1,1,53,62,0.060000," ","int((e*x^2+d*x+c)/(b*x+a)^(1/2),x)","\frac{2 \sqrt{b x +a}\, \left(3 e \,x^{2} b^{2}-4 a b e x +5 b^{2} d x +8 a^{2} e -10 a b d +15 b^{2} c \right)}{15 b^{3}}"," ",0,"2/15*(b*x+a)^(1/2)*(3*b^2*e*x^2-4*a*b*e*x+5*b^2*d*x+8*a^2*e-10*a*b*d+15*b^2*c)/b^3","A"
2,1,194,143,0.048000," ","int((e*x^2+d*x+c)^2/(b*x+a)^(1/2),x)","\frac{2 \sqrt{b x +a}\, \left(35 e^{2} x^{4} b^{4}-40 a \,b^{3} e^{2} x^{3}+90 b^{4} d e \,x^{3}+48 a^{2} b^{2} e^{2} x^{2}-108 a \,b^{3} d e \,x^{2}+126 b^{4} c e \,x^{2}+63 b^{4} d^{2} x^{2}-64 a^{3} b \,e^{2} x +144 a^{2} b^{2} d e x -168 a \,b^{3} c e x -84 a \,b^{3} d^{2} x +210 b^{4} c d x +128 a^{4} e^{2}-288 a^{3} b d e +336 a^{2} b^{2} c e +168 a^{2} b^{2} d^{2}-420 a \,b^{3} c d +315 c^{2} b^{4}\right)}{315 b^{5}}"," ",0,"2/315*(b*x+a)^(1/2)*(35*b^4*e^2*x^4-40*a*b^3*e^2*x^3+90*b^4*d*e*x^3+48*a^2*b^2*e^2*x^2-108*a*b^3*d*e*x^2+126*b^4*c*e*x^2+63*b^4*d^2*x^2-64*a^3*b*e^2*x+144*a^2*b^2*d*e*x-168*a*b^3*c*e*x-84*a*b^3*d^2*x+210*b^4*c*d*x+128*a^4*e^2-288*a^3*b*d*e+336*a^2*b^2*c*e+168*a^2*b^2*d^2-420*a*b^3*c*d+315*b^4*c^2)/b^5","A"
3,1,495,250,0.052000," ","int((e*x^2+d*x+c)^3/(b*x+a)^(1/2),x)","\frac{2 \sqrt{b x +a}\, \left(1155 e^{3} x^{6} b^{6}-1260 a \,b^{5} e^{3} x^{5}+4095 b^{6} d \,e^{2} x^{5}+1400 a^{2} b^{4} e^{3} x^{4}-4550 a \,b^{5} d \,e^{2} x^{4}+5005 b^{6} c \,e^{2} x^{4}+5005 b^{6} d^{2} e \,x^{4}-1600 a^{3} b^{3} e^{3} x^{3}+5200 a^{2} b^{4} d \,e^{2} x^{3}-5720 a \,b^{5} c \,e^{2} x^{3}-5720 a \,b^{5} d^{2} e \,x^{3}+12870 b^{6} c d e \,x^{3}+2145 b^{6} d^{3} x^{3}+1920 a^{4} b^{2} e^{3} x^{2}-6240 a^{3} b^{3} d \,e^{2} x^{2}+6864 a^{2} b^{4} c \,e^{2} x^{2}+6864 a^{2} b^{4} d^{2} e \,x^{2}-15444 a \,b^{5} c d e \,x^{2}-2574 a \,b^{5} d^{3} x^{2}+9009 b^{6} c^{2} e \,x^{2}+9009 b^{6} c \,d^{2} x^{2}-2560 a^{5} b \,e^{3} x +8320 a^{4} b^{2} d \,e^{2} x -9152 a^{3} b^{3} c \,e^{2} x -9152 a^{3} b^{3} d^{2} e x +20592 a^{2} b^{4} c d e x +3432 a^{2} b^{4} d^{3} x -12012 a \,b^{5} c^{2} e x -12012 a \,b^{5} c \,d^{2} x +15015 b^{6} c^{2} d x +5120 a^{6} e^{3}-16640 a^{5} b d \,e^{2}+18304 a^{4} b^{2} c \,e^{2}+18304 a^{4} b^{2} d^{2} e -41184 a^{3} b^{3} c d e -6864 a^{3} b^{3} d^{3}+24024 a^{2} b^{4} c^{2} e +24024 a^{2} b^{4} c \,d^{2}-30030 a \,b^{5} c^{2} d +15015 c^{3} b^{6}\right)}{15015 b^{7}}"," ",0,"2/15015*(b*x+a)^(1/2)*(1155*b^6*e^3*x^6-1260*a*b^5*e^3*x^5+4095*b^6*d*e^2*x^5+1400*a^2*b^4*e^3*x^4-4550*a*b^5*d*e^2*x^4+5005*b^6*c*e^2*x^4+5005*b^6*d^2*e*x^4-1600*a^3*b^3*e^3*x^3+5200*a^2*b^4*d*e^2*x^3-5720*a*b^5*c*e^2*x^3-5720*a*b^5*d^2*e*x^3+12870*b^6*c*d*e*x^3+2145*b^6*d^3*x^3+1920*a^4*b^2*e^3*x^2-6240*a^3*b^3*d*e^2*x^2+6864*a^2*b^4*c*e^2*x^2+6864*a^2*b^4*d^2*e*x^2-15444*a*b^5*c*d*e*x^2-2574*a*b^5*d^3*x^2+9009*b^6*c^2*e*x^2+9009*b^6*c*d^2*x^2-2560*a^5*b*e^3*x+8320*a^4*b^2*d*e^2*x-9152*a^3*b^3*c*e^2*x-9152*a^3*b^3*d^2*e*x+20592*a^2*b^4*c*d*e*x+3432*a^2*b^4*d^3*x-12012*a*b^5*c^2*e*x-12012*a*b^5*c*d^2*x+15015*b^6*c^2*d*x+5120*a^6*e^3-16640*a^5*b*d*e^2+18304*a^4*b^2*c*e^2+18304*a^4*b^2*d^2*e-41184*a^3*b^3*c*d*e-6864*a^3*b^3*d^3+24024*a^2*b^4*c^2*e+24024*a^2*b^4*c*d^2-30030*a*b^5*c^2*d+15015*b^6*c^3)/b^7","A"
4,1,91,100,0.045000," ","int((f*x^3+e*x^2+d*x+c)/(b*x+a)^(1/2),x)","-\frac{2 \sqrt{b x +a}\, \left(-15 f \,x^{3} b^{3}+18 a \,b^{2} f \,x^{2}-21 b^{3} e \,x^{2}-24 a^{2} b f x +28 a \,b^{2} e x -35 b^{3} d x +48 a^{3} f -56 a^{2} b e +70 a \,b^{2} d -105 b^{3} c \right)}{105 b^{4}}"," ",0,"-2/105*(b*x+a)^(1/2)*(-15*b^3*f*x^3+18*a*b^2*f*x^2-21*b^3*e*x^2-24*a^2*b*f*x+28*a*b^2*e*x-35*b^3*d*x+48*a^3*f-56*a^2*b*e+70*a*b^2*d-105*b^3*c)/b^4","A"
5,1,447,294,0.047000," ","int((f*x^3+e*x^2+d*x+c)^2/(b*x+a)^(1/2),x)","\frac{2 \sqrt{b x +a}\, \left(3465 f^{2} x^{6} b^{6}-3780 a \,b^{5} f^{2} x^{5}+8190 b^{6} e f \,x^{5}+4200 a^{2} b^{4} f^{2} x^{4}-9100 a \,b^{5} e f \,x^{4}+10010 b^{6} d f \,x^{4}+5005 b^{6} e^{2} x^{4}-4800 a^{3} b^{3} f^{2} x^{3}+10400 a^{2} b^{4} e f \,x^{3}-11440 a \,b^{5} d f \,x^{3}-5720 a \,b^{5} e^{2} x^{3}+12870 b^{6} c f \,x^{3}+12870 b^{6} d e \,x^{3}+5760 a^{4} b^{2} f^{2} x^{2}-12480 a^{3} b^{3} e f \,x^{2}+13728 a^{2} b^{4} d f \,x^{2}+6864 a^{2} b^{4} e^{2} x^{2}-15444 a \,b^{5} c f \,x^{2}-15444 a \,b^{5} d e \,x^{2}+18018 b^{6} c e \,x^{2}+9009 b^{6} d^{2} x^{2}-7680 a^{5} b \,f^{2} x +16640 a^{4} b^{2} e f x -18304 a^{3} b^{3} d f x -9152 a^{3} b^{3} e^{2} x +20592 a^{2} b^{4} c f x +20592 a^{2} b^{4} d e x -24024 a \,b^{5} c e x -12012 a \,b^{5} d^{2} x +30030 b^{6} c d x +15360 a^{6} f^{2}-33280 a^{5} b e f +36608 a^{4} b^{2} d f +18304 a^{4} b^{2} e^{2}-41184 a^{3} b^{3} c f -41184 a^{3} b^{3} d e +48048 a^{2} b^{4} c e +24024 a^{2} b^{4} d^{2}-60060 a \,b^{5} c d +45045 c^{2} b^{6}\right)}{45045 b^{7}}"," ",0,"2/45045*(b*x+a)^(1/2)*(3465*b^6*f^2*x^6-3780*a*b^5*f^2*x^5+8190*b^6*e*f*x^5+4200*a^2*b^4*f^2*x^4-9100*a*b^5*e*f*x^4+10010*b^6*d*f*x^4+5005*b^6*e^2*x^4-4800*a^3*b^3*f^2*x^3+10400*a^2*b^4*e*f*x^3-11440*a*b^5*d*f*x^3-5720*a*b^5*e^2*x^3+12870*b^6*c*f*x^3+12870*b^6*d*e*x^3+5760*a^4*b^2*f^2*x^2-12480*a^3*b^3*e*f*x^2+13728*a^2*b^4*d*f*x^2+6864*a^2*b^4*e^2*x^2-15444*a*b^5*c*f*x^2-15444*a*b^5*d*e*x^2+18018*b^6*c*e*x^2+9009*b^6*d^2*x^2-7680*a^5*b*f^2*x+16640*a^4*b^2*e*f*x-18304*a^3*b^3*d*f*x-9152*a^3*b^3*e^2*x+20592*a^2*b^4*c*f*x+20592*a^2*b^4*d*e*x-24024*a*b^5*c*e*x-12012*a*b^5*d^2*x+30030*b^6*c*d*x+15360*a^6*f^2-33280*a^5*b*e*f+36608*a^4*b^2*d*f+18304*a^4*b^2*e^2-41184*a^3*b^3*c*f-41184*a^3*b^3*d*e+48048*a^2*b^4*c*e+24024*a^2*b^4*d^2-60060*a*b^5*c*d+45045*b^6*c^2)/b^7","A"
6,1,1417,672,0.053000," ","int((f*x^3+e*x^2+d*x+c)^3/(b*x+a)^(1/2),x)","-\frac{2 \sqrt{b x +a}\, \left(-255255 f^{3} x^{9} b^{9}+270270 a \,b^{8} f^{3} x^{8}-855855 b^{9} e \,f^{2} x^{8}-288288 a^{2} b^{7} f^{3} x^{7}+912912 a \,b^{8} e \,f^{2} x^{7}-969969 b^{9} d \,f^{2} x^{7}-969969 b^{9} e^{2} f \,x^{7}+310464 a^{3} b^{6} f^{3} x^{6}-983136 a^{2} b^{7} e \,f^{2} x^{6}+1044582 a \,b^{8} d \,f^{2} x^{6}+1044582 a \,b^{8} e^{2} f \,x^{6}-1119195 b^{9} c \,f^{2} x^{6}-2238390 b^{9} d e f \,x^{6}-373065 b^{9} e^{3} x^{6}-338688 a^{4} b^{5} f^{3} x^{5}+1072512 a^{3} b^{6} e \,f^{2} x^{5}-1139544 a^{2} b^{7} d \,f^{2} x^{5}-1139544 a^{2} b^{7} e^{2} f \,x^{5}+1220940 a \,b^{8} c \,f^{2} x^{5}+2441880 a \,b^{8} d e f \,x^{5}+406980 a \,b^{8} e^{3} x^{5}-2645370 b^{9} c e f \,x^{5}-1322685 b^{9} d^{2} f \,x^{5}-1322685 b^{9} d \,e^{2} x^{5}+376320 a^{5} b^{4} f^{3} x^{4}-1191680 a^{4} b^{5} e \,f^{2} x^{4}+1266160 a^{3} b^{6} d \,f^{2} x^{4}+1266160 a^{3} b^{6} e^{2} f \,x^{4}-1356600 a^{2} b^{7} c \,f^{2} x^{4}-2713200 a^{2} b^{7} d e f \,x^{4}-452200 a^{2} b^{7} e^{3} x^{4}+2939300 a \,b^{8} c e f \,x^{4}+1469650 a \,b^{8} d^{2} f \,x^{4}+1469650 a \,b^{8} d \,e^{2} x^{4}-3233230 b^{9} c d f \,x^{4}-1616615 b^{9} c \,e^{2} x^{4}-1616615 b^{9} d^{2} e \,x^{4}-430080 a^{6} b^{3} f^{3} x^{3}+1361920 a^{5} b^{4} e \,f^{2} x^{3}-1447040 a^{4} b^{5} d \,f^{2} x^{3}-1447040 a^{4} b^{5} e^{2} f \,x^{3}+1550400 a^{3} b^{6} c \,f^{2} x^{3}+3100800 a^{3} b^{6} d e f \,x^{3}+516800 a^{3} b^{6} e^{3} x^{3}-3359200 a^{2} b^{7} c e f \,x^{3}-1679600 a^{2} b^{7} d^{2} f \,x^{3}-1679600 a^{2} b^{7} d \,e^{2} x^{3}+3695120 a \,b^{8} c d f \,x^{3}+1847560 a \,b^{8} c \,e^{2} x^{3}+1847560 a \,b^{8} d^{2} e \,x^{3}-2078505 b^{9} c^{2} f \,x^{3}-4157010 b^{9} c d e \,x^{3}-692835 b^{9} d^{3} x^{3}+516096 a^{7} b^{2} f^{3} x^{2}-1634304 a^{6} b^{3} e \,f^{2} x^{2}+1736448 a^{5} b^{4} d \,f^{2} x^{2}+1736448 a^{5} b^{4} e^{2} f \,x^{2}-1860480 a^{4} b^{5} c \,f^{2} x^{2}-3720960 a^{4} b^{5} d e f \,x^{2}-620160 a^{4} b^{5} e^{3} x^{2}+4031040 a^{3} b^{6} c e f \,x^{2}+2015520 a^{3} b^{6} d^{2} f \,x^{2}+2015520 a^{3} b^{6} d \,e^{2} x^{2}-4434144 a^{2} b^{7} c d f \,x^{2}-2217072 a^{2} b^{7} c \,e^{2} x^{2}-2217072 a^{2} b^{7} d^{2} e \,x^{2}+2494206 a \,b^{8} c^{2} f \,x^{2}+4988412 a \,b^{8} c d e \,x^{2}+831402 a \,b^{8} d^{3} x^{2}-2909907 b^{9} c^{2} e \,x^{2}-2909907 b^{9} c \,d^{2} x^{2}-688128 a^{8} b \,f^{3} x +2179072 a^{7} b^{2} e \,f^{2} x -2315264 a^{6} b^{3} d \,f^{2} x -2315264 a^{6} b^{3} e^{2} f x +2480640 a^{5} b^{4} c \,f^{2} x +4961280 a^{5} b^{4} d e f x +826880 a^{5} b^{4} e^{3} x -5374720 a^{4} b^{5} c e f x -2687360 a^{4} b^{5} d^{2} f x -2687360 a^{4} b^{5} d \,e^{2} x +5912192 a^{3} b^{6} c d f x +2956096 a^{3} b^{6} c \,e^{2} x +2956096 a^{3} b^{6} d^{2} e x -3325608 a^{2} b^{7} c^{2} f x -6651216 a^{2} b^{7} c d e x -1108536 a^{2} b^{7} d^{3} x +3879876 a \,b^{8} c^{2} e x +3879876 a \,b^{8} c \,d^{2} x -4849845 b^{9} c^{2} d x +1376256 a^{9} f^{3}-4358144 a^{8} b e \,f^{2}+4630528 a^{7} b^{2} d \,f^{2}+4630528 a^{7} b^{2} e^{2} f -4961280 a^{6} b^{3} c \,f^{2}-9922560 a^{6} b^{3} d e f -1653760 a^{6} b^{3} e^{3}+10749440 a^{5} b^{4} c e f +5374720 a^{5} b^{4} d^{2} f +5374720 a^{5} b^{4} d \,e^{2}-11824384 a^{4} b^{5} c d f -5912192 a^{4} b^{5} c \,e^{2}-5912192 a^{4} b^{5} d^{2} e +6651216 a^{3} b^{6} c^{2} f +13302432 a^{3} b^{6} c d e +2217072 a^{3} b^{6} d^{3}-7759752 a^{2} b^{7} c^{2} e -7759752 a^{2} b^{7} c \,d^{2}+9699690 a \,b^{8} c^{2} d -4849845 c^{3} b^{9}\right)}{4849845 b^{10}}"," ",0,"-2/4849845*(b*x+a)^(1/2)*(-255255*b^9*f^3*x^9+270270*a*b^8*f^3*x^8-855855*b^9*e*f^2*x^8-288288*a^2*b^7*f^3*x^7+912912*a*b^8*e*f^2*x^7-969969*b^9*d*f^2*x^7-969969*b^9*e^2*f*x^7+310464*a^3*b^6*f^3*x^6-983136*a^2*b^7*e*f^2*x^6+1044582*a*b^8*d*f^2*x^6+1044582*a*b^8*e^2*f*x^6-1119195*b^9*c*f^2*x^6-2238390*b^9*d*e*f*x^6-373065*b^9*e^3*x^6-338688*a^4*b^5*f^3*x^5+1072512*a^3*b^6*e*f^2*x^5-1139544*a^2*b^7*d*f^2*x^5-1139544*a^2*b^7*e^2*f*x^5+1220940*a*b^8*c*f^2*x^5+2441880*a*b^8*d*e*f*x^5+406980*a*b^8*e^3*x^5-2645370*b^9*c*e*f*x^5-1322685*b^9*d^2*f*x^5-1322685*b^9*d*e^2*x^5+376320*a^5*b^4*f^3*x^4-1191680*a^4*b^5*e*f^2*x^4+1266160*a^3*b^6*d*f^2*x^4+1266160*a^3*b^6*e^2*f*x^4-1356600*a^2*b^7*c*f^2*x^4-2713200*a^2*b^7*d*e*f*x^4-452200*a^2*b^7*e^3*x^4+2939300*a*b^8*c*e*f*x^4+1469650*a*b^8*d^2*f*x^4+1469650*a*b^8*d*e^2*x^4-3233230*b^9*c*d*f*x^4-1616615*b^9*c*e^2*x^4-1616615*b^9*d^2*e*x^4-430080*a^6*b^3*f^3*x^3+1361920*a^5*b^4*e*f^2*x^3-1447040*a^4*b^5*d*f^2*x^3-1447040*a^4*b^5*e^2*f*x^3+1550400*a^3*b^6*c*f^2*x^3+3100800*a^3*b^6*d*e*f*x^3+516800*a^3*b^6*e^3*x^3-3359200*a^2*b^7*c*e*f*x^3-1679600*a^2*b^7*d^2*f*x^3-1679600*a^2*b^7*d*e^2*x^3+3695120*a*b^8*c*d*f*x^3+1847560*a*b^8*c*e^2*x^3+1847560*a*b^8*d^2*e*x^3-2078505*b^9*c^2*f*x^3-4157010*b^9*c*d*e*x^3-692835*b^9*d^3*x^3+516096*a^7*b^2*f^3*x^2-1634304*a^6*b^3*e*f^2*x^2+1736448*a^5*b^4*d*f^2*x^2+1736448*a^5*b^4*e^2*f*x^2-1860480*a^4*b^5*c*f^2*x^2-3720960*a^4*b^5*d*e*f*x^2-620160*a^4*b^5*e^3*x^2+4031040*a^3*b^6*c*e*f*x^2+2015520*a^3*b^6*d^2*f*x^2+2015520*a^3*b^6*d*e^2*x^2-4434144*a^2*b^7*c*d*f*x^2-2217072*a^2*b^7*c*e^2*x^2-2217072*a^2*b^7*d^2*e*x^2+2494206*a*b^8*c^2*f*x^2+4988412*a*b^8*c*d*e*x^2+831402*a*b^8*d^3*x^2-2909907*b^9*c^2*e*x^2-2909907*b^9*c*d^2*x^2-688128*a^8*b*f^3*x+2179072*a^7*b^2*e*f^2*x-2315264*a^6*b^3*d*f^2*x-2315264*a^6*b^3*e^2*f*x+2480640*a^5*b^4*c*f^2*x+4961280*a^5*b^4*d*e*f*x+826880*a^5*b^4*e^3*x-5374720*a^4*b^5*c*e*f*x-2687360*a^4*b^5*d^2*f*x-2687360*a^4*b^5*d*e^2*x+5912192*a^3*b^6*c*d*f*x+2956096*a^3*b^6*c*e^2*x+2956096*a^3*b^6*d^2*e*x-3325608*a^2*b^7*c^2*f*x-6651216*a^2*b^7*c*d*e*x-1108536*a^2*b^7*d^3*x+3879876*a*b^8*c^2*e*x+3879876*a*b^8*c*d^2*x-4849845*b^9*c^2*d*x+1376256*a^9*f^3-4358144*a^8*b*e*f^2+4630528*a^7*b^2*d*f^2+4630528*a^7*b^2*e^2*f-4961280*a^6*b^3*c*f^2-9922560*a^6*b^3*d*e*f-1653760*a^6*b^3*e^3+10749440*a^5*b^4*c*e*f+5374720*a^5*b^4*d^2*f+5374720*a^5*b^4*d*e^2-11824384*a^4*b^5*c*d*f-5912192*a^4*b^5*c*e^2-5912192*a^4*b^5*d^2*e+6651216*a^3*b^6*c^2*f+13302432*a^3*b^6*c*d*e+2217072*a^3*b^6*d^3-7759752*a^2*b^7*c^2*e-7759752*a^2*b^7*c*d^2+9699690*a*b^8*c^2*d-4849845*b^9*c^3)/b^10","B"
7,1,186,112,0.050000," ","int((d*x+c)/(b*x^3+a),x)","\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"1/3*c/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*c/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*c/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*d/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*d/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*d*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
8,1,238,136,0.047000," ","int((d*x+c)/(b*x^3+a)^2,x)","\frac{d \,x^{2}}{3 \left(b \,x^{3}+a \right) a}+\frac{c x}{3 \left(b \,x^{3}+a \right) a}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}"," ",0,"1/3*c*x/a/(b*x^3+a)+2/9*c/a/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/9*c/a/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9*c/a/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*d*x^2/a/(b*x^3+a)-1/9*d/a/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18*d/a/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9*d/a*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
9,1,272,160,0.055000," ","int((d*x+c)/(b*x^3+a)^3,x)","\frac{d \,x^{2}}{6 \left(b \,x^{3}+a \right)^{2} a}+\frac{c x}{6 \left(b \,x^{3}+a \right)^{2} a}+\frac{2 d \,x^{2}}{9 \left(b \,x^{3}+a \right) a^{2}}+\frac{5 c x}{18 \left(b \,x^{3}+a \right) a^{2}}+\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}"," ",0,"1/6*c/a*x/(b*x^3+a)^2+5/18*c/a^2*x/(b*x^3+a)+5/27*c/a^2/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-5/54*c/a^2/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27*c/a^2/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/6*d/a*x^2/(b*x^3+a)^2+2/9*d/a^2*x^2/(b*x^3+a)-2/27*d/a^2/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/27*d/a^2/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27*d/a^2*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
10,1,306,183,0.053000," ","int((d*x+c)/(b*x^3+a)^4,x)","\frac{d \,x^{2}}{9 \left(b \,x^{3}+a \right)^{3} a}+\frac{c x}{9 \left(b \,x^{3}+a \right)^{3} a}+\frac{7 d \,x^{2}}{54 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 c x}{27 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{14 d \,x^{2}}{81 \left(b \,x^{3}+a \right) a^{3}}+\frac{20 c x}{81 \left(b \,x^{3}+a \right) a^{3}}+\frac{40 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{40 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}-\frac{20 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{14 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}-\frac{14 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}+\frac{7 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}"," ",0,"1/9*c/a*x/(b*x^3+a)^3+4/27*c/a^2*x/(b*x^3+a)^2+20/81*c/a^3*x/(b*x^3+a)+40/243*c/a^3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-20/243*c/a^3/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+40/243*c/a^3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9*d/a*x^2/(b*x^3+a)^3+7/54*d/a^2*x^2/(b*x^3+a)^2+14/81*d/a^3*x^2/(b*x^3+a)-14/243*d/a^3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/243*d/a^3/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/243*d/a^3*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
11,1,186,112,0.053000," ","int((b*x+a)/(e*x^3+d),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{a \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{a \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}-\frac{b \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{b \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}"," ",0,"1/3*a/e/(d/e)^(2/3)*ln(x+(d/e)^(1/3))-1/6*a/e/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))+1/3*a/e/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))-1/3*b/e/(d/e)^(1/3)*ln(x+(d/e)^(1/3))+1/6*b/e/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))+1/3*b*3^(1/2)/e/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))","A"
12,1,188,112,0.046000," ","int((b*x+a)/(-e*x^3+d),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{a \ln \left(x -\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{a \ln \left(x^{2}+\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}-\frac{b \ln \left(x -\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{b \ln \left(x^{2}+\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}"," ",0,"-1/3*a/e/(d/e)^(2/3)*ln(x-(d/e)^(1/3))+1/6*a/e/(d/e)^(2/3)*ln(x^2+(d/e)^(1/3)*x+(d/e)^(2/3))+1/3*a/e/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x+1))-1/3*b/e/(d/e)^(1/3)*ln(x-(d/e)^(1/3))+1/6*b/e/(d/e)^(1/3)*ln(x^2+(d/e)^(1/3)*x+(d/e)^(2/3))-1/3*b*3^(1/2)/e/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x+1))","A"
13,1,17,16,0.045000," ","int((x+1)/(x^3+1),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}"," ",0,"2/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
14,1,17,16,0.044000," ","int((1-x)/(-x^3+1),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}"," ",0,"2/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
15,1,17,18,0.047000," ","int((x+1)/(-x^3+1),x)","-\frac{2 \ln \left(x -1\right)}{3}+\frac{\ln \left(x^{2}+x +1\right)}{3}"," ",0,"-2/3*ln(x-1)+1/3*ln(x^2+x+1)","A"
16,1,19,18,0.043000," ","int((1-x)/(x^3+1),x)","\frac{2 \ln \left(x +1\right)}{3}-\frac{\ln \left(x^{2}-x +1\right)}{3}"," ",0,"2/3*ln(x+1)-1/3*ln(x^2-x+1)","A"
17,1,33,34,0.050000," ","int((3-x)/(-x^3+1),x)","\frac{4 \sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\frac{2 \ln \left(x -1\right)}{3}+\frac{\ln \left(x^{2}+x +1\right)}{3}"," ",0,"-2/3*ln(x-1)+1/3*ln(x^2+x+1)+4/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
18,1,35,26,0.074000," ","int((d*x+c)/(d^3*x^3+c^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 d^{2} x -c d \right) \sqrt{3}}{3 c d}\right)}{3 c d}"," ",0,"2/3*3^(1/2)/c/d*arctan(1/3*(2*d^2*x-c*d)*3^(1/2)/c/d)","A"
19,1,34,26,0.043000," ","int((-d*x+c)/(-d^3*x^3+c^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 d^{2} x +c d \right) \sqrt{3}}{3 c d}\right)}{3 c d}"," ",0,"2/3*3^(1/2)/c/d*arctan(1/3*(2*d^2*x+c*d)*3^(1/2)/c/d)","A"
20,1,195,28,0.063000," ","int((a^(1/3)*b^(1/3)*B+b^(2/3)*B*x)/(b*x^3+a),x)","\frac{\sqrt{3}\, B \,a^{\frac{1}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}+\frac{B \,a^{\frac{1}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}-\frac{B \,a^{\frac{1}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{1}{3}}}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{1}{3}}}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{1}{3}}}"," ",0,"1/3*B/b^(2/3)*a^(1/3)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*B/b^(2/3)*a^(1/3)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*B/b^(2/3)*a^(1/3)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*B/b^(1/3)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*B/b^(1/3)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*B/b^(1/3)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","B"
21,1,228,30,0.058000," ","int((a^(1/3)*(-b)^(1/3)*B-(-b)^(2/3)*B*x)/(b*x^3+a),x)","\frac{\left(-1\right)^{\frac{1}{3}} \sqrt{3}\, B \,a^{\frac{1}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}+\frac{\left(-1\right)^{\frac{1}{3}} B \,a^{\frac{1}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}-\frac{\left(-1\right)^{\frac{1}{3}} B \,a^{\frac{1}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}-\frac{\left(-1\right)^{\frac{1}{3}} \left(-b \right)^{\frac{1}{3}} \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{2}{3}}}+\frac{\left(-1\right)^{\frac{1}{3}} \left(-b \right)^{\frac{1}{3}} B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{2}{3}}}-\frac{\left(-1\right)^{\frac{1}{3}} \left(-b \right)^{\frac{1}{3}} B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{2}{3}}}"," ",0,"1/3*B/b^(2/3)*(-1)^(1/3)*a^(1/3)/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*B/b^(2/3)*(-1)^(1/3)*a^(1/3)/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*B/b^(2/3)*(-1)^(1/3)*a^(1/3)/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*B/b^(2/3)*(-1)^(1/3)*(-b)^(1/3)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6*B/b^(2/3)*(-1)^(1/3)*(-b)^(1/3)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*B/b^(2/3)*(-1)^(1/3)*(-b)^(1/3)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","B"
22,1,94,81,0.048000," ","int(-C*x^2/(b*x^3+a)+(C*x^2+B*x)/(b*x^3+a),x)","\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"-1/3*B/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*B/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*B*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
23,1,94,81,0.049000," ","int(-C*x^2/(b*x^3+a)+(C*x^2+A)/(b*x^3+a),x)","\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}"," ",0,"1/3*A/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*A/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*A/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
24,1,186,112,0.045000," ","int(-C*x^2/(b*x^3+a)+(C*x^2+B*x+A)/(b*x^3+a),x)","\frac{\sqrt{3}\, A \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{A \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{A \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"1/3/(a/b)^(2/3)*A/b*ln(x+(a/b)^(1/3))-1/6/(a/b)^(2/3)*A/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/(a/b)^(2/3)*3^(1/2)*A/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/(a/b)^(1/3)*B/b*ln(x+(a/b)^(1/3))+1/6/(a/b)^(1/3)*B/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*3^(1/2)/(a/b)^(1/3)*B/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
25,1,108,95,0.049000," ","int((c*x^2+b*x)/(e*x^3+d),x)","\frac{\sqrt{3}\, b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}-\frac{b \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{b \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{c \ln \left(e \,x^{3}+d \right)}{3 e}"," ",0,"-1/3/(d/e)^(1/3)*b/e*ln(x+(d/e)^(1/3))+1/6/(d/e)^(1/3)*b/e*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))+1/3*3^(1/2)/(d/e)^(1/3)*b/e*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))+1/3*c*ln(e*x^3+d)/e","A"
26,1,111,96,0.045000," ","int((c*x^2+a)/(-e*x^3+d),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{a \ln \left(x -\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{a \ln \left(x^{2}+\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{c \ln \left(e \,x^{3}-d \right)}{3 e}"," ",0,"-1/3/(d/e)^(2/3)*a/e*ln(x-(d/e)^(1/3))+1/6/(d/e)^(2/3)*a/e*ln(x^2+(d/e)^(1/3)*x+(d/e)^(2/3))+1/3/(d/e)^(2/3)*3^(1/2)*a/e*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x+1))-1/3*c/e*ln(e*x^3-d)","A"
27,1,43,34,0.053000," ","int((b^2*x^2+2*a^2)/(b^3*x^3+a^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 b^{2} x -a b \right) \sqrt{3}}{3 a b}\right)}{3 b}+\frac{\ln \left(b x +a \right)}{b}"," ",0,"2/3*3^(1/2)/b*arctan(1/3*(2*b^2*x-a*b)*3^(1/2)/a/b)+ln(b*x+a)/b","A"
28,1,45,36,0.058000," ","int((b^2*x^2+2*a^2)/(-b^3*x^3+a^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 b^{2} x +a b \right) \sqrt{3}}{3 a b}\right)}{3 b}-\frac{\ln \left(b x -a \right)}{b}"," ",0,"-1/b*ln(b*x-a)+2/3*3^(1/2)/b*arctan(1/3*(2*b^2*x+a*b)*3^(1/2)/a/b)","A"
29,1,117,37,0.056000," ","int((8*C+b^(2/3)*C*x^2)/(b*x^3+8),x)","\frac{C \ln \left(b \,x^{3}+8\right)}{3 b^{\frac{1}{3}}}+\frac{8^{\frac{1}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{8^{\frac{2}{3}} x}{4 \left(\frac{1}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{1}{b}\right)^{\frac{2}{3}} b}+\frac{8^{\frac{1}{3}} C \ln \left(x +8^{\frac{1}{3}} \left(\frac{1}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{1}{b}\right)^{\frac{2}{3}} b}-\frac{8^{\frac{1}{3}} C \ln \left(x^{2}-8^{\frac{1}{3}} \left(\frac{1}{b}\right)^{\frac{1}{3}} x +8^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{1}{b}\right)^{\frac{2}{3}} b}"," ",0,"1/3*C/b*8^(1/3)/(1/b)^(2/3)*ln(x+8^(1/3)*(1/b)^(1/3))-1/6*C/b*8^(1/3)/(1/b)^(2/3)*ln(x^2-8^(1/3)*(1/b)^(1/3)*x+8^(2/3)*(1/b)^(2/3))+1/3*C/b*8^(1/3)/(1/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(1/4*8^(2/3)/(1/b)^(1/3)*x-1))+1/3*C/b^(1/3)*ln(b*x^3+8)","B"
30,1,84,34,0.045000," ","int((a^(2/3)*C+2*C*x^2)/(8*x^3+a),x)","\frac{8^{\frac{2}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,8^{\frac{1}{3}} x}{a^{\frac{1}{3}}}-1\right)}{3}\right)}{24}+\frac{8^{\frac{2}{3}} C \ln \left(x +\frac{8^{\frac{2}{3}} a^{\frac{1}{3}}}{8}\right)}{24}-\frac{8^{\frac{2}{3}} C \ln \left(x^{2}-\frac{8^{\frac{2}{3}} a^{\frac{1}{3}} x}{8}+\frac{8^{\frac{1}{3}} a^{\frac{2}{3}}}{8}\right)}{48}+\frac{C \ln \left(8 x^{3}+a \right)}{12}"," ",0,"1/24*C*8^(2/3)*ln(x+1/8*8^(2/3)*a^(1/3))-1/48*C*8^(2/3)*ln(x^2-1/8*8^(2/3)*a^(1/3)*x+1/8*8^(1/3)*a^(2/3))+1/24*C*8^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2*8^(1/3)/a^(1/3)*x-1))+1/12*C*ln(8*x^3+a)","B"
31,1,122,46,0.051000," ","int((8*C+(-b)^(2/3)*C*x^2)/(b*x^3-8),x)","-\frac{8^{\frac{1}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{8^{\frac{2}{3}} x}{4 \left(\frac{1}{b}\right)^{\frac{1}{3}}}+1\right)}{3}\right)}{3 \left(\frac{1}{b}\right)^{\frac{2}{3}} b}+\frac{8^{\frac{1}{3}} C \ln \left(x -8^{\frac{1}{3}} \left(\frac{1}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{1}{b}\right)^{\frac{2}{3}} b}-\frac{8^{\frac{1}{3}} C \ln \left(x^{2}+8^{\frac{1}{3}} \left(\frac{1}{b}\right)^{\frac{1}{3}} x +8^{\frac{2}{3}} \left(\frac{1}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{1}{b}\right)^{\frac{2}{3}} b}+\frac{\left(-b \right)^{\frac{2}{3}} C \ln \left(b \,x^{3}-8\right)}{3 b}"," ",0,"1/3*C/b*8^(1/3)/(1/b)^(2/3)*ln(x-8^(1/3)*(1/b)^(1/3))-1/6*C/b*8^(1/3)/(1/b)^(2/3)*ln(x^2+8^(1/3)*(1/b)^(1/3)*x+8^(2/3)*(1/b)^(2/3))-1/3*C/b*8^(1/3)/(1/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(1/4*8^(2/3)/(1/b)^(1/3)*x+1))+1/3*C*(-b)^(2/3)/b*ln(b*x^3-8)","B"
32,1,110,36,0.052000," ","int(((-a)^(2/3)*C+2*C*x^2)/(-8*x^3+a),x)","-\frac{C \ln \left(8 x^{3}-a \right)}{12}+\frac{\left(-a \right)^{\frac{2}{3}} 8^{\frac{2}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,8^{\frac{1}{3}} x}{a^{\frac{1}{3}}}+1\right)}{3}\right)}{24 a^{\frac{2}{3}}}-\frac{\left(-a \right)^{\frac{2}{3}} 8^{\frac{2}{3}} C \ln \left(x -\frac{8^{\frac{2}{3}} a^{\frac{1}{3}}}{8}\right)}{24 a^{\frac{2}{3}}}+\frac{\left(-a \right)^{\frac{2}{3}} 8^{\frac{2}{3}} C \ln \left(x^{2}+\frac{8^{\frac{2}{3}} a^{\frac{1}{3}} x}{8}+\frac{8^{\frac{1}{3}} a^{\frac{2}{3}}}{8}\right)}{48 a^{\frac{2}{3}}}"," ",0,"-1/24*C*(-a)^(2/3)*8^(2/3)/a^(2/3)*ln(x-1/8*8^(2/3)*a^(1/3))+1/48*C*(-a)^(2/3)*8^(2/3)/a^(2/3)*ln(x^2+1/8*8^(2/3)*a^(1/3)*x+1/8*8^(1/3)*a^(2/3))+1/24*C*(-a)^(2/3)*8^(2/3)/a^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2*8^(1/3)/a^(1/3)*x+1))-1/12*C*ln(8*x^3-a)","B"
33,1,87,43,0.051000," ","int((2*(a/b)^(2/3)*C+C*x^2)/(b*x^3+a),x)","\frac{2 \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 b}+\frac{2 C \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 b}-\frac{C \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"2/3*C*ln(x+(a/b)^(1/3))/b-1/3*C/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C/b*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b*ln(b*x^3+a)","A"
34,1,135,46,0.049000," ","int((2*(-a/b)^(2/3)*C+C*x^2)/(-b*x^3+a),x)","\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} \sqrt{3}\, C \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{C \ln \left(b \,x^{3}-a \right)}{3 b}"," ",0,"-2/3*C*(-a/b)^(2/3)/b/(a/b)^(2/3)*ln(x-(a/b)^(1/3))+1/3*C*(-a/b)^(2/3)/b/(a/b)^(2/3)*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C*(-a/b)^(2/3)/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*(1+2/(a/b)^(1/3)*x)*3^(1/2))-1/3*C/b*ln(b*x^3-a)","B"
35,1,132,47,0.043000," ","int((2*(-a/b)^(2/3)*C+C*x^2)/(b*x^3+a),x)","\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"2/3*C*(-a/b)^(2/3)/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/3*C*(-a/b)^(2/3)/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C*(-a/b)^(2/3)/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b*ln(b*x^3+a)","B"
36,1,90,46,0.050000," ","int((2*(a/b)^(2/3)*C+C*x^2)/(-b*x^3+a),x)","\frac{2 \sqrt{3}\, C \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 b}-\frac{2 C \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 b}+\frac{C \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 b}-\frac{C \ln \left(b \,x^{3}-a \right)}{3 b}"," ",0,"-2/3*C/b*ln(x-(a/b)^(1/3))+1/3*C/b*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))/b*3^(1/2)-1/3*C/b*ln(b*x^3-a)","A"
37,1,117,44,0.056000," ","int((2*a^(2/3)*C+b^(2/3)*C*x^2)/(b*x^3+a),x)","\frac{2 \sqrt{3}\, C \,a^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{2 C \,a^{\frac{2}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{C \,a^{\frac{2}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b^{\frac{1}{3}}}"," ",0,"2/3*C*a^(2/3)/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/3*C*a^(2/3)/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C*a^(2/3)/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b^(1/3)*ln(b*x^3+a)","B"
38,1,122,53,0.054000," ","int((-2*a^(2/3)*C-(-b)^(2/3)*C*x^2)/(b*x^3+a),x)","-\frac{2 \sqrt{3}\, C \,a^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{2 C \,a^{\frac{2}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \,a^{\frac{2}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\left(-b \right)^{\frac{2}{3}} C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"-2/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x+(a/b)^(1/3))+1/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-2/3/(a/b)^(2/3)*3^(1/2)*C*a^(2/3)/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*C*(-b)^(2/3)/b*ln(b*x^3+a)","B"
39,1,32,33,0.046000," ","int((x^2-3)/(x^3-1),x)","\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)-\frac{2 \ln \left(x -1\right)}{3}+\frac{5 \ln \left(x^{2}+x +1\right)}{6}"," ",0,"-2/3*ln(x-1)+5/6*ln(x^2+x+1)+3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
40,1,310,51,0.056000," ","int((a^(1/3)*b^(1/3)*B+2*a^(2/3)*C+b^(2/3)*B*x+b^(2/3)*C*x^2)/(b*x^3+a),x)","\frac{\sqrt{3}\, B \,a^{\frac{1}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}+\frac{B \,a^{\frac{1}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}-\frac{B \,a^{\frac{1}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{\frac{2}{3}}}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{1}{3}}}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{1}{3}}}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{1}{3}}}+\frac{2 \sqrt{3}\, C \,a^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{2 C \,a^{\frac{2}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{C \,a^{\frac{2}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b^{\frac{1}{3}}}"," ",0,"1/3/(a/b)^(2/3)*B*a^(1/3)/b^(2/3)*ln(x+(a/b)^(1/3))+2/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x+(a/b)^(1/3))-1/6/(a/b)^(2/3)*B*a^(1/3)/b^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/(a/b)^(2/3)*3^(1/2)*B*a^(1/3)/b^(2/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/3/(a/b)^(2/3)*3^(1/2)*C*a^(2/3)/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/(a/b)^(1/3)*B/b^(1/3)*ln(x+(a/b)^(1/3))+1/6/(a/b)^(1/3)*B/b^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*3^(1/2)/(a/b)^(1/3)*B/b^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b^(1/3)*ln(b*x^3+a)","B"
41,1,345,67,0.054000," ","int((a^(1/3)*(-b)^(1/3)*B-2*a^(2/3)*C-(-b)^(2/3)*B*x-(-b)^(2/3)*C*x^2)/(b*x^3+a),x)","-\frac{2 \sqrt{3}\, C \,a^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{2 C \,a^{\frac{2}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \,a^{\frac{2}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, \left(-b \right)^{\frac{1}{3}} B \,a^{\frac{1}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\left(-b \right)^{\frac{1}{3}} B \,a^{\frac{1}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\left(-b \right)^{\frac{1}{3}} B \,a^{\frac{1}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\left(-b \right)^{\frac{2}{3}} \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{\left(-b \right)^{\frac{2}{3}} B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\left(-b \right)^{\frac{2}{3}} B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\left(-b \right)^{\frac{2}{3}} C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^(1/3)*(-b)^(1/3)*B-2/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x+(a/b)^(1/3))-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^(1/3)*(-b)^(1/3)*B+1/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^(1/3)*(-b)^(1/3)*B-2/3/(a/b)^(2/3)*3^(1/2)*C*a^(2/3)/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*B*(-b)^(2/3)/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6*B*(-b)^(2/3)/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*B*(-b)^(2/3)*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*(-b)^(2/3)*C/b*ln(b*x^3+a)","B"
42,1,12,11,0.045000," ","int((C^2*x^2+B*C*x+B^2)/(C^3*x^3-B^3),x)","\frac{\ln \left(-C x +B \right)}{C}"," ",0,"ln(-C*x+B)/C","A"
43,1,218,15,0.049000," ","int((a^(2/3)*C-a^(1/3)*b^(1/3)*C*x+b^(2/3)*C*x^2)/(b*x^3+a),x)","\frac{\sqrt{3}\, C \,a^{\frac{2}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \,a^{\frac{2}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{C \,a^{\frac{2}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\sqrt{3}\, C \,a^{\frac{1}{3}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{2}{3}}}+\frac{C \,a^{\frac{1}{3}} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{2}{3}}}-\frac{C \,a^{\frac{1}{3}} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{\frac{2}{3}}}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b^{\frac{1}{3}}}"," ",0,"1/3/(a/b)^(2/3)*C*a^(2/3)/b*ln(x+(a/b)^(1/3))-1/6/(a/b)^(2/3)*C*a^(2/3)/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/(a/b)^(2/3)*3^(1/2)*C*a^(2/3)/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b^(2/3)*a^(1/3)/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6*C/b^(2/3)*a^(1/3)/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*C/b^(2/3)*a^(1/3)*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b^(1/3)*ln(b*x^3+a)","B"
44,1,121,60,0.051000," ","int(((a/b)^(1/3)*B+2*(a/b)^(2/3)*C+B*x+C*x^2)/(b*x^3+a),x)","\frac{2 \sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{2 \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 b}+\frac{2 C \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 b}-\frac{C \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"2/3*C/b*ln(x+(a/b)^(1/3))-1/3*C/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*3^(1/2)*C/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/3*3^(1/2)/(a/b)^(1/3)*B/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b*ln(b*x^3+a)","A"
45,1,345,65,0.049000," ","int(((-a/b)^(1/3)*B+2*(-a/b)^(2/3)*C+B*x+C*x^2)/(-b*x^3+a),x)","\frac{\sqrt{3}\, \left(-\frac{a}{b}\right)^{\frac{1}{3}} B \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\sqrt{3}\, B \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} B \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{B \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} B \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{B \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} \sqrt{3}\, C \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{C \ln \left(b \,x^{3}-a \right)}{3 b}"," ",0,"-2/3*(-a/b)^(2/3)/(a/b)^(2/3)*C/b*ln(x-(a/b)^(1/3))-1/3/b/(a/b)^(2/3)*ln(x-(a/b)^(1/3))*(-a/b)^(1/3)*B+1/3*(-a/b)^(2/3)/(a/b)^(2/3)*C/b*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))+1/6/b/(a/b)^(2/3)*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))*(-a/b)^(1/3)*B+2/3*(-a/b)^(2/3)/(a/b)^(2/3)*3^(1/2)*C/b*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))*(-a/b)^(1/3)*B-1/3*B/b/(a/b)^(1/3)*ln(x-(a/b)^(1/3))+1/6*B/b/(a/b)^(1/3)*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*B*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))-1/3*C/b*ln(b*x^3-a)","B"
46,1,340,67,0.050000," ","int((-(-a/b)^(1/3)*B+2*(-a/b)^(2/3)*C+B*x+C*x^2)/(b*x^3+a),x)","-\frac{\sqrt{3}\, \left(-\frac{a}{b}\right)^{\frac{1}{3}} B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, B \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{B \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{B \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{2 \left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{\left(-\frac{a}{b}\right)^{\frac{2}{3}} C \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"2/3*(-a/b)^(2/3)/(a/b)^(2/3)*C/b*ln(x+(a/b)^(1/3))-1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*(-a/b)^(1/3)*B-1/3*(-a/b)^(2/3)/(a/b)^(2/3)*C/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*(-a/b)^(1/3)*B+2/3*(-a/b)^(2/3)/(a/b)^(2/3)*3^(1/2)*C/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*(-a/b)^(1/3)*B-1/3/(a/b)^(1/3)*B/b*ln(x+(a/b)^(1/3))+1/6/(a/b)^(1/3)*B/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*3^(1/2)/(a/b)^(1/3)*B/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b*ln(b*x^3+a)","B"
47,1,124,64,0.051000," ","int((-(a/b)^(1/3)*B+2*(a/b)^(2/3)*C+B*x+C*x^2)/(-b*x^3+a),x)","-\frac{2 \sqrt{3}\, B \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{2 \sqrt{3}\, C \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 b}-\frac{2 C \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 b}+\frac{C \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 b}-\frac{C \ln \left(b \,x^{3}-a \right)}{3 b}"," ",0,"-2/3*C/b*ln(x-(a/b)^(1/3))+1/3*C/b*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*3^(1/2)*C/b*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))-2/3*3^(1/2)/(a/b)^(1/3)*B/b*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))-1/3*C/b*ln(b*x^3-a)","A"
48,1,36,28,0.054000," ","int((c*x^2+a*x+a)/(-x^3+1),x)","-\frac{2 a \ln \left(x -1\right)}{3}+\frac{a \ln \left(x^{2}+x +1\right)}{3}-\frac{c \ln \left(x -1\right)}{3}-\frac{c \ln \left(x^{2}+x +1\right)}{3}"," ",0,"-1/3*ln(x-1)*c-2/3*ln(x-1)*a+1/3*ln(x^2+x+1)*a-1/3*ln(x^2+x+1)*c","A"
49,1,87,49,0.049000," ","int((c*x^2+b*x+a)/(-x^3+1),x)","\frac{\sqrt{3}\, a \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\frac{a \ln \left(x -1\right)}{3}+\frac{a \ln \left(x^{2}+x +1\right)}{6}-\frac{\sqrt{3}\, b \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\frac{b \ln \left(x -1\right)}{3}+\frac{b \ln \left(x^{2}+x +1\right)}{6}-\frac{c \ln \left(x -1\right)}{3}-\frac{c \ln \left(x^{2}+x +1\right)}{3}"," ",0,"-1/3*c*ln(x-1)-1/3*ln(x-1)*b-1/3*a*ln(x-1)+1/6*a*ln(x^2+x+1)+1/6*ln(x^2+x+1)*b-1/3*c*ln(x^2+x+1)+1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))*a-1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))*b","A"
50,1,7,8,0.054000," ","int((x^2+x+1)/(-x^3+1),x)","-\ln \left(x -1\right)"," ",0,"-ln(x-1)","A"
51,1,33,27,0.053000," ","int((3*x^2-x+1)/(-x^3+1),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\ln \left(x -1\right)-\ln \left(x^{2}+x +1\right)"," ",0,"-ln(x-1)-ln(x^2+x+1)+2/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
52,1,17,18,0.050000," ","int((4*x^2+x+1)/(-x^3+1),x)","-2 \ln \left(x -1\right)-\ln \left(x^{2}+x +1\right)"," ",0,"-2*ln(x-1)-ln(x^2+x+1)","A"
53,1,98,97,0.045000," ","int((b*x^3+a)^3*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)","\frac{1}{14} b^{4} d \,x^{14}+\frac{1}{13} b^{4} c \,x^{13}+\frac{4}{11} a \,b^{3} d \,x^{11}+\frac{2}{5} a \,b^{3} c \,x^{10}+\frac{3}{4} a^{2} b^{2} d \,x^{8}+\frac{6}{7} a^{2} b^{2} c \,x^{7}+\frac{4}{5} a^{3} b d \,x^{5}+a^{3} b c \,x^{4}+\frac{1}{2} a^{4} d \,x^{2}+a^{4} c x"," ",0,"a^4*c*x+1/2*a^4*d*x^2+a^3*b*c*x^4+4/5*a^3*b*d*x^5+6/7*a^2*b^2*c*x^7+3/4*a^2*b^2*d*x^8+2/5*a*b^3*c*x^10+4/11*a*b^3*d*x^11+1/13*b^4*c*x^13+1/14*b^4*d*x^14","A"
54,1,75,74,0.050000," ","int((b*x^3+a)^2*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)","\frac{1}{11} b^{3} d \,x^{11}+\frac{1}{10} b^{3} c \,x^{10}+\frac{3}{8} a \,b^{2} d \,x^{8}+\frac{3}{7} a \,b^{2} c \,x^{7}+\frac{3}{5} a^{2} b d \,x^{5}+\frac{3}{4} a^{2} b c \,x^{4}+\frac{1}{2} a^{3} d \,x^{2}+a^{3} c x"," ",0,"a^3*c*x+1/2*a^3*d*x^2+3/4*a^2*b*c*x^4+3/5*a^2*b*d*x^5+3/7*a*b^2*c*x^7+3/8*a*b^2*d*x^8+1/10*b^3*c*x^10+1/11*b^3*d*x^11","A"
55,1,51,50,0.041000," ","int((b*x^3+a)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)","\frac{1}{8} b^{2} d \,x^{8}+\frac{1}{7} b^{2} c \,x^{7}+\frac{2}{5} a b d \,x^{5}+\frac{1}{2} a b c \,x^{4}+\frac{1}{2} a^{2} d \,x^{2}+a^{2} c x"," ",0,"a^2*c*x+1/2*a^2*d*x^2+1/2*a*b*c*x^4+2/5*a*b*d*x^5+1/7*b^2*c*x^7+1/8*b^2*d*x^8","A"
56,1,11,10,0.043000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a),x)","\frac{1}{2} d \,x^{2}+c x"," ",0,"c*x+1/2*d*x^2","A"
57,1,186,112,0.046000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^2,x)","\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"1/3/(a/b)^(2/3)/b*c*ln(x+(a/b)^(1/3))-1/6*c/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*c/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*d/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*d/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*d*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
58,1,238,136,0.046000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^3,x)","\frac{d \,x^{2}}{3 \left(b \,x^{3}+a \right) a}+\frac{c x}{3 \left(b \,x^{3}+a \right) a}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}"," ",0,"1/3*c*x/a/(b*x^3+a)+2/9/(a/b)^(2/3)/a/b*c*ln(x+(a/b)^(1/3))-1/9*c/a/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9*c/a/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(b*x^3+a)/a*d*x^2-1/9*d/a/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18*d/a/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9*d/a*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
59,1,1618,441,0.052000," ","int((b*x^3+a)^(3/2)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) a c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) a d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) b c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) b d"," ",0,"b*d*(2/19*b*x^8*(b*x^3+a)^(1/2)+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(2/17*b*x^7*(b*x^3+a)^(1/2)+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+a*d*(2/13*b*x^5*(b*x^3+a)^(1/2)+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+a*c*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
60,1,1546,416,0.062000," ","int((b*x^3+a)^(1/2)*(b*d*x^4+b*c*x^3+a*d*x+a*c),x)","\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) a c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) a d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) b c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) b d"," ",0,"b*d*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+a*d*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+a*c*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
61,1,1480,389,0.055000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) b c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{21 \sqrt{b \,x^{3}+a}\, b^{2}}\right) b d -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a d}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"b*d*(2/7*(b*x^3+a)^(1/2)/b*x^2+8/21*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*a*d*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*a*c*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
62,1,1536,364,0.052000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(3/2),x)","\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) a c +\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) a d +\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) b c +\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) b d"," ",0,"b*d*(-2/3/b*x^2/((x^3+a/b)*b)^(1/2)-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+a*d*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+a*c*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
63,1,1662,389,0.052000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(5/2),x)","\left(\frac{14 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}-\frac{14 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) a c +\left(\frac{10 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}+\frac{10 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) a d +\left(\frac{4 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}\right) b c +\left(\frac{8 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}\right) b d"," ",0,"b*d*(-2/9*x^2/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+8/27/b/a*x^2/((x^3+a/b)*b)^(1/2)+8/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(-2/9*x/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+4/27/b/a*x/((x^3+a/b)*b)^(1/2)-4/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+a*d*(2/9/a*x^2/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+10/27/a^2*x^2/((x^3+a/b)*b)^(1/2)+10/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+a*c*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^2*x+14/27/((x^3+a/b)*b)^(1/2)/a^2*x-14/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
64,1,1782,414,0.128000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(7/2),x)","\left(\frac{182 x}{405 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{15 \left(x^{3}+\frac{a}{b}\right)^{3} a \,b^{3}}+\frac{26 \sqrt{b \,x^{3}+a}\, x}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b^{2}}-\frac{182 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{1215 \sqrt{b \,x^{3}+a}\, a^{3} b}\right) a c +\left(\frac{22 x^{2}}{81 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{15 \left(x^{3}+\frac{a}{b}\right)^{3} a \,b^{3}}+\frac{22 \sqrt{b \,x^{3}+a}\, x^{2}}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b^{2}}+\frac{22 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{243 \sqrt{b \,x^{3}+a}\, a^{3} b}\right) a d +\left(\frac{28 x}{405 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2} b}+\frac{4 \sqrt{b \,x^{3}+a}\, x}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{3}}-\frac{28 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{1215 \sqrt{b \,x^{3}+a}\, a^{2} b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{15 \left(x^{3}+\frac{a}{b}\right)^{3} b^{4}}\right) b c +\left(\frac{8 x^{2}}{81 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2} b}+\frac{8 \sqrt{b \,x^{3}+a}\, x^{2}}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{15 \left(x^{3}+\frac{a}{b}\right)^{3} b^{4}}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{243 \sqrt{b \,x^{3}+a}\, a^{2} b^{2}}\right) b d"," ",0,"b*d*(-2/15*x^2/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^3+8/135/a*x^2/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+8/81/b/a^2*x^2/((x^3+a/b)*b)^(1/2)+8/243*I/a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(-2/15*x/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^3+4/135/a*x/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+28/405/b/a^2*x/((x^3+a/b)*b)^(1/2)-28/1215*I/a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+a*d*(2/15/a*x^2/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^3+22/135/a^2*x^2/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+22/81/a^3*x^2/((x^3+a/b)*b)^(1/2)+22/243*I/a^3*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+a*c*(2/15/a*x/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^3+26/135/a^2*x/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+182/405/a^3*x/((x^3+a/b)*b)^(1/2)-182/1215*I/a^3*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
65,1,1902,437,0.131000," ","int((b*d*x^4+b*c*x^3+a*d*x+a*c)/(b*x^3+a)^(9/2),x)","\left(\frac{494 x}{1215 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{4}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{21 \left(x^{3}+\frac{a}{b}\right)^{4} a \,b^{4}}+\frac{38 \sqrt{b \,x^{3}+a}\, x}{315 \left(x^{3}+\frac{a}{b}\right)^{3} a^{2} b^{3}}+\frac{494 \sqrt{b \,x^{3}+a}\, x}{2835 \left(x^{3}+\frac{a}{b}\right)^{2} a^{3} b^{2}}-\frac{494 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3645 \sqrt{b \,x^{3}+a}\, a^{4} b}\right) a c +\left(\frac{374 x^{2}}{1701 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{4}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{21 \left(x^{3}+\frac{a}{b}\right)^{4} a \,b^{4}}+\frac{34 \sqrt{b \,x^{3}+a}\, x^{2}}{315 \left(x^{3}+\frac{a}{b}\right)^{3} a^{2} b^{3}}+\frac{374 \sqrt{b \,x^{3}+a}\, x^{2}}{2835 \left(x^{3}+\frac{a}{b}\right)^{2} a^{3} b^{2}}+\frac{374 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{5103 \sqrt{b \,x^{3}+a}\, a^{4} b}\right) a d +\left(\frac{52 x}{1215 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3} b}+\frac{4 \sqrt{b \,x^{3}+a}\, x}{315 \left(x^{3}+\frac{a}{b}\right)^{3} a \,b^{4}}+\frac{52 \sqrt{b \,x^{3}+a}\, x}{2835 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b^{3}}-\frac{52 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3645 \sqrt{b \,x^{3}+a}\, a^{3} b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{21 \left(x^{3}+\frac{a}{b}\right)^{4} b^{5}}\right) b c +\left(\frac{88 x^{2}}{1701 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3} b}+\frac{8 \sqrt{b \,x^{3}+a}\, x^{2}}{315 \left(x^{3}+\frac{a}{b}\right)^{3} a \,b^{4}}+\frac{88 \sqrt{b \,x^{3}+a}\, x^{2}}{2835 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{21 \left(x^{3}+\frac{a}{b}\right)^{4} b^{5}}+\frac{88 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{5103 \sqrt{b \,x^{3}+a}\, a^{3} b^{2}}\right) b d"," ",0,"b*d*(-2/21*x^2/b^5*(b*x^3+a)^(1/2)/(x^3+a/b)^4+8/315/a*x^2/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^3+88/2835/a^2*x^2/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+88/1701/b/a^3*x^2/((x^3+a/b)*b)^(1/2)+88/5103*I/a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+b*c*(-2/21*x/b^5*(b*x^3+a)^(1/2)/(x^3+a/b)^4+4/315/a*x/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^3+52/2835/a^2*x/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^2+52/1215/b/a^3*x/((x^3+a/b)*b)^(1/2)-52/3645*I/a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+a*d*(2/21/a*x^2/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^4+34/315/a^2*x^2/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^3+374/2835/a^3*x^2/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+374/1701/a^4*x^2/((x^3+a/b)*b)^(1/2)+374/5103*I/a^4*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+a*c*(2/21/a*x/b^4*(b*x^3+a)^(1/2)/(x^3+a/b)^4+38/315/a^2*x/b^3*(b*x^3+a)^(1/2)/(x^3+a/b)^3+494/2835/a^3*x/b^2*(b*x^3+a)^(1/2)/(x^3+a/b)^2+494/1215/a^4*x/((x^3+a/b)*b)^(1/2)-494/3645*I/a^4*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
66,1,1491,446,0.061000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{21 \sqrt{b \,x^{3}+a}\, b^{2}}\right) g -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) d}{3 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, e}{3 b}"," ",0,"g*(2/7*(b*x^3+a)^(1/2)/b*x^2+8/21*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/3*e*(b*x^3+a)^(1/2)/b-2/3*I*d*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*c*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
67,1,1547,457,0.059000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) c +\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) d +\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) f +\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) g -\frac{2 e}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"g*(-2/3/((x^3+a/b)*b)^(1/2)/b*x^2-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*e/b/(b*x^3+a)^(1/2)+d*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
68,1,1673,488,0.063000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(5/2),x)","\left(\frac{14 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}-\frac{14 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) c +\left(\frac{10 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{2}}+\frac{10 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a^{2} b}\right) d +\left(\frac{4 x}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}\right) f +\left(\frac{8 x^{2}}{27 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a b}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{9 \left(x^{3}+\frac{a}{b}\right)^{2} b^{3}}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{81 \sqrt{b \,x^{3}+a}\, a \,b^{2}}\right) g -\frac{2 e}{9 \left(b \,x^{3}+a \right)^{\frac{3}{2}} b}"," ",0,"g*(-2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/b^3*x^2+8/27/((x^3+a/b)*b)^(1/2)/a/b*x^2+8/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/b^3*x+4/27/((x^3+a/b)*b)^(1/2)/a/b*x-4/81*I/b^2/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/9*e/b/(b*x^3+a)^(3/2)+d*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^2*x^2+10/27/((x^3+a/b)*b)^(1/2)/a^2*x^2+10/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/9*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^2*x+14/27/((x^3+a/b)*b)^(1/2)/a^2*x-14/81*I/a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
69,1,1793,529,0.065000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^(7/2),x)","\left(\frac{182 x}{405 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{15 \left(x^{3}+\frac{a}{b}\right)^{3} a \,b^{3}}+\frac{26 \sqrt{b \,x^{3}+a}\, x}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b^{2}}-\frac{182 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{1215 \sqrt{b \,x^{3}+a}\, a^{3} b}\right) c +\left(\frac{22 x^{2}}{81 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{15 \left(x^{3}+\frac{a}{b}\right)^{3} a \,b^{3}}+\frac{22 \sqrt{b \,x^{3}+a}\, x^{2}}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a^{2} b^{2}}+\frac{22 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{243 \sqrt{b \,x^{3}+a}\, a^{3} b}\right) d +\left(\frac{28 x}{405 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2} b}+\frac{4 \sqrt{b \,x^{3}+a}\, x}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{3}}-\frac{28 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{1215 \sqrt{b \,x^{3}+a}\, a^{2} b^{2}}-\frac{2 \sqrt{b \,x^{3}+a}\, x}{15 \left(x^{3}+\frac{a}{b}\right)^{3} b^{4}}\right) f +\left(\frac{8 x^{2}}{81 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2} b}+\frac{8 \sqrt{b \,x^{3}+a}\, x^{2}}{135 \left(x^{3}+\frac{a}{b}\right)^{2} a \,b^{3}}-\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{15 \left(x^{3}+\frac{a}{b}\right)^{3} b^{4}}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{243 \sqrt{b \,x^{3}+a}\, a^{2} b^{2}}\right) g -\frac{2 e}{15 \left(b \,x^{3}+a \right)^{\frac{5}{2}} b}"," ",0,"g*(-2/15*(b*x^3+a)^(1/2)/(x^3+a/b)^3/b^4*x^2+8/135*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^3*x^2+8/81/((x^3+a/b)*b)^(1/2)/a^2/b*x^2+8/243*I/a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-2/15*(b*x^3+a)^(1/2)/(x^3+a/b)^3/b^4*x+4/135*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a/b^3*x+28/405/((x^3+a/b)*b)^(1/2)/a^2/b*x-28/1215*I/a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/15*e/b/(b*x^3+a)^(5/2)+d*(2/15*(b*x^3+a)^(1/2)/(x^3+a/b)^3/a/b^3*x^2+22/135*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a^2/b^2*x^2+22/81/((x^3+a/b)*b)^(1/2)/a^3*x^2+22/243*I/a^3*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/15*(b*x^3+a)^(1/2)/(x^3+a/b)^3/a/b^3*x+26/135*(b*x^3+a)^(1/2)/(x^3+a/b)^2/a^2/b^2*x+182/405/((x^3+a/b)*b)^(1/2)/a^3*x-182/1215*I/a^3*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
70,1,211,135,0.049000," ","int((b*x+a)^2/(d*x^3+c),x)","\frac{\sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{a^{2} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{a^{2} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{2 \sqrt{3}\, a b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}-\frac{2 a b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{a b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{b^{2} \ln \left(d \,x^{3}+c \right)}{3 d}"," ",0,"1/3*a^2/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))-1/6*a^2/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/3*a^2/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))-2/3*a*b/d/(c/d)^(1/3)*ln(x+(c/d)^(1/3))+1/3*a*b/d/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+2/3*a*b*3^(1/2)/d/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))+1/3*b^2*ln(d*x^3+c)/d","A"
71,1,325,174,0.051000," ","int((b*x+a)^3/(d*x^3+c),x)","\frac{\sqrt{3}\, a^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{a^{3} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{a^{3} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{\sqrt{3}\, a^{2} b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{c}{d}\right)^{\frac{1}{3}} d}-\frac{a^{2} b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{\left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{a^{2} b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{2 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{a \,b^{2} \ln \left(d \,x^{3}+c \right)}{d}-\frac{\sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{b^{3} c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{b^{3} c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{b^{3} x}{d}"," ",0,"b^3*x/d+1/3/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a^3-1/3/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*b^3*c-1/6/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a^3+1/6/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b^3*c+1/3/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a^3-1/3/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b^3*c-1/d*a^2*b/(c/d)^(1/3)*ln(x+(c/d)^(1/3))+1/2/d*a^2*b/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))+1/d*a^2*b*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))+a*b^2*ln(d*x^3+c)/d","A"
72,1,446,228,0.051000," ","int((b*x+a)^4/(d*x^3+c),x)","\frac{b^{4} x^{2}}{2 d}+\frac{\sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{a^{4} \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}-\frac{a^{4} \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{2}{3}} d}+\frac{4 \sqrt{3}\, a^{3} b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}-\frac{4 a^{3} b \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{2 a^{3} b \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d}+\frac{2 a^{2} b^{2} \ln \left(d \,x^{3}+c \right)}{d}-\frac{4 \sqrt{3}\, a \,b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}-\frac{4 a \,b^{3} c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{2 a \,b^{3} c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{2}{3}} d^{2}}+\frac{4 a \,b^{3} x}{d}-\frac{\sqrt{3}\, b^{4} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{c}{d}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d^{2}}+\frac{b^{4} c \ln \left(x +\left(\frac{c}{d}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{c}{d}\right)^{\frac{1}{3}} d^{2}}-\frac{b^{4} c \ln \left(x^{2}-\left(\frac{c}{d}\right)^{\frac{1}{3}} x +\left(\frac{c}{d}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{c}{d}\right)^{\frac{1}{3}} d^{2}}"," ",0,"1/2*b^4*x^2/d+4*a*b^3*x/d+1/3/d/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a^4-4/3/d^2/(c/d)^(2/3)*ln(x+(c/d)^(1/3))*a*b^3*c-1/6/d/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a^4+2/3/d^2/(c/d)^(2/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a*b^3*c+1/3/d/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a^4-4/3/d^2/(c/d)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a*b^3*c-4/3/d/(c/d)^(1/3)*ln(x+(c/d)^(1/3))*a^3*b+1/3/d^2/(c/d)^(1/3)*ln(x+(c/d)^(1/3))*b^4*c+2/3/d/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*a^3*b-1/6/d^2/(c/d)^(1/3)*ln(x^2-(c/d)^(1/3)*x+(c/d)^(2/3))*b^4*c+4/3/d*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*a^3*b-1/3/d^2*3^(1/2)/(c/d)^(1/3)*arctan(1/3*3^(1/2)*(2/(c/d)^(1/3)*x-1))*b^4*c+2*a^2*b^2*ln(d*x^3+c)/d","A"
73,1,444,216,0.071000," ","int((c*x^2+b*x+a)^2/(e*x^3+d),x)","\frac{c^{2} x^{2}}{2 e}+\frac{\sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{a^{2} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{a^{2} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{2 \sqrt{3}\, a b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}-\frac{2 a b \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{a b \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{2 a c \ln \left(e \,x^{3}+d \right)}{3 e}+\frac{b^{2} \ln \left(e \,x^{3}+d \right)}{3 e}-\frac{2 \sqrt{3}\, b c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}-\frac{2 b c d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{b c d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{2 b c x}{e}-\frac{\sqrt{3}\, c^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}+\frac{c^{2} d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{c^{2} d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}"," ",0,"1/2*c^2*x^2/e+2*b*c*x/e+1/3/e/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a^2-2/3/e^2/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*b*c*d-1/6/e/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^2+1/3/e^2/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*b*c*d+1/3/e/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^2-2/3/e^2/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*b*c*d-2/3/e/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*a*b+1/3/e^2/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*c^2*d+1/3/e/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a*b-1/6/e^2/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*c^2*d+2/3/e*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a*b-1/3/e^2*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*c^2*d+2/3/e*ln(e*x^3+d)*a*c+1/3/e*ln(e*x^3+d)*b^2","B"
74,1,837,355,0.052000," ","int((c*x^2+b*x+a)^3/(e*x^3+d),x)","\frac{c^{3} x^{4}}{4 e}+\frac{b \,c^{2} x^{3}}{e}+\frac{3 a \,c^{2} x^{2}}{2 e}+\frac{3 b^{2} c \,x^{2}}{2 e}+\frac{\sqrt{3}\, a^{3} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{a^{3} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{a^{3} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{\sqrt{3}\, a^{2} b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e}-\frac{a^{2} b \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{a^{2} b \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{2 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{a^{2} c \ln \left(e \,x^{3}+d \right)}{e}+\frac{a \,b^{2} \ln \left(e \,x^{3}+d \right)}{e}-\frac{2 \sqrt{3}\, a b c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}-\frac{2 a b c d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{a b c d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{6 a b c x}{e}-\frac{\sqrt{3}\, a \,c^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}+\frac{a \,c^{2} d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{a \,c^{2} d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{2 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{\sqrt{3}\, b^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}-\frac{b^{3} d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{b^{3} d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{b^{3} x}{e}-\frac{\sqrt{3}\, b^{2} c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}+\frac{b^{2} c d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{b^{2} c d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{2 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{b \,c^{2} d \ln \left(e \,x^{3}+d \right)}{e^{2}}+\frac{\sqrt{3}\, c^{3} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}+\frac{c^{3} d^{2} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}-\frac{c^{3} d^{2} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}-\frac{c^{3} d x}{e^{2}}"," ",0,"-2/e^2/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a*b*c*d-1/2/e^2/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*b^2*c*d+1/e*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^2*b+1/e^2/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*a*c^2*d+1/e^2/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*b^2*c*d-1/2/e^2/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a*c^2*d-1/3/e^2/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*b^3*d+1/3/e^3/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*c^3*d^2-2/e^2/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a*b*c*d+1/e^2/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a*b*c*d-1/e^2*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a*c^2*d-1/e^2*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*b^2*c*d-1/6/e/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^3+1/e*ln(e*x^3+d)*a^2*c+1/e*ln(e*x^3+d)*a*b^2+1/3/e/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a^3+3/2/e*x^2*a*c^2+3/2/e*x^2*b^2*c-1/e^2*c^3*d*x+6/e*a*b*c*x-1/e/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*a^2*b+1/2/e/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^2*b-1/e^2*ln(e*x^3+d)*b*c^2*d+1/3/e^3/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*c^3*d^2+1/6/e^2/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*b^3*d-1/6/e^3/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*c^3*d^2+1/3/e/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^3-1/3/e^2/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*b^3*d+1/e*b^3*x+1/4*c^3*x^4/e+b*c^2*x^3/e","B"
75,1,1339,568,0.056000," ","int((c*x^2+b*x+a)^4/(e*x^3+d),x)","\frac{c^{4} x^{6}}{6 e}+\frac{4 b \,c^{3} x^{5}}{5 e}+\frac{a \,c^{3} x^{4}}{e}+\frac{3 b^{2} c^{2} x^{4}}{2 e}+\frac{4 a b \,c^{2} x^{3}}{e}+\frac{4 b^{3} c \,x^{3}}{3 e}-\frac{c^{4} d \,x^{3}}{3 e^{2}}+\frac{3 a^{2} c^{2} x^{2}}{e}+\frac{6 a \,b^{2} c \,x^{2}}{e}+\frac{b^{4} x^{2}}{2 e}-\frac{2 b \,c^{3} d \,x^{2}}{e^{2}}+\frac{\sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{a^{4} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}-\frac{a^{4} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{2}{3}} e}+\frac{4 \sqrt{3}\, a^{3} b \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}-\frac{4 a^{3} b \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{2 a^{3} b \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e}+\frac{4 a^{3} c \ln \left(e \,x^{3}+d \right)}{3 e}+\frac{2 a^{2} b^{2} \ln \left(e \,x^{3}+d \right)}{e}-\frac{4 \sqrt{3}\, a^{2} b c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}-\frac{4 a^{2} b c d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{2 a^{2} b c d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{12 a^{2} b c x}{e}-\frac{2 \sqrt{3}\, a^{2} c^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}+\frac{2 a^{2} c^{2} d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{a^{2} c^{2} d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{4 \sqrt{3}\, a \,b^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}-\frac{4 a \,b^{3} d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{2 a \,b^{3} d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{2}}+\frac{4 a \,b^{3} x}{e}-\frac{4 \sqrt{3}\, a \,b^{2} c d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}+\frac{4 a \,b^{2} c d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{2 a \,b^{2} c d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{4 a b \,c^{2} d \ln \left(e \,x^{3}+d \right)}{e^{2}}+\frac{4 \sqrt{3}\, a \,c^{3} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}+\frac{4 a \,c^{3} d^{2} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}-\frac{2 a \,c^{3} d^{2} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}-\frac{4 a \,c^{3} d x}{e^{2}}-\frac{\sqrt{3}\, b^{4} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}+\frac{b^{4} d \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{b^{4} d \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{2}}-\frac{4 b^{3} c d \ln \left(e \,x^{3}+d \right)}{3 e^{2}}+\frac{2 \sqrt{3}\, b^{2} c^{2} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}+\frac{2 b^{2} c^{2} d^{2} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}-\frac{b^{2} c^{2} d^{2} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{\left(\frac{d}{e}\right)^{\frac{2}{3}} e^{3}}-\frac{6 b^{2} c^{2} d x}{e^{2}}+\frac{4 \sqrt{3}\, b \,c^{3} d^{2} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{d}{e}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{3}}-\frac{4 b \,c^{3} d^{2} \ln \left(x +\left(\frac{d}{e}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{3}}+\frac{2 b \,c^{3} d^{2} \ln \left(x^{2}-\left(\frac{d}{e}\right)^{\frac{1}{3}} x +\left(\frac{d}{e}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{d}{e}\right)^{\frac{1}{3}} e^{3}}+\frac{c^{4} d^{2} \ln \left(e \,x^{3}+d \right)}{3 e^{3}}"," ",0,"-4/e^2/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^2*b*c*d-4/e^2*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a*b^2*c*d-1/e^2/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^2*c^2*d-1/3/e^2*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*b^4*d-4/e^2*ln(e*x^3+d)*a*b*c^2*d+2/3/e^3/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*b*c^3*d^2+4/3/e*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^3*b+2/e^2/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*a^2*c^2*d-4/3/e^3/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*b*c^3*d^2+2/e^3/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*b^2*c^2*d^2+2/3/e^2/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a*b^3*d-2/3/e^3/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a*c^3*d^2-1/e^3/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*b^2*c^2*d^2-4/3/e^2/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a*b^3*d+4/3/e^3/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a*c^3*d^2+1/2/e*x^2*b^4-4/3/e^2/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a*b^3*d+4/3/e^3/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a*c^3*d^2+2/e^3/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*b^2*c^2*d^2+4/e^2/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*a*b^2*c*d-2/e^2/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a*b^2*c*d-2/e^2*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^2*c^2*d+4/3/e^3*3^(1/2)/(d/e)^(1/3)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*b*c^3*d^2-4/e^2/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a^2*b*c*d+2/e^2/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^2*b*c*d+4/3/e*x^3*b^3*c+3/e*x^2*a^2*c^2+4/e*a*b^3*x+1/e*x^4*a*c^3+3/2/e*x^4*b^2*c^2+4/3/e*ln(e*x^3+d)*a^3*c+2/e*ln(e*x^3+d)*a^2*b^2+1/3/e^3*ln(e*x^3+d)*c^4*d^2+1/3/e/(d/e)^(2/3)*ln(x+(d/e)^(1/3))*a^4-1/3/e^2*x^3*c^4*d-1/6/e/(d/e)^(2/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^4+1/6*c^4*x^6/e+2/3/e/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*a^3*b-1/6/e^2/(d/e)^(1/3)*ln(x^2-(d/e)^(1/3)*x+(d/e)^(2/3))*b^4*d-4/3/e/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*a^3*b-4/3/e^2*ln(e*x^3+d)*b^3*c*d+1/3/e^2/(d/e)^(1/3)*ln(x+(d/e)^(1/3))*b^4*d-2/e^2*x^2*b*c^3*d+12/e*a^2*b*c*x-4/e^2*a*c^3*d*x-6/e^2*b^2*c^2*d*x+4/e*x^3*a*b*c^2+6/e*x^2*a*b^2*c+1/3/e/(d/e)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(d/e)^(1/3)*x-1))*a^4+4/5*b*c^3*x^5/e","B"
76,1,38,37,0.052000," ","int((x^4+2*x^2)/(x^3+1),x)","\frac{x^{2}}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}+\ln \left(x +1\right)+\frac{\ln \left(x^{2}-x +1\right)}{2}"," ",0,"1/2*x^2+ln(x+1)+1/2*ln(x^2-x+1)-1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
77,1,38,39,0.052000," ","int((x^4+2*x^2)/(-x^3+1),x)","-\frac{x^{2}}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\ln \left(x -1\right)-\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"-1/2*x^2-ln(x-1)-1/2*ln(x^2+x+1)-1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
78,1,38,37,0.047000," ","int((4*x^3-x+1)/(x^3+1),x)","4 x -\frac{4 \sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}-\frac{2 \ln \left(x +1\right)}{3}+\frac{\ln \left(x^{2}-x +1\right)}{3}"," ",0,"4*x-2/3*ln(x+1)+1/3*ln(x^2-x+1)-4/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
79,1,407,190,0.111000," ","int((1+x+3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \sqrt{3}\, \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*((-3/2-1/2*I*3^(1/2))*EllipticE(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+(1/2+1/2*I*3^(1/2))*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))+2*3^(1/2)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
80,1,368,217,0.129000," ","int((1-x+3^(1/2))/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)+\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right)}{3 \sqrt{-x^{3}+1}}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*((-3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2)))-2*I*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
81,1,407,120,0.069000," ","int((1-x+3^(1/2))/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \sqrt{3}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right)}{\sqrt{x^{3}-1}}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*((3/2-1/2*I*3^(1/2))*EllipticE(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+(-1/2+1/2*I*3^(1/2))*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))+2*3^(1/2)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","B"
82,1,370,115,0.065000," ","int((1+x+3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)-\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right)}{3 \sqrt{-x^{3}-1}}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*((3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2)))-2*I*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","B"
83,1,1003,346,0.268000," ","int((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3+a)^(1/2),x)","-\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*a^(1/3)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*a^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
84,1,949,359,0.293000," ","int((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3+a)^(1/2),x)","\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}+a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}+a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)*b/(a*b^2)^(1/3))^(1/2)/(-b*x^3+a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*a^(1/3)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)*b/(a*b^2)^(1/3))^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*a^(1/3)*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)*b/(a*b^2)^(1/3))^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
85,1,952,206,0.115000," ","int((-b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(b*x^3-a)^(1/2),x)","\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}-a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}-a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*a^(1/3)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*a^(1/3)*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
86,1,1012,201,0.108000," ","int((b^(1/3)*x+a^(1/3)*(1+3^(1/2)))/(-b*x^3-a)^(1/2),x)","-\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}-a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*a^(1/3)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*a^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
87,1,1004,386,0.201000," ","int((1+(1/a*b)^(1/3)*x+3^(1/2))/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}-\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}+a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*(1/a*b)^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
88,1,950,399,0.187000," ","int((1-(1/a*b)^(1/3)*x+3^(1/2))/(-b*x^3+a)^(1/2),x)","\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}+a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}"," ",0,"-2/3*I*(1/a*b)^(1/3)*3^(1/2)/b*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
89,1,953,211,0.097000," ","int((1-(1/a*b)^(1/3)*x+3^(1/2))/(b*x^3-a)^(1/2),x)","\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}-a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}-a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}-a}\, b}"," ",0,"-2/3*I*(1/a*b)^(1/3)*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
90,1,1013,208,0.080000," ","int((1+(1/a*b)^(1/3)*x+3^(1/2))/(-b*x^3-a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*(1/a*b)^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
91,1,407,104,0.108000," ","int((1+x-3^(1/2))/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \sqrt{3}\, \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right)}{\sqrt{x^{3}+1}}"," ",0,"2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*((-3/2-1/2*I*3^(1/2))*EllipticE(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+(1/2+1/2*I*3^(1/2))*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))-2*3^(1/2)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
92,1,368,119,0.107000," ","int((1-x-3^(1/2))/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}+\frac{2 i \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)+\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right)}{3 \sqrt{-x^{3}+1}}"," ",0,"-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*((-3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2)))+2*I*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","B"
93,1,407,218,0.066000," ","int((1-x-3^(1/2))/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \sqrt{3}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right)}{\sqrt{x^{3}-1}}"," ",0,"2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*((3/2-1/2*I*3^(1/2))*EllipticE(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+(-1/2+1/2*I*3^(1/2))*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))-2*3^(1/2)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
94,1,370,209,0.063000," ","int((1+x-3^(1/2))/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}+\frac{2 i \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)-\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right)}{3 \sqrt{-x^{3}-1}}"," ",0,"-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*((3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2)))+2*I*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
95,1,407,103,0.074000," ","int((-1-x+3^(1/2))/(x^3+1)^(1/2),x)","-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \sqrt{3}\, \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}-\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right)}{\sqrt{x^{3}+1}}"," ",0,"-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))-2*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*((-3/2-1/2*I*3^(1/2))*EllipticE(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+(1/2+1/2*I*3^(1/2))*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))+2*3^(1/2)*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","B"
96,1,368,120,0.065000," ","int((-1+x+3^(1/2))/(-x^3+1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}+1}}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)+\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right)}{3 \sqrt{-x^{3}+1}}"," ",0,"2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))-2/3*I*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*((-3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2)))-2*I*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","B"
97,1,407,217,0.064000," ","int((-1+x+3^(1/2))/(x^3-1)^(1/2),x)","-\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \sqrt{3}\, \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right)}{\sqrt{x^{3}-1}}"," ",0,"-2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+2*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*((3/2-1/2*I*3^(1/2))*EllipticE(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+(-1/2+1/2*I*3^(1/2))*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))+2*3^(1/2)*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
98,1,370,210,0.064000," ","int((-1-x+3^(1/2))/(-x^3-1)^(1/2),x)","\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{-x^{3}-1}}+\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)-\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right)}{3 \sqrt{-x^{3}-1}}"," ",0,"2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))+2/3*I*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*((3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2)))-2*I*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
99,1,1003,189,0.244000," ","int((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3+a)^(1/2),x)","\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*a^(1/3)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*a^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
100,1,949,196,0.224000," ","int((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3+a)^(1/2),x)","-\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}+a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}+a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*a^(1/3)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*a^(1/3)*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
101,1,952,375,0.076000," ","int((-b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(b*x^3-a)^(1/2),x)","-\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}-a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}-a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*a^(1/3)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*a^(1/3)*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
102,1,1012,366,0.087000," ","int((b^(1/3)*x+a^(1/3)*(1-3^(1/2)))/(-b*x^3-a)^(1/2),x)","\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}-a}\, b^{\frac{2}{3}}}"," ",0,"-2/3*I/b^(2/3)*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*a^(1/3)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*a^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
103,1,1004,196,0.180000," ","int((1+(1/a*b)^(1/3)*x-3^(1/2))/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}+a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*(1/a*b)^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
104,1,950,203,0.180000," ","int((1-(1/a*b)^(1/3)*x-3^(1/2))/(-b*x^3+a)^(1/2),x)","-\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}+a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}"," ",0,"-2/3*I*(1/a*b)^(1/3)*3^(1/2)/b*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
105,1,953,415,0.078000," ","int((1-(1/a*b)^(1/3)*x-3^(1/2))/(b*x^3-a)^(1/2),x)","-\frac{2 i \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{b \,x^{3}-a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}-a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}-a}\, b}"," ",0,"-2/3*I*(1/a*b)^(1/3)*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))-2*I*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+2/3*I*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","B"
106,1,1013,406,0.092000," ","int((1+(1/a*b)^(1/3)*x-3^(1/2))/(-b*x^3-a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}+\frac{2 i \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{\sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \left(\frac{b}{a}\right)^{\frac{1}{3}} \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}"," ",0,"-2/3*I*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*I*(1/a*b)^(1/3)*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2*I*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","B"
107,1,720,364,0.047000," ","int((d*x+c)/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) d}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*I*d*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*c*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","A"
108,1,681,377,0.049000," ","int((d*x+c)/(-b*x^3+a)^(1/2),x)","\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}+a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) d}{3 \sqrt{-b \,x^{3}+a}\, b}"," ",0,"2/3*I*d*3^(1/2)/b*(a*b^2)^(1/3)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+2/3*I*c*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(-b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","A"
109,1,683,389,0.053000," ","int((d*x+c)/(b*x^3-a)^(1/2),x)","\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}-a}\, b}+\frac{2 i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}} \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{-\frac{i \left(x +\frac{\left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) d}{3 \sqrt{b \,x^{3}-a}\, b}"," ",0,"2/3*I*d*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*((-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))+1/b*(a*b^2)^(1/3)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2)))+2/3*I*c*3^(1/2)*(a*b^2)^(1/3)/b*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)*((x-(a*b^2)^(1/3)/b)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b))^(1/2)*(I*(x+1/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2)/(b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(-I*(x+1/2*(a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)*3^(1/2)/(a*b^2)^(1/3)*b)^(1/2),(-I*3^(1/2)*(a*b^2)^(1/3)/(-3/2*(a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(a*b^2)^(1/3)/b)/b)^(1/2))","A"
110,1,726,382,0.052000," ","int((d*x+c)/(-b*x^3-a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{-b \,x^{3}-a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) d}{3 \sqrt{-b \,x^{3}-a}\, b}"," ",0,"-2/3*I*d*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*c*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(-b*x^3-a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","A"
111,1,291,204,0.049000," ","int((d*x+c)/(x^3+1)^(1/2),x)","\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, c \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}+1}}+\frac{2 \left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}-\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x -\frac{1}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x +1}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right) d}{\sqrt{x^{3}+1}}"," ",0,"2*d*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*((-3/2-1/2*I*3^(1/2))*EllipticE(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))+(1/2+1/2*I*3^(1/2))*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)))+2*c*(3/2-1/2*I*3^(1/2))*((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2-1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x-1/2+1/2*I*3^(1/2))/(-3/2+1/2*I*3^(1/2)))^(1/2)/(x^3+1)^(1/2)*EllipticF(((x+1)/(3/2-1/2*I*3^(1/2)))^(1/2),((-3/2+1/2*I*3^(1/2))/(-3/2-1/2*I*3^(1/2)))^(1/2))","A"
112,1,267,229,0.049000," ","int((d*x+c)/(-x^3+1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}+1}}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x -1}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x +\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(-\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)+\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x +\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{-\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right) d}{3 \sqrt{-x^{3}+1}}"," ",0,"-2/3*I*d*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*((-3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))+EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2)))-2/3*I*c*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x-1)/(-3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x+1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3+1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(-3/2+1/2*I*3^(1/2)))^(1/2))","A"
113,1,291,227,0.049000," ","int((d*x+c)/(x^3-1)^(1/2),x)","\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, c \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)}{\sqrt{x^{3}-1}}+\frac{2 \left(-\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}-\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\, \sqrt{\frac{x +\frac{1}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \left(\left(\frac{3}{2}-\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)+\left(-\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticF \left(\sqrt{\frac{x -1}{-\frac{3}{2}-\frac{i \sqrt{3}}{2}}}, \sqrt{\frac{\frac{3}{2}+\frac{i \sqrt{3}}{2}}{\frac{3}{2}-\frac{i \sqrt{3}}{2}}}\right)\right) d}{\sqrt{x^{3}-1}}"," ",0,"2*d*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*((3/2-1/2*I*3^(1/2))*EllipticE(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))+(-1/2+1/2*I*3^(1/2))*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)))+2*c*(-3/2-1/2*I*3^(1/2))*((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2-1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2)*((x+1/2+1/2*I*3^(1/2))/(3/2+1/2*I*3^(1/2)))^(1/2)/(x^3-1)^(1/2)*EllipticF(((x-1)/(-3/2-1/2*I*3^(1/2)))^(1/2),((3/2+1/2*I*3^(1/2))/(3/2-1/2*I*3^(1/2)))^(1/2))","A"
114,1,269,221,0.047000," ","int((d*x+c)/(-x^3-1)^(1/2),x)","-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)}{3 \sqrt{-x^{3}-1}}-\frac{2 i \sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \sqrt{\frac{x +1}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\, \sqrt{-i \left(x -\frac{1}{2}+\frac{i \sqrt{3}}{2}\right) \sqrt{3}}\, \left(\left(\frac{3}{2}+\frac{i \sqrt{3}}{2}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)-\EllipticF \left(\frac{\sqrt{3}\, \sqrt{i \left(x -\frac{1}{2}-\frac{i \sqrt{3}}{2}\right) \sqrt{3}}}{3}, \sqrt{\frac{i \sqrt{3}}{\frac{3}{2}+\frac{i \sqrt{3}}{2}}}\right)\right) d}{3 \sqrt{-x^{3}-1}}"," ",0,"-2/3*I*d*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*((3/2+1/2*I*3^(1/2))*EllipticE(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))-EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2)))-2/3*I*c*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2)*((x+1)/(3/2+1/2*I*3^(1/2)))^(1/2)*(-I*(x-1/2+1/2*I*3^(1/2))*3^(1/2))^(1/2)/(-x^3-1)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x-1/2-1/2*I*3^(1/2))*3^(1/2))^(1/2),(I*3^(1/2)/(3/2+1/2*I*3^(1/2)))^(1/2))","A"
115,1,101,57,0.046000," ","int((d*x+c)/(-b*x^4+a),x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}"," ",0,"1/4*c*(a/b)^(1/4)/a*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*c*(a/b)^(1/4)/a*arctan(x/(a/b)^(1/4))-1/4*d/(a*b)^(1/2)*ln((-a+x^2*(a*b)^(1/2))/(-a-x^2*(a*b)^(1/2)))","A"
116,1,151,144,0.045000," ","int((d*x+c)/(b*x^4+a),x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}"," ",0,"1/8*c*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*c*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*c*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/2*d/(a*b)^(1/2)*arctan(x^2*(1/a*b)^(1/2))","A"
117,1,142,78,0.050000," ","int((d*x+c)/(-b*x^4+a)^2,x)","-\frac{d \,x^{2}}{4 \left(b \,x^{4}-a \right) a}-\frac{c x}{4 \left(b \,x^{4}-a \right) a}-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}"," ",0,"-1/4*c*x/a/(b*x^4-a)+3/16*c/a^2*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+3/8*c/a^2*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)-1/4*d*x^2/a/(b*x^4-a)-1/8*d/a/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))","A"
118,1,188,164,0.052000," ","int((d*x+c)/(b*x^4+a)^2,x)","\frac{d \,x^{2}}{4 \left(b \,x^{4}+a \right) a}+\frac{c x}{4 \left(b \,x^{4}+a \right) a}+\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}"," ",0,"1/4*c*x/a/(b*x^4+a)+3/32*c/a^2*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16*c/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/16*c/a^2*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*d*x^2/a/(b*x^4+a)+1/4*d/a/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)","A"
119,1,180,102,0.049000," ","int((d*x+c)/(-b*x^4+a)^3,x)","\frac{d \,x^{2}}{8 \left(b \,x^{4}-a \right)^{2} a}+\frac{c x}{8 \left(b \,x^{4}-a \right)^{2} a}-\frac{3 d \,x^{2}}{16 \left(b \,x^{4}-a \right) a^{2}}-\frac{7 c x}{32 \left(b \,x^{4}-a \right) a^{2}}-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}"," ",0,"1/8*c*x/a/(b*x^4-a)^2-7/32*c/a^2*x/(b*x^4-a)+21/128*c/a^3*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+21/64*c/a^3*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/8*d*x^2/a/(b*x^4-a)^2-3/16*d/a^2*x^2/(b*x^4-a)-3/32*d/a^2/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))","A"
120,1,222,187,0.049000," ","int((d*x+c)/(b*x^4+a)^3,x)","\frac{d \,x^{2}}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{c x}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{3 d \,x^{2}}{16 \left(b \,x^{4}+a \right) a^{2}}+\frac{7 c x}{32 \left(b \,x^{4}+a \right) a^{2}}+\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}"," ",0,"1/8*c*x/a/(b*x^4+a)^2+7/32*c/a^2*x/(b*x^4+a)+21/256*c/a^3*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+21/128*c/a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+21/128*c/a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/8*d*x^2/a/(b*x^4+a)^2+3/16*d/a^2*x^2/(b*x^4+a)+3/16*d/a^2/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)","A"
121,1,177,126,0.064000," ","int((d*x+c)/(-b*x^4+a)^4,x)","-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{-\frac{5 b^{2} d \,x^{10}}{32 a^{3}}-\frac{77 b^{2} c \,x^{9}}{384 a^{3}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{33 b c \,x^{5}}{64 a^{2}}-\frac{11 d \,x^{2}}{32 a}-\frac{51 c x}{128 a}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(-5/32*d/a^3*b^2*x^10-77/384*c/a^3*b^2*x^9+5/12/a^2*d*b*x^6+33/64/a^2*c*b*x^5-11/32*d/a*x^2-51/128*c/a*x)/(b*x^4-a)^3+77/512/a^4*c*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+77/256/a^4*c*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)-5/64/a^3*d/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))","A"
122,1,225,210,0.070000," ","int((d*x+c)/(b*x^4+a)^4,x)","\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{5 b^{2} d \,x^{10}}{32 a^{3}}+\frac{77 b^{2} c \,x^{9}}{384 a^{3}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{33 b c \,x^{5}}{64 a^{2}}+\frac{11 d \,x^{2}}{32 a}+\frac{51 c x}{128 a}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(5/32/a^3*b^2*d*x^10+77/384/a^3*b^2*c*x^9+5/12/a^2*b*d*x^6+33/64/a^2*b*c*x^5+11/32/a*d*x^2+51/128/a*c*x)/(b*x^4+a)^3+77/1024/a^4*c*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+77/512/a^4*c*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+77/512/a^4*c*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+5/32/a^3*d/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)","A"
123,1,44,18,0.044000," ","int((d*x+c)/(-x^4+1),x)","\frac{c \arctan \left(x \right)}{2}-\frac{c \ln \left(x -1\right)}{4}+\frac{c \ln \left(x +1\right)}{4}-\frac{d \ln \left(x -1\right)}{4}-\frac{d \ln \left(x +1\right)}{4}+\frac{d \ln \left(x^{2}+1\right)}{4}"," ",0,"-1/4*c*ln(x-1)-1/4*ln(x-1)*d+1/4*ln(x+1)*c-1/4*ln(x+1)*d+1/4*d*ln(x^2+1)+1/2*c*arctan(x)","B"
124,1,68,71,0.046000," ","int((d*x+c)/(x^4+1),x)","\frac{\sqrt{2}\, c \arctan \left(\sqrt{2}\, x -1\right)}{4}+\frac{\sqrt{2}\, c \arctan \left(\sqrt{2}\, x +1\right)}{4}+\frac{\sqrt{2}\, c \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{8}+\frac{d \arctan \left(x^{2}\right)}{2}"," ",0,"1/4*c*arctan(2^(1/2)*x-1)*2^(1/2)+1/8*c*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))+1/4*c*arctan(2^(1/2)*x+1)*2^(1/2)+1/2*d*arctan(x^2)","A"
125,1,161,78,0.045000," ","int((e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/4*(a/b)^(1/4)/a*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*(a/b)^(1/4)/a*c*arctan(1/(a/b)^(1/4)*x)-1/4/(a*b)^(1/2)*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2*e/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/4*e/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
126,1,280,186,0.046000," ","int((e*x^2+d*x+c)/(b*x^4+a),x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}"," ",0,"1/8*(a/b)^(1/4)*2^(1/2)/a*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/2/(a*b)^(1/2)*d*arctan((1/a*b)^(1/2)*x^2)+1/8*e/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
127,1,228,106,0.055000," ","int((e*x^2+d*x+c)/(-b*x^4+a)^2,x)","-\frac{e \,x^{3}}{4 \left(b \,x^{4}-a \right) a}-\frac{d \,x^{2}}{4 \left(b \,x^{4}-a \right) a}-\frac{c x}{4 \left(b \,x^{4}-a \right) a}-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}"," ",0,"-1/4/(b*x^4-a)/a*c*x+3/16*(a/b)^(1/4)/a^2*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+3/8*(a/b)^(1/4)/a^2*c*arctan(1/(a/b)^(1/4)*x)-1/4/(b*x^4-a)/a*d*x^2-1/8/(a*b)^(1/2)/a*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/4*e*x^3/a/(b*x^4-a)-1/8*e/a/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/16*e/a/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
128,1,344,215,0.049000," ","int((e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{e \,x^{3}}{4 \left(b \,x^{4}+a \right) a}+\frac{d \,x^{2}}{4 \left(b \,x^{4}+a \right) a}+\frac{c x}{4 \left(b \,x^{4}+a \right) a}+\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}"," ",0,"1/4/(b*x^4+a)/a*c*x+3/32*(a/b)^(1/4)*2^(1/2)/a^2*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4/(b*x^4+a)/a*d*x^2+1/4/(a*b)^(1/2)/a*d*arctan((1/a*b)^(1/2)*x^2)+1/4*e*x^3/a/(b*x^4+a)+1/32*e/a/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16*e/a/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16*e/a/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
129,1,286,137,0.052000," ","int((e*x^2+d*x+c)/(-b*x^4+a)^3,x)","\frac{e \,x^{3}}{8 \left(b \,x^{4}-a \right)^{2} a}+\frac{d \,x^{2}}{8 \left(b \,x^{4}-a \right)^{2} a}-\frac{5 e \,x^{3}}{32 \left(b \,x^{4}-a \right) a^{2}}+\frac{c x}{8 \left(b \,x^{4}-a \right)^{2} a}-\frac{3 d \,x^{2}}{16 \left(b \,x^{4}-a \right) a^{2}}-\frac{7 c x}{32 \left(b \,x^{4}-a \right) a^{2}}-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}-\frac{5 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}"," ",0,"1/8/(b*x^4-a)^2/a*c*x-7/32/(b*x^4-a)/a^2*c*x+21/128*(a/b)^(1/4)/a^3*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+21/64*(a/b)^(1/4)/a^3*c*arctan(1/(a/b)^(1/4)*x)+1/8/(b*x^4-a)^2/a*d*x^2-3/16/(b*x^4-a)/a^2*d*x^2-3/32/(a*b)^(1/2)/a^2*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+1/8*e*x^3/a/(b*x^4-a)^2-5/32*e/a^2*x^3/(b*x^4-a)-5/64*e/a^2/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+5/128*e/a^2/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
130,1,396,246,0.051000," ","int((e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{e \,x^{3}}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{d \,x^{2}}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{5 e \,x^{3}}{32 \left(b \,x^{4}+a \right) a^{2}}+\frac{c x}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{3 d \,x^{2}}{16 \left(b \,x^{4}+a \right) a^{2}}+\frac{7 c x}{32 \left(b \,x^{4}+a \right) a^{2}}+\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}"," ",0,"1/8/(b*x^4+a)^2/a*c*x+7/32/(b*x^4+a)/a^2*c*x+21/256*(a/b)^(1/4)*2^(1/2)/a^3*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/8/(b*x^4+a)^2/a*d*x^2+3/16/(b*x^4+a)/a^2*d*x^2+3/16/(a*b)^(1/2)/a^2*d*arctan((1/a*b)^(1/2)*x^2)+1/8*e*x^3/a/(b*x^4+a)^2+5/32*e/a^2*x^3/(b*x^4+a)+5/256*e/a^2/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/128*e/a^2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/128*e/a^2/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
131,1,274,167,0.061000," ","int((e*x^2+d*x+c)/(-b*x^4+a)^4,x)","-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}-\frac{15 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{-\frac{15 b^{2} e \,x^{11}}{128 a^{3}}-\frac{5 b^{2} d \,x^{10}}{32 a^{3}}-\frac{77 b^{2} c \,x^{9}}{384 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{33 b c \,x^{5}}{64 a^{2}}-\frac{113 e \,x^{3}}{384 a}-\frac{11 d \,x^{2}}{32 a}-\frac{51 c x}{128 a}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(-15/128*e/a^3*b^2*x^11-5/32/a^3*b^2*d*x^10-77/384/a^3*b^2*c*x^9+21/64/a^2*b*e*x^7+5/12/a^2*b*d*x^6+33/64/a^2*b*c*x^5-113/384/a*e*x^3-11/32/a*d*x^2-51/128/a*c*x)/(b*x^4-a)^3+77/512*(a/b)^(1/4)/a^4*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+77/256*(a/b)^(1/4)/a^4*c*arctan(1/(a/b)^(1/4)*x)-5/64/(a*b)^(1/2)/a^3*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-15/256/a^3*e/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+15/512/a^3*e/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
132,1,394,275,0.065000," ","int((e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{15 b^{2} e \,x^{11}}{128 a^{3}}+\frac{5 b^{2} d \,x^{10}}{32 a^{3}}+\frac{77 b^{2} c \,x^{9}}{384 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{33 b c \,x^{5}}{64 a^{2}}+\frac{113 e \,x^{3}}{384 a}+\frac{11 d \,x^{2}}{32 a}+\frac{51 c x}{128 a}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(15/128/a^3*b^2*e*x^11+5/32/a^3*b^2*d*x^10+77/384/a^3*b^2*c*x^9+21/64/a^2*b*e*x^7+5/12/a^2*b*d*x^6+33/64/a^2*b*c*x^5+113/384/a*e*x^3+11/32/a*d*x^2+51/128/a*c*x)/(b*x^4+a)^3+77/1024*(a/b)^(1/4)*2^(1/2)/a^4*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+5/32/(a*b)^(1/2)/a^3*d*arctan((1/a*b)^(1/2)*x^2)+15/1024/a^3*e/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
133,1,24,24,0.045000," ","int(a*(f*x^4+e)^2,x)","\left(\frac{1}{9} f^{2} x^{9}+\frac{2}{5} e f \,x^{5}+e^{2} x \right) a"," ",0,"a*(1/9*f^2*x^9+2/5*e*f*x^5+e^2*x)","A"
134,1,27,27,0.041000," ","int(b*x*(f*x^4+e)^2,x)","\left(\frac{1}{10} f^{2} x^{10}+\frac{1}{3} e f \,x^{6}+\frac{1}{2} e^{2} x^{2}\right) b"," ",0,"b*(1/10*f^2*x^10+1/3*e*f*x^6+1/2*e^2*x^2)","A"
135,1,51,50,0.048000," ","int((b*x+a)*(f*x^4+e)^2,x)","\frac{1}{10} b \,f^{2} x^{10}+\frac{1}{9} a \,f^{2} x^{9}+\frac{1}{3} b e f \,x^{6}+\frac{2}{5} a e f \,x^{5}+\frac{1}{2} b \,e^{2} x^{2}+a \,e^{2} x"," ",0,"a*e^2*x+1/2*b*e^2*x^2+2/5*a*e*f*x^5+1/3*b*e*f*x^6+1/9*a*f^2*x^9+1/10*b*f^2*x^10","A"
136,1,27,27,0.042000," ","int(c*x^2*(f*x^4+e)^2,x)","\left(\frac{1}{11} f^{2} x^{11}+\frac{2}{7} e f \,x^{7}+\frac{1}{3} e^{2} x^{3}\right) c"," ",0,"c*(1/11*f^2*x^11+2/7*e*f*x^7+1/3*e^2*x^3)","A"
137,1,51,50,0.044000," ","int((c*x^2+a)*(f*x^4+e)^2,x)","\frac{1}{11} c \,f^{2} x^{11}+\frac{1}{9} a \,f^{2} x^{9}+\frac{2}{7} c e f \,x^{7}+\frac{2}{5} a e f \,x^{5}+\frac{1}{3} c \,e^{2} x^{3}+a \,e^{2} x"," ",0,"a*e^2*x+1/3*c*e^2*x^3+2/5*a*e*f*x^5+2/7*c*e*f*x^7+1/9*a*f^2*x^9+1/11*c*f^2*x^11","A"
138,1,54,53,0.039000," ","int((c*x^2+b*x)*(f*x^4+e)^2,x)","\frac{1}{11} c \,f^{2} x^{11}+\frac{1}{10} b \,f^{2} x^{10}+\frac{2}{7} c e f \,x^{7}+\frac{1}{3} b e f \,x^{6}+\frac{1}{3} c \,e^{2} x^{3}+\frac{1}{2} b \,e^{2} x^{2}"," ",0,"1/2*b*e^2*x^2+1/3*c*e^2*x^3+1/3*b*e*f*x^6+2/7*c*e*f*x^7+1/10*b*f^2*x^10+1/11*c*f^2*x^11","A"
139,1,77,76,0.043000," ","int((c*x^2+b*x+a)*(f*x^4+e)^2,x)","\frac{1}{11} c \,f^{2} x^{11}+\frac{1}{10} b \,f^{2} x^{10}+\frac{1}{9} a \,f^{2} x^{9}+\frac{2}{7} c e f \,x^{7}+\frac{1}{3} b e f \,x^{6}+\frac{2}{5} a e f \,x^{5}+\frac{1}{3} c \,e^{2} x^{3}+\frac{1}{2} b \,e^{2} x^{2}+a \,e^{2} x"," ",0,"a*e^2*x+1/2*b*e^2*x^2+1/3*c*e^2*x^3+2/5*a*e*f*x^5+1/3*b*e*f*x^6+2/7*c*e*f*x^7+1/9*a*f^2*x^9+1/10*b*f^2*x^10+1/11*c*f^2*x^11","A"
140,1,27,15,0.044000," ","int(d*x^3*(f*x^4+e)^2,x)","\left(\frac{1}{12} f^{2} x^{12}+\frac{1}{4} e f \,x^{8}+\frac{1}{4} e^{2} x^{4}\right) d"," ",0,"d*(1/12*f^2*x^12+1/4*e*f*x^8+1/4*e^2*x^4)","A"
141,1,51,39,0.043000," ","int((d*x^3+a)*(f*x^4+e)^2,x)","\frac{1}{12} d \,f^{2} x^{12}+\frac{1}{9} a \,f^{2} x^{9}+\frac{1}{4} d e f \,x^{8}+\frac{2}{5} a e f \,x^{5}+\frac{1}{4} d \,e^{2} x^{4}+a \,e^{2} x"," ",0,"1/12*d*f^2*x^12+1/9*a*f^2*x^9+1/4*d*e*f*x^8+2/5*a*e*f*x^5+1/4*d*e^2*x^4+a*e^2*x","A"
142,1,54,42,0.039000," ","int((d*x^3+b*x)*(f*x^4+e)^2,x)","\frac{1}{12} d \,f^{2} x^{12}+\frac{1}{10} b \,f^{2} x^{10}+\frac{1}{4} d e f \,x^{8}+\frac{1}{3} b e f \,x^{6}+\frac{1}{4} d \,e^{2} x^{4}+\frac{1}{2} b \,e^{2} x^{2}"," ",0,"1/12*d*f^2*x^12+1/10*b*f^2*x^10+1/4*d*e*f*x^8+1/3*b*e*f*x^6+1/4*d*e^2*x^4+1/2*b*e^2*x^2","A"
143,1,77,65,0.044000," ","int((d*x^3+b*x+a)*(f*x^4+e)^2,x)","\frac{1}{12} d \,f^{2} x^{12}+\frac{1}{10} b \,f^{2} x^{10}+\frac{1}{9} a \,f^{2} x^{9}+\frac{1}{4} d e f \,x^{8}+\frac{1}{3} b e f \,x^{6}+\frac{2}{5} a e f \,x^{5}+\frac{1}{4} d \,e^{2} x^{4}+\frac{1}{2} b \,e^{2} x^{2}+a \,e^{2} x"," ",0,"1/12*d*f^2*x^12+1/10*b*f^2*x^10+1/9*a*f^2*x^9+1/4*d*e*f*x^8+1/3*b*e*f*x^6+2/5*a*e*f*x^5+1/4*d*e^2*x^4+1/2*b*e^2*x^2+a*e^2*x","A"
144,1,54,42,0.043000," ","int((d*x^3+c*x^2)*(f*x^4+e)^2,x)","\frac{1}{12} d \,f^{2} x^{12}+\frac{1}{11} c \,f^{2} x^{11}+\frac{1}{4} d e f \,x^{8}+\frac{2}{7} c e f \,x^{7}+\frac{1}{4} d \,e^{2} x^{4}+\frac{1}{3} c \,e^{2} x^{3}"," ",0,"1/12*d*f^2*x^12+1/11*c*f^2*x^11+1/4*d*e*f*x^8+2/7*c*e*f*x^7+1/4*d*e^2*x^4+1/3*c*e^2*x^3","A"
145,1,77,65,0.043000," ","int((d*x^3+c*x^2+a)*(f*x^4+e)^2,x)","\frac{1}{12} d \,f^{2} x^{12}+\frac{1}{11} c \,f^{2} x^{11}+\frac{1}{9} a \,f^{2} x^{9}+\frac{1}{4} d e f \,x^{8}+\frac{2}{7} c e f \,x^{7}+\frac{2}{5} a e f \,x^{5}+\frac{1}{4} d \,e^{2} x^{4}+\frac{1}{3} c \,e^{2} x^{3}+a \,e^{2} x"," ",0,"1/12*d*f^2*x^12+1/11*c*f^2*x^11+1/9*a*f^2*x^9+1/4*d*e*f*x^8+2/7*c*e*f*x^7+2/5*a*e*f*x^5+1/4*d*e^2*x^4+1/3*c*e^2*x^3+a*e^2*x","A"
146,1,80,68,0.038000," ","int((d*x^3+c*x^2+b*x)*(f*x^4+e)^2,x)","\frac{1}{12} d \,f^{2} x^{12}+\frac{1}{11} c \,f^{2} x^{11}+\frac{1}{10} b \,f^{2} x^{10}+\frac{1}{4} d e f \,x^{8}+\frac{2}{7} c e f \,x^{7}+\frac{1}{3} b e f \,x^{6}+\frac{1}{4} d \,e^{2} x^{4}+\frac{1}{3} c \,e^{2} x^{3}+\frac{1}{2} b \,e^{2} x^{2}"," ",0,"1/12*d*f^2*x^12+1/11*c*f^2*x^11+1/10*b*f^2*x^10+1/4*d*e*f*x^8+2/7*c*e*f*x^7+1/3*b*e*f*x^6+1/4*d*e^2*x^4+1/3*c*e^2*x^3+1/2*b*e^2*x^2","A"
147,1,103,91,0.040000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x)","\frac{1}{12} b^{2} f \,x^{12}+\frac{1}{11} b^{2} e \,x^{11}+\frac{1}{10} b^{2} d \,x^{10}+\frac{1}{9} b^{2} c \,x^{9}+\frac{1}{4} a b f \,x^{8}+\frac{2}{7} a b e \,x^{7}+\frac{1}{3} a b d \,x^{6}+\frac{2}{5} a b c \,x^{5}+\frac{1}{4} a^{2} f \,x^{4}+\frac{1}{3} a^{2} e \,x^{3}+\frac{1}{2} a^{2} d \,x^{2}+a^{2} c x"," ",0,"1/12*b^2*f*x^12+1/11*b^2*e*x^11+1/10*b^2*d*x^10+1/9*b^2*c*x^9+1/4*f*a*b*x^8+2/7*a*b*e*x^7+1/3*a*b*d*x^6+2/5*a*b*c*x^5+1/4*f*a^2*x^4+1/3*a^2*e*x^3+1/2*a^2*d*x^2+a^2*c*x","A"
148,1,151,127,0.049000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x)","\frac{1}{16} b^{3} f \,x^{16}+\frac{1}{15} b^{3} e \,x^{15}+\frac{1}{14} b^{3} d \,x^{14}+\frac{1}{13} b^{3} c \,x^{13}+\frac{1}{4} a \,b^{2} f \,x^{12}+\frac{3}{11} a \,b^{2} e \,x^{11}+\frac{3}{10} a \,b^{2} d \,x^{10}+\frac{1}{3} a \,b^{2} c \,x^{9}+\frac{3}{8} a^{2} b f \,x^{8}+\frac{3}{7} a^{2} b e \,x^{7}+\frac{1}{2} a^{2} b d \,x^{6}+\frac{3}{5} a^{2} b c \,x^{5}+\frac{1}{4} a^{3} f \,x^{4}+\frac{1}{3} a^{3} e \,x^{3}+\frac{1}{2} a^{3} d \,x^{2}+a^{3} c x"," ",0,"1/16*b^3*f*x^16+1/15*b^3*e*x^15+1/14*b^3*d*x^14+1/13*b^3*c*x^13+1/4*a*b^2*f*x^12+3/11*a*b^2*e*x^11+3/10*a*b^2*d*x^10+1/3*a*b^2*c*x^9+3/8*f*a^2*b*x^8+3/7*a^2*b*e*x^7+1/2*a^2*b*d*x^6+3/5*a^2*b*c*x^5+1/4*f*a^3*x^4+1/3*a^3*e*x^3+1/2*a^3*d*x^2+a^3*c*x","A"
149,1,248,115,0.052000," ","int((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x)","-\frac{f \,x^{4}}{4 \left(b \,x^{4}-a \right) a}-\frac{e \,x^{3}}{4 \left(b \,x^{4}-a \right) a}-\frac{d \,x^{2}}{4 \left(b \,x^{4}-a \right) a}-\frac{c x}{4 \left(b \,x^{4}-a \right) a}-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}"," ",0,"-1/4/(b*x^4-a)/a*c*x+3/16*(a/b)^(1/4)/a^2*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+3/8*(a/b)^(1/4)/a^2*c*arctan(1/(a/b)^(1/4)*x)-1/4/(b*x^4-a)/a*d*x^2-1/8/(a*b)^(1/2)/a*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/4/(b*x^4-a)/a*e*x^3-1/8/(a/b)^(1/4)/a/b*e*arctan(1/(a/b)^(1/4)*x)+1/16/(a/b)^(1/4)/a/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4*f*x^4/a/(b*x^4-a)","B"
150,1,326,146,0.054000," ","int((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x)","\frac{f \,x^{4}}{8 \left(b \,x^{4}-a \right)^{2} a}+\frac{e \,x^{3}}{8 \left(b \,x^{4}-a \right)^{2} a}-\frac{f \,x^{4}}{8 \left(b \,x^{4}-a \right) a^{2}}+\frac{d \,x^{2}}{8 \left(b \,x^{4}-a \right)^{2} a}-\frac{5 e \,x^{3}}{32 \left(b \,x^{4}-a \right) a^{2}}+\frac{c x}{8 \left(b \,x^{4}-a \right)^{2} a}-\frac{3 d \,x^{2}}{16 \left(b \,x^{4}-a \right) a^{2}}-\frac{7 c x}{32 \left(b \,x^{4}-a \right) a^{2}}-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}-\frac{5 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}"," ",0,"1/8/(b*x^4-a)^2/a*c*x-7/32/(b*x^4-a)/a^2*c*x+21/128*(a/b)^(1/4)/a^3*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+21/64*(a/b)^(1/4)/a^3*c*arctan(1/(a/b)^(1/4)*x)+1/8/(b*x^4-a)^2/a*d*x^2-3/16/(b*x^4-a)/a^2*d*x^2-3/32/(a*b)^(1/2)/a^2*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+1/8/(b*x^4-a)^2/a*e*x^3-5/32/(b*x^4-a)/a^2*e*x^3-5/64/(a/b)^(1/4)/a^2/b*e*arctan(1/(a/b)^(1/4)*x)+5/128/(a/b)^(1/4)/a^2/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/8*f*x^4/a/(b*x^4-a)^2-1/8*f/a^2*x^4/(b*x^4-a)","B"
151,1,280,176,0.058000," ","int((f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x)","-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}-\frac{15 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{-\frac{15 b^{2} e \,x^{11}}{128 a^{3}}-\frac{5 b^{2} d \,x^{10}}{32 a^{3}}-\frac{77 b^{2} c \,x^{9}}{384 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{33 b c \,x^{5}}{64 a^{2}}-\frac{113 e \,x^{3}}{384 a}-\frac{11 d \,x^{2}}{32 a}-\frac{51 c x}{128 a}-\frac{f}{12 b}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(-15/128/a^3*b^2*e*x^11-5/32/a^3*b^2*d*x^10-77/384/a^3*b^2*c*x^9+21/64/a^2*b*e*x^7+5/12/a^2*b*d*x^6+33/64/a^2*b*c*x^5-113/384/a*e*x^3-11/32/a*d*x^2-51/128/a*c*x-1/12*f/b)/(b*x^4-a)^3+77/512*(a/b)^(1/4)/a^4*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+77/256*(a/b)^(1/4)/a^4*c*arctan(1/(a/b)^(1/4)*x)-5/64/(a*b)^(1/2)/a^3*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-15/256/(a/b)^(1/4)/a^3/b*e*arctan(1/(a/b)^(1/4)*x)+15/512/(a/b)^(1/4)/a^3/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
152,1,114,72,0.045000," ","int(a/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}"," ",0,"1/24*a*3^(1/2)*6^(1/4)*2^(1/2)*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*a*3^(1/2)*6^(1/4)*2^(1/2)*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/48*a*3^(1/2)*6^(1/4)*2^(1/2)*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))","A"
153,1,16,15,0.039000," ","int(b*x/(3*x^4+2),x)","\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}"," ",0,"1/12*b*arctan(1/2*6^(1/2)*x^2)*6^(1/2)","A"
154,1,129,87,0.049000," ","int((b*x+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}"," ",0,"1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)","A"
155,1,114,72,0.043000," ","int(c*x^2/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}"," ",0,"1/72*c*3^(1/2)*6^(3/4)*2^(1/2)*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*c*3^(1/2)*6^(3/4)*2^(1/2)*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*c*3^(1/2)*6^(3/4)*2^(1/2)*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))","A"
156,1,226,104,0.043000," ","int((c*x^2+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}"," ",0,"1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))","B"
157,1,129,87,0.047000," ","int((c*x^2+b*x)/(3*x^4+2),x)","\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}"," ",0,"1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))","A"
158,1,241,119,0.048000," ","int((c*x^2+b*x+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}"," ",0,"1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))","B"
159,1,12,11,0.046000," ","int(d*x^3/(3*x^4+2),x)","\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/12*d*ln(3*x^4+2)","A"
160,1,125,83,0.048000," ","int((d*x^3+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*d*ln(3*x^4+2)","A"
161,1,28,27,0.047000," ","int((d*x^3+b*x)/(3*x^4+2),x)","\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/12*d*ln(3*x^4+2)+1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)","A"
162,1,140,98,0.045000," ","int((d*x^3+b*x+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)+1/12*d*ln(3*x^4+2)","A"
163,1,125,83,0.041000," ","int((d*x^3+c*x^2)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*d*ln(3*x^4+2)","A"
164,1,237,115,0.047000," ","int((d*x^3+c*x^2+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*d*ln(3*x^4+2)","B"
165,1,140,98,0.046000," ","int((d*x^3+c*x^2+b*x)/(3*x^4+2),x)","\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*d*ln(3*x^4+2)","A"
166,1,252,130,0.046000," ","int((d*x^3+c*x^2+b*x+a)/(3*x^4+2),x)","\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{24}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, a \ln \left(\frac{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{48}+\frac{\sqrt{6}\, b \arctan \left(\frac{\sqrt{6}\, x^{2}}{2}\right)}{12}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}-1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, \sqrt{3}\, 6^{\frac{3}{4}} x}{6}+1\right)}{72}+\frac{\sqrt{3}\, 6^{\frac{3}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}-\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}{x^{2}+\frac{\sqrt{3}\, 6^{\frac{1}{4}} \sqrt{2}\, x}{3}+\frac{\sqrt{6}}{3}}\right)}{144}+\frac{d \ln \left(3 x^{4}+2\right)}{12}"," ",0,"1/48*3^(1/2)*6^(1/4)*2^(1/2)*a*ln((x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/24*3^(1/2)*6^(1/4)*2^(1/2)*a*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/12*6^(1/2)*b*arctan(1/2*6^(1/2)*x^2)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x+1)+1/72*3^(1/2)*6^(3/4)*2^(1/2)*c*arctan(1/6*2^(1/2)*3^(1/2)*6^(3/4)*x-1)+1/144*3^(1/2)*6^(3/4)*2^(1/2)*c*ln((x^2-1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2))/(x^2+1/3*3^(1/2)*6^(1/4)*2^(1/2)*x+1/3*6^(1/2)))+1/12*d*ln(3*x^4+2)","A"
167,1,7,8,0.043000," ","int((x^3+x^2+x+1)/(-x^4+1),x)","-\ln \left(x -1\right)"," ",0,"-ln(x-1)","A"
168,1,102,41,0.046000," ","int((x^3+x^2+x+1)/(x^4+1),x)","\frac{\arctan \left(x^{2}\right)}{2}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{2}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{2}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{8}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{8}+\frac{\ln \left(x^{4}+1\right)}{4}"," ",0,"1/2*2^(1/2)*arctan(2^(1/2)*x-1)+1/8*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))+1/2*2^(1/2)*arctan(2^(1/2)*x+1)+1/2*arctan(x^2)+1/8*2^(1/2)*ln((x^2-2^(1/2)*x+1)/(x^2+2^(1/2)*x+1))+1/4*ln(x^4+1)","B"
169,1,171,84,0.049000," ","int((x^3+x^2+x+1)/(-b*x^4+a),x)","-\frac{\ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{\arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{\ln \left(b \,x^{4}-a \right)}{4 b}"," ",0,"1/4*(a/b)^(1/4)/a*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*(a/b)^(1/4)/a*arctan(1/(a/b)^(1/4)*x)-1/4/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/4/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b*ln(b*x^4-a)","B"
170,1,286,184,0.047000," ","int((x^3+x^2+x+1)/(b*x^4+a),x)","\frac{\arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\ln \left(b \,x^{4}+a \right)}{4 b}"," ",0,"1/8*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/2/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+1/8/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*ln(b*x^4+a)/b","A"
171,1,244,108,0.047000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{f \ln \left(b \,x^{4}-a \right)}{4 b}-\frac{g x}{b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 b}"," ",0,"-g*x/b+1/2/b*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*g+1/2*c*(a/b)^(1/4)/a*arctan(1/(a/b)^(1/4)*x)+1/4/b*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*g+1/4*c*(a/b)^(1/4)/a*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4*d/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2*e/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/4*e/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b*f*ln(b*x^4-a)","B"
172,1,289,132,0.052000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}+\frac{-\frac{e \,x^{3}}{4 a}-\frac{d \,x^{2}}{4 a}-\frac{f}{4 b}-\frac{\left(a g +b c \right) x}{4 a b}}{b \,x^{4}-a}"," ",0,"(-1/4/a*e*x^3-1/4/a*d*x^2-1/4*(a*g+b*c)/a/b*x-1/4/b*f)/(b*x^4-a)-1/8/b/a*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*g+3/8*(a/b)^(1/4)/a^2*c*arctan(1/(a/b)^(1/4)*x)-1/16/b/a*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*g+3/16*(a/b)^(1/4)/a^2*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/8/(a*b)^(1/2)/a*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/8/(a/b)^(1/4)/a/b*e*arctan(1/(a/b)^(1/4)*x)+1/16/(a/b)^(1/4)/a/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
173,1,328,179,0.072000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x)","-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}-\frac{5 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}-\frac{\frac{5 b e \,x^{7}}{32 a^{2}}+\frac{3 b d \,x^{6}}{16 a^{2}}-\frac{9 e \,x^{3}}{32 a}-\frac{\left(a g -7 b c \right) x^{5}}{32 a^{2}}-\frac{5 d \,x^{2}}{16 a}-\frac{f}{8 b}-\frac{\left(3 a g +11 b c \right) x}{32 a b}}{\left(b \,x^{4}-a \right)^{2}}"," ",0,"-(5/32/a^2*b*e*x^7+3/16/a^2*b*d*x^6-1/32*(a*g-7*b*c)/a^2*x^5-9/32/a*e*x^3-5/16/a*d*x^2-1/32*(3*a*g+11*b*c)/a/b*x-1/8/b*f)/(b*x^4-a)^2-3/64/a^2/b*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*g+21/64*(a/b)^(1/4)/a^3*c*arctan(1/(a/b)^(1/4)*x)-3/128/a^2/b*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*g+21/128*(a/b)^(1/4)/a^3*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-3/32/(a*b)^(1/2)/a^2*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-5/64/(a/b)^(1/4)/a^2/b*e*arctan(1/(a/b)^(1/4)*x)+5/128/(a/b)^(1/4)/a^2/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
174,1,368,219,0.059000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x)","-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}-\frac{15 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{-\frac{15 b^{2} e \,x^{11}}{128 a^{3}}-\frac{5 b^{2} d \,x^{10}}{32 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{7 \left(a g -11 b c \right) b \,x^{9}}{384 a^{3}}+\frac{5 b d \,x^{6}}{12 a^{2}}-\frac{113 e \,x^{3}}{384 a}-\frac{3 \left(a g -11 b c \right) x^{5}}{64 a^{2}}-\frac{11 d \,x^{2}}{32 a}-\frac{f}{12 b}-\frac{\left(7 a g +51 b c \right) x}{128 a b}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(-15/128/a^3*b^2*e*x^11-5/32/a^3*b^2*d*x^10+7/384*(a*g-11*b*c)/a^3*b*x^9+21/64/a^2*b*e*x^7+5/12/a^2*b*d*x^6-3/64/a^2*(a*g-11*b*c)*x^5-113/384/a*e*x^3-11/32/a*d*x^2-1/128*(7*a*g+51*b*c)/a/b*x-1/12/b*f)/(b*x^4-a)^3-7/256/a^3/b*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*g+77/256*(a/b)^(1/4)/a^4*c*arctan(1/(a/b)^(1/4)*x)-7/512/a^3/b*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*g+77/512*(a/b)^(1/4)/a^4*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-5/64/(a*b)^(1/2)/a^3*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-15/256/(a/b)^(1/4)/a^3/b*e*arctan(1/(a/b)^(1/4)*x)+15/512/(a/b)^(1/4)/a^3/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
175,1,429,226,0.055000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{f \ln \left(b \,x^{4}+a \right)}{4 b}+\frac{g x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/b*g*x-1/4/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*g+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*c-1/8/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*g+1/8*(a/b)^(1/4)*2^(1/2)/a*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*g+1/4*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*c+1/2*d/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+1/8/b*e/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/b*e/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*f*ln(b*x^4+a)/b","A"
176,1,482,248,0.053000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{\frac{e \,x^{3}}{4 a}+\frac{d \,x^{2}}{4 a}-\frac{f}{4 b}-\frac{\left(a g -b c \right) x}{4 a b}}{b \,x^{4}+a}"," ",0,"(1/4/a*e*x^3+1/4/a*d*x^2-1/4*(a*g-b*c)/a/b*x-1/4/b*f)/(b*x^4+a)+1/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*g+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/32/b/a*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*g+3/32*(a/b)^(1/4)*2^(1/2)/a^2*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*g+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/(a*b)^(1/2)/a*d*arctan((1/a*b)^(1/2)*x^2)+1/32/(a/b)^(1/4)*2^(1/2)/a/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
177,1,519,298,0.062000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}+\frac{\frac{5 b e \,x^{7}}{32 a^{2}}+\frac{3 b d \,x^{6}}{16 a^{2}}+\frac{9 e \,x^{3}}{32 a}+\frac{\left(a g +7 b c \right) x^{5}}{32 a^{2}}+\frac{5 d \,x^{2}}{16 a}-\frac{f}{8 b}-\frac{\left(3 a g -11 b c \right) x}{32 a b}}{\left(b \,x^{4}+a \right)^{2}}"," ",0,"(5/32/a^2*b*e*x^7+3/16/a^2*b*d*x^6+1/32*(a*g+7*b*c)/a^2*x^5+9/32/a*e*x^3+5/16/a*d*x^2-1/32*(3*a*g-11*b*c)/a/b*x-1/8/b*f)/(b*x^4+a)^2+3/128/a^2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*g+21/128*c/a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/128/a^2/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*g+21/128*c/a^3*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/256/a^2/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*g+21/256*c/a^3*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16/(a*b)^(1/2)/a^2*d*arctan((1/a*b)^(1/2)*x^2)+5/256/a^2/b*e/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
178,1,560,337,0.064000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{15 b^{2} e \,x^{11}}{128 a^{3}}+\frac{5 b^{2} d \,x^{10}}{32 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{7 \left(a g +11 b c \right) b \,x^{9}}{384 a^{3}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{113 e \,x^{3}}{384 a}+\frac{3 \left(a g +11 b c \right) x^{5}}{64 a^{2}}+\frac{11 d \,x^{2}}{32 a}-\frac{f}{12 b}-\frac{\left(7 a g -51 b c \right) x}{128 a b}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(15/128/a^3*b^2*e*x^11+5/32/a^3*b^2*d*x^10+7/384*(a*g+11*b*c)/a^3*b*x^9+21/64/a^2*b*e*x^7+5/12/a^2*b*d*x^6+3/64/a^2*(a*g+11*b*c)*x^5+113/384/a*e*x^3+11/32/a*d*x^2-1/128*(7*a*g-51*b*c)/a/b*x-1/12/b*f)/(b*x^4+a)^3+7/512/a^3/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*g+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+7/512/a^3/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*g+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+7/1024/a^3/b*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*g+77/1024*(a/b)^(1/4)*2^(1/2)/a^4*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/32/(a*b)^(1/2)/a^3*d*arctan((1/a*b)^(1/2)*x^2)+15/1024/a^3*e/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+15/512/(a/b)^(1/4)*2^(1/2)/a^3/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
179,1,8,9,0.046000," ","int((-x^4+1)^3/(x^3+x^2+x+1)^3,x)","-\frac{\left(x -1\right)^{4}}{4}"," ",0,"-1/4*(x-1)^4","A"
180,1,8,9,0.043000," ","int((-x^4+1)^2/(x^3+x^2+x+1)^2,x)","\frac{\left(x -1\right)^{3}}{3}"," ",0,"1/3*(x-1)^3","A"
181,1,8,7,0.041000," ","int((-x^4+1)/(x^3+x^2+x+1),x)","-\frac{1}{2} x^{2}+x"," ",0,"x-1/2*x^2","A"
182,1,7,8,0.045000," ","int((x^3+x^2+x+1)/(-x^4+1),x)","-\ln \left(x -1\right)"," ",0,"-ln(x-1)","A"
183,1,8,7,0.042000," ","int((x^3+x^2+x+1)^2/(-x^4+1)^2,x)","-\frac{1}{x -1}"," ",0,"-1/(x-1)","A"
184,1,8,9,0.038000," ","int((x^3+x^2+x+1)^3/(-x^4+1)^3,x)","\frac{1}{2 \left(x -1\right)^{2}}"," ",0,"1/2/(x-1)^2","A"
185,1,8,9,0.045000," ","int((x^3+x^2+x+1)^4/(-x^4+1)^4,x)","-\frac{1}{3 \left(x -1\right)^{3}}"," ",0,"-1/3/(x-1)^3","A"
186,1,296,123,0.047000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{a h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}\, b}-\frac{h \,x^{2}}{2 b}-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{f \ln \left(b \,x^{4}-a \right)}{4 b}-\frac{g x}{b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 b}"," ",0,"-1/2*h*x^2/b-1/b*g*x+1/2*(a/b)^(1/4)/b*g*arctan(1/(a/b)^(1/4)*x)+1/2*(a/b)^(1/4)/a*c*arctan(1/(a/b)^(1/4)*x)+1/4*(a/b)^(1/4)/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/4*(a/b)^(1/4)/a*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))*a*h-1/4/(a*b)^(1/2)*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2/(a/b)^(1/4)/b*e*arctan(1/(a/b)^(1/4)*x)+1/4/(a/b)^(1/4)/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b*f*ln(b*x^4-a)","B"
187,1,367,144,0.054000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{i \,x^{3}}{3 b}-\frac{a h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}\, b}-\frac{h \,x^{2}}{2 b}-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}-\frac{a i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{a i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{f \ln \left(b \,x^{4}-a \right)}{4 b}-\frac{g x}{b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 b}"," ",0,"-1/3*i*x^3/b-1/2/b*h*x^2-1/b*g*x+1/4*(a/b)^(1/4)/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/4*(a/b)^(1/4)/a*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*(a/b)^(1/4)/b*g*arctan(1/(a/b)^(1/4)*x)+1/2*(a/b)^(1/4)/a*c*arctan(1/(a/b)^(1/4)*x)-1/4/(a*b)^(1/2)*a/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/4/(a*b)^(1/2)*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+1/4/b^2/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*a*i+1/4/(a/b)^(1/4)/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/2/b^2/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*a*i-1/2/(a/b)^(1/4)/b*e*arctan(1/(a/b)^(1/4)*x)-1/4/b*f*ln(b*x^4-a)","B"
188,1,393,159,0.052000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{j \,x^{4}}{4 b}-\frac{i \,x^{3}}{3 b}-\frac{a h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}\, b}-\frac{h \,x^{2}}{2 b}-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}-\frac{a i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{a i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{a j \ln \left(b \,x^{4}-a \right)}{4 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{f \ln \left(b \,x^{4}-a \right)}{4 b}-\frac{g x}{b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 b}"," ",0,"-1/4*j*x^4/b-1/3/b*i*x^3-1/2/b*h*x^2-1/b*g*x+1/2*(a/b)^(1/4)/b*g*arctan(1/(a/b)^(1/4)*x)+1/2*(a/b)^(1/4)/a*c*arctan(1/(a/b)^(1/4)*x)+1/4*(a/b)^(1/4)/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/4*(a/b)^(1/4)/a*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/(a*b)^(1/2)*a/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/4/(a*b)^(1/2)*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2/(a/b)^(1/4)*a/b^2*i*arctan(1/(a/b)^(1/4)*x)-1/2/(a/b)^(1/4)/b*e*arctan(1/(a/b)^(1/4)*x)+1/4/(a/b)^(1/4)*a/b^2*i*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/4/(a/b)^(1/4)/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b^2*ln(b*x^4-a)*a*j-1/4/b*f*ln(b*x^4-a)","B"
189,1,462,242,0.047000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x)","-\frac{a h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}\, b}+\frac{h \,x^{2}}{2 b}+\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{f \ln \left(b \,x^{4}+a \right)}{4 b}+\frac{g x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/2/b*h*x^2+1/b*g*x-1/4*(a/b)^(1/4)*2^(1/2)/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/8*(a/b)^(1/4)*2^(1/2)/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/8*(a/b)^(1/4)*2^(1/2)/a*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4*(a/b)^(1/4)*2^(1/2)/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/2/b/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)*a*h+1/2/(a*b)^(1/2)*d*arctan((1/a*b)^(1/2)*x^2)+1/8/(a/b)^(1/4)*2^(1/2)/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4/b*f*ln(b*x^4+a)","A"
190,1,603,287,0.056000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x)","\frac{i \,x^{3}}{3 b}-\frac{a h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}\, b}+\frac{h \,x^{2}}{2 b}+\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}-\frac{\sqrt{2}\, a i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{f \ln \left(b \,x^{4}+a \right)}{4 b}+\frac{g x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/3/b*i*x^3+1/2/b*h*x^2+1/b*g*x-1/4*(a/b)^(1/4)*2^(1/2)/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/8*(a/b)^(1/4)*2^(1/2)/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/8*(a/b)^(1/4)*2^(1/2)/a*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4*(a/b)^(1/4)*2^(1/2)/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/2/(a*b)^(1/2)*a/b*h*arctan((1/a*b)^(1/2)*x^2)+1/2/(a*b)^(1/2)*d*arctan((1/a*b)^(1/2)*x^2)-1/8/b^2/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*a*i+1/8/(a/b)^(1/4)*2^(1/2)/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*a*i+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/4/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*a*i+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/b*f*ln(b*x^4+a)","B"
191,1,627,303,0.049000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a),x)","\frac{j \,x^{4}}{4 b}+\frac{i \,x^{3}}{3 b}-\frac{a h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}\, b}+\frac{h \,x^{2}}{2 b}+\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}-\frac{\sqrt{2}\, a i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{a j \ln \left(b \,x^{4}+a \right)}{4 b^{2}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{f \ln \left(b \,x^{4}+a \right)}{4 b}+\frac{g x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/4/b*j*x^4+1/3/b*i*x^3+1/2/b*h*x^2+1/b*g*x-1/4*(a/b)^(1/4)*2^(1/2)/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/8*(a/b)^(1/4)*2^(1/2)/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/8*(a/b)^(1/4)*2^(1/2)/a*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4*(a/b)^(1/4)*2^(1/2)/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/2/(a*b)^(1/2)*a/b*h*arctan((1/a*b)^(1/2)*x^2)+1/2/(a*b)^(1/2)*d*arctan((1/a*b)^(1/2)*x^2)-1/4/(a/b)^(1/4)*2^(1/2)*a/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/4/(a/b)^(1/4)*2^(1/2)*a/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/(a/b)^(1/4)*2^(1/2)/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/8/(a/b)^(1/4)*2^(1/2)*a/b^2*i*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/8/(a/b)^(1/4)*2^(1/2)/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/b^2*ln(b*x^4+a)*a*j+1/4/b*f*ln(b*x^4+a)","B"
192,1,340,144,0.053000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}+\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, b}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}+\frac{-\frac{e \,x^{3}}{4 a}-\frac{\left(a h +b d \right) x^{2}}{4 a b}-\frac{f}{4 b}-\frac{\left(a g +b c \right) x}{4 a b}}{b \,x^{4}-a}"," ",0,"(-1/4/a*e*x^3-1/4*(a*h+b*d)/a/b*x^2-1/4*(a*g+b*c)/a/b*x-1/4/b*f)/(b*x^4-a)-1/8*(a/b)^(1/4)/a/b*g*arctan(1/(a/b)^(1/4)*x)+3/8*(a/b)^(1/4)/a^2*c*arctan(1/(a/b)^(1/4)*x)-1/16/b/a*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*g+3/16/a^2*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*c+1/8/b/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))*h-1/8/(a*b)^(1/2)/a*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/8/b/a*e/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/16/(a/b)^(1/4)/a/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
193,1,409,163,0.051000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}+\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, b}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}+\frac{3 i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{-\frac{\left(a i +b e \right) x^{3}}{4 a b}-\frac{\left(a h +b d \right) x^{2}}{4 a b}-\frac{f}{4 b}-\frac{\left(a g +b c \right) x}{4 a b}}{b \,x^{4}-a}"," ",0,"(-1/4*(a*i+b*e)/a/b*x^3-1/4*(a*h+b*d)/a/b*x^2-1/4*(a*g+b*c)/a/b*x-1/4/b*f)/(b*x^4-a)-1/8*(a/b)^(1/4)/a/b*g*arctan(1/(a/b)^(1/4)*x)+3/8*(a/b)^(1/4)/a^2*c*arctan(1/(a/b)^(1/4)*x)-1/16*(a/b)^(1/4)/a/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+3/16*(a/b)^(1/4)/a^2*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/8/(a*b)^(1/2)/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/8/(a*b)^(1/2)/a*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+3/8/b^2/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*i-1/8/(a/b)^(1/4)/a/b*e*arctan(1/(a/b)^(1/4)*x)-3/16/b^2/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*i+1/16/(a/b)^(1/4)/a/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
194,1,431,183,0.060000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^2,x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, a}+\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{8 \sqrt{a b}\, b}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 a^{2}}+\frac{3 i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{3 i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{j \ln \left(b \,x^{4}-a \right)}{4 b^{2}}+\frac{-\frac{\left(a i +b e \right) x^{3}}{4 a b}-\frac{\left(a h +b d \right) x^{2}}{4 a b}-\frac{\left(a g +b c \right) x}{4 a b}-\frac{a j +b f}{4 b^{2}}}{b \,x^{4}-a}"," ",0,"(-1/4*(a*i+b*e)/a/b*x^3-1/4*(a*h+b*d)/a/b*x^2-1/4*(a*g+b*c)/a/b*x-1/4*(a*j+b*f)/b^2)/(b*x^4-a)-1/8*(a/b)^(1/4)/a/b*g*arctan(1/(a/b)^(1/4)*x)+3/8*(a/b)^(1/4)/a^2*c*arctan(1/(a/b)^(1/4)*x)-1/16*(a/b)^(1/4)/a/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+3/16*(a/b)^(1/4)/a^2*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/8/(a*b)^(1/2)/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/8/(a*b)^(1/2)/a*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+3/8/(a/b)^(1/4)/b^2*i*arctan(1/(a/b)^(1/4)*x)-1/8/(a/b)^(1/4)/a/b*e*arctan(1/(a/b)^(1/4)*x)-3/16/(a/b)^(1/4)/b^2*i*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/16/(a/b)^(1/4)/a/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/4/b^2*j*ln(b*x^4-a)","B"
195,1,515,260,0.056000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{\frac{e \,x^{3}}{4 a}-\frac{\left(a h -b d \right) x^{2}}{4 a b}-\frac{f}{4 b}-\frac{\left(a g -b c \right) x}{4 a b}}{b \,x^{4}+a}"," ",0,"(1/4/a*e*x^3-1/4*(a*h-b*d)/a/b*x^2-1/4*(a*g-b*c)/a/b*x-1/4/b*f)/(b*x^4+a)+1/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*g+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/b/a*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*g+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/32*(a/b)^(1/4)*2^(1/2)/a/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/32*(a/b)^(1/4)*2^(1/2)/a^2*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/b/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)*h+1/4/(a*b)^(1/2)/a*d*arctan((1/a*b)^(1/2)*x^2)+1/32/(a/b)^(1/4)*2^(1/2)/a/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
196,1,654,302,0.054000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{-\frac{\left(a i -b e \right) x^{3}}{4 a b}-\frac{\left(a h -b d \right) x^{2}}{4 a b}-\frac{f}{4 b}-\frac{\left(a g -b c \right) x}{4 a b}}{b \,x^{4}+a}"," ",0,"(-1/4*(a*i-b*e)/a/b*x^3-1/4*(a*h-b*d)/a/b*x^2-1/4*(a*g-b*c)/a/b*x-1/4/b*f)/(b*x^4+a)+1/16*(a/b)^(1/4)*2^(1/2)/a/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/32*(a/b)^(1/4)*2^(1/2)/a/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/32*(a/b)^(1/4)*2^(1/2)/a^2*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16*(a/b)^(1/4)*2^(1/2)/a/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4/(a*b)^(1/2)/b*h*arctan((1/a*b)^(1/2)*x^2)+1/4/(a*b)^(1/2)/a*d*arctan((1/a*b)^(1/2)*x^2)+3/32/b^2/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*i+1/32/(a/b)^(1/4)*2^(1/2)/a/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*i+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/16/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*i+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)","B"
197,1,675,322,0.063000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{j \ln \left(b \,x^{4}+a \right)}{4 b^{2}}+\frac{-\frac{\left(a i -b e \right) x^{3}}{4 a b}-\frac{\left(a h -b d \right) x^{2}}{4 a b}-\frac{\left(a g -b c \right) x}{4 a b}+\frac{a j -b f}{4 b^{2}}}{b \,x^{4}+a}"," ",0,"(-1/4*(a*i-b*e)/a/b*x^3-1/4*(a*h-b*d)/a/b*x^2-1/4*(a*g-b*c)/a/b*x+1/4*(a*j-b*f)/b^2)/(b*x^4+a)+1/16*(a/b)^(1/4)*2^(1/2)/a/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16*(a/b)^(1/4)*2^(1/2)/a/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/32*(a/b)^(1/4)*2^(1/2)/a/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/32*(a/b)^(1/4)*2^(1/2)/a^2*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4/(a*b)^(1/2)/b*h*arctan((1/a*b)^(1/2)*x^2)+1/4/(a*b)^(1/2)/a*d*arctan((1/a*b)^(1/2)*x^2)+3/16/(a/b)^(1/4)*2^(1/2)/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/32/(a/b)^(1/4)*2^(1/2)/b^2*i*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/32/(a/b)^(1/4)*2^(1/2)/a/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16/(a/b)^(1/4)*2^(1/2)/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*j*ln(b*x^4+a)/b^2","B"
198,1,389,199,0.062000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x)","\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a b}-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}-\frac{5 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}-\frac{\frac{5 b e \,x^{7}}{32 a^{2}}-\frac{\left(a h -3 b d \right) x^{6}}{16 a^{2}}-\frac{9 e \,x^{3}}{32 a}-\frac{\left(a g -7 b c \right) x^{5}}{32 a^{2}}-\frac{\left(a h +5 b d \right) x^{2}}{16 a b}-\frac{f}{8 b}-\frac{\left(3 a g +11 b c \right) x}{32 a b}}{\left(b \,x^{4}-a \right)^{2}}"," ",0,"-(5/32/a^2*b*e*x^7-1/16*(a*h-3*b*d)/a^2*x^6-1/32*(a*g-7*b*c)/a^2*x^5-9/32/a*e*x^3-1/16*(a*h+5*b*d)/a/b*x^2-1/32*(3*a*g+11*b*c)/a/b*x-1/8/b*f)/(b*x^4-a)^2-3/64*(a/b)^(1/4)/a^2/b*g*arctan(1/(a/b)^(1/4)*x)+21/64*(a/b)^(1/4)/a^3*c*arctan(1/(a/b)^(1/4)*x)-3/128*(a/b)^(1/4)/a^2/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+21/128*(a/b)^(1/4)/a^3*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/32/a/b/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))*h-3/32/(a*b)^(1/2)/a^2*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-5/64/(a/b)^(1/4)/a^2/b*e*arctan(1/(a/b)^(1/4)*x)+5/128/(a/b)^(1/4)/a^2/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
199,1,472,226,0.063000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x)","\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a b}-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}+\frac{3 i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}-\frac{3 i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}-\frac{5 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}-\frac{-\frac{\left(3 a i -5 b e \right) x^{7}}{32 a^{2}}-\frac{\left(a h -3 b d \right) x^{6}}{16 a^{2}}-\frac{\left(a g -7 b c \right) x^{5}}{32 a^{2}}-\frac{\left(a i +9 b e \right) x^{3}}{32 a b}-\frac{\left(a h +5 b d \right) x^{2}}{16 a b}-\frac{f}{8 b}-\frac{\left(3 a g +11 b c \right) x}{32 a b}}{\left(b \,x^{4}-a \right)^{2}}"," ",0,"-(-1/32*(3*a*i-5*b*e)/a^2*x^7-1/16*(a*h-3*b*d)/a^2*x^6-1/32*(a*g-7*b*c)/a^2*x^5-1/32*(a*i+9*b*e)/a/b*x^3-1/16*(a*h+5*b*d)/a/b*x^2-1/32*(3*a*g+11*b*c)/a/b*x-1/8/b*f)/(b*x^4-a)^2-3/64*(a/b)^(1/4)/a^2/b*g*arctan(1/(a/b)^(1/4)*x)+21/64*(a/b)^(1/4)/a^3*c*arctan(1/(a/b)^(1/4)*x)-3/128*(a/b)^(1/4)/a^2/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+21/128*(a/b)^(1/4)/a^3*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/32/(a*b)^(1/2)/a/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-3/32/(a*b)^(1/2)/a^2*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+3/64/a/b^2/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*i-5/64/(a/b)^(1/4)/a^2/b*e*arctan(1/(a/b)^(1/4)*x)-3/128/a/b^2/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*i+5/128/(a/b)^(1/4)/a^2/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
200,1,488,243,0.061000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^3,x)","\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a b}-\frac{3 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{32 \sqrt{a b}\, a^{2}}+\frac{3 i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}-\frac{3 i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}-\frac{5 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{2} b}-\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{64 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{128 a^{3}}-\frac{-\frac{\left(3 a i -5 b e \right) x^{7}}{32 a^{2}}-\frac{\left(a h -3 b d \right) x^{6}}{16 a^{2}}-\frac{j \,x^{4}}{4 b}-\frac{\left(a g -7 b c \right) x^{5}}{32 a^{2}}-\frac{\left(a i +9 b e \right) x^{3}}{32 a b}-\frac{\left(a h +5 b d \right) x^{2}}{16 a b}-\frac{\left(3 a g +11 b c \right) x}{32 a b}+\frac{a j -b f}{8 b^{2}}}{\left(b \,x^{4}-a \right)^{2}}"," ",0,"-(-1/32*(3*a*i-5*b*e)/a^2*x^7-1/16*(a*h-3*b*d)/a^2*x^6-1/32*(a*g-7*b*c)/a^2*x^5-1/4/b*j*x^4-1/32*(a*i+9*b*e)/a/b*x^3-1/16*(a*h+5*b*d)/a/b*x^2-1/32*(3*a*g+11*b*c)/a/b*x+1/8*(a*j-b*f)/b^2)/(b*x^4-a)^2-3/64*(a/b)^(1/4)/a^2/b*g*arctan(1/(a/b)^(1/4)*x)+21/64*(a/b)^(1/4)/a^3*c*arctan(1/(a/b)^(1/4)*x)-3/128*(a/b)^(1/4)/a^2/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+21/128*(a/b)^(1/4)/a^3*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/32/(a*b)^(1/2)/a/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-3/32/(a*b)^(1/2)/a^2*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+3/64/(a/b)^(1/4)/a/b^2*i*arctan(1/(a/b)^(1/4)*x)-5/64/(a/b)^(1/4)/a^2/b*e*arctan(1/(a/b)^(1/4)*x)-3/128/(a/b)^(1/4)/a/b^2*i*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+5/128/(a/b)^(1/4)/a^2/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","B"
201,1,561,317,0.058000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a b}+\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}+\frac{\frac{5 b e \,x^{7}}{32 a^{2}}+\frac{\left(a h +3 b d \right) x^{6}}{16 a^{2}}+\frac{9 e \,x^{3}}{32 a}+\frac{\left(a g +7 b c \right) x^{5}}{32 a^{2}}-\frac{\left(a h -5 b d \right) x^{2}}{16 a b}-\frac{f}{8 b}-\frac{\left(3 a g -11 b c \right) x}{32 a b}}{\left(b \,x^{4}+a \right)^{2}}"," ",0,"(5/32/a^2*b*e*x^7+1/16*(a*h+3*b*d)/a^2*x^6+1/32*(a*g+7*b*c)/a^2*x^5+9/32/a*e*x^3-1/16*(a*h-5*b*d)/a/b*x^2-1/32*(3*a*g-11*b*c)/a/b*x-1/8/b*f)/(b*x^4+a)^2+3/128*(a/b)^(1/4)*2^(1/2)/a^2/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/256*(a/b)^(1/4)*2^(1/2)/a^2/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+21/256*(a/b)^(1/4)*2^(1/2)/a^3*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/128*(a/b)^(1/4)*2^(1/2)/a^2/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/a/b/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)*h+3/16/(a*b)^(1/2)/a^2*d*arctan((1/a*b)^(1/2)*x^2)+5/256/(a/b)^(1/4)*2^(1/2)/a^2/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
202,1,716,367,0.061000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a b}+\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}+\frac{\frac{\left(3 a i +5 b e \right) x^{7}}{32 a^{2}}+\frac{\left(a h +3 b d \right) x^{6}}{16 a^{2}}+\frac{\left(a g +7 b c \right) x^{5}}{32 a^{2}}-\frac{\left(a i -9 b e \right) x^{3}}{32 a b}-\frac{\left(a h -5 b d \right) x^{2}}{16 a b}-\frac{f}{8 b}-\frac{\left(3 a g -11 b c \right) x}{32 a b}}{\left(b \,x^{4}+a \right)^{2}}"," ",0,"(1/32*(3*a*i+5*b*e)/a^2*x^7+1/16*(a*h+3*b*d)/a^2*x^6+1/32*(a*g+7*b*c)/a^2*x^5-1/32*(a*i-9*b*e)/a/b*x^3-1/16*(a*h-5*b*d)/a/b*x^2-1/32*(3*a*g-11*b*c)/a/b*x-1/8/b*f)/(b*x^4+a)^2+3/128*(a/b)^(1/4)*2^(1/2)/a^2/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/128*(a/b)^(1/4)*2^(1/2)/a^2/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/256*(a/b)^(1/4)*2^(1/2)/a^2/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+21/256*(a/b)^(1/4)*2^(1/2)/a^3*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16/(a*b)^(1/2)/a/b*h*arctan((1/a*b)^(1/2)*x^2)+3/16/(a*b)^(1/2)/a^2*d*arctan((1/a*b)^(1/2)*x^2)+3/128/a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*i+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/128/a/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*i+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/256/a/b^2/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*i+5/256/(a/b)^(1/4)*2^(1/2)/a^2/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))","A"
203,1,731,384,0.059000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a b}+\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}+\frac{\frac{\left(3 a i +5 b e \right) x^{7}}{32 a^{2}}+\frac{\left(a h +3 b d \right) x^{6}}{16 a^{2}}-\frac{j \,x^{4}}{4 b}+\frac{\left(a g +7 b c \right) x^{5}}{32 a^{2}}-\frac{\left(a i -9 b e \right) x^{3}}{32 a b}-\frac{\left(a h -5 b d \right) x^{2}}{16 a b}-\frac{\left(3 a g -11 b c \right) x}{32 a b}-\frac{a j +b f}{8 b^{2}}}{\left(b \,x^{4}+a \right)^{2}}"," ",0,"(1/32*(3*a*i+5*b*e)/a^2*x^7+1/16*(a*h+3*b*d)/a^2*x^6+1/32*(a*g+7*b*c)/a^2*x^5-1/4/b*j*x^4-1/32*(a*i-9*b*e)/a/b*x^3-1/16*(a*h-5*b*d)/a/b*x^2-1/32*(3*a*g-11*b*c)/a/b*x-1/8*(a*j+b*f)/b^2)/(b*x^4+a)^2+3/128*(a/b)^(1/4)*2^(1/2)/a^2/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/256*(a/b)^(1/4)*2^(1/2)/a^2/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+21/256*(a/b)^(1/4)*2^(1/2)/a^3*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/128*(a/b)^(1/4)*2^(1/2)/a^2/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/(a*b)^(1/2)/a/b*h*arctan((1/a*b)^(1/2)*x^2)+3/16/(a*b)^(1/2)/a^2*d*arctan((1/a*b)^(1/2)*x^2)+3/256/(a/b)^(1/4)*2^(1/2)/a/b^2*i*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/256/(a/b)^(1/4)*2^(1/2)/a^2/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/128/(a/b)^(1/4)*2^(1/2)/a/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+3/128/(a/b)^(1/4)*2^(1/2)/a/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)","A"
204,1,434,246,0.064000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x)","\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{2} b}-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}-\frac{15 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{-\frac{15 b^{2} e \,x^{11}}{128 a^{3}}+\frac{\left(a h -5 b d \right) b \,x^{10}}{32 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{7 \left(a g -11 b c \right) b \,x^{9}}{384 a^{3}}-\frac{\left(a h -5 b d \right) x^{6}}{12 a^{2}}-\frac{113 e \,x^{3}}{384 a}-\frac{3 \left(a g -11 b c \right) x^{5}}{64 a^{2}}-\frac{\left(a h +11 b d \right) x^{2}}{32 a b}-\frac{f}{12 b}-\frac{\left(7 a g +51 b c \right) x}{128 a b}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(-15/128/a^3*b^2*e*x^11+1/32*(a*h-5*b*d)/a^3*b*x^10+7/384*(a*g-11*b*c)/a^3*b*x^9+21/64/a^2*b*e*x^7-1/12/a^2*(a*h-5*b*d)*x^6-3/64*(a*g-11*b*c)/a^2*x^5-113/384/a*e*x^3-1/32*(a*h+11*b*d)/a/b*x^2-1/128*(7*a*g+51*b*c)/a/b*x-1/12/b*f)/(b*x^4-a)^3-7/256*(a/b)^(1/4)/a^3/b*g*arctan(1/(a/b)^(1/4)*x)+77/256*(a/b)^(1/4)/a^4*c*arctan(1/(a/b)^(1/4)*x)-7/512*(a/b)^(1/4)/a^3/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+77/512*(a/b)^(1/4)/a^4*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/64/a^2/b/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))*h-5/64/(a*b)^(1/2)/a^3*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-15/256/(a/b)^(1/4)/a^3/b*e*arctan(1/(a/b)^(1/4)*x)+15/512/(a/b)^(1/4)/a^3/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
205,1,522,281,0.059000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x)","\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{2} b}-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}+\frac{5 i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}-\frac{5 i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}-\frac{15 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{\frac{5 \left(a i -3 b e \right) b \,x^{11}}{128 a^{3}}+\frac{\left(a h -5 b d \right) b \,x^{10}}{32 a^{3}}+\frac{7 \left(a g -11 b c \right) b \,x^{9}}{384 a^{3}}-\frac{7 \left(a i -3 b e \right) x^{7}}{64 a^{2}}-\frac{\left(a h -5 b d \right) x^{6}}{12 a^{2}}-\frac{3 \left(a g -11 b c \right) x^{5}}{64 a^{2}}-\frac{\left(5 a i +113 b e \right) x^{3}}{384 a b}-\frac{\left(a h +11 b d \right) x^{2}}{32 a b}-\frac{f}{12 b}-\frac{\left(7 a g +51 b c \right) x}{128 a b}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(5/128*(a*i-3*b*e)/a^3*b*x^11+1/32*(a*h-5*b*d)/a^3*b*x^10+7/384*(a*g-11*b*c)/a^3*b*x^9-7/64/a^2*(a*i-3*b*e)*x^7-1/12*(a*h-5*b*d)/a^2*x^6-3/64*(a*g-11*b*c)/a^2*x^5-1/384*(5*a*i+113*b*e)/a/b*x^3-1/32*(a*h+11*b*d)/a/b*x^2-1/128*(7*a*g+51*b*c)/a/b*x-1/12/b*f)/(b*x^4-a)^3-7/512*(a/b)^(1/4)/a^3/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+77/512*(a/b)^(1/4)/a^4*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-7/256*(a/b)^(1/4)/a^3/b*g*arctan(1/(a/b)^(1/4)*x)+77/256*(a/b)^(1/4)/a^4*c*arctan(1/(a/b)^(1/4)*x)+1/64/(a*b)^(1/2)/a^2/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-5/64/(a*b)^(1/2)/a^3*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-5/512/a^2/b^2/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))*i+15/512/(a/b)^(1/4)/a^3/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+5/256/a^2/b^2/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)*i-15/256/(a/b)^(1/4)/a^3/b*e*arctan(1/(a/b)^(1/4)*x)","A"
206,1,538,299,0.060000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(-b*x^4+a)^4,x)","\frac{h \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{2} b}-\frac{5 d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{64 \sqrt{a b}\, a^{3}}+\frac{5 i \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}-\frac{5 i \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}-\frac{15 e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{3} b}-\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} g \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{256 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{512 a^{4}}+\frac{\frac{5 \left(a i -3 b e \right) b \,x^{11}}{128 a^{3}}+\frac{\left(a h -5 b d \right) b \,x^{10}}{32 a^{3}}+\frac{7 \left(a g -11 b c \right) b \,x^{9}}{384 a^{3}}-\frac{7 \left(a i -3 b e \right) x^{7}}{64 a^{2}}-\frac{\left(a h -5 b d \right) x^{6}}{12 a^{2}}-\frac{j \,x^{4}}{8 b}-\frac{3 \left(a g -11 b c \right) x^{5}}{64 a^{2}}-\frac{\left(5 a i +113 b e \right) x^{3}}{384 a b}-\frac{\left(a h +11 b d \right) x^{2}}{32 a b}-\frac{\left(7 a g +51 b c \right) x}{128 a b}+\frac{a j -2 b f}{24 b^{2}}}{\left(b \,x^{4}-a \right)^{3}}"," ",0,"(5/128*(a*i-3*b*e)/a^3*b*x^11+1/32*(a*h-5*b*d)/a^3*b*x^10+7/384*(a*g-11*b*c)/a^3*b*x^9-7/64*(a*i-3*b*e)/a^2*x^7-1/12*(a*h-5*b*d)/a^2*x^6-3/64*(a*g-11*b*c)/a^2*x^5-1/8/b*j*x^4-1/384*(5*a*i+113*b*e)/a/b*x^3-1/32*(a*h+11*b*d)/a/b*x^2-1/128*(7*a*g+51*b*c)/a/b*x+1/24*(a*j-2*b*f)/b^2)/(b*x^4-a)^3-7/256*(a/b)^(1/4)/a^3/b*g*arctan(1/(a/b)^(1/4)*x)+77/256*(a/b)^(1/4)/a^4*c*arctan(1/(a/b)^(1/4)*x)-7/512*(a/b)^(1/4)/a^3/b*g*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+77/512*(a/b)^(1/4)/a^4*c*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/64/(a*b)^(1/2)/a^2/b*h*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-5/64/(a*b)^(1/2)/a^3*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))+5/256/(a/b)^(1/4)/a^2/b^2*i*arctan(1/(a/b)^(1/4)*x)-15/256/(a/b)^(1/4)/a^3/b*e*arctan(1/(a/b)^(1/4)*x)-5/512/(a/b)^(1/4)/a^2/b^2*i*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+15/512/(a/b)^(1/4)/a^3/b*e*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))","A"
207,1,607,362,0.070000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{2} b}+\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{15 b^{2} e \,x^{11}}{128 a^{3}}+\frac{\left(a h +5 b d \right) b \,x^{10}}{32 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{7 \left(a g +11 b c \right) b \,x^{9}}{384 a^{3}}+\frac{\left(a h +5 b d \right) x^{6}}{12 a^{2}}+\frac{113 e \,x^{3}}{384 a}+\frac{3 \left(a g +11 b c \right) x^{5}}{64 a^{2}}-\frac{\left(a h -11 b d \right) x^{2}}{32 a b}-\frac{f}{12 b}-\frac{\left(7 a g -51 b c \right) x}{128 a b}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(15/128/a^3*b^2*e*x^11+1/32*(a*h+5*b*d)/a^3*b*x^10+7/384*(a*g+11*b*c)/a^3*b*x^9+21/64/a^2*b*e*x^7+1/12/a^2*(a*h+5*b*d)*x^6+3/64/a^2*(a*g+11*b*c)*x^5+113/384/a*e*x^3-1/32*(a*h-11*b*d)/a/b*x^2-1/128*(7*a*g-51*b*c)/a/b*x-1/12/b*f)/(b*x^4+a)^3+7/512/a^3/b*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*g+77/512/a^4*c*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+7/1024*(a/b)^(1/4)*2^(1/2)/a^3/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+77/1024/a^4*c*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+7/512*(a/b)^(1/4)*2^(1/2)/a^3/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/32/a^2/b/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)*h+5/32/(a*b)^(1/2)/a^3*d*arctan((1/a*b)^(1/2)*x^2)+15/1024/a^3*e/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
208,1,767,416,0.066000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{2} b}+\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{5 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{5 \left(a i +3 b e \right) b \,x^{11}}{128 a^{3}}+\frac{\left(a h +5 b d \right) b \,x^{10}}{32 a^{3}}+\frac{7 \left(a g +11 b c \right) b \,x^{9}}{384 a^{3}}+\frac{7 \left(a i +3 b e \right) x^{7}}{64 a^{2}}+\frac{\left(a h +5 b d \right) x^{6}}{12 a^{2}}+\frac{3 \left(a g +11 b c \right) x^{5}}{64 a^{2}}-\frac{\left(5 a i -113 b e \right) x^{3}}{384 a b}-\frac{\left(a h -11 b d \right) x^{2}}{32 a b}-\frac{f}{12 b}-\frac{\left(7 a g -51 b c \right) x}{128 a b}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(5/128*(a*i+3*b*e)/a^3*b*x^11+1/32*(a*h+5*b*d)/a^3*b*x^10+7/384*(a*g+11*b*c)/a^3*b*x^9+7/64*(a*i+3*b*e)/a^2*x^7+1/12*(a*h+5*b*d)/a^2*x^6+3/64*(a*g+11*b*c)/a^2*x^5-1/384*(5*a*i-113*b*e)/a/b*x^3-1/32*(a*h-11*b*d)/a/b*x^2-1/128*(7*a*g-51*b*c)/a/b*x-1/12/b*f)/(b*x^4+a)^3+7/1024*(a/b)^(1/4)*2^(1/2)/a^3/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+77/1024*(a/b)^(1/4)*2^(1/2)/a^4*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+7/512*(a/b)^(1/4)*2^(1/2)/a^3/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+7/512*(a/b)^(1/4)*2^(1/2)/a^3/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/32/(a*b)^(1/2)/a^2/b*h*arctan((1/a*b)^(1/2)*x^2)+5/32/(a*b)^(1/2)/a^3*d*arctan((1/a*b)^(1/2)*x^2)+5/1024/a^2/b^2/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))*i+15/1024/(a/b)^(1/4)*2^(1/2)/a^3/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/512/a^2/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)*i+15/512/(a/b)^(1/4)*2^(1/2)/a^3/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+5/512/a^2/b^2/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)*i+15/512/(a/b)^(1/4)*2^(1/2)/a^3/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)","A"
209,1,783,434,0.067000," ","int((j*x^7+i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{h \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{2} b}+\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{5 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, i \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, i \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, g \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{5 \left(a i +3 b e \right) b \,x^{11}}{128 a^{3}}+\frac{\left(a h +5 b d \right) b \,x^{10}}{32 a^{3}}+\frac{7 \left(a g +11 b c \right) b \,x^{9}}{384 a^{3}}+\frac{7 \left(a i +3 b e \right) x^{7}}{64 a^{2}}+\frac{\left(a h +5 b d \right) x^{6}}{12 a^{2}}-\frac{j \,x^{4}}{8 b}+\frac{3 \left(a g +11 b c \right) x^{5}}{64 a^{2}}-\frac{\left(5 a i -113 b e \right) x^{3}}{384 a b}-\frac{\left(a h -11 b d \right) x^{2}}{32 a b}-\frac{\left(7 a g -51 b c \right) x}{128 a b}-\frac{a j +2 b f}{24 b^{2}}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(5/128*(a*i+3*b*e)/a^3*b*x^11+1/32*(a*h+5*b*d)/a^3*b*x^10+7/384*(a*g+11*b*c)/a^3*b*x^9+7/64*(a*i+3*b*e)/a^2*x^7+1/12*(a*h+5*b*d)/a^2*x^6+3/64*(a*g+11*b*c)/a^2*x^5-1/8/b*j*x^4-1/384*(5*a*i-113*b*e)/a/b*x^3-1/32*(a*h-11*b*d)/a/b*x^2-1/128*(7*a*g-51*b*c)/a/b*x-1/24*(a*j+2*b*f)/b^2)/(b*x^4+a)^3+7/512*(a/b)^(1/4)*2^(1/2)/a^3/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+7/512*(a/b)^(1/4)*2^(1/2)/a^3/b*g*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+77/512*(a/b)^(1/4)*2^(1/2)/a^4*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+7/1024*(a/b)^(1/4)*2^(1/2)/a^3/b*g*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+77/1024*(a/b)^(1/4)*2^(1/2)/a^4*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/32/(a*b)^(1/2)/a^2/b*h*arctan((1/a*b)^(1/2)*x^2)+5/32/(a*b)^(1/2)/a^3*d*arctan((1/a*b)^(1/2)*x^2)+5/1024/(a/b)^(1/4)*2^(1/2)/a^2/b^2*i*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+15/1024/(a/b)^(1/4)*2^(1/2)/a^3/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/512/(a/b)^(1/4)*2^(1/2)/a^2/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+15/512/(a/b)^(1/4)*2^(1/2)/a^3/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/512/(a/b)^(1/4)*2^(1/2)/a^2/b^2*i*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+15/512/(a/b)^(1/4)*2^(1/2)/a^3/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
210,1,96,124,0.152000," ","int((d*x+c)/(b*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}"," ",0,"1/2*d*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)+c/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
211,1,90,67,0.168000," ","int((d*x+c)/(-b*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}+a}}+\frac{d \arctan \left(\frac{\sqrt{b}\, x^{2}}{\sqrt{-b \,x^{4}+a}}\right)}{2 \sqrt{b}}"," ",0,"1/2*d*arctan(1/(-b*x^4+a)^(1/2)*b^(1/2)*x^2)/b^(1/2)+c/(1/a^(1/2)*b^(1/2))^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4+a)^(1/2)*EllipticF((1/a^(1/2)*b^(1/2))^(1/2)*x,I)","A"
212,1,95,69,0.174000," ","int((d*x+c)/(b*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{\sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{\sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}-a}}+\frac{d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}-a}\right)}{2 \sqrt{b}}"," ",0,"1/2*d*ln(b^(1/2)*x^2+(b*x^4-a)^(1/2))/b^(1/2)+c/(-1/a^(1/2)*b^(1/2))^(1/2)*(1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(-1/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4-a)^(1/2)*EllipticF(x*(-1/a^(1/2)*b^(1/2))^(1/2),I)","A"
213,1,101,130,0.184000," ","int((d*x+c)/(-b*x^4-a)^(1/2),x)","\frac{\sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{-\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{-b \,x^{4}-a}}+\frac{d \arctan \left(\frac{\sqrt{b}\, x^{2}}{\sqrt{-b \,x^{4}-a}}\right)}{2 \sqrt{b}}"," ",0,"1/2*d*arctan(x^2*b^(1/2)/(-b*x^4-a)^(1/2))/b^(1/2)+c/(-I/a^(1/2)*b^(1/2))^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(-b*x^4-a)^(1/2)*EllipticF(x*(-I/a^(1/2)*b^(1/2))^(1/2),I)","C"
214,1,193,261,0.235000," ","int((e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}"," ",0,"I*e*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I))+1/2/b^(1/2)*d*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+c/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
215,1,13,12,0.047000," ","int((-b*g*x^4+a*g)/(b*x^4+a)^(3/2),x)","\frac{g x}{\sqrt{b \,x^{4}+a}}"," ",0,"g*x/(b*x^4+a)^(1/2)","A"
216,1,24,25,0.048000," ","int((-b*g*x^4+a*g+e*x)/(b*x^4+a)^(3/2),x)","\frac{\left(2 a g +e x \right) x}{2 \sqrt{b \,x^{4}+a}\, a}"," ",0,"1/2*x*(2*a*g+e*x)/(b*x^4+a)^(1/2)/a","A"
217,1,24,23,0.048000," ","int((-b*g*x^4+f*x^3+a*g)/(b*x^4+a)^(3/2),x)","\frac{2 b g x -f}{2 \sqrt{b \,x^{4}+a}\, b}"," ",0,"1/2*(2*b*g*x-f)/b/(b*x^4+a)^(1/2)","A"
218,1,35,34,0.044000," ","int((-b*g*x^4+f*x^3+a*g+e*x)/(b*x^4+a)^(3/2),x)","\frac{2 a b g x +b e \,x^{2}-a f}{2 \sqrt{b \,x^{4}+a}\, a b}"," ",0,"1/2*(2*a*b*g*x+b*e*x^2-a*f)/a/b/(b*x^4+a)^(1/2)","A"
219,1,11,10,0.048000," ","int((x^4-1)/(x^4+1)^(3/2),x)","-\frac{x}{\sqrt{x^{4}+1}}"," ",0,"-1/(x^4+1)^(1/2)*x","A"
220,1,516,369,0.204000," ","int((i*x^6+h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, i \,x^{3}}{5 b}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} i \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} i \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a g \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{\sqrt{b \,x^{4}+a}\, h \,x^{2}}{4 b}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{a h \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 b^{\frac{3}{2}}}+\frac{d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, g x}{3 b}+\frac{\sqrt{b \,x^{4}+a}\, f}{2 b}"," ",0,"1/5*i*x^3*(b*x^4+a)^(1/2)/b-3/5*I*i*a^(3/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+3/5*I*i*a^(3/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*h*x^2*(b*x^4+a)^(1/2)/b-1/4*h*a/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*g*x*(b*x^4+a)^(1/2)/b-1/3*g*a/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*f*(b*x^4+a)^(1/2)/b+I*e*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I))+1/2/b^(1/2)*d*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+c/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
221,1,173,77,0.122000," ","int((x+1)/(x^5+1),x)","\frac{\arctan \left(\frac{4 x -\sqrt{5}-1}{\sqrt{10-2 \sqrt{5}}}\right)}{\sqrt{10-2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{4 x -\sqrt{5}-1}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}+\frac{\arctan \left(\frac{4 x +\sqrt{5}-1}{\sqrt{10+2 \sqrt{5}}}\right)}{\sqrt{10+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{4 x +\sqrt{5}-1}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}-\frac{\sqrt{5}\, \ln \left(2 x^{2}-\sqrt{5}\, x -x +2\right)}{10}+\frac{\sqrt{5}\, \ln \left(2 x^{2}+\sqrt{5}\, x -x +2\right)}{10}"," ",0,"1/10*5^(1/2)*ln(2*x^2+5^(1/2)*x-x+2)+1/(10+2*5^(1/2))^(1/2)*arctan((4*x+5^(1/2)-1)/(10+2*5^(1/2))^(1/2))-1/5/(10+2*5^(1/2))^(1/2)*arctan((4*x+5^(1/2)-1)/(10+2*5^(1/2))^(1/2))*5^(1/2)-1/10*5^(1/2)*ln(-5^(1/2)*x+2*x^2-x+2)+1/(10-2*5^(1/2))^(1/2)*arctan((4*x-5^(1/2)-1)/(10-2*5^(1/2))^(1/2))+1/5/(10-2*5^(1/2))^(1/2)*arctan((4*x-5^(1/2)-1)/(10-2*5^(1/2))^(1/2))*5^(1/2)","B"
222,1,169,77,0.112000," ","int((1-x)/(-x^5+1),x)","\frac{\arctan \left(\frac{4 x +1-\sqrt{5}}{\sqrt{10+2 \sqrt{5}}}\right)}{\sqrt{10+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{4 x +1-\sqrt{5}}{\sqrt{10+2 \sqrt{5}}}\right)}{5 \sqrt{10+2 \sqrt{5}}}+\frac{\arctan \left(\frac{4 x +1+\sqrt{5}}{\sqrt{10-2 \sqrt{5}}}\right)}{\sqrt{10-2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{4 x +1+\sqrt{5}}{\sqrt{10-2 \sqrt{5}}}\right)}{5 \sqrt{10-2 \sqrt{5}}}-\frac{\sqrt{5}\, \ln \left(2 x^{2}-\sqrt{5}\, x +x +2\right)}{10}+\frac{\sqrt{5}\, \ln \left(2 x^{2}+\sqrt{5}\, x +x +2\right)}{10}"," ",0,"-1/10*5^(1/2)*ln(-5^(1/2)*x+2*x^2+x+2)+1/(10+2*5^(1/2))^(1/2)*arctan((4*x+1-5^(1/2))/(10+2*5^(1/2))^(1/2))-1/5/(10+2*5^(1/2))^(1/2)*arctan((4*x+1-5^(1/2))/(10+2*5^(1/2))^(1/2))*5^(1/2)+1/10*5^(1/2)*ln(5^(1/2)*x+2*x^2+x+2)+1/(10-2*5^(1/2))^(1/2)*arctan((4*x+1+5^(1/2))/(10-2*5^(1/2))^(1/2))+1/5/(10-2*5^(1/2))^(1/2)*arctan((4*x+1+5^(1/2))/(10-2*5^(1/2))^(1/2))*5^(1/2)","B"
223,1,266,194,0.046000," ","int(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{18}}{18 b}-\frac{a f \,x^{15}}{15 b^{2}}+\frac{e \,x^{15}}{15 b}+\frac{a^{2} f \,x^{12}}{12 b^{3}}-\frac{a e \,x^{12}}{12 b^{2}}+\frac{d \,x^{12}}{12 b}-\frac{a^{3} f \,x^{9}}{9 b^{4}}+\frac{a^{2} e \,x^{9}}{9 b^{3}}-\frac{a d \,x^{9}}{9 b^{2}}+\frac{c \,x^{9}}{9 b}+\frac{a^{4} f \,x^{6}}{6 b^{5}}-\frac{a^{3} e \,x^{6}}{6 b^{4}}+\frac{a^{2} d \,x^{6}}{6 b^{3}}-\frac{a c \,x^{6}}{6 b^{2}}-\frac{a^{5} f \,x^{3}}{3 b^{6}}+\frac{a^{4} e \,x^{3}}{3 b^{5}}-\frac{a^{3} d \,x^{3}}{3 b^{4}}+\frac{a^{2} c \,x^{3}}{3 b^{3}}+\frac{a^{6} f \ln \left(b \,x^{3}+a \right)}{3 b^{7}}-\frac{a^{5} e \ln \left(b \,x^{3}+a \right)}{3 b^{6}}+\frac{a^{4} d \ln \left(b \,x^{3}+a \right)}{3 b^{5}}-\frac{a^{3} c \ln \left(b \,x^{3}+a \right)}{3 b^{4}}"," ",0,"1/18*f*x^18/b-1/15/b^2*x^15*a*f+1/15/b*x^15*e+1/12/b^3*x^12*a^2*f-1/12/b^2*x^12*a*e+1/12/b*x^12*d-1/9/b^4*x^9*a^3*f+1/9/b^3*x^9*a^2*e-1/9/b^2*x^9*a*d+1/9/b*x^9*c+1/6/b^5*x^6*a^4*f-1/6/b^4*x^6*a^3*e+1/6/b^3*x^6*a^2*d-1/6/b^2*x^6*a*c-1/3/b^6*x^3*a^5*f+1/3/b^5*x^3*a^4*e-1/3/b^4*x^3*a^3*d+1/3/b^3*x^3*a^2*c+1/3*a^6/b^7*ln(b*x^3+a)*f-1/3*a^5/b^6*ln(b*x^3+a)*e+1/3*a^4/b^5*ln(b*x^3+a)*d-1/3*a^3/b^4*ln(b*x^3+a)*c","A"
224,1,218,158,0.046000," ","int(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{15}}{15 b}-\frac{a f \,x^{12}}{12 b^{2}}+\frac{e \,x^{12}}{12 b}+\frac{a^{2} f \,x^{9}}{9 b^{3}}-\frac{a e \,x^{9}}{9 b^{2}}+\frac{d \,x^{9}}{9 b}-\frac{a^{3} f \,x^{6}}{6 b^{4}}+\frac{a^{2} e \,x^{6}}{6 b^{3}}-\frac{a d \,x^{6}}{6 b^{2}}+\frac{c \,x^{6}}{6 b}+\frac{a^{4} f \,x^{3}}{3 b^{5}}-\frac{a^{3} e \,x^{3}}{3 b^{4}}+\frac{a^{2} d \,x^{3}}{3 b^{3}}-\frac{a c \,x^{3}}{3 b^{2}}-\frac{a^{5} f \ln \left(b \,x^{3}+a \right)}{3 b^{6}}+\frac{a^{4} e \ln \left(b \,x^{3}+a \right)}{3 b^{5}}-\frac{a^{3} d \ln \left(b \,x^{3}+a \right)}{3 b^{4}}+\frac{a^{2} c \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/15*f*x^15/b-1/12/b^2*x^12*a*f+1/12/b*x^12*e+1/9/b^3*x^9*a^2*f-1/9/b^2*x^9*a*e+1/9/b*x^9*d-1/6/b^4*x^6*a^3*f+1/6/b^3*x^6*a^2*e-1/6/b^2*x^6*a*d+1/6/b*x^6*c+1/3/b^5*x^3*a^4*f-1/3/b^4*x^3*a^3*e+1/3/b^3*x^3*a^2*d-1/3/b^2*x^3*a*c-1/3*a^5/b^6*ln(b*x^3+a)*f+1/3*a^4/b^5*ln(b*x^3+a)*e-1/3*a^3/b^4*ln(b*x^3+a)*d+1/3*a^2/b^3*ln(b*x^3+a)*c","A"
225,1,170,122,0.050000," ","int(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{12}}{12 b}-\frac{a f \,x^{9}}{9 b^{2}}+\frac{e \,x^{9}}{9 b}+\frac{a^{2} f \,x^{6}}{6 b^{3}}-\frac{a e \,x^{6}}{6 b^{2}}+\frac{d \,x^{6}}{6 b}-\frac{a^{3} f \,x^{3}}{3 b^{4}}+\frac{a^{2} e \,x^{3}}{3 b^{3}}-\frac{a d \,x^{3}}{3 b^{2}}+\frac{c \,x^{3}}{3 b}+\frac{a^{4} f \ln \left(b \,x^{3}+a \right)}{3 b^{5}}-\frac{a^{3} e \ln \left(b \,x^{3}+a \right)}{3 b^{4}}+\frac{a^{2} d \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{a c \ln \left(b \,x^{3}+a \right)}{3 b^{2}}"," ",0,"1/12*f*x^12/b-1/9/b^2*x^9*a*f+1/9/b*x^9*e+1/6/b^3*x^6*a^2*f-1/6/b^2*x^6*a*e+1/6/b*x^6*d-1/3/b^4*x^3*a^3*f+1/3/b^3*x^3*a^2*e-1/3/b^2*x^3*a*d+1/3/b*x^3*c+1/3*a^4/b^5*ln(b*x^3+a)*f-1/3*a^3/b^4*ln(b*x^3+a)*e+1/3*a^2/b^3*ln(b*x^3+a)*d-1/3*a/b^2*ln(b*x^3+a)*c","A"
226,1,124,88,0.044000," ","int(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{9}}{9 b}-\frac{a f \,x^{6}}{6 b^{2}}+\frac{e \,x^{6}}{6 b}+\frac{a^{2} f \,x^{3}}{3 b^{3}}-\frac{a e \,x^{3}}{3 b^{2}}+\frac{d \,x^{3}}{3 b}-\frac{a^{3} f \ln \left(b \,x^{3}+a \right)}{3 b^{4}}+\frac{a^{2} e \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{a d \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{c \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"1/9/b*f*x^9-1/6/b^2*x^6*a*f+1/6/b*x^6*e+1/3/b^3*x^3*a^2*f-1/3/b^2*x^3*a*e+1/3/b*x^3*d-1/3/b^4*ln(b*x^3+a)*a^3*f+1/3/b^3*ln(b*x^3+a)*a^2*e-1/3/b^2*ln(b*x^3+a)*a*d+1/3*c*ln(b*x^3+a)/b","A"
227,1,97,74,0.050000," ","int((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a),x)","\frac{f \,x^{6}}{6 b}-\frac{a f \,x^{3}}{3 b^{2}}+\frac{e \,x^{3}}{3 b}+\frac{a^{2} f \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{a e \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{c \ln \left(x \right)}{a}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{d \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"1/6*f*x^6/b-1/3/b^2*x^3*a*f+1/3*e*x^3/b+1/3*a^2/b^3*ln(b*x^3+a)*f-1/3*a*e*ln(b*x^3+a)/b^2+1/3*d*ln(b*x^3+a)/b-1/3*c*ln(b*x^3+a)/a+c*ln(x)/a","A"
228,1,94,75,0.056000," ","int((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a),x)","\frac{f \,x^{3}}{3 b}-\frac{a f \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{d \ln \left(x \right)}{a}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a}-\frac{b c \ln \left(x \right)}{a^{2}}+\frac{b c \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{e \ln \left(b \,x^{3}+a \right)}{3 b}-\frac{c}{3 a \,x^{3}}"," ",0,"1/3/b*f*x^3-1/3*a/b^2*ln(b*x^3+a)*f+1/3*e*ln(b*x^3+a)/b-1/3*d*ln(b*x^3+a)/a+1/3/a^2*b*ln(b*x^3+a)*c-1/3/a*c/x^3+d*ln(x)/a-1/a^2*ln(x)*b*c","A"
229,1,116,89,0.052000," ","int((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a),x)","\frac{e \ln \left(x \right)}{a}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a}-\frac{b d \ln \left(x \right)}{a^{2}}+\frac{b d \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{b^{2} c \ln \left(x \right)}{a^{3}}-\frac{b^{2} c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}+\frac{f \ln \left(b \,x^{3}+a \right)}{3 b}-\frac{d}{3 a \,x^{3}}+\frac{b c}{3 a^{2} x^{3}}-\frac{c}{6 a \,x^{6}}"," ",0,"1/3/b*ln(b*x^3+a)*f-1/3*e*ln(b*x^3+a)/a+1/3/a^2*b*ln(b*x^3+a)*d-1/3/a^3*b^2*ln(b*x^3+a)*c-1/6*c/a/x^6-1/3/a/x^3*d+1/3/a^2/x^3*b*c+e*ln(x)/a-1/a^2*ln(x)*b*d+1/a^3*ln(x)*b^2*c","A"
230,1,161,121,0.049000," ","int((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a),x)","\frac{f \ln \left(x \right)}{a}-\frac{f \ln \left(b \,x^{3}+a \right)}{3 a}-\frac{b e \ln \left(x \right)}{a^{2}}+\frac{b e \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{b^{2} d \ln \left(x \right)}{a^{3}}-\frac{b^{2} d \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{b^{3} c \ln \left(x \right)}{a^{4}}+\frac{b^{3} c \ln \left(b \,x^{3}+a \right)}{3 a^{4}}-\frac{e}{3 a \,x^{3}}+\frac{b d}{3 a^{2} x^{3}}-\frac{b^{2} c}{3 a^{3} x^{3}}-\frac{d}{6 a \,x^{6}}+\frac{b c}{6 a^{2} x^{6}}-\frac{c}{9 a \,x^{9}}"," ",0,"-1/3/a*ln(b*x^3+a)*f+1/3/a^2*ln(b*x^3+a)*b*e-1/3/a^3*ln(b*x^3+a)*b^2*d+1/3/a^4*ln(b*x^3+a)*b^3*c-1/9/a*c/x^9-1/6/a/x^6*d+1/6/a^2/x^6*b*c-1/3/a/x^3*e+1/3/a^2/x^3*b*d-1/3/a^3/x^3*b^2*c+1/a*ln(x)*f-1/a^2*ln(x)*b*e+1/a^3*ln(x)*b^2*d-1/a^4*ln(x)*b^3*c","A"
231,1,210,155,0.057000," ","int((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a),x)","-\frac{b f \ln \left(x \right)}{a^{2}}+\frac{b f \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{b^{2} e \ln \left(x \right)}{a^{3}}-\frac{b^{2} e \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{b^{3} d \ln \left(x \right)}{a^{4}}+\frac{b^{3} d \ln \left(b \,x^{3}+a \right)}{3 a^{4}}+\frac{b^{4} c \ln \left(x \right)}{a^{5}}-\frac{b^{4} c \ln \left(b \,x^{3}+a \right)}{3 a^{5}}-\frac{f}{3 a \,x^{3}}+\frac{b e}{3 a^{2} x^{3}}-\frac{b^{2} d}{3 a^{3} x^{3}}+\frac{b^{3} c}{3 a^{4} x^{3}}-\frac{e}{6 a \,x^{6}}+\frac{b d}{6 a^{2} x^{6}}-\frac{b^{2} c}{6 a^{3} x^{6}}-\frac{d}{9 a \,x^{9}}+\frac{b c}{9 a^{2} x^{9}}-\frac{c}{12 a \,x^{12}}"," ",0,"1/3*b/a^2*ln(b*x^3+a)*f-1/3*b^2/a^3*ln(b*x^3+a)*e+1/3*b^3/a^4*ln(b*x^3+a)*d-1/3*b^4/a^5*ln(b*x^3+a)*c-1/12*c/a/x^12-1/9/a/x^9*d+1/9/a^2/x^9*b*c-1/6/a/x^6*e+1/6/a^2/x^6*b*d-1/6/a^3/x^6*b^2*c-1/3/a/x^3*f+1/3/a^2/x^3*b*e-1/3/a^3/x^3*b^2*d+1/3/a^4/x^3*b^3*c-1/a^2*b*ln(x)*f+1/a^3*b^2*ln(x)*e-1/a^4*b^3*ln(x)*d+1/a^5*b^4*ln(x)*c","A"
232,1,260,194,0.053000," ","int((f*x^9+e*x^6+d*x^3+c)/x^16/(b*x^3+a),x)","\frac{b^{2} f \ln \left(x \right)}{a^{3}}-\frac{b^{2} f \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{b^{3} e \ln \left(x \right)}{a^{4}}+\frac{b^{3} e \ln \left(b \,x^{3}+a \right)}{3 a^{4}}+\frac{b^{4} d \ln \left(x \right)}{a^{5}}-\frac{b^{4} d \ln \left(b \,x^{3}+a \right)}{3 a^{5}}-\frac{b^{5} c \ln \left(x \right)}{a^{6}}+\frac{b^{5} c \ln \left(b \,x^{3}+a \right)}{3 a^{6}}+\frac{b f}{3 a^{2} x^{3}}-\frac{b^{2} e}{3 a^{3} x^{3}}+\frac{b^{3} d}{3 a^{4} x^{3}}-\frac{b^{4} c}{3 a^{5} x^{3}}-\frac{f}{6 a \,x^{6}}+\frac{b e}{6 a^{2} x^{6}}-\frac{b^{2} d}{6 a^{3} x^{6}}+\frac{b^{3} c}{6 a^{4} x^{6}}-\frac{e}{9 a \,x^{9}}+\frac{b d}{9 a^{2} x^{9}}-\frac{b^{2} c}{9 a^{3} x^{9}}-\frac{d}{12 a \,x^{12}}+\frac{b c}{12 a^{2} x^{12}}-\frac{c}{15 a \,x^{15}}"," ",0,"-1/3*b^2/a^3*ln(b*x^3+a)*f+1/3*b^3/a^4*ln(b*x^3+a)*e-1/3*b^4/a^5*ln(b*x^3+a)*d+1/3*b^5/a^6*ln(b*x^3+a)*c-1/15*c/a/x^15-1/12/a/x^12*d+1/12/a^2/x^12*b*c-1/9/a/x^9*e+1/9/a^2/x^9*b*d-1/9/a^3/x^9*b^2*c-1/6/a/x^6*f+1/6/a^2/x^6*b*e-1/6/a^3/x^6*b^2*d+1/6/a^4/x^6*b^3*c+1/a^3*b^2*ln(x)*f-1/a^4*b^3*ln(x)*e+1/a^5*b^4*ln(x)*d-1/a^6*b^5*ln(x)*c+1/3/a^2*b/x^3*f-1/3/a^3*b^2/x^3*e+1/3/a^4*b^3/x^3*d-1/3/a^5*b^4/x^3*c","A"
233,1,592,302,0.049000," ","int(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{16}}{16 b}-\frac{a f \,x^{13}}{13 b^{2}}+\frac{e \,x^{13}}{13 b}+\frac{a^{2} f \,x^{10}}{10 b^{3}}-\frac{a e \,x^{10}}{10 b^{2}}+\frac{d \,x^{10}}{10 b}-\frac{a^{3} f \,x^{7}}{7 b^{4}}+\frac{a^{2} e \,x^{7}}{7 b^{3}}-\frac{a d \,x^{7}}{7 b^{2}}+\frac{c \,x^{7}}{7 b}+\frac{a^{4} f \,x^{4}}{4 b^{5}}-\frac{a^{3} e \,x^{4}}{4 b^{4}}+\frac{a^{2} d \,x^{4}}{4 b^{3}}-\frac{a c \,x^{4}}{4 b^{2}}+\frac{\sqrt{3}\, a^{6} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}+\frac{a^{6} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}-\frac{a^{6} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}-\frac{\sqrt{3}\, a^{5} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{a^{5} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{a^{5} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{a^{5} f x}{b^{6}}+\frac{\sqrt{3}\, a^{4} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{a^{4} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{a^{4} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{a^{4} e x}{b^{5}}-\frac{\sqrt{3}\, a^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} d x}{b^{4}}+\frac{a^{2} c x}{b^{3}}"," ",0,"1/3*a^6/b^7/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a^5/b^6/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3*a^4/b^5/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3*a^3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/10/b^2*x^10*a*e-1/b^4*a^3*d*x-1/13/b^2*x^13*a*f+1/10/b^3*x^10*a^2*f+1/b^5*a^4*e*x+1/4/b^3*x^4*a^2*d-1/4/b^2*x^4*a*c-1/b^6*a^5*f*x+1/4/b^5*x^4*a^4*f-1/4/b^4*x^4*a^3*e-1/7/b^2*x^7*a*d+1/b^3*a^2*c*x-1/7/b^4*x^7*a^3*f+1/7/b^3*x^7*a^2*e+1/3*a^6/b^7/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+1/3*a^4/b^5/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-1/3*a^3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/6*a^6/b^7/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/3*a^5/b^6/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/6*a^5/b^6/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6*a^4/b^5/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6*a^3/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/7/b*x^7*c+1/13/b*x^13*e+1/10/b*x^10*d+1/16*f*x^16/b","A"
234,1,554,269,0.050000," ","int(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{14}}{14 b}-\frac{a f \,x^{11}}{11 b^{2}}+\frac{e \,x^{11}}{11 b}+\frac{a^{2} f \,x^{8}}{8 b^{3}}-\frac{a e \,x^{8}}{8 b^{2}}+\frac{d \,x^{8}}{8 b}-\frac{a^{3} f \,x^{5}}{5 b^{4}}+\frac{a^{2} e \,x^{5}}{5 b^{3}}-\frac{a d \,x^{5}}{5 b^{2}}+\frac{c \,x^{5}}{5 b}+\frac{a^{4} f \,x^{2}}{2 b^{5}}-\frac{a^{3} e \,x^{2}}{2 b^{4}}+\frac{a^{2} d \,x^{2}}{2 b^{3}}-\frac{a c \,x^{2}}{2 b^{2}}-\frac{\sqrt{3}\, a^{5} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{a^{5} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}-\frac{a^{5} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{\sqrt{3}\, a^{4} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{a^{4} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{a^{4} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{\sqrt{3}\, a^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{a^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{a^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{\sqrt{3}\, a^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"-1/3*a^5/b^6*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a^3/b^4*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3*a^2/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3*a^4/b^5*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/5/b^4*x^5*a^3*f-1/11/b^2*x^11*a*f-1/5/b^2*x^5*a*d+1/5/b^3*x^5*a^2*e+1/8/b^3*x^8*a^2*f-1/8/b^2*x^8*a*e-1/2/b^4*x^2*a^3*e+1/2/b^3*x^2*a^2*d+1/2/b^5*x^2*a^4*f-1/2/b^2*x^2*a*c+1/6*a^4/b^5/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6*a^3/b^4/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6*a^2/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3*a^5/b^6/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-1/3*a^4/b^5/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+1/3*a^3/b^4/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-1/3*a^2/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-1/6*a^5/b^6/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/11/b*x^11*e+1/8/b*x^8*d+1/5/b*x^5*c+1/14*f*x^14/b","B"
235,1,544,267,0.045000," ","int(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{13}}{13 b}-\frac{a f \,x^{10}}{10 b^{2}}+\frac{e \,x^{10}}{10 b}+\frac{a^{2} f \,x^{7}}{7 b^{3}}-\frac{a e \,x^{7}}{7 b^{2}}+\frac{d \,x^{7}}{7 b}-\frac{a^{3} f \,x^{4}}{4 b^{4}}+\frac{a^{2} e \,x^{4}}{4 b^{3}}-\frac{a d \,x^{4}}{4 b^{2}}+\frac{c \,x^{4}}{4 b}-\frac{\sqrt{3}\, a^{5} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{a^{5} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{a^{5} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{\sqrt{3}\, a^{4} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{a^{4} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{a^{4} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{a^{4} f x}{b^{5}}-\frac{\sqrt{3}\, a^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} e x}{b^{4}}+\frac{\sqrt{3}\, a^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} d x}{b^{3}}-\frac{a c x}{b^{2}}"," ",0,"-1/3*a^5/b^6/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a^3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3*a^2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3*a^4/b^5/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/7/b^2*x^7*a*e-1/4/b^4*x^4*a^3*f-1/b^4*a^3*e*x+1/b^3*a^2*d*x-1/b^2*a*c*x+1/b^5*a^4*f*x+1/4/b^3*x^4*a^2*e-1/4/b^2*x^4*a*d-1/10/b^2*x^10*a*f+1/7/b^3*x^7*a^2*f-1/3*a^5/b^6/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-1/6*a^2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3*a^3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+1/3*a^2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+1/6*a^5/b^6/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/3*a^4/b^5/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e-1/6*a^4/b^5/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/6*a^3/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/10/b*x^10*e+1/7/b*x^7*d+1/4/b*x^4*c+1/13*f*x^13/b","B"
236,1,502,235,0.047000," ","int(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{11}}{11 b}-\frac{a f \,x^{8}}{8 b^{2}}+\frac{e \,x^{8}}{8 b}+\frac{a^{2} f \,x^{5}}{5 b^{3}}-\frac{a e \,x^{5}}{5 b^{2}}+\frac{d \,x^{5}}{5 b}-\frac{a^{3} f \,x^{2}}{2 b^{4}}+\frac{a^{2} e \,x^{2}}{2 b^{3}}-\frac{a d \,x^{2}}{2 b^{2}}+\frac{c \,x^{2}}{2 b}+\frac{\sqrt{3}\, a^{4} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{a^{4} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{a^{4} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{\sqrt{3}\, a^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{a^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{a^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{\sqrt{3}\, a^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{\sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}"," ",0,"1/11/b*f*x^11-1/8/b^2*x^8*a*f+1/8/b*x^8*e+1/5/b^3*x^5*a^2*f-1/5/b^2*x^5*a*e+1/5/b*x^5*d-1/2/b^4*x^2*a^3*f+1/2/b^3*x^2*a^2*e-1/2/b^2*x^2*a*d+1/2/b*x^2*c-1/3*a^4/b^5/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/3*a^3/b^4/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-1/3*a^2/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/3*a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/6*a^4/b^5/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6*a^3/b^4/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/6*a^2/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/6*a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3*a^4/b^5*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a^3/b^4*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3*a^2/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3*a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
237,1,492,232,0.046000," ","int(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{10}}{10 b}-\frac{a f \,x^{7}}{7 b^{2}}+\frac{e \,x^{7}}{7 b}+\frac{a^{2} f \,x^{4}}{4 b^{3}}-\frac{a e \,x^{4}}{4 b^{2}}+\frac{d \,x^{4}}{4 b}+\frac{\sqrt{3}\, a^{4} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{a^{4} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{a^{4} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{\sqrt{3}\, a^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} f x}{b^{4}}+\frac{\sqrt{3}\, a^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} e x}{b^{3}}-\frac{\sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a d x}{b^{2}}+\frac{c x}{b}"," ",0,"1/10*f*x^10/b-1/7/b^2*x^7*a*f+1/7/b*x^7*e+1/4/b^3*x^4*a^2*f-1/4/b^2*x^4*a*e+1/4/b*x^4*d-1/b^4*a^3*f*x+1/b^3*a^2*e*x-1/b^2*a*d*x+1/b*c*x+1/3*a^4/b^5/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-1/3*a^3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/3*a^2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-1/3*a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/6*a^4/b^5/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6*a^3/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6*a^2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6*a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3*a^4/b^5/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a^3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3*a^2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3*a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
238,1,450,202,0.046000," ","int(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{8}}{8 b}-\frac{a f \,x^{5}}{5 b^{2}}+\frac{e \,x^{5}}{5 b}+\frac{a^{2} f \,x^{2}}{2 b^{3}}-\frac{a e \,x^{2}}{2 b^{2}}+\frac{d \,x^{2}}{2 b}-\frac{\sqrt{3}\, a^{3} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{a^{3} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{a^{3} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{\sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"1/8*f*x^8/b-1/5/b^2*x^5*a*f+1/5/b*x^5*e+1/2/b^3*x^2*a^2*f-1/2/b^2*x^2*a*e+1/2/b*d*x^2+1/3/b^4/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*a^3*f-1/3/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*a^2*e+1/3/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*a*d-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-1/6/b^4/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^3*f+1/6/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*e-1/6/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*d+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/b^4*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^3*f+1/3/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*e-1/3/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*d+1/3/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
239,1,442,199,0.043000," ","int((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a),x)","\frac{f \,x^{7}}{7 b}-\frac{a f \,x^{4}}{4 b^{2}}+\frac{e \,x^{4}}{4 b}-\frac{\sqrt{3}\, a^{3} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a^{3} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{\sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} f x}{b^{3}}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a e x}{b^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{d x}{b}"," ",0,"1/7/b*f*x^7-1/4/b^2*x^4*a*f+1/4/b*x^4*e+1/b^3*a^2*f*x-1/b^2*a*e*x+1/b*d*x-1/3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^3*f+1/3/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^2*e-1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*d+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+1/6/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^3*f-1/6/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*e+1/6/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*d-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^3*f+1/3/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*e-1/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*d+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
240,1,419,187,0.049000," ","int((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a),x)","\frac{f \,x^{5}}{5 b}-\frac{a f \,x^{2}}{2 b^{2}}+\frac{e \,x^{2}}{2 b}+\frac{\sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{\sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{c}{a x}"," ",0,"1/5/b*f*x^5-1/2/b^2*x^2*a*f+1/2*e*x^2/b-1/3*a^2/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/3*a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/6*a^2/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6*a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3*a^2/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/a*c/x","B"
241,1,414,184,0.055000," ","int((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a),x)","\frac{f \,x^{4}}{4 b}+\frac{\sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{\sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a f x}{b^{2}}-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{e x}{b}-\frac{c}{2 a \,x^{2}}"," ",0,"1/4*f*x^4/b-1/b^2*a*f*x+e*x/b+1/3*a^2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-1/3*a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/6*a^2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6*a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3*a^2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/2*c/a/x^2","B"
242,1,412,186,0.057000," ","int((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a),x)","\frac{f \,x^{2}}{2 b}-\frac{\sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{\sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{d}{a x}+\frac{b c}{a^{2} x}-\frac{c}{4 a \,x^{4}}"," ",0,"1/2*f*x^2/b+1/3*a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-1/3/a^2*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-1/6*a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6/a^2*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3*a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/3/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3/a^2*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/4*c/a/x^4-d/a/x+1/a^2/x*b*c","B"
243,1,410,184,0.051000," ","int((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a),x)","-\frac{\sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{\sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{f x}{b}-\frac{d}{2 a \,x^{2}}+\frac{b c}{2 a^{2} x^{2}}-\frac{c}{5 a \,x^{5}}"," ",0,"1/b*f*x-1/3*a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+1/3/a^2*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+1/6*a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/6/a^2*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3*a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3/a^2*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/5/a*c/x^5-1/2*d/a/x^2+1/2/a^2/x^2*b*c","B"
244,1,440,202,0.048000," ","int((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a),x)","-\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{\sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{\sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{e}{a x}+\frac{b d}{a^{2} x}-\frac{b^{2} c}{a^{3} x}-\frac{d}{4 a \,x^{4}}+\frac{b c}{4 a^{2} x^{4}}-\frac{c}{7 a \,x^{7}}"," ",0,"-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-1/3/a^2*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/3/a^3*b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/6/a^2*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/6/a^3*b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3/a^2*3^(1/2)*b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/a^3*3^(1/2)*b^2/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/7/a*c/x^7-1/4/a/x^4*d+1/4/a^2/x^4*b*c-e/a/x+1/a^2/x*b*d-1/a^3/x*b^2*c","B"
245,1,441,203,0.061000," ","int((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a),x)","-\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{\sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{\sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{e}{2 a \,x^{2}}+\frac{b d}{2 a^{2} x^{2}}-\frac{b^{2} c}{2 a^{3} x^{2}}-\frac{d}{5 a \,x^{5}}+\frac{b c}{5 a^{2} x^{5}}-\frac{c}{8 a \,x^{8}}"," ",0,"1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/3/a^2*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-1/3/a^3*b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6/a^2*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6/a^3*b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3/a^2*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/a^3*b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/8*c/a/x^8-1/5/a/x^5*d+1/5/a^2/x^5*b*c-1/2/a/x^2*e+1/2/a^2/x^2*b*d-1/2/a^3/x^2*b^2*c","B"
246,1,491,235,0.062000," ","int((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a),x)","-\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{\sqrt{3}\, b e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{b e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{b e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{\sqrt{3}\, b^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{b^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{b^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{\sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{b^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{b^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{f}{a x}+\frac{b e}{a^{2} x}-\frac{b^{2} d}{a^{3} x}+\frac{b^{3} c}{a^{4} x}-\frac{e}{4 a \,x^{4}}+\frac{b d}{4 a^{2} x^{4}}-\frac{b^{2} c}{4 a^{3} x^{4}}-\frac{d}{7 a \,x^{7}}+\frac{b c}{7 a^{2} x^{7}}-\frac{c}{10 a \,x^{10}}"," ",0,"1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-1/3/a^2*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+1/3/a^3*b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-1/3/a^4*b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6/a^2*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6/a^3*b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6/a^4*b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/3/a^2*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/a^3*b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3/a^4*b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/10*c/a/x^10-1/7/a/x^7*d+1/7/a^2/x^7*b*c-1/4/a/x^4*e+1/4/a^2/x^4*b*d-1/4/a^3/x^4*b^2*c-1/a/x*f+1/a^2/x*b*e-1/a^3/x*b^2*d+1/a^4/x*b^3*c","B"
247,1,493,236,0.054000," ","int((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a),x)","-\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{\sqrt{3}\, b e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{b e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{b e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{\sqrt{3}\, b^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{b^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{b^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{\sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{b^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{b^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{f}{2 a \,x^{2}}+\frac{b e}{2 a^{2} x^{2}}-\frac{b^{2} d}{2 a^{3} x^{2}}+\frac{b^{3} c}{2 a^{4} x^{2}}-\frac{e}{5 a \,x^{5}}+\frac{b d}{5 a^{2} x^{5}}-\frac{b^{2} c}{5 a^{3} x^{5}}-\frac{d}{8 a \,x^{8}}+\frac{b c}{8 a^{2} x^{8}}-\frac{c}{11 a \,x^{11}}"," ",0,"-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+1/3/a^2*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e-1/3/a^3*b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+1/3/a^4*b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6/a^2*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/6/a^3*b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/6/a^4*b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/3/a^2*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/a^3*b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3/a^4*b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/11/a*c/x^11-1/8/a/x^8*d+1/8/a^2/x^8*b*c-1/5/a/x^5*e+1/5/a^2/x^5*b*d-1/5/a^3/x^5*b^2*c-1/2/a/x^2*f+1/2/a^2/x^2*b*e-1/2/a^3/x^2*b^2*d+1/2/a^4/x^2*b^3*c","B"
248,1,546,270,0.053000," ","int((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a),x)","\frac{\sqrt{3}\, b f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{b f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{b f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{\sqrt{3}\, b^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{b^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{b^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{\sqrt{3}\, b^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{b^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{b^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{\sqrt{3}\, b^{4} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{b^{4} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{b^{4} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{b f}{a^{2} x}-\frac{b^{2} e}{a^{3} x}+\frac{b^{3} d}{a^{4} x}-\frac{b^{4} c}{a^{5} x}-\frac{f}{4 a \,x^{4}}+\frac{b e}{4 a^{2} x^{4}}-\frac{b^{2} d}{4 a^{3} x^{4}}+\frac{b^{3} c}{4 a^{4} x^{4}}-\frac{e}{7 a \,x^{7}}+\frac{b d}{7 a^{2} x^{7}}-\frac{b^{2} c}{7 a^{3} x^{7}}-\frac{d}{10 a \,x^{10}}+\frac{b c}{10 a^{2} x^{10}}-\frac{c}{13 a \,x^{13}}"," ",0,"1/3/a^2*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3/a^3*b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3/a^4*b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/a^5*b^4*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/7/a^3/x^7*b^2*c+1/a^4*b^3/x*d-1/a^5*b^4/x*c+1/a^2*b/x*f-1/a^3*b^2/x*e+1/4/a^2/x^4*b*e-1/4/a^3/x^4*b^2*d+1/4/a^4/x^4*b^3*c+1/10/a^2/x^10*b*c+1/7/a^2/x^7*b*d-1/13*c/a/x^13-1/7/a/x^7*e-1/10/a/x^10*d+1/6/a^4*b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/6/a^5*b^4/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/a^2*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/3/a^3*b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-1/3/a^4*b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/3/a^5*b^4/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/6/a^2*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6/a^3*b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/4/a/x^4*f","B"
249,1,548,270,0.056000," ","int((f*x^9+e*x^6+d*x^3+c)/x^15/(b*x^3+a),x)","\frac{\sqrt{3}\, b f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{b f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{b f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{\sqrt{3}\, b^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{b^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{b^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{\sqrt{3}\, b^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{b^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{b^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{\sqrt{3}\, b^{4} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}-\frac{b^{4} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}+\frac{b^{4} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}+\frac{b f}{2 a^{2} x^{2}}-\frac{b^{2} e}{2 a^{3} x^{2}}+\frac{b^{3} d}{2 a^{4} x^{2}}-\frac{b^{4} c}{2 a^{5} x^{2}}-\frac{f}{5 a \,x^{5}}+\frac{b e}{5 a^{2} x^{5}}-\frac{b^{2} d}{5 a^{3} x^{5}}+\frac{b^{3} c}{5 a^{4} x^{5}}-\frac{e}{8 a \,x^{8}}+\frac{b d}{8 a^{2} x^{8}}-\frac{b^{2} c}{8 a^{3} x^{8}}-\frac{d}{11 a \,x^{11}}+\frac{b c}{11 a^{2} x^{11}}-\frac{c}{14 a \,x^{14}}"," ",0,"1/3/a^2*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3/a^3*b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/3/a^4*b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/a^5*b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/2/a^5*b^4/x^2*c+1/11/a^2/x^11*b*c+1/8/a^2/x^8*b*d-1/8/a^3/x^8*b^2*c+1/5/a^2/x^5*b*e+1/2/a^2*b/x^2*f-1/2/a^3*b^2/x^2*e+1/2/a^4*b^3/x^2*d-1/5/a^3/x^5*b^2*d+1/5/a^4/x^5*b^3*c-1/11/a/x^11*d-1/14*c/a/x^14-1/3/a^5*b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/8/a/x^8*e-1/6/a^4*b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/6/a^5*b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3/a^2*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-1/3/a^3*b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e-1/5/a/x^5*f-1/6/a^2*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6/a^3*b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/3/a^4*b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d","B"
250,1,600,305,0.056000," ","int((f*x^9+e*x^6+d*x^3+c)/x^17/(b*x^3+a),x)","-\frac{\sqrt{3}\, b^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{b^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{b^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{\sqrt{3}\, b^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{b^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{b^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{\sqrt{3}\, b^{4} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{b^{4} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{b^{4} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{\sqrt{3}\, b^{5} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{b^{5} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}+\frac{b^{5} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{b^{2} f}{a^{3} x}+\frac{b^{3} e}{a^{4} x}-\frac{b^{4} d}{a^{5} x}+\frac{b^{5} c}{a^{6} x}+\frac{b f}{4 a^{2} x^{4}}-\frac{b^{2} e}{4 a^{3} x^{4}}+\frac{b^{3} d}{4 a^{4} x^{4}}-\frac{b^{4} c}{4 a^{5} x^{4}}-\frac{f}{7 a \,x^{7}}+\frac{b e}{7 a^{2} x^{7}}-\frac{b^{2} d}{7 a^{3} x^{7}}+\frac{b^{3} c}{7 a^{4} x^{7}}-\frac{e}{10 a \,x^{10}}+\frac{b d}{10 a^{2} x^{10}}-\frac{b^{2} c}{10 a^{3} x^{10}}-\frac{d}{13 a \,x^{13}}+\frac{b c}{13 a^{2} x^{13}}-\frac{c}{16 a \,x^{16}}"," ",0,"-1/10/a^3/x^10*b^2*c+1/7/a^2/x^7*b*e-1/7/a^3/x^7*b^2*d+1/7/a^4/x^7*b^3*c-1/a^3*b^2/x*f+1/a^4*b^3/x*e-1/a^5*b^4/x*d+1/a^6*b^5/x*c+1/4/a^2*b/x^4*f-1/4/a^3*b^2/x^4*e+1/4/a^4*b^3/x^4*d-1/4/a^5*b^4/x^4*c+1/13/a^2/x^13*b*c+1/10/a^2/x^10*b*d-1/16*c/a/x^16-1/3/a^3*b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/3/a^4*b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/a^5*b^4*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3/a^6*b^5*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/7/a/x^7*f-1/13/a/x^13*d-1/3/a^4*b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+1/3/a^5*b^4/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-1/10/a/x^10*e+1/6/a^6*b^5/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3/a^6*b^5/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-1/6/a^3*b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6/a^4*b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/6/a^5*b^4/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/3/a^3*b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f","A"
251,1,288,206,0.065000," ","int(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{15}}{15 b^{2}}-\frac{a f \,x^{12}}{6 b^{3}}+\frac{e \,x^{12}}{12 b^{2}}+\frac{a^{2} f \,x^{9}}{3 b^{4}}-\frac{2 a e \,x^{9}}{9 b^{3}}+\frac{d \,x^{9}}{9 b^{2}}-\frac{2 a^{3} f \,x^{6}}{3 b^{5}}+\frac{a^{2} e \,x^{6}}{2 b^{4}}-\frac{a d \,x^{6}}{3 b^{3}}+\frac{c \,x^{6}}{6 b^{2}}+\frac{5 a^{4} f \,x^{3}}{3 b^{6}}-\frac{4 a^{3} e \,x^{3}}{3 b^{5}}+\frac{a^{2} d \,x^{3}}{b^{4}}-\frac{2 a c \,x^{3}}{3 b^{3}}-\frac{a^{6} f}{3 \left(b \,x^{3}+a \right) b^{7}}+\frac{a^{5} e}{3 \left(b \,x^{3}+a \right) b^{6}}-\frac{2 a^{5} f \ln \left(b \,x^{3}+a \right)}{b^{7}}-\frac{a^{4} d}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{5 a^{4} e \ln \left(b \,x^{3}+a \right)}{3 b^{6}}+\frac{a^{3} c}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{4 a^{3} d \ln \left(b \,x^{3}+a \right)}{3 b^{5}}+\frac{a^{2} c \ln \left(b \,x^{3}+a \right)}{b^{4}}"," ",0,"1/15*f*x^15/b^2-1/6/b^3*x^12*a*f+1/12/b^2*x^12*e+1/3/b^4*x^9*a^2*f-2/9/b^3*x^9*a*e+1/9/b^2*x^9*d-2/3/b^5*x^6*a^3*f+1/2/b^4*x^6*a^2*e-1/3/b^3*x^6*a*d+1/6/b^2*x^6*c+5/3/b^6*x^3*a^4*f-4/3/b^5*x^3*a^3*e+1/b^4*x^3*a^2*d-2/3/b^3*x^3*a*c-2*a^5/b^7*ln(b*x^3+a)*f+5/3*a^4/b^6*ln(b*x^3+a)*e-4/3*a^3/b^5*ln(b*x^3+a)*d+a^2/b^4*ln(b*x^3+a)*c-1/3*a^6/b^7/(b*x^3+a)*f+1/3*a^5/b^6/(b*x^3+a)*e-1/3*a^4/b^5/(b*x^3+a)*d+1/3*a^3/b^4/(b*x^3+a)*c","A"
252,1,240,168,0.059000," ","int(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{12}}{12 b^{2}}-\frac{2 a f \,x^{9}}{9 b^{3}}+\frac{e \,x^{9}}{9 b^{2}}+\frac{a^{2} f \,x^{6}}{2 b^{4}}-\frac{a e \,x^{6}}{3 b^{3}}+\frac{d \,x^{6}}{6 b^{2}}-\frac{4 a^{3} f \,x^{3}}{3 b^{5}}+\frac{a^{2} e \,x^{3}}{b^{4}}-\frac{2 a d \,x^{3}}{3 b^{3}}+\frac{c \,x^{3}}{3 b^{2}}+\frac{a^{5} f}{3 \left(b \,x^{3}+a \right) b^{6}}-\frac{a^{4} e}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{5 a^{4} f \ln \left(b \,x^{3}+a \right)}{3 b^{6}}+\frac{a^{3} d}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{4 a^{3} e \ln \left(b \,x^{3}+a \right)}{3 b^{5}}-\frac{a^{2} c}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a^{2} d \ln \left(b \,x^{3}+a \right)}{b^{4}}-\frac{2 a c \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/12*f*x^12/b^2-2/9/b^3*x^9*a*f+1/9/b^2*x^9*e+1/2/b^4*x^6*a^2*f-1/3/b^3*x^6*a*e+1/6/b^2*x^6*d-4/3*a^3/b^5*f*x^3+a^2/b^4*e*x^3-2/3*a/b^3*d*x^3+1/3/b^2*c*x^3+5/3*a^4/b^6*ln(b*x^3+a)*f-4/3*a^3/b^5*ln(b*x^3+a)*e+a^2/b^4*ln(b*x^3+a)*d-2/3*a/b^3*ln(b*x^3+a)*c+1/3*a^5/b^6/(b*x^3+a)*f-1/3*a^4/b^5/(b*x^3+a)*e+1/3*a^3/b^4/(b*x^3+a)*d-1/3*a^2/b^3/(b*x^3+a)*c","A"
253,1,192,130,0.056000," ","int(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{9}}{9 b^{2}}-\frac{a f \,x^{6}}{3 b^{3}}+\frac{e \,x^{6}}{6 b^{2}}+\frac{a^{2} f \,x^{3}}{b^{4}}-\frac{2 a e \,x^{3}}{3 b^{3}}+\frac{d \,x^{3}}{3 b^{2}}-\frac{a^{4} f}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{a^{3} e}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{4 a^{3} f \ln \left(b \,x^{3}+a \right)}{3 b^{5}}-\frac{a^{2} d}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a^{2} e \ln \left(b \,x^{3}+a \right)}{b^{4}}+\frac{a c}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{2 a d \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{c \ln \left(b \,x^{3}+a \right)}{3 b^{2}}"," ",0,"1/9/b^2*f*x^9-1/3/b^3*x^6*a*f+1/6/b^2*x^6*e+1/b^4*x^3*a^2*f-2/3/b^3*x^3*a*e+1/3/b^2*x^3*d-4/3/b^5*ln(b*x^3+a)*a^3*f+1/b^4*ln(b*x^3+a)*a^2*e-2/3/b^3*ln(b*x^3+a)*a*d+1/3/b^2*ln(b*x^3+a)*c-1/3/b^5*a^4/(b*x^3+a)*f+1/3/b^4*a^3/(b*x^3+a)*e-1/3/b^3*a^2/(b*x^3+a)*d+1/3/b^2*a/(b*x^3+a)*c","A"
254,1,142,95,0.066000," ","int(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{6}}{6 b^{2}}-\frac{2 a f \,x^{3}}{3 b^{3}}+\frac{e \,x^{3}}{3 b^{2}}+\frac{a^{3} f}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{a^{2} e}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a^{2} f \ln \left(b \,x^{3}+a \right)}{b^{4}}+\frac{a d}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{2 a e \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{c}{3 \left(b \,x^{3}+a \right) b}+\frac{d \ln \left(b \,x^{3}+a \right)}{3 b^{2}}"," ",0,"1/6*f*x^6/b^2-2/3/b^3*x^3*a*f+1/3/b^2*x^3*e+1/b^4*ln(b*x^3+a)*a^2*f-2/3/b^3*ln(b*x^3+a)*a*e+1/3/b^2*ln(b*x^3+a)*d+1/3/b^4/(b*x^3+a)*a^3*f-1/3/b^3/(b*x^3+a)*a^2*e+1/3/b^2/(b*x^3+a)*a*d-1/3/b/(b*x^3+a)*c","A"
255,1,125,94,0.062000," ","int((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a)^2,x)","\frac{f \,x^{3}}{3 b^{2}}-\frac{a^{2} f}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a e}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{2 a f \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{c}{3 \left(b \,x^{3}+a \right) a}+\frac{c \ln \left(x \right)}{a^{2}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{d}{3 \left(b \,x^{3}+a \right) b}+\frac{e \ln \left(b \,x^{3}+a \right)}{3 b^{2}}"," ",0,"1/3/b^2*f*x^3-2/3*a/b^3*ln(b*x^3+a)*f+1/3/b^2*ln(b*x^3+a)*e-1/3*c*ln(b*x^3+a)/a^2-1/3*a^2/b^3/(b*x^3+a)*f+1/3*a/b^2/(b*x^3+a)*e-1/3/b/(b*x^3+a)*d+1/3/a/(b*x^3+a)*c+1/a^2*c*ln(x)","A"
256,1,132,103,0.059000," ","int((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a)^2,x)","\frac{a f}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{d}{3 \left(b \,x^{3}+a \right) a}-\frac{b c}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{d \ln \left(x \right)}{a^{2}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{2 b c \ln \left(x \right)}{a^{3}}+\frac{2 b c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{e}{3 \left(b \,x^{3}+a \right) b}+\frac{f \ln \left(b \,x^{3}+a \right)}{3 b^{2}}-\frac{c}{3 a^{2} x^{3}}"," ",0,"1/3*f*ln(b*x^3+a)/b^2-1/3*d*ln(b*x^3+a)/a^2+2/3*b*c*ln(b*x^3+a)/a^3+1/3*a/b^2/(b*x^3+a)*f-1/3/b/(b*x^3+a)*e+1/3/a/(b*x^3+a)*d-1/3/a^2*b/(b*x^3+a)*c-1/3/a^2*c/x^3+d*ln(x)/a^2-2*b*c*ln(x)/a^3","A"
257,1,167,122,0.066000," ","int((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a)^2,x)","\frac{e}{3 \left(b \,x^{3}+a \right) a}-\frac{b d}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{e \ln \left(x \right)}{a^{2}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{b^{2} c}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{2 b d \ln \left(x \right)}{a^{3}}+\frac{2 b d \ln \left(b \,x^{3}+a \right)}{3 a^{3}}+\frac{3 b^{2} c \ln \left(x \right)}{a^{4}}-\frac{b^{2} c \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{f}{3 \left(b \,x^{3}+a \right) b}-\frac{d}{3 a^{2} x^{3}}+\frac{2 b c}{3 a^{3} x^{3}}-\frac{c}{6 a^{2} x^{6}}"," ",0,"-1/3*e*ln(b*x^3+a)/a^2+2/3/a^3*ln(b*x^3+a)*b*d-1/a^4*ln(b*x^3+a)*b^2*c-1/3/b/(b*x^3+a)*f+1/3/a/(b*x^3+a)*e-1/3/a^2*b/(b*x^3+a)*d+1/3/a^3*b^2/(b*x^3+a)*c-1/6*c/a^2/x^6-1/3/a^2/x^3*d+2/3/a^3/x^3*b*c+e*ln(x)/a^2-2/a^3*ln(x)*b*d+3/a^4*ln(x)*b^2*c","A"
258,1,229,166,0.063000," ","int((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a)^2,x)","\frac{f}{3 \left(b \,x^{3}+a \right) a}-\frac{b e}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{f \ln \left(x \right)}{a^{2}}-\frac{f \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{b^{2} d}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{2 b e \ln \left(x \right)}{a^{3}}+\frac{2 b e \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{b^{3} c}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{3 b^{2} d \ln \left(x \right)}{a^{4}}-\frac{b^{2} d \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{4 b^{3} c \ln \left(x \right)}{a^{5}}+\frac{4 b^{3} c \ln \left(b \,x^{3}+a \right)}{3 a^{5}}-\frac{e}{3 a^{2} x^{3}}+\frac{2 b d}{3 a^{3} x^{3}}-\frac{b^{2} c}{a^{4} x^{3}}-\frac{d}{6 a^{2} x^{6}}+\frac{b c}{3 a^{3} x^{6}}-\frac{c}{9 a^{2} x^{9}}"," ",0,"-1/3/a^2*ln(b*x^3+a)*f+2/3*b/a^3*ln(b*x^3+a)*e-b^2/a^4*ln(b*x^3+a)*d+4/3*b^3/a^5*ln(b*x^3+a)*c+1/3/a/(b*x^3+a)*f-1/3*b/a^2/(b*x^3+a)*e+1/3*b^2/a^3/(b*x^3+a)*d-1/3*b^3/a^4/(b*x^3+a)*c-1/9/a^2*c/x^9-1/6/a^2/x^6*d+1/3/a^3/x^6*b*c-1/3/a^2/x^3*e+2/3/a^3/x^3*b*d-1/a^4/x^3*b^2*c+1/a^2*ln(x)*f-2/a^3*ln(x)*b*e+3/a^4*ln(x)*b^2*d-4/a^5*ln(x)*b^3*c","A"
259,1,282,203,0.069000," ","int((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a)^2,x)","-\frac{b f}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} e}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{2 b f \ln \left(x \right)}{a^{3}}+\frac{2 b f \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{b^{3} d}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{3 b^{2} e \ln \left(x \right)}{a^{4}}-\frac{b^{2} e \ln \left(b \,x^{3}+a \right)}{a^{4}}+\frac{b^{4} c}{3 \left(b \,x^{3}+a \right) a^{5}}-\frac{4 b^{3} d \ln \left(x \right)}{a^{5}}+\frac{4 b^{3} d \ln \left(b \,x^{3}+a \right)}{3 a^{5}}+\frac{5 b^{4} c \ln \left(x \right)}{a^{6}}-\frac{5 b^{4} c \ln \left(b \,x^{3}+a \right)}{3 a^{6}}-\frac{f}{3 a^{2} x^{3}}+\frac{2 b e}{3 a^{3} x^{3}}-\frac{b^{2} d}{a^{4} x^{3}}+\frac{4 b^{3} c}{3 a^{5} x^{3}}-\frac{e}{6 a^{2} x^{6}}+\frac{b d}{3 a^{3} x^{6}}-\frac{b^{2} c}{2 a^{4} x^{6}}-\frac{d}{9 a^{2} x^{9}}+\frac{2 b c}{9 a^{3} x^{9}}-\frac{c}{12 a^{2} x^{12}}"," ",0,"2/3/a^3*b*ln(b*x^3+a)*f-1/a^4*b^2*ln(b*x^3+a)*e+4/3/a^5*b^3*ln(b*x^3+a)*d-5/3/a^6*b^4*ln(b*x^3+a)*c-1/3/a^2*b/(b*x^3+a)*f+1/3/a^3*b^2/(b*x^3+a)*e-1/3/a^4*b^3/(b*x^3+a)*d+1/3/a^5*b^4/(b*x^3+a)*c-1/12*c/a^2/x^12-1/9/a^2/x^9*d+2/9/a^3/x^9*b*c-1/6/a^2/x^6*e+1/3/a^3/x^6*b*d-1/2/a^4/x^6*b^2*c-1/3/a^2/x^3*f+2/3/a^3/x^3*b*e-1/a^4/x^3*b^2*d+4/3/a^5/x^3*b^3*c-2*b/a^3*ln(x)*f+3*b^2/a^4*ln(x)*e-4*b^3/a^5*ln(x)*d+5*b^4/a^6*ln(x)*c","A"
260,1,622,320,0.053000," ","int(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{13}}{13 b^{2}}-\frac{a f \,x^{10}}{5 b^{3}}+\frac{e \,x^{10}}{10 b^{2}}+\frac{3 a^{2} f \,x^{7}}{7 b^{4}}-\frac{2 a e \,x^{7}}{7 b^{3}}+\frac{d \,x^{7}}{7 b^{2}}-\frac{a^{3} f \,x^{4}}{b^{5}}+\frac{3 a^{2} e \,x^{4}}{4 b^{4}}-\frac{a d \,x^{4}}{2 b^{3}}+\frac{c \,x^{4}}{4 b^{2}}+\frac{a^{5} f x}{3 \left(b \,x^{3}+a \right) b^{6}}-\frac{a^{4} e x}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{a^{3} d x}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{a^{2} c x}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{16 \sqrt{3}\, a^{5} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}-\frac{16 a^{5} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}+\frac{8 a^{5} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}+\frac{13 \sqrt{3}\, a^{4} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{13 a^{4} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{13 a^{4} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{5 a^{4} f x}{b^{6}}-\frac{10 \sqrt{3}\, a^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{10 a^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{5 a^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{4 a^{3} e x}{b^{5}}+\frac{7 \sqrt{3}\, a^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 a^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{3 a^{2} d x}{b^{4}}-\frac{2 a c x}{b^{3}}"," ",0,"-10/9*a^3/b^5*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+7/9*a^2/b^4*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-16/9*a^5/b^7*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+13/9*a^4/b^6*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+3/7/b^4*x^7*a^2*f-1/5/b^3*x^10*a*f-1/2/b^3*x^4*a*d+3/4/b^4*x^4*a^2*e-2/7/b^3*x^7*a*e-1/b^5*x^4*a^3*f+5*a^4/b^6*f*x-4*a^3/b^5*e*x+3*a^2/b^4*d*x-2*a/b^3*c*x-16/9*a^5/b^7*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+8/9*a^5/b^7*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+13/9*a^4/b^6*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-13/18*a^4/b^6*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-10/9*a^3/b^5*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/18*a^2/b^4*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/10/b^2*x^10*e+1/7/b^2*x^7*d+1/4/b^2*x^4*c+7/9*a^2/b^4*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/3*a^3/b^4*x/(b*x^3+a)*d-1/3*a^2/b^3*x/(b*x^3+a)*c+1/3*a^5/b^6*x/(b*x^3+a)*f-1/3*a^4/b^5*x/(b*x^3+a)*e+5/9*a^3/b^5*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/13*f*x^13/b^2","A"
261,1,584,286,0.054000," ","int(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{11}}{11 b^{2}}-\frac{a f \,x^{8}}{4 b^{3}}+\frac{e \,x^{8}}{8 b^{2}}+\frac{3 a^{2} f \,x^{5}}{5 b^{4}}-\frac{2 a e \,x^{5}}{5 b^{3}}+\frac{d \,x^{5}}{5 b^{2}}-\frac{a^{4} f \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{a^{3} e \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{a^{2} d \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a c \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{2 a^{3} f \,x^{2}}{b^{5}}+\frac{3 a^{2} e \,x^{2}}{2 b^{4}}-\frac{a d \,x^{2}}{b^{3}}+\frac{c \,x^{2}}{2 b^{2}}+\frac{14 \sqrt{3}\, a^{4} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}-\frac{14 a^{4} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{7 a^{4} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}-\frac{11 \sqrt{3}\, a^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{11 a^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{11 a^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{8 \sqrt{3}\, a^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{8 a^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{4 a^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{5 \sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"1/3*a^3/b^4*x^2/(b*x^3+a)*e-1/3*a^2/b^3*x^2/(b*x^3+a)*d+1/3*a/b^2*x^2/(b*x^3+a)*c+4/9*a^2/b^4*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/9*a^4/b^6*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-5/9*a/b^3*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-11/9*a^3/b^5*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+8/9*a^2/b^4*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/4/b^3*x^8*a*f+3/2/b^4*x^2*a^2*e-1/b^3*x^2*a*d-2/b^5*x^2*a^3*f+3/5*a^2/b^4*f*x^5-2/5*a/b^3*e*x^5+1/5/b^2*d*x^5-8/9*a^2/b^4*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-14/9*a^4/b^6*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/9*a^4/b^6*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+11/9*a^3/b^5*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-11/18*a^3/b^5*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*a^4/b^5*x^2/(b*x^3+a)*f+1/2/b^2*x^2*c+5/9*a/b^3*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18*a/b^3*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/8/b^2*x^8*e+1/11*f*x^11/b^2","B"
262,1,567,281,0.055000," ","int(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{10}}{10 b^{2}}-\frac{2 a f \,x^{7}}{7 b^{3}}+\frac{e \,x^{7}}{7 b^{2}}+\frac{3 a^{2} f \,x^{4}}{4 b^{4}}-\frac{a e \,x^{4}}{2 b^{3}}+\frac{d \,x^{4}}{4 b^{2}}-\frac{a^{4} f x}{3 \left(b \,x^{3}+a \right) b^{5}}+\frac{a^{3} e x}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{a^{2} d x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a c x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{13 \sqrt{3}\, a^{4} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{13 a^{4} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{13 a^{4} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{10 \sqrt{3}\, a^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{10 a^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{5 a^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{4 a^{3} f x}{b^{5}}+\frac{7 \sqrt{3}\, a^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 a^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{3 a^{2} e x}{b^{4}}-\frac{4 \sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{2 a d x}{b^{3}}+\frac{c x}{b^{2}}"," ",0,"-4/9*a/b^3*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+13/9*a^4/b^6*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-10/9*a^3/b^5*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+7/9*a^2/b^4*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2/b^3*x^4*a*e-4/b^5*a^3*f*x+3/b^4*a^2*e*x-2/b^3*a*d*x+3/4/b^4*x^4*a^2*f-2/7*a/b^3*f*x^7+2/9*a/b^3*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9*a/b^3*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/7/b^2*e*x^7-1/3*a^4/b^5*x/(b*x^3+a)*f+1/3*a^3/b^4*x/(b*x^3+a)*e-1/3*a^2/b^3*x/(b*x^3+a)*d-13/18*a^4/b^6*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*a/b^2*x/(b*x^3+a)*c+13/9*a^4/b^6*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/4/b^2*x^4*d+1/b^2*c*x-10/9*a^3/b^5*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/9*a^3/b^5*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/9*a^2/b^4*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/18*a^2/b^4*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/10*f*x^10/b^2","B"
263,1,529,251,0.058000," ","int(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{8}}{8 b^{2}}-\frac{2 a f \,x^{5}}{5 b^{3}}+\frac{e \,x^{5}}{5 b^{2}}+\frac{a^{3} f \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{a^{2} e \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a d \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{c \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{3 a^{2} f \,x^{2}}{2 b^{4}}-\frac{a e \,x^{2}}{b^{3}}+\frac{d \,x^{2}}{2 b^{2}}-\frac{11 \sqrt{3}\, a^{3} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{11 a^{3} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{11 a^{3} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{8 \sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{8 a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{4 a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{5 \sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}"," ",0,"1/8*f*x^8/b^2-2/5/b^3*x^5*a*f+1/5/b^2*x^5*e+3/2/b^4*x^2*a^2*f-1/b^3*x^2*a*e+1/2/b^2*x^2*d+1/3/b^4*x^2/(b*x^3+a)*a^3*f-1/3/b^3*x^2/(b*x^3+a)*a^2*e+1/3/b^2*x^2/(b*x^3+a)*a*d-1/3/b*x^2/(b*x^3+a)*c+11/9/b^5*a^3*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-11/18/b^5*a^3*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-11/9/b^5*a^3*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-8/9/b^4*a^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+4/9/b^4*a^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+8/9/b^4*a^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+5/9/b^3*a*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18/b^3*a*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/b^3*a*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","B"
264,1,514,243,0.053000," ","int(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{7}}{7 b^{2}}-\frac{a f \,x^{4}}{2 b^{3}}+\frac{e \,x^{4}}{4 b^{2}}+\frac{a^{3} f x}{3 \left(b \,x^{3}+a \right) b^{4}}-\frac{a^{2} e x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a d x}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{c x}{3 \left(b \,x^{3}+a \right) b}-\frac{10 \sqrt{3}\, a^{3} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{10 a^{3} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{5 a^{3} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{7 \sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{3 a^{2} f x}{b^{4}}-\frac{4 \sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{2 a e x}{b^{3}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{d x}{b^{2}}"," ",0,"1/7/b^2*f*x^7-1/2/b^3*x^4*a*f+1/4/b^2*x^4*e+3/b^4*a^2*f*x-2/b^3*a*e*x+1/b^2*d*x+1/3/b^4*x/(b*x^3+a)*a^3*f-1/3/b^3*x/(b*x^3+a)*a^2*e+1/3/b^2*x/(b*x^3+a)*a*d-1/3/b*x/(b*x^3+a)*c-10/9/b^5*a^3*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/9/b^5*a^3*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-10/9/b^5*a^3*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+7/9/b^4*a^2*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/18/b^4*a^2*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/9/b^4*a^2*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-4/9/b^3*a*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+2/9/b^3*a*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/b^3*a*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/b^2*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","B"
265,1,495,226,0.054000," ","int(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{5}}{5 b^{2}}-\frac{a^{2} f \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a e \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{c \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{d \,x^{2}}{3 \left(b \,x^{3}+a \right) b}-\frac{a f \,x^{2}}{b^{3}}+\frac{e \,x^{2}}{2 b^{2}}+\frac{8 \sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{8 a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{4 a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{5 \sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}"," ",0,"1/5/b^2*f*x^5-1/b^3*x^2*a*f+1/2/b^2*x^2*e-1/3/b^3*a^2*x^2/(b*x^3+a)*f+1/3/b^2*a*x^2/(b*x^3+a)*e-1/3/b*x^2/(b*x^3+a)*d+1/3/a*x^2/(b*x^3+a)*c-8/9/b^4*a^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+5/9/b^3*a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-2/9/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-1/9/b/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+4/9/b^4*a^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-5/18/b^3*a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/9/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/18/b/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+8/9/b^4*a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-5/9/b^3*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+2/9/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/9/b/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
266,1,482,221,0.055000," ","int((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^2,x)","\frac{f \,x^{4}}{4 b^{2}}-\frac{a^{2} f x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a e x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{c x}{3 \left(b \,x^{3}+a \right) a}-\frac{d x}{3 \left(b \,x^{3}+a \right) b}+\frac{7 \sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{4 \sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{2 a f x}{b^{3}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{e x}{b^{2}}"," ",0,"1/4*f*x^4/b^2-2/b^3*a*f*x+1/b^2*e*x-1/3/b^3*a^2*x/(b*x^3+a)*f+1/3/b^2*a*x/(b*x^3+a)*e-1/3/b*x/(b*x^3+a)*d+1/3/a*x/(b*x^3+a)*c+7/9/b^4*a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-4/9/b^3*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-7/18/b^4*a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+2/9/b^3*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+7/9/b^4*a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-4/9/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
267,1,474,222,0.058000," ","int((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a)^2,x)","\frac{a f \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{d \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{b c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{e \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{f \,x^{2}}{2 b^{2}}-\frac{5 \sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{4 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{c}{a^{2} x}"," ",0,"1/2*f*x^2/b^2+1/3*a/b^2*x^2/(b*x^3+a)*f-1/3/b*x^2/(b*x^3+a)*e+1/3/a*x^2/(b*x^3+a)*d-1/3/a^2*b*x^2/(b*x^3+a)*c+5/9*a/b^3*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18*a/b^3*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9*a/b^3*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/a/b*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18/a/b*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/a/b*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/a^2*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-2/9/a^2*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/a^2*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/a^2*c/x","B"
268,1,463,217,0.061000," ","int((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a)^2,x)","\frac{a f x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{d x}{3 \left(b \,x^{3}+a \right) a}-\frac{b c x}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{e x}{3 \left(b \,x^{3}+a \right) b}-\frac{4 \sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{f x}{b^{2}}-\frac{c}{2 a^{2} x^{2}}"," ",0,"1/b^2*f*x+1/3*a/b^2*x/(b*x^3+a)*f-1/3/b*x/(b*x^3+a)*e+1/3/a*x/(b*x^3+a)*d-1/3/a^2*b*x/(b*x^3+a)*c-4/9*a/b^3*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+2/9*a/b^3*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9*a/b^3*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/a/b*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/9/a/b*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a/b*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-5/9/a^2*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/18/a^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/a^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/b^2*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2/a^2*c/x^2","B"
269,1,486,226,0.066000," ","int((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a)^2,x)","\frac{e \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{b d \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{f \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{4 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{7 \sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{7 b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{d}{a^{2} x}+\frac{2 b c}{a^{3} x}-\frac{c}{4 a^{2} x^{4}}"," ",0,"-1/3/b*x^2/(b*x^3+a)*f+1/3/a*x^2/(b*x^3+a)*e-1/3/a^2*b*x^2/(b*x^3+a)*d+1/3/a^3*b^2*x^2/(b*x^3+a)*c-2/9/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-1/9/a/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+4/9/a^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-7/9/a^3*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/9/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/18/a/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-2/9/a^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+7/18/a^3*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+2/9/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/9/a/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-4/9/a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+7/9/a^3*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/4*c/a^2/x^4-d/a^2/x+2/a^3/x*b*c","B"
270,1,477,225,0.055000," ","int((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a)^2,x)","\frac{e x}{3 \left(b \,x^{3}+a \right) a}-\frac{b d x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} c x}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{f x}{3 \left(b \,x^{3}+a \right) b}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{8 \sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{8 b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{4 b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{d}{2 a^{2} x^{2}}+\frac{b c}{a^{3} x^{2}}-\frac{c}{5 a^{2} x^{5}}"," ",0,"-1/3/b*x/(b*x^3+a)*f+1/3/a*x/(b*x^3+a)*e-1/3/a^2*b*x/(b*x^3+a)*d+1/3/a^3*b^2*x/(b*x^3+a)*c+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+2/9/a/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e-5/9/a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+8/9/a^3*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/9/a/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+5/18/a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-4/9/a^3*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+2/9/a/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-5/9/a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+8/9/a^3*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/5/a^2*c/x^5-1/2*d/a^2/x^2+1/a^3/x^2*b*c","B"
271,1,529,252,0.069000," ","int((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a)^2,x)","\frac{f \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{b e \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} d \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{b^{3} c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{4 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{7 \sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{7 b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{10 \sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{10 b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{5 b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{e}{a^{2} x}+\frac{2 b d}{a^{3} x}-\frac{3 b^{2} c}{a^{4} x}-\frac{d}{4 a^{2} x^{4}}+\frac{b c}{2 a^{3} x^{4}}-\frac{c}{7 a^{2} x^{7}}"," ",0,"1/3/a*x^2/(b*x^3+a)*f-1/3/a^2*x^2/(b*x^3+a)*b*e+1/3/a^3*x^2/(b*x^3+a)*b^2*d-1/3/a^4*x^2/(b*x^3+a)*b^3*c+4/9/a^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-2/9/a^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/a^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-7/9/a^3*b*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/18/a^3*b*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/9/a^3*b*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+10/9/a^4*b^2*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/9/a^4*b^2*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-10/9/a^4*b^2*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/a*f/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18/a*f/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/a*f*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/7/a^2*c/x^7-1/4/a^2/x^4*d+1/2/a^3/x^4*b*c-e/a^2/x+2/a^3/x*b*d-3/a^4/x*b^2*c","B"
272,1,520,251,0.063000," ","int((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a)^2,x)","\frac{f x}{3 \left(b \,x^{3}+a \right) a}-\frac{b e x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} d x}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{b^{3} c x}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{5 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{8 \sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{8 b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{4 b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{11 \sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{11 b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{11 b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{e}{2 a^{2} x^{2}}+\frac{b d}{a^{3} x^{2}}-\frac{3 b^{2} c}{2 a^{4} x^{2}}-\frac{d}{5 a^{2} x^{5}}+\frac{2 b c}{5 a^{3} x^{5}}-\frac{c}{8 a^{2} x^{8}}"," ",0,"1/3/a*x/(b*x^3+a)*f-1/3/a^2*x/(b*x^3+a)*b*e+1/3/a^3*x/(b*x^3+a)*b^2*d-1/3/a^4*x/(b*x^3+a)*b^3*c-5/9/a^2*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/18/a^2*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/a^2*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+8/9/a^3*b*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-4/9/a^3*b*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+8/9/a^3*b*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-11/9/a^4*b^2*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+11/18/a^4*b^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-11/9/a^4*b^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/a*f/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/9/a*f/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a*f/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/8*c/a^2/x^8-1/5/a^2/x^5*d+2/5/a^3/x^5*b*c-1/2/a^2/x^2*e+1/a^3/x^2*b*d-3/2/a^4/x^2*b^2*c","B"
273,1,575,288,0.063000," ","int((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a)^2,x)","-\frac{b f \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} e \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{b^{3} d \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{b^{4} c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{5}}-\frac{4 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{7 \sqrt{3}\, b e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 b e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{7 b e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{10 \sqrt{3}\, b^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{10 b^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{5 b^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{13 \sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{13 b^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{13 b^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{f}{a^{2} x}+\frac{2 b e}{a^{3} x}-\frac{3 b^{2} d}{a^{4} x}+\frac{4 b^{3} c}{a^{5} x}-\frac{e}{4 a^{2} x^{4}}+\frac{b d}{2 a^{3} x^{4}}-\frac{3 b^{2} c}{4 a^{4} x^{4}}-\frac{d}{7 a^{2} x^{7}}+\frac{2 b c}{7 a^{3} x^{7}}-\frac{c}{10 a^{2} x^{10}}"," ",0,"4/a^5/x*b^3*c+4/9/a^2*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-2/9/a^2*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/7/a^3/x^7*b*c+1/2/a^3/x^4*b*d-3/4/a^4/x^4*b^2*c+2/a^3/x*b*e-3/a^4/x*b^2*d-1/3*b/a^2*x^2/(b*x^3+a)*f+1/3*b^2/a^3*x^2/(b*x^3+a)*e-10/9*b^2/a^4*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+13/9*b^3/a^5*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+7/9*b/a^3*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/a^2/x*f-1/4/a^2/x^4*e-1/7/a^2/x^7*d-1/10*c/a^2/x^10-1/3*b^3/a^4*x^2/(b*x^3+a)*d+1/3*b^4/a^5*x^2/(b*x^3+a)*c-4/9/a^2*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-7/9*b/a^3*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/18*b/a^3*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+10/9*b^2/a^4*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/9*b^2/a^4*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-13/9*b^3/a^5*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+13/18*b^3/a^5*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))","A"
274,1,566,287,0.058000," ","int((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a)^2,x)","-\frac{b f x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{b^{2} e x}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{b^{3} d x}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{b^{4} c x}{3 \left(b \,x^{3}+a \right) a^{5}}-\frac{5 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{8 \sqrt{3}\, b e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{8 b e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{4 b e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{11 \sqrt{3}\, b^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{11 b^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{11 b^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{14 \sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}+\frac{14 b^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}-\frac{7 b^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}-\frac{f}{2 a^{2} x^{2}}+\frac{b e}{a^{3} x^{2}}-\frac{3 b^{2} d}{2 a^{4} x^{2}}+\frac{2 b^{3} c}{a^{5} x^{2}}-\frac{e}{5 a^{2} x^{5}}+\frac{2 b d}{5 a^{3} x^{5}}-\frac{3 b^{2} c}{5 a^{4} x^{5}}-\frac{d}{8 a^{2} x^{8}}+\frac{b c}{4 a^{3} x^{8}}-\frac{c}{11 a^{2} x^{11}}"," ",0,"5/18/a^2*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/a^3/x^2*b*e-3/2/a^4/x^2*b^2*d+2/a^5/x^2*b^3*c+1/4/a^3/x^8*b*c+2/5/a^3/x^5*b*d-3/5/a^4/x^5*b^2*c-5/9/a^2*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/3*b/a^2*x/(b*x^3+a)*f+1/3*b^2/a^3*x/(b*x^3+a)*e-1/3*b^3/a^4*x/(b*x^3+a)*d+11/18*b^2/a^4*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/9*b^3/a^5*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/9*b^3/a^5*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*b^4/a^5*x/(b*x^3+a)*c-1/5/a^2/x^5*e-1/2/a^2/x^2*f-1/8/a^2/x^8*d-5/9/a^2*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+8/9*b/a^3*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-4/9*b/a^3*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-11/9*b^2/a^4*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+8/9*b/a^3*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-11/9*b^2/a^4*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+14/9*b^3/a^5*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/11*c/a^2/x^11","A"
275,1,631,327,0.063000," ","int((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a)^2,x)","\frac{b^{2} f \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{3}}-\frac{b^{3} e \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{4}}+\frac{b^{4} d \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{5}}-\frac{b^{5} c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{6}}+\frac{7 \sqrt{3}\, b f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 b f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{7 b f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{10 \sqrt{3}\, b^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{10 b^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{5 b^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{13 \sqrt{3}\, b^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{13 b^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{13 b^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{16 \sqrt{3}\, b^{4} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}+\frac{16 b^{4} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{8 b^{4} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}+\frac{2 b f}{a^{3} x}-\frac{3 b^{2} e}{a^{4} x}+\frac{4 b^{3} d}{a^{5} x}-\frac{5 b^{4} c}{a^{6} x}-\frac{f}{4 a^{2} x^{4}}+\frac{b e}{2 a^{3} x^{4}}-\frac{3 b^{2} d}{4 a^{4} x^{4}}+\frac{b^{3} c}{a^{5} x^{4}}-\frac{e}{7 a^{2} x^{7}}+\frac{2 b d}{7 a^{3} x^{7}}-\frac{3 b^{2} c}{7 a^{4} x^{7}}-\frac{d}{10 a^{2} x^{10}}+\frac{b c}{5 a^{3} x^{10}}-\frac{c}{13 a^{2} x^{13}}"," ",0,"-3/4/a^4/x^4*b^2*d+1/a^5/x^4*b^3*c+2*b/a^3/x*f-3*b^2/a^4/x*e+4*b^3/a^5/x*d-5*b^4/a^6/x*c+1/5/a^3/x^10*b*c+2/7/a^3/x^7*b*d-3/7/a^4/x^7*b^2*c+1/2/a^3/x^4*b*e-1/10/a^2/x^10*d+1/3*b^2/a^3*x^2/(b*x^3+a)*f-1/3*b^3/a^4*x^2/(b*x^3+a)*e+7/9*b/a^3*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-10/9*b^2/a^4*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+13/9*b^3/a^5*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-16/9*b^4/a^6*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/7/a^2/x^7*e-1/4/a^2/x^4*f+1/3*b^4/a^5*x^2/(b*x^3+a)*d-1/3*b^5/a^6*x^2/(b*x^3+a)*c+10/9*b^2/a^4*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/9*b^2/a^4*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-13/9*b^3/a^5*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+13/18*b^3/a^5*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+16/9*b^4/a^6*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-8/9*b^4/a^6*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-7/9*b/a^3*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/18*b/a^3*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/13*c/a^2/x^13","A"
276,1,361,250,0.061000," ","int(x^14*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{15}}{15 b^{3}}-\frac{a f \,x^{12}}{4 b^{4}}+\frac{e \,x^{12}}{12 b^{3}}+\frac{2 a^{2} f \,x^{9}}{3 b^{5}}-\frac{a e \,x^{9}}{3 b^{4}}+\frac{d \,x^{9}}{9 b^{3}}-\frac{5 a^{3} f \,x^{6}}{3 b^{6}}+\frac{a^{2} e \,x^{6}}{b^{5}}-\frac{a d \,x^{6}}{2 b^{4}}+\frac{c \,x^{6}}{6 b^{3}}+\frac{5 a^{4} f \,x^{3}}{b^{7}}-\frac{10 a^{3} e \,x^{3}}{3 b^{6}}+\frac{2 a^{2} d \,x^{3}}{b^{5}}-\frac{a c \,x^{3}}{b^{4}}+\frac{a^{7} f}{6 \left(b \,x^{3}+a \right)^{2} b^{8}}-\frac{a^{6} e}{6 \left(b \,x^{3}+a \right)^{2} b^{7}}+\frac{a^{5} d}{6 \left(b \,x^{3}+a \right)^{2} b^{6}}-\frac{a^{4} c}{6 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{7 a^{6} f}{3 \left(b \,x^{3}+a \right) b^{8}}+\frac{2 a^{5} e}{\left(b \,x^{3}+a \right) b^{7}}-\frac{7 a^{5} f \ln \left(b \,x^{3}+a \right)}{b^{8}}-\frac{5 a^{4} d}{3 \left(b \,x^{3}+a \right) b^{6}}+\frac{5 a^{4} e \ln \left(b \,x^{3}+a \right)}{b^{7}}+\frac{4 a^{3} c}{3 \left(b \,x^{3}+a \right) b^{5}}-\frac{10 a^{3} d \ln \left(b \,x^{3}+a \right)}{3 b^{6}}+\frac{2 a^{2} c \ln \left(b \,x^{3}+a \right)}{b^{5}}"," ",0,"1/6*a^7/b^8/(b*x^3+a)^2*f-1/6*a^6/b^7/(b*x^3+a)^2*e+1/6*a^5/b^6/(b*x^3+a)^2*d+5/b^7*x^3*a^4*f-10/3/b^6*x^3*a^3*e+2/b^5*x^3*a^2*d-1/b^4*x^3*a*c-1/4/b^4*x^12*a*f+2/3/b^5*x^9*a^2*f-1/3/b^4*x^9*a*e-5/3/b^6*x^6*a^3*f+1/b^5*x^6*a^2*e-1/2/b^4*x^6*a*d+5*a^4/b^7*ln(b*x^3+a)*e-10/3*a^3/b^6*ln(b*x^3+a)*d+2*a^2/b^5*ln(b*x^3+a)*c-1/6*a^4/b^5/(b*x^3+a)^2*c-7/3*a^6/b^8/(b*x^3+a)*f+2*a^5/b^7/(b*x^3+a)*e-5/3*a^4/b^6/(b*x^3+a)*d+4/3*a^3/b^5/(b*x^3+a)*c-7*a^5/b^8*ln(b*x^3+a)*f+1/12/b^3*x^12*e+1/9/b^3*x^9*d+1/6/b^3*x^6*c+1/15*f*x^15/b^3","A"
277,1,313,212,0.061000," ","int(x^11*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{12}}{12 b^{3}}-\frac{a f \,x^{9}}{3 b^{4}}+\frac{e \,x^{9}}{9 b^{3}}+\frac{a^{2} f \,x^{6}}{b^{5}}-\frac{a e \,x^{6}}{2 b^{4}}+\frac{d \,x^{6}}{6 b^{3}}-\frac{10 a^{3} f \,x^{3}}{3 b^{6}}+\frac{2 a^{2} e \,x^{3}}{b^{5}}-\frac{a d \,x^{3}}{b^{4}}+\frac{c \,x^{3}}{3 b^{3}}-\frac{a^{6} f}{6 \left(b \,x^{3}+a \right)^{2} b^{7}}+\frac{a^{5} e}{6 \left(b \,x^{3}+a \right)^{2} b^{6}}-\frac{a^{4} d}{6 \left(b \,x^{3}+a \right)^{2} b^{5}}+\frac{a^{3} c}{6 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{2 a^{5} f}{\left(b \,x^{3}+a \right) b^{7}}-\frac{5 a^{4} e}{3 \left(b \,x^{3}+a \right) b^{6}}+\frac{5 a^{4} f \ln \left(b \,x^{3}+a \right)}{b^{7}}+\frac{4 a^{3} d}{3 \left(b \,x^{3}+a \right) b^{5}}-\frac{10 a^{3} e \ln \left(b \,x^{3}+a \right)}{3 b^{6}}-\frac{a^{2} c}{\left(b \,x^{3}+a \right) b^{4}}+\frac{2 a^{2} d \ln \left(b \,x^{3}+a \right)}{b^{5}}-\frac{a c \ln \left(b \,x^{3}+a \right)}{b^{4}}"," ",0,"1/12*f*x^12/b^3-1/3/b^4*x^9*a*f+1/9/b^3*x^9*e+1/b^5*x^6*a^2*f-1/2/b^4*x^6*a*e+1/6/b^3*x^6*d-10/3/b^6*x^3*a^3*f+2/b^5*x^3*a^2*e-1/b^4*x^3*a*d+1/3/b^3*x^3*c-1/6*a^6/b^7/(b*x^3+a)^2*f+1/6*a^5/b^6/(b*x^3+a)^2*e-1/6*a^4/b^5/(b*x^3+a)^2*d+1/6*a^3/b^4/(b*x^3+a)^2*c+5*a^4/b^7*ln(b*x^3+a)*f-10/3*a^3/b^6*ln(b*x^3+a)*e+2*a^2/b^5*ln(b*x^3+a)*d-a/b^4*ln(b*x^3+a)*c+2*a^5/b^7/(b*x^3+a)*f-5/3*a^4/b^6/(b*x^3+a)*e+4/3*a^3/b^5/(b*x^3+a)*d-a^2/b^4/(b*x^3+a)*c","A"
278,1,266,174,0.058000," ","int(x^8*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{9}}{9 b^{3}}-\frac{a f \,x^{6}}{2 b^{4}}+\frac{e \,x^{6}}{6 b^{3}}+\frac{2 a^{2} f \,x^{3}}{b^{5}}-\frac{a e \,x^{3}}{b^{4}}+\frac{d \,x^{3}}{3 b^{3}}+\frac{a^{5} f}{6 \left(b \,x^{3}+a \right)^{2} b^{6}}-\frac{a^{4} e}{6 \left(b \,x^{3}+a \right)^{2} b^{5}}+\frac{a^{3} d}{6 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{a^{2} c}{6 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{5 a^{4} f}{3 \left(b \,x^{3}+a \right) b^{6}}+\frac{4 a^{3} e}{3 \left(b \,x^{3}+a \right) b^{5}}-\frac{10 a^{3} f \ln \left(b \,x^{3}+a \right)}{3 b^{6}}-\frac{a^{2} d}{\left(b \,x^{3}+a \right) b^{4}}+\frac{2 a^{2} e \ln \left(b \,x^{3}+a \right)}{b^{5}}+\frac{2 a c}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{a d \ln \left(b \,x^{3}+a \right)}{b^{4}}+\frac{c \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/9/b^3*f*x^9-1/2/b^4*x^6*a*f+1/6/b^3*x^6*e+2/b^5*x^3*a^2*f-1/b^4*x^3*a*e+1/3/b^3*x^3*d+1/6/b^6*a^5/(b*x^3+a)^2*f-1/6/b^5*a^4/(b*x^3+a)^2*e+1/6/b^4*a^3/(b*x^3+a)^2*d-1/6/b^3*a^2/(b*x^3+a)^2*c-10/3/b^6*ln(b*x^3+a)*a^3*f+2/b^5*ln(b*x^3+a)*a^2*e-1/b^4*ln(b*x^3+a)*a*d+1/3/b^3*ln(b*x^3+a)*c-5/3/b^6*a^4/(b*x^3+a)*f+4/3/b^5*a^3/(b*x^3+a)*e-1/b^4*a^2/(b*x^3+a)*d+2/3/b^3*a/(b*x^3+a)*c","A"
279,1,213,137,0.072000," ","int(x^5*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{6}}{6 b^{3}}-\frac{a f \,x^{3}}{b^{4}}+\frac{e \,x^{3}}{3 b^{3}}-\frac{a^{4} f}{6 \left(b \,x^{3}+a \right)^{2} b^{5}}+\frac{a^{3} e}{6 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{a^{2} d}{6 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{a c}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{4 a^{3} f}{3 \left(b \,x^{3}+a \right) b^{5}}-\frac{a^{2} e}{\left(b \,x^{3}+a \right) b^{4}}+\frac{2 a^{2} f \ln \left(b \,x^{3}+a \right)}{b^{5}}+\frac{2 a d}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{a e \ln \left(b \,x^{3}+a \right)}{b^{4}}-\frac{c}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{d \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/6*f*x^6/b^3-1/b^4*x^3*a*f+1/3/b^3*x^3*e-1/6/b^5*a^4/(b*x^3+a)^2*f+1/6/b^4*a^3/(b*x^3+a)^2*e-1/6/b^3*a^2/(b*x^3+a)^2*d+1/6/b^2*a/(b*x^3+a)^2*c+2/b^5*ln(b*x^3+a)*a^2*f-1/b^4*ln(b*x^3+a)*a*e+1/3/b^3*ln(b*x^3+a)*d+4/3/b^5/(b*x^3+a)*a^3*f-1/b^4/(b*x^3+a)*a^2*e+2/3/b^3/(b*x^3+a)*a*d-1/3/b^2/(b*x^3+a)*c","A"
280,1,156,102,0.062000," ","int(x^2*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{3}}{3 b^{3}}+\frac{a^{3} f}{6 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{a^{2} e}{6 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{a d}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{c}{6 \left(b \,x^{3}+a \right)^{2} b}-\frac{a^{2} f}{\left(b \,x^{3}+a \right) b^{4}}+\frac{2 a e}{3 \left(b \,x^{3}+a \right) b^{3}}-\frac{a f \ln \left(b \,x^{3}+a \right)}{b^{4}}-\frac{d}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{e \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"1/3/b^3*f*x^3+1/6/b^4/(b*x^3+a)^2*a^3*f-1/6/b^3/(b*x^3+a)^2*a^2*e+1/6/b^2/(b*x^3+a)^2*a*d-1/6/b/(b*x^3+a)^2*c-1/b^4*ln(b*x^3+a)*a*f+1/3/b^3*ln(b*x^3+a)*e-1/b^4/(b*x^3+a)*a^2*f+2/3/b^3/(b*x^3+a)*a*e-1/3/b^2/(b*x^3+a)*d","A"
281,1,147,108,0.062000," ","int((f*x^9+e*x^6+d*x^3+c)/x/(b*x^3+a)^3,x)","-\frac{a^{2} f}{6 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{a e}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{c}{6 \left(b \,x^{3}+a \right)^{2} a}-\frac{d}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{2 a f}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{c}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{c \ln \left(x \right)}{a^{3}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{e}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{f \ln \left(b \,x^{3}+a \right)}{3 b^{3}}"," ",0,"-1/6*a^2/b^3/(b*x^3+a)^2*f+1/6*a/b^2/(b*x^3+a)^2*e-1/6/b/(b*x^3+a)^2*d+1/6/a/(b*x^3+a)^2*c+1/3/b^3*ln(b*x^3+a)*f-1/3*c*ln(b*x^3+a)/a^3+2/3*a/b^3/(b*x^3+a)*f-1/3/b^2/(b*x^3+a)*e+1/3/a^2/(b*x^3+a)*c+c*ln(x)/a^3","A"
282,1,163,126,0.059000," ","int((f*x^9+e*x^6+d*x^3+c)/x^4/(b*x^3+a)^3,x)","\frac{a f}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{d}{6 \left(b \,x^{3}+a \right)^{2} a}-\frac{b c}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{e}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{d}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{2 b c}{3 \left(b \,x^{3}+a \right) a^{3}}+\frac{d \ln \left(x \right)}{a^{3}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{3 b c \ln \left(x \right)}{a^{4}}+\frac{b c \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{f}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{c}{3 a^{3} x^{3}}"," ",0,"1/6*a/b^2/(b*x^3+a)^2*f-1/6/b/(b*x^3+a)^2*e+1/6/a/(b*x^3+a)^2*d-1/6/a^2*b/(b*x^3+a)^2*c-1/3*d*ln(b*x^3+a)/a^3+b*c*ln(b*x^3+a)/a^4-1/3/b^2/(b*x^3+a)*f+1/3/a^2/(b*x^3+a)*d-2/3/a^3*b/(b*x^3+a)*c-1/3/a^3*c/x^3+d*ln(x)/a^3-3*b*c*ln(x)/a^4","A"
283,1,213,153,0.059000," ","int((f*x^9+e*x^6+d*x^3+c)/x^7/(b*x^3+a)^3,x)","\frac{e}{6 \left(b \,x^{3}+a \right)^{2} a}-\frac{b d}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b^{2} c}{6 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{f}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{e}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{2 b d}{3 \left(b \,x^{3}+a \right) a^{3}}+\frac{e \ln \left(x \right)}{a^{3}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{3}}+\frac{b^{2} c}{\left(b \,x^{3}+a \right) a^{4}}-\frac{3 b d \ln \left(x \right)}{a^{4}}+\frac{b d \ln \left(b \,x^{3}+a \right)}{a^{4}}+\frac{6 b^{2} c \ln \left(x \right)}{a^{5}}-\frac{2 b^{2} c \ln \left(b \,x^{3}+a \right)}{a^{5}}-\frac{d}{3 a^{3} x^{3}}+\frac{b c}{a^{4} x^{3}}-\frac{c}{6 a^{3} x^{6}}"," ",0,"-1/6/b/(b*x^3+a)^2*f+1/6/a/(b*x^3+a)^2*e-1/6/a^2*b/(b*x^3+a)^2*d+1/6/a^3*b^2/(b*x^3+a)^2*c-1/3*e*ln(b*x^3+a)/a^3+1/a^4*ln(b*x^3+a)*b*d-2/a^5*ln(b*x^3+a)*b^2*c+1/3/a^2/(b*x^3+a)*e-2/3/a^3*b/(b*x^3+a)*d+1/a^4*b^2/(b*x^3+a)*c-1/6*c/a^3/x^6-1/3/a^3/x^3*d+1/a^4/x^3*b*c+e*ln(x)/a^3-3/a^4*ln(x)*b*d+6/a^5*ln(x)*b^2*c","A"
284,1,293,206,0.067000," ","int((f*x^9+e*x^6+d*x^3+c)/x^10/(b*x^3+a)^3,x)","\frac{f}{6 \left(b \,x^{3}+a \right)^{2} a}-\frac{b e}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b^{2} d}{6 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{b^{3} c}{6 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{f}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{2 b e}{3 \left(b \,x^{3}+a \right) a^{3}}+\frac{f \ln \left(x \right)}{a^{3}}-\frac{f \ln \left(b \,x^{3}+a \right)}{3 a^{3}}+\frac{b^{2} d}{\left(b \,x^{3}+a \right) a^{4}}-\frac{3 b e \ln \left(x \right)}{a^{4}}+\frac{b e \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{4 b^{3} c}{3 \left(b \,x^{3}+a \right) a^{5}}+\frac{6 b^{2} d \ln \left(x \right)}{a^{5}}-\frac{2 b^{2} d \ln \left(b \,x^{3}+a \right)}{a^{5}}-\frac{10 b^{3} c \ln \left(x \right)}{a^{6}}+\frac{10 b^{3} c \ln \left(b \,x^{3}+a \right)}{3 a^{6}}-\frac{e}{3 a^{3} x^{3}}+\frac{b d}{a^{4} x^{3}}-\frac{2 b^{2} c}{a^{5} x^{3}}-\frac{d}{6 a^{3} x^{6}}+\frac{b c}{2 a^{4} x^{6}}-\frac{c}{9 a^{3} x^{9}}"," ",0,"1/6/a/(b*x^3+a)^2*f-1/6/a^2*b/(b*x^3+a)^2*e+1/6/a^3*b^2/(b*x^3+a)^2*d-1/6/a^4*b^3/(b*x^3+a)^2*c-1/3/a^3*ln(b*x^3+a)*f+1/a^4*b*ln(b*x^3+a)*e-2/a^5*b^2*ln(b*x^3+a)*d+10/3/a^6*b^3*ln(b*x^3+a)*c+1/3/a^2/(b*x^3+a)*f-2/3/a^3*b/(b*x^3+a)*e+1/a^4*b^2/(b*x^3+a)*d-4/3/a^5*b^3/(b*x^3+a)*c-1/9/a^3*c/x^9-1/6/a^3/x^6*d+1/2/a^4/x^6*b*c-1/3/a^3/x^3*e+1/a^4/x^3*b*d-2/a^5/x^3*b^2*c+1/a^3*ln(x)*f-3/a^4*ln(x)*b*e+6/a^5*ln(x)*b^2*d-10/a^6*ln(x)*b^3*c","A"
285,1,349,245,0.063000," ","int((f*x^9+e*x^6+d*x^3+c)/x^13/(b*x^3+a)^3,x)","-\frac{b f}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b^{2} e}{6 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{b^{3} d}{6 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{b^{4} c}{6 \left(b \,x^{3}+a \right)^{2} a^{5}}-\frac{2 b f}{3 \left(b \,x^{3}+a \right) a^{3}}+\frac{b^{2} e}{\left(b \,x^{3}+a \right) a^{4}}-\frac{3 b f \ln \left(x \right)}{a^{4}}+\frac{b f \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{4 b^{3} d}{3 \left(b \,x^{3}+a \right) a^{5}}+\frac{6 b^{2} e \ln \left(x \right)}{a^{5}}-\frac{2 b^{2} e \ln \left(b \,x^{3}+a \right)}{a^{5}}+\frac{5 b^{4} c}{3 \left(b \,x^{3}+a \right) a^{6}}-\frac{10 b^{3} d \ln \left(x \right)}{a^{6}}+\frac{10 b^{3} d \ln \left(b \,x^{3}+a \right)}{3 a^{6}}+\frac{15 b^{4} c \ln \left(x \right)}{a^{7}}-\frac{5 b^{4} c \ln \left(b \,x^{3}+a \right)}{a^{7}}-\frac{f}{3 a^{3} x^{3}}+\frac{b e}{a^{4} x^{3}}-\frac{2 b^{2} d}{a^{5} x^{3}}+\frac{10 b^{3} c}{3 a^{6} x^{3}}-\frac{e}{6 a^{3} x^{6}}+\frac{b d}{2 a^{4} x^{6}}-\frac{b^{2} c}{a^{5} x^{6}}-\frac{d}{9 a^{3} x^{9}}+\frac{b c}{3 a^{4} x^{9}}-\frac{c}{12 a^{3} x^{12}}"," ",0,"-1/9/a^3/x^9*d-1/6/a^3/x^6*e-1/3/a^3/x^3*f-10*b^3/a^6*ln(x)*d+15*b^4/a^7*ln(x)*c+1/a^4*b*ln(b*x^3+a)*f-2/a^5*b^2*ln(b*x^3+a)*e+10/3/a^6*b^3*ln(b*x^3+a)*d-5/a^7*b^4*ln(b*x^3+a)*c+1/3/a^4/x^9*b*c+1/2/a^4/x^6*b*d-1/a^5/x^6*b^2*c+1/a^4/x^3*b*e-2/a^5/x^3*b^2*d+10/3/a^6/x^3*b^3*c-1/6/a^2*b/(b*x^3+a)^2*f+1/6/a^3*b^2/(b*x^3+a)^2*e-1/6/a^4*b^3/(b*x^3+a)^2*d+1/6/a^5*b^4/(b*x^3+a)^2*c-2/3/a^3*b/(b*x^3+a)*f+1/a^4*b^2/(b*x^3+a)*e-4/3/a^5*b^3/(b*x^3+a)*d+5/3/a^6*b^4/(b*x^3+a)*c-3*b/a^4*ln(x)*f+6*b^2/a^5*ln(x)*e-1/12*c/a^3/x^12","A"
286,1,706,365,0.066000," ","int(x^12*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{13}}{13 b^{3}}-\frac{3 a f \,x^{10}}{10 b^{4}}+\frac{e \,x^{10}}{10 b^{3}}+\frac{6 a^{2} f \,x^{7}}{7 b^{5}}-\frac{3 a e \,x^{7}}{7 b^{4}}+\frac{d \,x^{7}}{7 b^{3}}+\frac{37 a^{5} f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{6}}-\frac{31 a^{4} e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{5}}+\frac{25 a^{3} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{19 a^{2} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{5 a^{3} f \,x^{4}}{2 b^{6}}+\frac{3 a^{2} e \,x^{4}}{2 b^{5}}-\frac{3 a d \,x^{4}}{4 b^{4}}+\frac{c \,x^{4}}{4 b^{3}}+\frac{17 a^{6} f x}{9 \left(b \,x^{3}+a \right)^{2} b^{7}}-\frac{14 a^{5} e x}{9 \left(b \,x^{3}+a \right)^{2} b^{6}}+\frac{11 a^{4} d x}{9 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{8 a^{3} c x}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{152 \sqrt{3}\, a^{5} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{8}}-\frac{152 a^{5} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{8}}+\frac{76 a^{5} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{8}}+\frac{104 \sqrt{3}\, a^{4} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}+\frac{104 a^{4} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}-\frac{52 a^{4} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}+\frac{15 a^{4} f x}{b^{7}}-\frac{65 \sqrt{3}\, a^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{65 a^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{65 a^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{10 a^{3} e x}{b^{6}}+\frac{35 \sqrt{3}\, a^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{35 a^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{35 a^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{6 a^{2} d x}{b^{5}}-\frac{3 a c x}{b^{4}}"," ",0,"35/27*a^2/b^5*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-65/27*a^3/b^6*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-8/9*a^3/b^4/(b*x^3+a)^2*c*x+76/27*a^5/b^8*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+104/27*a^4/b^7*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+3/2/b^5*x^4*a^2*e-3/4/b^4*x^4*a*d-3/10/b^4*x^10*a*f+6/7/b^5*x^7*a^2*f-3/7/b^4*x^7*a*e-5/2/b^6*x^4*a^3*f+15/b^7*a^4*f*x-10/b^6*a^3*e*x+6/b^5*a^2*d*x-3/b^4*a*c*x-152/27*a^5/b^8*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+104/27*a^4/b^7*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/10/b^3*x^10*e+1/7/b^3*x^7*d+1/4/b^3*x^4*c+35/27*a^2/b^5*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-35/54*a^2/b^5*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-65/27*a^3/b^6*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+65/54*a^3/b^6*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-52/27*a^4/b^7*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+37/18*a^5/b^6/(b*x^3+a)^2*x^4*f-31/18*a^4/b^5/(b*x^3+a)^2*x^4*e+25/18*a^3/b^4/(b*x^3+a)^2*x^4*d-19/18*a^2/b^3/(b*x^3+a)^2*x^4*c+17/9*a^6/b^7/(b*x^3+a)^2*f*x-14/9*a^5/b^6/(b*x^3+a)^2*e*x+11/9*a^4/b^5/(b*x^3+a)^2*d*x-152/27*a^5/b^8*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/13*f*x^13/b^3","A"
287,1,668,333,0.068000," ","int(x^10*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{11}}{11 b^{3}}-\frac{3 a f \,x^{8}}{8 b^{4}}+\frac{e \,x^{8}}{8 b^{3}}-\frac{16 a^{4} f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{5}}+\frac{13 a^{3} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{10 a^{2} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{7 a c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{6 a^{2} f \,x^{5}}{5 b^{5}}-\frac{3 a e \,x^{5}}{5 b^{4}}+\frac{d \,x^{5}}{5 b^{3}}-\frac{29 a^{5} f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{6}}+\frac{23 a^{4} e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{17 a^{3} d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{11 a^{2} c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{5 a^{3} f \,x^{2}}{b^{6}}+\frac{3 a^{2} e \,x^{2}}{b^{5}}-\frac{3 a d \,x^{2}}{2 b^{4}}+\frac{c \,x^{2}}{2 b^{3}}+\frac{119 \sqrt{3}\, a^{4} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{7}}-\frac{119 a^{4} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{7}}+\frac{119 a^{4} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{7}}-\frac{77 \sqrt{3}\, a^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{77 a^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}-\frac{77 a^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{44 \sqrt{3}\, a^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{44 a^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{22 a^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{20 \sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{20 a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{10 a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}"," ",0,"119/27*a^4/b^7*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-77/27*a^3/b^6*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-20/27*a/b^4*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+44/27*a^2/b^5*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-3/8/b^4*x^8*a*f+6/5/b^5*x^5*a^2*f+3/b^5*x^2*a^2*e-3/2/b^4*x^2*a*d-5/b^6*x^2*a^3*f-3/5/b^4*x^5*a*e+1/11*f*x^11/b^3-119/27*a^4/b^7*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+11/18*a^2/b^3/(b*x^3+a)^2*x^2*c-17/18*a^3/b^4/(b*x^3+a)^2*x^2*d+22/27*a^2/b^5*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/8/b^3*x^8*e+1/5/b^3*x^5*d+1/2/b^3*x^2*c+20/27*a/b^4*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-10/9*a^2/b^3/(b*x^3+a)^2*x^5*d-10/27*a/b^4*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-77/54*a^3/b^6*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-44/27*a^2/b^5*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+13/9*a^3/b^4/(b*x^3+a)^2*x^5*e-16/9*a^4/b^5/(b*x^3+a)^2*x^5*f+119/54*a^4/b^7*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+77/27*a^3/b^6*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/9*a/b^2/(b*x^3+a)^2*x^5*c-29/18*a^5/b^6/(b*x^3+a)^2*x^2*f+23/18*a^4/b^5/(b*x^3+a)^2*x^2*e","B"
288,1,651,326,0.064000," ","int(x^9*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{10}}{10 b^{3}}-\frac{3 a f \,x^{7}}{7 b^{4}}+\frac{e \,x^{7}}{7 b^{3}}-\frac{31 a^{4} f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{5}}+\frac{25 a^{3} e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{19 a^{2} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{13 a c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{3 a^{2} f \,x^{4}}{2 b^{5}}-\frac{3 a e \,x^{4}}{4 b^{4}}+\frac{d \,x^{4}}{4 b^{3}}-\frac{14 a^{5} f x}{9 \left(b \,x^{3}+a \right)^{2} b^{6}}+\frac{11 a^{4} e x}{9 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{8 a^{3} d x}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{5 a^{2} c x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{104 \sqrt{3}\, a^{4} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}+\frac{104 a^{4} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}-\frac{52 a^{4} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{7}}-\frac{65 \sqrt{3}\, a^{3} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{65 a^{3} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{65 a^{3} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{10 a^{3} f x}{b^{6}}+\frac{35 \sqrt{3}\, a^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{35 a^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{35 a^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{6 a^{2} e x}{b^{5}}-\frac{14 \sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{3 a d x}{b^{4}}+\frac{c x}{b^{3}}"," ",0,"-14/27*a/b^4*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+104/27*a^4/b^7*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-65/27*a^3/b^6*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+35/27*a^2/b^5*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-14/27*a/b^4*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+7/27*a/b^4*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-31/18*a^4/b^5/(b*x^3+a)^2*x^4*f-10/b^6*a^3*f*x+6/b^5*a^2*e*x-3/b^4*a*d*x-3/4/b^4*x^4*a*e-3/7/b^4*x^7*a*f+3/2/b^5*x^4*a^2*f+1/10*f*x^10/b^3+104/27*a^4/b^7*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-52/27*a^4/b^7*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-65/27*a^3/b^6*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+65/54*a^3/b^6*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/7/b^3*x^7*e+1/4/b^3*x^4*d+1/b^3*c*x+35/27*a^2/b^5*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-35/54*a^2/b^5*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-19/18*a^2/b^3/(b*x^3+a)^2*x^4*d+13/18*a/b^2/(b*x^3+a)^2*x^4*c+11/9*a^4/b^5/(b*x^3+a)^2*e*x-8/9*a^3/b^4/(b*x^3+a)^2*d*x+5/9*a^2/b^3/(b*x^3+a)^2*c*x+25/18*a^3/b^4/(b*x^3+a)^2*x^4*e-14/9*a^5/b^6/(b*x^3+a)^2*f*x","A"
289,1,611,296,0.061000," ","int(x^7*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{8}}{8 b^{3}}+\frac{13 a^{3} f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{10 a^{2} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{7 a d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{4 c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b}-\frac{3 a f \,x^{5}}{5 b^{4}}+\frac{e \,x^{5}}{5 b^{3}}+\frac{23 a^{4} f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{17 a^{3} e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{11 a^{2} d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{5 a c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{3 a^{2} f \,x^{2}}{b^{5}}-\frac{3 a e \,x^{2}}{2 b^{4}}+\frac{d \,x^{2}}{2 b^{3}}-\frac{77 \sqrt{3}\, a^{3} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{77 a^{3} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}-\frac{77 a^{3} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{6}}+\frac{44 \sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{44 a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{22 a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{20 \sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{20 a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{10 a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"44/27/b^5*a^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-20/27/b^4*a*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-77/27/b^6*a^3*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-3/2/b^4*x^2*a*e-3/5/b^4*x^5*a*f+3/b^5*x^2*a^2*f-4/9/b/(b*x^3+a)^2*x^5*c-5/27/b^3*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+5/54/b^3*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/5/b^3*x^5*e+1/2/b^3*x^2*d+1/8*f*x^8/b^3+13/9/b^4/(b*x^3+a)^2*x^5*a^3*f-10/9/b^3/(b*x^3+a)^2*x^5*a^2*e+7/9/b^2/(b*x^3+a)^2*x^5*a*d+23/18/b^5/(b*x^3+a)^2*x^2*a^4*f-17/18/b^4/(b*x^3+a)^2*x^2*a^3*e-77/54/b^6*a^3*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-44/27/b^5*a^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+22/27/b^5*a^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+20/27/b^4*a*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-10/27/b^4*a*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/b^3*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+11/18/b^3/(b*x^3+a)^2*x^2*a^2*d-5/18/b^2/(b*x^3+a)^2*x^2*a*c+77/27/b^6*a^3*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))","B"
290,1,596,289,0.053000," ","int(x^6*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{f \,x^{7}}{7 b^{3}}+\frac{25 a^{3} f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}-\frac{19 a^{2} e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{13 a d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{7 c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b}-\frac{3 a f \,x^{4}}{4 b^{4}}+\frac{e \,x^{4}}{4 b^{3}}+\frac{11 a^{4} f x}{9 \left(b \,x^{3}+a \right)^{2} b^{5}}-\frac{8 a^{3} e x}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{5 a^{2} d x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{2 a c x}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{65 \sqrt{3}\, a^{3} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}-\frac{65 a^{3} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{65 a^{3} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{6}}+\frac{35 \sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{35 a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{35 a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{6 a^{2} f x}{b^{5}}-\frac{14 \sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{3 a e x}{b^{4}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{d x}{b^{3}}"," ",0,"65/54/b^6*a^3*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+35/27/b^5*a^2*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-14/27/b^4*a*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-3/b^4*a*e*x-3/4/b^4*x^4*a*f+2/27/b^3*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/18/b/(b*x^3+a)^2*x^4*c+6/b^5*a^2*f*x-1/27/b^3*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-8/9/b^4/(b*x^3+a)^2*a^3*e*x+1/7/b^3*f*x^7+13/18/b^2/(b*x^3+a)^2*x^4*a*d-35/54/b^5*a^2*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-2/9/b^2/(b*x^3+a)^2*a*c*x+11/9/b^5/(b*x^3+a)^2*a^4*f*x+1/4/b^3*x^4*e+7/27/b^4*a*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/b^3*d*x+2/27/b^3*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-65/27/b^6*a^3*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-65/27/b^6*a^3*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+35/27/b^5*a^2*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-14/27/b^4*a*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+25/18/b^4/(b*x^3+a)^2*x^4*a^3*f-19/18/b^3/(b*x^3+a)^2*x^4*a^2*e+5/9/b^3/(b*x^3+a)^2*a^2*d*x","B"
291,1,574,269,0.063000," ","int(x^4*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","-\frac{10 a^{2} f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{7 a e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{4 d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{f \,x^{5}}{5 b^{3}}-\frac{17 a^{3} f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{11 a^{2} e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{5 a d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b}-\frac{3 a f \,x^{2}}{2 b^{4}}+\frac{e \,x^{2}}{2 b^{3}}+\frac{44 \sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{44 a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}+\frac{22 a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{5}}-\frac{20 \sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{20 a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{10 a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"1/5/b^3*f*x^5-3/2/b^4*x^2*a*f+1/2/b^3*x^2*e-10/9/b^3/(b*x^3+a)^2*a^2*x^5*f+7/9/b^2/(b*x^3+a)^2*a*x^5*e-4/9/b/(b*x^3+a)^2*x^5*d+1/9/(b*x^3+a)^2/a*x^5*c-17/18/b^4/(b*x^3+a)^2*x^2*a^3*f+11/18/b^3/(b*x^3+a)^2*x^2*a^2*e-5/18/b^2/(b*x^3+a)^2*x^2*a*d-1/18/b/(b*x^3+a)^2*x^2*c-44/27/b^5*a^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+20/27/b^4*a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-1/27/b^2/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+22/27/b^5*a^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-10/27/b^4*a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/54/b^2/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+44/27/b^5*a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-20/27/b^4*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/27/b^2/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
292,1,561,262,0.065000," ","int(x^3*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","-\frac{19 a^{2} f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}+\frac{13 a e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{7 d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{f \,x^{4}}{4 b^{3}}-\frac{8 a^{3} f x}{9 \left(b \,x^{3}+a \right)^{2} b^{4}}+\frac{5 a^{2} e x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{2 a d x}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{c x}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{35 \sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}+\frac{35 a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{35 a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{5}}-\frac{14 \sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{3 a f x}{b^{4}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{e x}{b^{3}}"," ",0,"1/4*f*x^4/b^3-3/b^4*a*f*x+1/b^3*e*x-19/18/b^3/(b*x^3+a)^2*x^4*a^2*f+13/18/b^2/(b*x^3+a)^2*x^4*a*e-7/18/b/(b*x^3+a)^2*x^4*d+1/18/(b*x^3+a)^2/a*x^4*c-8/9/b^4/(b*x^3+a)^2*a^3*f*x+5/9/b^3/(b*x^3+a)^2*a^2*e*x-2/9/b^2/(b*x^3+a)^2*a*d*x-1/9/b/(b*x^3+a)^2*c*x+35/27/b^5*a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-14/27/b^4*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+2/27/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+1/27/b^2/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-35/54/b^5*a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+7/27/b^4*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/27/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-1/54/b^2/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+35/27/b^5*a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-14/27/b^4*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+2/27/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/27/b^2/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
293,1,550,256,0.059000," ","int(x*(f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{7 a f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a}+\frac{2 b c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{4 e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{11 a^{2} f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{5 a e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{7 c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{f \,x^{2}}{2 b^{3}}-\frac{20 \sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{20 a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}-\frac{10 a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4}}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{5 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}"," ",0,"1/2*f*x^2/b^3+7/9/b^2/(b*x^3+a)^2*a*x^5*f-4/9/b/(b*x^3+a)^2*x^5*e+1/9/(b*x^3+a)^2/a*x^5*d+2/9*b/(b*x^3+a)^2/a^2*x^5*c+11/18/b^3/(b*x^3+a)^2*a^2*x^2*f-5/18/b^2/(b*x^3+a)^2*a*x^2*e-1/18/b/(b*x^3+a)^2*x^2*d+7/18/(b*x^3+a)^2/a*x^2*c+20/27/b^4*a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-1/27/b^2/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-2/27/b/a^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-10/27/b^4*a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/54/b^2/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/27/b/a^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-20/27/b^4*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/27/b^2/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+2/27/b/a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
294,1,539,249,0.062000," ","int((f*x^9+e*x^6+d*x^3+c)/(b*x^3+a)^3,x)","\frac{13 a f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 b c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{7 e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{5 a^{2} f x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{2 a e x}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{4 c x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{d x}{9 \left(b \,x^{3}+a \right)^{2} b}-\frac{14 \sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{f x}{b^{3}}"," ",0,"1/b^3*f*x+13/18/b^2/(b*x^3+a)^2*x^4*a*f-7/18/b/(b*x^3+a)^2*x^4*e+1/18/(b*x^3+a)^2/a*x^4*d+5/18*b/(b*x^3+a)^2/a^2*x^4*c+5/9/b^3/(b*x^3+a)^2*a^2*f*x-2/9/b^2/(b*x^3+a)^2*a*e*x-1/9/b/(b*x^3+a)^2*d*x+4/9/(b*x^3+a)^2/a*x*c-14/27/b^4*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+2/27/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/27/b^2/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+5/27/b/a^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c+7/27/b^4*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/27/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/54/b^2/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-5/54/b/a^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-14/27/b^4*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+2/27/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+1/27/b^2/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+5/27/b/a^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c","B"
295,1,547,260,0.116000," ","int((f*x^9+e*x^6+d*x^3+c)/x^2/(b*x^3+a)^3,x)","\frac{e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a}+\frac{2 b d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b^{2} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{4 f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b}-\frac{5 a f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{7 d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{13 b c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{14 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{5 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{c}{a^{3} x}"," ",0,"-4/9/(b*x^3+a)^2/b*x^5*f+1/9/a/(b*x^3+a)^2*x^5*e+2/9/a^2/(b*x^3+a)^2*b*x^5*d-5/9/a^3/(b*x^3+a)^2*b^2*x^5*c-5/18*a/(b*x^3+a)^2/b^2*x^2*f-1/18/(b*x^3+a)^2/b*x^2*e+7/18/a/(b*x^3+a)^2*x^2*d-13/18/a^2/(b*x^3+a)^2*b*x^2*c-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-1/27/a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e-2/27/a^2/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+14/27/a^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/54/a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/27/a^2/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-7/27/a^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/27/a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+2/27/a^2/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-14/27/a^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/a^3*c/x","B"
296,1,539,256,0.061000," ","int((f*x^9+e*x^6+d*x^3+c)/x^3/(b*x^3+a)^3,x)","\frac{e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 b d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{11 b^{2} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{7 f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b}-\frac{2 a f x}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{4 d x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{7 b c x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{e x}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{20 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{c}{2 a^{3} x^{2}}"," ",0,"-7/18/(b*x^3+a)^2/b*x^4*f+1/18/a/(b*x^3+a)^2*x^4*e+5/18/a^2/(b*x^3+a)^2*b*x^4*d-11/18/a^3/(b*x^3+a)^2*b^2*x^4*c-2/9*a/(b*x^3+a)^2/b^2*x*f-1/9/(b*x^3+a)^2/b*x*e+4/9/a/(b*x^3+a)^2*x*d-7/9/a^2/(b*x^3+a)^2*b*x*c+2/27/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+1/27/a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+5/27/a^2/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-20/27/a^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/27/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/54/a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-5/54/a^2/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+10/27/a^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+2/27/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/27/a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e+5/27/a^2/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-20/27/a^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/2*c/a^3/x^2","B"
297,1,574,272,0.066000," ","int((f*x^9+e*x^6+d*x^3+c)/x^5/(b*x^3+a)^3,x)","\frac{f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a}+\frac{2 b e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b^{2} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{8 b^{3} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{7 e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{13 b d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{19 b^{2} c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{14 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{35 \sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{35 b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{35 b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{d}{a^{3} x}+\frac{3 b c}{a^{4} x}-\frac{c}{4 a^{3} x^{4}}"," ",0,"1/9/a/(b*x^3+a)^2*x^5*f+2/9/a^2/(b*x^3+a)^2*x^5*b*e-5/9/a^3/(b*x^3+a)^2*x^5*b^2*d+8/9/a^4/(b*x^3+a)^2*x^5*b^3*c-1/18/(b*x^3+a)^2/b*x^2*f+7/18/a/(b*x^3+a)^2*x^2*e-13/18/a^2/(b*x^3+a)^2*b*x^2*d+19/18/a^3/(b*x^3+a)^2*c*x^2*b^2-1/27/a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-2/27/a^2/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+14/27/a^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d-35/27/a^4*b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/54/a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/27/a^2/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-7/27/a^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+35/54/a^4*b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/27/a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+2/27/a^2/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-14/27/a^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+35/27/a^4*b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/4*c/a^3/x^4-d/a^3/x+3/a^4/x*b*c","B"
298,1,566,269,0.063000," ","int((f*x^9+e*x^6+d*x^3+c)/x^6/(b*x^3+a)^3,x)","\frac{f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 b e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{11 b^{2} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{17 b^{3} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{4 e x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{7 b d x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{10 b^{2} c x}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{f x}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{20 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{44 \sqrt{3}\, b c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{44 b c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{22 b c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{d}{2 a^{3} x^{2}}+\frac{3 b c}{2 a^{4} x^{2}}-\frac{c}{5 a^{3} x^{5}}"," ",0,"1/18/a/(b*x^3+a)^2*x^4*f+5/18/a^2/(b*x^3+a)^2*x^4*b*e-11/18/a^3/(b*x^3+a)^2*x^4*b^2*d+17/18/a^4/(b*x^3+a)^2*x^4*b^3*c-1/9/(b*x^3+a)^2/b*x*f+4/9/a/(b*x^3+a)^2*x*e-7/9/a^2/(b*x^3+a)^2*b*x*d+10/9/a^3/(b*x^3+a)^2*x*b^2*c+1/27/a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f+5/27/a^2/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e-20/27/a^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d+44/27/a^4*b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/54/a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-5/54/a^2/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+10/27/a^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d-22/27/a^4*b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/27/a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+5/27/a^2/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-20/27/a^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+44/27/a^4*b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/5/a^3*c/x^5-1/2*d/a^3/x^2+3/2/a^4/x^2*b*c","B"
299,1,611,296,0.069000," ","int((f*x^9+e*x^6+d*x^3+c)/x^8/(b*x^3+a)^3,x)","\frac{2 b f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b^{2} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{8 b^{3} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{11 b^{4} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{5}}+\frac{7 f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{13 b e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{19 b^{2} d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{25 b^{3} c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{14 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{35 \sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{35 b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{35 b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{65 \sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{65 b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{65 b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{e}{a^{3} x}+\frac{3 b d}{a^{4} x}-\frac{6 b^{2} c}{a^{5} x}-\frac{d}{4 a^{3} x^{4}}+\frac{3 b c}{4 a^{4} x^{4}}-\frac{c}{7 a^{3} x^{7}}"," ",0,"2/9/a^2/(b*x^3+a)^2*x^5*b*f-5/9/a^3/(b*x^3+a)^2*x^5*e*b^2+8/9/a^4/(b*x^3+a)^2*x^5*d*b^3-11/9/a^5/(b*x^3+a)^2*x^5*c*b^4-13/18/a^2/(b*x^3+a)^2*x^2*b*e+19/18/a^3/(b*x^3+a)^2*x^2*b^2*d-25/18/a^4/(b*x^3+a)^2*x^2*b^3*c-14/27/a^3*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-35/27/a^4*b*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+35/54/a^4*b*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+65/27/a^5*b^2*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-65/54/a^5*b^2*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+3/4/a^4/x^4*b*c+3/a^4/x*b*d-6/a^5/x*b^2*c+7/18/a/(b*x^3+a)^2*x^2*f+14/27/a^3*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-7/27/a^3*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+35/27/a^4*b*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-65/27/a^5*b^2*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/27/a^2*f*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/7/a^3*c/x^7-1/4/a^3/x^4*d-e/a^3/x-2/27/a^2*f/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/27/a^2*f/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))","B"
300,1,603,293,0.062000," ","int((f*x^9+e*x^6+d*x^3+c)/x^9/(b*x^3+a)^3,x)","\frac{5 b f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{11 b^{2} e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{17 b^{3} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{23 b^{4} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{5}}+\frac{4 f x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{7 b e x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{10 b^{2} d x}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{13 b^{3} c x}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{5 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{20 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{44 \sqrt{3}\, b d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{44 b d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{22 b d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{77 \sqrt{3}\, b^{2} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}-\frac{77 b^{2} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}+\frac{77 b^{2} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}-\frac{e}{2 a^{3} x^{2}}+\frac{3 b d}{2 a^{4} x^{2}}-\frac{3 b^{2} c}{a^{5} x^{2}}-\frac{d}{5 a^{3} x^{5}}+\frac{3 b c}{5 a^{4} x^{5}}-\frac{c}{8 a^{3} x^{8}}"," ",0,"10/27/a^3*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-3/a^5/x^2*b^2*c+3/5/a^4/x^5*b*c+4/9/a/(b*x^3+a)^2*f*x-20/27/a^3*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+3/2/a^4/x^2*b*d-1/2/a^3/x^2*e+5/27/a^2*f/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+44/27/a^4*b*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-77/27/a^5*b^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/5/a^3/x^5*d+5/18/a^2/(b*x^3+a)^2*x^4*b*f-11/18/a^3/(b*x^3+a)^2*x^4*b^2*e+17/18/a^4/(b*x^3+a)^2*x^4*b^3*d-23/18/a^5/(b*x^3+a)^2*x^4*b^4*c-20/27/a^3*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+44/27/a^4*b*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-22/27/a^4*b*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-77/27/a^5*b^2*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+77/54/a^5*b^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/a^2*f/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-5/54/a^2*f/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+10/9/a^3/(b*x^3+a)^2*b^2*d*x-13/9/a^4/(b*x^3+a)^2*b^3*c*x-7/9/a^2/(b*x^3+a)^2*b*e*x-1/8*c/a^3/x^8","B"
301,1,659,333,0.075000," ","int((f*x^9+e*x^6+d*x^3+c)/x^11/(b*x^3+a)^3,x)","-\frac{5 b^{2} f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{8 b^{3} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{11 b^{4} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{5}}+\frac{14 b^{5} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{6}}-\frac{13 b f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{19 b^{2} e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{25 b^{3} d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{31 b^{4} c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{5}}-\frac{14 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{35 \sqrt{3}\, b e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{35 b e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{35 b e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{65 \sqrt{3}\, b^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{65 b^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{65 b^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{104 \sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{104 b^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}+\frac{52 b^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{f}{a^{3} x}+\frac{3 b e}{a^{4} x}-\frac{6 b^{2} d}{a^{5} x}+\frac{10 b^{3} c}{a^{6} x}-\frac{e}{4 a^{3} x^{4}}+\frac{3 b d}{4 a^{4} x^{4}}-\frac{3 b^{2} c}{2 a^{5} x^{4}}-\frac{d}{7 a^{3} x^{7}}+\frac{3 b c}{7 a^{4} x^{7}}-\frac{c}{10 a^{3} x^{10}}"," ",0,"-7/27/a^3*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+3/7/a^4/x^7*b*c+3/4/a^4/x^4*b*d-3/2/a^5/x^4*b^2*c+3/a^4/x*b*e-6/a^5/x*b^2*d+10/a^6/x*b^3*c+14/27/a^3*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+35/27/a^4*b*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-65/27/a^5*b^2*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+104/27/a^6*b^3*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/7/a^3/x^7*d-1/4/a^3/x^4*e-1/a^3/x*f-1/10*c/a^3/x^10-5/9/a^3*b^2/(b*x^3+a)^2*x^5*f+8/9/a^4*b^3/(b*x^3+a)^2*x^5*e-11/9/a^5*b^4/(b*x^3+a)^2*x^5*d+14/9/a^6*b^5/(b*x^3+a)^2*x^5*c-13/18/a^2*b/(b*x^3+a)^2*x^2*f+19/18/a^3*b^2/(b*x^3+a)^2*x^2*e-25/18/a^4*b^3/(b*x^3+a)^2*x^2*d+31/18/a^5*b^4/(b*x^3+a)^2*x^2*c-14/27/a^3*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-35/27/a^4*b*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+35/54/a^4*b*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+65/27/a^5*b^2*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-65/54/a^5*b^2*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-104/27/a^6*b^3*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+52/27/a^6*b^3*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))","A"
302,1,651,330,0.066000," ","int((f*x^9+e*x^6+d*x^3+c)/x^12/(b*x^3+a)^3,x)","-\frac{11 b^{2} f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{17 b^{3} e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{23 b^{4} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{5}}+\frac{29 b^{5} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{6}}-\frac{7 b f x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{10 b^{2} e x}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{13 b^{3} d x}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{16 b^{4} c x}{9 \left(b \,x^{3}+a \right)^{2} a^{5}}-\frac{20 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{44 \sqrt{3}\, b e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{44 b e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{22 b e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{77 \sqrt{3}\, b^{2} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}-\frac{77 b^{2} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}+\frac{77 b^{2} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{5}}+\frac{119 \sqrt{3}\, b^{3} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{6}}+\frac{119 b^{3} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{6}}-\frac{119 b^{3} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{6}}-\frac{f}{2 a^{3} x^{2}}+\frac{3 b e}{2 a^{4} x^{2}}-\frac{3 b^{2} d}{a^{5} x^{2}}+\frac{5 b^{3} c}{a^{6} x^{2}}-\frac{e}{5 a^{3} x^{5}}+\frac{3 b d}{5 a^{4} x^{5}}-\frac{6 b^{2} c}{5 a^{5} x^{5}}-\frac{d}{8 a^{3} x^{8}}+\frac{3 b c}{8 a^{4} x^{8}}-\frac{c}{11 a^{3} x^{11}}"," ",0,"3/5/a^4/x^5*b*d-6/5/a^5/x^5*b^2*c+3/2/a^4/x^2*b*e-3/a^5/x^2*b^2*d+5/a^6/x^2*b^3*c-20/27/a^3*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+10/27/a^3*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+3/8/a^4/x^8*b*c-119/54/a^6*b^3*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+29/18/a^6*b^5/(b*x^3+a)^2*x^4*c-7/9/a^2*b/(b*x^3+a)^2*f*x+10/9/a^3*b^2/(b*x^3+a)^2*e*x-13/9/a^4*b^3/(b*x^3+a)^2*d*x-11/18/a^3*b^2/(b*x^3+a)^2*x^4*f+17/18/a^4*b^3/(b*x^3+a)^2*x^4*e-23/18/a^5*b^4/(b*x^3+a)^2*x^4*d-1/8/a^3/x^8*d-1/5/a^3/x^5*e-1/2/a^3/x^2*f+44/27/a^4*b*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-77/27/a^5*b^2*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+16/9/a^5*b^4/(b*x^3+a)^2*c*x-20/27/a^3*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+44/27/a^4*b*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-22/27/a^4*b*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+119/27/a^6*b^3*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/11*c/a^3/x^11-77/27/a^5*b^2*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+77/54/a^5*b^2*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+119/27/a^6*b^3*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))","A"
303,1,716,374,0.071000," ","int((f*x^9+e*x^6+d*x^3+c)/x^14/(b*x^3+a)^3,x)","\frac{8 b^{3} f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{4}}-\frac{11 b^{4} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{5}}+\frac{14 b^{5} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{6}}-\frac{17 b^{6} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{7}}+\frac{19 b^{2} f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{25 b^{3} e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{4}}+\frac{31 b^{4} d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{5}}-\frac{37 b^{5} c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{6}}+\frac{35 \sqrt{3}\, b f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{35 b f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{35 b f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{65 \sqrt{3}\, b^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{65 b^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}-\frac{65 b^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{5}}+\frac{104 \sqrt{3}\, b^{3} d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{104 b^{3} d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}+\frac{52 b^{3} d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{6}}-\frac{152 \sqrt{3}\, b^{4} c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{7}}+\frac{152 b^{4} c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{7}}-\frac{76 b^{4} c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{7}}+\frac{3 b f}{a^{4} x}-\frac{6 b^{2} e}{a^{5} x}+\frac{10 b^{3} d}{a^{6} x}-\frac{15 b^{4} c}{a^{7} x}-\frac{f}{4 a^{3} x^{4}}+\frac{3 b e}{4 a^{4} x^{4}}-\frac{3 b^{2} d}{2 a^{5} x^{4}}+\frac{5 b^{3} c}{2 a^{6} x^{4}}-\frac{e}{7 a^{3} x^{7}}+\frac{3 b d}{7 a^{4} x^{7}}-\frac{6 b^{2} c}{7 a^{5} x^{7}}-\frac{d}{10 a^{3} x^{10}}+\frac{3 b c}{10 a^{4} x^{10}}-\frac{c}{13 a^{3} x^{13}}"," ",0,"-1/10/a^3/x^10*d+3/4/a^4/x^4*b*e-3/2/a^5/x^4*b^2*d+5/2/a^6/x^4*b^3*c+3/7/a^4/x^7*b*d-6/7/a^5/x^7*b^2*c+3/10/a^4/x^10*b*c+3*b/a^4/x*f-6*b^2/a^5/x*e+10*b^3/a^6/x*d-15*b^4/a^7/x*c-1/7/a^3/x^7*e-1/4/a^3/x^4*f-104/27/a^6*b^3*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+52/27/a^6*b^3*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+152/27/a^7*b^4*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-76/27/a^7*b^4*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+8/9/a^4*b^3/(b*x^3+a)^2*x^5*f-11/9/a^5*b^4/(b*x^3+a)^2*x^5*e+14/9/a^6*b^5/(b*x^3+a)^2*x^5*d-17/9/a^7*b^6/(b*x^3+a)^2*x^5*c+19/18/a^3*b^2/(b*x^3+a)^2*x^2*f-25/18/a^4*b^3/(b*x^3+a)^2*x^2*e+31/18/a^5*b^4/(b*x^3+a)^2*x^2*d-37/18/a^6*b^5/(b*x^3+a)^2*x^2*c+35/27/a^4*b*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-65/27/a^5*b^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+104/27/a^6*b^3*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-152/27/a^7*b^4*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/13*c/a^3/x^13+35/54/a^4*b*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+65/27/a^5*b^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-65/54/a^5*b^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-35/27/a^4*b*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))","A"
304,1,45,44,0.047000," ","int((1-x)*x^4/(x^3+1),x)","-\frac{x^{3}}{3}+\frac{x^{2}}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}+\frac{2 \ln \left(x +1\right)}{3}+\frac{\ln \left(x^{2}-x +1\right)}{6}"," ",0,"-1/3*x^3+1/2*x^2+2/3*ln(x+1)+1/6*ln(x^2-x+1)-1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
305,1,25,24,0.046000," ","int((1-x)*x^3/(x^3+1),x)","-\frac{x^{2}}{2}+x -\frac{2 \ln \left(x +1\right)}{3}+\frac{\ln \left(x^{2}-x +1\right)}{3}"," ",0,"x-1/2*x^2-2/3*ln(x+1)+1/3*ln(x^2-x+1)","A"
306,1,38,37,0.048000," ","int((1-x)*x^2/(x^3+1),x)","-x +\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}+\frac{2 \ln \left(x +1\right)}{3}+\frac{\ln \left(x^{2}-x +1\right)}{6}"," ",0,"-x+2/3*ln(x+1)+1/6*ln(x^2-x+1)+1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
307,1,35,34,0.052000," ","int((1-x)*x/(x^3+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}-\frac{2 \ln \left(x +1\right)}{3}-\frac{\ln \left(x^{2}-x +1\right)}{6}"," ",0,"-2/3*ln(x+1)-1/6*ln(x^2-x+1)+1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
308,1,37,36,0.051000," ","int((1-x)/x/(x^3+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}+\ln \left(x \right)-\frac{2 \ln \left(x +1\right)}{3}-\frac{\ln \left(x^{2}-x +1\right)}{6}"," ",0,"-2/3*ln(x+1)+ln(x)-1/6*ln(x^2-x+1)-1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
309,1,44,43,0.049000," ","int((1-x)/x^2/(x^3+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}-\ln \left(x \right)+\frac{2 \ln \left(x +1\right)}{3}+\frac{\ln \left(x^{2}-x +1\right)}{6}-\frac{1}{x}"," ",0,"2/3*ln(x+1)-1/x-ln(x)+1/6*ln(x^2-x+1)-1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
310,1,27,26,0.046000," ","int((1-x)/x^3/(x^3+1),x)","-\frac{2 \ln \left(x +1\right)}{3}+\frac{\ln \left(x^{2}-x +1\right)}{3}+\frac{1}{x}-\frac{1}{2 x^{2}}"," ",0,"-1/2/x^2+1/x-2/3*ln(x+1)+1/3*ln(x^2-x+1)","A"
311,1,35,34,0.051000," ","int(x*(2*x+1)/(x^3+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{3}+\frac{\ln \left(x +1\right)}{3}+\frac{5 \ln \left(x^{2}-x +1\right)}{6}"," ",0,"1/3*ln(x+1)+5/6*ln(x^2-x+1)+1/3*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
312,1,33,34,0.063000," ","int(x*(2*x+1)/(-x^3+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{3}-\ln \left(x -1\right)-\frac{\ln \left(x^{2}+x +1\right)}{2}"," ",0,"-ln(x-1)-1/2*ln(x^2+x+1)-1/3*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))","A"
313,1,44,43,0.041000," ","int(x^2*(e*x^2+d*x+c)*(b*x^3+a),x)","\frac{1}{8} b e \,x^{8}+\frac{1}{7} b d \,x^{7}+\frac{1}{6} b c \,x^{6}+\frac{1}{5} a e \,x^{5}+\frac{1}{4} a d \,x^{4}+\frac{1}{3} a c \,x^{3}"," ",0,"1/3*a*c*x^3+1/4*a*d*x^4+1/5*a*e*x^5+1/6*b*c*x^6+1/7*b*d*x^7+1/8*b*e*x^8","A"
314,1,44,43,0.048000," ","int(x*(e*x^2+d*x+c)*(b*x^3+a),x)","\frac{1}{7} b e \,x^{7}+\frac{1}{6} b d \,x^{6}+\frac{1}{5} b c \,x^{5}+\frac{1}{4} a e \,x^{4}+\frac{1}{3} a d \,x^{3}+\frac{1}{2} a c \,x^{2}"," ",0,"1/2*a*c*x^2+1/3*a*d*x^3+1/4*a*e*x^4+1/5*b*c*x^5+1/6*b*d*x^6+1/7*b*e*x^7","A"
315,1,41,40,0.045000," ","int((e*x^2+d*x+c)*(b*x^3+a),x)","\frac{1}{6} b e \,x^{6}+\frac{1}{5} b d \,x^{5}+\frac{1}{4} b c \,x^{4}+\frac{1}{3} a e \,x^{3}+\frac{1}{2} a d \,x^{2}+a c x"," ",0,"a*c*x+1/2*a*d*x^2+1/3*a*e*x^3+1/4*b*c*x^4+1/5*b*d*x^5+1/6*b*e*x^6","A"
316,1,39,38,0.048000," ","int((e*x^2+d*x+c)*(b*x^3+a)/x,x)","\frac{b e \,x^{5}}{5}+\frac{b d \,x^{4}}{4}+\frac{b c \,x^{3}}{3}+\frac{a e \,x^{2}}{2}+a c \ln \left(x \right)+a d x"," ",0,"a*d*x+1/2*a*e*x^2+1/3*b*c*x^3+1/4*b*d*x^4+1/5*b*e*x^5+a*c*ln(x)","A"
317,1,39,38,0.058000," ","int((e*x^2+d*x+c)*(b*x^3+a)/x^2,x)","\frac{b e \,x^{4}}{4}+\frac{b d \,x^{3}}{3}+\frac{b c \,x^{2}}{2}+a d \ln \left(x \right)+a e x -\frac{a c}{x}"," ",0,"-a*c/x+a*e*x+1/2*b*c*x^2+1/3*b*d*x^3+1/4*b*e*x^4+a*d*ln(x)","A"
318,1,39,38,0.056000," ","int((e*x^2+d*x+c)*(b*x^3+a)/x^3,x)","\frac{b e \,x^{3}}{3}+\frac{b d \,x^{2}}{2}+a e \ln \left(x \right)+b c x -\frac{a d}{x}-\frac{a c}{2 x^{2}}"," ",0,"-1/2*a*c/x^2-a*d/x+b*c*x+1/2*b*d*x^2+1/3*b*e*x^3+a*e*ln(x)","A"
319,1,80,68,0.049000," ","int(x^2*(e*x^2+d*x+c)*(b*x^3+a)^2,x)","\frac{1}{11} b^{2} e \,x^{11}+\frac{1}{10} b^{2} d \,x^{10}+\frac{1}{9} b^{2} c \,x^{9}+\frac{1}{4} a b e \,x^{8}+\frac{2}{7} a b d \,x^{7}+\frac{1}{3} a b c \,x^{6}+\frac{1}{5} a^{2} e \,x^{5}+\frac{1}{4} a^{2} d \,x^{4}+\frac{1}{3} a^{2} c \,x^{3}"," ",0,"1/11*b^2*e*x^11+1/10*b^2*d*x^10+1/9*b^2*c*x^9+1/4*a*b*e*x^8+2/7*a*b*d*x^7+1/3*a*b*c*x^6+1/5*a^2*e*x^5+1/4*a^2*d*x^4+1/3*a^2*c*x^3","A"
320,1,80,68,0.046000," ","int(x*(e*x^2+d*x+c)*(b*x^3+a)^2,x)","\frac{1}{10} b^{2} e \,x^{10}+\frac{1}{9} b^{2} d \,x^{9}+\frac{1}{8} b^{2} c \,x^{8}+\frac{2}{7} a b e \,x^{7}+\frac{1}{3} a b d \,x^{6}+\frac{2}{5} a b c \,x^{5}+\frac{1}{4} a^{2} e \,x^{4}+\frac{1}{3} a^{2} d \,x^{3}+\frac{1}{2} a^{2} c \,x^{2}"," ",0,"1/10*b^2*e*x^10+1/9*b^2*d*x^9+1/8*b^2*c*x^8+2/7*a*b*e*x^7+1/3*a*b*d*x^6+2/5*a*b*c*x^5+1/4*a^2*e*x^4+1/3*a^2*d*x^3+1/2*a^2*c*x^2","A"
321,1,77,65,0.043000," ","int((e*x^2+d*x+c)*(b*x^3+a)^2,x)","\frac{1}{9} b^{2} e \,x^{9}+\frac{1}{8} b^{2} d \,x^{8}+\frac{1}{7} b^{2} c \,x^{7}+\frac{1}{3} a b e \,x^{6}+\frac{2}{5} a b d \,x^{5}+\frac{1}{2} a b c \,x^{4}+\frac{1}{3} a^{2} e \,x^{3}+\frac{1}{2} a^{2} d \,x^{2}+a^{2} c x"," ",0,"1/9*b^2*e*x^9+1/8*b^2*d*x^8+1/7*b^2*c*x^7+1/3*a*b*e*x^6+2/5*a*b*d*x^5+1/2*a*b*c*x^4+1/3*a^2*e*x^3+1/2*a^2*d*x^2+a^2*c*x","A"
322,1,75,74,0.040000," ","int((e*x^2+d*x+c)*(b*x^3+a)^2/x,x)","\frac{b^{2} e \,x^{8}}{8}+\frac{b^{2} d \,x^{7}}{7}+\frac{b^{2} c \,x^{6}}{6}+\frac{2 a b e \,x^{5}}{5}+\frac{a b d \,x^{4}}{2}+\frac{2 a b c \,x^{3}}{3}+\frac{a^{2} e \,x^{2}}{2}+a^{2} c \ln \left(x \right)+a^{2} d x"," ",0,"a^2*d*x+1/2*a^2*e*x^2+2/3*a*b*c*x^3+1/2*a*b*d*x^4+2/5*a*b*e*x^5+1/6*b^2*c*x^6+1/7*b^2*d*x^7+1/8*b^2*e*x^8+a^2*c*ln(x)","A"
323,1,74,73,0.058000," ","int((e*x^2+d*x+c)*(b*x^3+a)^2/x^2,x)","\frac{b^{2} e \,x^{7}}{7}+\frac{b^{2} d \,x^{6}}{6}+\frac{b^{2} c \,x^{5}}{5}+\frac{a b e \,x^{4}}{2}+\frac{2 a b d \,x^{3}}{3}+a b c \,x^{2}+a^{2} d \ln \left(x \right)+a^{2} e x -\frac{a^{2} c}{x}"," ",0,"-a^2*c/x+a^2*e*x+a*b*c*x^2+2/3*a*b*d*x^3+1/2*a*b*e*x^4+1/5*b^2*c*x^5+1/6*b^2*d*x^6+1/7*b^2*e*x^7+a^2*d*ln(x)","A"
324,1,75,74,0.052000," ","int((e*x^2+d*x+c)*(b*x^3+a)^2/x^3,x)","\frac{b^{2} e \,x^{6}}{6}+\frac{b^{2} d \,x^{5}}{5}+\frac{b^{2} c \,x^{4}}{4}+\frac{2 a b e \,x^{3}}{3}+a b d \,x^{2}+a^{2} e \ln \left(x \right)+2 a b c x -\frac{a^{2} d}{x}-\frac{a^{2} c}{2 x^{2}}"," ",0,"-1/2*a^2*c/x^2-a^2*d/x+2*a*b*c*x+a*b*d*x^2+2/3*a*b*e*x^3+1/4*b^2*c*x^4+1/5*b^2*d*x^5+1/6*b^2*e*x^6+a^2*e*ln(x)","A"
325,1,116,92,0.043000," ","int(x^2*(e*x^2+d*x+c)*(b*x^3+a)^3,x)","\frac{1}{14} b^{3} e \,x^{14}+\frac{1}{13} b^{3} d \,x^{13}+\frac{1}{12} b^{3} c \,x^{12}+\frac{3}{11} a \,b^{2} e \,x^{11}+\frac{3}{10} a \,b^{2} d \,x^{10}+\frac{1}{3} a \,b^{2} c \,x^{9}+\frac{3}{8} a^{2} b e \,x^{8}+\frac{3}{7} a^{2} b d \,x^{7}+\frac{1}{2} a^{2} b c \,x^{6}+\frac{1}{5} a^{3} e \,x^{5}+\frac{1}{4} a^{3} d \,x^{4}+\frac{1}{3} a^{3} c \,x^{3}"," ",0,"1/14*b^3*e*x^14+1/13*b^3*d*x^13+1/12*b^3*c*x^12+3/11*a*b^2*e*x^11+3/10*a*b^2*d*x^10+1/3*a*b^2*c*x^9+3/8*a^2*b*e*x^8+3/7*a^2*b*d*x^7+1/2*a^2*b*c*x^6+1/5*a^3*e*x^5+1/4*a^3*d*x^4+1/3*a^3*c*x^3","A"
326,1,116,92,0.040000," ","int(x*(e*x^2+d*x+c)*(b*x^3+a)^3,x)","\frac{1}{13} b^{3} e \,x^{13}+\frac{1}{12} b^{3} d \,x^{12}+\frac{1}{11} b^{3} c \,x^{11}+\frac{3}{10} a \,b^{2} e \,x^{10}+\frac{1}{3} a \,b^{2} d \,x^{9}+\frac{3}{8} a \,b^{2} c \,x^{8}+\frac{3}{7} a^{2} b e \,x^{7}+\frac{1}{2} a^{2} b d \,x^{6}+\frac{3}{5} a^{2} b c \,x^{5}+\frac{1}{4} a^{3} e \,x^{4}+\frac{1}{3} a^{3} d \,x^{3}+\frac{1}{2} a^{3} c \,x^{2}"," ",0,"1/13*b^3*e*x^13+1/12*b^3*d*x^12+1/11*b^3*c*x^11+3/10*a*b^2*e*x^10+1/3*a*b^2*d*x^9+3/8*a*b^2*c*x^8+3/7*a^2*b*e*x^7+1/2*a^2*b*d*x^6+3/5*a^2*b*c*x^5+1/4*a^3*e*x^4+1/3*a^3*d*x^3+1/2*a^3*c*x^2","A"
327,1,113,89,0.052000," ","int((e*x^2+d*x+c)*(b*x^3+a)^3,x)","\frac{1}{12} b^{3} e \,x^{12}+\frac{1}{11} b^{3} d \,x^{11}+\frac{1}{10} b^{3} c \,x^{10}+\frac{1}{3} a \,b^{2} e \,x^{9}+\frac{3}{8} a \,b^{2} d \,x^{8}+\frac{3}{7} a \,b^{2} c \,x^{7}+\frac{1}{2} a^{2} b e \,x^{6}+\frac{3}{5} a^{2} b d \,x^{5}+\frac{3}{4} a^{2} b c \,x^{4}+\frac{1}{3} a^{3} e \,x^{3}+\frac{1}{2} a^{3} d \,x^{2}+a^{3} c x"," ",0,"1/12*b^3*e*x^12+1/11*b^3*d*x^11+1/10*b^3*c*x^10+1/3*a*b^2*e*x^9+3/8*a*b^2*d*x^8+3/7*a*b^2*c*x^7+1/2*a^2*b*e*x^6+3/5*a^2*b*d*x^5+3/4*a^2*b*c*x^4+1/3*a^3*e*x^3+1/2*a^3*d*x^2+a^3*c*x","A"
328,1,110,109,0.048000," ","int((e*x^2+d*x+c)*(b*x^3+a)^3/x,x)","\frac{b^{3} e \,x^{11}}{11}+\frac{b^{3} d \,x^{10}}{10}+\frac{b^{3} c \,x^{9}}{9}+\frac{3 a \,b^{2} e \,x^{8}}{8}+\frac{3 a \,b^{2} d \,x^{7}}{7}+\frac{a \,b^{2} c \,x^{6}}{2}+\frac{3 a^{2} b e \,x^{5}}{5}+\frac{3 a^{2} b d \,x^{4}}{4}+a^{2} b c \,x^{3}+\frac{a^{3} e \,x^{2}}{2}+a^{3} c \ln \left(x \right)+a^{3} d x"," ",0,"a^3*d*x+1/2*a^3*e*x^2+a^2*b*c*x^3+3/4*a^2*b*d*x^4+3/5*a^2*b*e*x^5+1/2*a*b^2*c*x^6+3/7*a*b^2*d*x^7+3/8*a*b^2*e*x^8+1/9*b^3*c*x^9+1/10*b^3*d*x^10+1/11*b^3*e*x^11+a^3*c*ln(x)","A"
329,1,110,109,0.050000," ","int((e*x^2+d*x+c)*(b*x^3+a)^3/x^2,x)","\frac{b^{3} e \,x^{10}}{10}+\frac{b^{3} d \,x^{9}}{9}+\frac{b^{3} c \,x^{8}}{8}+\frac{3 a \,b^{2} e \,x^{7}}{7}+\frac{a \,b^{2} d \,x^{6}}{2}+\frac{3 a \,b^{2} c \,x^{5}}{5}+\frac{3 a^{2} b e \,x^{4}}{4}+a^{2} b d \,x^{3}+\frac{3 a^{2} b c \,x^{2}}{2}+a^{3} d \ln \left(x \right)+a^{3} e x -\frac{a^{3} c}{x}"," ",0,"-a^3*c/x+a^3*e*x+3/2*a^2*b*c*x^2+a^2*b*d*x^3+3/4*a^2*b*e*x^4+3/5*a*b^2*c*x^5+1/2*a*b^2*d*x^6+3/7*a*b^2*e*x^7+1/8*b^3*c*x^8+1/9*b^3*d*x^9+1/10*b^3*e*x^10+a^3*d*ln(x)","A"
330,1,111,110,0.046000," ","int((e*x^2+d*x+c)*(b*x^3+a)^3/x^3,x)","\frac{b^{3} e \,x^{9}}{9}+\frac{b^{3} d \,x^{8}}{8}+\frac{b^{3} c \,x^{7}}{7}+\frac{a \,b^{2} e \,x^{6}}{2}+\frac{3 a \,b^{2} d \,x^{5}}{5}+\frac{3 a \,b^{2} c \,x^{4}}{4}+a^{2} b e \,x^{3}+\frac{3 a^{2} b d \,x^{2}}{2}+a^{3} e \ln \left(x \right)+3 a^{2} b c x -\frac{a^{3} d}{x}-\frac{a^{3} c}{2 x^{2}}"," ",0,"-1/2*a^3*c/x^2-a^3*d/x+3*a^2*b*c*x+3/2*a^2*b*d*x^2+a^2*b*e*x^3+3/4*a*b^2*c*x^4+3/5*a*b^2*d*x^5+1/2*a*b^2*e*x^6+1/7*b^3*c*x^7+1/8*b^3*d*x^8+1/9*b^3*e*x^9+a^3*e*ln(x)","A"
331,1,152,116,0.040000," ","int(x^2*(e*x^2+d*x+c)*(b*x^3+a)^4,x)","\frac{1}{17} b^{4} e \,x^{17}+\frac{1}{16} b^{4} d \,x^{16}+\frac{1}{15} b^{4} c \,x^{15}+\frac{2}{7} a \,b^{3} e \,x^{14}+\frac{4}{13} a \,b^{3} d \,x^{13}+\frac{1}{3} a \,b^{3} c \,x^{12}+\frac{6}{11} a^{2} b^{2} e \,x^{11}+\frac{3}{5} a^{2} b^{2} d \,x^{10}+\frac{2}{3} a^{2} b^{2} c \,x^{9}+\frac{1}{2} a^{3} b e \,x^{8}+\frac{4}{7} a^{3} b d \,x^{7}+\frac{2}{3} a^{3} b c \,x^{6}+\frac{1}{5} a^{4} e \,x^{5}+\frac{1}{4} a^{4} d \,x^{4}+\frac{1}{3} a^{4} c \,x^{3}"," ",0,"1/17*b^4*e*x^17+1/16*b^4*d*x^16+1/15*b^4*c*x^15+2/7*a*b^3*e*x^14+4/13*a*b^3*d*x^13+1/3*a*b^3*c*x^12+6/11*a^2*b^2*e*x^11+3/5*a^2*b^2*d*x^10+2/3*a^2*b^2*c*x^9+1/2*a^3*b*e*x^8+4/7*a^3*b*d*x^7+2/3*a^3*b*c*x^6+1/5*a^4*e*x^5+1/4*a^4*d*x^4+1/3*a^4*c*x^3","A"
332,1,152,116,0.041000," ","int(x*(e*x^2+d*x+c)*(b*x^3+a)^4,x)","\frac{1}{16} b^{4} e \,x^{16}+\frac{1}{15} b^{4} d \,x^{15}+\frac{1}{14} b^{4} c \,x^{14}+\frac{4}{13} a \,b^{3} e \,x^{13}+\frac{1}{3} a \,b^{3} d \,x^{12}+\frac{4}{11} a \,b^{3} c \,x^{11}+\frac{3}{5} a^{2} b^{2} e \,x^{10}+\frac{2}{3} a^{2} b^{2} d \,x^{9}+\frac{3}{4} a^{2} b^{2} c \,x^{8}+\frac{4}{7} a^{3} b e \,x^{7}+\frac{2}{3} a^{3} b d \,x^{6}+\frac{4}{5} a^{3} b c \,x^{5}+\frac{1}{4} a^{4} e \,x^{4}+\frac{1}{3} a^{4} d \,x^{3}+\frac{1}{2} a^{4} c \,x^{2}"," ",0,"1/16*b^4*e*x^16+1/15*b^4*d*x^15+1/14*b^4*c*x^14+4/13*a*b^3*e*x^13+1/3*a*b^3*d*x^12+4/11*a*b^3*c*x^11+3/5*a^2*b^2*e*x^10+2/3*a^2*b^2*d*x^9+3/4*a^2*b^2*c*x^8+4/7*a^3*b*e*x^7+2/3*a^3*b*d*x^6+4/5*a^3*b*c*x^5+1/4*a^4*e*x^4+1/3*a^4*d*x^3+1/2*a^4*c*x^2","A"
333,1,148,112,0.040000," ","int((e*x^2+d*x+c)*(b*x^3+a)^4,x)","\frac{1}{15} b^{4} e \,x^{15}+\frac{1}{14} b^{4} d \,x^{14}+\frac{1}{13} b^{4} c \,x^{13}+\frac{1}{3} a \,b^{3} e \,x^{12}+\frac{4}{11} a \,b^{3} d \,x^{11}+\frac{2}{5} a \,b^{3} c \,x^{10}+\frac{2}{3} a^{2} b^{2} e \,x^{9}+\frac{3}{4} a^{2} b^{2} d \,x^{8}+\frac{6}{7} a^{2} b^{2} c \,x^{7}+\frac{2}{3} a^{3} b e \,x^{6}+\frac{4}{5} a^{3} b d \,x^{5}+a^{3} b c \,x^{4}+\frac{1}{3} a^{4} e \,x^{3}+\frac{1}{2} a^{4} d \,x^{2}+a^{4} c x"," ",0,"1/15*b^4*e*x^15+1/14*b^4*d*x^14+1/13*b^4*c*x^13+1/3*a*b^3*e*x^12+4/11*a*b^3*d*x^11+2/5*a*b^3*c*x^10+2/3*a^2*b^2*e*x^9+3/4*a^2*b^2*d*x^8+6/7*a^2*b^2*c*x^7+2/3*a^3*b*e*x^6+4/5*a^3*b*d*x^5+a^3*b*c*x^4+1/3*a^4*e*x^3+1/2*a^4*d*x^2+a^4*c*x","A"
334,1,145,144,0.044000," ","int((e*x^2+d*x+c)*(b*x^3+a)^4/x,x)","\frac{b^{4} e \,x^{14}}{14}+\frac{b^{4} d \,x^{13}}{13}+\frac{b^{4} c \,x^{12}}{12}+\frac{4 a \,b^{3} e \,x^{11}}{11}+\frac{2 a \,b^{3} d \,x^{10}}{5}+\frac{4 a \,b^{3} c \,x^{9}}{9}+\frac{3 a^{2} b^{2} e \,x^{8}}{4}+\frac{6 a^{2} b^{2} d \,x^{7}}{7}+a^{2} b^{2} c \,x^{6}+\frac{4 a^{3} b e \,x^{5}}{5}+a^{3} b d \,x^{4}+\frac{4 a^{3} b c \,x^{3}}{3}+\frac{a^{4} e \,x^{2}}{2}+a^{4} c \ln \left(x \right)+a^{4} d x"," ",0,"a^4*d*x+1/2*a^4*e*x^2+4/3*a^3*b*c*x^3+a^3*b*d*x^4+4/5*a^3*b*e*x^5+a^2*b^2*c*x^6+6/7*a^2*b^2*d*x^7+3/4*a^2*b^2*e*x^8+4/9*a*b^3*c*x^9+2/5*a*b^3*d*x^10+4/11*a*b^3*e*x^11+1/12*b^4*c*x^12+1/13*b^4*d*x^13+1/14*b^4*e*x^14+a^4*c*ln(x)","A"
335,1,145,144,0.052000," ","int((e*x^2+d*x+c)*(b*x^3+a)^4/x^2,x)","\frac{b^{4} e \,x^{13}}{13}+\frac{b^{4} d \,x^{12}}{12}+\frac{b^{4} c \,x^{11}}{11}+\frac{2 a \,b^{3} e \,x^{10}}{5}+\frac{4 a \,b^{3} d \,x^{9}}{9}+\frac{a \,b^{3} c \,x^{8}}{2}+\frac{6 a^{2} b^{2} e \,x^{7}}{7}+a^{2} b^{2} d \,x^{6}+\frac{6 a^{2} b^{2} c \,x^{5}}{5}+a^{3} b e \,x^{4}+\frac{4 a^{3} b d \,x^{3}}{3}+2 a^{3} b c \,x^{2}+a^{4} d \ln \left(x \right)+a^{4} e x -\frac{a^{4} c}{x}"," ",0,"-a^4*c/x+a^4*e*x+2*a^3*b*c*x^2+4/3*a^3*b*d*x^3+a^3*b*e*x^4+6/5*a^2*b^2*c*x^5+a^2*b^2*d*x^6+6/7*a^2*b^2*e*x^7+1/2*a*b^3*c*x^8+4/9*a*b^3*d*x^9+2/5*a*b^3*e*x^10+1/11*b^4*c*x^11+1/12*b^4*d*x^12+1/13*b^4*e*x^13+a^4*d*ln(x)","A"
336,1,147,146,0.051000," ","int((e*x^2+d*x+c)*(b*x^3+a)^4/x^3,x)","\frac{b^{4} e \,x^{12}}{12}+\frac{b^{4} d \,x^{11}}{11}+\frac{b^{4} c \,x^{10}}{10}+\frac{4 a \,b^{3} e \,x^{9}}{9}+\frac{a \,b^{3} d \,x^{8}}{2}+\frac{4 a \,b^{3} c \,x^{7}}{7}+a^{2} b^{2} e \,x^{6}+\frac{6 a^{2} b^{2} d \,x^{5}}{5}+\frac{3 a^{2} b^{2} c \,x^{4}}{2}+\frac{4 a^{3} b e \,x^{3}}{3}+2 a^{3} b d \,x^{2}+a^{4} e \ln \left(x \right)+4 a^{3} b c x -\frac{a^{4} d}{x}-\frac{a^{4} c}{2 x^{2}}"," ",0,"-1/2*a^4*c/x^2-a^4*d/x+4*a^3*b*c*x+2*a^3*b*d*x^2+4/3*a^3*b*e*x^3+3/2*a^2*b^2*c*x^4+6/5*a^2*b^2*d*x^5+a^2*b^2*e*x^6+4/7*a*b^3*c*x^7+1/2*a*b^3*d*x^8+4/9*a*b^3*e*x^9+1/10*b^4*c*x^10+1/11*b^4*d*x^11+1/12*b^4*e*x^12+a^4*e*ln(x)","A"
337,1,231,151,0.044000," ","int(x^3*(e*x^2+d*x+c)/(b*x^3+a),x)","\frac{e \,x^{3}}{3 b}+\frac{d \,x^{2}}{2 b}-\frac{\sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a e \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{c x}{b}"," ",0,"1/3/b*e*x^3+1/2/b*d*x^2+1/b*c*x-1/3/(a/b)^(2/3)*a/b^2*c*ln(x+(a/b)^(1/3))+1/6*a/b^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*a/b^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*a/b^2*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6*a/b^2*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*a/b^2*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*a/b^2*e*ln(b*x^3+a)","A"
338,1,221,141,0.049000," ","int(x^2*(e*x^2+d*x+c)/(b*x^3+a),x)","\frac{e \,x^{2}}{2 b}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{c \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{d x}{b}"," ",0,"1/2/b*e*x^2+1/b*d*x-1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*d+1/6/(a/b)^(2/3)*a/b^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*d+1/3/b^2*a*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6/b^2*a*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/b^2*a*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b*c*ln(b*x^3+a)","A"
339,1,209,132,0.046000," ","int(x*(e*x^2+d*x+c)/(b*x^3+a),x)","-\frac{\sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{e x}{b}"," ",0,"1/b*e*x-1/3/(a/b)^(2/3)*a/b^2*e*ln(x+(a/b)^(1/3))+1/6/(a/b)^(2/3)*a/b^2*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a/b)^(2/3)*3^(1/2)*a/b^2*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/b*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6/b*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b*d*ln(b*x^3+a)","A"
340,1,200,126,0.046000," ","int((e*x^2+d*x+c)/(b*x^3+a),x)","\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{e \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/3*d/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6*d/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*d*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b*e*ln(b*x^3+a)","A"
341,1,207,133,0.053000," ","int((e*x^2+d*x+c)/x/(b*x^3+a),x)","\frac{c \ln \left(x \right)}{a}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"1/3/(a/b)^(2/3)/b*d*ln(x+(a/b)^(1/3))-1/6/(a/b)^(2/3)/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/(a/b)^(2/3)*3^(1/2)/b*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/(a/b)^(1/3)/b*e*ln(x+(a/b)^(1/3))+1/6/(a/b)^(1/3)/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*3^(1/2)/(a/b)^(1/3)/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a*c*ln(b*x^3+a)+1/a*c*ln(x)","A"
342,1,216,142,0.049000," ","int((e*x^2+d*x+c)/x^2/(b*x^3+a),x)","-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{d \ln \left(x \right)}{a}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c}{a x}"," ",0,"1/3*e/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/6*e/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*e/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/a*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-1/6/a*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/a*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a*d*ln(b*x^3+a)-1/a*c/x+1/a*d*ln(x)","A"
343,1,225,151,0.218000," ","int((e*x^2+d*x+c)/x^3/(b*x^3+a),x)","-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{e \ln \left(x \right)}{a}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a}-\frac{d}{a x}-\frac{c}{2 a \,x^{2}}"," ",0,"-1/3/(a/b)^(2/3)/a*c*ln(x+(a/b)^(1/3))+1/6/(a/b)^(2/3)/a*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a/b)^(2/3)*3^(1/2)/a*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(a/b)^(1/3)/a*d*ln(x+(a/b)^(1/3))-1/6/(a/b)^(1/3)/a*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3*3^(1/2)/(a/b)^(1/3)/a*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a*e*ln(b*x^3+a)+1/a*e*ln(x)-1/2/a*c/x^2-1/a*d/x","A"
344,1,219,141,0.053000," ","int(x^2*(e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{-\frac{e \,x^{2}}{3 b}-\frac{d x}{3 b}-\frac{c}{3 b}}{b \,x^{3}+a}"," ",0,"(-1/3/b*e*x^2-1/3/b*d*x-1/3*c/b)/(b*x^3+a)+1/9/(a/b)^(2/3)/b^2*d*ln(x+(a/b)^(1/3))-1/18/(a/b)^(2/3)/b^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/(a/b)^(2/3)*3^(1/2)/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
345,1,228,147,0.052000," ","int(x*(e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{\frac{c \,x^{2}}{3 a}-\frac{e x}{3 b}-\frac{d}{3 b}}{b \,x^{3}+a}"," ",0,"(1/3*c/a*x^2-1/3/b*e*x-1/3*d/b)/(b*x^3+a)+1/9/b^2*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/b/a*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18/(a/b)^(1/3)/a/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b/a*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
346,1,253,146,0.045000," ","int((e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{d \,x^{2}}{3 \left(b \,x^{3}+a \right) a}+\frac{c x}{3 \left(b \,x^{3}+a \right) a}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{e}{3 \left(b \,x^{3}+a \right) b}"," ",0,"1/3/(b*x^3+a)/a*c*x+2/9/(a/b)^(2/3)/a/b*c*ln(x+(a/b)^(1/3))-1/9/(a/b)^(2/3)/a/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/(a/b)^(2/3)*3^(1/2)/a/b*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(b*x^3+a)/a*d*x^2-1/9*d/a/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18*d/a/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9*d/a*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*e/b/(b*x^3+a)","A"
347,1,274,167,0.058000," ","int((e*x^2+d*x+c)/x/(b*x^3+a)^2,x)","\frac{e \,x^{2}}{3 \left(b \,x^{3}+a \right) a}+\frac{d x}{3 \left(b \,x^{3}+a \right) a}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{c}{3 \left(b \,x^{3}+a \right) a}+\frac{c \ln \left(x \right)}{a^{2}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{2}}"," ",0,"1/3/(b*x^3+a)/a*e*x^2+1/3/a*x/(b*x^3+a)*d+1/3/a/(b*x^3+a)*c+2/9/a/b*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/9/a/b*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a/b*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/(a/b)^(1/3)/a/b*e*ln(x+(a/b)^(1/3))+1/18/(a/b)^(1/3)/a/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9*3^(1/2)/(a/b)^(1/3)/a/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^2*c*ln(b*x^3+a)+1/a^2*c*ln(x)","A"
348,1,275,176,0.061000," ","int((e*x^2+d*x+c)/x^2/(b*x^3+a)^2,x)","-\frac{b c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{e x}{3 \left(b \,x^{3}+a \right) a}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{d}{3 \left(b \,x^{3}+a \right) a}-\frac{4 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{d \ln \left(x \right)}{a^{2}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{c}{a^{2} x}"," ",0,"-1/3/a^2/(b*x^3+a)*b*c*x^2+1/3/(b*x^3+a)/a*e*x+1/3/a/(b*x^3+a)*d+2/9/(a/b)^(2/3)/a/b*e*ln(x+(a/b)^(1/3))-1/9/(a/b)^(2/3)/a/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/(a/b)^(2/3)*3^(1/2)/a/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/a^2*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-2/9/a^2*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9*3^(1/2)/(a/b)^(1/3)/a^2*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^2*d*ln(b*x^3+a)-1/a^2*c/x+1/a^2*d*ln(x)","A"
349,1,276,185,0.059000," ","int((e*x^2+d*x+c)/x^3/(b*x^3+a)^2,x)","-\frac{b d \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{b c x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{e}{3 \left(b \,x^{3}+a \right) a}-\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{4 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{e \ln \left(x \right)}{a^{2}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{d}{a^{2} x}-\frac{c}{2 a^{2} x^{2}}"," ",0,"-1/3/(b*x^3+a)/a^2*b*d*x^2-1/3/a^2*b*x/(b*x^3+a)*c+1/3/a/(b*x^3+a)*e-5/9/a^2*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+5/18/a^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/a^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/(a/b)^(1/3)/a^2*d*ln(x+(a/b)^(1/3))-2/9/(a/b)^(1/3)/a^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9*3^(1/2)/(a/b)^(1/3)/a^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^2*e*ln(b*x^3+a)-1/a^2*d/x+1/a^2*e*ln(x)-1/2/a^2*c/x^2","A"
350,1,289,203,0.058000," ","int((e*x^2+d*x+c)/x^4/(b*x^3+a)^2,x)","-\frac{b e \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{b d x}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{b c}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{4 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 b c \ln \left(x \right)}{a^{3}}+\frac{2 b c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{e}{a^{2} x}-\frac{d}{2 a^{2} x^{2}}-\frac{c}{3 a^{2} x^{3}}"," ",0,"-1/3/(b*x^3+a)/a^2*b*e*x^2-1/3/(b*x^3+a)/a^2*b*d*x-1/3*b/a^2/(b*x^3+a)*c-5/9/(a/b)^(2/3)/a^2*d*ln(x+(a/b)^(1/3))+5/18/(a/b)^(2/3)/a^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/(a/b)^(2/3)*3^(1/2)/a^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/(a/b)^(1/3)/a^2*e*ln(x+(a/b)^(1/3))-2/9/a^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/a^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/3/a^3*b*c*ln(b*x^3+a)-1/a^2*e/x-1/3/a^2*c/x^3-1/2/a^2*d/x^2-2/a^3*b*c*ln(x)","A"
351,1,255,164,0.057000," ","int(x^2*(e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{\frac{e \,x^{5}}{9 a}+\frac{d \,x^{4}}{18 a}-\frac{e \,x^{2}}{18 b}-\frac{d x}{9 b}-\frac{c}{6 b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/9/a*e*x^5+1/18*d/a*x^4-1/18/b*e*x^2-1/9/b*d*x-1/6/b*c)/(b*x^3+a)^2+1/27/(a/b)^(2/3)/a/b^2*d*ln(x+(a/b)^(1/3))-1/54/(a/b)^(2/3)/a/b^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/27/(a/b)^(2/3)*3^(1/2)/a/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/27/a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*e+1/54/a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/27/a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e","A"
352,1,256,183,0.054000," ","int(x*(e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{\frac{2 b c \,x^{5}}{9 a^{2}}+\frac{e \,x^{4}}{18 a}+\frac{7 c \,x^{2}}{18 a}-\frac{e x}{9 b}-\frac{d}{6 b}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(2/9/a^2*c*b*x^5+1/18/a*e*x^4+7/18/a*c*x^2-1/9/b*e*x-1/6/b*d)/(b*x^3+a)^2+1/27/(a/b)^(2/3)/a/b^2*e*ln(x+(a/b)^(1/3))-1/54/(a/b)^(2/3)/a/b^2*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/27/(a/b)^(2/3)*3^(1/2)/a/b^2*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/27/(a/b)^(1/3)/a^2/b*c*ln(x+(a/b)^(1/3))+1/27/(a/b)^(1/3)/a^2/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27*3^(1/2)/(a/b)^(1/3)/a^2/b*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
353,1,308,170,0.049000," ","int((e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{e \,x^{3}}{6 \left(b \,x^{3}+a \right)^{2} a}+\frac{d \,x^{2}}{6 \left(b \,x^{3}+a \right)^{2} a}+\frac{c x}{6 \left(b \,x^{3}+a \right)^{2} a}+\frac{2 d \,x^{2}}{9 \left(b \,x^{3}+a \right) a^{2}}+\frac{5 c x}{18 \left(b \,x^{3}+a \right) a^{2}}-\frac{e}{6 \left(b \,x^{3}+a \right) a b}+\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}"," ",0,"1/6/(b*x^3+a)^2/a*c*x+5/18*c/a^2*x/(b*x^3+a)+5/27/(a/b)^(2/3)/a^2/b*c*ln(x+(a/b)^(1/3))-5/54/(a/b)^(2/3)/a^2/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/6/a/(b*x^3+a)^2*x^2*d+2/9*d/a^2*x^2/(b*x^3+a)-2/27/a^2/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/27/a^2/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+2/27/a^2/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/6*e/a*x^3/(b*x^3+a)^2-1/6*e/a/b/(b*x^3+a)","A"
354,1,331,200,0.073000," ","int((e*x^2+d*x+c)/x/(b*x^3+a)^3,x)","\frac{2 b e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{5 b d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b c \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{7 e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}+\frac{4 d x}{9 \left(b \,x^{3}+a \right)^{2} a}+\frac{c}{2 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{c \ln \left(x \right)}{a^{3}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}"," ",0,"2/9/a^2/(b*x^3+a)^2*b*e*x^5+5/18/(b*x^3+a)^2/a^2*b*d*x^4+1/3/a^2/(b*x^3+a)^2*x^3*c*b+7/18/a/(b*x^3+a)^2*e*x^2+4/9/(b*x^3+a)^2/a*d*x+1/2/(b*x^3+a)^2/a*c+5/27/(a/b)^(2/3)/a^2/b*d*ln(x+(a/b)^(1/3))-5/54/(a/b)^(2/3)/a^2/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/27/a^2*e/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/27/a^2*e/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27/a^2*e*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^3*c*ln(b*x^3+a)+1/a^3*c*ln(x)","A"
355,1,334,210,0.061000," ","int((e*x^2+d*x+c)/x^2/(b*x^3+a)^3,x)","-\frac{5 b^{2} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{5 b e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b d \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{13 b c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 e x}{9 \left(b \,x^{3}+a \right)^{2} a}+\frac{d}{2 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{14 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{d \ln \left(x \right)}{a^{3}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{c}{a^{3} x}"," ",0,"-5/9/(b*x^3+a)^2/a^3*b^2*c*x^5+5/18/(b*x^3+a)^2/a^2*b*e*x^4+1/3/a^2/(b*x^3+a)^2*b*d*x^3-13/18/(b*x^3+a)^2/a^2*b*c*x^2+4/9/(b*x^3+a)^2/a*e*x+1/2/(b*x^3+a)^2/a*d+5/27/(a/b)^(2/3)/a^2/b*e*ln(x+(a/b)^(1/3))-5/54/(a/b)^(2/3)/a^2/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+14/27/a^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-7/27/a^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-14/27/a^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/3/a^3*d*ln(b*x^3+a)-1/a^3*c/x+1/a^3*d*ln(x)","A"
356,1,337,217,0.065000," ","int((e*x^2+d*x+c)/x^3/(b*x^3+a)^3,x)","-\frac{5 b^{2} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{11 b^{2} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{b e \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{13 b d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{7 b c x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{e}{2 \left(b \,x^{3}+a \right)^{2} a}-\frac{20 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{14 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{e \ln \left(x \right)}{a^{3}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{d}{a^{3} x}-\frac{c}{2 a^{3} x^{2}}"," ",0,"-5/9/(b*x^3+a)^2/a^3*b^2*d*x^5-11/18/(b*x^3+a)^2/a^3*b^2*c*x^4+1/3*b/a^2/(b*x^3+a)^2*e*x^3-13/18/(b*x^3+a)^2/a^2*b*d*x^2-7/9/(b*x^3+a)^2/a^2*b*c*x+1/2/a/(b*x^3+a)^2*e-20/27/(a/b)^(2/3)/a^3*c*ln(x+(a/b)^(1/3))+10/27/(a/b)^(2/3)/a^3*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-20/27/(a/b)^(2/3)*3^(1/2)/a^3*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+14/27/a^3*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-7/27/a^3*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27/a^3*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^3*e*ln(b*x^3+a)-1/a^3*d/x+1/a^3*e*ln(x)-1/2/a^3*c/x^2","A"
357,1,351,239,0.063000," ","int((e*x^2+d*x+c)/x^4/(b*x^3+a)^3,x)","-\frac{5 b^{2} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{11 b^{2} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{2 b^{2} c \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{3}}-\frac{13 b e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{7 b d x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b c}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{20 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{14 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{3 b c \ln \left(x \right)}{a^{4}}+\frac{b c \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{e}{a^{3} x}-\frac{d}{2 a^{3} x^{2}}-\frac{c}{3 a^{3} x^{3}}"," ",0,"-5/9/(b*x^3+a)^2/a^3*b^2*e*x^5-11/18/(b*x^3+a)^2/a^3*b^2*d*x^4-2/3/a^3*b^2/(b*x^3+a)^2*x^3*c-13/18/a^2/(b*x^3+a)^2*x^2*b*e-7/9/(b*x^3+a)^2/a^2*b*d*x-5/6/(b*x^3+a)^2/a^2*b*c-20/27/(a/b)^(2/3)/a^3*d*ln(x+(a/b)^(1/3))+10/27/(a/b)^(2/3)/a^3*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-20/27/(a/b)^(2/3)*3^(1/2)/a^3*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+14/27/a^3*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-7/27/(a/b)^(1/3)/a^3*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27*3^(1/2)/(a/b)^(1/3)/a^3*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/a^4*b*c*ln(b*x^3+a)-1/3/a^3*c/x^3-1/2/a^3*d/x^2-1/a^3*e/x-3/a^4*b*c*ln(x)","A"
358,1,275,195,0.056000," ","int(x^2*(e*x^2+d*x+c)/(b*x^3+a)^4,x)","\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2}}+\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2}}-\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{486 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2}}+\frac{4 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b^{2}}-\frac{4 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b^{2}}+\frac{2 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b^{2}}+\frac{\frac{4 b e \,x^{8}}{81 a^{2}}+\frac{5 b d \,x^{7}}{162 a^{2}}+\frac{11 e \,x^{5}}{81 a}+\frac{13 d \,x^{4}}{162 a}-\frac{2 e \,x^{2}}{81 b}-\frac{5 d x}{81 b}-\frac{c}{9 b}}{\left(b \,x^{3}+a \right)^{3}}"," ",0,"(4/81/a^2*b*e*x^8+5/162/a^2*d*b*x^7+11/81/a*e*x^5+13/162/a*d*x^4-2/81/b*e*x^2-5/81/b*d*x-1/9/b*c)/(b*x^3+a)^3+5/243/a^2/b^2*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-5/486/a^2/b^2*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/243/a^2/b^2*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-4/243/a^2/b^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+2/243/a^2/b^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+4/243/a^2/b^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
359,1,278,212,0.055000," ","int(x*(e*x^2+d*x+c)/(b*x^3+a)^4,x)","\frac{5 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2}}+\frac{5 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2}}-\frac{5 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{486 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2}}+\frac{14 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}-\frac{14 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}+\frac{7 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}+\frac{\frac{14 b^{2} c \,x^{8}}{81 a^{3}}+\frac{5 b e \,x^{7}}{162 a^{2}}+\frac{77 b c \,x^{5}}{162 a^{2}}+\frac{13 e \,x^{4}}{162 a}+\frac{67 c \,x^{2}}{162 a}-\frac{5 e x}{81 b}-\frac{d}{9 b}}{\left(b \,x^{3}+a \right)^{3}}"," ",0,"(14/81*c/a^3*b^2*x^8+5/162/a^2*b*e*x^7+77/162/a^2*b*c*x^5+13/162/a*e*x^4+67/162/a*c*x^2-5/81/b*e*x-1/9/b*d)/(b*x^3+a)^3+5/243/a^2/b^2*e/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-5/486/a^2/b^2*e/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/243/a^2/b^2*e/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-14/243/a^3/b*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/243/a^3/b*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/243/a^3/b*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
360,1,360,193,0.055000," ","int((e*x^2+d*x+c)/(b*x^3+a)^4,x)","\frac{e \,x^{3}}{9 \left(b \,x^{3}+a \right)^{3} a}+\frac{d \,x^{2}}{9 \left(b \,x^{3}+a \right)^{3} a}+\frac{e \,x^{3}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{c x}{9 \left(b \,x^{3}+a \right)^{3} a}+\frac{7 d \,x^{2}}{54 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 c x}{27 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{14 d \,x^{2}}{81 \left(b \,x^{3}+a \right) a^{3}}+\frac{20 c x}{81 \left(b \,x^{3}+a \right) a^{3}}-\frac{e}{9 \left(b \,x^{3}+a \right) a^{2} b}+\frac{40 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{40 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}-\frac{20 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{14 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}-\frac{14 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}+\frac{7 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}"," ",0,"1/9*c/a*x/(b*x^3+a)^3+4/27*c/a^2*x/(b*x^3+a)^2+20/81*c/a^3*x/(b*x^3+a)+40/243*c/a^3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-20/243*c/a^3/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+40/243*c/a^3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9*d/a*x^2/(b*x^3+a)^3+7/54*d/a^2*x^2/(b*x^3+a)^2+14/81*d/a^3*x^2/(b*x^3+a)-14/243*d/a^3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/243*d/a^3/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/243*d/a^3*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9*e/a*x^3/(b*x^3+a)^3+1/9*e/a^2*x^3/(b*x^3+a)^2-1/9*e/a^2/b/(b*x^3+a)","A"
361,1,394,232,0.063000," ","int((e*x^2+d*x+c)/x/(b*x^3+a)^4,x)","\frac{14 b^{2} e \,x^{8}}{81 \left(b \,x^{3}+a \right)^{3} a^{3}}+\frac{20 b^{2} d \,x^{7}}{81 \left(b \,x^{3}+a \right)^{3} a^{3}}+\frac{b^{2} c \,x^{6}}{3 \left(b \,x^{3}+a \right)^{3} a^{3}}+\frac{77 b e \,x^{5}}{162 \left(b \,x^{3}+a \right)^{3} a^{2}}+\frac{52 b d \,x^{4}}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}+\frac{5 b c \,x^{3}}{6 \left(b \,x^{3}+a \right)^{3} a^{2}}+\frac{67 e \,x^{2}}{162 \left(b \,x^{3}+a \right)^{3} a}+\frac{41 d x}{81 \left(b \,x^{3}+a \right)^{3} a}+\frac{11 c}{18 \left(b \,x^{3}+a \right)^{3} a}+\frac{40 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{40 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}-\frac{20 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{14 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}-\frac{14 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}+\frac{7 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b}+\frac{c \ln \left(x \right)}{a^{4}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{4}}"," ",0,"14/81/a^3/(b*x^3+a)^3*b^2*e*x^8+20/81/a^3/(b*x^3+a)^3*b^2*d*x^7+1/3/a^3/(b*x^3+a)^3*b^2*c*x^6+77/162/a^2/(b*x^3+a)^3*b*e*x^5+52/81/a^2/(b*x^3+a)^3*b*d*x^4+5/6/a^2/(b*x^3+a)^3*b*c*x^3+67/162/a/(b*x^3+a)^3*e*x^2+41/81/a/(b*x^3+a)^3*d*x+11/18/a/(b*x^3+a)^3*c+40/243/a^3*d/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-20/243/a^3*d/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+40/243/a^3*d/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-14/243/a^3*e/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+7/243/a^3*e/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/243/a^3*e*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*c*ln(b*x^3+a)/a^4+c*ln(x)/a^4","A"
362,1,397,242,0.067000," ","int((e*x^2+d*x+c)/x^2/(b*x^3+a)^4,x)","-\frac{59 b^{3} c \,x^{8}}{81 \left(b \,x^{3}+a \right)^{3} a^{4}}+\frac{20 b^{2} e \,x^{7}}{81 \left(b \,x^{3}+a \right)^{3} a^{3}}+\frac{b^{2} d \,x^{6}}{3 \left(b \,x^{3}+a \right)^{3} a^{3}}-\frac{142 b^{2} c \,x^{5}}{81 \left(b \,x^{3}+a \right)^{3} a^{3}}+\frac{52 b e \,x^{4}}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}+\frac{5 b d \,x^{3}}{6 \left(b \,x^{3}+a \right)^{3} a^{2}}-\frac{92 b c \,x^{2}}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}+\frac{41 e x}{81 \left(b \,x^{3}+a \right)^{3} a}+\frac{11 d}{18 \left(b \,x^{3}+a \right)^{3} a}+\frac{40 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}+\frac{40 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}-\frac{20 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b}-\frac{140 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{140 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{70 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{d \ln \left(x \right)}{a^{4}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{4}}-\frac{c}{a^{4} x}"," ",0,"-59/81/a^4/(b*x^3+a)^3*b^3*c*x^8+20/81/a^3/(b*x^3+a)^3*b^2*e*x^7+1/3/a^3/(b*x^3+a)^3*b^2*d*x^6-142/81/a^3/(b*x^3+a)^3*b^2*c*x^5+52/81/a^2/(b*x^3+a)^3*b*e*x^4+5/6/a^2/(b*x^3+a)^3*b*d*x^3-92/81/a^2/(b*x^3+a)^3*b*c*x^2+41/81/a/(b*x^3+a)^3*e*x+11/18/a/(b*x^3+a)^3*d+40/243/a^3*e/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-20/243/a^3*e/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+40/243/a^3*e/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+140/243/a^4*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-70/243/a^4*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-140/243/a^4*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*d*ln(b*x^3+a)/a^4-c/a^4/x+d*ln(x)/a^4","A"
363,1,400,249,0.067000," ","int((e*x^2+d*x+c)/x^3/(b*x^3+a)^4,x)","-\frac{59 b^{3} d \,x^{8}}{81 \left(b \,x^{3}+a \right)^{3} a^{4}}-\frac{139 b^{3} c \,x^{7}}{162 \left(b \,x^{3}+a \right)^{3} a^{4}}+\frac{b^{2} e \,x^{6}}{3 \left(b \,x^{3}+a \right)^{3} a^{3}}-\frac{142 b^{2} d \,x^{5}}{81 \left(b \,x^{3}+a \right)^{3} a^{3}}-\frac{329 b^{2} c \,x^{4}}{162 \left(b \,x^{3}+a \right)^{3} a^{3}}+\frac{5 b e \,x^{3}}{6 \left(b \,x^{3}+a \right)^{3} a^{2}}-\frac{92 b d \,x^{2}}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}-\frac{104 b c x}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}+\frac{11 e}{18 \left(b \,x^{3}+a \right)^{3} a}-\frac{220 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{220 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{110 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{140 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{140 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{70 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{e \ln \left(x \right)}{a^{4}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{4}}-\frac{d}{a^{4} x}-\frac{c}{2 a^{4} x^{2}}"," ",0,"-59/81/a^4*b^3/(b*x^3+a)^3*d*x^8-139/162/a^4*b^3/(b*x^3+a)^3*c*x^7+1/3/a^3*b^2/(b*x^3+a)^3*e*x^6-142/81/a^3*b^2/(b*x^3+a)^3*d*x^5-329/162/a^3*b^2/(b*x^3+a)^3*c*x^4+5/6/a^2*b/(b*x^3+a)^3*e*x^3-92/81/a^2*b/(b*x^3+a)^3*d*x^2-104/81/a^2*b/(b*x^3+a)^3*c*x+11/18/a/(b*x^3+a)^3*e-220/243/a^4*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+110/243/a^4*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-220/243/a^4*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+140/243/a^4*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-70/243/a^4*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-140/243/a^4*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*e*ln(b*x^3+a)/a^4-1/2*c/a^4/x^2-d/a^4/x+e*ln(x)/a^4","A"
364,1,415,277,0.066000," ","int((e*x^2+d*x+c)/x^4/(b*x^3+a)^4,x)","-\frac{59 b^{3} e \,x^{8}}{81 \left(b \,x^{3}+a \right)^{3} a^{4}}-\frac{139 b^{3} d \,x^{7}}{162 \left(b \,x^{3}+a \right)^{3} a^{4}}-\frac{b^{3} c \,x^{6}}{\left(b \,x^{3}+a \right)^{3} a^{4}}-\frac{142 b^{2} e \,x^{5}}{81 \left(b \,x^{3}+a \right)^{3} a^{3}}-\frac{329 b^{2} d \,x^{4}}{162 \left(b \,x^{3}+a \right)^{3} a^{3}}-\frac{7 b^{2} c \,x^{3}}{3 \left(b \,x^{3}+a \right)^{3} a^{3}}-\frac{92 b e \,x^{2}}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}-\frac{104 b d x}{81 \left(b \,x^{3}+a \right)^{3} a^{2}}-\frac{13 b c}{9 \left(b \,x^{3}+a \right)^{3} a^{2}}-\frac{220 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{220 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}+\frac{110 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}}-\frac{140 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}+\frac{140 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{70 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{243 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}}-\frac{4 b c \ln \left(x \right)}{a^{5}}+\frac{4 b c \ln \left(b \,x^{3}+a \right)}{3 a^{5}}-\frac{e}{a^{4} x}-\frac{d}{2 a^{4} x^{2}}-\frac{c}{3 a^{4} x^{3}}"," ",0,"-59/81/a^4*b^3/(b*x^3+a)^3*e*x^8-139/162/a^4*b^3/(b*x^3+a)^3*d*x^7-1/a^4*b^3/(b*x^3+a)^3*c*x^6-142/81/a^3*b^2/(b*x^3+a)^3*e*x^5-329/162/a^3*b^2/(b*x^3+a)^3*d*x^4-7/3/a^3*b^2/(b*x^3+a)^3*c*x^3-92/81/a^2*b/(b*x^3+a)^3*e*x^2-104/81/a^2*b/(b*x^3+a)^3*d*x-13/9/a^2*b/(b*x^3+a)^3*c-220/243/a^4*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+110/243/a^4*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-220/243/a^4*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+140/243/a^4*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-70/243/a^4*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-140/243/a^4*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/3*b*c*ln(b*x^3+a)/a^5-1/3*c/a^4/x^3-1/2*d/a^4/x^2-e/a^4/x-4*b*c*ln(x)/a^5","A"
365,1,29,26,0.052000," ","int((2*a*x-x^2)/(a^3+x^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(-a +2 x \right) \sqrt{3}}{3 a}\right)}{3}-\ln \left(a +x \right)"," ",0,"-ln(a+x)+2/3*3^(1/2)*arctan(1/3*(2*x-a)*3^(1/2)/a)","A"
366,1,29,26,0.052000," ","int((2*a-x)*x/(a^3+x^3),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(-a +2 x \right) \sqrt{3}}{3 a}\right)}{3}-\ln \left(a +x \right)"," ",0,"2/3*3^(1/2)*arctan(1/3*(-a+2*x)*3^(1/2)/a)-ln(a+x)","A"
367,1,29,28,0.049000," ","int((2*a*x+x^2)/(a^3-x^3),x)","-\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(a +2 x \right) \sqrt{3}}{3 a}\right)}{3}-\ln \left(-a +x \right)"," ",0,"-2/3*arctan(1/3*(a+2*x)/a*3^(1/2))*3^(1/2)-ln(x-a)","A"
368,1,29,28,0.058000," ","int(x*(2*a+x)/(a^3-x^3),x)","-\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(a +2 x \right) \sqrt{3}}{3 a}\right)}{3}-\ln \left(-a +x \right)"," ",0,"-2/3*3^(1/2)*arctan(1/3*(a+2*x)*3^(1/2)/a)-ln(-a+x)","A"
369,1,87,43,0.049000," ","int(x*(-2*(a/b)^(1/3)*C+C*x)/(b*x^3+a),x)","-\frac{2 \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 b}+\frac{2 C \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 b}-\frac{C \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"2/3*C/b*ln(x+(a/b)^(1/3))-1/3*C/b*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-2/3*3^(1/2)*C/b*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b*ln(b*x^3+a)","A"
370,1,135,46,0.052000," ","int(x*(-2*(-a/b)^(1/3)*C+C*x)/(-b*x^3+a),x)","\frac{2 \left(-\frac{a}{b}\right)^{\frac{1}{3}} \sqrt{3}\, C \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{2 \left(-\frac{a}{b}\right)^{\frac{1}{3}} C \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} C \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{C \ln \left(b \,x^{3}-a \right)}{3 b}"," ",0,"2/3*C*(-a/b)^(1/3)/b/(a/b)^(1/3)*ln(x-(a/b)^(1/3))-1/3*C*(-a/b)^(1/3)/b/(a/b)^(1/3)*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C*(-a/b)^(1/3)*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))-1/3*C/b*ln(b*x^3-a)","B"
371,1,132,47,0.056000," ","int(x*(2*(-a/b)^(1/3)*C+C*x)/(b*x^3+a),x)","\frac{2 \left(-\frac{a}{b}\right)^{\frac{1}{3}} \sqrt{3}\, C \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{2 \left(-\frac{a}{b}\right)^{\frac{1}{3}} C \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{\left(-\frac{a}{b}\right)^{\frac{1}{3}} C \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{C \ln \left(b \,x^{3}+a \right)}{3 b}"," ",0,"-2/3*C*(-a/b)^(1/3)/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/3*C*(-a/b)^(1/3)/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/3*C*(-a/b)^(1/3)*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*C/b*ln(b*x^3+a)","B"
372,1,90,46,0.051000," ","int(x*(2*(a/b)^(1/3)*C+C*x)/(-b*x^3+a),x)","-\frac{2 \sqrt{3}\, C \arctan \left(\frac{\left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}+1\right) \sqrt{3}}{3}\right)}{3 b}-\frac{2 C \ln \left(x -\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 b}+\frac{C \ln \left(x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{3 b}-\frac{C \ln \left(b \,x^{3}-a \right)}{3 b}"," ",0,"-2/3*C/b*ln(x-(a/b)^(1/3))+1/3*C/b*ln(x^2+(a/b)^(1/3)*x+(a/b)^(2/3))-2/3*3^(1/2)*C/b*arctan(1/3*(2/(a/b)^(1/3)*x+1)*3^(1/2))-1/3*C/b*ln(b*x^3-a)","A"
373,1,80,79,0.046000," ","int(x^4*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b h \,x^{13}}{13}+\frac{b g \,x^{12}}{12}+\frac{b f \,x^{11}}{11}+\frac{\left(a h +b e \right) x^{10}}{10}+\frac{a e \,x^{7}}{7}+\frac{\left(a g +b d \right) x^{9}}{9}+\frac{a d \,x^{6}}{6}+\frac{\left(a f +b c \right) x^{8}}{8}+\frac{a c \,x^{5}}{5}"," ",0,"1/5*a*c*x^5+1/6*a*d*x^6+1/7*a*e*x^7+1/8*(a*f+b*c)*x^8+1/9*(a*g+b*d)*x^9+1/10*(a*h+b*e)*x^10+1/11*b*f*x^11+1/12*b*g*x^12+1/13*b*h*x^13","A"
374,1,80,79,0.048000," ","int(x^3*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b h \,x^{12}}{12}+\frac{b g \,x^{11}}{11}+\frac{b f \,x^{10}}{10}+\frac{\left(a h +b e \right) x^{9}}{9}+\frac{a e \,x^{6}}{6}+\frac{\left(a g +b d \right) x^{8}}{8}+\frac{a d \,x^{5}}{5}+\frac{\left(a f +b c \right) x^{7}}{7}+\frac{a c \,x^{4}}{4}"," ",0,"1/4*a*c*x^4+1/5*a*d*x^5+1/6*a*e*x^6+1/7*(a*f+b*c)*x^7+1/8*(a*g+b*d)*x^8+1/9*(a*h+b*e)*x^9+1/10*b*f*x^10+1/11*b*g*x^11+1/12*b*h*x^12","A"
375,1,80,79,0.046000," ","int(x^2*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b h \,x^{11}}{11}+\frac{b g \,x^{10}}{10}+\frac{b f \,x^{9}}{9}+\frac{\left(a h +b e \right) x^{8}}{8}+\frac{a e \,x^{5}}{5}+\frac{\left(a g +b d \right) x^{7}}{7}+\frac{a d \,x^{4}}{4}+\frac{\left(a f +b c \right) x^{6}}{6}+\frac{a c \,x^{3}}{3}"," ",0,"1/3*a*c*x^3+1/4*a*d*x^4+1/5*a*e*x^5+1/6*(a*f+b*c)*x^6+1/7*(a*g+b*d)*x^7+1/8*(a*h+b*e)*x^8+1/9*b*f*x^9+1/10*b*g*x^10+1/11*b*h*x^11","A"
376,1,80,79,0.046000," ","int(x*(b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b h \,x^{10}}{10}+\frac{b g \,x^{9}}{9}+\frac{b f \,x^{8}}{8}+\frac{\left(a h +b e \right) x^{7}}{7}+\frac{a e \,x^{4}}{4}+\frac{\left(a g +b d \right) x^{6}}{6}+\frac{a d \,x^{3}}{3}+\frac{\left(a f +b c \right) x^{5}}{5}+\frac{a c \,x^{2}}{2}"," ",0,"1/2*a*c*x^2+1/3*a*d*x^3+1/4*a*e*x^4+1/5*(a*f+b*c)*x^5+1/6*(a*g+b*d)*x^6+1/7*(a*h+b*e)*x^7+1/8*b*f*x^8+1/9*b*g*x^9+1/10*b*h*x^10","A"
377,1,77,76,0.040000," ","int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b h \,x^{9}}{9}+\frac{b g \,x^{8}}{8}+\frac{b f \,x^{7}}{7}+\frac{\left(a h +b e \right) x^{6}}{6}+\frac{a e \,x^{3}}{3}+\frac{\left(a g +b d \right) x^{5}}{5}+\frac{a d \,x^{2}}{2}+\frac{\left(a f +b c \right) x^{4}}{4}+a c x"," ",0,"a*c*x+1/2*a*d*x^2+1/3*a*e*x^3+1/4*(a*f+b*c)*x^4+1/5*(a*g+b*d)*x^5+1/6*(a*h+b*e)*x^6+1/7*b*f*x^7+1/8*b*g*x^8+1/9*b*h*x^9","A"
378,1,81,74,0.049000," ","int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x)","\frac{b h \,x^{8}}{8}+\frac{b g \,x^{7}}{7}+\frac{b f \,x^{6}}{6}+\frac{a h \,x^{5}}{5}+\frac{b e \,x^{5}}{5}+\frac{a g \,x^{4}}{4}+\frac{b d \,x^{4}}{4}+\frac{a f \,x^{3}}{3}+\frac{b c \,x^{3}}{3}+\frac{a e \,x^{2}}{2}+a c \ln \left(x \right)+a d x"," ",0,"1/8*b*h*x^8+1/7*b*g*x^7+1/6*b*f*x^6+1/5*x^5*a*h+1/5*b*e*x^5+1/4*x^4*a*g+1/4*b*d*x^4+1/3*x^3*a*f+1/3*b*c*x^3+1/2*a*e*x^2+a*d*x+a*c*ln(x)","A"
379,1,81,74,0.051000," ","int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x)","\frac{b h \,x^{7}}{7}+\frac{b g \,x^{6}}{6}+\frac{b f \,x^{5}}{5}+\frac{a h \,x^{4}}{4}+\frac{b e \,x^{4}}{4}+\frac{a g \,x^{3}}{3}+\frac{b d \,x^{3}}{3}+\frac{a f \,x^{2}}{2}+\frac{b c \,x^{2}}{2}+a d \ln \left(x \right)+a e x -\frac{a c}{x}"," ",0,"1/7*b*h*x^7+1/6*b*g*x^6+1/5*b*f*x^5+1/4*x^4*a*h+1/4*b*e*x^4+1/3*x^3*a*g+1/3*b*d*x^3+1/2*x^2*a*f+1/2*b*c*x^2+a*e*x-a*c/x+a*d*ln(x)","A"
380,1,78,74,0.051000," ","int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x)","\frac{b h \,x^{6}}{6}+\frac{b g \,x^{5}}{5}+\frac{b f \,x^{4}}{4}+\frac{a h \,x^{3}}{3}+\frac{b e \,x^{3}}{3}+\frac{a g \,x^{2}}{2}+\frac{b d \,x^{2}}{2}+a e \ln \left(x \right)+a f x +b c x -\frac{a d}{x}-\frac{a c}{2 x^{2}}"," ",0,"1/6*b*h*x^6+1/5*b*g*x^5+1/4*b*f*x^4+1/3*x^3*a*h+1/3*b*e*x^3+1/2*x^2*a*g+1/2*b*d*x^2+a*f*x+b*c*x-1/2*a*c/x^2-a*d/x+a*e*ln(x)","A"
381,1,76,74,0.048000," ","int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x)","\frac{b h \,x^{5}}{5}+\frac{b g \,x^{4}}{4}+\frac{b f \,x^{3}}{3}+\frac{a h \,x^{2}}{2}+\frac{b e \,x^{2}}{2}+a f \ln \left(x \right)+a g x +b c \ln \left(x \right)+b d x -\frac{a e}{x}-\frac{a d}{2 x^{2}}-\frac{a c}{3 x^{3}}"," ",0,"1/5*b*h*x^5+1/4*b*g*x^4+1/3*b*f*x^3+1/2*x^2*a*h+1/2*b*e*x^2+a*g*x+x*b*d-1/3*a*c/x^3-1/2*a*d/x^2-a*e/x+ln(x)*a*f+ln(x)*b*c","A"
382,1,76,75,0.051000," ","int((b*x^3+a)*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x)","\frac{b h \,x^{4}}{4}+\frac{b g \,x^{3}}{3}+\frac{b f \,x^{2}}{2}+a g \ln \left(x \right)+a h x +b d \ln \left(x \right)+b e x -\frac{a f}{x}-\frac{b c}{x}-\frac{a e}{2 x^{2}}-\frac{a d}{3 x^{3}}-\frac{a c}{4 x^{4}}"," ",0,"1/4*b*h*x^4+1/3*b*g*x^3+1/2*b*f*x^2+a*h*x+b*e*x-1/4*a*c/x^4-1/3*a*d/x^3-1/2*a*e/x^2-1/x*a*f-1/x*b*c+ln(x)*a*g+ln(x)*b*d","A"
383,1,152,139,0.043000," ","int(x^4*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{2} h \,x^{16}}{16}+\frac{b^{2} g \,x^{15}}{15}+\frac{b^{2} f \,x^{14}}{14}+\frac{\left(2 a b h +b^{2} e \right) x^{13}}{13}+\frac{\left(2 a b g +b^{2} d \right) x^{12}}{12}+\frac{\left(2 a b f +c \,b^{2}\right) x^{11}}{11}+\frac{a^{2} e \,x^{7}}{7}+\frac{\left(a^{2} h +2 b e a \right) x^{10}}{10}+\frac{a^{2} d \,x^{6}}{6}+\frac{\left(a^{2} g +2 b d a \right) x^{9}}{9}+\frac{a^{2} c \,x^{5}}{5}+\frac{\left(a^{2} f +2 a b c \right) x^{8}}{8}"," ",0,"1/16*b^2*h*x^16+1/15*b^2*g*x^15+1/14*b^2*f*x^14+1/13*(2*a*b*h+b^2*e)*x^13+1/12*(2*a*b*g+b^2*d)*x^12+1/11*(2*a*b*f+b^2*c)*x^11+1/10*(a^2*h+2*a*b*e)*x^10+1/9*(a^2*g+2*a*b*d)*x^9+1/8*(a^2*f+2*a*b*c)*x^8+1/7*a^2*e*x^7+1/6*a^2*d*x^6+1/5*a^2*c*x^5","A"
384,1,152,139,0.042000," ","int(x^3*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{2} h \,x^{15}}{15}+\frac{b^{2} g \,x^{14}}{14}+\frac{b^{2} f \,x^{13}}{13}+\frac{\left(2 a b h +b^{2} e \right) x^{12}}{12}+\frac{\left(2 a b g +b^{2} d \right) x^{11}}{11}+\frac{\left(2 a b f +c \,b^{2}\right) x^{10}}{10}+\frac{a^{2} e \,x^{6}}{6}+\frac{\left(a^{2} h +2 b e a \right) x^{9}}{9}+\frac{a^{2} d \,x^{5}}{5}+\frac{\left(a^{2} g +2 b d a \right) x^{8}}{8}+\frac{a^{2} c \,x^{4}}{4}+\frac{\left(a^{2} f +2 a b c \right) x^{7}}{7}"," ",0,"1/15*b^2*h*x^15+1/14*b^2*g*x^14+1/13*b^2*f*x^13+1/12*(2*a*b*h+b^2*e)*x^12+1/11*(2*a*b*g+b^2*d)*x^11+1/10*(2*a*b*f+b^2*c)*x^10+1/9*(a^2*h+2*a*b*e)*x^9+1/8*(a^2*g+2*a*b*d)*x^8+1/7*(a^2*f+2*a*b*c)*x^7+1/6*a^2*e*x^6+1/5*a^2*d*x^5+1/4*a^2*c*x^4","A"
385,1,152,134,0.042000," ","int(x^2*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{2} h \,x^{14}}{14}+\frac{b^{2} g \,x^{13}}{13}+\frac{b^{2} f \,x^{12}}{12}+\frac{\left(2 a b h +b^{2} e \right) x^{11}}{11}+\frac{\left(2 a b g +b^{2} d \right) x^{10}}{10}+\frac{\left(2 a b f +c \,b^{2}\right) x^{9}}{9}+\frac{a^{2} e \,x^{5}}{5}+\frac{\left(a^{2} h +2 b e a \right) x^{8}}{8}+\frac{a^{2} d \,x^{4}}{4}+\frac{\left(a^{2} g +2 b d a \right) x^{7}}{7}+\frac{a^{2} c \,x^{3}}{3}+\frac{\left(a^{2} f +2 a b c \right) x^{6}}{6}"," ",0,"1/14*b^2*h*x^14+1/13*b^2*g*x^13+1/12*b^2*f*x^12+1/11*(2*a*b*h+b^2*e)*x^11+1/10*(2*a*b*g+b^2*d)*x^10+1/9*(2*a*b*f+b^2*c)*x^9+1/8*(a^2*h+2*a*b*e)*x^8+1/7*(a^2*g+2*a*b*d)*x^7+1/6*(a^2*f+2*a*b*c)*x^6+1/5*a^2*e*x^5+1/4*a^2*d*x^4+1/3*a^2*c*x^3","A"
386,1,152,134,0.037000," ","int(x*(b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{2} h \,x^{13}}{13}+\frac{b^{2} g \,x^{12}}{12}+\frac{b^{2} f \,x^{11}}{11}+\frac{\left(2 a b h +b^{2} e \right) x^{10}}{10}+\frac{\left(2 a b g +b^{2} d \right) x^{9}}{9}+\frac{\left(2 a b f +c \,b^{2}\right) x^{8}}{8}+\frac{a^{2} e \,x^{4}}{4}+\frac{\left(a^{2} h +2 b e a \right) x^{7}}{7}+\frac{a^{2} d \,x^{3}}{3}+\frac{\left(a^{2} g +2 b d a \right) x^{6}}{6}+\frac{a^{2} c \,x^{2}}{2}+\frac{\left(a^{2} f +2 a b c \right) x^{5}}{5}"," ",0,"1/13*b^2*h*x^13+1/12*b^2*g*x^12+1/11*b^2*f*x^11+1/10*(2*a*b*h+b^2*e)*x^10+1/9*(2*a*b*g+b^2*d)*x^9+1/8*(2*a*b*f+b^2*c)*x^8+1/7*(a^2*h+2*a*b*e)*x^7+1/6*(a^2*g+2*a*b*d)*x^6+1/5*(a^2*f+2*a*b*c)*x^5+1/4*a^2*e*x^4+1/3*a^2*d*x^3+1/2*a^2*c*x^2","A"
387,1,149,131,0.043000," ","int((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{2} h \,x^{12}}{12}+\frac{b^{2} g \,x^{11}}{11}+\frac{b^{2} f \,x^{10}}{10}+\frac{\left(2 a b h +b^{2} e \right) x^{9}}{9}+\frac{\left(2 a b g +b^{2} d \right) x^{8}}{8}+\frac{\left(2 a b f +c \,b^{2}\right) x^{7}}{7}+\frac{a^{2} e \,x^{3}}{3}+\frac{\left(a^{2} h +2 b e a \right) x^{6}}{6}+\frac{a^{2} d \,x^{2}}{2}+\frac{\left(a^{2} g +2 b d a \right) x^{5}}{5}+a^{2} c x +\frac{\left(a^{2} f +2 a b c \right) x^{4}}{4}"," ",0,"1/12*b^2*h*x^12+1/11*b^2*g*x^11+1/10*b^2*f*x^10+1/9*(2*a*b*h+b^2*e)*x^9+1/8*(2*a*b*g+b^2*d)*x^8+1/7*(2*a*b*f+b^2*c)*x^7+1/6*(a^2*h+2*a*b*e)*x^6+1/5*(a^2*g+2*a*b*d)*x^5+1/4*(a^2*f+2*a*b*c)*x^4+1/3*a^2*e*x^3+1/2*a^2*d*x^2+a^2*c*x","A"
388,1,153,129,0.045000," ","int((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x)","\frac{b^{2} h \,x^{11}}{11}+\frac{b^{2} g \,x^{10}}{10}+\frac{b^{2} f \,x^{9}}{9}+\frac{a b h \,x^{8}}{4}+\frac{b^{2} e \,x^{8}}{8}+\frac{2 a b g \,x^{7}}{7}+\frac{b^{2} d \,x^{7}}{7}+\frac{a b f \,x^{6}}{3}+\frac{b^{2} c \,x^{6}}{6}+\frac{a^{2} h \,x^{5}}{5}+\frac{2 a b e \,x^{5}}{5}+\frac{a^{2} g \,x^{4}}{4}+\frac{a b d \,x^{4}}{2}+\frac{a^{2} f \,x^{3}}{3}+\frac{2 a b c \,x^{3}}{3}+\frac{a^{2} e \,x^{2}}{2}+a^{2} c \ln \left(x \right)+a^{2} d x"," ",0,"1/11*b^2*h*x^11+1/10*b^2*g*x^10+1/9*x^9*f*b^2+1/4*x^8*a*b*h+1/8*b^2*e*x^8+2/7*x^7*a*b*g+1/7*b^2*d*x^7+1/3*x^6*a*b*f+1/6*b^2*c*x^6+1/5*x^5*a^2*h+2/5*a*b*e*x^5+1/4*x^4*a^2*g+1/2*a*b*d*x^4+1/3*x^3*a^2*f+2/3*a*b*c*x^3+1/2*a^2*e*x^2+a^2*d*x+a^2*c*ln(x)","A"
389,1,152,129,0.052000," ","int((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x)","\frac{b^{2} h \,x^{10}}{10}+\frac{b^{2} g \,x^{9}}{9}+\frac{b^{2} f \,x^{8}}{8}+\frac{2 a b h \,x^{7}}{7}+\frac{b^{2} e \,x^{7}}{7}+\frac{a b g \,x^{6}}{3}+\frac{b^{2} d \,x^{6}}{6}+\frac{2 a b f \,x^{5}}{5}+\frac{b^{2} c \,x^{5}}{5}+\frac{a^{2} h \,x^{4}}{4}+\frac{a b e \,x^{4}}{2}+\frac{a^{2} g \,x^{3}}{3}+\frac{2 a b d \,x^{3}}{3}+\frac{a^{2} f \,x^{2}}{2}+a b c \,x^{2}+a^{2} d \ln \left(x \right)+a^{2} e x -\frac{a^{2} c}{x}"," ",0,"1/10*b^2*h*x^10+1/9*b^2*g*x^9+1/8*b^2*f*x^8+2/7*x^7*a*b*h+1/7*b^2*e*x^7+1/3*x^6*a*b*g+1/6*b^2*d*x^6+2/5*x^5*a*b*f+1/5*b^2*c*x^5+1/4*x^4*a^2*h+1/2*a*b*e*x^4+1/3*x^3*a^2*g+2/3*a*b*d*x^3+1/2*a^2*f*x^2+a*b*c*x^2+a^2*e*x-a^2*c/x+a^2*d*ln(x)","A"
390,1,150,129,0.050000," ","int((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x)","\frac{b^{2} h \,x^{9}}{9}+\frac{b^{2} g \,x^{8}}{8}+\frac{b^{2} f \,x^{7}}{7}+\frac{a b h \,x^{6}}{3}+\frac{b^{2} e \,x^{6}}{6}+\frac{2 a b g \,x^{5}}{5}+\frac{b^{2} d \,x^{5}}{5}+\frac{a b f \,x^{4}}{2}+\frac{b^{2} c \,x^{4}}{4}+\frac{a^{2} h \,x^{3}}{3}+\frac{2 a b e \,x^{3}}{3}+\frac{a^{2} g \,x^{2}}{2}+a b d \,x^{2}+a^{2} e \ln \left(x \right)+a^{2} f x +2 a b c x -\frac{a^{2} d}{x}-\frac{a^{2} c}{2 x^{2}}"," ",0,"1/9*b^2*h*x^9+1/8*b^2*g*x^8+1/7*b^2*f*x^7+1/3*x^6*a*b*h+1/6*b^2*e*x^6+2/5*x^5*a*b*g+1/5*b^2*d*x^5+1/2*x^4*a*b*f+1/4*b^2*c*x^4+1/3*x^3*a^2*h+2/3*a*b*e*x^3+1/2*x^2*a^2*g+a*b*d*x^2+a^2*f*x+2*a*b*c*x-1/2*a^2*c/x^2-a^2*d/x+a^2*e*ln(x)","A"
391,1,149,134,0.049000," ","int((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x)","\frac{b^{2} h \,x^{8}}{8}+\frac{b^{2} g \,x^{7}}{7}+\frac{b^{2} f \,x^{6}}{6}+\frac{2 a b h \,x^{5}}{5}+\frac{b^{2} e \,x^{5}}{5}+\frac{a b g \,x^{4}}{2}+\frac{b^{2} d \,x^{4}}{4}+\frac{2 a b f \,x^{3}}{3}+\frac{b^{2} c \,x^{3}}{3}+\frac{a^{2} h \,x^{2}}{2}+a b e \,x^{2}+a^{2} f \ln \left(x \right)+a^{2} g x +2 a b c \ln \left(x \right)+2 a b d x -\frac{a^{2} e}{x}-\frac{a^{2} d}{2 x^{2}}-\frac{a^{2} c}{3 x^{3}}"," ",0,"1/8*b^2*h*x^8+1/7*b^2*g*x^7+1/6*b^2*f*x^6+2/5*x^5*a*b*h+1/5*x^5*b^2*e+1/2*x^4*a*b*g+1/4*x^4*b^2*d+2/3*x^3*a*b*f+1/3*b^2*c*x^3+1/2*x^2*a^2*h+a*b*e*x^2+a^2*g*x+2*b*d*a*x-1/3*a^2*c/x^3-1/2*a^2*d/x^2-a^2*e/x+ln(x)*a^2*f+2*ln(x)*a*b*c","A"
392,1,149,134,0.054000," ","int((b*x^3+a)^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x)","\frac{b^{2} h \,x^{7}}{7}+\frac{b^{2} g \,x^{6}}{6}+\frac{b^{2} f \,x^{5}}{5}+\frac{a b h \,x^{4}}{2}+\frac{b^{2} e \,x^{4}}{4}+\frac{2 a b g \,x^{3}}{3}+\frac{b^{2} d \,x^{3}}{3}+a b f \,x^{2}+\frac{b^{2} c \,x^{2}}{2}+a^{2} g \ln \left(x \right)+a^{2} h x +2 a b d \ln \left(x \right)+2 a b e x -\frac{a^{2} f}{x}-\frac{2 a b c}{x}-\frac{a^{2} e}{2 x^{2}}-\frac{a^{2} d}{3 x^{3}}-\frac{a^{2} c}{4 x^{4}}"," ",0,"1/7*b^2*h*x^7+1/6*b^2*g*x^6+1/5*b^2*f*x^5+1/2*x^4*a*b*h+1/4*x^4*b^2*e+2/3*x^3*a*b*g+1/3*x^3*b^2*d+x^2*a*b*f+1/2*b^2*c*x^2+a^2*h*x+2*a*b*e*x-1/4*a^2*c/x^4-1/3*a^2*d/x^3-1/2*a^2*e/x^2-a^2/x*f-2*a/x*b*c+ln(x)*a^2*g+2*ln(x)*a*b*d","A"
393,1,224,193,0.037000," ","int(x^4*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{3} h \,x^{19}}{19}+\frac{b^{3} g \,x^{18}}{18}+\frac{b^{3} f \,x^{17}}{17}+\frac{\left(3 a \,b^{2} h +b^{3} e \right) x^{16}}{16}+\frac{\left(3 a \,b^{2} g +b^{3} d \right) x^{15}}{15}+\frac{\left(3 a \,b^{2} f +b^{3} c \right) x^{14}}{14}+\frac{\left(3 a^{2} b h +3 a e \,b^{2}\right) x^{13}}{13}+\frac{\left(3 a^{2} b g +3 a \,b^{2} d \right) x^{12}}{12}+\frac{a^{3} e \,x^{7}}{7}+\frac{\left(3 a^{2} b f +3 a \,b^{2} c \right) x^{11}}{11}+\frac{a^{3} d \,x^{6}}{6}+\frac{\left(a^{3} h +3 a^{2} b e \right) x^{10}}{10}+\frac{a^{3} c \,x^{5}}{5}+\frac{\left(a^{3} g +3 a^{2} d b \right) x^{9}}{9}+\frac{\left(a^{3} f +3 a^{2} c b \right) x^{8}}{8}"," ",0,"1/19*b^3*h*x^19+1/18*b^3*g*x^18+1/17*b^3*f*x^17+1/16*(3*a*b^2*h+b^3*e)*x^16+1/15*(3*a*b^2*g+b^3*d)*x^15+1/14*(3*a*b^2*f+b^3*c)*x^14+1/13*(3*a^2*b*h+3*a*b^2*e)*x^13+1/12*(3*a^2*b*g+3*a*b^2*d)*x^12+1/11*(3*a^2*b*f+3*a*b^2*c)*x^11+1/10*(a^3*h+3*a^2*b*e)*x^10+1/9*(a^3*g+3*a^2*b*d)*x^9+1/8*(a^3*f+3*a^2*b*c)*x^8+1/7*a^3*e*x^7+1/6*a^3*d*x^6+1/5*a^3*c*x^5","A"
394,1,224,193,0.045000," ","int(x^3*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{3} h \,x^{18}}{18}+\frac{b^{3} g \,x^{17}}{17}+\frac{b^{3} f \,x^{16}}{16}+\frac{\left(3 a \,b^{2} h +b^{3} e \right) x^{15}}{15}+\frac{\left(3 a \,b^{2} g +b^{3} d \right) x^{14}}{14}+\frac{\left(3 a \,b^{2} f +b^{3} c \right) x^{13}}{13}+\frac{\left(3 a^{2} b h +3 a e \,b^{2}\right) x^{12}}{12}+\frac{\left(3 a^{2} b g +3 a \,b^{2} d \right) x^{11}}{11}+\frac{a^{3} e \,x^{6}}{6}+\frac{\left(3 a^{2} b f +3 a \,b^{2} c \right) x^{10}}{10}+\frac{a^{3} d \,x^{5}}{5}+\frac{\left(a^{3} h +3 a^{2} b e \right) x^{9}}{9}+\frac{a^{3} c \,x^{4}}{4}+\frac{\left(a^{3} g +3 a^{2} d b \right) x^{8}}{8}+\frac{\left(a^{3} f +3 a^{2} c b \right) x^{7}}{7}"," ",0,"1/18*b^3*h*x^18+1/17*b^3*g*x^17+1/16*b^3*f*x^16+1/15*(3*a*b^2*h+b^3*e)*x^15+1/14*(3*a*b^2*g+b^3*d)*x^14+1/13*(3*a*b^2*f+b^3*c)*x^13+1/12*(3*a^2*b*h+3*a*b^2*e)*x^12+1/11*(3*a^2*b*g+3*a*b^2*d)*x^11+1/10*(3*a^2*b*f+3*a*b^2*c)*x^10+1/9*(a^3*h+3*a^2*b*e)*x^9+1/8*(a^3*g+3*a^2*b*d)*x^8+1/7*(a^3*f+3*a^2*b*c)*x^7+1/6*a^3*e*x^6+1/5*a^3*d*x^5+1/4*a^3*c*x^4","A"
395,1,224,182,0.048000," ","int(x^2*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{3} h \,x^{17}}{17}+\frac{b^{3} g \,x^{16}}{16}+\frac{b^{3} f \,x^{15}}{15}+\frac{\left(3 a \,b^{2} h +b^{3} e \right) x^{14}}{14}+\frac{\left(3 a \,b^{2} g +b^{3} d \right) x^{13}}{13}+\frac{\left(3 a \,b^{2} f +b^{3} c \right) x^{12}}{12}+\frac{\left(3 a^{2} b h +3 a e \,b^{2}\right) x^{11}}{11}+\frac{\left(3 a^{2} b g +3 a \,b^{2} d \right) x^{10}}{10}+\frac{a^{3} e \,x^{5}}{5}+\frac{\left(3 a^{2} b f +3 a \,b^{2} c \right) x^{9}}{9}+\frac{a^{3} d \,x^{4}}{4}+\frac{\left(a^{3} h +3 a^{2} b e \right) x^{8}}{8}+\frac{a^{3} c \,x^{3}}{3}+\frac{\left(a^{3} g +3 a^{2} d b \right) x^{7}}{7}+\frac{\left(a^{3} f +3 a^{2} c b \right) x^{6}}{6}"," ",0,"1/17*b^3*h*x^17+1/16*b^3*g*x^16+1/15*b^3*f*x^15+1/14*(3*a*b^2*h+b^3*e)*x^14+1/13*(3*a*b^2*g+b^3*d)*x^13+1/12*(3*a*b^2*f+b^3*c)*x^12+1/11*(3*a^2*b*h+3*a*b^2*e)*x^11+1/10*(3*a^2*b*g+3*a*b^2*d)*x^10+1/9*(3*a^2*b*f+3*a*b^2*c)*x^9+1/8*(a^3*h+3*a^2*b*e)*x^8+1/7*(a^3*g+3*a^2*b*d)*x^7+1/6*(a^3*f+3*a^2*b*c)*x^6+1/5*a^3*e*x^5+1/4*a^3*d*x^4+1/3*a^3*c*x^3","A"
396,1,224,182,0.039000," ","int(x*(b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{3} h \,x^{16}}{16}+\frac{b^{3} g \,x^{15}}{15}+\frac{b^{3} f \,x^{14}}{14}+\frac{\left(3 a \,b^{2} h +b^{3} e \right) x^{13}}{13}+\frac{\left(3 a \,b^{2} g +b^{3} d \right) x^{12}}{12}+\frac{\left(3 a \,b^{2} f +b^{3} c \right) x^{11}}{11}+\frac{\left(3 a^{2} b h +3 a e \,b^{2}\right) x^{10}}{10}+\frac{\left(3 a^{2} b g +3 a \,b^{2} d \right) x^{9}}{9}+\frac{a^{3} e \,x^{4}}{4}+\frac{\left(3 a^{2} b f +3 a \,b^{2} c \right) x^{8}}{8}+\frac{a^{3} d \,x^{3}}{3}+\frac{\left(a^{3} h +3 a^{2} b e \right) x^{7}}{7}+\frac{a^{3} c \,x^{2}}{2}+\frac{\left(a^{3} g +3 a^{2} d b \right) x^{6}}{6}+\frac{\left(a^{3} f +3 a^{2} c b \right) x^{5}}{5}"," ",0,"1/16*b^3*h*x^16+1/15*b^3*g*x^15+1/14*b^3*f*x^14+1/13*(3*a*b^2*h+b^3*e)*x^13+1/12*(3*a*b^2*g+b^3*d)*x^12+1/11*(3*a*b^2*f+b^3*c)*x^11+1/10*(3*a^2*b*h+3*a*b^2*e)*x^10+1/9*(3*a^2*b*g+3*a*b^2*d)*x^9+1/8*(3*a^2*b*f+3*a*b^2*c)*x^8+1/7*(a^3*h+3*a^2*b*e)*x^7+1/6*(a^3*g+3*a^2*b*d)*x^6+1/5*(a^3*f+3*a^2*b*c)*x^5+1/4*a^3*e*x^4+1/3*a^3*d*x^3+1/2*a^3*c*x^2","A"
397,1,221,179,0.042000," ","int((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c),x)","\frac{b^{3} h \,x^{15}}{15}+\frac{b^{3} g \,x^{14}}{14}+\frac{b^{3} f \,x^{13}}{13}+\frac{\left(3 a \,b^{2} h +b^{3} e \right) x^{12}}{12}+\frac{\left(3 a \,b^{2} g +b^{3} d \right) x^{11}}{11}+\frac{\left(3 a \,b^{2} f +b^{3} c \right) x^{10}}{10}+\frac{\left(3 a^{2} b h +3 a e \,b^{2}\right) x^{9}}{9}+\frac{\left(3 a^{2} b g +3 a \,b^{2} d \right) x^{8}}{8}+\frac{a^{3} e \,x^{3}}{3}+\frac{\left(3 a^{2} b f +3 a \,b^{2} c \right) x^{7}}{7}+\frac{a^{3} d \,x^{2}}{2}+\frac{\left(a^{3} h +3 a^{2} b e \right) x^{6}}{6}+a^{3} c x +\frac{\left(a^{3} g +3 a^{2} d b \right) x^{5}}{5}+\frac{\left(a^{3} f +3 a^{2} c b \right) x^{4}}{4}"," ",0,"1/15*b^3*h*x^15+1/14*b^3*g*x^14+1/13*b^3*f*x^13+1/12*(3*a*b^2*h+b^3*e)*x^12+1/11*(3*a*b^2*g+b^3*d)*x^11+1/10*(3*a*b^2*f+b^3*c)*x^10+1/9*(3*a^2*b*h+3*a*b^2*e)*x^9+1/8*(3*a^2*b*g+3*a*b^2*d)*x^8+1/7*(3*a^2*b*f+3*a*b^2*c)*x^7+1/6*(a^3*h+3*a^2*b*e)*x^6+1/5*(a^3*g+3*a^2*b*d)*x^5+1/4*(a^3*f+3*a^2*b*c)*x^4+1/3*a^3*e*x^3+1/2*a^3*d*x^2+a^3*c*x","A"
398,1,224,176,0.047000," ","int((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x,x)","\frac{b^{3} h \,x^{14}}{14}+\frac{b^{3} g \,x^{13}}{13}+\frac{b^{3} f \,x^{12}}{12}+\frac{3 a \,b^{2} h \,x^{11}}{11}+\frac{b^{3} e \,x^{11}}{11}+\frac{3 a \,b^{2} g \,x^{10}}{10}+\frac{b^{3} d \,x^{10}}{10}+\frac{a \,b^{2} f \,x^{9}}{3}+\frac{b^{3} c \,x^{9}}{9}+\frac{3 a^{2} b h \,x^{8}}{8}+\frac{3 a \,b^{2} e \,x^{8}}{8}+\frac{3 a^{2} b g \,x^{7}}{7}+\frac{3 a \,b^{2} d \,x^{7}}{7}+\frac{a^{2} b f \,x^{6}}{2}+\frac{a \,b^{2} c \,x^{6}}{2}+\frac{a^{3} h \,x^{5}}{5}+\frac{3 a^{2} b e \,x^{5}}{5}+\frac{a^{3} g \,x^{4}}{4}+\frac{3 a^{2} b d \,x^{4}}{4}+\frac{a^{3} f \,x^{3}}{3}+a^{2} b c \,x^{3}+\frac{a^{3} e \,x^{2}}{2}+a^{3} c \ln \left(x \right)+a^{3} d x"," ",0,"1/14*b^3*h*x^14+1/13*b^3*g*x^13+1/12*x^12*f*b^3+3/11*x^11*a*b^2*h+1/11*b^3*e*x^11+3/10*x^10*a*b^2*g+1/10*b^3*d*x^10+1/3*x^9*a*b^2*f+1/9*b^3*c*x^9+3/8*x^8*a^2*b*h+3/8*a*b^2*e*x^8+3/7*x^7*a^2*b*g+3/7*a*b^2*d*x^7+1/2*x^6*a^2*b*f+1/2*a*b^2*c*x^6+1/5*x^5*a^3*h+3/5*a^2*b*e*x^5+1/4*x^4*a^3*g+3/4*a^2*b*d*x^4+1/3*x^3*a^3*f+a^2*b*c*x^3+1/2*a^3*e*x^2+a^3*d*x+a^3*c*ln(x)","A"
399,1,224,176,0.052000," ","int((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x)","\frac{b^{3} h \,x^{13}}{13}+\frac{b^{3} g \,x^{12}}{12}+\frac{b^{3} f \,x^{11}}{11}+\frac{3 a \,b^{2} h \,x^{10}}{10}+\frac{b^{3} e \,x^{10}}{10}+\frac{a \,b^{2} g \,x^{9}}{3}+\frac{b^{3} d \,x^{9}}{9}+\frac{3 a \,b^{2} f \,x^{8}}{8}+\frac{b^{3} c \,x^{8}}{8}+\frac{3 a^{2} b h \,x^{7}}{7}+\frac{3 a \,b^{2} e \,x^{7}}{7}+\frac{a^{2} b g \,x^{6}}{2}+\frac{a \,b^{2} d \,x^{6}}{2}+\frac{3 a^{2} b f \,x^{5}}{5}+\frac{3 a \,b^{2} c \,x^{5}}{5}+\frac{a^{3} h \,x^{4}}{4}+\frac{3 a^{2} b e \,x^{4}}{4}+\frac{a^{3} g \,x^{3}}{3}+a^{2} b d \,x^{3}+\frac{a^{3} f \,x^{2}}{2}+\frac{3 a^{2} b c \,x^{2}}{2}+a^{3} d \ln \left(x \right)+a^{3} e x -\frac{a^{3} c}{x}"," ",0,"1/13*b^3*h*x^13+1/12*b^3*g*x^12+1/11*b^3*f*x^11+3/10*x^10*a*b^2*h+1/10*b^3*e*x^10+1/3*x^9*a*b^2*g+1/9*b^3*d*x^9+3/8*x^8*a*b^2*f+1/8*b^3*c*x^8+3/7*x^7*a^2*b*h+3/7*a*b^2*e*x^7+1/2*x^6*a^2*b*g+1/2*a*b^2*d*x^6+3/5*x^5*a^2*b*f+3/5*a*b^2*c*x^5+1/4*x^4*a^3*h+3/4*a^2*b*e*x^4+1/3*x^3*a^3*g+a^2*b*d*x^3+1/2*x^2*a^3*f+3/2*a^2*b*c*x^2+a^3*e*x-a^3*c/x+a^3*d*ln(x)","A"
400,1,222,176,0.058000," ","int((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x)","\frac{b^{3} h \,x^{12}}{12}+\frac{b^{3} g \,x^{11}}{11}+\frac{b^{3} f \,x^{10}}{10}+\frac{a \,b^{2} h \,x^{9}}{3}+\frac{b^{3} e \,x^{9}}{9}+\frac{3 a \,b^{2} g \,x^{8}}{8}+\frac{b^{3} d \,x^{8}}{8}+\frac{3 a \,b^{2} f \,x^{7}}{7}+\frac{b^{3} c \,x^{7}}{7}+\frac{a^{2} b h \,x^{6}}{2}+\frac{a \,b^{2} e \,x^{6}}{2}+\frac{3 a^{2} b g \,x^{5}}{5}+\frac{3 a \,b^{2} d \,x^{5}}{5}+\frac{3 a^{2} b f \,x^{4}}{4}+\frac{3 a \,b^{2} c \,x^{4}}{4}+\frac{a^{3} h \,x^{3}}{3}+a^{2} b e \,x^{3}+\frac{a^{3} g \,x^{2}}{2}+\frac{3 a^{2} b d \,x^{2}}{2}+a^{3} e \ln \left(x \right)+a^{3} f x +3 a^{2} b c x -\frac{a^{3} d}{x}-\frac{a^{3} c}{2 x^{2}}"," ",0,"1/12*b^3*h*x^12+1/11*b^3*g*x^11+1/10*b^3*f*x^10+1/3*x^9*a*b^2*h+1/9*b^3*e*x^9+3/8*x^8*a*b^2*g+1/8*b^3*d*x^8+3/7*x^7*a*b^2*f+1/7*b^3*c*x^7+1/2*x^6*a^2*b*h+1/2*a*b^2*e*x^6+3/5*x^5*a^2*b*g+3/5*a*b^2*d*x^5+3/4*x^4*a^2*b*f+3/4*a*b^2*c*x^4+1/3*x^3*a^3*h+a^2*b*e*x^3+1/2*x^2*a^3*g+3/2*a^2*b*d*x^2+a^3*f*x+3*a^2*b*c*x-1/2*a^3*c/x^2-a^3*d/x+a^3*e*ln(x)","A"
401,1,220,187,0.050000," ","int((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x)","\frac{b^{3} h \,x^{11}}{11}+\frac{b^{3} g \,x^{10}}{10}+\frac{b^{3} f \,x^{9}}{9}+\frac{3 a \,b^{2} h \,x^{8}}{8}+\frac{b^{3} e \,x^{8}}{8}+\frac{3 a \,b^{2} g \,x^{7}}{7}+\frac{b^{3} d \,x^{7}}{7}+\frac{a \,b^{2} f \,x^{6}}{2}+\frac{b^{3} c \,x^{6}}{6}+\frac{3 a^{2} b h \,x^{5}}{5}+\frac{3 a \,b^{2} e \,x^{5}}{5}+\frac{3 a^{2} b g \,x^{4}}{4}+\frac{3 a \,b^{2} d \,x^{4}}{4}+a^{2} b f \,x^{3}+a \,b^{2} c \,x^{3}+\frac{a^{3} h \,x^{2}}{2}+\frac{3 a^{2} b e \,x^{2}}{2}+a^{3} f \ln \left(x \right)+a^{3} g x +3 a^{2} b c \ln \left(x \right)+3 a^{2} b d x -\frac{a^{3} e}{x}-\frac{a^{3} d}{2 x^{2}}-\frac{a^{3} c}{3 x^{3}}"," ",0,"1/11*b^3*h*x^11+1/10*b^3*g*x^10+1/9*b^3*f*x^9+3/8*x^8*a*b^2*h+1/8*x^8*b^3*e+3/7*x^7*a*b^2*g+1/7*x^7*b^3*d+1/2*x^6*a*b^2*f+1/6*x^6*b^3*c+3/5*x^5*a^2*b*h+3/5*x^5*a*b^2*e+3/4*x^4*a^2*b*g+3/4*x^4*a*b^2*d+x^3*a^2*b*f+a*b^2*c*x^3+1/2*x^2*a^3*h+3/2*x^2*a^2*b*e+a^3*g*x+3*a^2*d*b*x-1/3*a^3*c/x^3-1/2*a^3*d/x^2-a^3*e/x+ln(x)*a^3*f+3*ln(x)*a^2*b*c","A"
402,1,220,187,0.046000," ","int((b*x^3+a)^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x)","\frac{b^{3} h \,x^{10}}{10}+\frac{b^{3} g \,x^{9}}{9}+\frac{b^{3} f \,x^{8}}{8}+\frac{3 a \,b^{2} h \,x^{7}}{7}+\frac{b^{3} e \,x^{7}}{7}+\frac{a \,b^{2} g \,x^{6}}{2}+\frac{b^{3} d \,x^{6}}{6}+\frac{3 a \,b^{2} f \,x^{5}}{5}+\frac{b^{3} c \,x^{5}}{5}+\frac{3 a^{2} b h \,x^{4}}{4}+\frac{3 a \,b^{2} e \,x^{4}}{4}+a^{2} b g \,x^{3}+a \,b^{2} d \,x^{3}+\frac{3 a^{2} b f \,x^{2}}{2}+\frac{3 a \,b^{2} c \,x^{2}}{2}+a^{3} g \ln \left(x \right)+a^{3} h x +3 a^{2} b d \ln \left(x \right)+3 a^{2} b e x -\frac{a^{3} f}{x}-\frac{3 a^{2} b c}{x}-\frac{a^{3} e}{2 x^{2}}-\frac{a^{3} d}{3 x^{3}}-\frac{a^{3} c}{4 x^{4}}"," ",0,"1/10*b^3*h*x^10+1/9*b^3*g*x^9+1/8*b^3*f*x^8+3/7*x^7*a*b^2*h+1/7*x^7*b^3*e+1/2*x^6*a*b^2*g+1/6*x^6*b^3*d+3/5*x^5*a*b^2*f+1/5*x^5*b^3*c+3/4*x^4*a^2*b*h+3/4*x^4*a*b^2*e+x^3*a^2*b*g+x^3*a*b^2*d+3/2*x^2*a^2*b*f+3/2*a*b^2*c*x^2+a^3*h*x+3*a^2*b*e*x-1/4*a^3*c/x^4-1/3*a^3*d/x^3-1/2*a^3*e/x^2-a^3/x*f-3*a^2/x*b*c+ln(x)*a^3*g+3*ln(x)*a^2*b*d","A"
403,1,533,265,0.049000," ","int(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x)","\frac{h \,x^{7}}{7 b}+\frac{g \,x^{6}}{6 b}+\frac{f \,x^{5}}{5 b}-\frac{a h \,x^{4}}{4 b^{2}}+\frac{e \,x^{4}}{4 b}-\frac{a g \,x^{3}}{3 b^{2}}+\frac{d \,x^{3}}{3 b}-\frac{a f \,x^{2}}{2 b^{2}}+\frac{c \,x^{2}}{2 b}-\frac{\sqrt{3}\, a^{3} h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{a^{3} h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a^{3} h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{\sqrt{3}\, a^{2} e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{\sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} g \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{a^{2} h x}{b^{3}}-\frac{\sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a d \ln \left(b \,x^{3}+a \right)}{3 b^{2}}-\frac{a e x}{b^{2}}"," ",0,"1/3*a^2/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3*a^3/b^4/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h-1/3*a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3*a^2/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/2*a/b^2*f*x^2+1/b^3*a^2*h*x-1/b^2*a*e*x-1/3/b^2*x^3*a*g-1/3*a/b^2*ln(b*x^3+a)*d-1/4/b^2*x^4*a*h+1/3*a^2/b^3*ln(b*x^3+a)*g-1/6*a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/6*a^2/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/3*a^2/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/3*a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/6*a^2/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6*a^3/b^4/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-1/3*a^3/b^4/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h+1/3*a^2/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/4/b*x^4*e+1/3/b*x^3*d+1/2/b*c*x^2+1/5/b*f*x^5+1/6*g*x^6/b+1/7*h*x^7/b","B"
404,1,505,249,0.049000," ","int(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x)","\frac{h \,x^{6}}{6 b}+\frac{g \,x^{5}}{5 b}+\frac{f \,x^{4}}{4 b}-\frac{a h \,x^{3}}{3 b^{2}}+\frac{e \,x^{3}}{3 b}-\frac{a g \,x^{2}}{2 b^{2}}+\frac{d \,x^{2}}{2 b}+\frac{\sqrt{3}\, a^{2} f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{\sqrt{3}\, a^{2} g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} h \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{\sqrt{3}\, a c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a e \ln \left(b \,x^{3}+a \right)}{3 b^{2}}-\frac{a f x}{b^{2}}+\frac{c x}{b}"," ",0,"1/6*h*x^6/b+1/5*g*x^5/b+1/4/b*f*x^4-1/3/b^2*x^3*a*h+1/3/b*e*x^3-1/2/b^2*x^2*a*g+1/2/b*d*x^2-a/b^2*f*x+1/b*c*x+1/3/(a/b)^(2/3)*a^2/b^3*f*ln(x+(a/b)^(1/3))-1/3/(a/b)^(2/3)*a/b^2*c*ln(x+(a/b)^(1/3))-1/6/(a/b)^(2/3)*a^2/b^3*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/6/(a/b)^(2/3)*a/b^2*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/(a/b)^(2/3)*3^(1/2)*a^2/b^3*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3*a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/3*a^2/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*g+1/3*a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/6*a^2/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g-1/6*a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/3*a^2/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g-1/3*3^(1/2)/(a/b)^(1/3)*a/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*a^2/b^3*ln(b*x^3+a)*h-1/3*a/b^2*e*ln(b*x^3+a)","B"
405,1,483,232,0.047000," ","int(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x)","\frac{h \,x^{5}}{5 b}+\frac{g \,x^{4}}{4 b}+\frac{f \,x^{3}}{3 b}-\frac{a h \,x^{2}}{2 b^{2}}+\frac{e \,x^{2}}{2 b}+\frac{\sqrt{3}\, a^{2} g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{\sqrt{3}\, a^{2} h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{a^{2} h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{a^{2} h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{\sqrt{3}\, a d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a f \ln \left(b \,x^{3}+a \right)}{3 b^{2}}-\frac{a g x}{b^{2}}+\frac{c \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{d x}{b}"," ",0,"1/5*h*x^5/b+1/4*g*x^4/b+1/3/b*f*x^3-1/2/b^2*x^2*a*h+1/2/b*e*x^2-1/b^2*a*g*x+1/b*d*x+1/3/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^2*g-1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*d-1/6/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*g+1/6/(a/b)^(2/3)*a/b^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*g-1/3/(a/b)^(2/3)*3^(1/2)*a/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*a^2*h+1/3/b^2*a*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/6/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*h-1/6/b^2*a*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*h-1/3/b^2*a*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/b^2*ln(b*x^3+a)*a*f+1/3/b*c*ln(b*x^3+a)","B"
406,1,455,214,0.044000," ","int(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x)","\frac{h \,x^{4}}{4 b}+\frac{g \,x^{3}}{3 b}+\frac{f \,x^{2}}{2 b}+\frac{\sqrt{3}\, a^{2} h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{a^{2} h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{a^{2} h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{\sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a g \ln \left(b \,x^{3}+a \right)}{3 b^{2}}-\frac{a h x}{b^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{e x}{b}"," ",0,"1/4*h*x^4/b+1/3*g*x^3/b+1/2/b*f*x^2-1/b^2*a*h*x+1/b*e*x+1/3/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a^2*h-1/3/(a/b)^(2/3)*a/b^2*e*ln(x+(a/b)^(1/3))-1/6/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2*h+1/6/(a/b)^(2/3)*a/b^2*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a^2*h-1/3/(a/b)^(2/3)*3^(1/2)*a/b^2*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(a/b)^(1/3)*a/b^2*f*ln(x+(a/b)^(1/3))-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c-1/6/(a/b)^(1/3)*a/b^2*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c-1/3*3^(1/2)/(a/b)^(1/3)*a/b^2*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/3/b^2*ln(b*x^3+a)*a*g+1/3/b*d*ln(b*x^3+a)","B"
407,1,429,200,0.049000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a),x)","\frac{h \,x^{3}}{3 b}+\frac{g \,x^{2}}{2 b}-\frac{\sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a h \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{e \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{f x}{b}"," ",0,"1/3*h*x^3/b+1/2*g*x^2/b+1/b*f*x-1/3/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*a*f+1/3/(a/b)^(2/3)/b*c*ln(x+(a/b)^(1/3))+1/6/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*f-1/6/(a/b)^(2/3)/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/(a/b)^(2/3)*3^(1/2)*a/b^2*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/(a/b)^(2/3)*3^(1/2)/b*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*a*g-1/3/(a/b)^(1/3)/b*d*ln(x+(a/b)^(1/3))-1/6/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a*g+1/6/(a/b)^(1/3)/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*a*g+1/3*3^(1/2)/(a/b)^(1/3)/b*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/b^2*ln(b*x^3+a)*a*h+1/3/b*e*ln(b*x^3+a)","B"
408,1,426,201,0.051000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a),x)","\frac{h \,x^{2}}{2 b}-\frac{\sqrt{3}\, a g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, a h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{a h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{a h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{c \ln \left(x \right)}{a}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{f \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{g x}{b}"," ",0,"1/2/b*h*x^2+1/b*g*x-1/3/b^2*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*g+1/3/(a/b)^(2/3)/b*d*ln(x+(a/b)^(1/3))+1/6/b^2*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g-1/6/(a/b)^(2/3)/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/b^2*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+1/3/(a/b)^(2/3)*3^(1/2)/b*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b^2*a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*h-1/3/(a/b)^(1/3)/b*e*ln(x+(a/b)^(1/3))-1/6/b^2*a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h+1/6/(a/b)^(1/3)/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/b^2*a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/3*3^(1/2)/(a/b)^(1/3)/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b*f*ln(b*x^3+a)-1/3/a*c*ln(b*x^3+a)+1/a*c*ln(x)","B"
409,1,423,199,0.056000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a),x)","-\frac{\sqrt{3}\, a h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{a h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{a h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{d \ln \left(x \right)}{a}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{g \ln \left(b \,x^{3}+a \right)}{3 b}+\frac{h x}{b}-\frac{c}{a x}"," ",0,"h*x/b-1/3/b^2*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h+1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+1/6/b^2*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-1/3/b^2*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/3/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/3/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3/b*ln(b*x^3+a)*g-1/3/a*d*ln(b*x^3+a)-1/a*c/x+1/a*d*ln(x)","B"
410,1,423,204,0.050000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a),x)","-\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{e \ln \left(x \right)}{a}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{h \ln \left(b \,x^{3}+a \right)}{3 b}-\frac{d}{a x}-\frac{c}{2 a \,x^{2}}"," ",0,"1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*f-1/3/(a/b)^(2/3)/a*c*ln(x+(a/b)^(1/3))-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/6/(a/b)^(2/3)/a*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-1/3/(a/b)^(2/3)*3^(1/2)/a*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*g+1/3/(a/b)^(1/3)/a*d*ln(x+(a/b)^(1/3))+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g-1/6/(a/b)^(1/3)/a*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g-1/3*3^(1/2)/(a/b)^(1/3)/a*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b*ln(b*x^3+a)*h-1/3/a*e*ln(b*x^3+a)+1/a*e*ln(x)-1/2/a*c/x^2-1/a*d/x","B"
411,1,442,218,0.056000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a),x)","-\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} a}-\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} a}+\frac{f \ln \left(x \right)}{a}-\frac{f \ln \left(b \,x^{3}+a \right)}{3 a}-\frac{b c \ln \left(x \right)}{a^{2}}+\frac{b c \ln \left(b \,x^{3}+a \right)}{3 a^{2}}+\frac{\sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}-\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{2}{3}} b}+\frac{\sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}+\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{6 \left(\frac{a}{b}\right)^{\frac{1}{3}} b}-\frac{e}{a x}-\frac{d}{2 a \,x^{2}}-\frac{c}{3 a \,x^{3}}"," ",0,"1/3/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*g-1/3/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*d-1/6/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g+1/6/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+1/3/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g-1/3/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d-1/3/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*h+1/3/(a/b)^(1/3)/a*e*ln(x+(a/b)^(1/3))+1/6/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-1/6/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e+1/3*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h-1/3/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-1/3/a*ln(b*x^3+a)*f+1/3/a^2*b*ln(b*x^3+a)*c-1/a*e/x-1/3/a*c/x^3-1/2/a*d/x^2+1/a*ln(x)*f-1/a^2*ln(x)*b*c","B"
412,1,562,272,0.060000," ","int(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{h \,x^{4}}{4 b^{2}}+\frac{a f \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{c \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{g \,x^{3}}{3 b^{2}}-\frac{a^{2} h x}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a e x}{3 \left(b \,x^{3}+a \right) b^{2}}+\frac{f \,x^{2}}{2 b^{2}}-\frac{a^{2} g}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{7 \sqrt{3}\, a^{2} h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a^{2} h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{7 a^{2} h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{a d}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{4 \sqrt{3}\, a e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{5 \sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{2 a g \ln \left(b \,x^{3}+a \right)}{3 b^{3}}-\frac{2 a h x}{b^{3}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{d \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{e x}{b^{2}}"," ",0,"-5/9/b^3*a*f*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-4/9/b^3*e*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+7/9/b^4*a^2*h/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-7/18/b^4*a^2*h/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/b^3*e*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/b^2*e*x-1/3/b/(b*x^3+a)*c*x^2-1/3/b^3/(b*x^3+a)*a^2*g+1/3/b^2/(b*x^3+a)*d*a-2/b^3*a*h*x-2/9/b^2*c/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*c/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-2/3/b^3*ln(b*x^3+a)*a*g+2/9/b^2*c*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/b^3*e*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/9/b^3*a*f/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18/b^3*a*f/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/b^2/(b*x^3+a)*x^2*a*f-1/3/b^3/(b*x^3+a)*a^2*h*x+1/3/b^2/(b*x^3+a)*a*e*x+7/9/b^4*a^2*h/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+1/3/b^2*ln(b*x^3+a)*d+1/2/b^2*f*x^2+1/3*g*x^3/b^2+1/4*h*x^4/b^2","B"
413,1,533,248,0.058000," ","int(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{a g \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{d \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{h \,x^{3}}{3 b^{2}}+\frac{a f x}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{c x}{3 \left(b \,x^{3}+a \right) b}+\frac{g \,x^{2}}{2 b^{2}}-\frac{a^{2} h}{3 \left(b \,x^{3}+a \right) b^{3}}+\frac{a e}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{4 \sqrt{3}\, a f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{5 \sqrt{3}\, a g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{2 a h \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{e \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{f x}{b^{2}}"," ",0,"1/3*h*x^3/b^2+1/2*g*x^2/b^2+1/b^2*f*x+1/3/b^2/(b*x^3+a)*x^2*a*g-1/3/b/(b*x^3+a)*x^2*d+1/3/b^2/(b*x^3+a)*a*f*x-1/3/(b*x^3+a)/b*c*x-1/3/b^3/(b*x^3+a)*a^2*h+1/3/b^2/(b*x^3+a)*a*e-4/9/b^3*a*f/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+2/9/b^3*a*f/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/b^3*a*f/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/b^2*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+5/9/b^3*a*g/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18/b^3*a*g/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/b^3*a*g*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/3/b^3*ln(b*x^3+a)*a*h+1/3/b^2*ln(b*x^3+a)*e","B"
414,1,506,234,0.056000," ","int(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{a h \,x^{2}}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{e \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{a g x}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{d x}{3 \left(b \,x^{3}+a \right) b}+\frac{h \,x^{2}}{2 b^{2}}+\frac{a f}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{4 \sqrt{3}\, a g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{5 \sqrt{3}\, a h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 a h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 a h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{c}{3 \left(b \,x^{3}+a \right) b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{f \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{g x}{b^{2}}"," ",0,"1/2*h*x^2/b^2+g*x/b^2+1/3/b^2/(b*x^3+a)*x^2*a*h-1/3/b/(b*x^3+a)*x^2*e+1/3/b^2/(b*x^3+a)*a*g*x-1/3/b/(b*x^3+a)*x*d+1/3/b^2/(b*x^3+a)*a*f-1/3/b/(b*x^3+a)*c-4/9/b^3*a*g/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+2/9/b^3*a*g/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/b^3*a*g/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/b^2*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2*d/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/(a/b)^(2/3)*3^(1/2)/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+5/9/b^3*a*h/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-5/18/b^3*a*h/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/b^3*a*h*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2*e/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/9/b^2*e/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3/b^2*f*ln(b*x^3+a)","B"
415,1,502,230,0.050000," ","int(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{c \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{f \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{a h x}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{e x}{3 \left(b \,x^{3}+a \right) b}+\frac{a g}{3 \left(b \,x^{3}+a \right) b^{2}}-\frac{4 \sqrt{3}\, a h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{4 a h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 a h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{d}{3 \left(b \,x^{3}+a \right) b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{g \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{h x}{b^{2}}"," ",0,"h*x/b^2-1/3/(b*x^3+a)/b*f*x^2+1/3/(b*x^3+a)/a*x^2*c+1/3/b^2/(b*x^3+a)*a*h*x-1/3/b/(b*x^3+a)*e*x+1/3/b^2/(b*x^3+a)*a*g-1/3/b/(b*x^3+a)*d-4/9/b^3*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*e+2/9/b^3*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*e-4/9/b^3*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*e-2/9/(a/b)^(1/3)/b^2*f*ln(x+(a/b)^(1/3))-1/9/b/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/9/(a/b)^(1/3)/b^2*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/18/(a/b)^(1/3)/a/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9*3^(1/2)/(a/b)^(1/3)/b^2*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/b/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/3*g*ln(b*x^3+a)/b^2","B"
416,1,462,217,0.048000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^2,x)","\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 \sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{h \ln \left(b \,x^{3}+a \right)}{3 b^{2}}+\frac{-\frac{\left(a g -b d \right) x^{2}}{3 a b}-\frac{\left(a f -b c \right) x}{3 a b}+\frac{a h -b e}{3 b^{2}}}{b \,x^{3}+a}"," ",0,"(-1/3*(a*g-b*d)/a/b*x^2-1/3*(a*f-b*c)/a/b*x+1/3*(a*h-b*e)/b^2)/(b*x^3+a)+1/9/(a/b)^(2/3)/b^2*f*ln(x+(a/b)^(1/3))+2/9/b/a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/18/(a/b)^(2/3)/b^2*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/9/b/a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/9/(a/b)^(2/3)*3^(1/2)/b^2*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/b/a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-2/9/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*g-1/9/b/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*d+1/9/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g+1/18/b/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*d+2/9/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+1/9/b/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*d+1/3*h*ln(b*x^3+a)/b^2","B"
417,1,507,230,0.061000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a)^2,x)","\frac{e \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{h \,x^{2}}{3 \left(b \,x^{3}+a \right) b}+\frac{d x}{3 \left(b \,x^{3}+a \right) a}-\frac{g x}{3 \left(b \,x^{3}+a \right) b}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{c}{3 \left(b \,x^{3}+a \right) a}+\frac{c \ln \left(x \right)}{a^{2}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{f}{3 \left(b \,x^{3}+a \right) b}+\frac{\sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{2 \sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}-\frac{2 h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}+\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}"," ",0,"-1/3/(b*x^3+a)/b*x^2*h+1/3/(b*x^3+a)/a*e*x^2-1/3/(b*x^3+a)/b*x*g+1/3/a*x/(b*x^3+a)*d-1/3/(b*x^3+a)/b*f+1/3/a/(b*x^3+a)*c+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*g+2/9/a/b*d/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g-1/9/(a/b)^(2/3)/a/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+2/9/a/b*d/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/9/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*h-1/9/(a/b)^(1/3)/a/b*e*ln(x+(a/b)^(1/3))+1/9/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h+1/18/(a/b)^(1/3)/a/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/9*3^(1/2)/(a/b)^(1/3)/a/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^2*c*ln(b*x^3+a)+1/a^2*c*ln(x)","B"
418,1,517,242,0.061000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a)^2,x)","\frac{f \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{b c \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{e x}{3 \left(b \,x^{3}+a \right) a}-\frac{h x}{3 \left(b \,x^{3}+a \right) b}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{d}{3 \left(b \,x^{3}+a \right) a}-\frac{4 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{d \ln \left(x \right)}{a^{2}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{g}{3 \left(b \,x^{3}+a \right) b}+\frac{\sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}+\frac{h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}-\frac{c}{a^{2} x}"," ",0,"1/3/a/(b*x^3+a)*x^2*f-1/3/a^2/(b*x^3+a)*b*c*x^2-1/3/(b*x^3+a)/b*x*h+1/3/(b*x^3+a)/a*e*x-1/3/(b*x^3+a)/b*g+1/3/a/(b*x^3+a)*d+1/9/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h+2/9/(a/b)^(2/3)/a/b*e*ln(x+(a/b)^(1/3))-1/18/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-1/9/(a/b)^(2/3)/a/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+2/9/(a/b)^(2/3)*3^(1/2)/a/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/(a/b)^(1/3)/a/b*f*ln(x+(a/b)^(1/3))+4/9/a^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/18/a/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-2/9/a^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+1/9*3^(1/2)/(a/b)^(1/3)/a/b*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-4/9/a^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-1/3/a^2*d*ln(b*x^3+a)-1/a^2*c/x+1/a^2*d*ln(x)","B"
419,1,527,245,0.066000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a)^2,x)","\frac{g \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{b d \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{f x}{3 \left(b \,x^{3}+a \right) a}-\frac{b c x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{e}{3 \left(b \,x^{3}+a \right) a}-\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{4 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{e \ln \left(x \right)}{a^{2}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{h}{3 \left(b \,x^{3}+a \right) b}-\frac{d}{a^{2} x}-\frac{c}{2 a^{2} x^{2}}"," ",0,"1/3/a/(b*x^3+a)*x^2*g-1/3/(b*x^3+a)/a^2*b*d*x^2+1/3/a/(b*x^3+a)*f*x-1/3/(b*x^3+a)/a^2*b*c*x-1/3/(b*x^3+a)/b*h+1/3/(b*x^3+a)/a*e-5/9/(a/b)^(2/3)/a^2*c*ln(x+(a/b)^(1/3))+5/18/(a/b)^(2/3)/a^2*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/(a/b)^(2/3)*3^(1/2)/a^2*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/(a/b)^(2/3)/a/b*f*ln(x+(a/b)^(1/3))-1/9/a*f/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a*f/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/(a/b)^(1/3)/a^2*d*ln(x+(a/b)^(1/3))-2/9/(a/b)^(1/3)/a^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9*3^(1/2)/(a/b)^(1/3)/a^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/a*g/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18/a*g/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/9/a*g*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^2*e*ln(b*x^3+a)-1/a^2*d/x+1/a^2*e*ln(x)-1/2/a^2*c/x^2","B"
420,1,561,275,0.062000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a)^2,x)","\frac{h \,x^{2}}{3 \left(b \,x^{3}+a \right) a}-\frac{b e \,x^{2}}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{g x}{3 \left(b \,x^{3}+a \right) a}-\frac{b d x}{3 \left(b \,x^{3}+a \right) a^{2}}+\frac{2 \sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{2 g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}-\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b}+\frac{\sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}-\frac{h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b}+\frac{f}{3 \left(b \,x^{3}+a \right) a}-\frac{b c}{3 \left(b \,x^{3}+a \right) a^{2}}-\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}+\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{18 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}}-\frac{4 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{4 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}-\frac{2 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{9 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2}}+\frac{f \ln \left(x \right)}{a^{2}}-\frac{f \ln \left(b \,x^{3}+a \right)}{3 a^{2}}-\frac{2 b c \ln \left(x \right)}{a^{3}}+\frac{2 b c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{e}{a^{2} x}-\frac{d}{2 a^{2} x^{2}}-\frac{c}{3 a^{2} x^{3}}"," ",0,"-1/2/a^2*d/x^2-1/a^2*e/x+1/3/a/(b*x^3+a)*x^2*h+1/3/a/(b*x^3+a)*g*x+4/9/(a/b)^(1/3)/a^2*e*ln(x+(a/b)^(1/3))+5/18/(a/b)^(2/3)/a^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/9/(a/b)^(2/3)/a^2*d*ln(x+(a/b)^(1/3))-2/9/(a/b)^(1/3)/a^2*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-4/9/a^2*e*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/a^2*ln(x)*f+1/3/a/(b*x^3+a)*f-1/3/a^2*ln(b*x^3+a)*f-1/3/a^2*c/x^3-1/3/(b*x^3+a)/a^2*b*c+2/9/a*g/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/9/a*h*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/a*h/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/18/a*h/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a*g/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-5/9/(a/b)^(2/3)*3^(1/2)/a^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/9/a*g/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/3/a^2/(b*x^3+a)*b*e*x^2-1/3/(b*x^3+a)/a^2*b*d*x-2/a^3*b*c*ln(x)+2/3/a^3*b*c*ln(b*x^3+a)","B"
421,1,619,284,0.064000," ","int(x^4*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{4 f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{13 a h \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{7 e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{2 a g \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{d \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} b}-\frac{5 a f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{5 a^{2} h x}{9 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{2 a e x}{9 \left(b \,x^{3}+a \right)^{2} b^{2}}+\frac{a^{2} g}{2 \left(b \,x^{3}+a \right)^{2} b^{3}}-\frac{a d}{6 \left(b \,x^{3}+a \right)^{2} b^{2}}-\frac{14 \sqrt{3}\, a h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}-\frac{14 a h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{7 a h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4}}+\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{5 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{g \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{h x}{b^{3}}"," ",0,"1/27/b^2/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c+1/2/b^3/(b*x^3+a)^2*a^2*g+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f-4/9/b/(b*x^3+a)^2*f*x^5-1/3/b/(b*x^3+a)^2*x^3*d-1/6/b^2/(b*x^3+a)^2*d*a-1/18/b/(b*x^3+a)^2*x^2*c-14/27/b^4*a/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/9/(b*x^3+a)^2/a*c*x^5-1/27/(a/b)^(2/3)/b^3*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-7/18/(b*x^3+a)^2/b*e*x^4+2/27/(a/b)^(2/3)/b^3*e*ln(x+(a/b)^(1/3))+1/3*g*ln(b*x^3+a)/b^3-5/18/b^2/(b*x^3+a)^2*x^2*a*f+2/3/b^2/(b*x^3+a)^2*x^3*a*g+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f-14/27/b^4*a/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h-1/27/b^2/a/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*c+1/54/b^2/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+5/9/b^3/(b*x^3+a)^2*a^2*h*x+13/18/b^2/(b*x^3+a)^2*x^4*a*h+7/27/b^4*a/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-2/9/(b*x^3+a)^2*a/b^2*e*x+2/27/(a/b)^(2/3)*3^(1/2)/b^3*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+h*x/b^3","B"
422,1,515,264,0.060000," ","int(x^3*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{5 \sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{h \ln \left(b \,x^{3}+a \right)}{3 b^{3}}+\frac{-\frac{\left(4 a g -b d \right) x^{5}}{9 a b}-\frac{\left(7 a f -b c \right) x^{4}}{18 a b}+\frac{\left(2 a h -b e \right) x^{3}}{3 b^{2}}-\frac{\left(5 a g +b d \right) x^{2}}{18 b^{2}}-\frac{\left(2 a f +b c \right) x}{9 b^{2}}+\frac{\left(3 a h -b e \right) a}{6 b^{3}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(-1/9*(4*a*g-b*d)/a/b*x^5-1/18*(7*a*f-b*c)/a/b*x^4+1/3*(2*a*h-b*e)/b^2*x^3-1/18*(5*a*g+b*d)/b^2*x^2-1/9*(2*a*f+b*c)/b^2*x+1/6*a*(3*a*h-b*e)/b^3)/(b*x^3+a)^2+2/27/(a/b)^(2/3)/b^3*f*ln(x+(a/b)^(1/3))+1/27/a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*c-1/27/(a/b)^(2/3)/b^3*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/54/a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*c+2/27/(a/b)^(2/3)*3^(1/2)/b^3*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/27/a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*c-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*g-1/27/(a/b)^(1/3)/a/b^2*d*ln(x+(a/b)^(1/3))+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g+1/54/(a/b)^(1/3)/a/b^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+1/27*3^(1/2)/(a/b)^(1/3)/a/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/3*h*ln(b*x^3+a)/b^3","A"
423,1,490,245,0.057000," ","int(x^2*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{5 \sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}-\frac{5 h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{5 h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{3}}+\frac{-\frac{\left(4 a h -b e \right) x^{5}}{9 a b}-\frac{f \,x^{3}}{3 b}-\frac{\left(7 a g -b d \right) x^{4}}{18 a b}-\frac{\left(5 a h +b e \right) x^{2}}{18 b^{2}}-\frac{\left(2 a g +b d \right) x}{9 b^{2}}-\frac{a f +b c}{6 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(-1/9*(4*a*h-b*e)/a/b*x^5-1/18*(7*a*g-b*d)/a/b*x^4-1/3/b*f*x^3-1/18*(5*a*h+b*e)/b^2*x^2-1/9*(2*a*g+b*d)/b^2*x-1/6*(a*f+b*c)/b^2)/(b*x^3+a)^2+2/27/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*g+1/27/(a/b)^(2/3)/a/b^2*d*ln(x+(a/b)^(1/3))-1/27/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g-1/54/(a/b)^(2/3)/a/b^2*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+1/27/(a/b)^(2/3)*3^(1/2)/a/b^2*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-5/27/b^3/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*h-1/27/(a/b)^(1/3)/a/b^2*e*ln(x+(a/b)^(1/3))+5/54/b^3/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h+1/54/(a/b)^(1/3)/a/b^2*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/b^3*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/27*3^(1/2)/(a/b)^(1/3)/a/b^2*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
424,1,498,264,0.056000," ","int(x*(h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{2 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{2 \sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{2 h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}-\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{3}}+\frac{\frac{\left(a f +2 b c \right) x^{5}}{9 a^{2}}-\frac{g \,x^{3}}{3 b}-\frac{\left(7 a h -b e \right) x^{4}}{18 a b}-\frac{\left(a f -7 b c \right) x^{2}}{18 a b}-\frac{\left(2 a h +b e \right) x}{9 b^{2}}-\frac{a g +b d}{6 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/9*(a*f+2*b*c)/a^2*x^5-1/18*(7*a*h-b*e)/a/b*x^4-1/3/b*g*x^3-1/18*(a*f-7*b*c)/a/b*x^2-1/9*(2*a*h+b*e)/b^2*x-1/6*(a*g+b*d)/b^2)/(b*x^3+a)^2+2/27/b^3/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h+1/27/(a/b)^(2/3)/a/b^2*e*ln(x+(a/b)^(1/3))-1/27/b^3/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-1/54/(a/b)^(2/3)/a/b^2*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/27/b^3/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+1/27/(a/b)^(2/3)*3^(1/2)/a/b^2*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/27/(a/b)^(1/3)/a/b^2*f*ln(x+(a/b)^(1/3))-2/27/(a/b)^(1/3)/a^2/b*c*ln(x+(a/b)^(1/3))+1/54/b^2/a/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f+1/27/(a/b)^(1/3)/a^2/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/27/b^2/a*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+2/27*3^(1/2)/(a/b)^(1/3)/a^2/b*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
425,1,506,253,0.057000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/(b*x^3+a)^3,x)","\frac{\sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{\frac{\left(a g +2 b d \right) x^{5}}{9 a^{2}}-\frac{h \,x^{3}}{3 b}+\frac{\left(a f +5 b c \right) x^{4}}{18 a^{2}}-\frac{\left(a g -7 b d \right) x^{2}}{18 a b}-\frac{\left(a f -4 b c \right) x}{9 a b}-\frac{a h +b e}{6 b^{2}}}{\left(b \,x^{3}+a \right)^{2}}"," ",0,"(1/9*(a*g+2*b*d)/a^2*x^5+1/18*(a*f+5*b*c)/a^2*x^4-1/3/b*h*x^3-1/18*(a*g-7*b*d)/a/b*x^2-1/9*(a*f-4*b*c)/a/b*x-1/6*(a*h+b*e)/b^2)/(b*x^3+a)^2+1/27/(a/b)^(2/3)/a/b^2*f*ln(x+(a/b)^(1/3))+5/27/(a/b)^(2/3)/a^2/b*c*ln(x+(a/b)^(1/3))-1/54/(a/b)^(2/3)/a/b^2*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-5/54/(a/b)^(2/3)/a^2/b*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/27/(a/b)^(2/3)*3^(1/2)/a/b^2*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/27/a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*g-2/27/(a/b)^(1/3)/a^2/b*d*ln(x+(a/b)^(1/3))+1/54/a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g+1/27/(a/b)^(1/3)/a^2/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/27/a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+2/27*3^(1/2)/(a/b)^(1/3)/a^2/b*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))","A"
426,1,618,286,0.068000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x/(b*x^3+a)^3,x)","\frac{h \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a}+\frac{2 b e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{g \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 b d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b c \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{7 e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{h \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} b}+\frac{4 d x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{g x}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{c}{2 \left(b \,x^{3}+a \right)^{2} a}-\frac{f}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{\sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{\sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}-\frac{h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{c \ln \left(x \right)}{a^{3}}-\frac{c \ln \left(b \,x^{3}+a \right)}{3 a^{3}}"," ",0,"1/9/a/(b*x^3+a)^2*x^5*h+1/18/a/(b*x^3+a)^2*x^4*g-1/18/(b*x^3+a)^2/b*x^2*h-1/9/(b*x^3+a)^2/b*x*g+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/27*3^(1/2)/(a/b)^(1/3)/a^2/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+4/9/(b*x^3+a)^2/a*d*x+7/18/(b*x^3+a)^2/a*e*x^2+1/2/(b*x^3+a)^2/a*c+5/27/(a/b)^(2/3)/a^2/b*d*ln(x+(a/b)^(1/3))-2/27/(a/b)^(1/3)/a^2/b*e*ln(x+(a/b)^(1/3))+1/27/(a/b)^(1/3)/a^2/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/3/(b*x^3+a)^2/a^2*b*c*x^3+2/9/(b*x^3+a)^2/a^2*b*e*x^5-1/6/(b*x^3+a)^2/b*f+1/a^3*c*ln(x)-1/3/a^3*c*ln(b*x^3+a)+1/27/a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*g+1/27/a/b^2*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+5/18/(b*x^3+a)^2/a^2*b*d*x^4-5/54/(a/b)^(2/3)/a^2/b*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/54/a/b^2/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h+1/27/a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*g-1/54/a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*g-1/27/a/b^2/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*h","B"
427,1,622,301,0.064000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^2/(b*x^3+a)^3,x)","\frac{2 b f \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b^{2} c \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{h \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a}+\frac{5 b e \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{b d \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{7 f \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{13 b c \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 e x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{h x}{9 \left(b \,x^{3}+a \right)^{2} b}+\frac{d}{2 \left(b \,x^{3}+a \right)^{2} a}-\frac{g}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{\sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}-\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{2}}+\frac{5 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{14 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{d \ln \left(x \right)}{a^{3}}-\frac{d \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{c}{a^{3} x}"," ",0,"1/2/(b*x^3+a)^2/a*d+1/18/a/(b*x^3+a)^2*x^4*h+7/18/a/(b*x^3+a)^2*f*x^2-1/9/(b*x^3+a)^2/b*x*h-5/9/(b*x^3+a)^2/a^3*b^2*c*x^5+4/9/(b*x^3+a)^2/a*e*x-7/27/(a/b)^(1/3)/a^3*c*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/27/(a/b)^(1/3)/a^3*c*ln(x+(a/b)^(1/3))+5/18/(b*x^3+a)^2/a^2*b*e*x^4-5/54/(a/b)^(2/3)/a^2/b*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-1/a^3*c/x-14/27*3^(1/2)/(a/b)^(1/3)/a^3*c*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+2/9/a^2/(b*x^3+a)^2*x^5*b*f-1/6/(b*x^3+a)^2/b*g+1/3/(b*x^3+a)^2/a^2*b*d*x^3+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+1/27/a/b^2/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*h+2/27/a^2/b*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))*f+1/a^3*d*ln(x)-1/3/a^3*d*ln(b*x^3+a)-13/18/(b*x^3+a)^2/a^2*b*c*x^2+5/27/(a/b)^(2/3)/a^2/b*e*ln(x+(a/b)^(1/3))+1/27/a/b^2/(a/b)^(2/3)*ln(x+(a/b)^(1/3))*h-1/54/a/b^2/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*h-2/27/a^2/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))*f+1/27/a^2/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*f","B"
428,1,626,297,0.066000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^3/(b*x^3+a)^3,x)","\frac{2 b g \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b^{2} d \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{5 b f \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{11 b^{2} c \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{b e \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{7 g \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{13 b d \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 f x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{7 b c x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{e}{2 \left(b \,x^{3}+a \right)^{2} a}-\frac{h}{6 \left(b \,x^{3}+a \right)^{2} b}+\frac{5 \sqrt{3}\, f \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 f \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 f \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{20 \sqrt{3}\, c \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 c \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 c \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{14 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{e \ln \left(x \right)}{a^{3}}-\frac{e \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{d}{a^{3} x}-\frac{c}{2 a^{3} x^{2}}"," ",0,"10/27/a^3*c/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/27/a^3*d/(a/b)^(1/3)*ln(x+(a/b)^(1/3))-7/27/a^3*d/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+7/18/a/(b*x^3+a)^2*x^2*g-20/27/a^3*c/(a/b)^(2/3)*ln(x+(a/b)^(1/3))+4/9/(b*x^3+a)^2/a*f*x+5/27/(a/b)^(2/3)*3^(1/2)/a^2/b*f*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/6/(b*x^3+a)^2/b*h+1/2/a/(b*x^3+a)^2*e+5/18/(b*x^3+a)^2/a^2*b*f*x^4+2/27/a^2*g*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/a^3*d/x+1/a^3*e*ln(x)-1/3/a^3*e*ln(b*x^3+a)-20/27/a^3*c/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-2/27/a^2*g/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/27/a^2*g/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-14/27/a^3*d*3^(1/2)/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2/a^3*c/x^2+5/27/(a/b)^(2/3)/a^2/b*f*ln(x+(a/b)^(1/3))-5/54/(a/b)^(2/3)/a^2/b*f*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2/9/a^2/(b*x^3+a)^2*x^5*b*g-5/9/a^3/(b*x^3+a)^2*b^2*d*x^5-11/18/a^3/(b*x^3+a)^2*b^2*c*x^4+1/3/a^2/(b*x^3+a)^2*x^3*b*e-13/18/a^2/(b*x^3+a)^2*b*d*x^2-7/9/a^2/(b*x^3+a)^2*b*c*x","B"
429,1,680,330,0.070000," ","int((h*x^5+g*x^4+f*x^3+e*x^2+d*x+c)/x^4/(b*x^3+a)^3,x)","\frac{2 b h \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{5 b^{2} e \,x^{5}}{9 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{5 b g \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{11 b^{2} d \,x^{4}}{18 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{b f \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{2}}-\frac{2 b^{2} c \,x^{3}}{3 \left(b \,x^{3}+a \right)^{2} a^{3}}+\frac{7 h \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a}-\frac{13 b e \,x^{2}}{18 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{4 g x}{9 \left(b \,x^{3}+a \right)^{2} a}-\frac{7 b d x}{9 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{f}{2 \left(b \,x^{3}+a \right)^{2} a}-\frac{5 b c}{6 \left(b \,x^{3}+a \right)^{2} a^{2}}+\frac{5 \sqrt{3}\, g \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{5 g \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}-\frac{5 g \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b}+\frac{2 \sqrt{3}\, h \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{2 h \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}+\frac{h \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b}-\frac{20 \sqrt{3}\, d \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{20 d \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}+\frac{10 d \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3}}-\frac{14 \sqrt{3}\, e \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 x}{\left(\frac{a}{b}\right)^{\frac{1}{3}}}-1\right)}{3}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{14 e \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}-\frac{7 e \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)}{27 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3}}+\frac{f \ln \left(x \right)}{a^{3}}-\frac{f \ln \left(b \,x^{3}+a \right)}{3 a^{3}}-\frac{3 b c \ln \left(x \right)}{a^{4}}+\frac{b c \ln \left(b \,x^{3}+a \right)}{a^{4}}-\frac{e}{a^{3} x}-\frac{d}{2 a^{3} x^{2}}-\frac{c}{3 a^{3} x^{3}}"," ",0,"-5/9/(b*x^3+a)^2/a^3*b^2*e*x^5-14/27*3^(1/2)/(a/b)^(1/3)/a^3*e*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-7/27/(a/b)^(1/3)/a^3*e*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+14/27/(a/b)^(1/3)/a^3*e*ln(x+(a/b)^(1/3))-5/6/(b*x^3+a)^2/a^2*b*c-20/27/(a/b)^(2/3)/a^3*d*ln(x+(a/b)^(1/3))+10/27/(a/b)^(2/3)/a^3*d*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1/a^3*ln(x)*f+1/2/a/(b*x^3+a)^2*f-1/3/a^3*ln(b*x^3+a)*f-11/18/(b*x^3+a)^2/a^3*b^2*d*x^4-20/27/(a/b)^(2/3)*3^(1/2)/a^3*d*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/3/a^3*c/x^3+7/18/a/(b*x^3+a)^2*x^2*h+4/9/a/(b*x^3+a)^2*g*x+2/27/a^2*h*3^(1/2)/b/(a/b)^(1/3)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))+5/27/a^2*g/b/(a/b)^(2/3)*3^(1/2)*arctan(1/3*3^(1/2)*(2/(a/b)^(1/3)*x-1))-1/2/a^3*d/x^2-1/a^3*e/x-13/18/(b*x^3+a)^2/a^2*b*e*x^2-5/54/a^2*g/b/(a/b)^(2/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+5/27/a^2*g/b/(a/b)^(2/3)*ln(x+(a/b)^(1/3))-7/9/(b*x^3+a)^2/a^2*b*d*x+5/18/a^2/(b*x^3+a)^2*x^4*b*g+1/3/a^2/(b*x^3+a)^2*x^3*b*f+2/9/a^2/(b*x^3+a)^2*x^5*b*h-2/27/a^2*h/b/(a/b)^(1/3)*ln(x+(a/b)^(1/3))+1/27/a^2*h/b/(a/b)^(1/3)*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-2/3/(b*x^3+a)^2/a^3*b^2*c*x^3-3/a^4*b*c*ln(x)+1/a^4*b*c*ln(b*x^3+a)","B"
430,1,793,435,0.079000," ","int(x^3*(e*x^2+d*x+c)/(b*x^3+a)^(1/2),x)","\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{21 \sqrt{b \,x^{3}+a}\, b^{2}}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{3}}{9 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a}{9 b^{2}}\right) e"," ",0,"e*(2/9/b*x^3*(b*x^3+a)^(1/2)-4/9*a*(b*x^3+a)^(1/2)/b^2)+d*(2/7*(b*x^3+a)^(1/2)/b*x^2+8/21*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","A"
431,1,773,416,0.056000," ","int(x^2*(e*x^2+d*x+c)/(b*x^3+a)^(1/2),x)","\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{21 \sqrt{b \,x^{3}+a}\, b^{2}}\right) e +\frac{2 \sqrt{b \,x^{3}+a}\, c}{3 b}"," ",0,"e*(2/7*(b*x^3+a)^(1/2)/b*x^2+8/21*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/3*c*(b*x^3+a)^(1/2)/b","A"
432,1,753,399,0.049000," ","int(x*(e*x^2+d*x+c)/(b*x^3+a)^(1/2),x)","\left(\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{15 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b}\right) e -\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) c}{3 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, d}{3 b}"," ",0,"e*(2/5*(b*x^3+a)^(1/2)/b*x+4/15*I*a/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/3*d*(b*x^3+a)^(1/2)/b-2/3*I*c*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","A"
433,1,735,379,0.051000," ","int((e*x^2+d*x+c)/(b*x^3+a)^(1/2),x)","-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, c \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) d}{3 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, e}{3 b}"," ",0,"2/3*(b*x^3+a)^(1/2)/b*e-2/3*I*d*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*c*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))","A"
434,1,740,384,0.046000," ","int((e*x^2+d*x+c)/x/(b*x^3+a)^(1/2),x)","-\frac{2 c \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, d \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) e}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*I*e*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*I*d*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))-2/3*c*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)","A"
435,1,759,407,0.060000," ","int((e*x^2+d*x+c)/x^2/(b*x^3+a)^(1/2),x)","-\frac{2 d \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, e \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{3 \sqrt{b \,x^{3}+a}\, b}+\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{a x}\right) c"," ",0,"-2/3*I*e*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+c*(-(b*x^3+a)^(1/2)/a/x-1/3*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))-2/3*d*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)","A"
436,1,778,425,0.059000," ","int((e*x^2+d*x+c)/x^3/(b*x^3+a)^(1/2),x)","-\frac{2 e \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}+\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{6 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{2 a \,x^{2}}\right) c +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{3 \sqrt{b \,x^{3}+a}\, a}-\frac{\sqrt{b \,x^{3}+a}}{a x}\right) d"," ",0,"c*(-1/2*(b*x^3+a)^(1/2)/a/x^2+1/6*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-(b*x^3+a)^(1/2)/a/x-1/3*I/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))-2/3*e*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)","A"
437,1,836,446,0.086000," ","int(x^5*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(\frac{2 a}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}}{3 b^{2}}\right) c +\left(\frac{2 a x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{45 \sqrt{b \,x^{3}+a}\, b^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b^{2}}\right) d +\left(\frac{2 a \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7 b^{2}}+\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{63 \sqrt{b \,x^{3}+a}\, b^{3}}\right) e"," ",0,"e*(2/3/b^2*a*x^2/((x^3+a/b)*b)^(1/2)+2/7*(b*x^3+a)^(1/2)/b^2*x^2+80/63*I*a/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/3/((x^3+a/b)*b)^(1/2)*a/b^2*x+2/5*(b*x^3+a)^(1/2)/b^2*x+32/45*I*a/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(2/3/b^2*a/((x^3+a/b)*b)^(1/2)+2/3*(b*x^3+a)^(1/2)/b^2)","A"
438,1,817,430,0.053000," ","int(x^4*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) c +\left(\frac{2 a}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}}{3 b^{2}}\right) d +\left(\frac{2 a x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{45 \sqrt{b \,x^{3}+a}\, b^{3}}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5 b^{2}}\right) e"," ",0,"e*(2/3/((x^3+a/b)*b)^(1/2)*a/b^2*x+2/5*(b*x^3+a)^(1/2)/b^2*x+32/45*I*a/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(2/3/((x^3+a/b)*b)^(1/2)*a/b^2+2/3*(b*x^3+a)^(1/2)/b^2)+c*(-2/3/((x^3+a/b)*b)^(1/2)/b*x^2-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","A"
439,1,800,404,0.054000," ","int(x^3*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) c +\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) d +\left(\frac{2 a}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b^{2}}+\frac{2 \sqrt{b \,x^{3}+a}}{3 b^{2}}\right) e"," ",0,"e*(2/3/((x^3+a/b)*b)^(1/2)*a/b^2+2/3*(b*x^3+a)^(1/2)/b^2)+d*(-2/3/((x^3+a/b)*b)^(1/2)/b*x^2-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","A"
440,1,779,388,0.059000," ","int(x^2*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) d +\left(-\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) e -\frac{2 c}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"e*(-2/3/((x^3+a/b)*b)^(1/2)/b*x^2-8/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*c/b/(b*x^3+a)^(1/2)","B"
441,1,782,422,0.130000," ","int(x*(e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) c +\left(-\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, b}-\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, b^{2}}\right) e -\frac{2 d}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"e*(-2/3/((x^3+a/b)*b)^(1/2)/b*x-4/9*I/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))-2/3*d/b/(b*x^3+a)^(1/2)+c*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","A"
442,1,785,399,0.052000," ","int((e*x^2+d*x+c)/(b*x^3+a)^(3/2),x)","\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) c +\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) d -\frac{2 e}{3 \sqrt{b \,x^{3}+a}\, b}"," ",0,"-2/3*e/b/(b*x^3+a)^(1/2)+d*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","A"
443,1,810,434,0.049000," ","int((e*x^2+d*x+c)/x/(b*x^3+a)^(3/2),x)","\left(-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}\right) c +\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) d +\left(\frac{2 x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}+\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) e"," ",0,"e*(2/3/((x^3+a/b)*b)^(1/2)/a*x^2+2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(2/3/a/((x^3+a/b)*b)^(1/2)-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2))","A"
444,1,825,455,0.056000," ","int((e*x^2+d*x+c)/x^2/(b*x^3+a)^(3/2),x)","\left(-\frac{2 b \,x^{2}}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a^{2}}-\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{9 \sqrt{b \,x^{3}+a}\, a^{2}}-\frac{\sqrt{b \,x^{3}+a}}{a^{2} x}\right) c +\left(-\frac{2 \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 a^{\frac{3}{2}}}+\frac{2}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}\right) d +\left(\frac{2 x}{3 \sqrt{\left(x^{3}+\frac{a}{b}\right) b}\, a}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{9 \sqrt{b \,x^{3}+a}\, a b}\right) e"," ",0,"e*(2/3/((x^3+a/b)*b)^(1/2)/a*x-2/9*I/a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-2/3/((x^3+a/b)*b)^(1/2)/a^2*b*x^2-(b*x^3+a)^(1/2)/a^2/x-5/9*I/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/3/((x^3+a/b)*b)^(1/2)/a-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2))","A"
445,1,1674,573,0.090000," ","int(x^3*(g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{6}}{15}+\frac{2 \sqrt{b \,x^{3}+a}\, a \,x^{3}}{45 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a^{2}}{45 b^{2}}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{7}}{17}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187 b}-\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{48 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{8}}{19}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247 b}-\frac{60 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b^{2}}-\frac{80 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{3}}\right) g"," ",0,"g*(2/19*(b*x^3+a)^(1/2)*x^8+6/247*(b*x^3+a)^(1/2)*a/b*x^5-60/1729*(b*x^3+a)^(1/2)*a^2/b^2*x^2-80/1729*I*a^3/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/17*(b*x^3+a)^(1/2)*x^7+6/187*(b*x^3+a)^(1/2)*a/b*x^4-48/935*(b*x^3+a)^(1/2)*a^2/b^2*x-32/935*I*a^3/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+e*(2/15*x^6*(b*x^3+a)^(1/2)+2/45*a/b*x^3*(b*x^3+a)^(1/2)-4/45*a^2/b^2*(b*x^3+a)^(1/2))+d*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
446,1,1197,525,0.058000," ","int(x^2*(g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{6}}{15}+\frac{2 \sqrt{b \,x^{3}+a}\, a \,x^{3}}{45 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a^{2}}{45 b^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{7}}{17}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187 b}-\frac{32 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{48 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b^{2}}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} c}{9 b}"," ",0,"g*(2/17*(b*x^3+a)^(1/2)*x^7+6/187*(b*x^3+a)^(1/2)*a/b*x^4-48/935*(b*x^3+a)^(1/2)*a^2/b^2*x-32/935*I*a^3/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+f*(2/15*(b*x^3+a)^(1/2)*x^6+2/45*(b*x^3+a)^(1/2)*a/b*x^3-4/45*(b*x^3+a)^(1/2)*a^2/b^2)+e*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/9*c/b*(b*x^3+a)^(3/2)","B"
447,1,1311,513,0.053000," ","int(x*(g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{6}}{15}+\frac{2 \sqrt{b \,x^{3}+a}\, a \,x^{3}}{45 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a^{2}}{45 b^{2}}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} d}{9 b}"," ",0,"g*(2/15*(b*x^3+a)^(1/2)*x^6+2/45*(b*x^3+a)^(1/2)*a/b*x^3-4/45*(b*x^3+a)^(1/2)*a^2/b^2)+f*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/9*d/b*(b*x^3+a)^(3/2)+c*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
448,1,1557,491,0.053000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2),x)","\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{5}}{13}+\frac{6 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91 b}+\frac{8 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b^{2}}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} e}{9 b}"," ",0,"g*(2/13*(b*x^3+a)^(1/2)*x^5+6/91*(b*x^3+a)^(1/2)*a/b*x^2+8/91*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/9*e/b*(b*x^3+a)^(3/2)+d*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
449,1,1118,468,0.056000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x,x)","\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) c +\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{4}}{11}+\frac{4 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{6 \sqrt{b \,x^{3}+a}\, a x}{55 b}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} f}{9 b}"," ",0,"g*(2/11*(b*x^3+a)^(1/2)*x^4+6/55*(b*x^3+a)^(1/2)*a/b*x+4/55*I*a^2/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/9*f/b*(b*x^3+a)^(3/2)+e*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","B"
450,1,1248,486,0.062000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^2,x)","\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) c +\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) d +\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) f +\frac{2 \left(b \,x^{3}+a \right)^{\frac{3}{2}} g}{9 b}"," ",0,"2/9*g/b*(b*x^3+a)^(3/2)+f*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","B"
451,1,1529,490,0.060000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^3,x)","\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) c +\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) d +\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) e +\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, x^{2}}{7}-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}\, b}\right) g"," ",0,"g*(2/7*(b*x^3+a)^(1/2)*x^2-2/7*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","B"
452,1,1114,485,0.061000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^4,x)","\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) c +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) d +\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) e +\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) f +\left(-\frac{2 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{5 \sqrt{b \,x^{3}+a}\, b}+\frac{2 \sqrt{b \,x^{3}+a}\, x}{5}\right) g"," ",0,"g*(2/5*(b*x^3+a)^(1/2)*x-2/5*I*a*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+d*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+e*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","B"
453,1,1286,532,0.074000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^5,x)","\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) c +\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) d +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) e +\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) f +\left(-\frac{2 \sqrt{a}\, \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{2 \sqrt{b \,x^{3}+a}}{3}\right) g"," ",0,"c*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+e*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+f*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+g*(-2/3*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2)+2/3*(b*x^3+a)^(1/2))","B"
454,1,1571,500,0.059000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^6,x)","\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{20 a \,x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 x^{5}}\right) c +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) d +\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) e +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) f +\left(-\frac{\sqrt{b \,x^{3}+a}}{x}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right)}{\sqrt{b \,x^{3}+a}}\right) g"," ",0,"c*(-1/5*(b*x^3+a)^(1/2)/x^5-3/20*(b*x^3+a)^(1/2)/a*b/x^2+1/20*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+f*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+g*(-(b*x^3+a)^(1/2)/x-I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
455,1,1180,503,0.064000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^7,x)","\left(\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{12 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b}{12 a \,x^{3}}-\frac{\sqrt{b \,x^{3}+a}}{6 x^{6}}\right) c +\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{20 a \,x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 x^{5}}\right) d +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) e +\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) f +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{2 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}}{2 x^{2}}\right) g"," ",0,"d*(-1/5*(b*x^3+a)^(1/2)/x^5-3/20*(b*x^3+a)^(1/2)/a*b/x^2+1/20*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+e*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+g*(-1/2*(b*x^3+a)^(1/2)/x^2-1/2*I*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(1/12*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2)-1/6*(b*x^3+a)^(1/2)/x^6-1/12*(b*x^3+a)^(1/2)/a*b/x^3)","B"
456,1,1376,549,0.063000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^8,x)","\left(\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{15 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a^{2} x}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{56 a \,x^{4}}-\frac{\sqrt{b \,x^{3}+a}}{7 x^{7}}\right) c +\left(\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{12 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b}{12 a \,x^{3}}-\frac{\sqrt{b \,x^{3}+a}}{6 x^{6}}\right) d +\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{20 a \,x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 x^{5}}\right) e +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) f +\left(-\frac{b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{\sqrt{b \,x^{3}+a}}{3 x^{3}}\right) g"," ",0,"e*(-1/5*(b*x^3+a)^(1/2)/x^5-3/20*(b*x^3+a)^(1/2)/a*b/x^2+1/20*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+f*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+g*(-1/3*b*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2)-1/3*(b*x^3+a)^(1/2)/x^3)+c*(-1/7*(b*x^3+a)^(1/2)/x^7-3/56/a*b*(b*x^3+a)^(1/2)/x^4+15/112/a^2*b^2*(b*x^3+a)^(1/2)/x+5/112*I*b^2/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(1/12*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2)-1/6*(b*x^3+a)^(1/2)/x^6-1/12*(b*x^3+a)^(1/2)/a*b/x^3)","B"
457,1,1679,579,0.059000," ","int((g*x^4+f*x^3+e*x^2+d*x+c)*(b*x^3+a)^(1/2)/x^9,x)","\left(-\frac{7 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{21 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a^{2} x^{2}}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{80 a \,x^{5}}-\frac{\sqrt{b \,x^{3}+a}}{8 x^{8}}\right) c +\left(\frac{5 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{15 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a^{2} x}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{56 a \,x^{4}}-\frac{\sqrt{b \,x^{3}+a}}{7 x^{7}}\right) d +\left(\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{12 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b}{12 a \,x^{3}}-\frac{\sqrt{b \,x^{3}+a}}{6 x^{6}}\right) e +\left(\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{20 a \,x^{2}}-\frac{\sqrt{b \,x^{3}+a}}{5 x^{5}}\right) f +\left(-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}\, a}-\frac{3 \sqrt{b \,x^{3}+a}\, b}{8 a x}-\frac{\sqrt{b \,x^{3}+a}}{4 x^{4}}\right) g"," ",0,"f*(-1/5*(b*x^3+a)^(1/2)/x^5-3/20*(b*x^3+a)^(1/2)/a*b/x^2+1/20*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+g*(-1/4*(b*x^3+a)^(1/2)/x^4-3/8*(b*x^3+a)^(1/2)/a*b/x-1/8*I*b/a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(-1/8*(b*x^3+a)^(1/2)/x^8-3/80*(b*x^3+a)^(1/2)/a*b/x^5+21/320*(b*x^3+a)^(1/2)/a^2*b^2/x^2-7/320*I*b^2/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-1/7*(b*x^3+a)^(1/2)/x^7-3/56*(b*x^3+a)^(1/2)/a*b/x^4+15/112*(b*x^3+a)^(1/2)/a^2*b^2/x+5/112*I*b^2/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(1/12*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(3/2)-1/6*(b*x^3+a)^(1/2)/x^6-1/12*(b*x^3+a)^(1/2)/a*b/x^3)","B"
458,1,1764,627,0.084000," ","int(x^3*(b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{9}}{21}+\frac{16 \sqrt{b \,x^{3}+a}\, a \,x^{6}}{105}+\frac{2 \sqrt{b \,x^{3}+a}\, a^{2} x^{3}}{105 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a^{3}}{105 b^{2}}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{10}}{23}+\frac{52 \sqrt{b \,x^{3}+a}\, a \,x^{7}}{391}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{4}}{4301 b}-\frac{288 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{4} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{21505 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{432 \sqrt{b \,x^{3}+a}\, a^{3} x}{21505 b^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{11}}{25}+\frac{56 \sqrt{b \,x^{3}+a}\, a \,x^{8}}{475}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{5}}{6175 b}-\frac{108 \sqrt{b \,x^{3}+a}\, a^{3} x^{2}}{8645 b^{2}}-\frac{144 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{4}}{8645 \sqrt{b \,x^{3}+a}\, b^{3}}\right) g"," ",0,"g*(2/25*b*x^11*(b*x^3+a)^(1/2)+56/475*(b*x^3+a)^(1/2)*a*x^8+54/6175*(b*x^3+a)^(1/2)*a^2/b*x^5-108/8645*(b*x^3+a)^(1/2)*a^3/b^2*x^2-144/8645*I*a^4/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/23*(b*x^3+a)^(1/2)*b*x^10+52/391*(b*x^3+a)^(1/2)*a*x^7+54/4301*(b*x^3+a)^(1/2)*a^2/b*x^4-432/21505*(b*x^3+a)^(1/2)*a^3/b^2*x-288/21505*I*a^4/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+e*(2/21*b*x^9*(b*x^3+a)^(1/2)+16/105*a*x^6*(b*x^3+a)^(1/2)+2/105*a^2/b*x^3*(b*x^3+a)^(1/2)-4/105*a^3/b^2*(b*x^3+a)^(1/2))+d*(2/19*b*x^8*(b*x^3+a)^(1/2)+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/17*b*x^7*(b*x^3+a)^(1/2)+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
459,1,1269,579,0.060000," ","int(x^2*(b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{9}}{21}+\frac{16 \sqrt{b \,x^{3}+a}\, a \,x^{6}}{105}+\frac{2 \sqrt{b \,x^{3}+a}\, a^{2} x^{3}}{105 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a^{3}}{105 b^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{10}}{23}+\frac{52 \sqrt{b \,x^{3}+a}\, a \,x^{7}}{391}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{4}}{4301 b}-\frac{288 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{4} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{21505 \sqrt{b \,x^{3}+a}\, b^{3}}-\frac{432 \sqrt{b \,x^{3}+a}\, a^{3} x}{21505 b^{2}}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} c}{15 b}"," ",0,"g*(2/23*(b*x^3+a)^(1/2)*b*x^10+52/391*(b*x^3+a)^(1/2)*a*x^7+54/4301*(b*x^3+a)^(1/2)*a^2/b*x^4-432/21505*(b*x^3+a)^(1/2)*a^3/b^2*x-288/21505*I*a^4/b^3*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+f*(2/21*(b*x^3+a)^(1/2)*b*x^9+16/105*(b*x^3+a)^(1/2)*a*x^6+2/105*(b*x^3+a)^(1/2)*a^2/b*x^3-4/105*(b*x^3+a)^(1/2)*a^3/b^2)+e*(2/19*(b*x^3+a)^(1/2)*b*x^8+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/17*(b*x^3+a)^(1/2)*b*x^7+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/15*c/b*(b*x^3+a)^(5/2)","B"
460,1,1383,565,0.054000," ","int(x*(b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{9}}{21}+\frac{16 \sqrt{b \,x^{3}+a}\, a \,x^{6}}{105}+\frac{2 \sqrt{b \,x^{3}+a}\, a^{2} x^{3}}{105 b}-\frac{4 \sqrt{b \,x^{3}+a}\, a^{3}}{105 b^{2}}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} d}{15 b}"," ",0,"g*(2/21*(b*x^3+a)^(1/2)*b*x^9+16/105*(b*x^3+a)^(1/2)*a*x^6+2/105*(b*x^3+a)^(1/2)*a^2/b*x^3-4/105*(b*x^3+a)^(1/2)*a^3/b^2)+f*(2/19*(b*x^3+a)^(1/2)*b*x^8+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(2/17*(b*x^3+a)^(1/2)*b*x^7+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/15*d/b*(b*x^3+a)^(5/2)+c*(2/13*b*x^5*(b*x^3+a)^(1/2)+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
461,1,1629,542,0.060000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c),x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{8}}{19}+\frac{44 \sqrt{b \,x^{3}+a}\, a \,x^{5}}{247}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x^{2}}{1729 b}+\frac{72 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{3}}{1729 \sqrt{b \,x^{3}+a}\, b^{2}}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} e}{15 b}"," ",0,"g*(2/19*(b*x^3+a)^(1/2)*b*x^8+44/247*(b*x^3+a)^(1/2)*a*x^5+54/1729*(b*x^3+a)^(1/2)*a^2/b*x^2+72/1729*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/17*(b*x^3+a)^(1/2)*b*x^7+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/15*e/b*(b*x^3+a)^(5/2)+d*(2/13*(b*x^3+a)^(1/2)*b*x^5+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
462,1,1188,520,0.055000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x,x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{7}}{17}+\frac{40 \sqrt{b \,x^{3}+a}\, a \,x^{4}}{187}+\frac{36 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{935 \sqrt{b \,x^{3}+a}\, b^{2}}+\frac{54 \sqrt{b \,x^{3}+a}\, a^{2} x}{935 b}\right) g +\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} f}{15 b}"," ",0,"g*(2/17*(b*x^3+a)^(1/2)*b*x^7+40/187*(b*x^3+a)^(1/2)*a*x^4+54/935*(b*x^3+a)^(1/2)*a^2/b*x+36/935*I*a^3/b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+2/15*f/b*(b*x^3+a)^(5/2)+e*(2/13*(b*x^3+a)^(1/2)*b*x^5+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","B"
463,1,1317,534,0.057000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^2,x)","\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) f +\frac{2 \left(b \,x^{3}+a \right)^{\frac{5}{2}} g}{15 b}"," ",0,"2/15*g/b*(b*x^3+a)^(5/2)+f*(2/13*(b*x^3+a)^(1/2)*b*x^5+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-a*(b*x^3+a)^(1/2)/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","B"
464,1,1613,538,0.059000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^3,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) c +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{5}}{13}+\frac{32 \sqrt{b \,x^{3}+a}\, a \,x^{2}}{91}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a^{2}}{91 \sqrt{b \,x^{3}+a}\, b}\right) g"," ",0,"g*(2/13*(b*x^3+a)^(1/2)*b*x^5+32/91*(b*x^3+a)^(1/2)*a*x^2-18/91*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/2*a*(b*x^3+a)^(1/2)/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-(b*x^3+a)^(1/2)*a/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","B"
465,1,1193,534,0.057000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^4,x)","\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) c +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) d +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{4}}{11}-\frac{18 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{55 \sqrt{b \,x^{3}+a}\, b}+\frac{28 \sqrt{b \,x^{3}+a}\, a x}{55}\right) g"," ",0,"g*(2/11*(b*x^3+a)^(1/2)*b*x^4+28/55*(b*x^3+a)^(1/2)*a*x-18/55*I*a^2*3^(1/2)*(-a*b^2)^(1/3)/b*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+d*(-1/2*(b*x^3+a)^(1/2)*a/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+e*(-(b*x^3+a)^(1/2)*a/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","B"
466,1,1342,577,0.060000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^5,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) c +\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) d +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) e +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{3}}{9}-\frac{2 a^{\frac{3}{2}} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{3}+\frac{8 \sqrt{b \,x^{3}+a}\, a}{9}\right) g"," ",0,"c*(-1/4*a*(b*x^3+a)^(1/2)/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+e*(-1/2*(b*x^3+a)^(1/2)*a/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+f*(-(b*x^3+a)^(1/2)*a/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+g*(2/9*(b*x^3+a)^(1/2)*b*x^3+8/9*(b*x^3+a)^(1/2)*a-2/3*a^(3/2)*arctanh((b*x^3+a)^(1/2)/a^(1/2)))","B"
467,1,1606,535,0.063000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^6,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) c +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) d +\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) e +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) f +\left(\frac{2 \sqrt{b \,x^{3}+a}\, b \,x^{2}}{7}-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) a}{7 \sqrt{b \,x^{3}+a}}-\frac{\sqrt{b \,x^{3}+a}\, a}{x}\right) g"," ",0,"c*(-1/5*a*(b*x^3+a)^(1/2)/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-1/4*(b*x^3+a)^(1/2)*a/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+f*(-1/2*(b*x^3+a)^(1/2)*a/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+g*(-(b*x^3+a)^(1/2)*a/x+2/7*(b*x^3+a)^(1/2)*b*x^2-9/7*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))","B"
468,1,1196,532,0.067000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^7,x)","\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{5 \sqrt{b \,x^{3}+a}\, b}{12 x^{3}}-\frac{\sqrt{b \,x^{3}+a}\, a}{6 x^{6}}\right) c +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) d +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) e +\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) f +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, a \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{10 \sqrt{b \,x^{3}+a}}+\frac{2 \sqrt{b \,x^{3}+a}\, b x}{5}-\frac{\sqrt{b \,x^{3}+a}\, a}{2 x^{2}}\right) g"," ",0,"d*(-1/5*(b*x^3+a)^(1/2)*a/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+e*(-1/4*(b*x^3+a)^(1/2)*a/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+g*(-1/2*(b*x^3+a)^(1/2)*a/x^2+2/5*(b*x^3+a)^(1/2)*b*x-9/10*I*a*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/6*a*(b*x^3+a)^(1/2)/x^6-5/12*(b*x^3+a)^(1/2)*b/x^3-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2))","B"
469,1,1375,580,0.060000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^8,x)","\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) c +\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{5 \sqrt{b \,x^{3}+a}\, b}{12 x^{3}}-\frac{\sqrt{b \,x^{3}+a}\, a}{6 x^{6}}\right) d +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) e +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) f +\left(-\sqrt{a}\, b \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)+\frac{2 \sqrt{b \,x^{3}+a}\, b}{3}-\frac{\sqrt{b \,x^{3}+a}\, a}{3 x^{3}}\right) g"," ",0,"e*(-1/5*(b*x^3+a)^(1/2)*a/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+f*(-1/4*(b*x^3+a)^(1/2)*a/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+g*(-1/3*(b*x^3+a)^(1/2)*a/x^3+2/3*(b*x^3+a)^(1/2)*b-b*arctanh((b*x^3+a)^(1/2)/a^(1/2))*a^(1/2))+c*(-1/7*a*(b*x^3+a)^(1/2)/x^7-17/56*b*(b*x^3+a)^(1/2)/x^4-27/112*b^2/a*(b*x^3+a)^(1/2)/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(-1/6*(b*x^3+a)^(1/2)*a/x^6-5/12*(b*x^3+a)^(1/2)*b/x^3-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2))","B"
470,1,1663,549,0.059000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^9,x)","\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a \,x^{2}}-\frac{19 \sqrt{b \,x^{3}+a}\, b}{80 x^{5}}-\frac{\sqrt{b \,x^{3}+a}\, a}{8 x^{8}}\right) c +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) d +\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{5 \sqrt{b \,x^{3}+a}\, b}{12 x^{3}}-\frac{\sqrt{b \,x^{3}+a}\, a}{6 x^{6}}\right) e +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) f +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b}{8 \sqrt{b \,x^{3}+a}}-\frac{11 \sqrt{b \,x^{3}+a}\, b}{8 x}-\frac{\sqrt{b \,x^{3}+a}\, a}{4 x^{4}}\right) g"," ",0,"f*(-1/5*(b*x^3+a)^(1/2)*a/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+g*(-1/4*(b*x^3+a)^(1/2)*a/x^4-11/8*(b*x^3+a)^(1/2)*b/x-9/8*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(-1/8*a*(b*x^3+a)^(1/2)/x^8-19/80*b*(b*x^3+a)^(1/2)/x^5-27/320*b^2/a*(b*x^3+a)^(1/2)/x^2+9/320*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-1/7*(b*x^3+a)^(1/2)*a/x^7-17/56*(b*x^3+a)^(1/2)*b/x^4-27/112*(b*x^3+a)^(1/2)/a*b^2/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(-1/6*(b*x^3+a)^(1/2)*a/x^6-5/12*(b*x^3+a)^(1/2)*b/x^3-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2))","B"
471,1,1273,554,0.095000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^10,x)","\left(\frac{b^{3} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{24 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b^{2}}{24 a \,x^{3}}-\frac{7 \sqrt{b \,x^{3}+a}\, b}{36 x^{6}}-\frac{\sqrt{b \,x^{3}+a}\, a}{9 x^{9}}\right) c +\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a \,x^{2}}-\frac{19 \sqrt{b \,x^{3}+a}\, b}{80 x^{5}}-\frac{\sqrt{b \,x^{3}+a}\, a}{8 x^{8}}\right) d +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) e +\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{5 \sqrt{b \,x^{3}+a}\, b}{12 x^{3}}-\frac{\sqrt{b \,x^{3}+a}\, a}{6 x^{6}}\right) f +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{20 \sqrt{b \,x^{3}+a}}-\frac{13 \sqrt{b \,x^{3}+a}\, b}{20 x^{2}}-\frac{\sqrt{b \,x^{3}+a}\, a}{5 x^{5}}\right) g"," ",0,"g*(-1/5*(b*x^3+a)^(1/2)*a/x^5-13/20*(b*x^3+a)^(1/2)*b/x^2-9/20*I*b*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-1/8*(b*x^3+a)^(1/2)*a/x^8-19/80*(b*x^3+a)^(1/2)*b/x^5-27/320*(b*x^3+a)^(1/2)/a*b^2/x^2+9/320*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/9*a*(b*x^3+a)^(1/2)/x^9-7/36*b*(b*x^3+a)^(1/2)/x^6-1/24*b^2/a*(b*x^3+a)^(1/2)/x^3+1/24/a^(3/2)*b^3*arctanh((b*x^3+a)^(1/2)/a^(1/2)))+e*(-1/7*(b*x^3+a)^(1/2)*a/x^7-17/56*(b*x^3+a)^(1/2)*b/x^4-27/112*(b*x^3+a)^(1/2)/a*b^2/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+f*(-1/6*(b*x^3+a)^(1/2)*a/x^6-5/12*(b*x^3+a)^(1/2)*b/x^3-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2))","B"
472,1,1470,598,0.060000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^11,x)","\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{3}}{448 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{27 \sqrt{b \,x^{3}+a}\, b^{3}}{448 a^{2} x}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{1120 a \,x^{4}}-\frac{23 \sqrt{b \,x^{3}+a}\, b}{140 x^{7}}-\frac{\sqrt{b \,x^{3}+a}\, a}{10 x^{10}}\right) c +\left(\frac{b^{3} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{24 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b^{2}}{24 a \,x^{3}}-\frac{7 \sqrt{b \,x^{3}+a}\, b}{36 x^{6}}-\frac{\sqrt{b \,x^{3}+a}\, a}{9 x^{9}}\right) d +\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a \,x^{2}}-\frac{19 \sqrt{b \,x^{3}+a}\, b}{80 x^{5}}-\frac{\sqrt{b \,x^{3}+a}\, a}{8 x^{8}}\right) e +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) f +\left(-\frac{b^{2} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{5 \sqrt{b \,x^{3}+a}\, b}{12 x^{3}}-\frac{\sqrt{b \,x^{3}+a}\, a}{6 x^{6}}\right) g"," ",0,"e*(-1/8*(b*x^3+a)^(1/2)*a/x^8-19/80*(b*x^3+a)^(1/2)*b/x^5-27/320*(b*x^3+a)^(1/2)/a*b^2/x^2+9/320*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+c*(-1/10*a*(b*x^3+a)^(1/2)/x^10-23/140*b*(b*x^3+a)^(1/2)/x^7-27/1120*b^2/a*(b*x^3+a)^(1/2)/x^4+27/448*b^3/a^2*(b*x^3+a)^(1/2)/x+9/448*I*b^3/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+d*(-1/9*(b*x^3+a)^(1/2)*a/x^9-7/36*(b*x^3+a)^(1/2)*b/x^6-1/24*(b*x^3+a)^(1/2)/a*b^2/x^3+1/24/a^(3/2)*b^3*arctanh((b*x^3+a)^(1/2)/a^(1/2)))+f*(-1/7*(b*x^3+a)^(1/2)*a/x^7-17/56*(b*x^3+a)^(1/2)*b/x^4-27/112*(b*x^3+a)^(1/2)/a*b^2/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+g*(-1/6*(b*x^3+a)^(1/2)*a/x^6-5/12*(b*x^3+a)^(1/2)*b/x^3-1/4*b^2*arctanh((b*x^3+a)^(1/2)/a^(1/2))/a^(1/2))","B"
473,1,1773,628,0.099000," ","int((b*x^3+a)^(3/2)*(g*x^4+f*x^3+e*x^2+d*x+c)/x^12,x)","\left(-\frac{63 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{3} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{7040 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{189 \sqrt{b \,x^{3}+a}\, b^{3}}{7040 a^{2} x^{2}}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{1760 a \,x^{5}}-\frac{25 \sqrt{b \,x^{3}+a}\, b}{176 x^{8}}-\frac{\sqrt{b \,x^{3}+a}\, a}{11 x^{11}}\right) c +\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{3}}{448 \sqrt{b \,x^{3}+a}\, a^{2}}+\frac{27 \sqrt{b \,x^{3}+a}\, b^{3}}{448 a^{2} x}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{1120 a \,x^{4}}-\frac{23 \sqrt{b \,x^{3}+a}\, b}{140 x^{7}}-\frac{\sqrt{b \,x^{3}+a}\, a}{10 x^{10}}\right) d +\left(\frac{b^{3} \arctanh \left(\frac{\sqrt{b \,x^{3}+a}}{\sqrt{a}}\right)}{24 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{3}+a}\, b^{2}}{24 a \,x^{3}}-\frac{7 \sqrt{b \,x^{3}+a}\, b}{36 x^{6}}-\frac{\sqrt{b \,x^{3}+a}\, a}{9 x^{9}}\right) e +\left(\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, b^{2} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{320 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{320 a \,x^{2}}-\frac{19 \sqrt{b \,x^{3}+a}\, b}{80 x^{5}}-\frac{\sqrt{b \,x^{3}+a}\, a}{8 x^{8}}\right) f +\left(-\frac{9 i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}} \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \sqrt{\frac{x -\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{b}}{-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}}}\, \sqrt{-\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}\, \left(\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \EllipticE \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)+\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}} \EllipticF \left(\frac{\sqrt{3}\, \sqrt{\frac{i \left(x +\frac{\left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}-\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) \sqrt{3}\, b}{\left(-a \,b^{2}\right)^{\frac{1}{3}}}}}{3}, \sqrt{\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{\left(-\frac{3 \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}+\frac{i \sqrt{3}\, \left(-a \,b^{2}\right)^{\frac{1}{3}}}{2 b}\right) b}}\right)}{b}\right) b^{2}}{112 \sqrt{b \,x^{3}+a}\, a}-\frac{27 \sqrt{b \,x^{3}+a}\, b^{2}}{112 a x}-\frac{17 \sqrt{b \,x^{3}+a}\, b}{56 x^{4}}-\frac{\sqrt{b \,x^{3}+a}\, a}{7 x^{7}}\right) g"," ",0,"f*(-1/8*(b*x^3+a)^(1/2)*a/x^8-19/80*(b*x^3+a)^(1/2)*b/x^5-27/320*(b*x^3+a)^(1/2)/a*b^2/x^2+9/320*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))+d*(-1/10*(b*x^3+a)^(1/2)*a/x^10-23/140*(b*x^3+a)^(1/2)*b/x^7-27/1120*(b*x^3+a)^(1/2)/a*b^2/x^4+27/448*(b*x^3+a)^(1/2)/a^2*b^3/x+9/448*I*b^3/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+e*(-1/9*(b*x^3+a)^(1/2)*a/x^9-7/36*(b*x^3+a)^(1/2)*b/x^6-1/24*(b*x^3+a)^(1/2)/a*b^2/x^3+1/24/a^(3/2)*b^3*arctanh((b*x^3+a)^(1/2)/a^(1/2)))+g*(-1/7*(b*x^3+a)^(1/2)*a/x^7-17/56*(b*x^3+a)^(1/2)*b/x^4-27/112*(b*x^3+a)^(1/2)/a*b^2/x-9/112*I/a*b^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*((-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*EllipticE(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))+(-a*b^2)^(1/3)/b*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2))))+c*(-1/11*a*(b*x^3+a)^(1/2)/x^11-25/176*b*(b*x^3+a)^(1/2)/x^8-27/1760*b^2/a*(b*x^3+a)^(1/2)/x^5+189/7040*b^3/a^2*(b*x^3+a)^(1/2)/x^2-63/7040*I*b^3/a^2*3^(1/2)*(-a*b^2)^(1/3)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)*((x-(-a*b^2)^(1/3)/b)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b))^(1/2)*(-I*(x+1/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2)/(b*x^3+a)^(1/2)*EllipticF(1/3*3^(1/2)*(I*(x+1/2*(-a*b^2)^(1/3)/b-1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)*3^(1/2)/(-a*b^2)^(1/3)*b)^(1/2),(I*3^(1/2)*(-a*b^2)^(1/3)/(-3/2*(-a*b^2)^(1/3)/b+1/2*I*3^(1/2)*(-a*b^2)^(1/3)/b)/b)^(1/2)))","B"
474,0,0,94,0.459000," ","int((e*x^2+d*x+c)*(b*x^3+a)^p,x)","\int \left(e \,x^{2}+d x +c \right) \left(b \,x^{3}+a \right)^{p}\, dx"," ",0,"int((e*x^2+d*x+c)*(b*x^3+a)^p,x)","F"
475,0,0,97,0.473000," ","int(x*(e*x^2+d*x+c)*(b*x^3+a)^p,x)","\int \left(e \,x^{2}+d x +c \right) x \left(b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x*(e*x^2+d*x+c)*(b*x^3+a)^p,x)","F"
476,0,0,97,0.476000," ","int(x^2*(e*x^2+d*x+c)*(b*x^3+a)^p,x)","\int \left(e \,x^{2}+d x +c \right) x^{2} \left(b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x^2*(e*x^2+d*x+c)*(b*x^3+a)^p,x)","F"
477,1,55,54,0.043000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a),x)","\frac{1}{8} b f \,x^{8}+\frac{1}{7} b e \,x^{7}+\frac{1}{6} b d \,x^{6}+\frac{1}{5} b c \,x^{5}+\frac{1}{4} a f \,x^{4}+\frac{1}{3} a e \,x^{3}+\frac{1}{2} a d \,x^{2}+a c x"," ",0,"a*c*x+1/2*a*d*x^2+1/3*a*e*x^3+1/4*a*f*x^4+1/5*b*c*x^5+1/6*b*d*x^6+1/7*b*e*x^7+1/8*b*f*x^8","A"
478,1,58,57,0.045000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a),x)","\frac{1}{11} b f \,x^{11}+\frac{1}{10} b e \,x^{10}+\frac{1}{9} b d \,x^{9}+\frac{1}{8} b c \,x^{8}+\frac{1}{7} a f \,x^{7}+\frac{1}{6} a e \,x^{6}+\frac{1}{5} a d \,x^{5}+\frac{1}{4} a c \,x^{4}"," ",0,"1/4*a*c*x^4+1/5*a*d*x^5+1/6*a*e*x^6+1/7*a*f*x^7+1/8*b*c*x^8+1/9*b*d*x^9+1/10*b*e*x^10+1/11*b*f*x^11","A"
479,1,103,91,0.043000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x)","\frac{1}{12} b^{2} f \,x^{12}+\frac{1}{11} b^{2} e \,x^{11}+\frac{1}{10} b^{2} d \,x^{10}+\frac{1}{9} b^{2} c \,x^{9}+\frac{1}{4} a b f \,x^{8}+\frac{2}{7} a b e \,x^{7}+\frac{1}{3} a b d \,x^{6}+\frac{2}{5} a b c \,x^{5}+\frac{1}{4} a^{2} f \,x^{4}+\frac{1}{3} a^{2} e \,x^{3}+\frac{1}{2} a^{2} d \,x^{2}+a^{2} c x"," ",0,"1/12*b^2*f*x^12+1/11*b^2*e*x^11+1/10*b^2*d*x^10+1/9*b^2*c*x^9+1/4*a*b*f*x^8+2/7*a*b*e*x^7+1/3*a*b*d*x^6+2/5*a*b*c*x^5+1/4*f*a^2*x^4+1/3*a^2*e*x^3+1/2*a^2*d*x^2+a^2*c*x","A"
480,1,106,94,0.043000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^2,x)","\frac{1}{15} b^{2} f \,x^{15}+\frac{1}{14} b^{2} e \,x^{14}+\frac{1}{13} b^{2} d \,x^{13}+\frac{1}{12} b^{2} c \,x^{12}+\frac{2}{11} a b f \,x^{11}+\frac{1}{5} a b e \,x^{10}+\frac{2}{9} a b d \,x^{9}+\frac{1}{4} a b c \,x^{8}+\frac{1}{7} a^{2} f \,x^{7}+\frac{1}{6} a^{2} e \,x^{6}+\frac{1}{5} a^{2} d \,x^{5}+\frac{1}{4} a^{2} c \,x^{4}"," ",0,"1/15*b^2*f*x^15+1/14*b^2*e*x^14+1/13*b^2*d*x^13+1/12*c*b^2*x^12+2/11*a*b*f*x^11+1/5*a*b*e*x^10+2/9*a*b*d*x^9+1/4*a*b*c*x^8+1/7*a^2*f*x^7+1/6*a^2*e*x^6+1/5*a^2*d*x^5+1/4*a^2*c*x^4","A"
481,1,151,127,0.043000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x)","\frac{1}{16} b^{3} f \,x^{16}+\frac{1}{15} b^{3} e \,x^{15}+\frac{1}{14} b^{3} d \,x^{14}+\frac{1}{13} b^{3} c \,x^{13}+\frac{1}{4} a \,b^{2} f \,x^{12}+\frac{3}{11} a \,b^{2} e \,x^{11}+\frac{3}{10} a \,b^{2} d \,x^{10}+\frac{1}{3} a \,b^{2} c \,x^{9}+\frac{3}{8} a^{2} b f \,x^{8}+\frac{3}{7} a^{2} b e \,x^{7}+\frac{1}{2} a^{2} b d \,x^{6}+\frac{3}{5} a^{2} b c \,x^{5}+\frac{1}{4} a^{3} f \,x^{4}+\frac{1}{3} a^{3} e \,x^{3}+\frac{1}{2} a^{3} d \,x^{2}+a^{3} c x"," ",0,"1/16*b^3*f*x^16+1/15*b^3*e*x^15+1/14*b^3*d*x^14+1/13*b^3*c*x^13+1/4*a*b^2*f*x^12+3/11*a*b^2*e*x^11+3/10*a*b^2*d*x^10+1/3*a*b^2*c*x^9+3/8*a^2*b*f*x^8+3/7*a^2*b*e*x^7+1/2*a^2*b*d*x^6+3/5*a^2*b*c*x^5+1/4*a^3*f*x^4+1/3*a^3*e*x^3+1/2*a^3*d*x^2+a^3*c*x","A"
482,1,154,130,0.043000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^3,x)","\frac{1}{19} b^{3} f \,x^{19}+\frac{1}{18} b^{3} e \,x^{18}+\frac{1}{17} b^{3} d \,x^{17}+\frac{1}{16} b^{3} c \,x^{16}+\frac{1}{5} a \,b^{2} f \,x^{15}+\frac{3}{14} a \,b^{2} e \,x^{14}+\frac{3}{13} a \,b^{2} d \,x^{13}+\frac{1}{4} a \,b^{2} c \,x^{12}+\frac{3}{11} a^{2} b f \,x^{11}+\frac{3}{10} a^{2} b e \,x^{10}+\frac{1}{3} a^{2} b d \,x^{9}+\frac{3}{8} a^{2} b c \,x^{8}+\frac{1}{7} a^{3} f \,x^{7}+\frac{1}{6} a^{3} e \,x^{6}+\frac{1}{5} a^{3} d \,x^{5}+\frac{1}{4} a^{3} c \,x^{4}"," ",0,"1/19*b^3*f*x^19+1/18*b^3*e*x^18+1/17*b^3*d*x^17+1/16*b^3*c*x^16+1/5*a*b^2*f*x^15+3/14*a*b^2*e*x^14+3/13*a*b^2*d*x^13+1/4*a*b^2*c*x^12+3/11*a^2*b*f*x^11+3/10*a^2*b*e*x^10+1/3*a^2*b*d*x^9+3/8*a^2*c*b*x^8+1/7*a^3*f*x^7+1/6*a^3*e*x^6+1/5*a^3*d*x^5+1/4*a^3*c*x^4","A"
483,1,199,163,0.043000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x)","\frac{1}{20} b^{4} f \,x^{20}+\frac{1}{19} b^{4} e \,x^{19}+\frac{1}{18} b^{4} d \,x^{18}+\frac{1}{17} b^{4} c \,x^{17}+\frac{1}{4} a \,b^{3} f \,x^{16}+\frac{4}{15} a \,b^{3} e \,x^{15}+\frac{2}{7} a \,b^{3} d \,x^{14}+\frac{4}{13} a \,b^{3} c \,x^{13}+\frac{1}{2} a^{2} b^{2} f \,x^{12}+\frac{6}{11} a^{2} b^{2} e \,x^{11}+\frac{3}{5} a^{2} b^{2} d \,x^{10}+\frac{2}{3} a^{2} b^{2} c \,x^{9}+\frac{1}{2} a^{3} b f \,x^{8}+\frac{4}{7} a^{3} b e \,x^{7}+\frac{2}{3} a^{3} b d \,x^{6}+\frac{4}{5} a^{3} b c \,x^{5}+\frac{1}{4} a^{4} f \,x^{4}+\frac{1}{3} a^{4} e \,x^{3}+\frac{1}{2} a^{4} d \,x^{2}+a^{4} c x"," ",0,"1/20*f*b^4*x^20+1/19*b^4*e*x^19+1/18*b^4*d*x^18+1/17*b^4*c*x^17+1/4*f*a*b^3*x^16+4/15*a*b^3*e*x^15+2/7*a*b^3*d*x^14+4/13*a*b^3*c*x^13+1/2*f*b^2*a^2*x^12+6/11*a^2*b^2*e*x^11+3/5*a^2*b^2*d*x^10+2/3*a^2*b^2*c*x^9+1/2*a^3*b*f*x^8+4/7*a^3*b*e*x^7+2/3*a^3*b*d*x^6+4/5*a^3*b*c*x^5+1/4*a^4*f*x^4+1/3*a^4*e*x^3+1/2*a^4*d*x^2+a^4*c*x","A"
484,1,202,166,0.043000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^4,x)","\frac{1}{23} b^{4} f \,x^{23}+\frac{1}{22} b^{4} e \,x^{22}+\frac{1}{21} b^{4} d \,x^{21}+\frac{1}{20} b^{4} c \,x^{20}+\frac{4}{19} a \,b^{3} f \,x^{19}+\frac{2}{9} a \,b^{3} e \,x^{18}+\frac{4}{17} a \,b^{3} d \,x^{17}+\frac{1}{4} a \,b^{3} c \,x^{16}+\frac{2}{5} a^{2} b^{2} f \,x^{15}+\frac{3}{7} a^{2} b^{2} e \,x^{14}+\frac{6}{13} a^{2} b^{2} d \,x^{13}+\frac{1}{2} a^{2} b^{2} c \,x^{12}+\frac{4}{11} a^{3} b f \,x^{11}+\frac{2}{5} a^{3} b e \,x^{10}+\frac{4}{9} a^{3} b d \,x^{9}+\frac{1}{2} a^{3} b c \,x^{8}+\frac{1}{7} a^{4} f \,x^{7}+\frac{1}{6} a^{4} e \,x^{6}+\frac{1}{5} a^{4} d \,x^{5}+\frac{1}{4} a^{4} c \,x^{4}"," ",0,"1/23*b^4*f*x^23+1/22*b^4*e*x^22+1/21*b^4*d*x^21+1/20*c*b^4*x^20+4/19*a*b^3*f*x^19+2/9*a*b^3*e*x^18+4/17*a*b^3*d*x^17+1/4*a*b^3*c*x^16+2/5*a^2*b^2*f*x^15+3/7*a^2*b^2*e*x^14+6/13*a^2*b^2*d*x^13+1/2*c*b^2*a^2*x^12+4/11*a^3*b*f*x^11+2/5*a^3*b*e*x^10+4/9*a^3*b*d*x^9+1/2*c*a^3*b*x^8+1/7*a^4*f*x^7+1/6*a^4*e*x^6+1/5*a^4*d*x^5+1/4*c*a^4*x^4","A"
485,1,177,93,0.046000," ","int((f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{d \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} c \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 a}-\frac{e \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{e \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}-\frac{f \ln \left(b \,x^{4}-a \right)}{4 b}"," ",0,"1/4*c*(a/b)^(1/4)/a*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))+1/2*c*(a/b)^(1/4)/a*arctan(1/(a/b)^(1/4)*x)-1/4/(a*b)^(1/2)*d*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2*e/b/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/4*e/b/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4*f/b*ln(b*x^4-a)","A"
486,1,208,118,0.044000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(-b*x^4+a),x)","-\frac{f \,x^{3}}{3 b}-\frac{a e \ln \left(\frac{\sqrt{a b}\, x^{2}-a}{-\sqrt{a b}\, x^{2}-a}\right)}{4 \sqrt{a b}\, b}-\frac{e \,x^{2}}{2 b}-\frac{a f \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{a f \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{c \ln \left(b \,x^{4}-a \right)}{4 b}-\frac{d x}{b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} d \arctan \left(\frac{x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{2 b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} d \ln \left(\frac{x +\left(\frac{a}{b}\right)^{\frac{1}{4}}}{x -\left(\frac{a}{b}\right)^{\frac{1}{4}}}\right)}{4 b}"," ",0,"-1/3/b*f*x^3-1/2/b*e*x^2-1/b*d*x+1/2/b*d*(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/4/b*d*(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b*a*e/(a*b)^(1/2)*ln(((a*b)^(1/2)*x^2-a)/(-(a*b)^(1/2)*x^2-a))-1/2/b^2*a*f/(a/b)^(1/4)*arctan(1/(a/b)^(1/4)*x)+1/4/b^2*a*f/(a/b)^(1/4)*ln((x+(a/b)^(1/4))/(x-(a/b)^(1/4)))-1/4/b*c*ln(b*x^4-a)","A"
487,1,294,200,0.052000," ","int((f*x^3+e*x^2+d*x+c)/(b*x^4+a),x)","\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 a}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b}+\frac{f \ln \left(b \,x^{4}+a \right)}{4 b}"," ",0,"1/8*c*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*c*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*(a/b)^(1/4)*2^(1/2)/a*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/2*d/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+1/8*e/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/4*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/4*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4/b*f*ln(b*x^4+a)","A"
488,1,325,224,0.053000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a),x)","\frac{f \,x^{3}}{3 b}-\frac{a e \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{2 \sqrt{a b}\, b}+\frac{e \,x^{2}}{2 b}-\frac{\sqrt{2}\, a f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}-\frac{\sqrt{2}\, a f \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{c \ln \left(b \,x^{4}+a \right)}{4 b}+\frac{d x}{b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{4 b}-\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{8 b}"," ",0,"1/3/b*f*x^3+1/2/b*e*x^2+1/b*d*x-1/4/b*d*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)-1/8/b*d*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/b*d*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/2/b*a*e/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)-1/8/b^2*a*f/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))-1/4/b^2*a*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)-1/4/b^2*a*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*c*ln(b*x^4+a)/b","A"
489,1,362,225,0.049000," ","int((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{f \,x^{4}}{4 \left(b \,x^{4}+a \right) a}+\frac{e \,x^{3}}{4 \left(b \,x^{4}+a \right) a}+\frac{d \,x^{2}}{4 \left(b \,x^{4}+a \right) a}+\frac{c x}{4 \left(b \,x^{4}+a \right) a}+\frac{d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, a}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{\sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} a b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a^{2}}"," ",0,"1/4/(b*x^4+a)/a*c*x+3/32*(a/b)^(1/4)*2^(1/2)/a^2*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/16*(a/b)^(1/4)*2^(1/2)/a^2*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4/(b*x^4+a)/a*d*x^2+1/4/(a*b)^(1/2)/a*d*arctan((1/a*b)^(1/2)*x^2)+1/4/(b*x^4+a)/a*e*x^3+1/32/(a/b)^(1/4)*2^(1/2)/a/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/(a/b)^(1/4)*2^(1/2)/a/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4*f*x^4/a/(b*x^4+a)","A"
490,1,334,222,0.054000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^2,x)","\frac{e \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{4 \sqrt{a b}\, b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 a b}+\frac{\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 a b}+\frac{3 \sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{16 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{3 \sqrt{2}\, f \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{32 \left(\frac{a}{b}\right)^{\frac{1}{4}} b^{2}}+\frac{-\frac{f \,x^{3}}{4 b}-\frac{e \,x^{2}}{4 b}-\frac{d x}{4 b}-\frac{c}{4 b}}{b \,x^{4}+a}"," ",0,"(-1/4/b*f*x^3-1/4/b*e*x^2-1/4/b*d*x-1/4/b*c)/(b*x^4+a)+1/32/b*d*(a/b)^(1/4)/a*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+1/16/b*d*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+1/16/b*d*(a/b)^(1/4)/a*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/4/b*e/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+3/32/b^2*f/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/16/b^2*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/16/b^2*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
491,1,432,256,0.052000," ","int((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{f \,x^{4}}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{e \,x^{3}}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{f \,x^{4}}{8 \left(b \,x^{4}+a \right) a^{2}}+\frac{d \,x^{2}}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{5 e \,x^{3}}{32 \left(b \,x^{4}+a \right) a^{2}}+\frac{c x}{8 \left(b \,x^{4}+a \right)^{2} a}+\frac{3 d \,x^{2}}{16 \left(b \,x^{4}+a \right) a^{2}}+\frac{7 c x}{32 \left(b \,x^{4}+a \right) a^{2}}+\frac{3 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a^{2}}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{5 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{3}}+\frac{21 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{3}}"," ",0,"1/8*c*x/a/(b*x^4+a)^2+7/32*c/a^2*x/(b*x^4+a)+21/256*(a/b)^(1/4)*2^(1/2)/a^3*c*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+21/128*(a/b)^(1/4)*2^(1/2)/a^3*c*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/8*d*x^2/a/(b*x^4+a)^2+3/16*d/a^2*x^2/(b*x^4+a)+3/16/(a*b)^(1/2)/a^2*d*arctan((1/a*b)^(1/2)*x^2)+1/8*e*x^3/a/(b*x^4+a)^2+5/32*e/a^2*x^3/(b*x^4+a)+5/256/(a/b)^(1/4)*2^(1/2)/a^2/b*e*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/128/(a/b)^(1/4)*2^(1/2)/a^2/b*e*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/8*f*x^4/a/(b*x^4+a)^2+1/8*f/a^2*x^4/(b*x^4+a)","A"
492,1,373,250,0.060000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^3,x)","\frac{e \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{16 \sqrt{a b}\, a b}+\frac{3 \sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \sqrt{2}\, f \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 \left(\frac{a}{b}\right)^{\frac{1}{4}} a \,b^{2}}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{128 a^{2} b}+\frac{3 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{256 a^{2} b}+\frac{\frac{3 f \,x^{7}}{32 a}+\frac{e \,x^{6}}{16 a}+\frac{d \,x^{5}}{32 a}-\frac{f \,x^{3}}{32 b}-\frac{e \,x^{2}}{16 b}-\frac{3 d x}{32 b}-\frac{c}{8 b}}{\left(b \,x^{4}+a \right)^{2}}"," ",0,"(3/32*f/a*x^7+1/16/a*e*x^6+1/32*d/a*x^5-1/32/b*f*x^3-1/16/b*e*x^2-3/32/b*d*x-1/8/b*c)/(b*x^4+a)^2+3/256/b/a^2*d*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/128/b/a^2*d*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/128/b/a^2*d*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/16/b/a*e/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+3/256/b^2/a*f/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+3/128/b^2/a*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+3/128/b^2/a*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
493,1,400,285,0.063000," ","int((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{5 d \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{3}}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{15 \sqrt{2}\, e \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{3} b}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{4}}+\frac{77 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, c \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{4}}+\frac{\frac{15 b^{2} e \,x^{11}}{128 a^{3}}+\frac{5 b^{2} d \,x^{10}}{32 a^{3}}+\frac{77 b^{2} c \,x^{9}}{384 a^{3}}+\frac{21 b e \,x^{7}}{64 a^{2}}+\frac{5 b d \,x^{6}}{12 a^{2}}+\frac{33 b c \,x^{5}}{64 a^{2}}+\frac{113 e \,x^{3}}{384 a}+\frac{11 d \,x^{2}}{32 a}+\frac{51 c x}{128 a}-\frac{f}{12 b}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(15/128/a^3*b^2*e*x^11+5/32*d/a^3*b^2*x^10+77/384*c/a^3*b^2*x^9+21/64/a^2*b*e*x^7+5/12/a^2*d*b*x^6+33/64/a^2*c*b*x^5+113/384/a*e*x^3+11/32*d/a*x^2+51/128*c/a*x-1/12/b*f)/(b*x^4+a)^3+77/1024/a^4*c*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+77/512/a^4*c*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+77/512/a^4*c*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+5/32/a^3*d/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+15/1024/a^3*e/b/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+15/512/a^3*e/b/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
494,1,403,288,0.065000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^4,x)","\frac{e \arctan \left(\sqrt{\frac{b}{a}}\, x^{2}\right)}{32 \sqrt{a b}\, a^{2} b}+\frac{5 \sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, f \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{5 \sqrt{2}\, f \ln \left(\frac{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 \left(\frac{a}{b}\right)^{\frac{1}{4}} a^{2} b^{2}}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}-1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \arctan \left(\frac{\sqrt{2}\, x}{\left(\frac{a}{b}\right)^{\frac{1}{4}}}+1\right)}{512 a^{3} b}+\frac{7 \left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, d \ln \left(\frac{x^{2}+\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}{x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{4}} \sqrt{2}\, x +\sqrt{\frac{a}{b}}}\right)}{1024 a^{3} b}+\frac{\frac{5 b f \,x^{11}}{128 a^{2}}+\frac{b e \,x^{10}}{32 a^{2}}+\frac{7 b d \,x^{9}}{384 a^{2}}+\frac{7 f \,x^{7}}{64 a}+\frac{e \,x^{6}}{12 a}+\frac{3 d \,x^{5}}{64 a}-\frac{5 f \,x^{3}}{384 b}-\frac{e \,x^{2}}{32 b}-\frac{7 d x}{128 b}-\frac{c}{12 b}}{\left(b \,x^{4}+a \right)^{3}}"," ",0,"(5/128*f/a^2*b*x^11+1/32/a^2*b*e*x^10+7/384/a^2*d*b*x^9+7/64/a*f*x^7+1/12/a*e*x^6+3/64/a*d*x^5-5/384/b*f*x^3-1/32/b*e*x^2-7/128/b*d*x-1/12/b*c)/(b*x^4+a)^3+7/1024/a^3/b*d*(a/b)^(1/4)*2^(1/2)*ln((x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+7/512/a^3/b*d*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+7/512/a^3/b*d*(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)+1/32/a^2/b*e/(a*b)^(1/2)*arctan((1/a*b)^(1/2)*x^2)+5/1024/a^2/b^2*f/(a/b)^(1/4)*2^(1/2)*ln((x^2-(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2))/(x^2+(a/b)^(1/4)*2^(1/2)*x+(a/b)^(1/2)))+5/512/a^2/b^2*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x+1)+5/512/a^2/b^2*f/(a/b)^(1/4)*2^(1/2)*arctan(2^(1/2)/(a/b)^(1/4)*x-1)","A"
495,1,390,394,0.207000," ","int(x^4*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, e \,x^{7}}{9}+\frac{\sqrt{b \,x^{4}+a}\, c \,x^{5}}{7}+\frac{2 \sqrt{b \,x^{4}+a}\, a e \,x^{3}}{45 b}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}-\frac{\sqrt{b \,x^{4}+a}\, a d \,x^{2}}{16 b}-\frac{a^{2} d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{2 \sqrt{b \,x^{4}+a}\, a c x}{21 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} d \,x^{2}}{8 b}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} \left(-3 b \,x^{4}+2 a \right) f}{30 b^{2}}"," ",0,"-1/30*f*(b*x^4+a)^(3/2)*(-3*b*x^4+2*a)/b^2+1/9*e*x^7*(b*x^4+a)^(1/2)+2/45*a*e*x^3*(b*x^4+a)^(1/2)/b-2/15*I*e*a^(5/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+2/15*I*e*a^(5/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*d*x^2*(b*x^4+a)^(3/2)/b-1/16*a*d*x^2*(b*x^4+a)^(1/2)/b-1/16*d*a^2/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/7*c*x^5*(b*x^4+a)^(1/2)+2/21*a*c*x*(b*x^4+a)^(1/2)/b-2/21*c*a^2/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
496,1,380,374,0.189000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, f \,x^{7}}{9}+\frac{\sqrt{b \,x^{4}+a}\, d \,x^{5}}{7}+\frac{2 \sqrt{b \,x^{4}+a}\, a f \,x^{3}}{45 b}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}-\frac{\sqrt{b \,x^{4}+a}\, a e \,x^{2}}{16 b}-\frac{a^{2} e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{2 \sqrt{b \,x^{4}+a}\, a d x}{21 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} e \,x^{2}}{8 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} c}{6 b}"," ",0,"1/9*f*x^7*(b*x^4+a)^(1/2)+2/45*a*f*x^3*(b*x^4+a)^(1/2)/b-2/15*I*f*a^(5/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+2/15*I*f*a^(5/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*e*x^2*(b*x^4+a)^(3/2)/b-1/16*a*e*x^2*(b*x^4+a)^(1/2)/b-1/16*e*a^2/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/7*d*x^5*(b*x^4+a)^(1/2)+2/21*a*d*x*(b*x^4+a)^(1/2)/b-2/21*d*a^2/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*c/b*(b*x^4+a)^(3/2)","C"
497,1,361,353,0.169000," ","int(x^2*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, e \,x^{5}}{7}+\frac{\sqrt{b \,x^{4}+a}\, c \,x^{3}}{5}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}-\frac{\sqrt{b \,x^{4}+a}\, a f \,x^{2}}{16 b}-\frac{a^{2} f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 b^{\frac{3}{2}}}+\frac{2 \sqrt{b \,x^{4}+a}\, a e x}{21 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} f \,x^{2}}{8 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} d}{6 b}"," ",0,"1/8*f*x^2*(b*x^4+a)^(3/2)/b-1/16*a*f*x^2*(b*x^4+a)^(1/2)/b-1/16*f*a^2/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/7*e*x^5*(b*x^4+a)^(1/2)+2/21*a*e*x*(b*x^4+a)^(1/2)/b-2/21*e*a^2/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*d/b*(b*x^4+a)^(3/2)+1/5*c*x^3*(b*x^4+a)^(1/2)+2/5*I*c*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*c*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
498,1,337,338,0.165000," ","int(x*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, f \,x^{5}}{7}+\frac{\sqrt{b \,x^{4}+a}\, d \,x^{3}}{5}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, c \,x^{2}}{4}+\frac{a c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 \sqrt{b}}+\frac{2 \sqrt{b \,x^{4}+a}\, a f x}{21 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} e}{6 b}"," ",0,"1/7*f*x^5*(b*x^4+a)^(1/2)+2/21*a*f*x*(b*x^4+a)^(1/2)/b-2/21*f*a^2/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*e*(b*x^4+a)^(3/2)/b+1/5*x^3*d*(b*x^4+a)^(1/2)+2/5*I*d*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*d*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*c*x^2*(b*x^4+a)^(1/2)+1/4*c*a/b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))","C"
499,1,313,319,0.180000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, e \,x^{3}}{5}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, d \,x^{2}}{4}+\frac{a d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, c x}{3}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} f}{6 b}"," ",0,"1/6*f*(b*x^4+a)^(3/2)/b+1/5*e*x^3*(b*x^4+a)^(1/2)+2/5*I*e*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*e*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*d*x^2*(b*x^4+a)^(1/2)+1/4*d*a/b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*c*x*(b*x^4+a)^(1/2)+2/3*c*a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
500,1,339,329,0.197000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x,x)","\frac{\sqrt{b \,x^{4}+a}\, f \,x^{3}}{5}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, e \,x^{2}}{4}+\frac{a e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 \sqrt{b}}-\frac{\sqrt{a}\, c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, d x}{3}+\frac{\sqrt{b \,x^{4}+a}\, c}{2}"," ",0,"1/5*x^3*f*(b*x^4+a)^(1/2)+2/5*I*f*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*f*a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*e*x^2*(b*x^4+a)^(1/2)+1/4*e*a/b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*d*x*(b*x^4+a)^(1/2)+2/3*d*a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*c*(b*x^4+a)^(1/2)-1/2*c*a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
501,1,339,329,0.201000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^2,x)","\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, f \,x^{2}}{4}+\frac{a f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 \sqrt{b}}-\frac{\sqrt{a}\, d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, e x}{3}+\frac{\sqrt{b \,x^{4}+a}\, d}{2}-\frac{\sqrt{b \,x^{4}+a}\, c}{x}"," ",0,"1/4*x^2*f*(b*x^4+a)^(1/2)+1/4*f*a/b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*e*x*(b*x^4+a)^(1/2)+2/3*e*a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-c/x*(b*x^4+a)^(1/2)+2*I*c*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2*I*c*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*d*(b*x^4+a)^(1/2)-1/2*d*a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
502,1,360,330,0.178000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^3,x)","\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{2}}{2 a}-\frac{\sqrt{a}\, e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{\sqrt{b}\, c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, f x}{3}+\frac{\sqrt{b \,x^{4}+a}\, e}{2}-\frac{\sqrt{b \,x^{4}+a}\, d}{x}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} c}{2 a \,x^{2}}"," ",0,"1/3*f*x*(b*x^4+a)^(1/2)+2/3*f*a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c/a/x^2*(b*x^4+a)^(3/2)+1/2*c/a*b*x^2*(b*x^4+a)^(1/2)+1/2*c*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-d/x*(b*x^4+a)^(1/2)+2*I*d*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2*I*d*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e*(b*x^4+a)^(1/2)-1/2*e*a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
503,1,362,343,0.197000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^4,x)","-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{2}}{2 a}+\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{\sqrt{a}\, f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{\sqrt{b}\, d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, f}{2}-\frac{\sqrt{b \,x^{4}+a}\, e}{x}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} d}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, c}{3 x^{3}}"," ",0,"-1/3*c/x^3*(b*x^4+a)^(1/2)+2/3*c*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*d/a/x^2*(b*x^4+a)^(3/2)+1/2*d/a*b*x^2*(b*x^4+a)^(1/2)+1/2*d*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-e*(b*x^4+a)^(1/2)/x+2*I*e*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2*I*e*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*f*(b*x^4+a)^(1/2)-1/2*f*a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
504,1,385,321,0.196000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^5,x)","-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, \sqrt{b}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{2}}{2 a}+\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{b c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}}+\frac{\sqrt{b}\, e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, b c}{4 a}-\frac{\sqrt{b \,x^{4}+a}\, f}{x}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} e}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, d}{3 x^{3}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} c}{4 a \,x^{4}}"," ",0,"-1/4*c/a/x^4*(b*x^4+a)^(3/2)-1/4*c/a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)+1/4*c/a*b*(b*x^4+a)^(1/2)-1/3*d/x^3*(b*x^4+a)^(1/2)+2/3*d*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*e/a/x^2*(b*x^4+a)^(3/2)+1/2*e/a*b*x^2*(b*x^4+a)^(1/2)+1/2*e*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-f/x*(b*x^4+a)^(1/2)+2*I*f*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2*I*f*b^(1/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
505,1,404,344,0.198000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^6,x)","-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{2}}{2 a}+\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{b d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}}+\frac{\sqrt{b}\, f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, b d}{4 a}-\frac{2 \sqrt{b \,x^{4}+a}\, b c}{5 a x}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} f}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, e}{3 x^{3}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} d}{4 a \,x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, c}{5 x^{5}}"," ",0,"-1/5*c/x^5*(b*x^4+a)^(1/2)-2/5*b*c*(b*x^4+a)^(1/2)/a/x+2/5*I*c*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*c*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/4*d/a/x^4*(b*x^4+a)^(3/2)-1/4*d/a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)+1/4*d/a*b*(b*x^4+a)^(1/2)-1/3*e/x^3*(b*x^4+a)^(1/2)+2/3*e*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*f/a/x^2*(b*x^4+a)^(3/2)+1/2*f/a*b*x^2*(b*x^4+a)^(1/2)+1/2*f*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))","C"
506,1,361,340,0.190000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^7,x)","-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{b e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}}+\frac{\sqrt{b \,x^{4}+a}\, b e}{4 a}-\frac{2 \sqrt{b \,x^{4}+a}\, b d}{5 a x}-\frac{\sqrt{b \,x^{4}+a}\, f}{3 x^{3}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} e}{4 a \,x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, d}{5 x^{5}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} c}{6 a \,x^{6}}"," ",0,"-1/5*d/x^5*(b*x^4+a)^(1/2)-2/5*b*d*(b*x^4+a)^(1/2)/a/x+2/5*I*d*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*d*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/4*e/a/x^4*(b*x^4+a)^(3/2)-1/4*e/a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)+1/4*e/a*b*(b*x^4+a)^(1/2)-1/3*f/x^3*(b*x^4+a)^(1/2)+2/3*f*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/6*c*(b*x^4+a)^(3/2)/x^6/a","C"
507,1,385,359,0.192000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^8,x)","-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}-\frac{b f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4 \sqrt{a}}+\frac{\sqrt{b \,x^{4}+a}\, b f}{4 a}-\frac{2 \sqrt{b \,x^{4}+a}\, b e}{5 a x}-\frac{2 \sqrt{b \,x^{4}+a}\, b c}{21 a \,x^{3}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} f}{4 a \,x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, e}{5 x^{5}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} d}{6 a \,x^{6}}-\frac{\sqrt{b \,x^{4}+a}\, c}{7 x^{7}}"," ",0,"-1/5*e/x^5*(b*x^4+a)^(1/2)-2/5*b*e*(b*x^4+a)^(1/2)/a/x+2/5*I*e*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*e*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/4*f/a/x^4*(b*x^4+a)^(3/2)-1/4*f/a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)+1/4*f/a*b*(b*x^4+a)^(1/2)-1/7*c/x^7*(b*x^4+a)^(1/2)-2/21*b*c*(b*x^4+a)^(1/2)/a/x^3-2/21*c*b^2/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/6*d*(b*x^4+a)^(3/2)/x^6/a","C"
508,1,408,380,0.183000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^9,x)","-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{b^{2} c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{4}+a}\, b^{2} c}{16 a^{2}}-\frac{2 \sqrt{b \,x^{4}+a}\, b f}{5 a x}-\frac{2 \sqrt{b \,x^{4}+a}\, b d}{21 a \,x^{3}}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} b c}{16 a^{2} x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, f}{5 x^{5}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} e}{6 a \,x^{6}}-\frac{\sqrt{b \,x^{4}+a}\, d}{7 x^{7}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} c}{8 a \,x^{8}}"," ",0,"-1/5*f/x^5*(b*x^4+a)^(1/2)-2/5*b*f*(b*x^4+a)^(1/2)/a/x+2/5*I*f*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-2/5*I*f*b^(3/2)/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/8*c/a/x^8*(b*x^4+a)^(3/2)+1/16*c/a^2*b/x^4*(b*x^4+a)^(3/2)+1/16*c/a^(3/2)*b^2*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/16*c/a^2*b^2*(b*x^4+a)^(1/2)-1/7*d/x^7*(b*x^4+a)^(1/2)-2/21*b*d*(b*x^4+a)^(1/2)/a/x^3-2/21*d*b^2/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/6*e*(b*x^4+a)^(3/2)/x^6/a","C"
509,1,429,401,0.210000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(1/2)/x^10,x)","-\frac{2 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{21 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}-\frac{2 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}+\frac{b^{2} d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{16 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{4}+a}\, b^{2} d}{16 a^{2}}+\frac{2 \sqrt{b \,x^{4}+a}\, b^{2} c}{15 a^{2} x}-\frac{2 \sqrt{b \,x^{4}+a}\, b e}{21 a \,x^{3}}-\frac{2 \sqrt{b \,x^{4}+a}\, b c}{45 a \,x^{5}}+\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} b d}{16 a^{2} x^{4}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} f}{6 a \,x^{6}}-\frac{\sqrt{b \,x^{4}+a}\, e}{7 x^{7}}-\frac{\left(b \,x^{4}+a \right)^{\frac{3}{2}} d}{8 a \,x^{8}}-\frac{\sqrt{b \,x^{4}+a}\, c}{9 x^{9}}"," ",0,"-1/8*d/a/x^8*(b*x^4+a)^(3/2)+1/16*d/a^2*b/x^4*(b*x^4+a)^(3/2)+1/16*d/a^(3/2)*b^2*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/16*d/a^2*b^2*(b*x^4+a)^(1/2)-1/9*c/x^9*(b*x^4+a)^(1/2)-2/45*b*c*(b*x^4+a)^(1/2)/a/x^5+2/15*b^2*c*(b*x^4+a)^(1/2)/a^2/x-2/15*I*c*b^(5/2)/a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+2/15*I*c*b^(5/2)/a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/7*e/x^7*(b*x^4+a)^(1/2)-2/21*b*e*(b*x^4+a)^(1/2)/a/x^3-2/21*e*b^2/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/6*f*(b*x^4+a)^(3/2)/x^6/a","C"
510,1,462,444,0.202000," ","int(x^4*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x)","\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{11}}{13}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{10}}{12}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{9}}{11}+\frac{5 \sqrt{b \,x^{4}+a}\, a e \,x^{7}}{39}+\frac{7 \sqrt{b \,x^{4}+a}\, a d \,x^{6}}{48}+\frac{13 \sqrt{b \,x^{4}+a}\, a c \,x^{5}}{77}+\frac{4 \sqrt{b \,x^{4}+a}\, a^{2} e \,x^{3}}{195 b}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{7}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{65 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{7}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{65 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{3} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{\sqrt{b \,x^{4}+a}\, a^{2} d \,x^{2}}{32 b}-\frac{a^{3} d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{32 b^{\frac{3}{2}}}+\frac{4 \sqrt{b \,x^{4}+a}\, a^{2} c x}{77 b}-\frac{\sqrt{b \,x^{4}+a}\, \left(-5 b \,x^{4}+2 a \right) \left(b^{2} x^{8}+2 a b \,x^{4}+a^{2}\right) f}{70 b^{2}}"," ",0,"-1/70*f*(b*x^4+a)^(1/2)*(-5*b*x^4+2*a)*(b^2*x^8+2*a*b*x^4+a^2)/b^2+1/13*e*b*x^11*(b*x^4+a)^(1/2)+5/39*e*a*x^7*(b*x^4+a)^(1/2)+4/195*a^2*e*x^3*(b*x^4+a)^(1/2)/b-4/65*I*e*a^(7/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+4/65*I*e*a^(7/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/12*d*b*x^10*(b*x^4+a)^(1/2)+7/48*d*a*x^6*(b*x^4+a)^(1/2)+1/32*a^2*d*x^2*(b*x^4+a)^(1/2)/b-1/32*d/b^(3/2)*a^3*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/11*c*b*x^9*(b*x^4+a)^(1/2)+13/77*c*a*x^5*(b*x^4+a)^(1/2)+4/77*a^2*c*x*(b*x^4+a)^(1/2)/b-4/77*c*a^3/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
511,1,434,424,0.186000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{11}}{13}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{10}}{12}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{9}}{11}+\frac{5 \sqrt{b \,x^{4}+a}\, a f \,x^{7}}{39}+\frac{7 \sqrt{b \,x^{4}+a}\, a e \,x^{6}}{48}+\frac{13 \sqrt{b \,x^{4}+a}\, a d \,x^{5}}{77}+\frac{4 \sqrt{b \,x^{4}+a}\, a^{2} f \,x^{3}}{195 b}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{7}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{65 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{7}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{65 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{3} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{\sqrt{b \,x^{4}+a}\, a^{2} e \,x^{2}}{32 b}-\frac{a^{3} e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{32 b^{\frac{3}{2}}}+\frac{4 \sqrt{b \,x^{4}+a}\, a^{2} d x}{77 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{5}{2}} c}{10 b}"," ",0,"1/13*f*b*x^11*(b*x^4+a)^(1/2)+5/39*f*a*x^7*(b*x^4+a)^(1/2)+4/195*a^2*f*x^3*(b*x^4+a)^(1/2)/b-4/65*I*f*a^(7/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+4/65*I*f*a^(7/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/12*e*b*x^10*(b*x^4+a)^(1/2)+7/48*e*a*x^6*(b*x^4+a)^(1/2)+1/32*a^2*e*x^2*(b*x^4+a)^(1/2)/b-1/32*e/b^(3/2)*a^3*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/11*d*b*x^9*(b*x^4+a)^(1/2)+13/77*d*a*x^5*(b*x^4+a)^(1/2)+4/77*a^2*d*x*(b*x^4+a)^(1/2)/b-4/77*d*a^3/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/10*c/b*(b*x^4+a)^(5/2)","C"
512,1,413,403,0.207000," ","int(x^2*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{10}}{12}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{9}}{11}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{7}}{9}+\frac{7 \sqrt{b \,x^{4}+a}\, a f \,x^{6}}{48}+\frac{13 \sqrt{b \,x^{4}+a}\, a e \,x^{5}}{77}+\frac{11 \sqrt{b \,x^{4}+a}\, a c \,x^{3}}{45}-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{3} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, a^{2} f \,x^{2}}{32 b}-\frac{a^{3} f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{32 b^{\frac{3}{2}}}+\frac{4 \sqrt{b \,x^{4}+a}\, a^{2} e x}{77 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{5}{2}} d}{10 b}"," ",0,"1/12*f*b*x^10*(b*x^4+a)^(1/2)+7/48*f*a*x^6*(b*x^4+a)^(1/2)+1/32*a^2*f*x^2*(b*x^4+a)^(1/2)/b-1/32*f/b^(3/2)*a^3*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/11*e*b*x^9*(b*x^4+a)^(1/2)+13/77*e*a*x^5*(b*x^4+a)^(1/2)+4/77*a^2*e*x*(b*x^4+a)^(1/2)/b-4/77*e*a^3/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/10*d/b*(b*x^4+a)^(5/2)+1/9*c*b*x^7*(b*x^4+a)^(1/2)+11/45*c*a*x^3*(b*x^4+a)^(1/2)+4/15*I*c*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*c*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
513,1,392,385,0.166000," ","int(x*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{9}}{11}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{7}}{9}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{6}}{8}+\frac{13 \sqrt{b \,x^{4}+a}\, a f \,x^{5}}{77}+\frac{11 \sqrt{b \,x^{4}+a}\, a d \,x^{3}}{45}-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{3} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{5 \sqrt{b \,x^{4}+a}\, a c \,x^{2}}{16}+\frac{3 a^{2} c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 \sqrt{b}}+\frac{4 \sqrt{b \,x^{4}+a}\, a^{2} f x}{77 b}+\frac{\left(b \,x^{4}+a \right)^{\frac{5}{2}} e}{10 b}"," ",0,"1/11*f*b*x^9*(b*x^4+a)^(1/2)+13/77*f*a*x^5*(b*x^4+a)^(1/2)+4/77*a^2*f*x*(b*x^4+a)^(1/2)/b-4/77*f*a^3/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/10*e*(b*x^4+a)^(5/2)/b+1/9*d*b*x^7*(b*x^4+a)^(1/2)+11/45*d*a*x^3*(b*x^4+a)^(1/2)+4/15*I*d*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*d*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*c*b*x^6*(b*x^4+a)^(1/2)+5/16*a*c*x^2*(b*x^4+a)^(1/2)+3/16*c*a^2*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)","C"
514,1,368,362,0.180000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2),x)","\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{7}}{9}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{6}}{8}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{5}}{7}+\frac{11 \sqrt{b \,x^{4}+a}\, a e \,x^{3}}{45}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{5 \sqrt{b \,x^{4}+a}\, a d \,x^{2}}{16}+\frac{3 a^{2} d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 \sqrt{b}}+\frac{3 \sqrt{b \,x^{4}+a}\, a c x}{7}+\frac{\left(b \,x^{4}+a \right)^{\frac{5}{2}} f}{10 b}"," ",0,"1/10*f*(b*x^4+a)^(5/2)/b+1/9*e*b*x^7*(b*x^4+a)^(1/2)+11/45*e*a*x^3*(b*x^4+a)^(1/2)+4/15*I*e*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*e*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*d*b*x^6*(b*x^4+a)^(1/2)+5/16*a*d*x^2*(b*x^4+a)^(1/2)+3/16*d*a^2*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)+1/7*c*b*x^5*(b*x^4+a)^(1/2)+3/7*c*a*x*(b*x^4+a)^(1/2)+4/7*c*a^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
515,1,411,379,0.182000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x,x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{7}}{9}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{6}}{8}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{5}}{7}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{4}}{6}+\frac{11 \sqrt{b \,x^{4}+a}\, a f \,x^{3}}{45}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{5}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{5 \sqrt{b \,x^{4}+a}\, a e \,x^{2}}{16}+\frac{3 a^{2} e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 \sqrt{b}}-\frac{a^{\frac{3}{2}} c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{3 \sqrt{b \,x^{4}+a}\, a d x}{7}+\frac{2 \sqrt{b \,x^{4}+a}\, a c}{3}"," ",0,"1/9*f*b*x^7*(b*x^4+a)^(1/2)+11/45*f*a*x^3*(b*x^4+a)^(1/2)+4/15*I*f*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*f*a^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/8*e*b*x^6*(b*x^4+a)^(1/2)+5/16*e*a*x^2*(b*x^4+a)^(1/2)+3/16*e*a^2*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)+1/7*d*b*x^5*(b*x^4+a)^(1/2)+3/7*d*a*x*(b*x^4+a)^(1/2)+4/7*d*a^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*c*b*x^4*(b*x^4+a)^(1/2)+2/3*c*a*(b*x^4+a)^(1/2)-1/2*c*a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
516,1,411,380,0.207000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^2,x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{6}}{8}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{5}}{7}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{4}}{6}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{3}}{5}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{5 \sqrt{b \,x^{4}+a}\, a f \,x^{2}}{16}+\frac{3 a^{2} f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{16 \sqrt{b}}-\frac{a^{\frac{3}{2}} d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{3 \sqrt{b \,x^{4}+a}\, a e x}{7}+\frac{2 \sqrt{b \,x^{4}+a}\, a d}{3}-\frac{\sqrt{b \,x^{4}+a}\, a c}{x}"," ",0,"1/8*f*b*x^6*(b*x^4+a)^(1/2)+5/16*f*a*x^2*(b*x^4+a)^(1/2)+3/16*f*a^2*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)+1/7*e*b*x^5*(b*x^4+a)^(1/2)+3/7*e*a*x*(b*x^4+a)^(1/2)+4/7*e*a^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-c*a*(b*x^4+a)^(1/2)/x+1/5*c*b*x^3*(b*x^4+a)^(1/2)+12/5*I*c*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*c*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*d*b*x^4*(b*x^4+a)^(1/2)+2/3*d*a*(b*x^4+a)^(1/2)-1/2*d*a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
517,1,409,382,0.212000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^3,x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{5}}{7}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{4}}{6}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{3}}{5}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{2} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b c \,x^{2}}{4}-\frac{a^{\frac{3}{2}} e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{3 a \sqrt{b}\, c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4}+\frac{3 \sqrt{b \,x^{4}+a}\, a f x}{7}+\frac{2 \sqrt{b \,x^{4}+a}\, a e}{3}-\frac{\sqrt{b \,x^{4}+a}\, a d}{x}-\frac{\sqrt{b \,x^{4}+a}\, a c}{2 x^{2}}"," ",0,"1/7*f*b*x^5*(b*x^4+a)^(1/2)+3/7*f*a*x*(b*x^4+a)^(1/2)+4/7*f*a^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*c*b*x^2*(b*x^4+a)^(1/2)+3/4*c*a*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*c*a/x^2*(b*x^4+a)^(1/2)-d*a*(b*x^4+a)^(1/2)/x+1/5*d*b*x^3*(b*x^4+a)^(1/2)+12/5*I*d*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*d*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*e*b*x^4*(b*x^4+a)^(1/2)+2/3*e*a*(b*x^4+a)^(1/2)-1/2*e*a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
518,1,408,384,0.215000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^4,x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{4}}{6}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{3}}{5}-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a b c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b d \,x^{2}}{4}-\frac{a^{\frac{3}{2}} f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2}+\frac{3 a \sqrt{b}\, d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4}+\frac{\sqrt{b \,x^{4}+a}\, b c x}{3}+\frac{2 \sqrt{b \,x^{4}+a}\, a f}{3}-\frac{\sqrt{b \,x^{4}+a}\, a e}{x}-\frac{\sqrt{b \,x^{4}+a}\, a d}{2 x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{3 x^{3}}"," ",0,"-1/3*c*a*(b*x^4+a)^(1/2)/x^3+1/3*c*b*x*(b*x^4+a)^(1/2)+4/3*c*a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*d*b*x^2*(b*x^4+a)^(1/2)+3/4*d*a*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*d*a/x^2*(b*x^4+a)^(1/2)-e*a*(b*x^4+a)^(1/2)/x+1/5*e*b*x^3*(b*x^4+a)^(1/2)+12/5*I*e*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*e*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/6*f*b*x^4*(b*x^4+a)^(1/2)+2/3*f*a*(b*x^4+a)^(1/2)-1/2*f*a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
519,1,409,366,0.185000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^5,x)","\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{3}}{5}-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} \sqrt{b}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a b d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b e \,x^{2}}{4}+\frac{3 a \sqrt{b}\, e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4}-\frac{3 \sqrt{a}\, b c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4}+\frac{\sqrt{b \,x^{4}+a}\, b d x}{3}+\frac{\sqrt{b \,x^{4}+a}\, b c}{2}-\frac{\sqrt{b \,x^{4}+a}\, a f}{x}-\frac{\sqrt{b \,x^{4}+a}\, a e}{2 x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{3 x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{4 x^{4}}"," ",0,"1/2*c*b*(b*x^4+a)^(1/2)-1/4*c*a/x^4*(b*x^4+a)^(1/2)-3/4*c*a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/3*d*a*(b*x^4+a)^(1/2)/x^3+1/3*d*b*x*(b*x^4+a)^(1/2)+4/3*d*a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*e*b*x^2*(b*x^4+a)^(1/2)+3/4*e*a*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*e*a/x^2*(b*x^4+a)^(1/2)-f*a*(b*x^4+a)^(1/2)/x+1/5*f*b*x^3*(b*x^4+a)^(1/2)+12/5*I*f*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*f*a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
520,1,409,367,0.211000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^6,x)","\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a b e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{\sqrt{b \,x^{4}+a}\, b f \,x^{2}}{4}+\frac{3 a \sqrt{b}\, f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4}-\frac{3 \sqrt{a}\, b d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4}+\frac{\sqrt{b \,x^{4}+a}\, b e x}{3}+\frac{\sqrt{b \,x^{4}+a}\, b d}{2}-\frac{7 \sqrt{b \,x^{4}+a}\, b c}{5 x}-\frac{\sqrt{b \,x^{4}+a}\, a f}{2 x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{3 x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{4 x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{5 x^{5}}"," ",0,"-1/5*c*a*(b*x^4+a)^(1/2)/x^5-7/5*c*b*(b*x^4+a)^(1/2)/x+12/5*I*c*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*c*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*d*b*(b*x^4+a)^(1/2)-1/4*d*a/x^4*(b*x^4+a)^(1/2)-3/4*d*a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/3*e*a*(b*x^4+a)^(1/2)/x^3+1/3*e*b*x*(b*x^4+a)^(1/2)+4/3*e*a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*f*b*x^2*(b*x^4+a)^(1/2)+3/4*f*a*b^(1/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*f*a/x^2*(b*x^4+a)^(1/2)","C"
521,1,408,372,0.209000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^7,x)","\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a b f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{3 \sqrt{a}\, b e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4}+\frac{b^{\frac{3}{2}} c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, b f x}{3}+\frac{\sqrt{b \,x^{4}+a}\, b e}{2}-\frac{7 \sqrt{b \,x^{4}+a}\, b d}{5 x}-\frac{2 \sqrt{b \,x^{4}+a}\, b c}{3 x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{3 x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{4 x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{5 x^{5}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{6 x^{6}}"," ",0,"-1/5*d*a*(b*x^4+a)^(1/2)/x^5-7/5*d*b*(b*x^4+a)^(1/2)/x+12/5*I*d*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*d*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e*b*(b*x^4+a)^(1/2)-1/4*e*a/x^4*(b*x^4+a)^(1/2)-3/4*e*a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/3*f*a*(b*x^4+a)^(1/2)/x^3+1/3*f*b*x*(b*x^4+a)^(1/2)+4/3*f*a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*c*b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/6*c*a/x^6*(b*x^4+a)^(1/2)-2/3*c*b/x^2*(b*x^4+a)^(1/2)","C"
522,1,411,388,0.220000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^8,x)","-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{3 \sqrt{a}\, b f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4}+\frac{b^{\frac{3}{2}} d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}+\frac{\sqrt{b \,x^{4}+a}\, b f}{2}-\frac{7 \sqrt{b \,x^{4}+a}\, b e}{5 x}-\frac{2 \sqrt{b \,x^{4}+a}\, b d}{3 x^{2}}-\frac{3 \sqrt{b \,x^{4}+a}\, b c}{7 x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{4 x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{5 x^{5}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{6 x^{6}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{7 x^{7}}"," ",0,"-1/5*e*a*(b*x^4+a)^(1/2)/x^5-7/5*b*e*(b*x^4+a)^(1/2)/x+12/5*I*e*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*e*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*f*b*(b*x^4+a)^(1/2)-1/4*f*a/x^4*(b*x^4+a)^(1/2)-3/4*f*a^(1/2)*b*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/7*c*a*(b*x^4+a)^(1/2)/x^7-3/7*c*b*(b*x^4+a)^(1/2)/x^3+4/7*c*b^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*d*b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/6*d*a/x^6*(b*x^4+a)^(1/2)-2/3*d*b/x^2*(b*x^4+a)^(1/2)","C"
523,1,416,361,0.206000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^9,x)","-\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{12 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, b^{\frac{3}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{3 b^{2} c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{16 \sqrt{a}}+\frac{b^{\frac{3}{2}} e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}-\frac{7 \sqrt{b \,x^{4}+a}\, b f}{5 x}-\frac{2 \sqrt{b \,x^{4}+a}\, b e}{3 x^{2}}-\frac{3 \sqrt{b \,x^{4}+a}\, b d}{7 x^{3}}-\frac{5 \sqrt{b \,x^{4}+a}\, b c}{16 x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{5 x^{5}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{6 x^{6}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{7 x^{7}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{8 x^{8}}"," ",0,"-1/5*f*a*(b*x^4+a)^(1/2)/x^5-7/5*f*b*(b*x^4+a)^(1/2)/x+12/5*I*f*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-12/5*I*f*b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/8*c*a/x^8*(b*x^4+a)^(1/2)-5/16*c*b/x^4*(b*x^4+a)^(1/2)-3/16*c*b^2/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/7*d*a*(b*x^4+a)^(1/2)/x^7-3/7*d*b*(b*x^4+a)^(1/2)/x^3+4/7*d*b^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e*b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/6*e*a/x^6*(b*x^4+a)^(1/2)-2/3*e*b/x^2*(b*x^4+a)^(1/2)","C"
524,1,437,385,0.213000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^10,x)","-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{3 b^{2} d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{16 \sqrt{a}}+\frac{b^{\frac{3}{2}} f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} c}{15 a x}-\frac{2 \sqrt{b \,x^{4}+a}\, b f}{3 x^{2}}-\frac{3 \sqrt{b \,x^{4}+a}\, b e}{7 x^{3}}-\frac{5 \sqrt{b \,x^{4}+a}\, b d}{16 x^{4}}-\frac{11 \sqrt{b \,x^{4}+a}\, b c}{45 x^{5}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{6 x^{6}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{7 x^{7}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{8 x^{8}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{9 x^{9}}"," ",0,"-1/8*d*a/x^8*(b*x^4+a)^(1/2)-5/16*d*b/x^4*(b*x^4+a)^(1/2)-3/16*d*b^2/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/9*c*a*(b*x^4+a)^(1/2)/x^9-11/45*c*b*(b*x^4+a)^(1/2)/x^5-4/15*b^2*c*(b*x^4+a)^(1/2)/a/x+4/15*I*c/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*c/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/7*e*a*(b*x^4+a)^(1/2)/x^7-3/7*e*b*(b*x^4+a)^(1/2)/x^3+4/7*e*b^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*f*b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/6*f*a/x^6*(b*x^4+a)^(1/2)-2/3*f*b/x^2*(b*x^4+a)^(1/2)","C"
525,1,417,383,0.190000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^11,x)","-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{2} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{7 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{3 b^{2} e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{16 \sqrt{a}}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} d}{15 a x}-\frac{3 \sqrt{b \,x^{4}+a}\, b f}{7 x^{3}}-\frac{5 \sqrt{b \,x^{4}+a}\, b e}{16 x^{4}}-\frac{11 \sqrt{b \,x^{4}+a}\, b d}{45 x^{5}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{7 x^{7}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{8 x^{8}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{9 x^{9}}-\frac{\sqrt{b \,x^{4}+a}\, \left(b^{2} x^{8}+2 a b \,x^{4}+a^{2}\right) c}{10 a \,x^{10}}"," ",0,"-1/8*e*a/x^8*(b*x^4+a)^(1/2)-5/16*e*b/x^4*(b*x^4+a)^(1/2)-3/16*e*b^2/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/9*d*a*(b*x^4+a)^(1/2)/x^9-11/45*d*b*(b*x^4+a)^(1/2)/x^5-4/15*b^2*d*(b*x^4+a)^(1/2)/a/x+4/15*I*d/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*d/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/7*f*a*(b*x^4+a)^(1/2)/x^7-3/7*f*b*(b*x^4+a)^(1/2)/x^3+4/7*f*b^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/10*c*(b*x^4+a)^(1/2)/x^10/a*(b^2*x^8+2*a*b*x^4+a^2)","C"
526,1,441,404,0.219000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^12,x)","-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{3} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}-\frac{3 b^{2} f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{16 \sqrt{a}}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} e}{15 a x}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} c}{77 a \,x^{3}}-\frac{5 \sqrt{b \,x^{4}+a}\, b f}{16 x^{4}}-\frac{11 \sqrt{b \,x^{4}+a}\, b e}{45 x^{5}}-\frac{13 \sqrt{b \,x^{4}+a}\, b c}{77 x^{7}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{8 x^{8}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{9 x^{9}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{11 x^{11}}-\frac{\sqrt{b \,x^{4}+a}\, \left(b^{2} x^{8}+2 a b \,x^{4}+a^{2}\right) d}{10 a \,x^{10}}"," ",0,"-1/8*f*a/x^8*(b*x^4+a)^(1/2)-5/16*f*b/x^4*(b*x^4+a)^(1/2)-3/16*f*b^2/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/9*e*a*(b*x^4+a)^(1/2)/x^9-11/45*e*b*(b*x^4+a)^(1/2)/x^5-4/15*b^2*e*(b*x^4+a)^(1/2)/a/x+4/15*I*e/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*e/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/11*c*a*(b*x^4+a)^(1/2)/x^11-13/77*c*b*(b*x^4+a)^(1/2)/x^7-4/77*b^2*c*(b*x^4+a)^(1/2)/a/x^3-4/77*c/a*b^3/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/10*d*(b*x^4+a)^(1/2)/x^10/a*(b^2*x^8+2*a*b*x^4+a^2)","C"
527,1,462,425,0.203000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^13,x)","-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{5}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{15 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{3} d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{b^{3} c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{3}{2}}}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} f}{15 a x}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} d}{77 a \,x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, b^{2} c}{32 a \,x^{4}}-\frac{11 \sqrt{b \,x^{4}+a}\, b f}{45 x^{5}}-\frac{13 \sqrt{b \,x^{4}+a}\, b d}{77 x^{7}}-\frac{7 \sqrt{b \,x^{4}+a}\, b c}{48 x^{8}}-\frac{\sqrt{b \,x^{4}+a}\, a f}{9 x^{9}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{11 x^{11}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{12 x^{12}}-\frac{\sqrt{b \,x^{4}+a}\, \left(b^{2} x^{8}+2 a b \,x^{4}+a^{2}\right) e}{10 a \,x^{10}}"," ",0,"-7/48*c*b/x^8*(b*x^4+a)^(1/2)-1/32*b^2*c*(b*x^4+a)^(1/2)/a/x^4+1/32*c/a^(3/2)*b^3*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/12*c*a/x^12*(b*x^4+a)^(1/2)-1/9*f*a*(b*x^4+a)^(1/2)/x^9-11/45*f*b*(b*x^4+a)^(1/2)/x^5-4/15*b^2*f*(b*x^4+a)^(1/2)/a/x+4/15*I*f/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-4/15*I*f/a^(1/2)*b^(5/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/11*d*a*(b*x^4+a)^(1/2)/x^11-13/77*d*b*(b*x^4+a)^(1/2)/x^7-4/77*b^2*d*(b*x^4+a)^(1/2)/a/x^3-4/77*d/a*b^3/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/10*e*(b*x^4+a)^(1/2)/x^10/a*(b^2*x^8+2*a*b*x^4+a^2)","C"
528,1,483,446,0.219000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^(3/2)/x^14,x)","-\frac{4 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{3} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{77 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{7}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{65 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}-\frac{4 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{7}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{65 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}+\frac{b^{3} d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{32 a^{\frac{3}{2}}}+\frac{4 \sqrt{b \,x^{4}+a}\, b^{3} c}{65 a^{2} x}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} e}{77 a \,x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, b^{2} d}{32 a \,x^{4}}-\frac{4 \sqrt{b \,x^{4}+a}\, b^{2} c}{195 a \,x^{5}}-\frac{13 \sqrt{b \,x^{4}+a}\, b e}{77 x^{7}}-\frac{7 \sqrt{b \,x^{4}+a}\, b d}{48 x^{8}}-\frac{5 \sqrt{b \,x^{4}+a}\, b c}{39 x^{9}}-\frac{\sqrt{b \,x^{4}+a}\, a e}{11 x^{11}}-\frac{\sqrt{b \,x^{4}+a}\, a d}{12 x^{12}}-\frac{\sqrt{b \,x^{4}+a}\, \left(b^{2} x^{8}+2 a b \,x^{4}+a^{2}\right) f}{10 a \,x^{10}}-\frac{\sqrt{b \,x^{4}+a}\, a c}{13 x^{13}}"," ",0,"-7/48*d*b/x^8*(b*x^4+a)^(1/2)-1/32*b^2*d*(b*x^4+a)^(1/2)/a/x^4+1/32*d/a^(3/2)*b^3*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/12*d*a/x^12*(b*x^4+a)^(1/2)-1/13*c*a*(b*x^4+a)^(1/2)/x^13-5/39*c*b*(b*x^4+a)^(1/2)/x^9-4/195*b^2*c*(b*x^4+a)^(1/2)/a/x^5+4/65*b^3*c*(b*x^4+a)^(1/2)/a^2/x-4/65*I*c*b^(7/2)/a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+4/65*I*c*b^(7/2)/a^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/11*e*a*(b*x^4+a)^(1/2)/x^11-13/77*e*b*(b*x^4+a)^(1/2)/x^7-4/77*b^2*e*(b*x^4+a)^(1/2)/a/x^3-4/77*e/a*b^3/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/10*f*(b*x^4+a)^(1/2)/x^10/a*(b^2*x^8+2*a*b*x^4+a^2)","C"
529,1,335,345,0.226000," ","int(x^4*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, e \,x^{3}}{5 b}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{\sqrt{b \,x^{4}+a}\, d \,x^{2}}{4 b}-\frac{a d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 b^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{4}+a}\, c x}{3 b}-\frac{\sqrt{b \,x^{4}+a}\, \left(-b \,x^{4}+2 a \right) f}{6 b^{2}}"," ",0,"-1/6*f*(b*x^4+a)^(1/2)*(-b*x^4+2*a)/b^2+1/5*e*x^3*(b*x^4+a)^(1/2)/b-3/5*I*e*a^(3/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+3/5*I*e*a^(3/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*d*x^2/b*(b*x^4+a)^(1/2)-1/4*d*a/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*c*x*(b*x^4+a)^(1/2)/b-1/3*c*a/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
530,1,325,324,0.166000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","\frac{\sqrt{b \,x^{4}+a}\, f \,x^{3}}{5 b}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a^{\frac{3}{2}} f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{\sqrt{b \,x^{4}+a}\, e \,x^{2}}{4 b}-\frac{a e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 b^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{4}+a}\, d x}{3 b}+\frac{\sqrt{b \,x^{4}+a}\, c}{2 b}"," ",0,"1/5*f*x^3*(b*x^4+a)^(1/2)/b-3/5*I*f*a^(3/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+3/5*I*f*a^(3/2)/b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/4*e*x^2/b*(b*x^4+a)^(1/2)-1/4*e*a/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*d*x*(b*x^4+a)^(1/2)/b-1/3*d*a/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*c/b*(b*x^4+a)^(1/2)","C"
531,1,248,304,0.189000," ","int(x^2*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{\sqrt{b \,x^{4}+a}\, f \,x^{2}}{4 b}-\frac{a f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 b^{\frac{3}{2}}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, c}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, e x}{3 b}+\frac{\sqrt{b \,x^{4}+a}\, d}{2 b}"," ",0,"1/4*f*x^2/b*(b*x^4+a)^(1/2)-1/4*f*a/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/3*e*x*(b*x^4+a)^(1/2)/b-1/3*e*a/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*d/b*(b*x^4+a)^(1/2)+I*c*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I))","C"
532,1,229,295,0.168000," ","int(x*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, d}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, f x}{3 b}+\frac{\sqrt{b \,x^{4}+a}\, e}{2 b}"," ",0,"1/3*f*x*(b*x^4+a)^(1/2)/b-1/3*f*a/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e*(b*x^4+a)^(1/2)/b+I*d*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I))+1/2*c*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)","C"
533,1,208,276,0.175000," ","int((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}+\frac{d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, e}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}+\frac{\sqrt{b \,x^{4}+a}\, f}{2 b}"," ",0,"1/2*(b*x^4+a)^(1/2)/b*f+I*e*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I))+1/2/b^(1/2)*d*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+c/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
534,1,222,281,0.420000," ","int((f*x^3+e*x^2+d*x+c)/x/(b*x^4+a)^(1/2),x)","\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}+\frac{e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right) \sqrt{a}\, f}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{b}}"," ",0,"I*f*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I))+1/2*e*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)+d/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
535,1,299,303,0.204000," ","int((f*x^3+e*x^2+d*x+c)/x^2/(b*x^4+a)^(1/2),x)","-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}+\frac{f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 \sqrt{b}}-\frac{\sqrt{b \,x^{4}+a}\, c}{a x}"," ",0,"1/2*f*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))/b^(1/2)+e/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-c*(b*x^4+a)^(1/2)/a/x+I*c/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-I*c/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*d/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
536,1,293,298,0.180000," ","int((f*x^3+e*x^2+d*x+c)/x^3/(b*x^4+a)^(1/2),x)","-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}}-\frac{e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b \,x^{4}+a}\, d}{a x}-\frac{\sqrt{b \,x^{4}+a}\, c}{2 a \,x^{2}}"," ",0,"f/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c*(b*x^4+a)^(1/2)/a/x^2-d*(b*x^4+a)^(1/2)/a/x+I*d/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-I*d/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*e/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
537,1,316,317,0.179000," ","int((f*x^3+e*x^2+d*x+c)/x^4/(b*x^4+a)^(1/2),x)","-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}-\frac{f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 \sqrt{a}}-\frac{\sqrt{b \,x^{4}+a}\, e}{a x}-\frac{\sqrt{b \,x^{4}+a}\, d}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, c}{3 a \,x^{3}}"," ",0,"-1/3*c*(b*x^4+a)^(1/2)/a/x^3-1/3*c/a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*d*(b*x^4+a)^(1/2)/a/x^2-e*(b*x^4+a)^(1/2)/a/x+I*e/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-I*e/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*f/a^(1/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
538,1,335,336,0.211000," ","int((f*x^3+e*x^2+d*x+c)/x^5/(b*x^4+a)^(1/2),x)","-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}}-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{b c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4 a^{\frac{3}{2}}}-\frac{\sqrt{b \,x^{4}+a}\, f}{a x}-\frac{\sqrt{b \,x^{4}+a}\, e}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, d}{3 a \,x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, c}{4 a \,x^{4}}"," ",0,"-1/4*c*(b*x^4+a)^(1/2)/a/x^4+1/4*c*b/a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/3*d*(b*x^4+a)^(1/2)/a/x^3-1/3*d/a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*e*(b*x^4+a)^(1/2)/a/x^2-f*(b*x^4+a)^(1/2)/a/x+I*f/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-I*f/a^(1/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
539,1,354,357,0.188000," ","int((f*x^3+e*x^2+d*x+c)/x^6/(b*x^4+a)^(1/2),x)","-\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{3 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b^{\frac{3}{2}} c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{5 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}+\frac{b d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{4 a^{\frac{3}{2}}}+\frac{3 \sqrt{b \,x^{4}+a}\, b c}{5 a^{2} x}-\frac{\sqrt{b \,x^{4}+a}\, f}{2 a \,x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, e}{3 a \,x^{3}}-\frac{\sqrt{b \,x^{4}+a}\, d}{4 a \,x^{4}}-\frac{\sqrt{b \,x^{4}+a}\, c}{5 a \,x^{5}}"," ",0,"-1/5*c*(b*x^4+a)^(1/2)/a/x^5+3/5*b*c*(b*x^4+a)^(1/2)/a^2/x-3/5*I*c/a^(3/2)*b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+3/5*I*c/a^(3/2)*b^(3/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/4*d*(b*x^4+a)^(1/2)/a/x^4+1/4*d*b/a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)-1/3*e*(b*x^4+a)^(1/2)/a/x^3-1/3*e/a*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*f*(b*x^4+a)^(1/2)/a/x^2","C"
540,1,378,351,0.193000," ","int(x^6*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","\frac{f \,x^{6}}{4 \sqrt{b \,x^{4}+a}\, b}-\frac{c \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}+\frac{3 a f \,x^{2}}{4 \sqrt{b \,x^{4}+a}\, b^{2}}+\frac{a e x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b^{2}}-\frac{5 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{6 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{2}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{3 a f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{4 b^{\frac{5}{2}}}+\frac{\sqrt{b \,x^{4}+a}\, e x}{3 b^{2}}+\frac{\left(b \,x^{4}+2 a \right) d}{2 \sqrt{b \,x^{4}+a}\, b^{2}}"," ",0,"1/4*f*x^6/b/(b*x^4+a)^(1/2)+3/4*f*a/b^2*x^2/(b*x^4+a)^(1/2)-3/4*f*a/b^(5/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))+1/2*e/b^2*a*x/((x^4+a/b)*b)^(1/2)+1/3*e*x*(b*x^4+a)^(1/2)/b^2-5/6*e*a/b^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*d*(b*x^4+2*a)/(b*x^4+a)^(1/2)/b^2-1/2*c/b*x^3/((x^4+a/b)*b)^(1/2)+3/2*I*c/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*c/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
541,1,358,333,0.191000," ","int(x^5*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","-\frac{d \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}-\frac{c \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, b}+\frac{a f x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b^{2}}-\frac{5 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, a f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{6 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{2}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}+\frac{c \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{\sqrt{b \,x^{4}+a}\, f x}{3 b^{2}}+\frac{\left(b \,x^{4}+2 a \right) e}{2 \sqrt{b \,x^{4}+a}\, b^{2}}"," ",0,"1/2*f/b^2*a*x/((x^4+a/b)*b)^(1/2)+1/3*f*x*(b*x^4+a)^(1/2)/b^2-5/6*f*a/b^2/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e*(b*x^4+2*a)/(b*x^4+a)^(1/2)/b^2-1/2*d/b*x^3/((x^4+a/b)*b)^(1/2)+3/2*I*d/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*d/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c*x^2/b/(b*x^4+a)^(1/2)+1/2*c/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))","C"
542,1,340,308,0.168000," ","int(x^4*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","-\frac{e \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}-\frac{d \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, b}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{c x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{d \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 b^{\frac{3}{2}}}+\frac{\left(b \,x^{4}+2 a \right) f}{2 \sqrt{b \,x^{4}+a}\, b^{2}}"," ",0,"1/2*f*(b*x^4+2*a)/(b*x^4+a)^(1/2)/b^2-1/2*e/b*x^3/((x^4+a/b)*b)^(1/2)+3/2*I*e/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*e/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*d*x^2/b/(b*x^4+a)^(1/2)+1/2*d/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*c/b*x/((x^4+a/b)*b)^(1/2)+1/2*c/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
543,1,331,298,0.174000," ","int(x^3*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","-\frac{f \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}-\frac{e \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, b}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{a}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b^{\frac{3}{2}}}-\frac{d x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{e \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 b^{\frac{3}{2}}}-\frac{c}{2 \sqrt{b \,x^{4}+a}\, b}"," ",0,"-1/2*f/b*x^3/((x^4+a/b)*b)^(1/2)+3/2*I*f/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*f/b^(3/2)*a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*e*x^2/b/(b*x^4+a)^(1/2)+1/2*e/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*d/b*x/((x^4+a/b)*b)^(1/2)+1/2*d/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c/b/(b*x^4+a)^(1/2)","C"
544,1,331,325,0.176000," ","int(x^2*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","\frac{c \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}-\frac{f \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, b}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}\, \sqrt{b}}-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}\, \sqrt{b}}-\frac{e x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}+\frac{f \ln \left(\sqrt{b}\, x^{2}+\sqrt{b \,x^{4}+a}\right)}{2 b^{\frac{3}{2}}}-\frac{d}{2 \sqrt{b \,x^{4}+a}\, b}"," ",0,"-1/2*f*x^2/b/(b*x^4+a)^(1/2)+1/2*f/b^(3/2)*ln(b^(1/2)*x^2+(b*x^4+a)^(1/2))-1/2*e/b*x/((x^4+a/b)*b)^(1/2)+1/2*e/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*d/b/(b*x^4+a)^(1/2)+1/2*c/a*x^3/((x^4+a/b)*b)^(1/2)-1/2*I*c/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*I*c/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)","C"
545,1,250,303,0.168000," ","int(x*(f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","\frac{c \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, a}+\left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}\, \sqrt{b}}\right) d +\left(-\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, b}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, b}\right) f -\frac{e}{2 \sqrt{b \,x^{4}+a}\, b}"," ",0,"f*(-1/2/b*x/((x^4+a/b)*b)^(1/2)+1/2/b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I))-1/2*e/b/(b*x^4+a)^(1/2)+d*(1/2/a*x^3/((x^4+a/b)*b)^(1/2)-1/2*I/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)))+1/2*c/(b*x^4+a)^(1/2)/a*x^2","C"
546,1,250,279,0.170000," ","int((f*x^3+e*x^2+d*x+c)/(b*x^4+a)^(3/2),x)","\frac{d \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, a}+\left(\frac{x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}\right) c +\left(\frac{x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \left(-\EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)+\EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}\, \sqrt{b}}\right) e -\frac{f}{2 \sqrt{b \,x^{4}+a}\, b}"," ",0,"-1/2*f/b/(b*x^4+a)^(1/2)+e*(1/2/((x^4+a/b)*b)^(1/2)/a*x^3-1/2*I/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*(EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)))+1/2*d/(b*x^4+a)^(1/2)/a*x^2+c*(1/2/a*x/((x^4+a/b)*b)^(1/2)+1/2/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I))","C"
547,1,336,315,0.164000," ","int((f*x^3+e*x^2+d*x+c)/x/(b*x^4+a)^(3/2),x)","\frac{f \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}+\frac{e \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, a}+\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, f \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}\, \sqrt{b}}-\frac{i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, \sqrt{a}\, \sqrt{b}}+\frac{d x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}-\frac{c \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}}}+\frac{c}{2 \sqrt{b \,x^{4}+a}\, a}"," ",0,"1/2*f/a*x^3/((x^4+a/b)*b)^(1/2)-1/2*I*f/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*I*f/a^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)/b^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e/(b*x^4+a)^(1/2)/a*x^2+1/2*d/a*x/((x^4+a/b)*b)^(1/2)+1/2*d/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*c/a/(b*x^4+a)^(1/2)-1/2*c/a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
548,1,355,334,0.191000," ","int((f*x^3+e*x^2+d*x+c)/x^2/(b*x^4+a)^(3/2),x)","-\frac{b c \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a^{2}}+\frac{f \,x^{2}}{2 \sqrt{b \,x^{4}+a}\, a}+\frac{e x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, c \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}-\frac{d \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}}}+\frac{d}{2 \sqrt{b \,x^{4}+a}\, a}-\frac{\sqrt{b \,x^{4}+a}\, c}{a^{2} x}"," ",0,"1/2*f/(b*x^4+a)^(1/2)/a*x^2+1/2*e/a*x/((x^4+a/b)*b)^(1/2)+1/2*e/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c*b/a^2*x^3/((x^4+a/b)*b)^(1/2)-c*(b*x^4+a)^(1/2)/a^2/x+3/2*I*c/a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*c/a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*d/a/(b*x^4+a)^(1/2)-1/2*d/a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
549,1,363,353,0.190000," ","int((f*x^3+e*x^2+d*x+c)/x^3/(b*x^4+a)^(3/2),x)","-\frac{b d \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a^{2}}+\frac{f x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a}+\frac{\sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, f \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, d \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, d \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}-\frac{e \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}}}+\frac{e}{2 \sqrt{b \,x^{4}+a}\, a}-\frac{\sqrt{b \,x^{4}+a}\, d}{a^{2} x}-\frac{\left(2 b \,x^{4}+a \right) c}{2 \sqrt{b \,x^{4}+a}\, a^{2} x^{2}}"," ",0,"1/2*f/a*x/((x^4+a/b)*b)^(1/2)+1/2*f/a/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*c/x^2*(2*b*x^4+a)/(b*x^4+a)^(1/2)/a^2-1/2*d*b/a^2*x^3/((x^4+a/b)*b)^(1/2)-d*(b*x^4+a)^(1/2)/a^2/x+3/2*I*d/a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*d/a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*e/a/(b*x^4+a)^(1/2)-1/2*e/a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
550,1,383,369,0.186000," ","int((f*x^3+e*x^2+d*x+c)/x^4/(b*x^4+a)^(3/2),x)","-\frac{b e \,x^{3}}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a^{2}}-\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, e \EllipticE \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}+\frac{3 i \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{b}\, e \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{2 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{\frac{3}{2}}}-\frac{b c x}{2 \sqrt{\left(x^{4}+\frac{a}{b}\right) b}\, a^{2}}-\frac{5 \sqrt{-\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, \sqrt{\frac{i \sqrt{b}\, x^{2}}{\sqrt{a}}+1}\, b c \EllipticF \left(\sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, x , i\right)}{6 \sqrt{\frac{i \sqrt{b}}{\sqrt{a}}}\, \sqrt{b \,x^{4}+a}\, a^{2}}-\frac{f \ln \left(\frac{2 a +2 \sqrt{b \,x^{4}+a}\, \sqrt{a}}{x^{2}}\right)}{2 a^{\frac{3}{2}}}+\frac{f}{2 \sqrt{b \,x^{4}+a}\, a}-\frac{\sqrt{b \,x^{4}+a}\, e}{a^{2} x}-\frac{\left(2 b \,x^{4}+a \right) d}{2 \sqrt{b \,x^{4}+a}\, a^{2} x^{2}}-\frac{\sqrt{b \,x^{4}+a}\, c}{3 a^{2} x^{3}}"," ",0,"-1/3*c*(b*x^4+a)^(1/2)/a^2/x^3-1/2*c*b/a^2*x/((x^4+a/b)*b)^(1/2)-5/6*c/a^2*b/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-1/2*d/x^2*(2*b*x^4+a)/(b*x^4+a)^(1/2)/a^2-1/2*e*b/a^2*x^3/((x^4+a/b)*b)^(1/2)-e*(b*x^4+a)^(1/2)/a^2/x+3/2*I*e/a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticF((I/a^(1/2)*b^(1/2))^(1/2)*x,I)-3/2*I*e/a^(3/2)*b^(1/2)/(I/a^(1/2)*b^(1/2))^(1/2)*(-I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)*(I/a^(1/2)*b^(1/2)*x^2+1)^(1/2)/(b*x^4+a)^(1/2)*EllipticE((I/a^(1/2)*b^(1/2))^(1/2)*x,I)+1/2*f/a/(b*x^4+a)^(1/2)-1/2*f/a^(3/2)*ln((2*a+2*(b*x^4+a)^(1/2)*a^(1/2))/x^2)","C"
551,0,0,261,0.469000," ","int((g*x)^m*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x)","\int \left(f \,x^{3}+e \,x^{2}+d x +c \right) \left(g x \right)^{m} \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int((g*x)^m*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x)","F"
552,0,0,131,0.469000," ","int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x)","\int \left(f \,x^{3}+e \,x^{2}+d x +c \right) \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int((f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x)","F"
553,0,0,161,0.477000," ","int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x)","\int \left(f \,x^{3}+e \,x^{2}+d x +c \right) x^{3} \left(b \,x^{4}+a \right)^{p}\, dx"," ",0,"int(x^3*(f*x^3+e*x^2+d*x+c)*(b*x^4+a)^p,x)","F"
554,1,7,8,0.037000," ","int((x^4+x^3+x^2+x+1)/(-x^5+1),x)","-\ln \left(x -1\right)"," ",0,"-ln(x-1)","A"
555,1,9,8,0.042000," ","int((-32*x^5+48*x^4-72*x^3+108*x^2-162*x+243)/(-64*x^6+729),x)","\frac{\ln \left(2 x +3\right)}{2}"," ",0,"1/2*ln(3+2*x)","A"
556,1,9,8,0.041000," ","int((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729),x)","-\frac{\ln \left(2 x -3\right)}{2}"," ",0,"-1/2*ln(-3+2*x)","A"
557,1,18,6,0.047000," ","int((16*x^4+36*x^2+81)/(-64*x^6+729),x)","-\frac{\ln \left(2 x -3\right)}{12}+\frac{\ln \left(2 x +3\right)}{12}"," ",0,"1/12*ln(2*x+3)-1/12*ln(2*x-3)","B"
558,1,17,16,0.045000," ","int((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{9}"," ",0,"1/9*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))","A"
559,1,39,38,0.051000," ","int((3-2*x)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{486}+\frac{\ln \left(2 x +3\right)}{486}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{972}"," ",0,"-1/972*ln(4*x^2-6*x+9)+1/486*ln(2*x+3)+1/486*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))","A"
560,1,39,38,0.049000," ","int((2*x+3)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{486}-\frac{\ln \left(2 x -3\right)}{486}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{972}"," ",0,"1/486*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/972*ln(4*x^2+6*x+9)-1/486*ln(2*x-3)","A"
561,1,47,46,0.048000," ","int((4*x^2-6*x+9)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{162}-\frac{\ln \left(2 x -3\right)}{324}+\frac{\ln \left(2 x +3\right)}{108}-\frac{\ln \left(4 x^{2}+6 x +9\right)}{324}"," ",0,"1/108*ln(2*x+3)-1/324*ln(4*x^2+6*x+9)+1/162*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/324*ln(2*x-3)","A"
562,1,47,46,0.050000," ","int((4*x^2+6*x+9)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{162}-\frac{\ln \left(2 x -3\right)}{108}+\frac{\ln \left(2 x +3\right)}{324}+\frac{\ln \left(4 x^{2}-6 x +9\right)}{324}"," ",0,"1/324*ln(4*x^2-6*x+9)+1/162*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/324*ln(2*x+3)-1/108*ln(2*x-3)","A"
563,1,39,38,0.049000," ","int((-8*x^3+27)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{54}+\frac{\ln \left(2 x +3\right)}{54}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{108}"," ",0,"-1/108*ln(4*x^2-6*x+9)+1/54*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/54*ln(2*x+3)","A"
564,1,39,38,0.052000," ","int((8*x^3+24*x^2+36*x+27)/(-64*x^6+729),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{54}-\frac{\ln \left(2 x -3\right)}{18}+\frac{\ln \left(4 x^{2}-6 x +9\right)}{36}"," ",0,"1/36*ln(4*x^2-6*x+9)+1/54*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/18*ln(2*x-3)","A"
565,1,85,84,0.056000," ","int((-32*x^5+48*x^4-72*x^3+108*x^2-162*x+243)/(-64*x^6+729)^2,x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{26244}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{8748}-\frac{\ln \left(2 x -3\right)}{17496}+\frac{5 \ln \left(2 x +3\right)}{17496}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{17496}-\frac{\ln \left(4 x^{2}+6 x +9\right)}{17496}-\frac{1}{2916 \left(2 x +3\right)}"," ",0,"-1/17496*ln(4*x^2-6*x+9)+1/26244*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/2916/(2*x+3)+5/17496*ln(2*x+3)-1/17496*ln(4*x^2+6*x+9)+1/8748*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/17496*ln(2*x-3)","A"
566,1,85,84,0.049000," ","int((32*x^5+48*x^4+72*x^3+108*x^2+162*x+243)/(-64*x^6+729)^2,x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{8748}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{26244}-\frac{5 \ln \left(2 x -3\right)}{17496}+\frac{\ln \left(2 x +3\right)}{17496}+\frac{\ln \left(4 x^{2}-6 x +9\right)}{17496}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{17496}-\frac{1}{2916 \left(2 x -3\right)}"," ",0,"1/17496*ln(4*x^2-6*x+9)+1/8748*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/17496*ln(2*x+3)+1/17496*ln(4*x^2+6*x+9)+1/26244*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/2916/(2*x-3)-5/17496*ln(2*x-3)","A"
567,1,68,57,0.056000," ","int((16*x^4+36*x^2+81)/(-64*x^6+729)^2,x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{39366}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{39366}-\frac{\ln \left(2 x -3\right)}{17496}+\frac{\ln \left(2 x +3\right)}{17496}-\frac{1}{17496 \left(2 x +3\right)}-\frac{1}{17496 \left(2 x -3\right)}"," ",0,"1/39366*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/17496/(2*x+3)+1/17496*ln(2*x+3)+1/39366*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/17496/(2*x-3)-1/17496*ln(2*x-3)","A"
568,1,73,74,0.058000," ","int((-16*x^4-24*x^3+54*x+81)/(-64*x^6+729)^2,x)","\frac{x}{17496 x^{2}-26244 x +39366}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{13122}-\frac{\ln \left(2 x -3\right)}{26244}+\frac{\ln \left(2 x +3\right)}{78732}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{157464}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{52488}"," ",0,"1/17496*x/(x^2-3/2*x+9/4)-1/157464*ln(4*x^2-6*x+9)+1/13122*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/78732*ln(2*x+3)+1/52488*ln(4*x^2+6*x+9)-1/26244*ln(2*x-3)","A"
569,1,115,118,0.067000," ","int((3-2*x)/(-64*x^6+729)^2,x)","\frac{x}{944784 x^{2}+1417176 x +2125764}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{4251528}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{472392}-\frac{\ln \left(2 x -3\right)}{4251528}+\frac{\ln \left(2 x +3\right)}{472392}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{944784}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{8503056}-\frac{\frac{x}{4}-\frac{3}{4}}{708588 \left(x^{2}-\frac{3}{2} x +\frac{9}{4}\right)}-\frac{1}{708588 \left(2 x +3\right)}"," ",0,"-1/708588*(1/4*x-3/4)/(x^2-3/2*x+9/4)-1/944784*ln(4*x^2-6*x+9)+1/4251528*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/708588/(2*x+3)+1/472392*ln(2*x+3)+1/944784*x/(x^2+3/2*x+9/4)+1/8503056*ln(4*x^2+6*x+9)+1/472392*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/4251528*ln(2*x-3)","A"
570,1,115,118,0.066000," ","int((2*x+3)/(-64*x^6+729)^2,x)","\frac{x}{944784 x^{2}-1417176 x +2125764}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{472392}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{4251528}-\frac{\ln \left(2 x -3\right)}{472392}+\frac{\ln \left(2 x +3\right)}{4251528}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{8503056}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{944784}+\frac{-\frac{x}{4}-\frac{3}{4}}{708588 x^{2}+1062882 x +1594323}-\frac{1}{708588 \left(2 x -3\right)}"," ",0,"1/944784/(x^2-3/2*x+9/4)*x-1/8503056*ln(4*x^2-6*x+9)+1/472392*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/4251528*ln(2*x+3)+1/708588*(-1/4*x-3/4)/(x^2+3/2*x+9/4)+1/944784*ln(4*x^2+6*x+9)+1/4251528*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/708588/(2*x-3)-1/472392*ln(2*x-3)","A"
571,1,111,112,0.060000," ","int((4*x^2-6*x+9)/(-64*x^6+729)^2,x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{1417176}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{157464}-\frac{\ln \left(2 x -3\right)}{354294}+\frac{\ln \left(2 x +3\right)}{118098}-\frac{\ln \left(4 x^{2}-6 x +9\right)}{944784}-\frac{5 \ln \left(4 x^{2}+6 x +9\right)}{2834352}-\frac{1}{157464 \left(2 x +3\right)}-\frac{-3 x -\frac{9}{4}}{708588 \left(x^{2}+\frac{3}{2} x +\frac{9}{4}\right)}-\frac{1}{472392 \left(2 x -3\right)}"," ",0,"-1/944784*ln(4*x^2-6*x+9)+1/1417176*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/157464/(2*x+3)+1/118098*ln(2*x+3)-1/708588*(-3*x-9/4)/(x^2+3/2*x+9/4)-5/2834352*ln(4*x^2+6*x+9)+1/157464*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/472392/(2*x-3)-1/354294*ln(2*x-3)","A"
572,1,111,112,0.061000," ","int((4*x^2+6*x+9)/(-64*x^6+729)^2,x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{157464}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{1417176}-\frac{\ln \left(2 x -3\right)}{118098}+\frac{\ln \left(2 x +3\right)}{354294}+\frac{5 \ln \left(4 x^{2}-6 x +9\right)}{2834352}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{944784}+\frac{3 x -\frac{9}{4}}{708588 x^{2}-1062882 x +1594323}-\frac{1}{472392 \left(2 x +3\right)}-\frac{1}{157464 \left(2 x -3\right)}"," ",0,"1/708588*(3*x-9/4)/(x^2-3/2*x+9/4)+5/2834352*ln(4*x^2-6*x+9)+1/157464*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/472392/(2*x+3)+1/354294*ln(2*x+3)+1/944784*ln(4*x^2+6*x+9)+1/1417176*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/157464/(2*x-3)-1/118098*ln(2*x-3)","A"
573,1,102,87,0.062000," ","int((-8*x^3+27)/(-64*x^6+729)^2,x)","\frac{7 \sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{472392}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{157464}-\frac{\ln \left(2 x -3\right)}{157464}+\frac{7 \ln \left(2 x +3\right)}{472392}-\frac{7 \ln \left(4 x^{2}-6 x +9\right)}{944784}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{314928}-\frac{-\frac{3 x}{4}-\frac{9}{8}}{118098 \left(x^{2}-\frac{3}{2} x +\frac{9}{4}\right)}-\frac{1}{78732 \left(2 x +3\right)}"," ",0,"-1/118098*(-3/4*x-9/8)/(x^2-3/2*x+9/4)-7/944784*ln(4*x^2-6*x+9)+7/472392*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-1/78732/(2*x+3)+7/472392*ln(2*x+3)+1/314928*ln(4*x^2+6*x+9)+1/157464*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/157464*ln(2*x-3)","A"
574,1,102,103,0.060000," ","int((8*x^3+24*x^2+36*x+27)/(-64*x^6+729)^2,x)","\frac{11 \sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{472392}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{472392}-\frac{7 \ln \left(2 x -3\right)}{157464}+\frac{\ln \left(2 x +3\right)}{472392}+\frac{17 \ln \left(4 x^{2}-6 x +9\right)}{944784}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{314928}+\frac{\frac{9 x}{4}-\frac{27}{8}}{118098 x^{2}-177147 x +\frac{531441}{2}}-\frac{1}{26244 \left(2 x -3\right)}"," ",0,"1/118098*(9/4*x-27/8)/(x^2-3/2*x+9/4)+17/944784*ln(4*x^2-6*x+9)+11/472392*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))+1/472392*ln(2*x+3)+1/314928*ln(4*x^2+6*x+9)-1/472392*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/26244/(2*x-3)-7/157464*ln(2*x-3)","A"
575,1,76,75,0.050000," ","int(x*(-2*x^3+27)/(-64*x^6+729),x)","\frac{5 \sqrt{3}\, \arctan \left(\frac{\left(8 x -6\right) \sqrt{3}}{18}\right)}{288}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(8 x +6\right) \sqrt{3}}{18}\right)}{96}-\frac{\ln \left(2 x -3\right)}{96}-\frac{5 \ln \left(2 x +3\right)}{288}+\frac{5 \ln \left(4 x^{2}-6 x +9\right)}{576}+\frac{\ln \left(4 x^{2}+6 x +9\right)}{192}"," ",0,"5/576*ln(4*x^2-6*x+9)+5/288*3^(1/2)*arctan(1/18*(8*x-6)*3^(1/2))-5/288*ln(2*x+3)+1/192*ln(4*x^2+6*x+9)-1/96*3^(1/2)*arctan(1/18*(8*x+6)*3^(1/2))-1/96*ln(2*x-3)","A"
576,0,0,164,0.648000," ","int((c*x)^m*(d+e*x^n+f*x^(2*n)+g*x^(3*n))/(b*x^n+a),x)","\int \frac{\left(e \,x^{n}+f \,x^{2 n}+g \,x^{3 n}+d \right) \left(c x \right)^{m}}{b \,x^{n}+a}\, dx"," ",0,"int((c*x)^m*(d+e*x^n+f*x^(2*n)+g*x^(3*n))/(b*x^n+a),x)","F"
577,1,130,82,0.063000," ","int((c+d*x^(n-1))*(b*x^n+a)^3,x)","\frac{3 a^{2} b c x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{3 a \,b^{2} c x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}+\frac{b^{3} c x \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n +1}+a^{3} c x +\frac{a^{3} d \,{\mathrm e}^{n \ln \left(x \right)}}{n}+\frac{3 a^{2} b d \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n}+\frac{a \,b^{2} d \,{\mathrm e}^{3 n \ln \left(x \right)}}{n}+\frac{b^{3} d \,{\mathrm e}^{4 n \ln \left(x \right)}}{4 n}"," ",0,"a^3*c*x+a^3*d/n*exp(n*ln(x))+a*b^2*d/n*exp(n*ln(x))^3+b^3*c/(3*n+1)*x*exp(n*ln(x))^3+1/4*b^3*d/n*exp(n*ln(x))^4+3/2*a^2*d*b/n*exp(n*ln(x))^2+3*a*b^2*c/(2*n+1)*x*exp(n*ln(x))^2+3*a^2*c*b/(n+1)*x*exp(n*ln(x))","A"
578,1,87,59,0.063000," ","int((c+d*x^(n-1))*(b*x^n+a)^2,x)","\frac{2 a b c x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+\frac{b^{2} c x \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n +1}+a^{2} c x +\frac{a^{2} d \,{\mathrm e}^{n \ln \left(x \right)}}{n}+\frac{a b d \,{\mathrm e}^{2 n \ln \left(x \right)}}{n}+\frac{b^{2} d \,{\mathrm e}^{3 n \ln \left(x \right)}}{3 n}"," ",0,"a^2*c*x+a^2*d/n*exp(n*ln(x))+b*d*a/n*exp(n*ln(x))^2+c*b^2/(2*n+1)*x*exp(n*ln(x))^2+1/3*b^2*d/n*exp(n*ln(x))^3+2*a*b*c/(n+1)*x*exp(n*ln(x))","A"
579,1,45,39,0.056000," ","int((c+d*x^(n-1))*(b*x^n+a),x)","\frac{b c x \,{\mathrm e}^{n \ln \left(x \right)}}{n +1}+a c x +\frac{a d \,{\mathrm e}^{n \ln \left(x \right)}}{n}+\frac{b d \,{\mathrm e}^{2 n \ln \left(x \right)}}{2 n}"," ",0,"a*c*x+a*d/n*exp(n*ln(x))+b*c/(n+1)*x*exp(n*ln(x))+1/2*b*d/n*exp(n*ln(x))^2","A"
580,1,13,12,0.043000," ","int(c+d*x^(n-1),x)","c x +\frac{d \,x^{n}}{n}"," ",0,"c*x+d*x^n/n","A"
581,0,0,44,0.780000," ","int((c+d*x^(n-1))/(b*x^n+a),x)","\int \frac{d \,x^{n -1}+c}{b \,x^{n}+a}\, dx"," ",0,"int((c+d*x^(n-1))/(b*x^n+a),x)","F"
582,0,0,46,1.034000," ","int((d*x^(n-1)+c)/(b*x^n+a)^2,x)","\int \frac{d \,x^{n -1}+c}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((d*x^(n-1)+c)/(b*x^n+a)^2,x)","F"
583,0,0,46,0.707000," ","int((d*x^(n-1)+c)/(b*x^n+a)^3,x)","\int \frac{d \,x^{n -1}+c}{\left(b \,x^{n}+a \right)^{3}}\, dx"," ",0,"int((d*x^(n-1)+c)/(b*x^n+a)^3,x)","F"
584,0,0,289,0.695000," ","int((c*x)^m*(e*x^n+f*x^(2*n)+g*x^(3*n)+d)/(b*x^n+a)^(1/2),x)","\int \frac{\left(e \,x^{n}+f \,x^{2 n}+g \,x^{3 n}+d \right) \left(c x \right)^{m}}{\sqrt{b \,x^{n}+a}}\, dx"," ",0,"int((c*x)^m*(e*x^n+f*x^(2*n)+g*x^(3*n)+d)/(b*x^n+a)^(1/2),x)","F"
585,0,0,39,0.691000," ","int((-a*h*x^(-1+1/4*n)+b*f*x^(1/2*n-1)+b*g*x^(n-1)+b*h*x^(-1+5/4*n))/(b*x^n+a)^(3/2),x)","\int \frac{-a h \,x^{\frac{n}{4}-1}+b f \,x^{\frac{n}{2}-1}+b g \,x^{n -1}+b h \,x^{\frac{5 n}{4}-1}}{\left(b \,x^{n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((-a*h*x^(-1+1/4*n)+b*f*x^(1/2*n-1)+b*g*x^(n-1)+b*h*x^(-1+5/4*n))/(b*x^n+a)^(3/2),x)","F"
586,0,0,281,0.740000," ","int((c*x)^m*(g*x^3+f*x^2+e*x+d)*(b*x^n+a)^p,x)","\int \left(g \,x^{3}+f \,x^{2}+e x +d \right) \left(c x \right)^{m} \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((c*x)^m*(g*x^3+f*x^2+e*x+d)*(b*x^n+a)^p,x)","F"
587,0,0,305,0.664000," ","int((c*x)^m*(b*x^n+a)^p*(e*x^n+f*x^(2*n)+g*x^(3*n)+d),x)","\int \left(e \,x^{n}+f \,x^{2 n}+g \,x^{3 n}+d \right) \left(c x \right)^{m} \left(b \,x^{n}+a \right)^{p}\, dx"," ",0,"int((c*x)^m*(b*x^n+a)^p*(e*x^n+f*x^(2*n)+g*x^(3*n)+d),x)","F"
588,0,0,150,0.651000," ","int((c+d*x^(1/2*n)+e*x^n+f*x^(3/2*n))/(b*x^n+a)^2,x)","\int \frac{d \,x^{\frac{n}{2}}+e \,x^{n}+f \,x^{\frac{3 n}{2}}+c}{\left(b \,x^{n}+a \right)^{2}}\, dx"," ",0,"int((c+d*x^(1/2*n)+e*x^n+f*x^(3/2*n))/(b*x^n+a)^2,x)","F"
589,1,21,20,0.052000," ","int((a*c+2*(a*d+b*c)*x^2+3*b*d*x^4)/(b*x^2+a)^(1/2)/(d*x^2+c)^(1/2),x)","\sqrt{b \,x^{2}+a}\, \sqrt{d \,x^{2}+c}\, x"," ",0,"x*(b*x^2+a)^(1/2)*(d*x^2+c)^(1/2)","A"
590,-1,0,73,180.000000," ","int((x^3+1)/(-x^4+1)/(x^4+1)^(1/4),x)","\int \frac{x^{3}+1}{\left(-x^{4}+1\right) \left(x^{4}+1\right)^{\frac{1}{4}}}\, dx"," ",0,"int((x^3+1)/(-x^4+1)/(x^4+1)^(1/4),x)","F"
591,0,0,28,1.082000," ","int((b*x^n+a)^((-n-1)/n)*(d*x^n+c)^((-n-1)/n)*(a*c-b*d*x^(2*n)),x)","\int \left(-b d \,x^{2 n}+a c \right) \left(b \,x^{n}+a \right)^{\frac{-n -1}{n}} \left(d \,x^{n}+c \right)^{\frac{-n -1}{n}}\, dx"," ",0,"int((b*x^n+a)^((-n-1)/n)*(d*x^n+c)^((-n-1)/n)*(a*c-b*d*x^(2*n)),x)","F"
592,1,138,46,0.575000," ","int((h*x)^(-n*p-n-1)*(b*x^n+a)^p*(d*x^n+c)^p*(-b*d*x^(2*n)+a*c),x)","-\frac{\left(a d \,x^{n}+b c \,x^{n}+b d \,x^{2 n}+a c \right) x \left(b \,x^{n}+a \right)^{p} \left(d \,x^{n}+c \right)^{p} {\mathrm e}^{-\frac{\left(n p +n +1\right) \left(-i \pi  \,\mathrm{csgn}\left(i h \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i h x \right)+i \pi  \,\mathrm{csgn}\left(i h \right) \mathrm{csgn}\left(i h x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i h x \right)^{2}-i \pi  \mathrm{csgn}\left(i h x \right)^{3}+2 \ln \left(h \right)+2 \ln \left(x \right)\right)}{2}}}{\left(p +1\right) n}"," ",0,"-(b*x^n+a)^p*exp(-1/2*(n*p+n+1)*(-I*Pi*csgn(I*h*x)^3+I*Pi*csgn(I*h*x)^2*csgn(I*h)+I*Pi*csgn(I*h*x)^2*csgn(I*x)-I*Pi*csgn(I*h*x)*csgn(I*h)*csgn(I*x)+2*ln(h)+2*ln(x)))*(b*d*(x^n)^2+a*d*x^n+b*c*x^n+a*c)*x/(p+1)/n*(d*x^n+c)^p","C"
593,1,52,31,0.171000," ","int((b*x^n+a)^p*(d*x^n+c)^p*(e+(a*d+b*c)*e*(n*p+n+1)*x^n/a/c+b*d*e*(2*n*p+2*n+1)*x^(2*n)/a/c),x)","\frac{\left(a d \,x^{n}+b c \,x^{n}+b d \,x^{2 n}+a c \right) e x \left(b \,x^{n}+a \right)^{p} \left(d \,x^{n}+c \right)^{p}}{a c}"," ",0,"(b*x^n+a)^p*(b*d*(x^n)^2+a*d*x^n+b*c*x^n+a*c)*e*x/a/c*(d*x^n+c)^p","A"
594,1,136,45,0.502000," ","int((h*x)^m*(b*x^n+a)^p*(d*x^n+c)^p*(e+(a*d+b*c)*e*(n*p+m+n+1)*x^n/a/c/(m+1)+b*d*e*(2*n*p+m+2*n+1)*x^(2*n)/a/c/(m+1)),x)","\frac{\left(a d \,x^{n}+b c \,x^{n}+b d \,x^{2 n}+a c \right) e x \left(b \,x^{n}+a \right)^{p} \left(d \,x^{n}+c \right)^{p} {\mathrm e}^{\frac{\left(-i \pi  \,\mathrm{csgn}\left(i h \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i h x \right)+i \pi  \,\mathrm{csgn}\left(i h \right) \mathrm{csgn}\left(i h x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i h x \right)^{2}-i \pi  \mathrm{csgn}\left(i h x \right)^{3}+2 \ln \left(h \right)+2 \ln \left(x \right)\right) m}{2}}}{\left(m +1\right) a c}"," ",0,"(b*x^n+a)^p*exp(1/2*m*(-I*Pi*csgn(I*h)*csgn(I*x)*csgn(I*h*x)+I*Pi*csgn(I*h)*csgn(I*h*x)^2+I*Pi*csgn(I*x)*csgn(I*h*x)^2-I*Pi*csgn(I*h*x)^3+2*ln(h)+2*ln(x)))*(b*d*(x^n)^2+a*d*x^n+b*c*x^n+a*c)*e*x/a/c/(m+1)*(d*x^n+c)^p","C"