3.61.75 \(\int \frac {10251562500+655560624846 x+956153602500 x^2+537220650631 x^3+421106423750 x^4+300666345007 x^5+66719025000 x^6+19129907088 x^7+11418525000 x^8+2315325870 x^9+309318750 x^{10}+199763982 x^{11}+32805000 x^{12}+1653372 x^{13}+1822500 x^{14}+157464 x^{15}+6561 x^{17}+(10251562500+105583541256 x+50497830000 x^2+249324860016 x^3+101333160000 x^4+109725878352 x^5+54772425000 x^6+19766210568 x^7+9979237500 x^8+3136702320 x^9+576450000 x^{10}+279578952 x^{11}+65610000 x^{12}+4408992 x^{13}+3645000 x^{14}+419904 x^{15}+17496 x^{17}) \log (x)+(3417187500+13317516882 x+23856525000 x^2+45764940852 x^3+33720862500 x^4+27268993494 x^5+16890562500 x^6+8088703996 x^7+3671500000 x^8+1634486040 x^9+452250000 x^{10}+157425444 x^{11}+54675000 x^{12}+5143824 x^{13}+3037500 x^{14}+489888 x^{15}+20412 x^{17}) \log ^2(x)+(379687500+89282088 x+5287275000 x^2+2516210568 x^3+6271425000 x^4+3315266496 x^5+3215250000 x^6+1703927664 x^7+958687500 x^8+414657360 x^9+191625000 x^{10}+48700296 x^{11}+24300000 x^{12}+3429216 x^{13}+1350000 x^{14}+326592 x^{15}+13608 x^{17}) \log ^3(x)+(37200870 x+562443750 x^2+289046070 x^3+829575000 x^4+368861040 x^5+536625000 x^6+203719860 x^7+201000000 x^8+60273900 x^9+46343750 x^{10}+10916790 x^{11}+6075000 x^{12}+1428840 x^{13}+337500 x^{14}+136080 x^{15}+5670 x^{17}) \log ^4(x)+(9920232 x+32805000 x^2+26453952 x^3+65610000 x^4+30862944 x^5+54675000 x^6+20575296 x^7+24300000 x^8+8573040 x^9+6075000 x^{10}+2286144 x^{11}+810000 x^{12}+381024 x^{13}+45000 x^{14}+36288 x^{15}+1512 x^{17}) \log ^5(x)+(1653372 x+1822500 x^2+4408992 x^3+3645000 x^4+5143824 x^5+3037500 x^6+3429216 x^7+1350000 x^8+1428840 x^9+337500 x^{10}+381024 x^{11}+45000 x^{12}+63504 x^{13}+2500 x^{14}+6048 x^{15}+252 x^{17}) \log ^6(x)+(157464 x+419904 x^3+489888 x^5+326592 x^7+136080 x^9+36288 x^{11}+6048 x^{13}+576 x^{15}+24 x^{17}) \log ^7(x)+(6561 x+17496 x^3+20412 x^5+13608 x^7+5670 x^9+1512 x^{11}+252 x^{13}+24 x^{15}+x^{17}) \log ^8(x)}{43046721 x+6454383750 x^2+247181588131 x^3+393768923750 x^4+225959313757 x^5+58365900000 x^6+19129907088 x^7+10532587500 x^8+2315325870 x^9+309318750 x^{10}+199763982 x^{11}+32805000 x^{12}+1653372 x^{13}+1822500 x^{14}+157464 x^{15}+6561 x^{17}+(114791256 x+9491580000 x^2+73543610016 x^3+67161285000 x^4+62850878352 x^5+44141175000 x^6+19766210568 x^7+8840175000 x^8+3136702320 x^9+576450000 x^{10}+279578952 x^{11}+65610000 x^{12}+4408992 x^{13}+3645000 x^{14}+419904 x^{15}+17496 x^{17}) \log (x)+(133923132 x+5631525000 x^2+19397753352 x^3+17773987500 x^4+19944774744 x^5+11828062500 x^6+8088703996 x^7+3123062500 x^8+1634486040 x^9+452250000 x^{10}+157425444 x^{11}+54675000 x^{12}+5143824 x^{13}+3037500 x^{14}+489888 x^{15}+20412 x^{17}) \log ^2(x)+(89282088 x+1743525000 x^2+2516210568 x^3+2980800000 x^4+3315266496 x^5+2146500000 x^6+1703927664 x^7+841500000 x^8+414657360 x^9+191625000 x^{10}+48700296 x^{11}+24300000 x^{12}+3429216 x^{13}+1350000 x^{14}+326592 x^{15}+13608 x^{17}) \log ^3(x)+(37200870 x+309318750 x^2+289046070 x^3+576450000 x^4+368861040 x^5+452250000 x^6+203719860 x^7+191625000 x^8+60273900 x^9+46343750 x^{10}+10916790 x^{11}+6075000 x^{12}+1428840 x^{13}+337500 x^{14}+136080 x^{15}+5670 x^{17}) \log ^4(x)+(9920232 x+32805000 x^2+26453952 x^3+65610000 x^4+30862944 x^5+54675000 x^6+20575296 x^7+24300000 x^8+8573040 x^9+6075000 x^{10}+2286144 x^{11}+810000 x^{12}+381024 x^{13}+45000 x^{14}+36288 x^{15}+1512 x^{17}) \log ^5(x)+(1653372 x+1822500 x^2+4408992 x^3+3645000 x^4+5143824 x^5+3037500 x^6+3429216 x^7+1350000 x^8+1428840 x^9+337500 x^{10}+381024 x^{11}+45000 x^{12}+63504 x^{13}+2500 x^{14}+6048 x^{15}+252 x^{17}) \log ^6(x)+(157464 x+419904 x^3+489888 x^5+326592 x^7+136080 x^9+36288 x^{11}+6048 x^{13}+576 x^{15}+24 x^{17}) \log ^7(x)+(6561 x+17496 x^3+20412 x^5+13608 x^7+5670 x^9+1512 x^{11}+252 x^{13}+24 x^{15}+x^{17}) \log ^8(x)} \, dx\)
Optimal. Leaf size=29 \[ x-\frac {3}{x+\left (x+\frac {1}{625} \left (3+x^2\right )^2 (3+\log (x))^2\right )^2} \]
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Rubi [F] time = 180.00, antiderivative size = 0, normalized size of antiderivative = 0.00,
number of steps used = 0, number of rules used = 0, integrand size = 0, \(\frac {\text {number of rules}}{\text {integrand size}}\) = 0.000, Rules used =
{} \begin {gather*} \text {\$Aborted} \end {gather*}
Verification is not applicable to the result.
[In]
Int[(10251562500 + 655560624846*x + 956153602500*x^2 + 537220650631*x^3 + 421106423750*x^4 + 300666345007*x^5
+ 66719025000*x^6 + 19129907088*x^7 + 11418525000*x^8 + 2315325870*x^9 + 309318750*x^10 + 199763982*x^11 + 328
05000*x^12 + 1653372*x^13 + 1822500*x^14 + 157464*x^15 + 6561*x^17 + (10251562500 + 105583541256*x + 504978300
00*x^2 + 249324860016*x^3 + 101333160000*x^4 + 109725878352*x^5 + 54772425000*x^6 + 19766210568*x^7 + 99792375
00*x^8 + 3136702320*x^9 + 576450000*x^10 + 279578952*x^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 4199
04*x^15 + 17496*x^17)*Log[x] + (3417187500 + 13317516882*x + 23856525000*x^2 + 45764940852*x^3 + 33720862500*x
^4 + 27268993494*x^5 + 16890562500*x^6 + 8088703996*x^7 + 3671500000*x^8 + 1634486040*x^9 + 452250000*x^10 + 1
57425444*x^11 + 54675000*x^12 + 5143824*x^13 + 3037500*x^14 + 489888*x^15 + 20412*x^17)*Log[x]^2 + (379687500
+ 89282088*x + 5287275000*x^2 + 2516210568*x^3 + 6271425000*x^4 + 3315266496*x^5 + 3215250000*x^6 + 1703927664
*x^7 + 958687500*x^8 + 414657360*x^9 + 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000
*x^14 + 326592*x^15 + 13608*x^17)*Log[x]^3 + (37200870*x + 562443750*x^2 + 289046070*x^3 + 829575000*x^4 + 368
861040*x^5 + 536625000*x^6 + 203719860*x^7 + 201000000*x^8 + 60273900*x^9 + 46343750*x^10 + 10916790*x^11 + 60
75000*x^12 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17)*Log[x]^4 + (9920232*x + 32805000*x^2 + 2645
3952*x^3 + 65610000*x^4 + 30862944*x^5 + 54675000*x^6 + 20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075000*x^
10 + 2286144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x^14 + 36288*x^15 + 1512*x^17)*Log[x]^5 + (1653372*x + 1
822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*x^7 + 1350000*x^8 + 1428840*x^9 +
337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048*x^15 + 252*x^17)*Log[x]^6 + (157464*x
+ 419904*x^3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13 + 576*x^15 + 24*x^17)*Log[x]^7 +
(6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 252*x^13 + 24*x^15 + x^17)*Log[x]^8)/(430
46721*x + 6454383750*x^2 + 247181588131*x^3 + 393768923750*x^4 + 225959313757*x^5 + 58365900000*x^6 + 19129907
088*x^7 + 10532587500*x^8 + 2315325870*x^9 + 309318750*x^10 + 199763982*x^11 + 32805000*x^12 + 1653372*x^13 +
1822500*x^14 + 157464*x^15 + 6561*x^17 + (114791256*x + 9491580000*x^2 + 73543610016*x^3 + 67161285000*x^4 + 6
2850878352*x^5 + 44141175000*x^6 + 19766210568*x^7 + 8840175000*x^8 + 3136702320*x^9 + 576450000*x^10 + 279578
952*x^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17)*Log[x] + (133923132*x + 563
1525000*x^2 + 19397753352*x^3 + 17773987500*x^4 + 19944774744*x^5 + 11828062500*x^6 + 8088703996*x^7 + 3123062
500*x^8 + 1634486040*x^9 + 452250000*x^10 + 157425444*x^11 + 54675000*x^12 + 5143824*x^13 + 3037500*x^14 + 489
888*x^15 + 20412*x^17)*Log[x]^2 + (89282088*x + 1743525000*x^2 + 2516210568*x^3 + 2980800000*x^4 + 3315266496*
x^5 + 2146500000*x^6 + 1703927664*x^7 + 841500000*x^8 + 414657360*x^9 + 191625000*x^10 + 48700296*x^11 + 24300
000*x^12 + 3429216*x^13 + 1350000*x^14 + 326592*x^15 + 13608*x^17)*Log[x]^3 + (37200870*x + 309318750*x^2 + 28
9046070*x^3 + 576450000*x^4 + 368861040*x^5 + 452250000*x^6 + 203719860*x^7 + 191625000*x^8 + 60273900*x^9 + 4
6343750*x^10 + 10916790*x^11 + 6075000*x^12 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17)*Log[x]^4 +
(9920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54675000*x^6 + 20575296*x^7 + 243000
00*x^8 + 8573040*x^9 + 6075000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x^14 + 36288*x^15 + 151
2*x^17)*Log[x]^5 + (1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*
x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048*x^15
+ 252*x^17)*Log[x]^6 + (157464*x + 419904*x^3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13
+ 576*x^15 + 24*x^17)*Log[x]^7 + (6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 252*x^13
+ 24*x^15 + x^17)*Log[x]^8),x]
[Out]
$Aborted
Rubi steps
Aborted
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Mathematica [B] time = 0.82, size = 242, normalized size = 8.34 \begin {gather*} x-\frac {1171875}{6561+491875 x+399373 x^2+67500 x^3+4374 x^4+11250 x^5+972 x^6+81 x^8+8748 \log (x)+67500 x \log (x)+11664 x^2 \log (x)+45000 x^3 \log (x)+5832 x^4 \log (x)+7500 x^5 \log (x)+1296 x^6 \log (x)+108 x^8 \log (x)+4374 \log ^2(x)+11250 x \log ^2(x)+5832 x^2 \log ^2(x)+7500 x^3 \log ^2(x)+2916 x^4 \log ^2(x)+1250 x^5 \log ^2(x)+648 x^6 \log ^2(x)+54 x^8 \log ^2(x)+972 \log ^3(x)+1296 x^2 \log ^3(x)+648 x^4 \log ^3(x)+144 x^6 \log ^3(x)+12 x^8 \log ^3(x)+81 \log ^4(x)+108 x^2 \log ^4(x)+54 x^4 \log ^4(x)+12 x^6 \log ^4(x)+x^8 \log ^4(x)} \end {gather*}
Antiderivative was successfully verified.
[In]
Integrate[(10251562500 + 655560624846*x + 956153602500*x^2 + 537220650631*x^3 + 421106423750*x^4 + 30066634500
7*x^5 + 66719025000*x^6 + 19129907088*x^7 + 11418525000*x^8 + 2315325870*x^9 + 309318750*x^10 + 199763982*x^11
+ 32805000*x^12 + 1653372*x^13 + 1822500*x^14 + 157464*x^15 + 6561*x^17 + (10251562500 + 105583541256*x + 504
97830000*x^2 + 249324860016*x^3 + 101333160000*x^4 + 109725878352*x^5 + 54772425000*x^6 + 19766210568*x^7 + 99
79237500*x^8 + 3136702320*x^9 + 576450000*x^10 + 279578952*x^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14
+ 419904*x^15 + 17496*x^17)*Log[x] + (3417187500 + 13317516882*x + 23856525000*x^2 + 45764940852*x^3 + 3372086
2500*x^4 + 27268993494*x^5 + 16890562500*x^6 + 8088703996*x^7 + 3671500000*x^8 + 1634486040*x^9 + 452250000*x^
10 + 157425444*x^11 + 54675000*x^12 + 5143824*x^13 + 3037500*x^14 + 489888*x^15 + 20412*x^17)*Log[x]^2 + (3796
87500 + 89282088*x + 5287275000*x^2 + 2516210568*x^3 + 6271425000*x^4 + 3315266496*x^5 + 3215250000*x^6 + 1703
927664*x^7 + 958687500*x^8 + 414657360*x^9 + 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1
350000*x^14 + 326592*x^15 + 13608*x^17)*Log[x]^3 + (37200870*x + 562443750*x^2 + 289046070*x^3 + 829575000*x^4
+ 368861040*x^5 + 536625000*x^6 + 203719860*x^7 + 201000000*x^8 + 60273900*x^9 + 46343750*x^10 + 10916790*x^1
1 + 6075000*x^12 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17)*Log[x]^4 + (9920232*x + 32805000*x^2
+ 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54675000*x^6 + 20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075
000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x^14 + 36288*x^15 + 1512*x^17)*Log[x]^5 + (1653372
*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*x^7 + 1350000*x^8 + 1428840
*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048*x^15 + 252*x^17)*Log[x]^6 + (157
464*x + 419904*x^3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13 + 576*x^15 + 24*x^17)*Log[x
]^7 + (6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 252*x^13 + 24*x^15 + x^17)*Log[x]^8
)/(43046721*x + 6454383750*x^2 + 247181588131*x^3 + 393768923750*x^4 + 225959313757*x^5 + 58365900000*x^6 + 19
129907088*x^7 + 10532587500*x^8 + 2315325870*x^9 + 309318750*x^10 + 199763982*x^11 + 32805000*x^12 + 1653372*x
^13 + 1822500*x^14 + 157464*x^15 + 6561*x^17 + (114791256*x + 9491580000*x^2 + 73543610016*x^3 + 67161285000*x
^4 + 62850878352*x^5 + 44141175000*x^6 + 19766210568*x^7 + 8840175000*x^8 + 3136702320*x^9 + 576450000*x^10 +
279578952*x^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17)*Log[x] + (133923132*x
+ 5631525000*x^2 + 19397753352*x^3 + 17773987500*x^4 + 19944774744*x^5 + 11828062500*x^6 + 8088703996*x^7 + 3
123062500*x^8 + 1634486040*x^9 + 452250000*x^10 + 157425444*x^11 + 54675000*x^12 + 5143824*x^13 + 3037500*x^14
+ 489888*x^15 + 20412*x^17)*Log[x]^2 + (89282088*x + 1743525000*x^2 + 2516210568*x^3 + 2980800000*x^4 + 33152
66496*x^5 + 2146500000*x^6 + 1703927664*x^7 + 841500000*x^8 + 414657360*x^9 + 191625000*x^10 + 48700296*x^11 +
24300000*x^12 + 3429216*x^13 + 1350000*x^14 + 326592*x^15 + 13608*x^17)*Log[x]^3 + (37200870*x + 309318750*x^
2 + 289046070*x^3 + 576450000*x^4 + 368861040*x^5 + 452250000*x^6 + 203719860*x^7 + 191625000*x^8 + 60273900*x
^9 + 46343750*x^10 + 10916790*x^11 + 6075000*x^12 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17)*Log[
x]^4 + (9920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54675000*x^6 + 20575296*x^7 +
24300000*x^8 + 8573040*x^9 + 6075000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x^14 + 36288*x^15
+ 1512*x^17)*Log[x]^5 + (1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^6 + 34
29216*x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048
*x^15 + 252*x^17)*Log[x]^6 + (157464*x + 419904*x^3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048
*x^13 + 576*x^15 + 24*x^17)*Log[x]^7 + (6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 25
2*x^13 + 24*x^15 + x^17)*Log[x]^8),x]
[Out]
x - 1171875/(6561 + 491875*x + 399373*x^2 + 67500*x^3 + 4374*x^4 + 11250*x^5 + 972*x^6 + 81*x^8 + 8748*Log[x]
+ 67500*x*Log[x] + 11664*x^2*Log[x] + 45000*x^3*Log[x] + 5832*x^4*Log[x] + 7500*x^5*Log[x] + 1296*x^6*Log[x] +
108*x^8*Log[x] + 4374*Log[x]^2 + 11250*x*Log[x]^2 + 5832*x^2*Log[x]^2 + 7500*x^3*Log[x]^2 + 2916*x^4*Log[x]^2
+ 1250*x^5*Log[x]^2 + 648*x^6*Log[x]^2 + 54*x^8*Log[x]^2 + 972*Log[x]^3 + 1296*x^2*Log[x]^3 + 648*x^4*Log[x]^
3 + 144*x^6*Log[x]^3 + 12*x^8*Log[x]^3 + 81*Log[x]^4 + 108*x^2*Log[x]^4 + 54*x^4*Log[x]^4 + 12*x^6*Log[x]^4 +
x^8*Log[x]^4)
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fricas [B] time = 1.22, size = 352, normalized size = 12.14 \begin {gather*} \frac {81 \, x^{9} + 972 \, x^{7} + 11250 \, x^{6} + 4374 \, x^{5} + {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \relax (x)^{4} + 67500 \, x^{4} + 12 \, {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \relax (x)^{3} + 399373 \, x^{3} + 2 \, {\left (27 \, x^{9} + 324 \, x^{7} + 625 \, x^{6} + 1458 \, x^{5} + 3750 \, x^{4} + 2916 \, x^{3} + 5625 \, x^{2} + 2187 \, x\right )} \log \relax (x)^{2} + 491875 \, x^{2} + 12 \, {\left (9 \, x^{9} + 108 \, x^{7} + 625 \, x^{6} + 486 \, x^{5} + 3750 \, x^{4} + 972 \, x^{3} + 5625 \, x^{2} + 729 \, x\right )} \log \relax (x) + 6561 \, x - 1171875}{81 \, x^{8} + 972 \, x^{6} + 11250 \, x^{5} + {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \relax (x)^{4} + 4374 \, x^{4} + 12 \, {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \relax (x)^{3} + 67500 \, x^{3} + 2 \, {\left (27 \, x^{8} + 324 \, x^{6} + 625 \, x^{5} + 1458 \, x^{4} + 3750 \, x^{3} + 2916 \, x^{2} + 5625 \, x + 2187\right )} \log \relax (x)^{2} + 399373 \, x^{2} + 12 \, {\left (9 \, x^{8} + 108 \, x^{6} + 625 \, x^{5} + 486 \, x^{4} + 3750 \, x^{3} + 972 \, x^{2} + 5625 \, x + 729\right )} \log \relax (x) + 491875 \, x + 6561} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((10251562500+655560624846*x+421106423750*x^4+537220650631*x^3+956153602500*x^2+66719025000*x^6+30066
6345007*x^5+19129907088*x^7+11418525000*x^8+309318750*x^10+2315325870*x^9+157464*x^15+199763982*x^11+32805000*
x^12+1653372*x^13+1822500*x^14+6561*x^17+(x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+13608*x^7+20412*x^5+17496*x
^3+6561*x)*log(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489888*x^5+419904*x^3+157464*
x)*log(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x^10+1428840*x^9+1350000*x^
8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)*log(x)^6+(1512*x^17+36288
*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300000*x^8+20575296*x^7+54675
000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*log(x)^5+(5670*x^17+136080*x^15+337500*
x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+201000000*x^8+203719860*x^7+536625000*
x^6+368861040*x^5+829575000*x^4+289046070*x^3+562443750*x^2+37200870*x)*log(x)^4+(13608*x^17+326592*x^15+13500
00*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+958687500*x^8+1703927664*x^7+321
5250000*x^6+3315266496*x^5+6271425000*x^4+2516210568*x^3+5287275000*x^2+89282088*x+379687500)*log(x)^3+(20412*
x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486040*x^9+36715000
00*x^8+8088703996*x^7+16890562500*x^6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516
882*x+3417187500)*log(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+5764
50000*x^10+3136702320*x^9+9979237500*x^8+19766210568*x^7+54772425000*x^6+109725878352*x^5+101333160000*x^4+249
324860016*x^3+50497830000*x^2+105583541256*x+10251562500)*log(x))/((x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+1
3608*x^7+20412*x^5+17496*x^3+6561*x)*log(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489
888*x^5+419904*x^3+157464*x)*log(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x
^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)
*log(x)^6+(1512*x^17+36288*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300
000*x^8+20575296*x^7+54675000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*log(x)^5+(567
0*x^17+136080*x^15+337500*x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+191625000*x^
8+203719860*x^7+452250000*x^6+368861040*x^5+576450000*x^4+289046070*x^3+309318750*x^2+37200870*x)*log(x)^4+(13
608*x^17+326592*x^15+1350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+841500
000*x^8+1703927664*x^7+2146500000*x^6+3315266496*x^5+2980800000*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*
log(x)^3+(20412*x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486
040*x^9+3123062500*x^8+8088703996*x^7+11828062500*x^6+19944774744*x^5+17773987500*x^4+19397753352*x^3+56315250
00*x^2+133923132*x)*log(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+57
6450000*x^10+3136702320*x^9+8840175000*x^8+19766210568*x^7+44141175000*x^6+62850878352*x^5+67161285000*x^4+735
43610016*x^3+9491580000*x^2+114791256*x)*log(x)+6561*x^17+157464*x^15+1822500*x^14+1653372*x^13+32805000*x^12+
199763982*x^11+309318750*x^10+2315325870*x^9+10532587500*x^8+19129907088*x^7+58365900000*x^6+225959313757*x^5+
393768923750*x^4+247181588131*x^3+6454383750*x^2+43046721*x),x, algorithm="fricas")
[Out]
(81*x^9 + 972*x^7 + 11250*x^6 + 4374*x^5 + (x^9 + 12*x^7 + 54*x^5 + 108*x^3 + 81*x)*log(x)^4 + 67500*x^4 + 12*
(x^9 + 12*x^7 + 54*x^5 + 108*x^3 + 81*x)*log(x)^3 + 399373*x^3 + 2*(27*x^9 + 324*x^7 + 625*x^6 + 1458*x^5 + 37
50*x^4 + 2916*x^3 + 5625*x^2 + 2187*x)*log(x)^2 + 491875*x^2 + 12*(9*x^9 + 108*x^7 + 625*x^6 + 486*x^5 + 3750*
x^4 + 972*x^3 + 5625*x^2 + 729*x)*log(x) + 6561*x - 1171875)/(81*x^8 + 972*x^6 + 11250*x^5 + (x^8 + 12*x^6 + 5
4*x^4 + 108*x^2 + 81)*log(x)^4 + 4374*x^4 + 12*(x^8 + 12*x^6 + 54*x^4 + 108*x^2 + 81)*log(x)^3 + 67500*x^3 + 2
*(27*x^8 + 324*x^6 + 625*x^5 + 1458*x^4 + 3750*x^3 + 2916*x^2 + 5625*x + 2187)*log(x)^2 + 399373*x^2 + 12*(9*x
^8 + 108*x^6 + 625*x^5 + 486*x^4 + 3750*x^3 + 972*x^2 + 5625*x + 729)*log(x) + 491875*x + 6561)
________________________________________________________________________________________
giac [F(-1)] time = 0.00, size = 0, normalized size = 0.00 \begin {gather*} \text {Timed out} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((10251562500+655560624846*x+421106423750*x^4+537220650631*x^3+956153602500*x^2+66719025000*x^6+30066
6345007*x^5+19129907088*x^7+11418525000*x^8+309318750*x^10+2315325870*x^9+157464*x^15+199763982*x^11+32805000*
x^12+1653372*x^13+1822500*x^14+6561*x^17+(x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+13608*x^7+20412*x^5+17496*x
^3+6561*x)*log(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489888*x^5+419904*x^3+157464*
x)*log(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x^10+1428840*x^9+1350000*x^
8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)*log(x)^6+(1512*x^17+36288
*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300000*x^8+20575296*x^7+54675
000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*log(x)^5+(5670*x^17+136080*x^15+337500*
x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+201000000*x^8+203719860*x^7+536625000*
x^6+368861040*x^5+829575000*x^4+289046070*x^3+562443750*x^2+37200870*x)*log(x)^4+(13608*x^17+326592*x^15+13500
00*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+958687500*x^8+1703927664*x^7+321
5250000*x^6+3315266496*x^5+6271425000*x^4+2516210568*x^3+5287275000*x^2+89282088*x+379687500)*log(x)^3+(20412*
x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486040*x^9+36715000
00*x^8+8088703996*x^7+16890562500*x^6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516
882*x+3417187500)*log(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+5764
50000*x^10+3136702320*x^9+9979237500*x^8+19766210568*x^7+54772425000*x^6+109725878352*x^5+101333160000*x^4+249
324860016*x^3+50497830000*x^2+105583541256*x+10251562500)*log(x))/((x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+1
3608*x^7+20412*x^5+17496*x^3+6561*x)*log(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489
888*x^5+419904*x^3+157464*x)*log(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x
^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)
*log(x)^6+(1512*x^17+36288*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300
000*x^8+20575296*x^7+54675000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*log(x)^5+(567
0*x^17+136080*x^15+337500*x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+191625000*x^
8+203719860*x^7+452250000*x^6+368861040*x^5+576450000*x^4+289046070*x^3+309318750*x^2+37200870*x)*log(x)^4+(13
608*x^17+326592*x^15+1350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+841500
000*x^8+1703927664*x^7+2146500000*x^6+3315266496*x^5+2980800000*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*
log(x)^3+(20412*x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486
040*x^9+3123062500*x^8+8088703996*x^7+11828062500*x^6+19944774744*x^5+17773987500*x^4+19397753352*x^3+56315250
00*x^2+133923132*x)*log(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+57
6450000*x^10+3136702320*x^9+8840175000*x^8+19766210568*x^7+44141175000*x^6+62850878352*x^5+67161285000*x^4+735
43610016*x^3+9491580000*x^2+114791256*x)*log(x)+6561*x^17+157464*x^15+1822500*x^14+1653372*x^13+32805000*x^12+
199763982*x^11+309318750*x^10+2315325870*x^9+10532587500*x^8+19129907088*x^7+58365900000*x^6+225959313757*x^5+
393768923750*x^4+247181588131*x^3+6454383750*x^2+43046721*x),x, algorithm="giac")
[Out]
Timed out
________________________________________________________________________________________
maple [B] time = 0.18, size = 243, normalized size = 8.38
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| method |
result |
size |
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| risch |
\(x -\frac {1171875}{6561+491875 x +12 x^{8} \ln \relax (x )^{3}+11664 x^{2} \ln \relax (x )+12 x^{6} \ln \relax (x )^{4}+5832 x^{2} \ln \relax (x )^{2}+108 x^{2} \ln \relax (x )^{4}+81 x^{8}+81 \ln \relax (x )^{4}+972 \ln \relax (x )^{3}+8748 \ln \relax (x )+4374 \ln \relax (x )^{2}+4374 x^{4}+67500 x^{3}+399373 x^{2}+972 x^{6}+11250 x^{5}+45000 x^{3} \ln \relax (x )+54 x^{8} \ln \relax (x )^{2}+648 x^{6} \ln \relax (x )^{2}+1296 x^{6} \ln \relax (x )+648 x^{4} \ln \relax (x )^{3}+144 x^{6} \ln \relax (x )^{3}+7500 x^{5} \ln \relax (x )+2916 x^{4} \ln \relax (x )^{2}+11250 x \ln \relax (x )^{2}+108 x^{8} \ln \relax (x )+5832 x^{4} \ln \relax (x )+67500 x \ln \relax (x )+x^{8} \ln \relax (x )^{4}+54 x^{4} \ln \relax (x )^{4}+1250 x^{5} \ln \relax (x )^{2}+1296 x^{2} \ln \relax (x )^{3}+7500 x^{3} \ln \relax (x )^{2}}\) |
\(243\) |
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Verification of antiderivative is not currently implemented for this CAS.
[In]
int((10251562500+655560624846*x+6561*x^17+1653372*x^13+1822500*x^14+32805000*x^12+199763982*x^11+157464*x^15+3
09318750*x^10+2315325870*x^9+19129907088*x^7+11418525000*x^8+421106423750*x^4+537220650631*x^3+956153602500*x^
2+66719025000*x^6+300666345007*x^5+(13608*x^17+326592*x^15+1350000*x^14+3429216*x^13+24300000*x^12+48700296*x^
11+191625000*x^10+414657360*x^9+958687500*x^8+1703927664*x^7+3215250000*x^6+3315266496*x^5+6271425000*x^4+2516
210568*x^3+5287275000*x^2+89282088*x+379687500)*ln(x)^3+(20412*x^17+489888*x^15+3037500*x^14+5143824*x^13+5467
5000*x^12+157425444*x^11+452250000*x^10+1634486040*x^9+3671500000*x^8+8088703996*x^7+16890562500*x^6+272689934
94*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516882*x+3417187500)*ln(x)^2+(17496*x^17+419904*x^
15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+576450000*x^10+3136702320*x^9+9979237500*x^8+1976621
0568*x^7+54772425000*x^6+109725878352*x^5+101333160000*x^4+249324860016*x^3+50497830000*x^2+105583541256*x+102
51562500)*ln(x)+(x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+13608*x^7+20412*x^5+17496*x^3+6561*x)*ln(x)^8+(24*x^
17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489888*x^5+419904*x^3+157464*x)*ln(x)^7+(252*x^17+6048*
x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5
143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)*ln(x)^6+(1512*x^17+36288*x^15+45000*x^14+381024*x^13
+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300000*x^8+20575296*x^7+54675000*x^6+30862944*x^5+6561000
0*x^4+26453952*x^3+32805000*x^2+9920232*x)*ln(x)^5+(5670*x^17+136080*x^15+337500*x^14+1428840*x^13+6075000*x^1
2+10916790*x^11+46343750*x^10+60273900*x^9+201000000*x^8+203719860*x^7+536625000*x^6+368861040*x^5+829575000*x
^4+289046070*x^3+562443750*x^2+37200870*x)*ln(x)^4)/((x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+13608*x^7+20412
*x^5+17496*x^3+6561*x)*ln(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489888*x^5+419904*
x^3+157464*x)*ln(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x^10+1428840*x^9+
1350000*x^8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)*ln(x)^6+(1512*x
^17+36288*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300000*x^8+20575296*
x^7+54675000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*ln(x)^5+(5670*x^17+136080*x^15
+337500*x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+191625000*x^8+203719860*x^7+45
2250000*x^6+368861040*x^5+576450000*x^4+289046070*x^3+309318750*x^2+37200870*x)*ln(x)^4+(13608*x^17+326592*x^1
5+1350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+841500000*x^8+1703927664*
x^7+2146500000*x^6+3315266496*x^5+2980800000*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*ln(x)^3+(20412*x^17
+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486040*x^9+3123062500*x
^8+8088703996*x^7+11828062500*x^6+19944774744*x^5+17773987500*x^4+19397753352*x^3+5631525000*x^2+133923132*x)*
ln(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+576450000*x^10+31367023
20*x^9+8840175000*x^8+19766210568*x^7+44141175000*x^6+62850878352*x^5+67161285000*x^4+73543610016*x^3+94915800
00*x^2+114791256*x)*ln(x)+6561*x^17+157464*x^15+1822500*x^14+1653372*x^13+32805000*x^12+199763982*x^11+3093187
50*x^10+2315325870*x^9+10532587500*x^8+19129907088*x^7+58365900000*x^6+225959313757*x^5+393768923750*x^4+24718
1588131*x^3+6454383750*x^2+43046721*x),x,method=_RETURNVERBOSE)
[Out]
x-1171875/(6561+491875*x+12*x^8*ln(x)^3+11664*x^2*ln(x)+12*x^6*ln(x)^4+5832*x^2*ln(x)^2+108*x^2*ln(x)^4+81*x^8
+81*ln(x)^4+972*ln(x)^3+8748*ln(x)+4374*ln(x)^2+4374*x^4+67500*x^3+399373*x^2+972*x^6+11250*x^5+45000*x^3*ln(x
)+54*x^8*ln(x)^2+648*x^6*ln(x)^2+1296*x^6*ln(x)+648*x^4*ln(x)^3+144*x^6*ln(x)^3+7500*x^5*ln(x)+2916*x^4*ln(x)^
2+11250*x*ln(x)^2+108*x^8*ln(x)+5832*x^4*ln(x)+67500*x*ln(x)+x^8*ln(x)^4+54*x^4*ln(x)^4+1250*x^5*ln(x)^2+1296*
x^2*ln(x)^3+7500*x^3*ln(x)^2)
________________________________________________________________________________________
maxima [B] time = 1.05, size = 352, normalized size = 12.14 \begin {gather*} \frac {81 \, x^{9} + 972 \, x^{7} + 11250 \, x^{6} + 4374 \, x^{5} + {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \relax (x)^{4} + 67500 \, x^{4} + 12 \, {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \relax (x)^{3} + 399373 \, x^{3} + 2 \, {\left (27 \, x^{9} + 324 \, x^{7} + 625 \, x^{6} + 1458 \, x^{5} + 3750 \, x^{4} + 2916 \, x^{3} + 5625 \, x^{2} + 2187 \, x\right )} \log \relax (x)^{2} + 491875 \, x^{2} + 12 \, {\left (9 \, x^{9} + 108 \, x^{7} + 625 \, x^{6} + 486 \, x^{5} + 3750 \, x^{4} + 972 \, x^{3} + 5625 \, x^{2} + 729 \, x\right )} \log \relax (x) + 6561 \, x - 1171875}{81 \, x^{8} + 972 \, x^{6} + 11250 \, x^{5} + {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \relax (x)^{4} + 4374 \, x^{4} + 12 \, {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \relax (x)^{3} + 67500 \, x^{3} + 2 \, {\left (27 \, x^{8} + 324 \, x^{6} + 625 \, x^{5} + 1458 \, x^{4} + 3750 \, x^{3} + 2916 \, x^{2} + 5625 \, x + 2187\right )} \log \relax (x)^{2} + 399373 \, x^{2} + 12 \, {\left (9 \, x^{8} + 108 \, x^{6} + 625 \, x^{5} + 486 \, x^{4} + 3750 \, x^{3} + 972 \, x^{2} + 5625 \, x + 729\right )} \log \relax (x) + 491875 \, x + 6561} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((10251562500+655560624846*x+421106423750*x^4+537220650631*x^3+956153602500*x^2+66719025000*x^6+30066
6345007*x^5+19129907088*x^7+11418525000*x^8+309318750*x^10+2315325870*x^9+157464*x^15+199763982*x^11+32805000*
x^12+1653372*x^13+1822500*x^14+6561*x^17+(x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+13608*x^7+20412*x^5+17496*x
^3+6561*x)*log(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489888*x^5+419904*x^3+157464*
x)*log(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x^10+1428840*x^9+1350000*x^
8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)*log(x)^6+(1512*x^17+36288
*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300000*x^8+20575296*x^7+54675
000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*log(x)^5+(5670*x^17+136080*x^15+337500*
x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+201000000*x^8+203719860*x^7+536625000*
x^6+368861040*x^5+829575000*x^4+289046070*x^3+562443750*x^2+37200870*x)*log(x)^4+(13608*x^17+326592*x^15+13500
00*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+958687500*x^8+1703927664*x^7+321
5250000*x^6+3315266496*x^5+6271425000*x^4+2516210568*x^3+5287275000*x^2+89282088*x+379687500)*log(x)^3+(20412*
x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486040*x^9+36715000
00*x^8+8088703996*x^7+16890562500*x^6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516
882*x+3417187500)*log(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+5764
50000*x^10+3136702320*x^9+9979237500*x^8+19766210568*x^7+54772425000*x^6+109725878352*x^5+101333160000*x^4+249
324860016*x^3+50497830000*x^2+105583541256*x+10251562500)*log(x))/((x^17+24*x^15+252*x^13+1512*x^11+5670*x^9+1
3608*x^7+20412*x^5+17496*x^3+6561*x)*log(x)^8+(24*x^17+576*x^15+6048*x^13+36288*x^11+136080*x^9+326592*x^7+489
888*x^5+419904*x^3+157464*x)*log(x)^7+(252*x^17+6048*x^15+2500*x^14+63504*x^13+45000*x^12+381024*x^11+337500*x
^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+1653372*x)
*log(x)^6+(1512*x^17+36288*x^15+45000*x^14+381024*x^13+810000*x^12+2286144*x^11+6075000*x^10+8573040*x^9+24300
000*x^8+20575296*x^7+54675000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+9920232*x)*log(x)^5+(567
0*x^17+136080*x^15+337500*x^14+1428840*x^13+6075000*x^12+10916790*x^11+46343750*x^10+60273900*x^9+191625000*x^
8+203719860*x^7+452250000*x^6+368861040*x^5+576450000*x^4+289046070*x^3+309318750*x^2+37200870*x)*log(x)^4+(13
608*x^17+326592*x^15+1350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657360*x^9+841500
000*x^8+1703927664*x^7+2146500000*x^6+3315266496*x^5+2980800000*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*
log(x)^3+(20412*x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+157425444*x^11+452250000*x^10+1634486
040*x^9+3123062500*x^8+8088703996*x^7+11828062500*x^6+19944774744*x^5+17773987500*x^4+19397753352*x^3+56315250
00*x^2+133923132*x)*log(x)^2+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+57
6450000*x^10+3136702320*x^9+8840175000*x^8+19766210568*x^7+44141175000*x^6+62850878352*x^5+67161285000*x^4+735
43610016*x^3+9491580000*x^2+114791256*x)*log(x)+6561*x^17+157464*x^15+1822500*x^14+1653372*x^13+32805000*x^12+
199763982*x^11+309318750*x^10+2315325870*x^9+10532587500*x^8+19129907088*x^7+58365900000*x^6+225959313757*x^5+
393768923750*x^4+247181588131*x^3+6454383750*x^2+43046721*x),x, algorithm="maxima")
[Out]
(81*x^9 + 972*x^7 + 11250*x^6 + 4374*x^5 + (x^9 + 12*x^7 + 54*x^5 + 108*x^3 + 81*x)*log(x)^4 + 67500*x^4 + 12*
(x^9 + 12*x^7 + 54*x^5 + 108*x^3 + 81*x)*log(x)^3 + 399373*x^3 + 2*(27*x^9 + 324*x^7 + 625*x^6 + 1458*x^5 + 37
50*x^4 + 2916*x^3 + 5625*x^2 + 2187*x)*log(x)^2 + 491875*x^2 + 12*(9*x^9 + 108*x^7 + 625*x^6 + 486*x^5 + 3750*
x^4 + 972*x^3 + 5625*x^2 + 729*x)*log(x) + 6561*x - 1171875)/(81*x^8 + 972*x^6 + 11250*x^5 + (x^8 + 12*x^6 + 5
4*x^4 + 108*x^2 + 81)*log(x)^4 + 4374*x^4 + 12*(x^8 + 12*x^6 + 54*x^4 + 108*x^2 + 81)*log(x)^3 + 67500*x^3 + 2
*(27*x^8 + 324*x^6 + 625*x^5 + 1458*x^4 + 3750*x^3 + 2916*x^2 + 5625*x + 2187)*log(x)^2 + 399373*x^2 + 12*(9*x
^8 + 108*x^6 + 625*x^5 + 486*x^4 + 3750*x^3 + 972*x^2 + 5625*x + 729)*log(x) + 491875*x + 6561)
________________________________________________________________________________________
mupad [F] time = 0.00, size = -1, normalized size = -0.03 result too large to
display
Verification of antiderivative is not currently implemented for this CAS.
[In]
int((655560624846*x + log(x)^6*(1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^
6 + 3429216*x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14
+ 6048*x^15 + 252*x^17) + log(x)^5*(9920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54
675000*x^6 + 20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^
13 + 45000*x^14 + 36288*x^15 + 1512*x^17) + log(x)^8*(6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 +
1512*x^11 + 252*x^13 + 24*x^15 + x^17) + log(x)*(105583541256*x + 50497830000*x^2 + 249324860016*x^3 + 1013331
60000*x^4 + 109725878352*x^5 + 54772425000*x^6 + 19766210568*x^7 + 9979237500*x^8 + 3136702320*x^9 + 576450000
*x^10 + 279578952*x^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17 + 10251562500)
+ log(x)^7*(157464*x + 419904*x^3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13 + 576*x^15
+ 24*x^17) + log(x)^2*(13317516882*x + 23856525000*x^2 + 45764940852*x^3 + 33720862500*x^4 + 27268993494*x^5 +
16890562500*x^6 + 8088703996*x^7 + 3671500000*x^8 + 1634486040*x^9 + 452250000*x^10 + 157425444*x^11 + 546750
00*x^12 + 5143824*x^13 + 3037500*x^14 + 489888*x^15 + 20412*x^17 + 3417187500) + log(x)^3*(89282088*x + 528727
5000*x^2 + 2516210568*x^3 + 6271425000*x^4 + 3315266496*x^5 + 3215250000*x^6 + 1703927664*x^7 + 958687500*x^8
+ 414657360*x^9 + 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000*x^14 + 326592*x^15 +
13608*x^17 + 379687500) + log(x)^4*(37200870*x + 562443750*x^2 + 289046070*x^3 + 829575000*x^4 + 368861040*x^
5 + 536625000*x^6 + 203719860*x^7 + 201000000*x^8 + 60273900*x^9 + 46343750*x^10 + 10916790*x^11 + 6075000*x^1
2 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17) + 956153602500*x^2 + 537220650631*x^3 + 421106423750
*x^4 + 300666345007*x^5 + 66719025000*x^6 + 19129907088*x^7 + 11418525000*x^8 + 2315325870*x^9 + 309318750*x^1
0 + 199763982*x^11 + 32805000*x^12 + 1653372*x^13 + 1822500*x^14 + 157464*x^15 + 6561*x^17 + 10251562500)/(430
46721*x + log(x)^6*(1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*
x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048*x^15
+ 252*x^17) + log(x)^5*(9920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54675000*x^6 +
20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x
^14 + 36288*x^15 + 1512*x^17) + log(x)^8*(6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 +
252*x^13 + 24*x^15 + x^17) + log(x)*(114791256*x + 9491580000*x^2 + 73543610016*x^3 + 67161285000*x^4 + 628508
78352*x^5 + 44141175000*x^6 + 19766210568*x^7 + 8840175000*x^8 + 3136702320*x^9 + 576450000*x^10 + 279578952*x
^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17) + log(x)^7*(157464*x + 419904*x^
3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13 + 576*x^15 + 24*x^17) + log(x)^2*(133923132*
x + 5631525000*x^2 + 19397753352*x^3 + 17773987500*x^4 + 19944774744*x^5 + 11828062500*x^6 + 8088703996*x^7 +
3123062500*x^8 + 1634486040*x^9 + 452250000*x^10 + 157425444*x^11 + 54675000*x^12 + 5143824*x^13 + 3037500*x^1
4 + 489888*x^15 + 20412*x^17) + log(x)^4*(37200870*x + 309318750*x^2 + 289046070*x^3 + 576450000*x^4 + 3688610
40*x^5 + 452250000*x^6 + 203719860*x^7 + 191625000*x^8 + 60273900*x^9 + 46343750*x^10 + 10916790*x^11 + 607500
0*x^12 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17) + log(x)^3*(89282088*x + 1743525000*x^2 + 25162
10568*x^3 + 2980800000*x^4 + 3315266496*x^5 + 2146500000*x^6 + 1703927664*x^7 + 841500000*x^8 + 414657360*x^9
+ 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000*x^14 + 326592*x^15 + 13608*x^17) + 6
454383750*x^2 + 247181588131*x^3 + 393768923750*x^4 + 225959313757*x^5 + 58365900000*x^6 + 19129907088*x^7 + 1
0532587500*x^8 + 2315325870*x^9 + 309318750*x^10 + 199763982*x^11 + 32805000*x^12 + 1653372*x^13 + 1822500*x^1
4 + 157464*x^15 + 6561*x^17),x)
[Out]
int((655560624846*x + log(x)^6*(1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^
6 + 3429216*x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14
+ 6048*x^15 + 252*x^17) + log(x)^5*(9920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54
675000*x^6 + 20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^
13 + 45000*x^14 + 36288*x^15 + 1512*x^17) + log(x)^8*(6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 +
1512*x^11 + 252*x^13 + 24*x^15 + x^17) + log(x)*(105583541256*x + 50497830000*x^2 + 249324860016*x^3 + 1013331
60000*x^4 + 109725878352*x^5 + 54772425000*x^6 + 19766210568*x^7 + 9979237500*x^8 + 3136702320*x^9 + 576450000
*x^10 + 279578952*x^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17 + 10251562500)
+ log(x)^7*(157464*x + 419904*x^3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13 + 576*x^15
+ 24*x^17) + log(x)^2*(13317516882*x + 23856525000*x^2 + 45764940852*x^3 + 33720862500*x^4 + 27268993494*x^5 +
16890562500*x^6 + 8088703996*x^7 + 3671500000*x^8 + 1634486040*x^9 + 452250000*x^10 + 157425444*x^11 + 546750
00*x^12 + 5143824*x^13 + 3037500*x^14 + 489888*x^15 + 20412*x^17 + 3417187500) + log(x)^3*(89282088*x + 528727
5000*x^2 + 2516210568*x^3 + 6271425000*x^4 + 3315266496*x^5 + 3215250000*x^6 + 1703927664*x^7 + 958687500*x^8
+ 414657360*x^9 + 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000*x^14 + 326592*x^15 +
13608*x^17 + 379687500) + log(x)^4*(37200870*x + 562443750*x^2 + 289046070*x^3 + 829575000*x^4 + 368861040*x^
5 + 536625000*x^6 + 203719860*x^7 + 201000000*x^8 + 60273900*x^9 + 46343750*x^10 + 10916790*x^11 + 6075000*x^1
2 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17) + 956153602500*x^2 + 537220650631*x^3 + 421106423750
*x^4 + 300666345007*x^5 + 66719025000*x^6 + 19129907088*x^7 + 11418525000*x^8 + 2315325870*x^9 + 309318750*x^1
0 + 199763982*x^11 + 32805000*x^12 + 1653372*x^13 + 1822500*x^14 + 157464*x^15 + 6561*x^17 + 10251562500)/(430
46721*x + log(x)^6*(1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*
x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 381024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048*x^15
+ 252*x^17) + log(x)^5*(9920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 54675000*x^6 +
20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075000*x^10 + 2286144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x
^14 + 36288*x^15 + 1512*x^17) + log(x)^8*(6561*x + 17496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 +
252*x^13 + 24*x^15 + x^17) + log(x)*(114791256*x + 9491580000*x^2 + 73543610016*x^3 + 67161285000*x^4 + 628508
78352*x^5 + 44141175000*x^6 + 19766210568*x^7 + 8840175000*x^8 + 3136702320*x^9 + 576450000*x^10 + 279578952*x
^11 + 65610000*x^12 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17) + log(x)^7*(157464*x + 419904*x^
3 + 489888*x^5 + 326592*x^7 + 136080*x^9 + 36288*x^11 + 6048*x^13 + 576*x^15 + 24*x^17) + log(x)^2*(133923132*
x + 5631525000*x^2 + 19397753352*x^3 + 17773987500*x^4 + 19944774744*x^5 + 11828062500*x^6 + 8088703996*x^7 +
3123062500*x^8 + 1634486040*x^9 + 452250000*x^10 + 157425444*x^11 + 54675000*x^12 + 5143824*x^13 + 3037500*x^1
4 + 489888*x^15 + 20412*x^17) + log(x)^4*(37200870*x + 309318750*x^2 + 289046070*x^3 + 576450000*x^4 + 3688610
40*x^5 + 452250000*x^6 + 203719860*x^7 + 191625000*x^8 + 60273900*x^9 + 46343750*x^10 + 10916790*x^11 + 607500
0*x^12 + 1428840*x^13 + 337500*x^14 + 136080*x^15 + 5670*x^17) + log(x)^3*(89282088*x + 1743525000*x^2 + 25162
10568*x^3 + 2980800000*x^4 + 3315266496*x^5 + 2146500000*x^6 + 1703927664*x^7 + 841500000*x^8 + 414657360*x^9
+ 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000*x^14 + 326592*x^15 + 13608*x^17) + 6
454383750*x^2 + 247181588131*x^3 + 393768923750*x^4 + 225959313757*x^5 + 58365900000*x^6 + 19129907088*x^7 + 1
0532587500*x^8 + 2315325870*x^9 + 309318750*x^10 + 199763982*x^11 + 32805000*x^12 + 1653372*x^13 + 1822500*x^1
4 + 157464*x^15 + 6561*x^17), x)
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sympy [B] time = 3.94, size = 170, normalized size = 5.86 \begin {gather*} x - \frac {1171875}{81 x^{8} + 972 x^{6} + 11250 x^{5} + 4374 x^{4} + 67500 x^{3} + 399373 x^{2} + 491875 x + \left (x^{8} + 12 x^{6} + 54 x^{4} + 108 x^{2} + 81\right ) \log {\relax (x )}^{4} + \left (12 x^{8} + 144 x^{6} + 648 x^{4} + 1296 x^{2} + 972\right ) \log {\relax (x )}^{3} + \left (54 x^{8} + 648 x^{6} + 1250 x^{5} + 2916 x^{4} + 7500 x^{3} + 5832 x^{2} + 11250 x + 4374\right ) \log {\relax (x )}^{2} + \left (108 x^{8} + 1296 x^{6} + 7500 x^{5} + 5832 x^{4} + 45000 x^{3} + 11664 x^{2} + 67500 x + 8748\right ) \log {\relax (x )} + 6561} \end {gather*}
Verification of antiderivative is not currently implemented for this CAS.
[In]
integrate((10251562500+655560624846*x+421106423750*x**4+537220650631*x**3+956153602500*x**2+66719025000*x**6+3
00666345007*x**5+19129907088*x**7+11418525000*x**8+309318750*x**10+2315325870*x**9+157464*x**15+199763982*x**1
1+32805000*x**12+1653372*x**13+1822500*x**14+6561*x**17+(x**17+24*x**15+252*x**13+1512*x**11+5670*x**9+13608*x
**7+20412*x**5+17496*x**3+6561*x)*ln(x)**8+(24*x**17+576*x**15+6048*x**13+36288*x**11+136080*x**9+326592*x**7+
489888*x**5+419904*x**3+157464*x)*ln(x)**7+(252*x**17+6048*x**15+2500*x**14+63504*x**13+45000*x**12+381024*x**
11+337500*x**10+1428840*x**9+1350000*x**8+3429216*x**7+3037500*x**6+5143824*x**5+3645000*x**4+4408992*x**3+182
2500*x**2+1653372*x)*ln(x)**6+(1512*x**17+36288*x**15+45000*x**14+381024*x**13+810000*x**12+2286144*x**11+6075
000*x**10+8573040*x**9+24300000*x**8+20575296*x**7+54675000*x**6+30862944*x**5+65610000*x**4+26453952*x**3+328
05000*x**2+9920232*x)*ln(x)**5+(5670*x**17+136080*x**15+337500*x**14+1428840*x**13+6075000*x**12+10916790*x**1
1+46343750*x**10+60273900*x**9+201000000*x**8+203719860*x**7+536625000*x**6+368861040*x**5+829575000*x**4+2890
46070*x**3+562443750*x**2+37200870*x)*ln(x)**4+(13608*x**17+326592*x**15+1350000*x**14+3429216*x**13+24300000*
x**12+48700296*x**11+191625000*x**10+414657360*x**9+958687500*x**8+1703927664*x**7+3215250000*x**6+3315266496*
x**5+6271425000*x**4+2516210568*x**3+5287275000*x**2+89282088*x+379687500)*ln(x)**3+(20412*x**17+489888*x**15+
3037500*x**14+5143824*x**13+54675000*x**12+157425444*x**11+452250000*x**10+1634486040*x**9+3671500000*x**8+808
8703996*x**7+16890562500*x**6+27268993494*x**5+33720862500*x**4+45764940852*x**3+23856525000*x**2+13317516882*
x+3417187500)*ln(x)**2+(17496*x**17+419904*x**15+3645000*x**14+4408992*x**13+65610000*x**12+279578952*x**11+57
6450000*x**10+3136702320*x**9+9979237500*x**8+19766210568*x**7+54772425000*x**6+109725878352*x**5+101333160000
*x**4+249324860016*x**3+50497830000*x**2+105583541256*x+10251562500)*ln(x))/((x**17+24*x**15+252*x**13+1512*x*
*11+5670*x**9+13608*x**7+20412*x**5+17496*x**3+6561*x)*ln(x)**8+(24*x**17+576*x**15+6048*x**13+36288*x**11+136
080*x**9+326592*x**7+489888*x**5+419904*x**3+157464*x)*ln(x)**7+(252*x**17+6048*x**15+2500*x**14+63504*x**13+4
5000*x**12+381024*x**11+337500*x**10+1428840*x**9+1350000*x**8+3429216*x**7+3037500*x**6+5143824*x**5+3645000*
x**4+4408992*x**3+1822500*x**2+1653372*x)*ln(x)**6+(1512*x**17+36288*x**15+45000*x**14+381024*x**13+810000*x**
12+2286144*x**11+6075000*x**10+8573040*x**9+24300000*x**8+20575296*x**7+54675000*x**6+30862944*x**5+65610000*x
**4+26453952*x**3+32805000*x**2+9920232*x)*ln(x)**5+(5670*x**17+136080*x**15+337500*x**14+1428840*x**13+607500
0*x**12+10916790*x**11+46343750*x**10+60273900*x**9+191625000*x**8+203719860*x**7+452250000*x**6+368861040*x**
5+576450000*x**4+289046070*x**3+309318750*x**2+37200870*x)*ln(x)**4+(13608*x**17+326592*x**15+1350000*x**14+34
29216*x**13+24300000*x**12+48700296*x**11+191625000*x**10+414657360*x**9+841500000*x**8+1703927664*x**7+214650
0000*x**6+3315266496*x**5+2980800000*x**4+2516210568*x**3+1743525000*x**2+89282088*x)*ln(x)**3+(20412*x**17+48
9888*x**15+3037500*x**14+5143824*x**13+54675000*x**12+157425444*x**11+452250000*x**10+1634486040*x**9+31230625
00*x**8+8088703996*x**7+11828062500*x**6+19944774744*x**5+17773987500*x**4+19397753352*x**3+5631525000*x**2+13
3923132*x)*ln(x)**2+(17496*x**17+419904*x**15+3645000*x**14+4408992*x**13+65610000*x**12+279578952*x**11+57645
0000*x**10+3136702320*x**9+8840175000*x**8+19766210568*x**7+44141175000*x**6+62850878352*x**5+67161285000*x**4
+73543610016*x**3+9491580000*x**2+114791256*x)*ln(x)+6561*x**17+157464*x**15+1822500*x**14+1653372*x**13+32805
000*x**12+199763982*x**11+309318750*x**10+2315325870*x**9+10532587500*x**8+19129907088*x**7+58365900000*x**6+2
25959313757*x**5+393768923750*x**4+247181588131*x**3+6454383750*x**2+43046721*x),x)
[Out]
x - 1171875/(81*x**8 + 972*x**6 + 11250*x**5 + 4374*x**4 + 67500*x**3 + 399373*x**2 + 491875*x + (x**8 + 12*x*
*6 + 54*x**4 + 108*x**2 + 81)*log(x)**4 + (12*x**8 + 144*x**6 + 648*x**4 + 1296*x**2 + 972)*log(x)**3 + (54*x*
*8 + 648*x**6 + 1250*x**5 + 2916*x**4 + 7500*x**3 + 5832*x**2 + 11250*x + 4374)*log(x)**2 + (108*x**8 + 1296*x
**6 + 7500*x**5 + 5832*x**4 + 45000*x**3 + 11664*x**2 + 67500*x + 8748)*log(x) + 6561)
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