1,1,39,44,0.006000," ","int((b*x^6+a*x^3)^(5/3),x)","-\frac{\left(b \,x^{3}+a \right) \left(-8 b \,x^{3}+3 a \right) \left(b \,x^{6}+a \,x^{3}\right)^{\frac{5}{3}}}{88 b^{2} x^{5}}"," ",0,"-1/88*(b*x^3+a)*(-8*b*x^3+3*a)*(b*x^6+a*x^3)^(5/3)/b^2/x^5","A"
2,1,29,21,0.004000," ","int((b*x^6+a*x^3)^(2/3),x)","\frac{\left(b \,x^{3}+a \right) \left(b \,x^{6}+a \,x^{3}\right)^{\frac{2}{3}}}{5 b \,x^{2}}"," ",0,"1/5*(b*x^3+a)/b/x^2*(b*x^6+a*x^3)^(2/3)","A"
3,1,27,21,0.004000," ","int(1/(b*x^6+a*x^3)^(2/3),x)","-\frac{\left(b \,x^{3}+a \right) x}{\left(b \,x^{6}+a \,x^{3}\right)^{\frac{2}{3}} a}"," ",0,"-x*(b*x^3+a)/a/(b*x^6+a*x^3)^(2/3)","A"
4,1,46,65,0.004000," ","int(1/(b*x^6+a*x^3)^(5/3),x)","-\frac{\left(b \,x^{3}+a \right) \left(-9 b^{2} x^{6}-6 b \,x^{3} a +a^{2}\right) x}{4 \left(b \,x^{6}+a \,x^{3}\right)^{\frac{5}{3}} a^{3}}"," ",0,"-1/4*x*(b*x^3+a)*(-9*b^2*x^6-6*a*b*x^3+a^2)/a^3/(b*x^6+a*x^3)^(5/3)","A"
5,1,38,39,0.007000," ","int(1/(x^6-x^3),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{\ln \left(x^{2}+x +1\right)}{6}+\frac{1}{2 x^{2}}"," ",0,"-1/6*ln(x^2+x+1)-1/3*arctan(1/3*(2*x+1)*3^(1/2))*3^(1/2)+1/3*ln(x-1)+1/2/x^2","A"
6,1,36,53,0.003000," ","int(x^5*((b*x^3+a)^2)^(1/2),x)","\frac{\left(2 b \,x^{3}+3 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x^{6}}{18 b \,x^{3}+18 a}"," ",0,"1/18*x^6*(2*b*x^3+3*a)*((b*x^3+a)^2)^(1/2)/(b*x^3+a)","A"
7,1,36,53,0.001000," ","int(x^4*((b*x^3+a)^2)^(1/2),x)","\frac{\left(5 b \,x^{3}+8 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x^{5}}{40 b \,x^{3}+40 a}"," ",0,"1/40*x^5*(5*b*x^3+8*a)*((b*x^3+a)^2)^(1/2)/(b*x^3+a)","A"
8,1,36,53,0.003000," ","int(x^3*((b*x^3+a)^2)^(1/2),x)","\frac{\left(4 b \,x^{3}+7 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x^{4}}{28 b \,x^{3}+28 a}"," ",0,"1/28*x^4*(4*b*x^3+7*a)*((b*x^3+a)^2)^(1/2)/(b*x^3+a)","A"
9,1,35,23,0.003000," ","int(x^2*((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+2 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x^{3}}{6 b \,x^{3}+6 a}"," ",0,"1/6*x^3*(b*x^3+2*a)*((b*x^3+a)^2)^(1/2)/(b*x^3+a)","A"
10,1,36,53,0.007000," ","int(x*((b*x^3+a)^2)^(1/2),x)","\frac{\left(2 b \,x^{3}+5 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x^{2}}{10 b \,x^{3}+10 a}"," ",0,"1/10*x^2*(2*b*x^3+5*a)*((b*x^3+a)^2)^(1/2)/(b*x^3+a)","A"
11,1,33,50,0.001000," ","int(((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+4 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x}{4 b \,x^{3}+4 a}"," ",0,"1/4*x*(b*x^3+4*a)*((b*x^3+a)^2)^(1/2)/(b*x^3+a)","A"
12,1,34,51,0.010000," ","int(((b*x^3+a)^2)^(1/2)/x,x)","\frac{\sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(b \,x^{3}+3 a \ln \left(x \right)\right)}{3 b \,x^{3}+3 a}"," ",0,"1/3*((b*x^3+a)^2)^(1/2)*(b*x^3+3*a*ln(x))/(b*x^3+a)","A"
13,1,36,53,0.001000," ","int(((b*x^3+a)^2)^(1/2)/x^2,x)","-\frac{\left(-b \,x^{3}+2 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{2 \left(b \,x^{3}+a \right) x}"," ",0,"-1/2*(-b*x^3+2*a)*((b*x^3+a)^2)^(1/2)/x/(b*x^3+a)","A"
14,1,34,50,0.003000," ","int(((b*x^3+a)^2)^(1/2)/x^3,x)","-\frac{\left(-2 b \,x^{3}+a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{2 \left(b \,x^{3}+a \right) x^{2}}"," ",0,"-1/2*(-2*b*x^3+a)*((b*x^3+a)^2)^(1/2)/x^2/(b*x^3+a)","A"
15,1,38,51,0.009000," ","int(((b*x^3+a)^2)^(1/2)/x^4,x)","\frac{\sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(3 b \,x^{3} \ln \left(x \right)-a \right)}{3 \left(b \,x^{3}+a \right) x^{3}}"," ",0,"1/3*((b*x^3+a)^2)^(1/2)*(3*b*ln(x)*x^3-a)/(b*x^3+a)/x^3","A"
16,1,34,53,0.003000," ","int(((b*x^3+a)^2)^(1/2)/x^5,x)","-\frac{\left(4 b \,x^{3}+a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{4 \left(b \,x^{3}+a \right) x^{4}}"," ",0,"-1/4*(4*b*x^3+a)*((b*x^3+a)^2)^(1/2)/x^4/(b*x^3+a)","A"
17,1,36,53,0.003000," ","int(((b*x^3+a)^2)^(1/2)/x^6,x)","-\frac{\left(5 b \,x^{3}+2 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{10 \left(b \,x^{3}+a \right) x^{5}}"," ",0,"-1/10*(5*b*x^3+2*a)*((b*x^3+a)^2)^(1/2)/x^5/(b*x^3+a)","A"
18,1,34,53,0.003000," ","int(((b*x^3+a)^2)^(1/2)/x^7,x)","-\frac{\left(2 b \,x^{3}+a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{6 \left(b \,x^{3}+a \right) x^{6}}"," ",0,"-1/6*(2*b*x^3+a)*((b*x^3+a)^2)^(1/2)/x^6/(b*x^3+a)","A"
19,1,36,53,0.003000," ","int(((b*x^3+a)^2)^(1/2)/x^8,x)","-\frac{\left(7 b \,x^{3}+4 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{28 \left(b \,x^{3}+a \right) x^{7}}"," ",0,"-1/28*(7*b*x^3+4*a)*((b*x^3+a)^2)^(1/2)/x^7/(b*x^3+a)","A"
20,1,36,53,0.003000," ","int(((b*x^3+a)^2)^(1/2)/x^9,x)","-\frac{\left(8 b \,x^{3}+5 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{40 \left(b \,x^{3}+a \right) x^{8}}"," ",0,"-1/40*(8*b*x^3+5*a)*((b*x^3+a)^2)^(1/2)/x^8/(b*x^3+a)","A"
21,1,36,53,0.004000," ","int(((b*x^3+a)^2)^(1/2)/x^10,x)","-\frac{\left(3 b \,x^{3}+2 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{18 \left(b \,x^{3}+a \right) x^{9}}"," ",0,"-1/18*(3*b*x^3+2*a)*((b*x^3+a)^2)^(1/2)/x^9/(b*x^3+a)","A"
22,1,36,53,0.004000," ","int(((b*x^3+a)^2)^(1/2)/x^11,x)","-\frac{\left(10 b \,x^{3}+7 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}}{70 \left(b \,x^{3}+a \right) x^{10}}"," ",0,"-1/70*(10*b*x^3+7*a)*((b*x^3+a)^2)^(1/2)/x^10/(b*x^3+a)","A"
23,1,58,115,0.007000," ","int(x^9*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(1040 b^{3} x^{9}+3705 a \,b^{2} x^{6}+4560 a^{2} b \,x^{3}+1976 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{10}}{19760 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/19760*x^10*(1040*b^3*x^9+3705*a*b^2*x^6+4560*a^2*b*x^3+1976*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
24,1,58,80,0.008000," ","int(x^8*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(10 b^{3} x^{9}+36 a \,b^{2} x^{6}+45 a^{2} b \,x^{3}+20 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{9}}{180 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/180*x^9*(10*b^3*x^9+36*a*b^2*x^6+45*a^2*b*x^3+20*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
25,1,58,115,0.007000," ","int(x^7*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(616 b^{3} x^{9}+2244 a \,b^{2} x^{6}+2856 a^{2} b \,x^{3}+1309 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{8}}{10472 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/10472*x^8*(616*b^3*x^9+2244*a*b^2*x^6+2856*a^2*b*x^3+1309*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
26,1,58,115,0.008000," ","int(x^6*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(455 b^{3} x^{9}+1680 a \,b^{2} x^{6}+2184 a^{2} b \,x^{3}+1040 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{7}}{7280 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/7280*x^7*(455*b^3*x^9+1680*a*b^2*x^6+2184*a^2*b*x^3+1040*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
27,1,58,52,0.007000," ","int(x^5*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(4 b^{3} x^{9}+15 a \,b^{2} x^{6}+20 a^{2} b \,x^{3}+10 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{6}}{60 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/60*x^6*(4*b^3*x^9+15*a*b^2*x^6+20*a^2*b*x^3+10*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
28,1,58,115,0.007000," ","int(x^4*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(220 b^{3} x^{9}+840 a \,b^{2} x^{6}+1155 a^{2} b \,x^{3}+616 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{5}}{3080 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/3080*x^5*(220*b^3*x^9+840*a*b^2*x^6+1155*a^2*b*x^3+616*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
29,1,58,115,0.007000," ","int(x^3*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(140 b^{3} x^{9}+546 a \,b^{2} x^{6}+780 a^{2} b \,x^{3}+455 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{4}}{1820 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/1820*x^4*(140*b^3*x^9+546*a*b^2*x^6+780*a^2*b*x^3+455*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
30,1,57,32,0.007000," ","int(x^2*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(b^{3} x^{9}+4 a \,b^{2} x^{6}+6 a^{2} b \,x^{3}+4 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{3}}{12 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/12*x^3*(b^3*x^9+4*a*b^2*x^6+6*a^2*b*x^3+4*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
31,1,58,115,0.005000," ","int(x*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(40 b^{3} x^{9}+165 a \,b^{2} x^{6}+264 a^{2} b \,x^{3}+220 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x^{2}}{440 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/440*x^2*(40*b^3*x^9+165*a*b^2*x^6+264*a^2*b*x^3+220*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
32,1,56,148,0.003000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(14 b^{3} x^{9}+60 a \,b^{2} x^{6}+105 a^{2} b \,x^{3}+140 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x}{140 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/140*x*(14*b^3*x^9+60*a*b^2*x^6+105*a^2*b*x^3+140*a^3)*((b*x^3+a)^2)^(3/2)/(b*x^3+a)^3","A"
33,1,57,112,0.010000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} \left(2 b^{3} x^{9}+9 a \,b^{2} x^{6}+18 a^{2} b \,x^{3}+18 a^{3} \ln \left(x \right)\right)}{18 \left(b \,x^{3}+a \right)^{3}}"," ",0,"1/18*((b*x^3+a)^2)^(3/2)*(2*b^3*x^9+9*a*b^2*x^6+18*a^2*b*x^3+18*a^3*ln(x))/(b*x^3+a)^3","A"
34,1,58,115,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^2,x)","-\frac{\left(-5 b^{3} x^{9}-24 a \,b^{2} x^{6}-60 a^{2} b \,x^{3}+40 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{40 \left(b \,x^{3}+a \right)^{3} x}"," ",0,"-1/40*(-5*b^3*x^9-24*a*b^2*x^6-60*a^2*b*x^3+40*a^3)*((b*x^3+a)^2)^(3/2)/x/(b*x^3+a)^3","A"
35,1,58,113,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^3,x)","-\frac{\left(-4 b^{3} x^{9}-21 a \,b^{2} x^{6}-84 a^{2} b \,x^{3}+14 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{28 \left(b \,x^{3}+a \right)^{3} x^{2}}"," ",0,"-1/28*(-4*b^3*x^9-21*a*b^2*x^6-84*a^2*b*x^3+14*a^3)*((b*x^3+a)^2)^(3/2)/x^2/(b*x^3+a)^3","A"
36,1,59,113,0.010000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^4,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} \left(b^{3} x^{9}+6 a \,b^{2} x^{6}+18 a^{2} b \,x^{3} \ln \left(x \right)-2 a^{3}\right)}{6 \left(b \,x^{3}+a \right)^{3} x^{3}}"," ",0,"1/6*((b*x^3+a)^2)^(3/2)*(b^3*x^9+6*a*b^2*x^6+18*a^2*b*ln(x)*x^3-2*a^3)/(b*x^3+a)^3/x^3","A"
37,1,58,115,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^5,x)","-\frac{\left(-4 b^{3} x^{9}-30 a \,b^{2} x^{6}+60 a^{2} b \,x^{3}+5 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{20 \left(b \,x^{3}+a \right)^{3} x^{4}}"," ",0,"-1/20*(-4*b^3*x^9-30*a*b^2*x^6+60*a^2*b*x^3+5*a^3)*((b*x^3+a)^2)^(3/2)/x^4/(b*x^3+a)^3","A"
38,1,58,113,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^6,x)","-\frac{\left(-5 b^{3} x^{9}-60 a \,b^{2} x^{6}+30 a^{2} b \,x^{3}+4 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{20 \left(b \,x^{3}+a \right)^{3} x^{5}}"," ",0,"-1/20*(-5*b^3*x^9-60*a*b^2*x^6+30*a^2*b*x^3+4*a^3)*((b*x^3+a)^2)^(3/2)/x^5/(b*x^3+a)^3","A"
39,1,60,114,0.012000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^7,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} \left(2 b^{3} x^{9}+18 a \,b^{2} x^{6} \ln \left(x \right)-6 a^{2} b \,x^{3}-a^{3}\right)}{6 \left(b \,x^{3}+a \right)^{3} x^{6}}"," ",0,"1/6*((b*x^3+a)^2)^(3/2)*(2*b^3*x^9+18*a*b^2*ln(x)*x^6-6*a^2*b*x^3-a^3)/(b*x^3+a)^3/x^6","A"
40,1,58,115,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^8,x)","-\frac{\left(-14 b^{3} x^{9}+84 a \,b^{2} x^{6}+21 a^{2} b \,x^{3}+4 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{28 \left(b \,x^{3}+a \right)^{3} x^{7}}"," ",0,"-1/28*(-14*b^3*x^9+84*a*b^2*x^6+21*a^2*b*x^3+4*a^3)*((b*x^3+a)^2)^(3/2)/x^7/(b*x^3+a)^3","A"
41,1,58,112,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^9,x)","-\frac{\left(-40 b^{3} x^{9}+60 a \,b^{2} x^{6}+24 a^{2} b \,x^{3}+5 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{40 \left(b \,x^{3}+a \right)^{3} x^{8}}"," ",0,"-1/40*(-40*b^3*x^9+60*a*b^2*x^6+24*a^2*b*x^3+5*a^3)*((b*x^3+a)^2)^(3/2)/x^8/(b*x^3+a)^3","A"
42,1,60,113,0.013000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^10,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} \left(18 b^{3} x^{9} \ln \left(x \right)-18 a \,b^{2} x^{6}-9 a^{2} b \,x^{3}-2 a^{3}\right)}{18 \left(b \,x^{3}+a \right)^{3} x^{9}}"," ",0,"1/18*((b*x^3+a)^2)^(3/2)*(18*b^3*ln(x)*x^9-18*a*b^2*x^6-9*a^2*b*x^3-2*a^3)/(b*x^3+a)^3/x^9","A"
43,1,58,115,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^11,x)","-\frac{\left(140 b^{3} x^{9}+105 a \,b^{2} x^{6}+60 a^{2} b \,x^{3}+14 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{140 \left(b \,x^{3}+a \right)^{3} x^{10}}"," ",0,"-1/140*(140*b^3*x^9+105*a*b^2*x^6+60*a^2*b*x^3+14*a^3)*((b*x^3+a)^2)^(3/2)/x^10/(b*x^3+a)^3","A"
44,1,58,115,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^12,x)","-\frac{\left(220 b^{3} x^{9}+264 a \,b^{2} x^{6}+165 a^{2} b \,x^{3}+40 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{440 \left(b \,x^{3}+a \right)^{3} x^{11}}"," ",0,"-1/440*(220*b^3*x^9+264*a*b^2*x^6+165*a^2*b*x^3+40*a^3)*((b*x^3+a)^2)^(3/2)/x^11/(b*x^3+a)^3","A"
45,1,56,28,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^13,x)","-\frac{\left(4 b^{3} x^{9}+6 a \,b^{2} x^{6}+4 a^{2} b \,x^{3}+a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{12 \left(b \,x^{3}+a \right)^{3} x^{12}}"," ",0,"-1/12*(4*b^3*x^9+6*a*b^2*x^6+4*a^2*b*x^3+a^3)*((b*x^3+a)^2)^(3/2)/x^12/(b*x^3+a)^3","A"
46,1,58,115,0.010000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^14,x)","-\frac{\left(455 b^{3} x^{9}+780 a \,b^{2} x^{6}+546 a^{2} b \,x^{3}+140 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{1820 \left(b \,x^{3}+a \right)^{3} x^{13}}"," ",0,"-1/1820*(455*b^3*x^9+780*a*b^2*x^6+546*a^2*b*x^3+140*a^3)*((b*x^3+a)^2)^(3/2)/x^13/(b*x^3+a)^3","A"
47,1,58,115,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^15,x)","-\frac{\left(616 b^{3} x^{9}+1155 a \,b^{2} x^{6}+840 a^{2} b \,x^{3}+220 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{3080 \left(b \,x^{3}+a \right)^{3} x^{14}}"," ",0,"-1/3080*(616*b^3*x^9+1155*a*b^2*x^6+840*a^2*b*x^3+220*a^3)*((b*x^3+a)^2)^(3/2)/x^14/(b*x^3+a)^3","A"
48,1,58,58,0.012000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^16,x)","-\frac{\left(10 b^{3} x^{9}+20 a \,b^{2} x^{6}+15 a^{2} b \,x^{3}+4 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{60 \left(b \,x^{3}+a \right)^{3} x^{15}}"," ",0,"-1/60*(10*b^3*x^9+20*a*b^2*x^6+15*a^2*b*x^3+4*a^3)*((b*x^3+a)^2)^(3/2)/x^15/(b*x^3+a)^3","A"
49,1,58,115,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(3/2)/x^17,x)","-\frac{\left(1040 b^{3} x^{9}+2184 a \,b^{2} x^{6}+1680 a^{2} b \,x^{3}+455 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}}}{7280 \left(b \,x^{3}+a \right)^{3} x^{16}}"," ",0,"-1/7280*(1040*b^3*x^9+2184*a*b^2*x^6+1680*a^2*b*x^3+455*a^3)*((b*x^3+a)^2)^(3/2)/x^16/(b*x^3+a)^3","A"
50,1,80,177,0.013000," ","int(x^13*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(71162 b^{5} x^{15}+396865 a \,b^{4} x^{12}+897260 a^{2} b^{3} x^{9}+1031849 a^{3} b^{2} x^{6}+606970 a^{4} b \,x^{3}+147407 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{14}}{2063698 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/2063698*x^14*(71162*b^5*x^15+396865*a*b^4*x^12+897260*a^2*b^3*x^9+1031849*a^3*b^2*x^6+606970*a^4*b*x^3+147407*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
51,1,80,177,0.010000," ","int(x^12*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(54340 b^{5} x^{15}+304304 a \,b^{4} x^{12}+691600 a^{2} b^{3} x^{9}+800800 a^{3} b^{2} x^{6}+475475 a^{4} b \,x^{3}+117040 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{13}}{1521520 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/1521520*x^13*(54340*b^5*x^15+304304*a*b^4*x^12+691600*a^2*b^3*x^9+800800*a^3*b^2*x^6+475475*a^4*b*x^3+117040*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
52,1,80,108,0.012000," ","int(x^11*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(56 b^{5} x^{15}+315 a \,b^{4} x^{12}+720 a^{2} b^{3} x^{9}+840 a^{3} b^{2} x^{6}+504 a^{4} b \,x^{3}+126 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{12}}{1512 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/1512*x^12*(56*b^5*x^15+315*a*b^4*x^12+720*a^2*b^3*x^9+840*a^3*b^2*x^6+504*a^4*b*x^3+126*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
53,1,80,177,0.010000," ","int(x^10*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(30107 b^{5} x^{15}+170170 a \,b^{4} x^{12}+391391 a^{2} b^{3} x^{9}+460460 a^{3} b^{2} x^{6}+279565 a^{4} b \,x^{3}+71162 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{11}}{782782 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/782782*x^11*(30107*b^5*x^15+170170*a*b^4*x^12+391391*a^2*b^3*x^9+460460*a^3*b^2*x^6+279565*a^4*b*x^3+71162*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
54,1,80,177,0.008000," ","int(x^9*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(21736 b^{5} x^{15}+123500 a \,b^{4} x^{12}+286000 a^{2} b^{3} x^{9}+339625 a^{3} b^{2} x^{6}+209000 a^{4} b \,x^{3}+54340 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{10}}{543400 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/543400*x^10*(21736*b^5*x^15+123500*a*b^4*x^12+286000*a^2*b^3*x^9+339625*a^3*b^2*x^6+209000*a^4*b*x^3+54340*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
55,1,80,80,0.009000," ","int(x^8*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(21 b^{5} x^{15}+120 a \,b^{4} x^{12}+280 a^{2} b^{3} x^{9}+336 a^{3} b^{2} x^{6}+210 a^{4} b \,x^{3}+56 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{9}}{504 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/504*x^9*(21*b^5*x^15+120*a*b^4*x^12+280*a^2*b^3*x^9+336*a^3*b^2*x^6+210*a^4*b*x^3+56*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
56,1,80,177,0.008000," ","int(x^7*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(10472 b^{5} x^{15}+60214 a \,b^{4} x^{12}+141680 a^{2} b^{3} x^{9}+172040 a^{3} b^{2} x^{6}+109480 a^{4} b \,x^{3}+30107 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{8}}{240856 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/240856*x^8*(10472*b^5*x^15+60214*a*b^4*x^12+141680*a^2*b^3*x^9+172040*a^3*b^2*x^6+109480*a^4*b*x^3+30107*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
57,1,80,177,0.009000," ","int(x^6*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(6916 b^{5} x^{15}+40040 a \,b^{4} x^{12}+95095 a^{2} b^{3} x^{9}+117040 a^{3} b^{2} x^{6}+76076 a^{4} b \,x^{3}+21736 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{7}}{152152 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/152152*x^7*(6916*b^5*x^15+40040*a*b^4*x^12+95095*a^2*b^3*x^9+117040*a^3*b^2*x^6+76076*a^4*b*x^3+21736*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
58,1,80,52,0.009000," ","int(x^5*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(6 b^{5} x^{15}+35 a \,b^{4} x^{12}+84 a^{2} b^{3} x^{9}+105 a^{3} b^{2} x^{6}+70 a^{4} b \,x^{3}+21 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{6}}{126 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/126*x^6*(6*b^5*x^15+35*a*b^4*x^12+84*a^2*b^3*x^9+105*a^3*b^2*x^6+70*a^4*b*x^3+21*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
59,1,80,177,0.009000," ","int(x^4*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(2618 b^{5} x^{15}+15400 a \,b^{4} x^{12}+37400 a^{2} b^{3} x^{9}+47600 a^{3} b^{2} x^{6}+32725 a^{4} b \,x^{3}+10472 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{5}}{52360 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/52360*x^5*(2618*b^5*x^15+15400*a*b^4*x^12+37400*a^2*b^3*x^9+47600*a^3*b^2*x^6+32725*a^4*b*x^3+10472*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
60,1,80,176,0.008000," ","int(x^3*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(1456 b^{5} x^{15}+8645 a \,b^{4} x^{12}+21280 a^{2} b^{3} x^{9}+27664 a^{3} b^{2} x^{6}+19760 a^{4} b \,x^{3}+6916 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{4}}{27664 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/27664*x^4*(1456*b^5*x^15+8645*a*b^4*x^12+21280*a^2*b^3*x^9+27664*a^3*b^2*x^6+19760*a^4*b*x^3+6916*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
61,1,79,32,0.009000," ","int(x^2*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(b^{5} x^{15}+6 a \,b^{4} x^{12}+15 a^{2} b^{3} x^{9}+20 a^{3} b^{2} x^{6}+15 a^{4} b \,x^{3}+6 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{3}}{18 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/18*x^3*(b^5*x^15+6*a*b^4*x^12+15*a^2*b^3*x^9+20*a^3*b^2*x^6+15*a^4*b*x^3+6*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","B"
62,1,80,176,0.005000," ","int(x*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(308 b^{5} x^{15}+1870 a \,b^{4} x^{12}+4760 a^{2} b^{3} x^{9}+6545 a^{3} b^{2} x^{6}+5236 a^{4} b \,x^{3}+2618 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x^{2}}{5236 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/5236*x^2*(308*b^5*x^15+1870*a*b^4*x^12+4760*a^2*b^3*x^9+6545*a^3*b^2*x^6+5236*a^4*b*x^3+2618*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
63,1,78,227,0.004000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(91 b^{5} x^{15}+560 a \,b^{4} x^{12}+1456 a^{2} b^{3} x^{9}+2080 a^{3} b^{2} x^{6}+1820 a^{4} b \,x^{3}+1456 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x}{1456 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/1456*x*(91*b^5*x^15+560*a*b^4*x^12+1456*a^2*b^3*x^9+2080*a^3*b^2*x^6+1820*a^4*b*x^3+1456*a^5)*((b*x^3+a)^2)^(5/2)/(b*x^3+a)^5","A"
64,1,79,175,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} \left(12 b^{5} x^{15}+75 a \,b^{4} x^{12}+200 a^{2} b^{3} x^{9}+300 a^{3} b^{2} x^{6}+300 a^{4} b \,x^{3}+180 a^{5} \ln \left(x \right)\right)}{180 \left(b \,x^{3}+a \right)^{5}}"," ",0,"1/180*((b*x^3+a)^2)^(5/2)*(12*b^5*x^15+75*a*b^4*x^12+200*a^2*b^3*x^9+300*a^3*b^2*x^6+300*a^4*b*x^3+180*a^5*ln(x))/(b*x^3+a)^5","A"
65,1,80,177,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^2,x)","-\frac{\left(-22 b^{5} x^{15}-140 a \,b^{4} x^{12}-385 a^{2} b^{3} x^{9}-616 a^{3} b^{2} x^{6}-770 a^{4} b \,x^{3}+308 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{308 \left(b \,x^{3}+a \right)^{5} x}"," ",0,"-1/308*(-22*b^5*x^15-140*a*b^4*x^12-385*a^2*b^3*x^9-616*a^3*b^2*x^6-770*a^4*b*x^3+308*a^5)*((b*x^3+a)^2)^(5/2)/x/(b*x^3+a)^5","A"
66,1,80,175,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^3,x)","-\frac{\left(-14 b^{5} x^{15}-91 a \,b^{4} x^{12}-260 a^{2} b^{3} x^{9}-455 a^{3} b^{2} x^{6}-910 a^{4} b \,x^{3}+91 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{182 \left(b \,x^{3}+a \right)^{5} x^{2}}"," ",0,"-1/182*(-14*b^5*x^15-91*a*b^4*x^12-260*a^2*b^3*x^9-455*a^3*b^2*x^6-910*a^4*b*x^3+91*a^5)*((b*x^3+a)^2)^(5/2)/x^2/(b*x^3+a)^5","A"
67,1,82,176,0.011000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^4,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} x^{15}+20 a \,b^{4} x^{12}+60 a^{2} b^{3} x^{9}+120 a^{3} b^{2} x^{6}+180 a^{4} b \,x^{3} \ln \left(x \right)-12 a^{5}\right)}{36 \left(b \,x^{3}+a \right)^{5} x^{3}}"," ",0,"1/36*((b*x^3+a)^2)^(5/2)*(3*b^5*x^15+20*a*b^4*x^12+60*a^2*b^3*x^9+120*a^3*b^2*x^6+180*a^4*b*ln(x)*x^3-12*a^5)/(b*x^3+a)^5/x^3","A"
68,1,80,177,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^5,x)","-\frac{\left(-8 b^{5} x^{15}-55 a \,b^{4} x^{12}-176 a^{2} b^{3} x^{9}-440 a^{3} b^{2} x^{6}+440 a^{4} b \,x^{3}+22 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{88 \left(b \,x^{3}+a \right)^{5} x^{4}}"," ",0,"-1/88*(-8*b^5*x^15-55*a*b^4*x^12-176*a^2*b^3*x^9-440*a^3*b^2*x^6+440*a^4*b*x^3+22*a^5)*((b*x^3+a)^2)^(5/2)/x^4/(b*x^3+a)^5","A"
69,1,80,175,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^6,x)","-\frac{\left(-7 b^{5} x^{15}-50 a \,b^{4} x^{12}-175 a^{2} b^{3} x^{9}-700 a^{3} b^{2} x^{6}+175 a^{4} b \,x^{3}+14 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{70 \left(b \,x^{3}+a \right)^{5} x^{5}}"," ",0,"-1/70*(-7*b^5*x^15-50*a*b^4*x^12-175*a^2*b^3*x^9-700*a^3*b^2*x^6+175*a^4*b*x^3+14*a^5)*((b*x^3+a)^2)^(5/2)/x^5/(b*x^3+a)^5","A"
70,1,82,176,0.013000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^7,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} \left(2 b^{5} x^{15}+15 a \,b^{4} x^{12}+60 a^{2} b^{3} x^{9}+180 a^{3} b^{2} x^{6} \ln \left(x \right)-30 a^{4} b \,x^{3}-3 a^{5}\right)}{18 \left(b \,x^{3}+a \right)^{5} x^{6}}"," ",0,"1/18*((b*x^3+a)^2)^(5/2)*(2*b^5*x^15+15*a*b^4*x^12+60*a^2*b^3*x^9+180*a^3*b^2*ln(x)*x^6-30*a^4*b*x^3-3*a^5)/(b*x^3+a)^5/x^6","A"
71,1,80,176,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^8,x)","-\frac{\left(-7 b^{5} x^{15}-56 a \,b^{4} x^{12}-280 a^{2} b^{3} x^{9}+560 a^{3} b^{2} x^{6}+70 a^{4} b \,x^{3}+8 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{56 \left(b \,x^{3}+a \right)^{5} x^{7}}"," ",0,"-1/56*(-7*b^5*x^15-56*a*b^4*x^12-280*a^2*b^3*x^9+560*a^3*b^2*x^6+70*a^4*b*x^3+8*a^5)*((b*x^3+a)^2)^(5/2)/x^7/(b*x^3+a)^5","A"
72,1,80,175,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^9,x)","-\frac{\left(-8 b^{5} x^{15}-70 a \,b^{4} x^{12}-560 a^{2} b^{3} x^{9}+280 a^{3} b^{2} x^{6}+56 a^{4} b \,x^{3}+7 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{56 \left(b \,x^{3}+a \right)^{5} x^{8}}"," ",0,"-1/56*(-8*b^5*x^15-70*a*b^4*x^12-560*a^2*b^3*x^9+280*a^3*b^2*x^6+56*a^4*b*x^3+7*a^5)*((b*x^3+a)^2)^(5/2)/x^8/(b*x^3+a)^5","A"
73,1,82,176,0.012000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^10,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} \left(3 b^{5} x^{15}+30 a \,b^{4} x^{12}+180 a^{2} b^{3} x^{9} \ln \left(x \right)-60 a^{3} b^{2} x^{6}-15 a^{4} b \,x^{3}-2 a^{5}\right)}{18 \left(b \,x^{3}+a \right)^{5} x^{9}}"," ",0,"1/18*((b*x^3+a)^2)^(5/2)*(3*b^5*x^15+30*a*b^4*x^12+180*a^2*b^3*ln(x)*x^9-60*a^3*b^2*x^6-15*a^4*b*x^3-2*a^5)/(b*x^3+a)^5/x^9","A"
74,1,80,177,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^11,x)","-\frac{\left(-14 b^{5} x^{15}-175 a \,b^{4} x^{12}+700 a^{2} b^{3} x^{9}+175 a^{3} b^{2} x^{6}+50 a^{4} b \,x^{3}+7 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{70 \left(b \,x^{3}+a \right)^{5} x^{10}}"," ",0,"-1/70*(-14*b^5*x^15-175*a*b^4*x^12+700*a^2*b^3*x^9+175*a^3*b^2*x^6+50*a^4*b*x^3+7*a^5)*((b*x^3+a)^2)^(5/2)/x^10/(b*x^3+a)^5","A"
75,1,80,175,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^12,x)","-\frac{\left(-22 b^{5} x^{15}-440 a \,b^{4} x^{12}+440 a^{2} b^{3} x^{9}+176 a^{3} b^{2} x^{6}+55 a^{4} b \,x^{3}+8 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{88 \left(b \,x^{3}+a \right)^{5} x^{11}}"," ",0,"-1/88*(-22*b^5*x^15-440*a*b^4*x^12+440*a^2*b^3*x^9+176*a^3*b^2*x^6+55*a^4*b*x^3+8*a^5)*((b*x^3+a)^2)^(5/2)/x^11/(b*x^3+a)^5","A"
76,1,82,176,0.013000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^13,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} \left(12 b^{5} x^{15}+180 a \,b^{4} x^{12} \ln \left(x \right)-120 a^{2} b^{3} x^{9}-60 a^{3} b^{2} x^{6}-20 a^{4} b \,x^{3}-3 a^{5}\right)}{36 \left(b \,x^{3}+a \right)^{5} x^{12}}"," ",0,"1/36*((b*x^3+a)^2)^(5/2)*(12*b^5*x^15+180*a*b^4*ln(x)*x^12-120*a^2*b^3*x^9-60*a^3*b^2*x^6-20*a^4*b*x^3-3*a^5)/(b*x^3+a)^5/x^12","A"
77,1,80,177,0.006000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^14,x)","-\frac{\left(-91 b^{5} x^{15}+910 a \,b^{4} x^{12}+455 a^{2} b^{3} x^{9}+260 a^{3} b^{2} x^{6}+91 a^{4} b \,x^{3}+14 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{182 \left(b \,x^{3}+a \right)^{5} x^{13}}"," ",0,"-1/182*(-91*b^5*x^15+910*a*b^4*x^12+455*a^2*b^3*x^9+260*a^3*b^2*x^6+91*a^4*b*x^3+14*a^5)*((b*x^3+a)^2)^(5/2)/x^13/(b*x^3+a)^5","A"
78,1,80,174,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^15,x)","-\frac{\left(-308 b^{5} x^{15}+770 a \,b^{4} x^{12}+616 a^{2} b^{3} x^{9}+385 a^{3} b^{2} x^{6}+140 a^{4} b \,x^{3}+22 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{308 \left(b \,x^{3}+a \right)^{5} x^{14}}"," ",0,"-1/308*(-308*b^5*x^15+770*a*b^4*x^12+616*a^2*b^3*x^9+385*a^3*b^2*x^6+140*a^4*b*x^3+22*a^5)*((b*x^3+a)^2)^(5/2)/x^14/(b*x^3+a)^5","A"
79,1,82,175,0.014000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^16,x)","\frac{\left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} \left(180 b^{5} x^{15} \ln \left(x \right)-300 a \,b^{4} x^{12}-300 a^{2} b^{3} x^{9}-200 a^{3} b^{2} x^{6}-75 a^{4} b \,x^{3}-12 a^{5}\right)}{180 \left(b \,x^{3}+a \right)^{5} x^{15}}"," ",0,"1/180*((b*x^3+a)^2)^(5/2)*(180*b^5*ln(x)*x^15-300*a*b^4*x^12-300*a^2*b^3*x^9-200*a^3*b^2*x^6-75*a^4*b*x^3-12*a^5)/(b*x^3+a)^5/x^15","A"
80,1,80,177,0.009000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^17,x)","-\frac{\left(1456 b^{5} x^{15}+1820 a \,b^{4} x^{12}+2080 a^{2} b^{3} x^{9}+1456 a^{3} b^{2} x^{6}+560 a^{4} b \,x^{3}+91 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{1456 \left(b \,x^{3}+a \right)^{5} x^{16}}"," ",0,"-1/1456*(1456*b^5*x^15+1820*a*b^4*x^12+2080*a^2*b^3*x^9+1456*a^3*b^2*x^6+560*a^4*b*x^3+91*a^5)*((b*x^3+a)^2)^(5/2)/x^16/(b*x^3+a)^5","A"
81,1,80,177,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^18,x)","-\frac{\left(2618 b^{5} x^{15}+5236 a \,b^{4} x^{12}+6545 a^{2} b^{3} x^{9}+4760 a^{3} b^{2} x^{6}+1870 a^{4} b \,x^{3}+308 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{5236 \left(b \,x^{3}+a \right)^{5} x^{17}}"," ",0,"-1/5236*(2618*b^5*x^15+5236*a*b^4*x^12+6545*a^2*b^3*x^9+4760*a^3*b^2*x^6+1870*a^4*b*x^3+308*a^5)*((b*x^3+a)^2)^(5/2)/x^17/(b*x^3+a)^5","A"
82,1,78,28,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^19,x)","-\frac{\left(6 b^{5} x^{15}+15 a \,b^{4} x^{12}+20 a^{2} b^{3} x^{9}+15 a^{3} b^{2} x^{6}+6 a^{4} b \,x^{3}+a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{18 \left(b \,x^{3}+a \right)^{5} x^{18}}"," ",0,"-1/18*(6*b^5*x^15+15*a*b^4*x^12+20*a^2*b^3*x^9+15*a^3*b^2*x^6+6*a^4*b*x^3+a^5)*((b*x^3+a)^2)^(5/2)/x^18/(b*x^3+a)^5","B"
83,1,80,177,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^20,x)","-\frac{\left(6916 b^{5} x^{15}+19760 a \,b^{4} x^{12}+27664 a^{2} b^{3} x^{9}+21280 a^{3} b^{2} x^{6}+8645 a^{4} b \,x^{3}+1456 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{27664 \left(b \,x^{3}+a \right)^{5} x^{19}}"," ",0,"-1/27664*(6916*b^5*x^15+19760*a*b^4*x^12+27664*a^2*b^3*x^9+21280*a^3*b^2*x^6+8645*a^4*b*x^3+1456*a^5)*((b*x^3+a)^2)^(5/2)/x^19/(b*x^3+a)^5","A"
84,1,80,177,0.009000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^21,x)","-\frac{\left(10472 b^{5} x^{15}+32725 a \,b^{4} x^{12}+47600 a^{2} b^{3} x^{9}+37400 a^{3} b^{2} x^{6}+15400 a^{4} b \,x^{3}+2618 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{52360 \left(b \,x^{3}+a \right)^{5} x^{20}}"," ",0,"-1/52360*(10472*b^5*x^15+32725*a*b^4*x^12+47600*a^2*b^3*x^9+37400*a^3*b^2*x^6+15400*a^4*b*x^3+2618*a^5)*((b*x^3+a)^2)^(5/2)/x^20/(b*x^3+a)^5","A"
85,1,80,58,0.007000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^22,x)","-\frac{\left(21 b^{5} x^{15}+70 a \,b^{4} x^{12}+105 a^{2} b^{3} x^{9}+84 a^{3} b^{2} x^{6}+35 a^{4} b \,x^{3}+6 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{126 \left(b \,x^{3}+a \right)^{5} x^{21}}"," ",0,"-1/126*(21*b^5*x^15+70*a*b^4*x^12+105*a^2*b^3*x^9+84*a^3*b^2*x^6+35*a^4*b*x^3+6*a^5)*((b*x^3+a)^2)^(5/2)/x^21/(b*x^3+a)^5","A"
86,1,80,177,0.010000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^23,x)","-\frac{\left(21736 b^{5} x^{15}+76076 a \,b^{4} x^{12}+117040 a^{2} b^{3} x^{9}+95095 a^{3} b^{2} x^{6}+40040 a^{4} b \,x^{3}+6916 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{152152 \left(b \,x^{3}+a \right)^{5} x^{22}}"," ",0,"-1/152152*(21736*b^5*x^15+76076*a*b^4*x^12+117040*a^2*b^3*x^9+95095*a^3*b^2*x^6+40040*a^4*b*x^3+6916*a^5)*((b*x^3+a)^2)^(5/2)/x^22/(b*x^3+a)^5","A"
87,1,80,177,0.008000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^24,x)","-\frac{\left(30107 b^{5} x^{15}+109480 a \,b^{4} x^{12}+172040 a^{2} b^{3} x^{9}+141680 a^{3} b^{2} x^{6}+60214 a^{4} b \,x^{3}+10472 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{240856 \left(b \,x^{3}+a \right)^{5} x^{23}}"," ",0,"-1/240856*(30107*b^5*x^15+109480*a*b^4*x^12+172040*a^2*b^3*x^9+141680*a^3*b^2*x^6+60214*a^4*b*x^3+10472*a^5)*((b*x^3+a)^2)^(5/2)/x^23/(b*x^3+a)^5","A"
88,1,80,89,0.010000," ","int((b^2*x^6+2*a*b*x^3+a^2)^(5/2)/x^25,x)","-\frac{\left(56 b^{5} x^{15}+210 a \,b^{4} x^{12}+336 a^{2} b^{3} x^{9}+280 a^{3} b^{2} x^{6}+120 a^{4} b \,x^{3}+21 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}}}{504 \left(b \,x^{3}+a \right)^{5} x^{24}}"," ",0,"-1/504*(56*b^5*x^15+210*a*b^4*x^12+336*a^2*b^3*x^9+280*a^3*b^2*x^6+120*a^4*b*x^3+21*a^5)*((b*x^3+a)^2)^(5/2)/x^24/(b*x^3+a)^5","A"
89,1,113,158,0.010000," ","int(x^4/((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \left(3 \left(\frac{a}{b}\right)^{\frac{1}{3}} b \,x^{2}+2 \sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+2 a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-a \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right)}{6 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2}}"," ",0,"1/6*(b*x^3+a)*(3*x^2*b*(a/b)^(1/3)+2*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*3^(1/2)*a+2*ln(x+(a/b)^(1/3))*a-ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a)/((b*x^3+a)^2)^(1/2)/b^2/(a/b)^(1/3)","A"
90,1,110,155,0.007000," ","int(x^3/((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \left(2 \sqrt{3}\, a \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-2 a \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+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 x \right)}{6 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2}}"," ",0,"1/6*(b*x^3+a)*(6*x*b*(a/b)^(2/3)+2*3^(1/2)*a*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-2*a*ln(x+(a/b)^(1/3))+a*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))/((b*x^3+a)^2)^(1/2)/b^2/(a/b)^(2/3)","A"
91,1,32,31,0.007000," ","int(x^2/((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \ln \left(b \,x^{3}+a \right)}{3 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, b}"," ",0,"1/3*(b*x^3+a)*ln(b*x^3+a)/b/((b*x^3+a)^2)^(1/2)","A"
92,1,97,132,0.004000," ","int(x/((b*x^3+a)^2)^(1/2),x)","-\frac{\left(b \,x^{3}+a \right) \left(2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+2 \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-\ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right)}{6 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(\frac{a}{b}\right)^{\frac{1}{3}} b}"," ",0,"-1/6*(b*x^3+a)*(2*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+2*ln(x+(a/b)^(1/3))-ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))/((b*x^3+a)^2)^(1/2)/b/(a/b)^(1/3)","A"
93,1,97,132,0.004000," ","int(1/((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \left(-2 \sqrt{3}\, \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+2 \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-\ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right)}{6 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(\frac{a}{b}\right)^{\frac{2}{3}} b}"," ",0,"1/6*(b*x^3+a)*(-2*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+2*ln(x+(a/b)^(1/3))-ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))/((b*x^3+a)^2)^(1/2)/b/(a/b)^(2/3)","A"
94,1,39,56,0.008000," ","int(1/x/((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \left(3 \ln \left(x \right)-\ln \left(b \,x^{3}+a \right)\right)}{3 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, a}"," ",0,"1/3*(b*x^3+a)*(3*ln(x)-ln(b*x^3+a))/((b*x^3+a)^2)^(1/2)/a","A"
95,1,111,160,0.007000," ","int(1/x^2/((b*x^3+a)^2)^(1/2),x)","-\frac{\left(b \,x^{3}+a \right) \left(-2 \sqrt{3}\, x \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-2 x \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+x \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}}\right)}{6 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(\frac{a}{b}\right)^{\frac{1}{3}} a x}"," ",0,"-1/6*(b*x^3+a)*(-2*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x+ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x-2*ln(x+(a/b)^(1/3))*x+6*(a/b)^(1/3))/((b*x^3+a)^2)^(1/2)/a/x/(a/b)^(1/3)","A"
96,1,117,161,0.013000," ","int(1/x^3/((b*x^3+a)^2)^(1/2),x)","\frac{\left(b \,x^{3}+a \right) \left(2 \sqrt{3}\, x^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-2 x^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+x^{2} \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}}\right)}{6 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,x^{2}}"," ",0,"1/6*(b*x^3+a)*(2*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^2+ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^2-2*ln(x+(a/b)^(1/3))*x^2-3*(a/b)^(2/3))/((b*x^3+a)^2)^(1/2)/x^2/a/(a/b)^(2/3)","A"
97,1,51,88,0.014000," ","int(1/x^4/((b*x^3+a)^2)^(1/2),x)","-\frac{\left(b \,x^{3}+a \right) \left(3 b \,x^{3} \ln \left(x \right)-b \,x^{3} \ln \left(b \,x^{3}+a \right)+a \right)}{3 \sqrt{\left(b \,x^{3}+a \right)^{2}}\, a^{2} x^{3}}"," ",0,"-1/3*(b*x^3+a)*(3*b*x^3*ln(x)-b*ln(b*x^3+a)*x^3+a)/((b*x^3+a)^2)^(1/2)/a^2/x^3","A"
98,1,299,182,0.025000," ","int(x^4/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(-2 \sqrt{3}\, b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-2 b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+b^{2} x^{6} \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} x^{5}-4 \sqrt{3}\, a b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-4 a b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+2 a b \,x^{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{1}{3}} a b \,x^{2}-2 \sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-2 a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right) \left(b \,x^{3}+a \right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a \,b^{2}}"," ",0,"1/54*(-2*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^6*b^2-2*ln(x+(a/b)^(1/3))*x^6*b^2+ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^6*b^2+6*(a/b)^(1/3)*x^5*b^2-4*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^3*a*b-4*ln(x+(a/b)^(1/3))*x^3*a*b+2*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^3*a*b-3*(a/b)^(1/3)*x^2*a*b-2*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*a^2-2*ln(x+(a/b)^(1/3))*a^2+ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^2)*(b*x^3+a)/(a/b)^(1/3)/b^2/a/((b*x^3+a)^2)^(3/2)","A"
99,1,299,178,0.014000," ","int(x^3/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(-2 \sqrt{3}\, b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+2 b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-4 \sqrt{3}\, a b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+4 a b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-2 a b \,x^{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^{2} x^{4}-2 \sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+2 a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-a^{2} \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 b x \right) \left(b \,x^{3}+a \right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a \,b^{2}}"," ",0,"1/54*(-2*3^(1/2)*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+2*b^2*x^6*ln(x+(a/b)^(1/3))-b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+3*(a/b)^(2/3)*x^4*b^2-4*3^(1/2)*a*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+4*a*b*x^3*ln(x+(a/b)^(1/3))-2*a*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-6*(a/b)^(2/3)*x*a*b-2*3^(1/2)*a^2*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+2*a^2*ln(x+(a/b)^(1/3))-a^2*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(2/3)/b^2/a/((b*x^3+a)^2)^(3/2)","A"
100,1,24,25,0.006000," ","int(x^2/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","-\frac{b \,x^{3}+a}{6 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} b}"," ",0,"-1/6*(b*x^3+a)/b/((b*x^3+a)^2)^(3/2)","A"
101,1,301,179,0.010000," ","int(x/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(-4 \sqrt{3}\, b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-4 b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+2 b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+12 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2} x^{5}-8 \sqrt{3}\, a b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-8 a b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+4 a b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+21 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b \,x^{2}-4 \sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-4 a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+2 a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right) \left(b \,x^{3}+a \right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a^{2} b}"," ",0,"1/54*(-4*3^(1/2)*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-4*b^2*x^6*ln(x+(a/b)^(1/3))+2*b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+12*(a/b)^(1/3)*b^2*x^5-8*3^(1/2)*a*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-8*a*b*x^3*ln(x+(a/b)^(1/3))+4*a*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+21*(a/b)^(1/3)*a*b*x^2-4*3^(1/2)*a^2*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-4*a^2*ln(x+(a/b)^(1/3))+2*a^2*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(1/3)/b/a^2/((b*x^3+a)^2)^(3/2)","A"
102,1,299,233,0.010000," ","int(1/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(-10 \sqrt{3}\, b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+10 b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-5 b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-20 \sqrt{3}\, a b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+20 a b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-10 a b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+15 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2} x^{4}-10 \sqrt{3}\, a^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+10 a^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-5 a^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+24 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b x \right) \left(b \,x^{3}+a \right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a^{2} b}"," ",0,"1/54*(-10*3^(1/2)*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+10*b^2*x^6*ln(x+(a/b)^(1/3))-5*b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+15*(a/b)^(2/3)*b^2*x^4-20*3^(1/2)*a*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+20*a*b*x^3*ln(x+(a/b)^(1/3))-10*a*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+24*(a/b)^(2/3)*a*b*x-10*3^(1/2)*a^2*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+10*a^2*ln(x+(a/b)^(1/3))-5*a^2*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(2/3)/b/a^2/((b*x^3+a)^2)^(3/2)","A"
103,1,107,97,0.017000," ","int(1/x/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(6 b^{2} x^{6} \ln \left(x \right)-2 b^{2} x^{6} \ln \left(b \,x^{3}+a \right)+12 a b \,x^{3} \ln \left(x \right)-4 a b \,x^{3} \ln \left(b \,x^{3}+a \right)+2 a b \,x^{3}+6 a^{2} \ln \left(x \right)-2 a^{2} \ln \left(b \,x^{3}+a \right)+3 a^{2}\right) \left(b \,x^{3}+a \right)}{6 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a^{3}}"," ",0,"1/6*(6*ln(x)*x^6*b^2-2*ln(b*x^3+a)*x^6*b^2+12*ln(x)*x^3*a*b-4*ln(b*x^3+a)*x^3*a*b+2*a*b*x^3+6*ln(x)*a^2-2*ln(b*x^3+a)*a^2+3*a^2)*(b*x^3+a)/a^3/((b*x^3+a)^2)^(3/2)","A"
104,1,316,205,0.020000," ","int(1/x^2/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","-\frac{\left(-28 \sqrt{3}\, b^{2} x^{7} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-28 b^{2} x^{7} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+14 b^{2} x^{7} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+84 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{2} x^{6}-56 \sqrt{3}\, a b \,x^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-56 a b \,x^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+28 a b \,x^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+147 \left(\frac{a}{b}\right)^{\frac{1}{3}} a b \,x^{3}-28 \sqrt{3}\, a^{2} x \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-28 a^{2} x \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+14 a^{2} x \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^{2}\right) \left(b \,x^{3}+a \right)}{54 \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} x}"," ",0,"-1/54*(-28*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^7*b^2-28*ln(x+(a/b)^(1/3))*x^7*b^2+14*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^7*b^2+84*(a/b)^(1/3)*x^6*b^2-56*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^4*a*b-56*ln(x+(a/b)^(1/3))*x^4*a*b+28*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^4*a*b+147*(a/b)^(1/3)*x^3*a*b-28*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x*a^2-28*ln(x+(a/b)^(1/3))*x*a^2+14*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x*a^2+54*(a/b)^(1/3)*a^2)*(b*x^3+a)/(a/b)^(1/3)/x/a^3/((b*x^3+a)^2)^(3/2)","A"
105,1,322,205,0.018000," ","int(1/x^3/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","-\frac{\left(-40 \sqrt{3}\, b^{2} x^{8} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+40 b^{2} x^{8} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-20 b^{2} x^{8} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-80 \sqrt{3}\, a b \,x^{5} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+80 a b \,x^{5} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-40 a b \,x^{5} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+60 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{2} x^{6}-40 \sqrt{3}\, a^{2} x^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+40 a^{2} x^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-20 a^{2} x^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+96 \left(\frac{a}{b}\right)^{\frac{2}{3}} a b \,x^{3}+27 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2}\right) \left(b \,x^{3}+a \right)}{54 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a^{3} x^{2}}"," ",0,"-1/54*(-40*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^8*b^2+40*ln(x+(a/b)^(1/3))*x^8*b^2-20*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^8*b^2+60*(a/b)^(2/3)*x^6*b^2-80*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^5*a*b+80*ln(x+(a/b)^(1/3))*x^5*a*b-40*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^5*a*b+96*(a/b)^(2/3)*x^3*a*b-40*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^2*a^2+40*ln(x+(a/b)^(1/3))*x^2*a^2-20*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^2*a^2+27*(a/b)^(2/3)*a^2)*(b*x^3+a)/(a/b)^(2/3)/x^2/a^3/((b*x^3+a)^2)^(3/2)","A"
106,1,133,130,0.024000," ","int(1/x^4/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","-\frac{\left(18 b^{3} x^{9} \ln \left(x \right)-6 b^{3} x^{9} \ln \left(b \,x^{3}+a \right)+36 a \,b^{2} x^{6} \ln \left(x \right)-12 a \,b^{2} x^{6} \ln \left(b \,x^{3}+a \right)+6 a \,b^{2} x^{6}+18 a^{2} b \,x^{3} \ln \left(x \right)-6 a^{2} b \,x^{3} \ln \left(b \,x^{3}+a \right)+9 a^{2} b \,x^{3}+2 a^{3}\right) \left(b \,x^{3}+a \right)}{6 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} a^{4} x^{3}}"," ",0,"-1/6*(18*b^3*x^9*ln(x)-6*ln(b*x^3+a)*x^9*b^3+36*a*b^2*x^6*ln(x)-12*ln(b*x^3+a)*x^6*a*b^2+6*a*b^2*x^6+18*a^2*b*x^3*ln(x)-6*ln(b*x^3+a)*x^3*a^2*b+9*a^2*b*x^3+2*a^3)*(b*x^3+a)/x^3/a^4/((b*x^3+a)^2)^(3/2)","A"
107,1,519,235,0.023000," ","int(x^6/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(-20 \sqrt{3}\, b^{4} x^{12} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+20 b^{4} x^{12} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-10 b^{4} x^{12} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-80 \sqrt{3}\, a \,b^{3} x^{9} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+80 a \,b^{3} x^{9} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-40 a \,b^{3} x^{9} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+30 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4} x^{10}-120 \sqrt{3}\, a^{2} b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+120 a^{2} b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-60 a^{2} b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+108 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{3} x^{7}-80 \sqrt{3}\, a^{3} b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+80 a^{3} b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-40 a^{3} b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-225 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2} x^{4}-20 \sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+20 a^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-10 a^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-60 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b x \right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{2} b^{3}}"," ",0,"1/2916*(-20*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^12*b^4+20*ln(x+(a/b)^(1/3))*x^12*b^4-10*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^12*b^4+30*(a/b)^(2/3)*x^10*b^4-80*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^9*a*b^3+80*ln(x+(a/b)^(1/3))*x^9*a*b^3-40*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^9*a*b^3+108*(a/b)^(2/3)*x^7*a*b^3-120*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^6*a^2*b^2+120*ln(x+(a/b)^(1/3))*x^6*a^2*b^2-60*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^6*a^2*b^2-225*(a/b)^(2/3)*x^4*a^2*b^2-80*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^3*a^3*b+80*ln(x+(a/b)^(1/3))*x^3*a^3*b-40*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^3*a^3*b-60*(a/b)^(2/3)*x*a^3*b-20*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*a^4+20*ln(x+(a/b)^(1/3))*a^4-10*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*a^4)*(b*x^3+a)/(a/b)^(2/3)/b^3/a^2/((b*x^3+a)^2)^(5/2)","B"
108,1,32,52,0.009000," ","int(x^5/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","-\frac{\left(b \,x^{3}+a \right) \left(4 b \,x^{3}+a \right)}{36 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} b^{2}}"," ",0,"-1/36*(b*x^3+a)*(4*b*x^3+a)/b^2/((b*x^3+a)^2)^(5/2)","A"
109,1,521,244,0.022000," ","int(x^4/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(-28 \sqrt{3}\, b^{4} x^{12} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-28 b^{4} x^{12} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+14 b^{4} x^{12} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+84 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4} x^{11}-112 \sqrt{3}\, a \,b^{3} x^{9} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-112 a \,b^{3} x^{9} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+56 a \,b^{3} x^{9} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+315 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{3} x^{8}-168 \sqrt{3}\, a^{2} b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-168 a^{2} b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+84 a^{2} b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+432 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b^{2} x^{5}-112 \sqrt{3}\, a^{3} b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-112 a^{3} b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+56 a^{3} b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-42 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b \,x^{2}-28 \sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-28 a^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+14 a^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{3} b^{2}}"," ",0,"1/2916*(-28*3^(1/2)*b^4*x^12*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-28*b^4*x^12*ln(x+(a/b)^(1/3))+14*b^4*x^12*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+84*(a/b)^(1/3)*x^11*b^4-112*3^(1/2)*a*b^3*x^9*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-112*a*b^3*x^9*ln(x+(a/b)^(1/3))+56*a*b^3*x^9*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+315*(a/b)^(1/3)*x^8*a*b^3-168*3^(1/2)*a^2*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-168*a^2*b^2*x^6*ln(x+(a/b)^(1/3))+84*a^2*b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+432*(a/b)^(1/3)*x^5*a^2*b^2-112*3^(1/2)*a^3*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-112*a^3*b*x^3*ln(x+(a/b)^(1/3))+56*a^3*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-42*(a/b)^(1/3)*x^2*a^3*b-28*3^(1/2)*a^4*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-28*a^4*ln(x+(a/b)^(1/3))+14*a^4*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(1/3)/b^2/a^3/((b*x^3+a)^2)^(5/2)","B"
110,1,519,236,0.019000," ","int(x^3/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(-40 \sqrt{3}\, b^{4} x^{12} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+40 b^{4} x^{12} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-20 b^{4} x^{12} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-160 \sqrt{3}\, a \,b^{3} x^{9} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+160 a \,b^{3} x^{9} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-80 a \,b^{3} x^{9} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+60 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4} x^{10}-240 \sqrt{3}\, a^{2} b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+240 a^{2} b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-120 a^{2} b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+216 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{3} x^{7}-160 \sqrt{3}\, a^{3} b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+160 a^{3} b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-80 a^{3} b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+279 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2} x^{4}-40 \sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+40 a^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-20 a^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-120 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b x \right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{3} b^{2}}"," ",0,"1/2916*(-40*3^(1/2)*b^4*x^12*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+40*b^4*x^12*ln(x+(a/b)^(1/3))-20*b^4*x^12*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+60*(a/b)^(2/3)*b^4*x^10-160*3^(1/2)*a*b^3*x^9*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+160*a*b^3*x^9*ln(x+(a/b)^(1/3))-80*a*b^3*x^9*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+216*(a/b)^(2/3)*a*b^3*x^7-240*3^(1/2)*a^2*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+240*a^2*b^2*x^6*ln(x+(a/b)^(1/3))-120*a^2*b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+279*(a/b)^(2/3)*a^2*b^2*x^4-160*3^(1/2)*a^3*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+160*a^3*b*x^3*ln(x+(a/b)^(1/3))-80*a^3*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))-120*(a/b)^(2/3)*a^3*b*x-40*3^(1/2)*a^4*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+40*a^4*ln(x+(a/b)^(1/3))-20*a^4*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(2/3)/b^2/a^3/((b*x^3+a)^2)^(5/2)","B"
111,1,24,34,0.009000," ","int(x^2/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","-\frac{b \,x^{3}+a}{12 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} b}"," ",0,"-1/12*(b*x^3+a)/b/((b*x^3+a)^2)^(5/2)","A"
112,1,521,235,0.011000," ","int(x/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(-140 \sqrt{3}\, b^{4} x^{12} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-140 b^{4} x^{12} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+70 b^{4} x^{12} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+420 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4} x^{11}-560 \sqrt{3}\, a \,b^{3} x^{9} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-560 a \,b^{3} x^{9} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+280 a \,b^{3} x^{9} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+1575 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{3} x^{8}-840 \sqrt{3}\, a^{2} b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-840 a^{2} b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+420 a^{2} b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+2160 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b^{2} x^{5}-560 \sqrt{3}\, a^{3} b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-560 a^{3} b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+280 a^{3} b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+1248 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b \,x^{2}-140 \sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-140 a^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+70 a^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)\right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{4} b}"," ",0,"1/2916*(-140*3^(1/2)*b^4*x^12*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-140*b^4*x^12*ln(x+(a/b)^(1/3))+70*b^4*x^12*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+420*(a/b)^(1/3)*b^4*x^11-560*3^(1/2)*a*b^3*x^9*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-560*a*b^3*x^9*ln(x+(a/b)^(1/3))+280*a*b^3*x^9*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1575*(a/b)^(1/3)*a*b^3*x^8-840*3^(1/2)*a^2*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-840*a^2*b^2*x^6*ln(x+(a/b)^(1/3))+420*a^2*b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2160*(a/b)^(1/3)*a^2*b^2*x^5-560*3^(1/2)*a^3*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-560*a^3*b*x^3*ln(x+(a/b)^(1/3))+280*a^3*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1248*(a/b)^(1/3)*a^3*b*x^2-140*3^(1/2)*a^4*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))-140*a^4*ln(x+(a/b)^(1/3))+70*a^4*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(1/3)/b/a^4/((b*x^3+a)^2)^(5/2)","B"
113,1,519,303,0.008000," ","int(1/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(-440 \sqrt{3}\, b^{4} x^{12} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+440 b^{4} x^{12} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-220 b^{4} x^{12} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-1760 \sqrt{3}\, a \,b^{3} x^{9} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+1760 a \,b^{3} x^{9} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-880 a \,b^{3} x^{9} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+660 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4} x^{10}-2640 \sqrt{3}\, a^{2} b^{2} x^{6} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+2640 a^{2} b^{2} x^{6} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-1320 a^{2} b^{2} x^{6} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+2376 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{3} x^{7}-1760 \sqrt{3}\, a^{3} b \,x^{3} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+1760 a^{3} b \,x^{3} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-880 a^{3} b \,x^{3} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+3069 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2} x^{4}-440 \sqrt{3}\, a^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+440 a^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-220 a^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+1596 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b x \right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{4} b}"," ",0,"1/2916*(-440*3^(1/2)*b^4*x^12*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+440*b^4*x^12*ln(x+(a/b)^(1/3))-220*b^4*x^12*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+660*(a/b)^(2/3)*b^4*x^10-1760*3^(1/2)*a*b^3*x^9*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+1760*a*b^3*x^9*ln(x+(a/b)^(1/3))-880*a*b^3*x^9*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+2376*(a/b)^(2/3)*a*b^3*x^7-2640*3^(1/2)*a^2*b^2*x^6*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+2640*a^2*b^2*x^6*ln(x+(a/b)^(1/3))-1320*a^2*b^2*x^6*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+3069*(a/b)^(2/3)*a^2*b^2*x^4-1760*3^(1/2)*a^3*b*x^3*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+1760*a^3*b*x^3*ln(x+(a/b)^(1/3))-880*a^3*b*x^3*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))+1596*(a/b)^(2/3)*a^3*b*x-440*3^(1/2)*a^4*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))+440*a^4*ln(x+(a/b)^(1/3))-220*a^4*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3)))*(b*x^3+a)/(a/b)^(2/3)/b/a^4/((b*x^3+a)^2)^(5/2)","A"
114,1,193,147,0.024000," ","int(1/x/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(36 b^{4} x^{12} \ln \left(x \right)-12 b^{4} x^{12} \ln \left(b \,x^{3}+a \right)+144 a \,b^{3} x^{9} \ln \left(x \right)-48 a \,b^{3} x^{9} \ln \left(b \,x^{3}+a \right)+12 a \,b^{3} x^{9}+216 a^{2} b^{2} x^{6} \ln \left(x \right)-72 a^{2} b^{2} x^{6} \ln \left(b \,x^{3}+a \right)+42 a^{2} b^{2} x^{6}+144 a^{3} b \,x^{3} \ln \left(x \right)-48 a^{3} b \,x^{3} \ln \left(b \,x^{3}+a \right)+52 a^{3} b \,x^{3}+36 a^{4} \ln \left(x \right)-12 a^{4} \ln \left(b \,x^{3}+a \right)+25 a^{4}\right) \left(b \,x^{3}+a \right)}{36 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{5}}"," ",0,"1/36*(36*ln(x)*x^12*b^4-12*ln(b*x^3+a)*x^12*b^4+144*ln(x)*x^9*a*b^3-48*ln(b*x^3+a)*x^9*a*b^3+12*x^9*a*b^3+216*ln(x)*x^6*a^2*b^2-72*ln(b*x^3+a)*x^6*a^2*b^2+42*x^6*a^2*b^2+144*ln(x)*x^3*a^3*b-48*ln(b*x^3+a)*x^3*a^3*b+52*x^3*a^3*b+36*ln(x)*a^4-12*ln(b*x^3+a)*a^4+25*a^4)*(b*x^3+a)/a^5/((b*x^3+a)^2)^(5/2)","A"
115,1,536,261,0.025000," ","int(1/x^2/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","-\frac{\left(-1820 \sqrt{3}\, b^{4} x^{13} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-1820 b^{4} x^{13} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+910 b^{4} x^{13} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+5460 \left(\frac{a}{b}\right)^{\frac{1}{3}} b^{4} x^{12}-7280 \sqrt{3}\, a \,b^{3} x^{10} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-7280 a \,b^{3} x^{10} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+3640 a \,b^{3} x^{10} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+20475 \left(\frac{a}{b}\right)^{\frac{1}{3}} a \,b^{3} x^{9}-10920 \sqrt{3}\, a^{2} b^{2} x^{7} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-10920 a^{2} b^{2} x^{7} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+5460 a^{2} b^{2} x^{7} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+28080 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{2} b^{2} x^{6}-7280 \sqrt{3}\, a^{3} b \,x^{4} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-7280 a^{3} b \,x^{4} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+3640 a^{3} b \,x^{4} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+16224 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{3} b \,x^{3}-1820 \sqrt{3}\, a^{4} x \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)-1820 a^{4} x \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)+910 a^{4} x \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+2916 \left(\frac{a}{b}\right)^{\frac{1}{3}} a^{4}\right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{1}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{5} x}"," ",0,"-1/2916*(-1820*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^13*b^4-1820*ln(x+(a/b)^(1/3))*x^13*b^4+910*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^13*b^4+5460*(a/b)^(1/3)*x^12*b^4-7280*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^10*a*b^3-7280*ln(x+(a/b)^(1/3))*x^10*a*b^3+3640*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^10*a*b^3+20475*(a/b)^(1/3)*x^9*a*b^3-10920*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^7*a^2*b^2-10920*ln(x+(a/b)^(1/3))*x^7*a^2*b^2+5460*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^7*a^2*b^2+28080*(a/b)^(1/3)*x^6*a^2*b^2-7280*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^4*a^3*b-7280*ln(x+(a/b)^(1/3))*x^4*a^3*b+3640*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^4*a^3*b+16224*(a/b)^(1/3)*x^3*a^3*b-1820*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x*a^4-1820*ln(x+(a/b)^(1/3))*x*a^4+910*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x*a^4+2916*(a/b)^(1/3)*a^4)*(b*x^3+a)/(a/b)^(1/3)/x/a^5/((b*x^3+a)^2)^(5/2)","B"
116,1,542,261,0.025000," ","int(1/x^3/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","-\frac{\left(-3080 \sqrt{3}\, b^{4} x^{14} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+3080 b^{4} x^{14} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-1540 b^{4} x^{14} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)-12320 \sqrt{3}\, a \,b^{3} x^{11} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+12320 a \,b^{3} x^{11} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-6160 a \,b^{3} x^{11} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+4620 \left(\frac{a}{b}\right)^{\frac{2}{3}} b^{4} x^{12}-18480 \sqrt{3}\, a^{2} b^{2} x^{8} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+18480 a^{2} b^{2} x^{8} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-9240 a^{2} b^{2} x^{8} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+16632 \left(\frac{a}{b}\right)^{\frac{2}{3}} a \,b^{3} x^{9}-12320 \sqrt{3}\, a^{3} b \,x^{5} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+12320 a^{3} b \,x^{5} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-6160 a^{3} b \,x^{5} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+21483 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{2} b^{2} x^{6}-3080 \sqrt{3}\, a^{4} x^{2} \arctan \left(\frac{\sqrt{3}\, \left(-2 x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)}{3 \left(\frac{a}{b}\right)^{\frac{1}{3}}}\right)+3080 a^{4} x^{2} \ln \left(x +\left(\frac{a}{b}\right)^{\frac{1}{3}}\right)-1540 a^{4} x^{2} \ln \left(x^{2}-\left(\frac{a}{b}\right)^{\frac{1}{3}} x +\left(\frac{a}{b}\right)^{\frac{2}{3}}\right)+11172 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{3} b \,x^{3}+1458 \left(\frac{a}{b}\right)^{\frac{2}{3}} a^{4}\right) \left(b \,x^{3}+a \right)}{2916 \left(\frac{a}{b}\right)^{\frac{2}{3}} \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{5} x^{2}}"," ",0,"-1/2916*(-3080*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^14*b^4+3080*ln(x+(a/b)^(1/3))*x^14*b^4-1540*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^14*b^4+4620*(a/b)^(2/3)*x^12*b^4-12320*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^11*a*b^3+12320*ln(x+(a/b)^(1/3))*x^11*a*b^3-6160*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^11*a*b^3+16632*(a/b)^(2/3)*x^9*a*b^3-18480*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^8*a^2*b^2+18480*ln(x+(a/b)^(1/3))*x^8*a^2*b^2-9240*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^8*a^2*b^2+21483*(a/b)^(2/3)*x^6*a^2*b^2-12320*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^5*a^3*b+12320*ln(x+(a/b)^(1/3))*x^5*a^3*b-6160*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^5*a^3*b+11172*(a/b)^(2/3)*x^3*a^3*b-3080*3^(1/2)*arctan(1/3*3^(1/2)*(-2*x+(a/b)^(1/3))/(a/b)^(1/3))*x^2*a^4+3080*ln(x+(a/b)^(1/3))*x^2*a^4-1540*ln(x^2-(a/b)^(1/3)*x+(a/b)^(2/3))*x^2*a^4+1458*(a/b)^(2/3)*a^4)*(b*x^3+a)/(a/b)^(2/3)/x^2/a^5/((b*x^3+a)^2)^(5/2)","B"
117,1,219,183,0.021000," ","int(1/x^4/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","-\frac{\left(180 b^{5} x^{15} \ln \left(x \right)-60 b^{5} x^{15} \ln \left(b \,x^{3}+a \right)+720 a \,b^{4} x^{12} \ln \left(x \right)-240 a \,b^{4} x^{12} \ln \left(b \,x^{3}+a \right)+60 a \,b^{4} x^{12}+1080 a^{2} b^{3} x^{9} \ln \left(x \right)-360 a^{2} b^{3} x^{9} \ln \left(b \,x^{3}+a \right)+210 a^{2} b^{3} x^{9}+720 a^{3} b^{2} x^{6} \ln \left(x \right)-240 a^{3} b^{2} x^{6} \ln \left(b \,x^{3}+a \right)+260 a^{3} b^{2} x^{6}+180 a^{4} b \,x^{3} \ln \left(x \right)-60 a^{4} b \,x^{3} \ln \left(b \,x^{3}+a \right)+125 a^{4} b \,x^{3}+12 a^{5}\right) \left(b \,x^{3}+a \right)}{36 \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} a^{6} x^{3}}"," ",0,"-1/36*(180*b^5*x^15*ln(x)-60*ln(b*x^3+a)*x^15*b^5+720*a*b^4*x^12*ln(x)-240*ln(b*x^3+a)*x^12*a*b^4+60*a*b^4*x^12+1080*a^2*b^3*x^9*ln(x)-360*ln(b*x^3+a)*x^9*a^2*b^3+210*a^2*b^3*x^9+720*a^3*b^2*x^6*ln(x)-240*ln(b*x^3+a)*x^6*a^3*b^2+260*a^3*b^2*x^6+180*a^4*b*x^3*ln(x)-60*ln(b*x^3+a)*x^3*a^4*b+125*a^4*b*x^3+12*a^5)*(b*x^3+a)/x^3/a^6/((b*x^3+a)^2)^(5/2)","A"
118,1,453,247,0.008000," ","int((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\frac{\left(b^{5} m^{5} x^{15}+35 b^{5} m^{4} x^{15}+445 b^{5} m^{3} x^{15}+5 a \,b^{4} m^{5} x^{12}+2485 b^{5} m^{2} x^{15}+190 a \,b^{4} m^{4} x^{12}+5714 b^{5} m \,x^{15}+2555 a \,b^{4} m^{3} x^{12}+3640 b^{5} x^{15}+10 a^{2} b^{3} m^{5} x^{9}+14810 a \,b^{4} m^{2} x^{12}+410 a^{2} b^{3} m^{4} x^{9}+34840 a \,b^{4} m \,x^{12}+5950 a^{2} b^{3} m^{3} x^{9}+22400 a \,b^{4} x^{12}+10 a^{3} b^{2} m^{5} x^{6}+36550 a^{2} b^{3} m^{2} x^{9}+440 a^{3} b^{2} m^{4} x^{6}+89240 a^{2} b^{3} m \,x^{9}+6970 a^{3} b^{2} m^{3} x^{6}+58240 a^{2} b^{3} x^{9}+5 a^{4} b \,m^{5} x^{3}+47260 a^{3} b^{2} m^{2} x^{6}+235 a^{4} b \,m^{4} x^{3}+123920 a^{3} b^{2} m \,x^{6}+4085 a^{4} b \,m^{3} x^{3}+83200 a^{3} b^{2} x^{6}+a^{5} m^{5}+31685 a^{4} b \,m^{2} x^{3}+50 a^{5} m^{4}+100630 a^{4} b m \,x^{3}+955 a^{5} m^{3}+72800 a^{4} b \,x^{3}+8650 a^{5} m^{2}+36824 a^{5} m +58240 a^{5}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{5}{2}} x \left(d x \right)^{m}}{\left(m +1\right) \left(m +4\right) \left(m +7\right) \left(m +10\right) \left(m +13\right) \left(m +16\right) \left(b \,x^{3}+a \right)^{5}}"," ",0,"x*(b^5*m^5*x^15+35*b^5*m^4*x^15+445*b^5*m^3*x^15+5*a*b^4*m^5*x^12+2485*b^5*m^2*x^15+190*a*b^4*m^4*x^12+5714*b^5*m*x^15+2555*a*b^4*m^3*x^12+3640*b^5*x^15+10*a^2*b^3*m^5*x^9+14810*a*b^4*m^2*x^12+410*a^2*b^3*m^4*x^9+34840*a*b^4*m*x^12+5950*a^2*b^3*m^3*x^9+22400*a*b^4*x^12+10*a^3*b^2*m^5*x^6+36550*a^2*b^3*m^2*x^9+440*a^3*b^2*m^4*x^6+89240*a^2*b^3*m*x^9+6970*a^3*b^2*m^3*x^6+58240*a^2*b^3*x^9+5*a^4*b*m^5*x^3+47260*a^3*b^2*m^2*x^6+235*a^4*b*m^4*x^3+123920*a^3*b^2*m*x^6+4085*a^4*b*m^3*x^3+83200*a^3*b^2*x^6+a^5*m^5+31685*a^4*b*m^2*x^3+50*a^5*m^4+100630*a^4*b*m*x^3+955*a^5*m^3+72800*a^4*b*x^3+8650*a^5*m^2+36824*a^5*m+58240*a^5)*(d*x)^m*((b*x^3+a)^2)^(5/2)/(m+1)/(m+4)/(m+7)/(m+10)/(m+13)/(16+m)/(b*x^3+a)^5","A"
119,1,199,161,0.015000," ","int((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\frac{\left(b^{3} m^{3} x^{9}+12 b^{3} m^{2} x^{9}+39 b^{3} m \,x^{9}+3 a \,b^{2} m^{3} x^{6}+28 b^{3} x^{9}+45 a \,b^{2} m^{2} x^{6}+162 a \,b^{2} m \,x^{6}+3 a^{2} b \,m^{3} x^{3}+120 a \,b^{2} x^{6}+54 a^{2} b \,m^{2} x^{3}+261 a^{2} b m \,x^{3}+a^{3} m^{3}+210 a^{2} b \,x^{3}+21 a^{3} m^{2}+138 a^{3} m +280 a^{3}\right) \left(\left(b \,x^{3}+a \right)^{2}\right)^{\frac{3}{2}} x \left(d x \right)^{m}}{\left(m +10\right) \left(m +7\right) \left(m +4\right) \left(m +1\right) \left(b \,x^{3}+a \right)^{3}}"," ",0,"x*(b^3*m^3*x^9+12*b^3*m^2*x^9+39*b^3*m*x^9+3*a*b^2*m^3*x^6+28*b^3*x^9+45*a*b^2*m^2*x^6+162*a*b^2*m*x^6+3*a^2*b*m^3*x^3+120*a*b^2*x^6+54*a^2*b*m^2*x^3+261*a^2*b*m*x^3+a^3*m^3+210*a^2*b*x^3+21*a^3*m^2+138*a^3*m+280*a^3)*(d*x)^m*((b*x^3+a)^2)^(3/2)/(m+10)/(m+7)/(m+4)/(m+1)/(b*x^3+a)^3","A"
120,1,56,75,0.003000," ","int((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x)","\frac{\left(b m \,x^{3}+b \,x^{3}+a m +4 a \right) \sqrt{\left(b \,x^{3}+a \right)^{2}}\, x \left(d x \right)^{m}}{\left(m +4\right) \left(m +1\right) \left(b \,x^{3}+a \right)}"," ",0,"x*(b*m*x^3+b*x^3+a*m+4*a)*(d*x)^m*((b*x^3+a)^2)^(1/2)/(m+4)/(m+1)/(b*x^3+a)","A"
121,0,0,60,0.033000," ","int((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{b^{2} x^{6}+2 a b \,x^{3}+a^{2}}}\, dx"," ",0,"int((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(1/2),x)","F"
122,0,0,60,0.023000," ","int((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(3/2),x)","F"
123,0,0,60,0.030000," ","int((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","\int \frac{\left(d x \right)^{m}}{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{\frac{5}{2}}}\, dx"," ",0,"int((d*x)^m/(b^2*x^6+2*a*b*x^3+a^2)^(5/2),x)","F"
124,0,0,77,0.135000," ","int((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","\int \left(d x \right)^{m} \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}\, dx"," ",0,"int((d*x)^m*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","F"
125,1,150,166,0.014000," ","int(x^11*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","-\frac{\left(-4 b^{3} p^{3} x^{9}-12 b^{3} p^{2} x^{9}-11 b^{3} p \,x^{9}-3 b^{3} x^{9}+6 a \,b^{2} p^{2} x^{6}+9 a \,b^{2} p \,x^{6}+3 a \,b^{2} x^{6}-6 a^{2} b p \,x^{3}-3 a^{2} b \,x^{3}+3 a^{3}\right) \left(b \,x^{3}+a \right) \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{6 \left(4 p^{4}+20 p^{3}+35 p^{2}+25 p +6\right) b^{4}}"," ",0,"-1/6*(b^2*x^6+2*a*b*x^3+a^2)^p*(-4*b^3*p^3*x^9-12*b^3*p^2*x^9-11*b^3*p*x^9-3*b^3*x^9+6*a*b^2*p^2*x^6+9*a*b^2*p*x^6+3*a*b^2*x^6-6*a^2*b*p*x^3-3*a^2*b*x^3+3*a^3)*(b*x^3+a)/b^4/(4*p^4+20*p^3+35*p^2+25*p+6)","A"
126,1,96,124,0.007000," ","int(x^8*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","\frac{\left(b \,x^{3}+a \right) \left(2 b^{2} p^{2} x^{6}+3 b^{2} p \,x^{6}+b^{2} x^{6}-2 a b p \,x^{3}-a b \,x^{3}+a^{2}\right) \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{3 \left(4 p^{3}+12 p^{2}+11 p +3\right) b^{3}}"," ",0,"1/3*(b*x^3+a)*(2*b^2*p^2*x^6+3*b^2*p*x^6+b^2*x^6-2*a*b*p*x^3-a*b*x^3+a^2)*(b^2*x^6+2*a*b*x^3+a^2)^p/b^3/(4*p^3+12*p^2+11*p+3)","A"
127,1,60,80,0.007000," ","int(x^5*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","-\frac{\left(-2 x^{3} p b -b \,x^{3}+a \right) \left(b \,x^{3}+a \right) \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{6 \left(2 p^{2}+3 p +1\right) b^{2}}"," ",0,"-1/6*(b^2*x^6+2*a*b*x^3+a^2)^p*(-2*b*p*x^3-b*x^3+a)*(b*x^3+a)/b^2/(2*p^2+3*p+1)","A"
128,0,0,58,0.057000," ","int(x^4*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","\int x^{4} \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}\, dx"," ",0,"int(x^4*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","F"
129,0,0,58,0.043000," ","int(x^3*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","\int x^{3} \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}\, dx"," ",0,"int(x^3*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","F"
130,1,40,39,0.007000," ","int(x^2*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","\frac{\left(b \,x^{3}+a \right) \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{3 \left(2 p +1\right) b}"," ",0,"1/3*(b*x^3+a)*(b^2*x^6+2*a*b*x^3+a^2)^p/b/(1+2*p)","A"
131,0,0,54,0.030000," ","int(x*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","\int x \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}\, dx"," ",0,"int(x*(b^2*x^6+2*a*b*x^3+a^2)^p,x)","F"
132,0,0,51,0.014000," ","int((b^2*x^6+2*a*b*x^3+a^2)^p,x)","\int \left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}\, dx"," ",0,"int((b^2*x^6+2*a*b*x^3+a^2)^p,x)","F"
133,0,0,63,0.023000," ","int((b^2*x^6+2*a*b*x^3+a^2)^p/x,x)","\int \frac{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{x}\, dx"," ",0,"int((b^2*x^6+2*a*b*x^3+a^2)^p/x,x)","F"
134,0,0,58,0.038000," ","int((b^2*x^6+2*a*b*x^3+a^2)^p/x^2,x)","\int \frac{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int((b^2*x^6+2*a*b*x^3+a^2)^p/x^2,x)","F"
135,0,0,58,0.046000," ","int((b^2*x^6+2*a*b*x^3+a^2)^p/x^3,x)","\int \frac{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{x^{3}}\, dx"," ",0,"int((b^2*x^6+2*a*b*x^3+a^2)^p/x^3,x)","F"
136,0,0,64,0.047000," ","int((b^2*x^6+2*a*b*x^3+a^2)^p/x^4,x)","\int \frac{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{x^{4}}\, dx"," ",0,"int((b^2*x^6+2*a*b*x^3+a^2)^p/x^4,x)","F"
137,0,0,58,0.056000," ","int((b^2*x^6+2*a*b*x^3+a^2)^p/x^5,x)","\int \frac{\left(b^{2} x^{6}+2 a b \,x^{3}+a^{2}\right)^{p}}{x^{5}}\, dx"," ",0,"int((b^2*x^6+2*a*b*x^3+a^2)^p/x^5,x)","F"
138,1,111,71,0.006000," ","int(x^8/(c*x^6+b*x^3+a),x)","\frac{x^{3}}{3 c}-\frac{2 a \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b \ln \left(c \,x^{6}+b \,x^{3}+a \right)}{6 c^{2}}"," ",0,"1/3*x^3/c-1/6*b*ln(c*x^6+b*x^3+a)/c^2-2/3/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))*a+1/3/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))*b^2","A"
139,1,60,55,0.003000," ","int(x^5/(c*x^6+b*x^3+a),x)","-\frac{b \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{6}+b \,x^{3}+a \right)}{6 c}"," ",0,"1/6*ln(c*x^6+b*x^3+a)/c-1/3*b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))","A"
140,1,37,32,0.002000," ","int(x^2/(c*x^6+b*x^3+a),x)","\frac{2 \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}}"," ",0,"2/3/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))","A"
141,1,66,61,0.007000," ","int(1/x/(c*x^6+b*x^3+a),x)","-\frac{b \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{6}+b \,x^{3}+a \right)}{6 a}"," ",0,"ln(x)/a-1/6*ln(c*x^6+b*x^3+a)/a-1/3/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))","A"
142,1,119,79,0.009000," ","int(1/x^4/(c*x^6+b*x^3+a),x)","-\frac{2 c \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{3}+b}{\sqrt{4 a c -b^{2}}}\right)}{3 \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(c \,x^{6}+b \,x^{3}+a \right)}{6 a^{2}}-\frac{1}{3 a \,x^{3}}"," ",0,"-1/3/a/x^3-b*ln(x)/a^2+1/6*b*ln(c*x^6+b*x^3+a)/a^2-2/3/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))*c+1/3/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^3+b)/(4*a*c-b^2)^(1/2))*b^2","A"
143,1,61,501,0.141000," ","int(x^7/(c*x^6+b*x^3+a),x)","\frac{x^{2}}{2 c}-\frac{\left(\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{4} b +\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right) a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{3 c \left(2 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b \right)}"," ",0,"1/2*x^2/c-1/3/c*sum((_R^4*b+_R*a)/(2*_R^5*c+_R^2*b)*ln(x-_R),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
144,1,59,498,0.005000," ","int(x^6/(c*x^6+b*x^3+a),x)","\frac{x}{c}+\frac{\left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{3} b -a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{3 c \left(2 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b \right)}"," ",0,"x/c+1/3/c*sum((-_R^3*b-a)/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
145,1,43,421,0.004000," ","int(x^4/(c*x^6+b*x^3+a),x)","\frac{\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{4} \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{6 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +3 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b}"," ",0,"1/3*sum(_R^4/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
146,1,43,421,0.003000," ","int(x^3/(c*x^6+b*x^3+a),x)","\frac{\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{3} \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{6 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +3 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b}"," ",0,"1/3*sum(_R^3/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
147,1,41,421,0.004000," ","int(x/(c*x^6+b*x^3+a),x)","\frac{\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{6 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +3 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b}"," ",0,"1/3*sum(_R/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
148,1,40,421,0.002000," ","int(1/(c*x^6+b*x^3+a),x)","\frac{\ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{6 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +3 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b}"," ",0,"1/3*sum(1/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
149,1,61,474,0.006000," ","int(1/x^2/(c*x^6+b*x^3+a),x)","-\frac{\left(\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{4} c +\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right) b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{3 a \left(2 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b \right)}-\frac{1}{a x}"," ",0,"-1/3/a*sum((_R^4*c+_R*b)/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))-1/a/x","C"
150,1,62,474,0.005000," ","int(1/x^3/(c*x^6+b*x^3+a),x)","\frac{\left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{3} c -b \right) \ln \left(-\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)+x \right)}{3 a \left(2 \RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{5} c +\RootOf \left(c \,\textit{\_Z}^{6}+b \,\textit{\_Z}^{3}+a \right)^{2} b \right)}-\frac{1}{2 a \,x^{2}}"," ",0,"1/3/a*sum((-_R^3*c-b)/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))-1/2/a/x^2","C"
151,1,28,27,0.005000," ","int(x^11/(x^6+4*x^3+3),x)","\frac{x^{6}}{6}-\frac{4 x^{3}}{3}-\frac{\ln \left(x^{3}+1\right)}{6}+\frac{9 \ln \left(x^{3}+3\right)}{2}"," ",0,"-4/3*x^3+1/6*x^6-1/6*ln(x^3+1)+9/2*ln(x^3+3)","A"
152,1,23,22,0.006000," ","int(x^8/(x^6+4*x^3+3),x)","\frac{x^{3}}{3}+\frac{\ln \left(x^{3}+1\right)}{6}-\frac{3 \ln \left(x^{3}+3\right)}{2}"," ",0,"1/3*x^3+1/6*ln(x^3+1)-3/2*ln(x^3+3)","A"
153,1,18,17,0.004000," ","int(x^5/(x^6+4*x^3+3),x)","-\frac{\ln \left(x^{3}+1\right)}{6}+\frac{\ln \left(x^{3}+3\right)}{2}"," ",0,"-1/6*ln(x^3+1)+1/2*ln(x^3+3)","A"
154,1,18,8,0.003000," ","int(x^2/(x^6+4*x^3+3),x)","\frac{\ln \left(x^{3}+1\right)}{6}-\frac{\ln \left(x^{3}+3\right)}{6}"," ",0,"1/6*ln(x^3+1)-1/6*ln(x^3+3)","B"
155,1,31,21,0.010000," ","int(1/x/(x^6+4*x^3+3),x)","\frac{\ln \left(x \right)}{3}-\frac{\ln \left(x +1\right)}{6}+\frac{\ln \left(x^{3}+3\right)}{18}-\frac{\ln \left(x^{2}-x +1\right)}{6}"," ",0,"1/3*ln(x)-1/6*ln(x+1)+1/18*ln(x^3+3)-1/6*ln(x^2-x+1)","A"
156,1,36,26,0.010000," ","int(1/x^4/(x^6+4*x^3+3),x)","-\frac{4 \ln \left(x \right)}{9}+\frac{\ln \left(x +1\right)}{6}-\frac{\ln \left(x^{3}+3\right)}{54}+\frac{\ln \left(x^{2}-x +1\right)}{6}-\frac{1}{9 x^{3}}"," ",0,"-1/9/x^3-4/9*ln(x)+1/6*ln(x+1)-1/54*ln(x^3+3)+1/6*ln(x^2-x+1)","A"
157,1,41,31,0.008000," ","int(1/x^7/(x^6+4*x^3+3),x)","\frac{13 \ln \left(x \right)}{27}-\frac{\ln \left(x +1\right)}{6}+\frac{\ln \left(x^{3}+3\right)}{162}-\frac{\ln \left(x^{2}-x +1\right)}{6}+\frac{4}{27 x^{3}}-\frac{1}{18 x^{6}}"," ",0,"-1/18/x^6+4/27/x^3+13/27*ln(x)-1/6*ln(x+1)+1/162*ln(x^3+3)-1/6*ln(x^2-x+1)","A"
158,1,94,92,0.010000," ","int(x^10/(x^6+4*x^3+3),x)","\frac{x^{5}}{5}-2 x^{2}+\frac{9 \,3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x +1\right)}{6}-\frac{3 \,3^{\frac{2}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{2}+\frac{3 \,3^{\frac{2}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{4}-\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"1/5*x^5-2*x^2+1/6*ln(x+1)-3/2*3^(2/3)*ln(3^(1/3)+x)+3/4*3^(2/3)*ln(3^(2/3)-3^(1/3)*x+x^2)+9/2*3^(1/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/12*ln(x^2-x+1)-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
159,1,92,90,0.007000," ","int(x^9/(x^6+4*x^3+3),x)","\frac{x^{4}}{4}-4 x +\frac{3 \,3^{\frac{5}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(x +1\right)}{6}+\frac{3 \,3^{\frac{1}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{2}-\frac{3 \,3^{\frac{1}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{4}+\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"1/4*x^4-4*x-1/6*ln(x+1)+3/2*3^(1/3)*ln(x+3^(1/3))-3/4*3^(1/3)*ln(x^2-3^(1/3)*x+3^(2/3))+3/2*3^(5/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))+1/12*ln(x^2-x+1)-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
160,1,89,87,0.007000," ","int(x^7/(x^6+4*x^3+3),x)","\frac{x^{2}}{2}-\frac{3 \,3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{2}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(x +1\right)}{6}+\frac{3^{\frac{2}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{2}-\frac{3^{\frac{2}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{4}+\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"1/2*x^2-1/6*ln(x+1)+1/2*3^(2/3)*ln(x+3^(1/3))-1/4*3^(2/3)*ln(x^2-3^(1/3)*x+3^(2/3))-3/2*3^(1/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))+1/12*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
161,1,85,83,0.007000," ","int(x^6/(x^6+4*x^3+3),x)","x -\frac{3^{\frac{5}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{2}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x +1\right)}{6}-\frac{3^{\frac{1}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{2}+\frac{3^{\frac{1}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{4}-\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"x+1/6*ln(x+1)-1/2*3^(1/3)*ln(x+3^(1/3))+1/4*3^(1/3)*ln(x^2-3^(1/3)*x+3^(2/3))-1/2*3^(5/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/12*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
162,1,84,82,0.006000," ","int(x^4/(x^6+4*x^3+3),x)","\frac{3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x +1\right)}{6}-\frac{3^{\frac{2}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{6}+\frac{3^{\frac{2}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{12}-\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"1/6*ln(x+1)-1/6*3^(2/3)*ln(x+3^(1/3))+1/12*3^(2/3)*ln(x^2-3^(1/3)*x+3^(2/3))+1/2*3^(1/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/12*ln(x^2-x+1)-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
163,1,84,82,0.007000," ","int(x^3/(x^6+4*x^3+3),x)","\frac{3^{\frac{5}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{6}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(x +1\right)}{6}+\frac{3^{\frac{1}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{6}-\frac{3^{\frac{1}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{12}+\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"-1/6*ln(x+1)+1/6*3^(1/3)*ln(x+3^(1/3))-1/12*3^(1/3)*ln(x^2-3^(1/3)*x+3^(2/3))+1/6*3^(5/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))+1/12*ln(x^2-x+1)-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
164,1,84,82,0.005000," ","int(x/(x^6+4*x^3+3),x)","-\frac{3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{6}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(x +1\right)}{6}+\frac{3^{\frac{2}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{18}-\frac{3^{\frac{2}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{36}+\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"-1/6*ln(x+1)+1/18*3^(2/3)*ln(x+3^(1/3))-1/36*3^(2/3)*ln(x^2-3^(1/3)*x+3^(2/3))-1/6*3^(1/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))+1/12*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
165,1,84,82,0.007000," ","int(1/(x^6+4*x^3+3),x)","-\frac{3^{\frac{5}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{18}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x +1\right)}{6}-\frac{3^{\frac{1}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{18}+\frac{3^{\frac{1}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{36}-\frac{\ln \left(x^{2}-x +1\right)}{12}"," ",0,"1/6*ln(x+1)-1/18*3^(1/3)*ln(x+3^(1/3))+1/36*3^(1/3)*ln(x^2-3^(1/3)*x+3^(2/3))-1/18*3^(5/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/12*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
166,1,89,87,0.007000," ","int(1/x^2/(x^6+4*x^3+3),x)","\frac{3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{18}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x +1\right)}{6}-\frac{3^{\frac{2}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{54}+\frac{3^{\frac{2}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{108}-\frac{\ln \left(x^{2}-x +1\right)}{12}-\frac{1}{3 x}"," ",0,"1/6*ln(x+1)-1/3/x-1/54*3^(2/3)*ln(x+3^(1/3))+1/108*3^(2/3)*ln(x^2-3^(1/3)*x+3^(2/3))+1/18*3^(1/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/12*ln(x^2-x+1)-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
167,1,89,87,0.008000," ","int(1/x^3/(x^6+4*x^3+3),x)","\frac{3^{\frac{5}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{54}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(x +1\right)}{6}+\frac{3^{\frac{1}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{54}-\frac{3^{\frac{1}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{108}+\frac{\ln \left(x^{2}-x +1\right)}{12}-\frac{1}{6 x^{2}}"," ",0,"-1/6*ln(x+1)+1/54*3^(1/3)*ln(x+3^(1/3))-1/108*3^(1/3)*ln(x^2-3^(1/3)*x+3^(2/3))+1/54*3^(5/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/6/x^2+1/12*ln(x^2-x+1)-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
168,1,94,92,0.011000," ","int(1/x^5/(x^6+4*x^3+3),x)","-\frac{3^{\frac{1}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{54}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\ln \left(x +1\right)}{6}+\frac{3^{\frac{2}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{162}-\frac{3^{\frac{2}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{324}+\frac{\ln \left(x^{2}-x +1\right)}{12}+\frac{4}{9 x}-\frac{1}{12 x^{4}}"," ",0,"-1/12/x^4+4/9/x-1/6*ln(x+1)+1/162*3^(2/3)*ln(x+3^(1/3))-1/324*3^(2/3)*ln(x^2-3^(1/3)*x+3^(2/3))-1/54*3^(1/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))+1/12*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
169,1,94,92,0.014000," ","int(1/x^6/(x^6+4*x^3+3),x)","-\frac{3^{\frac{5}{6}} \arctan \left(\frac{\sqrt{3}\, \left(\frac{2 \,3^{\frac{2}{3}} x}{3}-1\right)}{3}\right)}{162}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\ln \left(x +1\right)}{6}-\frac{3^{\frac{1}{3}} \ln \left(x +3^{\frac{1}{3}}\right)}{162}+\frac{3^{\frac{1}{3}} \ln \left(x^{2}-3^{\frac{1}{3}} x +3^{\frac{2}{3}}\right)}{324}-\frac{\ln \left(x^{2}-x +1\right)}{12}+\frac{2}{9 x^{2}}-\frac{1}{15 x^{5}}"," ",0,"-1/15/x^5+2/9/x^2+1/6*ln(x+1)-1/162*3^(1/3)*ln(x+3^(1/3))+1/324*3^(1/3)*ln(x^2-3^(1/3)*x+3^(2/3))-1/162*3^(5/6)*arctan(1/3*3^(1/2)*(2/3*3^(2/3)*x-1))-1/12*ln(x^2-x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
170,1,44,290,0.013000," ","int(x^6/(x^6-x^3+1),x)","x +\frac{\left(\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{3}-1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-3 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}}"," ",0,"x+1/3*sum((_R^3-1)/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))","C"
171,1,33,32,0.005000," ","int(x^5/(x^6-x^3+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{3}-1\right) \sqrt{3}}{3}\right)}{9}+\frac{\ln \left(x^{6}-x^{3}+1\right)}{6}"," ",0,"1/6*ln(x^6-x^3+1)+1/9*3^(1/2)*arctan(1/3*(2*x^3-1)*3^(1/2))","A"
172,1,40,289,0.007000," ","int(x^4/(x^6-x^3+1),x)","\frac{\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{4} \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-3 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}}"," ",0,"1/3*sum(_R^4/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))","C"
173,1,40,289,0.007000," ","int(x^3/(x^6-x^3+1),x)","\frac{\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{3} \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-3 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}}"," ",0,"1/3*sum(_R^3/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))","C"
174,1,19,18,0.001000," ","int(x^2/(x^6-x^3+1),x)","\frac{2 \sqrt{3}\, \arctan \left(\frac{\left(2 x^{3}-1\right) \sqrt{3}}{3}\right)}{9}"," ",0,"2/9*3^(1/2)*arctan(1/3*(2*x^3-1)*3^(1/2))","A"
175,1,38,261,0.007000," ","int(x/(x^6-x^3+1),x)","\frac{\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-3 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}}"," ",0,"1/3*sum(_R/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))","C"
176,1,37,130,0.007000," ","int(1/(x^6-x^3+1),x)","\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-3 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}}"," ",0,"1/3*sum(1/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))","C"
177,1,35,34,0.006000," ","int(1/x/(x^6-x^3+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{3}-1\right) \sqrt{3}}{3}\right)}{9}+\ln \left(x \right)-\frac{\ln \left(x^{6}-x^{3}+1\right)}{6}"," ",0,"-1/6*ln(x^6-x^3+1)+1/9*3^(1/2)*arctan(1/3*(2*x^3-1)*3^(1/2))+ln(x)","A"
178,1,50,294,0.009000," ","int(1/x^2/(x^6-x^3+1),x)","-\frac{\left(\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{4}-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)\right) \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{3 \left(2 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}\right)}-\frac{1}{x}"," ",0,"-1/3*sum((_R^4-_R)/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))-1/x","C"
179,1,50,294,0.009000," ","int(1/x^3/(x^6-x^3+1),x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{3}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-3 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}}-\frac{1}{2 x^{2}}"," ",0,"1/3*sum((-_R^3+1)/(2*_R^5-_R^2)*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))-1/2/x^2","C"
180,1,40,39,0.007000," ","int(1/x^4/(x^6-x^3+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{3}-1\right) \sqrt{3}}{3}\right)}{9}+\ln \left(x \right)-\frac{\ln \left(x^{6}-x^{3}+1\right)}{6}-\frac{1}{3 x^{3}}"," ",0,"-1/6*ln(x^6-x^3+1)-1/9*3^(1/2)*arctan(1/3*(2*x^3-1)*3^(1/2))-1/3/x^3+ln(x)","A"
181,1,51,299,0.010000," ","int(1/x^5/(x^6-x^3+1),x)","-\frac{\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{4} \ln \left(-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)+x \right)}{3 \left(2 \RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{5}-\RootOf \left(\textit{\_Z}^{6}-\textit{\_Z}^{3}+1\right)^{2}\right)}-\frac{1}{x}-\frac{1}{4 x^{4}}"," ",0,"-1/3*sum(1/(2*_R^5-_R^2)*_R^4*ln(-_R+x),_R=RootOf(_Z^6-_Z^3+1))-1/4/x^4-1/x","C"
182,1,33,267,0.007000," ","int(1/(x^6+x^3+2),x)","\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)^{5}+3 \RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)^{2}}"," ",0,"1/3*sum(1/(2*_R^5+_R^2)*ln(-_R+x),_R=RootOf(_Z^6+_Z^3+2))","C"
183,1,19,18,0.003000," ","int(x^2/(x^6+x^3+2),x)","\frac{2 \sqrt{7}\, \arctan \left(\frac{\left(2 x^{3}+1\right) \sqrt{7}}{7}\right)}{21}"," ",0,"2/21*arctan(1/7*(2*x^3+1)*7^(1/2))*7^(1/2)","A"
184,1,36,283,0.006000," ","int(x^3/(x^6+x^3+2),x)","\frac{\RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)^{3} \ln \left(-\RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)+x \right)}{6 \RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)^{5}+3 \RootOf \left(\textit{\_Z}^{6}+\textit{\_Z}^{3}+2\right)^{2}}"," ",0,"1/3*sum(_R^3/(2*_R^5+_R^2)*ln(-_R+x),_R=RootOf(_Z^6+_Z^3+2))","C"
185,0,0,205,0.053000," ","int(x^14*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{14}\, dx"," ",0,"int(x^14*(c*x^6+b*x^3+a)^(1/2),x)","F"
186,0,0,149,0.046000," ","int(x^11*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{11}\, dx"," ",0,"int(x^11*(c*x^6+b*x^3+a)^(1/2),x)","F"
187,0,0,131,0.032000," ","int(x^8*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{8}\, dx"," ",0,"int(x^8*(c*x^6+b*x^3+a)^(1/2),x)","F"
188,0,0,90,0.028000," ","int(x^5*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{5}\, dx"," ",0,"int(x^5*(c*x^6+b*x^3+a)^(1/2),x)","F"
189,0,0,69,0.026000," ","int(x^2*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{2}\, dx"," ",0,"int(x^2*(c*x^6+b*x^3+a)^(1/2),x)","F"
190,0,0,85,0.036000," ","int((c*x^6+b*x^3+a)^(1/2)/x,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x,x)","F"
191,0,0,88,0.043000," ","int((c*x^6+b*x^3+a)^(1/2)/x^4,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{4}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^4,x)","F"
192,0,0,74,0.039000," ","int((c*x^6+b*x^3+a)^(1/2)/x^7,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{7}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^7,x)","F"
193,0,0,98,0.050000," ","int((c*x^6+b*x^3+a)^(1/2)/x^10,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{10}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^10,x)","F"
194,0,0,139,0.060000," ","int((c*x^6+b*x^3+a)^(1/2)/x^13,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{13}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^13,x)","F"
195,0,0,173,0.061000," ","int((c*x^6+b*x^3+a)^(1/2)/x^16,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{16}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^16,x)","F"
196,0,0,116,0.045000," ","int(x^3*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{3}\, dx"," ",0,"int(x^3*(c*x^6+b*x^3+a)^(1/2),x)","F"
197,0,0,116,0.043000," ","int(x*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, x\, dx"," ",0,"int(x*(c*x^6+b*x^3+a)^(1/2),x)","F"
198,0,0,113,0.033000," ","int((c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2),x)","F"
199,0,0,116,0.046000," ","int((c*x^6+b*x^3+a)^(1/2)/x^2,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{2}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^2,x)","F"
200,0,0,116,0.039000," ","int((c*x^6+b*x^3+a)^(1/2)/x^3,x)","\int \frac{\sqrt{c \,x^{6}+b \,x^{3}+a}}{x^{3}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(1/2)/x^3,x)","F"
201,0,0,263,0.049000," ","int(x^14*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{14}\, dx"," ",0,"int(x^14*(c*x^6+b*x^3+a)^(3/2),x)","F"
202,0,0,197,0.032000," ","int(x^11*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{11}\, dx"," ",0,"int(x^11*(c*x^6+b*x^3+a)^(3/2),x)","F"
203,0,0,178,0.031000," ","int(x^8*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{8}\, dx"," ",0,"int(x^8*(c*x^6+b*x^3+a)^(3/2),x)","F"
204,0,0,128,0.036000," ","int(x^5*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{5}\, dx"," ",0,"int(x^5*(c*x^6+b*x^3+a)^(3/2),x)","F"
205,0,0,106,0.033000," ","int(x^2*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{2}\, dx"," ",0,"int(x^2*(c*x^6+b*x^3+a)^(3/2),x)","F"
206,0,0,127,0.042000," ","int((c*x^6+b*x^3+a)^(3/2)/x,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x,x)","F"
207,0,0,122,0.065000," ","int((c*x^6+b*x^3+a)^(3/2)/x^4,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{4}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^4,x)","F"
208,0,0,123,0.056000," ","int((c*x^6+b*x^3+a)^(3/2)/x^7,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{7}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^7,x)","F"
209,0,0,135,0.056000," ","int((c*x^6+b*x^3+a)^(3/2)/x^10,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{10}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^10,x)","F"
210,0,0,115,0.051000," ","int((c*x^6+b*x^3+a)^(3/2)/x^13,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{13}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^13,x)","F"
211,0,0,140,0.065000," ","int((c*x^6+b*x^3+a)^(3/2)/x^16,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{16}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^16,x)","F"
212,0,0,190,0.078000," ","int((c*x^6+b*x^3+a)^(3/2)/x^19,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{19}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^19,x)","F"
213,0,0,225,0.093000," ","int((c*x^6+b*x^3+a)^(3/2)/x^22,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{22}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^22,x)","F"
214,0,0,117,0.045000," ","int(x^3*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{3}\, dx"," ",0,"int(x^3*(c*x^6+b*x^3+a)^(3/2),x)","F"
215,0,0,117,0.043000," ","int(x*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x\, dx"," ",0,"int(x*(c*x^6+b*x^3+a)^(3/2),x)","F"
216,0,0,114,0.038000," ","int((c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2),x)","F"
217,0,0,117,0.046000," ","int((c*x^6+b*x^3+a)^(3/2)/x^2,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^2,x)","F"
218,0,0,117,0.042000," ","int((c*x^6+b*x^3+a)^(3/2)/x^3,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^(3/2)/x^3,x)","F"
219,0,0,149,0.036000," ","int(x^14/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x^{14}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x^14/(c*x^6+b*x^3+a)^(1/2),x)","F"
220,0,0,103,0.040000," ","int(x^11/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x^{11}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x^11/(c*x^6+b*x^3+a)^(1/2),x)","F"
221,0,0,86,0.027000," ","int(x^8/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x^{8}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x^8/(c*x^6+b*x^3+a)^(1/2),x)","F"
222,0,0,54,0.024000," ","int(x^5/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x^{5}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x^5/(c*x^6+b*x^3+a)^(1/2),x)","F"
223,0,0,33,0.020000," ","int(x^2/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x^{2}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x^2/(c*x^6+b*x^3+a)^(1/2),x)","F"
224,0,0,34,0.020000," ","int(1/x/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x}\, dx"," ",0,"int(1/x/(c*x^6+b*x^3+a)^(1/2),x)","F"
225,0,0,58,0.033000," ","int(1/x^4/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{4}}\, dx"," ",0,"int(1/x^4/(c*x^6+b*x^3+a)^(1/2),x)","F"
226,0,0,90,0.037000," ","int(1/x^7/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{7}}\, dx"," ",0,"int(1/x^7/(c*x^6+b*x^3+a)^(1/2),x)","F"
227,0,0,123,0.042000," ","int(1/x^10/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{10}}\, dx"," ",0,"int(1/x^10/(c*x^6+b*x^3+a)^(1/2),x)","F"
228,0,0,166,0.046000," ","int(1/x^13/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{13}}\, dx"," ",0,"int(1/x^13/(c*x^6+b*x^3+a)^(1/2),x)","F"
229,0,0,116,0.023000," ","int(x^3/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x^{3}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x^3/(c*x^6+b*x^3+a)^(1/2),x)","F"
230,0,0,116,0.020000," ","int(x/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{x}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(x/(c*x^6+b*x^3+a)^(1/2),x)","F"
231,0,0,113,0.024000," ","int(1/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int(1/(c*x^6+b*x^3+a)^(1/2),x)","F"
232,0,0,116,0.048000," ","int(1/x^2/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{2}}\, dx"," ",0,"int(1/x^2/(c*x^6+b*x^3+a)^(1/2),x)","F"
233,0,0,116,0.048000," ","int(1/x^3/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{1}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, x^{3}}\, dx"," ",0,"int(1/x^3/(c*x^6+b*x^3+a)^(1/2),x)","F"
234,0,0,173,0.065000," ","int(x^14/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{x^{14}}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^14/(c*x^6+b*x^3+a)^(3/2),x)","F"
235,0,0,119,0.055000," ","int(x^11/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{x^{11}}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^11/(c*x^6+b*x^3+a)^(3/2),x)","F"
236,0,0,102,0.028000," ","int(x^8/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{x^{8}}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^8/(c*x^6+b*x^3+a)^(3/2),x)","F"
237,1,38,35,0.006000," ","int(x^5/(c*x^6+b*x^3+a)^(3/2),x)","-\frac{2 \left(b \,x^{3}+2 a \right)}{3 \sqrt{c \,x^{6}+b \,x^{3}+a}\, \left(4 a c -b^{2}\right)}"," ",0,"-2/3/(c*x^6+b*x^3+a)^(1/2)*(b*x^3+2*a)/(4*a*c-b^2)","A"
238,1,37,34,0.006000," ","int(x^2/(c*x^6+b*x^3+a)^(3/2),x)","\frac{\frac{4 c \,x^{3}}{3}+\frac{2 b}{3}}{\sqrt{c \,x^{6}+b \,x^{3}+a}\, \left(4 a c -b^{2}\right)}"," ",0,"2/3/(c*x^6+b*x^3+a)^(1/2)*(2*c*x^3+b)/(4*a*c-b^2)","A"
239,0,0,78,0.062000," ","int(1/x/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x}\, dx"," ",0,"int(1/x/(c*x^6+b*x^3+a)^(3/2),x)","F"
240,0,0,124,0.087000," ","int(1/x^4/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{4}}\, dx"," ",0,"int(1/x^4/(c*x^6+b*x^3+a)^(3/2),x)","F"
241,0,0,176,0.098000," ","int(1/x^7/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{7}}\, dx"," ",0,"int(1/x^7/(c*x^6+b*x^3+a)^(3/2),x)","F"
242,0,0,230,0.133000," ","int(1/x^10/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{10}}\, dx"," ",0,"int(1/x^10/(c*x^6+b*x^3+a)^(3/2),x)","F"
243,0,0,119,0.031000," ","int(x^3/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{x^{3}}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(c*x^6+b*x^3+a)^(3/2),x)","F"
244,0,0,119,0.030000," ","int(x/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{x}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(c*x^6+b*x^3+a)^(3/2),x)","F"
245,0,0,116,0.031000," ","int(1/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(c*x^6+b*x^3+a)^(3/2),x)","F"
246,0,0,119,0.063000," ","int(1/x^2/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{2}}\, dx"," ",0,"int(1/x^2/(c*x^6+b*x^3+a)^(3/2),x)","F"
247,0,0,119,0.081000," ","int(1/x^3/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{1}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} x^{3}}\, dx"," ",0,"int(1/x^3/(c*x^6+b*x^3+a)^(3/2),x)","F"
248,1,301,101,0.008000," ","int((d*x)^m*(c*x^6+b*x^3+a)^2,x)","\frac{\left(c^{2} m^{4} x^{12}+22 c^{2} m^{3} x^{12}+159 c^{2} m^{2} x^{12}+2 b c \,m^{4} x^{9}+418 c^{2} m \,x^{12}+50 b c \,m^{3} x^{9}+280 c^{2} x^{12}+390 b c \,m^{2} x^{9}+2 a c \,m^{4} x^{6}+b^{2} m^{4} x^{6}+1070 b c m \,x^{9}+56 a c \,m^{3} x^{6}+28 b^{2} m^{3} x^{6}+728 b c \,x^{9}+498 a c \,m^{2} x^{6}+249 b^{2} m^{2} x^{6}+2 a b \,m^{4} x^{3}+1484 a c m \,x^{6}+742 b^{2} m \,x^{6}+62 a b \,m^{3} x^{3}+1040 a c \,x^{6}+520 b^{2} x^{6}+642 a b \,m^{2} x^{3}+a^{2} m^{4}+2402 a b m \,x^{3}+34 a^{2} m^{3}+1820 a b \,x^{3}+411 a^{2} m^{2}+2074 a^{2} m +3640 a^{2}\right) x \left(d x \right)^{m}}{\left(m +13\right) \left(m +10\right) \left(m +7\right) \left(m +4\right) \left(m +1\right)}"," ",0,"x*(c^2*m^4*x^12+22*c^2*m^3*x^12+159*c^2*m^2*x^12+2*b*c*m^4*x^9+418*c^2*m*x^12+50*b*c*m^3*x^9+280*c^2*x^12+390*b*c*m^2*x^9+2*a*c*m^4*x^6+b^2*m^4*x^6+1070*b*c*m*x^9+56*a*c*m^3*x^6+28*b^2*m^3*x^6+728*b*c*x^9+498*a*c*m^2*x^6+249*b^2*m^2*x^6+2*a*b*m^4*x^3+1484*a*c*m*x^6+742*b^2*m*x^6+62*a*b*m^3*x^3+1040*a*c*x^6+520*b^2*x^6+642*a*b*m^2*x^3+a^2*m^4+2402*a*b*m*x^3+34*a^2*m^3+1820*a*b*x^3+411*a^2*m^2+2074*a^2*m+3640*a^2)*(d*x)^m/(m+13)/(m+10)/(m+7)/(m+4)/(m+1)","B"
249,1,78,52,0.003000," ","int((d*x)^m*(c*x^6+b*x^3+a),x)","\frac{\left(c \,m^{2} x^{6}+5 c m \,x^{6}+4 c \,x^{6}+b \,m^{2} x^{3}+8 b m \,x^{3}+7 b \,x^{3}+a \,m^{2}+11 a m +28 a \right) x \left(d x \right)^{m}}{\left(m +7\right) \left(m +4\right) \left(m +1\right)}"," ",0,"x*(c*m^2*x^6+5*c*m*x^6+4*c*x^6+b*m^2*x^3+8*b*m*x^3+7*b*x^3+a*m^2+11*a*m+28*a)*(d*x)^m/(m+7)/(m+4)/(m+1)","A"
250,0,0,157,0.045000," ","int((d*x)^m/(c*x^6+b*x^3+a),x)","\int \frac{\left(d x \right)^{m}}{c \,x^{6}+b \,x^{3}+a}\, dx"," ",0,"int((d*x)^m/(c*x^6+b*x^3+a),x)","F"
251,0,0,289,0.026000," ","int((d*x)^m/(c*x^6+b*x^3+a)^2,x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{6}+b \,x^{3}+a \right)^{2}}\, dx"," ",0,"int((d*x)^m/(c*x^6+b*x^3+a)^2,x)","F"
252,0,0,136,0.017000," ","int((d*x)^m*(c*x^6+b*x^3+a)^(3/2),x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}} \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^6+b*x^3+a)^(3/2),x)","F"
253,0,0,135,0.013000," ","int((d*x)^m*(c*x^6+b*x^3+a)^(1/2),x)","\int \sqrt{c \,x^{6}+b \,x^{3}+a}\, \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(c*x^6+b*x^3+a)^(1/2),x)","F"
254,0,0,135,0.013000," ","int((d*x)^m/(c*x^6+b*x^3+a)^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{c \,x^{6}+b \,x^{3}+a}}\, dx"," ",0,"int((d*x)^m/(c*x^6+b*x^3+a)^(1/2),x)","F"
255,0,0,138,0.011000," ","int((d*x)^m/(c*x^6+b*x^3+a)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(c \,x^{6}+b \,x^{3}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(c*x^6+b*x^3+a)^(3/2),x)","F"
256,0,0,143,0.068000," ","int((d*x)^m*(c*x^6+b*x^3+a)^p,x)","\int \left(d x \right)^{m} \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int((d*x)^m*(c*x^6+b*x^3+a)^p,x)","F"
257,0,0,207,0.026000," ","int(x^8*(c*x^6+b*x^3+a)^p,x)","\int x^{8} \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x^8*(c*x^6+b*x^3+a)^p,x)","F"
258,0,0,146,0.039000," ","int(x^5*(c*x^6+b*x^3+a)^p,x)","\int x^{5} \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x^5*(c*x^6+b*x^3+a)^p,x)","F"
259,0,0,117,0.029000," ","int(x^2*(c*x^6+b*x^3+a)^p,x)","\int x^{2} \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x^2*(c*x^6+b*x^3+a)^p,x)","F"
260,0,0,124,0.033000," ","int(x^4*(c*x^6+b*x^3+a)^p,x)","\int x^{4} \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x^4*(c*x^6+b*x^3+a)^p,x)","F"
261,0,0,124,0.032000," ","int(x^3*(c*x^6+b*x^3+a)^p,x)","\int x^{3} \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x^3*(c*x^6+b*x^3+a)^p,x)","F"
262,0,0,124,0.026000," ","int(x*(c*x^6+b*x^3+a)^p,x)","\int x \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int(x*(c*x^6+b*x^3+a)^p,x)","F"
263,0,0,121,0.016000," ","int((c*x^6+b*x^3+a)^p,x)","\int \left(c \,x^{6}+b \,x^{3}+a \right)^{p}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p,x)","F"
264,0,0,147,0.017000," ","int((c*x^6+b*x^3+a)^p/x,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x,x)","F"
265,0,0,124,0.030000," ","int((c*x^6+b*x^3+a)^p/x^2,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x^{2}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x^2,x)","F"
266,0,0,124,0.036000," ","int((c*x^6+b*x^3+a)^p/x^3,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x^{3}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x^3,x)","F"
267,0,0,152,0.033000," ","int((c*x^6+b*x^3+a)^p/x^4,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x^{4}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x^4,x)","F"
268,0,0,124,0.038000," ","int((c*x^6+b*x^3+a)^p/x^5,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x^{5}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x^5,x)","F"
269,0,0,124,0.043000," ","int((c*x^6+b*x^3+a)^p/x^6,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x^{6}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x^6,x)","F"
270,0,0,156,0.045000," ","int((c*x^6+b*x^3+a)^p/x^7,x)","\int \frac{\left(c \,x^{6}+b \,x^{3}+a \right)^{p}}{x^{7}}\, dx"," ",0,"int((c*x^6+b*x^3+a)^p/x^7,x)","F"
271,0,0,30,0.025000," ","int(x^m/(x^8+2*x^4+1),x)","\int \frac{x^{m}}{x^{8}+2 x^{4}+1}\, dx"," ",0,"int(x^m/(x^8+2*x^4+1),x)","F"
272,1,25,24,0.009000," ","int(x^9/(x^8+2*x^4+1),x)","\frac{x^{2}}{2}+\frac{x^{2}}{4 x^{4}+4}-\frac{3 \arctan \left(x^{2}\right)}{4}"," ",0,"1/2*x^2+1/4*x^2/(x^4+1)-3/4*arctan(x^2)","A"
273,1,19,18,0.007000," ","int(x^7/(x^8+2*x^4+1),x)","\frac{\ln \left(x^{4}+1\right)}{4}+\frac{1}{4 x^{4}+4}"," ",0,"1/4/(x^4+1)+1/4*ln(x^4+1)","A"
274,1,20,19,0.006000," ","int(x^5/(x^8+2*x^4+1),x)","-\frac{x^{2}}{4 \left(x^{4}+1\right)}+\frac{\arctan \left(x^{2}\right)}{4}"," ",0,"-1/4/(x^4+1)*x^2+1/4*arctan(x^2)","A"
275,1,10,9,0.003000," ","int(x^3/(x^8+2*x^4+1),x)","-\frac{1}{4 \left(x^{4}+1\right)}"," ",0,"-1/4/(x^4+1)","A"
276,1,20,19,0.004000," ","int(x/(x^8+2*x^4+1),x)","\frac{x^{2}}{4 x^{4}+4}+\frac{\arctan \left(x^{2}\right)}{4}"," ",0,"1/4/(x^4+1)*x^2+1/4*arctan(x^2)","A"
277,1,21,20,0.013000," ","int(1/x/(x^8+2*x^4+1),x)","\ln \left(x \right)-\frac{\ln \left(x^{4}+1\right)}{4}+\frac{1}{4 x^{4}+4}"," ",0,"1/4/(x^4+1)+ln(x)-1/4*ln(x^4+1)","A"
278,1,25,24,0.010000," ","int(1/x^3/(x^8+2*x^4+1),x)","-\frac{x^{2}}{4 \left(x^{4}+1\right)}-\frac{3 \arctan \left(x^{2}\right)}{4}-\frac{1}{2 x^{2}}"," ",0,"-1/2/x^2-1/4/(x^4+1)*x^2-3/4*arctan(x^2)","A"
279,1,28,27,0.015000," ","int(1/x^5/(x^8+2*x^4+1),x)","-2 \ln \left(x \right)+\frac{\ln \left(x^{4}+1\right)}{2}-\frac{1}{4 x^{4}}-\frac{1}{4 \left(x^{4}+1\right)}"," ",0,"-1/4/x^4-1/4/(x^4+1)-2*ln(x)+1/2*ln(x^4+1)","A"
280,1,28,29,0.012000," ","int(1/x^7/(x^8+2*x^4+1),x)","\frac{x^{2}}{4 x^{4}+4}+\frac{5 \arctan \left(x^{2}\right)}{4}+\frac{1}{x^{2}}-\frac{1}{6 x^{6}}"," ",0,"-1/6/x^6+1/x^2+1/4/(x^4+1)*x^2+5/4*arctan(x^2)","A"
281,1,69,75,0.010000," ","int(x^8/(x^8+2*x^4+1),x)","x +\frac{x}{4 x^{4}+4}-\frac{5 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}-\frac{5 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}-\frac{5 \sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{32}"," ",0,"x+1/4*x/(x^4+1)-5/32*2^(1/2)*ln((1+x^2+2^(1/2)*x)/(1+x^2-2^(1/2)*x))-5/16*arctan(-1+2^(1/2)*x)*2^(1/2)-5/16*arctan(1+2^(1/2)*x)*2^(1/2)","A"
282,1,70,72,0.008000," ","int(x^6/(x^8+2*x^4+1),x)","-\frac{x^{3}}{4 \left(x^{4}+1\right)}+\frac{3 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}+\frac{3 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}+\frac{3 \sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{32}"," ",0,"-1/4*x^3/(x^4+1)+3/16*2^(1/2)*arctan(2^(1/2)*x-1)+3/32*2^(1/2)*ln((x^2-2^(1/2)*x+1)/(x^2+2^(1/2)*x+1))+3/16*2^(1/2)*arctan(2^(1/2)*x+1)","A"
283,1,68,70,0.006000," ","int(x^4/(x^8+2*x^4+1),x)","-\frac{x}{4 \left(x^{4}+1\right)}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{32}"," ",0,"-1/4/(x^4+1)*x+1/32*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))+1/16*2^(1/2)*arctan(2^(1/2)*x-1)+1/16*2^(1/2)*arctan(2^(1/2)*x+1)","A"
284,1,70,72,0.007000," ","int(x^2/(x^8+2*x^4+1),x)","\frac{x^{3}}{4 x^{4}+4}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}+\frac{\sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}+\frac{\sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{32}"," ",0,"1/4/(x^4+1)*x^3+1/16*2^(1/2)*arctan(2^(1/2)*x-1)+1/32*2^(1/2)*ln((x^2-2^(1/2)*x+1)/(x^2+2^(1/2)*x+1))+1/16*2^(1/2)*arctan(2^(1/2)*x+1)","A"
285,1,68,70,0.004000," ","int(1/(x^8+2*x^4+1),x)","\frac{x}{4 x^{4}+4}+\frac{3 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}+\frac{3 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}+\frac{3 \sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{32}"," ",0,"1/4/(x^4+1)*x+3/16*2^(1/2)*arctan(2^(1/2)*x-1)+3/32*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))+3/16*2^(1/2)*arctan(2^(1/2)*x+1)","A"
286,1,75,77,0.009000," ","int(1/x^2/(x^8+2*x^4+1),x)","-\frac{x^{3}}{4 \left(x^{4}+1\right)}-\frac{5 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}-\frac{5 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}-\frac{5 \sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{32}-\frac{1}{x}"," ",0,"-1/x-1/4/(x^4+1)*x^3-5/16*2^(1/2)*arctan(2^(1/2)*x-1)-5/32*2^(1/2)*ln((x^2-2^(1/2)*x+1)/(x^2+2^(1/2)*x+1))-5/16*2^(1/2)*arctan(2^(1/2)*x+1)","A"
287,1,73,77,0.010000," ","int(1/x^4/(x^8+2*x^4+1),x)","-\frac{x}{4 \left(x^{4}+1\right)}-\frac{7 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}-\frac{7 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}-\frac{7 \sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{32}-\frac{1}{3 x^{3}}"," ",0,"-1/3/x^3-1/4/(x^4+1)*x-7/32*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))-7/16*2^(1/2)*arctan(2^(1/2)*x+1)-7/16*2^(1/2)*arctan(2^(1/2)*x-1)","A"
288,1,80,82,0.012000," ","int(1/x^6/(x^8+2*x^4+1),x)","\frac{x^{3}}{4 x^{4}+4}+\frac{9 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}+\frac{9 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}+\frac{9 \sqrt{2}\, \ln \left(\frac{x^{2}-\sqrt{2}\, x +1}{x^{2}+\sqrt{2}\, x +1}\right)}{32}+\frac{2}{x}-\frac{1}{5 x^{5}}"," ",0,"-1/5/x^5+2/x+1/4/(x^4+1)*x^3+9/32*2^(1/2)*ln((x^2-2^(1/2)*x+1)/(x^2+2^(1/2)*x+1))+9/16*2^(1/2)*arctan(2^(1/2)*x+1)+9/16*2^(1/2)*arctan(2^(1/2)*x-1)","A"
289,1,78,82,0.010000," ","int(1/x^8/(x^8+2*x^4+1),x)","\frac{x}{4 x^{4}+4}+\frac{11 \sqrt{2}\, \arctan \left(\sqrt{2}\, x -1\right)}{16}+\frac{11 \sqrt{2}\, \arctan \left(\sqrt{2}\, x +1\right)}{16}+\frac{11 \sqrt{2}\, \ln \left(\frac{x^{2}+\sqrt{2}\, x +1}{x^{2}-\sqrt{2}\, x +1}\right)}{32}+\frac{2}{3 x^{3}}-\frac{1}{7 x^{7}}"," ",0,"-1/7/x^7+2/3/x^3+1/4/(x^4+1)*x+11/16*2^(1/2)*arctan(2^(1/2)*x-1)+11/32*2^(1/2)*ln((x^2+2^(1/2)*x+1)/(x^2-2^(1/2)*x+1))+11/16*2^(1/2)*arctan(2^(1/2)*x+1)","A"
290,0,0,28,0.020000," ","int(x^m/(x^8-2*x^4+1),x)","\int \frac{x^{m}}{x^{8}-2 x^{4}+1}\, dx"," ",0,"int(x^m/(x^8-2*x^4+1),x)","F"
291,1,41,26,0.009000," ","int(x^9/(x^8-2*x^4+1),x)","\frac{x^{2}}{2}+\frac{3 \ln \left(x^{2}-1\right)}{8}-\frac{3 \ln \left(x^{2}+1\right)}{8}-\frac{1}{8 \left(x^{2}+1\right)}-\frac{1}{8 \left(x^{2}-1\right)}"," ",0,"1/2*x^2-1/8/(x^2+1)-3/8*ln(x^2+1)-1/8/(x^2-1)+3/8*ln(x^2-1)","A"
292,1,19,22,0.006000," ","int(x^7/(x^8-2*x^4+1),x)","\frac{\ln \left(x^{4}-1\right)}{4}-\frac{1}{4 \left(x^{4}-1\right)}"," ",0,"-1/4/(x^4-1)+1/4*ln(x^4-1)","A"
293,1,36,21,0.009000," ","int(x^5/(x^8-2*x^4+1),x)","\frac{\ln \left(x^{2}-1\right)}{8}-\frac{\ln \left(x^{2}+1\right)}{8}-\frac{1}{8 \left(x^{2}+1\right)}-\frac{1}{8 \left(x^{2}-1\right)}"," ",0,"-1/8/(x^2+1)-1/8*ln(x^2+1)-1/8/(x^2-1)+1/8*ln(x^2-1)","A"
294,1,10,11,0.003000," ","int(x^3/(x^8-2*x^4+1),x)","-\frac{1}{4 \left(x^{4}-1\right)}"," ",0,"-1/4/(x^4-1)","A"
295,1,36,21,0.010000," ","int(x/(x^8-2*x^4+1),x)","-\frac{\ln \left(x^{2}-1\right)}{8}+\frac{\ln \left(x^{2}+1\right)}{8}-\frac{1}{8 \left(x^{2}+1\right)}-\frac{1}{8 \left(x^{2}-1\right)}"," ",0,"-1/8/(x^2+1)+1/8*ln(x^2+1)-1/8/(x^2-1)-1/8*ln(x^2-1)","A"
296,1,47,24,0.015000," ","int(1/x/(x^8-2*x^4+1),x)","\ln \left(x \right)-\frac{\ln \left(x -1\right)}{4}-\frac{\ln \left(x +1\right)}{4}-\frac{\ln \left(x^{2}+1\right)}{4}+\frac{1}{16 x +16}+\frac{1}{8 x^{2}+8}-\frac{1}{16 \left(x -1\right)}"," ",0,"ln(x)+1/16/(x+1)-1/4*ln(x+1)-1/4*ln(x^2+1)+1/8/(x^2+1)-1/16/(x-1)-1/4*ln(x-1)","A"
297,1,50,26,0.017000," ","int(1/x^3/(x^8-2*x^4+1),x)","-\frac{3 \ln \left(x -1\right)}{8}-\frac{3 \ln \left(x +1\right)}{8}+\frac{3 \ln \left(x^{2}+1\right)}{8}-\frac{1}{2 x^{2}}+\frac{1}{16 x +16}-\frac{1}{8 \left(x^{2}+1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/2/x^2+1/16/(x+1)-3/8*ln(x+1)+3/8*ln(x^2+1)-1/8/(x^2+1)-1/16/(x-1)-3/8*ln(x-1)","A"
298,1,54,31,0.018000," ","int(1/x^5/(x^8-2*x^4+1),x)","2 \ln \left(x \right)-\frac{\ln \left(x -1\right)}{2}-\frac{\ln \left(x +1\right)}{2}-\frac{\ln \left(x^{2}+1\right)}{2}-\frac{1}{4 x^{4}}+\frac{1}{16 x +16}+\frac{1}{8 x^{2}+8}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/4/x^4+2*ln(x)+1/16/(x+1)-1/2*ln(x+1)-1/2*ln(x^2+1)+1/8/(x^2+1)-1/16/(x-1)-1/2*ln(x-1)","A"
299,1,55,31,0.020000," ","int(1/x^7/(x^8-2*x^4+1),x)","-\frac{5 \ln \left(x -1\right)}{8}-\frac{5 \ln \left(x +1\right)}{8}+\frac{5 \ln \left(x^{2}+1\right)}{8}-\frac{1}{x^{2}}-\frac{1}{6 x^{6}}+\frac{1}{16 x +16}-\frac{1}{8 \left(x^{2}+1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/6/x^6-1/x^2+1/16/(x+1)-5/8*ln(x+1)+5/8*ln(x^2+1)-1/8/(x^2+1)-1/16/(x-1)-5/8*ln(x-1)","A"
300,1,43,26,0.013000," ","int(x^8/(x^8-2*x^4+1),x)","x +\frac{x}{8 x^{2}+8}-\frac{5 \arctan \left(x \right)}{8}+\frac{5 \ln \left(x -1\right)}{16}-\frac{5 \ln \left(x +1\right)}{16}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"x-1/16/(x+1)-5/16*ln(x+1)+1/8/(x^2+1)*x-5/8*arctan(x)-1/16/(x-1)+5/16*ln(x-1)","A"
301,1,42,23,0.015000," ","int(x^6/(x^8-2*x^4+1),x)","-\frac{x}{8 \left(x^{2}+1\right)}+\frac{3 \arctan \left(x \right)}{8}+\frac{3 \ln \left(x -1\right)}{16}-\frac{3 \ln \left(x +1\right)}{16}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/16/(x+1)-3/16*ln(x+1)-1/8/(x^2+1)*x+3/8*arctan(x)-1/16/(x-1)+3/16*ln(x-1)","A"
302,1,42,21,0.013000," ","int(x^4/(x^8-2*x^4+1),x)","\frac{x}{8 x^{2}+8}-\frac{\arctan \left(x \right)}{8}+\frac{\ln \left(x -1\right)}{16}-\frac{\ln \left(x +1\right)}{16}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/16/(x+1)-1/16*ln(x+1)+1/8/(x^2+1)*x-1/8*arctan(x)-1/16/(x-1)+1/16*ln(x-1)","A"
303,1,42,23,0.010000," ","int(x^2/(x^8-2*x^4+1),x)","-\frac{x}{8 \left(x^{2}+1\right)}-\frac{\arctan \left(x \right)}{8}-\frac{\ln \left(x -1\right)}{16}+\frac{\ln \left(x +1\right)}{16}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/16/(x+1)+1/16*ln(x+1)-1/8/(x^2+1)*x-1/8*arctan(x)-1/16/(x-1)-1/16*ln(x-1)","A"
304,1,42,21,0.013000," ","int(1/(x^8-2*x^4+1),x)","\frac{x}{8 x^{2}+8}+\frac{3 \arctan \left(x \right)}{8}-\frac{3 \ln \left(x -1\right)}{16}+\frac{3 \ln \left(x +1\right)}{16}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/16/(x+1)+3/16*ln(x+1)+1/8/(x^2+1)*x+3/8*arctan(x)-1/16/(x-1)-3/16*ln(x-1)","A"
305,1,47,28,0.014000," ","int(1/x^2/(x^8-2*x^4+1),x)","-\frac{x}{8 \left(x^{2}+1\right)}-\frac{5 \arctan \left(x \right)}{8}-\frac{5 \ln \left(x -1\right)}{16}+\frac{5 \ln \left(x +1\right)}{16}-\frac{1}{x}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/x-1/16/(x+1)+5/16*ln(x+1)-1/8/(x^2+1)*x-5/8*arctan(x)-1/16/(x-1)-5/16*ln(x-1)","A"
306,1,47,28,0.013000," ","int(1/x^4/(x^8-2*x^4+1),x)","\frac{x}{8 x^{2}+8}+\frac{7 \arctan \left(x \right)}{8}-\frac{7 \ln \left(x -1\right)}{16}+\frac{7 \ln \left(x +1\right)}{16}-\frac{1}{3 x^{3}}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/3/x^3-1/16/(x+1)+7/16*ln(x+1)+1/8/(x^2+1)*x+7/8*arctan(x)-1/16/(x-1)-7/16*ln(x-1)","A"
307,1,52,33,0.020000," ","int(1/x^6/(x^8-2*x^4+1),x)","-\frac{x}{8 \left(x^{2}+1\right)}-\frac{9 \arctan \left(x \right)}{8}-\frac{9 \ln \left(x -1\right)}{16}+\frac{9 \ln \left(x +1\right)}{16}-\frac{2}{x}-\frac{1}{5 x^{5}}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/5/x^5-2/x-1/16/(x+1)+9/16*ln(x+1)-1/8/(x^2+1)*x-9/8*arctan(x)-1/16/(x-1)-9/16*ln(x-1)","A"
308,1,52,33,0.016000," ","int(1/x^8/(x^8-2*x^4+1),x)","\frac{x}{8 x^{2}+8}+\frac{11 \arctan \left(x \right)}{8}-\frac{11 \ln \left(x -1\right)}{16}+\frac{11 \ln \left(x +1\right)}{16}-\frac{2}{3 x^{3}}-\frac{1}{7 x^{7}}-\frac{1}{16 \left(x +1\right)}-\frac{1}{16 \left(x -1\right)}"," ",0,"-1/7/x^7-2/3/x^3-1/16/(x+1)+11/16*ln(x+1)+1/8/(x^2+1)*x+11/8*arctan(x)-1/16/(x-1)-11/16*ln(x-1)","A"
309,0,0,147,0.016000," ","int(x^m/(c*x^8+b*x^4+a),x)","\int \frac{x^{m}}{c \,x^{8}+b \,x^{4}+a}\, dx"," ",0,"int(x^m/(c*x^8+b*x^4+a),x)","F"
310,1,111,71,0.006000," ","int(x^11/(c*x^8+b*x^4+a),x)","\frac{x^{4}}{4 c}-\frac{a \arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{4 \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b \ln \left(c \,x^{8}+b \,x^{4}+a \right)}{8 c^{2}}"," ",0,"1/4*x^4/c-1/8*b*ln(c*x^8+b*x^4+a)/c^2-1/2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))*a+1/4/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))*b^2","A"
311,1,360,151,0.030000," ","int(x^9/(c*x^8+b*x^4+a),x)","\frac{\sqrt{2}\, a \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{x^{2}}{2 c}"," ",0,"1/2/c*x^2+1/4/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a-1/4/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(c*x^2*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2-1/4/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b+1/2/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*a-1/4/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(c*x^2*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2))*b^2","B"
312,1,60,55,0.004000," ","int(x^7/(c*x^8+b*x^4+a),x)","-\frac{b \arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{4 \sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{8}+b \,x^{4}+a \right)}{8 c}"," ",0,"1/8*ln(c*x^8+b*x^4+a)/c-1/4*b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))","A"
313,1,216,119,0.018000," ","int(x^5/(c*x^8+b*x^4+a),x)","\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-1/4*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)+1/4/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)*b+1/4*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)+1/4/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)*b","A"
314,1,37,32,0.003000," ","int(x^3/(c*x^8+b*x^4+a),x)","\frac{\arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}}"," ",0,"1/2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))","A"
315,1,120,119,0.013000," ","int(x/(c*x^8+b*x^4+a),x)","-\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}"," ",0,"-1/2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)-1/2*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)","A"
316,1,66,61,0.008000," ","int(1/x/(c*x^8+b*x^4+a),x)","-\frac{b \arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{4 \sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{8}+b \,x^{4}+a \right)}{8 a}"," ",0,"1/a*ln(x)-1/8*ln(c*x^8+b*x^4+a)/a-1/4/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))","A"
317,1,240,142,0.025000," ","int(1/x^3/(c*x^8+b*x^4+a),x)","\frac{\sqrt{2}\, b c \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, b c \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}+\frac{\sqrt{2}\, c \arctanh \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{\sqrt{2}\, c \arctan \left(\frac{\sqrt{2}\, c \,x^{2}}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{4 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, a}-\frac{1}{2 a \,x^{2}}"," ",0,"1/4/a*c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)+1/4/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)*b-1/4/a*c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)+1/4/a*c/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x^2)*b-1/2/a/x^2","A"
318,1,119,79,0.010000," ","int(1/x^5/(c*x^8+b*x^4+a),x)","-\frac{c \arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{2 \sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} \arctan \left(\frac{2 c \,x^{4}+b}{\sqrt{4 a c -b^{2}}}\right)}{4 \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(c \,x^{8}+b \,x^{4}+a \right)}{8 a^{2}}-\frac{1}{4 a \,x^{4}}"," ",0,"-1/4/x^4/a-1/a^2*b*ln(x)+1/8*b*ln(c*x^8+b*x^4+a)/a^2-1/2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))*c+1/4/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x^4+b)/(4*a*c-b^2)^(1/2))*b^2","A"
319,1,63,301,0.038000," ","int(x^10/(c*x^8+b*x^4+a),x)","\frac{x^{3}}{3 c}-\frac{\left(\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{6} b +\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{2} a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{4 c \left(2 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}"," ",0,"1/3/c*x^3-1/4/c*sum((_R^6*b+_R^2*a)/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
320,1,59,298,0.007000," ","int(x^8/(c*x^8+b*x^4+a),x)","\frac{x}{c}+\frac{\left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{4} b -a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{4 c \left(2 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}"," ",0,"1/c*x+1/4/c*sum((-_R^4*b-a)/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
321,1,43,245,0.003000," ","int(x^6/(c*x^8+b*x^4+a),x)","\frac{\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{6} \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +4 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/4*sum(_R^6/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
322,1,43,245,0.003000," ","int(x^4/(c*x^8+b*x^4+a),x)","\frac{\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{4} \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +4 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/4*sum(_R^4/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
323,1,43,245,0.003000," ","int(x^2/(c*x^8+b*x^4+a),x)","\frac{\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{2} \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +4 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/4*sum(_R^2/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
324,1,40,245,0.003000," ","int(1/(c*x^8+b*x^4+a),x)","\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +4 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b}"," ",0,"1/4*sum(1/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
325,1,63,283,0.009000," ","int(1/x^2/(c*x^8+b*x^4+a),x)","-\frac{\left(\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{6} c +\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{2} b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{4 a \left(2 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}-\frac{1}{a x}"," ",0,"-1/a/x-1/4/a*sum((_R^6*c+_R^2*b)/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
326,1,62,283,0.012000," ","int(1/x^4/(c*x^8+b*x^4+a),x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{4} c -b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)+x \right)}{4 a \left(2 \RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{7} c +\RootOf \left(\textit{\_Z}^{8} c +b \,\textit{\_Z}^{4}+a \right)^{3} b \right)}-\frac{1}{3 a \,x^{3}}"," ",0,"-1/3/a/x^3+1/4/a*sum((-_R^4*c-b)/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
327,0,0,107,0.026000," ","int(x^m/(x^8+x^4+1),x)","\int \frac{x^{m}}{x^{8}+x^{4}+1}\, dx"," ",0,"int(x^m/(x^8+x^4+1),x)","F"
328,1,36,35,0.004000," ","int(x^11/(x^8+x^4+1),x)","\frac{x^{4}}{4}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}+1\right) \sqrt{3}}{3}\right)}{12}-\frac{\ln \left(x^{8}+x^{4}+1\right)}{8}"," ",0,"1/4*x^4-1/8*ln(x^8+x^4+1)-1/12*arctan(1/3*(2*x^4+1)*3^(1/2))*3^(1/2)","A"
329,1,43,42,0.006000," ","int(x^9/(x^8+x^4+1),x)","\frac{x^{2}}{2}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{6}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}+1\right) \sqrt{3}}{3}\right)}{6}"," ",0,"1/2*x^2-1/6*3^(1/2)*arctan(1/3*(2*x^2+1)*3^(1/2))-1/6*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))","A"
330,1,31,30,0.003000," ","int(x^7/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}+1\right) \sqrt{3}}{3}\right)}{12}+\frac{\ln \left(x^{8}+x^{4}+1\right)}{8}"," ",0,"1/8*ln(x^8+x^4+1)-1/12*3^(1/2)*arctan(1/3*(2*x^4+1)*3^(1/2))","A"
331,1,62,61,0.004000," ","int(x^5/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}+1\right) \sqrt{3}}{3}\right)}{12}+\frac{\ln \left(x^{4}-x^{2}+1\right)}{8}-\frac{\ln \left(x^{4}+x^{2}+1\right)}{8}"," ",0,"-1/8*ln(x^4+x^2+1)+1/12*3^(1/2)*arctan(1/3*(2*x^2+1)*3^(1/2))+1/8*ln(x^4-x^2+1)+1/12*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))","A"
332,1,19,18,0.001000," ","int(x^3/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}+1\right) \sqrt{3}}{3}\right)}{6}"," ",0,"1/6*3^(1/2)*arctan(1/3*(2*x^4+1)*3^(1/2))","A"
333,1,62,61,0.004000," ","int(x/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}+1\right) \sqrt{3}}{3}\right)}{12}-\frac{\ln \left(x^{4}-x^{2}+1\right)}{8}+\frac{\ln \left(x^{4}+x^{2}+1\right)}{8}"," ",0,"1/8*ln(x^4+x^2+1)+1/12*3^(1/2)*arctan(1/3*(2*x^2+1)*3^(1/2))-1/8*ln(x^4-x^2+1)+1/12*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))","A"
334,1,87,32,0.008000," ","int(1/x/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{12}+\ln \left(x \right)-\frac{\ln \left(x^{2}-x +1\right)}{8}-\frac{\ln \left(x^{2}+x +1\right)}{8}-\frac{\ln \left(x^{4}-x^{2}+1\right)}{8}"," ",0,"ln(x)-1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-1/8*ln(x^4-x^2+1)-1/12*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))-1/8*ln(x^2-x+1)+1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","B"
335,1,57,42,0.006000," ","int(1/x^3/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{6}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{6}-\frac{1}{2 x^{2}}"," ",0,"1/6*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-1/6*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))-1/2/x^2-1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
336,1,94,39,0.010000," ","int(1/x^5/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{12}-\ln \left(x \right)+\frac{\ln \left(x^{2}-x +1\right)}{8}+\frac{\ln \left(x^{2}+x +1\right)}{8}+\frac{\ln \left(x^{4}-x^{2}+1\right)}{8}-\frac{1}{4 x^{4}}"," ",0,"-1/4/x^4-ln(x)+1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/8*ln(x^4-x^2+1)-1/12*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))+1/8*ln(x^2-x+1)+1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","B"
337,1,95,71,0.009000," ","int(1/x^7/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{2}-1\right) \sqrt{3}}{3}\right)}{12}-\frac{\ln \left(x^{2}-x +1\right)}{8}-\frac{\ln \left(x^{2}+x +1\right)}{8}+\frac{\ln \left(x^{4}-x^{2}+1\right)}{8}+\frac{1}{2 x^{2}}-\frac{1}{6 x^{6}}"," ",0,"-1/6/x^6+1/2/x^2-1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/8*ln(x^4-x^2+1)+1/12*3^(1/2)*arctan(1/3*(2*x^2-1)*3^(1/2))-1/8*ln(x^2-x+1)+1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
338,1,110,109,0.045000," ","int(x^8/(x^8+x^4+1),x)","x -\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}-\frac{\arctan \left(2 x -\sqrt{3}\right)}{4}-\frac{\arctan \left(2 x +\sqrt{3}\right)}{4}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{24}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{24}+\frac{\ln \left(x^{2}-x +1\right)}{8}-\frac{\ln \left(x^{2}+x +1\right)}{8}"," ",0,"x-1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/24*ln(1+x^2-x*3^(1/2))*3^(1/2)-1/4*arctan(2*x-3^(1/2))-1/24*ln(1+x^2+x*3^(1/2))*3^(1/2)-1/4*arctan(2*x+3^(1/2))+1/8*ln(x^2-x+1)-1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
339,1,67,66,0.013000," ","int(x^6/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{12}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{12}"," ",0,"1/6*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/12*3^(1/2)*ln(x^2-3^(1/2)*x+1)-1/12*3^(1/2)*ln(x^2+3^(1/2)*x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
340,1,109,108,0.015000," ","int(x^4/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}+\frac{\arctan \left(2 x -\sqrt{3}\right)}{4}+\frac{\arctan \left(2 x +\sqrt{3}\right)}{4}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{24}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{24}-\frac{\ln \left(x^{2}-x +1\right)}{8}+\frac{\ln \left(x^{2}+x +1\right)}{8}"," ",0,"1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/24*3^(1/2)*ln(x^2-3^(1/2)*x+1)+1/4*arctan(2*x-3^(1/2))-1/24*3^(1/2)*ln(x^2+3^(1/2)*x+1)+1/4*arctan(2*x+3^(1/2))-1/8*ln(x^2-x+1)-1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
341,1,109,108,0.010000," ","int(x^2/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}+\frac{\arctan \left(2 x -\sqrt{3}\right)}{4}+\frac{\arctan \left(2 x +\sqrt{3}\right)}{4}-\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{24}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{24}+\frac{\ln \left(x^{2}-x +1\right)}{8}-\frac{\ln \left(x^{2}+x +1\right)}{8}"," ",0,"-1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-1/24*3^(1/2)*ln(x^2-3^(1/2)*x+1)+1/4*arctan(2*x-3^(1/2))+1/24*3^(1/2)*ln(x^2+3^(1/2)*x+1)+1/4*arctan(2*x+3^(1/2))+1/8*ln(x^2-x+1)-1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
342,1,67,66,0.010000," ","int(1/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}-\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{12}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{12}"," ",0,"1/6*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-1/12*3^(1/2)*ln(x^2-3^(1/2)*x+1)+1/12*3^(1/2)*ln(x^2+3^(1/2)*x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
343,1,114,113,0.013000," ","int(1/x^2/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}-\frac{\arctan \left(2 x -\sqrt{3}\right)}{4}-\frac{\arctan \left(2 x +\sqrt{3}\right)}{4}-\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{24}+\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{24}-\frac{\ln \left(x^{2}-x +1\right)}{8}+\frac{\ln \left(x^{2}+x +1\right)}{8}-\frac{1}{x}"," ",0,"1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-1/x-1/24*3^(1/2)*ln(x^2-3^(1/2)*x+1)-1/4*arctan(2*x-3^(1/2))+1/24*3^(1/2)*ln(x^2+3^(1/2)*x+1)-1/4*arctan(2*x+3^(1/2))-1/8*ln(x^2-x+1)-1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
344,1,114,113,0.013000," ","int(1/x^4/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}-\frac{\arctan \left(2 x -\sqrt{3}\right)}{4}-\frac{\arctan \left(2 x +\sqrt{3}\right)}{4}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{24}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{24}+\frac{\ln \left(x^{2}-x +1\right)}{8}-\frac{\ln \left(x^{2}+x +1\right)}{8}-\frac{1}{3 x^{3}}"," ",0,"-1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))-1/3/x^3+1/24*3^(1/2)*ln(x^2-3^(1/2)*x+1)-1/4*arctan(2*x-3^(1/2))-1/24*3^(1/2)*ln(x^2+3^(1/2)*x+1)-1/4*arctan(2*x+3^(1/2))+1/8*ln(x^2-x+1)-1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
345,1,75,74,0.013000," ","int(1/x^6/(x^8+x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{6}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{12}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{12}+\frac{1}{x}-\frac{1}{5 x^{5}}"," ",0,"-1/5/x^5+1/x+1/6*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/12*3^(1/2)*ln(x^2-3^(1/2)*x+1)-1/12*3^(1/2)*ln(x^2+3^(1/2)*x+1)+1/6*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
346,1,119,118,0.013000," ","int(1/x^8/(x^8+x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x +1\right) \sqrt{3}}{3}\right)}{12}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x -1\right) \sqrt{3}}{3}\right)}{12}+\frac{\arctan \left(2 x -\sqrt{3}\right)}{4}+\frac{\arctan \left(2 x +\sqrt{3}\right)}{4}+\frac{\sqrt{3}\, \ln \left(x^{2}-\sqrt{3}\, x +1\right)}{24}-\frac{\sqrt{3}\, \ln \left(x^{2}+\sqrt{3}\, x +1\right)}{24}-\frac{\ln \left(x^{2}-x +1\right)}{8}+\frac{\ln \left(x^{2}+x +1\right)}{8}+\frac{1}{3 x^{3}}-\frac{1}{7 x^{7}}"," ",0,"-1/7/x^7+1/3/x^3+1/8*ln(x^2+x+1)-1/12*3^(1/2)*arctan(1/3*(2*x+1)*3^(1/2))+1/24*3^(1/2)*ln(x^2-3^(1/2)*x+1)+1/4*arctan(2*x-3^(1/2))-1/24*3^(1/2)*ln(x^2+3^(1/2)*x+1)+1/4*arctan(2*x+3^(1/2))-1/8*ln(x^2-x+1)-1/12*3^(1/2)*arctan(1/3*(2*x-1)*3^(1/2))","A"
347,0,0,107,0.020000," ","int(x^m/(x^8-x^4+1),x)","\int \frac{x^{m}}{x^{8}-x^{4}+1}\, dx"," ",0,"int(x^m/(x^8-x^4+1),x)","F"
348,1,38,37,0.006000," ","int(x^11/(x^8-x^4+1),x)","\frac{x^{4}}{4}-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}-1\right) \sqrt{3}}{3}\right)}{12}+\frac{\ln \left(x^{8}-x^{4}+1\right)}{8}"," ",0,"1/4*x^4+1/8*ln(x^8-x^4+1)-1/12*3^(1/2)*arctan(1/3*(2*x^4-1)*3^(1/2))","A"
349,1,44,43,0.010000," ","int(x^9/(x^8-x^4+1),x)","\frac{x^{2}}{2}+\frac{\sqrt{3}\, \ln \left(x^{4}-\sqrt{3}\, x^{2}+1\right)}{12}-\frac{\sqrt{3}\, \ln \left(x^{4}+\sqrt{3}\, x^{2}+1\right)}{12}"," ",0,"1/2*x^2+1/12*ln(1+x^4-x^2*3^(1/2))*3^(1/2)-1/12*ln(1+x^4+x^2*3^(1/2))*3^(1/2)","A"
350,1,33,32,0.004000," ","int(x^7/(x^8-x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}-1\right) \sqrt{3}}{3}\right)}{12}+\frac{\ln \left(x^{8}-x^{4}+1\right)}{8}"," ",0,"1/8*ln(x^8-x^4+1)+1/12*3^(1/2)*arctan(1/3*(2*x^4-1)*3^(1/2))","A"
351,1,65,64,0.007000," ","int(x^5/(x^8-x^4+1),x)","\frac{\arctan \left(2 x^{2}-\sqrt{3}\right)}{4}+\frac{\arctan \left(2 x^{2}+\sqrt{3}\right)}{4}+\frac{\sqrt{3}\, \ln \left(x^{4}-\sqrt{3}\, x^{2}+1\right)}{24}-\frac{\sqrt{3}\, \ln \left(x^{4}+\sqrt{3}\, x^{2}+1\right)}{24}"," ",0,"1/4*arctan(2*x^2-3^(1/2))+1/4*arctan(2*x^2+3^(1/2))+1/24*3^(1/2)*ln(x^4-3^(1/2)*x^2+1)-1/24*3^(1/2)*ln(x^4+3^(1/2)*x^2+1)","A"
352,1,19,18,0.001000," ","int(x^3/(x^8-x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}-1\right) \sqrt{3}}{3}\right)}{6}"," ",0,"1/6*3^(1/2)*arctan(1/3*(2*x^4-1)*3^(1/2))","A"
353,1,65,64,0.008000," ","int(x/(x^8-x^4+1),x)","\frac{\arctan \left(2 x^{2}-\sqrt{3}\right)}{4}+\frac{\arctan \left(2 x^{2}+\sqrt{3}\right)}{4}-\frac{\sqrt{3}\, \ln \left(x^{4}-\sqrt{3}\, x^{2}+1\right)}{24}+\frac{\sqrt{3}\, \ln \left(x^{4}+\sqrt{3}\, x^{2}+1\right)}{24}"," ",0,"1/4*arctan(2*x^2-3^(1/2))+1/4*arctan(2*x^2+3^(1/2))-1/24*3^(1/2)*ln(x^4-3^(1/2)*x^2+1)+1/24*3^(1/2)*ln(x^4+3^(1/2)*x^2+1)","A"
354,1,35,34,0.006000," ","int(1/x/(x^8-x^4+1),x)","\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}-1\right) \sqrt{3}}{3}\right)}{12}+\ln \left(x \right)-\frac{\ln \left(x^{8}-x^{4}+1\right)}{8}"," ",0,"ln(x)-1/8*ln(x^8-x^4+1)+1/12*3^(1/2)*arctan(1/3*(2*x^4-1)*3^(1/2))","A"
355,1,44,43,0.010000," ","int(1/x^3/(x^8-x^4+1),x)","-\frac{\sqrt{3}\, \ln \left(x^{4}-\sqrt{3}\, x^{2}+1\right)}{12}+\frac{\sqrt{3}\, \ln \left(x^{4}+\sqrt{3}\, x^{2}+1\right)}{12}-\frac{1}{2 x^{2}}"," ",0,"-1/2/x^2-1/12*3^(1/2)*ln(x^4-3^(1/2)*x^2+1)+1/12*3^(1/2)*ln(x^4+3^(1/2)*x^2+1)","A"
356,1,40,39,0.007000," ","int(1/x^5/(x^8-x^4+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{\left(2 x^{4}-1\right) \sqrt{3}}{3}\right)}{12}+\ln \left(x \right)-\frac{\ln \left(x^{8}-x^{4}+1\right)}{8}-\frac{1}{4 x^{4}}"," ",0,"-1/4/x^4+ln(x)-1/8*ln(x^8-x^4+1)-1/12*3^(1/2)*arctan(1/3*(2*x^4-1)*3^(1/2))","A"
357,1,75,74,0.011000," ","int(1/x^7/(x^8-x^4+1),x)","-\frac{\arctan \left(2 x^{2}-\sqrt{3}\right)}{4}-\frac{\arctan \left(2 x^{2}+\sqrt{3}\right)}{4}-\frac{\sqrt{3}\, \ln \left(x^{4}-\sqrt{3}\, x^{2}+1\right)}{24}+\frac{\sqrt{3}\, \ln \left(x^{4}+\sqrt{3}\, x^{2}+1\right)}{24}-\frac{1}{2 x^{2}}-\frac{1}{6 x^{6}}"," ",0,"-1/6/x^6-1/2/x^2-1/4*arctan(2*x^2-3^(1/2))-1/4*arctan(2*x^2+3^(1/2))-1/24*3^(1/2)*ln(x^4-3^(1/2)*x^2+1)+1/24*3^(1/2)*ln(x^4+3^(1/2)*x^2+1)","A"
358,1,44,308,0.016000," ","int(x^8/(x^8-x^4+1),x)","x +\frac{\left(\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{4}-1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{7}-4 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{3}}"," ",0,"x+1/4*sum((_R^4-1)/(2*_R^7-_R^3)*ln(-_R+x),_R=RootOf(_Z^8-_Z^4+1))","C"
359,1,32,235,0.013000," ","int(x^6/(x^8-x^4+1),x)","\frac{\RootOf \left(9 \textit{\_Z}^{4}+1\right) \ln \left(9 \RootOf \left(9 \textit{\_Z}^{4}+1\right)^{3} x -3 \RootOf \left(9 \textit{\_Z}^{4}+1\right)^{2}+x^{2}\right)}{4}"," ",0,"1/4*sum(_R*ln(9*_R^3*x-3*_R^2+x^2),_R=RootOf(9*_Z^4+1))","C"
360,1,40,315,0.012000," ","int(x^4/(x^8-x^4+1),x)","\frac{\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{4} \ln \left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{7}-4 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{3}}"," ",0,"1/4*sum(_R^4/(2*_R^7-_R^3)*ln(-_R+x),_R=RootOf(_Z^8-_Z^4+1))","C"
361,1,40,307,0.013000," ","int(x^2/(x^8-x^4+1),x)","\frac{\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{2} \ln \left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{7}-4 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{3}}"," ",0,"1/4*sum(_R^2/(2*_R^7-_R^3)*ln(-_R+x),_R=RootOf(_Z^8-_Z^4+1))","C"
362,1,30,235,0.006000," ","int(1/(x^8-x^4+1),x)","\frac{\RootOf \left(9 \textit{\_Z}^{4}+1\right) \ln \left(3 \RootOf \left(9 \textit{\_Z}^{4}+1\right)^{2}+3 \RootOf \left(9 \textit{\_Z}^{4}+1\right) x +x^{2}\right)}{4}"," ",0,"1/4*sum(_R*ln(3*_R^2+3*_R*x+x^2),_R=RootOf(9*_Z^4+1))","C"
363,1,52,312,0.016000," ","int(1/x^2/(x^8-x^4+1),x)","-\frac{\left(\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{6}-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)+x \right)}{4 \left(2 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{7}-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{3}\right)}-\frac{1}{x}"," ",0,"-1/x-1/4*sum((_R^6-_R^2)/(2*_R^7-_R^3)*ln(-_R+x),_R=RootOf(_Z^8-_Z^4+1))","C"
364,1,50,304,0.014000," ","int(1/x^4/(x^8-x^4+1),x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{4}+1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{7}-4 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{3}}-\frac{1}{3 x^{3}}"," ",0,"-1/3/x^3+1/4*sum((-_R^4+1)/(2*_R^7-_R^3)*ln(-_R+x),_R=RootOf(_Z^8-_Z^4+1))","C"
365,1,43,245,0.011000," ","int(1/x^6/(x^8-x^4+1),x)","-\frac{\RootOf \left(9 \textit{\_Z}^{4}+1\right) \ln \left(9 \RootOf \left(9 \textit{\_Z}^{4}+1\right)^{3} x -3 \RootOf \left(9 \textit{\_Z}^{4}+1\right)^{2}+x^{2}\right)}{4}-\frac{1}{x}-\frac{1}{5 x^{5}}"," ",0,"-1/5/x^5-1/x-1/4*sum(_R*ln(9*_R^3*x-3*_R^2+x^2),_R=RootOf(9*_Z^4+1))","C"
366,1,51,309,0.019000," ","int(1/x^8/(x^8-x^4+1),x)","-\frac{\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{4} \ln \left(-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)+x \right)}{4 \left(2 \RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{7}-\RootOf \left(\textit{\_Z}^{8}-\textit{\_Z}^{4}+1\right)^{3}\right)}-\frac{1}{3 x^{3}}-\frac{1}{7 x^{7}}"," ",0,"-1/7/x^7-1/3/x^3-1/4*sum(1/(2*_R^7-_R^3)*_R^4*ln(-_R+x),_R=RootOf(_Z^8-_Z^4+1))","C"
367,0,0,101,0.019000," ","int(x^m/(x^8+3*x^4+1),x)","\int \frac{x^{m}}{x^{8}+3 x^{4}+1}\, dx"," ",0,"int(x^m/(x^8+3*x^4+1),x)","F"
368,1,38,48,0.004000," ","int(x^11/(x^8+3*x^4+1),x)","\frac{x^{4}}{4}-\frac{7 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}+3\right) \sqrt{5}}{5}\right)}{20}-\frac{3 \ln \left(x^{8}+3 x^{4}+1\right)}{8}"," ",0,"1/4*x^4-3/8*ln(x^8+3*x^4+1)-7/20*arctanh(1/5*(2*x^4+3)*5^(1/2))*5^(1/2)","A"
369,1,117,51,0.050000," ","int(x^9/(x^8+3*x^4+1),x)","\frac{x^{2}}{2}+\frac{7 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{5 \left(-2+2 \sqrt{5}\right)}-\frac{3 \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{-2+2 \sqrt{5}}-\frac{7 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{5 \left(2+2 \sqrt{5}\right)}-\frac{3 \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{2+2 \sqrt{5}}"," ",0,"1/2*x^2-7/5*5^(1/2)/(2+2*5^(1/2))*arctan(4*x^2/(2+2*5^(1/2)))-3/(2+2*5^(1/2))*arctan(4*x^2/(2+2*5^(1/2)))+7/5*5^(1/2)/(-2+2*5^(1/2))*arctan(4*x^2/(-2+2*5^(1/2)))-3/(-2+2*5^(1/2))*arctan(4*x^2/(-2+2*5^(1/2)))","B"
370,1,33,43,0.003000," ","int(x^7/(x^8+3*x^4+1),x)","\frac{3 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}+3\right) \sqrt{5}}{5}\right)}{20}+\frac{\ln \left(x^{8}+3 x^{4}+1\right)}{8}"," ",0,"1/8*ln(x^8+3*x^4+1)+3/20*arctanh(1/5*(2*x^4+3)*5^(1/2))*5^(1/2)","A"
371,1,110,46,0.024000," ","int(x^5/(x^8+3*x^4+1),x)","\frac{\arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{-2+2 \sqrt{5}}-\frac{3 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{5 \left(-2+2 \sqrt{5}\right)}+\frac{\arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{2+2 \sqrt{5}}+\frac{3 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{5 \left(2+2 \sqrt{5}\right)}"," ",0,"1/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)+3/5*5^(1/2)/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)+1/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)-3/5*5^(1/2)/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)","B"
372,1,19,18,0.001000," ","int(x^3/(x^8+3*x^4+1),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}+3\right) \sqrt{5}}{5}\right)}{10}"," ",0,"-1/10*arctanh(1/5*(2*x^4+3)*5^(1/2))*5^(1/2)","A"
373,1,60,46,0.016000," ","int(x/(x^8+3*x^4+1),x)","\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{5 \left(-2+2 \sqrt{5}\right)}-\frac{2 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{5 \left(2+2 \sqrt{5}\right)}"," ",0,"-2/5*5^(1/2)/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)+2/5*5^(1/2)/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)","A"
374,1,35,45,0.009000," ","int(1/x/(x^8+3*x^4+1),x)","\frac{3 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}+3\right) \sqrt{5}}{5}\right)}{20}+\ln \left(x \right)-\frac{\ln \left(x^{8}+3 x^{4}+1\right)}{8}"," ",0,"ln(x)-1/8*ln(x^8+3*x^4+1)+3/20*arctanh(1/5*(2*x^4+3)*5^(1/2))*5^(1/2)","A"
375,1,117,54,0.028000," ","int(1/x^3/(x^8+3*x^4+1),x)","-\frac{\arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{-2+2 \sqrt{5}}-\frac{3 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{5 \left(-2+2 \sqrt{5}\right)}-\frac{\arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{2+2 \sqrt{5}}+\frac{3 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{5 \left(2+2 \sqrt{5}\right)}-\frac{1}{2 x^{2}}"," ",0,"-1/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)+3/5*5^(1/2)/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)-1/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)-3/5*5^(1/2)/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)-1/2/x^2","B"
376,1,42,52,0.010000," ","int(1/x^5/(x^8+3*x^4+1),x)","-\frac{7 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}+3\right) \sqrt{5}}{5}\right)}{20}-3 \ln \left(x \right)+\frac{3 \ln \left(x^{8}+3 x^{4}+1\right)}{8}-\frac{1}{4 x^{4}}"," ",0,"-1/4/x^4-3*ln(x)+3/8*ln(x^8+3*x^4+1)-7/20*arctanh(1/5*(2*x^4+3)*5^(1/2))*5^(1/2)","A"
377,1,122,56,0.027000," ","int(1/x^7/(x^8+3*x^4+1),x)","\frac{7 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{5 \left(-2+2 \sqrt{5}\right)}+\frac{3 \arctan \left(\frac{4 x^{2}}{-2+2 \sqrt{5}}\right)}{-2+2 \sqrt{5}}-\frac{7 \sqrt{5}\, \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{5 \left(2+2 \sqrt{5}\right)}+\frac{3 \arctan \left(\frac{4 x^{2}}{2+2 \sqrt{5}}\right)}{2+2 \sqrt{5}}+\frac{3}{2 x^{2}}-\frac{1}{6 x^{6}}"," ",0,"-1/6/x^6+3/2/x^2-7/5*5^(1/2)/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)+3/(2+2*5^(1/2))*arctan(4/(2+2*5^(1/2))*x^2)+7/5*5^(1/2)/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)+3/(-2+2*5^(1/2))*arctan(4/(-2+2*5^(1/2))*x^2)","B"
378,1,46,302,0.013000," ","int(x^8/(x^8+3*x^4+1),x)","x +\frac{\left(-3 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{4}-1\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+12 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}}"," ",0,"x+1/4*sum((-3*_R^4-1)/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))","C"
379,1,40,293,0.013000," ","int(x^6/(x^8+3*x^4+1),x)","\frac{\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{6} \ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+12 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}}"," ",0,"1/4*sum(_R^6/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))","C"
380,1,40,293,0.016000," ","int(x^4/(x^8+3*x^4+1),x)","\frac{\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{4} \ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+12 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}}"," ",0,"1/4*sum(_R^4/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))","C"
381,1,40,293,0.010000," ","int(x^2/(x^8+3*x^4+1),x)","\frac{\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{2} \ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+12 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}}"," ",0,"1/4*sum(_R^2/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))","C"
382,1,37,221,0.010000," ","int(1/(x^8+3*x^4+1),x)","\frac{\ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+12 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}}"," ",0,"1/4*sum(1/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))","C"
383,1,52,270,0.013000," ","int(1/x^2/(x^8+3*x^4+1),x)","-\frac{\left(\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{6}+3 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{4 \left(2 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+3 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}\right)}-\frac{1}{x}"," ",0,"-1/4*sum((_R^6+3*_R^2)/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))-1/x","C"
384,1,50,306,0.012000," ","int(1/x^4/(x^8+3*x^4+1),x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{4}-3\right) \ln \left(-\RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)+x \right)}{8 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{7}+12 \RootOf \left(\textit{\_Z}^{8}+3 \textit{\_Z}^{4}+1\right)^{3}}-\frac{1}{3 x^{3}}"," ",0,"1/4*sum((-_R^4-3)/(2*_R^7+3*_R^3)*ln(-_R+x),_R=RootOf(_Z^8+3*_Z^4+1))-1/3/x^3","C"
385,0,0,101,0.018000," ","int(x^m/(x^8-3*x^4+1),x)","\int \frac{x^{m}}{x^{8}-3 x^{4}+1}\, dx"," ",0,"int(x^m/(x^8-3*x^4+1),x)","F"
386,1,38,48,0.004000," ","int(x^11/(x^8-3*x^4+1),x)","\frac{x^{4}}{4}-\frac{7 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}-3\right) \sqrt{5}}{5}\right)}{20}+\frac{3 \ln \left(x^{8}-3 x^{4}+1\right)}{8}"," ",0,"1/4*x^4+3/8*ln(x^8-3*x^4+1)-7/20*5^(1/2)*arctanh(1/5*(2*x^4-3)*5^(1/2))","A"
387,1,67,51,0.006000," ","int(x^9/(x^8-3*x^4+1),x)","\frac{x^{2}}{2}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{5}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{5}+\frac{\ln \left(x^{4}-x^{2}-1\right)}{4}-\frac{\ln \left(x^{4}+x^{2}-1\right)}{4}"," ",0,"1/2*x^2-1/4*ln(x^4+x^2-1)-1/5*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))+1/4*ln(x^4-x^2-1)-1/5*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))","A"
388,1,33,43,0.003000," ","int(x^7/(x^8-3*x^4+1),x)","-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}-3\right) \sqrt{5}}{5}\right)}{20}+\frac{\ln \left(x^{8}-3 x^{4}+1\right)}{8}"," ",0,"1/8*ln(x^8-3*x^4+1)-3/20*5^(1/2)*arctanh(1/5*(2*x^4-3)*5^(1/2))","A"
389,1,62,46,0.003000," ","int(x^5/(x^8-3*x^4+1),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{20}-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{20}+\frac{\ln \left(x^{4}-x^{2}-1\right)}{8}-\frac{\ln \left(x^{4}+x^{2}-1\right)}{8}"," ",0,"-1/8*ln(x^4+x^2-1)-1/20*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))+1/8*ln(x^4-x^2-1)-1/20*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))","A"
390,1,19,18,0.003000," ","int(x^3/(x^8-3*x^4+1),x)","-\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{4}-3\right) \sqrt{5}}{5}\right)}{10}"," ",0,"-1/10*5^(1/2)*arctanh(1/5*(2*x^4-3)*5^(1/2))","A"
391,1,62,46,0.004000," ","int(x/(x^8-3*x^4+1),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{20}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{20}+\frac{\ln \left(x^{4}-x^{2}-1\right)}{8}-\frac{\ln \left(x^{4}+x^{2}-1\right)}{8}"," ",0,"-1/8*ln(x^4+x^2-1)+1/20*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))+1/8*ln(x^4-x^2-1)+1/20*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))","A"
392,1,64,45,0.010000," ","int(1/x/(x^8-3*x^4+1),x)","-\frac{3 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{20}+\frac{3 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{20}+\ln \left(x \right)-\frac{\ln \left(x^{4}-x^{2}-1\right)}{8}-\frac{\ln \left(x^{4}+x^{2}-1\right)}{8}"," ",0,"ln(x)-1/8*ln(x^4-x^2-1)-3/20*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))-1/8*ln(x^4+x^2-1)+3/20*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))","A"
393,1,67,54,0.007000," ","int(1/x^3/(x^8-3*x^4+1),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{5}+\frac{\sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{5}+\frac{\ln \left(x^{4}-x^{2}-1\right)}{4}-\frac{\ln \left(x^{4}+x^{2}-1\right)}{4}-\frac{1}{2 x^{2}}"," ",0,"1/4*ln(x^4-x^2-1)+1/5*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))-1/4*ln(x^4+x^2-1)+1/5*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))-1/2/x^2","A"
394,1,71,52,0.012000," ","int(1/x^5/(x^8-3*x^4+1),x)","-\frac{7 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{20}+\frac{7 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{20}+3 \ln \left(x \right)-\frac{3 \ln \left(x^{4}-x^{2}-1\right)}{8}-\frac{3 \ln \left(x^{4}+x^{2}-1\right)}{8}-\frac{1}{4 x^{4}}"," ",0,"-1/4/x^4+3*ln(x)-3/8*ln(x^4-x^2-1)-7/20*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))-3/8*ln(x^4+x^2-1)+7/20*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))","A"
395,1,72,56,0.009000," ","int(1/x^7/(x^8-3*x^4+1),x)","\frac{11 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}-1\right) \sqrt{5}}{5}\right)}{20}+\frac{11 \sqrt{5}\, \arctanh \left(\frac{\left(2 x^{2}+1\right) \sqrt{5}}{5}\right)}{20}+\frac{5 \ln \left(x^{4}-x^{2}-1\right)}{8}-\frac{5 \ln \left(x^{4}+x^{2}-1\right)}{8}-\frac{3}{2 x^{2}}-\frac{1}{6 x^{6}}"," ",0,"-1/6/x^6-3/2/x^2+5/8*ln(x^4-x^2-1)+11/20*5^(1/2)*arctanh(1/5*(2*x^2-1)*5^(1/2))-5/8*ln(x^4+x^2-1)+11/20*5^(1/2)*arctanh(1/5*(2*x^2+1)*5^(1/2))","A"
396,1,205,122,0.061000," ","int(x^8/(x^8-3*x^4+1),x)","x +\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}-\frac{2 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}-\frac{2 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}-\frac{\arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}-\frac{2 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}-\frac{2 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}"," ",0,"x-2/5*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2*x/(2+2*5^(1/2))^(1/2))-1/(2+2*5^(1/2))^(1/2)*arctanh(2*x/(2+2*5^(1/2))^(1/2))+1/(-2+2*5^(1/2))^(1/2)*arctan(2*x/(-2+2*5^(1/2))^(1/2))-2/5*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2*x/(-2+2*5^(1/2))^(1/2))+1/(-2+2*5^(1/2))^(1/2)*arctanh(2*x/(-2+2*5^(1/2))^(1/2))-2/5*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2*x/(-2+2*5^(1/2))^(1/2))-2/5*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2*x/(2+2*5^(1/2))^(1/2))-1/(2+2*5^(1/2))^(1/2)*arctan(2*x/(2+2*5^(1/2))^(1/2))","A"
397,1,206,117,0.030000," ","int(x^6/(x^8-3*x^4+1),x)","-\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}+\frac{3 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}-\frac{\arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}-\frac{3 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{3 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}+\frac{3 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}"," ",0,"-1/2/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-3/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+1/2/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)-3/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)-1/2/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+3/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+1/2/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)+3/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
398,1,206,123,0.040000," ","int(x^4/(x^8-3*x^4+1),x)","\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{\arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}"," ",0,"-1/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-1/2/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+1/2/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)-1/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+1/2/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)-1/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)-1/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)-1/2/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
399,1,110,97,0.029000," ","int(x^2/(x^8-3*x^4+1),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}-\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}"," ",0,"-1/5*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-1/5*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+1/5*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+1/5*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
400,1,206,117,0.029000," ","int(1/(x^8-3*x^4+1),x)","\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{\arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}+\frac{\sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}"," ",0,"-1/2/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+1/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+1/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+1/2/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+1/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+1/2/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)-1/2/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)+1/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
401,1,211,122,0.029000," ","int(1/x^2/(x^8-3*x^4+1),x)","\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}+\frac{3 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{\arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}-\frac{3 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{3 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}+\frac{3 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{1}{x}"," ",0,"1/2/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-3/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-1/2/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)-3/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)-1/x+1/2/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+3/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)-1/2/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)+3/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
402,1,209,132,0.030000," ","int(1/x^4/(x^8-3*x^4+1),x)","\frac{2 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}+\frac{\arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}+\frac{2 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}-\frac{\arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}+\frac{2 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{5 \sqrt{-2+2 \sqrt{5}}}+\frac{\arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{\sqrt{-2+2 \sqrt{5}}}+\frac{2 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{5 \sqrt{2+2 \sqrt{5}}}-\frac{\arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{\sqrt{2+2 \sqrt{5}}}-\frac{1}{3 x^{3}}"," ",0,"2/5*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-1/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+2/5*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+1/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+2/5*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+1/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+2/5*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)-1/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)-1/3/x^3","A"
403,1,216,125,0.039000," ","int(1/x^6/(x^8-3*x^4+1),x)","\frac{7 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{3 \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}-\frac{7 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}+\frac{3 \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}-\frac{7 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}-\frac{3 \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}+\frac{7 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{3 \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}-\frac{3}{x}-\frac{1}{5 x^{5}}"," ",0,"-1/5/x^5-3/x-7/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+3/2/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-7/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)-3/2/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+7/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+3/2/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+7/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)-3/2/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
404,1,216,137,0.043000," ","int(1/x^8/(x^8-3*x^4+1),x)","\frac{11 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{5 \arctanh \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}+\frac{11 \sqrt{5}\, \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{5 \arctanh \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}+\frac{11 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{10 \sqrt{-2+2 \sqrt{5}}}+\frac{5 \arctan \left(\frac{2 x}{\sqrt{-2+2 \sqrt{5}}}\right)}{2 \sqrt{-2+2 \sqrt{5}}}+\frac{11 \sqrt{5}\, \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{10 \sqrt{2+2 \sqrt{5}}}-\frac{5 \arctan \left(\frac{2 x}{\sqrt{2+2 \sqrt{5}}}\right)}{2 \sqrt{2+2 \sqrt{5}}}-\frac{1}{x^{3}}-\frac{1}{7 x^{7}}"," ",0,"-1/7/x^7-1/x^3+11/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)-5/2/(2+2*5^(1/2))^(1/2)*arctanh(2/(2+2*5^(1/2))^(1/2)*x)+11/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+5/2/(-2+2*5^(1/2))^(1/2)*arctan(2/(-2+2*5^(1/2))^(1/2)*x)+11/10*5^(1/2)/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+5/2/(-2+2*5^(1/2))^(1/2)*arctanh(2/(-2+2*5^(1/2))^(1/2)*x)+11/10*5^(1/2)/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)-5/2/(2+2*5^(1/2))^(1/2)*arctan(2/(2+2*5^(1/2))^(1/2)*x)","A"
405,1,18,17,0.005000," ","int(x^3/(x^8+3*x^4+2),x)","\frac{\ln \left(x^{4}+1\right)}{4}-\frac{\ln \left(x^{4}+2\right)}{4}"," ",0,"1/4*ln(x^4+1)-1/4*ln(x^4+2)","A"
406,1,23,22,0.006000," ","int(x^11/(x^8+3*x^4+2),x)","\frac{x^{4}}{4}+\frac{\ln \left(x^{4}+1\right)}{4}-\ln \left(x^{4}+2\right)"," ",0,"1/4*x^4+1/4*ln(x^4+1)-ln(x^4+2)","A"
407,1,31,30,0.003000," ","int(x^9/(x^10+x^5+2),x)","-\frac{\sqrt{7}\, \arctan \left(\frac{\left(2 x^{5}+1\right) \sqrt{7}}{7}\right)}{35}+\frac{\ln \left(x^{10}+x^{5}+2\right)}{10}"," ",0,"1/10*ln(x^10+x^5+2)-1/35*arctan(1/7*(2*x^5+1)*7^(1/2))*7^(1/2)","A"
408,1,19,18,0.001000," ","int(x^4/(x^10+x^5+2),x)","\frac{2 \sqrt{7}\, \arctan \left(\frac{\left(2 x^{5}+1\right) \sqrt{7}}{7}\right)}{35}"," ",0,"2/35*7^(1/2)*arctan(1/7*(2*x^5+1)*7^(1/2))","A"
409,1,66,32,0.039000," ","int(1/x/(x^10+x^5+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{2 \sqrt{3}\, x^{5}}{3}+\frac{\sqrt{3}}{3}\right)}{15}+\ln \left(x \right)-\frac{\ln \left(x^{2}+x +1\right)}{10}-\frac{\ln \left(4 x^{8}-4 x^{7}+4 x^{5}-4 x^{4}+4 x^{3}-4 x +4\right)}{10}"," ",0,"-1/10*ln(4*x^8-4*x^7+4*x^5-4*x^4+4*x^3-4*x+4)-1/15*3^(1/2)*arctan(2/3*3^(1/2)*x^5+1/3*3^(1/2))+ln(x)-1/10*ln(x^2+x+1)","B"
410,1,73,39,0.024000," ","int(1/x^6/(x^10+x^5+1),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{2 \sqrt{3}\, x^{5}}{3}+\frac{\sqrt{3}}{3}\right)}{15}-\ln \left(x \right)+\frac{\ln \left(x^{2}+x +1\right)}{10}+\frac{\ln \left(4 x^{8}-4 x^{7}+4 x^{5}-4 x^{4}+4 x^{3}-4 x +4\right)}{10}-\frac{1}{5 x^{5}}"," ",0,"1/10*ln(4*x^8-4*x^7+4*x^5-4*x^4+4*x^3-4*x+4)-1/15*3^(1/2)*arctan(2/3*3^(1/2)*x^5+1/3*3^(1/2))-1/5/x^5-ln(x)+1/10*ln(x^2+x+1)","A"
411,1,66,32,0.022000," ","int(1/(x^11+x^6+x),x)","-\frac{\sqrt{3}\, \arctan \left(\frac{2 \sqrt{3}\, x^{5}}{3}+\frac{\sqrt{3}}{3}\right)}{15}+\ln \left(x \right)-\frac{\ln \left(x^{2}+x +1\right)}{10}-\frac{\ln \left(4 x^{8}-4 x^{7}+4 x^{5}-4 x^{4}+4 x^{3}-4 x +4\right)}{10}"," ",0,"-1/15*3^(1/2)*arctan(2/3*3^(1/2)*x^5+1/3*3^(1/2))+ln(x)-1/10*ln(x^2+x+1)-1/10*ln(4*x^8-4*x^7+4*x^5-4*x^4+4*x^3-4*x+4)","B"
412,1,236,135,0.006000," ","int(x^3/(c+a/x^2+b/x),x)","\frac{x^{4}}{4 c}-\frac{b \,x^{3}}{3 c^{2}}-\frac{5 a^{2} b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{5 a \,b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{4}}-\frac{a \,x^{2}}{2 c^{2}}-\frac{b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{5}}+\frac{b^{2} x^{2}}{2 c^{3}}+\frac{a^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{3}}-\frac{3 a \,b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{4}}+\frac{2 a b x}{c^{3}}+\frac{b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{5}}-\frac{b^{3} x}{c^{4}}"," ",0,"1/4/c*x^4-1/3*b*x^3/c^2-1/2/c^2*x^2*a+1/2/c^3*x^2*b^2+2/c^3*a*b*x-1/c^4*b^3*x+1/2/c^3*ln(c*x^2+b*x+a)*a^2-3/2/c^4*ln(c*x^2+b*x+a)*a*b^2+1/2/c^5*ln(c*x^2+b*x+a)*b^4-5/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b+5/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^3-1/c^5/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5","A"
413,1,190,108,0.003000," ","int(x^2/(c+a/x^2+b/x),x)","\frac{x^{3}}{3 c}+\frac{2 a^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{4 a \,b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{4}}-\frac{b \,x^{2}}{2 c^{2}}+\frac{a b \ln \left(c \,x^{2}+b x +a \right)}{c^{3}}-\frac{a x}{c^{2}}-\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{4}}+\frac{b^{2} x}{c^{3}}"," ",0,"1/3/c*x^3-1/2*b*x^2/c^2-1/c^2*a*x+1/c^3*b^2*x+1/c^3*ln(c*x^2+b*x+a)*a*b-1/2/c^4*ln(c*x^2+b*x+a)*b^3+2/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2-4/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2+1/c^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","A"
414,1,132,81,0.005000," ","int(x/(c+a/x^2+b/x),x)","\frac{3 a b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{3}}+\frac{x^{2}}{2 c}-\frac{a \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}+\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 c^{3}}-\frac{b x}{c^{2}}"," ",0,"1/2/c*x^2-b*x/c^2-1/2/c^2*ln(c*x^2+b*x+a)*a+1/2/c^3*ln(c*x^2+b*x+a)*b^2+3/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b-1/c^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","A"
415,1,101,64,0.003000," ","int(1/(c+a/x^2+b/x),x)","-\frac{2 a \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b \ln \left(c \,x^{2}+b x +a \right)}{2 c^{2}}+\frac{x}{c}"," ",0,"1/c*x-1/2*b*ln(c*x^2+b*x+a)/c^2-2/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a+1/c^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2","A"
416,1,56,50,0.003000," ","int(1/(c+a/x^2+b/x)/x,x)","-\frac{b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, c}+\frac{\ln \left(c \,x^{2}+b x +a \right)}{2 c}"," ",0,"1/2*ln(c*x^2+b*x+a)/c-b/c/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
417,1,35,32,0.001000," ","int(1/(c+a/x^2+b/x)/x^2,x)","\frac{2 \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}}"," ",0,"2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
418,1,62,56,0.006000," ","int(1/(c+a/x^2+b/x)/x^3,x)","-\frac{b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{\ln \left(x \right)}{a}-\frac{\ln \left(c \,x^{2}+b x +a \right)}{2 a}"," ",0,"1/a*ln(x)-1/2*ln(c*x^2+b*x+a)/a-1/a*b/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
419,1,112,75,0.006000," ","int(1/(c+a/x^2+b/x)/x^4,x)","-\frac{2 c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a}+\frac{b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b \ln \left(x \right)}{a^{2}}+\frac{b \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2}}-\frac{1}{a x}"," ",0,"-1/a/x-1/a^2*b*ln(x)+1/2*b*ln(c*x^2+b*x+a)/a^2-2/a/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c+1/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2","A"
420,1,150,96,0.007000," ","int(1/(c+a/x^2+b/x)/x^5,x)","\frac{3 b c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{3}}-\frac{c \ln \left(x \right)}{a^{2}}+\frac{c \ln \left(c \,x^{2}+b x +a \right)}{2 a^{2}}+\frac{b^{2} \ln \left(x \right)}{a^{3}}-\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 a^{3}}+\frac{b}{a^{2} x}-\frac{1}{2 a \,x^{2}}"," ",0,"-1/2/a/x^2-1/a^2*ln(x)*c+1/a^3*ln(x)*b^2+b/a^2/x+1/2/a^2*c*ln(c*x^2+b*x+a)-1/2/a^3*ln(c*x^2+b*x+a)*b^2+3/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c-1/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","A"
421,1,214,127,0.010000," ","int(1/(c+a/x^2+b/x)/x^6,x)","\frac{2 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{2}}-\frac{4 b^{2} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{3}}+\frac{b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\sqrt{4 a c -b^{2}}\, a^{4}}+\frac{2 b c \ln \left(x \right)}{a^{3}}-\frac{b c \ln \left(c \,x^{2}+b x +a \right)}{a^{3}}-\frac{b^{3} \ln \left(x \right)}{a^{4}}+\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{2 a^{4}}+\frac{c}{a^{2} x}-\frac{b^{2}}{a^{3} x}+\frac{b}{2 a^{2} x^{2}}-\frac{1}{3 a \,x^{3}}"," ",0,"-1/3/a/x^3+1/a^2/x*c-1/a^3/x*b^2+2*b/a^3*ln(x)*c-b^3/a^4*ln(x)+1/2*b/a^2/x^2-1/a^3*c*ln(c*x^2+b*x+a)*b+1/2/a^4*ln(c*x^2+b*x+a)*b^3+2/a^2/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2-4/a^3/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c+1/a^4/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","A"
422,1,434,188,0.013000," ","int(x/(c+a/x^2+b/x)^2,x)","-\frac{5 a^{2} b x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{30 a^{2} b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{5 a \,b^{3} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{20 a \,b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}-\frac{b^{5} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{4}}+\frac{3 b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{4}}-\frac{2 a^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{4 a^{2} b^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{4 a^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}-\frac{a \,b^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{4}}+\frac{7 a \,b^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{3}}-\frac{3 b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) c^{4}}+\frac{x^{2}}{2 c^{2}}-\frac{2 b x}{c^{3}}"," ",0,"1/2/c^2*x^2-2/c^3*b*x-5/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*b*x*a^2+5/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^3*x*a-1/c^4/(c*x^2+b*x+a)/(4*a*c-b^2)*b^5*x-2/c^2/(c*x^2+b*x+a)*a^3/(4*a*c-b^2)+4/c^3/(c*x^2+b*x+a)*a^2/(4*a*c-b^2)*b^2-1/c^4/(c*x^2+b*x+a)*a/(4*a*c-b^2)*b^4-4/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a^2+7/c^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*b^2-3/2/c^4/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^4+30/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b-20/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^3+3/c^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5","B"
423,1,352,146,0.012000," ","int(1/(c+a/x^2+b/x)^2,x)","\frac{2 a^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c}-\frac{12 a^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}-\frac{4 a \,b^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{12 a \,b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{b^{4} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{2 b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{3}}-\frac{3 a^{2} b}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{2}}+\frac{a \,b^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) c^{3}}-\frac{4 a b \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{2}}+\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c^{3}}+\frac{x}{c^{2}}"," ",0,"x/c^2+2/c/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a^2-4/c^2/(c*x^2+b*x+a)/(4*a*c-b^2)*x*a*b^2+1/c^3/(c*x^2+b*x+a)/(4*a*c-b^2)*x*b^4-3/c^2/(c*x^2+b*x+a)*a^2*b/(4*a*c-b^2)+1/c^3/(c*x^2+b*x+a)*a*b^3/(4*a*c-b^2)-4/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a*b+1/c^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3-12/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2+12/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^2-2/c^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
424,1,209,108,0.010000," ","int(1/(c+a/x^2+b/x)^2/x,x)","-\frac{6 a b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c}+\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} c^{2}}+\frac{2 a \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) c}-\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) c^{2}}+\frac{\frac{\left(3 a c -b^{2}\right) b x}{\left(4 a c -b^{2}\right) c^{2}}+\frac{\left(2 a c -b^{2}\right) a}{\left(4 a c -b^{2}\right) c^{2}}}{c \,x^{2}+b x +a}"," ",0,"((3*a*c-b^2)/(4*a*c-b^2)*b/c^2*x+(2*a*c-b^2)/(4*a*c-b^2)*a/c^2)/(c*x^2+b*x+a)+2/c/(4*a*c-b^2)*ln(c*x^2+b*x+a)*a-1/2/c^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2-6/c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b+1/c^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","A"
425,1,97,67,0.007000," ","int(1/(c+a/x^2+b/x)^2/x^2,x)","\frac{4 a \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{\frac{a b}{\left(4 a c -b^{2}\right) c}-\frac{\left(2 a c -b^{2}\right) x}{\left(4 a c -b^{2}\right) c}}{c \,x^{2}+b x +a}"," ",0,"(-(2*a*c-b^2)/(4*a*c-b^2)/c*x+1/c*a*b/(4*a*c-b^2))/(c*x^2+b*x+a)+4*a/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
426,1,70,62,0.003000," ","int(1/(c+a/x^2+b/x)^2/x^3,x)","-\frac{2 b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{-b x -2 a}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)}"," ",0,"(-b*x-2*a)/(4*a*c-b^2)/(c*x^2+b*x+a)-2*b/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
427,1,68,63,0.003000," ","int(1/(c+a/x^2+b/x)^2/x^4,x)","\frac{4 c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}}}+\frac{2 c x +b}{\left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)}"," ",0,"(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)+4*c/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
428,1,237,102,0.013000," ","int(1/(c+a/x^2+b/x)^2/x^5,x)","-\frac{b c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}-\frac{6 b c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}-\frac{2 c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a}+\frac{b^{2} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) a^{2}}+\frac{2 c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right)}+\frac{\ln \left(x \right)}{a^{2}}"," ",0,"ln(x)/a^2-1/a/(c*x^2+b*x+a)*b*c/(4*a*c-b^2)*x+2/(c*x^2+b*x+a)/(4*a*c-b^2)*c-1/a/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2-2/a/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)+1/2/a^2/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^2-6/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c+1/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3","B"
429,1,328,144,0.014000," ","int(1/(c+a/x^2+b/x)^2/x^6,x)","-\frac{2 c^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}-\frac{12 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a}+\frac{b^{2} c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{12 b^{2} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{2 b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}-\frac{3 b c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{3}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{4 b c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{3}}-\frac{2 b \ln \left(x \right)}{a^{3}}-\frac{1}{a^{2} x}"," ",0,"-1/a^2/x-2*b*ln(x)/a^3-2/a/(c*x^2+b*x+a)*c^2/(4*a*c-b^2)*x+1/a^2/(c*x^2+b*x+a)*c/(4*a*c-b^2)*x*b^2-3/a/(c*x^2+b*x+a)*b/(4*a*c-b^2)*c+1/a^2/(c*x^2+b*x+a)*b^3/(4*a*c-b^2)+4/a^2/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b-1/a^3/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^3-12/a/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^2+12/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c-2/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4","B"
430,1,418,194,0.017000," ","int(1/(c+a/x^2+b/x)^2/x^7,x)","\frac{3 b \,c^{2} x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{30 b \,c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{2}}-\frac{b^{3} c x}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{20 b^{3} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{3}}+\frac{3 b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{3}{2}} a^{4}}-\frac{2 c^{2}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a}+\frac{4 b^{2} c}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{2}}+\frac{4 c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{2}}-\frac{b^{4}}{\left(c \,x^{2}+b x +a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{7 b^{2} c \ln \left(c \,x^{2}+b x +a \right)}{\left(4 a c -b^{2}\right) a^{3}}+\frac{3 b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(4 a c -b^{2}\right) a^{4}}-\frac{2 c \ln \left(x \right)}{a^{3}}+\frac{3 b^{2} \ln \left(x \right)}{a^{4}}+\frac{2 b}{a^{3} x}-\frac{1}{2 a^{2} x^{2}}"," ",0,"-1/2/a^2/x^2-2/a^3*ln(x)*c+3/a^4*ln(x)*b^2+2/a^3*b/x+3/a^2/(c*x^2+b*x+a)*b*c^2/(4*a*c-b^2)*x-1/a^3/(c*x^2+b*x+a)*b^3*c/(4*a*c-b^2)*x-2/a/(c*x^2+b*x+a)/(4*a*c-b^2)*c^2+4/a^2/(c*x^2+b*x+a)/(4*a*c-b^2)*b^2*c-1/a^3/(c*x^2+b*x+a)/(4*a*c-b^2)*b^4+4/a^2/(4*a*c-b^2)*c^2*ln(c*x^2+b*x+a)-7/a^3/(4*a*c-b^2)*c*ln(c*x^2+b*x+a)*b^2+3/2/a^4/(4*a*c-b^2)*ln(c*x^2+b*x+a)*b^4+30/a^2/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2-20/a^3/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c+3/a^4/(4*a*c-b^2)^(3/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5","B"
431,1,1040,228,0.017000," ","int(1/(c+a/x^2+b/x)^3,x)","\frac{18 a^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{51 a^{2} b^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{24 a \,b^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{3 b^{6} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{21 a^{3} b \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{41 a^{2} b^{3} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{17 a \,b^{5} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{5 b^{7} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{14 a^{4} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{71 a^{3} b^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{38 a^{2} b^{4} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{5 a \,b^{6} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}-\frac{29 a^{4} b}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{18 a^{3} b^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{60 a^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c}-\frac{5 a^{2} b^{5}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{90 a^{2} b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{30 a \,b^{4} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{3 b^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{4}}-\frac{24 a^{2} b \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{12 a \,b^{3} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}-\frac{3 b^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{4}}+\frac{x}{c^{3}}"," ",0,"x/c^3+18/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^3-51/c/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a^2*b^2+24/c^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a*b^4-3/c^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^6-21/c/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^3-41/2/c^2/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a^2+17/c^3/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a-5/2/c^4/(c*x^2+b*x+a)^2*b^7/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+14/c/(c*x^2+b*x+a)^2*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x-71/c^2/(c*x^2+b*x+a)^2*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2+38/c^3/(c*x^2+b*x+a)^2*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4-5/c^4/(c*x^2+b*x+a)^2*a/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^6-29/c^2/(c*x^2+b*x+a)^2*b*a^4/(16*a^2*c^2-8*a*b^2*c+b^4)+18/c^3/(c*x^2+b*x+a)^2*b^3*a^3/(16*a^2*c^2-8*a*b^2*c+b^4)-5/2/c^4/(c*x^2+b*x+a)^2*b^5*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)-24/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a^2*b+12/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a*b^3-3/2/c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^5-60/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^3+90/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b^2-30/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^4+3/c^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6","B"
432,1,530,180,0.016000," ","int(1/(c+a/x^2+b/x)^3/x,x)","-\frac{30 a^{2} b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c}+\frac{10 a \,b^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{2}}-\frac{b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, c^{3}}+\frac{8 a^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{4 a \,b^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\frac{\left(25 a^{2} c^{2}-15 a \,b^{2} c +2 b^{4}\right) b \,x^{3}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(31 a^{2} c^{2}-22 a \,b^{2} c +3 b^{4}\right) a b x}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{3 \left(8 a^{2} c^{2}-7 a \,b^{2} c +b^{4}\right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}+\frac{\left(32 a^{3} c^{3}+11 a^{2} b^{2} c^{2}-19 a \,b^{4} c +3 b^{6}\right) x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{3}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(1/c^2*b*(25*a^2*c^2-15*a*b^2*c+2*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/2*(32*a^3*c^3+11*a^2*b^2*c^2-19*a*b^4*c+3*b^6)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+a*b*(31*a^2*c^2-22*a*b^2*c+3*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^3*x+3/2*a^2*(8*a^2*c^2-7*a*b^2*c+b^4)/c^3/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+8/c/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a^2-4/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*a*b^2+1/2/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^4-30/c/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a^2*b+10/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*b^3-1/c^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5","B"
433,1,260,105,0.010000," ","int(1/(c+a/x^2+b/x)^3/x^2,x)","\frac{12 a^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{\left(10 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) x^{3}}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}+\frac{\left(10 a c -b^{2}\right) a^{2} b}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}+\frac{\left(2 a^{2} c^{2}+8 a \,b^{2} c -b^{4}\right) b \,x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}-\frac{\left(6 a^{2} c^{2}-10 a \,b^{2} c +b^{4}\right) a x}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c^{2}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(-1/c*(10*a^2*c^2-8*a*b^2*c+b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/2*b*(2*a^2*c^2+8*a*b^2*c-b^4)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-a*(6*a^2*c^2-10*a*b^2*c+b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/c^2*x+1/2*a^2*b*(10*a*c-b^2)/c^2/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+12*a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
434,1,223,99,0.012000," ","int(1/(c+a/x^2+b/x)^3/x^3,x)","-\frac{6 a b \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{-\frac{3 a b c \,x^{3}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{\left(5 a c +b^{2}\right) a b x}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(8 a c +b^{2}\right) a^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}-\frac{\left(16 a^{2} c^{2}+a \,b^{2} c +b^{4}\right) x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) c}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(-3*a*b*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/2*(16*a^2*c^2+a*b^2*c+b^4)/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-(5*a*c+b^2)*a*b/c/(16*a^2*c^2-8*a*b^2*c+b^4)*x-1/2*a^2*(8*a*c+b^2)/c/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2-6*a*b/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","B"
435,1,262,109,0.010000," ","int(1/(c+a/x^2+b/x)^3/x^4,x)","\frac{4 a c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{2 b^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}}+\frac{\frac{\left(2 a c +b^{2}\right) c \,x^{3}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{3 a^{2} b}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{3 \left(2 a c +b^{2}\right) b \,x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(2 a c -5 b^{2}\right) a x}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}}{\left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"(c*(2*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+3/2*b*(2*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-a*(2*a*c-5*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x+3*a^2*b/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*x^2+b*x+a)^2+4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*a*c+2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2","B"
436,1,130,95,0.005000," ","int(1/(c+a/x^2+b/x)^3/x^5,x)","-\frac{3 b c x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}-\frac{6 b c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}-\frac{3 b^{2}}{2 \left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{-b x -2 a}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"1/2*(-b*x-2*a)/(4*a*c-b^2)/(c*x^2+b*x+a)^2-3/(4*a*c-b^2)^2*b/(c*x^2+b*x+a)*c*x-3/2/(4*a*c-b^2)^2*b^2/(c*x^2+b*x+a)-6/(4*a*c-b^2)^(5/2)*b*c*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
437,1,129,97,0.004000," ","int(1/(c+a/x^2+b/x)^3/x^6,x)","\frac{6 c^{2} x}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{12 c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(4 a c -b^{2}\right)^{\frac{5}{2}}}+\frac{3 b c}{\left(4 a c -b^{2}\right)^{2} \left(c \,x^{2}+b x +a \right)}+\frac{2 c x +b}{2 \left(4 a c -b^{2}\right) \left(c \,x^{2}+b x +a \right)^{2}}"," ",0,"1/2*(2*c*x+b)/(4*a*c-b^2)/(c*x^2+b*x+a)^2+6*c^2/(4*a*c-b^2)^2/(c*x^2+b*x+a)*x+3*c/(4*a*c-b^2)^2/(c*x^2+b*x+a)*b+12*c^2/(4*a*c-b^2)^(5/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))","A"
438,1,781,175,0.017000," ","int(1/(c+a/x^2+b/x)^3/x^7,x)","-\frac{7 b \,c^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{b^{3} c^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{29 b^{2} c^{2} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{2 b^{4} c \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{8 c^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{6 b^{3} c x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{b^{5} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{b \,c^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{12 a \,c^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 b^{4}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{30 b \,c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}+\frac{10 b^{3} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{b^{5} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}-\frac{21 b^{2} c}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{8 c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{4 b^{2} c \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{b^{4} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{\ln \left(x \right)}{a^{3}}"," ",0,"ln(x)/a^3-7/a/(c*x^2+b*x+a)^2*b*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+1/a^2/(c*x^2+b*x+a)^2*b^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+8/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-29/2/a/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2+2/a^2/(c*x^2+b*x+a)^2*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^4-1/(c*x^2+b*x+a)^2*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^2-6/a/(c*x^2+b*x+a)^2*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c+1/a^2/(c*x^2+b*x+a)^2*b^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x+12*a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2-21/2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c+3/2/a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4-8/a/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^2+b*x+a)+4/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^2+b*x+a)*b^2-1/2/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^4-30/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b*c^2+10/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^3*c-1/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^5","B"
439,1,954,229,0.023000," ","int(1/(c+a/x^2+b/x)^3/x^8,x)","-\frac{14 c^{4} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{13 b^{2} c^{3} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{2 b^{4} c^{2} x^{3}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{37 b \,c^{3} x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{55 b^{3} c^{2} x^{2}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{4 b^{5} c \,x^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{7 b^{2} c^{2} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{12 b^{4} c x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{2 b^{6} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}-\frac{18 c^{3} x}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{18 b^{3} c}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}-\frac{60 c^{3} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a}-\frac{5 b^{5}}{2 \left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{90 b^{2} c^{2} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{2}}-\frac{30 b^{4} c \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{3}}+\frac{3 b^{6} \arctan \left(\frac{2 c x +b}{\sqrt{4 a c -b^{2}}}\right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) \sqrt{4 a c -b^{2}}\, a^{4}}-\frac{29 b \,c^{2}}{\left(c \,x^{2}+b x +a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{24 b \,c^{2} \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{12 b^{3} c \ln \left(c \,x^{2}+b x +a \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{3}}+\frac{3 b^{5} \ln \left(c \,x^{2}+b x +a \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{4}}-\frac{3 b \ln \left(x \right)}{a^{4}}-\frac{1}{a^{3} x}"," ",0,"-1/a^3/x-3*b*ln(x)/a^4-14/a/(c*x^2+b*x+a)^2*c^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+13/a^2/(c*x^2+b*x+a)^2*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^2-2/a^3/(c*x^2+b*x+a)^2*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^4-37/a/(c*x^2+b*x+a)^2*b*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+55/2/a^2/(c*x^2+b*x+a)^2*b^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-4/a^3/(c*x^2+b*x+a)^2*b^5*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-18/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^3-7/a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2*c^2+12/a^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4*c-2/a^3/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^6-29/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b*c^2+18/a/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c-5/2/a^2/(c*x^2+b*x+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*b^5+24/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2*ln(c*x^2+b*x+a)*b-12/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)*c*ln(c*x^2+b*x+a)*b^3+3/2/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)*ln(c*x^2+b*x+a)*b^5-60/a/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*c^3+90/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^2*c^2-30/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^4*c+3/a^4/(16*a^2*c^2-8*a*b^2*c+b^4)/(4*a*c-b^2)^(1/2)*arctan((2*c*x+b)/(4*a*c-b^2)^(1/2))*b^6","B"
440,1,31,30,0.006000," ","int(x^2/(15+2/x^2+13/x),x)","\frac{x^{3}}{45}-\frac{13 x^{2}}{450}+\frac{139 x}{3375}+\frac{\ln \left(5 x +1\right)}{4375}-\frac{16 \ln \left(3 x +2\right)}{567}"," ",0,"139/3375*x-13/450*x^2+1/45*x^3-16/567*ln(2+3*x)+1/4375*ln(1+5*x)","A"
441,1,26,25,0.004000," ","int(x/(15+2/x^2+13/x),x)","\frac{x^{2}}{30}-\frac{13 x}{225}-\frac{\ln \left(5 x +1\right)}{875}+\frac{8 \ln \left(3 x +2\right)}{189}"," ",0,"-13/225*x+1/30*x^2+8/189*ln(3*x+2)-1/875*ln(5*x+1)","A"
442,1,21,20,0.006000," ","int(1/(15+2/x^2+13/x),x)","\frac{x}{15}+\frac{\ln \left(5 x +1\right)}{175}-\frac{4 \ln \left(3 x +2\right)}{63}"," ",0,"1/15*x-4/63*ln(3*x+2)+1/175*ln(5*x+1)","A"
443,1,18,17,0.006000," ","int(1/(15+2/x^2+13/x)/x,x)","-\frac{\ln \left(5 x +1\right)}{35}+\frac{2 \ln \left(3 x +2\right)}{21}"," ",0,"2/21*ln(3*x+2)-1/35*ln(5*x+1)","A"
444,1,18,19,0.006000," ","int(1/(15+2/x^2+13/x)/x^2,x)","\frac{\ln \left(5 x +1\right)}{7}-\frac{\ln \left(3 x +2\right)}{7}"," ",0,"-1/7*ln(3*x+2)+1/7*ln(5*x+1)","A"
445,1,22,21,0.007000," ","int(1/(15+2/x^2+13/x)/x^3,x)","\frac{\ln \left(x \right)}{2}-\frac{5 \ln \left(5 x +1\right)}{7}+\frac{3 \ln \left(3 x +2\right)}{14}"," ",0,"1/2*ln(x)+3/14*ln(3*x+2)-5/7*ln(5*x+1)","A"
446,1,27,26,0.009000," ","int(1/(15+2/x^2+13/x)/x^4,x)","-\frac{13 \ln \left(x \right)}{4}+\frac{25 \ln \left(5 x +1\right)}{7}-\frac{9 \ln \left(3 x +2\right)}{28}-\frac{1}{2 x}"," ",0,"-1/2/x-13/4*ln(x)-9/28*ln(3*x+2)+25/7*ln(5*x+1)","A"
447,1,32,31,0.007000," ","int(1/(15+2/x^2+13/x)/x^5,x)","\frac{139 \ln \left(x \right)}{8}-\frac{125 \ln \left(5 x +1\right)}{7}+\frac{27 \ln \left(3 x +2\right)}{56}+\frac{13}{4 x}-\frac{1}{4 x^{2}}"," ",0,"-1/4/x^2+13/4/x+139/8*ln(x)+27/56*ln(3*x+2)-125/7*ln(5*x+1)","A"
448,1,37,36,0.007000," ","int(1/(15+2/x^2+13/x)/x^6,x)","-\frac{1417 \ln \left(x \right)}{16}+\frac{625 \ln \left(5 x +1\right)}{7}-\frac{81 \ln \left(3 x +2\right)}{112}-\frac{139}{8 x}+\frac{13}{8 x^{2}}-\frac{1}{6 x^{3}}"," ",0,"-1/6/x^3+13/8/x^2-139/8/x-1417/16*ln(x)-81/112*ln(3*x+2)+625/7*ln(5*x+1)","A"
449,1,701,174,0.019000," ","int((a+c/x^2+b/x)^(5/2),x)","\frac{\left(\frac{a \,x^{2}+b x +c}{x^{2}}\right)^{\frac{5}{2}} \left(-720 a^{\frac{7}{2}} c^{\frac{9}{2}} x^{4} \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)+960 a^{3} b \,c^{4} x^{4} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)-360 a^{\frac{5}{2}} b^{2} c^{\frac{7}{2}} x^{4} \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)+15 a^{\frac{3}{2}} b^{4} c^{\frac{5}{2}} x^{4} \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)+600 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{7}{2}} b \,c^{3} x^{5}-30 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{5}{2}} b^{3} c^{2} x^{5}+280 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{7}{2}} b \,c^{2} x^{5}+720 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{7}{2}} c^{4} x^{4}-10 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{3} c \,x^{5}+660 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{5}{2}} b^{2} c^{3} x^{4}-30 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{3}{2}} b^{4} c^{2} x^{4}+152 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{7}{2}} b c \,x^{5}+240 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{7}{2}} c^{3} x^{4}-6 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{5}{2}} b^{3} x^{5}+260 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{5}{2}} b^{2} c^{2} x^{4}-10 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{4} c \,x^{4}+144 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{7}{2}} c^{2} x^{4}+148 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{5}{2}} b^{2} c \,x^{4}-6 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{3}{2}} b^{4} x^{4}-152 \left(a \,x^{2}+b x +c \right)^{\frac{7}{2}} a^{\frac{5}{2}} b c \,x^{3}+6 \left(a \,x^{2}+b x +c \right)^{\frac{7}{2}} a^{\frac{3}{2}} b^{3} x^{3}-144 \left(a \,x^{2}+b x +c \right)^{\frac{7}{2}} a^{\frac{5}{2}} c^{2} x^{2}+4 \left(a \,x^{2}+b x +c \right)^{\frac{7}{2}} a^{\frac{3}{2}} b^{2} c \,x^{2}+16 \left(a \,x^{2}+b x +c \right)^{\frac{7}{2}} a^{\frac{3}{2}} b \,c^{2} x -96 \left(a \,x^{2}+b x +c \right)^{\frac{7}{2}} a^{\frac{3}{2}} c^{3}\right) x}{384 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{3}{2}} c^{4}}"," ",0,"1/384*((a*x^2+b*x+c)/x^2)^(5/2)*x*(720*a^(7/2)*(a*x^2+b*x+c)^(1/2)*x^4*c^4+6*a^(3/2)*(a*x^2+b*x+c)^(7/2)*x^3*b^3-6*a^(3/2)*(a*x^2+b*x+c)^(5/2)*x^4*b^4-720*ln((2*c+b*x+2*c^(1/2)*(a*x^2+b*x+c)^(1/2))/x)*c^(9/2)*a^(7/2)*x^4-6*a^(5/2)*(a*x^2+b*x+c)^(5/2)*x^5*b^3+144*a^(7/2)*(a*x^2+b*x+c)^(5/2)*x^4*c^2-144*a^(5/2)*(a*x^2+b*x+c)^(7/2)*x^2*c^2+240*a^(7/2)*(a*x^2+b*x+c)^(3/2)*x^4*c^3-360*ln((2*c+b*x+2*c^(1/2)*(a*x^2+b*x+c)^(1/2))/x)*c^(7/2)*a^(5/2)*x^4*b^2+660*a^(5/2)*(a*x^2+b*x+c)^(1/2)*x^4*b^2*c^3+960*ln(1/2*(2*(a*x^2+b*x+c)^(1/2)*a^(1/2)+2*a*x+b)/a^(1/2))*a^3*x^4*b*c^4+148*a^(5/2)*(a*x^2+b*x+c)^(5/2)*x^4*b^2*c+280*a^(7/2)*(a*x^2+b*x+c)^(3/2)*x^5*b*c^2-10*a^(5/2)*(a*x^2+b*x+c)^(3/2)*x^5*b^3*c+15*ln((2*c+b*x+2*c^(1/2)*(a*x^2+b*x+c)^(1/2))/x)*c^(5/2)*a^(3/2)*x^4*b^4+260*a^(5/2)*(a*x^2+b*x+c)^(3/2)*x^4*b^2*c^2+600*a^(7/2)*(a*x^2+b*x+c)^(1/2)*x^5*b*c^3-30*a^(5/2)*(a*x^2+b*x+c)^(1/2)*x^5*b^3*c^2+152*a^(7/2)*(a*x^2+b*x+c)^(5/2)*x^5*b*c-152*a^(5/2)*(a*x^2+b*x+c)^(7/2)*x^3*b*c+4*a^(3/2)*(a*x^2+b*x+c)^(7/2)*x^2*b^2*c-10*a^(3/2)*(a*x^2+b*x+c)^(3/2)*x^4*b^4*c+16*a^(3/2)*(a*x^2+b*x+c)^(7/2)*x*b*c^2-30*a^(3/2)*(a*x^2+b*x+c)^(1/2)*x^4*b^4*c^2-96*(a*x^2+b*x+c)^(7/2)*c^3*a^(3/2))/(a*x^2+b*x+c)^(5/2)/c^4/a^(3/2)","B"
450,1,334,119,0.007000," ","int((a+c/x^2+b/x)^(3/2),x)","-\frac{\left(\frac{a \,x^{2}+b x +c}{x^{2}}\right)^{\frac{3}{2}} \left(12 a^{\frac{5}{2}} c^{\frac{5}{2}} x^{2} \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)-12 a^{2} b \,c^{2} x^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 a^{\frac{3}{2}} b^{2} c^{\frac{3}{2}} x^{2} \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)-6 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{5}{2}} b c \,x^{3}-2 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{5}{2}} b \,x^{3}-12 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{5}{2}} c^{2} x^{2}-6 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{3}{2}} b^{2} c \,x^{2}-4 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{5}{2}} c \,x^{2}-2 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{3}{2}} b^{2} x^{2}+2 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{3}{2}} b x +4 \left(a \,x^{2}+b x +c \right)^{\frac{5}{2}} a^{\frac{3}{2}} c \right) x}{8 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{\frac{3}{2}} c^{2}}"," ",0,"-1/8*((a*x^2+b*x+c)/x^2)^(3/2)*x*(12*a^(5/2)*c^(5/2)*ln((b*x+2*c+2*(a*x^2+b*x+c)^(1/2)*c^(1/2))/x)*x^2-2*a^(5/2)*(a*x^2+b*x+c)^(3/2)*x^3*b-4*a^(5/2)*(a*x^2+b*x+c)^(3/2)*x^2*c-6*a^(5/2)*(a*x^2+b*x+c)^(1/2)*x^3*b*c+3*a^(3/2)*c^(3/2)*ln((b*x+2*c+2*(a*x^2+b*x+c)^(1/2)*c^(1/2))/x)*x^2*b^2-12*a^(5/2)*(a*x^2+b*x+c)^(1/2)*x^2*c^2+2*a^(3/2)*(a*x^2+b*x+c)^(5/2)*x*b-2*a^(3/2)*(a*x^2+b*x+c)^(3/2)*x^2*b^2+4*(a*x^2+b*x+c)^(5/2)*c*a^(3/2)-6*a^(3/2)*(a*x^2+b*x+c)^(1/2)*x^2*b^2*c-12*a^2*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*x^2*b*c^2)/(a*x^2+b*x+c)^(3/2)/c^2/a^(3/2)","B"
451,1,121,85,0.007000," ","int((a+c/x^2+b/x)^(1/2),x)","\frac{\sqrt{\frac{a \,x^{2}+b x +c}{x^{2}}}\, \left(-2 \sqrt{a}\, \sqrt{c}\, \ln \left(\frac{b x +2 c +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{c}}{x}\right)+b \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}\right) x}{2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}"," ",0,"1/2*((a*x^2+b*x+c)/x^2)^(1/2)*x*(-2*c^(1/2)*ln((b*x+2*c+2*(a*x^2+b*x+c)^(1/2)*c^(1/2))/x)*a^(1/2)+b*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/(a*x^2+b*x+c)^(1/2)/a^(1/2)","A"
452,1,88,55,0.005000," ","int(1/(a+c/x^2+b/x)^(1/2),x)","\frac{\sqrt{a \,x^{2}+b x +c}\, \left(-a b \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+2 \sqrt{a \,x^{2}+b x +c}\, a^{\frac{3}{2}}\right)}{2 \sqrt{\frac{a \,x^{2}+b x +c}{x^{2}}}\, a^{\frac{5}{2}} x}"," ",0,"1/2*(a*x^2+b*x+c)^(1/2)*(2*(a*x^2+b*x+c)^(1/2)*a^(3/2)-b*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*a)/((a*x^2+b*x+c)/x^2)^(1/2)/x/a^(5/2)","A"
453,1,197,119,0.008000," ","int(1/(a+c/x^2+b/x)^(3/2),x)","\frac{\left(a \,x^{2}+b x +c \right) \left(8 a^{\frac{7}{2}} c \,x^{2}-2 a^{\frac{5}{2}} b^{2} x^{2}+20 a^{\frac{5}{2}} b c x -6 a^{\frac{3}{2}} b^{3} x -12 \sqrt{a \,x^{2}+b x +c}\, a^{2} b c \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+3 \sqrt{a \,x^{2}+b x +c}\, a \,b^{3} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+16 a^{\frac{5}{2}} c^{2}-6 a^{\frac{3}{2}} b^{2} c \right)}{2 \left(\frac{a \,x^{2}+b x +c}{x^{2}}\right)^{\frac{3}{2}} \left(4 a c -b^{2}\right) a^{\frac{7}{2}} x^{3}}"," ",0,"1/2*(a*x^2+b*x+c)/a^(7/2)*(8*a^(7/2)*x^2*c-2*a^(5/2)*x^2*b^2+20*a^(5/2)*x*b*c-6*a^(3/2)*x*b^3+16*a^(5/2)*c^2-6*a^(3/2)*b^2*c-12*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*(a*x^2+b*x+c)^(1/2)*a^2*b*c+3*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*(a*x^2+b*x+c)^(1/2)*a*b^3)/((a*x^2+b*x+c)/x^2)^(3/2)/x^3/(4*a*c-b^2)","A"
454,1,376,198,0.012000," ","int(1/(a+c/x^2+b/x)^(5/2),x)","-\frac{\left(a \,x^{2}+b x +c \right) \left(-96 a^{\frac{13}{2}} c^{2} x^{4}+48 a^{\frac{11}{2}} b^{2} c \,x^{4}-6 a^{\frac{9}{2}} b^{4} x^{4}-512 a^{\frac{11}{2}} b \,c^{2} x^{3}+296 a^{\frac{9}{2}} b^{3} c \,x^{3}-40 a^{\frac{7}{2}} b^{5} x^{3}-384 a^{\frac{11}{2}} c^{3} x^{2}-96 a^{\frac{9}{2}} b^{2} c^{2} x^{2}+180 a^{\frac{7}{2}} b^{4} c \,x^{2}-30 a^{\frac{5}{2}} b^{6} x^{2}-624 a^{\frac{9}{2}} b \,c^{3} x +420 a^{\frac{7}{2}} b^{3} c^{2} x -60 a^{\frac{5}{2}} b^{5} c x -256 a^{\frac{9}{2}} c^{4}+200 a^{\frac{7}{2}} b^{2} c^{3}-30 a^{\frac{5}{2}} b^{4} c^{2}+240 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{4} b \,c^{2} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)-120 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{3} b^{3} c \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)+15 \left(a \,x^{2}+b x +c \right)^{\frac{3}{2}} a^{2} b^{5} \ln \left(\frac{2 a x +b +2 \sqrt{a \,x^{2}+b x +c}\, \sqrt{a}}{2 \sqrt{a}}\right)\right)}{6 \left(\frac{a \,x^{2}+b x +c}{x^{2}}\right)^{\frac{5}{2}} \left(4 a c -b^{2}\right)^{2} a^{\frac{11}{2}} x^{5}}"," ",0,"-1/6*(a*x^2+b*x+c)*(-96*a^(13/2)*x^4*c^2+48*a^(11/2)*x^4*b^2*c-512*a^(11/2)*x^3*b*c^2-6*a^(9/2)*x^4*b^4-384*a^(11/2)*x^2*c^3+296*a^(9/2)*x^3*b^3*c-96*a^(9/2)*x^2*b^2*c^2-40*a^(7/2)*x^3*b^5-624*a^(9/2)*x*b*c^3+180*a^(7/2)*x^2*b^4*c-256*a^(9/2)*c^4+420*a^(7/2)*x*b^3*c^2-30*a^(5/2)*x^2*b^6+200*a^(7/2)*b^2*c^3-60*a^(5/2)*x*b^5*c+240*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*(a*x^2+b*x+c)^(3/2)*a^4*b*c^2-120*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*(a*x^2+b*x+c)^(3/2)*a^3*b^3*c+15*ln(1/2*(2*a*x+b+2*(a*x^2+b*x+c)^(1/2)*a^(1/2))/a^(1/2))*(a*x^2+b*x+c)^(3/2)*a^2*b^5-30*a^(5/2)*b^4*c^2)/a^(11/2)/((a*x^2+b*x+c)/x^2)^(5/2)/x^5/(4*a*c-b^2)^2","A"
455,1,40,69,0.013000," ","int((a^2+b^2/x^2+2*a*b/x)^(1/2),x)","\frac{\sqrt{\frac{a^{2} x^{2}+2 a x b +b^{2}}{x^{2}}}\, \left(a x +b \ln \left(x \right)\right) x}{a x +b}"," ",0,"((a^2*x^2+2*a*b*x+b^2)/x^2)^(1/2)/(a*x+b)*x*(a*x+b*ln(x))","A"
456,1,343,144,0.011000," ","int(1/(c+a/x^4+b/x^2),x)","\frac{\sqrt{2}\, a \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}+\frac{\sqrt{2}\, a \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{\sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}-\frac{\sqrt{2}\, b^{2} \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b^{2} \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{-4 a c +b^{2}}\, \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{\sqrt{2}\, b \arctanh \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(-b +\sqrt{-4 a c +b^{2}}\right) c}\, c}-\frac{\sqrt{2}\, b \arctan \left(\frac{\sqrt{2}\, c x}{\sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}}\right)}{2 \sqrt{\left(b +\sqrt{-4 a c +b^{2}}\right) c}\, c}+\frac{x}{c}"," ",0,"1/c*x+1/2/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctanh(2^(1/2)/((-b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2-1/2/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b+1/(-4*a*c+b^2)^(1/2)*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*a-1/2/(-4*a*c+b^2)^(1/2)/c*2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*arctan(2^(1/2)/((b+(-4*a*c+b^2)^(1/2))*c)^(1/2)*c*x)*b^2","B"
457,1,59,498,0.006000," ","int(1/(c+a/x^6+b/x^3),x)","\frac{x}{c}+\frac{\left(-\RootOf \left(\textit{\_Z}^{6} c +\textit{\_Z}^{3} b +a \right)^{3} b -a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{6} c +\textit{\_Z}^{3} b +a \right)+x \right)}{3 c \left(2 \RootOf \left(\textit{\_Z}^{6} c +\textit{\_Z}^{3} b +a \right)^{5} c +\RootOf \left(\textit{\_Z}^{6} c +\textit{\_Z}^{3} b +a \right)^{2} b \right)}"," ",0,"1/c*x+1/3/c*sum((-_R^3*b-a)/(2*_R^5*c+_R^2*b)*ln(-_R+x),_R=RootOf(_Z^6*c+_Z^3*b+a))","C"
458,1,59,298,0.004000," ","int(1/(c+a/x^8+b/x^4),x)","\frac{x}{c}+\frac{\left(-\RootOf \left(\textit{\_Z}^{8} c +\textit{\_Z}^{4} b +a \right)^{4} b -a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{8} c +\textit{\_Z}^{4} b +a \right)+x \right)}{4 c \left(2 \RootOf \left(\textit{\_Z}^{8} c +\textit{\_Z}^{4} b +a \right)^{7} c +\RootOf \left(\textit{\_Z}^{8} c +\textit{\_Z}^{4} b +a \right)^{3} b \right)}"," ",0,"1/c*x+1/4/c*sum((-_R^4*b-a)/(2*_R^7*c+_R^3*b)*ln(-_R+x),_R=RootOf(_Z^8*c+_Z^4*b+a))","C"
459,1,84,78,0.007000," ","int((a+c*x+b*x^(1/2))^(1/2)/x,x)","-2 \sqrt{a}\, \ln \left(\frac{b \sqrt{x}+2 a +2 \sqrt{c x +b \sqrt{x}+a}\, \sqrt{a}}{\sqrt{x}}\right)+\frac{b \ln \left(\frac{c \sqrt{x}+\frac{b}{2}}{\sqrt{c}}+\sqrt{c x +b \sqrt{x}+a}\right)}{\sqrt{c}}+2 \sqrt{c x +b \sqrt{x}+a}"," ",0,"2*(a+c*x+b*x^(1/2))^(1/2)+b*ln((1/2*b+c*x^(1/2))/c^(1/2)+(a+c*x+b*x^(1/2))^(1/2))/c^(1/2)-2*a^(1/2)*ln((2*a+b*x^(1/2)+2*a^(1/2)*(a+c*x+b*x^(1/2))^(1/2))/x^(1/2))","A"
460,1,52,32,0.001000," ","int((1/4*b^2/c+c*x+b*x^(1/2))^2,x)","\frac{b^{2} x^{2}}{2}+\frac{\left(\frac{8 c^{2} x^{\frac{5}{2}}}{5}+\frac{2 b^{2} x^{\frac{3}{2}}}{3}\right) b}{2 c}+\frac{\left(c x +\frac{b^{2}}{4 c}\right)^{3}}{3 c}"," ",0,"1/2*b^2*x^2+1/2*b/c*(8/5*c^2*x^(5/2)+2/3*x^(3/2)*b^2)+1/3*(1/4*b^2/c+c*x)^3/c","A"
461,1,50,63,0.011000," ","int(1/(a^2+b^2*x+2*a*b*x^(1/2))^(1/2),x)","\frac{2 \sqrt{b^{2} x +2 a b \sqrt{x}+a^{2}}\, \left(-a \ln \left(b \sqrt{x}+a \right)+b \sqrt{x}\right)}{\left(b \sqrt{x}+a \right) b^{2}}"," ",0,"2*(a^2+b^2*x+2*a*b*x^(1/2))^(1/2)*(b*x^(1/2)-a*ln(a+b*x^(1/2)))/(a+b*x^(1/2))/b^2","A"
462,1,109,107,0.016000," ","int((a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(7/2),x)","\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(36 b^{7} x^{\frac{10}{3}}+280 a \,b^{6} x^{3}+945 a^{2} b^{5} x^{\frac{8}{3}}+1800 a^{3} b^{4} x^{\frac{7}{3}}+2100 a^{4} b^{3} x^{2}+1512 a^{5} b^{2} x^{\frac{5}{3}}+630 a^{6} b \,x^{\frac{4}{3}}+120 a^{7} x \right)}{120 b \,x^{\frac{1}{3}}+120 a}"," ",0,"1/120*(a^2+2*a*b*x^(1/3)+b^2*x^(2/3))^(1/2)*(36*b^7*x^(10/3)+945*a^2*b^5*x^(8/3)+1800*a^3*b^4*x^(7/3)+1512*a^5*b^2*x^(5/3)+630*a^6*b*x^(4/3)+280*a*b^6*x^3+2100*a^4*b^3*x^2+120*a^7*x)/(a+b*x^(1/3))","A"
463,1,87,107,0.002000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(5/2),x)","\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(21 b^{5} x^{\frac{8}{3}}+120 a \,b^{4} x^{\frac{7}{3}}+280 a^{2} b^{3} x^{2}+336 a^{3} b^{2} x^{\frac{5}{3}}+210 a^{4} b \,x^{\frac{4}{3}}+56 a^{5} x \right)}{56 b \,x^{\frac{1}{3}}+56 a}"," ",0,"1/56*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(21*b^5*x^(8/3)+120*a*b^4*x^(7/3)+336*a^3*b^2*x^(5/3)+210*a^4*b*x^(4/3)+280*a^2*b^3*x^2+56*a^5*x)/(b*x^(1/3)+a)","A"
464,1,65,107,0.003000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(3/2),x)","\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(10 b^{3} x^{2}+36 a \,b^{2} x^{\frac{5}{3}}+45 a^{2} b \,x^{\frac{4}{3}}+20 a^{3} x \right)}{20 b \,x^{\frac{1}{3}}+20 a}"," ",0,"1/20*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(36*a*b^2*x^(5/3)+45*a^2*b*x^(4/3)+10*b^3*x^2+20*a^3*x)/(b*x^(1/3)+a)","A"
465,1,43,68,0.003000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2),x)","\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(3 b \,x^{\frac{4}{3}}+4 a x \right)}{4 b \,x^{\frac{1}{3}}+4 a}"," ",0,"1/4*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(3*b*x^(4/3)+4*a*x)/(b*x^(1/3)+a)","A"
466,1,103,115,0.018000," ","int(1/(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2),x)","\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(4 a^{2} \ln \left(b \,x^{\frac{1}{3}}+a \right)-2 a^{2} \ln \left(b^{2} x^{\frac{2}{3}}-a b \,x^{\frac{1}{3}}+a^{2}\right)+2 a^{2} \ln \left(b^{3} x +a^{3}\right)+3 b^{2} x^{\frac{2}{3}}-6 a b \,x^{\frac{1}{3}}\right)}{2 \left(b \,x^{\frac{1}{3}}+a \right) b^{3}}"," ",0,"1/2*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(3*b^2*x^(2/3)-6*a*b*x^(1/3)+2*a^2*ln(b^3*x+a^3)-2*a^2*ln(b^2*x^(2/3)-a*b*x^(1/3)+a^2)+4*a^2*ln(b*x^(1/3)+a))/(b*x^(1/3)+a)/b^3","A"
467,1,92,104,0.008000," ","int(1/(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(3/2),x)","\frac{3 \sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(2 b^{2} x^{\frac{2}{3}} \ln \left(b \,x^{\frac{1}{3}}+a \right)+4 a b \,x^{\frac{1}{3}} \ln \left(b \,x^{\frac{1}{3}}+a \right)+2 a^{2} \ln \left(b \,x^{\frac{1}{3}}+a \right)+4 a b \,x^{\frac{1}{3}}+3 a^{2}\right)}{2 \left(b \,x^{\frac{1}{3}}+a \right)^{3} b^{3}}"," ",0,"3/2*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(2*x^(2/3)*ln(b*x^(1/3)+a)*b^2+4*x^(1/3)*ln(b*x^(1/3)+a)*a*b+4*a*b*x^(1/3)+2*a^2*ln(b*x^(1/3)+a)+3*a^2)/(b*x^(1/3)+a)^3/b^3","A"
468,1,54,107,0.009000," ","int(1/(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(5/2),x)","-\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(6 b^{2} x^{\frac{2}{3}}+4 a b \,x^{\frac{1}{3}}+a^{2}\right)}{4 \left(b \,x^{\frac{1}{3}}+a \right)^{5} b^{3}}"," ",0,"-1/4*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(6*b^2*x^(2/3)+4*a*b*x^(1/3)+a^2)/(b*x^(1/3)+a)^5/b^3","A"
469,1,54,107,0.007000," ","int(1/(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(7/2),x)","-\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(15 b^{2} x^{\frac{2}{3}}+6 a b \,x^{\frac{1}{3}}+a^{2}\right)}{20 \left(b \,x^{\frac{1}{3}}+a \right)^{7} b^{3}}"," ",0,"-1/20*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(15*b^2*x^(2/3)+6*a*b*x^(1/3)+a^2)/(b*x^(1/3)+a)^7/b^3","A"
470,1,54,107,0.007000," ","int(1/(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(9/2),x)","-\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(28 b^{2} x^{\frac{2}{3}}+8 a b \,x^{\frac{1}{3}}+a^{2}\right)}{56 \left(b \,x^{\frac{1}{3}}+a \right)^{9} b^{3}}"," ",0,"-1/56*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(28*b^2*x^(2/3)+8*a*b*x^(1/3)+a^2)/(b*x^(1/3)+a)^9/b^3","A"
471,1,54,107,0.007000," ","int(1/(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(11/2),x)","-\frac{\sqrt{b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}}\, \left(45 b^{2} x^{\frac{2}{3}}+10 a b \,x^{\frac{1}{3}}+a^{2}\right)}{120 \left(b \,x^{\frac{1}{3}}+a \right)^{11} b^{3}}"," ",0,"-1/120*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^(1/2)*(45*b^2*x^(2/3)+10*a*b*x^(1/3)+a^2)/(b*x^(1/3)+a)^11/b^3","A"
472,0,0,73,0.030000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p*(d*x)^m,x)","\int \left(d x \right)^{m} \left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}\, dx"," ",0,"int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p*(d*x)^m,x)","F"
473,0,0,414,0.009000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p*x^2,x)","\int x^{2} \left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}\, dx"," ",0,"int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p*x^2,x)","F"
474,0,0,275,0.007000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p*x,x)","\int x \left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}\, dx"," ",0,"int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p*x,x)","F"
475,0,0,124,0.006000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p,x)","\int \left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}\, dx"," ",0,"int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p,x)","F"
476,0,0,63,0.009000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p/x,x)","\int \frac{\left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}}{x}\, dx"," ",0,"int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p/x,x)","F"
477,0,0,69,0.008000," ","int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p/x^2,x)","\int \frac{\left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int((b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p/x^2,x)","F"
478,0,0,124,0.011000," ","int(1/x^2*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p-2/3*b^3*(1-2*p)*(1-p)*p*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p/a^3/x,x)","\int -\frac{2 \left(-2 p +1\right) \left(-p +1\right) b^{3} p \left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}}{3 a^{3} x}+\frac{\left(b^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+a^{2}\right)^{p}}{x^{2}}\, dx"," ",0,"int(1/x^2*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p-2/3*b^3*(1-2*p)*(1-p)*p*(b^2*x^(2/3)+2*a*b*x^(1/3)+a^2)^p/a^3/x,x)","F"
479,1,114,142,0.016000," ","int(1/(a^2+2*a*b*x^(1/4)+b^2*x^(1/2))^(3/2),x)","\frac{2 \sqrt{b^{2} \sqrt{x}+2 a b \,x^{\frac{1}{4}}+a^{2}}\, \left(-6 a \,b^{2} \sqrt{x}\, \ln \left(b \,x^{\frac{1}{4}}+a \right)-12 a^{2} b \,x^{\frac{1}{4}} \ln \left(b \,x^{\frac{1}{4}}+a \right)-6 a^{3} \ln \left(b \,x^{\frac{1}{4}}+a \right)+2 b^{3} x^{\frac{3}{4}}+4 a \,b^{2} \sqrt{x}-4 a^{2} b \,x^{\frac{1}{4}}-5 a^{3}\right)}{\left(b \,x^{\frac{1}{4}}+a \right)^{3} b^{4}}"," ",0,"2*(a^2+2*a*b*x^(1/4)+b^2*x^(1/2))^(1/2)*(2*x^(3/4)*b^3-6*x^(1/2)*ln(a+b*x^(1/4))*a*b^2+4*x^(1/2)*a*b^2-12*x^(1/4)*ln(a+b*x^(1/4))*a^2*b-4*x^(1/4)*a^2*b-6*ln(a+b*x^(1/4))*a^3-5*a^3)/(a+b*x^(1/4))^3/b^4","A"
480,1,174,216,0.016000," ","int(1/(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))^(5/2),x)","\frac{\sqrt{b^{2} x^{\frac{1}{3}}+2 a b \,x^{\frac{1}{6}}+a^{2}}\, \left(-60 a \,b^{4} x^{\frac{2}{3}} \ln \left(b \,x^{\frac{1}{6}}+a \right)-240 a^{2} b^{3} \sqrt{x}\, \ln \left(b \,x^{\frac{1}{6}}+a \right)-360 a^{3} b^{2} x^{\frac{1}{3}} \ln \left(b \,x^{\frac{1}{6}}+a \right)-240 a^{4} b \,x^{\frac{1}{6}} \ln \left(b \,x^{\frac{1}{6}}+a \right)-60 a^{5} \ln \left(b \,x^{\frac{1}{6}}+a \right)+12 b^{5} x^{\frac{5}{6}}+48 a \,b^{4} x^{\frac{2}{3}}-48 a^{2} b^{3} \sqrt{x}-252 a^{3} b^{2} x^{\frac{1}{3}}-248 a^{4} b \,x^{\frac{1}{6}}-77 a^{5}\right)}{2 \left(b \,x^{\frac{1}{6}}+a \right)^{5} b^{6}}"," ",0,"1/2*(a^2+2*a*b*x^(1/6)+b^2*x^(1/3))^(1/2)*(12*x^(5/6)*b^5-60*x^(2/3)*ln(a+b*x^(1/6))*a*b^4+48*x^(2/3)*a*b^4-240*x^(1/2)*ln(a+b*x^(1/6))*a^2*b^3-48*x^(1/2)*a^2*b^3-360*x^(1/3)*ln(a+b*x^(1/6))*a^3*b^2-252*x^(1/3)*a^3*b^2-240*x^(1/6)*ln(a+b*x^(1/6))*a^4*b-248*x^(1/6)*a^4*b-60*ln(a+b*x^(1/6))*a^5-77*a^5)/(a+b*x^(1/6))^5/b^6","A"
481,1,68,147,0.030000," ","int((a^2+b^2/x+2*a*b/x^(1/2))^(3/2),x)","\frac{\sqrt{\frac{a^{2} x^{\frac{3}{2}}+2 a b x +b^{2} \sqrt{x}}{x^{\frac{3}{2}}}}\, \left(a^{3} x^{\frac{3}{2}}+3 a \,b^{2} \sqrt{x}\, \ln \left(x \right)+6 a^{2} b x -2 b^{3}\right)}{a \sqrt{x}+b}"," ",0,"((a^2*x^(3/2)+b^2*x^(1/2)+2*a*x*b)/x^(3/2))^(1/2)*(3*a*b^2*ln(x)*x^(1/2)+6*a^2*b*x+x^(3/2)*a^3-2*b^3)/(a*x^(1/2)+b)","A"
482,1,115,307,0.028000," ","int((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(7/2),x)","\frac{\left(\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{7}{2}} \left(4 a^{7} x^{\frac{10}{3}}+140 a^{4} b^{3} x^{\frac{7}{3}} \ln \left(x \right)+42 a^{6} b \,x^{3}+252 a^{5} b^{2} x^{\frac{8}{3}}-420 a^{3} b^{4} x^{2}-126 a^{2} b^{5} x^{\frac{5}{3}}-28 a \,b^{6} x^{\frac{4}{3}}-3 b^{7} x \right)}{4 \left(a \,x^{\frac{1}{3}}+b \right)^{7}}"," ",0,"1/4*((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(7/2)*(42*a^6*b*x^3+140*a^4*b^3*ln(x)*x^(7/3)+252*a^5*b^2*x^(8/3)+4*a^7*x^(10/3)-28*a*b^6*x^(4/3)-420*a^3*b^4*x^2-126*a^2*b^5*x^(5/3)-3*b^7*x)/(b+a*x^(1/3))^7","A"
483,1,91,227,0.010000," ","int((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x)","\frac{\left(\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{5}{2}} \left(2 a^{5} x^{\frac{5}{3}}+20 a^{2} b^{3} x^{\frac{2}{3}} \ln \left(x \right)+15 a^{4} b \,x^{\frac{4}{3}}+60 a^{3} b^{2} x -30 a \,b^{4} x^{\frac{1}{3}}-3 b^{5}\right) x}{2 \left(a \,x^{\frac{1}{3}}+b \right)^{5}}"," ",0,"1/2*((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(5/2)*x*(15*a^4*b*x^(4/3)+60*a^3*b^2*x+20*a^2*b^3*ln(x)*x^(2/3)+2*a^5*x^(5/3)-30*a*b^4*x^(1/3)-3*b^5)/(a*x^(1/3)+b)^5","A"
484,1,69,146,0.005000," ","int((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x)","\frac{\left(\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}} \left(2 a^{3} x +2 b^{3} \ln \left(x \right)+9 a^{2} b \,x^{\frac{2}{3}}+18 a \,b^{2} x^{\frac{1}{3}}\right) x}{2 \left(a \,x^{\frac{1}{3}}+b \right)^{3}}"," ",0,"1/2*((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(3/2)*x*(9*a^2*b*x^(2/3)+18*a*b^2*x^(1/3)+2*b^3*ln(x)+2*a^3*x)/(a*x^(1/3)+b)^3","A"
485,1,50,68,0.005000," ","int((a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(1/2),x)","\frac{\sqrt{\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}}\, \left(2 a x +3 b \,x^{\frac{2}{3}}\right) x^{\frac{1}{3}}}{2 a \,x^{\frac{1}{3}}+2 b}"," ",0,"1/2*((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(1/2)*x^(1/3)*(3*x^(2/3)*b+2*a*x)/(a*x^(1/3)+b)","A"
486,1,78,150,0.006000," ","int(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(1/2),x)","-\frac{\left(a \,x^{\frac{1}{3}}+b \right) \left(-2 a^{3} x +6 b^{3} \ln \left(a \,x^{\frac{1}{3}}+b \right)+3 a^{2} b \,x^{\frac{2}{3}}-6 a \,b^{2} x^{\frac{1}{3}}\right)}{2 \sqrt{\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}}\, a^{4} x^{\frac{1}{3}}}"," ",0,"-1/2/((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(1/2)/x^(1/3)*(a*x^(1/3)+b)*(3*a^2*b*x^(2/3)-6*a*b^2*x^(1/3)+6*b^3*ln(a*x^(1/3)+b)-2*a^3*x)/a^4","A"
487,1,141,238,0.011000," ","int(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(3/2),x)","\frac{\left(2 a^{5} x^{\frac{5}{3}}-60 a^{2} b^{3} x^{\frac{2}{3}} \ln \left(a \,x^{\frac{1}{3}}+b \right)-5 a^{4} b \,x^{\frac{4}{3}}-120 a \,b^{4} x^{\frac{1}{3}} \ln \left(a \,x^{\frac{1}{3}}+b \right)+20 a^{3} b^{2} x -60 b^{5} \ln \left(a \,x^{\frac{1}{3}}+b \right)+63 a^{2} b^{3} x^{\frac{2}{3}}+6 a \,b^{4} x^{\frac{1}{3}}-27 b^{5}\right) \left(a \,x^{\frac{1}{3}}+b \right)}{2 \left(\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{3}{2}} a^{6} x}"," ",0,"1/2/((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(3/2)/x*(2*a^5*x^(5/3)-5*a^4*b*x^(4/3)-60*x^(2/3)*ln(a*x^(1/3)+b)*a^2*b^3+63*x^(2/3)*a^2*b^3-120*x^(1/3)*ln(a*x^(1/3)+b)*a*b^4+6*a*b^4*x^(1/3)-60*ln(a*x^(1/3)+b)*b^5+20*a^3*b^2*x-27*b^5)*(a*x^(1/3)+b)/a^6","A"
488,1,199,326,0.013000," ","int(1/(a^2+b^2/x^(2/3)+2*a*b/x^(1/3))^(5/2),x)","\frac{\left(4 a^{7} x^{\frac{7}{3}}-420 a^{4} b^{3} x^{\frac{4}{3}} \ln \left(a \,x^{\frac{1}{3}}+b \right)-14 a^{6} b \,x^{2}-1680 a^{3} b^{4} x \ln \left(a \,x^{\frac{1}{3}}+b \right)+84 a^{5} b^{2} x^{\frac{5}{3}}-2520 a^{2} b^{5} x^{\frac{2}{3}} \ln \left(a \,x^{\frac{1}{3}}+b \right)+556 a^{4} b^{3} x^{\frac{4}{3}}-1680 a \,b^{6} x^{\frac{1}{3}} \ln \left(a \,x^{\frac{1}{3}}+b \right)+544 a^{3} b^{4} x -420 b^{7} \ln \left(a \,x^{\frac{1}{3}}+b \right)-444 a^{2} b^{5} x^{\frac{2}{3}}-856 a \,b^{6} x^{\frac{1}{3}}-319 b^{7}\right) \left(a \,x^{\frac{1}{3}}+b \right)}{4 \left(\frac{a^{2} x^{\frac{2}{3}}+2 a b \,x^{\frac{1}{3}}+b^{2}}{x^{\frac{2}{3}}}\right)^{\frac{5}{2}} a^{8} x^{\frac{5}{3}}}"," ",0,"1/4/((a^2*x^(2/3)+2*a*b*x^(1/3)+b^2)/x^(2/3))^(5/2)/x^(5/3)*(4*x^(7/3)*a^7+84*a^5*b^2*x^(5/3)-420*x^(4/3)*ln(a*x^(1/3)+b)*a^4*b^3+556*x^(4/3)*a^4*b^3-2520*x^(2/3)*ln(a*x^(1/3)+b)*a^2*b^5-444*x^(2/3)*a^2*b^5-1680*x^(1/3)*ln(a*x^(1/3)+b)*a*b^6-1680*x*ln(a*x^(1/3)+b)*a^3*b^4-14*a^6*b*x^2-856*x^(1/3)*a*b^6-420*ln(a*x^(1/3)+b)*b^7+544*x*a^3*b^4-319*b^7)*(a*x^(1/3)+b)/a^8","A"
489,1,94,227,0.036000," ","int((a^2+2*a*b/x^(1/4)+b^2/x^(1/2))^(5/2),x)","\frac{\sqrt{\frac{a^{2} x^{\frac{3}{4}}+2 a b \sqrt{x}+b^{2} x^{\frac{1}{4}}}{x^{\frac{3}{4}}}}\, \left(3 a^{5} x^{\frac{5}{4}}+15 a \,b^{4} x^{\frac{1}{4}} \ln \left(x \right)+20 a^{4} b x +60 a^{3} b^{2} x^{\frac{3}{4}}+120 a^{2} b^{3} \sqrt{x}-12 b^{5}\right)}{3 a \,x^{\frac{1}{4}}+3 b}"," ",0,"1/3*((a^2*x^(3/4)+b^2*x^(1/4)+2*a*b*x^(1/2))/x^(3/4))^(1/2)*(20*x*a^4*b+15*ln(x)*x^(1/4)*a*b^4+120*a^2*b^3*x^(1/2)+60*x^(3/4)*a^3*b^2+3*x^(5/4)*a^5-12*b^5)/(a*x^(1/4)+b)","A"
490,1,91,226,0.026000," ","int((a^2+b^2/x^(2/5)+2*a*b/x^(1/5))^(5/2),x)","\frac{\left(\frac{a^{2} x^{\frac{2}{5}}+2 a b \,x^{\frac{1}{5}}+b^{2}}{x^{\frac{2}{5}}}\right)^{\frac{5}{2}} \left(12 a^{5} x +12 b^{5} \ln \left(x \right)+75 a^{4} b \,x^{\frac{4}{5}}+200 a^{3} b^{2} x^{\frac{3}{5}}+300 a^{2} b^{3} x^{\frac{2}{5}}+300 a \,b^{4} x^{\frac{1}{5}}\right) x}{12 \left(a \,x^{\frac{1}{5}}+b \right)^{5}}"," ",0,"1/12*((a^2*x^(2/5)+2*a*b*x^(1/5)+b^2)/x^(2/5))^(5/2)*x*(75*a^4*b*x^(4/5)+200*a^3*b^2*x^(3/5)+300*a^2*b^3*x^(2/5)+12*b^5*ln(x)+300*a*b^4*x^(1/5)+12*a^5*x)/(x^(1/5)*a+b)^5","A"
491,1,152,178,0.012000," ","int(1/(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))^(5/2),x)","\frac{5 \sqrt{b^{2} x^{\frac{2}{5}}+2 a b \,x^{\frac{1}{5}}+a^{2}}\, \left(12 b^{4} x^{\frac{4}{5}} \ln \left(b \,x^{\frac{1}{5}}+a \right)+48 a \,b^{3} x^{\frac{3}{5}} \ln \left(b \,x^{\frac{1}{5}}+a \right)+72 a^{2} b^{2} x^{\frac{2}{5}} \ln \left(b \,x^{\frac{1}{5}}+a \right)+48 a^{3} b \,x^{\frac{1}{5}} \ln \left(b \,x^{\frac{1}{5}}+a \right)+12 a^{4} \ln \left(b \,x^{\frac{1}{5}}+a \right)+48 a \,b^{3} x^{\frac{3}{5}}+108 a^{2} b^{2} x^{\frac{2}{5}}+88 a^{3} b \,x^{\frac{1}{5}}+25 a^{4}\right)}{12 \left(b \,x^{\frac{1}{5}}+a \right)^{5} b^{5}}"," ",0,"5/12*(a^2+2*a*b*x^(1/5)+b^2*x^(2/5))^(1/2)*(12*x^(4/5)*ln(a+b*x^(1/5))*b^4+48*x^(3/5)*ln(a+b*x^(1/5))*a*b^3+48*x^(3/5)*a*b^3+72*x^(2/5)*ln(a+b*x^(1/5))*a^2*b^2+108*x^(2/5)*a^2*b^2+48*x^(1/5)*ln(a+b*x^(1/5))*a^3*b+88*x^(1/5)*a^3*b+12*ln(a+b*x^(1/5))*a^4+25*a^4)/(a+b*x^(1/5))^5/b^5","A"
492,1,116,307,0.032000," ","int((a^2+b^2/x^(1/3)+2*a*b/x^(1/6))^(7/2),x)","\frac{\sqrt{\frac{a^{2} \sqrt{x}+2 a b \,x^{\frac{1}{3}}+b^{2} x^{\frac{1}{6}}}{\sqrt{x}}}\, \left(10 a^{7} x^{\frac{7}{6}}+70 a \,b^{6} x^{\frac{1}{6}} \ln \left(x \right)+84 a^{6} b x +315 a^{5} b^{2} x^{\frac{5}{6}}+700 a^{4} b^{3} x^{\frac{2}{3}}+1050 a^{3} b^{4} \sqrt{x}+1260 a^{2} b^{5} x^{\frac{1}{3}}-60 b^{7}\right)}{10 a \,x^{\frac{1}{6}}+10 b}"," ",0,"1/10*((a^2*x^(1/2)+2*a*b*x^(1/3)+b^2*x^(1/6))/x^(1/2))^(1/2)*(84*a^6*b*x+315*a^5*b^2*x^(5/6)+70*a*b^6*ln(x)*x^(1/6)+1050*a^3*b^4*x^(1/2)+1260*a^2*b^5*x^(1/3)+700*a^4*b^3*x^(2/3)+10*a^7*x^(7/6)-60*b^7)/(a*x^(1/6)+b)","A"
493,1,62,44,0.030000," ","int(x^(-1+4*n)/(b*x^n+c*x^(2*n)),x)","\left(-\frac{b \,{\mathrm e}^{2 n \ln \left(x \right)}}{c^{2} n}+\frac{{\mathrm e}^{3 n \ln \left(x \right)}}{2 c n}\right) {\mathrm e}^{-n \ln \left(x \right)}+\frac{b^{2} \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{c^{3} n}"," ",0,"(1/2/c/n*exp(n*ln(x))^3-b/c^2/n*exp(n*ln(x))^2)/exp(n*ln(x))+b^2/c^3/n*ln(c*exp(n*ln(x))+b)","A"
494,1,33,28,0.024000," ","int(x^(-1+3*n)/(b*x^n+c*x^(2*n)),x)","-\frac{b \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{c^{2} n}+\frac{{\mathrm e}^{n \ln \left(x \right)}}{c n}"," ",0,"1/c/n*exp(n*ln(x))-b/c^2/n*ln(c*exp(n*ln(x))+b)","A"
495,1,18,15,0.022000," ","int(x^(-1+2*n)/(b*x^n+c*x^(2*n)),x)","\frac{\ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{c n}"," ",0,"1/c/n*ln(c*exp(n*ln(x))+b)","A"
496,1,26,23,0.020000," ","int(x^(-1+n)/(b*x^n+c*x^(2*n)),x)","\frac{\ln \left(x \right)}{b}-\frac{\ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{b n}"," ",0,"ln(x)/b-1/b/n*ln(c*exp(n*ln(x))+b)","A"
497,1,69,57,0.024000," ","int(x^(-1-n)/(b*x^n+c*x^(2*n)),x)","\left(\frac{c^{2} {\mathrm e}^{2 n \ln \left(x \right)} \ln \left(x \right)}{b^{3}}+\frac{c \,{\mathrm e}^{n \ln \left(x \right)}}{b^{2} n}-\frac{1}{2 b n}\right) {\mathrm e}^{-2 n \ln \left(x \right)}-\frac{c^{2} \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{b^{3} n}"," ",0,"(c/b^2/n*exp(n*ln(x))-1/2/b/n+c^2/b^3*ln(x)*exp(n*ln(x))^2)/exp(n*ln(x))^2-c^2/b^3/n*ln(c*exp(n*ln(x))+b)","A"
498,1,88,76,0.031000," ","int(x^(-1-2*n)/(b*x^n+c*x^(2*n)),x)","\left(-\frac{c^{3} {\mathrm e}^{3 n \ln \left(x \right)} \ln \left(x \right)}{b^{4}}+\frac{c \,{\mathrm e}^{n \ln \left(x \right)}}{2 b^{2} n}-\frac{c^{2} {\mathrm e}^{2 n \ln \left(x \right)}}{b^{3} n}-\frac{1}{3 b n}\right) {\mathrm e}^{-3 n \ln \left(x \right)}+\frac{c^{3} \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{b^{4} n}"," ",0,"(-1/3/b/n+1/2/b^2*c/n*exp(n*ln(x))-c^2/b^3/n*exp(n*ln(x))^2-c^3/b^4*ln(x)*exp(n*ln(x))^3)/exp(n*ln(x))^3+c^3/b^4/n*ln(c*exp(n*ln(x))+b)","A"
499,1,105,93,0.032000," ","int(x^(-1-3*n)/(b*x^n+c*x^(2*n)),x)","\left(\frac{c^{4} {\mathrm e}^{4 n \ln \left(x \right)} \ln \left(x \right)}{b^{5}}+\frac{c \,{\mathrm e}^{n \ln \left(x \right)}}{3 b^{2} n}-\frac{c^{2} {\mathrm e}^{2 n \ln \left(x \right)}}{2 b^{3} n}+\frac{c^{3} {\mathrm e}^{3 n \ln \left(x \right)}}{b^{4} n}-\frac{1}{4 b n}\right) {\mathrm e}^{-4 n \ln \left(x \right)}-\frac{c^{4} \ln \left(c \,{\mathrm e}^{n \ln \left(x \right)}+b \right)}{b^{5} n}"," ",0,"(c^3/b^4/n*exp(n*ln(x))^3-1/4/b/n+1/3/b^2*c/n*exp(n*ln(x))-1/2*c^2/b^3/n*exp(n*ln(x))^2+c^4/b^5*ln(x)*exp(n*ln(x))^4)/exp(n*ln(x))^4-c^4/b^5/n*ln(c*exp(n*ln(x))+b)","A"
500,1,54,167,0.121000," ","int(x^(-1+1/4*n)/(b*x^n+c*x^(2*n)),x)","\RootOf \left(b^{7} n^{4} \textit{\_Z}^{4}+c^{3}\right) \ln \left(-\frac{\RootOf \left(b^{7} n^{4} \textit{\_Z}^{4}+c^{3}\right) b^{2} n}{c}+x^{\frac{n}{4}}\right)-\frac{4 x^{-\frac{3 n}{4}}}{3 b n}"," ",0,"-4/3/b/n/(x^(1/4*n))^3+sum(_R*ln(x^(1/4*n)-b^2*n/c*_R),_R=RootOf(_Z^4*b^7*n^4+c^3))","C"
501,1,54,115,0.069000," ","int(x^(-1+1/3*n)/(b*x^n+c*x^(2*n)),x)","\RootOf \left(b^{5} n^{3} \textit{\_Z}^{3}+c^{2}\right) \ln \left(-\frac{\RootOf \left(b^{5} n^{3} \textit{\_Z}^{3}+c^{2}\right) b^{2} n}{c}+x^{\frac{n}{3}}\right)-\frac{3 x^{-\frac{2 n}{3}}}{2 b n}"," ",0,"-3/2/b/n/(x^(1/3*n))^2+sum(_R*ln(x^(1/3*n)-_R*b^2/c*n),_R=RootOf(_Z^3*b^5*n^3+c^2))","C"
502,1,79,42,0.073000," ","int(x^(-1+1/2*n)/(b*x^n+c*x^(2*n)),x)","-\frac{2 x^{-\frac{n}{2}}}{b n}+\frac{\sqrt{-b c}\, \ln \left(x^{\frac{n}{2}}-\frac{\sqrt{-b c}}{c}\right)}{b^{2} n}-\frac{\sqrt{-b c}\, \ln \left(x^{\frac{n}{2}}+\frac{\sqrt{-b c}}{c}\right)}{b^{2} n}"," ",0,"-2/b/n/(x^(1/2*n))+1/b^2*(-b*c)^(1/2)/n*ln(x^(1/2*n)-(-b*c)^(1/2)/c)-1/b^2*(-b*c)^(1/2)/n*ln(x^(1/2*n)+(-b*c)^(1/2)/c)","A"
503,1,97,58,0.095000," ","int(x^(-1-1/2*n)/(b*x^n+c*x^(2*n)),x)","-\frac{2 x^{-\frac{3 n}{2}}}{3 b n}+\frac{2 c \,x^{-\frac{n}{2}}}{b^{2} n}-\frac{\sqrt{-b c}\, c \ln \left(x^{\frac{n}{2}}-\frac{\sqrt{-b c}}{c}\right)}{b^{3} n}+\frac{\sqrt{-b c}\, c \ln \left(x^{\frac{n}{2}}+\frac{\sqrt{-b c}}{c}\right)}{b^{3} n}"," ",0,"2*c/b^2/n/(x^(1/2*n))-2/3/b/n/(x^(1/2*n))^3+1/b^3*(-b*c)^(1/2)*c/n*ln(x^(1/2*n)+(-b*c)^(1/2)/c)-1/b^3*(-b*c)^(1/2)*c/n*ln(x^(1/2*n)-(-b*c)^(1/2)/c)","A"
504,1,73,137,0.079000," ","int(x^(-1-1/3*n)/(b*x^n+c*x^(2*n)),x)","\RootOf \left(b^{7} n^{3} \textit{\_Z}^{3}+c^{4}\right) \ln \left(\frac{\RootOf \left(b^{7} n^{3} \textit{\_Z}^{3}+c^{4}\right)^{2} b^{5} n^{2}}{c^{3}}+x^{\frac{n}{3}}\right)-\frac{3 x^{-\frac{4 n}{3}}}{4 b n}+\frac{3 c \,x^{-\frac{n}{3}}}{b^{2} n}"," ",0,"3*c/b^2/n/(x^(1/3*n))-3/4/b/n/(x^(1/3*n))^4+sum(_R*ln(x^(1/3*n)+b^5*n^2/c^3*_R^2),_R=RootOf(_Z^3*b^7*n^3+c^4))","C"
505,1,73,195,0.092000," ","int(x^(-1-1/4*n)/(b*x^n+c*x^(2*n)),x)","\RootOf \left(b^{9} n^{4} \textit{\_Z}^{4}+c^{5}\right) \ln \left(\frac{\RootOf \left(b^{9} n^{4} \textit{\_Z}^{4}+c^{5}\right)^{3} b^{7} n^{3}}{c^{4}}+x^{\frac{n}{4}}\right)-\frac{4 x^{-\frac{5 n}{4}}}{5 b n}+\frac{4 c \,x^{-\frac{n}{4}}}{b^{2} n}"," ",0,"4*c/b^2/n/(x^(1/4*n))-4/5/b/n/(x^(1/4*n))^5+sum(_R*ln(x^(1/4*n)+b^7*n^3/c^4*_R^3),_R=RootOf(_Z^4*b^9*n^4+c^5))","C"
506,0,0,38,0.098000," ","int(x^(-1-n*(-1+p))*(b*x^n+c*x^(2*n))^p,x)","\int x^{-\left(p -1\right) n -1} \left(b \,x^{n}+c \,x^{2 n}\right)^{p}\, dx"," ",0,"int(x^(-1-n*(-1+p))*(b*x^n+c*x^(2*n))^p,x)","F"
507,0,0,40,0.070000," ","int(x^(-1-n*(2*p+1))*(b*x^n+c*x^(2*n))^p,x)","\int x^{-\left(2 p +1\right) n -1} \left(b \,x^{n}+c \,x^{2 n}\right)^{p}\, dx"," ",0,"int(x^(-1-n*(2*p+1))*(b*x^n+c*x^(2*n))^p,x)","F"
508,1,208,104,0.047000," ","int(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(5/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{5} x^{2 n}}{2 \left(b \,x^{n}+a \right) n}+\frac{5 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{4} b \,x^{3 n}}{3 \left(b \,x^{n}+a \right) n}+\frac{5 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3} b^{2} x^{4 n}}{2 \left(b \,x^{n}+a \right) n}+\frac{2 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b^{3} x^{5 n}}{\left(b \,x^{n}+a \right) n}+\frac{5 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{4} x^{6 n}}{6 \left(b \,x^{n}+a \right) n}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{5} x^{7 n}}{7 \left(b \,x^{n}+a \right) n}"," ",0,"1/7*((a+b*x^n)^2)^(1/2)/(a+b*x^n)*b^5/n*(x^n)^7+5/6*((a+b*x^n)^2)^(1/2)/(a+b*x^n)*a*b^4/n*(x^n)^6+2*((a+b*x^n)^2)^(1/2)/(a+b*x^n)*a^2*b^3/n*(x^n)^5+5/2*((a+b*x^n)^2)^(1/2)/(a+b*x^n)*a^3*b^2/n*(x^n)^4+5/3*((a+b*x^n)^2)^(1/2)/(a+b*x^n)*a^4*b/n*(x^n)^3+1/2*((a+b*x^n)^2)^(1/2)/(a+b*x^n)*a^5/n*(x^n)^2","A"
509,1,135,104,0.026000," ","int(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3} x^{2 n}}{2 \left(b \,x^{n}+a \right) n}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b \,x^{3 n}}{\left(b \,x^{n}+a \right) n}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x^{4 n}}{4 \left(b \,x^{n}+a \right) n}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x^{5 n}}{5 \left(b \,x^{n}+a \right) n}"," ",0,"1/5*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b^3/n*(x^n)^5+3/4*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*b^2/n*(x^n)^4+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^2*b/n*(x^n)^3+1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^3/n*(x^n)^2","A"
510,1,64,91,0.023000," ","int(x^(-1+2*n)*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,x^{2 n}}{2 \left(b \,x^{n}+a \right) n}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b \,x^{3 n}}{3 \left(b \,x^{n}+a \right) n}"," ",0,"1/3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b/n*(x^n)^3+1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a/n*(x^n)^2","A"
511,1,71,86,0.030000," ","int(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \ln \left(x^{n}+\frac{a}{b}\right)}{\left(b \,x^{n}+a \right) b^{2} n}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, x^{n}}{\left(b \,x^{n}+a \right) b n}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)/b/n*x^n-((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a/b^2/n*ln(x^n+a/b)","A"
512,1,37,44,0.026000," ","int(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x)","-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \left(2 b \,x^{n}+a \right)}{2 \left(b \,x^{n}+a \right)^{3} b^{2} n}"," ",0,"-1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)^3*(2*b*x^n+a)/b^2/n","A"
513,1,37,80,0.030000," ","int(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(5/2),x)","-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \left(4 b \,x^{n}+a \right)}{12 \left(b \,x^{n}+a \right)^{5} b^{2} n}"," ",0,"-1/12*((b*x^n+a)^2)^(1/2)/(b*x^n+a)^5*(4*b*x^n+a)/b^2/n","A"
514,1,37,80,0.032000," ","int(x^(-1+2*n)/(a^2+2*a*b*x^n+b^2*x^(2*n))^(7/2),x)","-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \left(6 b \,x^{n}+a \right)}{30 \left(b \,x^{n}+a \right)^{7} b^{2} n}"," ",0,"-1/30*((b*x^n+a)^2)^(1/2)/(b*x^n+a)^7*(6*b*x^n+a)/b^2/n","A"
515,1,132,104,0.043000," ","int((d*x)^m*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \left(b m \,x^{n}+a m +a n +b \,x^{n}+a \right) x \,{\mathrm e}^{\frac{\left(-i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)+i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)^{2}-i \pi  \mathrm{csgn}\left(i d x \right)^{3}+2 \ln \left(d \right)+2 \ln \left(x \right)\right) m}{2}}}{\left(b \,x^{n}+a \right) \left(m +1\right) \left(m +n +1\right)}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)*x*(m*b*x^n+a*m+a*n+b*x^n+a)/(m+1)/(1+m+n)*exp(1/2*m*(-I*Pi*csgn(I*d*x)^3+I*Pi*csgn(I*d*x)^2*csgn(I*d)+I*Pi*csgn(I*d*x)^2*csgn(I*x)-I*Pi*csgn(I*d*x)*csgn(I*d)*csgn(I*x)+2*ln(d)+2*ln(x)))","C"
516,1,61,87,0.016000," ","int(x^2*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b \,x^{3} x^{n}}{\left(b \,x^{n}+a \right) \left(n +3\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,x^{3}}{3 b \,x^{n}+3 a}"," ",0,"1/3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*x^3+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b/(3+n)*x^3*x^n","A"
517,1,61,87,0.015000," ","int(x*(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b \,x^{2} x^{n}}{\left(b \,x^{n}+a \right) \left(n +2\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,x^{2}}{2 b \,x^{n}+2 a}"," ",0,"1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*x^2+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b/(2+n)*x^2*x^n","A"
518,1,56,84,0.016000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b x \,x^{n}}{\left(b \,x^{n}+a \right) \left(n +1\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a x}{b \,x^{n}+a}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*x+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b/(1+n)*x*x^n","A"
519,1,54,81,0.017000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x,x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \ln \left(x \right)}{b \,x^{n}+a}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b \,x^{n}}{\left(b \,x^{n}+a \right) n}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*ln(x)+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b/n*x^n","A"
520,1,61,90,0.017000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x^2,x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b \,x^{n}}{\left(b \,x^{n}+a \right) \left(n -1\right) x}-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a}{\left(b \,x^{n}+a \right) x}"," ",0,"-((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a/x+((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(-1+n)*b/x*x^n","A"
521,1,61,90,0.020000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2)/x^3,x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b \,x^{n}}{\left(b \,x^{n}+a \right) \left(n -2\right) x^{2}}-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a}{2 \left(b \,x^{n}+a \right) x^{2}}"," ",0,"-1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a/x^2+((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(-2+n)*b/x^2*x^n","A"
522,1,532,230,0.059000," ","int((d*x)^m*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \left(3 a^{2} b \,m^{3} x^{n}+15 a^{2} b \,m^{2} n \,x^{n}+18 a^{2} b m \,n^{2} x^{n}+3 a \,b^{2} m^{3} x^{2 n}+12 a \,b^{2} m^{2} n \,x^{2 n}+9 a \,b^{2} m \,n^{2} x^{2 n}+b^{3} m^{3} x^{3 n}+3 b^{3} m^{2} n \,x^{3 n}+2 b^{3} m \,n^{2} x^{3 n}+a^{3} m^{3}+6 a^{3} m^{2} n +11 a^{3} m \,n^{2}+6 a^{3} n^{3}+9 a^{2} b \,m^{2} x^{n}+30 a^{2} b m n \,x^{n}+18 a^{2} b \,n^{2} x^{n}+9 a \,b^{2} m^{2} x^{2 n}+24 a \,b^{2} m n \,x^{2 n}+9 a \,b^{2} n^{2} x^{2 n}+3 b^{3} m^{2} x^{3 n}+6 b^{3} m n \,x^{3 n}+2 b^{3} n^{2} x^{3 n}+3 a^{3} m^{2}+12 a^{3} m n +11 a^{3} n^{2}+9 a^{2} b m \,x^{n}+15 a^{2} b n \,x^{n}+9 a \,b^{2} m \,x^{2 n}+12 a \,b^{2} n \,x^{2 n}+3 b^{3} m \,x^{3 n}+3 b^{3} n \,x^{3 n}+3 a^{3} m +6 a^{3} n +3 a^{2} b \,x^{n}+3 a \,b^{2} x^{2 n}+b^{3} x^{3 n}+a^{3}\right) x \,{\mathrm e}^{\frac{\left(-i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)+i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)^{2}-i \pi  \mathrm{csgn}\left(i d x \right)^{3}+2 \ln \left(d \right)+2 \ln \left(x \right)\right) m}{2}}}{\left(b \,x^{n}+a \right) \left(m +1\right) \left(m +n +1\right) \left(m +2 n +1\right) \left(m +3 n +1\right)}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)*x*(b^3*(x^n)^3+a^3*m^3+3*a^3*m^2+11*a^3*n^2+6*a^3*n+6*a^3*n^3+a^3+15*a^2*b*n*x^n+3*b^3*m^2*n*(x^n)^3+2*b^3*m*n^2*(x^n)^3+3*a*b^2*m^3*(x^n)^2+6*b^3*m*n*(x^n)^3+3*a^2*b*m^3*x^n+9*a*b^2*m^2*(x^n)^2+9*a*b^2*n^2*(x^n)^2+9*a^2*b*m^2*x^n+18*a^2*b*n^2*x^n+9*m*a*b^2*(x^n)^2+12*a*b^2*(x^n)^2*n+9*m*a^2*b*x^n+12*a*b^2*m^2*n*(x^n)^2+b^3*m^3*(x^n)^3+3*b^3*m^2*(x^n)^3+2*b^3*n^2*(x^n)^3+3*m*b^3*(x^n)^3+3*b^3*(x^n)^3*n+3*a^2*b*x^n+3*(x^n)^2*a*b^2+6*a^3*m^2*n+11*a^3*m*n^2+12*a^3*m*n+9*a*b^2*m*n^2*(x^n)^2+15*a^2*b*m^2*n*x^n+18*a^2*b*m*n^2*x^n+3*m*a^3+24*a*b^2*m*n*(x^n)^2+30*a^2*b*m*n*x^n)/(m+1)/(m+n+1)/(1+m+2*n)/(1+m+3*n)*exp(1/2*(-I*Pi*csgn(I*d)*csgn(I*x)*csgn(I*d*x)+I*Pi*csgn(I*d)*csgn(I*d*x)^2+I*Pi*csgn(I*x)*csgn(I*d*x)^2-I*Pi*csgn(I*d*x)^3+2*ln(d)+2*ln(x))*m)","C"
523,1,146,200,0.017000," ","int(x^2*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x)","\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b \,x^{3} x^{n}}{\left(b \,x^{n}+a \right) \left(n +3\right)}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x^{3} x^{2 n}}{\left(b \,x^{n}+a \right) \left(2 n +3\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x^{3} x^{3 n}}{3 \left(b \,x^{n}+a \right) \left(n +1\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3} x^{3}}{3 b \,x^{n}+3 a}"," ",0,"1/3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*x^3*a^3+1/3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b^3*x^3/(n+1)*(x^n)^3+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*b^2/(3+2*n)*x^3*(x^n)^2+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^2*b/(n+3)*x^3*x^n","A"
524,1,145,199,0.017000," ","int(x*(a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x)","\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b \,x^{2} x^{n}}{\left(b \,x^{n}+a \right) \left(n +2\right)}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x^{2} x^{2 n}}{2 \left(b \,x^{n}+a \right) \left(n +1\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x^{2} x^{3 n}}{\left(b \,x^{n}+a \right) \left(3 n +2\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3} x^{2}}{2 b \,x^{n}+2 a}"," ",0,"1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*x^2*a^3+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b^3/(2+3*n)*x^2*(x^n)^3+3/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*b^2*x^2/(n+1)*(x^n)^2+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^2*b/(n+2)*x^2*x^n","A"
525,1,138,198,0.016000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2),x)","\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b x \,x^{n}}{\left(b \,x^{n}+a \right) \left(n +1\right)}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x \,x^{2 n}}{\left(b \,x^{n}+a \right) \left(2 n +1\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x \,x^{3 n}}{\left(b \,x^{n}+a \right) \left(3 n +1\right)}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3} x}{b \,x^{n}+a}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^3*x+((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b^3/(1+3*n)*x*(x^n)^3+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*b^2/(1+2*n)*x*(x^n)^2+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^2*b/(n+1)*x*x^n","A"
526,1,127,184,0.019000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x,x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3} \ln \left(x \right)}{b \,x^{n}+a}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b \,x^{n}}{\left(b \,x^{n}+a \right) n}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x^{2 n}}{2 \left(b \,x^{n}+a \right) n}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x^{3 n}}{3 \left(b \,x^{n}+a \right) n}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^3*ln(x)+1/3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*b^3/n*(x^n)^3+3/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a*b^2/n*(x^n)^2+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^2*b/n*x^n","A"
527,1,147,204,0.025000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x^2,x)","\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b \,x^{n}}{\left(b \,x^{n}+a \right) \left(n -1\right) x}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x^{2 n}}{\left(b \,x^{n}+a \right) \left(2 n -1\right) x}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x^{3 n}}{\left(b \,x^{n}+a \right) \left(3 n -1\right) x}-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3}}{\left(b \,x^{n}+a \right) x}"," ",0,"-((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^3/x+((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(-1+3*n)*b^3/x*(x^n)^3+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(-1+2*n)*a*b^2/x*(x^n)^2+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(n-1)*a^2*b/x*x^n","A"
528,1,145,206,0.026000," ","int((a^2+2*a*b*x^n+b^2*x^(2*n))^(3/2)/x^3,x)","\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{2} b \,x^{n}}{\left(b \,x^{n}+a \right) \left(n -2\right) x^{2}}+\frac{3 \sqrt{\left(b \,x^{n}+a \right)^{2}}\, a \,b^{2} x^{2 n}}{2 \left(b \,x^{n}+a \right) \left(n -1\right) x^{2}}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, b^{3} x^{3 n}}{\left(b \,x^{n}+a \right) \left(3 n -2\right) x^{2}}-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, a^{3}}{2 \left(b \,x^{n}+a \right) x^{2}}"," ",0,"-1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)*a^3/x^2+((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(-2+3*n)*b^3/x^2*(x^n)^3+3/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(n-1)*a*b^2/x^2*(x^n)^2+3*((b*x^n+a)^2)^(1/2)/(b*x^n+a)/(n-2)*a^2*b/x^2*x^n","A"
529,0,0,76,0.070000," ","int((d*x)^m/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}}}\, dx"," ",0,"int((d*x)^m/(a^2+2*a*b*x^n+b^2*x^(2*n))^(1/2),x)","F"
530,0,0,62,0.021000," ","int(x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","\int \frac{x^{2}}{\sqrt{2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}}}\, dx"," ",0,"int(x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","F"
531,0,0,62,0.023000," ","int(x/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","\int \frac{x}{\sqrt{2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}}}\, dx"," ",0,"int(x/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","F"
532,0,0,55,0.020000," ","int(1/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","\int \frac{1}{\sqrt{2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}}}\, dx"," ",0,"int(1/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","F"
533,1,66,81,0.020000," ","int(1/x/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \ln \left(x \right)}{\left(b \,x^{n}+a \right) a}-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \ln \left(x^{n}+\frac{a}{b}\right)}{\left(b \,x^{n}+a \right) a n}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)/a*ln(x)-((b*x^n+a)^2)^(1/2)/(b*x^n+a)/a/n*ln(x^n+a/b)","A"
534,0,0,62,0.023000," ","int(1/x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","\int \frac{1}{\sqrt{2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}}\, x^{2}}\, dx"," ",0,"int(1/x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","F"
535,0,0,62,0.023000," ","int(1/x^3/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","\int \frac{1}{\sqrt{2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}}\, x^{3}}\, dx"," ",0,"int(1/x^3/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2),x)","F"
536,0,0,76,0.040000," ","int((d*x)^m/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","F"
537,0,0,62,0.083000," ","int(x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\int \frac{x^{2}}{\left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","F"
538,0,0,62,0.077000," ","int(x/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\int \frac{x}{\left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","F"
539,0,0,57,0.089000," ","int(1/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\int \frac{1}{\left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","F"
540,1,104,149,0.021000," ","int(1/x/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \ln \left(x \right)}{\left(b \,x^{n}+a \right) a^{3}}+\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \left(2 b \,x^{n}+3 a \right)}{2 \left(b \,x^{n}+a \right)^{3} a^{2} n}-\frac{\sqrt{\left(b \,x^{n}+a \right)^{2}}\, \ln \left(x^{n}+\frac{a}{b}\right)}{\left(b \,x^{n}+a \right) a^{3} n}"," ",0,"((b*x^n+a)^2)^(1/2)/(b*x^n+a)/a^3*ln(x)+1/2*((b*x^n+a)^2)^(1/2)/(b*x^n+a)^3*(2*b*x^n+3*a)/a^2/n-((b*x^n+a)^2)^(1/2)/(b*x^n+a)/a^3/n*ln(x^n+a/b)","A"
541,0,0,62,0.079000," ","int(1/x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\int \frac{1}{\left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{\frac{3}{2}} x^{2}}\, dx"," ",0,"int(1/x^2/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","F"
542,0,0,62,0.078000," ","int(1/x^3/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","\int \frac{1}{\left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{\frac{3}{2}} x^{3}}\, dx"," ",0,"int(1/x^3/(2*a*b*x^n+b^2*x^(2*n)+a^2)^(3/2),x)","F"
543,0,0,54,0.279000," ","int((a^2+b^2/(x^(2/(2*p+1)))+2*a*b/(x^(1/(2*p+1))))^p,x)","\int \left(2 a b \,x^{-\frac{1}{2 p +1}}+b^{2} x^{-\frac{2}{2 p +1}}+a^{2}\right)^{p}\, dx"," ",0,"int((a^2+b^2/(x^(2/(2*p+1)))+2*a*b/(x^(1/(2*p+1))))^p,x)","F"
544,1,51,43,0.043000," ","int(1/((2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2*(n+1)/n)),x)","\left(\frac{b x \,{\mathrm e}^{n \ln \left(x \right)}}{a}+x \right) {\mathrm e}^{-\frac{\left(n +1\right) \ln \left(2 a b \,{\mathrm e}^{n \ln \left(x \right)}+b^{2} {\mathrm e}^{2 n \ln \left(x \right)}+a^{2}\right)}{2 n}}"," ",0,"(x+1/a*b*x*exp(n*ln(x)))/exp(1/2*(n+1)/n*ln(a^2+2*a*b*exp(n*ln(x))+b^2*exp(n*ln(x))^2))","A"
545,0,0,130,0.282000," ","int((a^2+b^2/(x^(1/(p+1)))+2*a*b/(x^(1/2/(p+1))))^p,x)","\int \left(2 a b \,x^{-\frac{1}{2 \left(p +1\right)}}+b^{2} x^{-\frac{1}{p +1}}+a^{2}\right)^{p}\, dx"," ",0,"int((a^2+b^2/(x^(1/(p+1)))+2*a*b/(x^(1/2/(p+1))))^p,x)","F"
546,0,0,94,0.111000," ","int(1/((2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2*(2*n+1)/n)),x)","\int \left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{-\frac{2 n +1}{2 n}}\, dx"," ",0,"int(1/((2*a*b*x^n+b^2*x^(2*n)+a^2)^(1/2*(2*n+1)/n)),x)","F"
547,0,0,119,0.052000," ","int((d*x)^(-1-2*n*(p+1))*(2*a*b*x^n+b^2*x^(2*n)+a^2)^p,x)","\int \left(d x \right)^{-2 \left(p +1\right) n -1} \left(2 a b \,x^{n}+b^{2} x^{2 n}+a^{2}\right)^{p}\, dx"," ",0,"int((d*x)^(-1-2*n*(p+1))*(2*a*b*x^n+b^2*x^(2*n)+a^2)^p,x)","F"
548,1,148,101,0.073000," ","int(x^(2*n-1)*(2*a*b*x^n+b^2*x^(2*n)+a^2)^p,x)","-\frac{\left(-2 a b p \,x^{n}-2 b^{2} p \,x^{2 n}-b^{2} x^{2 n}+a^{2}\right) {\mathrm e}^{\frac{\left(-i \pi  \mathrm{csgn}\left(i \left(b \,x^{n}+a \right)\right)^{2} \mathrm{csgn}\left(i \left(b \,x^{n}+a \right)^{2}\right)+2 i \pi  \,\mathrm{csgn}\left(i \left(b \,x^{n}+a \right)\right) \mathrm{csgn}\left(i \left(b \,x^{n}+a \right)^{2}\right)^{2}-i \pi  \mathrm{csgn}\left(i \left(b \,x^{n}+a \right)^{2}\right)^{3}+4 \ln \left(b \,x^{n}+a \right)\right) p}{2}}}{2 \left(2 p +1\right) \left(p +1\right) b^{2} n}"," ",0,"-1/2*(-2*b^2*p*(x^n)^2-2*a*p*x^n*b-b^2*(x^n)^2+a^2)/(2*p+1)/(p+1)/n/b^2*exp(1/2*p*(-I*Pi*csgn(I*(b*x^n+a)^2)^3+2*I*Pi*csgn(I*(b*x^n+a)^2)^2*csgn(I*(b*x^n+a))-I*Pi*csgn(I*(b*x^n+a)^2)*csgn(I*(b*x^n+a))^2+4*ln(b*x^n+a)))","C"
549,1,973,103,0.164000," ","int(x^(-1+4*n)/(a+b*x^n+c*x^(2*n)),x)","\frac{4 a^{2} c^{2} n^{2} \ln \left(x \right)}{4 a \,c^{4} n^{2}-b^{2} c^{3} n^{2}}-\frac{5 a \,b^{2} c \,n^{2} \ln \left(x \right)}{4 a \,c^{4} n^{2}-b^{2} c^{3} n^{2}}+\frac{b^{4} n^{2} \ln \left(x \right)}{4 a \,c^{4} n^{2}-b^{2} c^{3} n^{2}}-\frac{2 a^{2} \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{\left(4 a c -b^{2}\right) c n}-\frac{2 a^{2} \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{\left(4 a c -b^{2}\right) c n}+\frac{5 a \,b^{2} \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) c^{2} n}+\frac{5 a \,b^{2} \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) c^{2} n}-\frac{b^{4} \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) c^{3} n}-\frac{b^{4} \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) c^{3} n}-\frac{a \ln \left(x \right)}{c^{2}}+\frac{b^{2} \ln \left(x \right)}{c^{3}}-\frac{b \,x^{n}}{c^{2} n}+\frac{x^{2 n}}{2 c n}-\frac{\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}\, \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) c^{3} n}+\frac{\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}\, \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) c^{3} n}"," ",0,"-1/c^2*ln(x)*a+1/c^3*ln(x)*b^2+1/2/c/n*(x^n)^2-b*x^n/c^2/n+4/(4*a*c^4*n^2-b^2*c^3*n^2)*n^2*ln(x)*a^2*c^2-5/(4*a*c^4*n^2-b^2*c^3*n^2)*n^2*ln(x)*a*b^2*c+1/(4*a*c^4*n^2-b^2*c^3*n^2)*n^2*ln(x)*b^4-2/c/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*a^2+5/2/c^2/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*a*b^2-1/2/c^3/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*b^4+1/2/c^3/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2)-2/c/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*a^2+5/2/c^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*a*b^2-1/2/c^3/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*b^4-1/2/c^3/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/c/b/(3*a*c-b^2))*(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2)","B"
550,1,664,81,0.127000," ","int(x^(3*n-1)/(a+b*x^n+c*x^(2*n)),x)","\frac{4 a b c \,n^{2} \ln \left(x \right)}{4 a \,c^{3} n^{2}-b^{2} c^{2} n^{2}}-\frac{b^{3} n^{2} \ln \left(x \right)}{4 a \,c^{3} n^{2}-b^{2} c^{2} n^{2}}-\frac{2 a b \ln \left(x^{n}-\frac{-2 a b c +b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{\left(4 a c -b^{2}\right) c n}-\frac{2 a b \ln \left(x^{n}+\frac{2 a b c -b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{\left(4 a c -b^{2}\right) c n}+\frac{b^{3} \ln \left(x^{n}-\frac{-2 a b c +b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) c^{2} n}+\frac{b^{3} \ln \left(x^{n}+\frac{2 a b c -b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) c^{2} n}-\frac{b \ln \left(x \right)}{c^{2}}+\frac{x^{n}}{c n}+\frac{\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}\, \ln \left(x^{n}-\frac{-2 a b c +b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) c^{2} n}-\frac{\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}\, \ln \left(x^{n}+\frac{2 a b c -b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) c^{2} n}"," ",0,"-b/c^2*ln(x)+x^n/c/n+4/(4*a*c^3*n^2-b^2*c^2*n^2)*n^2*ln(x)*a*b*c-1/(4*a*c^3*n^2-b^2*c^2*n^2)*n^2*ln(x)*b^3-2/c/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a*b*c+b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/c/(2*a*c-b^2))*a*b+1/2/c^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a*b*c+b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/c/(2*a*c-b^2))*b^3+1/2/c^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a*b*c+b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/c/(2*a*c-b^2))*(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2)-2/c/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a*b*c-b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/c/(2*a*c-b^2))*a*b+1/2/c^2/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a*b*c-b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/c/(2*a*c-b^2))*b^3-1/2/c^2/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a*b*c-b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/c/(2*a*c-b^2))*(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2)","B"
551,1,402,62,0.101000," ","int(x^(2*n-1)/(a+b*x^n+c*x^(2*n)),x)","-\frac{4 a c \,n^{2} \ln \left(x \right)}{4 a \,c^{2} n^{2}-b^{2} c \,n^{2}}+\frac{b^{2} n^{2} \ln \left(x \right)}{4 a \,c^{2} n^{2}-b^{2} c \,n^{2}}+\frac{2 a \ln \left(x^{n}-\frac{-b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{\left(4 a c -b^{2}\right) n}+\frac{2 a \ln \left(x^{n}+\frac{b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{\left(4 a c -b^{2}\right) n}-\frac{b^{2} \ln \left(x^{n}-\frac{-b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) c n}-\frac{b^{2} \ln \left(x^{n}+\frac{b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) c n}+\frac{\ln \left(x \right)}{c}+\frac{\sqrt{-4 a \,b^{2} c +b^{4}}\, \ln \left(x^{n}-\frac{-b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) c n}-\frac{\sqrt{-4 a \,b^{2} c +b^{4}}\, \ln \left(x^{n}+\frac{b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) c n}"," ",0,"1/c*ln(x)-4/(4*a*c^2*n^2-b^2*c*n^2)*n^2*ln(x)*a*c+1/(4*a*c^2*n^2-b^2*c*n^2)*n^2*ln(x)*b^2+2/(4*a*c-b^2)/n*ln(x^n-1/2*(-b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*a-1/2/(4*a*c-b^2)/c/n*ln(x^n-1/2*(-b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*b^2+1/2/(4*a*c-b^2)/c/n*ln(x^n-1/2*(-b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*(-4*a*b^2*c+b^4)^(1/2)+2/(4*a*c-b^2)/n*ln(x^n+1/2*(b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*a-1/2/(4*a*c-b^2)/c/n*ln(x^n+1/2*(b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*b^2-1/2/(4*a*c-b^2)/c/n*ln(x^n+1/2*(b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*(-4*a*b^2*c+b^4)^(1/2)","B"
552,1,113,35,0.063000," ","int(x^(n-1)/(a+b*x^n+c*x^(2*n)),x)","-\frac{\ln \left(x^{n}+\frac{-4 a c +b^{2}+\sqrt{-4 a c +b^{2}}\, b}{2 \sqrt{-4 a c +b^{2}}\, c}\right)}{\sqrt{-4 a c +b^{2}}\, n}+\frac{\ln \left(x^{n}+\frac{4 a c -b^{2}+\sqrt{-4 a c +b^{2}}\, b}{2 \sqrt{-4 a c +b^{2}}\, c}\right)}{\sqrt{-4 a c +b^{2}}\, n}"," ",0,"-1/(-4*a*c+b^2)^(1/2)/n*ln(x^n+1/2*((-4*a*c+b^2)^(1/2)*b-4*a*c+b^2)/c/(-4*a*c+b^2)^(1/2))+1/(-4*a*c+b^2)^(1/2)/n*ln(x^n+1/2*((-4*a*c+b^2)^(1/2)*b+4*a*c-b^2)/c/(-4*a*c+b^2)^(1/2))","B"
553,1,658,92,0.148000," ","int(x^(-1-n)/(a+b*x^n+c*x^(2*n)),x)","-\frac{4 a b c \,n^{2} \ln \left(x \right)}{4 a^{3} c \,n^{2}-a^{2} b^{2} n^{2}}+\frac{b^{3} n^{2} \ln \left(x \right)}{4 a^{3} c \,n^{2}-a^{2} b^{2} n^{2}}+\frac{2 b c \ln \left(x^{n}-\frac{-2 a b c +b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{\left(4 a c -b^{2}\right) a n}+\frac{2 b c \ln \left(x^{n}+\frac{2 a b c -b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{\left(4 a c -b^{2}\right) a n}-\frac{b^{3} \ln \left(x^{n}-\frac{-2 a b c +b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{2} n}-\frac{b^{3} \ln \left(x^{n}+\frac{2 a b c -b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{2} n}-\frac{x^{-n}}{a n}+\frac{\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}\, \ln \left(x^{n}-\frac{-2 a b c +b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{2} n}-\frac{\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}\, \ln \left(x^{n}+\frac{2 a b c -b^{3}+\sqrt{-16 a^{3} c^{3}+20 b^{2} a^{2} c^{2}-8 b^{4} a c +b^{6}}}{2 \left(2 a c -b^{2}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{2} n}"," ",0,"-1/a/n/(x^n)-4/(4*a^3*c*n^2-a^2*b^2*n^2)*n^2*ln(x)*a*b*c+1/(4*a^3*c*n^2-a^2*b^2*n^2)*n^2*ln(x)*b^3+2/a/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a*b*c+b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/(2*a*c-b^2)/c)*b*c-1/2/a^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a*b*c+b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/(2*a*c-b^2)/c)*b^3+1/2/a^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a*b*c+b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/(2*a*c-b^2)/c)*(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2)+2/a/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a*b*c-b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/(2*a*c-b^2)/c)*b*c-1/2/a^2/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a*b*c-b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/(2*a*c-b^2)/c)*b^3-1/2/a^2/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a*b*c-b^3+(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2))/(2*a*c-b^2)/c)*(-16*a^3*c^3+20*a^2*b^2*c^2-8*a*b^4*c+b^6)^(1/2)","B"
554,1,958,120,0.174000," ","int(x^(-1-2*n)/(a+b*x^n+c*x^(2*n)),x)","-\frac{4 a^{2} c^{2} n^{2} \ln \left(x \right)}{4 a^{4} c \,n^{2}-a^{3} b^{2} n^{2}}+\frac{5 a \,b^{2} c \,n^{2} \ln \left(x \right)}{4 a^{4} c \,n^{2}-a^{3} b^{2} n^{2}}-\frac{b^{4} n^{2} \ln \left(x \right)}{4 a^{4} c \,n^{2}-a^{3} b^{2} n^{2}}+\frac{2 c^{2} \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{\left(4 a c -b^{2}\right) a n}+\frac{2 c^{2} \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{\left(4 a c -b^{2}\right) a n}-\frac{5 b^{2} c \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) a^{2} n}-\frac{5 b^{2} c \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) a^{2} n}+\frac{b^{4} \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) a^{3} n}+\frac{b^{4} \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) a^{3} n}-\frac{x^{-2 n}}{2 a n}+\frac{b \,x^{-n}}{a^{2} n}-\frac{\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}\, \ln \left(x^{n}-\frac{-3 a \,b^{2} c +b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) a^{3} n}+\frac{\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}\, \ln \left(x^{n}+\frac{3 a \,b^{2} c -b^{4}+\sqrt{-36 a^{3} b^{2} c^{3}+33 a^{2} b^{4} c^{2}-10 a \,b^{6} c +b^{8}}}{2 \left(3 a c -b^{2}\right) b c}\right)}{2 \left(4 a c -b^{2}\right) a^{3} n}"," ",0,"b/a^2/n/(x^n)-1/2/a/n/(x^n)^2-4/(4*a^4*c*n^2-a^3*b^2*n^2)*n^2*ln(x)*a^2*c^2+5/(4*a^4*c*n^2-a^3*b^2*n^2)*n^2*ln(x)*a*b^2*c-1/(4*a^4*c*n^2-a^3*b^2*n^2)*n^2*ln(x)*b^4+2/a/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*c^2-5/2/a^2/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*b^2*c+1/2/a^3/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*b^4+1/2/a^3/(4*a*c-b^2)/n*ln(x^n+1/2*(3*a*b^2*c-b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2)+2/a/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*c^2-5/2/a^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*b^2*c+1/2/a^3/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*b^4-1/2/a^3/(4*a*c-b^2)/n*ln(x^n-1/2*(-3*a*b^2*c+b^4+(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2))/(3*a*c-b^2)/b/c)*(-36*a^3*b^2*c^3+33*a^2*b^4*c^2-10*a*b^6*c+b^8)^(1/2)","B"
555,1,1300,158,0.201000," ","int(x^(-1-3*n)/(a+b*x^n+c*x^(2*n)),x)","\frac{8 a^{2} b \,c^{2} n^{2} \ln \left(x \right)}{4 a^{5} c \,n^{2}-a^{4} b^{2} n^{2}}-\frac{6 a \,b^{3} c \,n^{2} \ln \left(x \right)}{4 a^{5} c \,n^{2}-a^{4} b^{2} n^{2}}+\frac{b^{5} n^{2} \ln \left(x \right)}{4 a^{5} c \,n^{2}-a^{4} b^{2} n^{2}}-\frac{4 b \,c^{2} \ln \left(x^{n}-\frac{-2 a^{2} b \,c^{2}+4 a \,b^{3} c -b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{\left(4 a c -b^{2}\right) a^{2} n}-\frac{4 b \,c^{2} \ln \left(x^{n}+\frac{2 a^{2} b \,c^{2}-4 a \,b^{3} c +b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{\left(4 a c -b^{2}\right) a^{2} n}+\frac{3 b^{3} c \ln \left(x^{n}-\frac{-2 a^{2} b \,c^{2}+4 a \,b^{3} c -b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{\left(4 a c -b^{2}\right) a^{3} n}+\frac{3 b^{3} c \ln \left(x^{n}+\frac{2 a^{2} b \,c^{2}-4 a \,b^{3} c +b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{\left(4 a c -b^{2}\right) a^{3} n}-\frac{b^{5} \ln \left(x^{n}-\frac{-2 a^{2} b \,c^{2}+4 a \,b^{3} c -b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{4} n}-\frac{b^{5} \ln \left(x^{n}+\frac{2 a^{2} b \,c^{2}-4 a \,b^{3} c +b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{4} n}-\frac{x^{-3 n}}{3 a n}+\frac{b \,x^{-2 n}}{2 a^{2} n}+\frac{c \,x^{-n}}{a^{2} n}-\frac{b^{2} x^{-n}}{a^{3} n}-\frac{\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}\, \ln \left(x^{n}-\frac{-2 a^{2} b \,c^{2}+4 a \,b^{3} c -b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{4} n}+\frac{\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}\, \ln \left(x^{n}+\frac{2 a^{2} b \,c^{2}-4 a \,b^{3} c +b^{5}+\sqrt{-16 a^{5} c^{5}+68 a^{4} b^{2} c^{4}-96 a^{3} b^{4} c^{3}+52 a^{2} b^{6} c^{2}-12 a \,b^{8} c +b^{10}}}{2 \left(2 a^{2} c^{2}-4 a \,b^{2} c +b^{4}\right) c}\right)}{2 \left(4 a c -b^{2}\right) a^{4} n}"," ",0,"1/a^2/n/(x^n)*c-1/a^3/n/(x^n)*b^2+1/2/a^2*b/n/(x^n)^2-1/3/a/n/(x^n)^3+8/(4*a^5*c*n^2-a^4*b^2*n^2)*n^2*ln(x)*a^2*b*c^2-6/(4*a^5*c*n^2-a^4*b^2*n^2)*n^2*ln(x)*a*b^3*c+1/(4*a^5*c*n^2-a^4*b^2*n^2)*n^2*ln(x)*b^5-4/a^2/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a^2*b*c^2-4*a*b^3*c+b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*b*c^2+3/a^3/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a^2*b*c^2-4*a*b^3*c+b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*b^3*c-1/2/a^4/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a^2*b*c^2-4*a*b^3*c+b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*b^5+1/2/a^4/(4*a*c-b^2)/n*ln(x^n+1/2*(2*a^2*b*c^2-4*a*b^3*c+b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2)-4/a^2/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a^2*b*c^2+4*a*b^3*c-b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*b*c^2+3/a^3/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a^2*b*c^2+4*a*b^3*c-b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*b^3*c-1/2/a^4/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a^2*b*c^2+4*a*b^3*c-b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*b^5-1/2/a^4/(4*a*c-b^2)/n*ln(x^n-1/2*(-2*a^2*b*c^2+4*a*b^3*c-b^5+(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2))/c/(2*a^2*c^2-4*a*b^2*c+b^4))*(-16*a^5*c^5+68*a^4*b^2*c^4-96*a^3*b^4*c^3+52*a^2*b^6*c^2-12*a*b^8*c+b^10)^(1/2)","B"
556,1,280,273,0.747000," ","int(x^(-1+1/4*n)/(a+b*x^n+c*x^(2*n)),x)","\RootOf \left(\left(256 a^{7} c^{4} n^{8}-256 a^{6} b^{2} c^{3} n^{8}+96 a^{5} b^{4} c^{2} n^{8}-16 a^{4} b^{6} c \,n^{8}+a^{3} b^{8} n^{8}\right) \textit{\_Z}^{8}+\left(-48 a^{3} b \,c^{3} n^{4}+40 a^{2} b^{3} c^{2} n^{4}-11 a \,b^{5} c \,n^{4}+b^{7} n^{4}\right) \textit{\_Z}^{4}+c^{3}\right) \ln \left(\left(\frac{16 a^{5} b \,c^{2} n^{5}}{a \,c^{2}-b^{2} c}-\frac{8 a^{4} b^{3} c \,n^{5}}{a \,c^{2}-b^{2} c}+\frac{a^{3} b^{5} n^{5}}{a \,c^{2}-b^{2} c}\right) \RootOf \left(\left(256 a^{7} c^{4} n^{8}-256 a^{6} b^{2} c^{3} n^{8}+96 a^{5} b^{4} c^{2} n^{8}-16 a^{4} b^{6} c \,n^{8}+a^{3} b^{8} n^{8}\right) \textit{\_Z}^{8}+\left(-48 a^{3} b \,c^{3} n^{4}+40 a^{2} b^{3} c^{2} n^{4}-11 a \,b^{5} c \,n^{4}+b^{7} n^{4}\right) \textit{\_Z}^{4}+c^{3}\right)^{5}+\left(\frac{2 a^{2} c^{2} n}{a \,c^{2}-b^{2} c}-\frac{4 a \,b^{2} c n}{a \,c^{2}-b^{2} c}+\frac{b^{4} n}{a \,c^{2}-b^{2} c}\right) \RootOf \left(\left(256 a^{7} c^{4} n^{8}-256 a^{6} b^{2} c^{3} n^{8}+96 a^{5} b^{4} c^{2} n^{8}-16 a^{4} b^{6} c \,n^{8}+a^{3} b^{8} n^{8}\right) \textit{\_Z}^{8}+\left(-48 a^{3} b \,c^{3} n^{4}+40 a^{2} b^{3} c^{2} n^{4}-11 a \,b^{5} c \,n^{4}+b^{7} n^{4}\right) \textit{\_Z}^{4}+c^{3}\right)+x^{\frac{n}{4}}\right)"," ",0,"sum(_R*ln(x^(1/4*n)+(16/(a*c^2-b^2*c)*n^5*b*a^5*c^2-8/(a*c^2-b^2*c)*n^5*b^3*a^4*c+1/(a*c^2-b^2*c)*n^5*b^5*a^3)*_R^5+(2/(a*c^2-b^2*c)*n*a^2*c^2-4/(a*c^2-b^2*c)*n*b^2*a*c+1/(a*c^2-b^2*c)*n*b^4)*_R),_R=RootOf((256*a^7*c^4*n^8-256*a^6*b^2*c^3*n^8+96*a^5*b^4*c^2*n^8-16*a^4*b^6*c*n^8+a^3*b^8*n^8)*_Z^8+(-48*a^3*b*c^3*n^4+40*a^2*b^3*c^2*n^4-11*a*b^5*c*n^4+b^7*n^4)*_Z^4+c^3))","C"
557,1,260,465,0.461000," ","int(x^(-1+1/3*n)/(a+b*x^n+c*x^(2*n)),x)","\RootOf \left(\left(64 a^{5} c^{3} n^{6}-48 a^{4} b^{2} c^{2} n^{6}+12 a^{3} b^{4} c \,n^{6}-a^{2} b^{6} n^{6}\right) \textit{\_Z}^{6}+\left(16 a^{2} b \,c^{2} n^{3}-8 a \,b^{3} c \,n^{3}+b^{5} n^{3}\right) \textit{\_Z}^{3}+c^{2}\right) \ln \left(\left(-\frac{16 a^{4} b \,c^{2} n^{4}}{2 a \,c^{2}-b^{2} c}+\frac{8 a^{3} b^{3} c \,n^{4}}{2 a \,c^{2}-b^{2} c}-\frac{a^{2} b^{5} n^{4}}{2 a \,c^{2}-b^{2} c}\right) \RootOf \left(\left(64 a^{5} c^{3} n^{6}-48 a^{4} b^{2} c^{2} n^{6}+12 a^{3} b^{4} c \,n^{6}-a^{2} b^{6} n^{6}\right) \textit{\_Z}^{6}+\left(16 a^{2} b \,c^{2} n^{3}-8 a \,b^{3} c \,n^{3}+b^{5} n^{3}\right) \textit{\_Z}^{3}+c^{2}\right)^{4}+\left(\frac{4 a^{2} c^{2} n}{2 a \,c^{2}-b^{2} c}-\frac{5 a \,b^{2} c n}{2 a \,c^{2}-b^{2} c}+\frac{b^{4} n}{2 a \,c^{2}-b^{2} c}\right) \RootOf \left(\left(64 a^{5} c^{3} n^{6}-48 a^{4} b^{2} c^{2} n^{6}+12 a^{3} b^{4} c \,n^{6}-a^{2} b^{6} n^{6}\right) \textit{\_Z}^{6}+\left(16 a^{2} b \,c^{2} n^{3}-8 a \,b^{3} c \,n^{3}+b^{5} n^{3}\right) \textit{\_Z}^{3}+c^{2}\right)+x^{\frac{n}{3}}\right)"," ",0,"sum(_R*ln(x^(1/3*n)+(-16/(2*a*c^2-b^2*c)*n^4*b*a^4*c^2+8/(2*a*c^2-b^2*c)*n^4*b^3*a^3*c-1/(2*a*c^2-b^2*c)*n^4*b^5*a^2)*_R^4+(4/(2*a*c^2-b^2*c)*n*a^2*c^2-5/(2*a*c^2-b^2*c)*n*b^2*a*c+1/(2*a*c^2-b^2*c)*n*b^4)*_R),_R=RootOf((64*a^5*c^3*n^6-48*a^4*b^2*c^2*n^6+12*a^3*b^4*c*n^6-a^2*b^6*n^6)*_Z^6+(16*a^2*b*c^2*n^3-8*a*b^3*c*n^3+b^5*n^3)*_Z^3+c^2))","C"
558,1,114,129,0.194000," ","int(x^(-1+1/2*n)/(a+b*x^n+c*x^(2*n)),x)","\RootOf \left(\left(16 a^{3} c^{2} n^{4}-8 a^{2} b^{2} c \,n^{4}+a \,b^{4} n^{4}\right) \textit{\_Z}^{4}+\left(-4 a b c \,n^{2}+b^{3} n^{2}\right) \textit{\_Z}^{2}+c \right) \ln \left(\left(4 a^{2} b \,n^{3}-\frac{a \,b^{3} n^{3}}{c}\right) \RootOf \left(\left(16 a^{3} c^{2} n^{4}-8 a^{2} b^{2} c \,n^{4}+a \,b^{4} n^{4}\right) \textit{\_Z}^{4}+\left(-4 a b c \,n^{2}+b^{3} n^{2}\right) \textit{\_Z}^{2}+c \right)^{3}+\left(2 a n -\frac{b^{2} n}{c}\right) \RootOf \left(\left(16 a^{3} c^{2} n^{4}-8 a^{2} b^{2} c \,n^{4}+a \,b^{4} n^{4}\right) \textit{\_Z}^{4}+\left(-4 a b c \,n^{2}+b^{3} n^{2}\right) \textit{\_Z}^{2}+c \right)+x^{\frac{n}{2}}\right)"," ",0,"sum(_R*ln(x^(1/2*n)+(4*n^3*b*a^2-1/c*n^3*b^3*a)*_R^3+(2*a*n-1/c*n*b^2)*_R),_R=RootOf((16*a^3*c^2*n^4-8*a^2*b^2*c*n^4+a*b^4*n^4)*_Z^4+(-4*a*b*c*n^2+b^3*n^2)*_Z^2+c))","C"
559,1,268,170,0.348000," ","int(x^(-1-1/2*n)/(a+b*x^n+c*x^(2*n)),x)","\RootOf \left(\left(16 a^{5} c^{2} n^{4}-8 a^{4} b^{2} c \,n^{4}+a^{3} b^{4} n^{4}\right) \textit{\_Z}^{4}+c^{3}+\left(12 a^{2} b \,c^{2} n^{2}-7 a \,b^{3} c \,n^{2}+b^{5} n^{2}\right) \textit{\_Z}^{2}\right) \ln \left(\left(-\frac{8 a^{5} c^{2} n^{3}}{a \,c^{3}-b^{2} c^{2}}+\frac{6 a^{4} b^{2} c \,n^{3}}{a \,c^{3}-b^{2} c^{2}}-\frac{a^{3} b^{4} n^{3}}{a \,c^{3}-b^{2} c^{2}}\right) \RootOf \left(\left(16 a^{5} c^{2} n^{4}-8 a^{4} b^{2} c \,n^{4}+a^{3} b^{4} n^{4}\right) \textit{\_Z}^{4}+c^{3}+\left(12 a^{2} b \,c^{2} n^{2}-7 a \,b^{3} c \,n^{2}+b^{5} n^{2}\right) \textit{\_Z}^{2}\right)^{3}+\left(-\frac{5 a^{2} b \,c^{2} n}{a \,c^{3}-b^{2} c^{2}}+\frac{5 a \,b^{3} c n}{a \,c^{3}-b^{2} c^{2}}-\frac{b^{5} n}{a \,c^{3}-b^{2} c^{2}}\right) \RootOf \left(\left(16 a^{5} c^{2} n^{4}-8 a^{4} b^{2} c \,n^{4}+a^{3} b^{4} n^{4}\right) \textit{\_Z}^{4}+c^{3}+\left(12 a^{2} b \,c^{2} n^{2}-7 a \,b^{3} c \,n^{2}+b^{5} n^{2}\right) \textit{\_Z}^{2}\right)+x^{\frac{n}{2}}\right)-\frac{2 x^{-\frac{n}{2}}}{a n}"," ",0,"-2/a/n/(x^(1/2*n))+sum(_R*ln(x^(1/2*n)+(-8/(a*c^3-b^2*c^2)*n^3*a^5*c^2+6/(a*c^3-b^2*c^2)*n^3*b^2*a^4*c-1/(a*c^3-b^2*c^2)*n^3*b^4*a^3)*_R^3+(-5/(a*c^3-b^2*c^2)*n*b*a^2*c^2+5/(a*c^3-b^2*c^2)*n*b^3*a*c-1/(a*c^3-b^2*c^2)*n*b^5)*_R),_R=RootOf((16*a^5*c^2*n^4-8*a^4*b^2*c*n^4+a^3*b^4*n^4)*_Z^4+(12*a^2*b*c^2*n^2-7*a*b^3*c*n^2+b^5*n^2)*_Z^2+c^3))","C"
560,1,534,570,0.750000," ","int(x^(-1-1/3*n)/(a+b*x^n+c*x^(2*n)),x)","\RootOf \left(\left(64 a^{7} c^{3} n^{6}-48 a^{6} b^{2} c^{2} n^{6}+12 a^{5} b^{4} c \,n^{6}-a^{4} b^{6} n^{6}\right) \textit{\_Z}^{6}+c^{4}+\left(-32 a^{3} b \,c^{3} n^{3}+32 a^{2} b^{3} c^{2} n^{3}-10 a \,b^{5} c \,n^{3}+b^{7} n^{3}\right) \textit{\_Z}^{3}\right) \ln \left(\left(-\frac{64 a^{8} c^{4} n^{5}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}+\frac{112 a^{7} b^{2} c^{3} n^{5}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}-\frac{60 a^{6} b^{4} c^{2} n^{5}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}+\frac{13 a^{5} b^{6} c \,n^{5}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}-\frac{a^{4} b^{8} n^{5}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}\right) \RootOf \left(\left(64 a^{7} c^{3} n^{6}-48 a^{6} b^{2} c^{2} n^{6}+12 a^{5} b^{4} c \,n^{6}-a^{4} b^{6} n^{6}\right) \textit{\_Z}^{6}+c^{4}+\left(-32 a^{3} b \,c^{3} n^{3}+32 a^{2} b^{3} c^{2} n^{3}-10 a \,b^{5} c \,n^{3}+b^{7} n^{3}\right) \textit{\_Z}^{3}\right)^{5}+\left(\frac{28 a^{4} b \,c^{4} n^{2}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}-\frac{63 a^{3} b^{3} c^{3} n^{2}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}+\frac{42 a^{2} b^{5} c^{2} n^{2}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}-\frac{11 a \,b^{7} c \,n^{2}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}+\frac{b^{9} n^{2}}{2 a^{2} c^{5}-4 a \,b^{2} c^{4}+b^{4} c^{3}}\right) \RootOf \left(\left(64 a^{7} c^{3} n^{6}-48 a^{6} b^{2} c^{2} n^{6}+12 a^{5} b^{4} c \,n^{6}-a^{4} b^{6} n^{6}\right) \textit{\_Z}^{6}+c^{4}+\left(-32 a^{3} b \,c^{3} n^{3}+32 a^{2} b^{3} c^{2} n^{3}-10 a \,b^{5} c \,n^{3}+b^{7} n^{3}\right) \textit{\_Z}^{3}\right)^{2}+x^{\frac{n}{3}}\right)-\frac{3 x^{-\frac{n}{3}}}{a n}"," ",0,"-3/a/n/(x^(1/3*n))+sum(_R*ln(x^(1/3*n)+(-64/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^5*a^8*c^4+112/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^5*b^2*a^7*c^3-60/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^5*b^4*a^6*c^2+13/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^5*b^6*a^5*c-1/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^5*b^8*a^4)*_R^5+(28/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^2*b*a^4*c^4-63/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^2*b^3*a^3*c^3+42/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^2*b^5*a^2*c^2-11/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^2*b^7*a*c+1/(2*a^2*c^5-4*a*b^2*c^4+b^4*c^3)*n^2*b^9)*_R^2),_R=RootOf((64*a^7*c^3*n^6-48*a^6*b^2*c^2*n^6+12*a^5*b^4*c*n^6-a^4*b^6*n^6)*_Z^6+(-32*a^3*b*c^3*n^3+32*a^2*b^3*c^2*n^3-10*a*b^5*c*n^3+b^7*n^3)*_Z^3+c^4))","C"
561,1,630,344,1.215000," ","int(x^(-1-1/4*n)/(a+b*x^n+c*x^(2*n)),x)","\RootOf \left(\left(256 a^{9} c^{4} n^{8}-256 a^{8} b^{2} c^{3} n^{8}+96 a^{7} b^{4} c^{2} n^{8}-16 a^{6} b^{6} c \,n^{8}+a^{5} b^{8} n^{8}\right) \textit{\_Z}^{8}+c^{5}+\left(80 a^{4} b \,c^{4} n^{4}-120 a^{3} b^{3} c^{3} n^{4}+61 a^{2} b^{5} c^{2} n^{4}-13 a \,b^{7} c \,n^{4}+b^{9} n^{4}\right) \textit{\_Z}^{4}\right) \ln \left(\left(-\frac{128 a^{10} c^{5} n^{7}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}+\frac{352 a^{9} b^{2} c^{4} n^{7}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}-\frac{280 a^{8} b^{4} c^{3} n^{7}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}+\frac{98 a^{7} b^{6} c^{2} n^{7}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}-\frac{16 a^{6} b^{8} c \,n^{7}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}+\frac{a^{5} b^{10} n^{7}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}\right) \RootOf \left(\left(256 a^{9} c^{4} n^{8}-256 a^{8} b^{2} c^{3} n^{8}+96 a^{7} b^{4} c^{2} n^{8}-16 a^{6} b^{6} c \,n^{8}+a^{5} b^{8} n^{8}\right) \textit{\_Z}^{8}+c^{5}+\left(80 a^{4} b \,c^{4} n^{4}-120 a^{3} b^{3} c^{3} n^{4}+61 a^{2} b^{5} c^{2} n^{4}-13 a \,b^{7} c \,n^{4}+b^{9} n^{4}\right) \textit{\_Z}^{4}\right)^{7}+\left(-\frac{36 a^{5} b \,c^{5} n^{3}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}+\frac{129 a^{4} b^{3} c^{4} n^{3}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}-\frac{138 a^{3} b^{5} c^{3} n^{3}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}+\frac{63 a^{2} b^{7} c^{2} n^{3}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}-\frac{13 a \,b^{9} c \,n^{3}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}+\frac{b^{11} n^{3}}{a^{2} c^{6}-3 a \,b^{2} c^{5}+b^{4} c^{4}}\right) \RootOf \left(\left(256 a^{9} c^{4} n^{8}-256 a^{8} b^{2} c^{3} n^{8}+96 a^{7} b^{4} c^{2} n^{8}-16 a^{6} b^{6} c \,n^{8}+a^{5} b^{8} n^{8}\right) \textit{\_Z}^{8}+c^{5}+\left(80 a^{4} b \,c^{4} n^{4}-120 a^{3} b^{3} c^{3} n^{4}+61 a^{2} b^{5} c^{2} n^{4}-13 a \,b^{7} c \,n^{4}+b^{9} n^{4}\right) \textit{\_Z}^{4}\right)^{3}+x^{\frac{n}{4}}\right)-\frac{4 x^{-\frac{n}{4}}}{a n}"," ",0,"-4/a/n/(x^(1/4*n))+sum(_R*ln(x^(1/4*n)+(-128/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^7*a^10*c^5+352/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^7*b^2*a^9*c^4-280/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^7*b^4*a^8*c^3+98/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^7*b^6*a^7*c^2-16/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^7*b^8*a^6*c+1/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^7*b^10*a^5)*_R^7+(-36/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^3*b*a^5*c^5+129/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^3*b^3*a^4*c^4-138/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^3*b^5*a^3*c^3+63/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^3*b^7*a^2*c^2-13/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^3*b^9*a*c+1/(a^2*c^6-3*a*b^2*c^5+b^4*c^4)*n^3*b^11)*_R^3),_R=RootOf((256*a^9*c^4*n^8-256*a^8*b^2*c^3*n^8+96*a^7*b^4*c^2*n^8-16*a^6*b^6*c*n^8+a^5*b^8*n^8)*_Z^8+(80*a^4*b*c^4*n^4-120*a^3*b^3*c^3*n^4+61*a^2*b^5*c^2*n^4-13*a*b^7*c*n^4+b^9*n^4)*_Z^4+c^5))","C"
562,0,0,132,0.042000," ","int(x^2/(a+b*x^n+c*x^(2*n)),x)","\int \frac{x^{2}}{b \,x^{n}+c \,x^{2 n}+a}\, dx"," ",0,"int(x^2/(a+b*x^n+c*x^(2*n)),x)","F"
563,0,0,132,0.033000," ","int(x/(b*x^n+c*x^(2*n)+a),x)","\int \frac{x}{b \,x^{n}+c \,x^{2 n}+a}\, dx"," ",0,"int(x/(b*x^n+c*x^(2*n)+a),x)","F"
564,0,0,120,0.026000," ","int(1/(b*x^n+c*x^(2*n)+a),x)","\int \frac{1}{b \,x^{n}+c \,x^{2 n}+a}\, dx"," ",0,"int(1/(b*x^n+c*x^(2*n)+a),x)","F"
565,1,397,68,0.096000," ","int(1/x/(b*x^n+c*x^(2*n)+a),x)","\frac{4 a c \,n^{2} \ln \left(x \right)}{4 a^{2} c \,n^{2}-a \,b^{2} n^{2}}-\frac{b^{2} n^{2} \ln \left(x \right)}{4 a^{2} c \,n^{2}-a \,b^{2} n^{2}}+\frac{b^{2} \ln \left(x^{n}-\frac{-b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) a n}+\frac{b^{2} \ln \left(x^{n}+\frac{b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) a n}-\frac{2 c \ln \left(x^{n}-\frac{-b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{\left(4 a c -b^{2}\right) n}-\frac{2 c \ln \left(x^{n}+\frac{b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{\left(4 a c -b^{2}\right) n}+\frac{\sqrt{-4 a \,b^{2} c +b^{4}}\, \ln \left(x^{n}-\frac{-b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) a n}-\frac{\sqrt{-4 a \,b^{2} c +b^{4}}\, \ln \left(x^{n}+\frac{b^{2}+\sqrt{-4 a \,b^{2} c +b^{4}}}{2 b c}\right)}{2 \left(4 a c -b^{2}\right) a n}"," ",0,"4/(4*a^2*c*n^2-a*b^2*n^2)*n^2*ln(x)*a*c-1/(4*a^2*c*n^2-a*b^2*n^2)*n^2*ln(x)*b^2-2/(4*a*c-b^2)/n*ln(x^n-1/2*(-b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*c+1/2/a/(4*a*c-b^2)/n*ln(x^n-1/2*(-b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*b^2+1/2/a/(4*a*c-b^2)/n*ln(x^n-1/2*(-b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*(-4*a*b^2*c+b^4)^(1/2)-2/(4*a*c-b^2)/n*ln(x^n+1/2*(b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*c+1/2/a/(4*a*c-b^2)/n*ln(x^n+1/2*(b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*b^2-1/2/a/(4*a*c-b^2)/n*ln(x^n+1/2*(b^2+(-4*a*b^2*c+b^4)^(1/2))/b/c)*(-4*a*b^2*c+b^4)^(1/2)","B"
566,0,0,132,0.036000," ","int(1/x^2/(b*x^n+c*x^(2*n)+a),x)","\int \frac{1}{\left(b \,x^{n}+c \,x^{2 n}+a \right) x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^n+c*x^(2*n)+a),x)","F"
567,0,0,130,0.040000," ","int(1/x^3/(b*x^n+c*x^(2*n)+a),x)","\int \frac{1}{\left(b \,x^{n}+c \,x^{2 n}+a \right) x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^n+c*x^(2*n)+a),x)","F"
568,0,0,128,0.083000," ","int(x^3*(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \sqrt{b \,x^{n}+c \,x^{2 n}+a}\, x^{3}\, dx"," ",0,"int(x^3*(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
569,0,0,128,0.064000," ","int(x^2*(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \sqrt{b \,x^{n}+c \,x^{2 n}+a}\, x^{2}\, dx"," ",0,"int(x^2*(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
570,0,0,128,0.069000," ","int(x*(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \sqrt{b \,x^{n}+c \,x^{2 n}+a}\, x\, dx"," ",0,"int(x*(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
571,0,0,121,0.068000," ","int((b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \sqrt{b \,x^{n}+c \,x^{2 n}+a}\, dx"," ",0,"int((b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
572,1,125,99,0.115000," ","int((b*x^n+c*x^(2*n)+a)^(1/2)/x,x)","-\frac{\sqrt{a}\, \ln \left(\left(b \,{\mathrm e}^{n \ln \left(x \right)}+2 a +2 \sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}\, \sqrt{a}\right) {\mathrm e}^{-n \ln \left(x \right)}\right)}{n}+\frac{b \ln \left(\frac{c \,{\mathrm e}^{n \ln \left(x \right)}+\frac{b}{2}}{\sqrt{c}}+\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}\right)}{2 \sqrt{c}\, n}+\frac{\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}}{n}"," ",0,"1/n*(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2)+1/2/n*b*ln((1/2*b+c*exp(n*ln(x)))/c^(1/2)+(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2))/c^(1/2)-1/n*a^(1/2)*ln((2*a+b*exp(n*ln(x))+2*a^(1/2)*(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2))/exp(n*ln(x)))","A"
573,0,0,128,0.069000," ","int((b*x^n+c*x^(2*n)+a)^(1/2)/x^2,x)","\int \frac{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}{x^{2}}\, dx"," ",0,"int((b*x^n+c*x^(2*n)+a)^(1/2)/x^2,x)","F"
574,0,0,128,0.069000," ","int((b*x^n+c*x^(2*n)+a)^(1/2)/x^3,x)","\int \frac{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}{x^{3}}\, dx"," ",0,"int((b*x^n+c*x^(2*n)+a)^(1/2)/x^3,x)","F"
575,0,0,129,0.054000," ","int(x^3*(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} x^{3}\, dx"," ",0,"int(x^3*(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
576,0,0,129,0.054000," ","int(x^2*(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} x^{2}\, dx"," ",0,"int(x^2*(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
577,0,0,129,0.053000," ","int(x*(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} x\, dx"," ",0,"int(x*(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
578,0,0,122,0.055000," ","int((b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}\, dx"," ",0,"int((b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
579,1,209,147,0.047000," ","int((b*x^n+c*x^(2*n)+a)^(3/2)/x,x)","-\frac{a^{\frac{3}{2}} \ln \left(\left(b \,{\mathrm e}^{n \ln \left(x \right)}+2 a +2 \sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}\, \sqrt{a}\right) {\mathrm e}^{-n \ln \left(x \right)}\right)}{n}+\frac{3 a b \ln \left(\frac{c \,{\mathrm e}^{n \ln \left(x \right)}+\frac{b}{2}}{\sqrt{c}}+\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}\right)}{4 \sqrt{c}\, n}-\frac{b^{3} \ln \left(\frac{c \,{\mathrm e}^{n \ln \left(x \right)}+\frac{b}{2}}{\sqrt{c}}+\sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}\right)}{16 c^{\frac{3}{2}} n}+\frac{\left(14 b c \,{\mathrm e}^{n \ln \left(x \right)}+8 c^{2} {\mathrm e}^{2 n \ln \left(x \right)}+32 a c +3 b^{2}\right) \sqrt{b \,{\mathrm e}^{n \ln \left(x \right)}+c \,{\mathrm e}^{2 n \ln \left(x \right)}+a}}{24 c n}"," ",0,"1/24*(8*c^2*exp(n*ln(x))^2+14*b*c*exp(n*ln(x))+32*a*c+3*b^2)*(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2)/c/n+3/4/c^(1/2)/n*a*b*ln((c*exp(n*ln(x))+1/2*b)/c^(1/2)+(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2))-1/16/c^(3/2)/n*b^3*ln((c*exp(n*ln(x))+1/2*b)/c^(1/2)+(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2))-1/n*a^(3/2)*ln((2*a+b*exp(n*ln(x))+2*a^(1/2)*(a+b*exp(n*ln(x))+c*exp(n*ln(x))^2)^(1/2))/exp(n*ln(x)))","A"
580,0,0,129,0.061000," ","int((b*x^n+c*x^(2*n)+a)^(3/2)/x^2,x)","\int \frac{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}{x^{2}}\, dx"," ",0,"int((b*x^n+c*x^(2*n)+a)^(3/2)/x^2,x)","F"
581,0,0,129,0.060000," ","int((b*x^n+c*x^(2*n)+a)^(3/2)/x^3,x)","\int \frac{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}{x^{3}}\, dx"," ",0,"int((b*x^n+c*x^(2*n)+a)^(3/2)/x^3,x)","F"
582,0,0,128,0.019000," ","int(x^3/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{x^{3}}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}\, dx"," ",0,"int(x^3/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
583,0,0,128,0.019000," ","int(x^2/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{x^{2}}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}\, dx"," ",0,"int(x^2/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
584,0,0,128,0.018000," ","int(x/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{x}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}\, dx"," ",0,"int(x/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
585,0,0,121,0.018000," ","int(1/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}\, dx"," ",0,"int(1/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
586,0,0,39,0.036000," ","int(1/x/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}\, x}\, dx"," ",0,"int(1/x/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
587,0,0,128,0.019000," ","int(1/x^2/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}\, x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
588,0,0,128,0.019000," ","int(1/x^3/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{1}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}\, x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
589,0,0,131,0.013000," ","int(x^3/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{x^{3}}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^3/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
590,0,0,131,0.014000," ","int(x^2/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{x^{2}}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x^2/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
591,0,0,131,0.013000," ","int(x/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{x}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(x/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
592,0,0,124,0.013000," ","int(1/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{1}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int(1/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
593,0,0,88,0.013000," ","int(1/x/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{1}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} x}\, dx"," ",0,"int(1/x/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
594,0,0,131,0.016000," ","int(1/x^2/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{1}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} x^{2}}\, dx"," ",0,"int(1/x^2/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
595,0,0,131,0.015000," ","int(1/x^3/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{1}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} x^{3}}\, dx"," ",0,"int(1/x^3/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
596,1,3798,182,0.113000," ","int((d*x)^m*(b*x^n+c*x^(2*n)+a)^3,x)","\text{output too large to display}"," 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5+57*a^2*c*m^5*n*(x^n)^2+411*a^2*c*m^4*n^2*(x^n)^2+1383*a^2*c*m^3*n^3*(x^n)^2+2106*a^2*c*m^2*n^4*(x^n)^2+1080*a^2*c*m*n^5*(x^n)^2+372*b^3*n^3*(x^n)^3+3*(x^n)^2*a^2*c+3*(x^n)^4*a*c^2+3*(x^n)^4*b^2*c+6096*a*b*c*m*n^4*(x^n)^3+508*b^3*n^4*(x^n)^3+6*m*c^3*(x^n)^6+15*c^3*(x^n)^6*n+726*a*b*c*m^4*n^2*(x^n)^3+2232*a*b*c*m^3*n^3*(x^n)^3+3048*a*b*c*m^2*n^4*(x^n)^3+921*a*c^2*m^3*n^3*(x^n)^4+1188*a*c^2*m^2*n^4*(x^n)^4+540*a*c^2*m*n^5*(x^n)^4+51*b^2*c*m^5*n*(x^n)^4+321*b^2*c*m^4*n^2*(x^n)^4+921*b^2*c*m^3*n^3*(x^n)^4+1188*b^2*c*m^2*n^4*(x^n)^4+540*b^2*c*m*n^5*(x^n)^4+240*b*c^2*m^4*n*(x^n)^5+1140*b*c^2*m^3*n^2*(x^n)^5+2340*b*c^2*m^2*n^3*(x^n)^5+1944*b*c^2*m*n^4*(x^n)^5+6*a*b*c*m^6*(x^n)^3+255*a*c^2*m^4*n*(x^n)^4+285*a*b^2*m*n*(x^n)^2+300*a^2*b*m*n*x^n)/(m+1)/(m+n+1)/(m+2*n+1)/(m+3*n+1)/(1+m+4*n)/(1+m+5*n)/(1+m+6*n)*exp(1/2*(-I*Pi*csgn(I*d)*csgn(I*x)*csgn(I*d*x)+I*Pi*csgn(I*d)*csgn(I*d*x)^2+I*Pi*csgn(I*x)*csgn(I*d*x)^2-I*Pi*csgn(I*d*x)^3+2*ln(d)+2*ln(x))*m)","C"
597,1,1065,117,0.071000," ","int((d*x)^m*(b*x^n+c*x^(2*n)+a)^2,x)","\frac{\left(2 a b \,m^{4} x^{n}+18 a b \,m^{3} n \,x^{n}+52 a b \,m^{2} n^{2} x^{n}+48 a b m \,n^{3} x^{n}+2 a c \,m^{4} x^{2 n}+16 a c \,m^{3} n \,x^{2 n}+38 a c \,m^{2} n^{2} x^{2 n}+24 a c m \,n^{3} x^{2 n}+b^{2} m^{4} x^{2 n}+8 b^{2} m^{3} n \,x^{2 n}+19 b^{2} m^{2} n^{2} x^{2 n}+12 b^{2} m \,n^{3} x^{2 n}+2 b c \,m^{4} x^{3 n}+14 b c \,m^{3} n \,x^{3 n}+28 b c \,m^{2} n^{2} x^{3 n}+16 b c m \,n^{3} x^{3 n}+c^{2} m^{4} x^{4 n}+6 c^{2} m^{3} n \,x^{4 n}+11 c^{2} m^{2} n^{2} x^{4 n}+6 c^{2} m \,n^{3} x^{4 n}+a^{2} m^{4}+10 a^{2} m^{3} n +35 a^{2} m^{2} n^{2}+50 a^{2} m \,n^{3}+24 a^{2} n^{4}+8 a b \,m^{3} x^{n}+54 a b \,m^{2} n \,x^{n}+104 a b m \,n^{2} x^{n}+48 a b \,n^{3} x^{n}+8 a c \,m^{3} x^{2 n}+48 a c \,m^{2} n \,x^{2 n}+76 a c m \,n^{2} x^{2 n}+24 a c \,n^{3} x^{2 n}+4 b^{2} m^{3} x^{2 n}+24 b^{2} m^{2} n \,x^{2 n}+38 b^{2} m \,n^{2} x^{2 n}+12 b^{2} n^{3} x^{2 n}+8 b c \,m^{3} x^{3 n}+42 b c \,m^{2} n \,x^{3 n}+56 b c m \,n^{2} x^{3 n}+16 b c \,n^{3} x^{3 n}+4 c^{2} m^{3} x^{4 n}+18 c^{2} m^{2} n \,x^{4 n}+22 c^{2} m \,n^{2} x^{4 n}+6 c^{2} n^{3} x^{4 n}+4 a^{2} m^{3}+30 a^{2} m^{2} n +70 a^{2} m \,n^{2}+50 a^{2} n^{3}+12 a b \,m^{2} x^{n}+54 a b m n \,x^{n}+52 a b \,n^{2} x^{n}+12 a c \,m^{2} x^{2 n}+48 a c m n \,x^{2 n}+38 a c \,n^{2} x^{2 n}+6 b^{2} m^{2} x^{2 n}+24 b^{2} m n \,x^{2 n}+19 b^{2} n^{2} x^{2 n}+12 b c \,m^{2} x^{3 n}+42 b c m n \,x^{3 n}+28 b c \,n^{2} x^{3 n}+6 c^{2} m^{2} x^{4 n}+18 c^{2} m n \,x^{4 n}+11 c^{2} n^{2} x^{4 n}+6 a^{2} m^{2}+30 a^{2} m n +35 a^{2} n^{2}+8 a b m \,x^{n}+18 a b n \,x^{n}+8 a c m \,x^{2 n}+16 a c n \,x^{2 n}+4 b^{2} m \,x^{2 n}+8 b^{2} n \,x^{2 n}+8 b c m \,x^{3 n}+14 b c n \,x^{3 n}+4 c^{2} m \,x^{4 n}+6 c^{2} n \,x^{4 n}+4 a^{2} m +10 a^{2} n +2 a b \,x^{n}+2 a c \,x^{2 n}+b^{2} x^{2 n}+2 b c \,x^{3 n}+c^{2} x^{4 n}+a^{2}\right) x \,{\mathrm e}^{\frac{\left(-i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)+i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)^{2}-i \pi  \mathrm{csgn}\left(i d x \right)^{3}+2 \ln \left(d \right)+2 \ln \left(x \right)\right) m}{2}}}{\left(m +1\right) \left(m +n +1\right) \left(m +2 n +1\right) \left(m +3 n +1\right) \left(m +4 n +1\right)}"," ",0,"x*(2*(x^n)^3*b*c+a^2+c^2*(x^n)^4+a^2*m^4+4*a^2*m^3+50*a^2*n^3+6*a^2*m^2+35*a^2*n^2+24*a^2*n^4+4*a^2*m+10*a^2*n+b^2*(x^n)^2+6*c^2*m^3*n*(x^n)^4+11*c^2*m^2*n^2*(x^n)^4+6*c^2*m*n^3*(x^n)^4+2*b*c*m^4*(x^n)^3+18*c^2*m^2*n*(x^n)^4+22*c^2*m*n^2*(x^n)^4+52*a*b*n^2*x^n+8*a*c*(x^n)^2*m+12*a*b*m^2*x^n+12*a*c*m^2*(x^n)^2+38*a*c*n^2*(x^n)^2+24*b^2*m*n*(x^n)^2+8*m*b*c*(x^n)^3+14*b*c*(x^n)^3*n+18*c^2*m*n*(x^n)^4+2*a*b*m^4*x^n+8*a*c*m^3*(x^n)^2+24*a*c*n^3*(x^n)^2+24*b^2*m^2*n*(x^n)^2+38*b^2*m*n^2*(x^n)^2+12*b*c*m^2*(x^n)^3+28*b*c*n^2*(x^n)^3+8*a*b*m^3*x^n+48*a*b*n^3*x^n+16*a*c*(x^n)^2*n+8*a*b*x^n*m+18*a*b*x^n*n+2*a*c*m^4*(x^n)^2+8*b^2*m^3*n*(x^n)^2+19*b^2*m^2*n^2*(x^n)^2+12*b^2*m*n^3*(x^n)^2+8*b*c*m^3*(x^n)^3+16*b*c*n^3*(x^n)^3+2*(x^n)^2*a*c+c^2*m^4*(x^n)^4+4*c^2*m^3*(x^n)^4+56*b*c*m*n^2*(x^n)^3+18*a*b*m^3*n*x^n+52*a*b*m^2*n^2*x^n+48*a*b*m*n^3*x^n+48*a*c*m^2*n*(x^n)^2+76*a*c*m*n^2*(x^n)^2+42*b*c*m*n*(x^n)^3+54*a*b*m^2*n*x^n+104*a*b*m*n^2*x^n+48*a*c*m*n*(x^n)^2+54*a*b*m*n*x^n+6*c^2*n^3*(x^n)^4+b^2*m^4*(x^n)^2+6*c^2*m^2*(x^n)^4+11*c^2*n^2*(x^n)^4+4*b^2*m^3*(x^n)^2+12*b^2*n^3*(x^n)^2+4*m*c^2*(x^n)^4+6*c^2*(x^n)^4*n+6*b^2*m^2*(x^n)^2+14*b*c*m^3*n*(x^n)^3+28*b*c*m^2*n^2*(x^n)^3+16*b*c*m*n^3*(x^n)^3+16*a*c*m^3*n*(x^n)^2+38*a*c*m^2*n^2*(x^n)^2+24*a*c*m*n^3*(x^n)^2+42*b*c*m^2*n*(x^n)^3+19*b^2*n^2*(x^n)^2+4*b^2*(x^n)^2*m+8*b^2*(x^n)^2*n+30*a^2*m*n+2*a*b*x^n+10*a^2*m^3*n+35*a^2*m^2*n^2+50*a^2*m*n^3+30*a^2*m^2*n+70*a^2*m*n^2)/(m+1)/(m+n+1)/(m+2*n+1)/(m+3*n+1)/(1+m+4*n)*exp(1/2*(-I*Pi*csgn(I*d)*csgn(I*x)*csgn(I*d*x)+I*Pi*csgn(I*d)*csgn(I*d*x)^2+I*Pi*csgn(I*x)*csgn(I*d*x)^2-I*Pi*csgn(I*d*x)^3+2*ln(d)+2*ln(x))*m)","C"
598,1,205,58,0.046000," ","int((d*x)^m*(b*x^n+c*x^(2*n)+a),x)","\frac{\left(b \,m^{2} x^{n}+2 b m n \,x^{n}+c \,m^{2} x^{2 n}+c m n \,x^{2 n}+a \,m^{2}+3 a m n +2 a \,n^{2}+2 b m \,x^{n}+2 b n \,x^{n}+2 c m \,x^{2 n}+c n \,x^{2 n}+2 a m +3 a n +b \,x^{n}+c \,x^{2 n}+a \right) x \,{\mathrm e}^{\frac{\left(-i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)+i \pi  \,\mathrm{csgn}\left(i d \right) \mathrm{csgn}\left(i d x \right)^{2}+i \pi  \,\mathrm{csgn}\left(i x \right) \mathrm{csgn}\left(i d x \right)^{2}-i \pi  \mathrm{csgn}\left(i d x \right)^{3}+2 \ln \left(d \right)+2 \ln \left(x \right)\right) m}{2}}}{\left(m +1\right) \left(m +n +1\right) \left(m +2 n +1\right)}"," ",0,"x*(c*m^2*(x^n)^2+c*m*n*(x^n)^2+b*m^2*x^n+2*b*m*n*x^n+2*m*c*(x^n)^2+c*(x^n)^2*n+a*m^2+3*a*m*n+2*a*n^2+2*b*m*x^n+2*b*x^n*n+c*(x^n)^2+2*a*m+3*a*n+b*x^n+a)/(m+1)/(m+n+1)/(m+2*n+1)*exp(1/2*(-I*Pi*csgn(I*d)*csgn(I*x)*csgn(I*d*x)+I*Pi*csgn(I*d)*csgn(I*d*x)^2+I*Pi*csgn(I*x)*csgn(I*d*x)^2-I*Pi*csgn(I*d*x)^3+2*ln(d)+2*ln(x))*m)","C"
599,0,0,167,0.034000," ","int((d*x)^m/(b*x^n+c*x^(2*n)+a),x)","\int \frac{\left(d x \right)^{m}}{b \,x^{n}+c \,x^{2 n}+a}\, dx"," ",0,"int((d*x)^m/(b*x^n+c*x^(2*n)+a),x)","F"
600,0,0,318,0.042000," ","int((d*x)^m/(b*x^n+c*x^(2*n)+a)^2,x)","\int \frac{\left(d x \right)^{m}}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{2}}\, dx"," ",0,"int((d*x)^m/(b*x^n+c*x^(2*n)+a)^2,x)","F"
601,0,0,595,0.055000," ","int((d*x)^m/(b*x^n+c*x^(2*n)+a)^3,x)","\int \frac{\left(d x \right)^{m}}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{3}}\, dx"," ",0,"int((d*x)^m/(b*x^n+c*x^(2*n)+a)^3,x)","F"
602,0,0,143,0.263000," ","int((d*x)^m*(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}} \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
603,0,0,142,0.147000," ","int((d*x)^m*(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \sqrt{b \,x^{n}+c \,x^{2 n}+a}\, \left(d x \right)^{m}\, dx"," ",0,"int((d*x)^m*(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
604,0,0,142,0.034000," ","int((d*x)^m/(b*x^n+c*x^(2*n)+a)^(1/2),x)","\int \frac{\left(d x \right)^{m}}{\sqrt{b \,x^{n}+c \,x^{2 n}+a}}\, dx"," ",0,"int((d*x)^m/(b*x^n+c*x^(2*n)+a)^(1/2),x)","F"
605,0,0,145,0.020000," ","int((d*x)^m/(b*x^n+c*x^(2*n)+a)^(3/2),x)","\int \frac{\left(d x \right)^{m}}{\left(b \,x^{n}+c \,x^{2 n}+a \right)^{\frac{3}{2}}}\, dx"," ",0,"int((d*x)^m/(b*x^n+c*x^(2*n)+a)^(3/2),x)","F"
606,0,0,150,0.052000," ","int((d*x)^m*(b*x^n+c*x^(2*n)+a)^p,x)","\int \left(d x \right)^{m} \left(b \,x^{n}+c \,x^{2 n}+a \right)^{p}\, dx"," ",0,"int((d*x)^m*(b*x^n+c*x^(2*n)+a)^p,x)","F"
607,1,298,40,0.002000," ","int((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{c \,e^{7} x^{8}}{8}+c d \,e^{6} x^{7}+\frac{\left(15 c \,d^{2} e^{5}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) e^{3}\right) x^{6}}{6}+\frac{\left(13 c \,d^{3} e^{4}+3 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) d \,e^{2}+\left(4 c \,d^{3} e +2 d e b \right) e^{3}\right) x^{5}}{5}+\left(c \,d^{4}+b \,d^{2}+a \right) d^{3} x +\frac{\left(4 c \,d^{4} e^{3}+3 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) d^{2} e +3 \left(4 c \,d^{3} e +2 d e b \right) d \,e^{2}+\left(c \,d^{4}+b \,d^{2}+a \right) e^{3}\right) x^{4}}{4}+\frac{\left(\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) d^{3}+3 \left(4 c \,d^{3} e +2 d e b \right) d^{2} e +3 \left(c \,d^{4}+b \,d^{2}+a \right) d \,e^{2}\right) x^{3}}{3}+\frac{\left(\left(4 c \,d^{3} e +2 d e b \right) d^{3}+3 \left(c \,d^{4}+b \,d^{2}+a \right) d^{2} e \right) x^{2}}{2}"," ",0,"1/8*e^7*c*x^8+d*e^6*c*x^7+1/6*(15*d^2*e^5*c+e^3*(6*c*d^2*e^2+b*e^2))*x^6+1/5*(13*d^3*c*e^4+3*d*e^2*(6*c*d^2*e^2+b*e^2)+e^3*(4*c*d^3*e+2*b*d*e))*x^5+1/4*(4*d^4*c*e^3+3*d^2*e*(6*c*d^2*e^2+b*e^2)+3*d*e^2*(4*c*d^3*e+2*b*d*e)+e^3*(c*d^4+b*d^2+a))*x^4+1/3*(d^3*(6*c*d^2*e^2+b*e^2)+3*d^2*e*(4*c*d^3*e+2*b*d*e)+3*d*e^2*(c*d^4+b*d^2+a))*x^3+1/2*(d^3*(4*c*d^3*e+2*b*d*e)+3*d^2*e*(c*d^4+b*d^2+a))*x^2+d^3*(c*d^4+b*d^2+a)*x","B"
608,1,1314,79,0.003000," ","int((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{c^{2} e^{11} x^{12}}{12}+c^{2} d \,e^{10} x^{11}+\frac{\left(27 c^{2} d^{2} e^{9}+\left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) e^{3}\right) x^{10}}{10}+\frac{\left(25 c^{2} d^{3} e^{8}+3 \left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) d \,e^{2}+\left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) e^{3}\right) x^{9}}{9}+\frac{\left(8 c^{2} d^{4} e^{7}+3 \left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) d^{2} e +3 \left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) d \,e^{2}+\left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) e^{3}\right) x^{8}}{8}+\frac{\left(\left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) d^{3}+3 \left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) d^{2} e +3 \left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) d \,e^{2}+\left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) e^{3}\right) x^{7}}{7}+\frac{\left(\left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) d^{3}+3 \left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) d^{2} e +3 \left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) d \,e^{2}+\left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) e^{3}\right) x^{6}}{6}+\frac{\left(\left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) d^{3}+3 \left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) d^{2} e +3 \left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) d \,e^{2}+2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) e^{3}\right) x^{5}}{5}+\left(c \,d^{4}+b \,d^{2}+a \right)^{2} d^{3} x +\frac{\left(\left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) d^{3}+3 \left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) d^{2} e +6 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) d \,e^{2}+\left(c \,d^{4}+b \,d^{2}+a \right)^{2} e^{3}\right) x^{4}}{4}+\frac{\left(\left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) d^{3}+6 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) d^{2} e +3 \left(c \,d^{4}+b \,d^{2}+a \right)^{2} d \,e^{2}\right) x^{3}}{3}+\frac{\left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) d^{3}+3 \left(c \,d^{4}+b \,d^{2}+a \right)^{2} d^{2} e \right) x^{2}}{2}"," ",0,"1/12*e^11*c^2*x^12+d*e^10*c^2*x^11+1/10*(27*d^2*e^9*c^2+e^3*(2*(6*c*d^2*e^2+b*e^2)*c*e^4+16*c^2*d^2*e^6))*x^10+1/9*(25*d^3*c^2*e^8+3*d*e^2*(2*(6*c*d^2*e^2+b*e^2)*c*e^4+16*c^2*d^2*e^6)+e^3*(2*(4*c*d^3*e+2*b*d*e)*c*e^4+8*(6*c*d^2*e^2+b*e^2)*c*d*e^3))*x^9+1/8*(8*d^4*c^2*e^7+3*d^2*e*(2*(6*c*d^2*e^2+b*e^2)*c*e^4+16*c^2*d^2*e^6)+3*d*e^2*(2*(4*c*d^3*e+2*b*d*e)*c*e^4+8*(6*c*d^2*e^2+b*e^2)*c*d*e^3)+e^3*(2*(c*d^4+b*d^2+a)*c*e^4+8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+(6*c*d^2*e^2+b*e^2)^2))*x^8+1/7*(d^3*(2*(6*c*d^2*e^2+b*e^2)*c*e^4+16*c^2*d^2*e^6)+3*d^2*e*(2*(4*c*d^3*e+2*b*d*e)*c*e^4+8*(6*c*d^2*e^2+b*e^2)*c*d*e^3)+3*d*e^2*(2*(c*d^4+b*d^2+a)*c*e^4+8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+(6*c*d^2*e^2+b*e^2)^2)+e^3*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2)))*x^7+1/6*(d^3*(2*(4*c*d^3*e+2*b*d*e)*c*e^4+8*(6*c*d^2*e^2+b*e^2)*c*d*e^3)+3*d^2*e*(2*(c*d^4+b*d^2+a)*c*e^4+8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+(6*c*d^2*e^2+b*e^2)^2)+3*d*e^2*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2))+e^3*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2))*x^6+1/5*(d^3*(2*(c*d^4+b*d^2+a)*c*e^4+8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+(6*c*d^2*e^2+b*e^2)^2)+3*d^2*e*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2))+3*d*e^2*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2)+2*e^3*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e))*x^5+1/4*(d^3*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2))+3*d^2*e*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2)+6*d*e^2*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e)+e^3*(c*d^4+b*d^2+a)^2)*x^4+1/3*(d^3*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2)+6*d^2*e*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e)+3*d*e^2*(c*d^4+b*d^2+a)^2)*x^3+1/2*(2*d^3*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e)+3*d^2*e*(c*d^4+b*d^2+a)^2)*x^2+d^3*(c*d^4+b*d^2+a)^2*x","B"
609,1,7550,124,0.003000," ","int((e*x+d)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
610,1,349,49,0.001000," ","int((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{c \,e^{7} f^{3} x^{8}}{8}+c d \,e^{6} f^{3} x^{7}+\left(c \,d^{4}+b \,d^{2}+a \right) d^{3} f^{3} x +\frac{\left(15 c \,d^{2} e^{5} f^{3}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) e^{3} f^{3}\right) x^{6}}{6}+\frac{\left(13 c \,d^{3} e^{4} f^{3}+3 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) d \,e^{2} f^{3}+\left(4 c \,d^{3} e +2 d e b \right) e^{3} f^{3}\right) x^{5}}{5}+\frac{\left(4 c \,d^{4} e^{3} f^{3}+3 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) d^{2} e \,f^{3}+3 \left(4 c \,d^{3} e +2 d e b \right) d \,e^{2} f^{3}+\left(c \,d^{4}+b \,d^{2}+a \right) e^{3} f^{3}\right) x^{4}}{4}+\frac{\left(\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) d^{3} f^{3}+3 \left(4 c \,d^{3} e +2 d e b \right) d^{2} e \,f^{3}+3 \left(c \,d^{4}+b \,d^{2}+a \right) d \,e^{2} f^{3}\right) x^{3}}{3}+\frac{\left(\left(4 c \,d^{3} e +2 d e b \right) d^{3} f^{3}+3 \left(c \,d^{4}+b \,d^{2}+a \right) d^{2} e \,f^{3}\right) x^{2}}{2}"," ",0,"1/8*e^7*f^3*c*x^8+d*f^3*e^6*c*x^7+1/6*(15*d^2*f^3*e^5*c+e^3*f^3*(6*c*d^2*e^2+b*e^2))*x^6+1/5*(13*d^3*f^3*c*e^4+3*d*f^3*e^2*(6*c*d^2*e^2+b*e^2)+e^3*f^3*(4*c*d^3*e+2*b*d*e))*x^5+1/4*(4*d^4*f^3*c*e^3+3*d^2*f^3*e*(6*c*d^2*e^2+b*e^2)+3*d*f^3*e^2*(4*c*d^3*e+2*b*d*e)+e^3*f^3*(c*d^4+b*d^2+a))*x^4+1/3*(d^3*f^3*(6*c*d^2*e^2+b*e^2)+3*d^2*f^3*e*(4*c*d^3*e+2*b*d*e)+3*d*f^3*e^2*(c*d^4+b*d^2+a))*x^3+1/2*(d^3*f^3*(4*c*d^3*e+2*b*d*e)+3*d^2*f^3*e*(c*d^4+b*d^2+a))*x^2+d^3*f^3*(c*d^4+b*d^2+a)*x","B"
611,1,1413,94,0.000000," ","int((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{c^{2} e^{11} f^{3} x^{12}}{12}+c^{2} d \,e^{10} f^{3} x^{11}+\frac{\left(27 c^{2} d^{2} e^{9} f^{3}+\left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) e^{3} f^{3}\right) x^{10}}{10}+\frac{\left(25 c^{2} d^{3} e^{8} f^{3}+3 \left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) d \,e^{2} f^{3}+\left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) e^{3} f^{3}\right) x^{9}}{9}+\frac{\left(8 c^{2} d^{4} e^{7} f^{3}+3 \left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) d^{2} e \,f^{3}+3 \left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) d \,e^{2} f^{3}+\left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) e^{3} f^{3}\right) x^{8}}{8}+\left(c \,d^{4}+b \,d^{2}+a \right)^{2} d^{3} f^{3} x +\frac{\left(\left(16 c^{2} d^{2} e^{6}+2 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c \,e^{4}\right) d^{3} f^{3}+3 \left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) d^{2} e \,f^{3}+3 \left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) d \,e^{2} f^{3}+\left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) e^{3} f^{3}\right) x^{7}}{7}+\frac{\left(\left(8 \left(6 c \,d^{2} e^{2}+b \,e^{2}\right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) c \,e^{4}\right) d^{3} f^{3}+3 \left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) d^{2} e \,f^{3}+3 \left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) d \,e^{2} f^{3}+\left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) e^{3} f^{3}\right) x^{6}}{6}+\frac{\left(\left(8 \left(4 c \,d^{3} e +2 d e b \right) c d \,e^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) c \,e^{4}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right)^{2}\right) d^{3} f^{3}+3 \left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) d^{2} e \,f^{3}+3 \left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) d \,e^{2} f^{3}+2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) e^{3} f^{3}\right) x^{5}}{5}+\frac{\left(\left(8 \left(c \,d^{4}+b \,d^{2}+a \right) c d \,e^{3}+2 \left(4 c \,d^{3} e +2 d e b \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)\right) d^{3} f^{3}+3 \left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) d^{2} e \,f^{3}+6 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) d \,e^{2} f^{3}+\left(c \,d^{4}+b \,d^{2}+a \right)^{2} e^{3} f^{3}\right) x^{4}}{4}+\frac{\left(\left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(6 c \,d^{2} e^{2}+b \,e^{2}\right)+\left(4 c \,d^{3} e +2 d e b \right)^{2}\right) d^{3} f^{3}+6 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) d^{2} e \,f^{3}+3 \left(c \,d^{4}+b \,d^{2}+a \right)^{2} d \,e^{2} f^{3}\right) x^{3}}{3}+\frac{\left(2 \left(c \,d^{4}+b \,d^{2}+a \right) \left(4 c \,d^{3} e +2 d e b \right) d^{3} f^{3}+3 \left(c \,d^{4}+b \,d^{2}+a \right)^{2} d^{2} e \,f^{3}\right) x^{2}}{2}"," ",0,"1/12*e^11*f^3*c^2*x^12+d*f^3*e^10*c^2*x^11+1/10*(27*d^2*f^3*e^9*c^2+e^3*f^3*(16*c^2*d^2*e^6+2*(6*c*d^2*e^2+b*e^2)*c*e^4))*x^10+1/9*(25*d^3*f^3*c^2*e^8+3*d*f^3*e^2*(16*c^2*d^2*e^6+2*(6*c*d^2*e^2+b*e^2)*c*e^4)+e^3*f^3*(8*(6*c*d^2*e^2+b*e^2)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*c*e^4))*x^9+1/8*(8*d^4*f^3*c^2*e^7+3*d^2*f^3*e*(16*c^2*d^2*e^6+2*(6*c*d^2*e^2+b*e^2)*c*e^4)+3*d*f^3*e^2*(8*(6*c*d^2*e^2+b*e^2)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*c*e^4)+e^3*f^3*(8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+2*(c*d^4+b*d^2+a)*c*e^4+(6*c*d^2*e^2+b*e^2)^2))*x^8+1/7*(d^3*f^3*(16*c^2*d^2*e^6+2*(6*c*d^2*e^2+b*e^2)*c*e^4)+3*d^2*f^3*e*(8*(6*c*d^2*e^2+b*e^2)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*c*e^4)+3*d*f^3*e^2*(8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+2*(c*d^4+b*d^2+a)*c*e^4+(6*c*d^2*e^2+b*e^2)^2)+e^3*f^3*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2)))*x^7+1/6*(d^3*f^3*(8*(6*c*d^2*e^2+b*e^2)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*c*e^4)+3*d^2*f^3*e*(8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+2*(c*d^4+b*d^2+a)*c*e^4+(6*c*d^2*e^2+b*e^2)^2)+3*d*f^3*e^2*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2))+e^3*f^3*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2))*x^6+1/5*(d^3*f^3*(8*(4*c*d^3*e+2*b*d*e)*c*d*e^3+2*(c*d^4+b*d^2+a)*c*e^4+(6*c*d^2*e^2+b*e^2)^2)+3*d^2*f^3*e*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2))+3*d*f^3*e^2*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2)+2*e^3*f^3*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e))*x^5+1/4*(d^3*f^3*(8*(c*d^4+b*d^2+a)*c*d*e^3+2*(4*c*d^3*e+2*b*d*e)*(6*c*d^2*e^2+b*e^2))+3*d^2*f^3*e*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2)+6*d*f^3*e^2*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e)+e^3*f^3*(c*d^4+b*d^2+a)^2)*x^4+1/3*(d^3*f^3*(2*(c*d^4+b*d^2+a)*(6*c*d^2*e^2+b*e^2)+(4*c*d^3*e+2*b*d*e)^2)+6*d^2*f^3*e*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e)+3*d*f^3*e^2*(c*d^4+b*d^2+a)^2)*x^3+1/2*(2*d^3*f^3*(c*d^4+b*d^2+a)*(4*c*d^3*e+2*b*d*e)+3*d^2*f^3*e*(c*d^4+b*d^2+a)^2)*x^2+d^3*f^3*(c*d^4+b*d^2+a)^2*x","B"
612,1,7697,145,0.003000," ","int((e*f*x+d*f)^3*(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"result too large to display","B"
613,1,158,158,0.069000," ","int((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{x}{c}+\frac{\left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b d e -b \,d^{2}-a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 c e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/c*x+1/2/c/e*sum((-_R^2*b*e^2-2*_R*b*d*e-b*d^2-a)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(c*e^4*_Z^4+4*c*d*e^3*_Z^3+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+c*d^4+b*d^2+a))","C"
614,1,151,73,0.003000," ","int((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} e^{3}+3 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} d \,e^{2}+3 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) d^{2} e +d^{3}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/e*sum((_R^3*e^3+3*_R^2*d*e^2+3*_R*d^2*e+d^3)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
615,1,140,129,0.006000," ","int((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} e^{2}+2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) d e +d^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/e*sum((_R^2*e^2+2*_R*d*e+d^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
616,1,129,39,0.007000," ","int((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e +d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/e*sum((_R*e+d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
617,1,184,86,0.011000," ","int(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\ln \left(e x +d \right)}{a e}+\frac{\left(-c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}-3 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}-c \,d^{3}+\left(-3 c \,d^{2}-b \right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e -b d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/a/e*sum((-c*e^3*_R^3-3*c*d*e^2*_R^2+e*(-3*c*d^2-b)*_R-c*d^3-b*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))+ln(e*x+d)/a/e","C"
618,1,168,159,0.010000," ","int(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e -c \,d^{2}-b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}-\frac{1}{\left(e x +d \right) a e}"," ",0,"1/2/a/e*sum((-_R^2*c*e^2-2*_R*c*d*e-c*d^2-b)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/a/e/(e*x+d)","C"
619,1,213,111,0.013000," ","int(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","-\frac{b \ln \left(e x +d \right)}{a^{2} e}-\frac{1}{2 \left(e x +d \right)^{2} a e}+\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} b c \,e^{3}+3 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c d \,e^{2}+b c \,d^{3}-a c d +b^{2} d +\left(3 b c \,d^{2}-a c +b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a^{2} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/a^2/e*sum((_R^3*b*c*e^3+3*_R^2*b*c*d*e^2+e*(3*b*c*d^2-a*c+b^2)*_R+b*c*d^3-a*c*d+b^2*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/2/a/e/(e*x+d)^2-b*ln(e*x+d)/a^2/e","C"
620,1,188,189,0.010000," ","int(1/(e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","-\frac{1}{3 \left(e x +d \right)^{3} a e}+\frac{b}{\left(e x +d \right) a^{2} e}+\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}+2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e +b c \,d^{2}-a c +b^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a^{2} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/a^2/e*sum((_R^2*b*c*e^2+2*_R*b*c*d*e+b*c*d^2-a*c+b^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/3/a/e/(e*x+d)^3+b/a^2/e/(e*x+d)","C"
621,1,323,227,0.020000," ","int((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b d e -b \,d^{2}+2 a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{-\frac{b \,e^{2} x^{3}}{2 \left(4 a c -b^{2}\right)}-\frac{3 b d e \,x^{2}}{2 \left(4 a c -b^{2}\right)}-\frac{\left(3 b \,d^{2}+2 a \right) x}{2 \left(4 a c -b^{2}\right)}-\frac{\left(b \,d^{2}+2 a \right) d}{2 \left(4 a c -b^{2}\right) e}}{c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a}"," ",0,"(-1/2*b*e^2/(4*a*c-b^2)*x^3-3/2*d*b*e/(4*a*c-b^2)*x^2-1/2*(3*b*d^2+2*a)/(4*a*c-b^2)*x-1/2*d/e*(b*d^2+2*a)/(4*a*c-b^2))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)+1/4/(4*a*c-b^2)/e*sum((-_R^2*b*e^2-2*_R*b*d*e-b*d^2+2*a)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
622,1,276,91,0.021000," ","int((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{b \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e -d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 \left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{-\frac{b e \,x^{2}}{2 \left(4 a c -b^{2}\right)}-\frac{b d x}{4 a c -b^{2}}-\frac{b \,d^{2}+2 a}{2 \left(4 a c -b^{2}\right) e}}{c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a}"," ",0,"(-1/2*b*e/(4*a*c-b^2)*x^2-b*d/(4*a*c-b^2)*x-1/2/e*(b*d^2+2*a)/(4*a*c-b^2))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)+1/2/(4*a*c-b^2)*b/e*sum((-_R*e-d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
623,1,319,213,0.022000," ","int((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{\left(2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}+4 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e +2 c \,d^{2}-b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{\frac{c \,e^{2} x^{3}}{4 a c -b^{2}}+\frac{3 c d e \,x^{2}}{4 a c -b^{2}}+\frac{\left(6 c \,d^{2}+b \right) x}{8 a c -2 b^{2}}+\frac{\left(2 c \,d^{2}+b \right) d}{2 \left(4 a c -b^{2}\right) e}}{c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a}"," ",0,"(c*e^2/(4*a*c-b^2)*x^3+3*d*c*e/(4*a*c-b^2)*x^2+1/2*(6*c*d^2+b)/(4*a*c-b^2)*x+1/2*d/e*(2*c*d^2+b)/(4*a*c-b^2))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)+1/4/(4*a*c-b^2)/e*sum((2*_R^2*c*e^2+4*_R*c*d*e+2*c*d^2-b)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
624,1,270,92,0.023000," ","int((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{c \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e +d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{\left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{\frac{c e \,x^{2}}{4 a c -b^{2}}+\frac{2 c d x}{4 a c -b^{2}}+\frac{2 c \,d^{2}+b}{2 \left(4 a c -b^{2}\right) e}}{c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a}"," ",0,"(c*e/(4*a*c-b^2)*x^2+2*c*d/(4*a*c-b^2)*x+1/2/e*(2*c*d^2+b)/(4*a*c-b^2))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)+c/(4*a*c-b^2)/e*sum((_R*e+d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
625,1,364,253,0.018000," ","int(1/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e -b c \,d^{2}+6 a c -b^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) a e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{-\frac{b c \,e^{2} x^{3}}{2 \left(4 a c -b^{2}\right) a}-\frac{3 b c d e \,x^{2}}{2 \left(4 a c -b^{2}\right) a}+\frac{\left(-3 b c \,d^{2}+2 a c -b^{2}\right) x}{2 \left(4 a c -b^{2}\right) a}+\frac{\left(-b c \,d^{2}+2 a c -b^{2}\right) d}{2 \left(4 a c -b^{2}\right) a e}}{c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a}"," ",0,"(-1/2*b*c*e^2/a/(4*a*c-b^2)*x^3-3/2*d*b*c*e/a/(4*a*c-b^2)*x^2+1/2*(-3*b*c*d^2+2*a*c-b^2)/a/(4*a*c-b^2)*x+1/2*d/e*(-b*c*d^2+2*a*c-b^2)/a/(4*a*c-b^2))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)+1/4/a/(4*a*c-b^2)/e*sum((-_R^2*b*c*e^2-2*_R*b*c*d*e-b*c*d^2+6*a*c-b^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
626,1,693,152,0.033000," ","int(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{b c e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{b c d x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}-\frac{b c \,d^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}-\frac{b^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}+\frac{c}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}+\frac{\ln \left(e x +d \right)}{a^{2} e}-\frac{\left(\left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} c \,e^{3}+3 \left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c d \,e^{2}+4 a \,c^{2} d^{3}-b^{2} c \,d^{3}+5 a b c d -b^{3} d +\left(12 a \,c^{2} d^{2}-3 b^{2} c \,d^{2}+5 a b c -b^{3}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 \left(4 a c -b^{2}\right) a^{2} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"-1/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*c*e/(4*a*c-b^2)*x^2-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*c*d/(4*a*c-b^2)*x-1/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b*c*d^2+1/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*c-1/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b^2-1/2/a^2/(4*a*c-b^2)/e*sum((c*e^3*(4*a*c-b^2)*_R^3+3*c*d*e^2*(4*a*c-b^2)*_R^2+e*(12*a*c^2*d^2-3*b^2*c*d^2+5*a*b*c-b^3)*_R+4*a*c^2*d^3-b^2*c*d^3+5*a*b*c*d-b^3*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))+ln(e*x+d)/a^2/e","C"
627,1,1304,300,0.032000," ","int(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{c^{2} e^{2} x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c \,e^{2} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 c^{2} d e \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{3 b^{2} c d e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 c^{2} d^{2} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{3 b^{2} c \,d^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{c^{2} d^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}+\frac{b^{2} c \,d^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e}-\frac{3 b c x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{3} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 b c d}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}+\frac{b^{3} d}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e}-\frac{\left(\left(10 a c -3 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}+10 a \,c^{2} d^{2}-3 b^{2} c \,d^{2}+2 \left(10 a c -3 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e +13 a b c -3 b^{3}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) a^{2} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}-\frac{1}{\left(e x +d \right) a^{2} e}"," ",0,"-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c^2*e^2/(4*a*c-b^2)*x^3+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*e^2/(4*a*c-b^2)*x^3*b^2-3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*c^2*e/(4*a*c-b^2)*x^2+3/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*c*e/(4*a*c-b^2)*x^2*b^2-3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*c^2*d^2+3/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^2*c*d^2-3/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b*c+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^3-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*c^2+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*b^2*c-3/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b*c+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b^3-1/4/a^2/(4*a*c-b^2)/e*sum((c*e^2*(10*a*c-3*b^2)*_R^2+2*c*d*e*(10*a*c-3*b^2)*_R+10*a*c^2*d^2-3*b^2*c*d^2+13*a*b*c-3*b^3)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/a^2/e/(e*x+d)","C"
628,1,1014,206,0.040000," ","int(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{c^{2} e \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{2 c^{2} d x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{b^{2} c d x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{c^{2} d^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}+\frac{b^{2} c \,d^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e}-\frac{3 b c}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}+\frac{b^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e}-\frac{2 b \ln \left(e x +d \right)}{a^{3} e}-\frac{1}{2 \left(e x +d \right)^{2} a^{2} e}+\frac{\left(\left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} b c \,e^{3}+3 \left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c d \,e^{2}+4 a b \,c^{2} d^{3}-b^{3} c \,d^{3}-3 a^{2} c^{2} d +5 a \,b^{2} c d -b^{4} d +\left(12 a b \,c^{2} d^{2}-3 b^{3} c \,d^{2}-3 a^{2} c^{2}+5 a \,b^{2} c -b^{4}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{\left(4 a c -b^{2}\right) a^{3} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c^2*e/(4*a*c-b^2)*x^2+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*e/(4*a*c-b^2)*x^2*b^2-2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c^2*d/(4*a*c-b^2)*x+1/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*d/(4*a*c-b^2)*x*b^2-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*c^2*d^2+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b^2*c*d^2-3/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b*c+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b^3+1/a^3/(4*a*c-b^2)/e*sum((b*c*e^3*(4*a*c-b^2)*_R^3+3*b*c*d*e^2*(4*a*c-b^2)*_R^2+e*(12*a*b*c^2*d^2-3*b^3*c*d^2-3*a^2*c^2+5*a*b^2*c-b^4)*_R+4*a*b*c^2*d^3-b^3*c*d^3-3*a^2*c^2*d+5*a*b^2*c*d-b^4*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/2/a^2/e/(e*x+d)^2-2*b*ln(e*x+d)/a^3/e","C"
629,1,1518,358,0.036000," ","int(1/(e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{3 b \,c^{2} e^{2} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{3} c \,e^{2} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{9 b \,c^{2} d e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 b^{3} c d e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{9 b \,c^{2} d^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{3 b^{3} c \,d^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}+\frac{3 b \,c^{2} d^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e}-\frac{b^{3} c \,d^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} e}-\frac{c^{2} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a}+\frac{2 b^{2} c x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2}}-\frac{b^{4} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3}}-\frac{c^{2} d}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e}+\frac{2 b^{2} c d}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e}-\frac{b^{4} d}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} e}-\frac{1}{3 \left(e x +d \right)^{3} a^{2} e}+\frac{2 b}{\left(e x +d \right) a^{3} e}+\frac{\left(\left(19 a c -5 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}+19 a b \,c^{2} d^{2}-5 b^{3} c \,d^{2}+2 \left(19 a c -5 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e -14 a^{2} c^{2}+24 a \,b^{2} c -5 b^{4}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) a^{3} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"3/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*c^2*e^2/(4*a*c-b^2)*x^3-1/2/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b^3*c*e^2/(4*a*c-b^2)*x^3+9/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*b*c^2*e/(4*a*c-b^2)*x^2-3/2/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*b^3*c*e/(4*a*c-b^2)*x^2+9/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b*c^2*d^2-3/2/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^3*c*d^2-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*c^2+2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^2*c-1/2/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^4+3/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*b*c^2-1/2/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*b^3*c-1/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*c^2+2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b^2*c-1/2/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b^4+1/4/a^3/(4*a*c-b^2)/e*sum((b*c*e^2*(19*a*c-5*b^2)*_R^2+2*d*e*b*c*(19*a*c-5*b^2)*_R+19*a*b*c^2*d^2-5*b^3*c*d^2-14*a^2*c^2+24*a*b^2*c-5*b^4)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/3/a^2/e/(e*x+d)^3+2/a^3*b/e/(e*x+d)","C"
630,1,704,293,0.050000," ","int((e*x+d)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\frac{3 \left(-4 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}-8 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e -4 b c \,d^{2}+4 a c +b^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{-\frac{3 b \,c^{2} e^{6} x^{7}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{21 b \,c^{2} d \,e^{5} x^{6}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{\left(-252 b c \,d^{2}+4 a c -19 b^{2}\right) c \,e^{4} x^{5}}{128 a^{2} c^{2}-64 a \,b^{2} c +8 b^{4}}+\frac{5 \left(-84 b c \,d^{2}+4 a c -19 b^{2}\right) c d \,e^{3} x^{4}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(420 b \,c^{2} d^{4}-40 a \,c^{2} d^{2}+190 b^{2} c \,d^{2}+16 a b c +5 b^{3}\right) e^{2} x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(252 b \,c^{2} d^{4}-40 a \,c^{2} d^{2}+190 b^{2} c \,d^{2}+48 a b c +15 b^{3}\right) d e \,x^{2}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(84 b \,c^{2} d^{6}-20 a \,c^{2} d^{4}+95 b^{2} c \,d^{4}+48 a b c \,d^{2}+15 b^{3} d^{2}+12 a^{2} c +3 a \,b^{2}\right) x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(12 b \,c^{2} d^{6}-4 a \,c^{2} d^{4}+19 b^{2} c \,d^{4}+16 a b c \,d^{2}+5 b^{3} d^{2}+12 a^{2} c +3 a \,b^{2}\right) d}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2}}"," ",0,"(-3/2*c^2*e^6*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7-21/2*c^2*d*e^5*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/8*(-252*b*c*d^2+4*a*c-19*b^2)*c*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+5/8*c*d*e^3*(-84*b*c*d^2+4*a*c-19*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-1/8*e^2*(420*b*c^2*d^4-40*a*c^2*d^2+190*b^2*c*d^2+16*a*b*c+5*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/8*d*e*(252*b*c^2*d^4-40*a*c^2*d^2+190*b^2*c*d^2+48*a*b*c+15*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-1/8*(84*b*c^2*d^6-20*a*c^2*d^4+95*b^2*c*d^4+48*a*b*c*d^2+15*b^3*d^2+12*a^2*c+3*a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x-1/8*d/e*(12*b*c^2*d^6-4*a*c^2*d^4+19*b^2*c*d^4+16*a*b*c*d^2+5*b^3*d^2+12*a^2*c+3*a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((-4*_R^2*b*c*e^2-8*_R*b*c*d*e-4*b*c*d^2+4*a*c+b^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
631,1,544,142,0.046000," ","int((e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\frac{3 b c \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e -d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{-\frac{3 b \,c^{2} e^{5} x^{6}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 b \,c^{2} d \,e^{4} x^{5}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{9 \left(10 c \,d^{2}+b \right) b c \,e^{3} x^{4}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 \left(10 c \,d^{2}+3 b \right) b c d \,e^{2} x^{3}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{\left(45 c^{2} d^{4}+27 b c \,d^{2}+5 a c +b^{2}\right) b e \,x^{2}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{\left(9 c^{2} d^{4}+9 b c \,d^{2}+5 a c +b^{2}\right) b d x}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}-\frac{6 b \,c^{2} d^{6}+9 b^{2} c \,d^{4}+10 a b c \,d^{2}+2 b^{3} d^{2}+8 a^{2} c +a \,b^{2}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2}}"," ",0,"(-3/2*c^2*e^5*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6-9*e^4*b*c^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-9/4*b*c*e^3*(10*c*d^2+b)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4-3*c*d*e^2*b*(10*c*d^2+3*b)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/2*b*e*(45*c^2*d^4+27*b*c*d^2+5*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2-d*b*(9*c^2*d^4+9*b*c*d^2+5*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x-1/4/e*(6*b*c^2*d^6+9*b^2*c*d^4+10*a*b*c*d^2+2*b^3*d^2+8*a^2*c+a*b^2)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2+3/2*b*c/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((-_R*e-d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
632,1,885,319,0.051000," ","int((e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\frac{\left(\left(20 a c +b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}+20 a \,c^{2} d^{2}+b^{2} c \,d^{2}+2 \left(20 a c +b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e -16 a b c +b^{3}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{\frac{\left(20 a c +b^{2}\right) c^{2} e^{6} x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{7 \left(20 a c +b^{2}\right) c^{2} d \,e^{5} x^{6}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(420 a \,c^{2} d^{2}+21 b^{2} c \,d^{2}+28 a b c +2 b^{3}\right) c \,e^{4} x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{5 \left(140 a \,c^{2} d^{2}+7 b^{2} c \,d^{2}+28 a b c +2 b^{3}\right) c d \,e^{3} x^{4}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(700 a \,c^{3} d^{4}+35 b^{2} c^{2} d^{4}+280 a b \,c^{2} d^{2}+20 b^{3} c \,d^{2}+36 a^{2} c^{2}+5 a \,b^{2} c +b^{4}\right) e^{2} x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(420 a \,c^{3} d^{4}+21 b^{2} c^{2} d^{4}+280 a b \,c^{2} d^{2}+20 b^{3} c \,d^{2}+108 a^{2} c^{2}+15 a \,b^{2} c +3 b^{4}\right) d e \,x^{2}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(140 a \,c^{3} d^{6}+7 b^{2} c^{2} d^{6}+140 a b \,c^{2} d^{4}+10 b^{3} c \,d^{4}+108 a^{2} c^{2} d^{2}+15 a \,b^{2} c \,d^{2}+3 b^{4} d^{2}+16 a^{2} b c -a \,b^{3}\right) x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a}+\frac{\left(20 a \,c^{3} d^{6}+b^{2} c^{2} d^{6}+28 a b \,c^{2} d^{4}+2 b^{3} c \,d^{4}+36 a^{2} c^{2} d^{2}+5 a \,b^{2} c \,d^{2}+b^{4} d^{2}+16 a^{2} b c -a \,b^{3}\right) d}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a e}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2}}"," ",0,"(1/8*c^2*e^6*(20*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^7+7/8*c^2*d*e^5*(20*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^6+1/8*(420*a*c^2*d^2+21*b^2*c*d^2+28*a*b*c+2*b^3)*c*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^5+5/8*c*d*e^3*(140*a*c^2*d^2+7*b^2*c*d^2+28*a*b*c+2*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^4+1/8*e^2*(700*a*c^3*d^4+35*b^2*c^2*d^4+280*a*b*c^2*d^2+20*b^3*c*d^2+36*a^2*c^2+5*a*b^2*c+b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^3+1/8*d*e*(420*a*c^3*d^4+21*b^2*c^2*d^4+280*a*b*c^2*d^2+20*b^3*c*d^2+108*a^2*c^2+15*a*b^2*c+3*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^2+1/8*(140*a*c^3*d^6+7*b^2*c^2*d^6+140*a*b*c^2*d^4+10*b^3*c*d^4+108*a^2*c^2*d^2+15*a*b^2*c*d^2+3*b^4*d^2+16*a^2*b*c-a*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x+1/8*d/e*(20*a*c^3*d^6+b^2*c^2*d^6+28*a*b*c^2*d^4+2*b^3*c*d^4+36*a^2*c^2*d^2+5*a*b^2*c*d^2+b^4*d^2+16*a^2*b*c-a*b^3)/(16*a^2*c^2-8*a*b^2*c+b^4)/a)/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2+1/16/(16*a^2*c^2-8*a*b^2*c+b^4)/a/e*sum((c*e^2*(20*a*c+b^2)*_R^2+2*c*d*e*(20*a*c+b^2)*_R+20*a*c^2*d^2+b^2*c*d^2-16*a*b*c+b^3)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
633,1,541,144,0.050000," ","int((e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\frac{3 c^{2} \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e +d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{\frac{3 c^{3} e^{5} x^{6}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{18 c^{3} d \,e^{4} x^{5}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{9 \left(10 c \,d^{2}+b \right) c^{2} e^{3} x^{4}}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{6 \left(10 c \,d^{2}+3 b \right) c^{2} d \,e^{2} x^{3}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{\left(45 c^{2} d^{4}+27 b c \,d^{2}+5 a c +b^{2}\right) c e \,x^{2}}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{2 \left(9 c^{2} d^{4}+9 b c \,d^{2}+5 a c +b^{2}\right) c d x}{16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}}+\frac{12 c^{3} d^{6}+18 b \,c^{2} d^{4}+20 a \,c^{2} d^{2}+4 b^{2} c \,d^{2}+10 a b c -b^{3}}{4 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2}}"," ",0,"(3*c^3*e^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+18*e^4*c^3*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+9/2*c^2*e^3*(10*c*d^2+b)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4+6*c^2*d*e^2*(10*c*d^2+3*b)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+c*e*(45*c^2*d^4+27*b*c*d^2+5*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2+2*c*d*(9*c^2*d^4+9*b*c*d^2+5*a*c+b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)*x+1/4/e*(12*c^3*d^6+18*b*c^2*d^4+20*a*c^2*d^2+4*b^2*c*d^2+10*a*b*c-b^3)/(16*a^2*c^2-8*a*b^2*c+b^4))/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2+3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((_R*e+d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
634,1,1010,389,0.052000," ","int(1/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\frac{3 \left(\left(-8 a c +b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}-8 a b \,c^{2} d^{2}+b^{3} c \,d^{2}+2 \left(-8 a c +b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e +28 a^{2} c^{2}-9 a \,b^{2} c +b^{4}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{16 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2} e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{-\frac{3 \left(8 a c -b^{2}\right) b \,c^{2} e^{6} x^{7}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{21 \left(8 a c -b^{2}\right) b \,c^{2} d \,e^{5} x^{6}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{\left(-504 a b \,c^{2} d^{2}+63 b^{3} c \,d^{2}+28 a^{2} c^{2}-49 a \,b^{2} c +6 b^{4}\right) c \,e^{4} x^{5}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{5 \left(-168 a b \,c^{2} d^{2}+21 b^{3} c \,d^{2}+28 a^{2} c^{2}-49 a \,b^{2} c +6 b^{4}\right) c d \,e^{3} x^{4}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{\left(840 a b \,c^{3} d^{4}-105 b^{3} c^{2} d^{4}-280 a^{2} c^{3} d^{2}+490 a \,b^{2} c^{2} d^{2}-60 b^{4} c \,d^{2}+4 a^{2} b \,c^{2}+20 a \,b^{3} c -3 b^{5}\right) e^{2} x^{3}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}-\frac{\left(504 a b \,c^{3} d^{4}-63 b^{3} c^{2} d^{4}-280 a^{2} c^{3} d^{2}+490 a \,b^{2} c^{2} d^{2}-60 b^{4} c \,d^{2}+12 a^{2} b \,c^{2}+60 a \,b^{3} c -9 b^{5}\right) d e \,x^{2}}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{\left(-168 a b \,c^{3} d^{6}+21 b^{3} c^{2} d^{6}+140 a^{2} c^{3} d^{4}-245 a \,b^{2} c^{2} d^{4}+30 b^{4} c \,d^{4}-12 a^{2} b \,c^{2} d^{2}-60 a \,b^{3} c \,d^{2}+9 b^{5} d^{2}+44 a^{3} c^{2}-37 a^{2} b^{2} c +5 a \,b^{4}\right) x}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2}}+\frac{\left(-24 a b \,c^{3} d^{6}+3 b^{3} c^{2} d^{6}+28 a^{2} c^{3} d^{4}-49 a \,b^{2} c^{2} d^{4}+6 b^{4} c \,d^{4}-4 a^{2} b \,c^{2} d^{2}-20 a \,b^{3} c \,d^{2}+3 b^{5} d^{2}+44 a^{3} c^{2}-37 a^{2} b^{2} c +5 a \,b^{4}\right) d}{8 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) a^{2} e}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2}}"," ",0,"(-3/8*c^2*e^6*b*(8*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2*x^7-21/8*c^2*d*e^5*b*(8*a*c-b^2)/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2*x^6+1/8*(-504*a*b*c^2*d^2+63*b^3*c*d^2+28*a^2*c^2-49*a*b^2*c+6*b^4)*c*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2*x^5+5/8*c*d*e^3*(-168*a*b*c^2*d^2+21*b^3*c*d^2+28*a^2*c^2-49*a*b^2*c+6*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2*x^4-1/8*e^2*(840*a*b*c^3*d^4-105*b^3*c^2*d^4-280*a^2*c^3*d^2+490*a*b^2*c^2*d^2-60*b^4*c*d^2+4*a^2*b*c^2+20*a*b^3*c-3*b^5)/a^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3-1/8*d*e*(504*a*b*c^3*d^4-63*b^3*c^2*d^4-280*a^2*c^3*d^2+490*a*b^2*c^2*d^2-60*b^4*c*d^2+12*a^2*b*c^2+60*a*b^3*c-9*b^5)/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2*x^2+1/8*(-168*a*b*c^3*d^6+21*b^3*c^2*d^6+140*a^2*c^3*d^4-245*a*b^2*c^2*d^4+30*b^4*c*d^4-12*a^2*b*c^2*d^2-60*a*b^3*c*d^2+9*b^5*d^2+44*a^3*c^2-37*a^2*b^2*c+5*a*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2*x+1/8*d/e*(-24*a*b*c^3*d^6+3*b^3*c^2*d^6+28*a^2*c^3*d^4-49*a*b^2*c^2*d^4+6*b^4*c*d^4-4*a^2*b*c^2*d^2-20*a*b^3*c*d^2+3*b^5*d^2+44*a^3*c^2-37*a^2*b^2*c+5*a*b^4)/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2)/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2+3/16/(16*a^2*c^2-8*a*b^2*c+b^4)/a^2/e*sum((b*c*e^2*(-8*a*c+b^2)*_R^2+2*b*c*d*e*(-8*a*c+b^2)*_R-8*a*b*c^2*d^2+b^3*c*d^2+28*a^2*c^2-9*a*b^2*c+b^4)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
635,1,4477,243,0.080000," ","int(1/(e*x+d)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"-1/2/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((c*e^3*(16*a^2*c^2-8*a*b^2*c+b^4)*_R^3+3*c*d*e^2*(16*a^2*c^2-8*a*b^2*c+b^4)*_R^2+e*(48*a^2*c^3*d^2-24*a*b^2*c^2*d^2+3*b^4*c*d^2+23*a^2*b*c^2-9*a*b^3*c+b^5)*_R+16*a^2*c^3*d^3-8*a*b^2*c^2*d^3+b^4*c*d^3+23*a^2*b*c^2*d-9*a*b^3*c*d+b^5*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^3*c-21/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b*c^3+3/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3*c^2-29/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2*c^2+4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4*c-6/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3*c-7/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b*c^3*d^6+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c^2*d^6-29/4/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c^2*d^4+1/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4*c*d^4-3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c*d^2-29/4/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^2-7/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*e^5*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e^5*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6-1/2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*c^2-1/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b*c^2-1/2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b*c^2*d^2+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^5+1/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^5+1/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^5*d^2+1/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^4+16/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+24/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*c^3*d^2+6*a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2+3/4/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4+4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4+16/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^3+4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*d^4-21/4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c+ln(e*x+d)/a^3/e-21/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*b*c^3*d*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+3/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*b^3*c^2*d*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-105/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b*d^2+15/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^3*d^2-70/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*d^3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b+10/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d^3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^3-29/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^2+4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^4-105/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*c^3*d^4+15/2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^3*c^2*d^4-87/2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2*c^2*d^2+6/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^4*c*d^2","C"
636,1,6821,437,0.071000," ","int(1/(e*x+d)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
637,1,5575,311,0.086000," ","int(1/(e*x+d)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
638,1,164,167,0.005000," ","int((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{f^{4} x}{c}+\frac{f^{4} \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b d e -b \,d^{2}-a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 c e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"f^4*x/c+1/2*f^4/c/e*sum((-_R^2*b*e^2-2*_R*b*d*e-b*d^2-a)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
639,1,154,79,0.005000," ","int((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{f^{3} \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} e^{3}+3 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} d \,e^{2}+3 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) d^{2} e +d^{3}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2*f^3/e*sum((_R^3*e^3+3*_R^2*d*e^2+3*_R*d^2*e+d^3)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
640,1,143,135,0.002000," ","int((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{f^{2} \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} e^{2}+2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) d e +d^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2*f^2/e*sum((_R^2*e^2+2*_R*d*e+d^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
641,1,130,40,0.005000," ","int((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{f \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e +d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2*f/e*sum((_R*e+d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
642,1,190,95,0.007000," ","int(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\ln \left(e x +d \right)}{a e f}+\frac{\left(-c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}-3 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}-c \,d^{3}+\left(-3 c \,d^{2}-b \right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e -b d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a e f \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/f/a/e*sum((-_R^3*c*e^3-3*_R^2*c*d*e^2-c*d^3+(-3*c*d^2-b)*_R*e-b*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))+ln(e*x+d)/a/e/f","C"
643,1,174,168,0.007000," ","int(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","\frac{\left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e -c \,d^{2}-b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a e \,f^{2} \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}-\frac{1}{\left(e x +d \right) a e \,f^{2}}"," ",0,"1/2/f^2/a/e*sum((-_R^2*c*e^2-2*_R*c*d*e-c*d^2-b)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/a/e/f^2/(e*x+d)","C"
644,1,222,123,0.008000," ","int(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","-\frac{b \ln \left(e x +d \right)}{a^{2} e \,f^{3}}-\frac{1}{2 \left(e x +d \right)^{2} a e \,f^{3}}+\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} b c \,e^{3}+3 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c d \,e^{2}+b c \,d^{3}-a c d +b^{2} d +\left(3 b c \,d^{2}-a c +b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a^{2} e \,f^{3} \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/f^3/a^2/e*sum((_R^3*b*c*e^3+3*_R^2*b*c*d*e^2+b*c*d^3-a*c*d+b^2*d+(3*b*c*d^2-a*c+b^2)*_R*e)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/2/a/e/f^3/(e*x+d)^2-b*ln(e*x+d)/a^2/e/f^3","C"
645,1,197,201,0.010000," ","int(1/(e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4),x)","-\frac{1}{3 \left(e x +d \right)^{3} a e \,f^{4}}+\frac{b}{\left(e x +d \right) a^{2} e \,f^{4}}+\frac{\left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}+2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e +b c \,d^{2}-a c +b^{2}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 a^{2} e \,f^{4} \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"1/2/f^4/a^2/e*sum((_R^2*b*c*e^2+2*_R*b*c*d*e+b*c*d^2-a*c+b^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/3/a/e/f^4/(e*x+d)^3+b/a^2/e/f^4/(e*x+d)","C"
646,1,695,236,0.018000," ","int((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{b \,e^{2} f^{4} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 b d e \,f^{4} x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{3 b \,d^{2} f^{4} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b \,d^{3} f^{4}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}-\frac{a \,f^{4} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{a d \,f^{4}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}+\frac{f^{4} \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b \,e^{2}-2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b d e -b \,d^{2}+2 a \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"-1/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*e^2/(4*a*c-b^2)*x^3-3/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*b*e/(4*a*c-b^2)*x^2-3/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b*d^2-f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*a-1/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*d^3/e*b-f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*d/e*a+1/4*f^4/(4*a*c-b^2)/e*sum((-_R^2*b*e^2-2*_R*b*d*e-b*d^2+2*a)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
647,1,500,97,0.020000," ","int((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{b e \,f^{3} x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b d \,f^{3} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}-\frac{b \,d^{2} f^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}+\frac{b \,f^{3} \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e -d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 \left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}-\frac{a \,f^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}"," ",0,"-1/2*f^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*e/(4*a*c-b^2)*x^2-f^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*d/(4*a*c-b^2)*x-1/2*f^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)/e*b*d^2-f^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)/e*a+1/2*f^3/(4*a*c-b^2)*b/e*sum((-_R*e-d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
648,1,693,222,0.017000," ","int((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{c \,e^{2} f^{2} x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{3 c d e \,f^{2} x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{3 c \,d^{2} f^{2} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c \,d^{3} f^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}+\frac{b \,f^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{b d \,f^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}+\frac{f^{2} \left(2 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}+4 \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e +2 c \,d^{2}-b \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*e^2/(4*a*c-b^2)*x^3+3*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*c*e/(4*a*c-b^2)*x^2+3*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*c*d^2+1/2*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b+f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*d^3/e*c+1/2*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*d/e*b+1/4*f^2/(4*a*c-b^2)/e*sum((2*_R^2*c*e^2+4*_R*c*d*e+2*c*d^2-b)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
649,1,484,92,0.024000," ","int((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{c e f \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{2 c d f x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right)}+\frac{c \,d^{2} f}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}+\frac{c f \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e +d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{\left(4 a c -b^{2}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}+\frac{b f}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e}"," ",0,"f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*e/(4*a*c-b^2)*x^2+2*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*d/(4*a*c-b^2)*x+f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)/e*c*d^2+1/2*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)/e*b+f*c/(4*a*c-b^2)/e*sum((_R*e+d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
650,1,714,164,0.030000," ","int(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{b c e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a f}-\frac{b c d x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a f}-\frac{b c \,d^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e f}-\frac{b^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e f}+\frac{c}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) e f}+\frac{\ln \left(e x +d \right)}{a^{2} e f}-\frac{\left(\left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} c \,e^{3}+3 \left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c d \,e^{2}+4 a \,c^{2} d^{3}-b^{2} c \,d^{3}+5 a b c d -b^{3} d +\left(12 a \,c^{2} d^{2}-3 b^{2} c \,d^{2}+5 a b c -b^{3}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 \left(4 a c -b^{2}\right) a^{2} e f \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"-1/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*c*e/(4*a*c-b^2)*x^2-1/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*c*d/(4*a*c-b^2)*x-1/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b*c*d^2+1/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*c-1/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b^2-1/2/f/a^2/(4*a*c-b^2)/e*sum(((4*a*c-b^2)*_R^3*c*e^3+3*(4*a*c-b^2)*_R^2*c*d*e^2+4*a*c^2*d^3-b^2*c*d^3+5*a*b*c*d-b^3*d+(12*a*c^2*d^2-3*b^2*c*d^2+5*a*b*c-b^3)*_R*e)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))+ln(e*x+d)/a^2/e/f","C"
651,1,1346,312,0.028000," ","int(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{c^{2} e^{2} x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{2}}+\frac{b^{2} c \,e^{2} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{2}}-\frac{3 c^{2} d e \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{2}}+\frac{3 b^{2} c d e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{2}}-\frac{3 c^{2} d^{2} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{2}}+\frac{3 b^{2} c \,d^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{2}}-\frac{c^{2} d^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e \,f^{2}}+\frac{b^{2} c \,d^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e \,f^{2}}-\frac{3 b c x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{2}}+\frac{b^{3} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{2}}-\frac{3 b c d}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e \,f^{2}}+\frac{b^{3} d}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e \,f^{2}}-\frac{\left(\left(10 a c -3 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} c \,e^{2}+10 a \,c^{2} d^{2}-3 b^{2} c \,d^{2}+2 \left(10 a c -3 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) c d e +13 a b c -3 b^{3}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) a^{2} e \,f^{2} \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}-\frac{1}{\left(e x +d \right) a^{2} e \,f^{2}}"," ",0,"-1/f^2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c^2*e^2/(4*a*c-b^2)*x^3+1/2/f^2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*e^2/(4*a*c-b^2)*x^3*b^2-3/f^2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*c^2*e/(4*a*c-b^2)*x^2+3/2/f^2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*c*e/(4*a*c-b^2)*x^2*b^2-3/f^2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*c^2*d^2+3/2/f^2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^2*c*d^2-3/2/f^2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b*c+1/2/f^2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^3-1/f^2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*c^2+1/2/f^2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*b^2*c-3/2/f^2/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b*c+1/2/f^2/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b^3-1/4/f^2/a^2/(4*a*c-b^2)/e*sum(((10*a*c-3*b^2)*_R^2*c*e^2+10*a*c^2*d^2-3*b^2*c*d^2+2*(10*a*c-3*b^2)*_R*c*d*e+13*a*b*c-3*b^3)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/f^2/a^2/e/(e*x+d)","C"
652,1,1047,221,0.034000," ","int(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","-\frac{c^{2} e \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{3}}+\frac{b^{2} c e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{3}}-\frac{2 c^{2} d x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{3}}+\frac{b^{2} c d x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{3}}-\frac{c^{2} d^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e \,f^{3}}+\frac{b^{2} c \,d^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e \,f^{3}}-\frac{3 b c}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e \,f^{3}}+\frac{b^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e \,f^{3}}-\frac{2 b \ln \left(e x +d \right)}{a^{3} e \,f^{3}}-\frac{1}{2 \left(e x +d \right)^{2} a^{2} e \,f^{3}}+\frac{\left(\left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3} b c \,e^{3}+3 \left(4 a c -b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c d \,e^{2}+4 a b \,c^{2} d^{3}-b^{3} c \,d^{3}-3 a^{2} c^{2} d +5 a \,b^{2} c d -b^{4} d +\left(12 a b \,c^{2} d^{2}-3 b^{3} c \,d^{2}-3 a^{2} c^{2}+5 a \,b^{2} c -b^{4}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{\left(4 a c -b^{2}\right) a^{3} e \,f^{3} \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"-1/f^3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c^2*e/(4*a*c-b^2)*x^2+1/2/f^3/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*e/(4*a*c-b^2)*x^2*b^2-2/f^3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c^2*d/(4*a*c-b^2)*x+1/f^3/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*c*d/(4*a*c-b^2)*x*b^2-1/f^3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*c^2*d^2+1/2/f^3/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b^2*c*d^2-3/2/f^3/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b*c+1/2/f^3/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/e/(4*a*c-b^2)*b^3+1/f^3/a^3/(4*a*c-b^2)/e*sum(((4*a*c-b^2)*_R^3*b*c*e^3+3*(4*a*c-b^2)*_R^2*b*c*d*e^2+4*a*b*c^2*d^3-b^3*c*d^3-3*a^2*c^2*d+5*a*b^2*c*d-b^4*d+(12*a*b*c^2*d^2-3*b^3*c*d^2-3*a^2*c^2+5*a*b^2*c-b^4)*_R*e)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/2/f^3/a^2/e/(e*x+d)^2-2*b*ln(e*x+d)/a^3/e/f^3","C"
653,1,1569,373,0.030000," ","int(1/(e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^2,x)","\frac{3 b \,c^{2} e^{2} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{4}}-\frac{b^{3} c \,e^{2} x^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} f^{4}}+\frac{9 b \,c^{2} d e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{4}}-\frac{3 b^{3} c d e \,x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} f^{4}}+\frac{9 b \,c^{2} d^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{4}}-\frac{3 b^{3} c \,d^{2} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} f^{4}}+\frac{3 b \,c^{2} d^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e \,f^{4}}-\frac{b^{3} c \,d^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} e \,f^{4}}-\frac{c^{2} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a \,f^{4}}+\frac{2 b^{2} c x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} f^{4}}-\frac{b^{4} x}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} f^{4}}-\frac{c^{2} d}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a e \,f^{4}}+\frac{2 b^{2} c d}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{2} e \,f^{4}}-\frac{b^{4} d}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right) \left(4 a c -b^{2}\right) a^{3} e \,f^{4}}-\frac{1}{3 \left(e x +d \right)^{3} a^{2} e \,f^{4}}+\frac{2 b}{\left(e x +d \right) a^{3} e \,f^{4}}+\frac{\left(\left(19 a c -5 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2} b c \,e^{2}+19 a b \,c^{2} d^{2}-5 b^{3} c \,d^{2}+2 \left(19 a c -5 b^{2}\right) \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) b c d e -14 a^{2} c^{2}+24 a \,b^{2} c -5 b^{4}\right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{4 \left(4 a c -b^{2}\right) a^{3} e \,f^{4} \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"3/2/f^4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b*c^2*e^2/(4*a*c-b^2)*x^3-1/2/f^4/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*b^3*c*e^2/(4*a*c-b^2)*x^3+9/2/f^4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*b*c^2*e/(4*a*c-b^2)*x^2-3/2/f^4/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d*b^3*c*e/(4*a*c-b^2)*x^2+9/2/f^4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b*c^2*d^2-3/2/f^4/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^3*c*d^2-1/f^4/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*c^2+2/f^4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^2*c-1/2/f^4/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)/(4*a*c-b^2)*x*b^4+3/2/f^4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*b*c^2-1/2/f^4/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d^3/e/(4*a*c-b^2)*b^3*c-1/f^4/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*c^2+2/f^4/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b^2*c-1/2/f^4/a^3/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)*d/e/(4*a*c-b^2)*b^4+1/4/f^4/a^3/(4*a*c-b^2)/e*sum(((19*a*c-5*b^2)*_R^2*b*c*e^2+19*a*b*c^2*d^2-5*b^3*c*d^2+2*(19*a*c-5*b^2)*_R*b*c*d*e-14*a^2*c^2+24*a*b^2*c-5*b^4)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-1/3/f^4/a^2/e/(e*x+d)^3+2/f^4/a^3*b/e/(e*x+d)","C"
654,1,3432,305,0.049000," ","int((e*f*x+d*f)^4/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"-95/4*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^2*c*d^2-2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a*b*c-63/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^5*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*c^2+5*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*c^2-95/4*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2*c-6*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b*c*d^2-2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d^3/e*a*b*c-105/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d^3*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b+5/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*a-95/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c*d*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^2-6*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a*b*c+3/16*f^4/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((-4*_R^2*b*c*e^2-8*_R*b*c*d*e-4*b*c*d^2+4*a*c+b^2)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))-15/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^3-21/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b*c^2*d^6+5/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*c^2*d^4-95/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2*c*d^4-3/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d^7/e*b*c^2+1/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d^5/e*a*c^2-19/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d^5/e*b^2*c-3/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d/e*a^2*c-3/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d/e*a*b^2+1/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5*a-19/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5*b^2-3/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e^6*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^7-5/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^3-15/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3*d^2-3/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a^2*c-3/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a*b^2-5/8*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*d^3/e*b^3-105/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b*c^2*d^4+5*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*a*c^2*d^2-21/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d*e^5*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6-63/2*f^4/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5*b*d^2","C"
655,1,2181,151,0.046000," ","int((e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","-\frac{3 b \,c^{2} e^{5} f^{3} x^{6}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 b \,c^{2} d \,e^{4} f^{3} x^{5}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{45 b \,c^{2} d^{2} e^{3} f^{3} x^{4}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{30 b \,c^{2} d^{3} e^{2} f^{3} x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 b^{2} c \,e^{3} f^{3} x^{4}}{4 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{45 b \,c^{2} d^{4} e \,f^{3} x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 b^{2} c d \,e^{2} f^{3} x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 b \,c^{2} d^{5} f^{3} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{27 b^{2} c \,d^{2} e \,f^{3} x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{3 b \,c^{2} d^{6} f^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}-\frac{9 b^{2} c \,d^{3} f^{3} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{5 a b c e \,f^{3} x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{b^{3} e \,f^{3} x^{2}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{9 b^{2} c \,d^{4} f^{3}}{4 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}-\frac{5 a b c d \,f^{3} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{b^{3} d \,f^{3} x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}-\frac{5 a b c \,d^{2} f^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}-\frac{b^{3} d^{2} f^{3}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}-\frac{2 a^{2} c \,f^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}-\frac{a \,b^{2} f^{3}}{4 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}+\frac{3 b c \,f^{3} \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e -d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{2 \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," 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656,1,4751,331,0.049000," ","int((e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," 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6*a^2*c^2-8*a*b^2*c+b^4)/a*x^7*b^2+27/2*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d*e/(16*a^2*c^2-8*a*b^2*c+b^4)*a*x^2*c^2+3/8*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d*e/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^2*b^4+7/8*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x*b^2*c^2*d^6+5/4*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x*b^3*c*d^4+5/2*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^3*b^3*c*d^2+21/8*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^5*e/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^2*b^2*c^2+5/2*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3*e/(16*a^2*c^2-8*a*b^2*c+b^4)/a*x^2*b^3*c-1/8*f^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3+1/16*f^2/(16*a^2*c^2-8*a*b^2*c+b^4)/a/e*sum(((20*a*c+b^2)*_R^2*c*e^2+20*a*c^2*d^2+b^2*c*d^2+2*(20*a*c+b^2)*_R*c*d*e-16*a*b*c+b^3)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
657,1,2132,145,0.053000," ","int((e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\frac{3 c^{3} e^{5} f \,x^{6}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{18 c^{3} d \,e^{4} f \,x^{5}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{45 c^{3} d^{2} e^{3} f \,x^{4}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{60 c^{3} d^{3} e^{2} f \,x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{9 b \,c^{2} e^{3} f \,x^{4}}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{45 c^{3} d^{4} e f \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{18 b \,c^{2} d \,e^{2} f \,x^{3}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{18 c^{3} d^{5} f x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{27 b \,c^{2} d^{2} e f \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{3 c^{3} d^{6} f}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}+\frac{18 b \,c^{2} d^{3} f x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{5 a \,c^{2} e f \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{b^{2} c e f \,x^{2}}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{9 b \,c^{2} d^{4} f}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}+\frac{10 a \,c^{2} d f x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{2 b^{2} c d f x}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right)}+\frac{5 a \,c^{2} d^{2} f}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}+\frac{b^{2} c \,d^{2} f}{\left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}+\frac{5 a b c f}{2 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}-\frac{b^{3} f}{4 \left(c \,e^{4} x^{4}+4 c d \,e^{3} x^{3}+6 c \,d^{2} e^{2} x^{2}+4 c \,d^{3} e x +b \,e^{2} x^{2}+c \,d^{4}+2 b d e x +b \,d^{2}+a \right)^{2} \left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e}+\frac{3 c^{2} f \left(\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right) e +d \right) \ln \left(-\RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+x \right)}{\left(16 a^{2} c^{2}-8 a \,b^{2} c +b^{4}\right) e \left(2 c \,e^{3} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{3}+6 c d \,e^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)^{2}+6 e c \,d^{2} \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+2 c \,d^{3}+b e \RootOf \left(\textit{\_Z}^{4} c \,e^{4}+4 \textit{\_Z}^{3} c d \,e^{3}+c \,d^{4}+b \,d^{2}+\left(6 c \,d^{2} e^{2}+b \,e^{2}\right) \textit{\_Z}^{2}+\left(4 c \,d^{3} e +2 d e b \right) \textit{\_Z} +a \right)+b d \right)}"," ",0,"3*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*e^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+18*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^4*c^3*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+45*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*d^2+9/2*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b+60*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*d^3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+18*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b+45*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*d^4+27*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*d^2+5*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*a+f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2+18*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*d^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x+18*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b+10*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*a+2*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2+3*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*c^3*d^6+9/2*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*b*c^2*d^4+5*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*a*c^2*d^2+f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*b^2*c*d^2+5/2*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*a*b*c-1/4*f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*b^3+3*f*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((_R*e+d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))","C"
658,1,4606,258,0.075000," ","int(1/(e*f*x+d*f)/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"-1/2/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*c^2-1/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b*c^2-1/2/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b*c^2*d^2+1/2/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^5+1/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^5+1/2/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^5*d^2+ln(e*x+d)/a^3/e/f-7/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*e^5*b/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+1/2/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*e^5*b^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^6+6/f*a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^2+3/4/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4+4/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4+16/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*c^3+4/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*c^3*d^4-21/4/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c-1/2/f/a^3/(16*a^2*c^2-8*a*b^2*c+b^4)/e*sum((c*e^3*(16*a^2*c^2-8*a*b^2*c+b^4)*_R^3+3*c*d*e^2*(16*a^2*c^2-8*a*b^2*c+b^4)*_R^2+e*(48*a^2*c^3*d^2-24*a*b^2*c^2*d^2+3*b^4*c*d^2+23*a^2*b*c^2-9*a*b^3*c+b^5)*_R+16*a^2*c^3*d^3-8*a*b^2*c^2*d^3+b^4*c*d^3+23*a^2*b*c^2*d-9*a*b^3*c*d+b^5*d)/(2*_R^3*c*e^3+6*_R^2*c*d*e^2+6*_R*c*d^2*e+2*c*d^3+_R*b*e+b*d)*ln(-_R+x),_R=RootOf(_Z^4*c*e^4+4*_Z^3*c*d*e^3+c*d^4+b*d^2+(6*c*d^2*e^2+b*e^2)*_Z^2+(4*c*d^3*e+2*b*d*e)*_Z+a))+10/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d^3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^3-29/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^2*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^2+4/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b^4-105/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b*c^3*d^4+15/2/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^3*c^2*d^4-87/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^2*c^2*d^2+6/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^4*c*d^2-21/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*b*c^3*d*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5+3/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*b^3*c^2*d*e^4/(16*a^2*c^2-8*a*b^2*c+b^4)*x^5-105/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b*d^2+15/2/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^3*d^2-70/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*d^3*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3*b+16/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*c^3*d*e^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^3+24/f/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*c^3*d^2+1/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^4-3/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e/(16*a^2*c^2-8*a*b^2*c+b^4)*x^2*b^3*c-21/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b*c^3+3/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^5/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3*c^2-29/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^2*c^2+4/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d^3/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^4*c-6/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*d/(16*a^2*c^2-8*a*b^2*c+b^4)*x*b^3*c-7/2/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b*c^3*d^6+1/2/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c^2*d^6-29/4/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^2*c^2*d^4+1/f/a^2/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^4*c*d^4-3/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2/e/(16*a^2*c^2-8*a*b^2*c+b^4)*b^3*c*d^2-29/4/f/a/(c*e^4*x^4+4*c*d*e^3*x^3+6*c*d^2*e^2*x^2+4*c*d^3*e*x+b*e^2*x^2+c*d^4+2*b*d*e*x+b*d^2+a)^2*e^3*c^2/(16*a^2*c^2-8*a*b^2*c+b^4)*x^4*b^2","C"
659,1,7019,452,0.070000," ","int(1/(e*f*x+d*f)^2/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
660,1,5737,329,0.082000," ","int(1/(e*f*x+d*f)^3/(a+b*(e*x+d)^2+c*(e*x+d)^4)^3,x)","\text{output too large to display}"," ",0,"result too large to display","C"
661,0,0,294,0.054000," ","int(x/(a+b*(e*x+d)^3+c*(e*x+d)^6)^(1/2),x)","\int \frac{x}{\sqrt{a +\left(e x +d \right)^{3} b +\left(e x +d \right)^{6} c}}\, dx"," ",0,"int(x/(a+b*(e*x+d)^3+c*(e*x+d)^6)^(1/2),x)","F"
662,0,0,344,0.058000," ","int(x^2/(a+(e*x+d)^3*b+(e*x+d)^6*c)^(1/2),x)","\int \frac{x^{2}}{\sqrt{a +\left(e x +d \right)^{3} b +\left(e x +d \right)^{6} c}}\, dx"," ",0,"int(x^2/(a+(e*x+d)^3*b+(e*x+d)^6*c)^(1/2),x)","F"
663,1,105,28,0.003000," ","int((3*x+2)^6*(1+(3*x+2)^7+(3*x+2)^14),x)","\frac{1162261467}{7} x^{21}+2324522934 x^{20}+15496819560 x^{19}+65431015920 x^{18}+196293047760 x^{17}+444930908256 x^{16}+790988281344 x^{15}+\frac{15819767221203}{14} x^{14}+1318314865122 x^{13}+1269491970942 x^{12}+1015602174288 x^{11}+677082445416 x^{10}+376174427616 x^{9}+173635132896 x^{8}+66158154783 x^{7}+20588764518 x^{6}+5149786572 x^{5}+1010576952 x^{4}+149902032 x^{3}+15808800 x^{2}+1056832 x"," ",0,"1162261467/7*x^21+2324522934*x^20+15496819560*x^19+65431015920*x^18+196293047760*x^17+444930908256*x^16+790988281344*x^15+15819767221203/14*x^14+1318314865122*x^13+1269491970942*x^12+1015602174288*x^11+677082445416*x^10+376174427616*x^9+173635132896*x^8+66158154783*x^7+20588764518*x^6+5149786572*x^5+1010576952*x^4+149902032*x^3+15808800*x^2+1056832*x","B"
664,1,175,46,0.003000," ","int((3*x+2)^6*(1+(3*x+2)^7+(3*x+2)^14)^2,x)","\frac{16677181699666569}{35} x^{35}+11118121133111046 x^{34}+126005372841925188 x^{33}+924039400840784712 x^{32}+4928210137817518464 x^{31}+\frac{101849676181562048256}{5} x^{30}+67899784121041365504 x^{29}+\frac{2625458326972530284475}{14} x^{28}+437576396725285446564 x^{27}+875152864622814086340 x^{26}+\frac{7584660010542711771792}{5} x^{25}+2298383223254096766840 x^{24}+3064515076512846852480 x^{23}+3614565944605222108800 x^{22}+\frac{26506949038858918036881}{7} x^{21}+3534290697929473864098 x^{20}+2945285062308448290360 x^{19}+2194577166014752240080 x^{18}+1463104032160519033200 x^{17}+872775774067455498528 x^{16}+465517091041681015296 x^{15}+221699757548270194389 x^{14}+94069263918929616324 x^{13}+35454069480572048124 x^{12}+11821487501620716192 x^{11}+\frac{17344958593049772048}{5} x^{10}+889942562270387136 x^{9}+197897276851452864 x^{8}+37727143432895007 x^{7}+6077684727888102 x^{6}+\frac{4057390785756924}{5} x^{5}+87406679578680 x^{4}+7299544818384 x^{3}+443569828128 x^{2}+17451466816 x"," ",0,"17451466816*x+16677181699666569/35*x^35+67899784121041365504*x^29+2625458326972530284475/14*x^28+875152864622814086340*x^26+2298383223254096766840*x^24+3614565944605222108800*x^22+3534290697929473864098*x^20+2194577166014752240080*x^18+872775774067455498528*x^16+11118121133111046*x^34+126005372841925188*x^33+924039400840784712*x^32+4928210137817518464*x^31+101849676181562048256/5*x^30+437576396725285446564*x^27+889942562270387136*x^9+11821487501620716192*x^11+94069263918929616324*x^13+465517091041681015296*x^15+1463104032160519033200*x^17+2945285062308448290360*x^19+26506949038858918036881/7*x^21+3064515076512846852480*x^23+7584660010542711771792/5*x^25+87406679578680*x^4+443569828128*x^2+6077684727888102*x^6+197897276851452864*x^8+17344958593049772048/5*x^10+35454069480572048124*x^12+221699757548270194389*x^14+7299544818384*x^3+4057390785756924/5*x^5+37727143432895007*x^7","B"