\(\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}[phone] x^{11}[phone] 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}[phone] x^{11}[phone] 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}[phone] x^{11}[phone] 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}[phone] x^{11}[phone] 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}[phone] 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}[phone] x^{11}[phone] 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}[phone] x^{11}[phone] 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}[phone] x^{11}[phone] 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}[phone] x^{11}[phone] 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}[phone] 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\) [75]

Optimal result

Integrand size = 1361, antiderivative size = 29 \[ \text {the integral} =x-\frac {3}{x+\left (x+\frac {1}{625} \left (3+x^2\right )^2 (3+\log (x))^2\right )^2} \] Output:

x-3/(x+(1/625*(3+ln(x))^2*(x^2+3)^2+x)^2)
                                                                                    
                                                                                    
 

Mathematica [B] (verified)

Leaf count is larger than twice the leaf count of optimal. \(242\) vs. \(2(29)=58\).

Time = 0.50 (sec) , antiderivative size = 242, normalized size of antiderivative = 8.34 \[ \text {the integral} =x-\frac {1171875}{6561+491875 x+399373 x^2+67500 x^3+4374 x^4+11250 x^5+972 x^6+81 x^8+8748 \log (x)+67500 x \log (x)+11664 x^2 \log (x)+45000 x^3 \log (x)+5832 x^4 \log (x)+7500 x^5 \log (x)+1296 x^6 \log (x)+108 x^8 \log (x)+4374 \log ^2(x)+11250 x \log ^2(x)+5832 x^2 \log ^2(x)+7500 x^3 \log ^2(x)+2916 x^4 \log ^2(x)+1250 x^5 \log ^2(x)+648 x^6 \log ^2(x)+54 x^8 \log ^2(x)+972 \log ^3(x)+1296 x^2 \log ^3(x)+648 x^4 \log ^3(x)+144 x^6 \log ^3(x)+12 x^8 \log ^3(x)+81 \log ^4(x)+108 x^2 \log ^4(x)+54 x^4 \log ^4(x)+12 x^6 \log ^4(x)+x^8 \log ^4(x)} \] Input:

Integrate[(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 + 101333 
160000*x^4 + 109725878352*x^5 + 54772425000*x^6 + 19766210568*x^7 + 997923 
7500*x^8 + 3136702320*x^9 + 576450000*x^10 + 279578952*x^11 + 65610000*x^1 
2 + 4408992*x^13 + 3645000*x^14 + 419904*x^15 + 17496*x^17)*Log[x] + (3417 
187500 + 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 + 514382 
4*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 + 1 
91625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000*x^1 
4 + 326592*x^15 + 13608*x^17)*Log[x]^3 + (37200870*x + 562443750*x^2 + 289 
046070*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[x]^4 + (9 
920232*x + 32805000*x^2 + 26453952*x^3 + 65610000*x^4 + 30862944*x^5 + 546 
75000*x^6 + 20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 6075000*x^10 + 228 
6144*x^11 + 810000*x^12 + 381024*x^13 + 45000*x^14 + 36288*x^15 + 1512*x^1 
7)*Log[x]^5 + (1653372*x + 1822500*x^2 + 4408992*x^3 + 3645000*x^4 + 51438 
24*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 + 17 
496*x^3 + 20412*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 252*x^13 + 24*x^1 
5 + x^17)*Log[x]^8)/(43046721*x + 6454383750*x^2 + 247181588131*x^3 + 3937 
68923750*x^4 + 225959313757*x^5 + 58365900000*x^6 + 19129907088*x^7 + 1053 
2587500*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 + 576 
450000*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 + 1939 
7753352*x^3 + 17773987500*x^4 + 19944774744*x^5 + 11828062500*x^6 + 808870 
3996*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^1 
7)*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 + 41 
4657360*x^9 + 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^1 
3 + 1350000*x^14 + 326592*x^15 + 13608*x^17)*Log[x]^3 + (37200870*x + 3093 
18750*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 + 308 
62944*x^5 + 54675000*x^6 + 20575296*x^7 + 24300000*x^8 + 8573040*x^9 + 607 
5000*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 + 3645 
000*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 + 60 
48*x^15 + 252*x^17)*Log[x]^6 + (157464*x + 419904*x^3 + 489888*x^5 + 32659 
2*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]
 

Output:

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] + 1 
08*x^8*Log[x] + 4374*Log[x]^2 + 11250*x*Log[x]^2 + 5832*x^2*Log[x]^2 + 750 
0*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)
 

Rubi [F]

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 {6561 x^{17}+157464 x^{15}+1822500 x^{14}+1653372 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+11418525000 x^8+19129907088 x^7+66719025000 x^6+300666345007 x^5+421106423750 x^4+537220650631 x^3+956153602500 x^2+655560624846 x+\left (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\right ) \log ^8(x)+\left (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\right ) \log ^7(x)+\left (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\right ) \log ^6(x)+\left (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\right ) \log ^5(x)+\left (5670 x^{17}+136080 x^{15}+337500 x^{14}+1428840 x^{13}+6075000 x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log ^4(x)+\left (13608 x^{17}+326592 x^{15}+1350000 x^{14}+3429216 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log ^3(x)+\left (20412 x^{17}+489888 x^{15}+3037500 x^{14}+5143824 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+3671500000 x^8+8088703996 x^7+16890562500 x^6+27268993494 x^5+33720862500 x^4+45764940852 x^3+23856525000 x^2+13317516882 x+3417187500\right ) \log ^2(x)+\left (17496 x^{17}+419904 x^{15}+3645000 x^{14}+4408992 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log (x)[phone]}{6561 x^{17}+157464 x^{15}+1822500 x^{14}+1653372 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] 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+\left (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\right ) \log ^8(x)+\left (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\right ) \log ^7(x)+\left (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\right ) \log ^6(x)+\left (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\right ) \log ^5(x)+\left (5670 x^{17}+136080 x^{15}+337500 x^{14}+1428840 x^{13}+6075000 x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log ^4(x)+\left (13608 x^{17}+326592 x^{15}+1350000 x^{14}+3429216 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log ^3(x)+\left (20412 x^{17}+489888 x^{15}+3037500 x^{14}+5143824 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log ^2(x)+\left (17496 x^{17}+419904 x^{15}+3645000 x^{14}+4408992 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] 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\right ) \log (x)} \, dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \frac {6561 x^{17}+157464 x^{15}+1822500 x^{14}+1653372 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+11418525000 x^8+19129907088 x^7+66719025000 x^6+300666345007 x^5+421106423750 x^4+537220650631 x^3+956153602500 x^2+\left (x^2+3\right )^8 x \log ^8(x)+24 \left (x^2+3\right )^8 x \log ^7(x)+4 \left (x^2+3\right )^6 \left (63 x^4+378 x^2+625 x+567\right ) x \log ^6(x)+72 \left (x^2+3\right )^6 \left (21 x^4+126 x^2+625 x+189\right ) x \log ^5(x)+10 \left (x^2+3\right )^3 \left (567 x^{10}+8505 x^8+33750 x^7+51030 x^6+303750 x^5+387465 x^4+989375 x^3+932760 x^2+2083125 x+137781\right ) x \log ^4(x)+12 \left (x^2+3\right )^3 \left (1134 x^{11}+17010 x^9+112500 x^8+102060 x^7+1012500 x^6+2649930 x^5+3818750 x^4+7490520 x^3+15146875 x^2+275562 x+1171875\right ) \log ^3(x)[phone] x+2 \left (10206 x^{17}+244944 x^{15}+1518750 x^{14}+2571912 x^{13}[phone] x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+1835750000 x^8+4044351998 x^7+8445281250 x^6+13634496747 x^5+16860431250 x^4+22882470426 x^3+11928262500 x^2+6658758441 x+1708593750\right ) \log ^2(x)+12 \left (1458 x^{17}+34992 x^{15}+303750 x^{14}+367416 x^{13}+5467500 x^{12}[phone] x^{11}[phone] x^{10}[phone] x^9+831603125 x^8+1647184214 x^7+4564368750 x^6+9143823196 x^5+8444430000 x^4+20777071668 x^3+4208152500 x^2+8798628438 x+854296875\right ) \log (x)[phone]}{x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7239

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )}+\frac {1171875 \left (108 x^{10}+1620 x^8-26250 x^7+9720 x^6-101250 x^5-2314590 x^4-2633125 x^3+2387490 x^2+4 \left (x^2+3\right )^5 \log ^3(x)+6 \left (x^2+3\right )^2 \left (6 x^6+54 x^4-625 x^3+162 x^2+625 x+162\right ) \log ^2(x)+4 \left (x^2+3\right )^2 \left (27 x^6+243 x^4-5000 x^3+729 x^2+7500 x+729\right ) \log (x)+1678125 x+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+972 x^6+11250 x^5+4374 x^4+67500 x^3+399373 x^2+\left (x^2+3\right )^4 \log ^4(x)+12 \left (x^2+3\right )^4 \log ^3(x)+2 \left (x^2+3\right )^2 \left (27 x^4+162 x^2+625 x+243\right ) \log ^2(x)+12 \left (x^2+3\right )^2 \left (9 x^4+54 x^2+625 x+81\right ) \log (x)+491875 x+6561\right )^2}+1\right )dx\)

\(\Big \downarrow \) 7293

\(\displaystyle \int \left (\frac {9375000 x}{\left (x^2+3\right ) \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )}+\frac {1171875 \left (108 x^{10}+4 x^{10} \log ^3(x)+36 x^{10} \log ^2(x)+108 x^{10} \log (x)+1620 x^8+60 x^8 \log ^3(x)+540 x^8 \log ^2(x)+1620 x^8 \log (x)-26250 x^7-3750 x^7 \log ^2(x)-20000 x^7 \log (x)+9720 x^6+360 x^6 \log ^3(x)+3240 x^6 \log ^2(x)+9720 x^6 \log (x)-101250 x^5-18750 x^5 \log ^2(x)-90000 x^5 \log (x)-2314590 x^4+1080 x^4 \log ^3(x)+9720 x^4 \log ^2(x)+29160 x^4 \log (x)-2633125 x^3-11250 x^3 \log ^2(x)+2387490 x^2+1620 x^2 \log ^3(x)+14580 x^2 \log ^2(x)+43740 x^2 \log (x)+1678125 x+972 \log ^3(x)+33750 x \log ^2(x)+8748 \log ^2(x)+270000 x \log (x)+26244 \log (x)+26244\right )}{\left (x^2+3\right ) x \left (81 x^8+x^8 \log ^4(x)+12 x^8 \log ^3(x)+54 x^8 \log ^2(x)+108 x^8 \log (x)+972 x^6+12 x^6 \log ^4(x)+144 x^6 \log ^3(x)+648 x^6 \log ^2(x)+1296 x^6 \log (x)+11250 x^5+1250 x^5 \log ^2(x)+7500 x^5 \log (x)+4374 x^4+54 x^4 \log ^4(x)+648 x^4 \log ^3(x)+2916 x^4 \log ^2(x)+5832 x^4 \log (x)+67500 x^3+7500 x^3 \log ^2(x)+45000 x^3 \log (x)+399373 x^2+108 x^2 \log ^4(x)+1296 x^2 \log ^3(x)+5832 x^2 \log ^2(x)+11664 x^2 \log (x)+491875 x+81 \log ^4(x)+972 \log ^3(x)+11250 x \log ^2(x)+4374 \log ^2(x)+67500 x \log (x)+8748 \log (x)+6561\right )^2}+1\right )dx\)

Input:

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 + 32805 
000*x^12 + 1653372*x^13 + 1822500*x^14 + 157464*x^15 + 6561*x^17 + (102515 
62500 + 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 + 44 
08992*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 + 2 
7268993494*x^5 + 16890562500*x^6 + 8088703996*x^7 + 3671500000*x^8 + 16344 
86040*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 + (379687500 + 892820 
88*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 + 1916250 
00*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 1350000*x^14 + 32 
6592*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 + 201 
000000*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 + 3429216*x^7 + 1350000*x^8 + 1428840*x^9 + 337500*x^10 + 3 
81024*x^11 + 45000*x^12 + 63504*x^13 + 2500*x^14 + 6048*x^15 + 252*x^17)*L 
og[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)/(43046721*x + 6454383750*x^2 + 247181588131*x^3 + 3937689237 
50*x^4 + 225959313757*x^5 + 58365900000*x^6 + 19129907088*x^7 + 1053258750 
0*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 + 94 
91580000*x^2 + 73543610016*x^3 + 67161285000*x^4 + 62850878352*x^5 + 44141 
175000*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 + 419 
904*x^15 + 17496*x^17)*Log[x] + (133923132*x + 5631525000*x^2 + 1939775335 
2*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 + 5 
4675000*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 + 3 
315266496*x^5 + 2146500000*x^6 + 1703927664*x^7 + 841500000*x^8 + 41465736 
0*x^9 + 191625000*x^10 + 48700296*x^11 + 24300000*x^12 + 3429216*x^13 + 13 
50000*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 + 2037 
19860*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 + 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^1 
5 + 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 + (65 
61*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]
 

Output:

$Aborted
 

Maple [B] (verified)

Leaf count of result is larger than twice the leaf count of optimal. \(242\) vs. \(2(27)=54\).

Time = 0.36 (sec) , antiderivative size = 243, normalized size of antiderivative = 8.38

\[x -\frac {1171875}{6561+491875 x +1296 x^{6} \ln \left (x \right )+648 x^{6} \ln \left (x \right )^{2}+1296 x^{2} \ln \left (x \right )^{3}+5832 x^{4} \ln \left (x \right )+2916 x^{4} \ln \left (x \right )^{2}+648 x^{4} \ln \left (x \right )^{3}+x^{8} \ln \left (x \right )^{4}+1250 x^{5} \ln \left (x \right )^{2}+144 x^{6} \ln \left (x \right )^{3}+108 x^{8} \ln \left (x \right )+54 x^{8} \ln \left (x \right )^{2}+12 x^{8} \ln \left (x \right )^{3}+7500 x^{3} \ln \left (x \right )^{2}+45000 x^{3} \ln \left (x \right )+12 x^{6} \ln \left (x \right )^{4}+5832 x^{2} \ln \left (x \right )^{2}+54 x^{4} \ln \left (x \right )^{4}+7500 x^{5} \ln \left (x \right )+108 x^{2} \ln \left (x \right )^{4}+81 x^{8}+11664 x^{2} \ln \left (x \right )+67500 x \ln \left (x \right )+11250 x \ln \left (x \right )^{2}+11250 x^{5}+8748 \ln \left (x \right )+972 x^{6}+81 \ln \left (x \right )^{4}+972 \ln \left (x \right )^{3}+4374 \ln \left (x \right )^{2}+399373 x^{2}+67500 x^{3}+4374 x^{4}}\]

Input:

int((10251562500+655560624846*x+6561*x^17+1822500*x^14+199763982*x^11+1141 
8525000*x^8+(13608*x^17+326592*x^15+1350000*x^14+3429216*x^13+24300000*x^1 
2+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 
[phone]*x[phone])*ln(x)^3+(20412*x^17+489888*x^15+3037500*x^14+514382 
4*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+4576 
4940852*x^3+23856525000*x^2+13317516882*x[phone])*ln(x)^2+(17496*x^17+ 
419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+5764500 
00*x^10+3136702320*x^9+9979237500*x^8+19766210568*x^7+54772425000*x^6+1097 
25878352*x^5+101333160000*x^4+249324860016*x^3+50497830000*x^2+10558354125 
6*x[phone])*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^1 
1+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+2057529 
6*x^7+54675000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32805000*x^2+992 
0232*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+201000000*x^8+203719860*x^7+53 
6625000*x^6+368861040*x^5+829575000*x^4+289046070*x^3+562443750*x^2+372008 
70*x)*ln(x)^4+300666345007*x^5+19129907088*x^7+66719025000*x^6+309318750*x 
^10+2315325870*x^9+1653372*x^13+32805000*x^12+157464*x^15+956153602500*x^2 
[phone]*x^3+421106423750*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+243000 
00*x^8+20575296*x^7+54675000*x^6+30862944*x^5+65610000*x^4+26453952*x^3+32 
805000*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+20 
3719860*x^7+452250000*x^6+368861040*x^5+576450000*x^4+289046070*x^3+309318 
750*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+841500000*x^8 
[phone]*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+31 
23062500*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+ 
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+32805000*x^12+199763982*x^11+3 
09318750*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+43046 
721*x),x)
 

Output:

x-1171875/(6561+491875*x+1296*x^6*ln(x)+648*x^6*ln(x)^2+1296*x^2*ln(x)^3+5 
832*x^4*ln(x)+2916*x^4*ln(x)^2+648*x^4*ln(x)^3+x^8*ln(x)^4+1250*x^5*ln(x)^ 
2+144*x^6*ln(x)^3+108*x^8*ln(x)+54*x^8*ln(x)^2+12*x^8*ln(x)^3+7500*x^3*ln( 
x)^2+45000*x^3*ln(x)+12*x^6*ln(x)^4+5832*x^2*ln(x)^2+54*x^4*ln(x)^4+7500*x 
^5*ln(x)+108*x^2*ln(x)^4+81*x^8+11664*x^2*ln(x)+67500*x*ln(x)+11250*x*ln(x 
)^2+11250*x^5+8748*ln(x)+972*x^6+81*ln(x)^4+972*ln(x)^3+4374*ln(x)^2+39937 
3*x^2+67500*x^3+4374*x^4)
 

Fricas [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 352 vs. \(2 (30) = 60\).

Time = 0.17 (sec) , antiderivative size = 352, normalized size of antiderivative = 12.14 \[ \text {the integral} =\frac {81 \, x^{9} + 972 \, x^{7} + 11250 \, x^{6} + 4374 \, x^{5} + {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \left (x\right )^{4} + 67500 \, x^{4} + 12 \, {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \left (x\right )^{3} + 399373 \, x^{3} + 2 \, {\left (27 \, x^{9} + 324 \, x^{7} + 625 \, x^{6} + 1458 \, x^{5} + 3750 \, x^{4} + 2916 \, x^{3} + 5625 \, x^{2} + 2187 \, x\right )} \log \left (x\right )^{2} + 491875 \, x^{2} + 12 \, {\left (9 \, x^{9} + 108 \, x^{7} + 625 \, x^{6} + 486 \, x^{5} + 3750 \, x^{4} + 972 \, x^{3} + 5625 \, x^{2} + 729 \, x\right )} \log \left (x\right ) + 6561 \, x - 1171875}{81 \, x^{8} + 972 \, x^{6} + 11250 \, x^{5} + {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \left (x\right )^{4} + 4374 \, x^{4} + 12 \, {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \left (x\right )^{3} + 67500 \, x^{3} + 2 \, {\left (27 \, x^{8} + 324 \, x^{6} + 625 \, x^{5} + 1458 \, x^{4} + 3750 \, x^{3} + 2916 \, x^{2} + 5625 \, x + 2187\right )} \log \left (x\right )^{2} + 399373 \, x^{2} + 12 \, {\left (9 \, x^{8} + 108 \, x^{6} + 625 \, x^{5} + 486 \, x^{4} + 3750 \, x^{3} + 972 \, x^{2} + 5625 \, x + 729\right )} \log \left (x\right ) + 491875 \, x + 6561} \] Input:

integrate((10251562500+655560624846*x+1822500*x^14+300666345007*x^5+956153 
602500*x^2+66719025000*x^6+19129907088*x^7+32805000*x^12+421106423750*x^4+ 
537220650631*x^3+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+6561000 
0*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[phone])*log(x)+(x^17+24*x^15+252*x^1 
3+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+51 
43824*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+54675000*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+3 
37500*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+1 
350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657 
360*x^9+958687500*x^8+1703927664*x^7+3215250000*x^6+3315266496*x^5+6271425 
000*x^4+2516210568*x^3+5287275000*x^2+89282088*x[phone])*log(x)^3+(2041 
2*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+8088703996*x^7+16890562500*x^ 
6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516 
882*x[phone])*log(x)^2+199763982*x^11+309318750*x^10+2315325870*x^9+11 
418525000*x^8+1653372*x^13+157464*x^15+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+38 
1024*x^11+337500*x^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5143 
824*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+8 
573040*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)*log(x)^5+(5670*x^17+136080*x^15+337 
500*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+28 
9046070*x^3+309318750*x^2+37200870*x)*log(x)^4+(13608*x^17+326592*x^15+135 
0000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+41465736 
0*x^9+841500000*x^8+1703927664*x^7+2146500000*x^6+3315266496*x^5+298080000 
0*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*log(x)^3+(20412*x^17+48988 
8*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+1994477474 
4*x^5+17773987500*x^4+19397753352*x^3+5631525000*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+576450000*x^10+3136702320*x^9+8840175000*x^8+19766210568*x^7+4414117 
5000*x^6+62850878352*x^5+67161285000*x^4+73543610016*x^3+9491580000*x^2+11 
4791256*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+1912990 
7088*x^7+58365900000*x^6+225959313757*x^5+393768923750*x^4+247181588131*x^ 
3+6454383750*x^2+43046721*x),x, algorithm="fricas")
 

Output:

(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 + 3750 
*x^4 + 2916*x^3 + 5625*x^2 + 2187*x)*log(x)^2 + 491875*x^2 + 12*(9*x^9 + 1 
08*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 + 54*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 + 1 
08*x^6 + 625*x^5 + 486*x^4 + 3750*x^3 + 972*x^2 + 5625*x + 729)*log(x) + 4 
91875*x + 6561)
 

Sympy [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 170 vs. \(2 (22) = 44\).

Time = 2.06 (sec) , antiderivative size = 170, normalized size of antiderivative = 5.86 \[ \text {the integral} =x - \frac {1171875}{81 x^{8} + 972 x^{6} + 11250 x^{5} + 4374 x^{4} + 67500 x^{3} + 399373 x^{2} + 491875 x + \left (x^{8} + 12 x^{6} + 54 x^{4} + 108 x^{2} + 81\right ) \log {\left (x \right )}^{4} + \left (12 x^{8} + 144 x^{6} + 648 x^{4} + 1296 x^{2} + 972\right ) \log {\left (x \right )}^{3} + \left (54 x^{8} + 648 x^{6} + 1250 x^{5} + 2916 x^{4} + 7500 x^{3} + 5832 x^{2} + 11250 x + 4374\right ) \log {\left (x \right )}^{2} + \left (108 x^{8} + 1296 x^{6} + 7500 x^{5} + 5832 x^{4} + 45000 x^{3} + 11664 x^{2} + 67500 x + 8748\right ) \log {\left (x \right )} + 6561} \] Input:

integrate((10251562500+655560624846*x[phone]*x**2+(20412*x**17+48988 
8*x**15+3037500*x**14+5143824*x**13+54675000*x**12+157425444*x**11+4522500 
00*x**10+1634486040*x**9+3671500000*x**8+8088703996*x**7+16890562500*x**6+ 
27268993494*x**5+33720862500*x**4+45764940852*x**3+23856525000*x**2+133175 
16882*x[phone])*ln(x)**2+(24*x**17+576*x**15+6048*x**13+36288*x**11+13 
6080*x**9+326592*x**7+489888*x**5+419904*x**3+157464*x)*ln(x)**7+(252*x**1 
7+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 
[phone]*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+602 
73900*x**9+201000000*x**8+203719860*x**7+536625000*x**6+368861040*x**5+829 
575000*x**4+289046070*x**3+562443750*x**2+37200870*x)*ln(x)**4+(13608*x**1 
7+326592*x**15+1350000*x**14+3429216*x**13+24300000*x**12+48700296*x**11+1 
91625000*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+8928208 
8*x[phone])*ln(x)**3+199763982*x**11+1653372*x**13+157464*x**15+6561*x* 
*17+309318750*x**10+2315325870*x**9+32805000*x**12+19129907088*x**7+300666 
345007*x**5+537220650631*x**3+(17496*x**17+419904*x**15+3645000*x**14+4408 
992*x**13+65610000*x**12+279578952*x**11+576450000*x**10+3136702320*x**9+9 
979237500*x**8+19766210568*x**7+54772425000*x**6+109725878352*x**5+1013331 
60000*x**4+249324860016*x**3+50497830000*x**2+105583541256*x[phone])* 
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+1822500*x**14+11418525000*x**8+421106423750*x 
**4+66719025000*x**6)/((x**17+24*x**15+252*x**13+1512*x**11+5670*x**9+1360 
8*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)*l 
n(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+51438 
24*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+60750 
00*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+4 
6343750*x**10+60273900*x**9+191625000*x**8+203719860*x**7+452250000*x**6+3 
68861040*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+3429216*x**13+24300000*x**12 
[phone]*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+174352 
5000*x**2+89282088*x)*ln(x)**3+(20412*x**17+489888*x**15+3037500*x**14+514 
3824*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+17773987 
500*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 
[phone]*x**10+3136702320*x**9+8840175000*x**8+19766210568*x**7+44141175 
000*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+3 
2805000*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 
[phone]*x**3+6454383750*x**2+43046721*x),x)
 

Output:

x - 1171875/(81*x**8 + 972*x**6 + 11250*x**5 + 4374*x**4 + 67500*x**3 + 39 
9373*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 + 43 
74)*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)
 

Maxima [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 352 vs. \(2 (30) = 60\).

Time = 0.68 (sec) , antiderivative size = 352, normalized size of antiderivative = 12.14 \[ \text {the integral} =\frac {81 \, x^{9} + 972 \, x^{7} + 11250 \, x^{6} + 4374 \, x^{5} + {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \left (x\right )^{4} + 67500 \, x^{4} + 12 \, {\left (x^{9} + 12 \, x^{7} + 54 \, x^{5} + 108 \, x^{3} + 81 \, x\right )} \log \left (x\right )^{3} + 399373 \, x^{3} + 2 \, {\left (27 \, x^{9} + 324 \, x^{7} + 625 \, x^{6} + 1458 \, x^{5} + 3750 \, x^{4} + 2916 \, x^{3} + 5625 \, x^{2} + 2187 \, x\right )} \log \left (x\right )^{2} + 491875 \, x^{2} + 12 \, {\left (9 \, x^{9} + 108 \, x^{7} + 625 \, x^{6} + 486 \, x^{5} + 3750 \, x^{4} + 972 \, x^{3} + 5625 \, x^{2} + 729 \, x\right )} \log \left (x\right ) + 6561 \, x - 1171875}{81 \, x^{8} + 972 \, x^{6} + 11250 \, x^{5} + {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \left (x\right )^{4} + 4374 \, x^{4} + 12 \, {\left (x^{8} + 12 \, x^{6} + 54 \, x^{4} + 108 \, x^{2} + 81\right )} \log \left (x\right )^{3} + 67500 \, x^{3} + 2 \, {\left (27 \, x^{8} + 324 \, x^{6} + 625 \, x^{5} + 1458 \, x^{4} + 3750 \, x^{3} + 2916 \, x^{2} + 5625 \, x + 2187\right )} \log \left (x\right )^{2} + 399373 \, x^{2} + 12 \, {\left (9 \, x^{8} + 108 \, x^{6} + 625 \, x^{5} + 486 \, x^{4} + 3750 \, x^{3} + 972 \, x^{2} + 5625 \, x + 729\right )} \log \left (x\right ) + 491875 \, x + 6561} \] Input:

integrate((10251562500+655560624846*x+1822500*x^14+300666345007*x^5+956153 
602500*x^2+66719025000*x^6+19129907088*x^7+32805000*x^12+421106423750*x^4+ 
537220650631*x^3+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+6561000 
0*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[phone])*log(x)+(x^17+24*x^15+252*x^1 
3+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+51 
43824*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+54675000*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+3 
37500*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+1 
350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657 
360*x^9+958687500*x^8+1703927664*x^7+3215250000*x^6+3315266496*x^5+6271425 
000*x^4+2516210568*x^3+5287275000*x^2+89282088*x[phone])*log(x)^3+(2041 
2*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+8088703996*x^7+16890562500*x^ 
6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516 
882*x[phone])*log(x)^2+199763982*x^11+309318750*x^10+2315325870*x^9+11 
418525000*x^8+1653372*x^13+157464*x^15+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+38 
1024*x^11+337500*x^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5143 
824*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+8 
573040*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)*log(x)^5+(5670*x^17+136080*x^15+337 
500*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+28 
9046070*x^3+309318750*x^2+37200870*x)*log(x)^4+(13608*x^17+326592*x^15+135 
0000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+41465736 
0*x^9+841500000*x^8+1703927664*x^7+2146500000*x^6+3315266496*x^5+298080000 
0*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*log(x)^3+(20412*x^17+48988 
8*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+1994477474 
4*x^5+17773987500*x^4+19397753352*x^3+5631525000*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+576450000*x^10+3136702320*x^9+8840175000*x^8+19766210568*x^7+4414117 
5000*x^6+62850878352*x^5+67161285000*x^4+73543610016*x^3+9491580000*x^2+11 
4791256*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+1912990 
7088*x^7+58365900000*x^6+225959313757*x^5+393768923750*x^4+247181588131*x^ 
3+6454383750*x^2+43046721*x),x, algorithm="maxima")
 

Output:

(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 + 3750 
*x^4 + 2916*x^3 + 5625*x^2 + 2187*x)*log(x)^2 + 491875*x^2 + 12*(9*x^9 + 1 
08*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 + 54*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 + 1 
08*x^6 + 625*x^5 + 486*x^4 + 3750*x^3 + 972*x^2 + 5625*x + 729)*log(x) + 4 
91875*x + 6561)
 

Giac [B] (verification not implemented)

Leaf count of result is larger than twice the leaf count of optimal. 242 vs. \(2 (30) = 60\).

Time = 6.65 (sec) , antiderivative size = 242, normalized size of antiderivative = 8.34 \[ \text {the integral} =x - \frac {1171875}{x^{8} \log \left (x\right )^{4} + 12 \, x^{8} \log \left (x\right )^{3} + 54 \, x^{8} \log \left (x\right )^{2} + 12 \, x^{6} \log \left (x\right )^{4} + 108 \, x^{8} \log \left (x\right ) + 144 \, x^{6} \log \left (x\right )^{3} + 81 \, x^{8} + 648 \, x^{6} \log \left (x\right )^{2} + 54 \, x^{4} \log \left (x\right )^{4} + 1296 \, x^{6} \log \left (x\right ) + 1250 \, x^{5} \log \left (x\right )^{2} + 648 \, x^{4} \log \left (x\right )^{3} + 972 \, x^{6} + 7500 \, x^{5} \log \left (x\right ) + 2916 \, x^{4} \log \left (x\right )^{2} + 108 \, x^{2} \log \left (x\right )^{4} + 11250 \, x^{5} + 5832 \, x^{4} \log \left (x\right ) + 7500 \, x^{3} \log \left (x\right )^{2} + 1296 \, x^{2} \log \left (x\right )^{3} + 4374 \, x^{4} + 45000 \, x^{3} \log \left (x\right ) + 5832 \, x^{2} \log \left (x\right )^{2} + 81 \, \log \left (x\right )^{4} + 67500 \, x^{3} + 11664 \, x^{2} \log \left (x\right ) + 11250 \, x \log \left (x\right )^{2} + 972 \, \log \left (x\right )^{3} + 399373 \, x^{2} + 67500 \, x \log \left (x\right ) + 4374 \, \log \left (x\right )^{2} + 491875 \, x + 8748 \, \log \left (x\right ) + 6561} \] Input:

integrate((10251562500+655560624846*x+1822500*x^14+300666345007*x^5+956153 
602500*x^2+66719025000*x^6+19129907088*x^7+32805000*x^12+421106423750*x^4+ 
537220650631*x^3+(17496*x^17+419904*x^15+3645000*x^14+4408992*x^13+6561000 
0*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[phone])*log(x)+(x^17+24*x^15+252*x^1 
3+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+51 
43824*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+54675000*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+3 
37500*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+1 
350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+414657 
360*x^9+958687500*x^8+1703927664*x^7+3215250000*x^6+3315266496*x^5+6271425 
000*x^4+2516210568*x^3+5287275000*x^2+89282088*x[phone])*log(x)^3+(2041 
2*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+8088703996*x^7+16890562500*x^ 
6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000*x^2+13317516 
882*x[phone])*log(x)^2+199763982*x^11+309318750*x^10+2315325870*x^9+11 
418525000*x^8+1653372*x^13+157464*x^15+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+38 
1024*x^11+337500*x^10+1428840*x^9+1350000*x^8+3429216*x^7+3037500*x^6+5143 
824*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+8 
573040*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)*log(x)^5+(5670*x^17+136080*x^15+337 
500*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+28 
9046070*x^3+309318750*x^2+37200870*x)*log(x)^4+(13608*x^17+326592*x^15+135 
0000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+191625000*x^10+41465736 
0*x^9+841500000*x^8+1703927664*x^7+2146500000*x^6+3315266496*x^5+298080000 
0*x^4+2516210568*x^3+1743525000*x^2+89282088*x)*log(x)^3+(20412*x^17+48988 
8*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+1994477474 
4*x^5+17773987500*x^4+19397753352*x^3+5631525000*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+576450000*x^10+3136702320*x^9+8840175000*x^8+19766210568*x^7+4414117 
5000*x^6+62850878352*x^5+67161285000*x^4+73543610016*x^3+9491580000*x^2+11 
4791256*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+1912990 
7088*x^7+58365900000*x^6+225959313757*x^5+393768923750*x^4+247181588131*x^ 
3+6454383750*x^2+43046721*x),x, algorithm="giac")
 

Output:

x - 1171875/(x^8*log(x)^4 + 12*x^8*log(x)^3 + 54*x^8*log(x)^2 + 12*x^6*log 
(x)^4 + 108*x^8*log(x) + 144*x^6*log(x)^3 + 81*x^8 + 648*x^6*log(x)^2 + 54 
*x^4*log(x)^4 + 1296*x^6*log(x) + 1250*x^5*log(x)^2 + 648*x^4*log(x)^3 + 9 
72*x^6 + 7500*x^5*log(x) + 2916*x^4*log(x)^2 + 108*x^2*log(x)^4 + 11250*x^ 
5 + 5832*x^4*log(x) + 7500*x^3*log(x)^2 + 1296*x^2*log(x)^3 + 4374*x^4 + 4 
5000*x^3*log(x) + 5832*x^2*log(x)^2 + 81*log(x)^4 + 67500*x^3 + 11664*x^2* 
log(x) + 11250*x*log(x)^2 + 972*log(x)^3 + 399373*x^2 + 67500*x*log(x) + 4 
374*log(x)^2 + 491875*x + 8748*log(x) + 6561)
 

Mupad [F(-1)]

Timed out. \[ \text {the integral} =\text {Too large to display} \] Input:

int((655560624846*x + log(x)^6*(1653372*x + 1822500*x^2 + 4408992*x^3 + 36 
45000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*x^7 + 1350000*x^8 + 142884 
0*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 + 204 
12*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 252*x^13 + 24*x^15 + x^17) + l 
og(x)*(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 + 440 
8992*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 + 2385652 
5000*x^2 + 45764940852*x^3 + 33720862500*x^4 + 27268993494*x^5 + 168905625 
00*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 + 3417187500) + log(x)^3*(89282088*x + 5287275000*x^2 + 2 
516210568*x^3 + 6271425000*x^4 + 3315266496*x^5 + 3215250000*x^6 + 1703927 
664*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 + 829575 
000*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) + 956153602500*x^2 + 53722065063 
1*x^3 + 421106423750*x^4 + 300666345007*x^5 + 66719025000*x^6 + 1912990708 
8*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)/(43046721*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 + 2645395 
2*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 + 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^1 
7) + log(x)*(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 + 4408 
992*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^1 
3 + 576*x^15 + 24*x^17) + log(x)^2*(133923132*x + 5631525000*x^2 + 1939775 
3352*x^3 + 17773987500*x^4 + 19944774744*x^5 + 11828062500*x^6 + 808870399 
6*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(x)^4*(37200870*x + 309318750*x^2 + 289046070*x^3 + 576450000*x^4 + 3 
68861040*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)^3*(89282088*x + 1743525000*x^2 + 2 
516210568*x^3 + 2980800000*x^4 + 3315266496*x^5 + 2146500000*x^6 + 1703927 
664*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) + 
 6454383750*x^2 + 247181588131*x^3 + 393768923750*x^4 + 225959313757*x^5 + 
 58365900000*x^6 + 19129907088*x^7 + 10532587500*x^8 + 2315325870*x^9 + 30 
9318750*x^10 + 199763982*x^11 + 32805000*x^12 + 1653372*x^13 + 1822500*x^1 
4 + 157464*x^15 + 6561*x^17),x)
 

Output:

int((655560624846*x + log(x)^6*(1653372*x + 1822500*x^2 + 4408992*x^3 + 36 
45000*x^4 + 5143824*x^5 + 3037500*x^6 + 3429216*x^7 + 1350000*x^8 + 142884 
0*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 + 204 
12*x^5 + 13608*x^7 + 5670*x^9 + 1512*x^11 + 252*x^13 + 24*x^15 + x^17) + l 
og(x)*(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 + 440 
8992*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 + 2385652 
5000*x^2 + 45764940852*x^3 + 33720862500*x^4 + 27268993494*x^5 + 168905625 
00*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 + 3417187500) + log(x)^3*(89282088*x + 5287275000*x^2 + 2 
516210568*x^3 + 6271425000*x^4 + 3315266496*x^5 + 3215250000*x^6 + 1703927 
664*x^7 + 958687500*x^8 + 414657360*x^9 + 191625000*x^10 + 48700296*x^1...
 

Reduce [B] (verification not implemented)

Time = 10.61 (sec) , antiderivative size = 600, normalized size of antiderivative = 20.69 \[ \text {the integral} =\text {Too large to display} \] Input:

int((10251562500+1822500*x^14+655560624846*x[phone]*x^5+956153602500 
*x^2+(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)*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+8 
29575000*x^4+289046070*x^3+562443750*x^2+37200870*x)*log(x)^4+(13608*x^17+ 
326592*x^15+1350000*x^14+3429216*x^13+24300000*x^12+48700296*x^11+19162500 
0*x^10+414657360*x^9+958687500*x^8+1703927664*x^7+3215250000*x^6+331526649 
6*x^5+6271425000*x^4+2516210568*x^3+5287275000*x^2+89282088*x[phone])*l 
og(x)^3+(20412*x^17+489888*x^15+3037500*x^14+5143824*x^13+54675000*x^12+15 
7425444*x^11+452250000*x^10+1634486040*x^9+3671500000*x^8+8088703996*x^7+1 
6890562500*x^6+27268993494*x^5+33720862500*x^4+45764940852*x^3+23856525000 
*x^2+13317516882*x[phone])*log(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 
[phone]*x^8+19766210568*x^7+54772425000*x^6+109725878352*x^5+101333160 
000*x^4+249324860016*x^3+50497830000*x^2+105583541256*x[phone])*log(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)*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+342 
9216*x^7+3037500*x^6+5143824*x^5+3645000*x^4+4408992*x^3+1822500*x^2+16533 
72*x)*log(x)^6+66719025000*x^6+11418525000*x^8+199763982*x^11+309318750*x^ 
10+32805000*x^12+19129907088*x^7+421106423750*x^4+537220650631*x^3+1653372 
*x^13+157464*x^15+6561*x^17+2315325870*x^9)/((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+15746 
4*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+54675000*x^6+30862944*x^5+65610000*x^4+2645 
3952*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+1916 
25000*x^8+203719860*x^7+452250000*x^6+368861040*x^5+576450000*x^4+28904607 
0*x^3+309318750*x^2+37200870*x)*log(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+ 
841500000*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+163 
4486040*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)*log(x)^2+(1749 
6*x^17+419904*x^15+3645000*x^14+4408992*x^13+65610000*x^12+279578952*x^11+ 
576450000*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+11479125 
6*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+6454 
383750*x^2+43046721*x),x)
 

Output:

(54*log(x)**4*x**9 - 625*log(x)**4*x**8 + 648*log(x)**4*x**7 - 7500*log(x) 
**4*x**6 + 2916*log(x)**4*x**5 - 33750*log(x)**4*x**4 + 5832*log(x)**4*x** 
3 - 67500*log(x)**4*x**2 + 4374*log(x)**4*x - 50625*log(x)**4 + 648*log(x) 
**3*x**9 - 7500*log(x)**3*x**8 + 7776*log(x)**3*x**7 - 90000*log(x)**3*x** 
6 + 34992*log(x)**3*x**5 - 405000*log(x)**3*x**4 + 69984*log(x)**3*x**3 - 
810000*log(x)**3*x**2 + 52488*log(x)**3*x - 607500*log(x)**3 + 2916*log(x) 
**2*x**9 - 33750*log(x)**2*x**8 + 34992*log(x)**2*x**7 - 337500*log(x)**2* 
x**6 - 623786*log(x)**2*x**5 - 1417500*log(x)**2*x**4 - 4372572*log(x)**2* 
x**3 - 3037500*log(x)**2*x**2 - 6795054*log(x)**2*x - 2733750*log(x)**2 + 
5832*log(x)*x**9 - 67500*log(x)*x**8 + 69984*log(x)*x**7 - 405000*log(x)*x 
**6 - 4372572*log(x)*x**5 - 1215000*log(x)*x**4 - 27495144*log(x)*x**3 - 3 
645000*log(x)*x**2 - 41715108*log(x)*x - 5467500*log(x) + 4374*x**9 - 5062 
5*x**8 + 52488*x**7 - 6795054*x**5 + 911250*x**4 - 20621358*x**3 - 2230468 
75*x**2 - 307067581*x - 67381875)/(54*(log(x)**4*x**8 + 12*log(x)**4*x**6 
+ 54*log(x)**4*x**4 + 108*log(x)**4*x**2 + 81*log(x)**4 + 12*log(x)**3*x** 
8 + 144*log(x)**3*x**6 + 648*log(x)**3*x**4 + 1296*log(x)**3*x**2 + 972*lo 
g(x)**3 + 54*log(x)**2*x**8 + 648*log(x)**2*x**6 + 1250*log(x)**2*x**5 + 2 
916*log(x)**2*x**4 + 7500*log(x)**2*x**3 + 5832*log(x)**2*x**2 + 11250*log 
(x)**2*x + 4374*log(x)**2 + 108*log(x)*x**8 + 1296*log(x)*x**6 + 7500*log( 
x)*x**5 + 5832*log(x)*x**4 + 45000*log(x)*x**3 + 11664*log(x)*x**2 + 67...