2))/(562500*x^3 + 303750*x^4 + 101250*x^5 + 303750*x^6 + 218 700*x^7 + 112266*x^8 + 105705*x^9 + 45927*x^10 + 13122*x^11 + 6561*x^12 + 390625)
Time = 0.23 (sec) , antiderivative size = 61, normalized size of antiderivative = 2.35 \[ \int \frac {\left (20503125000 x^7+18452812500 x^{10}+7971615000 x^{11}+1992903750 x^{12}+3985807500 x^{13}+1434890700 x^{14}-693530505 x^{16}-602654094 x^{17}-258280326 x^{18}-172186884 x^{19}\right ) \log (2)}{152587890625+439453125000 x^3+237304687500 x^4+79101562500 x^5+553710937500 x^6+512578125000 x^7+293878125000 x^8+485810156250 x^9+476697656250 x^{10}+330920437500 x^{11}+328796313750 x^{12}+271477777500 x^{13}+180099450000 x^{14}+137973893400 x^{15}+93382686756 x^{16}+53122842360 x^{17}+31210998489 x^{18}+15525517374 x^{19}+6356565801 x^{20}+2592369198 x^{21}+774840978 x^{22}+172186884 x^{23}+43046721 x^{24}} \, dx=\frac {6561 \,\mathrm {log}\left (2\right ) x^{8}}{6561 x^{12}+13122 x^{11}+45927 x^{10}+105705 x^{9}+112266 x^{8}+218700 x^{7}+303750 x^{6}+101250 x^{5}+303750 x^{4}+562500 x^{3}+390625} \] Input:
int((-172186884*x^19-258280326*x^18-602654094*x^17-693530505*x^16+14348907 00*x^14+3985807500*x^13+1992903750*x^12+7971615000*x^11+18452812500*x^10+2 0503125000*x^7)*log(2)/(43046721*x^24+172186884*x^23+774840978*x^22+259236 9198*x^21+6356565801*x^20+15525517374*x^19+31210998489*x^18+53122842360*x^ 17+93382686756*x^16+137973893400*x^15+180099450000*x^14+271477777500*x^13+ 328796313750*x^12+330920437500*x^11+476697656250*x^10+485810156250*x^9+293 878125000*x^8+512578125000*x^7+553710937500*x^6+79101562500*x^5+2373046875 00*x^4+439453125000*x^3+152587890625),x)
Output:
(6561*log(2)*x**8)/(6561*x**12 + 13122*x**11 + 45927*x**10 + 105705*x**9 + 112266*x**8 + 218700*x**7 + 303750*x**6 + 101250*x**5 + 303750*x**4 + 562 500*x**3 + 390625)