1,1,33,0,0.0325437,"\int x^2 \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[x^2*(a + b*x^3)*(A + B*x^3),x]","\frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9","\frac{1}{6} x^6 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{9} b B x^9",1,"(a*A*x^3)/3 + ((A*b + a*B)*x^6)/6 + (b*B*x^9)/9","A",3,2,18,0.1111,1,"{444, 43}"
2,1,33,0,0.0169825,"\int x \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[x*(a + b*x^3)*(A + B*x^3),x]","\frac{1}{5} x^5 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{8} b B x^8","\frac{1}{5} x^5 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{8} b B x^8",1,"(a*A*x^2)/2 + ((A*b + a*B)*x^5)/5 + (b*B*x^8)/8","A",2,1,16,0.06250,1,"{448}"
3,1,28,0,0.0129807,"\int \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[(a + b*x^3)*(A + B*x^3),x]","\frac{1}{4} x^4 (a B+A b)+a A x+\frac{1}{7} b B x^7","\frac{1}{4} x^4 (a B+A b)+a A x+\frac{1}{7} b B x^7",1,"a*A*x + ((A*b + a*B)*x^4)/4 + (b*B*x^7)/7","A",2,1,15,0.06667,1,"{373}"
4,1,29,0,0.0213559,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x,x]","\frac{1}{3} x^3 (a B+A b)+a A \log (x)+\frac{1}{6} b B x^6","\frac{1}{3} x^3 (a B+A b)+a A \log (x)+\frac{1}{6} b B x^6",1,"((A*b + a*B)*x^3)/3 + (b*B*x^6)/6 + a*A*Log[x]","A",3,2,18,0.1111,1,"{446, 76}"
5,1,31,0,0.0153374,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^2} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^2,x]","\frac{1}{2} x^2 (a B+A b)-\frac{a A}{x}+\frac{1}{5} b B x^5","\frac{1}{2} x^2 (a B+A b)-\frac{a A}{x}+\frac{1}{5} b B x^5",1,"-((a*A)/x) + ((A*b + a*B)*x^2)/2 + (b*B*x^5)/5","A",2,1,18,0.05556,1,"{448}"
6,1,28,0,0.0159127,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^3} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^3,x]","x (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{4} b B x^4","x (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{4} b B x^4",1,"-(a*A)/(2*x^2) + (A*b + a*B)*x + (b*B*x^4)/4","A",2,1,18,0.05556,1,"{448}"
7,1,29,0,0.0215009,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^4} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^4,x]","\log (x) (a B+A b)-\frac{a A}{3 x^3}+\frac{1}{3} b B x^3","\log (x) (a B+A b)-\frac{a A}{3 x^3}+\frac{1}{3} b B x^3",1,"-(a*A)/(3*x^3) + (b*B*x^3)/3 + (A*b + a*B)*Log[x]","A",3,2,18,0.1111,1,"{446, 76}"
8,1,31,0,0.0173916,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^5} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^5,x]","-\frac{a B+A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2","-\frac{a B+A b}{x}-\frac{a A}{4 x^4}+\frac{1}{2} b B x^2",1,"-(a*A)/(4*x^4) - (A*b + a*B)/x + (b*B*x^2)/2","A",2,1,18,0.05556,1,"{448}"
9,1,28,0,0.0164566,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^6} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^6,x]","-\frac{a B+A b}{2 x^2}-\frac{a A}{5 x^5}+b B x","-\frac{a B+A b}{2 x^2}-\frac{a A}{5 x^5}+b B x",1,"-(a*A)/(5*x^5) - (A*b + a*B)/(2*x^2) + b*B*x","A",2,1,18,0.05556,1,"{448}"
10,1,29,0,0.0211706,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^7} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^7,x]","-\frac{a B+A b}{3 x^3}-\frac{a A}{6 x^6}+b B \log (x)","-\frac{a B+A b}{3 x^3}-\frac{a A}{6 x^6}+b B \log (x)",1,"-(a*A)/(6*x^6) - (A*b + a*B)/(3*x^3) + b*B*Log[x]","A",3,2,18,0.1111,1,"{446, 76}"
11,1,42,0,0.0721012,"\int x^2 \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[x^2*(a + b*x^3)^2*(A + B*x^3),x]","\frac{\left(a+b x^3\right)^3 (A b-a B)}{9 b^2}+\frac{B \left(a+b x^3\right)^4}{12 b^2}","\frac{\left(a+b x^3\right)^3 (A b-a B)}{9 b^2}+\frac{B \left(a+b x^3\right)^4}{12 b^2}",1,"((A*b - a*B)*(a + b*x^3)^3)/(9*b^2) + (B*(a + b*x^3)^4)/(12*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
12,1,55,0,0.0337621,"\int x \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[x*(a + b*x^3)^2*(A + B*x^3),x]","\frac{1}{2} a^2 A x^2+\frac{1}{8} b x^8 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{11} b^2 B x^{11}","\frac{1}{2} a^2 A x^2+\frac{1}{8} b x^8 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{11} b^2 B x^{11}",1,"(a^2*A*x^2)/2 + (a*(2*A*b + a*B)*x^5)/5 + (b*(A*b + 2*a*B)*x^8)/8 + (b^2*B*x^11)/11","A",2,1,18,0.05556,1,"{448}"
13,1,50,0,0.0254353,"\int \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[(a + b*x^3)^2*(A + B*x^3),x]","a^2 A x+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{10} b^2 B x^{10}","a^2 A x+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{10} b^2 B x^{10}",1,"a^2*A*x + (a*(2*A*b + a*B)*x^4)/4 + (b*(A*b + 2*a*B)*x^7)/7 + (b^2*B*x^10)/10","A",2,1,17,0.05882,1,"{373}"
14,1,46,0,0.0326931,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x,x]","a^2 A \log (x)+\frac{2}{3} a A b x^3+\frac{B \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} A b^2 x^6","a^2 A \log (x)+\frac{2}{3} a A b x^3+\frac{B \left(a+b x^3\right)^3}{9 b}+\frac{1}{6} A b^2 x^6",1,"(2*a*A*b*x^3)/3 + (A*b^2*x^6)/6 + (B*(a + b*x^3)^3)/(9*b) + a^2*A*Log[x]","A",4,3,20,0.1500,1,"{446, 80, 43}"
15,1,53,0,0.0282968,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^2} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^2,x]","-\frac{a^2 A}{x}+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{8} b^2 B x^8","-\frac{a^2 A}{x}+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{8} b^2 B x^8",1,"-((a^2*A)/x) + (a*(2*A*b + a*B)*x^2)/2 + (b*(A*b + 2*a*B)*x^5)/5 + (b^2*B*x^8)/8","A",2,1,20,0.05000,1,"{448}"
16,1,50,0,0.0266763,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^3} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^3,x]","-\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7","-\frac{a^2 A}{2 x^2}+\frac{1}{4} b x^4 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{7} b^2 B x^7",1,"-(a^2*A)/(2*x^2) + a*(2*A*b + a*B)*x + (b*(A*b + 2*a*B)*x^4)/4 + (b^2*B*x^7)/7","A",2,1,20,0.05000,1,"{448}"
17,1,51,0,0.0500513,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^4} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^4,x]","-\frac{a^2 A}{3 x^3}+\frac{1}{3} b x^3 (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{6} b^2 B x^6","-\frac{a^2 A}{3 x^3}+\frac{1}{3} b x^3 (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{6} b^2 B x^6",1,"-(a^2*A)/(3*x^3) + (b*(A*b + 2*a*B)*x^3)/3 + (b^2*B*x^6)/6 + a*(2*A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
18,1,53,0,0.030959,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^5} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^5,x]","-\frac{a^2 A}{4 x^4}+\frac{1}{2} b x^2 (2 a B+A b)-\frac{a (a B+2 A b)}{x}+\frac{1}{5} b^2 B x^5","-\frac{a^2 A}{4 x^4}+\frac{1}{2} b x^2 (2 a B+A b)-\frac{a (a B+2 A b)}{x}+\frac{1}{5} b^2 B x^5",1,"-(a^2*A)/(4*x^4) - (a*(2*A*b + a*B))/x + (b*(A*b + 2*a*B)*x^2)/2 + (b^2*B*x^5)/5","A",2,1,20,0.05000,1,"{448}"
19,1,50,0,0.0283431,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^6} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^6,x]","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{2 x^2}+b x (2 a B+A b)+\frac{1}{4} b^2 B x^4",1,"-(a^2*A)/(5*x^5) - (a*(2*A*b + a*B))/(2*x^2) + b*(A*b + 2*a*B)*x + (b^2*B*x^4)/4","A",2,1,20,0.05000,1,"{448}"
20,1,51,0,0.0375813,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^7} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^7,x]","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{3 x^3}+b \log (x) (2 a B+A b)+\frac{1}{3} b^2 B x^3","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{3 x^3}+b \log (x) (2 a B+A b)+\frac{1}{3} b^2 B x^3",1,"-(a^2*A)/(6*x^6) - (a*(2*A*b + a*B))/(3*x^3) + (b^2*B*x^3)/3 + b*(A*b + 2*a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
21,1,53,0,0.0287355,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^8} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^8,x]","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{x}+\frac{1}{2} b^2 B x^2","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{x}+\frac{1}{2} b^2 B x^2",1,"-(a^2*A)/(7*x^7) - (a*(2*A*b + a*B))/(4*x^4) - (b*(A*b + 2*a*B))/x + (b^2*B*x^2)/2","A",2,1,20,0.05000,1,"{448}"
22,1,50,0,0.0287994,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^9} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^9,x]","-\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x","-\frac{a^2 A}{8 x^8}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B x",1,"-(a^2*A)/(8*x^8) - (a*(2*A*b + a*B))/(5*x^5) - (b*(A*b + 2*a*B))/(2*x^2) + b^2*B*x","A",2,1,20,0.05000,1,"{448}"
23,1,117,0,0.0975507,"\int x^9 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^9*(a + b*x^3)^5*(A + B*x^3),x]","\frac{10}{19} a^2 b^2 x^{19} (a B+A b)+\frac{5}{16} a^3 b x^{16} (a B+2 A b)+\frac{1}{13} a^4 x^{13} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{25} b^4 x^{25} (5 a B+A b)+\frac{5}{22} a b^3 x^{22} (2 a B+A b)+\frac{1}{28} b^5 B x^{28}","\frac{10}{19} a^2 b^2 x^{19} (a B+A b)+\frac{5}{16} a^3 b x^{16} (a B+2 A b)+\frac{1}{13} a^4 x^{13} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{25} b^4 x^{25} (5 a B+A b)+\frac{5}{22} a b^3 x^{22} (2 a B+A b)+\frac{1}{28} b^5 B x^{28}",1,"(a^5*A*x^10)/10 + (a^4*(5*A*b + a*B)*x^13)/13 + (5*a^3*b*(2*A*b + a*B)*x^16)/16 + (10*a^2*b^2*(A*b + a*B)*x^19)/19 + (5*a*b^3*(A*b + 2*a*B)*x^22)/22 + (b^4*(A*b + 5*a*B)*x^25)/25 + (b^5*B*x^28)/28","A",2,1,20,0.05000,1,"{448}"
24,1,95,0,0.2366157,"\int x^8 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^8*(a + b*x^3)^5*(A + B*x^3),x]","\frac{a^2 \left(a+b x^3\right)^6 (A b-a B)}{18 b^4}+\frac{\left(a+b x^3\right)^8 (A b-3 a B)}{24 b^4}-\frac{a \left(a+b x^3\right)^7 (2 A b-3 a B)}{21 b^4}+\frac{B \left(a+b x^3\right)^9}{27 b^4}","\frac{a^2 \left(a+b x^3\right)^6 (A b-a B)}{18 b^4}+\frac{\left(a+b x^3\right)^8 (A b-3 a B)}{24 b^4}-\frac{a \left(a+b x^3\right)^7 (2 A b-3 a B)}{21 b^4}+\frac{B \left(a+b x^3\right)^9}{27 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x^3)^6)/(18*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x^3)^7)/(21*b^4) + ((A*b - 3*a*B)*(a + b*x^3)^8)/(24*b^4) + (B*(a + b*x^3)^9)/(27*b^4)","A",3,2,20,0.1000,1,"{446, 76}"
25,1,117,0,0.0749274,"\int x^7 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^7*(a + b*x^3)^5*(A + B*x^3),x]","\frac{10}{17} a^2 b^2 x^{17} (a B+A b)+\frac{5}{14} a^3 b x^{14} (a B+2 A b)+\frac{1}{11} a^4 x^{11} (a B+5 A b)+\frac{1}{8} a^5 A x^8+\frac{1}{23} b^4 x^{23} (5 a B+A b)+\frac{1}{4} a b^3 x^{20} (2 a B+A b)+\frac{1}{26} b^5 B x^{26}","\frac{10}{17} a^2 b^2 x^{17} (a B+A b)+\frac{5}{14} a^3 b x^{14} (a B+2 A b)+\frac{1}{11} a^4 x^{11} (a B+5 A b)+\frac{1}{8} a^5 A x^8+\frac{1}{23} b^4 x^{23} (5 a B+A b)+\frac{1}{4} a b^3 x^{20} (2 a B+A b)+\frac{1}{26} b^5 B x^{26}",1,"(a^5*A*x^8)/8 + (a^4*(5*A*b + a*B)*x^11)/11 + (5*a^3*b*(2*A*b + a*B)*x^14)/14 + (10*a^2*b^2*(A*b + a*B)*x^17)/17 + (a*b^3*(A*b + 2*a*B)*x^20)/4 + (b^4*(A*b + 5*a*B)*x^23)/23 + (b^5*B*x^26)/26","A",2,1,20,0.05000,1,"{448}"
26,1,117,0,0.0681405,"\int x^6 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^6*(a + b*x^3)^5*(A + B*x^3),x]","\frac{5}{8} a^2 b^2 x^{16} (a B+A b)+\frac{5}{13} a^3 b x^{13} (a B+2 A b)+\frac{1}{10} a^4 x^{10} (a B+5 A b)+\frac{1}{7} a^5 A x^7+\frac{1}{22} b^4 x^{22} (5 a B+A b)+\frac{5}{19} a b^3 x^{19} (2 a B+A b)+\frac{1}{25} b^5 B x^{25}","\frac{5}{8} a^2 b^2 x^{16} (a B+A b)+\frac{5}{13} a^3 b x^{13} (a B+2 A b)+\frac{1}{10} a^4 x^{10} (a B+5 A b)+\frac{1}{7} a^5 A x^7+\frac{1}{22} b^4 x^{22} (5 a B+A b)+\frac{5}{19} a b^3 x^{19} (2 a B+A b)+\frac{1}{25} b^5 B x^{25}",1,"(a^5*A*x^7)/7 + (a^4*(5*A*b + a*B)*x^10)/10 + (5*a^3*b*(2*A*b + a*B)*x^13)/13 + (5*a^2*b^2*(A*b + a*B)*x^16)/8 + (5*a*b^3*(A*b + 2*a*B)*x^19)/19 + (b^4*(A*b + 5*a*B)*x^22)/22 + (b^5*B*x^25)/25","A",2,1,20,0.05000,1,"{448}"
27,1,67,0,0.1481731,"\int x^5 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^5*(a + b*x^3)^5*(A + B*x^3),x]","\frac{\left(a+b x^3\right)^7 (A b-2 a B)}{21 b^3}-\frac{a \left(a+b x^3\right)^6 (A b-a B)}{18 b^3}+\frac{B \left(a+b x^3\right)^8}{24 b^3}","\frac{\left(a+b x^3\right)^7 (A b-2 a B)}{21 b^3}-\frac{a \left(a+b x^3\right)^6 (A b-a B)}{18 b^3}+\frac{B \left(a+b x^3\right)^8}{24 b^3}",1,"-(a*(A*b - a*B)*(a + b*x^3)^6)/(18*b^3) + ((A*b - 2*a*B)*(a + b*x^3)^7)/(21*b^3) + (B*(a + b*x^3)^8)/(24*b^3)","A",3,2,20,0.1000,1,"{446, 76}"
28,1,117,0,0.0696903,"\int x^4 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^4*(a + b*x^3)^5*(A + B*x^3),x]","\frac{5}{7} a^2 b^2 x^{14} (a B+A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{1}{8} a^4 x^8 (a B+5 A b)+\frac{1}{5} a^5 A x^5+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{23} b^5 B x^{23}","\frac{5}{7} a^2 b^2 x^{14} (a B+A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{1}{8} a^4 x^8 (a B+5 A b)+\frac{1}{5} a^5 A x^5+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{23} b^5 B x^{23}",1,"(a^5*A*x^5)/5 + (a^4*(5*A*b + a*B)*x^8)/8 + (5*a^3*b*(2*A*b + a*B)*x^11)/11 + (5*a^2*b^2*(A*b + a*B)*x^14)/7 + (5*a*b^3*(A*b + 2*a*B)*x^17)/17 + (b^4*(A*b + 5*a*B)*x^20)/20 + (b^5*B*x^23)/23","A",2,1,20,0.05000,1,"{448}"
29,1,117,0,0.065377,"\int x^3 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^3*(a + b*x^3)^5*(A + B*x^3),x]","\frac{10}{13} a^2 b^2 x^{13} (a B+A b)+\frac{1}{2} a^3 b x^{10} (a B+2 A b)+\frac{1}{7} a^4 x^7 (a B+5 A b)+\frac{1}{4} a^5 A x^4+\frac{1}{19} b^4 x^{19} (5 a B+A b)+\frac{5}{16} a b^3 x^{16} (2 a B+A b)+\frac{1}{22} b^5 B x^{22}","\frac{10}{13} a^2 b^2 x^{13} (a B+A b)+\frac{1}{2} a^3 b x^{10} (a B+2 A b)+\frac{1}{7} a^4 x^7 (a B+5 A b)+\frac{1}{4} a^5 A x^4+\frac{1}{19} b^4 x^{19} (5 a B+A b)+\frac{5}{16} a b^3 x^{16} (2 a B+A b)+\frac{1}{22} b^5 B x^{22}",1,"(a^5*A*x^4)/4 + (a^4*(5*A*b + a*B)*x^7)/7 + (a^3*b*(2*A*b + a*B)*x^10)/2 + (10*a^2*b^2*(A*b + a*B)*x^13)/13 + (5*a*b^3*(A*b + 2*a*B)*x^16)/16 + (b^4*(A*b + 5*a*B)*x^19)/19 + (b^5*B*x^22)/22","A",2,1,20,0.05000,1,"{448}"
30,1,42,0,0.068837,"\int x^2 \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^2*(a + b*x^3)^5*(A + B*x^3),x]","\frac{\left(a+b x^3\right)^6 (A b-a B)}{18 b^2}+\frac{B \left(a+b x^3\right)^7}{21 b^2}","\frac{\left(a+b x^3\right)^6 (A b-a B)}{18 b^2}+\frac{B \left(a+b x^3\right)^7}{21 b^2}",1,"((A*b - a*B)*(a + b*x^3)^6)/(18*b^2) + (B*(a + b*x^3)^7)/(21*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
31,1,117,0,0.0632876,"\int x \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x*(a + b*x^3)^5*(A + B*x^3),x]","\frac{10}{11} a^2 b^2 x^{11} (a B+A b)+\frac{5}{8} a^3 b x^8 (a B+2 A b)+\frac{1}{5} a^4 x^5 (a B+5 A b)+\frac{1}{2} a^5 A x^2+\frac{1}{17} b^4 x^{17} (5 a B+A b)+\frac{5}{14} a b^3 x^{14} (2 a B+A b)+\frac{1}{20} b^5 B x^{20}","\frac{10}{11} a^2 b^2 x^{11} (a B+A b)+\frac{5}{8} a^3 b x^8 (a B+2 A b)+\frac{1}{5} a^4 x^5 (a B+5 A b)+\frac{1}{2} a^5 A x^2+\frac{1}{17} b^4 x^{17} (5 a B+A b)+\frac{5}{14} a b^3 x^{14} (2 a B+A b)+\frac{1}{20} b^5 B x^{20}",1,"(a^5*A*x^2)/2 + (a^4*(5*A*b + a*B)*x^5)/5 + (5*a^3*b*(2*A*b + a*B)*x^8)/8 + (10*a^2*b^2*(A*b + a*B)*x^11)/11 + (5*a*b^3*(A*b + 2*a*B)*x^14)/14 + (b^4*(A*b + 5*a*B)*x^17)/17 + (b^5*B*x^20)/20","A",2,1,18,0.05556,1,"{448}"
32,1,109,0,0.0554363,"\int \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[(a + b*x^3)^5*(A + B*x^3),x]","a^2 b^2 x^{10} (a B+A b)+\frac{5}{7} a^3 b x^7 (a B+2 A b)+\frac{1}{4} a^4 x^4 (a B+5 A b)+a^5 A x+\frac{1}{16} b^4 x^{16} (5 a B+A b)+\frac{5}{13} a b^3 x^{13} (2 a B+A b)+\frac{1}{19} b^5 B x^{19}","a^2 b^2 x^{10} (a B+A b)+\frac{5}{7} a^3 b x^7 (a B+2 A b)+\frac{1}{4} a^4 x^4 (a B+5 A b)+a^5 A x+\frac{1}{16} b^4 x^{16} (5 a B+A b)+\frac{5}{13} a b^3 x^{13} (2 a B+A b)+\frac{1}{19} b^5 B x^{19}",1,"a^5*A*x + (a^4*(5*A*b + a*B)*x^4)/4 + (5*a^3*b*(2*A*b + a*B)*x^7)/7 + a^2*b^2*(A*b + a*B)*x^10 + (5*a*b^3*(A*b + 2*a*B)*x^13)/13 + (b^4*(A*b + 5*a*B)*x^16)/16 + (b^5*B*x^19)/19","A",2,1,17,0.05882,1,"{373}"
33,1,88,0,0.0672439,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x,x]","\frac{10}{9} a^2 A b^3 x^9+\frac{5}{3} a^3 A b^2 x^6+\frac{5}{3} a^4 A b x^3+a^5 A \log (x)+\frac{5}{12} a A b^4 x^{12}+\frac{B \left(a+b x^3\right)^6}{18 b}+\frac{1}{15} A b^5 x^{15}","\frac{10}{9} a^2 A b^3 x^9+\frac{5}{3} a^3 A b^2 x^6+\frac{5}{3} a^4 A b x^3+a^5 A \log (x)+\frac{5}{12} a A b^4 x^{12}+\frac{B \left(a+b x^3\right)^6}{18 b}+\frac{1}{15} A b^5 x^{15}",1,"(5*a^4*A*b*x^3)/3 + (5*a^3*A*b^2*x^6)/3 + (10*a^2*A*b^3*x^9)/9 + (5*a*A*b^4*x^12)/12 + (A*b^5*x^15)/15 + (B*(a + b*x^3)^6)/(18*b) + a^5*A*Log[x]","A",4,3,20,0.1500,1,"{446, 80, 43}"
34,1,112,0,0.060787,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^2} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^2,x]","\frac{5}{4} a^2 b^2 x^8 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{2} a^4 x^2 (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{14} b^4 x^{14} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{17} b^5 B x^{17}","\frac{5}{4} a^2 b^2 x^8 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{2} a^4 x^2 (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{14} b^4 x^{14} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{17} b^5 B x^{17}",1,"-((a^5*A)/x) + (a^4*(5*A*b + a*B)*x^2)/2 + a^3*b*(2*A*b + a*B)*x^5 + (5*a^2*b^2*(A*b + a*B)*x^8)/4 + (5*a*b^3*(A*b + 2*a*B)*x^11)/11 + (b^4*(A*b + 5*a*B)*x^14)/14 + (b^5*B*x^17)/17","A",2,1,20,0.05000,1,"{448}"
35,1,112,0,0.0606458,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^3} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^3,x]","\frac{10}{7} a^2 b^2 x^7 (a B+A b)+\frac{5}{4} a^3 b x^4 (a B+2 A b)+a^4 x (a B+5 A b)-\frac{a^5 A}{2 x^2}+\frac{1}{13} b^4 x^{13} (5 a B+A b)+\frac{1}{2} a b^3 x^{10} (2 a B+A b)+\frac{1}{16} b^5 B x^{16}","\frac{10}{7} a^2 b^2 x^7 (a B+A b)+\frac{5}{4} a^3 b x^4 (a B+2 A b)+a^4 x (a B+5 A b)-\frac{a^5 A}{2 x^2}+\frac{1}{13} b^4 x^{13} (5 a B+A b)+\frac{1}{2} a b^3 x^{10} (2 a B+A b)+\frac{1}{16} b^5 B x^{16}",1,"-(a^5*A)/(2*x^2) + a^4*(5*A*b + a*B)*x + (5*a^3*b*(2*A*b + a*B)*x^4)/4 + (10*a^2*b^2*(A*b + a*B)*x^7)/7 + (a*b^3*(A*b + 2*a*B)*x^10)/2 + (b^4*(A*b + 5*a*B)*x^13)/13 + (b^5*B*x^16)/16","A",2,1,20,0.05000,1,"{448}"
36,1,113,0,0.1170538,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^4} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^4,x]","\frac{5}{3} a^2 b^2 x^6 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac{a^5 A}{3 x^3}+\frac{1}{12} b^4 x^{12} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{15} b^5 B x^{15}","\frac{5}{3} a^2 b^2 x^6 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac{a^5 A}{3 x^3}+\frac{1}{12} b^4 x^{12} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{15} b^5 B x^{15}",1,"-(a^5*A)/(3*x^3) + (5*a^3*b*(2*A*b + a*B)*x^3)/3 + (5*a^2*b^2*(A*b + a*B)*x^6)/3 + (5*a*b^3*(A*b + 2*a*B)*x^9)/9 + (b^4*(A*b + 5*a*B)*x^12)/12 + (b^5*B*x^15)/15 + a^4*(5*A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
37,1,113,0,0.0667424,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^5} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^5,x]","2 a^2 b^2 x^5 (a B+A b)+\frac{5}{2} a^3 b x^2 (a B+2 A b)-\frac{a^4 (a B+5 A b)}{x}-\frac{a^5 A}{4 x^4}+\frac{1}{11} b^4 x^{11} (5 a B+A b)+\frac{5}{8} a b^3 x^8 (2 a B+A b)+\frac{1}{14} b^5 B x^{14}","2 a^2 b^2 x^5 (a B+A b)+\frac{5}{2} a^3 b x^2 (a B+2 A b)-\frac{a^4 (a B+5 A b)}{x}-\frac{a^5 A}{4 x^4}+\frac{1}{11} b^4 x^{11} (5 a B+A b)+\frac{5}{8} a b^3 x^8 (2 a B+A b)+\frac{1}{14} b^5 B x^{14}",1,"-(a^5*A)/(4*x^4) - (a^4*(5*A*b + a*B))/x + (5*a^3*b*(2*A*b + a*B)*x^2)/2 + 2*a^2*b^2*(A*b + a*B)*x^5 + (5*a*b^3*(A*b + 2*a*B)*x^8)/8 + (b^4*(A*b + 5*a*B)*x^11)/11 + (b^5*B*x^14)/14","A",2,1,20,0.05000,1,"{448}"
38,1,113,0,0.062649,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^6} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^6,x]","\frac{5}{2} a^2 b^2 x^4 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)-\frac{a^5 A}{5 x^5}+\frac{1}{10} b^4 x^{10} (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{13} b^5 B x^{13}","\frac{5}{2} a^2 b^2 x^4 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b x (a B+2 A b)-\frac{a^5 A}{5 x^5}+\frac{1}{10} b^4 x^{10} (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{13} b^5 B x^{13}",1,"-(a^5*A)/(5*x^5) - (a^4*(5*A*b + a*B))/(2*x^2) + 5*a^3*b*(2*A*b + a*B)*x + (5*a^2*b^2*(A*b + a*B)*x^4)/2 + (5*a*b^3*(A*b + 2*a*B)*x^7)/7 + (b^4*(A*b + 5*a*B)*x^10)/10 + (b^5*B*x^13)/13","A",2,1,20,0.05000,1,"{448}"
39,1,114,0,0.1057997,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^7} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^7,x]","\frac{10}{3} a^2 b^2 x^3 (a B+A b)-\frac{a^4 (a B+5 A b)}{3 x^3}+5 a^3 b \log (x) (a B+2 A b)-\frac{a^5 A}{6 x^6}+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{12} b^5 B x^{12}","\frac{10}{3} a^2 b^2 x^3 (a B+A b)-\frac{a^4 (a B+5 A b)}{3 x^3}+5 a^3 b \log (x) (a B+2 A b)-\frac{a^5 A}{6 x^6}+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{12} b^5 B x^{12}",1,"-(a^5*A)/(6*x^6) - (a^4*(5*A*b + a*B))/(3*x^3) + (10*a^2*b^2*(A*b + a*B)*x^3)/3 + (5*a*b^3*(A*b + 2*a*B)*x^6)/6 + (b^4*(A*b + 5*a*B)*x^9)/9 + (b^5*B*x^12)/12 + 5*a^3*b*(2*A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
40,1,110,0,0.0671996,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^8} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^8,x]","5 a^2 b^2 x^2 (a B+A b)-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{x}-\frac{a^5 A}{7 x^7}+\frac{1}{8} b^4 x^8 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac{1}{11} b^5 B x^{11}","5 a^2 b^2 x^2 (a B+A b)-\frac{a^4 (a B+5 A b)}{4 x^4}-\frac{5 a^3 b (a B+2 A b)}{x}-\frac{a^5 A}{7 x^7}+\frac{1}{8} b^4 x^8 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac{1}{11} b^5 B x^{11}",1,"-(a^5*A)/(7*x^7) - (a^4*(5*A*b + a*B))/(4*x^4) - (5*a^3*b*(2*A*b + a*B))/x + 5*a^2*b^2*(A*b + a*B)*x^2 + a*b^3*(A*b + 2*a*B)*x^5 + (b^4*(A*b + 5*a*B)*x^8)/8 + (b^5*B*x^11)/11","A",2,1,20,0.05000,1,"{448}"
41,1,113,0,0.0623747,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^9} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^9,x]","10 a^2 b^2 x (a B+A b)-\frac{5 a^3 b (a B+2 A b)}{2 x^2}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{a^5 A}{8 x^8}+\frac{1}{7} b^4 x^7 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{10} b^5 B x^{10}","10 a^2 b^2 x (a B+A b)-\frac{5 a^3 b (a B+2 A b)}{2 x^2}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{a^5 A}{8 x^8}+\frac{1}{7} b^4 x^7 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{10} b^5 B x^{10}",1,"-(a^5*A)/(8*x^8) - (a^4*(5*A*b + a*B))/(5*x^5) - (5*a^3*b*(2*A*b + a*B))/(2*x^2) + 10*a^2*b^2*(A*b + a*B)*x + (5*a*b^3*(A*b + 2*a*B)*x^4)/4 + (b^4*(A*b + 5*a*B)*x^7)/7 + (b^5*B*x^10)/10","A",2,1,20,0.05000,1,"{448}"
42,1,114,0,0.1044867,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{10}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^10,x]","10 a^2 b^2 \log (x) (a B+A b)-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{6 x^6}-\frac{a^5 A}{9 x^9}+\frac{1}{6} b^4 x^6 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{9} b^5 B x^9","10 a^2 b^2 \log (x) (a B+A b)-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{6 x^6}-\frac{a^5 A}{9 x^9}+\frac{1}{6} b^4 x^6 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{9} b^5 B x^9",1,"-(a^5*A)/(9*x^9) - (a^4*(5*A*b + a*B))/(6*x^6) - (5*a^3*b*(2*A*b + a*B))/(3*x^3) + (5*a*b^3*(A*b + 2*a*B)*x^3)/3 + (b^4*(A*b + 5*a*B)*x^6)/6 + (b^5*B*x^9)/9 + 10*a^2*b^2*(A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
43,1,115,0,0.0631634,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{11}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^11,x]","-\frac{10 a^2 b^2 (a B+A b)}{x}-\frac{5 a^3 b (a B+2 A b)}{4 x^4}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^5 A}{10 x^{10}}+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{8} b^5 B x^8","-\frac{10 a^2 b^2 (a B+A b)}{x}-\frac{5 a^3 b (a B+2 A b)}{4 x^4}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^5 A}{10 x^{10}}+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{8} b^5 B x^8",1,"-(a^5*A)/(10*x^10) - (a^4*(5*A*b + a*B))/(7*x^7) - (5*a^3*b*(2*A*b + a*B))/(4*x^4) - (10*a^2*b^2*(A*b + a*B))/x + (5*a*b^3*(A*b + 2*a*B)*x^2)/2 + (b^4*(A*b + 5*a*B)*x^5)/5 + (b^5*B*x^8)/8","A",2,1,20,0.05000,1,"{448}"
44,1,109,0,0.064277,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{12}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^12,x]","-\frac{5 a^2 b^2 (a B+A b)}{x^2}-\frac{a^3 b (a B+2 A b)}{x^5}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{a^5 A}{11 x^{11}}+\frac{1}{4} b^4 x^4 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac{1}{7} b^5 B x^7","-\frac{5 a^2 b^2 (a B+A b)}{x^2}-\frac{a^3 b (a B+2 A b)}{x^5}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{a^5 A}{11 x^{11}}+\frac{1}{4} b^4 x^4 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac{1}{7} b^5 B x^7",1,"-(a^5*A)/(11*x^11) - (a^4*(5*A*b + a*B))/(8*x^8) - (a^3*b*(2*A*b + a*B))/x^5 - (5*a^2*b^2*(A*b + a*B))/x^2 + 5*a*b^3*(A*b + 2*a*B)*x + (b^4*(A*b + 5*a*B)*x^4)/4 + (b^5*B*x^7)/7","A",2,1,20,0.05000,1,"{448}"
45,1,114,0,0.0987126,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{13}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^13,x]","-\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{a^5 A}{12 x^{12}}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{6} b^5 B x^6","-\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{a^5 A}{12 x^{12}}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{6} b^5 B x^6",1,"-(a^5*A)/(12*x^12) - (a^4*(5*A*b + a*B))/(9*x^9) - (5*a^3*b*(2*A*b + a*B))/(6*x^6) - (10*a^2*b^2*(A*b + a*B))/(3*x^3) + (b^4*(A*b + 5*a*B)*x^3)/3 + (b^5*B*x^6)/6 + 5*a*b^3*(A*b + 2*a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
46,1,115,0,0.0621777,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{14}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^14,x]","-\frac{5 a^2 b^2 (a B+A b)}{2 x^4}-\frac{a^4 (a B+5 A b)}{10 x^{10}}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{a^5 A}{13 x^{13}}+\frac{1}{2} b^4 x^2 (5 a B+A b)-\frac{5 a b^3 (2 a B+A b)}{x}+\frac{1}{5} b^5 B x^5","-\frac{5 a^2 b^2 (a B+A b)}{2 x^4}-\frac{a^4 (a B+5 A b)}{10 x^{10}}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{a^5 A}{13 x^{13}}+\frac{1}{2} b^4 x^2 (5 a B+A b)-\frac{5 a b^3 (2 a B+A b)}{x}+\frac{1}{5} b^5 B x^5",1,"-(a^5*A)/(13*x^13) - (a^4*(5*A*b + a*B))/(10*x^10) - (5*a^3*b*(2*A*b + a*B))/(7*x^7) - (5*a^2*b^2*(A*b + a*B))/(2*x^4) - (5*a*b^3*(A*b + 2*a*B))/x + (b^4*(A*b + 5*a*B)*x^2)/2 + (b^5*B*x^5)/5","A",2,1,20,0.05000,1,"{448}"
47,1,110,0,0.0677994,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{15}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^15,x]","-\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{8 x^8}-\frac{a^5 A}{14 x^{14}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 x (5 a B+A b)+\frac{1}{4} b^5 B x^4","-\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{8 x^8}-\frac{a^5 A}{14 x^{14}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 x (5 a B+A b)+\frac{1}{4} b^5 B x^4",1,"-(a^5*A)/(14*x^14) - (a^4*(5*A*b + a*B))/(11*x^11) - (5*a^3*b*(2*A*b + a*B))/(8*x^8) - (2*a^2*b^2*(A*b + a*B))/x^5 - (5*a*b^3*(A*b + 2*a*B))/(2*x^2) + b^4*(A*b + 5*a*B)*x + (b^5*B*x^4)/4","A",2,1,20,0.05000,1,"{448}"
48,1,113,0,0.0911369,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{16}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^16,x]","-\frac{5 a^2 b^2 (a B+A b)}{3 x^6}-\frac{a^4 (a B+5 A b)}{12 x^{12}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{a^5 A}{15 x^{15}}-\frac{5 a b^3 (2 a B+A b)}{3 x^3}+b^4 \log (x) (5 a B+A b)+\frac{1}{3} b^5 B x^3","-\frac{5 a^2 b^2 (a B+A b)}{3 x^6}-\frac{a^4 (a B+5 A b)}{12 x^{12}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{a^5 A}{15 x^{15}}-\frac{5 a b^3 (2 a B+A b)}{3 x^3}+b^4 \log (x) (5 a B+A b)+\frac{1}{3} b^5 B x^3",1,"-(a^5*A)/(15*x^15) - (a^4*(5*A*b + a*B))/(12*x^12) - (5*a^3*b*(2*A*b + a*B))/(9*x^9) - (5*a^2*b^2*(A*b + a*B))/(3*x^6) - (5*a*b^3*(A*b + 2*a*B))/(3*x^3) + (b^5*B*x^3)/3 + b^4*(A*b + 5*a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
49,1,115,0,0.0615403,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{17}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^17,x]","-\frac{10 a^2 b^2 (a B+A b)}{7 x^7}-\frac{a^4 (a B+5 A b)}{13 x^{13}}-\frac{a^3 b (a B+2 A b)}{2 x^{10}}-\frac{a^5 A}{16 x^{16}}-\frac{5 a b^3 (2 a B+A b)}{4 x^4}-\frac{b^4 (5 a B+A b)}{x}+\frac{1}{2} b^5 B x^2","-\frac{10 a^2 b^2 (a B+A b)}{7 x^7}-\frac{a^4 (a B+5 A b)}{13 x^{13}}-\frac{a^3 b (a B+2 A b)}{2 x^{10}}-\frac{a^5 A}{16 x^{16}}-\frac{5 a b^3 (2 a B+A b)}{4 x^4}-\frac{b^4 (5 a B+A b)}{x}+\frac{1}{2} b^5 B x^2",1,"-(a^5*A)/(16*x^16) - (a^4*(5*A*b + a*B))/(13*x^13) - (a^3*b*(2*A*b + a*B))/(2*x^10) - (10*a^2*b^2*(A*b + a*B))/(7*x^7) - (5*a*b^3*(A*b + 2*a*B))/(4*x^4) - (b^4*(A*b + 5*a*B))/x + (b^5*B*x^2)/2","A",2,1,20,0.05000,1,"{448}"
50,1,110,0,0.0613283,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{18}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^18,x]","-\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{14 x^{14}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{17 x^{17}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{2 x^2}+b^5 B x","-\frac{5 a^2 b^2 (a B+A b)}{4 x^8}-\frac{a^4 (a B+5 A b)}{14 x^{14}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{17 x^{17}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{2 x^2}+b^5 B x",1,"-(a^5*A)/(17*x^17) - (a^4*(5*A*b + a*B))/(14*x^14) - (5*a^3*b*(2*A*b + a*B))/(11*x^11) - (5*a^2*b^2*(A*b + a*B))/(4*x^8) - (a*b^3*(A*b + 2*a*B))/x^5 - (b^4*(A*b + 5*a*B))/(2*x^2) + b^5*B*x","A",2,1,20,0.05000,1,"{448}"
51,1,91,0,0.0538979,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{19}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^19,x]","-\frac{5 a^2 b^3 B}{3 x^6}-\frac{10 a^3 b^2 B}{9 x^9}-\frac{5 a^4 b B}{12 x^{12}}-\frac{a^5 B}{15 x^{15}}-\frac{A \left(a+b x^3\right)^6}{18 a x^{18}}-\frac{5 a b^4 B}{3 x^3}+b^5 B \log (x)","-\frac{5 a^2 b^3 B}{3 x^6}-\frac{10 a^3 b^2 B}{9 x^9}-\frac{5 a^4 b B}{12 x^{12}}-\frac{a^5 B}{15 x^{15}}-\frac{A \left(a+b x^3\right)^6}{18 a x^{18}}-\frac{5 a b^4 B}{3 x^3}+b^5 B \log (x)",1,"-(a^5*B)/(15*x^15) - (5*a^4*b*B)/(12*x^12) - (10*a^3*b^2*B)/(9*x^9) - (5*a^2*b^3*B)/(3*x^6) - (5*a*b^4*B)/(3*x^3) - (A*(a + b*x^3)^6)/(18*a*x^18) + b^5*B*Log[x]","A",4,3,20,0.1500,1,"{446, 78, 43}"
52,1,113,0,0.0643632,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{20}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^20,x]","-\frac{a^2 b^2 (a B+A b)}{x^{10}}-\frac{a^4 (a B+5 A b)}{16 x^{16}}-\frac{5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{b^5 B}{x}","-\frac{a^2 b^2 (a B+A b)}{x^{10}}-\frac{a^4 (a B+5 A b)}{16 x^{16}}-\frac{5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{4 x^4}-\frac{b^5 B}{x}",1,"-(a^5*A)/(19*x^19) - (a^4*(5*A*b + a*B))/(16*x^16) - (5*a^3*b*(2*A*b + a*B))/(13*x^13) - (a^2*b^2*(A*b + a*B))/x^10 - (5*a*b^3*(A*b + 2*a*B))/(7*x^7) - (b^4*(A*b + 5*a*B))/(4*x^4) - (b^5*B)/x","A",2,1,20,0.05000,1,"{448}"
53,1,117,0,0.0588298,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{21}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^21,x]","-\frac{10 a^2 b^2 (a B+A b)}{11 x^{11}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{5 a^3 b (a B+2 A b)}{14 x^{14}}-\frac{a^5 A}{20 x^{20}}-\frac{5 a b^3 (2 a B+A b)}{8 x^8}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{b^5 B}{2 x^2}","-\frac{10 a^2 b^2 (a B+A b)}{11 x^{11}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{5 a^3 b (a B+2 A b)}{14 x^{14}}-\frac{a^5 A}{20 x^{20}}-\frac{5 a b^3 (2 a B+A b)}{8 x^8}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{b^5 B}{2 x^2}",1,"-(a^5*A)/(20*x^20) - (a^4*(5*A*b + a*B))/(17*x^17) - (5*a^3*b*(2*A*b + a*B))/(14*x^14) - (10*a^2*b^2*(A*b + a*B))/(11*x^11) - (5*a*b^3*(A*b + 2*a*B))/(8*x^8) - (b^4*(A*b + 5*a*B))/(5*x^5) - (b^5*B)/(2*x^2)","A",2,1,20,0.05000,1,"{448}"
54,1,48,0,0.031515,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{22}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^22,x]","\frac{\left(a+b x^3\right)^6 (A b-7 a B)}{126 a^2 x^{18}}-\frac{A \left(a+b x^3\right)^6}{21 a x^{21}}","\frac{\left(a+b x^3\right)^6 (A b-7 a B)}{126 a^2 x^{18}}-\frac{A \left(a+b x^3\right)^6}{21 a x^{21}}",1,"-(A*(a + b*x^3)^6)/(21*a*x^21) + ((A*b - 7*a*B)*(a + b*x^3)^6)/(126*a^2*x^18)","A",3,3,20,0.1500,1,"{446, 78, 37}"
55,1,117,0,0.0649493,"\int \frac{\left(a+b x^3\right)^5 \left(A+B x^3\right)}{x^{23}} \, dx","Int[((a + b*x^3)^5*(A + B*x^3))/x^23,x]","-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{22 x^{22}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{4 x^4}","-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{22 x^{22}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{4 x^4}",1,"-(a^5*A)/(22*x^22) - (a^4*(5*A*b + a*B))/(19*x^19) - (5*a^3*b*(2*A*b + a*B))/(16*x^16) - (10*a^2*b^2*(A*b + a*B))/(13*x^13) - (a*b^3*(A*b + 2*a*B))/(2*x^10) - (b^4*(A*b + 5*a*B))/(7*x^7) - (b^5*B)/(4*x^4)","A",2,1,20,0.05000,1,"{448}"
56,1,183,0,0.1491324,"\int \frac{x^6 \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^6*(A + B*x^3))/(a + b*x^3),x]","-\frac{a^{4/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{10/3}}+\frac{a^{4/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{10/3}}-\frac{a^{4/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{10/3}}+\frac{x^4 (A b-a B)}{4 b^2}-\frac{a x (A b-a B)}{b^3}+\frac{B x^7}{7 b}","-\frac{a^{4/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{10/3}}+\frac{a^{4/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{10/3}}-\frac{a^{4/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{10/3}}+\frac{x^4 (A b-a B)}{4 b^2}-\frac{a x (A b-a B)}{b^3}+\frac{B x^7}{7 b}",1,"-((a*(A*b - a*B)*x)/b^3) + ((A*b - a*B)*x^4)/(4*b^2) + (B*x^7)/(7*b) - (a^(4/3)*(A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(10/3)) + (a^(4/3)*(A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(10/3)) - (a^(4/3)*(A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(10/3))","A",9,8,20,0.4000,1,"{459, 302, 200, 31, 634, 617, 204, 628}"
57,1,54,0,0.0572361,"\int \frac{x^5 \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^5*(A + B*x^3))/(a + b*x^3),x]","\frac{x^3 (A b-a B)}{3 b^2}-\frac{a (A b-a B) \log \left(a+b x^3\right)}{3 b^3}+\frac{B x^6}{6 b}","\frac{x^3 (A b-a B)}{3 b^2}-\frac{a (A b-a B) \log \left(a+b x^3\right)}{3 b^3}+\frac{B x^6}{6 b}",1,"((A*b - a*B)*x^3)/(3*b^2) + (B*x^6)/(6*b) - (a*(A*b - a*B)*Log[a + b*x^3])/(3*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
58,1,167,0,0.1202355,"\int \frac{x^4 \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^4*(A + B*x^3))/(a + b*x^3),x]","-\frac{a^{2/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{8/3}}+\frac{a^{2/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{8/3}}+\frac{a^{2/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{8/3}}+\frac{x^2 (A b-a B)}{2 b^2}+\frac{B x^5}{5 b}","-\frac{a^{2/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{8/3}}+\frac{a^{2/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{8/3}}+\frac{a^{2/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{8/3}}+\frac{x^2 (A b-a B)}{2 b^2}+\frac{B x^5}{5 b}",1,"((A*b - a*B)*x^2)/(2*b^2) + (B*x^5)/(5*b) + (a^(2/3)*(A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(8/3)) + (a^(2/3)*(A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(8/3)) - (a^(2/3)*(A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(8/3))","A",8,8,20,0.4000,1,"{459, 321, 292, 31, 634, 617, 204, 628}"
59,1,162,0,0.1155213,"\int \frac{x^3 \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^3*(A + B*x^3))/(a + b*x^3),x]","\frac{\sqrt[3]{a} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{7/3}}+\frac{x (A b-a B)}{b^2}-\frac{\sqrt[3]{a} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{7/3}}+\frac{\sqrt[3]{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{7/3}}+\frac{B x^4}{4 b}","\frac{\sqrt[3]{a} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{7/3}}+\frac{x (A b-a B)}{b^2}-\frac{\sqrt[3]{a} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{7/3}}+\frac{\sqrt[3]{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{7/3}}+\frac{B x^4}{4 b}",1,"((A*b - a*B)*x)/b^2 + (B*x^4)/(4*b) + (a^(1/3)*(A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(7/3)) - (a^(1/3)*(A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(7/3)) + (a^(1/3)*(A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(7/3))","A",8,8,20,0.4000,1,"{459, 321, 200, 31, 634, 617, 204, 628}"
60,1,35,0,0.0327442,"\int \frac{x^2 \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^2*(A + B*x^3))/(a + b*x^3),x]","\frac{(A b-a B) \log \left(a+b x^3\right)}{3 b^2}+\frac{B x^3}{3 b}","\frac{(A b-a B) \log \left(a+b x^3\right)}{3 b^2}+\frac{B x^3}{3 b}",1,"(B*x^3)/(3*b) + ((A*b - a*B)*Log[a + b*x^3])/(3*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
61,1,150,0,0.0903092,"\int \frac{x \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x*(A + B*x^3))/(a + b*x^3),x]","\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{5/3}}-\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{5/3}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{5/3}}+\frac{B x^2}{2 b}","\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} b^{5/3}}-\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} b^{5/3}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} b^{5/3}}+\frac{B x^2}{2 b}",1,"(B*x^2)/(2*b) - ((A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*b^(5/3)) - ((A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*b^(5/3)) + ((A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*b^(5/3))","A",7,7,18,0.3889,1,"{459, 292, 31, 634, 617, 204, 628}"
62,1,145,0,0.0768879,"\int \frac{A+B x^3}{a+b x^3} \, dx","Int[(A + B*x^3)/(a + b*x^3),x]","-\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{4/3}}+\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{4/3}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3}}+\frac{B x}{b}","-\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} b^{4/3}}+\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} b^{4/3}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} b^{4/3}}+\frac{B x}{b}",1,"(B*x)/b - ((A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*b^(4/3)) + ((A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*b^(4/3)) - ((A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*b^(4/3))","A",7,7,17,0.4118,1,"{388, 200, 31, 634, 617, 204, 628}"
63,1,34,0,0.0333877,"\int \frac{A+B x^3}{x \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x*(a + b*x^3)),x]","\frac{A \log (x)}{a}-\frac{(A b-a B) \log \left(a+b x^3\right)}{3 a b}","\frac{A \log (x)}{a}-\frac{(A b-a B) \log \left(a+b x^3\right)}{3 a b}",1,"(A*Log[x])/a - ((A*b - a*B)*Log[a + b*x^3])/(3*a*b)","A",3,2,20,0.1000,1,"{446, 72}"
64,1,147,0,0.0856454,"\int \frac{A+B x^3}{x^2 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^2*(a + b*x^3)),x]","-\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} b^{2/3}}+\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} b^{2/3}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} b^{2/3}}-\frac{A}{a x}","-\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} b^{2/3}}+\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} b^{2/3}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} b^{2/3}}-\frac{A}{a x}",1,"-(A/(a*x)) + ((A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*b^(2/3)) + ((A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)*b^(2/3)) - ((A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*b^(2/3))","A",7,7,20,0.3500,1,"{453, 292, 31, 634, 617, 204, 628}"
65,1,149,0,0.0932772,"\int \frac{A+B x^3}{x^3 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^3*(a + b*x^3)),x]","\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3} \sqrt[3]{b}}-\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3} \sqrt[3]{b}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} \sqrt[3]{b}}-\frac{A}{2 a x^2}","\frac{(A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3} \sqrt[3]{b}}-\frac{(A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3} \sqrt[3]{b}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} \sqrt[3]{b}}-\frac{A}{2 a x^2}",1,"-A/(2*a*x^2) + ((A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*b^(1/3)) - ((A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)*b^(1/3)) + ((A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*b^(1/3))","A",7,7,20,0.3500,1,"{453, 200, 31, 634, 617, 204, 628}"
66,1,50,0,0.0490322,"\int \frac{A+B x^3}{x^4 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^4*(a + b*x^3)),x]","\frac{(A b-a B) \log \left(a+b x^3\right)}{3 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{3 a x^3}","\frac{(A b-a B) \log \left(a+b x^3\right)}{3 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{3 a x^3}",1,"-A/(3*a*x^3) - ((A*b - a*B)*Log[x])/a^2 + ((A*b - a*B)*Log[a + b*x^3])/(3*a^2)","A",3,2,20,0.1000,1,"{446, 77}"
67,1,165,0,0.1147875,"\int \frac{A+B x^3}{x^5 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^5*(a + b*x^3)),x]","\frac{\sqrt[3]{b} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{7/3}}+\frac{A b-a B}{a^2 x}-\frac{\sqrt[3]{b} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{7/3}}-\frac{\sqrt[3]{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{A}{4 a x^4}","\frac{\sqrt[3]{b} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{7/3}}+\frac{A b-a B}{a^2 x}-\frac{\sqrt[3]{b} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{7/3}}-\frac{\sqrt[3]{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3}}-\frac{A}{4 a x^4}",1,"-A/(4*a*x^4) + (A*b - a*B)/(a^2*x) - (b^(1/3)*(A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)) - (b^(1/3)*(A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(7/3)) + (b^(1/3)*(A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(7/3))","A",8,8,20,0.4000,1,"{453, 325, 292, 31, 634, 617, 204, 628}"
68,1,168,0,0.1188988,"\int \frac{A+B x^3}{x^6 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^6*(a + b*x^3)),x]","-\frac{b^{2/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{8/3}}+\frac{b^{2/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{8/3}}-\frac{b^{2/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3}}+\frac{A b-a B}{2 a^2 x^2}-\frac{A}{5 a x^5}","-\frac{b^{2/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{8/3}}+\frac{b^{2/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{8/3}}-\frac{b^{2/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3}}+\frac{A b-a B}{2 a^2 x^2}-\frac{A}{5 a x^5}",1,"-A/(5*a*x^5) + (A*b - a*B)/(2*a^2*x^2) - (b^(2/3)*(A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(8/3)) + (b^(2/3)*(A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(8/3)) - (b^(2/3)*(A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(8/3))","A",8,8,20,0.4000,1,"{453, 325, 200, 31, 634, 617, 204, 628}"
69,1,69,0,0.0640418,"\int \frac{A+B x^3}{x^7 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^7*(a + b*x^3)),x]","\frac{A b-a B}{3 a^2 x^3}-\frac{b (A b-a B) \log \left(a+b x^3\right)}{3 a^3}+\frac{b \log (x) (A b-a B)}{a^3}-\frac{A}{6 a x^6}","\frac{A b-a B}{3 a^2 x^3}-\frac{b (A b-a B) \log \left(a+b x^3\right)}{3 a^3}+\frac{b \log (x) (A b-a B)}{a^3}-\frac{A}{6 a x^6}",1,"-A/(6*a*x^6) + (A*b - a*B)/(3*a^2*x^3) + (b*(A*b - a*B)*Log[x])/a^3 - (b*(A*b - a*B)*Log[a + b*x^3])/(3*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
70,1,184,0,0.1338847,"\int \frac{A+B x^3}{x^8 \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^8*(a + b*x^3)),x]","-\frac{b^{4/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{10/3}}+\frac{b^{4/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{10/3}}+\frac{b^{4/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{10/3}}+\frac{A b-a B}{4 a^2 x^4}-\frac{b (A b-a B)}{a^3 x}-\frac{A}{7 a x^7}","-\frac{b^{4/3} (A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{10/3}}+\frac{b^{4/3} (A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{10/3}}+\frac{b^{4/3} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{10/3}}+\frac{A b-a B}{4 a^2 x^4}-\frac{b (A b-a B)}{a^3 x}-\frac{A}{7 a x^7}",1,"-A/(7*a*x^7) + (A*b - a*B)/(4*a^2*x^4) - (b*(A*b - a*B))/(a^3*x) + (b^(4/3)*(A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(10/3)) + (b^(4/3)*(A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(10/3)) - (b^(4/3)*(A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(10/3))","A",9,8,20,0.4000,1,"{453, 325, 292, 31, 634, 617, 204, 628}"
71,1,233,0,0.1380675,"\int \frac{x^9 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^9*(A + B*x^3))/(a + b*x^3)^2,x]","-\frac{a^{4/3} (7 A b-10 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 b^{13/3}}+\frac{a^{4/3} (7 A b-10 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 b^{13/3}}-\frac{a^{4/3} (7 A b-10 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} b^{13/3}}-\frac{x^7 (7 A b-10 a B)}{21 a b^2}+\frac{x^4 (7 A b-10 a B)}{12 b^3}-\frac{a x (7 A b-10 a B)}{3 b^4}+\frac{x^{10} (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{a^{4/3} (7 A b-10 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 b^{13/3}}+\frac{a^{4/3} (7 A b-10 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 b^{13/3}}-\frac{a^{4/3} (7 A b-10 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} b^{13/3}}-\frac{x^7 (7 A b-10 a B)}{21 a b^2}+\frac{x^4 (7 A b-10 a B)}{12 b^3}-\frac{a x (7 A b-10 a B)}{3 b^4}+\frac{x^{10} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"-(a*(7*A*b - 10*a*B)*x)/(3*b^4) + ((7*A*b - 10*a*B)*x^4)/(12*b^3) - ((7*A*b - 10*a*B)*x^7)/(21*a*b^2) + ((A*b - a*B)*x^10)/(3*a*b*(a + b*x^3)) - (a^(4/3)*(7*A*b - 10*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*b^(13/3)) + (a^(4/3)*(7*A*b - 10*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*b^(13/3)) - (a^(4/3)*(7*A*b - 10*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*b^(13/3))","A",9,8,20,0.4000,1,"{457, 302, 200, 31, 634, 617, 204, 628}"
72,1,82,0,0.0905451,"\int \frac{x^8 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^8*(A + B*x^3))/(a + b*x^3)^2,x]","-\frac{a^2 (A b-a B)}{3 b^4 \left(a+b x^3\right)}+\frac{x^3 (A b-2 a B)}{3 b^3}-\frac{a (2 A b-3 a B) \log \left(a+b x^3\right)}{3 b^4}+\frac{B x^6}{6 b^2}","-\frac{a^2 (A b-a B)}{3 b^4 \left(a+b x^3\right)}+\frac{x^3 (A b-2 a B)}{3 b^3}-\frac{a (2 A b-3 a B) \log \left(a+b x^3\right)}{3 b^4}+\frac{B x^6}{6 b^2}",1,"((A*b - 2*a*B)*x^3)/(3*b^3) + (B*x^6)/(6*b^2) - (a^2*(A*b - a*B))/(3*b^4*(a + b*x^3)) - (a*(2*A*b - 3*a*B)*Log[a + b*x^3])/(3*b^4)","A",3,2,20,0.1000,1,"{446, 77}"
73,1,215,0,0.1398651,"\int \frac{x^7 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^7*(A + B*x^3))/(a + b*x^3)^2,x]","-\frac{a^{2/3} (5 A b-8 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 b^{11/3}}+\frac{a^{2/3} (5 A b-8 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 b^{11/3}}+\frac{a^{2/3} (5 A b-8 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} b^{11/3}}-\frac{x^5 (5 A b-8 a B)}{15 a b^2}+\frac{x^2 (5 A b-8 a B)}{6 b^3}+\frac{x^8 (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{a^{2/3} (5 A b-8 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 b^{11/3}}+\frac{a^{2/3} (5 A b-8 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 b^{11/3}}+\frac{a^{2/3} (5 A b-8 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} b^{11/3}}-\frac{x^5 (5 A b-8 a B)}{15 a b^2}+\frac{x^2 (5 A b-8 a B)}{6 b^3}+\frac{x^8 (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((5*A*b - 8*a*B)*x^2)/(6*b^3) - ((5*A*b - 8*a*B)*x^5)/(15*a*b^2) + ((A*b - a*B)*x^8)/(3*a*b*(a + b*x^3)) + (a^(2/3)*(5*A*b - 8*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*b^(11/3)) + (a^(2/3)*(5*A*b - 8*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*b^(11/3)) - (a^(2/3)*(5*A*b - 8*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*b^(11/3))","A",9,8,20,0.4000,1,"{457, 302, 292, 31, 634, 617, 204, 628}"
74,1,213,0,0.1304092,"\int \frac{x^6 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^6*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{\sqrt[3]{a} (4 A b-7 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 b^{10/3}}-\frac{x^4 (4 A b-7 a B)}{12 a b^2}+\frac{x (4 A b-7 a B)}{3 b^3}-\frac{\sqrt[3]{a} (4 A b-7 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 b^{10/3}}+\frac{\sqrt[3]{a} (4 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} b^{10/3}}+\frac{x^7 (A b-a B)}{3 a b \left(a+b x^3\right)}","\frac{\sqrt[3]{a} (4 A b-7 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 b^{10/3}}-\frac{x^4 (4 A b-7 a B)}{12 a b^2}+\frac{x (4 A b-7 a B)}{3 b^3}-\frac{\sqrt[3]{a} (4 A b-7 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 b^{10/3}}+\frac{\sqrt[3]{a} (4 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} b^{10/3}}+\frac{x^7 (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((4*A*b - 7*a*B)*x)/(3*b^3) - ((4*A*b - 7*a*B)*x^4)/(12*a*b^2) + ((A*b - a*B)*x^7)/(3*a*b*(a + b*x^3)) + (a^(1/3)*(4*A*b - 7*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*b^(10/3)) - (a^(1/3)*(4*A*b - 7*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*b^(10/3)) + (a^(1/3)*(4*A*b - 7*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*b^(10/3))","A",9,8,20,0.4000,1,"{457, 302, 200, 31, 634, 617, 204, 628}"
75,1,60,0,0.0581286,"\int \frac{x^5 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^5*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{a (A b-a B)}{3 b^3 \left(a+b x^3\right)}+\frac{(A b-2 a B) \log \left(a+b x^3\right)}{3 b^3}+\frac{B x^3}{3 b^2}","\frac{a (A b-a B)}{3 b^3 \left(a+b x^3\right)}+\frac{(A b-2 a B) \log \left(a+b x^3\right)}{3 b^3}+\frac{B x^3}{3 b^2}",1,"(B*x^3)/(3*b^2) + (a*(A*b - a*B))/(3*b^3*(a + b*x^3)) + ((A*b - 2*a*B)*Log[a + b*x^3])/(3*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
76,1,196,0,0.1103493,"\int \frac{x^4 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^4*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{(2 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 \sqrt[3]{a} b^{8/3}}-\frac{x^2 (2 A b-5 a B)}{6 a b^2}-\frac{(2 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 \sqrt[3]{a} b^{8/3}}-\frac{(2 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{8/3}}+\frac{x^5 (A b-a B)}{3 a b \left(a+b x^3\right)}","\frac{(2 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 \sqrt[3]{a} b^{8/3}}-\frac{x^2 (2 A b-5 a B)}{6 a b^2}-\frac{(2 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 \sqrt[3]{a} b^{8/3}}-\frac{(2 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} b^{8/3}}+\frac{x^5 (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"-((2*A*b - 5*a*B)*x^2)/(6*a*b^2) + ((A*b - a*B)*x^5)/(3*a*b*(a + b*x^3)) - ((2*A*b - 5*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*b^(8/3)) - ((2*A*b - 5*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(1/3)*b^(8/3)) + ((2*A*b - 5*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(1/3)*b^(8/3))","A",8,8,20,0.4000,1,"{457, 321, 292, 31, 634, 617, 204, 628}"
77,1,190,0,0.1064469,"\int \frac{x^3 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^3*(A + B*x^3))/(a + b*x^3)^2,x]","-\frac{(A b-4 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{2/3} b^{7/3}}+\frac{(A b-4 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{2/3} b^{7/3}}-\frac{(A b-4 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{7/3}}-\frac{x (A b-4 a B)}{3 a b^2}+\frac{x^4 (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{(A b-4 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{2/3} b^{7/3}}+\frac{(A b-4 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{2/3} b^{7/3}}-\frac{(A b-4 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} b^{7/3}}-\frac{x (A b-4 a B)}{3 a b^2}+\frac{x^4 (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"-((A*b - 4*a*B)*x)/(3*a*b^2) + ((A*b - a*B)*x^4)/(3*a*b*(a + b*x^3)) - ((A*b - 4*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*b^(7/3)) + ((A*b - 4*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(2/3)*b^(7/3)) - ((A*b - 4*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(2/3)*b^(7/3))","A",8,8,20,0.4000,1,"{457, 321, 200, 31, 634, 617, 204, 628}"
78,1,41,0,0.0380932,"\int \frac{x^2 \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{B \log \left(a+b x^3\right)}{3 b^2}-\frac{A b-a B}{3 b^2 \left(a+b x^3\right)}","\frac{B \log \left(a+b x^3\right)}{3 b^2}-\frac{A b-a B}{3 b^2 \left(a+b x^3\right)}",1,"-(A*b - a*B)/(3*b^2*(a + b*x^3)) + (B*Log[a + b*x^3])/(3*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
79,1,171,0,0.0879305,"\int \frac{x \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{(2 a B+A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{4/3} b^{5/3}}-\frac{(2 a B+A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{4/3} b^{5/3}}-\frac{(2 a B+A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{5/3}}+\frac{x^2 (A b-a B)}{3 a b \left(a+b x^3\right)}","\frac{(2 a B+A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{4/3} b^{5/3}}-\frac{(2 a B+A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{4/3} b^{5/3}}-\frac{(2 a B+A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} b^{5/3}}+\frac{x^2 (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((A*b - a*B)*x^2)/(3*a*b*(a + b*x^3)) - ((A*b + 2*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*b^(5/3)) - ((A*b + 2*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(4/3)*b^(5/3)) + ((A*b + 2*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(4/3)*b^(5/3))","A",7,7,18,0.3889,1,"{457, 292, 31, 634, 617, 204, 628}"
80,1,169,0,0.0862685,"\int \frac{A+B x^3}{\left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(a + b*x^3)^2,x]","-\frac{(a B+2 A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{4/3}}+\frac{(a B+2 A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{4/3}}-\frac{(a B+2 A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{x (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{(a B+2 A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{5/3} b^{4/3}}+\frac{(a B+2 A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{5/3} b^{4/3}}-\frac{(a B+2 A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} b^{4/3}}+\frac{x (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((A*b - a*B)*x)/(3*a*b*(a + b*x^3)) - ((2*A*b + a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*b^(4/3)) + ((2*A*b + a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(5/3)*b^(4/3)) - ((2*A*b + a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(5/3)*b^(4/3))","A",7,7,17,0.4118,1,"{385, 200, 31, 634, 617, 204, 628}"
81,1,51,0,0.0458923,"\int \frac{A+B x^3}{x \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x*(a + b*x^3)^2),x]","-\frac{A \log \left(a+b x^3\right)}{3 a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{3 a b \left(a+b x^3\right)}","-\frac{A \log \left(a+b x^3\right)}{3 a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{3 a b \left(a+b x^3\right)}",1,"(A*b - a*B)/(3*a*b*(a + b*x^3)) + (A*Log[x])/a^2 - (A*Log[a + b*x^3])/(3*a^2)","A",3,2,20,0.1000,1,"{446, 77}"
82,1,196,0,0.1055516,"\int \frac{A+B x^3}{x^2 \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^2*(a + b*x^3)^2),x]","-\frac{(4 A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{7/3} b^{2/3}}+\frac{(4 A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{7/3} b^{2/3}}+\frac{(4 A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} b^{2/3}}-\frac{4 A b-a B}{3 a^2 b x}+\frac{A b-a B}{3 a b x \left(a+b x^3\right)}","-\frac{(4 A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{7/3} b^{2/3}}+\frac{(4 A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{7/3} b^{2/3}}+\frac{(4 A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} b^{2/3}}-\frac{4 A b-a B}{3 a^2 b x}+\frac{A b-a B}{3 a b x \left(a+b x^3\right)}",1,"-(4*A*b - a*B)/(3*a^2*b*x) + (A*b - a*B)/(3*a*b*x*(a + b*x^3)) + ((4*A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*b^(2/3)) + ((4*A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(7/3)*b^(2/3)) - ((4*A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(7/3)*b^(2/3))","A",8,8,20,0.4000,1,"{457, 325, 292, 31, 634, 617, 204, 628}"
83,1,196,0,0.102756,"\int \frac{A+B x^3}{x^3 \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^3*(a + b*x^3)^2),x]","\frac{(5 A b-2 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3} \sqrt[3]{b}}-\frac{5 A b-2 a B}{6 a^2 b x^2}-\frac{(5 A b-2 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3} \sqrt[3]{b}}+\frac{(5 A b-2 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{A b-a B}{3 a b x^2 \left(a+b x^3\right)}","\frac{(5 A b-2 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{8/3} \sqrt[3]{b}}-\frac{5 A b-2 a B}{6 a^2 b x^2}-\frac{(5 A b-2 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{8/3} \sqrt[3]{b}}+\frac{(5 A b-2 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{8/3} \sqrt[3]{b}}+\frac{A b-a B}{3 a b x^2 \left(a+b x^3\right)}",1,"-(5*A*b - 2*a*B)/(6*a^2*b*x^2) + (A*b - a*B)/(3*a*b*x^2*(a + b*x^3)) + ((5*A*b - 2*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(8/3)*b^(1/3)) - ((5*A*b - 2*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(8/3)*b^(1/3)) + ((5*A*b - 2*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(8/3)*b^(1/3))","A",8,8,20,0.4000,1,"{457, 325, 200, 31, 634, 617, 204, 628}"
84,1,76,0,0.0758433,"\int \frac{A+B x^3}{x^4 \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^4*(a + b*x^3)^2),x]","-\frac{A b-a B}{3 a^2 \left(a+b x^3\right)}+\frac{(2 A b-a B) \log \left(a+b x^3\right)}{3 a^3}-\frac{\log (x) (2 A b-a B)}{a^3}-\frac{A}{3 a^2 x^3}","-\frac{A b-a B}{3 a^2 \left(a+b x^3\right)}+\frac{(2 A b-a B) \log \left(a+b x^3\right)}{3 a^3}-\frac{\log (x) (2 A b-a B)}{a^3}-\frac{A}{3 a^2 x^3}",1,"-A/(3*a^2*x^3) - (A*b - a*B)/(3*a^2*(a + b*x^3)) - ((2*A*b - a*B)*Log[x])/a^3 + ((2*A*b - a*B)*Log[a + b*x^3])/(3*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
85,1,215,0,0.1266106,"\int \frac{A+B x^3}{x^5 \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^5*(a + b*x^3)^2),x]","\frac{\sqrt[3]{b} (7 A b-4 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{10/3}}-\frac{7 A b-4 a B}{12 a^2 b x^4}+\frac{7 A b-4 a B}{3 a^3 x}-\frac{\sqrt[3]{b} (7 A b-4 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{10/3}}-\frac{\sqrt[3]{b} (7 A b-4 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}+\frac{A b-a B}{3 a b x^4 \left(a+b x^3\right)}","\frac{\sqrt[3]{b} (7 A b-4 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{10/3}}-\frac{7 A b-4 a B}{12 a^2 b x^4}+\frac{7 A b-4 a B}{3 a^3 x}-\frac{\sqrt[3]{b} (7 A b-4 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{10/3}}-\frac{\sqrt[3]{b} (7 A b-4 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{10/3}}+\frac{A b-a B}{3 a b x^4 \left(a+b x^3\right)}",1,"-(7*A*b - 4*a*B)/(12*a^2*b*x^4) + (7*A*b - 4*a*B)/(3*a^3*x) + (A*b - a*B)/(3*a*b*x^4*(a + b*x^3)) - (b^(1/3)*(7*A*b - 4*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(10/3)) - (b^(1/3)*(7*A*b - 4*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(10/3)) + (b^(1/3)*(7*A*b - 4*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(10/3))","A",9,8,20,0.4000,1,"{457, 325, 292, 31, 634, 617, 204, 628}"
86,1,215,0,0.1270085,"\int \frac{A+B x^3}{x^6 \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^6*(a + b*x^3)^2),x]","-\frac{b^{2/3} (8 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{11/3}}+\frac{b^{2/3} (8 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{11/3}}-\frac{b^{2/3} (8 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{11/3}}+\frac{8 A b-5 a B}{6 a^3 x^2}-\frac{8 A b-5 a B}{15 a^2 b x^5}+\frac{A b-a B}{3 a b x^5 \left(a+b x^3\right)}","-\frac{b^{2/3} (8 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{18 a^{11/3}}+\frac{b^{2/3} (8 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{9 a^{11/3}}-\frac{b^{2/3} (8 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{11/3}}+\frac{8 A b-5 a B}{6 a^3 x^2}-\frac{8 A b-5 a B}{15 a^2 b x^5}+\frac{A b-a B}{3 a b x^5 \left(a+b x^3\right)}",1,"-(8*A*b - 5*a*B)/(15*a^2*b*x^5) + (8*A*b - 5*a*B)/(6*a^3*x^2) + (A*b - a*B)/(3*a*b*x^5*(a + b*x^3)) - (b^(2/3)*(8*A*b - 5*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(11/3)) + (b^(2/3)*(8*A*b - 5*a*B)*Log[a^(1/3) + b^(1/3)*x])/(9*a^(11/3)) - (b^(2/3)*(8*A*b - 5*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(18*a^(11/3))","A",9,8,20,0.4000,1,"{457, 325, 200, 31, 634, 617, 204, 628}"
87,1,97,0,0.0994124,"\int \frac{A+B x^3}{x^7 \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^7*(a + b*x^3)^2),x]","\frac{b (A b-a B)}{3 a^3 \left(a+b x^3\right)}+\frac{2 A b-a B}{3 a^3 x^3}-\frac{b (3 A b-2 a B) \log \left(a+b x^3\right)}{3 a^4}+\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{A}{6 a^2 x^6}","\frac{b (A b-a B)}{3 a^3 \left(a+b x^3\right)}+\frac{2 A b-a B}{3 a^3 x^3}-\frac{b (3 A b-2 a B) \log \left(a+b x^3\right)}{3 a^4}+\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{A}{6 a^2 x^6}",1,"-A/(6*a^2*x^6) + (2*A*b - a*B)/(3*a^3*x^3) + (b*(A*b - a*B))/(3*a^3*(a + b*x^3)) + (b*(3*A*b - 2*a*B)*Log[x])/a^4 - (b*(3*A*b - 2*a*B)*Log[a + b*x^3])/(3*a^4)","A",3,2,20,0.1000,1,"{446, 77}"
88,1,107,0,0.1401155,"\int \frac{x^{11} \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^11*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{a^2 (3 A b-4 a B)}{3 b^5 \left(a+b x^3\right)}+\frac{a^3 (A b-a B)}{6 b^5 \left(a+b x^3\right)^2}+\frac{x^3 (A b-3 a B)}{3 b^4}-\frac{a (A b-2 a B) \log \left(a+b x^3\right)}{b^5}+\frac{B x^6}{6 b^3}","-\frac{a^2 (3 A b-4 a B)}{3 b^5 \left(a+b x^3\right)}+\frac{a^3 (A b-a B)}{6 b^5 \left(a+b x^3\right)^2}+\frac{x^3 (A b-3 a B)}{3 b^4}-\frac{a (A b-2 a B) \log \left(a+b x^3\right)}{b^5}+\frac{B x^6}{6 b^3}",1,"((A*b - 3*a*B)*x^3)/(3*b^4) + (B*x^6)/(6*b^3) + (a^3*(A*b - a*B))/(6*b^5*(a + b*x^3)^2) - (a^2*(3*A*b - 4*a*B))/(3*b^5*(a + b*x^3)) - (a*(A*b - 2*a*B)*Log[a + b*x^3])/b^5","A",3,2,20,0.1000,1,"{446, 77}"
89,1,88,0,0.0878218,"\int \frac{x^8 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^8*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{a^2 (A b-a B)}{6 b^4 \left(a+b x^3\right)^2}+\frac{a (2 A b-3 a B)}{3 b^4 \left(a+b x^3\right)}+\frac{(A b-3 a B) \log \left(a+b x^3\right)}{3 b^4}+\frac{B x^3}{3 b^3}","-\frac{a^2 (A b-a B)}{6 b^4 \left(a+b x^3\right)^2}+\frac{a (2 A b-3 a B)}{3 b^4 \left(a+b x^3\right)}+\frac{(A b-3 a B) \log \left(a+b x^3\right)}{3 b^4}+\frac{B x^3}{3 b^3}",1,"(B*x^3)/(3*b^3) - (a^2*(A*b - a*B))/(6*b^4*(a + b*x^3)^2) + (a*(2*A*b - 3*a*B))/(3*b^4*(a + b*x^3)) + ((A*b - 3*a*B)*Log[a + b*x^3])/(3*b^4)","A",3,2,20,0.1000,1,"{446, 77}"
90,1,66,0,0.0678781,"\int \frac{x^5 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^5*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{A b-2 a B}{3 b^3 \left(a+b x^3\right)}+\frac{a (A b-a B)}{6 b^3 \left(a+b x^3\right)^2}+\frac{B \log \left(a+b x^3\right)}{3 b^3}","-\frac{A b-2 a B}{3 b^3 \left(a+b x^3\right)}+\frac{a (A b-a B)}{6 b^3 \left(a+b x^3\right)^2}+\frac{B \log \left(a+b x^3\right)}{3 b^3}",1,"(a*(A*b - a*B))/(6*b^3*(a + b*x^3)^2) - (A*b - 2*a*B)/(3*b^3*(a + b*x^3)) + (B*Log[a + b*x^3])/(3*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
91,1,32,0,0.022282,"\int \frac{x^2 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^2*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{\left(A+B x^3\right)^2}{6 \left(a+b x^3\right)^2 (A b-a B)}","-\frac{\left(A+B x^3\right)^2}{6 \left(a+b x^3\right)^2 (A b-a B)}",1,"-(A + B*x^3)^2/(6*(A*b - a*B)*(a + b*x^3)^2)","A",2,2,20,0.1000,1,"{444, 37}"
92,1,68,0,0.0583117,"\int \frac{A+B x^3}{x \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x*(a + b*x^3)^3),x]","\frac{A}{3 a^2 \left(a+b x^3\right)}-\frac{A \log \left(a+b x^3\right)}{3 a^3}+\frac{A \log (x)}{a^3}+\frac{A b-a B}{6 a b \left(a+b x^3\right)^2}","\frac{A}{3 a^2 \left(a+b x^3\right)}-\frac{A \log \left(a+b x^3\right)}{3 a^3}+\frac{A \log (x)}{a^3}+\frac{A b-a B}{6 a b \left(a+b x^3\right)^2}",1,"(A*b - a*B)/(6*a*b*(a + b*x^3)^2) + A/(3*a^2*(a + b*x^3)) + (A*Log[x])/a^3 - (A*Log[a + b*x^3])/(3*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
93,1,101,0,0.0998586,"\int \frac{A+B x^3}{x^4 \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^4*(a + b*x^3)^3),x]","-\frac{2 A b-a B}{3 a^3 \left(a+b x^3\right)}-\frac{A b-a B}{6 a^2 \left(a+b x^3\right)^2}+\frac{(3 A b-a B) \log \left(a+b x^3\right)}{3 a^4}-\frac{\log (x) (3 A b-a B)}{a^4}-\frac{A}{3 a^3 x^3}","-\frac{2 A b-a B}{3 a^3 \left(a+b x^3\right)}-\frac{A b-a B}{6 a^2 \left(a+b x^3\right)^2}+\frac{(3 A b-a B) \log \left(a+b x^3\right)}{3 a^4}-\frac{\log (x) (3 A b-a B)}{a^4}-\frac{A}{3 a^3 x^3}",1,"-A/(3*a^3*x^3) - (A*b - a*B)/(6*a^2*(a + b*x^3)^2) - (2*A*b - a*B)/(3*a^3*(a + b*x^3)) - ((3*A*b - a*B)*Log[x])/a^4 + ((3*A*b - a*B)*Log[a + b*x^3])/(3*a^4)","A",3,2,20,0.1000,1,"{446, 77}"
94,1,122,0,0.129556,"\int \frac{A+B x^3}{x^7 \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^7*(a + b*x^3)^3),x]","\frac{b (3 A b-2 a B)}{3 a^4 \left(a+b x^3\right)}+\frac{b (A b-a B)}{6 a^3 \left(a+b x^3\right)^2}+\frac{3 A b-a B}{3 a^4 x^3}-\frac{b (2 A b-a B) \log \left(a+b x^3\right)}{a^5}+\frac{3 b \log (x) (2 A b-a B)}{a^5}-\frac{A}{6 a^3 x^6}","\frac{b (3 A b-2 a B)}{3 a^4 \left(a+b x^3\right)}+\frac{b (A b-a B)}{6 a^3 \left(a+b x^3\right)^2}+\frac{3 A b-a B}{3 a^4 x^3}-\frac{b (2 A b-a B) \log \left(a+b x^3\right)}{a^5}+\frac{3 b \log (x) (2 A b-a B)}{a^5}-\frac{A}{6 a^3 x^6}",1,"-A/(6*a^3*x^6) + (3*A*b - a*B)/(3*a^4*x^3) + (b*(A*b - a*B))/(6*a^3*(a + b*x^3)^2) + (b*(3*A*b - 2*a*B))/(3*a^4*(a + b*x^3)) + (3*b*(2*A*b - a*B)*Log[x])/a^5 - (b*(2*A*b - a*B)*Log[a + b*x^3])/a^5","A",3,2,20,0.1000,1,"{446, 77}"
95,1,246,0,0.155731,"\int \frac{x^{10} \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^10*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{2 a^{2/3} (5 A b-11 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 b^{14/3}}+\frac{4 a^{2/3} (5 A b-11 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 b^{14/3}}+\frac{4 a^{2/3} (5 A b-11 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} b^{14/3}}+\frac{x^8 (5 A b-11 a B)}{18 a b^2 \left(a+b x^3\right)}-\frac{4 x^5 (5 A b-11 a B)}{45 a b^3}+\frac{2 x^2 (5 A b-11 a B)}{9 b^4}+\frac{x^{11} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","-\frac{2 a^{2/3} (5 A b-11 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 b^{14/3}}+\frac{4 a^{2/3} (5 A b-11 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 b^{14/3}}+\frac{4 a^{2/3} (5 A b-11 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} b^{14/3}}+\frac{x^8 (5 A b-11 a B)}{18 a b^2 \left(a+b x^3\right)}-\frac{4 x^5 (5 A b-11 a B)}{45 a b^3}+\frac{2 x^2 (5 A b-11 a B)}{9 b^4}+\frac{x^{11} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"(2*(5*A*b - 11*a*B)*x^2)/(9*b^4) - (4*(5*A*b - 11*a*B)*x^5)/(45*a*b^3) + ((A*b - a*B)*x^11)/(6*a*b*(a + b*x^3)^2) + ((5*A*b - 11*a*B)*x^8)/(18*a*b^2*(a + b*x^3)) + (4*a^(2/3)*(5*A*b - 11*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*b^(14/3)) + (4*a^(2/3)*(5*A*b - 11*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*b^(14/3)) - (2*a^(2/3)*(5*A*b - 11*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*b^(14/3))","A",10,9,20,0.4500,1,"{457, 288, 302, 292, 31, 634, 617, 204, 628}"
96,1,244,0,0.1653745,"\int \frac{x^9 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^9*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{7 \sqrt[3]{a} (2 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 b^{13/3}}+\frac{x^7 (2 A b-5 a B)}{9 a b^2 \left(a+b x^3\right)}-\frac{7 x^4 (2 A b-5 a B)}{36 a b^3}+\frac{7 x (2 A b-5 a B)}{9 b^4}-\frac{7 \sqrt[3]{a} (2 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 b^{13/3}}+\frac{7 \sqrt[3]{a} (2 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} b^{13/3}}+\frac{x^{10} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{7 \sqrt[3]{a} (2 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 b^{13/3}}+\frac{x^7 (2 A b-5 a B)}{9 a b^2 \left(a+b x^3\right)}-\frac{7 x^4 (2 A b-5 a B)}{36 a b^3}+\frac{7 x (2 A b-5 a B)}{9 b^4}-\frac{7 \sqrt[3]{a} (2 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 b^{13/3}}+\frac{7 \sqrt[3]{a} (2 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} b^{13/3}}+\frac{x^{10} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"(7*(2*A*b - 5*a*B)*x)/(9*b^4) - (7*(2*A*b - 5*a*B)*x^4)/(36*a*b^3) + ((A*b - a*B)*x^10)/(6*a*b*(a + b*x^3)^2) + ((2*A*b - 5*a*B)*x^7)/(9*a*b^2*(a + b*x^3)) + (7*a^(1/3)*(2*A*b - 5*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*b^(13/3)) - (7*a^(1/3)*(2*A*b - 5*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*b^(13/3)) + (7*a^(1/3)*(2*A*b - 5*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*b^(13/3))","A",10,9,20,0.4500,1,"{457, 288, 302, 200, 31, 634, 617, 204, 628}"
97,1,222,0,0.1399608,"\int \frac{x^7 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^7*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{5 (A b-4 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 \sqrt[3]{a} b^{11/3}}+\frac{x^5 (A b-4 a B)}{9 a b^2 \left(a+b x^3\right)}-\frac{5 x^2 (A b-4 a B)}{18 a b^3}-\frac{5 (A b-4 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 \sqrt[3]{a} b^{11/3}}-\frac{5 (A b-4 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} \sqrt[3]{a} b^{11/3}}+\frac{x^8 (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{5 (A b-4 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 \sqrt[3]{a} b^{11/3}}+\frac{x^5 (A b-4 a B)}{9 a b^2 \left(a+b x^3\right)}-\frac{5 x^2 (A b-4 a B)}{18 a b^3}-\frac{5 (A b-4 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 \sqrt[3]{a} b^{11/3}}-\frac{5 (A b-4 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} \sqrt[3]{a} b^{11/3}}+\frac{x^8 (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"(-5*(A*b - 4*a*B)*x^2)/(18*a*b^3) + ((A*b - a*B)*x^8)/(6*a*b*(a + b*x^3)^2) + ((A*b - 4*a*B)*x^5)/(9*a*b^2*(a + b*x^3)) - (5*(A*b - 4*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(1/3)*b^(11/3)) - (5*(A*b - 4*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(1/3)*b^(11/3)) + (5*(A*b - 4*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(1/3)*b^(11/3))","A",9,9,20,0.4500,1,"{457, 288, 321, 292, 31, 634, 617, 204, 628}"
98,1,220,0,0.1258023,"\int \frac{x^6 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^6*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{(A b-7 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{2/3} b^{10/3}}+\frac{2 (A b-7 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{2/3} b^{10/3}}-\frac{2 (A b-7 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{2/3} b^{10/3}}+\frac{x^4 (A b-7 a B)}{18 a b^2 \left(a+b x^3\right)}-\frac{2 x (A b-7 a B)}{9 a b^3}+\frac{x^7 (A b-a B)}{6 a b \left(a+b x^3\right)^2}","-\frac{(A b-7 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{2/3} b^{10/3}}+\frac{2 (A b-7 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{2/3} b^{10/3}}-\frac{2 (A b-7 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{2/3} b^{10/3}}+\frac{x^4 (A b-7 a B)}{18 a b^2 \left(a+b x^3\right)}-\frac{2 x (A b-7 a B)}{9 a b^3}+\frac{x^7 (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"(-2*(A*b - 7*a*B)*x)/(9*a*b^3) + ((A*b - a*B)*x^7)/(6*a*b*(a + b*x^3)^2) + ((A*b - 7*a*B)*x^4)/(18*a*b^2*(a + b*x^3)) - (2*(A*b - 7*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(2/3)*b^(10/3)) + (2*(A*b - 7*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(2/3)*b^(10/3)) - ((A*b - 7*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(2/3)*b^(10/3))","A",9,9,20,0.4500,1,"{457, 288, 321, 200, 31, 634, 617, 204, 628}"
99,1,201,0,0.1068893,"\int \frac{x^4 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^4*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{(5 a B+A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{4/3} b^{8/3}}-\frac{(5 a B+A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{4/3} b^{8/3}}-\frac{(5 a B+A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{8/3}}-\frac{x^2 (5 a B+A b)}{18 a b^2 \left(a+b x^3\right)}+\frac{x^5 (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{(5 a B+A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{4/3} b^{8/3}}-\frac{(5 a B+A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{4/3} b^{8/3}}-\frac{(5 a B+A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} b^{8/3}}-\frac{x^2 (5 a B+A b)}{18 a b^2 \left(a+b x^3\right)}+\frac{x^5 (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^5)/(6*a*b*(a + b*x^3)^2) - ((A*b + 5*a*B)*x^2)/(18*a*b^2*(a + b*x^3)) - ((A*b + 5*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(4/3)*b^(8/3)) - ((A*b + 5*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(4/3)*b^(8/3)) + ((A*b + 5*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(4/3)*b^(8/3))","A",8,8,20,0.4000,1,"{457, 288, 292, 31, 634, 617, 204, 628}"
100,1,199,0,0.1134008,"\int \frac{x^3 \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^3*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{(2 a B+A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{7/3}}+\frac{(2 a B+A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{7/3}}-\frac{(2 a B+A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{7/3}}-\frac{x (2 a B+A b)}{9 a b^2 \left(a+b x^3\right)}+\frac{x^4 (A b-a B)}{6 a b \left(a+b x^3\right)^2}","-\frac{(2 a B+A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{5/3} b^{7/3}}+\frac{(2 a B+A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{5/3} b^{7/3}}-\frac{(2 a B+A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} b^{7/3}}-\frac{x (2 a B+A b)}{9 a b^2 \left(a+b x^3\right)}+\frac{x^4 (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^4)/(6*a*b*(a + b*x^3)^2) - ((A*b + 2*a*B)*x)/(9*a*b^2*(a + b*x^3)) - ((A*b + 2*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*b^(7/3)) + ((A*b + 2*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(5/3)*b^(7/3)) - ((A*b + 2*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(5/3)*b^(7/3))","A",8,8,20,0.4000,1,"{457, 288, 200, 31, 634, 617, 204, 628}"
101,1,201,0,0.11535,"\int \frac{x \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{(a B+2 A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{7/3} b^{5/3}}-\frac{(a B+2 A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{5/3}}-\frac{(a B+2 A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{5/3}}+\frac{x^2 (a B+2 A b)}{9 a^2 b \left(a+b x^3\right)}+\frac{x^2 (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{(a B+2 A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{7/3} b^{5/3}}-\frac{(a B+2 A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{7/3} b^{5/3}}-\frac{(a B+2 A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} b^{5/3}}+\frac{x^2 (a B+2 A b)}{9 a^2 b \left(a+b x^3\right)}+\frac{x^2 (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^2)/(6*a*b*(a + b*x^3)^2) + ((2*A*b + a*B)*x^2)/(9*a^2*b*(a + b*x^3)) - ((2*A*b + a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*b^(5/3)) - ((2*A*b + a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(7/3)*b^(5/3)) + ((2*A*b + a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(7/3)*b^(5/3))","A",8,8,18,0.4444,1,"{457, 290, 292, 31, 634, 617, 204, 628}"
102,1,197,0,0.1025996,"\int \frac{A+B x^3}{\left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(a + b*x^3)^3,x]","-\frac{(a B+5 A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{4/3}}+\frac{(a B+5 A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{4/3}}-\frac{(a B+5 A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{4/3}}+\frac{x (a B+5 A b)}{18 a^2 b \left(a+b x^3\right)}+\frac{x (A b-a B)}{6 a b \left(a+b x^3\right)^2}","-\frac{(a B+5 A b) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{8/3} b^{4/3}}+\frac{(a B+5 A b) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{8/3} b^{4/3}}-\frac{(a B+5 A b) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} b^{4/3}}+\frac{x (a B+5 A b)}{18 a^2 b \left(a+b x^3\right)}+\frac{x (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x)/(6*a*b*(a + b*x^3)^2) + ((5*A*b + a*B)*x)/(18*a^2*b*(a + b*x^3)) - ((5*A*b + a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*b^(4/3)) + ((5*A*b + a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(8/3)*b^(4/3)) - ((5*A*b + a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(8/3)*b^(4/3))","A",8,8,17,0.4706,1,"{385, 199, 200, 31, 634, 617, 204, 628}"
103,1,227,0,0.1234697,"\int \frac{A+B x^3}{x^2 \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^2*(a + b*x^3)^3),x]","-\frac{(7 A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{10/3} b^{2/3}}+\frac{2 (7 A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{10/3} b^{2/3}}+\frac{2 (7 A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} b^{2/3}}+\frac{7 A b-a B}{18 a^2 b x \left(a+b x^3\right)}-\frac{2 (7 A b-a B)}{9 a^3 b x}+\frac{A b-a B}{6 a b x \left(a+b x^3\right)^2}","-\frac{(7 A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{10/3} b^{2/3}}+\frac{2 (7 A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{10/3} b^{2/3}}+\frac{2 (7 A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{10/3} b^{2/3}}+\frac{7 A b-a B}{18 a^2 b x \left(a+b x^3\right)}-\frac{2 (7 A b-a B)}{9 a^3 b x}+\frac{A b-a B}{6 a b x \left(a+b x^3\right)^2}",1,"(-2*(7*A*b - a*B))/(9*a^3*b*x) + (A*b - a*B)/(6*a*b*x*(a + b*x^3)^2) + (7*A*b - a*B)/(18*a^2*b*x*(a + b*x^3)) + (2*(7*A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(10/3)*b^(2/3)) + (2*(7*A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(10/3)*b^(2/3)) - ((7*A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(10/3)*b^(2/3))","A",9,9,20,0.4500,1,"{457, 290, 325, 292, 31, 634, 617, 204, 628}"
104,1,227,0,0.1310914,"\int \frac{A+B x^3}{x^3 \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^3*(a + b*x^3)^3),x]","\frac{5 (4 A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{11/3} \sqrt[3]{b}}+\frac{4 A b-a B}{9 a^2 b x^2 \left(a+b x^3\right)}-\frac{5 (4 A b-a B)}{18 a^3 b x^2}-\frac{5 (4 A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3} \sqrt[3]{b}}+\frac{5 (4 A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} \sqrt[3]{b}}+\frac{A b-a B}{6 a b x^2 \left(a+b x^3\right)^2}","\frac{5 (4 A b-a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{11/3} \sqrt[3]{b}}+\frac{4 A b-a B}{9 a^2 b x^2 \left(a+b x^3\right)}-\frac{5 (4 A b-a B)}{18 a^3 b x^2}-\frac{5 (4 A b-a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{11/3} \sqrt[3]{b}}+\frac{5 (4 A b-a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{11/3} \sqrt[3]{b}}+\frac{A b-a B}{6 a b x^2 \left(a+b x^3\right)^2}",1,"(-5*(4*A*b - a*B))/(18*a^3*b*x^2) + (A*b - a*B)/(6*a*b*x^2*(a + b*x^3)^2) + (4*A*b - a*B)/(9*a^2*b*x^2*(a + b*x^3)) + (5*(4*A*b - a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(11/3)*b^(1/3)) - (5*(4*A*b - a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(11/3)*b^(1/3)) + (5*(4*A*b - a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(11/3)*b^(1/3))","A",9,9,20,0.4500,1,"{457, 290, 325, 200, 31, 634, 617, 204, 628}"
105,1,246,0,0.1581775,"\int \frac{A+B x^3}{x^5 \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^5*(a + b*x^3)^3),x]","\frac{7 \sqrt[3]{b} (5 A b-2 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{13/3}}+\frac{5 A b-2 a B}{9 a^2 b x^4 \left(a+b x^3\right)}-\frac{7 (5 A b-2 a B)}{36 a^3 b x^4}+\frac{7 (5 A b-2 a B)}{9 a^4 x}-\frac{7 \sqrt[3]{b} (5 A b-2 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{13/3}}-\frac{7 \sqrt[3]{b} (5 A b-2 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{13/3}}+\frac{A b-a B}{6 a b x^4 \left(a+b x^3\right)^2}","\frac{7 \sqrt[3]{b} (5 A b-2 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{54 a^{13/3}}+\frac{5 A b-2 a B}{9 a^2 b x^4 \left(a+b x^3\right)}-\frac{7 (5 A b-2 a B)}{36 a^3 b x^4}+\frac{7 (5 A b-2 a B)}{9 a^4 x}-\frac{7 \sqrt[3]{b} (5 A b-2 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{13/3}}-\frac{7 \sqrt[3]{b} (5 A b-2 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{13/3}}+\frac{A b-a B}{6 a b x^4 \left(a+b x^3\right)^2}",1,"(-7*(5*A*b - 2*a*B))/(36*a^3*b*x^4) + (7*(5*A*b - 2*a*B))/(9*a^4*x) + (A*b - a*B)/(6*a*b*x^4*(a + b*x^3)^2) + (5*A*b - 2*a*B)/(9*a^2*b*x^4*(a + b*x^3)) - (7*b^(1/3)*(5*A*b - 2*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(13/3)) - (7*b^(1/3)*(5*A*b - 2*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(13/3)) + (7*b^(1/3)*(5*A*b - 2*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(54*a^(13/3))","A",10,9,20,0.4500,1,"{457, 290, 325, 292, 31, 634, 617, 204, 628}"
106,1,246,0,0.1416591,"\int \frac{A+B x^3}{x^6 \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^6*(a + b*x^3)^3),x]","-\frac{2 b^{2/3} (11 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{14/3}}+\frac{4 b^{2/3} (11 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{14/3}}-\frac{4 b^{2/3} (11 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{14/3}}+\frac{11 A b-5 a B}{18 a^2 b x^5 \left(a+b x^3\right)}+\frac{2 (11 A b-5 a B)}{9 a^4 x^2}-\frac{4 (11 A b-5 a B)}{45 a^3 b x^5}+\frac{A b-a B}{6 a b x^5 \left(a+b x^3\right)^2}","-\frac{2 b^{2/3} (11 A b-5 a B) \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{27 a^{14/3}}+\frac{4 b^{2/3} (11 A b-5 a B) \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{27 a^{14/3}}-\frac{4 b^{2/3} (11 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{14/3}}+\frac{11 A b-5 a B}{18 a^2 b x^5 \left(a+b x^3\right)}+\frac{2 (11 A b-5 a B)}{9 a^4 x^2}-\frac{4 (11 A b-5 a B)}{45 a^3 b x^5}+\frac{A b-a B}{6 a b x^5 \left(a+b x^3\right)^2}",1,"(-4*(11*A*b - 5*a*B))/(45*a^3*b*x^5) + (2*(11*A*b - 5*a*B))/(9*a^4*x^2) + (A*b - a*B)/(6*a*b*x^5*(a + b*x^3)^2) + (11*A*b - 5*a*B)/(18*a^2*b*x^5*(a + b*x^3)) - (4*b^(2/3)*(11*A*b - 5*a*B)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(14/3)) + (4*b^(2/3)*(11*A*b - 5*a*B)*Log[a^(1/3) + b^(1/3)*x])/(27*a^(14/3)) - (2*b^(2/3)*(11*A*b - 5*a*B)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(27*a^(14/3))","A",10,9,20,0.4500,1,"{457, 290, 325, 200, 31, 634, 617, 204, 628}"
107,1,70,0,0.0663375,"\int \frac{x^8}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^8/((a + b*x^3)*(c + d*x^3)),x]","\frac{a^2 \log \left(a+b x^3\right)}{3 b^2 (b c-a d)}-\frac{c^2 \log \left(c+d x^3\right)}{3 d^2 (b c-a d)}+\frac{x^3}{3 b d}","\frac{a^2 \log \left(a+b x^3\right)}{3 b^2 (b c-a d)}-\frac{c^2 \log \left(c+d x^3\right)}{3 d^2 (b c-a d)}+\frac{x^3}{3 b d}",1,"x^3/(3*b*d) + (a^2*Log[a + b*x^3])/(3*b^2*(b*c - a*d)) - (c^2*Log[c + d*x^3])/(3*d^2*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
108,1,301,0,0.3097253,"\int \frac{x^7}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^7/((a + b*x^3)*(c + d*x^3)),x]","\frac{a^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3} (b c-a d)}-\frac{a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3} (b c-a d)}-\frac{a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} (b c-a d)}-\frac{c^{5/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 d^{5/3} (b c-a d)}+\frac{c^{5/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 d^{5/3} (b c-a d)}+\frac{c^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^{5/3} (b c-a d)}+\frac{x^2}{2 b d}","\frac{a^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{5/3} (b c-a d)}-\frac{a^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{5/3} (b c-a d)}-\frac{a^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{5/3} (b c-a d)}-\frac{c^{5/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 d^{5/3} (b c-a d)}+\frac{c^{5/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 d^{5/3} (b c-a d)}+\frac{c^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^{5/3} (b c-a d)}+\frac{x^2}{2 b d}",1,"x^2/(2*b*d) - (a^(5/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(5/3)*(b*c - a*d)) + (c^(5/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d^(5/3)*(b*c - a*d)) - (a^(5/3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(5/3)*(b*c - a*d)) + (c^(5/3)*Log[c^(1/3) + d^(1/3)*x])/(3*d^(5/3)*(b*c - a*d)) + (a^(5/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(5/3)*(b*c - a*d)) - (c^(5/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*d^(5/3)*(b*c - a*d))","A",15,8,22,0.3636,1,"{479, 584, 292, 31, 634, 617, 204, 628}"
109,1,296,0,0.2668743,"\int \frac{x^6}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^6/((a + b*x^3)*(c + d*x^3)),x]","-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3} (b c-a d)}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{4/3} (b c-a d)}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} (b c-a d)}+\frac{c^{4/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 d^{4/3} (b c-a d)}-\frac{c^{4/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 d^{4/3} (b c-a d)}+\frac{c^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^{4/3} (b c-a d)}+\frac{x}{b d}","-\frac{a^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{4/3} (b c-a d)}+\frac{a^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{4/3} (b c-a d)}-\frac{a^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{4/3} (b c-a d)}+\frac{c^{4/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 d^{4/3} (b c-a d)}-\frac{c^{4/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 d^{4/3} (b c-a d)}+\frac{c^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^{4/3} (b c-a d)}+\frac{x}{b d}",1,"x/(b*d) - (a^(4/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(4/3)*(b*c - a*d)) + (c^(4/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d^(4/3)*(b*c - a*d)) + (a^(4/3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(4/3)*(b*c - a*d)) - (c^(4/3)*Log[c^(1/3) + d^(1/3)*x])/(3*d^(4/3)*(b*c - a*d)) - (a^(4/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(4/3)*(b*c - a*d)) + (c^(4/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*d^(4/3)*(b*c - a*d))","A",14,8,22,0.3636,1,"{479, 522, 200, 31, 634, 617, 204, 628}"
110,1,53,0,0.0500404,"\int \frac{x^5}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^5/((a + b*x^3)*(c + d*x^3)),x]","\frac{c \log \left(c+d x^3\right)}{3 d (b c-a d)}-\frac{a \log \left(a+b x^3\right)}{3 b (b c-a d)}","\frac{c \log \left(c+d x^3\right)}{3 d (b c-a d)}-\frac{a \log \left(a+b x^3\right)}{3 b (b c-a d)}",1,"-(a*Log[a + b*x^3])/(3*b*(b*c - a*d)) + (c*Log[c + d*x^3])/(3*d*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
111,1,288,0,0.1541597,"\int \frac{x^4}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^4/((a + b*x^3)*(c + d*x^3)),x]","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{2/3} (b c-a d)}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{2/3} (b c-a d)}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{2/3} (b c-a d)}+\frac{c^{2/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 d^{2/3} (b c-a d)}-\frac{c^{2/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 d^{2/3} (b c-a d)}-\frac{c^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^{2/3} (b c-a d)}","-\frac{a^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 b^{2/3} (b c-a d)}+\frac{a^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 b^{2/3} (b c-a d)}+\frac{a^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^{2/3} (b c-a d)}+\frac{c^{2/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 d^{2/3} (b c-a d)}-\frac{c^{2/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 d^{2/3} (b c-a d)}-\frac{c^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^{2/3} (b c-a d)}",1,"(a^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(2/3)*(b*c - a*d)) - (c^(2/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d^(2/3)*(b*c - a*d)) + (a^(2/3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(2/3)*(b*c - a*d)) - (c^(2/3)*Log[c^(1/3) + d^(1/3)*x])/(3*d^(2/3)*(b*c - a*d)) - (a^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(2/3)*(b*c - a*d)) + (c^(2/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*d^(2/3)*(b*c - a*d))","A",13,7,22,0.3182,1,"{481, 292, 31, 634, 617, 204, 628}"
112,1,288,0,0.1483881,"\int \frac{x^3}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^3/((a + b*x^3)*(c + d*x^3)),x]","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{b} (b c-a d)}-\frac{\sqrt[3]{c} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 \sqrt[3]{d} (b c-a d)}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{b} (b c-a d)}+\frac{\sqrt[3]{c} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 \sqrt[3]{d} (b c-a d)}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{b} (b c-a d)}-\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} \sqrt[3]{d} (b c-a d)}","\frac{\sqrt[3]{a} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{b} (b c-a d)}-\frac{\sqrt[3]{c} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 \sqrt[3]{d} (b c-a d)}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{b} (b c-a d)}+\frac{\sqrt[3]{c} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 \sqrt[3]{d} (b c-a d)}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{b} (b c-a d)}-\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} \sqrt[3]{d} (b c-a d)}",1,"(a^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^(1/3)*(b*c - a*d)) - (c^(1/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d^(1/3)*(b*c - a*d)) - (a^(1/3)*Log[a^(1/3) + b^(1/3)*x])/(3*b^(1/3)*(b*c - a*d)) + (c^(1/3)*Log[c^(1/3) + d^(1/3)*x])/(3*d^(1/3)*(b*c - a*d)) + (a^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*b^(1/3)*(b*c - a*d)) - (c^(1/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*d^(1/3)*(b*c - a*d))","A",13,7,22,0.3182,1,"{481, 200, 31, 634, 617, 204, 628}"
113,1,45,0,0.0308165,"\int \frac{x^2}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x^2/((a + b*x^3)*(c + d*x^3)),x]","\frac{\log \left(a+b x^3\right)}{3 (b c-a d)}-\frac{\log \left(c+d x^3\right)}{3 (b c-a d)}","\frac{\log \left(a+b x^3\right)}{3 (b c-a d)}-\frac{\log \left(c+d x^3\right)}{3 (b c-a d)}",1,"Log[a + b*x^3]/(3*(b*c - a*d)) - Log[c + d*x^3]/(3*(b*c - a*d))","A",4,3,22,0.1364,1,"{444, 36, 31}"
114,1,288,0,0.1430015,"\int \frac{x}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[x/((a + b*x^3)*(c + d*x^3)),x]","\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} (b c-a d)}-\frac{\sqrt[3]{d} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 \sqrt[3]{c} (b c-a d)}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} (b c-a d)}+\frac{\sqrt[3]{d} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 \sqrt[3]{c} (b c-a d)}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} (b c-a d)}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} \sqrt[3]{c} (b c-a d)}","\frac{\sqrt[3]{b} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 \sqrt[3]{a} (b c-a d)}-\frac{\sqrt[3]{d} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 \sqrt[3]{c} (b c-a d)}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 \sqrt[3]{a} (b c-a d)}+\frac{\sqrt[3]{d} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 \sqrt[3]{c} (b c-a d)}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} (b c-a d)}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} \sqrt[3]{c} (b c-a d)}",1,"-((b^(1/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*(b*c - a*d))) + (d^(1/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(1/3)*(b*c - a*d)) - (b^(1/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(1/3)*(b*c - a*d)) + (d^(1/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(1/3)*(b*c - a*d)) + (b^(1/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(1/3)*(b*c - a*d)) - (d^(1/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(1/3)*(b*c - a*d))","A",13,7,20,0.3500,1,"{482, 292, 31, 634, 617, 204, 628}"
115,1,288,0,0.1423171,"\int \frac{1}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)*(c + d*x^3)),x]","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} (b c-a d)}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} (b c-a d)}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} (b c-a d)}+\frac{d^{2/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} (b c-a d)}-\frac{d^{2/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} (b c-a d)}+\frac{d^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)}","-\frac{b^{2/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{2/3} (b c-a d)}+\frac{b^{2/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{2/3} (b c-a d)}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} (b c-a d)}+\frac{d^{2/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{2/3} (b c-a d)}-\frac{d^{2/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{2/3} (b c-a d)}+\frac{d^{2/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)}",1,"-((b^(2/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*(b*c - a*d))) + (d^(2/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*(b*c - a*d)) + (b^(2/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(2/3)*(b*c - a*d)) - (d^(2/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(2/3)*(b*c - a*d)) - (b^(2/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(2/3)*(b*c - a*d)) + (d^(2/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(2/3)*(b*c - a*d))","A",13,7,19,0.3684,1,"{391, 200, 31, 634, 617, 204, 628}"
116,1,62,0,0.0604353,"\int \frac{1}{x \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x*(a + b*x^3)*(c + d*x^3)),x]","-\frac{b \log \left(a+b x^3\right)}{3 a (b c-a d)}+\frac{d \log \left(c+d x^3\right)}{3 c (b c-a d)}+\frac{\log (x)}{a c}","-\frac{b \log \left(a+b x^3\right)}{3 a (b c-a d)}+\frac{d \log \left(c+d x^3\right)}{3 c (b c-a d)}+\frac{\log (x)}{a c}",1,"Log[x]/(a*c) - (b*Log[a + b*x^3])/(3*a*(b*c - a*d)) + (d*Log[c + d*x^3])/(3*c*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
117,1,299,0,0.2717759,"\int \frac{1}{x^2 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^2*(a + b*x^3)*(c + d*x^3)),x]","-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} (b c-a d)}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} (b c-a d)}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} (b c-a d)}+\frac{d^{4/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{4/3} (b c-a d)}-\frac{d^{4/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{4/3} (b c-a d)}-\frac{d^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{4/3} (b c-a d)}-\frac{1}{a c x}","-\frac{b^{4/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{4/3} (b c-a d)}+\frac{b^{4/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{4/3} (b c-a d)}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} (b c-a d)}+\frac{d^{4/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{4/3} (b c-a d)}-\frac{d^{4/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{4/3} (b c-a d)}-\frac{d^{4/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{4/3} (b c-a d)}-\frac{1}{a c x}",1,"-(1/(a*c*x)) + (b^(4/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*(b*c - a*d)) - (d^(4/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(4/3)*(b*c - a*d)) + (b^(4/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(4/3)*(b*c - a*d)) - (d^(4/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(4/3)*(b*c - a*d)) - (b^(4/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(4/3)*(b*c - a*d)) + (d^(4/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(4/3)*(b*c - a*d))","A",15,8,22,0.3636,1,"{480, 584, 292, 31, 634, 617, 204, 628}"
118,1,301,0,0.2548379,"\int \frac{1}{x^3 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^3*(a + b*x^3)*(c + d*x^3)),x]","\frac{b^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3} (b c-a d)}-\frac{b^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3} (b c-a d)}+\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} (b c-a d)}-\frac{d^{5/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{5/3} (b c-a d)}+\frac{d^{5/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{5/3} (b c-a d)}-\frac{d^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{5/3} (b c-a d)}-\frac{1}{2 a c x^2}","\frac{b^{5/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{5/3} (b c-a d)}-\frac{b^{5/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{5/3} (b c-a d)}+\frac{b^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} (b c-a d)}-\frac{d^{5/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{5/3} (b c-a d)}+\frac{d^{5/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{5/3} (b c-a d)}-\frac{d^{5/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{5/3} (b c-a d)}-\frac{1}{2 a c x^2}",1,"-1/(2*a*c*x^2) + (b^(5/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*(b*c - a*d)) - (d^(5/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(5/3)*(b*c - a*d)) - (b^(5/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(5/3)*(b*c - a*d)) + (d^(5/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(5/3)*(b*c - a*d)) + (b^(5/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(5/3)*(b*c - a*d)) - (d^(5/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(5/3)*(b*c - a*d))","A",14,8,22,0.3636,1,"{480, 522, 200, 31, 634, 617, 204, 628}"
119,1,87,0,0.0922362,"\int \frac{1}{x^4 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^4*(a + b*x^3)*(c + d*x^3)),x]","\frac{b^2 \log \left(a+b x^3\right)}{3 a^2 (b c-a d)}-\frac{\log (x) (a d+b c)}{a^2 c^2}-\frac{d^2 \log \left(c+d x^3\right)}{3 c^2 (b c-a d)}-\frac{1}{3 a c x^3}","\frac{b^2 \log \left(a+b x^3\right)}{3 a^2 (b c-a d)}-\frac{\log (x) (a d+b c)}{a^2 c^2}-\frac{d^2 \log \left(c+d x^3\right)}{3 c^2 (b c-a d)}-\frac{1}{3 a c x^3}",1,"-1/(3*a*c*x^3) - ((b*c + a*d)*Log[x])/(a^2*c^2) + (b^2*Log[a + b*x^3])/(3*a^2*(b*c - a*d)) - (d^2*Log[c + d*x^3])/(3*c^2*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
120,1,318,0,0.3798545,"\int \frac{1}{x^5 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^5*(a + b*x^3)*(c + d*x^3)),x]","\frac{b^{7/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{7/3} (b c-a d)}-\frac{b^{7/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{7/3} (b c-a d)}-\frac{b^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3} (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}-\frac{d^{7/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{7/3} (b c-a d)}+\frac{d^{7/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{7/3} (b c-a d)}+\frac{d^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{7/3} (b c-a d)}-\frac{1}{4 a c x^4}","\frac{b^{7/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{7/3} (b c-a d)}-\frac{b^{7/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{7/3} (b c-a d)}-\frac{b^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3} (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}-\frac{d^{7/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{7/3} (b c-a d)}+\frac{d^{7/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{7/3} (b c-a d)}+\frac{d^{7/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{7/3} (b c-a d)}-\frac{1}{4 a c x^4}",1,"-1/(4*a*c*x^4) + (b*c + a*d)/(a^2*c^2*x) - (b^(7/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)*(b*c - a*d)) + (d^(7/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(7/3)*(b*c - a*d)) - (b^(7/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(7/3)*(b*c - a*d)) + (d^(7/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(7/3)*(b*c - a*d)) + (b^(7/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(7/3)*(b*c - a*d)) - (d^(7/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(7/3)*(b*c - a*d))","A",16,9,22,0.4091,1,"{480, 583, 584, 292, 31, 634, 617, 204, 628}"
121,1,321,0,0.4556834,"\int \frac{1}{x^6 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^6*(a + b*x^3)*(c + d*x^3)),x]","-\frac{b^{8/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{8/3} (b c-a d)}+\frac{b^{8/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{8/3} (b c-a d)}-\frac{b^{8/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3} (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}+\frac{d^{8/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{8/3} (b c-a d)}-\frac{d^{8/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{8/3} (b c-a d)}+\frac{d^{8/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{8/3} (b c-a d)}-\frac{1}{5 a c x^5}","-\frac{b^{8/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{8/3} (b c-a d)}+\frac{b^{8/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{8/3} (b c-a d)}-\frac{b^{8/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3} (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}+\frac{d^{8/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{8/3} (b c-a d)}-\frac{d^{8/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{8/3} (b c-a d)}+\frac{d^{8/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{8/3} (b c-a d)}-\frac{1}{5 a c x^5}",1,"-1/(5*a*c*x^5) + (b*c + a*d)/(2*a^2*c^2*x^2) - (b^(8/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(8/3)*(b*c - a*d)) + (d^(8/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(8/3)*(b*c - a*d)) + (b^(8/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(8/3)*(b*c - a*d)) - (d^(8/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(8/3)*(b*c - a*d)) - (b^(8/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(8/3)*(b*c - a*d)) + (d^(8/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(8/3)*(b*c - a*d))","A",15,9,22,0.4091,1,"{480, 583, 522, 200, 31, 634, 617, 204, 628}"
122,1,119,0,0.1290993,"\int \frac{1}{x^7 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^7*(a + b*x^3)*(c + d*x^3)),x]","\frac{\log (x) \left(a^2 d^2+a b c d+b^2 c^2\right)}{a^3 c^3}-\frac{b^3 \log \left(a+b x^3\right)}{3 a^3 (b c-a d)}+\frac{a d+b c}{3 a^2 c^2 x^3}+\frac{d^3 \log \left(c+d x^3\right)}{3 c^3 (b c-a d)}-\frac{1}{6 a c x^6}","\frac{\log (x) \left(a^2 d^2+a b c d+b^2 c^2\right)}{a^3 c^3}-\frac{b^3 \log \left(a+b x^3\right)}{3 a^3 (b c-a d)}+\frac{a d+b c}{3 a^2 c^2 x^3}+\frac{d^3 \log \left(c+d x^3\right)}{3 c^3 (b c-a d)}-\frac{1}{6 a c x^6}",1,"-1/(6*a*c*x^6) + (b*c + a*d)/(3*a^2*c^2*x^3) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*Log[x])/(a^3*c^3) - (b^3*Log[a + b*x^3])/(3*a^3*(b*c - a*d)) + (d^3*Log[c + d*x^3])/(3*c^3*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
123,1,352,0,0.5009872,"\int \frac{1}{x^8 \left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[1/(x^8*(a + b*x^3)*(c + d*x^3)),x]","-\frac{a^2 d^2+a b c d+b^2 c^2}{a^3 c^3 x}-\frac{b^{10/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{10/3} (b c-a d)}+\frac{b^{10/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{10/3} (b c-a d)}+\frac{b^{10/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{10/3} (b c-a d)}+\frac{a d+b c}{4 a^2 c^2 x^4}+\frac{d^{10/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{10/3} (b c-a d)}-\frac{d^{10/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{10/3} (b c-a d)}-\frac{d^{10/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{10/3} (b c-a d)}-\frac{1}{7 a c x^7}","-\frac{a^2 d^2+a b c d+b^2 c^2}{a^3 c^3 x}-\frac{b^{10/3} \log \left(a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2\right)}{6 a^{10/3} (b c-a d)}+\frac{b^{10/3} \log \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{3 a^{10/3} (b c-a d)}+\frac{b^{10/3} \tan ^{-1}\left(\frac{\sqrt[3]{a}-2 \sqrt[3]{b} x}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{10/3} (b c-a d)}+\frac{a d+b c}{4 a^2 c^2 x^4}+\frac{d^{10/3} \log \left(c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2\right)}{6 c^{10/3} (b c-a d)}-\frac{d^{10/3} \log \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{3 c^{10/3} (b c-a d)}-\frac{d^{10/3} \tan ^{-1}\left(\frac{\sqrt[3]{c}-2 \sqrt[3]{d} x}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{10/3} (b c-a d)}-\frac{1}{7 a c x^7}",1,"-1/(7*a*c*x^7) + (b*c + a*d)/(4*a^2*c^2*x^4) - (b^2*c^2 + a*b*c*d + a^2*d^2)/(a^3*c^3*x) + (b^(10/3)*ArcTan[(a^(1/3) - 2*b^(1/3)*x)/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(10/3)*(b*c - a*d)) - (d^(10/3)*ArcTan[(c^(1/3) - 2*d^(1/3)*x)/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(10/3)*(b*c - a*d)) + (b^(10/3)*Log[a^(1/3) + b^(1/3)*x])/(3*a^(10/3)*(b*c - a*d)) - (d^(10/3)*Log[c^(1/3) + d^(1/3)*x])/(3*c^(10/3)*(b*c - a*d)) - (b^(10/3)*Log[a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2])/(6*a^(10/3)*(b*c - a*d)) + (d^(10/3)*Log[c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2])/(6*c^(10/3)*(b*c - a*d))","A",17,9,22,0.4091,1,"{480, 583, 584, 292, 31, 634, 617, 204, 628}"
124,1,148,0,0.0992086,"\int x^m \left(a+b x^3\right)^5 \left(A+B x^3\right) \, dx","Int[x^m*(a + b*x^3)^5*(A + B*x^3),x]","\frac{10 a^2 b^2 x^{m+10} (a B+A b)}{m+10}+\frac{a^4 x^{m+4} (a B+5 A b)}{m+4}+\frac{5 a^3 b x^{m+7} (a B+2 A b)}{m+7}+\frac{a^5 A x^{m+1}}{m+1}+\frac{5 a b^3 x^{m+13} (2 a B+A b)}{m+13}+\frac{b^4 x^{m+16} (5 a B+A b)}{m+16}+\frac{b^5 B x^{m+19}}{m+19}","\frac{10 a^2 b^2 x^{m+10} (a B+A b)}{m+10}+\frac{a^4 x^{m+4} (a B+5 A b)}{m+4}+\frac{5 a^3 b x^{m+7} (a B+2 A b)}{m+7}+\frac{a^5 A x^{m+1}}{m+1}+\frac{5 a b^3 x^{m+13} (2 a B+A b)}{m+13}+\frac{b^4 x^{m+16} (5 a B+A b)}{m+16}+\frac{b^5 B x^{m+19}}{m+19}",1,"(a^5*A*x^(1 + m))/(1 + m) + (a^4*(5*A*b + a*B)*x^(4 + m))/(4 + m) + (5*a^3*b*(2*A*b + a*B)*x^(7 + m))/(7 + m) + (10*a^2*b^2*(A*b + a*B)*x^(10 + m))/(10 + m) + (5*a*b^3*(A*b + 2*a*B)*x^(13 + m))/(13 + m) + (b^4*(A*b + 5*a*B)*x^(16 + m))/(16 + m) + (b^5*B*x^(19 + m))/(19 + m)","A",2,1,20,0.05000,1,"{448}"
125,1,71,0,0.0400606,"\int x^m \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[x^m*(a + b*x^3)^2*(A + B*x^3),x]","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+4} (a B+2 A b)}{m+4}+\frac{b x^{m+7} (2 a B+A b)}{m+7}+\frac{b^2 B x^{m+10}}{m+10}","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+4} (a B+2 A b)}{m+4}+\frac{b x^{m+7} (2 a B+A b)}{m+7}+\frac{b^2 B x^{m+10}}{m+10}",1,"(a^2*A*x^(1 + m))/(1 + m) + (a*(2*A*b + a*B)*x^(4 + m))/(4 + m) + (b*(A*b + 2*a*B)*x^(7 + m))/(7 + m) + (b^2*B*x^(10 + m))/(10 + m)","A",2,1,20,0.05000,1,"{448}"
126,1,45,0,0.0206881,"\int x^m \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[x^m*(a + b*x^3)*(A + B*x^3),x]","\frac{x^{m+4} (a B+A b)}{m+4}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+7}}{m+7}","\frac{x^{m+4} (a B+A b)}{m+4}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+7}}{m+7}",1,"(a*A*x^(1 + m))/(1 + m) + ((A*b + a*B)*x^(4 + m))/(4 + m) + (b*B*x^(7 + m))/(7 + m)","A",2,1,18,0.05556,1,"{448}"
127,1,66,0,0.0350864,"\int \frac{x^m \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^m*(A + B*x^3))/(a + b*x^3),x]","\frac{x^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a b (m+1)}+\frac{B x^{m+1}}{b (m+1)}","\frac{x^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a b (m+1)}+\frac{B x^{m+1}}{b (m+1)}",1,"(B*x^(1 + m))/(b*(1 + m)) + ((A*b - a*B)*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a*b*(1 + m))","A",2,2,20,0.1000,1,"{459, 364}"
128,1,93,0,0.0415492,"\int \frac{x^m \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^m*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{x^{m+1} (a B (m+1)+A b (2-m)) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{3 a^2 b (m+1)}+\frac{x^{m+1} (A b-a B)}{3 a b \left(a+b x^3\right)}","\frac{x^{m+1} (a B (m+1)+A b (2-m)) \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{3 a^2 b (m+1)}+\frac{x^{m+1} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((A*b - a*B)*x^(1 + m))/(3*a*b*(a + b*x^3)) + ((A*b*(2 - m) + a*B*(1 + m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(3*a^2*b*(1 + m))","A",2,2,20,0.1000,1,"{457, 364}"
129,1,93,0,0.0407562,"\int \frac{x^m \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^m*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{x^{m+1} (a B (m+1)+A b (5-m)) \, _2F_1\left(2,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{6 a^3 b (m+1)}+\frac{x^{m+1} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{x^{m+1} (a B (m+1)+A b (5-m)) \, _2F_1\left(2,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{6 a^3 b (m+1)}+\frac{x^{m+1} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^(1 + m))/(6*a*b*(a + b*x^3)^2) + ((A*b*(5 - m) + a*B*(1 + m))*x^(1 + m)*Hypergeometric2F1[2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(6*a^3*b*(1 + m))","A",2,2,20,0.1000,1,"{457, 364}"
130,1,112,0,0.0525424,"\int \frac{(e x)^m}{\left(a+b x^3\right) \left(c+d x^3\right)} \, dx","Int[(e*x)^m/((a + b*x^3)*(c + d*x^3)),x]","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a e (m+1) (b c-a d)}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{d x^3}{c}\right)}{c e (m+1) (b c-a d)}","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{a e (m+1) (b c-a d)}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{3};\frac{m+4}{3};-\frac{d x^3}{c}\right)}{c e (m+1) (b c-a d)}",1,"(b*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(a*(b*c - a*d)*e*(1 + m)) - (d*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/3, (4 + m)/3, -((d*x^3)/c)])/(c*(b*c - a*d)*e*(1 + m))","A",3,2,24,0.08333,1,"{482, 364}"
131,1,39,0,0.0154295,"\int x^{7/2} \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[x^(7/2)*(a + b*x^3)*(A + B*x^3),x]","\frac{2}{15} x^{15/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{21} b B x^{21/2}","\frac{2}{15} x^{15/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{21} b B x^{21/2}",1,"(2*a*A*x^(9/2))/9 + (2*(A*b + a*B)*x^(15/2))/15 + (2*b*B*x^(21/2))/21","A",2,1,20,0.05000,1,"{448}"
132,1,39,0,0.0158456,"\int x^{5/2} \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[x^(5/2)*(a + b*x^3)*(A + B*x^3),x]","\frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{19} b B x^{19/2}","\frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{19} b B x^{19/2}",1,"(2*a*A*x^(7/2))/7 + (2*(A*b + a*B)*x^(13/2))/13 + (2*b*B*x^(19/2))/19","A",2,1,20,0.05000,1,"{448}"
133,1,39,0,0.0153684,"\int x^{3/2} \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[x^(3/2)*(a + b*x^3)*(A + B*x^3),x]","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{17} b B x^{17/2}","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{17} b B x^{17/2}",1,"(2*a*A*x^(5/2))/5 + (2*(A*b + a*B)*x^(11/2))/11 + (2*b*B*x^(17/2))/17","A",2,1,20,0.05000,1,"{448}"
134,1,39,0,0.0160388,"\int \sqrt{x} \left(a+b x^3\right) \left(A+B x^3\right) \, dx","Int[Sqrt[x]*(a + b*x^3)*(A + B*x^3),x]","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{15} b B x^{15/2}","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{15} b B x^{15/2}",1,"(2*a*A*x^(3/2))/3 + (2*(A*b + a*B)*x^(9/2))/9 + (2*b*B*x^(15/2))/15","A",2,1,20,0.05000,1,"{448}"
135,1,37,0,0.0148383,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{\sqrt{x}} \, dx","Int[((a + b*x^3)*(A + B*x^3))/Sqrt[x],x]","\frac{2}{7} x^{7/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{13} b B x^{13/2}","\frac{2}{7} x^{7/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{13} b B x^{13/2}",1,"2*a*A*Sqrt[x] + (2*(A*b + a*B)*x^(7/2))/7 + (2*b*B*x^(13/2))/13","A",2,1,20,0.05000,1,"{448}"
136,1,37,0,0.0148993,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^{3/2}} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^(3/2),x]","\frac{2}{5} x^{5/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{11} b B x^{11/2}","\frac{2}{5} x^{5/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{11} b B x^{11/2}",1,"(-2*a*A)/Sqrt[x] + (2*(A*b + a*B)*x^(5/2))/5 + (2*b*B*x^(11/2))/11","A",2,1,20,0.05000,1,"{448}"
137,1,39,0,0.0150596,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^{5/2}} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^(5/2),x]","\frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{9} b B x^{9/2}","\frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{9} b B x^{9/2}",1,"(-2*a*A)/(3*x^(3/2)) + (2*(A*b + a*B)*x^(3/2))/3 + (2*b*B*x^(9/2))/9","A",2,1,20,0.05000,1,"{448}"
138,1,37,0,0.0161729,"\int \frac{\left(a+b x^3\right) \left(A+B x^3\right)}{x^{7/2}} \, dx","Int[((a + b*x^3)*(A + B*x^3))/x^(7/2),x]","2 \sqrt{x} (a B+A b)-\frac{2 a A}{5 x^{5/2}}+\frac{2}{7} b B x^{7/2}","2 \sqrt{x} (a B+A b)-\frac{2 a A}{5 x^{5/2}}+\frac{2}{7} b B x^{7/2}",1,"(-2*a*A)/(5*x^(5/2)) + 2*(A*b + a*B)*Sqrt[x] + (2*b*B*x^(7/2))/7","A",2,1,20,0.05000,1,"{448}"
139,1,63,0,0.0306103,"\int x^{7/2} \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[x^(7/2)*(a + b*x^3)^2*(A + B*x^3),x]","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{21} b x^{21/2} (2 a B+A b)+\frac{2}{15} a x^{15/2} (a B+2 A b)+\frac{2}{27} b^2 B x^{27/2}","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{21} b x^{21/2} (2 a B+A b)+\frac{2}{15} a x^{15/2} (a B+2 A b)+\frac{2}{27} b^2 B x^{27/2}",1,"(2*a^2*A*x^(9/2))/9 + (2*a*(2*A*b + a*B)*x^(15/2))/15 + (2*b*(A*b + 2*a*B)*x^(21/2))/21 + (2*b^2*B*x^(27/2))/27","A",2,1,22,0.04545,1,"{448}"
140,1,63,0,0.0309277,"\int x^{5/2} \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[x^(5/2)*(a + b*x^3)^2*(A + B*x^3),x]","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{19} b x^{19/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{25} b^2 B x^{25/2}","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{19} b x^{19/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{25} b^2 B x^{25/2}",1,"(2*a^2*A*x^(7/2))/7 + (2*a*(2*A*b + a*B)*x^(13/2))/13 + (2*b*(A*b + 2*a*B)*x^(19/2))/19 + (2*b^2*B*x^(25/2))/25","A",2,1,22,0.04545,1,"{448}"
141,1,63,0,0.0299877,"\int x^{3/2} \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[x^(3/2)*(a + b*x^3)^2*(A + B*x^3),x]","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{17} b x^{17/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{23} b^2 B x^{23/2}","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{17} b x^{17/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{23} b^2 B x^{23/2}",1,"(2*a^2*A*x^(5/2))/5 + (2*a*(2*A*b + a*B)*x^(11/2))/11 + (2*b*(A*b + 2*a*B)*x^(17/2))/17 + (2*b^2*B*x^(23/2))/23","A",2,1,22,0.04545,1,"{448}"
142,1,63,0,0.0290315,"\int \sqrt{x} \left(a+b x^3\right)^2 \left(A+B x^3\right) \, dx","Int[Sqrt[x]*(a + b*x^3)^2*(A + B*x^3),x]","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{15} b x^{15/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{21} b^2 B x^{21/2}","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{15} b x^{15/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{21} b^2 B x^{21/2}",1,"(2*a^2*A*x^(3/2))/3 + (2*a*(2*A*b + a*B)*x^(9/2))/9 + (2*b*(A*b + 2*a*B)*x^(15/2))/15 + (2*b^2*B*x^(21/2))/21","A",2,1,22,0.04545,1,"{448}"
143,1,61,0,0.0291588,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{\sqrt{x}} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/Sqrt[x],x]","2 a^2 A \sqrt{x}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{19} b^2 B x^{19/2}","2 a^2 A \sqrt{x}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{19} b^2 B x^{19/2}",1,"2*a^2*A*Sqrt[x] + (2*a*(2*A*b + a*B)*x^(7/2))/7 + (2*b*(A*b + 2*a*B)*x^(13/2))/13 + (2*b^2*B*x^(19/2))/19","A",2,1,22,0.04545,1,"{448}"
144,1,61,0,0.0303508,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^{3/2}} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^(3/2),x]","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2}","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2}",1,"(-2*a^2*A)/Sqrt[x] + (2*a*(2*A*b + a*B)*x^(5/2))/5 + (2*b*(A*b + 2*a*B)*x^(11/2))/11 + (2*b^2*B*x^(17/2))/17","A",2,1,22,0.04545,1,"{448}"
145,1,63,0,0.0301588,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^{5/2}} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^(5/2),x]","-\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}","-\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}",1,"(-2*a^2*A)/(3*x^(3/2)) + (2*a*(2*A*b + a*B)*x^(3/2))/3 + (2*b*(A*b + 2*a*B)*x^(9/2))/9 + (2*b^2*B*x^(15/2))/15","A",2,1,22,0.04545,1,"{448}"
146,1,61,0,0.0310831,"\int \frac{\left(a+b x^3\right)^2 \left(A+B x^3\right)}{x^{7/2}} \, dx","Int[((a + b*x^3)^2*(A + B*x^3))/x^(7/2),x]","-\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{7} b x^{7/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}","-\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{7} b x^{7/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}",1,"(-2*a^2*A)/(5*x^(5/2)) + 2*a*(2*A*b + a*B)*Sqrt[x] + (2*b*(A*b + 2*a*B)*x^(7/2))/7 + (2*b^2*B*x^(13/2))/13","A",2,1,22,0.04545,1,"{448}"
147,1,85,0,0.0436307,"\int x^{7/2} \left(a+b x^3\right)^3 \left(A+B x^3\right) \, dx","Int[x^(7/2)*(a + b*x^3)^3*(A + B*x^3),x]","\frac{2}{15} a^2 x^{15/2} (a B+3 A b)+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{27} b^2 x^{27/2} (3 a B+A b)+\frac{2}{7} a b x^{21/2} (a B+A b)+\frac{2}{33} b^3 B x^{33/2}","\frac{2}{15} a^2 x^{15/2} (a B+3 A b)+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{27} b^2 x^{27/2} (3 a B+A b)+\frac{2}{7} a b x^{21/2} (a B+A b)+\frac{2}{33} b^3 B x^{33/2}",1,"(2*a^3*A*x^(9/2))/9 + (2*a^2*(3*A*b + a*B)*x^(15/2))/15 + (2*a*b*(A*b + a*B)*x^(21/2))/7 + (2*b^2*(A*b + 3*a*B)*x^(27/2))/27 + (2*b^3*B*x^(33/2))/33","A",2,1,22,0.04545,1,"{448}"
148,1,85,0,0.0412137,"\int x^{5/2} \left(a+b x^3\right)^3 \left(A+B x^3\right) \, dx","Int[x^(5/2)*(a + b*x^3)^3*(A + B*x^3),x]","\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{7} a^3 A x^{7/2}+\frac{2}{25} b^2 x^{25/2} (3 a B+A b)+\frac{6}{19} a b x^{19/2} (a B+A b)+\frac{2}{31} b^3 B x^{31/2}","\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{7} a^3 A x^{7/2}+\frac{2}{25} b^2 x^{25/2} (3 a B+A b)+\frac{6}{19} a b x^{19/2} (a B+A b)+\frac{2}{31} b^3 B x^{31/2}",1,"(2*a^3*A*x^(7/2))/7 + (2*a^2*(3*A*b + a*B)*x^(13/2))/13 + (6*a*b*(A*b + a*B)*x^(19/2))/19 + (2*b^2*(A*b + 3*a*B)*x^(25/2))/25 + (2*b^3*B*x^(31/2))/31","A",2,1,22,0.04545,1,"{448}"
149,1,85,0,0.041957,"\int x^{3/2} \left(a+b x^3\right)^3 \left(A+B x^3\right) \, dx","Int[x^(3/2)*(a + b*x^3)^3*(A + B*x^3),x]","\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2}","\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{23} b^2 x^{23/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{29} b^3 B x^{29/2}",1,"(2*a^3*A*x^(5/2))/5 + (2*a^2*(3*A*b + a*B)*x^(11/2))/11 + (6*a*b*(A*b + a*B)*x^(17/2))/17 + (2*b^2*(A*b + 3*a*B)*x^(23/2))/23 + (2*b^3*B*x^(29/2))/29","A",2,1,22,0.04545,1,"{448}"
150,1,85,0,0.0405446,"\int \sqrt{x} \left(a+b x^3\right)^3 \left(A+B x^3\right) \, dx","Int[Sqrt[x]*(a + b*x^3)^3*(A + B*x^3),x]","\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{21} b^2 x^{21/2} (3 a B+A b)+\frac{2}{5} a b x^{15/2} (a B+A b)+\frac{2}{27} b^3 B x^{27/2}","\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{21} b^2 x^{21/2} (3 a B+A b)+\frac{2}{5} a b x^{15/2} (a B+A b)+\frac{2}{27} b^3 B x^{27/2}",1,"(2*a^3*A*x^(3/2))/3 + (2*a^2*(3*A*b + a*B)*x^(9/2))/9 + (2*a*b*(A*b + a*B)*x^(15/2))/5 + (2*b^2*(A*b + 3*a*B)*x^(21/2))/21 + (2*b^3*B*x^(27/2))/27","A",2,1,22,0.04545,1,"{448}"
151,1,83,0,0.0427669,"\int \frac{\left(a+b x^3\right)^3 \left(A+B x^3\right)}{\sqrt{x}} \, dx","Int[((a + b*x^3)^3*(A + B*x^3))/Sqrt[x],x]","\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+2 a^3 A \sqrt{x}+\frac{2}{19} b^2 x^{19/2} (3 a B+A b)+\frac{6}{13} a b x^{13/2} (a B+A b)+\frac{2}{25} b^3 B x^{25/2}","\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+2 a^3 A \sqrt{x}+\frac{2}{19} b^2 x^{19/2} (3 a B+A b)+\frac{6}{13} a b x^{13/2} (a B+A b)+\frac{2}{25} b^3 B x^{25/2}",1,"2*a^3*A*Sqrt[x] + (2*a^2*(3*A*b + a*B)*x^(7/2))/7 + (6*a*b*(A*b + a*B)*x^(13/2))/13 + (2*b^2*(A*b + 3*a*B)*x^(19/2))/19 + (2*b^3*B*x^(25/2))/25","A",2,1,22,0.04545,1,"{448}"
152,1,83,0,0.040886,"\int \frac{\left(a+b x^3\right)^3 \left(A+B x^3\right)}{x^{3/2}} \, dx","Int[((a + b*x^3)^3*(A + B*x^3))/x^(3/2),x]","\frac{2}{5} a^2 x^{5/2} (a B+3 A b)-\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2}","\frac{2}{5} a^2 x^{5/2} (a B+3 A b)-\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2}",1,"(-2*a^3*A)/Sqrt[x] + (2*a^2*(3*A*b + a*B)*x^(5/2))/5 + (6*a*b*(A*b + a*B)*x^(11/2))/11 + (2*b^2*(A*b + 3*a*B)*x^(17/2))/17 + (2*b^3*B*x^(23/2))/23","A",2,1,22,0.04545,1,"{448}"
153,1,85,0,0.0448236,"\int \frac{\left(a+b x^3\right)^3 \left(A+B x^3\right)}{x^{5/2}} \, dx","Int[((a + b*x^3)^3*(A + B*x^3))/x^(5/2),x]","\frac{2}{3} a^2 x^{3/2} (a B+3 A b)-\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{21} b^3 B x^{21/2}","\frac{2}{3} a^2 x^{3/2} (a B+3 A b)-\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{21} b^3 B x^{21/2}",1,"(-2*a^3*A)/(3*x^(3/2)) + (2*a^2*(3*A*b + a*B)*x^(3/2))/3 + (2*a*b*(A*b + a*B)*x^(9/2))/3 + (2*b^2*(A*b + 3*a*B)*x^(15/2))/15 + (2*b^3*B*x^(21/2))/21","A",2,1,22,0.04545,1,"{448}"
154,1,83,0,0.040558,"\int \frac{\left(a+b x^3\right)^3 \left(A+B x^3\right)}{x^{7/2}} \, dx","Int[((a + b*x^3)^3*(A + B*x^3))/x^(7/2),x]","2 a^2 \sqrt{x} (a B+3 A b)-\frac{2 a^3 A}{5 x^{5/2}}+\frac{2}{13} b^2 x^{13/2} (3 a B+A b)+\frac{6}{7} a b x^{7/2} (a B+A b)+\frac{2}{19} b^3 B x^{19/2}","2 a^2 \sqrt{x} (a B+3 A b)-\frac{2 a^3 A}{5 x^{5/2}}+\frac{2}{13} b^2 x^{13/2} (3 a B+A b)+\frac{6}{7} a b x^{7/2} (a B+A b)+\frac{2}{19} b^3 B x^{19/2}",1,"(-2*a^3*A)/(5*x^(5/2)) + 2*a^2*(3*A*b + a*B)*Sqrt[x] + (6*a*b*(A*b + a*B)*x^(7/2))/7 + (2*b^2*(A*b + 3*a*B)*x^(13/2))/13 + (2*b^3*B*x^(19/2))/19","A",2,1,22,0.04545,1,"{448}"
155,1,73,0,0.0476554,"\int \frac{x^{7/2} \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^(7/2)*(A + B*x^3))/(a + b*x^3),x]","\frac{2 x^{3/2} (A b-a B)}{3 b^2}-\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 b^{5/2}}+\frac{2 B x^{9/2}}{9 b}","\frac{2 x^{3/2} (A b-a B)}{3 b^2}-\frac{2 \sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 b^{5/2}}+\frac{2 B x^{9/2}}{9 b}",1,"(2*(A*b - a*B)*x^(3/2))/(3*b^2) + (2*B*x^(9/2))/(9*b) - (2*Sqrt[a]*(A*b - a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(3*b^(5/2))","A",5,5,22,0.2273,1,"{459, 321, 329, 275, 205}"
156,1,288,0,0.5190357,"\int \frac{x^{5/2} \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^(5/2)*(A + B*x^3))/(a + b*x^3),x]","\frac{2 \sqrt{x} (A b-a B)}{b^2}+\frac{\sqrt[6]{a} (A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} b^{13/6}}-\frac{\sqrt[6]{a} (A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} b^{13/6}}+\frac{\sqrt[6]{a} (A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 b^{13/6}}-\frac{\sqrt[6]{a} (A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 b^{13/6}}-\frac{2 \sqrt[6]{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 b^{13/6}}+\frac{2 B x^{7/2}}{7 b}","\frac{2 \sqrt{x} (A b-a B)}{b^2}+\frac{\sqrt[6]{a} (A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} b^{13/6}}-\frac{\sqrt[6]{a} (A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} b^{13/6}}+\frac{\sqrt[6]{a} (A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 b^{13/6}}-\frac{\sqrt[6]{a} (A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 b^{13/6}}-\frac{2 \sqrt[6]{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 b^{13/6}}+\frac{2 B x^{7/2}}{7 b}",1,"(2*(A*b - a*B)*Sqrt[x])/b^2 + (2*B*x^(7/2))/(7*b) + (a^(1/6)*(A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*b^(13/6)) - (a^(1/6)*(A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*b^(13/6)) - (2*a^(1/6)*(A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(3*b^(13/6)) + (a^(1/6)*(A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*b^(13/6)) - (a^(1/6)*(A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*b^(13/6))","A",13,9,22,0.4091,1,"{459, 321, 329, 209, 634, 618, 204, 628, 205}"
157,1,270,0,0.5507809,"\int \frac{x^{3/2} \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(x^(3/2)*(A + B*x^3))/(a + b*x^3),x]","\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} \sqrt[6]{a} b^{11/6}}-\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} \sqrt[6]{a} b^{11/6}}-\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 \sqrt[6]{a} b^{11/6}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 \sqrt[6]{a} b^{11/6}}+\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 \sqrt[6]{a} b^{11/6}}+\frac{2 B x^{5/2}}{5 b}","\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} \sqrt[6]{a} b^{11/6}}-\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} \sqrt[6]{a} b^{11/6}}-\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 \sqrt[6]{a} b^{11/6}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 \sqrt[6]{a} b^{11/6}}+\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 \sqrt[6]{a} b^{11/6}}+\frac{2 B x^{5/2}}{5 b}",1,"(2*B*x^(5/2))/(5*b) - ((A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(1/6)*b^(11/6)) + ((A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(1/6)*b^(11/6)) + (2*(A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(1/6)*b^(11/6)) + ((A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(1/6)*b^(11/6)) - ((A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(1/6)*b^(11/6))","A",12,8,22,0.3636,1,"{459, 329, 295, 634, 618, 204, 628, 205}"
158,1,53,0,0.0357264,"\int \frac{\sqrt{x} \left(A+B x^3\right)}{a+b x^3} \, dx","Int[(Sqrt[x]*(A + B*x^3))/(a + b*x^3),x]","\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 \sqrt{a} b^{3/2}}+\frac{2 B x^{3/2}}{3 b}","\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 \sqrt{a} b^{3/2}}+\frac{2 B x^{3/2}}{3 b}",1,"(2*B*x^(3/2))/(3*b) + (2*(A*b - a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(3*Sqrt[a]*b^(3/2))","A",4,4,22,0.1818,1,"{459, 329, 275, 205}"
159,1,268,0,0.4725922,"\int \frac{A+B x^3}{\sqrt{x} \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(Sqrt[x]*(a + b*x^3)),x]","-\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{5/6} b^{7/6}}+\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{5/6} b^{7/6}}-\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{5/6} b^{7/6}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 a^{5/6} b^{7/6}}+\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{5/6} b^{7/6}}+\frac{2 B \sqrt{x}}{b}","-\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{5/6} b^{7/6}}+\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{5/6} b^{7/6}}-\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{5/6} b^{7/6}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 a^{5/6} b^{7/6}}+\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{5/6} b^{7/6}}+\frac{2 B \sqrt{x}}{b}",1,"(2*B*Sqrt[x])/b - ((A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(5/6)*b^(7/6)) + ((A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(5/6)*b^(7/6)) + (2*(A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(5/6)*b^(7/6)) - ((A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(5/6)*b^(7/6)) + ((A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(5/6)*b^(7/6))","A",12,8,22,0.3636,1,"{459, 329, 209, 634, 618, 204, 628, 205}"
160,1,268,0,0.5520158,"\int \frac{A+B x^3}{x^{3/2} \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^(3/2)*(a + b*x^3)),x]","-\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{7/6} b^{5/6}}+\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{7/6} b^{5/6}}+\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{7/6} b^{5/6}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 a^{7/6} b^{5/6}}-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{7/6} b^{5/6}}-\frac{2 A}{a \sqrt{x}}","-\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{7/6} b^{5/6}}+\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{7/6} b^{5/6}}+\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{7/6} b^{5/6}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 a^{7/6} b^{5/6}}-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{7/6} b^{5/6}}-\frac{2 A}{a \sqrt{x}}",1,"(-2*A)/(a*Sqrt[x]) + ((A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(7/6)*b^(5/6)) - ((A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(7/6)*b^(5/6)) - (2*(A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(7/6)*b^(5/6)) - ((A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(7/6)*b^(5/6)) + ((A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(7/6)*b^(5/6))","A",12,8,22,0.3636,1,"{453, 329, 295, 634, 618, 204, 628, 205}"
161,1,53,0,0.0370199,"\int \frac{A+B x^3}{x^{5/2} \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^(5/2)*(a + b*x^3)),x]","-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 a^{3/2} \sqrt{b}}-\frac{2 A}{3 a x^{3/2}}","-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 a^{3/2} \sqrt{b}}-\frac{2 A}{3 a x^{3/2}}",1,"(-2*A)/(3*a*x^(3/2)) - (2*(A*b - a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(3*a^(3/2)*Sqrt[b])","A",4,4,22,0.1818,1,"{453, 329, 275, 205}"
162,1,270,0,0.4847339,"\int \frac{A+B x^3}{x^{7/2} \left(a+b x^3\right)} \, dx","Int[(A + B*x^3)/(x^(7/2)*(a + b*x^3)),x]","\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{11/6} \sqrt[6]{b}}-\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{11/6} \sqrt[6]{b}}+\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{11/6} \sqrt[6]{b}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 a^{11/6} \sqrt[6]{b}}-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{11/6} \sqrt[6]{b}}-\frac{2 A}{5 a x^{5/2}}","\frac{(A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{11/6} \sqrt[6]{b}}-\frac{(A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{2 \sqrt{3} a^{11/6} \sqrt[6]{b}}+\frac{(A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{11/6} \sqrt[6]{b}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{3 a^{11/6} \sqrt[6]{b}}-\frac{2 (A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{3 a^{11/6} \sqrt[6]{b}}-\frac{2 A}{5 a x^{5/2}}",1,"(-2*A)/(5*a*x^(5/2)) + ((A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(11/6)*b^(1/6)) - ((A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(11/6)*b^(1/6)) - (2*(A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(3*a^(11/6)*b^(1/6)) + ((A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(11/6)*b^(1/6)) - ((A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(2*Sqrt[3]*a^(11/6)*b^(1/6))","A",12,8,22,0.3636,1,"{453, 329, 209, 634, 618, 204, 628, 205}"
163,1,95,0,0.0550496,"\int \frac{x^{7/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^(7/2)*(A + B*x^3))/(a + b*x^3)^2,x]","-\frac{x^{3/2} (A b-3 a B)}{3 a b^2}+\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 \sqrt{a} b^{5/2}}+\frac{x^{9/2} (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{x^{3/2} (A b-3 a B)}{3 a b^2}+\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 \sqrt{a} b^{5/2}}+\frac{x^{9/2} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"-((A*b - 3*a*B)*x^(3/2))/(3*a*b^2) + ((A*b - a*B)*x^(9/2))/(3*a*b*(a + b*x^3)) + ((A*b - 3*a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(3*Sqrt[a]*b^(5/2))","A",5,5,22,0.2273,1,"{457, 321, 329, 275, 205}"
164,1,312,0,0.5015875,"\int \frac{x^{5/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^(5/2)*(A + B*x^3))/(a + b*x^3)^2,x]","-\frac{(A b-7 a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{5/6} b^{13/6}}+\frac{(A b-7 a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{5/6} b^{13/6}}-\frac{(A b-7 a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{5/6} b^{13/6}}+\frac{(A b-7 a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{5/6} b^{13/6}}+\frac{(A b-7 a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{5/6} b^{13/6}}-\frac{\sqrt{x} (A b-7 a B)}{3 a b^2}+\frac{x^{7/2} (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{(A b-7 a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{5/6} b^{13/6}}+\frac{(A b-7 a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{5/6} b^{13/6}}-\frac{(A b-7 a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{5/6} b^{13/6}}+\frac{(A b-7 a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{5/6} b^{13/6}}+\frac{(A b-7 a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{5/6} b^{13/6}}-\frac{\sqrt{x} (A b-7 a B)}{3 a b^2}+\frac{x^{7/2} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"-((A*b - 7*a*B)*Sqrt[x])/(3*a*b^2) + ((A*b - a*B)*x^(7/2))/(3*a*b*(a + b*x^3)) - ((A*b - 7*a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(5/6)*b^(13/6)) + ((A*b - 7*a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(5/6)*b^(13/6)) + ((A*b - 7*a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(9*a^(5/6)*b^(13/6)) - ((A*b - 7*a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(5/6)*b^(13/6)) + ((A*b - 7*a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(5/6)*b^(13/6))","A",13,9,22,0.4091,1,"{457, 321, 329, 209, 634, 618, 204, 628, 205}"
165,1,289,0,0.5493358,"\int \frac{x^{3/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(x^(3/2)*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{(5 a B+A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{7/6} b^{11/6}}-\frac{(5 a B+A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{7/6} b^{11/6}}-\frac{(5 a B+A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{7/6} b^{11/6}}+\frac{(5 a B+A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{7/6} b^{11/6}}+\frac{(5 a B+A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{7/6} b^{11/6}}+\frac{x^{5/2} (A b-a B)}{3 a b \left(a+b x^3\right)}","\frac{(5 a B+A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{7/6} b^{11/6}}-\frac{(5 a B+A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{7/6} b^{11/6}}-\frac{(5 a B+A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{7/6} b^{11/6}}+\frac{(5 a B+A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{7/6} b^{11/6}}+\frac{(5 a B+A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{7/6} b^{11/6}}+\frac{x^{5/2} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((A*b - a*B)*x^(5/2))/(3*a*b*(a + b*x^3)) - ((A*b + 5*a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(7/6)*b^(11/6)) + ((A*b + 5*a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(7/6)*b^(11/6)) + ((A*b + 5*a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(9*a^(7/6)*b^(11/6)) + ((A*b + 5*a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(7/6)*b^(11/6)) - ((A*b + 5*a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(7/6)*b^(11/6))","A",12,8,22,0.3636,1,"{457, 329, 295, 634, 618, 204, 628, 205}"
166,1,71,0,0.0418958,"\int \frac{\sqrt{x} \left(A+B x^3\right)}{\left(a+b x^3\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x^3))/(a + b*x^3)^2,x]","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 a^{3/2} b^{3/2}}+\frac{x^{3/2} (A b-a B)}{3 a b \left(a+b x^3\right)}","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 a^{3/2} b^{3/2}}+\frac{x^{3/2} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((A*b - a*B)*x^(3/2))/(3*a*b*(a + b*x^3)) + ((A*b + a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(3*a^(3/2)*b^(3/2))","A",4,4,22,0.1818,1,"{457, 329, 275, 205}"
167,1,289,0,0.4683677,"\int \frac{A+B x^3}{\sqrt{x} \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(Sqrt[x]*(a + b*x^3)^2),x]","-\frac{(a B+5 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{11/6} b^{7/6}}+\frac{(a B+5 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{11/6} b^{7/6}}-\frac{(a B+5 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{11/6} b^{7/6}}+\frac{(a B+5 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{11/6} b^{7/6}}+\frac{(a B+5 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{11/6} b^{7/6}}+\frac{\sqrt{x} (A b-a B)}{3 a b \left(a+b x^3\right)}","-\frac{(a B+5 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{11/6} b^{7/6}}+\frac{(a B+5 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{11/6} b^{7/6}}-\frac{(a B+5 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{11/6} b^{7/6}}+\frac{(a B+5 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{11/6} b^{7/6}}+\frac{(a B+5 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{11/6} b^{7/6}}+\frac{\sqrt{x} (A b-a B)}{3 a b \left(a+b x^3\right)}",1,"((A*b - a*B)*Sqrt[x])/(3*a*b*(a + b*x^3)) - ((5*A*b + a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(11/6)*b^(7/6)) + ((5*A*b + a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(11/6)*b^(7/6)) + ((5*A*b + a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(9*a^(11/6)*b^(7/6)) - ((5*A*b + a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(11/6)*b^(7/6)) + ((5*A*b + a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(11/6)*b^(7/6))","A",12,8,22,0.3636,1,"{457, 329, 209, 634, 618, 204, 628, 205}"
168,1,318,0,0.6864083,"\int \frac{A+B x^3}{x^{3/2} \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^(3/2)*(a + b*x^3)^2),x]","-\frac{(7 A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{13/6} b^{5/6}}+\frac{(7 A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{13/6} b^{5/6}}+\frac{(7 A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{13/6} b^{5/6}}-\frac{(7 A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{13/6} b^{5/6}}-\frac{(7 A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{13/6} b^{5/6}}-\frac{7 A b-a B}{3 a^2 b \sqrt{x}}+\frac{A b-a B}{3 a b \sqrt{x} \left(a+b x^3\right)}","-\frac{(7 A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{13/6} b^{5/6}}+\frac{(7 A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{13/6} b^{5/6}}+\frac{(7 A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{13/6} b^{5/6}}-\frac{(7 A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{13/6} b^{5/6}}-\frac{(7 A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{13/6} b^{5/6}}-\frac{7 A b-a B}{3 a^2 b \sqrt{x}}+\frac{A b-a B}{3 a b \sqrt{x} \left(a+b x^3\right)}",1,"-(7*A*b - a*B)/(3*a^2*b*Sqrt[x]) + (A*b - a*B)/(3*a*b*Sqrt[x]*(a + b*x^3)) + ((7*A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(13/6)*b^(5/6)) - ((7*A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(13/6)*b^(5/6)) - ((7*A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(9*a^(13/6)*b^(5/6)) - ((7*A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(13/6)*b^(5/6)) + ((7*A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(13/6)*b^(5/6))","A",13,9,22,0.4091,1,"{457, 325, 329, 295, 634, 618, 204, 628, 205}"
169,1,97,0,0.0571234,"\int \frac{A+B x^3}{x^{5/2} \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^(5/2)*(a + b*x^3)^2),x]","-\frac{3 A b-a B}{3 a^2 b x^{3/2}}-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 a^{5/2} \sqrt{b}}+\frac{A b-a B}{3 a b x^{3/2} \left(a+b x^3\right)}","-\frac{3 A b-a B}{3 a^2 b x^{3/2}}-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{3 a^{5/2} \sqrt{b}}+\frac{A b-a B}{3 a b x^{3/2} \left(a+b x^3\right)}",1,"-(3*A*b - a*B)/(3*a^2*b*x^(3/2)) + (A*b - a*B)/(3*a*b*x^(3/2)*(a + b*x^3)) - ((3*A*b - a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(3*a^(5/2)*Sqrt[b])","A",5,5,22,0.2273,1,"{457, 325, 329, 275, 205}"
170,1,318,0,0.5044902,"\int \frac{A+B x^3}{x^{7/2} \left(a+b x^3\right)^2} \, dx","Int[(A + B*x^3)/(x^(7/2)*(a + b*x^3)^2),x]","-\frac{11 A b-5 a B}{15 a^2 b x^{5/2}}+\frac{(11 A b-5 a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{17/6} \sqrt[6]{b}}-\frac{(11 A b-5 a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{17/6} \sqrt[6]{b}}+\frac{(11 A b-5 a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{17/6} \sqrt[6]{b}}-\frac{(11 A b-5 a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{17/6} \sqrt[6]{b}}-\frac{(11 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{17/6} \sqrt[6]{b}}+\frac{A b-a B}{3 a b x^{5/2} \left(a+b x^3\right)}","-\frac{11 A b-5 a B}{15 a^2 b x^{5/2}}+\frac{(11 A b-5 a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{17/6} \sqrt[6]{b}}-\frac{(11 A b-5 a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{12 \sqrt{3} a^{17/6} \sqrt[6]{b}}+\frac{(11 A b-5 a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{18 a^{17/6} \sqrt[6]{b}}-\frac{(11 A b-5 a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{18 a^{17/6} \sqrt[6]{b}}-\frac{(11 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{9 a^{17/6} \sqrt[6]{b}}+\frac{A b-a B}{3 a b x^{5/2} \left(a+b x^3\right)}",1,"-(11*A*b - 5*a*B)/(15*a^2*b*x^(5/2)) + (A*b - a*B)/(3*a*b*x^(5/2)*(a + b*x^3)) + ((11*A*b - 5*a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(17/6)*b^(1/6)) - ((11*A*b - 5*a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(18*a^(17/6)*b^(1/6)) - ((11*A*b - 5*a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(9*a^(17/6)*b^(1/6)) + ((11*A*b - 5*a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(17/6)*b^(1/6)) - ((11*A*b - 5*a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(12*Sqrt[3]*a^(17/6)*b^(1/6))","A",13,9,22,0.4091,1,"{457, 325, 329, 209, 634, 618, 204, 628, 205}"
171,1,104,0,0.0571408,"\int \frac{x^{7/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^(7/2)*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{12 a^{3/2} b^{5/2}}-\frac{x^{3/2} (3 a B+A b)}{12 a b^2 \left(a+b x^3\right)}+\frac{x^{9/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{12 a^{3/2} b^{5/2}}-\frac{x^{3/2} (3 a B+A b)}{12 a b^2 \left(a+b x^3\right)}+\frac{x^{9/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^(9/2))/(6*a*b*(a + b*x^3)^2) - ((A*b + 3*a*B)*x^(3/2))/(12*a*b^2*(a + b*x^3)) + ((A*b + 3*a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(12*a^(3/2)*b^(5/2))","A",5,5,22,0.2273,1,"{457, 288, 329, 275, 205}"
172,1,327,0,0.4933563,"\int \frac{x^{5/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^(5/2)*(A + B*x^3))/(a + b*x^3)^3,x]","-\frac{(7 a B+5 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{11/6} b^{13/6}}+\frac{(7 a B+5 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{11/6} b^{13/6}}-\frac{(7 a B+5 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{11/6} b^{13/6}}+\frac{(7 a B+5 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{11/6} b^{13/6}}+\frac{(7 a B+5 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{11/6} b^{13/6}}-\frac{\sqrt{x} (7 a B+5 A b)}{36 a b^2 \left(a+b x^3\right)}+\frac{x^{7/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","-\frac{(7 a B+5 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{11/6} b^{13/6}}+\frac{(7 a B+5 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{11/6} b^{13/6}}-\frac{(7 a B+5 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{11/6} b^{13/6}}+\frac{(7 a B+5 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{11/6} b^{13/6}}+\frac{(7 a B+5 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{11/6} b^{13/6}}-\frac{\sqrt{x} (7 a B+5 A b)}{36 a b^2 \left(a+b x^3\right)}+\frac{x^{7/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^(7/2))/(6*a*b*(a + b*x^3)^2) - ((5*A*b + 7*a*B)*Sqrt[x])/(36*a*b^2*(a + b*x^3)) - ((5*A*b + 7*a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(11/6)*b^(13/6)) + ((5*A*b + 7*a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(11/6)*b^(13/6)) + ((5*A*b + 7*a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(108*a^(11/6)*b^(13/6)) - ((5*A*b + 7*a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(11/6)*b^(13/6)) + ((5*A*b + 7*a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(11/6)*b^(13/6))","A",13,9,22,0.4091,1,"{457, 288, 329, 209, 634, 618, 204, 628, 205}"
173,1,327,0,0.5969999,"\int \frac{x^{3/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(x^(3/2)*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{(5 a B+7 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{13/6} b^{11/6}}-\frac{(5 a B+7 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{13/6} b^{11/6}}-\frac{(5 a B+7 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{13/6} b^{11/6}}+\frac{(5 a B+7 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{13/6} b^{11/6}}+\frac{(5 a B+7 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{13/6} b^{11/6}}+\frac{x^{5/2} (5 a B+7 A b)}{36 a^2 b \left(a+b x^3\right)}+\frac{x^{5/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{(5 a B+7 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{13/6} b^{11/6}}-\frac{(5 a B+7 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{13/6} b^{11/6}}-\frac{(5 a B+7 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{13/6} b^{11/6}}+\frac{(5 a B+7 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{13/6} b^{11/6}}+\frac{(5 a B+7 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{13/6} b^{11/6}}+\frac{x^{5/2} (5 a B+7 A b)}{36 a^2 b \left(a+b x^3\right)}+\frac{x^{5/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^(5/2))/(6*a*b*(a + b*x^3)^2) + ((7*A*b + 5*a*B)*x^(5/2))/(36*a^2*b*(a + b*x^3)) - ((7*A*b + 5*a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(13/6)*b^(11/6)) + ((7*A*b + 5*a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(13/6)*b^(11/6)) + ((7*A*b + 5*a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(108*a^(13/6)*b^(11/6)) + ((7*A*b + 5*a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(13/6)*b^(11/6)) - ((7*A*b + 5*a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(13/6)*b^(11/6))","A",13,9,22,0.4091,1,"{457, 290, 329, 295, 634, 618, 204, 628, 205}"
174,1,104,0,0.0595053,"\int \frac{\sqrt{x} \left(A+B x^3\right)}{\left(a+b x^3\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x^3))/(a + b*x^3)^3,x]","\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{12 a^{5/2} b^{3/2}}+\frac{x^{3/2} (a B+3 A b)}{12 a^2 b \left(a+b x^3\right)}+\frac{x^{3/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{12 a^{5/2} b^{3/2}}+\frac{x^{3/2} (a B+3 A b)}{12 a^2 b \left(a+b x^3\right)}+\frac{x^{3/2} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*x^(3/2))/(6*a*b*(a + b*x^3)^2) + ((3*A*b + a*B)*x^(3/2))/(12*a^2*b*(a + b*x^3)) + ((3*A*b + a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(12*a^(5/2)*b^(3/2))","A",5,5,22,0.2273,1,"{457, 290, 329, 275, 205}"
175,1,321,0,0.5220864,"\int \frac{A+B x^3}{\sqrt{x} \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(Sqrt[x]*(a + b*x^3)^3),x]","-\frac{5 (a B+11 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{17/6} b^{7/6}}+\frac{5 (a B+11 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{17/6} b^{7/6}}-\frac{5 (a B+11 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{17/6} b^{7/6}}+\frac{5 (a B+11 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{17/6} b^{7/6}}+\frac{5 (a B+11 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{17/6} b^{7/6}}+\frac{\sqrt{x} (a B+11 A b)}{36 a^2 b \left(a+b x^3\right)}+\frac{\sqrt{x} (A b-a B)}{6 a b \left(a+b x^3\right)^2}","-\frac{5 (a B+11 A b) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{17/6} b^{7/6}}+\frac{5 (a B+11 A b) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{17/6} b^{7/6}}-\frac{5 (a B+11 A b) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{17/6} b^{7/6}}+\frac{5 (a B+11 A b) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{17/6} b^{7/6}}+\frac{5 (a B+11 A b) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{17/6} b^{7/6}}+\frac{\sqrt{x} (a B+11 A b)}{36 a^2 b \left(a+b x^3\right)}+\frac{\sqrt{x} (A b-a B)}{6 a b \left(a+b x^3\right)^2}",1,"((A*b - a*B)*Sqrt[x])/(6*a*b*(a + b*x^3)^2) + ((11*A*b + a*B)*Sqrt[x])/(36*a^2*b*(a + b*x^3)) - (5*(11*A*b + a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(17/6)*b^(7/6)) + (5*(11*A*b + a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(17/6)*b^(7/6)) + (5*(11*A*b + a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(108*a^(17/6)*b^(7/6)) - (5*(11*A*b + a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(17/6)*b^(7/6)) + (5*(11*A*b + a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(17/6)*b^(7/6))","A",13,9,22,0.4091,1,"{457, 290, 329, 209, 634, 618, 204, 628, 205}"
176,1,351,0,0.6161172,"\int \frac{A+B x^3}{x^{3/2} \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^(3/2)*(a + b*x^3)^3),x]","-\frac{7 (13 A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{19/6} b^{5/6}}+\frac{7 (13 A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{19/6} b^{5/6}}+\frac{7 (13 A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{19/6} b^{5/6}}-\frac{7 (13 A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{19/6} b^{5/6}}-\frac{7 (13 A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{19/6} b^{5/6}}+\frac{13 A b-a B}{36 a^2 b \sqrt{x} \left(a+b x^3\right)}-\frac{7 (13 A b-a B)}{36 a^3 b \sqrt{x}}+\frac{A b-a B}{6 a b \sqrt{x} \left(a+b x^3\right)^2}","-\frac{7 (13 A b-a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{19/6} b^{5/6}}+\frac{7 (13 A b-a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{19/6} b^{5/6}}+\frac{7 (13 A b-a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{19/6} b^{5/6}}-\frac{7 (13 A b-a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{19/6} b^{5/6}}-\frac{7 (13 A b-a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{19/6} b^{5/6}}+\frac{13 A b-a B}{36 a^2 b \sqrt{x} \left(a+b x^3\right)}-\frac{7 (13 A b-a B)}{36 a^3 b \sqrt{x}}+\frac{A b-a B}{6 a b \sqrt{x} \left(a+b x^3\right)^2}",1,"(-7*(13*A*b - a*B))/(36*a^3*b*Sqrt[x]) + (A*b - a*B)/(6*a*b*Sqrt[x]*(a + b*x^3)^2) + (13*A*b - a*B)/(36*a^2*b*Sqrt[x]*(a + b*x^3)) + (7*(13*A*b - a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(19/6)*b^(5/6)) - (7*(13*A*b - a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(19/6)*b^(5/6)) - (7*(13*A*b - a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(108*a^(19/6)*b^(5/6)) - (7*(13*A*b - a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(19/6)*b^(5/6)) + (7*(13*A*b - a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(19/6)*b^(5/6))","A",14,10,22,0.4545,1,"{457, 290, 325, 329, 295, 634, 618, 204, 628, 205}"
177,1,130,0,0.0718134,"\int \frac{A+B x^3}{x^{5/2} \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^(5/2)*(a + b*x^3)^3),x]","\frac{5 A b-a B}{12 a^2 b x^{3/2} \left(a+b x^3\right)}-\frac{5 A b-a B}{4 a^3 b x^{3/2}}-\frac{(5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{4 a^{7/2} \sqrt{b}}+\frac{A b-a B}{6 a b x^{3/2} \left(a+b x^3\right)^2}","\frac{5 A b-a B}{12 a^2 b x^{3/2} \left(a+b x^3\right)}-\frac{5 A b-a B}{4 a^3 b x^{3/2}}-\frac{(5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a}}\right)}{4 a^{7/2} \sqrt{b}}+\frac{A b-a B}{6 a b x^{3/2} \left(a+b x^3\right)^2}",1,"-(5*A*b - a*B)/(4*a^3*b*x^(3/2)) + (A*b - a*B)/(6*a*b*x^(3/2)*(a + b*x^3)^2) + (5*A*b - a*B)/(12*a^2*b*x^(3/2)*(a + b*x^3)) - ((5*A*b - a*B)*ArcTan[(Sqrt[b]*x^(3/2))/Sqrt[a]])/(4*a^(7/2)*Sqrt[b])","A",6,6,22,0.2727,1,"{457, 290, 325, 329, 275, 205}"
178,1,351,0,0.5413746,"\int \frac{A+B x^3}{x^{7/2} \left(a+b x^3\right)^3} \, dx","Int[(A + B*x^3)/(x^(7/2)*(a + b*x^3)^3),x]","\frac{17 A b-5 a B}{36 a^2 b x^{5/2} \left(a+b x^3\right)}-\frac{11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac{11 (17 A b-5 a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{23/6} \sqrt[6]{b}}-\frac{11 (17 A b-5 a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{23/6} \sqrt[6]{b}}+\frac{11 (17 A b-5 a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{23/6} \sqrt[6]{b}}-\frac{11 (17 A b-5 a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{23/6} \sqrt[6]{b}}-\frac{11 (17 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{23/6} \sqrt[6]{b}}+\frac{A b-a B}{6 a b x^{5/2} \left(a+b x^3\right)^2}","\frac{17 A b-5 a B}{36 a^2 b x^{5/2} \left(a+b x^3\right)}-\frac{11 (17 A b-5 a B)}{180 a^3 b x^{5/2}}+\frac{11 (17 A b-5 a B) \log \left(-\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{23/6} \sqrt[6]{b}}-\frac{11 (17 A b-5 a B) \log \left(\sqrt{3} \sqrt[6]{a} \sqrt[6]{b} \sqrt{x}+\sqrt[3]{a}+\sqrt[3]{b} x\right)}{144 \sqrt{3} a^{23/6} \sqrt[6]{b}}+\frac{11 (17 A b-5 a B) \tan ^{-1}\left(\sqrt{3}-\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{216 a^{23/6} \sqrt[6]{b}}-\frac{11 (17 A b-5 a B) \tan ^{-1}\left(\frac{2 \sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}+\sqrt{3}\right)}{216 a^{23/6} \sqrt[6]{b}}-\frac{11 (17 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt[6]{b} \sqrt{x}}{\sqrt[6]{a}}\right)}{108 a^{23/6} \sqrt[6]{b}}+\frac{A b-a B}{6 a b x^{5/2} \left(a+b x^3\right)^2}",1,"(-11*(17*A*b - 5*a*B))/(180*a^3*b*x^(5/2)) + (A*b - a*B)/(6*a*b*x^(5/2)*(a + b*x^3)^2) + (17*A*b - 5*a*B)/(36*a^2*b*x^(5/2)*(a + b*x^3)) + (11*(17*A*b - 5*a*B)*ArcTan[Sqrt[3] - (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(23/6)*b^(1/6)) - (11*(17*A*b - 5*a*B)*ArcTan[Sqrt[3] + (2*b^(1/6)*Sqrt[x])/a^(1/6)])/(216*a^(23/6)*b^(1/6)) - (11*(17*A*b - 5*a*B)*ArcTan[(b^(1/6)*Sqrt[x])/a^(1/6)])/(108*a^(23/6)*b^(1/6)) + (11*(17*A*b - 5*a*B)*Log[a^(1/3) - Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(23/6)*b^(1/6)) - (11*(17*A*b - 5*a*B)*Log[a^(1/3) + Sqrt[3]*a^(1/6)*b^(1/6)*Sqrt[x] + b^(1/3)*x])/(144*Sqrt[3]*a^(23/6)*b^(1/6))","A",14,10,22,0.4545,1,"{457, 290, 325, 329, 209, 634, 618, 204, 628, 205}"
179,1,103,0,0.08424,"\int x^8 \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[x^8*Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{2 a^2 \left(a+b x^3\right)^{3/2} (A b-a B)}{9 b^4}+\frac{2 \left(a+b x^3\right)^{7/2} (A b-3 a B)}{21 b^4}-\frac{2 a \left(a+b x^3\right)^{5/2} (2 A b-3 a B)}{15 b^4}+\frac{2 B \left(a+b x^3\right)^{9/2}}{27 b^4}","\frac{2 a^2 \left(a+b x^3\right)^{3/2} (A b-a B)}{9 b^4}+\frac{2 \left(a+b x^3\right)^{7/2} (A b-3 a B)}{21 b^4}-\frac{2 a \left(a+b x^3\right)^{5/2} (2 A b-3 a B)}{15 b^4}+\frac{2 B \left(a+b x^3\right)^{9/2}}{27 b^4}",1,"(2*a^2*(A*b - a*B)*(a + b*x^3)^(3/2))/(9*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x^3)^(5/2))/(15*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(7/2))/(21*b^4) + (2*B*(a + b*x^3)^(9/2))/(27*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
180,1,73,0,0.0598291,"\int x^5 \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[x^5*Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{2 \left(a+b x^3\right)^{5/2} (A b-2 a B)}{15 b^3}-\frac{2 a \left(a+b x^3\right)^{3/2} (A b-a B)}{9 b^3}+\frac{2 B \left(a+b x^3\right)^{7/2}}{21 b^3}","\frac{2 \left(a+b x^3\right)^{5/2} (A b-2 a B)}{15 b^3}-\frac{2 a \left(a+b x^3\right)^{3/2} (A b-a B)}{9 b^3}+\frac{2 B \left(a+b x^3\right)^{7/2}}{21 b^3}",1,"(-2*a*(A*b - a*B)*(a + b*x^3)^(3/2))/(9*b^3) + (2*(A*b - 2*a*B)*(a + b*x^3)^(5/2))/(15*b^3) + (2*B*(a + b*x^3)^(7/2))/(21*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
181,1,46,0,0.0399213,"\int x^2 \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[x^2*Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{2 \left(a+b x^3\right)^{3/2} (A b-a B)}{9 b^2}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b^2}","\frac{2 \left(a+b x^3\right)^{3/2} (A b-a B)}{9 b^2}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b^2}",1,"(2*(A*b - a*B)*(a + b*x^3)^(3/2))/(9*b^2) + (2*B*(a + b*x^3)^(5/2))/(15*b^2)","A",3,2,22,0.09091,1,"{444, 43}"
182,1,64,0,0.0431833,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x,x]","\frac{2}{3} A \sqrt{a+b x^3}-\frac{2}{3} \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b}","\frac{2}{3} A \sqrt{a+b x^3}-\frac{2}{3} \sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b}",1,"(2*A*Sqrt[a + b*x^3])/3 + (2*B*(a + b*x^3)^(3/2))/(9*b) - (2*Sqrt[a]*A*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3","A",5,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
183,1,84,0,0.063156,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^4} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^4,x]","\frac{\sqrt{a+b x^3} (2 a B+A b)}{3 a}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{A \left(a+b x^3\right)^{3/2}}{3 a x^3}","\frac{\sqrt{a+b x^3} (2 a B+A b)}{3 a}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}-\frac{A \left(a+b x^3\right)^{3/2}}{3 a x^3}",1,"((A*b + 2*a*B)*Sqrt[a + b*x^3])/(3*a) - (A*(a + b*x^3)^(3/2))/(3*a*x^3) - ((A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a])","A",5,5,22,0.2273,1,"{446, 78, 50, 63, 208}"
184,1,88,0,0.0696097,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^7} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^7,x]","\frac{b (A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{\sqrt{a+b x^3} (A b-4 a B)}{12 a x^3}-\frac{A \left(a+b x^3\right)^{3/2}}{6 a x^6}","\frac{b (A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{3/2}}+\frac{\sqrt{a+b x^3} (A b-4 a B)}{12 a x^3}-\frac{A \left(a+b x^3\right)^{3/2}}{6 a x^6}",1,"((A*b - 4*a*B)*Sqrt[a + b*x^3])/(12*a*x^3) - (A*(a + b*x^3)^(3/2))/(6*a*x^6) + (b*(A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(12*a^(3/2))","A",5,5,22,0.2273,1,"{446, 78, 47, 63, 208}"
185,1,303,0,0.1509937,"\int x^3 \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[x^3*Sqrt[a + b*x^3]*(A + B*x^3),x]","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a x \sqrt{a+b x^3} (17 A b-8 a B)}{935 b^2}+\frac{2 x^4 \sqrt{a+b x^3} (17 A b-8 a B)}{187 b}+\frac{2 B x^4 \left(a+b x^3\right)^{3/2}}{17 b}","-\frac{4\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a x \sqrt{a+b x^3} (17 A b-8 a B)}{935 b^2}+\frac{2 x^4 \sqrt{a+b x^3} (17 A b-8 a B)}{187 b}+\frac{2 B x^4 \left(a+b x^3\right)^{3/2}}{17 b}",1,"(6*a*(17*A*b - 8*a*B)*x*Sqrt[a + b*x^3])/(935*b^2) + (2*(17*A*b - 8*a*B)*x^4*Sqrt[a + b*x^3])/(187*b) + (2*B*x^4*(a + b*x^3)^(3/2))/(17*b) - (4*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(17*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(935*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{459, 279, 321, 218}"
186,1,268,0,0.0911127,"\int \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \sqrt{a+b x^3} (11 A b-2 a B)}{55 b}+\frac{2 B x \left(a+b x^3\right)^{3/2}}{11 b}","\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \sqrt{a+b x^3} (11 A b-2 a B)}{55 b}+\frac{2 B x \left(a+b x^3\right)^{3/2}}{11 b}",1,"(2*(11*A*b - 2*a*B)*x*Sqrt[a + b*x^3])/(55*b) + (2*B*x*(a + b*x^3)^(3/2))/(11*b) + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(11*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(55*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,19,0.1579,1,"{388, 195, 218}"
187,1,269,0,0.0994994,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^3} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^3,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+5 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{x \sqrt{a+b x^3} (4 a B+5 A b)}{10 a}-\frac{A \left(a+b x^3\right)^{3/2}}{2 a x^2}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+5 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{10 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{x \sqrt{a+b x^3} (4 a B+5 A b)}{10 a}-\frac{A \left(a+b x^3\right)^{3/2}}{2 a x^2}",1,"((5*A*b + 4*a*B)*x*Sqrt[a + b*x^3])/(10*a) - (A*(a + b*x^3)^(3/2))/(2*a*x^2) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*(5*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(10*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{453, 195, 218}"
188,1,272,0,0.1025717,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^6} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^6,x]","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (A b-10 a B)}{20 a x^2}-\frac{A \left(a+b x^3\right)^{3/2}}{5 a x^5}","-\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (A b-10 a B)}{20 a x^2}-\frac{A \left(a+b x^3\right)^{3/2}}{5 a x^5}",1,"((A*b - 10*a*B)*Sqrt[a + b*x^3])/(20*a*x^2) - (A*(a + b*x^3)^(3/2))/(5*a*x^5) - (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*(A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(20*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{453, 277, 218}"
189,1,305,0,0.1381476,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^9} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^9,x]","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-16 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{320 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (7 A b-16 a B)}{320 a^2 x^2}+\frac{\sqrt{a+b x^3} (7 A b-16 a B)}{80 a x^5}-\frac{A \left(a+b x^3\right)^{3/2}}{8 a x^8}","\frac{3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-16 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{320 a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (7 A b-16 a B)}{320 a^2 x^2}+\frac{\sqrt{a+b x^3} (7 A b-16 a B)}{80 a x^5}-\frac{A \left(a+b x^3\right)^{3/2}}{8 a x^8}",1,"((7*A*b - 16*a*B)*Sqrt[a + b*x^3])/(80*a*x^5) + (3*b*(7*A*b - 16*a*B)*Sqrt[a + b*x^3])/(320*a^2*x^2) - (A*(a + b*x^3)^(3/2))/(8*a*x^8) + (3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(7*A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(320*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{453, 277, 325, 218}"
190,1,581,0,0.3551921,"\int x^4 \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[x^4*Sqrt[a + b*x^3]*(A + B*x^3),x]","-\frac{24 a^2 \sqrt{a+b x^3} (19 A b-10 a B)}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{8 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a x^2 \sqrt{a+b x^3} (19 A b-10 a B)}{1729 b^2}+\frac{2 x^5 \sqrt{a+b x^3} (19 A b-10 a B)}{247 b}+\frac{2 B x^5 \left(a+b x^3\right)^{3/2}}{19 b}","-\frac{24 a^2 \sqrt{a+b x^3} (19 A b-10 a B)}{1729 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{8 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{12 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a x^2 \sqrt{a+b x^3} (19 A b-10 a B)}{1729 b^2}+\frac{2 x^5 \sqrt{a+b x^3} (19 A b-10 a B)}{247 b}+\frac{2 B x^5 \left(a+b x^3\right)^{3/2}}{19 b}",1,"(6*a*(19*A*b - 10*a*B)*x^2*Sqrt[a + b*x^3])/(1729*b^2) + (2*(19*A*b - 10*a*B)*x^5*Sqrt[a + b*x^3])/(247*b) - (24*a^2*(19*A*b - 10*a*B)*Sqrt[a + b*x^3])/(1729*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*B*x^5*(a + b*x^3)^(3/2))/(19*b) + (12*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(19*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (8*Sqrt[2]*3^(3/4)*a^(7/3)*(19*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,22,0.2727,1,"{459, 279, 321, 303, 218, 1877}"
191,1,548,0,0.2413073,"\int x \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[x*Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3} (13 A b-4 a B)}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2 \sqrt{a+b x^3} (13 A b-4 a B)}{91 b}+\frac{2 B x^2 \left(a+b x^3\right)^{3/2}}{13 b}","\frac{2 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{6 a \sqrt{a+b x^3} (13 A b-4 a B)}{91 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2 \sqrt{a+b x^3} (13 A b-4 a B)}{91 b}+\frac{2 B x^2 \left(a+b x^3\right)^{3/2}}{13 b}",1,"(2*(13*A*b - 4*a*B)*x^2*Sqrt[a + b*x^3])/(91*b) + (6*a*(13*A*b - 4*a*B)*Sqrt[a + b*x^3])/(91*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*B*x^2*(a + b*x^3)^(3/2))/(13*b) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2]*3^(3/4)*a^(4/3)*(13*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,20,0.2500,1,"{459, 279, 303, 218, 1877}"
192,1,545,0,0.2485301,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^2} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^2,x]","\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+7 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+7 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt{a+b x^3} (2 a B+7 A b)}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{x^2 \sqrt{a+b x^3} (2 a B+7 A b)}{7 a}-\frac{A \left(a+b x^3\right)^{3/2}}{a x}","\frac{\sqrt{2} 3^{3/4} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+7 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+7 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{14 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt{a+b x^3} (2 a B+7 A b)}{7 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{x^2 \sqrt{a+b x^3} (2 a B+7 A b)}{7 a}-\frac{A \left(a+b x^3\right)^{3/2}}{a x}",1,"((7*A*b + 2*a*B)*x^2*Sqrt[a + b*x^3])/(7*a) + (3*(7*A*b + 2*a*B)*Sqrt[a + b*x^3])/(7*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(a*x) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(14*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (Sqrt[2]*3^(3/4)*a^(1/3)*(7*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{453, 279, 303, 218, 1877}"
193,1,546,0,0.251191,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^5} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^5,x]","\frac{3^{3/4} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3} (8 a B+A b)}{8 a x}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3} (8 a B+A b)}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \left(a+b x^3\right)^{3/2}}{4 a x^4}","\frac{3^{3/4} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{a+b x^3} (8 a B+A b)}{8 a x}+\frac{3 \sqrt[3]{b} \sqrt{a+b x^3} (8 a B+A b)}{8 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \left(a+b x^3\right)^{3/2}}{4 a x^4}",1,"-((A*b + 8*a*B)*Sqrt[a + b*x^3])/(8*a*x) + (3*b^(1/3)*(A*b + 8*a*B)*Sqrt[a + b*x^3])/(8*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(4*a*x^4) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*b^(1/3)*(A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{453, 277, 303, 218, 1877}"
194,1,581,0,0.3204453,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^8} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^8,x]","-\frac{3 b^{4/3} \sqrt{a+b x^3} (5 A b-14 a B)}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-14 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (5 A b-14 a B)}{112 a^2 x}+\frac{\sqrt{a+b x^3} (5 A b-14 a B)}{56 a x^4}-\frac{A \left(a+b x^3\right)^{3/2}}{7 a x^7}","-\frac{3 b^{4/3} \sqrt{a+b x^3} (5 A b-14 a B)}{112 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-14 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (5 A b-14 a B)}{112 a^2 x}+\frac{\sqrt{a+b x^3} (5 A b-14 a B)}{56 a x^4}-\frac{A \left(a+b x^3\right)^{3/2}}{7 a x^7}",1,"((5*A*b - 14*a*B)*Sqrt[a + b*x^3])/(56*a*x^4) + (3*b*(5*A*b - 14*a*B)*Sqrt[a + b*x^3])/(112*a^2*x) - (3*b^(4/3)*(5*A*b - 14*a*B)*Sqrt[a + b*x^3])/(112*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(7*a*x^7) + (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(5*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*b^(4/3)*(5*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(56*Sqrt[2]*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,22,0.2727,1,"{453, 277, 325, 303, 218, 1877}"
195,1,614,0,0.378772,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^{11}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^11,x]","\frac{3 b^{7/3} \sqrt{a+b x^3} (11 A b-20 a B)}{448 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3 b^2 \sqrt{a+b x^3} (11 A b-20 a B)}{448 a^3 x}+\frac{3^{3/4} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-20 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 \sqrt{2} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-20 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{896 a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (11 A b-20 a B)}{1120 a^2 x^4}+\frac{\sqrt{a+b x^3} (11 A b-20 a B)}{140 a x^7}-\frac{A \left(a+b x^3\right)^{3/2}}{10 a x^{10}}","\frac{3 b^{7/3} \sqrt{a+b x^3} (11 A b-20 a B)}{448 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3 b^2 \sqrt{a+b x^3} (11 A b-20 a B)}{448 a^3 x}+\frac{3^{3/4} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-20 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 \sqrt{2} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-20 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{896 a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 b \sqrt{a+b x^3} (11 A b-20 a B)}{1120 a^2 x^4}+\frac{\sqrt{a+b x^3} (11 A b-20 a B)}{140 a x^7}-\frac{A \left(a+b x^3\right)^{3/2}}{10 a x^{10}}",1,"((11*A*b - 20*a*B)*Sqrt[a + b*x^3])/(140*a*x^7) + (3*b*(11*A*b - 20*a*B)*Sqrt[a + b*x^3])/(1120*a^2*x^4) - (3*b^2*(11*A*b - 20*a*B)*Sqrt[a + b*x^3])/(448*a^3*x) + (3*b^(7/3)*(11*A*b - 20*a*B)*Sqrt[a + b*x^3])/(448*a^3*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (A*(a + b*x^3)^(3/2))/(10*a*x^10) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*(11*A*b - 20*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(896*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (3^(3/4)*b^(7/3)*(11*A*b - 20*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*Sqrt[2]*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,22,0.2727,1,"{453, 277, 325, 303, 218, 1877}"
196,1,103,0,0.0789919,"\int x^8 \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[x^8*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{2 a^2 \left(a+b x^3\right)^{5/2} (A b-a B)}{15 b^4}+\frac{2 \left(a+b x^3\right)^{9/2} (A b-3 a B)}{27 b^4}-\frac{2 a \left(a+b x^3\right)^{7/2} (2 A b-3 a B)}{21 b^4}+\frac{2 B \left(a+b x^3\right)^{11/2}}{33 b^4}","\frac{2 a^2 \left(a+b x^3\right)^{5/2} (A b-a B)}{15 b^4}+\frac{2 \left(a+b x^3\right)^{9/2} (A b-3 a B)}{27 b^4}-\frac{2 a \left(a+b x^3\right)^{7/2} (2 A b-3 a B)}{21 b^4}+\frac{2 B \left(a+b x^3\right)^{11/2}}{33 b^4}",1,"(2*a^2*(A*b - a*B)*(a + b*x^3)^(5/2))/(15*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x^3)^(7/2))/(21*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(9/2))/(27*b^4) + (2*B*(a + b*x^3)^(11/2))/(33*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
197,1,73,0,0.0575149,"\int x^5 \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[x^5*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{2 \left(a+b x^3\right)^{7/2} (A b-2 a B)}{21 b^3}-\frac{2 a \left(a+b x^3\right)^{5/2} (A b-a B)}{15 b^3}+\frac{2 B \left(a+b x^3\right)^{9/2}}{27 b^3}","\frac{2 \left(a+b x^3\right)^{7/2} (A b-2 a B)}{21 b^3}-\frac{2 a \left(a+b x^3\right)^{5/2} (A b-a B)}{15 b^3}+\frac{2 B \left(a+b x^3\right)^{9/2}}{27 b^3}",1,"(-2*a*(A*b - a*B)*(a + b*x^3)^(5/2))/(15*b^3) + (2*(A*b - 2*a*B)*(a + b*x^3)^(7/2))/(21*b^3) + (2*B*(a + b*x^3)^(9/2))/(27*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
198,1,46,0,0.0399532,"\int x^2 \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[x^2*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{2 \left(a+b x^3\right)^{5/2} (A b-a B)}{15 b^2}+\frac{2 B \left(a+b x^3\right)^{7/2}}{21 b^2}","\frac{2 \left(a+b x^3\right)^{5/2} (A b-a B)}{15 b^2}+\frac{2 B \left(a+b x^3\right)^{7/2}}{21 b^2}",1,"(2*(A*b - a*B)*(a + b*x^3)^(5/2))/(15*b^2) + (2*B*(a + b*x^3)^(7/2))/(21*b^2)","A",3,2,22,0.09091,1,"{444, 43}"
199,1,81,0,0.0566899,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x,x]","-\frac{2}{3} a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2}{9} A \left(a+b x^3\right)^{3/2}+\frac{2}{3} a A \sqrt{a+b x^3}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b}","-\frac{2}{3} a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)+\frac{2}{9} A \left(a+b x^3\right)^{3/2}+\frac{2}{3} a A \sqrt{a+b x^3}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b}",1,"(2*a*A*Sqrt[a + b*x^3])/3 + (2*A*(a + b*x^3)^(3/2))/9 + (2*B*(a + b*x^3)^(5/2))/(15*b) - (2*a^(3/2)*A*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3","A",6,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
200,1,110,0,0.0840313,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^4} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^4,x]","\frac{\left(a+b x^3\right)^{3/2} (2 a B+3 A b)}{9 a}+\frac{1}{3} \sqrt{a+b x^3} (2 a B+3 A b)-\frac{1}{3} \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)-\frac{A \left(a+b x^3\right)^{5/2}}{3 a x^3}","\frac{\left(a+b x^3\right)^{3/2} (2 a B+3 A b)}{9 a}+\frac{1}{3} \sqrt{a+b x^3} (2 a B+3 A b)-\frac{1}{3} \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)-\frac{A \left(a+b x^3\right)^{5/2}}{3 a x^3}",1,"((3*A*b + 2*a*B)*Sqrt[a + b*x^3])/3 + ((3*A*b + 2*a*B)*(a + b*x^3)^(3/2))/(9*a) - (A*(a + b*x^3)^(5/2))/(3*a*x^3) - (Sqrt[a]*(3*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/3","A",6,5,22,0.2273,1,"{446, 78, 50, 63, 208}"
201,1,115,0,0.0868472,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^7} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^7,x]","-\frac{\left(a+b x^3\right)^{3/2} (4 a B+A b)}{12 a x^3}+\frac{b \sqrt{a+b x^3} (4 a B+A b)}{4 a}-\frac{b (4 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{A \left(a+b x^3\right)^{5/2}}{6 a x^6}","-\frac{\left(a+b x^3\right)^{3/2} (4 a B+A b)}{12 a x^3}+\frac{b \sqrt{a+b x^3} (4 a B+A b)}{4 a}-\frac{b (4 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 \sqrt{a}}-\frac{A \left(a+b x^3\right)^{5/2}}{6 a x^6}",1,"(b*(A*b + 4*a*B)*Sqrt[a + b*x^3])/(4*a) - ((A*b + 4*a*B)*(a + b*x^3)^(3/2))/(12*a*x^3) - (A*(a + b*x^3)^(5/2))/(6*a*x^6) - (b*(A*b + 4*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*Sqrt[a])","A",6,6,22,0.2727,1,"{446, 78, 47, 50, 63, 208}"
202,1,336,0,0.1750039,"\int x^3 \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[x^3*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{54 a^2 x \sqrt{a+b x^3} (23 A b-8 a B)}{21505 b^2}-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (23 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21505 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^4 \left(a+b x^3\right)^{3/2} (23 A b-8 a B)}{391 b}+\frac{18 a x^4 \sqrt{a+b x^3} (23 A b-8 a B)}{4301 b}+\frac{2 B x^4 \left(a+b x^3\right)^{5/2}}{23 b}","\frac{54 a^2 x \sqrt{a+b x^3} (23 A b-8 a B)}{21505 b^2}-\frac{36\ 3^{3/4} \sqrt{2+\sqrt{3}} a^3 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (23 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21505 b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^4 \left(a+b x^3\right)^{3/2} (23 A b-8 a B)}{391 b}+\frac{18 a x^4 \sqrt{a+b x^3} (23 A b-8 a B)}{4301 b}+\frac{2 B x^4 \left(a+b x^3\right)^{5/2}}{23 b}",1,"(54*a^2*(23*A*b - 8*a*B)*x*Sqrt[a + b*x^3])/(21505*b^2) + (18*a*(23*A*b - 8*a*B)*x^4*Sqrt[a + b*x^3])/(4301*b) + (2*(23*A*b - 8*a*B)*x^4*(a + b*x^3)^(3/2))/(391*b) + (2*B*x^4*(a + b*x^3)^(5/2))/(23*b) - (36*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^3*(23*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(21505*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,22,0.1818,1,"{459, 279, 321, 218}"
203,1,299,0,0.1235658,"\int \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a+b x^3\right)^{3/2} (17 A b-2 a B)}{187 b}+\frac{18 a x \sqrt{a+b x^3} (17 A b-2 a B)}{935 b}+\frac{2 B x \left(a+b x^3\right)^{5/2}}{17 b}","\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} a^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{935 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \left(a+b x^3\right)^{3/2} (17 A b-2 a B)}{187 b}+\frac{18 a x \sqrt{a+b x^3} (17 A b-2 a B)}{935 b}+\frac{2 B x \left(a+b x^3\right)^{5/2}}{17 b}",1,"(18*a*(17*A*b - 2*a*B)*x*Sqrt[a + b*x^3])/(935*b) + (2*(17*A*b - 2*a*B)*x*(a + b*x^3)^(3/2))/(187*b) + (2*B*x*(a + b*x^3)^(5/2))/(17*b) + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*a^2*(17*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(935*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,19,0.1579,1,"{388, 195, 218}"
204,1,295,0,0.1266607,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^3} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^3,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+11 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{110 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{x \left(a+b x^3\right)^{3/2} (4 a B+11 A b)}{22 a}+\frac{9}{110} x \sqrt{a+b x^3} (4 a B+11 A b)-\frac{A \left(a+b x^3\right)^{5/2}}{2 a x^2}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+11 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{110 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{x \left(a+b x^3\right)^{3/2} (4 a B+11 A b)}{22 a}+\frac{9}{110} x \sqrt{a+b x^3} (4 a B+11 A b)-\frac{A \left(a+b x^3\right)^{5/2}}{2 a x^2}",1,"(9*(11*A*b + 4*a*B)*x*Sqrt[a + b*x^3])/110 + ((11*A*b + 4*a*B)*x*(a + b*x^3)^(3/2))/(22*a) - (A*(a + b*x^3)^(5/2))/(2*a*x^2) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*a*(11*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(110*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,22,0.1364,1,"{453, 195, 218}"
205,1,297,0,0.1209869,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^6} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^6,x]","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(a+b x^3\right)^{3/2} (2 a B+A b)}{4 a x^2}+\frac{9 b x \sqrt{a+b x^3} (2 a B+A b)}{20 a}-\frac{A \left(a+b x^3\right)^{5/2}}{5 a x^5}","\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(a+b x^3\right)^{3/2} (2 a B+A b)}{4 a x^2}+\frac{9 b x \sqrt{a+b x^3} (2 a B+A b)}{20 a}-\frac{A \left(a+b x^3\right)^{5/2}}{5 a x^5}",1,"(9*b*(A*b + 2*a*B)*x*Sqrt[a + b*x^3])/(20*a) - ((A*b + 2*a*B)*(a + b*x^3)^(3/2))/(4*a*x^2) - (A*(a + b*x^3)^(5/2))/(5*a*x^5) + (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(2/3)*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(20*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{453, 277, 195, 218}"
206,1,302,0,0.1261184,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^9} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^9,x]","-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-16 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{320 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(a+b x^3\right)^{3/2} (A b-16 a B)}{80 a x^5}+\frac{9 b \sqrt{a+b x^3} (A b-16 a B)}{320 a x^2}-\frac{A \left(a+b x^3\right)^{5/2}}{8 a x^8}","-\frac{9\ 3^{3/4} \sqrt{2+\sqrt{3}} b^{5/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-16 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{320 a \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(a+b x^3\right)^{3/2} (A b-16 a B)}{80 a x^5}+\frac{9 b \sqrt{a+b x^3} (A b-16 a B)}{320 a x^2}-\frac{A \left(a+b x^3\right)^{5/2}}{8 a x^8}",1,"(9*b*(A*b - 16*a*B)*Sqrt[a + b*x^3])/(320*a*x^2) + ((A*b - 16*a*B)*(a + b*x^3)^(3/2))/(80*a*x^5) - (A*(a + b*x^3)^(5/2))/(8*a*x^8) - (9*3^(3/4)*Sqrt[2 + Sqrt[3]]*b^(5/3)*(A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(320*a*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,22,0.1364,1,"{453, 277, 218}"
207,1,614,0,0.3701856,"\int x^4 \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[x^4*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{54 a^2 x^2 \sqrt{a+b x^3} (5 A b-2 a B)}{8645 b^2}-\frac{216 a^3 \sqrt{a+b x^3} (5 A b-2 a B)}{8645 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{72 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^5 \left(a+b x^3\right)^{3/2} (5 A b-2 a B)}{95 b}+\frac{18 a x^5 \sqrt{a+b x^3} (5 A b-2 a B)}{1235 b}+\frac{2 B x^5 \left(a+b x^3\right)^{5/2}}{25 b}","\frac{54 a^2 x^2 \sqrt{a+b x^3} (5 A b-2 a B)}{8645 b^2}-\frac{216 a^3 \sqrt{a+b x^3} (5 A b-2 a B)}{8645 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{72 \sqrt{2} 3^{3/4} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{108 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{10/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{8645 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^5 \left(a+b x^3\right)^{3/2} (5 A b-2 a B)}{95 b}+\frac{18 a x^5 \sqrt{a+b x^3} (5 A b-2 a B)}{1235 b}+\frac{2 B x^5 \left(a+b x^3\right)^{5/2}}{25 b}",1,"(54*a^2*(5*A*b - 2*a*B)*x^2*Sqrt[a + b*x^3])/(8645*b^2) + (18*a*(5*A*b - 2*a*B)*x^5*Sqrt[a + b*x^3])/(1235*b) - (216*a^3*(5*A*b - 2*a*B)*Sqrt[a + b*x^3])/(8645*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*(5*A*b - 2*a*B)*x^5*(a + b*x^3)^(3/2))/(95*b) + (2*B*x^5*(a + b*x^3)^(5/2))/(25*b) + (108*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(10/3)*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(8645*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (72*Sqrt[2]*3^(3/4)*a^(10/3)*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(8645*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,22,0.2727,1,"{459, 279, 321, 303, 218, 1877}"
208,1,581,0,0.2923005,"\int x \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[x*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{54 a^2 \sqrt{a+b x^3} (19 A b-4 a B)}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{18 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 \left(a+b x^3\right)^{3/2} (19 A b-4 a B)}{247 b}+\frac{18 a x^2 \sqrt{a+b x^3} (19 A b-4 a B)}{1729 b}+\frac{2 B x^2 \left(a+b x^3\right)^{5/2}}{19 b}","\frac{54 a^2 \sqrt{a+b x^3} (19 A b-4 a B)}{1729 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{18 \sqrt{2} 3^{3/4} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{1729 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 \left(a+b x^3\right)^{3/2} (19 A b-4 a B)}{247 b}+\frac{18 a x^2 \sqrt{a+b x^3} (19 A b-4 a B)}{1729 b}+\frac{2 B x^2 \left(a+b x^3\right)^{5/2}}{19 b}",1,"(18*a*(19*A*b - 4*a*B)*x^2*Sqrt[a + b*x^3])/(1729*b) + (54*a^2*(19*A*b - 4*a*B)*Sqrt[a + b*x^3])/(1729*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (2*(19*A*b - 4*a*B)*x^2*(a + b*x^3)^(3/2))/(247*b) + (2*B*x^2*(a + b*x^3)^(5/2))/(19*b) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(7/3)*(19*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (18*Sqrt[2]*3^(3/4)*a^(7/3)*(19*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,20,0.2500,1,"{459, 279, 303, 218, 1877}"
209,1,573,0,0.294175,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^2} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^2,x]","\frac{9 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+13 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+13 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{182 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a \sqrt{a+b x^3} (2 a B+13 A b)}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{x^2 \left(a+b x^3\right)^{3/2} (2 a B+13 A b)}{13 a}+\frac{9}{91} x^2 \sqrt{a+b x^3} (2 a B+13 A b)-\frac{A \left(a+b x^3\right)^{5/2}}{a x}","\frac{9 \sqrt{2} 3^{3/4} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+13 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+13 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{182 b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a \sqrt{a+b x^3} (2 a B+13 A b)}{91 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{x^2 \left(a+b x^3\right)^{3/2} (2 a B+13 A b)}{13 a}+\frac{9}{91} x^2 \sqrt{a+b x^3} (2 a B+13 A b)-\frac{A \left(a+b x^3\right)^{5/2}}{a x}",1,"(9*(13*A*b + 2*a*B)*x^2*Sqrt[a + b*x^3])/91 + (27*a*(13*A*b + 2*a*B)*Sqrt[a + b*x^3])/(91*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + ((13*A*b + 2*a*B)*x^2*(a + b*x^3)^(3/2))/(13*a) - (A*(a + b*x^3)^(5/2))/(a*x) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(182*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*Sqrt[2]*3^(3/4)*a^(4/3)*(13*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,22,0.2273,1,"{453, 279, 303, 218, 1877}"
210,1,578,0,0.2917307,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^5} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^5,x]","\frac{9\ 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+7 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt{2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+7 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{112 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(a+b x^3\right)^{3/2} (8 a B+7 A b)}{8 a x}+\frac{9 b x^2 \sqrt{a+b x^3} (8 a B+7 A b)}{56 a}+\frac{27 \sqrt[3]{b} \sqrt{a+b x^3} (8 a B+7 A b)}{56 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \left(a+b x^3\right)^{5/2}}{4 a x^4}","\frac{9\ 3^{3/4} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+7 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt{2} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+7 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{112 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(a+b x^3\right)^{3/2} (8 a B+7 A b)}{8 a x}+\frac{9 b x^2 \sqrt{a+b x^3} (8 a B+7 A b)}{56 a}+\frac{27 \sqrt[3]{b} \sqrt{a+b x^3} (8 a B+7 A b)}{56 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \left(a+b x^3\right)^{5/2}}{4 a x^4}",1,"(9*b*(7*A*b + 8*a*B)*x^2*Sqrt[a + b*x^3])/(56*a) + (27*b^(1/3)*(7*A*b + 8*a*B)*Sqrt[a + b*x^3])/(56*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - ((7*A*b + 8*a*B)*(a + b*x^3)^(3/2))/(8*a*x) - (A*(a + b*x^3)^(5/2))/(4*a*x^4) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*b^(1/3)*(7*A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(112*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*a^(1/3)*b^(1/3)*(7*A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(28*Sqrt[2]*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,22,0.2727,1,"{453, 277, 279, 303, 218, 1877}"
211,1,576,0,0.2966103,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^8} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^8,x]","\frac{9\ 3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a B+A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} \sqrt{a+b x^3} (14 a B+A b)}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\left(a+b x^3\right)^{3/2} (14 a B+A b)}{56 a x^4}-\frac{9 b \sqrt{a+b x^3} (14 a B+A b)}{112 a x}-\frac{A \left(a+b x^3\right)^{5/2}}{7 a x^7}","\frac{9\ 3^{3/4} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (14 a B+A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 b^{4/3} \sqrt{a+b x^3} (14 a B+A b)}{112 a \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\left(a+b x^3\right)^{3/2} (14 a B+A b)}{56 a x^4}-\frac{9 b \sqrt{a+b x^3} (14 a B+A b)}{112 a x}-\frac{A \left(a+b x^3\right)^{5/2}}{7 a x^7}",1,"(-9*b*(A*b + 14*a*B)*Sqrt[a + b*x^3])/(112*a*x) + (27*b^(4/3)*(A*b + 14*a*B)*Sqrt[a + b*x^3])/(112*a*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - ((A*b + 14*a*B)*(a + b*x^3)^(3/2))/(56*a*x^4) - (A*(a + b*x^3)^(5/2))/(7*a*x^7) - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(A*b + 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (9*3^(3/4)*b^(4/3)*(A*b + 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(56*Sqrt[2]*a^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,22,0.2273,1,"{453, 277, 303, 218, 1877}"
212,1,608,0,0.3546082,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{x^{11}} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/x^11,x]","\frac{27 b^2 \sqrt{a+b x^3} (A b-4 a B)}{448 a^2 x}-\frac{27 b^{7/3} \sqrt{a+b x^3} (A b-4 a B)}{448 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{9\ 3^{3/4} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 \sqrt{2} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{896 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(a+b x^3\right)^{3/2} (A b-4 a B)}{28 a x^7}+\frac{9 b \sqrt{a+b x^3} (A b-4 a B)}{224 a x^4}-\frac{A \left(a+b x^3\right)^{5/2}}{10 a x^{10}}","\frac{27 b^2 \sqrt{a+b x^3} (A b-4 a B)}{448 a^2 x}-\frac{27 b^{7/3} \sqrt{a+b x^3} (A b-4 a B)}{448 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{9\ 3^{3/4} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 \sqrt{2} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{7/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{896 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(a+b x^3\right)^{3/2} (A b-4 a B)}{28 a x^7}+\frac{9 b \sqrt{a+b x^3} (A b-4 a B)}{224 a x^4}-\frac{A \left(a+b x^3\right)^{5/2}}{10 a x^{10}}",1,"(9*b*(A*b - 4*a*B)*Sqrt[a + b*x^3])/(224*a*x^4) + (27*b^2*(A*b - 4*a*B)*Sqrt[a + b*x^3])/(448*a^2*x) - (27*b^(7/3)*(A*b - 4*a*B)*Sqrt[a + b*x^3])/(448*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + ((A*b - 4*a*B)*(a + b*x^3)^(3/2))/(28*a*x^7) - (A*(a + b*x^3)^(5/2))/(10*a*x^10) + (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(7/3)*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(896*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (9*3^(3/4)*b^(7/3)*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*Sqrt[2]*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,22,0.2727,1,"{453, 277, 325, 303, 218, 1877}"
213,1,103,0,0.073733,"\int \frac{x^8 \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^8*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{2 a^2 \sqrt{a+b x^3} (A b-a B)}{3 b^4}+\frac{2 \left(a+b x^3\right)^{5/2} (A b-3 a B)}{15 b^4}-\frac{2 a \left(a+b x^3\right)^{3/2} (2 A b-3 a B)}{9 b^4}+\frac{2 B \left(a+b x^3\right)^{7/2}}{21 b^4}","\frac{2 a^2 \sqrt{a+b x^3} (A b-a B)}{3 b^4}+\frac{2 \left(a+b x^3\right)^{5/2} (A b-3 a B)}{15 b^4}-\frac{2 a \left(a+b x^3\right)^{3/2} (2 A b-3 a B)}{9 b^4}+\frac{2 B \left(a+b x^3\right)^{7/2}}{21 b^4}",1,"(2*a^2*(A*b - a*B)*Sqrt[a + b*x^3])/(3*b^4) - (2*a*(2*A*b - 3*a*B)*(a + b*x^3)^(3/2))/(9*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(5/2))/(15*b^4) + (2*B*(a + b*x^3)^(7/2))/(21*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
214,1,73,0,0.0546994,"\int \frac{x^5 \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^5*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{2 \left(a+b x^3\right)^{3/2} (A b-2 a B)}{9 b^3}-\frac{2 a \sqrt{a+b x^3} (A b-a B)}{3 b^3}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b^3}","\frac{2 \left(a+b x^3\right)^{3/2} (A b-2 a B)}{9 b^3}-\frac{2 a \sqrt{a+b x^3} (A b-a B)}{3 b^3}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b^3}",1,"(-2*a*(A*b - a*B)*Sqrt[a + b*x^3])/(3*b^3) + (2*(A*b - 2*a*B)*(a + b*x^3)^(3/2))/(9*b^3) + (2*B*(a + b*x^3)^(5/2))/(15*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
215,1,46,0,0.0378856,"\int \frac{x^2 \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^2*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{a+b x^3} (A b-a B)}{3 b^2}+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b^2}","\frac{2 \sqrt{a+b x^3} (A b-a B)}{3 b^2}+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b^2}",1,"(2*(A*b - a*B)*Sqrt[a + b*x^3])/(3*b^2) + (2*B*(a + b*x^3)^(3/2))/(9*b^2)","A",3,2,22,0.09091,1,"{444, 43}"
216,1,48,0,0.0316857,"\int \frac{A+B x^3}{x \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x*Sqrt[a + b*x^3]),x]","\frac{2 B \sqrt{a+b x^3}}{3 b}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}","\frac{2 B \sqrt{a+b x^3}}{3 b}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 \sqrt{a}}",1,"(2*B*Sqrt[a + b*x^3])/(3*b) - (2*A*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*Sqrt[a])","A",4,4,22,0.1818,1,"{446, 80, 63, 208}"
217,1,58,0,0.0457008,"\int \frac{A+B x^3}{x^4 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^4*Sqrt[a + b*x^3]),x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{A \sqrt{a+b x^3}}{3 a x^3}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}-\frac{A \sqrt{a+b x^3}}{3 a x^3}",1,"-(A*Sqrt[a + b*x^3])/(3*a*x^3) + ((A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2))","A",4,4,22,0.1818,1,"{446, 78, 63, 208}"
218,1,90,0,0.0695414,"\int \frac{A+B x^3}{x^7 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^7*Sqrt[a + b*x^3]),x]","\frac{\sqrt{a+b x^3} (3 A b-4 a B)}{12 a^2 x^3}-\frac{b (3 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{5/2}}-\frac{A \sqrt{a+b x^3}}{6 a x^6}","\frac{\sqrt{a+b x^3} (3 A b-4 a B)}{12 a^2 x^3}-\frac{b (3 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{12 a^{5/2}}-\frac{A \sqrt{a+b x^3}}{6 a x^6}",1,"-(A*Sqrt[a + b*x^3])/(6*a*x^6) + ((3*A*b - 4*a*B)*Sqrt[a + b*x^3])/(12*a^2*x^3) - (b*(3*A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(12*a^(5/2))","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
219,1,270,0,0.1014759,"\int \frac{x^3 \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^3*(A + B*x^3))/Sqrt[a + b*x^3],x]","-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \sqrt{a+b x^3} (11 A b-8 a B)}{55 b^2}+\frac{2 B x^4 \sqrt{a+b x^3}}{11 b}","-\frac{4 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{55 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x \sqrt{a+b x^3} (11 A b-8 a B)}{55 b^2}+\frac{2 B x^4 \sqrt{a+b x^3}}{11 b}",1,"(2*(11*A*b - 8*a*B)*x*Sqrt[a + b*x^3])/(55*b^2) + (2*B*x^4*Sqrt[a + b*x^3])/(11*b) - (4*Sqrt[2 + Sqrt[3]]*a*(11*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(55*3^(1/4)*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{459, 321, 218}"
220,1,239,0,0.062515,"\int \frac{A+B x^3}{\sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 B x \sqrt{a+b x^3}}{5 b}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{5 \sqrt[4]{3} b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 B x \sqrt{a+b x^3}}{5 b}",1,"(2*B*x*Sqrt[a + b*x^3])/(5*b) + (2*Sqrt[2 + Sqrt[3]]*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(5*3^(1/4)*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,19,0.1053,1,"{388, 218}"
221,1,243,0,0.0689875,"\int \frac{A+B x^3}{x^3 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^3*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{A \sqrt{a+b x^3}}{2 a x^2}","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt[4]{3} a \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{A \sqrt{a+b x^3}}{2 a x^2}",1,"-(A*Sqrt[a + b*x^3])/(2*a*x^2) - (Sqrt[2 + Sqrt[3]]*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(1/4)*a*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,22,0.09091,1,"{453, 218}"
222,1,274,0,0.1017386,"\int \frac{A+B x^3}{x^6 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^6*Sqrt[a + b*x^3]),x]","\frac{\sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (7 A b-10 a B)}{20 a^2 x^2}-\frac{A \sqrt{a+b x^3}}{5 a x^5}","\frac{\sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{20 \sqrt[4]{3} a^2 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (7 A b-10 a B)}{20 a^2 x^2}-\frac{A \sqrt{a+b x^3}}{5 a x^5}",1,"-(A*Sqrt[a + b*x^3])/(5*a*x^5) + ((7*A*b - 10*a*B)*Sqrt[a + b*x^3])/(20*a^2*x^2) + (Sqrt[2 + Sqrt[3]]*b^(2/3)*(7*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(20*3^(1/4)*a^2*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{453, 325, 218}"
223,1,548,0,0.2454505,"\int \frac{x^4 \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(x^4*(A + B*x^3))/Sqrt[a + b*x^3],x]","-\frac{8 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 \sqrt{a+b x^3} (13 A b-10 a B)}{91 b^2}-\frac{8 a \sqrt{a+b x^3} (13 A b-10 a B)}{91 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^5 \sqrt{a+b x^3}}{13 b}","-\frac{8 \sqrt{2} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt[4]{3} \sqrt{2-\sqrt{3}} a^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{91 b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 \sqrt{a+b x^3} (13 A b-10 a B)}{91 b^2}-\frac{8 a \sqrt{a+b x^3} (13 A b-10 a B)}{91 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^5 \sqrt{a+b x^3}}{13 b}",1,"(2*(13*A*b - 10*a*B)*x^2*Sqrt[a + b*x^3])/(91*b^2) + (2*B*x^5*Sqrt[a + b*x^3])/(13*b) - (8*a*(13*A*b - 10*a*B)*Sqrt[a + b*x^3])/(91*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (4*3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(4/3)*(13*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (8*Sqrt[2]*a^(4/3)*(13*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*3^(1/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{459, 321, 303, 218, 1877}"
224,1,517,0,0.1861097,"\int \frac{x \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(x*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (7 A b-4 a B)}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^2 \sqrt{a+b x^3}}{7 b}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7 b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (7 A b-4 a B)}{7 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^2 \sqrt{a+b x^3}}{7 b}",1,"(2*B*x^2*Sqrt[a + b*x^3])/(7*b) + (2*(7*A*b - 4*a*B)*Sqrt[a + b*x^3])/(7*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2]*a^(1/3)*(7*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,20,0.2000,1,"{459, 303, 218, 1877}"
225,1,509,0,0.1951301,"\int \frac{A+B x^3}{x^2 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^2*Sqrt[a + b*x^3]),x]","\frac{\sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (2 a B+A b)}{a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \sqrt{a+b x^3}}{a x}","\frac{\sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2 a^{2/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (2 a B+A b)}{a b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \sqrt{a+b x^3}}{a x}",1,"-((A*Sqrt[a + b*x^3])/(a*x)) + ((A*b + 2*a*B)*Sqrt[a + b*x^3])/(a*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (Sqrt[2]*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*a^(2/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{453, 303, 218, 1877}"
226,1,550,0,0.2518131,"\int \frac{A+B x^3}{x^5 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^5*Sqrt[a + b*x^3]),x]","-\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-8 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (5 A b-8 a B)}{8 a^2 x}-\frac{\sqrt[3]{b} \sqrt{a+b x^3} (5 A b-8 a B)}{8 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \sqrt{a+b x^3}}{4 a x^4}","-\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-8 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16 a^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{a+b x^3} (5 A b-8 a B)}{8 a^2 x}-\frac{\sqrt[3]{b} \sqrt{a+b x^3} (5 A b-8 a B)}{8 a^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{A \sqrt{a+b x^3}}{4 a x^4}",1,"-(A*Sqrt[a + b*x^3])/(4*a*x^4) + ((5*A*b - 8*a*B)*Sqrt[a + b*x^3])/(8*a^2*x) - (b^(1/3)*(5*A*b - 8*a*B)*Sqrt[a + b*x^3])/(8*a^2*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(1/3)*(5*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (b^(1/3)*(5*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*a^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{453, 325, 303, 218, 1877}"
227,1,581,0,0.3076022,"\int \frac{A+B x^3}{x^8 \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(x^8*Sqrt[a + b*x^3]),x]","\frac{5 b^{4/3} \sqrt{a+b x^3} (11 A b-14 a B)}{112 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{5 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-14 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 b \sqrt{a+b x^3} (11 A b-14 a B)}{112 a^3 x}+\frac{\sqrt{a+b x^3} (11 A b-14 a B)}{56 a^2 x^4}-\frac{A \sqrt{a+b x^3}}{7 a x^7}","\frac{5 b^{4/3} \sqrt{a+b x^3} (11 A b-14 a B)}{112 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{5 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-14 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224 a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 b \sqrt{a+b x^3} (11 A b-14 a B)}{112 a^3 x}+\frac{\sqrt{a+b x^3} (11 A b-14 a B)}{56 a^2 x^4}-\frac{A \sqrt{a+b x^3}}{7 a x^7}",1,"-(A*Sqrt[a + b*x^3])/(7*a*x^7) + ((11*A*b - 14*a*B)*Sqrt[a + b*x^3])/(56*a^2*x^4) - (5*b*(11*A*b - 14*a*B)*Sqrt[a + b*x^3])/(112*a^3*x) + (5*b^(4/3)*(11*A*b - 14*a*B)*Sqrt[a + b*x^3])/(112*a^3*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (5*3^(1/4)*Sqrt[2 - Sqrt[3]]*b^(4/3)*(11*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (5*b^(4/3)*(11*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(56*Sqrt[2]*3^(1/4)*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,22,0.2273,1,"{453, 325, 303, 218, 1877}"
228,1,103,0,0.0767542,"\int \frac{x^8 \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^8*(A + B*x^3))/(a + b*x^3)^(3/2),x]","-\frac{2 a^2 (A b-a B)}{3 b^4 \sqrt{a+b x^3}}+\frac{2 \left(a+b x^3\right)^{3/2} (A b-3 a B)}{9 b^4}-\frac{2 a \sqrt{a+b x^3} (2 A b-3 a B)}{3 b^4}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b^4}","-\frac{2 a^2 (A b-a B)}{3 b^4 \sqrt{a+b x^3}}+\frac{2 \left(a+b x^3\right)^{3/2} (A b-3 a B)}{9 b^4}-\frac{2 a \sqrt{a+b x^3} (2 A b-3 a B)}{3 b^4}+\frac{2 B \left(a+b x^3\right)^{5/2}}{15 b^4}",1,"(-2*a^2*(A*b - a*B))/(3*b^4*Sqrt[a + b*x^3]) - (2*a*(2*A*b - 3*a*B)*Sqrt[a + b*x^3])/(3*b^4) + (2*(A*b - 3*a*B)*(a + b*x^3)^(3/2))/(9*b^4) + (2*B*(a + b*x^3)^(5/2))/(15*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
229,1,73,0,0.0548598,"\int \frac{x^5 \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^5*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{2 \sqrt{a+b x^3} (A b-2 a B)}{3 b^3}+\frac{2 a (A b-a B)}{3 b^3 \sqrt{a+b x^3}}+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b^3}","\frac{2 \sqrt{a+b x^3} (A b-2 a B)}{3 b^3}+\frac{2 a (A b-a B)}{3 b^3 \sqrt{a+b x^3}}+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b^3}",1,"(2*a*(A*b - a*B))/(3*b^3*Sqrt[a + b*x^3]) + (2*(A*b - 2*a*B)*Sqrt[a + b*x^3])/(3*b^3) + (2*B*(a + b*x^3)^(3/2))/(9*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
230,1,46,0,0.0365055,"\int \frac{x^2 \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^2*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{2 B \sqrt{a+b x^3}}{3 b^2}-\frac{2 (A b-a B)}{3 b^2 \sqrt{a+b x^3}}","\frac{2 B \sqrt{a+b x^3}}{3 b^2}-\frac{2 (A b-a B)}{3 b^2 \sqrt{a+b x^3}}",1,"(-2*(A*b - a*B))/(3*b^2*Sqrt[a + b*x^3]) + (2*B*Sqrt[a + b*x^3])/(3*b^2)","A",3,2,22,0.09091,1,"{444, 43}"
231,1,58,0,0.0397789,"\int \frac{A+B x^3}{x \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x*(a + b*x^3)^(3/2)),x]","\frac{2 (A b-a B)}{3 a b \sqrt{a+b x^3}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}","\frac{2 (A b-a B)}{3 a b \sqrt{a+b x^3}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{3/2}}",1,"(2*(A*b - a*B))/(3*a*b*Sqrt[a + b*x^3]) - (2*A*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(3/2))","A",4,4,22,0.1818,1,"{446, 78, 63, 208}"
232,1,86,0,0.0650946,"\int \frac{A+B x^3}{x^4 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^4*(a + b*x^3)^(3/2)),x]","-\frac{3 A b-2 a B}{3 a^2 \sqrt{a+b x^3}}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{5/2}}-\frac{A}{3 a x^3 \sqrt{a+b x^3}}","-\frac{3 A b-2 a B}{3 a^2 \sqrt{a+b x^3}}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{5/2}}-\frac{A}{3 a x^3 \sqrt{a+b x^3}}",1,"-(3*A*b - 2*a*B)/(3*a^2*Sqrt[a + b*x^3]) - A/(3*a*x^3*Sqrt[a + b*x^3]) + ((3*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(5/2))","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
233,1,120,0,0.0899382,"\int \frac{A+B x^3}{x^7 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^7*(a + b*x^3)^(3/2)),x]","\frac{\sqrt{a+b x^3} (5 A b-4 a B)}{4 a^3 x^3}-\frac{5 A b-4 a B}{6 a^2 x^3 \sqrt{a+b x^3}}-\frac{b (5 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{A}{6 a x^6 \sqrt{a+b x^3}}","\frac{b (5 A b-4 a B)}{4 a^3 \sqrt{a+b x^3}}+\frac{5 A b-4 a B}{12 a^2 x^3 \sqrt{a+b x^3}}-\frac{b (5 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{4 a^{7/2}}-\frac{A}{6 a x^6 \sqrt{a+b x^3}}",1,"-A/(6*a*x^6*Sqrt[a + b*x^3]) - (5*A*b - 4*a*B)/(6*a^2*x^3*Sqrt[a + b*x^3]) + ((5*A*b - 4*a*B)*Sqrt[a + b*x^3])/(4*a^3*x^3) - (b*(5*A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(4*a^(7/2))","A",6,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
234,1,300,0,0.139273,"\int \frac{x^6 \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^6*(A + B*x^3))/(a + b*x^3)^(3/2),x]","-\frac{32 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{165 \sqrt[4]{3} b^{10/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^4 (11 A b-14 a B)}{33 b^2 \sqrt{a+b x^3}}+\frac{16 x \sqrt{a+b x^3} (11 A b-14 a B)}{165 b^3}+\frac{2 B x^7}{11 b \sqrt{a+b x^3}}","-\frac{32 \sqrt{2+\sqrt{3}} a \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{165 \sqrt[4]{3} b^{10/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^4 (11 A b-14 a B)}{33 b^2 \sqrt{a+b x^3}}+\frac{16 x \sqrt{a+b x^3} (11 A b-14 a B)}{165 b^3}+\frac{2 B x^7}{11 b \sqrt{a+b x^3}}",1,"(-2*(11*A*b - 14*a*B)*x^4)/(33*b^2*Sqrt[a + b*x^3]) + (2*B*x^7)/(11*b*Sqrt[a + b*x^3]) + (16*(11*A*b - 14*a*B)*x*Sqrt[a + b*x^3])/(165*b^3) - (32*Sqrt[2 + Sqrt[3]]*a*(11*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(165*3^(1/4)*b^(10/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{459, 288, 321, 218}"
235,1,269,0,0.0995218,"\int \frac{x^3 \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^3*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x (5 A b-8 a B)}{15 b^2 \sqrt{a+b x^3}}+\frac{2 B x^4}{5 b \sqrt{a+b x^3}}","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{15 \sqrt[4]{3} b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x (5 A b-8 a B)}{15 b^2 \sqrt{a+b x^3}}+\frac{2 B x^4}{5 b \sqrt{a+b x^3}}",1,"(-2*(5*A*b - 8*a*B)*x)/(15*b^2*Sqrt[a + b*x^3]) + (2*B*x^4)/(5*b*Sqrt[a + b*x^3]) + (4*Sqrt[2 + Sqrt[3]]*(5*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(15*3^(1/4)*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{459, 288, 218}"
236,1,251,0,0.0631136,"\int \frac{A+B x^3}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(a + b*x^3)^(3/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (A b-a B)}{3 a b \sqrt{a+b x^3}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (A b-a B)}{3 a b \sqrt{a+b x^3}}",1,"(2*(A*b - a*B)*x)/(3*a*b*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",2,2,19,0.1053,1,"{385, 218}"
237,1,272,0,0.1008165,"\int \frac{A+B x^3}{x^3 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^3*(a + b*x^3)^(3/2)),x]","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} a^2 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{x (7 A b-4 a B)}{6 a^2 \sqrt{a+b x^3}}-\frac{A}{2 a x^2 \sqrt{a+b x^3}}","-\frac{\sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{6 \sqrt[4]{3} a^2 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{x (7 A b-4 a B)}{6 a^2 \sqrt{a+b x^3}}-\frac{A}{2 a x^2 \sqrt{a+b x^3}}",1,"-A/(2*a*x^2*Sqrt[a + b*x^3]) - ((7*A*b - 4*a*B)*x)/(6*a^2*Sqrt[a + b*x^3]) - (Sqrt[2 + Sqrt[3]]*(7*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(6*3^(1/4)*a^2*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{453, 199, 218}"
238,1,304,0,0.1357994,"\int \frac{A+B x^3}{x^6 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^6*(a + b*x^3)^(3/2)),x]","\frac{7 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{60 \sqrt[4]{3} a^3 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{7 \sqrt{a+b x^3} (13 A b-10 a B)}{60 a^3 x^2}-\frac{13 A b-10 a B}{15 a^2 x^2 \sqrt{a+b x^3}}-\frac{A}{5 a x^5 \sqrt{a+b x^3}}","\frac{7 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{60 \sqrt[4]{3} a^3 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{7 \sqrt{a+b x^3} (13 A b-10 a B)}{60 a^3 x^2}-\frac{13 A b-10 a B}{15 a^2 x^2 \sqrt{a+b x^3}}-\frac{A}{5 a x^5 \sqrt{a+b x^3}}",1,"-A/(5*a*x^5*Sqrt[a + b*x^3]) - (13*A*b - 10*a*B)/(15*a^2*x^2*Sqrt[a + b*x^3]) + (7*(13*A*b - 10*a*B)*Sqrt[a + b*x^3])/(60*a^3*x^2) + (7*Sqrt[2 + Sqrt[3]]*b^(2/3)*(13*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(60*3^(1/4)*a^3*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,22,0.1818,1,"{453, 290, 325, 218}"
239,1,547,0,0.2547658,"\int \frac{x^4 \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x^4*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{8 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^2 (7 A b-10 a B)}{21 b^2 \sqrt{a+b x^3}}+\frac{8 \sqrt{a+b x^3} (7 A b-10 a B)}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^5}{7 b \sqrt{a+b x^3}}","\frac{8 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{4 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^2 (7 A b-10 a B)}{21 b^2 \sqrt{a+b x^3}}+\frac{8 \sqrt{a+b x^3} (7 A b-10 a B)}{21 b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^5}{7 b \sqrt{a+b x^3}}",1,"(-2*(7*A*b - 10*a*B)*x^2)/(21*b^2*Sqrt[a + b*x^3]) + (2*B*x^5)/(7*b*Sqrt[a + b*x^3]) + (8*(7*A*b - 10*a*B)*Sqrt[a + b*x^3])/(21*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (4*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(3/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (8*Sqrt[2]*a^(1/3)*(7*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(21*3^(1/4)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{459, 288, 303, 218, 1877}"
240,1,524,0,0.1949622,"\int \frac{x \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(x*(A + B*x^3))/(a + b*x^3)^(3/2),x]","-\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (A b-4 a B)}{3 a b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2 (A b-a B)}{3 a b \sqrt{a+b x^3}}","-\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-4 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (A b-4 a B)}{3 a b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^2 (A b-a B)}{3 a b \sqrt{a+b x^3}}",1,"(2*(A*b - a*B)*x^2)/(3*a*b*Sqrt[a + b*x^3]) - (2*(A*b - 4*a*B)*Sqrt[a + b*x^3])/(3*a*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (Sqrt[2 - Sqrt[3]]*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(3/4)*a^(2/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (2*Sqrt[2]*(A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(2/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,20,0.2000,1,"{457, 303, 218, 1877}"
241,1,548,0,0.2438506,"\int \frac{A+B x^3}{x^2 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^2*(a + b*x^3)^(3/2)),x]","\frac{\sqrt{a+b x^3} (5 A b-2 a B)}{3 a^2 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{x^2 (5 A b-2 a B)}{3 a^2 \sqrt{a+b x^3}}-\frac{A}{a x \sqrt{a+b x^3}}","\frac{\sqrt{a+b x^3} (5 A b-2 a B)}{3 a^2 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} a^{5/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-2 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} a^{5/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{x^2 (5 A b-2 a B)}{3 a^2 \sqrt{a+b x^3}}-\frac{A}{a x \sqrt{a+b x^3}}",1,"-(A/(a*x*Sqrt[a + b*x^3])) - ((5*A*b - 2*a*B)*x^2)/(3*a^2*Sqrt[a + b*x^3]) + ((5*A*b - 2*a*B)*Sqrt[a + b*x^3])/(3*a^2*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (Sqrt[2 - Sqrt[3]]*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*a^(5/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (Sqrt[2]*(5*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*a^(5/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{453, 290, 303, 218, 1877}"
242,1,580,0,0.3036167,"\int \frac{A+B x^3}{x^5 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^5*(a + b*x^3)^(3/2)),x]","-\frac{5 \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-8 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 \sqrt{a+b x^3} (11 A b-8 a B)}{24 a^3 x}-\frac{5 \sqrt[3]{b} \sqrt{a+b x^3} (11 A b-8 a B)}{24 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{11 A b-8 a B}{12 a^2 x \sqrt{a+b x^3}}-\frac{A}{4 a x^4 \sqrt{a+b x^3}}","-\frac{5 \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-8 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} a^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{5 \sqrt{a+b x^3} (11 A b-8 a B)}{24 a^3 x}-\frac{5 \sqrt[3]{b} \sqrt{a+b x^3} (11 A b-8 a B)}{24 a^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{11 A b-8 a B}{12 a^2 x \sqrt{a+b x^3}}-\frac{A}{4 a x^4 \sqrt{a+b x^3}}",1,"-A/(4*a*x^4*Sqrt[a + b*x^3]) - (11*A*b - 8*a*B)/(12*a^2*x*Sqrt[a + b*x^3]) + (5*(11*A*b - 8*a*B)*Sqrt[a + b*x^3])/(24*a^3*x) - (5*b^(1/3)*(11*A*b - 8*a*B)*Sqrt[a + b*x^3])/(24*a^3*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (5*Sqrt[2 - Sqrt[3]]*b^(1/3)*(11*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*3^(3/4)*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (5*b^(1/3)*(11*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(12*Sqrt[2]*3^(1/4)*a^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,22,0.2727,1,"{453, 290, 325, 303, 218, 1877}"
243,1,611,0,0.3618236,"\int \frac{A+B x^3}{x^8 \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(x^8*(a + b*x^3)^(3/2)),x]","\frac{55 b^{4/3} \sqrt{a+b x^3} (17 A b-14 a B)}{336 a^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{55 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{168 \sqrt{2} \sqrt[4]{3} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{55 \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-14 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224\ 3^{3/4} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{55 b \sqrt{a+b x^3} (17 A b-14 a B)}{336 a^4 x}+\frac{11 \sqrt{a+b x^3} (17 A b-14 a B)}{168 a^3 x^4}-\frac{17 A b-14 a B}{21 a^2 x^4 \sqrt{a+b x^3}}-\frac{A}{7 a x^7 \sqrt{a+b x^3}}","\frac{55 b^{4/3} \sqrt{a+b x^3} (17 A b-14 a B)}{336 a^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{55 b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{168 \sqrt{2} \sqrt[4]{3} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{55 \sqrt{2-\sqrt{3}} b^{4/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-14 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{224\ 3^{3/4} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{55 b \sqrt{a+b x^3} (17 A b-14 a B)}{336 a^4 x}+\frac{11 \sqrt{a+b x^3} (17 A b-14 a B)}{168 a^3 x^4}-\frac{17 A b-14 a B}{21 a^2 x^4 \sqrt{a+b x^3}}-\frac{A}{7 a x^7 \sqrt{a+b x^3}}",1,"-A/(7*a*x^7*Sqrt[a + b*x^3]) - (17*A*b - 14*a*B)/(21*a^2*x^4*Sqrt[a + b*x^3]) + (11*(17*A*b - 14*a*B)*Sqrt[a + b*x^3])/(168*a^3*x^4) - (55*b*(17*A*b - 14*a*B)*Sqrt[a + b*x^3])/(336*a^4*x) + (55*b^(4/3)*(17*A*b - 14*a*B)*Sqrt[a + b*x^3])/(336*a^4*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (55*Sqrt[2 - Sqrt[3]]*b^(4/3)*(17*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*3^(3/4)*a^(11/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (55*b^(4/3)*(17*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(168*Sqrt[2]*3^(1/4)*a^(11/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,22,0.2727,1,"{453, 290, 325, 303, 218, 1877}"
244,1,103,0,0.0779481,"\int \frac{x^8 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^8*(A + B*x^3))/(a + b*x^3)^(5/2),x]","-\frac{2 a^2 (A b-a B)}{9 b^4 \left(a+b x^3\right)^{3/2}}+\frac{2 a (2 A b-3 a B)}{3 b^4 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (A b-3 a B)}{3 b^4}+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b^4}","-\frac{2 a^2 (A b-a B)}{9 b^4 \left(a+b x^3\right)^{3/2}}+\frac{2 a (2 A b-3 a B)}{3 b^4 \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (A b-3 a B)}{3 b^4}+\frac{2 B \left(a+b x^3\right)^{3/2}}{9 b^4}",1,"(-2*a^2*(A*b - a*B))/(9*b^4*(a + b*x^3)^(3/2)) + (2*a*(2*A*b - 3*a*B))/(3*b^4*Sqrt[a + b*x^3]) + (2*(A*b - 3*a*B)*Sqrt[a + b*x^3])/(3*b^4) + (2*B*(a + b*x^3)^(3/2))/(9*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
245,1,73,0,0.0555171,"\int \frac{x^5 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^5*(A + B*x^3))/(a + b*x^3)^(5/2),x]","-\frac{2 (A b-2 a B)}{3 b^3 \sqrt{a+b x^3}}+\frac{2 a (A b-a B)}{9 b^3 \left(a+b x^3\right)^{3/2}}+\frac{2 B \sqrt{a+b x^3}}{3 b^3}","-\frac{2 (A b-2 a B)}{3 b^3 \sqrt{a+b x^3}}+\frac{2 a (A b-a B)}{9 b^3 \left(a+b x^3\right)^{3/2}}+\frac{2 B \sqrt{a+b x^3}}{3 b^3}",1,"(2*a*(A*b - a*B))/(9*b^3*(a + b*x^3)^(3/2)) - (2*(A*b - 2*a*B))/(3*b^3*Sqrt[a + b*x^3]) + (2*B*Sqrt[a + b*x^3])/(3*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
246,1,46,0,0.0359458,"\int \frac{x^2 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^2*(A + B*x^3))/(a + b*x^3)^(5/2),x]","-\frac{2 (A b-a B)}{9 b^2 \left(a+b x^3\right)^{3/2}}-\frac{2 B}{3 b^2 \sqrt{a+b x^3}}","-\frac{2 (A b-a B)}{9 b^2 \left(a+b x^3\right)^{3/2}}-\frac{2 B}{3 b^2 \sqrt{a+b x^3}}",1,"(-2*(A*b - a*B))/(9*b^2*(a + b*x^3)^(3/2)) - (2*B)/(3*b^2*Sqrt[a + b*x^3])","A",3,2,22,0.09091,1,"{444, 43}"
247,1,77,0,0.0504637,"\int \frac{A+B x^3}{x \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(x*(a + b*x^3)^(5/2)),x]","\frac{2 A}{3 a^2 \sqrt{a+b x^3}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{5/2}}+\frac{2 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}","\frac{2 A}{3 a^2 \sqrt{a+b x^3}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{5/2}}+\frac{2 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B))/(9*a*b*(a + b*x^3)^(3/2)) + (2*A)/(3*a^2*Sqrt[a + b*x^3]) - (2*A*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(5/2))","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
248,1,113,0,0.0869774,"\int \frac{A+B x^3}{x^4 \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(x^4*(a + b*x^3)^(5/2)),x]","-\frac{5 A b-2 a B}{3 a^3 \sqrt{a+b x^3}}-\frac{5 A b-2 a B}{9 a^2 \left(a+b x^3\right)^{3/2}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{7/2}}-\frac{A}{3 a x^3 \left(a+b x^3\right)^{3/2}}","-\frac{5 A b-2 a B}{3 a^3 \sqrt{a+b x^3}}-\frac{5 A b-2 a B}{9 a^2 \left(a+b x^3\right)^{3/2}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^3}}{\sqrt{a}}\right)}{3 a^{7/2}}-\frac{A}{3 a x^3 \left(a+b x^3\right)^{3/2}}",1,"-(5*A*b - 2*a*B)/(9*a^2*(a + b*x^3)^(3/2)) - A/(3*a*x^3*(a + b*x^3)^(3/2)) - (5*A*b - 2*a*B)/(3*a^3*Sqrt[a + b*x^3]) + ((5*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^3]/Sqrt[a]])/(3*a^(7/2))","A",6,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
249,1,299,0,0.1316185,"\int \frac{x^6 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^6*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{32 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{135 \sqrt[4]{3} b^{10/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^4 (5 A b-14 a B)}{45 b^2 \left(a+b x^3\right)^{3/2}}-\frac{16 x (5 A b-14 a B)}{135 b^3 \sqrt{a+b x^3}}+\frac{2 B x^7}{5 b \left(a+b x^3\right)^{3/2}}","\frac{32 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (5 A b-14 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{135 \sqrt[4]{3} b^{10/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^4 (5 A b-14 a B)}{45 b^2 \left(a+b x^3\right)^{3/2}}-\frac{16 x (5 A b-14 a B)}{135 b^3 \sqrt{a+b x^3}}+\frac{2 B x^7}{5 b \left(a+b x^3\right)^{3/2}}",1,"(-2*(5*A*b - 14*a*B)*x^4)/(45*b^2*(a + b*x^3)^(3/2)) + (2*B*x^7)/(5*b*(a + b*x^3)^(3/2)) - (16*(5*A*b - 14*a*B)*x)/(135*b^3*Sqrt[a + b*x^3]) + (32*Sqrt[2 + Sqrt[3]]*(5*A*b - 14*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(135*3^(1/4)*b^(10/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,22,0.1364,1,"{459, 288, 218}"
250,1,283,0,0.1030118,"\int \frac{x^3 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^3*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x (8 a B+A b)}{27 a b^2 \sqrt{a+b x^3}}+\frac{2 x^4 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}","\frac{4 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (8 a B+A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a b^{7/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x (8 a B+A b)}{27 a b^2 \sqrt{a+b x^3}}+\frac{2 x^4 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*x^4)/(9*a*b*(a + b*x^3)^(3/2)) - (2*(A*b + 8*a*B)*x)/(27*a*b^2*Sqrt[a + b*x^3]) + (4*Sqrt[2 + Sqrt[3]]*(A*b + 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a*b^(7/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,22,0.1364,1,"{457, 288, 218}"
251,1,283,0,0.09851,"\int \frac{A+B x^3}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(a + b*x^3)^(5/2),x]","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+7 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^2 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (2 a B+7 A b)}{27 a^2 b \sqrt{a+b x^3}}+\frac{2 x (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}","\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (2 a B+7 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^2 b^{4/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x (2 a B+7 A b)}{27 a^2 b \sqrt{a+b x^3}}+\frac{2 x (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*x)/(9*a*b*(a + b*x^3)^(3/2)) + (2*(7*A*b + 2*a*B)*x)/(27*a^2*b*Sqrt[a + b*x^3]) + (2*Sqrt[2 + Sqrt[3]]*(7*A*b + 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a^2*b^(4/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,19,0.1579,1,"{385, 199, 218}"
252,1,300,0,0.1296285,"\int \frac{A+B x^3}{x^3 \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(x^3*(a + b*x^3)^(5/2)),x]","-\frac{7 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{54 \sqrt[4]{3} a^3 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{7 x (13 A b-4 a B)}{54 a^3 \sqrt{a+b x^3}}-\frac{x (13 A b-4 a B)}{18 a^2 \left(a+b x^3\right)^{3/2}}-\frac{A}{2 a x^2 \left(a+b x^3\right)^{3/2}}","-\frac{7 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (13 A b-4 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{54 \sqrt[4]{3} a^3 \sqrt[3]{b} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{7 x (13 A b-4 a B)}{54 a^3 \sqrt{a+b x^3}}-\frac{x (13 A b-4 a B)}{18 a^2 \left(a+b x^3\right)^{3/2}}-\frac{A}{2 a x^2 \left(a+b x^3\right)^{3/2}}",1,"-A/(2*a*x^2*(a + b*x^3)^(3/2)) - ((13*A*b - 4*a*B)*x)/(18*a^2*(a + b*x^3)^(3/2)) - (7*(13*A*b - 4*a*B)*x)/(54*a^3*Sqrt[a + b*x^3]) - (7*Sqrt[2 + Sqrt[3]]*(13*A*b - 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(54*3^(1/4)*a^3*b^(1/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,3,22,0.1364,1,"{453, 199, 218}"
253,1,334,0,0.1660227,"\int \frac{A+B x^3}{x^6 \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(x^6*(a + b*x^3)^(5/2)),x]","\frac{91 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{540 \sqrt[4]{3} a^4 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{91 \sqrt{a+b x^3} (19 A b-10 a B)}{540 a^4 x^2}-\frac{13 (19 A b-10 a B)}{135 a^3 x^2 \sqrt{a+b x^3}}-\frac{19 A b-10 a B}{45 a^2 x^2 \left(a+b x^3\right)^{3/2}}-\frac{A}{5 a x^5 \left(a+b x^3\right)^{3/2}}","\frac{91 \sqrt{2+\sqrt{3}} b^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (19 A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{540 \sqrt[4]{3} a^4 \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{91 \sqrt{a+b x^3} (19 A b-10 a B)}{540 a^4 x^2}-\frac{13 (19 A b-10 a B)}{135 a^3 x^2 \sqrt{a+b x^3}}-\frac{19 A b-10 a B}{45 a^2 x^2 \left(a+b x^3\right)^{3/2}}-\frac{A}{5 a x^5 \left(a+b x^3\right)^{3/2}}",1,"-A/(5*a*x^5*(a + b*x^3)^(3/2)) - (19*A*b - 10*a*B)/(45*a^2*x^2*(a + b*x^3)^(3/2)) - (13*(19*A*b - 10*a*B))/(135*a^3*x^2*Sqrt[a + b*x^3]) + (91*(19*A*b - 10*a*B)*Sqrt[a + b*x^3])/(540*a^4*x^2) + (91*Sqrt[2 + Sqrt[3]]*b^(2/3)*(19*A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(540*3^(1/4)*a^4*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,22,0.1818,1,"{453, 290, 325, 218}"
254,1,577,0,0.3179128,"\int \frac{x^7 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^7*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{80 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-16 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{189 \sqrt[4]{3} b^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{40 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-16 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{63\ 3^{3/4} b^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^5 (7 A b-16 a B)}{63 b^2 \left(a+b x^3\right)^{3/2}}-\frac{20 x^2 (7 A b-16 a B)}{189 b^3 \sqrt{a+b x^3}}+\frac{80 \sqrt{a+b x^3} (7 A b-16 a B)}{189 b^{11/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^8}{7 b \left(a+b x^3\right)^{3/2}}","\frac{80 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-16 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{189 \sqrt[4]{3} b^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{40 \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (7 A b-16 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{63\ 3^{3/4} b^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 x^5 (7 A b-16 a B)}{63 b^2 \left(a+b x^3\right)^{3/2}}-\frac{20 x^2 (7 A b-16 a B)}{189 b^3 \sqrt{a+b x^3}}+\frac{80 \sqrt{a+b x^3} (7 A b-16 a B)}{189 b^{11/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 B x^8}{7 b \left(a+b x^3\right)^{3/2}}",1,"(-2*(7*A*b - 16*a*B)*x^5)/(63*b^2*(a + b*x^3)^(3/2)) + (2*B*x^8)/(7*b*(a + b*x^3)^(3/2)) - (20*(7*A*b - 16*a*B)*x^2)/(189*b^3*Sqrt[a + b*x^3]) + (80*(7*A*b - 16*a*B)*Sqrt[a + b*x^3])/(189*b^(11/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (40*Sqrt[2 - Sqrt[3]]*a^(1/3)*(7*A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(63*3^(3/4)*b^(11/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (80*Sqrt[2]*a^(1/3)*(7*A*b - 16*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(189*3^(1/4)*b^(11/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,22,0.2273,1,"{459, 288, 303, 218, 1877}"
255,1,559,0,0.2650249,"\int \frac{x^4 \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x^4*(A + B*x^3))/(a + b*x^3)^(5/2),x]","-\frac{8 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^{2/3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{2/3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 (A b-10 a B)}{27 a b^2 \sqrt{a+b x^3}}-\frac{8 \sqrt{a+b x^3} (A b-10 a B)}{27 a b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^5 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}","-\frac{8 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-10 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^{2/3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{4 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (A b-10 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{2/3} b^{8/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 (A b-10 a B)}{27 a b^2 \sqrt{a+b x^3}}-\frac{8 \sqrt{a+b x^3} (A b-10 a B)}{27 a b^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{2 x^5 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*x^5)/(9*a*b*(a + b*x^3)^(3/2)) + (2*(A*b - 10*a*B)*x^2)/(27*a*b^2*Sqrt[a + b*x^3]) - (8*(A*b - 10*a*B)*Sqrt[a + b*x^3])/(27*a*b^(8/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (4*Sqrt[2 - Sqrt[3]]*(A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*a^(2/3)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (8*Sqrt[2]*(A*b - 10*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a^(2/3)*b^(8/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,22,0.2273,1,"{457, 288, 303, 218, 1877}"
256,1,563,0,0.2481839,"\int \frac{x \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(x*(A + B*x^3))/(a + b*x^3)^(5/2),x]","-\frac{2 \sqrt{a+b x^3} (4 a B+5 A b)}{27 a^2 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+5 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+5 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 (4 a B+5 A b)}{27 a^2 b \sqrt{a+b x^3}}+\frac{2 x^2 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}","-\frac{2 \sqrt{a+b x^3} (4 a B+5 A b)}{27 a^2 b^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{2 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+5 A b) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (4 a B+5 A b) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 x^2 (4 a B+5 A b)}{27 a^2 b \sqrt{a+b x^3}}+\frac{2 x^2 (A b-a B)}{9 a b \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*x^2)/(9*a*b*(a + b*x^3)^(3/2)) + (2*(5*A*b + 4*a*B)*x^2)/(27*a^2*b*Sqrt[a + b*x^3]) - (2*(5*A*b + 4*a*B)*Sqrt[a + b*x^3])/(27*a^2*b^(5/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (Sqrt[2 - Sqrt[3]]*(5*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*a^(5/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (2*Sqrt[2]*(5*A*b + 4*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a^(5/3)*b^(5/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,20,0.2500,1,"{457, 290, 303, 218, 1877}"
257,1,578,0,0.2997941,"\int \frac{A+B x^3}{x^2 \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(x^2*(a + b*x^3)^(5/2)),x]","\frac{5 \sqrt{a+b x^3} (11 A b-2 a B)}{27 a^3 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{5 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^{8/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-2 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{18\ 3^{3/4} a^{8/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 x^2 (11 A b-2 a B)}{27 a^3 \sqrt{a+b x^3}}-\frac{x^2 (11 A b-2 a B)}{9 a^2 \left(a+b x^3\right)^{3/2}}-\frac{A}{a x \left(a+b x^3\right)^{3/2}}","\frac{5 \sqrt{a+b x^3} (11 A b-2 a B)}{27 a^3 b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{5 \sqrt{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-2 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} a^{8/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (11 A b-2 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{18\ 3^{3/4} a^{8/3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{5 x^2 (11 A b-2 a B)}{27 a^3 \sqrt{a+b x^3}}-\frac{x^2 (11 A b-2 a B)}{9 a^2 \left(a+b x^3\right)^{3/2}}-\frac{A}{a x \left(a+b x^3\right)^{3/2}}",1,"-(A/(a*x*(a + b*x^3)^(3/2))) - ((11*A*b - 2*a*B)*x^2)/(9*a^2*(a + b*x^3)^(3/2)) - (5*(11*A*b - 2*a*B)*x^2)/(27*a^3*Sqrt[a + b*x^3]) + (5*(11*A*b - 2*a*B)*Sqrt[a + b*x^3])/(27*a^3*b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (5*Sqrt[2 - Sqrt[3]]*(11*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(18*3^(3/4)*a^(8/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (5*Sqrt[2]*(11*A*b - 2*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*a^(8/3)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,22,0.2273,1,"{453, 290, 303, 218, 1877}"
258,1,610,0,0.3556004,"\int \frac{A+B x^3}{x^5 \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(x^5*(a + b*x^3)^(5/2)),x]","-\frac{55 \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-8 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{144\ 3^{3/4} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 \sqrt{a+b x^3} (17 A b-8 a B)}{216 a^4 x}-\frac{55 \sqrt[3]{b} \sqrt{a+b x^3} (17 A b-8 a B)}{216 a^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{11 (17 A b-8 a B)}{108 a^3 x \sqrt{a+b x^3}}-\frac{17 A b-8 a B}{36 a^2 x \left(a+b x^3\right)^{3/2}}-\frac{A}{4 a x^4 \left(a+b x^3\right)^{3/2}}","-\frac{55 \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-8 a B) F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 \sqrt{2-\sqrt{3}} \sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} (17 A b-8 a B) E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{144\ 3^{3/4} a^{11/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{55 \sqrt{a+b x^3} (17 A b-8 a B)}{216 a^4 x}-\frac{55 \sqrt[3]{b} \sqrt{a+b x^3} (17 A b-8 a B)}{216 a^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{11 (17 A b-8 a B)}{108 a^3 x \sqrt{a+b x^3}}-\frac{17 A b-8 a B}{36 a^2 x \left(a+b x^3\right)^{3/2}}-\frac{A}{4 a x^4 \left(a+b x^3\right)^{3/2}}",1,"-A/(4*a*x^4*(a + b*x^3)^(3/2)) - (17*A*b - 8*a*B)/(36*a^2*x*(a + b*x^3)^(3/2)) - (11*(17*A*b - 8*a*B))/(108*a^3*x*Sqrt[a + b*x^3]) + (55*(17*A*b - 8*a*B)*Sqrt[a + b*x^3])/(216*a^4*x) - (55*b^(1/3)*(17*A*b - 8*a*B)*Sqrt[a + b*x^3])/(216*a^4*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (55*Sqrt[2 - Sqrt[3]]*b^(1/3)*(17*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(144*3^(3/4)*a^(11/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (55*b^(1/3)*(17*A*b - 8*a*B)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(108*Sqrt[2]*3^(1/4)*a^(11/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,22,0.2727,1,"{453, 290, 325, 303, 218, 1877}"
259,1,97,0,0.093991,"\int \frac{x^8 \sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[(x^8*Sqrt[c + d*x^3])/(4*c + d*x^3),x]","\frac{32 c^2 \sqrt{c+d x^3}}{3 d^3}-\frac{32 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d^3}-\frac{10 c \left(c+d x^3\right)^{3/2}}{9 d^3}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^3}","\frac{32 c^2 \sqrt{c+d x^3}}{3 d^3}-\frac{32 c^{5/2} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d^3}-\frac{10 c \left(c+d x^3\right)^{3/2}}{9 d^3}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^3}",1,"(32*c^2*Sqrt[c + d*x^3])/(3*d^3) - (10*c*(c + d*x^3)^(3/2))/(9*d^3) + (2*(c + d*x^3)^(5/2))/(15*d^3) - (32*c^(5/2)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(Sqrt[3]*d^3)","A",6,5,26,0.1923,1,"{446, 88, 50, 63, 203}"
260,1,76,0,0.0623822,"\int \frac{x^5 \sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[(x^5*Sqrt[c + d*x^3])/(4*c + d*x^3),x]","\frac{8 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d^2}-\frac{8 c \sqrt{c+d x^3}}{3 d^2}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^2}","\frac{8 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d^2}-\frac{8 c \sqrt{c+d x^3}}{3 d^2}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^2}",1,"(-8*c*Sqrt[c + d*x^3])/(3*d^2) + (2*(c + d*x^3)^(3/2))/(9*d^2) + (8*c^(3/2)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(Sqrt[3]*d^2)","A",5,5,26,0.1923,1,"{446, 80, 50, 63, 203}"
261,1,57,0,0.045898,"\int \frac{x^2 \sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[(x^2*Sqrt[c + d*x^3])/(4*c + d*x^3),x]","\frac{2 \sqrt{c+d x^3}}{3 d}-\frac{2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d}","\frac{2 \sqrt{c+d x^3}}{3 d}-\frac{2 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d}",1,"(2*Sqrt[c + d*x^3])/(3*d) - (2*Sqrt[c]*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(Sqrt[3]*d)","A",4,4,26,0.1538,1,"{444, 50, 63, 203}"
262,1,65,0,0.056413,"\int \frac{\sqrt{c+d x^3}}{x \left(4 c+d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x*(4*c + d*x^3)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{2 \sqrt{3} \sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{6 \sqrt{c}}","\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{2 \sqrt{3} \sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{6 \sqrt{c}}",1,"ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])]/(2*Sqrt[3]*Sqrt[c]) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(6*Sqrt[c])","A",6,5,26,0.1923,1,"{446, 83, 63, 208, 203}"
263,1,88,0,0.0769426,"\int \frac{\sqrt{c+d x^3}}{x^4 \left(4 c+d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^4*(4*c + d*x^3)),x]","-\frac{d \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{8 \sqrt{3} c^{3/2}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{24 c^{3/2}}-\frac{\sqrt{c+d x^3}}{12 c x^3}","-\frac{d \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{8 \sqrt{3} c^{3/2}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{24 c^{3/2}}-\frac{\sqrt{c+d x^3}}{12 c x^3}",1,"-Sqrt[c + d*x^3]/(12*c*x^3) - (d*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(8*Sqrt[3]*c^(3/2)) - (d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(24*c^(3/2))","A",7,6,26,0.2308,1,"{446, 99, 156, 63, 208, 203}"
264,1,689,0,0.4770174,"\int \frac{x^4 \sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[(x^4*Sqrt[c + d*x^3])/(4*c + d*x^3),x]","-\frac{2 \sqrt[3]{2} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{\sqrt{3} d^{5/3}}+\frac{2 \sqrt[3]{2} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d^{5/3}}-\frac{2 \sqrt[3]{2} c^{7/6} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{2 \sqrt[3]{2} c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 d^{5/3}}-\frac{50 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{25 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{50 c \sqrt{c+d x^3}}{7 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{2 x^2 \sqrt{c+d x^3}}{7 d}","-\frac{2 \sqrt[3]{2} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{\sqrt{3} d^{5/3}}+\frac{2 \sqrt[3]{2} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{\sqrt{3} d^{5/3}}-\frac{2 \sqrt[3]{2} c^{7/6} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{2 \sqrt[3]{2} c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 d^{5/3}}-\frac{50 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{25 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{50 c \sqrt{c+d x^3}}{7 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{2 x^2 \sqrt{c+d x^3}}{7 d}",1,"(2*x^2*Sqrt[c + d*x^3])/(7*d) - (50*c*Sqrt[c + d*x^3])/(7*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (2*2^(1/3)*c^(7/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(Sqrt[3]*d^(5/3)) + (2*2^(1/3)*c^(7/6)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(Sqrt[3]*d^(5/3)) - (2*2^(1/3)*c^(7/6)*ArcTanh[(c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(5/3) + (2*2^(1/3)*c^(7/6)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*d^(5/3)) + (25*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (50*Sqrt[2]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",7,6,26,0.2308,1,"{478, 584, 303, 218, 1877, 484}"
265,1,659,0,0.1674565,"\int \frac{x \sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[(x*Sqrt[c + d*x^3])/(4*c + d*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{\sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2^{2/3} \sqrt{3} d^{2/3}}-\frac{\sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{2^{2/3} \sqrt{3} d^{2/3}}+\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2^{2/3} d^{2/3}}-\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3\ 2^{2/3} d^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{\sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2^{2/3} \sqrt{3} d^{2/3}}-\frac{\sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{2^{2/3} \sqrt{3} d^{2/3}}+\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2^{2/3} d^{2/3}}-\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3\ 2^{2/3} d^{2/3}}",1,"(2*Sqrt[c + d*x^3])/(d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(2^(2/3)*Sqrt[3]*d^(2/3)) - (c^(1/6)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(2^(2/3)*Sqrt[3]*d^(2/3)) + (c^(1/6)*ArcTanh[(c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(2^(2/3)*d^(2/3)) - (c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*2^(2/3)*d^(2/3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (2*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",5,5,24,0.2083,1,"{489, 303, 218, 1877, 484}"
266,1,697,0,0.3838868,"\int \frac{\sqrt{c+d x^3}}{x^2 \left(4 c+d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^2*(4*c + d*x^3)),x]","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{2} \sqrt[4]{3} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{4\ 2^{2/3} \sqrt{3} c^{5/6}}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{4\ 2^{2/3} \sqrt{3} c^{5/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{4\ 2^{2/3} c^{5/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12\ 2^{2/3} c^{5/6}}-\frac{\sqrt{c+d x^3}}{4 c x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{4 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{2} \sqrt[4]{3} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{4\ 2^{2/3} \sqrt{3} c^{5/6}}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{4\ 2^{2/3} \sqrt{3} c^{5/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{4\ 2^{2/3} c^{5/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12\ 2^{2/3} c^{5/6}}-\frac{\sqrt{c+d x^3}}{4 c x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{4 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}",1,"-Sqrt[c + d*x^3]/(4*c*x) + (d^(1/3)*Sqrt[c + d*x^3])/(4*c*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(4*2^(2/3)*Sqrt[3]*c^(5/6)) + (d^(1/3)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(4*2^(2/3)*Sqrt[3]*c^(5/6)) - (d^(1/3)*ArcTanh[(c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(4*2^(2/3)*c^(5/6)) + (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(12*2^(2/3)*c^(5/6)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*Sqrt[2]*3^(1/4)*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",7,6,26,0.2308,1,"{475, 584, 303, 218, 1877, 484}"
267,1,66,0,0.0537595,"\int \frac{x^3 \sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[(x^3*Sqrt[c + d*x^3])/(4*c + d*x^3),x]","\frac{x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};1,-\frac{1}{2};\frac{7}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{16 c \sqrt{\frac{d x^3}{c}+1}}","\frac{x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};1,-\frac{1}{2};\frac{7}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{16 c \sqrt{\frac{d x^3}{c}+1}}",1,"(x^4*Sqrt[c + d*x^3]*AppellF1[4/3, 1, -1/2, 7/3, -(d*x^3)/(4*c), -((d*x^3)/c)])/(16*c*Sqrt[1 + (d*x^3)/c])","A",2,2,26,0.07692,1,"{511, 510}"
268,1,64,0,0.0280723,"\int \frac{\sqrt{c+d x^3}}{4 c+d x^3} \, dx","Int[Sqrt[c + d*x^3]/(4*c + d*x^3),x]","\frac{x \sqrt{c+d x^3} F_1\left(\frac{1}{3};1,-\frac{1}{2};\frac{4}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{4 c \sqrt{\frac{d x^3}{c}+1}}","\frac{x \sqrt{c+d x^3} F_1\left(\frac{1}{3};1,-\frac{1}{2};\frac{4}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{4 c \sqrt{\frac{d x^3}{c}+1}}",1,"(x*Sqrt[c + d*x^3]*AppellF1[1/3, 1, -1/2, 4/3, -(d*x^3)/(4*c), -((d*x^3)/c)])/(4*c*Sqrt[1 + (d*x^3)/c])","A",2,2,23,0.08696,1,"{430, 429}"
269,1,66,0,0.056457,"\int \frac{\sqrt{c+d x^3}}{x^3 \left(4 c+d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^3*(4*c + d*x^3)),x]","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{2}{3};1,-\frac{1}{2};\frac{1}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{8 c x^2 \sqrt{\frac{d x^3}{c}+1}}","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{2}{3};1,-\frac{1}{2};\frac{1}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{8 c x^2 \sqrt{\frac{d x^3}{c}+1}}",1,"-(Sqrt[c + d*x^3]*AppellF1[-2/3, 1, -1/2, 1/3, -(d*x^3)/(4*c), -((d*x^3)/c)])/(8*c*x^2*Sqrt[1 + (d*x^3)/c])","A",2,2,26,0.07692,1,"{511, 510}"
270,1,78,0,0.0741554,"\int \frac{x^8}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[x^8/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{32 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} d^3}-\frac{10 c \sqrt{c+d x^3}}{3 d^3}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^3}","\frac{32 c^{3/2} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} d^3}-\frac{10 c \sqrt{c+d x^3}}{3 d^3}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^3}",1,"(-10*c*Sqrt[c + d*x^3])/(3*d^3) + (2*(c + d*x^3)^(3/2))/(9*d^3) + (32*c^(3/2)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(3*Sqrt[3]*d^3)","A",5,4,26,0.1538,1,"{446, 88, 63, 203}"
271,1,59,0,0.0477036,"\int \frac{x^5}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[x^5/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{2 \sqrt{c+d x^3}}{3 d^2}-\frac{8 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} d^2}","\frac{2 \sqrt{c+d x^3}}{3 d^2}-\frac{8 \sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} d^2}",1,"(2*Sqrt[c + d*x^3])/(3*d^2) - (8*Sqrt[c]*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(3*Sqrt[3]*d^2)","A",4,4,26,0.1538,1,"{446, 80, 63, 203}"
272,1,40,0,0.0357859,"\int \frac{x^2}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[x^2/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} \sqrt{c} d}","\frac{2 \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} \sqrt{c} d}",1,"(2*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(3*Sqrt[3]*Sqrt[c]*d)","A",3,3,26,0.1154,1,"{444, 63, 203}"
273,1,65,0,0.0553441,"\int \frac{1}{x \sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[1/(x*Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{6 \sqrt{3} c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{6 c^{3/2}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{6 \sqrt{3} c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{6 c^{3/2}}",1,"-ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])]/(6*Sqrt[3]*c^(3/2)) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(6*c^(3/2))","A",6,5,26,0.1923,1,"{446, 86, 63, 208, 203}"
274,1,88,0,0.0769034,"\int \frac{1}{x^4 \sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[1/(x^4*Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","-\frac{\sqrt{c+d x^3}}{12 c^2 x^3}+\frac{d \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{24 \sqrt{3} c^{5/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{8 c^{5/2}}","-\frac{\sqrt{c+d x^3}}{12 c^2 x^3}+\frac{d \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{24 \sqrt{3} c^{5/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{8 c^{5/2}}",1,"-Sqrt[c + d*x^3]/(12*c^2*x^3) + (d*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(24*Sqrt[3]*c^(5/2)) + (d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(8*c^(5/2))","A",7,6,26,0.2308,1,"{446, 103, 156, 63, 208, 203}"
275,1,667,0,0.2350135,"\int \frac{x^4}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[x^4/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{5/3}}-\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} d^{5/3}}+\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 d^{5/3}}-\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{9 d^{5/3}}","\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{5/3}}-\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3 \sqrt{3} d^{5/3}}+\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 d^{5/3}}-\frac{2 \sqrt[3]{2} \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{9 d^{5/3}}",1,"(2*Sqrt[c + d*x^3])/(d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (2*2^(1/3)*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(3*Sqrt[3]*d^(5/3)) - (2*2^(1/3)*c^(1/6)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(3*Sqrt[3]*d^(5/3)) + (2*2^(1/3)*c^(1/6)*ArcTanh[(c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(3*d^(5/3)) - (2*2^(1/3)*c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(9*d^(5/3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (2*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",5,5,26,0.1923,1,"{483, 303, 218, 1877, 484}"
276,1,206,0,0.0324488,"\int \frac{x}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[x/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3\ 2^{2/3} \sqrt{3} c^{5/6} d^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3\ 2^{2/3} \sqrt{3} c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3\ 2^{2/3} c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{9\ 2^{2/3} c^{5/6} d^{2/3}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3\ 2^{2/3} \sqrt{3} c^{5/6} d^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{3\ 2^{2/3} \sqrt{3} c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3\ 2^{2/3} c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{9\ 2^{2/3} c^{5/6} d^{2/3}}",1,"-ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]]/(3*2^(2/3)*Sqrt[3]*c^(5/6)*d^(2/3)) + ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])]/(3*2^(2/3)*Sqrt[3]*c^(5/6)*d^(2/3)) - ArcTanh[(c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]]/(3*2^(2/3)*c^(5/6)*d^(2/3)) + ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(9*2^(2/3)*c^(5/6)*d^(2/3))","A",1,1,24,0.04167,1,"{484}"
277,1,697,0,0.3881167,"\int \frac{1}{x^2 \sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[1/(x^2*Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{4 c^2 x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{4 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{12\ 2^{2/3} \sqrt{3} c^{11/6}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{12\ 2^{2/3} \sqrt{3} c^{11/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{12\ 2^{2/3} c^{11/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{36\ 2^{2/3} c^{11/6}}","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{4 c^2 x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{4 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{12\ 2^{2/3} \sqrt{3} c^{11/6}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{3} \sqrt{c}}\right)}{12\ 2^{2/3} \sqrt{3} c^{11/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt[6]{c} \left(\sqrt[3]{c}-\sqrt[3]{2} \sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{12\ 2^{2/3} c^{11/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{36\ 2^{2/3} c^{11/6}}",1,"-Sqrt[c + d*x^3]/(4*c^2*x) + (d^(1/3)*Sqrt[c + d*x^3])/(4*c^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(12*2^(2/3)*Sqrt[3]*c^(11/6)) - (d^(1/3)*ArcTan[Sqrt[c + d*x^3]/(Sqrt[3]*Sqrt[c])])/(12*2^(2/3)*Sqrt[3]*c^(11/6)) + (d^(1/3)*ArcTanh[(c^(1/6)*(c^(1/3) - 2^(1/3)*d^(1/3)*x))/Sqrt[c + d*x^3]])/(12*2^(2/3)*c^(11/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(36*2^(2/3)*c^(11/6)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*Sqrt[2]*3^(1/4)*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",7,6,26,0.2308,1,"{480, 584, 303, 218, 1877, 484}"
278,1,66,0,0.0525761,"\int \frac{x^3}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[x^3/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{16 c \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{16 c \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 1, 1/2, 7/3, -(d*x^3)/(4*c), -((d*x^3)/c)])/(16*c*Sqrt[c + d*x^3])","A",2,2,26,0.07692,1,"{511, 510}"
279,1,64,0,0.0284523,"\int \frac{1}{\sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[1/(Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{4 c \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{4 c \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 1, 1/2, 4/3, -(d*x^3)/(4*c), -((d*x^3)/c)])/(4*c*Sqrt[c + d*x^3])","A",2,2,23,0.08696,1,"{430, 429}"
280,1,66,0,0.0563244,"\int \frac{1}{x^3 \sqrt{c+d x^3} \left(4 c+d x^3\right)} \, dx","Int[1/(x^3*Sqrt[c + d*x^3]*(4*c + d*x^3)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{8 c x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};-\frac{d x^3}{4 c},-\frac{d x^3}{c}\right)}{8 c x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 1, 1/2, 1/3, -(d*x^3)/(4*c), -((d*x^3)/c)])/(8*c*x^2*Sqrt[c + d*x^3])","A",2,2,26,0.07692,1,"{511, 510}"
281,1,127,0,0.0193199,"\int \frac{x}{\sqrt{1-x^3} \left(4-x^3\right)} \, dx","Int[x/(Sqrt[1 - x^3]*(4 - x^3)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{1-x^3}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x+1}{\sqrt{1-x^3}}\right)}{3\ 2^{2/3}}+\frac{\tanh ^{-1}\left(\sqrt{1-x^3}\right)}{9\ 2^{2/3}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} x\right)}{\sqrt{1-x^3}}\right)}{3\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{1-x^3}}{\sqrt{3}}\right)}{3\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[3]{2} x+1}{\sqrt{1-x^3}}\right)}{3\ 2^{2/3}}+\frac{\tanh ^{-1}\left(\sqrt{1-x^3}\right)}{9\ 2^{2/3}}",1,"-ArcTan[(Sqrt[3]*(1 - 2^(1/3)*x))/Sqrt[1 - x^3]]/(3*2^(2/3)*Sqrt[3]) + ArcTan[Sqrt[1 - x^3]/Sqrt[3]]/(3*2^(2/3)*Sqrt[3]) - ArcTanh[(1 + 2^(1/3)*x)/Sqrt[1 - x^3]]/(3*2^(2/3)) + ArcTanh[Sqrt[1 - x^3]]/(9*2^(2/3))","A",1,1,22,0.04545,1,"{484}"
282,1,111,0,0.0967581,"\int \frac{x^{11} \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x^11*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","-\frac{1024 c^3 \sqrt{c+d x^3}}{3 d^4}-\frac{38 c^2 \left(c+d x^3\right)^{3/2}}{3 d^4}+\frac{1024 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^4}-\frac{4 c \left(c+d x^3\right)^{5/2}}{5 d^4}-\frac{2 \left(c+d x^3\right)^{7/2}}{21 d^4}","-\frac{1024 c^3 \sqrt{c+d x^3}}{3 d^4}-\frac{38 c^2 \left(c+d x^3\right)^{3/2}}{3 d^4}+\frac{1024 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^4}-\frac{4 c \left(c+d x^3\right)^{5/2}}{5 d^4}-\frac{2 \left(c+d x^3\right)^{7/2}}{21 d^4}",1,"(-1024*c^3*Sqrt[c + d*x^3])/(3*d^4) - (38*c^2*(c + d*x^3)^(3/2))/(3*d^4) - (4*c*(c + d*x^3)^(5/2))/(5*d^4) - (2*(c + d*x^3)^(7/2))/(21*d^4) + (1024*c^(7/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^4","A",6,5,27,0.1852,1,"{446, 88, 50, 63, 206}"
283,1,90,0,0.0850978,"\int \frac{x^8 \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x^8*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","-\frac{128 c^2 \sqrt{c+d x^3}}{3 d^3}+\frac{128 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^3}-\frac{14 c \left(c+d x^3\right)^{3/2}}{9 d^3}-\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^3}","-\frac{128 c^2 \sqrt{c+d x^3}}{3 d^3}+\frac{128 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^3}-\frac{14 c \left(c+d x^3\right)^{3/2}}{9 d^3}-\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^3}",1,"(-128*c^2*Sqrt[c + d*x^3])/(3*d^3) - (14*c*(c + d*x^3)^(3/2))/(9*d^3) - (2*(c + d*x^3)^(5/2))/(15*d^3) + (128*c^(5/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^3","A",6,5,27,0.1852,1,"{446, 88, 50, 63, 206}"
284,1,69,0,0.0571967,"\int \frac{x^5 \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x^5*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","\frac{16 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^2}-\frac{16 c \sqrt{c+d x^3}}{3 d^2}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^2}","\frac{16 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^2}-\frac{16 c \sqrt{c+d x^3}}{3 d^2}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^2}",1,"(-16*c*Sqrt[c + d*x^3])/(3*d^2) - (2*(c + d*x^3)^(3/2))/(9*d^2) + (16*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^2","A",5,5,27,0.1852,1,"{446, 80, 50, 63, 206}"
285,1,50,0,0.0432402,"\int \frac{x^2 \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x^2*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d}-\frac{2 \sqrt{c+d x^3}}{3 d}","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d}-\frac{2 \sqrt{c+d x^3}}{3 d}",1,"(-2*Sqrt[c + d*x^3])/(3*d) + (2*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d","A",4,4,27,0.1481,1,"{444, 50, 63, 206}"
286,1,58,0,0.0540572,"\int \frac{\sqrt{c+d x^3}}{x \left(8 c-d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x*(8*c - d*x^3)),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12 \sqrt{c}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{4 \sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12 \sqrt{c}}",1,"ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(4*Sqrt[c]) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(12*Sqrt[c])","A",6,5,27,0.1852,1,"{446, 83, 63, 208, 206}"
287,1,81,0,0.0722102,"\int \frac{\sqrt{c+d x^3}}{x^4 \left(8 c-d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^4*(8*c - d*x^3)),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{32 c^{3/2}}-\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{3/2}}-\frac{\sqrt{c+d x^3}}{24 c x^3}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{32 c^{3/2}}-\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{3/2}}-\frac{\sqrt{c+d x^3}}{24 c x^3}",1,"-Sqrt[c + d*x^3]/(24*c*x^3) + (d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(32*c^(3/2)) - (5*d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(96*c^(3/2))","A",7,6,27,0.2222,1,"{446, 99, 156, 63, 208, 206}"
288,1,107,0,0.0940667,"\int \frac{\sqrt{c+d x^3}}{x^7 \left(8 c-d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^7*(8*c - d*x^3)),x]","\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{256 c^{5/2}}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{256 c^{5/2}}-\frac{d \sqrt{c+d x^3}}{64 c^2 x^3}-\frac{\sqrt{c+d x^3}}{48 c x^6}","\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{256 c^{5/2}}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{256 c^{5/2}}-\frac{d \sqrt{c+d x^3}}{64 c^2 x^3}-\frac{\sqrt{c+d x^3}}{48 c x^6}",1,"-Sqrt[c + d*x^3]/(48*c*x^6) - (d*Sqrt[c + d*x^3])/(64*c^2*x^3) + (d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(256*c^(5/2)) + (d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(256*c^(5/2))","A",8,7,27,0.2593,1,"{446, 99, 151, 156, 63, 208, 206}"
289,1,648,0,0.8878673,"\int \frac{x^7 \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x^7*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","-\frac{12248 c^2 \sqrt{c+d x^3}}{91 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{32 \sqrt{3} c^{13/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{8/3}}+\frac{32 c^{13/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{8/3}}-\frac{32 c^{13/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{8/3}}-\frac{12248 \sqrt{2} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{6124 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{214 c x^2 \sqrt{c+d x^3}}{91 d^2}-\frac{2 x^5 \sqrt{c+d x^3}}{13 d}","-\frac{12248 c^2 \sqrt{c+d x^3}}{91 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{32 \sqrt{3} c^{13/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{8/3}}+\frac{32 c^{13/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{8/3}}-\frac{32 c^{13/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{8/3}}-\frac{12248 \sqrt{2} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{6124 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{214 c x^2 \sqrt{c+d x^3}}{91 d^2}-\frac{2 x^5 \sqrt{c+d x^3}}{13 d}",1,"(-214*c*x^2*Sqrt[c + d*x^3])/(91*d^2) - (2*x^5*Sqrt[c + d*x^3])/(13*d) - (12248*c^2*Sqrt[c + d*x^3])/(91*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (32*Sqrt[3]*c^(13/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(8/3) + (32*c^(13/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/d^(8/3) - (32*c^(13/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^(8/3) + (6124*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (12248*Sqrt[2]*c^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*3^(1/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{478, 582, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
290,1,624,0,0.746765,"\int \frac{x^4 \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x^4*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","-\frac{4 \sqrt{3} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{4 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{5/3}}-\frac{4 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{5/3}}-\frac{118 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{59 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{118 c \sqrt{c+d x^3}}{7 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{2 x^2 \sqrt{c+d x^3}}{7 d}","-\frac{4 \sqrt{3} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{4 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{5/3}}-\frac{4 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{5/3}}-\frac{118 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{59 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{118 c \sqrt{c+d x^3}}{7 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{2 x^2 \sqrt{c+d x^3}}{7 d}",1,"(-2*x^2*Sqrt[c + d*x^3])/(7*d) - (118*c*Sqrt[c + d*x^3])/(7*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (4*Sqrt[3]*c^(7/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(5/3) + (4*c^(7/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/d^(5/3) - (4*c^(7/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^(5/3) + (59*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (118*Sqrt[2]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{478, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
291,1,601,0,0.5315861,"\int \frac{x \sqrt{c+d x^3}}{8 c-d x^3} \, dx","Int[(x*Sqrt[c + d*x^3])/(8*c - d*x^3),x]","-\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2 \sqrt{c+d x^3}}{d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt{3} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2 d^{2/3}}+\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{2 d^{2/3}}-\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2 d^{2/3}}","-\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2 \sqrt{c+d x^3}}{d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt{3} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2 d^{2/3}}+\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{2 d^{2/3}}-\frac{\sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2 d^{2/3}}",1,"(-2*Sqrt[c + d*x^3])/(d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (Sqrt[3]*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(2*d^(2/3)) + (c^(1/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(2*d^(2/3)) - (c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(2*d^(2/3)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (2*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",12,11,25,0.4400,1,"{489, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
292,1,632,0,0.7171227,"\int \frac{\sqrt{c+d x^3}}{x^2 \left(8 c-d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^2*(8*c - d*x^3)),x]","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{16 c^{5/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{16 c^{5/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{16 c^{5/6}}-\frac{\sqrt{c+d x^3}}{8 c x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{8 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{3} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{16 c^{5/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{16 c^{5/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{16 c^{5/6}}-\frac{\sqrt{c+d x^3}}{8 c x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{8 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}",1,"-Sqrt[c + d*x^3]/(8*c*x) + (d^(1/3)*Sqrt[c + d*x^3])/(8*c*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (Sqrt[3]*d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(16*c^(5/6)) + (d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(16*c^(5/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(16*c^(5/6)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{475, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
293,1,654,0,0.8375118,"\int \frac{\sqrt{c+d x^3}}{x^5 \left(8 c-d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^5*(8*c - d*x^3)),x]","\frac{d^{4/3} \sqrt{c+d x^3}}{16 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt{3} d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{128 c^{11/6}}+\frac{d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{128 c^{11/6}}-\frac{d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{128 c^{11/6}}+\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{d \sqrt{c+d x^3}}{16 c^2 x}-\frac{\sqrt{c+d x^3}}{32 c x^4}","\frac{d^{4/3} \sqrt{c+d x^3}}{16 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt{3} d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{128 c^{11/6}}+\frac{d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{128 c^{11/6}}-\frac{d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{128 c^{11/6}}+\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{d \sqrt{c+d x^3}}{16 c^2 x}-\frac{\sqrt{c+d x^3}}{32 c x^4}",1,"-Sqrt[c + d*x^3]/(32*c*x^4) - (d*Sqrt[c + d*x^3])/(16*c^2*x) + (d^(4/3)*Sqrt[c + d*x^3])/(16*c^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (Sqrt[3]*d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(128*c^(11/6)) + (d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(128*c^(11/6)) - (d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(128*c^(11/6)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(32*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*Sqrt[2]*3^(1/4)*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{475, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
294,1,678,0,0.9507182,"\int \frac{\sqrt{c+d x^3}}{x^8 \left(8 c-d x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^8*(8*c - d*x^3)),x]","-\frac{d^{7/3} \sqrt{c+d x^3}}{112 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{d^2 \sqrt{c+d x^3}}{112 c^3 x}-\frac{\sqrt{3} d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1024 c^{17/6}}+\frac{d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1024 c^{17/6}}-\frac{d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1024 c^{17/6}}-\frac{d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{224 c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{19 d \sqrt{c+d x^3}}{1792 c^2 x^4}-\frac{\sqrt{c+d x^3}}{56 c x^7}","-\frac{d^{7/3} \sqrt{c+d x^3}}{112 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{d^2 \sqrt{c+d x^3}}{112 c^3 x}-\frac{\sqrt{3} d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1024 c^{17/6}}+\frac{d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1024 c^{17/6}}-\frac{d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1024 c^{17/6}}-\frac{d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{56 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{224 c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{19 d \sqrt{c+d x^3}}{1792 c^2 x^4}-\frac{\sqrt{c+d x^3}}{56 c x^7}",1,"-Sqrt[c + d*x^3]/(56*c*x^7) - (19*d*Sqrt[c + d*x^3])/(1792*c^2*x^4) + (d^2*Sqrt[c + d*x^3])/(112*c^3*x) - (d^(7/3)*Sqrt[c + d*x^3])/(112*c^3*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (Sqrt[3]*d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(1024*c^(17/6)) + (d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(1024*c^(17/6)) - (d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1024*c^(17/6)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(224*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(56*Sqrt[2]*3^(1/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{475, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
295,1,130,0,0.1125463,"\int \frac{x^{11} \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x^11*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","-\frac{3072 c^4 \sqrt{c+d x^3}}{d^4}-\frac{1024 c^3 \left(c+d x^3\right)^{3/2}}{9 d^4}-\frac{38 c^2 \left(c+d x^3\right)^{5/2}}{5 d^4}+\frac{9216 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^4}-\frac{4 c \left(c+d x^3\right)^{7/2}}{7 d^4}-\frac{2 \left(c+d x^3\right)^{9/2}}{27 d^4}","-\frac{3072 c^4 \sqrt{c+d x^3}}{d^4}-\frac{1024 c^3 \left(c+d x^3\right)^{3/2}}{9 d^4}-\frac{38 c^2 \left(c+d x^3\right)^{5/2}}{5 d^4}+\frac{9216 c^{9/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^4}-\frac{4 c \left(c+d x^3\right)^{7/2}}{7 d^4}-\frac{2 \left(c+d x^3\right)^{9/2}}{27 d^4}",1,"(-3072*c^4*Sqrt[c + d*x^3])/d^4 - (1024*c^3*(c + d*x^3)^(3/2))/(9*d^4) - (38*c^2*(c + d*x^3)^(5/2))/(5*d^4) - (4*c*(c + d*x^3)^(7/2))/(7*d^4) - (2*(c + d*x^3)^(9/2))/(27*d^4) + (9216*c^(9/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^4","A",7,5,27,0.1852,1,"{446, 88, 50, 63, 206}"
296,1,109,0,0.1022589,"\int \frac{x^8 \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x^8*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","-\frac{384 c^3 \sqrt{c+d x^3}}{d^3}-\frac{128 c^2 \left(c+d x^3\right)^{3/2}}{9 d^3}+\frac{1152 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^3}-\frac{14 c \left(c+d x^3\right)^{5/2}}{15 d^3}-\frac{2 \left(c+d x^3\right)^{7/2}}{21 d^3}","-\frac{384 c^3 \sqrt{c+d x^3}}{d^3}-\frac{128 c^2 \left(c+d x^3\right)^{3/2}}{9 d^3}+\frac{1152 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^3}-\frac{14 c \left(c+d x^3\right)^{5/2}}{15 d^3}-\frac{2 \left(c+d x^3\right)^{7/2}}{21 d^3}",1,"(-384*c^3*Sqrt[c + d*x^3])/d^3 - (128*c^2*(c + d*x^3)^(3/2))/(9*d^3) - (14*c*(c + d*x^3)^(5/2))/(15*d^3) - (2*(c + d*x^3)^(7/2))/(21*d^3) + (1152*c^(7/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^3","A",7,5,27,0.1852,1,"{446, 88, 50, 63, 206}"
297,1,88,0,0.0716315,"\int \frac{x^5 \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x^5*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","-\frac{48 c^2 \sqrt{c+d x^3}}{d^2}+\frac{144 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^2}-\frac{16 c \left(c+d x^3\right)^{3/2}}{9 d^2}-\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^2}","-\frac{48 c^2 \sqrt{c+d x^3}}{d^2}+\frac{144 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^2}-\frac{16 c \left(c+d x^3\right)^{3/2}}{9 d^2}-\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^2}",1,"(-48*c^2*Sqrt[c + d*x^3])/d^2 - (16*c*(c + d*x^3)^(3/2))/(9*d^2) - (2*(c + d*x^3)^(5/2))/(15*d^2) + (144*c^(5/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^2","A",6,5,27,0.1852,1,"{446, 80, 50, 63, 206}"
298,1,67,0,0.0569293,"\int \frac{x^2 \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x^2*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","\frac{18 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d}-\frac{6 c \sqrt{c+d x^3}}{d}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d}","\frac{18 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d}-\frac{6 c \sqrt{c+d x^3}}{d}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d}",1,"(-6*c*Sqrt[c + d*x^3])/d - (2*(c + d*x^3)^(3/2))/(9*d) + (18*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d","A",5,4,27,0.1481,1,"{444, 50, 63, 206}"
299,1,73,0,0.0696853,"\int \frac{\left(c+d x^3\right)^{3/2}}{x \left(8 c-d x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x*(8*c - d*x^3)),x]","-\frac{2}{3} \sqrt{c+d x^3}+\frac{9}{4} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)-\frac{1}{12} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)","-\frac{2}{3} \sqrt{c+d x^3}+\frac{9}{4} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)-\frac{1}{12} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)",1,"(-2*Sqrt[c + d*x^3])/3 + (9*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/4 - (Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/12","A",7,6,27,0.2222,1,"{446, 84, 156, 63, 208, 206}"
300,1,78,0,0.0720884,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^4 \left(8 c-d x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^4*(8*c - d*x^3)),x]","-\frac{\sqrt{c+d x^3}}{24 x^3}+\frac{9 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{32 \sqrt{c}}-\frac{13 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 \sqrt{c}}","-\frac{\sqrt{c+d x^3}}{24 x^3}+\frac{9 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{32 \sqrt{c}}-\frac{13 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 \sqrt{c}}",1,"-Sqrt[c + d*x^3]/(24*x^3) + (9*d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(32*Sqrt[c]) - (13*d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(96*Sqrt[c])","A",7,6,27,0.2222,1,"{446, 98, 156, 63, 208, 206}"
301,1,104,0,0.0946632,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^7 \left(8 c-d x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^7*(8*c - d*x^3)),x]","\frac{9 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{256 c^{3/2}}-\frac{37 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{768 c^{3/2}}-\frac{11 d \sqrt{c+d x^3}}{192 c x^3}-\frac{\sqrt{c+d x^3}}{48 x^6}","\frac{9 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{256 c^{3/2}}-\frac{37 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{768 c^{3/2}}-\frac{11 d \sqrt{c+d x^3}}{192 c x^3}-\frac{\sqrt{c+d x^3}}{48 x^6}",1,"-Sqrt[c + d*x^3]/(48*x^6) - (11*d*Sqrt[c + d*x^3])/(192*c*x^3) + (9*d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(256*c^(3/2)) - (37*d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(768*c^(3/2))","A",8,7,27,0.2593,1,"{446, 98, 151, 156, 63, 208, 206}"
302,1,669,0,0.9662344,"\int \frac{x^7 \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","-\frac{36534 c^2 x^2 \sqrt{c+d x^3}}{1729 d^2}-\frac{2094648 c^3 \sqrt{c+d x^3}}{1729 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{288 \sqrt{3} c^{19/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{8/3}}+\frac{288 c^{19/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{8/3}}-\frac{288 c^{19/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{8/3}}-\frac{698216 \sqrt{2} 3^{3/4} c^{10/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1729 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{1047324 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{10/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1729 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2}{19} x^8 \sqrt{c+d x^3}-\frac{348 c x^5 \sqrt{c+d x^3}}{247 d}","-\frac{36534 c^2 x^2 \sqrt{c+d x^3}}{1729 d^2}-\frac{2094648 c^3 \sqrt{c+d x^3}}{1729 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{288 \sqrt{3} c^{19/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{8/3}}+\frac{288 c^{19/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{8/3}}-\frac{288 c^{19/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{8/3}}-\frac{698216 \sqrt{2} 3^{3/4} c^{10/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1729 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{1047324 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{10/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1729 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2}{19} x^8 \sqrt{c+d x^3}-\frac{348 c x^5 \sqrt{c+d x^3}}{247 d}",1,"(-36534*c^2*x^2*Sqrt[c + d*x^3])/(1729*d^2) - (348*c*x^5*Sqrt[c + d*x^3])/(247*d) - (2*x^8*Sqrt[c + d*x^3])/19 - (2094648*c^3*Sqrt[c + d*x^3])/(1729*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (288*Sqrt[3]*c^(19/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(8/3) + (288*c^(19/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/d^(8/3) - (288*c^(19/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^(8/3) + (1047324*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(10/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (698216*Sqrt[2]*3^(3/4)*c^(10/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(1729*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{477, 582, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
303,1,645,0,0.8272056,"\int \frac{x^4 \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","-\frac{13782 c^2 \sqrt{c+d x^3}}{91 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{36 \sqrt{3} c^{13/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{36 c^{13/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{5/3}}-\frac{36 c^{13/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{5/3}}-\frac{4594 \sqrt{2} 3^{3/4} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{6891 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2}{13} x^5 \sqrt{c+d x^3}-\frac{240 c x^2 \sqrt{c+d x^3}}{91 d}","-\frac{13782 c^2 \sqrt{c+d x^3}}{91 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{36 \sqrt{3} c^{13/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{36 c^{13/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{5/3}}-\frac{36 c^{13/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{5/3}}-\frac{4594 \sqrt{2} 3^{3/4} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{6891 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{91 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2}{13} x^5 \sqrt{c+d x^3}-\frac{240 c x^2 \sqrt{c+d x^3}}{91 d}",1,"(-240*c*x^2*Sqrt[c + d*x^3])/(91*d) - (2*x^5*Sqrt[c + d*x^3])/13 - (13782*c^2*Sqrt[c + d*x^3])/(91*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (36*Sqrt[3]*c^(13/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(5/3) + (36*c^(13/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/d^(5/3) - (36*c^(13/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^(5/3) + (6891*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (4594*Sqrt[2]*3^(3/4)*c^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(91*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{477, 582, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
304,1,627,0,0.7226073,"\int \frac{x \left(c+d x^3\right)^{3/2}}{8 c-d x^3} \, dx","Int[(x*(c + d*x^3)^(3/2))/(8*c - d*x^3),x]","-\frac{9 \sqrt{3} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2 d^{2/3}}+\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{2 d^{2/3}}-\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2 d^{2/3}}-\frac{44 \sqrt{2} 3^{3/4} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{66 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{132 c \sqrt{c+d x^3}}{7 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{2}{7} x^2 \sqrt{c+d x^3}","-\frac{9 \sqrt{3} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{2 d^{2/3}}+\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{2 d^{2/3}}-\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2 d^{2/3}}-\frac{44 \sqrt{2} 3^{3/4} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{66 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{132 c \sqrt{c+d x^3}}{7 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{2}{7} x^2 \sqrt{c+d x^3}",1,"(-2*x^2*Sqrt[c + d*x^3])/7 - (132*c*Sqrt[c + d*x^3])/(7*d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (9*Sqrt[3]*c^(7/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(2*d^(2/3)) + (9*c^(7/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(2*d^(2/3)) - (9*c^(7/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(2*d^(2/3)) + (66*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (44*Sqrt[2]*3^(3/4)*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,25,0.4800,1,"{477, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
305,1,626,0,0.7183767,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^2 \left(8 c-d x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)),x]","-\frac{5\ 3^{3/4} \sqrt[3]{c} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{8 x}-\frac{15 \sqrt[3]{d} \sqrt{c+d x^3}}{8 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{9}{16} \sqrt{3} \sqrt[6]{c} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)+\frac{9}{16} \sqrt[6]{c} \sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)-\frac{9}{16} \sqrt[6]{c} \sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)","-\frac{5\ 3^{3/4} \sqrt[3]{c} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{15 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{8 x}-\frac{15 \sqrt[3]{d} \sqrt{c+d x^3}}{8 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{9}{16} \sqrt{3} \sqrt[6]{c} \sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)+\frac{9}{16} \sqrt[6]{c} \sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)-\frac{9}{16} \sqrt[6]{c} \sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)",1,"-Sqrt[c + d*x^3]/(8*x) - (15*d^(1/3)*Sqrt[c + d*x^3])/(8*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (9*Sqrt[3]*c^(1/6)*d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/16 + (9*c^(1/6)*d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/16 - (9*c^(1/6)*d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/16 + (15*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (5*3^(3/4)*c^(1/3)*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{474, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
306,1,651,0,0.8442193,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^5 \left(8 c-d x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)),x]","-\frac{9 \sqrt{3} d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{128 c^{5/6}}+\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{128 c^{5/6}}-\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{128 c^{5/6}}+\frac{3^{3/4} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{3 d^{4/3} \sqrt{c+d x^3}}{16 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{3 d \sqrt{c+d x^3}}{16 c x}-\frac{\sqrt{c+d x^3}}{32 x^4}","-\frac{9 \sqrt{3} d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{128 c^{5/6}}+\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{128 c^{5/6}}-\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{128 c^{5/6}}+\frac{3^{3/4} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{3 d^{4/3} \sqrt{c+d x^3}}{16 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{3 d \sqrt{c+d x^3}}{16 c x}-\frac{\sqrt{c+d x^3}}{32 x^4}",1,"-Sqrt[c + d*x^3]/(32*x^4) - (3*d*Sqrt[c + d*x^3])/(16*c*x) + (3*d^(4/3)*Sqrt[c + d*x^3])/(16*c*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (9*Sqrt[3]*d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(128*c^(5/6)) + (9*d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(128*c^(5/6)) - (9*d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(128*c^(5/6)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(32*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (3^(3/4)*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*Sqrt[2]*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{474, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
307,1,675,0,0.9357199,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^8 \left(8 c-d x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)),x]","\frac{3 d^{7/3} \sqrt{c+d x^3}}{56 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{3 d^2 \sqrt{c+d x^3}}{56 c^2 x}-\frac{9 \sqrt{3} d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1024 c^{11/6}}+\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1024 c^{11/6}}-\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1024 c^{11/6}}+\frac{3^{3/4} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt{2} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{112 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{75 d \sqrt{c+d x^3}}{1792 c x^4}-\frac{\sqrt{c+d x^3}}{56 x^7}","\frac{3 d^{7/3} \sqrt{c+d x^3}}{56 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{3 d^2 \sqrt{c+d x^3}}{56 c^2 x}-\frac{9 \sqrt{3} d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1024 c^{11/6}}+\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1024 c^{11/6}}-\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1024 c^{11/6}}+\frac{3^{3/4} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt{2} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{112 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{75 d \sqrt{c+d x^3}}{1792 c x^4}-\frac{\sqrt{c+d x^3}}{56 x^7}",1,"-Sqrt[c + d*x^3]/(56*x^7) - (75*d*Sqrt[c + d*x^3])/(1792*c*x^4) - (3*d^2*Sqrt[c + d*x^3])/(56*c^2*x) + (3*d^(7/3)*Sqrt[c + d*x^3])/(56*c^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (9*Sqrt[3]*d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(1024*c^(11/6)) + (9*d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(1024*c^(11/6)) - (9*d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1024*c^(11/6)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(112*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (3^(3/4)*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(28*Sqrt[2]*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{474, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
308,1,90,0,0.0806504,"\int \frac{x^{11}}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^11/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{38 c^2 \sqrt{c+d x^3}}{d^4}+\frac{1024 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^4}-\frac{4 c \left(c+d x^3\right)^{3/2}}{3 d^4}-\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^4}","-\frac{38 c^2 \sqrt{c+d x^3}}{d^4}+\frac{1024 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^4}-\frac{4 c \left(c+d x^3\right)^{3/2}}{3 d^4}-\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^4}",1,"(-38*c^2*Sqrt[c + d*x^3])/d^4 - (4*c*(c + d*x^3)^(3/2))/(3*d^4) - (2*(c + d*x^3)^(5/2))/(15*d^4) + (1024*c^(5/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^4)","A",5,4,27,0.1481,1,"{446, 88, 63, 206}"
309,1,71,0,0.0689688,"\int \frac{x^8}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^8/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{128 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^3}-\frac{14 c \sqrt{c+d x^3}}{3 d^3}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^3}","\frac{128 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^3}-\frac{14 c \sqrt{c+d x^3}}{3 d^3}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^3}",1,"(-14*c*Sqrt[c + d*x^3])/(3*d^3) - (2*(c + d*x^3)^(3/2))/(9*d^3) + (128*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^3)","A",5,4,27,0.1481,1,"{446, 88, 63, 206}"
310,1,52,0,0.0442747,"\int \frac{x^5}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^5/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{16 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^2}-\frac{2 \sqrt{c+d x^3}}{3 d^2}","\frac{16 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^2}-\frac{2 \sqrt{c+d x^3}}{3 d^2}",1,"(-2*Sqrt[c + d*x^3])/(3*d^2) + (16*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^2)","A",4,4,27,0.1481,1,"{446, 80, 63, 206}"
311,1,33,0,0.0327539,"\int \frac{x^2}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^2/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 \sqrt{c} d}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 \sqrt{c} d}",1,"(2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*Sqrt[c]*d)","A",3,3,27,0.1111,1,"{444, 63, 206}"
312,1,58,0,0.0520377,"\int \frac{1}{x \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{36 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12 c^{3/2}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{36 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12 c^{3/2}}",1,"ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(36*c^(3/2)) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(12*c^(3/2))","A",6,5,27,0.1852,1,"{446, 86, 63, 208, 206}"
313,1,81,0,0.0731036,"\int \frac{1}{x^4 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^4*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{c+d x^3}}{24 c^2 x^3}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{288 c^{5/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{32 c^{5/2}}","-\frac{\sqrt{c+d x^3}}{24 c^2 x^3}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{288 c^{5/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{32 c^{5/2}}",1,"-Sqrt[c + d*x^3]/(24*c^2*x^3) + (d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(288*c^(5/2)) + (d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(32*c^(5/2))","A",7,6,27,0.2222,1,"{446, 103, 156, 63, 208, 206}"
314,1,107,0,0.0977468,"\int \frac{1}{x^7 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^7*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2304 c^{7/2}}-\frac{7 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{256 c^{7/2}}+\frac{5 d \sqrt{c+d x^3}}{192 c^3 x^3}-\frac{\sqrt{c+d x^3}}{48 c^2 x^6}","\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2304 c^{7/2}}-\frac{7 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{256 c^{7/2}}+\frac{5 d \sqrt{c+d x^3}}{192 c^3 x^3}-\frac{\sqrt{c+d x^3}}{48 c^2 x^6}",1,"-Sqrt[c + d*x^3]/(48*c^2*x^6) + (5*d*Sqrt[c + d*x^3])/(192*c^3*x^3) + (d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(2304*c^(7/2)) - (7*d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(256*c^(7/2))","A",8,7,27,0.2593,1,"{446, 103, 151, 156, 63, 208, 206}"
315,1,630,0,0.7231489,"\int \frac{x^7}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^7/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{32 c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{8/3}}+\frac{32 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{8/3}}-\frac{32 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{8/3}}-\frac{104 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{52 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2 x^2 \sqrt{c+d x^3}}{7 d^2}-\frac{104 c \sqrt{c+d x^3}}{7 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}","-\frac{32 c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{8/3}}+\frac{32 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{8/3}}-\frac{32 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{8/3}}-\frac{104 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{52 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2 x^2 \sqrt{c+d x^3}}{7 d^2}-\frac{104 c \sqrt{c+d x^3}}{7 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}",1,"(-2*x^2*Sqrt[c + d*x^3])/(7*d^2) - (104*c*Sqrt[c + d*x^3])/(7*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (32*c^(7/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3*Sqrt[3]*d^(8/3)) + (32*c^(7/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(9*d^(8/3)) - (32*c^(7/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^(8/3)) + (52*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (104*Sqrt[2]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{479, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
316,1,601,0,0.5814315,"\int \frac{x^4}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^4/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2 \sqrt{c+d x^3}}{d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{4 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{5/3}}+\frac{4 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{5/3}}-\frac{4 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{5/3}}","-\frac{2 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2 \sqrt{c+d x^3}}{d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{4 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{5/3}}+\frac{4 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{5/3}}-\frac{4 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{5/3}}",1,"(-2*Sqrt[c + d*x^3])/(d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (4*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3*Sqrt[3]*d^(5/3)) + (4*c^(1/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(9*d^(5/3)) - (4*c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^(5/3)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (2*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",12,11,27,0.4074,1,"{483, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
317,1,141,0,0.4134375,"\int \frac{x}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{6 \sqrt{3} c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{18 c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{18 c^{5/6} d^{2/3}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{6 \sqrt{3} c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{18 c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{18 c^{5/6} d^{2/3}}",1,"-ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]]/(6*Sqrt[3]*c^(5/6)*d^(2/3)) + ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])]/(18*c^(5/6)*d^(2/3)) - ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(18*c^(5/6)*d^(2/3))","A",8,7,25,0.2800,1,"{486, 444, 63, 206, 2138, 2145, 205}"
318,1,632,0,0.7233903,"\int \frac{1}{x^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^2*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{8 c^2 x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{8 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{48 \sqrt{3} c^{11/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{144 c^{11/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{144 c^{11/6}}","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{8 c^2 x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{8 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{48 \sqrt{3} c^{11/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{144 c^{11/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{144 c^{11/6}}",1,"-Sqrt[c + d*x^3]/(8*c^2*x) + (d^(1/3)*Sqrt[c + d*x^3])/(8*c^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(48*Sqrt[3]*c^(11/6)) + (d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(144*c^(11/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(144*c^(11/6)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{480, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
319,1,654,0,0.8303328,"\int \frac{1}{x^5 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^5*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{d^{4/3} \sqrt{c+d x^3}}{16 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{384 \sqrt{3} c^{17/6}}+\frac{d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1152 c^{17/6}}-\frac{d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1152 c^{17/6}}-\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{d \sqrt{c+d x^3}}{16 c^3 x}-\frac{\sqrt{c+d x^3}}{32 c^2 x^4}","-\frac{d^{4/3} \sqrt{c+d x^3}}{16 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{384 \sqrt{3} c^{17/6}}+\frac{d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1152 c^{17/6}}-\frac{d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1152 c^{17/6}}-\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{d \sqrt{c+d x^3}}{16 c^3 x}-\frac{\sqrt{c+d x^3}}{32 c^2 x^4}",1,"-Sqrt[c + d*x^3]/(32*c^2*x^4) + (d*Sqrt[c + d*x^3])/(16*c^3*x) - (d^(4/3)*Sqrt[c + d*x^3])/(16*c^3*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(384*Sqrt[3]*c^(17/6)) + (d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(1152*c^(17/6)) - (d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1152*c^(17/6)) + (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(32*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*Sqrt[2]*3^(1/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{480, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
320,1,678,0,0.9294796,"\int \frac{1}{x^8 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^8*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{3 d^{7/3} \sqrt{c+d x^3}}{56 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{3 d^2 \sqrt{c+d x^3}}{56 c^4 x}-\frac{d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3072 \sqrt{3} c^{23/6}}+\frac{d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9216 c^{23/6}}-\frac{d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9216 c^{23/6}}+\frac{3^{3/4} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt{2} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{112 c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{37 d \sqrt{c+d x^3}}{1792 c^3 x^4}-\frac{\sqrt{c+d x^3}}{56 c^2 x^7}","\frac{3 d^{7/3} \sqrt{c+d x^3}}{56 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{3 d^2 \sqrt{c+d x^3}}{56 c^4 x}-\frac{d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3072 \sqrt{3} c^{23/6}}+\frac{d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9216 c^{23/6}}-\frac{d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9216 c^{23/6}}+\frac{3^{3/4} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{28 \sqrt{2} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{112 c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{37 d \sqrt{c+d x^3}}{1792 c^3 x^4}-\frac{\sqrt{c+d x^3}}{56 c^2 x^7}",1,"-Sqrt[c + d*x^3]/(56*c^2*x^7) + (37*d*Sqrt[c + d*x^3])/(1792*c^3*x^4) - (3*d^2*Sqrt[c + d*x^3])/(56*c^4*x) + (3*d^(7/3)*Sqrt[c + d*x^3])/(56*c^4*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3072*Sqrt[3]*c^(23/6)) + (d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(9216*c^(23/6)) - (d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9216*c^(23/6)) - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(112*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (3^(3/4)*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(28*Sqrt[2]*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{480, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
321,1,66,0,0.05414,"\int \frac{x^3}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^3/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{32 c \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{32 c \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 1, 1/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(32*c*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
322,1,64,0,0.0282031,"\int \frac{1}{\left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/((8*c - d*x^3)*Sqrt[c + d*x^3]),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{8 c \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{8 c \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 1, 1/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(8*c*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{430, 429}"
323,1,66,0,0.0566818,"\int \frac{1}{x^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^3*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{16 c x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{16 c x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 1, 1/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(16*c*x^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
324,1,66,0,0.0589708,"\int \frac{1}{x^6 \left(8 c-d x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^6*(8*c - d*x^3)*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};1,\frac{1}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{40 c x^5 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};1,\frac{1}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{40 c x^5 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-5/3, 1, 1/2, -2/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(40*c*x^5*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
325,1,90,0,0.1035599,"\int \frac{x^{11}}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^11/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2 c^2}{27 d^4 \sqrt{c+d x^3}}+\frac{1024 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^4}-\frac{4 c \sqrt{c+d x^3}}{d^4}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^4}","\frac{2 c^2}{27 d^4 \sqrt{c+d x^3}}+\frac{1024 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^4}-\frac{4 c \sqrt{c+d x^3}}{d^4}-\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^4}",1,"(2*c^2)/(27*d^4*Sqrt[c + d*x^3]) - (4*c*Sqrt[c + d*x^3])/d^4 - (2*(c + d*x^3)^(3/2))/(9*d^4) + (1024*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*d^4)","A",7,5,27,0.1852,1,"{446, 87, 43, 63, 206}"
326,1,71,0,0.0732029,"\int \frac{x^8}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^8/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{2 c}{27 d^3 \sqrt{c+d x^3}}-\frac{2 \sqrt{c+d x^3}}{3 d^3}+\frac{128 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^3}","-\frac{2 c}{27 d^3 \sqrt{c+d x^3}}-\frac{2 \sqrt{c+d x^3}}{3 d^3}+\frac{128 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^3}",1,"(-2*c)/(27*d^3*Sqrt[c + d*x^3]) - (2*Sqrt[c + d*x^3])/(3*d^3) + (128*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*d^3)","A",5,4,27,0.1481,1,"{446, 87, 63, 206}"
327,1,52,0,0.0457229,"\int \frac{x^5}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^5/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2}{27 d^2 \sqrt{c+d x^3}}+\frac{16 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 \sqrt{c} d^2}","\frac{2}{27 d^2 \sqrt{c+d x^3}}+\frac{16 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 \sqrt{c} d^2}",1,"2/(27*d^2*Sqrt[c + d*x^3]) + (16*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*Sqrt[c]*d^2)","A",4,4,27,0.1481,1,"{446, 78, 63, 206}"
328,1,55,0,0.0486025,"\int \frac{x^2}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^2/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{3/2} d}-\frac{2}{27 c d \sqrt{c+d x^3}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{3/2} d}-\frac{2}{27 c d \sqrt{c+d x^3}}",1,"-2/(27*c*d*Sqrt[c + d*x^3]) + (2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*c^(3/2)*d)","A",4,4,27,0.1481,1,"{444, 51, 63, 206}"
329,1,76,0,0.0702243,"\int \frac{1}{x \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2}{27 c^2 \sqrt{c+d x^3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{324 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12 c^{5/2}}","\frac{2}{27 c^2 \sqrt{c+d x^3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{324 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{12 c^{5/2}}",1,"2/(27*c^2*Sqrt[c + d*x^3]) + ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(324*c^(5/2)) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(12*c^(5/2))","A",7,6,27,0.2222,1,"{446, 85, 156, 63, 208, 206}"
330,1,100,0,0.0950825,"\int \frac{1}{x^4 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^4*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{25 d}{216 c^3 \sqrt{c+d x^3}}-\frac{1}{24 c^2 x^3 \sqrt{c+d x^3}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2592 c^{7/2}}+\frac{11 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{7/2}}","-\frac{25 d}{216 c^3 \sqrt{c+d x^3}}-\frac{1}{24 c^2 x^3 \sqrt{c+d x^3}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2592 c^{7/2}}+\frac{11 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{7/2}}",1,"(-25*d)/(216*c^3*Sqrt[c + d*x^3]) - 1/(24*c^2*x^3*Sqrt[c + d*x^3]) + (d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(2592*c^(7/2)) + (11*d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(96*c^(7/2))","A",8,7,27,0.2593,1,"{446, 103, 152, 156, 63, 208, 206}"
331,1,128,0,0.1238155,"\int \frac{1}{x^7 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^7*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{245 d^2}{1728 c^4 \sqrt{c+d x^3}}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{20736 c^{9/2}}-\frac{109 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{768 c^{9/2}}+\frac{3 d}{64 c^3 x^3 \sqrt{c+d x^3}}-\frac{1}{48 c^2 x^6 \sqrt{c+d x^3}}","\frac{245 d^2}{1728 c^4 \sqrt{c+d x^3}}+\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{20736 c^{9/2}}-\frac{109 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{768 c^{9/2}}+\frac{3 d}{64 c^3 x^3 \sqrt{c+d x^3}}-\frac{1}{48 c^2 x^6 \sqrt{c+d x^3}}",1,"(245*d^2)/(1728*c^4*Sqrt[c + d*x^3]) - 1/(48*c^2*x^6*Sqrt[c + d*x^3]) + (3*d)/(64*c^3*x^3*Sqrt[c + d*x^3]) + (d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(20736*c^(9/2)) - (109*d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(768*c^(9/2))","A",9,8,27,0.2963,1,"{446, 103, 151, 152, 156, 63, 208, 206}"
332,1,629,0,0.7244229,"\int \frac{x^7}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^7/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{56 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{28 \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 x^2}{27 d^2 \sqrt{c+d x^3}}-\frac{56 \sqrt{c+d x^3}}{27 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{32 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} d^{8/3}}+\frac{32 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 d^{8/3}}-\frac{32 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^{8/3}}","-\frac{56 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{28 \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 x^2}{27 d^2 \sqrt{c+d x^3}}-\frac{56 \sqrt{c+d x^3}}{27 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{32 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} d^{8/3}}+\frac{32 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 d^{8/3}}-\frac{32 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^{8/3}}",1,"(2*x^2)/(27*d^2*Sqrt[c + d*x^3]) - (56*Sqrt[c + d*x^3])/(27*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (32*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(27*Sqrt[3]*d^(8/3)) + (32*c^(1/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(81*d^(8/3)) - (32*c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*d^(8/3)) + (28*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (56*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{470, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
333,1,635,0,0.7303869,"\int \frac{x^4}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^4/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} c^{5/6} d^{5/3}}+\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 c^{5/6} d^{5/3}}-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{5/6} d^{5/3}}+\frac{2 \sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{27 c d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{2 x^2}{27 c d \sqrt{c+d x^3}}","-\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} c^{5/6} d^{5/3}}+\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 c^{5/6} d^{5/3}}-\frac{4 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{5/6} d^{5/3}}+\frac{2 \sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{27 c d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{2 x^2}{27 c d \sqrt{c+d x^3}}",1,"(-2*x^2)/(27*c*d*Sqrt[c + d*x^3]) + (2*Sqrt[c + d*x^3])/(27*c*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (4*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(27*Sqrt[3]*c^(5/6)*d^(5/3)) + (4*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(81*c^(5/6)*d^(5/3)) - (4*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*c^(5/6)*d^(5/3)) - (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*c^(2/3)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (2*Sqrt[2]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*c^(2/3)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{471, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
334,1,632,0,0.7091471,"\int \frac{x}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{2 \sqrt{c+d x^3}}{27 c^2 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{54 \sqrt{3} c^{11/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{162 c^{11/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{162 c^{11/6} d^{2/3}}-\frac{2 \sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 x^2}{27 c^2 \sqrt{c+d x^3}}","-\frac{2 \sqrt{c+d x^3}}{27 c^2 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{54 \sqrt{3} c^{11/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{162 c^{11/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{162 c^{11/6} d^{2/3}}-\frac{2 \sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{2 x^2}{27 c^2 \sqrt{c+d x^3}}",1,"(2*x^2)/(27*c^2*Sqrt[c + d*x^3]) - (2*Sqrt[c + d*x^3])/(27*c^2*d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]]/(54*Sqrt[3]*c^(11/6)*d^(2/3)) + ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])]/(162*c^(11/6)*d^(2/3)) - ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(162*c^(11/6)*d^(2/3)) + (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*c^(5/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (2*Sqrt[2]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*c^(5/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,25,0.4800,1,"{472, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
335,1,653,0,0.8257697,"\int \frac{1}{x^2 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^2*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{43 \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{43 \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{144\ 3^{3/4} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{43 \sqrt{c+d x^3}}{216 c^3 x}+\frac{43 \sqrt[3]{d} \sqrt{c+d x^3}}{216 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{2}{27 c^2 x \sqrt{c+d x^3}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{432 \sqrt{3} c^{17/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1296 c^{17/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1296 c^{17/6}}","\frac{43 \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{43 \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{144\ 3^{3/4} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{43 \sqrt{c+d x^3}}{216 c^3 x}+\frac{43 \sqrt[3]{d} \sqrt{c+d x^3}}{216 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{2}{27 c^2 x \sqrt{c+d x^3}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{432 \sqrt{3} c^{17/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1296 c^{17/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1296 c^{17/6}}",1,"2/(27*c^2*x*Sqrt[c + d*x^3]) - (43*Sqrt[c + d*x^3])/(216*c^3*x) + (43*d^(1/3)*Sqrt[c + d*x^3])/(216*c^3*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(432*Sqrt[3]*c^(17/6)) + (d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(1296*c^(17/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1296*c^(17/6)) - (43*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(144*3^(3/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (43*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(108*Sqrt[2]*3^(1/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{472, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
336,1,675,0,0.9206851,"\int \frac{1}{x^5 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^5*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{113 d^{4/3} \sqrt{c+d x^3}}{432 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3456 \sqrt{3} c^{23/6}}+\frac{d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{10368 c^{23/6}}-\frac{d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{10368 c^{23/6}}-\frac{113 d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{216 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{113 \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{288\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{113 d \sqrt{c+d x^3}}{432 c^4 x}-\frac{91 \sqrt{c+d x^3}}{864 c^3 x^4}+\frac{2}{27 c^2 x^4 \sqrt{c+d x^3}}","-\frac{113 d^{4/3} \sqrt{c+d x^3}}{432 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3456 \sqrt{3} c^{23/6}}+\frac{d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{10368 c^{23/6}}-\frac{d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{10368 c^{23/6}}-\frac{113 d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{216 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{113 \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{288\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{113 d \sqrt{c+d x^3}}{432 c^4 x}-\frac{91 \sqrt{c+d x^3}}{864 c^3 x^4}+\frac{2}{27 c^2 x^4 \sqrt{c+d x^3}}",1,"2/(27*c^2*x^4*Sqrt[c + d*x^3]) - (91*Sqrt[c + d*x^3])/(864*c^3*x^4) + (113*d*Sqrt[c + d*x^3])/(432*c^4*x) - (113*d^(4/3)*Sqrt[c + d*x^3])/(432*c^4*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3456*Sqrt[3]*c^(23/6)) + (d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(10368*c^(23/6)) - (d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(10368*c^(23/6)) + (113*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(288*3^(3/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (113*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(216*Sqrt[2]*3^(1/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{472, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
337,1,699,0,1.0981379,"\int \frac{1}{x^8 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^8*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{953 d^{7/3} \sqrt{c+d x^3}}{3024 c^5 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{953 d^2 \sqrt{c+d x^3}}{3024 c^5 x}-\frac{d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27648 \sqrt{3} c^{29/6}}+\frac{d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{82944 c^{29/6}}-\frac{d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{82944 c^{29/6}}+\frac{953 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1512 \sqrt{2} \sqrt[4]{3} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{953 \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2016\ 3^{3/4} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{6095 d \sqrt{c+d x^3}}{48384 c^4 x^4}-\frac{139 \sqrt{c+d x^3}}{1512 c^3 x^7}+\frac{2}{27 c^2 x^7 \sqrt{c+d x^3}}","\frac{953 d^{7/3} \sqrt{c+d x^3}}{3024 c^5 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{953 d^2 \sqrt{c+d x^3}}{3024 c^5 x}-\frac{d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27648 \sqrt{3} c^{29/6}}+\frac{d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{82944 c^{29/6}}-\frac{d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{82944 c^{29/6}}+\frac{953 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1512 \sqrt{2} \sqrt[4]{3} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{953 \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2016\ 3^{3/4} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{6095 d \sqrt{c+d x^3}}{48384 c^4 x^4}-\frac{139 \sqrt{c+d x^3}}{1512 c^3 x^7}+\frac{2}{27 c^2 x^7 \sqrt{c+d x^3}}",1,"2/(27*c^2*x^7*Sqrt[c + d*x^3]) - (139*Sqrt[c + d*x^3])/(1512*c^3*x^7) + (6095*d*Sqrt[c + d*x^3])/(48384*c^4*x^4) - (953*d^2*Sqrt[c + d*x^3])/(3024*c^5*x) + (953*d^(7/3)*Sqrt[c + d*x^3])/(3024*c^5*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(27648*Sqrt[3]*c^(29/6)) + (d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(82944*c^(29/6)) - (d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(82944*c^(29/6)) - (953*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(2016*3^(3/4)*c^(14/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (953*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(1512*Sqrt[2]*3^(1/4)*c^(14/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",17,13,27,0.4815,1,"{472, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
338,1,66,0,0.0606034,"\int \frac{x^3}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^3/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{3}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{32 c^2 \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{3}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{32 c^2 \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 1, 3/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(32*c^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
339,1,64,0,0.0298604,"\int \frac{1}{\left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/((8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{3}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{8 c^2 \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{3}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{8 c^2 \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 1, 3/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(8*c^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{430, 429}"
340,1,66,0,0.0643902,"\int \frac{1}{x^3 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^3*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{3}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{16 c^2 x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{3}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{16 c^2 x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 1, 3/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(16*c^2*x^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
341,1,66,0,0.0637066,"\int \frac{1}{x^6 \left(8 c-d x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^6*(8*c - d*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};1,\frac{3}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{40 c^2 x^5 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};1,\frac{3}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{40 c^2 x^5 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-5/3, 1, 3/2, -2/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(40*c^2*x^5*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
342,1,737,0,0.2935668,"\int \frac{x \sqrt{a+b x^3}}{2 \left(5+3 \sqrt{3}\right) a+b x^3} \, dx","Int[(x*Sqrt[a + b*x^3])/(2*(5 + 3*Sqrt[3])*a + b*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}",1,"(2*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(3/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (a^(1/6)*ArcTan[((1 - Sqrt[3])*Sqrt[a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(Sqrt[2]*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,33,0.1515,1,"{489, 303, 218, 1877, 487}"
343,1,757,0,0.2875167,"\int \frac{x \sqrt{a-b x^3}}{2 \left(5+3 \sqrt{3}\right) a-b x^3} \, dx","Int[(x*Sqrt[a - b*x^3])/(2*(5 + 3*Sqrt[3])*a - b*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{2 \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}+\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{\sqrt{2} b^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{2 \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}+\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{\sqrt{2} b^{2/3}}",1,"(2*Sqrt[a - b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)) + (3^(3/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (a^(1/6)*ArcTan[((1 - Sqrt[3])*Sqrt[a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(Sqrt[2]*b^(2/3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",5,5,35,0.1429,1,"{489, 303, 218, 1877, 487}"
344,1,774,0,0.2805368,"\int \frac{x \sqrt{-a+b x^3}}{-2 \left(5+3 \sqrt{3}\right) a+b x^3} \, dx","Int[(x*Sqrt[-a + b*x^3])/(-2*(5 + 3*Sqrt[3])*a + b*x^3),x]","-\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{\sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}-\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}","-\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{2 \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{\sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}-\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}",1,"(-2*Sqrt[-a + b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)) + (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(Sqrt[2]*b^(2/3)) + (3^(3/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) - (a^(1/6)*ArcTanh[((1 - Sqrt[3])*Sqrt[-a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3]) - (2*Sqrt[2]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",5,5,35,0.1429,1,"{489, 304, 219, 1879, 488}"
345,1,768,0,0.283459,"\int \frac{x \sqrt{-a-b x^3}}{-2 \left(5+3 \sqrt{3}\right) a-b x^3} \, dx","Int[(x*Sqrt[-a - b*x^3])/(-2*(5 + 3*Sqrt[3])*a - b*x^3),x]","-\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}-\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}","-\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{2 \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}-\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}",1,"(-2*Sqrt[-a - b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)) + (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(Sqrt[2]*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (3^(3/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) - (a^(1/6)*ArcTanh[((1 - Sqrt[3])*Sqrt[-a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3]) - (2*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",5,5,37,0.1351,1,"{489, 304, 219, 1879, 488}"
346,1,738,0,0.2509736,"\int \frac{x \sqrt{a+b x^3}}{2 \left(5-3 \sqrt{3}\right) a+b x^3} \, dx","Int[(x*Sqrt[a + b*x^3])/(2*(5 - 3*Sqrt[3])*a + b*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{\sqrt{2} b^{2/3}}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{\sqrt{2} b^{2/3}}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}",1,"(2*Sqrt[a + b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(Sqrt[2]*b^(2/3)) - (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (3^(3/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (a^(1/6)*ArcTanh[((1 + Sqrt[3])*Sqrt[a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,33,0.1515,1,"{489, 303, 218, 1877, 487}"
347,1,758,0,0.2368218,"\int \frac{x \sqrt{a-b x^3}}{2 \left(5-3 \sqrt{3}\right) a-b x^3} \, dx","Int[(x*Sqrt[a - b*x^3])/(2*(5 - 3*Sqrt[3])*a - b*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{2 \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7-4 \sqrt{3}\right)}{b^{2/3} \sqrt{\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{a-b x^3}}+\frac{2 \sqrt{a-b x^3}}{b^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}-\frac{\sqrt[4]{3} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{3^{3/4} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}",1,"(2*Sqrt[a - b*x^3])/(b^(2/3)*((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)) - (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) - (3^(1/4)*a^(1/6)*ArcTan[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(Sqrt[2]*b^(2/3)) + (3^(3/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (a^(1/6)*ArcTanh[((1 + Sqrt[3])*Sqrt[a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 - 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[(a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*Sqrt[a - b*x^3])","A",5,5,35,0.1429,1,"{489, 303, 218, 1877, 487}"
348,1,774,0,0.2367779,"\int \frac{x \sqrt{-a+b x^3}}{2 \left(5-3 \sqrt{3}\right) a-b x^3} \, dx","Int[(x*Sqrt[-a + b*x^3])/(2*(5 - 3*Sqrt[3])*a - b*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{2 \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}-\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{\sqrt{2} b^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}+\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}{\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)^2}} \sqrt{b x^3-a}}+\frac{2 \sqrt{b x^3-a}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-\sqrt[3]{b} x\right)}-\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{\sqrt{2} b^{2/3}}",1,"(2*Sqrt[-a + b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)) - (3^(3/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (a^(1/6)*ArcTan[((1 + Sqrt[3])*Sqrt[-a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(Sqrt[2]*b^(2/3)) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) - b^(1/3)*x)*Sqrt[(a^(2/3) + a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) - b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) - b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) - b^(1/3)*x)^2)]*Sqrt[-a + b*x^3])","A",5,5,36,0.1389,1,"{489, 304, 219, 1879, 488}"
349,1,768,0,0.2305641,"\int \frac{x \sqrt{-a-b x^3}}{2 \left(5-3 \sqrt{3}\right) a+b x^3} \, dx","Int[(x*Sqrt[-a - b*x^3])/(2*(5 - 3*Sqrt[3])*a + b*x^3),x]","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}","\frac{2 \sqrt{2} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{\sqrt[4]{3} b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}-\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{b} x+\left(1+\sqrt{3}\right) \sqrt[3]{a}}{\sqrt[3]{b} x+\left(1-\sqrt{3}\right) \sqrt[3]{a}}\right)|-7+4 \sqrt{3}\right)}{b^{2/3} \sqrt{-\frac{\sqrt[3]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)^2}} \sqrt{-a-b x^3}}+\frac{2 \sqrt{-a-b x^3}}{b^{2/3} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+\sqrt[3]{b} x\right)}-\frac{3^{3/4} \sqrt[6]{a} \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}+\frac{\sqrt[6]{a} \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{\sqrt{2} \sqrt[4]{3} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{\sqrt{2} b^{2/3}}+\frac{\sqrt[4]{3} \sqrt[6]{a} \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} b^{2/3}}",1,"(2*Sqrt[-a - b*x^3])/(b^(2/3)*((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)) - (3^(3/4)*a^(1/6)*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) + (a^(1/6)*ArcTan[((1 + Sqrt[3])*Sqrt[-a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(Sqrt[2]*3^(1/4)*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(Sqrt[2]*b^(2/3)) + (3^(1/4)*a^(1/6)*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(2*Sqrt[2]*b^(2/3)) - (3^(1/4)*Sqrt[2 + Sqrt[3]]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticE[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3]) + (2*Sqrt[2]*a^(1/3)*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2]*EllipticF[ArcSin[((1 + Sqrt[3])*a^(1/3) + b^(1/3)*x)/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)], -7 + 4*Sqrt[3]])/(3^(1/4)*b^(2/3)*Sqrt[-((a^(1/3)*(a^(1/3) + b^(1/3)*x))/((1 - Sqrt[3])*a^(1/3) + b^(1/3)*x)^2)]*Sqrt[-a - b*x^3])","A",5,5,36,0.1389,1,"{489, 304, 219, 1879, 488}"
350,1,318,0,0.0638311,"\int \frac{x}{\sqrt{a+b x^3} \left(2 \left(5+3 \sqrt{3}\right) a+b x^3\right)} \, dx","Int[x/(Sqrt[a + b*x^3]*(2*(5 + 3*Sqrt[3])*a + b*x^3)),x]","-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}","-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}",1,"-((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTan[((1 - Sqrt[3])*Sqrt[a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3))","A",1,1,33,0.03030,1,"{487}"
351,1,324,0,0.0696075,"\int \frac{x}{\sqrt{a-b x^3} \left(2 \left(5+3 \sqrt{3}\right) a-b x^3\right)} \, dx","Int[x/(Sqrt[a - b*x^3]*(2*(5 + 3*Sqrt[3])*a - b*x^3)),x]","-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}","-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}",1,"-((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTan[((1 - Sqrt[3])*Sqrt[a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3))","A",1,1,35,0.02857,1,"{487}"
352,1,328,0,0.0667759,"\int \frac{x}{\sqrt{-a+b x^3} \left(-2 \left(5+3 \sqrt{3}\right) a+b x^3\right)} \, dx","Int[x/(Sqrt[-a + b*x^3]*(-2*(5 + 3*Sqrt[3])*a + b*x^3)),x]","\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}","\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}",1,"((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - Sqrt[3])*ArcTan[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTanh[((1 - Sqrt[3])*Sqrt[-a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3))","A",1,1,35,0.02857,1,"{488}"
353,1,330,0,0.0666485,"\int \frac{x}{\sqrt{-a-b x^3} \left(-2 \left(5+3 \sqrt{3}\right) a-b x^3\right)} \, dx","Int[x/(Sqrt[-a - b*x^3]*(-2*(5 + 3*Sqrt[3])*a - b*x^3)),x]","\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}","\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1+\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2-\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}",1,"((2 - Sqrt[3])*ArcTan[(3^(1/4)*a^(1/6)*((1 + Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 - Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 - Sqrt[3])*ArcTanh[((1 - Sqrt[3])*Sqrt[-a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3))","A",1,1,37,0.02703,1,"{488}"
354,1,310,0,0.0509157,"\int \frac{x}{\sqrt{a+b x^3} \left(2 \left(5-3 \sqrt{3}\right) a+b x^3\right)} \, dx","Int[x/(Sqrt[a + b*x^3]*(2*(5 - 3*Sqrt[3])*a + b*x^3)),x]","-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}","-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a+b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a+b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}",1,"-((2 + Sqrt[3])*ArcTan[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[a + b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) + ((2 + Sqrt[3])*ArcTanh[((1 + Sqrt[3])*Sqrt[a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3))","A",1,1,33,0.03030,1,"{487}"
355,1,316,0,0.0544255,"\int \frac{x}{\sqrt{a-b x^3} \left(2 \left(5-3 \sqrt{3}\right) a-b x^3\right)} \, dx","Int[x/(Sqrt[a - b*x^3]*(2*(5 - 3*Sqrt[3])*a - b*x^3)),x]","-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}","-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}+\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}",1,"-((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTan[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) + ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[a - b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) + ((2 + Sqrt[3])*ArcTanh[((1 + Sqrt[3])*Sqrt[a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3))","A",1,1,35,0.02857,1,"{487}"
356,1,320,0,0.0532115,"\int \frac{x}{\left(2 \left(5-3 \sqrt{3}\right) a-b x^3\right) \sqrt{-a+b x^3}} \, dx","Int[x/((2*(5 - 3*Sqrt[3])*a - b*x^3)*Sqrt[-a + b*x^3]),x]","\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}","\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{b x^3-a}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}-\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}+2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{b x^3-a}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}",1,"((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTan[((1 + Sqrt[3])*Sqrt[-a + b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) - b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) + 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a + b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3))","A",1,1,36,0.02778,1,"{488}"
357,1,322,0,0.0535043,"\int \frac{x}{\sqrt{-a-b x^3} \left(2 \left(5-3 \sqrt{3}\right) a+b x^3\right)} \, dx","Int[x/(Sqrt[-a - b*x^3]*(2*(5 - 3*Sqrt[3])*a + b*x^3)),x]","\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}","\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\sqrt[4]{3} \left(1-\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{2 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tan ^{-1}\left(\frac{\left(1+\sqrt{3}\right) \sqrt{-a-b x^3}}{\sqrt{2} 3^{3/4} \sqrt{a}}\right)}{3 \sqrt{2} 3^{3/4} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \sqrt[6]{a} \left(\left(1-\sqrt{3}\right) \sqrt[3]{a}-2 \sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{3 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}-\frac{\left(2+\sqrt{3}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{3} \left(1+\sqrt{3}\right) \sqrt[6]{a} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt{2} \sqrt{-a-b x^3}}\right)}{6 \sqrt{2} \sqrt[4]{3} a^{5/6} b^{2/3}}",1,"((2 + Sqrt[3])*ArcTan[(3^(1/4)*(1 - Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(2*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTan[((1 + Sqrt[3])*Sqrt[-a - b*x^3])/(Sqrt[2]*3^(3/4)*Sqrt[a])])/(3*Sqrt[2]*3^(3/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*a^(1/6)*((1 - Sqrt[3])*a^(1/3) - 2*b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(3*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3)) - ((2 + Sqrt[3])*ArcTanh[(3^(1/4)*(1 + Sqrt[3])*a^(1/6)*(a^(1/3) + b^(1/3)*x))/(Sqrt[2]*Sqrt[-a - b*x^3])])/(6*Sqrt[2]*3^(1/4)*a^(5/6)*b^(2/3))","A",1,1,36,0.02778,1,"{488}"
358,1,125,0,0.1294852,"\int \frac{x^8 \sqrt{c+d x^3}}{a+b x^3} \, dx","Int[(x^8*Sqrt[c + d*x^3])/(a + b*x^3),x]","\frac{2 a^2 \sqrt{c+d x^3}}{3 b^3}-\frac{2 a^2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2}}-\frac{2 \left(c+d x^3\right)^{3/2} (a d+b c)}{9 b^2 d^2}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 b d^2}","\frac{2 a^2 \sqrt{c+d x^3}}{3 b^3}-\frac{2 a^2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2}}-\frac{2 \left(c+d x^3\right)^{3/2} (a d+b c)}{9 b^2 d^2}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 b d^2}",1,"(2*a^2*Sqrt[c + d*x^3])/(3*b^3) - (2*(b*c + a*d)*(c + d*x^3)^(3/2))/(9*b^2*d^2) + (2*(c + d*x^3)^(5/2))/(15*b*d^2) - (2*a^2*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(7/2))","A",6,5,24,0.2083,1,"{446, 88, 50, 63, 208}"
359,1,93,0,0.0780381,"\int \frac{x^5 \sqrt{c+d x^3}}{a+b x^3} \, dx","Int[(x^5*Sqrt[c + d*x^3])/(a + b*x^3),x]","-\frac{2 a \sqrt{c+d x^3}}{3 b^2}+\frac{2 a \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2}}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b d}","-\frac{2 a \sqrt{c+d x^3}}{3 b^2}+\frac{2 a \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2}}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b d}",1,"(-2*a*Sqrt[c + d*x^3])/(3*b^2) + (2*(c + d*x^3)^(3/2))/(9*b*d) + (2*a*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(5/2))","A",5,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
360,1,70,0,0.0585363,"\int \frac{x^2 \sqrt{c+d x^3}}{a+b x^3} \, dx","Int[(x^2*Sqrt[c + d*x^3])/(a + b*x^3),x]","\frac{2 \sqrt{c+d x^3}}{3 b}-\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2}}","\frac{2 \sqrt{c+d x^3}}{3 b}-\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2}}",1,"(2*Sqrt[c + d*x^3])/(3*b) - (2*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(3/2))","A",4,4,24,0.1667,1,"{444, 50, 63, 208}"
361,1,85,0,0.0744782,"\int \frac{\sqrt{c+d x^3}}{x \left(a+b x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x*(a + b*x^3)),x]","\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a \sqrt{b}}-\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a}","\frac{2 \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a \sqrt{b}}-\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a}",1,"(-2*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a) + (2*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a*Sqrt[b])","A",6,4,24,0.1667,1,"{446, 83, 63, 208}"
362,1,115,0,0.1248718,"\int \frac{\sqrt{c+d x^3}}{x^4 \left(a+b x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^4*(a + b*x^3)),x]","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 \sqrt{c}}-\frac{2 \sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2}-\frac{\sqrt{c+d x^3}}{3 a x^3}","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 \sqrt{c}}-\frac{2 \sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2}-\frac{\sqrt{c+d x^3}}{3 a x^3}",1,"-Sqrt[c + d*x^3]/(3*a*x^3) + ((2*b*c - a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2*Sqrt[c]) - (2*Sqrt[b]*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2)","A",7,5,24,0.2083,1,"{446, 99, 156, 63, 208}"
363,1,64,0,0.0532768,"\int \frac{x^3 \sqrt{c+d x^3}}{a+b x^3} \, dx","Int[(x^3*Sqrt[c + d*x^3])/(a + b*x^3),x]","\frac{x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};1,-\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a \sqrt{\frac{d x^3}{c}+1}}","\frac{x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};1,-\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a \sqrt{\frac{d x^3}{c}+1}}",1,"(x^4*Sqrt[c + d*x^3]*AppellF1[4/3, 1, -1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
364,1,64,0,0.0373927,"\int \frac{x \sqrt{c+d x^3}}{a+b x^3} \, dx","Int[(x*Sqrt[c + d*x^3])/(a + b*x^3),x]","\frac{x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};1,-\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a \sqrt{\frac{d x^3}{c}+1}}","\frac{x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};1,-\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a \sqrt{\frac{d x^3}{c}+1}}",1,"(x^2*Sqrt[c + d*x^3]*AppellF1[2/3, 1, -1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*Sqrt[1 + (d*x^3)/c])","A",2,2,22,0.09091,1,"{511, 510}"
365,1,59,0,0.0258554,"\int \frac{\sqrt{c+d x^3}}{a+b x^3} \, dx","Int[Sqrt[c + d*x^3]/(a + b*x^3),x]","\frac{x \sqrt{c+d x^3} F_1\left(\frac{1}{3};1,-\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a \sqrt{\frac{d x^3}{c}+1}}","\frac{x \sqrt{c+d x^3} F_1\left(\frac{1}{3};1,-\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a \sqrt{\frac{d x^3}{c}+1}}",1,"(x*Sqrt[c + d*x^3]*AppellF1[1/3, 1, -1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*Sqrt[1 + (d*x^3)/c])","A",2,2,21,0.09524,1,"{430, 429}"
366,1,62,0,0.0520184,"\int \frac{\sqrt{c+d x^3}}{x^2 \left(a+b x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^2*(a + b*x^3)),x]","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{1}{3};1,-\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a x \sqrt{\frac{d x^3}{c}+1}}","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{1}{3};1,-\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a x \sqrt{\frac{d x^3}{c}+1}}",1,"-((Sqrt[c + d*x^3]*AppellF1[-1/3, 1, -1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*x*Sqrt[1 + (d*x^3)/c]))","A",2,2,24,0.08333,1,"{511, 510}"
367,1,64,0,0.0518778,"\int \frac{\sqrt{c+d x^3}}{x^3 \left(a+b x^3\right)} \, dx","Int[Sqrt[c + d*x^3]/(x^3*(a + b*x^3)),x]","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{2}{3};1,-\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a x^2 \sqrt{\frac{d x^3}{c}+1}}","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{2}{3};1,-\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a x^2 \sqrt{\frac{d x^3}{c}+1}}",1,"-(Sqrt[c + d*x^3]*AppellF1[-2/3, 1, -1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*x^2*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
368,1,154,0,0.1547696,"\int \frac{x^8 \left(c+d x^3\right)^{3/2}}{a+b x^3} \, dx","Int[(x^8*(c + d*x^3)^(3/2))/(a + b*x^3),x]","\frac{2 a^2 \left(c+d x^3\right)^{3/2}}{9 b^3}+\frac{2 a^2 \sqrt{c+d x^3} (b c-a d)}{3 b^4}-\frac{2 a^2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{9/2}}-\frac{2 \left(c+d x^3\right)^{5/2} (a d+b c)}{15 b^2 d^2}+\frac{2 \left(c+d x^3\right)^{7/2}}{21 b d^2}","\frac{2 a^2 \left(c+d x^3\right)^{3/2}}{9 b^3}+\frac{2 a^2 \sqrt{c+d x^3} (b c-a d)}{3 b^4}-\frac{2 a^2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{9/2}}-\frac{2 \left(c+d x^3\right)^{5/2} (a d+b c)}{15 b^2 d^2}+\frac{2 \left(c+d x^3\right)^{7/2}}{21 b d^2}",1,"(2*a^2*(b*c - a*d)*Sqrt[c + d*x^3])/(3*b^4) + (2*a^2*(c + d*x^3)^(3/2))/(9*b^3) - (2*(b*c + a*d)*(c + d*x^3)^(5/2))/(15*b^2*d^2) + (2*(c + d*x^3)^(7/2))/(21*b*d^2) - (2*a^2*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(9/2))","A",7,5,24,0.2083,1,"{446, 88, 50, 63, 208}"
369,1,120,0,0.103848,"\int \frac{x^5 \left(c+d x^3\right)^{3/2}}{a+b x^3} \, dx","Int[(x^5*(c + d*x^3)^(3/2))/(a + b*x^3),x]","-\frac{2 a \left(c+d x^3\right)^{3/2}}{9 b^2}-\frac{2 a \sqrt{c+d x^3} (b c-a d)}{3 b^3}+\frac{2 a (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2}}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 b d}","-\frac{2 a \left(c+d x^3\right)^{3/2}}{9 b^2}-\frac{2 a \sqrt{c+d x^3} (b c-a d)}{3 b^3}+\frac{2 a (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2}}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 b d}",1,"(-2*a*(b*c - a*d)*Sqrt[c + d*x^3])/(3*b^3) - (2*a*(c + d*x^3)^(3/2))/(9*b^2) + (2*(c + d*x^3)^(5/2))/(15*b*d) + (2*a*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(7/2))","A",6,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
370,1,96,0,0.0807584,"\int \frac{x^2 \left(c+d x^3\right)^{3/2}}{a+b x^3} \, dx","Int[(x^2*(c + d*x^3)^(3/2))/(a + b*x^3),x]","\frac{2 \sqrt{c+d x^3} (b c-a d)}{3 b^2}-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2}}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b}","\frac{2 \sqrt{c+d x^3} (b c-a d)}{3 b^2}-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2}}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b}",1,"(2*(b*c - a*d)*Sqrt[c + d*x^3])/(3*b^2) + (2*(c + d*x^3)^(3/2))/(9*b) - (2*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(5/2))","A",5,4,24,0.1667,1,"{444, 50, 63, 208}"
371,1,104,0,0.1120714,"\int \frac{\left(c+d x^3\right)^{3/2}}{x \left(a+b x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x*(a + b*x^3)),x]","\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a}+\frac{2 d \sqrt{c+d x^3}}{3 b}","\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a}+\frac{2 d \sqrt{c+d x^3}}{3 b}",1,"(2*d*Sqrt[c + d*x^3])/(3*b) - (2*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a) + (2*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a*b^(3/2))","A",7,5,24,0.2083,1,"{446, 84, 156, 63, 208}"
372,1,116,0,0.1454018,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^4 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^4*(a + b*x^3)),x]","-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b}}+\frac{\sqrt{c} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2}-\frac{c \sqrt{c+d x^3}}{3 a x^3}","-\frac{2 (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b}}+\frac{\sqrt{c} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2}-\frac{c \sqrt{c+d x^3}}{3 a x^3}",1,"-(c*Sqrt[c + d*x^3])/(3*a*x^3) + (Sqrt[c]*(2*b*c - 3*a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2) - (2*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*Sqrt[b])","A",7,5,24,0.2083,1,"{446, 98, 156, 63, 208}"
373,1,65,0,0.0561818,"\int \frac{x^3 \left(c+d x^3\right)^{3/2}}{a+b x^3} \, dx","Int[(x^3*(c + d*x^3)^(3/2))/(a + b*x^3),x]","\frac{c x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};1,-\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a \sqrt{\frac{d x^3}{c}+1}}","\frac{c x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};1,-\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a \sqrt{\frac{d x^3}{c}+1}}",1,"(c*x^4*Sqrt[c + d*x^3]*AppellF1[4/3, 1, -3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
374,1,65,0,0.0399799,"\int \frac{x \left(c+d x^3\right)^{3/2}}{a+b x^3} \, dx","Int[(x*(c + d*x^3)^(3/2))/(a + b*x^3),x]","\frac{c x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};1,-\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a \sqrt{\frac{d x^3}{c}+1}}","\frac{c x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};1,-\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a \sqrt{\frac{d x^3}{c}+1}}",1,"(c*x^2*Sqrt[c + d*x^3]*AppellF1[2/3, 1, -3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*Sqrt[1 + (d*x^3)/c])","A",2,2,22,0.09091,1,"{511, 510}"
375,1,60,0,0.0275824,"\int \frac{\left(c+d x^3\right)^{3/2}}{a+b x^3} \, dx","Int[(c + d*x^3)^(3/2)/(a + b*x^3),x]","\frac{c x \sqrt{c+d x^3} F_1\left(\frac{1}{3};1,-\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a \sqrt{\frac{d x^3}{c}+1}}","\frac{c x \sqrt{c+d x^3} F_1\left(\frac{1}{3};1,-\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a \sqrt{\frac{d x^3}{c}+1}}",1,"(c*x*Sqrt[c + d*x^3]*AppellF1[1/3, 1, -3/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*Sqrt[1 + (d*x^3)/c])","A",2,2,21,0.09524,1,"{430, 429}"
376,1,63,0,0.0578695,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^2 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^2*(a + b*x^3)),x]","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{1}{3};1,-\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a x \sqrt{\frac{d x^3}{c}+1}}","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{1}{3};1,-\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a x \sqrt{\frac{d x^3}{c}+1}}",1,"-((c*Sqrt[c + d*x^3]*AppellF1[-1/3, 1, -3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*x*Sqrt[1 + (d*x^3)/c]))","A",2,2,24,0.08333,1,"{511, 510}"
377,1,65,0,0.0577781,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^3 \left(a+b x^3\right)} \, dx","Int[(c + d*x^3)^(3/2)/(x^3*(a + b*x^3)),x]","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{2}{3};1,-\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a x^2 \sqrt{\frac{d x^3}{c}+1}}","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{2}{3};1,-\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a x^2 \sqrt{\frac{d x^3}{c}+1}}",1,"-(c*Sqrt[c + d*x^3]*AppellF1[-2/3, 1, -3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*x^2*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
378,1,104,0,0.1045881,"\int \frac{x^8}{\left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^8/((a + b*x^3)*Sqrt[c + d*x^3]),x]","-\frac{2 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} \sqrt{b c-a d}}-\frac{2 \sqrt{c+d x^3} (a d+b c)}{3 b^2 d^2}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b d^2}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} \sqrt{b c-a d}}-\frac{2 \sqrt{c+d x^3} (a d+b c)}{3 b^2 d^2}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b d^2}",1,"(-2*(b*c + a*d)*Sqrt[c + d*x^3])/(3*b^2*d^2) + (2*(c + d*x^3)^(3/2))/(9*b*d^2) - (2*a^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(5/2)*Sqrt[b*c - a*d])","A",5,4,24,0.1667,1,"{446, 88, 63, 208}"
379,1,74,0,0.0697095,"\int \frac{x^5}{\left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^5/((a + b*x^3)*Sqrt[c + d*x^3]),x]","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} \sqrt{b c-a d}}+\frac{2 \sqrt{c+d x^3}}{3 b d}","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} \sqrt{b c-a d}}+\frac{2 \sqrt{c+d x^3}}{3 b d}",1,"(2*Sqrt[c + d*x^3])/(3*b*d) + (2*a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{446, 80, 63, 208}"
380,1,51,0,0.0495318,"\int \frac{x^2}{\left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^2/((a + b*x^3)*Sqrt[c + d*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} \sqrt{b c-a d}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} \sqrt{b c-a d}}",1,"(-2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*Sqrt[b]*Sqrt[b*c - a*d])","A",3,3,24,0.1250,1,"{444, 63, 208}"
381,1,85,0,0.0758255,"\int \frac{1}{x \left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x*(a + b*x^3)*Sqrt[c + d*x^3]),x]","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a \sqrt{b c-a d}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a \sqrt{c}}","\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a \sqrt{b c-a d}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a \sqrt{c}}",1,"(-2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a*Sqrt[c]) + (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a*Sqrt[b*c - a*d])","A",6,4,24,0.1667,1,"{446, 86, 63, 208}"
382,1,117,0,0.1181765,"\int \frac{1}{x^4 \left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^4*(a + b*x^3)*Sqrt[c + d*x^3]),x]","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 c^{3/2}}-\frac{\sqrt{c+d x^3}}{3 a c x^3}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 c^{3/2}}-\frac{\sqrt{c+d x^3}}{3 a c x^3}",1,"-Sqrt[c + d*x^3]/(3*a*c*x^3) + ((2*b*c + a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2*c^(3/2)) - (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
383,1,64,0,0.0512265,"\int \frac{x^3}{\left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[x^3/((a + b*x^3)*Sqrt[c + d*x^3]),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 1, 1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
384,1,64,0,0.0370371,"\int \frac{x}{\left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[x/((a + b*x^3)*Sqrt[c + d*x^3]),x]","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a \sqrt{c+d x^3}}","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a \sqrt{c+d x^3}}",1,"(x^2*Sqrt[1 + (d*x^3)/c]*AppellF1[2/3, 1, 1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*Sqrt[c + d*x^3])","A",2,2,22,0.09091,1,"{511, 510}"
385,1,59,0,0.0263589,"\int \frac{1}{\left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/((a + b*x^3)*Sqrt[c + d*x^3]),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 1, 1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*Sqrt[c + d*x^3])","A",2,2,21,0.09524,1,"{430, 429}"
386,1,62,0,0.0534893,"\int \frac{1}{x^2 \left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^2*(a + b*x^3)*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a x \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a x \sqrt{c+d x^3}}",1,"-((Sqrt[1 + (d*x^3)/c]*AppellF1[-1/3, 1, 1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*x*Sqrt[c + d*x^3]))","A",2,2,24,0.08333,1,"{511, 510}"
387,1,64,0,0.0526242,"\int \frac{1}{x^3 \left(a+b x^3\right) \sqrt{c+d x^3}} \, dx","Int[1/(x^3*(a + b*x^3)*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 1, 1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*x^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
388,1,107,0,0.120525,"\int \frac{x^8}{\left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^8/((a + b*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{2 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} (b c-a d)^{3/2}}+\frac{2 c^2}{3 d^2 \sqrt{c+d x^3} (b c-a d)}+\frac{2 \sqrt{c+d x^3}}{3 b d^2}","-\frac{2 a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} (b c-a d)^{3/2}}+\frac{2 c^2}{3 d^2 \sqrt{c+d x^3} (b c-a d)}+\frac{2 \sqrt{c+d x^3}}{3 b d^2}",1,"(2*c^2)/(3*d^2*(b*c - a*d)*Sqrt[c + d*x^3]) + (2*Sqrt[c + d*x^3])/(3*b*d^2) - (2*a^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(3/2)*(b*c - a*d)^(3/2))","A",5,4,24,0.1667,1,"{446, 87, 63, 208}"
389,1,82,0,0.0736587,"\int \frac{x^5}{\left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^5/((a + b*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} (b c-a d)^{3/2}}-\frac{2 c}{3 d \sqrt{c+d x^3} (b c-a d)}","\frac{2 a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} (b c-a d)^{3/2}}-\frac{2 c}{3 d \sqrt{c+d x^3} (b c-a d)}",1,"(-2*c)/(3*d*(b*c - a*d)*Sqrt[c + d*x^3]) + (2*a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
390,1,77,0,0.0660656,"\int \frac{x^2}{\left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^2/((a + b*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2}{3 \sqrt{c+d x^3} (b c-a d)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 (b c-a d)^{3/2}}","\frac{2}{3 \sqrt{c+d x^3} (b c-a d)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 (b c-a d)^{3/2}}",1,"2/(3*(b*c - a*d)*Sqrt[c + d*x^3]) - (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{444, 51, 63, 208}"
391,1,114,0,0.1126874,"\int \frac{1}{x \left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^3)*(c + d*x^3)^(3/2)),x]","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a (b c-a d)^{3/2}}-\frac{2 d}{3 c \sqrt{c+d x^3} (b c-a d)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a c^{3/2}}","\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a (b c-a d)^{3/2}}-\frac{2 d}{3 c \sqrt{c+d x^3} (b c-a d)}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a c^{3/2}}",1,"(-2*d)/(3*c*(b*c - a*d)*Sqrt[c + d*x^3]) - (2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a*c^(3/2)) + (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 85, 156, 63, 208}"
392,1,158,0,0.2223245,"\int \frac{1}{x^4 \left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 (b c-a d)^{3/2}}+\frac{(3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 c^{5/2}}-\frac{d (b c-3 a d)}{3 a c^2 \sqrt{c+d x^3} (b c-a d)}-\frac{1}{3 a c x^3 \sqrt{c+d x^3}}","-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 (b c-a d)^{3/2}}+\frac{(3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 c^{5/2}}-\frac{d (b c-3 a d)}{3 a c^2 \sqrt{c+d x^3} (b c-a d)}-\frac{1}{3 a c x^3 \sqrt{c+d x^3}}",1,"-(d*(b*c - 3*a*d))/(3*a*c^2*(b*c - a*d)*Sqrt[c + d*x^3]) - 1/(3*a*c*x^3*Sqrt[c + d*x^3]) + ((2*b*c + 3*a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2*c^(5/2)) - (2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 152, 156, 63, 208}"
393,1,67,0,0.0570646,"\int \frac{x^3}{\left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x^3/((a + b*x^3)*(c + d*x^3)^(3/2)),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a c \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};1,\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a c \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 1, 3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a*c*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
394,1,67,0,0.0412375,"\int \frac{x}{\left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[x/((a + b*x^3)*(c + d*x^3)^(3/2)),x]","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};1,\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a c \sqrt{c+d x^3}}","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};1,\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a c \sqrt{c+d x^3}}",1,"(x^2*Sqrt[1 + (d*x^3)/c]*AppellF1[2/3, 1, 3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*c*Sqrt[c + d*x^3])","A",2,2,22,0.09091,1,"{511, 510}"
395,1,62,0,0.0288594,"\int \frac{1}{\left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/((a + b*x^3)*(c + d*x^3)^(3/2)),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};1,\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 1, 3/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*c*Sqrt[c + d*x^3])","A",2,2,21,0.09524,1,"{430, 429}"
396,1,65,0,0.0589631,"\int \frac{1}{x^2 \left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};1,\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c x \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};1,\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c x \sqrt{c+d x^3}}",1,"-((Sqrt[1 + (d*x^3)/c]*AppellF1[-1/3, 1, 3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*c*x*Sqrt[c + d*x^3]))","A",2,2,24,0.08333,1,"{511, 510}"
397,1,67,0,0.0572465,"\int \frac{1}{x^3 \left(a+b x^3\right) \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^3)*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a c x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};1,\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a c x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 1, 3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*c*x^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
398,1,117,0,0.0935964,"\int \frac{x^{11} \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^11*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","-\frac{3968 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^4}+\frac{7 x^6 \sqrt{c+d x^3}}{15 d^2}+\frac{2 c \sqrt{c+d x^3} \left(1146 c+47 d x^3\right)}{15 d^4}+\frac{x^9 \sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}","-\frac{3968 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^4}+\frac{7 x^6 \sqrt{c+d x^3}}{15 d^2}+\frac{2 c \sqrt{c+d x^3} \left(1146 c+47 d x^3\right)}{15 d^4}+\frac{x^9 \sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}",1,"(7*x^6*Sqrt[c + d*x^3])/(15*d^2) + (x^9*Sqrt[c + d*x^3])/(3*d*(8*c - d*x^3)) + (2*c*Sqrt[c + d*x^3]*(1146*c + 47*d*x^3))/(15*d^4) - (3968*c^(5/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^4)","A",6,6,27,0.2222,1,"{446, 97, 153, 147, 63, 206}"
399,1,102,0,0.0758963,"\int \frac{x^8 \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^8*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","-\frac{352 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^3}+\frac{64 c \left(c+d x^3\right)^{3/2}}{27 d^3 \left(8 c-d x^3\right)}+\frac{352 c \sqrt{c+d x^3}}{27 d^3}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^3}","-\frac{352 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^3}+\frac{64 c \left(c+d x^3\right)^{3/2}}{27 d^3 \left(8 c-d x^3\right)}+\frac{352 c \sqrt{c+d x^3}}{27 d^3}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 d^3}",1,"(352*c*Sqrt[c + d*x^3])/(27*d^3) + (2*(c + d*x^3)^(3/2))/(9*d^3) + (64*c*(c + d*x^3)^(3/2))/(27*d^3*(8*c - d*x^3)) - (352*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^3)","A",6,6,27,0.2222,1,"{446, 89, 80, 50, 63, 206}"
400,1,82,0,0.0585338,"\int \frac{x^5 \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^5*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","\frac{8 \left(c+d x^3\right)^{3/2}}{27 d^2 \left(8 c-d x^3\right)}+\frac{26 \sqrt{c+d x^3}}{27 d^2}-\frac{26 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^2}","\frac{8 \left(c+d x^3\right)^{3/2}}{27 d^2 \left(8 c-d x^3\right)}+\frac{26 \sqrt{c+d x^3}}{27 d^2}-\frac{26 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^2}",1,"(26*Sqrt[c + d*x^3])/(27*d^2) + (8*(c + d*x^3)^(3/2))/(27*d^2*(8*c - d*x^3)) - (26*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^2)","A",5,5,27,0.1852,1,"{446, 78, 50, 63, 206}"
401,1,64,0,0.0493253,"\int \frac{x^2 \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^2*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","\frac{\sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 \sqrt{c} d}","\frac{\sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 \sqrt{c} d}",1,"Sqrt[c + d*x^3]/(3*d*(8*c - d*x^3)) - ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(9*Sqrt[c]*d)","A",4,4,27,0.1481,1,"{444, 47, 63, 206}"
402,1,88,0,0.0723515,"\int \frac{\sqrt{c+d x^3}}{x \left(8 c-d x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x*(8*c - d*x^3)^2),x]","\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{288 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{3/2}}+\frac{\sqrt{c+d x^3}}{24 c \left(8 c-d x^3\right)}","\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{288 c^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{3/2}}+\frac{\sqrt{c+d x^3}}{24 c \left(8 c-d x^3\right)}",1,"Sqrt[c + d*x^3]/(24*c*(8*c - d*x^3)) + (5*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(288*c^(3/2)) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(96*c^(3/2))","A",7,6,27,0.2222,1,"{446, 99, 156, 63, 208, 206}"
403,1,124,0,0.1016209,"\int \frac{\sqrt{c+d x^3}}{x^4 \left(8 c-d x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^4*(8*c - d*x^3)^2),x]","\frac{d \sqrt{c+d x^3}}{96 c^2 \left(8 c-d x^3\right)}+\frac{7 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1152 c^{5/2}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{128 c^{5/2}}-\frac{\sqrt{c+d x^3}}{24 c x^3 \left(8 c-d x^3\right)}","\frac{d \sqrt{c+d x^3}}{96 c^2 \left(8 c-d x^3\right)}+\frac{7 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1152 c^{5/2}}-\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{128 c^{5/2}}-\frac{\sqrt{c+d x^3}}{24 c x^3 \left(8 c-d x^3\right)}",1,"(d*Sqrt[c + d*x^3])/(96*c^2*(8*c - d*x^3)) - Sqrt[c + d*x^3]/(24*c*x^3*(8*c - d*x^3)) + (7*d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1152*c^(5/2)) - (d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(128*c^(5/2))","A",8,7,27,0.2593,1,"{446, 99, 151, 156, 63, 208, 206}"
404,1,164,0,0.1313358,"\int \frac{\sqrt{c+d x^3}}{x^7 \left(8 c-d x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^7*(8*c - d*x^3)^2),x]","\frac{5 d^2 \sqrt{c+d x^3}}{1536 c^3 \left(8 c-d x^3\right)}+\frac{23 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{18432 c^{7/2}}-\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{2048 c^{7/2}}-\frac{7 d \sqrt{c+d x^3}}{384 c^2 x^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{48 c x^6 \left(8 c-d x^3\right)}","\frac{5 d^2 \sqrt{c+d x^3}}{1536 c^3 \left(8 c-d x^3\right)}+\frac{23 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{18432 c^{7/2}}-\frac{d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{2048 c^{7/2}}-\frac{7 d \sqrt{c+d x^3}}{384 c^2 x^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{48 c x^6 \left(8 c-d x^3\right)}",1,"(5*d^2*Sqrt[c + d*x^3])/(1536*c^3*(8*c - d*x^3)) - Sqrt[c + d*x^3]/(48*c*x^6*(8*c - d*x^3)) - (7*d*Sqrt[c + d*x^3])/(384*c^2*x^3*(8*c - d*x^3)) + (23*d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(18432*c^(7/2)) - (d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(2048*c^(7/2))","A",9,7,27,0.2593,1,"{446, 99, 151, 156, 63, 208, 206}"
405,1,663,0,0.8513781,"\int \frac{x^7 \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^7*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","\frac{76 c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{8/3}}-\frac{76 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{8/3}}+\frac{76 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{8/3}}+\frac{746 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{373 \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{13 x^2 \sqrt{c+d x^3}}{21 d^2}+\frac{746 c \sqrt{c+d x^3}}{21 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^5 \sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}","\frac{76 c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{8/3}}-\frac{76 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{8/3}}+\frac{76 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{8/3}}+\frac{746 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{21 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{373 \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7\ 3^{3/4} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{13 x^2 \sqrt{c+d x^3}}{21 d^2}+\frac{746 c \sqrt{c+d x^3}}{21 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^5 \sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}",1,"(13*x^2*Sqrt[c + d*x^3])/(21*d^2) + (746*c*Sqrt[c + d*x^3])/(21*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^5*Sqrt[c + d*x^3])/(3*d*(8*c - d*x^3)) + (76*c^(7/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3*Sqrt[3]*d^(8/3)) - (76*c^(7/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(9*d^(8/3)) + (76*c^(7/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^(8/3)) - (373*Sqrt[2 - Sqrt[3]]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(3/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (746*Sqrt[2]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(21*3^(1/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{467, 582, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
406,1,641,0,0.7310076,"\int \frac{x^4 \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^4*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","\frac{7 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{7 \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{7 \sqrt{c+d x^3}}{3 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{5 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{5/3}}-\frac{5 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{5/3}}+\frac{5 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{5/3}}+\frac{x^2 \sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}","\frac{7 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{7 \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2\ 3^{3/4} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{7 \sqrt{c+d x^3}}{3 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{5 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3 \sqrt{3} d^{5/3}}-\frac{5 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9 d^{5/3}}+\frac{5 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9 d^{5/3}}+\frac{x^2 \sqrt{c+d x^3}}{3 d \left(8 c-d x^3\right)}",1,"(7*Sqrt[c + d*x^3])/(3*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^2*Sqrt[c + d*x^3])/(3*d*(8*c - d*x^3)) + (5*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3*Sqrt[3]*d^(5/3)) - (5*c^(1/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(9*d^(5/3)) + (5*c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9*d^(5/3)) - (7*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(2*3^(3/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (7*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{467, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
407,1,644,0,0.7234174,"\int \frac{x \sqrt{c+d x^3}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x*Sqrt[c + d*x^3])/(8*c - d*x^3)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{48 \sqrt{3} c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{144 c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{144 c^{5/6} d^{2/3}}+\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} c^{2/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} c^{2/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt{c+d x^3}}{24 c d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^2 \sqrt{c+d x^3}}{24 c \left(8 c-d x^3\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{48 \sqrt{3} c^{5/6} d^{2/3}}-\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{144 c^{5/6} d^{2/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{144 c^{5/6} d^{2/3}}+\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} c^{2/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16\ 3^{3/4} c^{2/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt{c+d x^3}}{24 c d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^2 \sqrt{c+d x^3}}{24 c \left(8 c-d x^3\right)}",1,"Sqrt[c + d*x^3]/(24*c*d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^2*Sqrt[c + d*x^3])/(24*c*(8*c - d*x^3)) + ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]]/(48*Sqrt[3]*c^(5/6)*d^(2/3)) - ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])]/(144*c^(5/6)*d^(2/3)) + ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(144*c^(5/6)*d^(2/3)) - (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*3^(3/4)*c^(2/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + ((c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(12*Sqrt[2]*3^(1/4)*c^(2/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,25,0.4800,1,"{469, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
408,1,665,0,0.8241198,"\int \frac{\sqrt{c+d x^3}}{x^2 \left(8 c-d x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^2*(8*c - d*x^3)^2),x]","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{24 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32\ 3^{3/4} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{48 c^2 x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{48 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{48 \sqrt{3} c^{11/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{144 c^{11/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{144 c^{11/6}}+\frac{\sqrt{c+d x^3}}{24 c x \left(8 c-d x^3\right)}","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{24 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32\ 3^{3/4} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{48 c^2 x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{48 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{48 \sqrt{3} c^{11/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{144 c^{11/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{144 c^{11/6}}+\frac{\sqrt{c+d x^3}}{24 c x \left(8 c-d x^3\right)}",1,"-Sqrt[c + d*x^3]/(48*c^2*x) + (d^(1/3)*Sqrt[c + d*x^3])/(48*c^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + Sqrt[c + d*x^3]/(24*c*x*(8*c - d*x^3)) - (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(48*Sqrt[3]*c^(11/6)) + (d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(144*c^(11/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(144*c^(11/6)) - (Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(32*3^(3/4)*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(24*Sqrt[2]*3^(1/4)*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{469, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
409,1,687,0,0.9441787,"\int \frac{\sqrt{c+d x^3}}{x^5 \left(8 c-d x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^5*(8*c - d*x^3)^2),x]","\frac{d^{4/3} \sqrt{c+d x^3}}{96 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{17 d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3072 \sqrt{3} c^{17/6}}+\frac{17 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9216 c^{17/6}}-\frac{17 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9216 c^{17/6}}+\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{48 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{64\ 3^{3/4} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{d \sqrt{c+d x^3}}{96 c^3 x}-\frac{7 \sqrt{c+d x^3}}{768 c^2 x^4}+\frac{\sqrt{c+d x^3}}{24 c x^4 \left(8 c-d x^3\right)}","\frac{d^{4/3} \sqrt{c+d x^3}}{96 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{17 d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{3072 \sqrt{3} c^{17/6}}+\frac{17 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{9216 c^{17/6}}-\frac{17 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{9216 c^{17/6}}+\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{48 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{64\ 3^{3/4} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{d \sqrt{c+d x^3}}{96 c^3 x}-\frac{7 \sqrt{c+d x^3}}{768 c^2 x^4}+\frac{\sqrt{c+d x^3}}{24 c x^4 \left(8 c-d x^3\right)}",1,"(-7*Sqrt[c + d*x^3])/(768*c^2*x^4) - (d*Sqrt[c + d*x^3])/(96*c^3*x) + (d^(4/3)*Sqrt[c + d*x^3])/(96*c^3*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + Sqrt[c + d*x^3]/(24*c*x^4*(8*c - d*x^3)) - (17*d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(3072*Sqrt[3]*c^(17/6)) + (17*d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(9216*c^(17/6)) - (17*d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(9216*c^(17/6)) - (Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(64*3^(3/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(48*Sqrt[2]*3^(1/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{469, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
410,1,711,0,1.0714755,"\int \frac{\sqrt{c+d x^3}}{x^8 \left(8 c-d x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^8*(8*c - d*x^3)^2),x]","\frac{d^{7/3} \sqrt{c+d x^3}}{5376 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{d^2 \sqrt{c+d x^3}}{5376 c^4 x}-\frac{13 d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{12288 \sqrt{3} c^{23/6}}+\frac{13 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{36864 c^{23/6}}-\frac{13 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{36864 c^{23/6}}+\frac{d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2688 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{3584\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{53 d \sqrt{c+d x^3}}{21504 c^3 x^4}-\frac{5 \sqrt{c+d x^3}}{672 c^2 x^7}+\frac{\sqrt{c+d x^3}}{24 c x^7 \left(8 c-d x^3\right)}","\frac{d^{7/3} \sqrt{c+d x^3}}{5376 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{d^2 \sqrt{c+d x^3}}{5376 c^4 x}-\frac{13 d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{12288 \sqrt{3} c^{23/6}}+\frac{13 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{36864 c^{23/6}}-\frac{13 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{36864 c^{23/6}}+\frac{d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{2688 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{3584\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{53 d \sqrt{c+d x^3}}{21504 c^3 x^4}-\frac{5 \sqrt{c+d x^3}}{672 c^2 x^7}+\frac{\sqrt{c+d x^3}}{24 c x^7 \left(8 c-d x^3\right)}",1,"(-5*Sqrt[c + d*x^3])/(672*c^2*x^7) - (53*d*Sqrt[c + d*x^3])/(21504*c^3*x^4) - (d^2*Sqrt[c + d*x^3])/(5376*c^4*x) + (d^(7/3)*Sqrt[c + d*x^3])/(5376*c^4*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + Sqrt[c + d*x^3]/(24*c*x^7*(8*c - d*x^3)) - (13*d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(12288*Sqrt[3]*c^(23/6)) + (13*d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(36864*c^(23/6)) - (13*d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(36864*c^(23/6)) - (Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3584*3^(3/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(2688*Sqrt[2]*3^(1/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",17,13,27,0.4815,1,"{469, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
411,1,134,0,0.110103,"\int \frac{x^{11} \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^11*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","\frac{1664 c^3 \sqrt{c+d x^3}}{d^4}-\frac{4992 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^4}+\frac{3 x^6 \left(c+d x^3\right)^{3/2}}{7 d^2}+\frac{2 c \left(c+d x^3\right)^{3/2} \left(694 c+51 d x^3\right)}{21 d^4}+\frac{x^9 \left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}","\frac{1664 c^3 \sqrt{c+d x^3}}{d^4}-\frac{4992 c^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^4}+\frac{3 x^6 \left(c+d x^3\right)^{3/2}}{7 d^2}+\frac{2 c \left(c+d x^3\right)^{3/2} \left(694 c+51 d x^3\right)}{21 d^4}+\frac{x^9 \left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}",1,"(1664*c^3*Sqrt[c + d*x^3])/d^4 + (3*x^6*(c + d*x^3)^(3/2))/(7*d^2) + (x^9*(c + d*x^3)^(3/2))/(3*d*(8*c - d*x^3)) + (2*c*(c + d*x^3)^(3/2)*(694*c + 51*d*x^3))/(21*d^4) - (4992*c^(7/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^4","A",7,7,27,0.2593,1,"{446, 97, 153, 147, 50, 63, 206}"
412,1,119,0,0.0936134,"\int \frac{x^8 \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^8*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","\frac{160 c^2 \sqrt{c+d x^3}}{d^3}-\frac{480 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^3}+\frac{64 c \left(c+d x^3\right)^{5/2}}{27 d^3 \left(8 c-d x^3\right)}+\frac{160 c \left(c+d x^3\right)^{3/2}}{27 d^3}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^3}","\frac{160 c^2 \sqrt{c+d x^3}}{d^3}-\frac{480 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^3}+\frac{64 c \left(c+d x^3\right)^{5/2}}{27 d^3 \left(8 c-d x^3\right)}+\frac{160 c \left(c+d x^3\right)^{3/2}}{27 d^3}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 d^3}",1,"(160*c^2*Sqrt[c + d*x^3])/d^3 + (160*c*(c + d*x^3)^(3/2))/(27*d^3) + (2*(c + d*x^3)^(5/2))/(15*d^3) + (64*c*(c + d*x^3)^(5/2))/(27*d^3*(8*c - d*x^3)) - (480*c^(5/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^3","A",7,6,27,0.2222,1,"{446, 89, 80, 50, 63, 206}"
413,1,97,0,0.0748169,"\int \frac{x^5 \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^5*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","-\frac{42 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^2}+\frac{8 \left(c+d x^3\right)^{5/2}}{27 d^2 \left(8 c-d x^3\right)}+\frac{14 \left(c+d x^3\right)^{3/2}}{27 d^2}+\frac{14 c \sqrt{c+d x^3}}{d^2}","-\frac{42 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^2}+\frac{8 \left(c+d x^3\right)^{5/2}}{27 d^2 \left(8 c-d x^3\right)}+\frac{14 \left(c+d x^3\right)^{3/2}}{27 d^2}+\frac{14 c \sqrt{c+d x^3}}{d^2}",1,"(14*c*Sqrt[c + d*x^3])/d^2 + (14*(c + d*x^3)^(3/2))/(27*d^2) + (8*(c + d*x^3)^(5/2))/(27*d^2*(8*c - d*x^3)) - (42*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^2","A",6,5,27,0.1852,1,"{446, 78, 50, 63, 206}"
414,1,77,0,0.0600984,"\int \frac{x^2 \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^2*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","\frac{\left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}+\frac{\sqrt{c+d x^3}}{d}-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d}","\frac{\left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}+\frac{\sqrt{c+d x^3}}{d}-\frac{3 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d}",1,"Sqrt[c + d*x^3]/d + (c + d*x^3)^(3/2)/(3*d*(8*c - d*x^3)) - (3*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d","A",5,5,27,0.1852,1,"{444, 47, 50, 63, 206}"
415,1,85,0,0.0790129,"\int \frac{\left(c+d x^3\right)^{3/2}}{x \left(8 c-d x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x*(8*c - d*x^3)^2),x]","\frac{3 \sqrt{c+d x^3}}{8 \left(8 c-d x^3\right)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{32 \sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 \sqrt{c}}","\frac{3 \sqrt{c+d x^3}}{8 \left(8 c-d x^3\right)}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{32 \sqrt{c}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 \sqrt{c}}",1,"(3*Sqrt[c + d*x^3])/(8*(8*c - d*x^3)) - (3*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(32*Sqrt[c]) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(96*Sqrt[c])","A",7,6,27,0.2222,1,"{446, 98, 156, 63, 208, 206}"
416,1,121,0,0.1034577,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^4 \left(8 c-d x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^4*(8*c - d*x^3)^2),x]","\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{128 c^{3/2}}-\frac{7 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{384 c^{3/2}}+\frac{5 d \sqrt{c+d x^3}}{96 c \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{24 x^3 \left(8 c-d x^3\right)}","\frac{3 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{128 c^{3/2}}-\frac{7 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{384 c^{3/2}}+\frac{5 d \sqrt{c+d x^3}}{96 c \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{24 x^3 \left(8 c-d x^3\right)}",1,"(5*d*Sqrt[c + d*x^3])/(96*c*(8*c - d*x^3)) - Sqrt[c + d*x^3]/(24*x^3*(8*c - d*x^3)) + (3*d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(128*c^(3/2)) - (7*d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(384*c^(3/2))","A",8,7,27,0.2593,1,"{446, 98, 151, 156, 63, 208, 206}"
417,1,161,0,0.1334085,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^7 \left(8 c-d x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^7*(8*c - d*x^3)^2),x]","\frac{7 d^2 \sqrt{c+d x^3}}{512 c^2 \left(8 c-d x^3\right)}+\frac{15 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2048 c^{5/2}}-\frac{17 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{2048 c^{5/2}}-\frac{23 d \sqrt{c+d x^3}}{384 c x^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{48 x^6 \left(8 c-d x^3\right)}","\frac{7 d^2 \sqrt{c+d x^3}}{512 c^2 \left(8 c-d x^3\right)}+\frac{15 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2048 c^{5/2}}-\frac{17 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{2048 c^{5/2}}-\frac{23 d \sqrt{c+d x^3}}{384 c x^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{48 x^6 \left(8 c-d x^3\right)}",1,"(7*d^2*Sqrt[c + d*x^3])/(512*c^2*(8*c - d*x^3)) - Sqrt[c + d*x^3]/(48*x^6*(8*c - d*x^3)) - (23*d*Sqrt[c + d*x^3])/(384*c*x^3*(8*c - d*x^3)) + (15*d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(2048*c^(5/2)) - (17*d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(2048*c^(5/2))","A",9,7,27,0.2593,1,"{446, 98, 151, 156, 63, 208, 206}"
418,1,681,0,0.9390138,"\int \frac{x^7 \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^7*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","\frac{5906 c^2 \sqrt{c+d x^3}}{13 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{108 \sqrt{3} c^{13/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{8/3}}-\frac{108 c^{13/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{8/3}}+\frac{108 c^{13/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{8/3}}+\frac{5906 \sqrt{2} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2953 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{13 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{103 c x^2 \sqrt{c+d x^3}}{13 d^2}+\frac{x^5 \left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}+\frac{19 x^5 \sqrt{c+d x^3}}{39 d}","\frac{5906 c^2 \sqrt{c+d x^3}}{13 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{108 \sqrt{3} c^{13/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{8/3}}-\frac{108 c^{13/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{8/3}}+\frac{108 c^{13/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{8/3}}+\frac{5906 \sqrt{2} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{13 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{2953 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{13 d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{103 c x^2 \sqrt{c+d x^3}}{13 d^2}+\frac{x^5 \left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}+\frac{19 x^5 \sqrt{c+d x^3}}{39 d}",1,"(103*c*x^2*Sqrt[c + d*x^3])/(13*d^2) + (19*x^5*Sqrt[c + d*x^3])/(39*d) + (5906*c^2*Sqrt[c + d*x^3])/(13*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^5*(c + d*x^3)^(3/2))/(3*d*(8*c - d*x^3)) + (108*Sqrt[3]*c^(13/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(8/3) - (108*c^(13/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/d^(8/3) + (108*c^(13/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^(8/3) - (2953*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(13*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (5906*Sqrt[2]*c^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(13*3^(1/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,14,27,0.5185,1,"{467, 581, 582, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
419,1,657,0,0.8053188,"\int \frac{x^4 \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x^4*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","\frac{9 \sqrt{3} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}-\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{5/3}}+\frac{265 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{265 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{14 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{265 c \sqrt{c+d x^3}}{7 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^2 \left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}+\frac{13 x^2 \sqrt{c+d x^3}}{21 d}","\frac{9 \sqrt{3} c^{7/6} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{d^{5/3}}-\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{d^{5/3}}+\frac{9 c^{7/6} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{d^{5/3}}+\frac{265 \sqrt{2} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt[4]{3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{265 \sqrt[4]{3} \sqrt{2-\sqrt{3}} c^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{14 d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{265 c \sqrt{c+d x^3}}{7 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^2 \left(c+d x^3\right)^{3/2}}{3 d \left(8 c-d x^3\right)}+\frac{13 x^2 \sqrt{c+d x^3}}{21 d}",1,"(13*x^2*Sqrt[c + d*x^3])/(21*d) + (265*c*Sqrt[c + d*x^3])/(7*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^2*(c + d*x^3)^(3/2))/(3*d*(8*c - d*x^3)) + (9*Sqrt[3]*c^(7/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/d^(5/3) - (9*c^(7/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/d^(5/3) + (9*c^(7/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/d^(5/3) - (265*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(14*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (265*Sqrt[2]*c^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(7*3^(1/4)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{467, 581, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
420,1,638,0,0.7181715,"\int \frac{x \left(c+d x^3\right)^{3/2}}{\left(8 c-d x^3\right)^2} \, dx","Int[(x*(c + d*x^3)^(3/2))/(8*c - d*x^3)^2,x]","\frac{19 \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{19 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{19 \sqrt{c+d x^3}}{8 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{9 \sqrt{3} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{16 d^{2/3}}-\frac{9 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{16 d^{2/3}}+\frac{9 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{16 d^{2/3}}+\frac{3 x^2 \sqrt{c+d x^3}}{8 \left(8 c-d x^3\right)}","\frac{19 \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{19 \sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{19 \sqrt{c+d x^3}}{8 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{9 \sqrt{3} \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{16 d^{2/3}}-\frac{9 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{16 d^{2/3}}+\frac{9 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{16 d^{2/3}}+\frac{3 x^2 \sqrt{c+d x^3}}{8 \left(8 c-d x^3\right)}",1,"(19*Sqrt[c + d*x^3])/(8*d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (3*x^2*Sqrt[c + d*x^3])/(8*(8*c - d*x^3)) + (9*Sqrt[3]*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(16*d^(2/3)) - (9*c^(1/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(16*d^(2/3)) + (9*c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(16*d^(2/3)) - (19*3^(1/4)*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (19*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,25,0.4800,1,"{468, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
421,1,522,0,0.2560638,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^2 \left(8 c-d x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^2*(8*c - d*x^3)^2),x]","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} \sqrt[4]{3} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{16 c x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{16 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{3 \sqrt{c+d x^3}}{8 x \left(8 c-d x^3\right)}","\frac{\sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{8 \sqrt{2} \sqrt[4]{3} c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32 c^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{c+d x^3}}{16 c x}+\frac{\sqrt[3]{d} \sqrt{c+d x^3}}{16 c \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{3 \sqrt{c+d x^3}}{8 x \left(8 c-d x^3\right)}",1,"-Sqrt[c + d*x^3]/(16*c*x) + (d^(1/3)*Sqrt[c + d*x^3])/(16*c*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (3*Sqrt[c + d*x^3])/(8*x*(8*c - d*x^3)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(32*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(8*Sqrt[2]*3^(1/4)*c^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",6,6,27,0.2222,1,"{468, 21, 325, 303, 218, 1877}"
422,1,684,0,0.9404063,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^5 \left(8 c-d x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^5*(8*c - d*x^3)^2),x]","\frac{d^{4/3} \sqrt{c+d x^3}}{32 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{9 \sqrt{3} d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1024 c^{11/6}}+\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1024 c^{11/6}}-\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1024 c^{11/6}}+\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{64 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{d \sqrt{c+d x^3}}{32 c^2 x}+\frac{3 \sqrt{c+d x^3}}{8 x^4 \left(8 c-d x^3\right)}-\frac{13 \sqrt{c+d x^3}}{256 c x^4}","\frac{d^{4/3} \sqrt{c+d x^3}}{32 c^2 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{9 \sqrt{3} d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1024 c^{11/6}}+\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1024 c^{11/6}}-\frac{9 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1024 c^{11/6}}+\frac{d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{16 \sqrt{2} \sqrt[4]{3} c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{64 c^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{d \sqrt{c+d x^3}}{32 c^2 x}+\frac{3 \sqrt{c+d x^3}}{8 x^4 \left(8 c-d x^3\right)}-\frac{13 \sqrt{c+d x^3}}{256 c x^4}",1,"(-13*Sqrt[c + d*x^3])/(256*c*x^4) - (d*Sqrt[c + d*x^3])/(32*c^2*x) + (d^(4/3)*Sqrt[c + d*x^3])/(32*c^2*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (3*Sqrt[c + d*x^3])/(8*x^4*(8*c - d*x^3)) - (9*Sqrt[3]*d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(1024*c^(11/6)) + (9*d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(1024*c^(11/6)) - (9*d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1024*c^(11/6)) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(64*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(16*Sqrt[2]*3^(1/4)*c^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{468, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
423,1,708,0,1.0756475,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^8 \left(8 c-d x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^8*(8*c - d*x^3)^2),x]","\frac{19 d^{7/3} \sqrt{c+d x^3}}{1792 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{19 d^2 \sqrt{c+d x^3}}{1792 c^3 x}-\frac{9 \sqrt{3} d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{4096 c^{17/6}}+\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{4096 c^{17/6}}-\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{4096 c^{17/6}}+\frac{19 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{896 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{19 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{3584 c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{83 d \sqrt{c+d x^3}}{7168 c^2 x^4}+\frac{3 \sqrt{c+d x^3}}{8 x^7 \left(8 c-d x^3\right)}-\frac{11 \sqrt{c+d x^3}}{224 c x^7}","\frac{19 d^{7/3} \sqrt{c+d x^3}}{1792 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{19 d^2 \sqrt{c+d x^3}}{1792 c^3 x}-\frac{9 \sqrt{3} d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{4096 c^{17/6}}+\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{4096 c^{17/6}}-\frac{9 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{4096 c^{17/6}}+\frac{19 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{896 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{19 \sqrt[4]{3} \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{3584 c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{83 d \sqrt{c+d x^3}}{7168 c^2 x^4}+\frac{3 \sqrt{c+d x^3}}{8 x^7 \left(8 c-d x^3\right)}-\frac{11 \sqrt{c+d x^3}}{224 c x^7}",1,"(-11*Sqrt[c + d*x^3])/(224*c*x^7) - (83*d*Sqrt[c + d*x^3])/(7168*c^2*x^4) - (19*d^2*Sqrt[c + d*x^3])/(1792*c^3*x) + (19*d^(7/3)*Sqrt[c + d*x^3])/(1792*c^3*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (3*Sqrt[c + d*x^3])/(8*x^7*(8*c - d*x^3)) - (9*Sqrt[3]*d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(4096*c^(17/6)) + (9*d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(4096*c^(17/6)) - (9*d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(4096*c^(17/6)) - (19*3^(1/4)*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(3584*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (19*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(896*Sqrt[2]*3^(1/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",17,13,27,0.4815,1,"{468, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
424,1,95,0,0.0727786,"\int \frac{x^{11}}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^11/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{2944 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^4}+\frac{8 x^6 \sqrt{c+d x^3}}{27 d^2 \left(8 c-d x^3\right)}+\frac{2 \sqrt{c+d x^3} \left(170 c+7 d x^3\right)}{27 d^4}","-\frac{2944 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^4}+\frac{8 x^6 \sqrt{c+d x^3}}{27 d^2 \left(8 c-d x^3\right)}+\frac{2 \sqrt{c+d x^3} \left(170 c+7 d x^3\right)}{27 d^4}",1,"(8*x^6*Sqrt[c + d*x^3])/(27*d^2*(8*c - d*x^3)) + (2*Sqrt[c + d*x^3]*(170*c + 7*d*x^3))/(27*d^4) - (2944*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*d^4)","A",5,5,27,0.1852,1,"{446, 98, 147, 63, 206}"
425,1,83,0,0.0636044,"\int \frac{x^8}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^8/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{64 c \sqrt{c+d x^3}}{27 d^3 \left(8 c-d x^3\right)}+\frac{2 \sqrt{c+d x^3}}{3 d^3}-\frac{224 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^3}","\frac{64 c \sqrt{c+d x^3}}{27 d^3 \left(8 c-d x^3\right)}+\frac{2 \sqrt{c+d x^3}}{3 d^3}-\frac{224 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^3}",1,"(2*Sqrt[c + d*x^3])/(3*d^3) + (64*c*Sqrt[c + d*x^3])/(27*d^3*(8*c - d*x^3)) - (224*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*d^3)","A",5,5,27,0.1852,1,"{446, 89, 80, 63, 206}"
426,1,64,0,0.0506441,"\int \frac{x^5}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^5/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{8 \sqrt{c+d x^3}}{27 d^2 \left(8 c-d x^3\right)}-\frac{10 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 \sqrt{c} d^2}","\frac{8 \sqrt{c+d x^3}}{27 d^2 \left(8 c-d x^3\right)}-\frac{10 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 \sqrt{c} d^2}",1,"(8*Sqrt[c + d*x^3])/(27*d^2*(8*c - d*x^3)) - (10*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*Sqrt[c]*d^2)","A",4,4,27,0.1481,1,"{446, 78, 63, 206}"
427,1,67,0,0.0493981,"\int \frac{x^2}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^2/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{3/2} d}+\frac{\sqrt{c+d x^3}}{27 c d \left(8 c-d x^3\right)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{3/2} d}+\frac{\sqrt{c+d x^3}}{27 c d \left(8 c-d x^3\right)}",1,"Sqrt[c + d*x^3]/(27*c*d*(8*c - d*x^3)) + ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(81*c^(3/2)*d)","A",4,4,27,0.1481,1,"{444, 51, 63, 206}"
428,1,88,0,0.075345,"\int \frac{1}{x \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{\sqrt{c+d x^3}}{216 c^2 \left(8 c-d x^3\right)}+\frac{13 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2592 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{5/2}}","\frac{\sqrt{c+d x^3}}{216 c^2 \left(8 c-d x^3\right)}+\frac{13 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{2592 c^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{5/2}}",1,"Sqrt[c + d*x^3]/(216*c^2*(8*c - d*x^3)) + (13*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(2592*c^(5/2)) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(96*c^(5/2))","A",7,6,27,0.2222,1,"{446, 103, 156, 63, 208, 206}"
429,1,124,0,0.1012502,"\int \frac{1}{x^4 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^4*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{5 d \sqrt{c+d x^3}}{864 c^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{24 c^2 x^3 \left(8 c-d x^3\right)}+\frac{11 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{10368 c^{7/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{384 c^{7/2}}","\frac{5 d \sqrt{c+d x^3}}{864 c^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{24 c^2 x^3 \left(8 c-d x^3\right)}+\frac{11 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{10368 c^{7/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{384 c^{7/2}}",1,"(5*d*Sqrt[c + d*x^3])/(864*c^3*(8*c - d*x^3)) - Sqrt[c + d*x^3]/(24*c^2*x^3*(8*c - d*x^3)) + (11*d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(10368*c^(7/2)) + (d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(384*c^(7/2))","A",8,7,27,0.2593,1,"{446, 103, 151, 156, 63, 208, 206}"
430,1,164,0,0.1287091,"\int \frac{1}{x^7 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^7*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{35 d^2 \sqrt{c+d x^3}}{13824 c^4 \left(8 c-d x^3\right)}+\frac{31 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{165888 c^{9/2}}-\frac{19 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{6144 c^{9/2}}+\frac{3 d \sqrt{c+d x^3}}{128 c^3 x^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{48 c^2 x^6 \left(8 c-d x^3\right)}","-\frac{35 d^2 \sqrt{c+d x^3}}{13824 c^4 \left(8 c-d x^3\right)}+\frac{31 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{165888 c^{9/2}}-\frac{19 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{6144 c^{9/2}}+\frac{3 d \sqrt{c+d x^3}}{128 c^3 x^3 \left(8 c-d x^3\right)}-\frac{\sqrt{c+d x^3}}{48 c^2 x^6 \left(8 c-d x^3\right)}",1,"(-35*d^2*Sqrt[c + d*x^3])/(13824*c^4*(8*c - d*x^3)) - Sqrt[c + d*x^3]/(48*c^2*x^6*(8*c - d*x^3)) + (3*d*Sqrt[c + d*x^3])/(128*c^3*x^3*(8*c - d*x^3)) + (31*d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(165888*c^(9/2)) - (19*d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(6144*c^(9/2))","A",9,7,27,0.2593,1,"{446, 103, 151, 156, 63, 208, 206}"
431,1,641,0,0.7114938,"\int \frac{x^7}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^7/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{62 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{31 \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{8 x^2 \sqrt{c+d x^3}}{27 d^2 \left(8 c-d x^3\right)}+\frac{62 \sqrt{c+d x^3}}{27 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{44 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} d^{8/3}}-\frac{44 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 d^{8/3}}+\frac{44 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^{8/3}}","\frac{62 \sqrt{2} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{31 \sqrt{2-\sqrt{3}} \sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{8 x^2 \sqrt{c+d x^3}}{27 d^2 \left(8 c-d x^3\right)}+\frac{62 \sqrt{c+d x^3}}{27 d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{44 \sqrt[6]{c} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} d^{8/3}}-\frac{44 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 d^{8/3}}+\frac{44 \sqrt[6]{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 d^{8/3}}",1,"(62*Sqrt[c + d*x^3])/(27*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (8*x^2*Sqrt[c + d*x^3])/(27*d^2*(8*c - d*x^3)) + (44*c^(1/6)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(27*Sqrt[3]*d^(8/3)) - (44*c^(1/6)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(81*d^(8/3)) + (44*c^(1/6)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(81*d^(8/3)) - (31*Sqrt[2 - Sqrt[3]]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (62*Sqrt[2]*c^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{470, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
432,1,647,0,0.7145846,"\int \frac{x^4}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^4/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} c^{5/6} d^{5/3}}-\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 c^{5/6} d^{5/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{5/6} d^{5/3}}+\frac{\sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{18\ 3^{3/4} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt{c+d x^3}}{27 c d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^2 \sqrt{c+d x^3}}{27 c d \left(8 c-d x^3\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27 \sqrt{3} c^{5/6} d^{5/3}}-\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{81 c^{5/6} d^{5/3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{81 c^{5/6} d^{5/3}}+\frac{\sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{18\ 3^{3/4} c^{2/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{\sqrt{c+d x^3}}{27 c d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{x^2 \sqrt{c+d x^3}}{27 c d \left(8 c-d x^3\right)}",1,"Sqrt[c + d*x^3]/(27*c*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^2*Sqrt[c + d*x^3])/(27*c*d*(8*c - d*x^3)) + ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]]/(27*Sqrt[3]*c^(5/6)*d^(5/3)) - ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])]/(81*c^(5/6)*d^(5/3)) + ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(81*c^(5/6)*d^(5/3)) - (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(18*3^(3/4)*c^(2/3)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (Sqrt[2]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*c^(2/3)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,27,0.4444,1,"{471, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
433,1,644,0,0.6991683,"\int \frac{x}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{\sqrt{c+d x^3}}{216 c^2 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{432 \sqrt{3} c^{11/6} d^{2/3}}+\frac{7 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1296 c^{11/6} d^{2/3}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1296 c^{11/6} d^{2/3}}+\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{144\ 3^{3/4} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{x^2 \sqrt{c+d x^3}}{216 c^2 \left(8 c-d x^3\right)}","\frac{\sqrt{c+d x^3}}{216 c^2 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{432 \sqrt{3} c^{11/6} d^{2/3}}+\frac{7 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{1296 c^{11/6} d^{2/3}}-\frac{7 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{1296 c^{11/6} d^{2/3}}+\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{108 \sqrt{2} \sqrt[4]{3} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{144\ 3^{3/4} c^{5/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{x^2 \sqrt{c+d x^3}}{216 c^2 \left(8 c-d x^3\right)}",1,"Sqrt[c + d*x^3]/(216*c^2*d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (x^2*Sqrt[c + d*x^3])/(216*c^2*(8*c - d*x^3)) - (7*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(432*Sqrt[3]*c^(11/6)*d^(2/3)) + (7*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(1296*c^(11/6)*d^(2/3)) - (7*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(1296*c^(11/6)*d^(2/3)) - (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(144*3^(3/4)*c^(5/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + ((c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(108*Sqrt[2]*3^(1/4)*c^(5/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",14,12,25,0.4800,1,"{472, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
434,1,665,0,0.8283961,"\int \frac{1}{x^2 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^2*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{7 \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{216 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{7 \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{288\ 3^{3/4} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{7 \sqrt{c+d x^3}}{432 c^3 x}+\frac{7 \sqrt[3]{d} \sqrt{c+d x^3}}{432 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{\sqrt{c+d x^3}}{216 c^2 x \left(8 c-d x^3\right)}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{216 \sqrt{3} c^{17/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{648 c^{17/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{648 c^{17/6}}","\frac{7 \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{216 \sqrt{2} \sqrt[4]{3} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{7 \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{288\ 3^{3/4} c^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{7 \sqrt{c+d x^3}}{432 c^3 x}+\frac{7 \sqrt[3]{d} \sqrt{c+d x^3}}{432 c^3 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{\sqrt{c+d x^3}}{216 c^2 x \left(8 c-d x^3\right)}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{216 \sqrt{3} c^{17/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{648 c^{17/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{648 c^{17/6}}",1,"(-7*Sqrt[c + d*x^3])/(432*c^3*x) + (7*d^(1/3)*Sqrt[c + d*x^3])/(432*c^3*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + Sqrt[c + d*x^3]/(216*c^2*x*(8*c - d*x^3)) - (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(216*Sqrt[3]*c^(17/6)) + (d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(648*c^(17/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(648*c^(17/6)) - (7*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(288*3^(3/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (7*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(216*Sqrt[2]*3^(1/4)*c^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{472, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
435,1,687,0,0.9272767,"\int \frac{1}{x^5 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^5*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{5 d^{4/3} \sqrt{c+d x^3}}{864 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{25 d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27648 \sqrt{3} c^{23/6}}+\frac{25 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{82944 c^{23/6}}-\frac{25 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{82944 c^{23/6}}-\frac{5 d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{432 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{5 \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{576\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{5 d \sqrt{c+d x^3}}{864 c^4 x}+\frac{\sqrt{c+d x^3}}{216 c^2 x^4 \left(8 c-d x^3\right)}-\frac{31 \sqrt{c+d x^3}}{6912 c^3 x^4}","-\frac{5 d^{4/3} \sqrt{c+d x^3}}{864 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{25 d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{27648 \sqrt{3} c^{23/6}}+\frac{25 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{82944 c^{23/6}}-\frac{25 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{82944 c^{23/6}}-\frac{5 d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{432 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{5 \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{576\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{5 d \sqrt{c+d x^3}}{864 c^4 x}+\frac{\sqrt{c+d x^3}}{216 c^2 x^4 \left(8 c-d x^3\right)}-\frac{31 \sqrt{c+d x^3}}{6912 c^3 x^4}",1,"(-31*Sqrt[c + d*x^3])/(6912*c^3*x^4) + (5*d*Sqrt[c + d*x^3])/(864*c^4*x) - (5*d^(4/3)*Sqrt[c + d*x^3])/(864*c^4*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + Sqrt[c + d*x^3]/(216*c^2*x^4*(8*c - d*x^3)) - (25*d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(27648*Sqrt[3]*c^(23/6)) + (25*d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(82944*c^(23/6)) - (25*d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(82944*c^(23/6)) + (5*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(576*3^(3/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (5*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(432*Sqrt[2]*3^(1/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,13,27,0.4815,1,"{472, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
436,1,711,0,1.043717,"\int \frac{1}{x^8 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^8*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{289 d^{7/3} \sqrt{c+d x^3}}{48384 c^5 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{289 d^2 \sqrt{c+d x^3}}{48384 c^5 x}-\frac{17 d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{110592 \sqrt{3} c^{29/6}}+\frac{17 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{331776 c^{29/6}}-\frac{17 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{331776 c^{29/6}}+\frac{289 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{24192 \sqrt{2} \sqrt[4]{3} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{289 \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32256\ 3^{3/4} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{391 d \sqrt{c+d x^3}}{193536 c^4 x^4}+\frac{\sqrt{c+d x^3}}{216 c^2 x^7 \left(8 c-d x^3\right)}-\frac{17 \sqrt{c+d x^3}}{6048 c^3 x^7}","\frac{289 d^{7/3} \sqrt{c+d x^3}}{48384 c^5 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{289 d^2 \sqrt{c+d x^3}}{48384 c^5 x}-\frac{17 d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{110592 \sqrt{3} c^{29/6}}+\frac{17 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{331776 c^{29/6}}-\frac{17 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{331776 c^{29/6}}+\frac{289 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{24192 \sqrt{2} \sqrt[4]{3} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{289 \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{32256\ 3^{3/4} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{391 d \sqrt{c+d x^3}}{193536 c^4 x^4}+\frac{\sqrt{c+d x^3}}{216 c^2 x^7 \left(8 c-d x^3\right)}-\frac{17 \sqrt{c+d x^3}}{6048 c^3 x^7}",1,"(-17*Sqrt[c + d*x^3])/(6048*c^3*x^7) + (391*d*Sqrt[c + d*x^3])/(193536*c^4*x^4) - (289*d^2*Sqrt[c + d*x^3])/(48384*c^5*x) + (289*d^(7/3)*Sqrt[c + d*x^3])/(48384*c^5*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + Sqrt[c + d*x^3]/(216*c^2*x^7*(8*c - d*x^3)) - (17*d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(110592*Sqrt[3]*c^(29/6)) + (17*d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(331776*c^(29/6)) - (17*d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(331776*c^(29/6)) - (289*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(32256*3^(3/4)*c^(14/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (289*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(24192*Sqrt[2]*3^(1/4)*c^(14/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",17,13,27,0.4815,1,"{472, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
437,1,66,0,0.0544029,"\int \frac{x^6}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^6/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{x^7 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{7}{3};2,\frac{1}{2};\frac{10}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{448 c^2 \sqrt{c+d x^3}}","\frac{x^7 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{7}{3};2,\frac{1}{2};\frac{10}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{448 c^2 \sqrt{c+d x^3}}",1,"(x^7*Sqrt[1 + (d*x^3)/c]*AppellF1[7/3, 2, 1/2, 10/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(448*c^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
438,1,66,0,0.0549255,"\int \frac{x^3}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^3/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{1}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{256 c^2 \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{1}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{256 c^2 \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 2, 1/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(256*c^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
439,1,64,0,0.0283876,"\int \frac{1}{\left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/((8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{1}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{64 c^2 \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{1}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{64 c^2 \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 2, 1/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(64*c^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{430, 429}"
440,1,66,0,0.0551217,"\int \frac{1}{x^3 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^3*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{1}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{128 c^2 x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{1}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{128 c^2 x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 2, 1/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(128*c^2*x^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
441,1,66,0,0.0564458,"\int \frac{1}{x^6 \left(8 c-d x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^6*(8*c - d*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};2,\frac{1}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{320 c^2 x^5 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};2,\frac{1}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{320 c^2 x^5 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-5/3, 2, 1/2, -2/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(320*c^2*x^5*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
442,1,95,0,0.0757577,"\int \frac{x^{11}}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^11/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{8 x^6}{27 d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{2 \left(38 c+39 d x^3\right)}{81 d^4 \sqrt{c+d x^3}}-\frac{640 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 d^4}","\frac{8 x^6}{27 d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{2 \left(38 c+39 d x^3\right)}{81 d^4 \sqrt{c+d x^3}}-\frac{640 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 d^4}",1,"(8*x^6)/(27*d^2*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (2*(38*c + 39*d*x^3))/(81*d^4*Sqrt[c + d*x^3]) - (640*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(243*d^4)","A",5,5,27,0.1852,1,"{446, 98, 146, 63, 206}"
443,1,83,0,0.0651967,"\int \frac{x^8}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^8/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{64 c}{27 d^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{22}{81 d^3 \sqrt{c+d x^3}}-\frac{32 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 \sqrt{c} d^3}","\frac{64 c}{27 d^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{22}{81 d^3 \sqrt{c+d x^3}}-\frac{32 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 \sqrt{c} d^3}",1,"-22/(81*d^3*Sqrt[c + d*x^3]) + (64*c)/(27*d^3*(8*c - d*x^3)*Sqrt[c + d*x^3]) - (32*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(243*Sqrt[c]*d^3)","A",5,5,27,0.1852,1,"{446, 89, 78, 63, 206}"
444,1,85,0,0.0622635,"\int \frac{x^5}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^5/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{3/2} d^2}+\frac{8}{27 d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{2}{81 c d^2 \sqrt{c+d x^3}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{3/2} d^2}+\frac{8}{27 d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{2}{81 c d^2 \sqrt{c+d x^3}}",1,"-2/(81*c*d^2*Sqrt[c + d*x^3]) + 8/(27*d^2*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(243*c^(3/2)*d^2)","A",5,5,27,0.1852,1,"{446, 78, 51, 63, 206}"
445,1,88,0,0.0638284,"\int \frac{x^2}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^2/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{1}{81 c^2 d \sqrt{c+d x^3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{5/2} d}+\frac{1}{27 c d \left(8 c-d x^3\right) \sqrt{c+d x^3}}","-\frac{1}{81 c^2 d \sqrt{c+d x^3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{5/2} d}+\frac{1}{27 c d \left(8 c-d x^3\right) \sqrt{c+d x^3}}",1,"-1/(81*c^2*d*Sqrt[c + d*x^3]) + 1/(27*c*d*(8*c - d*x^3)*Sqrt[c + d*x^3]) + ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(243*c^(5/2)*d)","A",5,4,27,0.1481,1,"{444, 51, 63, 206}"
446,1,106,0,0.0949663,"\int \frac{1}{x \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{1}{216 c^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5}{648 c^3 \sqrt{c+d x^3}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{7776 c^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{7/2}}","\frac{1}{216 c^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5}{648 c^3 \sqrt{c+d x^3}}+\frac{7 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{7776 c^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{96 c^{7/2}}",1,"5/(648*c^3*Sqrt[c + d*x^3]) + 1/(216*c^2*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (7*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(7776*c^(7/2)) - ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]]/(96*c^(7/2))","A",8,7,27,0.2593,1,"{446, 103, 152, 156, 63, 208, 206}"
447,1,143,0,0.1248149,"\int \frac{1}{x^4 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^4*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{5 d}{864 c^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{35 d}{2592 c^4 \sqrt{c+d x^3}}-\frac{1}{24 c^2 x^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{31104 c^{9/2}}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{384 c^{9/2}}","\frac{5 d}{864 c^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{35 d}{2592 c^4 \sqrt{c+d x^3}}-\frac{1}{24 c^2 x^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{31104 c^{9/2}}+\frac{5 d \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{384 c^{9/2}}",1,"(-35*d)/(2592*c^4*Sqrt[c + d*x^3]) + (5*d)/(864*c^3*(8*c - d*x^3)*Sqrt[c + d*x^3]) - 1/(24*c^2*x^3*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (5*d*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(31104*c^(9/2)) + (5*d*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(384*c^(9/2))","A",9,8,27,0.2963,1,"{446, 103, 151, 152, 156, 63, 208, 206}"
448,1,185,0,0.162809,"\int \frac{1}{x^7 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^7*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{71 d^2}{13824 c^4 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{665 d^2}{41472 c^5 \sqrt{c+d x^3}}+\frac{13 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{497664 c^{11/2}}-\frac{33 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{2048 c^{11/2}}+\frac{17 d}{384 c^3 x^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{1}{48 c^2 x^6 \left(8 c-d x^3\right) \sqrt{c+d x^3}}","-\frac{71 d^2}{13824 c^4 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{665 d^2}{41472 c^5 \sqrt{c+d x^3}}+\frac{13 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{497664 c^{11/2}}-\frac{33 d^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{2048 c^{11/2}}+\frac{17 d}{384 c^3 x^3 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{1}{48 c^2 x^6 \left(8 c-d x^3\right) \sqrt{c+d x^3}}",1,"(665*d^2)/(41472*c^5*Sqrt[c + d*x^3]) - (71*d^2)/(13824*c^4*(8*c - d*x^3)*Sqrt[c + d*x^3]) - 1/(48*c^2*x^6*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (17*d)/(384*c^3*x^3*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (13*d^2*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(497664*c^(11/2)) - (33*d^2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(2048*c^(11/2))","A",10,8,27,0.2963,1,"{446, 103, 151, 152, 156, 63, 208, 206}"
449,1,668,0,0.801042,"\int \frac{x^7}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^7/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{81 \sqrt{3} c^{5/6} d^{8/3}}-\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{243 c^{5/6} d^{8/3}}+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{5/6} d^{8/3}}+\frac{2 \sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{81 \sqrt[4]{3} c^{2/3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27\ 3^{3/4} c^{2/3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{8 x^2}{27 d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{2 x^2}{81 c d^2 \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{81 c d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}","\frac{4 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{81 \sqrt{3} c^{5/6} d^{8/3}}-\frac{4 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{243 c^{5/6} d^{8/3}}+\frac{4 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{5/6} d^{8/3}}+\frac{2 \sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{81 \sqrt[4]{3} c^{2/3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{27\ 3^{3/4} c^{2/3} d^{8/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{8 x^2}{27 d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{2 x^2}{81 c d^2 \sqrt{c+d x^3}}+\frac{2 \sqrt{c+d x^3}}{81 c d^{8/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}",1,"(-2*x^2)/(81*c*d^2*Sqrt[c + d*x^3]) + (8*x^2)/(27*d^2*(8*c - d*x^3)*Sqrt[c + d*x^3]) + (2*Sqrt[c + d*x^3])/(81*c*d^(8/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) + (4*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(81*Sqrt[3]*c^(5/6)*d^(8/3)) - (4*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(243*c^(5/6)*d^(8/3)) + (4*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(243*c^(5/6)*d^(8/3)) - (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(27*3^(3/4)*c^(2/3)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (2*Sqrt[2]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(81*3^(1/4)*c^(2/3)*d^(8/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{470, 579, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
450,1,671,0,0.8004034,"\int \frac{x^4}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^4/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{\sqrt{c+d x^3}}{81 c^2 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{81 \sqrt{3} c^{11/6} d^{5/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{243 c^{11/6} d^{5/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{11/6} d^{5/3}}+\frac{\sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{81 \sqrt[4]{3} c^{5/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{54\ 3^{3/4} c^{5/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{x^2}{81 c^2 d \sqrt{c+d x^3}}+\frac{x^2}{27 c d \left(8 c-d x^3\right) \sqrt{c+d x^3}}","\frac{\sqrt{c+d x^3}}{81 c^2 d^{5/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{81 \sqrt{3} c^{11/6} d^{5/3}}+\frac{\tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{243 c^{11/6} d^{5/3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{243 c^{11/6} d^{5/3}}+\frac{\sqrt{2} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{81 \sqrt[4]{3} c^{5/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{\sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{54\ 3^{3/4} c^{5/3} d^{5/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{x^2}{81 c^2 d \sqrt{c+d x^3}}+\frac{x^2}{27 c d \left(8 c-d x^3\right) \sqrt{c+d x^3}}",1,"-x^2/(81*c^2*d*Sqrt[c + d*x^3]) + x^2/(27*c*d*(8*c - d*x^3)*Sqrt[c + d*x^3]) + Sqrt[c + d*x^3]/(81*c^2*d^(5/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]]/(81*Sqrt[3]*c^(11/6)*d^(5/3)) + ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])]/(243*c^(11/6)*d^(5/3)) - ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])]/(243*c^(11/6)*d^(5/3)) - (Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(54*3^(3/4)*c^(5/3)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (Sqrt[2]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(81*3^(1/4)*c^(5/3)*d^(5/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,27,0.4815,1,"{471, 579, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
451,1,665,0,0.7986922,"\int \frac{x}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{5 \sqrt{c+d x^3}}{648 c^3 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1296 \sqrt{3} c^{17/6} d^{2/3}}+\frac{5 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{3888 c^{17/6} d^{2/3}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{3888 c^{17/6} d^{2/3}}-\frac{5 \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{324 \sqrt{2} \sqrt[4]{3} c^{8/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{5 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{432\ 3^{3/4} c^{8/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{x^2}{216 c^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5 x^2}{648 c^3 \sqrt{c+d x^3}}","-\frac{5 \sqrt{c+d x^3}}{648 c^3 d^{2/3} \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{5 \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1296 \sqrt{3} c^{17/6} d^{2/3}}+\frac{5 \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{3888 c^{17/6} d^{2/3}}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{3888 c^{17/6} d^{2/3}}-\frac{5 \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{324 \sqrt{2} \sqrt[4]{3} c^{8/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{5 \sqrt{2-\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{432\ 3^{3/4} c^{8/3} d^{2/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{x^2}{216 c^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5 x^2}{648 c^3 \sqrt{c+d x^3}}",1,"(5*x^2)/(648*c^3*Sqrt[c + d*x^3]) + x^2/(216*c^2*(8*c - d*x^3)*Sqrt[c + d*x^3]) - (5*Sqrt[c + d*x^3])/(648*c^3*d^(2/3)*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (5*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(1296*Sqrt[3]*c^(17/6)*d^(2/3)) + (5*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(3888*c^(17/6)*d^(2/3)) - (5*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(3888*c^(17/6)*d^(2/3)) + (5*Sqrt[2 - Sqrt[3]]*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(432*3^(3/4)*c^(8/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (5*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(324*Sqrt[2]*3^(1/4)*c^(8/3)*d^(2/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",15,13,25,0.5200,1,"{472, 579, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
452,1,686,0,0.9226967,"\int \frac{1}{x^2 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^2*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{31 \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{648 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{31 \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{864\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{31 \sqrt{c+d x^3}}{1296 c^4 x}+\frac{31 \sqrt[3]{d} \sqrt{c+d x^3}}{1296 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{5}{648 c^3 x \sqrt{c+d x^3}}+\frac{1}{216 c^2 x \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1296 \sqrt{3} c^{23/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{3888 c^{23/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{3888 c^{23/6}}","\frac{31 \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{648 \sqrt{2} \sqrt[4]{3} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{31 \sqrt{2-\sqrt{3}} \sqrt[3]{d} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{864\ 3^{3/4} c^{11/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{31 \sqrt{c+d x^3}}{1296 c^4 x}+\frac{31 \sqrt[3]{d} \sqrt{c+d x^3}}{1296 c^4 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}+\frac{5}{648 c^3 x \sqrt{c+d x^3}}+\frac{1}{216 c^2 x \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{1296 \sqrt{3} c^{23/6}}+\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{3888 c^{23/6}}-\frac{\sqrt[3]{d} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{3888 c^{23/6}}",1,"5/(648*c^3*x*Sqrt[c + d*x^3]) + 1/(216*c^2*x*(8*c - d*x^3)*Sqrt[c + d*x^3]) - (31*Sqrt[c + d*x^3])/(1296*c^4*x) + (31*d^(1/3)*Sqrt[c + d*x^3])/(1296*c^4*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (d^(1/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(1296*Sqrt[3]*c^(23/6)) + (d^(1/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(3888*c^(23/6)) - (d^(1/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(3888*c^(23/6)) - (31*Sqrt[2 - Sqrt[3]]*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(864*3^(3/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (31*d^(1/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(648*Sqrt[2]*3^(1/4)*c^(11/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",16,14,27,0.5185,1,"{472, 579, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
453,1,708,0,1.0315424,"\int \frac{1}{x^5 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^5*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{77 d^{4/3} \sqrt{c+d x^3}}{2592 c^5 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{11 d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{82944 \sqrt{3} c^{29/6}}+\frac{11 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{248832 c^{29/6}}-\frac{11 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{248832 c^{29/6}}-\frac{77 d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1296 \sqrt{2} \sqrt[4]{3} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{77 \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1728\ 3^{3/4} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{77 d \sqrt{c+d x^3}}{2592 c^5 x}-\frac{253 \sqrt{c+d x^3}}{20736 c^4 x^4}+\frac{1}{216 c^2 x^4 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5}{648 c^3 x^4 \sqrt{c+d x^3}}","-\frac{77 d^{4/3} \sqrt{c+d x^3}}{2592 c^5 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{11 d^{4/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{82944 \sqrt{3} c^{29/6}}+\frac{11 d^{4/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{248832 c^{29/6}}-\frac{11 d^{4/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{248832 c^{29/6}}-\frac{77 d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1296 \sqrt{2} \sqrt[4]{3} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{77 \sqrt{2-\sqrt{3}} d^{4/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{1728\ 3^{3/4} c^{14/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{77 d \sqrt{c+d x^3}}{2592 c^5 x}-\frac{253 \sqrt{c+d x^3}}{20736 c^4 x^4}+\frac{1}{216 c^2 x^4 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5}{648 c^3 x^4 \sqrt{c+d x^3}}",1,"5/(648*c^3*x^4*Sqrt[c + d*x^3]) + 1/(216*c^2*x^4*(8*c - d*x^3)*Sqrt[c + d*x^3]) - (253*Sqrt[c + d*x^3])/(20736*c^4*x^4) + (77*d*Sqrt[c + d*x^3])/(2592*c^5*x) - (77*d^(4/3)*Sqrt[c + d*x^3])/(2592*c^5*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (11*d^(4/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(82944*Sqrt[3]*c^(29/6)) + (11*d^(4/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(248832*c^(29/6)) - (11*d^(4/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(248832*c^(29/6)) + (77*Sqrt[2 - Sqrt[3]]*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(1728*3^(3/4)*c^(14/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) - (77*d^(4/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(1296*Sqrt[2]*3^(1/4)*c^(14/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",17,14,27,0.5185,1,"{472, 579, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
454,1,732,0,1.1780122,"\int \frac{1}{x^8 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^8*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{5179 d^{7/3} \sqrt{c+d x^3}}{145152 c^6 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{5179 d^2 \sqrt{c+d x^3}}{145152 c^6 x}-\frac{7 d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{331776 \sqrt{3} c^{35/6}}+\frac{7 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{995328 c^{35/6}}-\frac{7 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{995328 c^{35/6}}+\frac{5179 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{72576 \sqrt{2} \sqrt[4]{3} c^{17/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{5179 \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{96768\ 3^{3/4} c^{17/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{8257 d \sqrt{c+d x^3}}{580608 c^5 x^4}-\frac{191 \sqrt{c+d x^3}}{18144 c^4 x^7}+\frac{1}{216 c^2 x^7 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5}{648 c^3 x^7 \sqrt{c+d x^3}}","\frac{5179 d^{7/3} \sqrt{c+d x^3}}{145152 c^6 \left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)}-\frac{5179 d^2 \sqrt{c+d x^3}}{145152 c^6 x}-\frac{7 d^{7/3} \tan ^{-1}\left(\frac{\sqrt{3} \sqrt[6]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\sqrt{c+d x^3}}\right)}{331776 \sqrt{3} c^{35/6}}+\frac{7 d^{7/3} \tanh ^{-1}\left(\frac{\left(\sqrt[3]{c}+\sqrt[3]{d} x\right)^2}{3 \sqrt[6]{c} \sqrt{c+d x^3}}\right)}{995328 c^{35/6}}-\frac{7 d^{7/3} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{3 \sqrt{c}}\right)}{995328 c^{35/6}}+\frac{5179 d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{72576 \sqrt{2} \sqrt[4]{3} c^{17/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}-\frac{5179 \sqrt{2-\sqrt{3}} d^{7/3} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} E\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{96768\ 3^{3/4} c^{17/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}+\frac{8257 d \sqrt{c+d x^3}}{580608 c^5 x^4}-\frac{191 \sqrt{c+d x^3}}{18144 c^4 x^7}+\frac{1}{216 c^2 x^7 \left(8 c-d x^3\right) \sqrt{c+d x^3}}+\frac{5}{648 c^3 x^7 \sqrt{c+d x^3}}",1,"5/(648*c^3*x^7*Sqrt[c + d*x^3]) + 1/(216*c^2*x^7*(8*c - d*x^3)*Sqrt[c + d*x^3]) - (191*Sqrt[c + d*x^3])/(18144*c^4*x^7) + (8257*d*Sqrt[c + d*x^3])/(580608*c^5*x^4) - (5179*d^2*Sqrt[c + d*x^3])/(145152*c^6*x) + (5179*d^(7/3)*Sqrt[c + d*x^3])/(145152*c^6*((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)) - (7*d^(7/3)*ArcTan[(Sqrt[3]*c^(1/6)*(c^(1/3) + d^(1/3)*x))/Sqrt[c + d*x^3]])/(331776*Sqrt[3]*c^(35/6)) + (7*d^(7/3)*ArcTanh[(c^(1/3) + d^(1/3)*x)^2/(3*c^(1/6)*Sqrt[c + d*x^3])])/(995328*c^(35/6)) - (7*d^(7/3)*ArcTanh[Sqrt[c + d*x^3]/(3*Sqrt[c])])/(995328*c^(35/6)) - (5179*Sqrt[2 - Sqrt[3]]*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticE[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(96768*3^(3/4)*c^(17/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3]) + (5179*d^(7/3)*(c^(1/3) + d^(1/3)*x)*Sqrt[(c^(2/3) - c^(1/3)*d^(1/3)*x + d^(2/3)*x^2)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*EllipticF[ArcSin[((1 - Sqrt[3])*c^(1/3) + d^(1/3)*x)/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)], -7 - 4*Sqrt[3]])/(72576*Sqrt[2]*3^(1/4)*c^(17/3)*Sqrt[(c^(1/3)*(c^(1/3) + d^(1/3)*x))/((1 + Sqrt[3])*c^(1/3) + d^(1/3)*x)^2]*Sqrt[c + d*x^3])","A",18,14,27,0.5185,1,"{472, 579, 583, 584, 303, 218, 1877, 486, 444, 63, 206, 2138, 2145, 205}"
455,1,66,0,0.0600647,"\int \frac{x^6}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^6/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{x^7 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{7}{3};2,\frac{3}{2};\frac{10}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{448 c^3 \sqrt{c+d x^3}}","\frac{2 x \left(4 c+d x^3\right)}{81 c d^2 \left(8 c-d x^3\right) \sqrt{c+d x^3}}-\frac{2 \sqrt{2+\sqrt{3}} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right) \sqrt{\frac{c^{2/3}-\sqrt[3]{c} \sqrt[3]{d} x+d^{2/3} x^2}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} F\left(\sin ^{-1}\left(\frac{\sqrt[3]{d} x+\left(1-\sqrt{3}\right) \sqrt[3]{c}}{\sqrt[3]{d} x+\left(1+\sqrt{3}\right) \sqrt[3]{c}}\right)|-7-4 \sqrt{3}\right)}{81 \sqrt[4]{3} c d^{7/3} \sqrt{\frac{\sqrt[3]{c} \left(\sqrt[3]{c}+\sqrt[3]{d} x\right)}{\left(\left(1+\sqrt{3}\right) \sqrt[3]{c}+\sqrt[3]{d} x\right)^2}} \sqrt{c+d x^3}}",1,"(x^7*Sqrt[1 + (d*x^3)/c]*AppellF1[7/3, 2, 3/2, 10/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(448*c^3*Sqrt[c + d*x^3])","C",2,2,27,0.07407,0,"{511, 510}"
456,1,66,0,0.058012,"\int \frac{x^3}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^3/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{3}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{256 c^3 \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{3}{2};\frac{7}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{256 c^3 \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 2, 3/2, 7/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(256*c^3*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
457,1,64,0,0.0294427,"\int \frac{1}{\left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/((8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{3}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{64 c^3 \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{3}{2};\frac{4}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{64 c^3 \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 2, 3/2, 4/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(64*c^3*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{430, 429}"
458,1,66,0,0.0574086,"\int \frac{1}{x^3 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^3*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{3}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{128 c^3 x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{3}{2};\frac{1}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{128 c^3 x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 2, 3/2, 1/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(128*c^3*x^2*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
459,1,66,0,0.0614282,"\int \frac{1}{x^6 \left(8 c-d x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^6*(8*c - d*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};2,\frac{3}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{320 c^3 x^5 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{5}{3};2,\frac{3}{2};-\frac{2}{3};\frac{d x^3}{8 c},-\frac{d x^3}{c}\right)}{320 c^3 x^5 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-5/3, 2, 3/2, -2/3, (d*x^3)/(8*c), -((d*x^3)/c)])/(320*c^3*x^5*Sqrt[c + d*x^3])","A",2,2,27,0.07407,1,"{511, 510}"
460,1,161,0,0.1922064,"\int \frac{x^8 \sqrt{c+d x^3}}{\left(a+b x^3\right)^2} \, dx","Int[(x^8*Sqrt[c + d*x^3])/(a + b*x^3)^2,x]","-\frac{a^2 \left(c+d x^3\right)^{3/2}}{3 b^2 \left(a+b x^3\right) (b c-a d)}-\frac{a \sqrt{c+d x^3} (4 b c-5 a d)}{3 b^3 (b c-a d)}+\frac{a (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2} \sqrt{b c-a d}}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b^2 d}","-\frac{a^2 \left(c+d x^3\right)^{3/2}}{3 b^2 \left(a+b x^3\right) (b c-a d)}-\frac{a \sqrt{c+d x^3} (4 b c-5 a d)}{3 b^3 (b c-a d)}+\frac{a (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2} \sqrt{b c-a d}}+\frac{2 \left(c+d x^3\right)^{3/2}}{9 b^2 d}",1,"-(a*(4*b*c - 5*a*d)*Sqrt[c + d*x^3])/(3*b^3*(b*c - a*d)) + (2*(c + d*x^3)^(3/2))/(9*b^2*d) - (a^2*(c + d*x^3)^(3/2))/(3*b^2*(b*c - a*d)*(a + b*x^3)) + (a*(4*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(7/2)*Sqrt[b*c - a*d])","A",6,6,24,0.2500,1,"{446, 89, 80, 50, 63, 208}"
461,1,136,0,0.1094998,"\int \frac{x^5 \sqrt{c+d x^3}}{\left(a+b x^3\right)^2} \, dx","Int[(x^5*Sqrt[c + d*x^3])/(a + b*x^3)^2,x]","\frac{\sqrt{c+d x^3} (2 b c-3 a d)}{3 b^2 (b c-a d)}-\frac{(2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} \sqrt{b c-a d}}+\frac{a \left(c+d x^3\right)^{3/2}}{3 b \left(a+b x^3\right) (b c-a d)}","\frac{\sqrt{c+d x^3} (2 b c-3 a d)}{3 b^2 (b c-a d)}-\frac{(2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} \sqrt{b c-a d}}+\frac{a \left(c+d x^3\right)^{3/2}}{3 b \left(a+b x^3\right) (b c-a d)}",1,"((2*b*c - 3*a*d)*Sqrt[c + d*x^3])/(3*b^2*(b*c - a*d)) + (a*(c + d*x^3)^(3/2))/(3*b*(b*c - a*d)*(a + b*x^3)) - ((2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(5/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
462,1,80,0,0.0651737,"\int \frac{x^2 \sqrt{c+d x^3}}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*Sqrt[c + d*x^3])/(a + b*x^3)^2,x]","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^3}}{3 b \left(a+b x^3\right)}","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^3}}{3 b \left(a+b x^3\right)}",1,"-Sqrt[c + d*x^3]/(3*b*(a + b*x^3)) - (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{444, 47, 63, 208}"
463,1,121,0,0.1178711,"\int \frac{\sqrt{c+d x^3}}{x \left(a+b x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x*(a + b*x^3)^2),x]","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b} \sqrt{b c-a d}}-\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2}+\frac{\sqrt{c+d x^3}}{3 a \left(a+b x^3\right)}","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b} \sqrt{b c-a d}}-\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2}+\frac{\sqrt{c+d x^3}}{3 a \left(a+b x^3\right)}",1,"Sqrt[c + d*x^3]/(3*a*(a + b*x^3)) - (2*Sqrt[c]*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2) + ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*Sqrt[b]*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 99, 156, 63, 208}"
464,1,161,0,0.2178794,"\int \frac{\sqrt{c+d x^3}}{x^4 \left(a+b x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^4*(a + b*x^3)^2),x]","-\frac{2 b \sqrt{c+d x^3}}{3 a^2 \left(a+b x^3\right)}-\frac{\sqrt{b} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 \sqrt{b c-a d}}+\frac{(4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3 \sqrt{c}}-\frac{\sqrt{c+d x^3}}{3 a x^3 \left(a+b x^3\right)}","-\frac{2 b \sqrt{c+d x^3}}{3 a^2 \left(a+b x^3\right)}-\frac{\sqrt{b} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 \sqrt{b c-a d}}+\frac{(4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3 \sqrt{c}}-\frac{\sqrt{c+d x^3}}{3 a x^3 \left(a+b x^3\right)}",1,"(-2*b*Sqrt[c + d*x^3])/(3*a^2*(a + b*x^3)) - Sqrt[c + d*x^3]/(3*a*x^3*(a + b*x^3)) + ((4*b*c - a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^3*Sqrt[c]) - (Sqrt[b]*(4*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^3*Sqrt[b*c - a*d])","A",8,6,24,0.2500,1,"{446, 99, 151, 156, 63, 208}"
465,1,64,0,0.0513995,"\int \frac{x^3 \sqrt{c+d x^3}}{\left(a+b x^3\right)^2} \, dx","Int[(x^3*Sqrt[c + d*x^3])/(a + b*x^3)^2,x]","\frac{x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};2,-\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 \sqrt{\frac{d x^3}{c}+1}}","\frac{x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};2,-\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 \sqrt{\frac{d x^3}{c}+1}}",1,"(x^4*Sqrt[c + d*x^3]*AppellF1[4/3, 2, -1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a^2*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
466,1,64,0,0.0407256,"\int \frac{x \sqrt{c+d x^3}}{\left(a+b x^3\right)^2} \, dx","Int[(x*Sqrt[c + d*x^3])/(a + b*x^3)^2,x]","\frac{x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};2,-\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 \sqrt{\frac{d x^3}{c}+1}}","\frac{x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};2,-\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 \sqrt{\frac{d x^3}{c}+1}}",1,"(x^2*Sqrt[c + d*x^3]*AppellF1[2/3, 2, -1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*Sqrt[1 + (d*x^3)/c])","A",2,2,22,0.09091,1,"{511, 510}"
467,1,59,0,0.0271805,"\int \frac{\sqrt{c+d x^3}}{\left(a+b x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(a + b*x^3)^2,x]","\frac{x \sqrt{c+d x^3} F_1\left(\frac{1}{3};2,-\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 \sqrt{\frac{d x^3}{c}+1}}","\frac{x \sqrt{c+d x^3} F_1\left(\frac{1}{3};2,-\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 \sqrt{\frac{d x^3}{c}+1}}",1,"(x*Sqrt[c + d*x^3]*AppellF1[1/3, 2, -1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*Sqrt[1 + (d*x^3)/c])","A",2,2,21,0.09524,1,"{430, 429}"
468,1,62,0,0.0544932,"\int \frac{\sqrt{c+d x^3}}{x^2 \left(a+b x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^2*(a + b*x^3)^2),x]","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{1}{3};2,-\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 x \sqrt{\frac{d x^3}{c}+1}}","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{1}{3};2,-\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 x \sqrt{\frac{d x^3}{c}+1}}",1,"-((Sqrt[c + d*x^3]*AppellF1[-1/3, 2, -1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*x*Sqrt[1 + (d*x^3)/c]))","A",2,2,24,0.08333,1,"{511, 510}"
469,1,64,0,0.0512235,"\int \frac{\sqrt{c+d x^3}}{x^3 \left(a+b x^3\right)^2} \, dx","Int[Sqrt[c + d*x^3]/(x^3*(a + b*x^3)^2),x]","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{2}{3};2,-\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 x^2 \sqrt{\frac{d x^3}{c}+1}}","-\frac{\sqrt{c+d x^3} F_1\left(-\frac{2}{3};2,-\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 x^2 \sqrt{\frac{d x^3}{c}+1}}",1,"-(Sqrt[c + d*x^3]*AppellF1[-2/3, 2, -1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*x^2*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
470,1,189,0,0.2370067,"\int \frac{x^8 \left(c+d x^3\right)^{3/2}}{\left(a+b x^3\right)^2} \, dx","Int[(x^8*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x]","-\frac{a^2 \left(c+d x^3\right)^{5/2}}{3 b^2 \left(a+b x^3\right) (b c-a d)}-\frac{a \left(c+d x^3\right)^{3/2} (4 b c-7 a d)}{9 b^3 (b c-a d)}-\frac{a \sqrt{c+d x^3} (4 b c-7 a d)}{3 b^4}+\frac{a (4 b c-7 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{9/2}}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 b^2 d}","-\frac{a^2 \left(c+d x^3\right)^{5/2}}{3 b^2 \left(a+b x^3\right) (b c-a d)}-\frac{a \left(c+d x^3\right)^{3/2} (4 b c-7 a d)}{9 b^3 (b c-a d)}-\frac{a \sqrt{c+d x^3} (4 b c-7 a d)}{3 b^4}+\frac{a (4 b c-7 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{9/2}}+\frac{2 \left(c+d x^3\right)^{5/2}}{15 b^2 d}",1,"-(a*(4*b*c - 7*a*d)*Sqrt[c + d*x^3])/(3*b^4) - (a*(4*b*c - 7*a*d)*(c + d*x^3)^(3/2))/(9*b^3*(b*c - a*d)) + (2*(c + d*x^3)^(5/2))/(15*b^2*d) - (a^2*(c + d*x^3)^(5/2))/(3*b^2*(b*c - a*d)*(a + b*x^3)) + (a*(4*b*c - 7*a*d)*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(9/2))","A",7,6,24,0.2500,1,"{446, 89, 80, 50, 63, 208}"
471,1,163,0,0.1368034,"\int \frac{x^5 \left(c+d x^3\right)^{3/2}}{\left(a+b x^3\right)^2} \, dx","Int[(x^5*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x]","\frac{\left(c+d x^3\right)^{3/2} (2 b c-5 a d)}{9 b^2 (b c-a d)}+\frac{\sqrt{c+d x^3} (2 b c-5 a d)}{3 b^3}-\frac{(2 b c-5 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2}}+\frac{a \left(c+d x^3\right)^{5/2}}{3 b \left(a+b x^3\right) (b c-a d)}","\frac{\left(c+d x^3\right)^{3/2} (2 b c-5 a d)}{9 b^2 (b c-a d)}+\frac{\sqrt{c+d x^3} (2 b c-5 a d)}{3 b^3}-\frac{(2 b c-5 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{7/2}}+\frac{a \left(c+d x^3\right)^{5/2}}{3 b \left(a+b x^3\right) (b c-a d)}",1,"((2*b*c - 5*a*d)*Sqrt[c + d*x^3])/(3*b^3) + ((2*b*c - 5*a*d)*(c + d*x^3)^(3/2))/(9*b^2*(b*c - a*d)) + (a*(c + d*x^3)^(5/2))/(3*b*(b*c - a*d)*(a + b*x^3)) - ((2*b*c - 5*a*d)*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(7/2))","A",6,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
472,1,94,0,0.0812484,"\int \frac{x^2 \left(c+d x^3\right)^{3/2}}{\left(a+b x^3\right)^2} \, dx","Int[(x^2*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x]","-\frac{d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{b^{5/2}}-\frac{\left(c+d x^3\right)^{3/2}}{3 b \left(a+b x^3\right)}+\frac{d \sqrt{c+d x^3}}{b^2}","-\frac{d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{b^{5/2}}-\frac{\left(c+d x^3\right)^{3/2}}{3 b \left(a+b x^3\right)}+\frac{d \sqrt{c+d x^3}}{b^2}",1,"(d*Sqrt[c + d*x^3])/b^2 - (c + d*x^3)^(3/2)/(3*b*(a + b*x^3)) - (d*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/b^(5/2)","A",5,5,24,0.2083,1,"{444, 47, 50, 63, 208}"
473,1,131,0,0.1396303,"\int \frac{\left(c+d x^3\right)^{3/2}}{x \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x*(a + b*x^3)^2),x]","\frac{\sqrt{b c-a d} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2}+\frac{\sqrt{c+d x^3} (b c-a d)}{3 a b \left(a+b x^3\right)}","\frac{\sqrt{b c-a d} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 b^{3/2}}-\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2}+\frac{\sqrt{c+d x^3} (b c-a d)}{3 a b \left(a+b x^3\right)}",1,"((b*c - a*d)*Sqrt[c + d*x^3])/(3*a*b*(a + b*x^3)) - (2*c^(3/2)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2) + (Sqrt[b*c - a*d]*(2*b*c + a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*b^(3/2))","A",7,5,24,0.2083,1,"{446, 98, 156, 63, 208}"
474,1,170,0,0.2579464,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^4 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^4*(a + b*x^3)^2),x]","-\frac{\sqrt{c+d x^3} (2 b c-a d)}{3 a^2 \left(a+b x^3\right)}+\frac{\sqrt{c} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3}-\frac{\sqrt{b c-a d} (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 \sqrt{b}}-\frac{c \sqrt{c+d x^3}}{3 a x^3 \left(a+b x^3\right)}","-\frac{\sqrt{c+d x^3} (2 b c-a d)}{3 a^2 \left(a+b x^3\right)}+\frac{\sqrt{c} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3}-\frac{\sqrt{b c-a d} (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 \sqrt{b}}-\frac{c \sqrt{c+d x^3}}{3 a x^3 \left(a+b x^3\right)}",1,"-((2*b*c - a*d)*Sqrt[c + d*x^3])/(3*a^2*(a + b*x^3)) - (c*Sqrt[c + d*x^3])/(3*a*x^3*(a + b*x^3)) + (Sqrt[c]*(4*b*c - 3*a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^3) - (Sqrt[b*c - a*d]*(4*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^3*Sqrt[b])","A",8,6,24,0.2500,1,"{446, 98, 151, 156, 63, 208}"
475,1,65,0,0.056264,"\int \frac{x^3 \left(c+d x^3\right)^{3/2}}{\left(a+b x^3\right)^2} \, dx","Int[(x^3*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x]","\frac{c x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};2,-\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 \sqrt{\frac{d x^3}{c}+1}}","\frac{c x^4 \sqrt{c+d x^3} F_1\left(\frac{4}{3};2,-\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 \sqrt{\frac{d x^3}{c}+1}}",1,"(c*x^4*Sqrt[c + d*x^3]*AppellF1[4/3, 2, -3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a^2*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
476,1,65,0,0.0405539,"\int \frac{x \left(c+d x^3\right)^{3/2}}{\left(a+b x^3\right)^2} \, dx","Int[(x*(c + d*x^3)^(3/2))/(a + b*x^3)^2,x]","\frac{c x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};2,-\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 \sqrt{\frac{d x^3}{c}+1}}","\frac{c x^2 \sqrt{c+d x^3} F_1\left(\frac{2}{3};2,-\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 \sqrt{\frac{d x^3}{c}+1}}",1,"(c*x^2*Sqrt[c + d*x^3]*AppellF1[2/3, 2, -3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*Sqrt[1 + (d*x^3)/c])","A",2,2,22,0.09091,1,"{511, 510}"
477,1,60,0,0.0267157,"\int \frac{\left(c+d x^3\right)^{3/2}}{\left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(a + b*x^3)^2,x]","\frac{c x \sqrt{c+d x^3} F_1\left(\frac{1}{3};2,-\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 \sqrt{\frac{d x^3}{c}+1}}","\frac{c x \sqrt{c+d x^3} F_1\left(\frac{1}{3};2,-\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 \sqrt{\frac{d x^3}{c}+1}}",1,"(c*x*Sqrt[c + d*x^3]*AppellF1[1/3, 2, -3/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*Sqrt[1 + (d*x^3)/c])","A",2,2,21,0.09524,1,"{430, 429}"
478,1,63,0,0.0569014,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^2 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^2*(a + b*x^3)^2),x]","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{1}{3};2,-\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 x \sqrt{\frac{d x^3}{c}+1}}","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{1}{3};2,-\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 x \sqrt{\frac{d x^3}{c}+1}}",1,"-((c*Sqrt[c + d*x^3]*AppellF1[-1/3, 2, -3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*x*Sqrt[1 + (d*x^3)/c]))","A",2,2,24,0.08333,1,"{511, 510}"
479,1,65,0,0.0553509,"\int \frac{\left(c+d x^3\right)^{3/2}}{x^3 \left(a+b x^3\right)^2} \, dx","Int[(c + d*x^3)^(3/2)/(x^3*(a + b*x^3)^2),x]","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{2}{3};2,-\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 x^2 \sqrt{\frac{d x^3}{c}+1}}","-\frac{c \sqrt{c+d x^3} F_1\left(-\frac{2}{3};2,-\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 x^2 \sqrt{\frac{d x^3}{c}+1}}",1,"-(c*Sqrt[c + d*x^3]*AppellF1[-2/3, 2, -3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*x^2*Sqrt[1 + (d*x^3)/c])","A",2,2,24,0.08333,1,"{511, 510}"
480,1,123,0,0.1436457,"\int \frac{x^8}{\left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^8/((a + b*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{a^2 \sqrt{c+d x^3}}{3 b^2 \left(a+b x^3\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} (b c-a d)^{3/2}}+\frac{2 \sqrt{c+d x^3}}{3 b^2 d}","-\frac{a^2 \sqrt{c+d x^3}}{3 b^2 \left(a+b x^3\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} (b c-a d)^{3/2}}+\frac{2 \sqrt{c+d x^3}}{3 b^2 d}",1,"(2*Sqrt[c + d*x^3])/(3*b^2*d) - (a^2*Sqrt[c + d*x^3])/(3*b^2*(b*c - a*d)*(a + b*x^3)) + (a*(4*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(5/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{446, 89, 80, 63, 208}"
481,1,99,0,0.0844353,"\int \frac{x^5}{\left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^5/((a + b*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{a \sqrt{c+d x^3}}{3 b \left(a+b x^3\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} (b c-a d)^{3/2}}","\frac{a \sqrt{c+d x^3}}{3 b \left(a+b x^3\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} (b c-a d)^{3/2}}",1,"(a*Sqrt[c + d*x^3])/(3*b*(b*c - a*d)*(a + b*x^3)) - ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
482,1,87,0,0.0726292,"\int \frac{x^2}{\left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^2/((a + b*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^3}}{3 \left(a+b x^3\right) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^3}}{3 \left(a+b x^3\right) (b c-a d)}",1,"-Sqrt[c + d*x^3]/(3*(b*c - a*d)*(a + b*x^3)) + (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{444, 51, 63, 208}"
483,1,132,0,0.1386603,"\int \frac{1}{x \left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x*(a + b*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 (b c-a d)^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^3}}{3 a \left(a+b x^3\right) (b c-a d)}","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 (b c-a d)^{3/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^3}}{3 a \left(a+b x^3\right) (b c-a d)}",1,"(b*Sqrt[c + d*x^3])/(3*a*(b*c - a*d)*(a + b*x^3)) - (2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2*Sqrt[c]) + (Sqrt[b]*(2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
484,1,185,0,0.2429821,"\int \frac{1}{x^4 \left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^4*(a + b*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^3} (2 b c-a d)}{3 a^2 c \left(a+b x^3\right) (b c-a d)}-\frac{\sqrt{c+d x^3}}{3 a c x^3 \left(a+b x^3\right)}","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^3} (2 b c-a d)}{3 a^2 c \left(a+b x^3\right) (b c-a d)}-\frac{\sqrt{c+d x^3}}{3 a c x^3 \left(a+b x^3\right)}",1,"-(b*(2*b*c - a*d)*Sqrt[c + d*x^3])/(3*a^2*c*(b*c - a*d)*(a + b*x^3)) - Sqrt[c + d*x^3]/(3*a*c*x^3*(a + b*x^3)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^3*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 151, 156, 63, 208}"
485,1,64,0,0.0523328,"\int \frac{x^3}{\left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x^3/((a + b*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 2, 1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
486,1,64,0,0.0393523,"\int \frac{x}{\left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[x/((a + b*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};2,\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 \sqrt{c+d x^3}}","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};2,\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 \sqrt{c+d x^3}}",1,"(x^2*Sqrt[1 + (d*x^3)/c]*AppellF1[2/3, 2, 1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*Sqrt[c + d*x^3])","A",2,2,22,0.09091,1,"{511, 510}"
487,1,59,0,0.0278168,"\int \frac{1}{\left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/((a + b*x^3)^2*Sqrt[c + d*x^3]),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 2, 1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*Sqrt[c + d*x^3])","A",2,2,21,0.09524,1,"{430, 429}"
488,1,62,0,0.0544206,"\int \frac{1}{x^2 \left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^2*(a + b*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};2,\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 x \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};2,\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 x \sqrt{c+d x^3}}",1,"-((Sqrt[1 + (d*x^3)/c]*AppellF1[-1/3, 2, 1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*x*Sqrt[c + d*x^3]))","A",2,2,24,0.08333,1,"{511, 510}"
489,1,64,0,0.0522244,"\int \frac{1}{x^3 \left(a+b x^3\right)^2 \sqrt{c+d x^3}} \, dx","Int[1/(x^3*(a + b*x^3)^2*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 2, 1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*x^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
490,1,149,0,0.1949396,"\int \frac{x^8}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^8/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{a^2 d^2+2 b^2 c^2}{3 b^2 d \sqrt{c+d x^3} (b c-a d)^2}-\frac{a^2}{3 b^2 \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{a (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} (b c-a d)^{5/2}}","-\frac{a^2 d^2+2 b^2 c^2}{3 b^2 d \sqrt{c+d x^3} (b c-a d)^2}-\frac{a^2}{3 b^2 \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{a (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} (b c-a d)^{5/2}}",1,"-(2*b^2*c^2 + a^2*d^2)/(3*b^2*d*(b*c - a*d)^2*Sqrt[c + d*x^3]) - a^2/(3*b^2*(b*c - a*d)*(a + b*x^3)*Sqrt[c + d*x^3]) + (a*(4*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*b^(3/2)*(b*c - a*d)^(5/2))","A",5,5,24,0.2083,1,"{446, 89, 78, 63, 208}"
491,1,134,0,0.1141006,"\int \frac{x^5}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^5/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{a}{3 b \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{a d+2 b c}{3 b \sqrt{c+d x^3} (b c-a d)^2}-\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} (b c-a d)^{5/2}}","\frac{a}{3 b \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{a d+2 b c}{3 b \sqrt{c+d x^3} (b c-a d)^2}-\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} (b c-a d)^{5/2}}",1,"(2*b*c + a*d)/(3*b*(b*c - a*d)^2*Sqrt[c + d*x^3]) + a/(3*b*(b*c - a*d)*(a + b*x^3)*Sqrt[c + d*x^3]) - ((2*b*c + a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*Sqrt[b]*(b*c - a*d)^(5/2))","A",5,5,24,0.2083,1,"{446, 78, 51, 63, 208}"
492,1,108,0,0.0913992,"\int \frac{x^2}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^2/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{d}{\sqrt{c+d x^3} (b c-a d)^2}-\frac{1}{3 \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}","-\frac{d}{\sqrt{c+d x^3} (b c-a d)^2}-\frac{1}{3 \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{\sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}",1,"-(d/((b*c - a*d)^2*Sqrt[c + d*x^3])) - 1/(3*(b*c - a*d)*(a + b*x^3)*Sqrt[c + d*x^3]) + (Sqrt[b]*d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(b*c - a*d)^(5/2)","A",5,4,24,0.1667,1,"{444, 51, 63, 208}"
493,1,172,0,0.2225977,"\int \frac{1}{x \left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{b^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 (b c-a d)^{5/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 c^{3/2}}+\frac{b}{3 a \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{d (2 a d+b c)}{3 a c \sqrt{c+d x^3} (b c-a d)^2}","\frac{b^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^2 (b c-a d)^{5/2}}-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^2 c^{3/2}}+\frac{b}{3 a \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}+\frac{d (2 a d+b c)}{3 a c \sqrt{c+d x^3} (b c-a d)^2}",1,"(d*(b*c + 2*a*d))/(3*a*c*(b*c - a*d)^2*Sqrt[c + d*x^3]) + b/(3*a*(b*c - a*d)*(a + b*x^3)*Sqrt[c + d*x^3]) - (2*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^2*c^(3/2)) + (b^(3/2)*(2*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^2*(b*c - a*d)^(5/2))","A",8,6,24,0.2500,1,"{446, 103, 152, 156, 63, 208}"
494,1,241,0,0.3569183,"\int \frac{1}{x^4 \left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{d \left(3 a^2 d^2-2 a b c d+2 b^2 c^2\right)}{3 a^2 c^2 \sqrt{c+d x^3} (b c-a d)^2}-\frac{b^{5/2} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 (b c-a d)^{5/2}}+\frac{(3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3 c^{5/2}}-\frac{b (2 b c-a d)}{3 a^2 c \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}-\frac{1}{3 a c x^3 \left(a+b x^3\right) \sqrt{c+d x^3}}","-\frac{d \left(3 a^2 d^2-2 a b c d+2 b^2 c^2\right)}{3 a^2 c^2 \sqrt{c+d x^3} (b c-a d)^2}-\frac{b^{5/2} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^3}}{\sqrt{b c-a d}}\right)}{3 a^3 (b c-a d)^{5/2}}+\frac{(3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^3}}{\sqrt{c}}\right)}{3 a^3 c^{5/2}}-\frac{b (2 b c-a d)}{3 a^2 c \left(a+b x^3\right) \sqrt{c+d x^3} (b c-a d)}-\frac{1}{3 a c x^3 \left(a+b x^3\right) \sqrt{c+d x^3}}",1,"-(d*(2*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2))/(3*a^2*c^2*(b*c - a*d)^2*Sqrt[c + d*x^3]) - (b*(2*b*c - a*d))/(3*a^2*c*(b*c - a*d)*(a + b*x^3)*Sqrt[c + d*x^3]) - 1/(3*a*c*x^3*(a + b*x^3)*Sqrt[c + d*x^3]) + ((4*b*c + 3*a*d)*ArcTanh[Sqrt[c + d*x^3]/Sqrt[c]])/(3*a^3*c^(5/2)) - (b^(5/2)*(4*b*c - 7*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^3])/Sqrt[b*c - a*d]])/(3*a^3*(b*c - a*d)^(5/2))","A",9,7,24,0.2917,1,"{446, 103, 151, 152, 156, 63, 208}"
495,1,67,0,0.0569109,"\int \frac{x^3}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x^3/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 c \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};2,\frac{3}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a^2 c \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 2, 3/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a^2*c*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
496,1,67,0,0.0425051,"\int \frac{x}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[x/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};2,\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 c \sqrt{c+d x^3}}","\frac{x^2 \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};2,\frac{3}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 c \sqrt{c+d x^3}}",1,"(x^2*Sqrt[1 + (d*x^3)/c]*AppellF1[2/3, 2, 3/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*c*Sqrt[c + d*x^3])","A",2,2,22,0.09091,1,"{511, 510}"
497,1,62,0,0.0275229,"\int \frac{1}{\left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/((a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};2,\frac{3}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 2, 3/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*c*Sqrt[c + d*x^3])","A",2,2,21,0.09524,1,"{430, 429}"
498,1,65,0,0.0583374,"\int \frac{1}{x^2 \left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};2,\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c x \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};2,\frac{3}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a^2 c x \sqrt{c+d x^3}}",1,"-((Sqrt[1 + (d*x^3)/c]*AppellF1[-1/3, 2, 3/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a^2*c*x*Sqrt[c + d*x^3]))","A",2,2,24,0.08333,1,"{511, 510}"
499,1,67,0,0.055826,"\int \frac{1}{x^3 \left(a+b x^3\right)^2 \left(c+d x^3\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^3)^2*(c + d*x^3)^(3/2)),x]","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 c x^2 \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};2,\frac{3}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a^2 c x^2 \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 2, 3/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a^2*c*x^2*Sqrt[c + d*x^3])","A",2,2,24,0.08333,1,"{511, 510}"
500,1,134,0,0.0791409,"\int (e x)^m \left(a+b x^3\right)^{5/2} \left(A+B x^3\right) \, dx","Int[(e*x)^m*(a + b*x^3)^(5/2)*(A + B*x^3),x]","\frac{2 B \left(a+b x^3\right)^{7/2} (e x)^{m+1}}{b e (2 m+23)}-\frac{a^2 \sqrt{a+b x^3} (e x)^{m+1} (2 a B (m+1)-A b (2 m+23)) \, _2F_1\left(-\frac{5}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+23) \sqrt{\frac{b x^3}{a}+1}}","\frac{2 B \left(a+b x^3\right)^{7/2} (e x)^{m+1}}{b e (2 m+23)}-\frac{a^2 \sqrt{a+b x^3} (e x)^{m+1} (2 a B (m+1)-A b (2 m+23)) \, _2F_1\left(-\frac{5}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+23) \sqrt{\frac{b x^3}{a}+1}}",1,"(2*B*(e*x)^(1 + m)*(a + b*x^3)^(7/2))/(b*e*(23 + 2*m)) - (a^2*(2*a*B*(1 + m) - A*b*(23 + 2*m))*(e*x)^(1 + m)*Sqrt[a + b*x^3]*Hypergeometric2F1[-5/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(b*e*(1 + m)*(23 + 2*m)*Sqrt[1 + (b*x^3)/a])","A",3,3,24,0.1250,1,"{459, 365, 364}"
501,1,132,0,0.0743111,"\int (e x)^m \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[(e*x)^m*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{2 B \left(a+b x^3\right)^{5/2} (e x)^{m+1}}{b e (2 m+17)}-\frac{a \sqrt{a+b x^3} (e x)^{m+1} (2 a B (m+1)-A b (2 m+17)) \, _2F_1\left(-\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+17) \sqrt{\frac{b x^3}{a}+1}}","\frac{2 B \left(a+b x^3\right)^{5/2} (e x)^{m+1}}{b e (2 m+17)}-\frac{a \sqrt{a+b x^3} (e x)^{m+1} (2 a B (m+1)-A b (2 m+17)) \, _2F_1\left(-\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+17) \sqrt{\frac{b x^3}{a}+1}}",1,"(2*B*(e*x)^(1 + m)*(a + b*x^3)^(5/2))/(b*e*(17 + 2*m)) - (a*(2*a*B*(1 + m) - A*b*(17 + 2*m))*(e*x)^(1 + m)*Sqrt[a + b*x^3]*Hypergeometric2F1[-3/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(b*e*(1 + m)*(17 + 2*m)*Sqrt[1 + (b*x^3)/a])","A",3,3,24,0.1250,1,"{459, 365, 364}"
502,1,131,0,0.073593,"\int (e x)^m \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[(e*x)^m*Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{2 B \left(a+b x^3\right)^{3/2} (e x)^{m+1}}{b e (2 m+11)}-\frac{\sqrt{a+b x^3} (e x)^{m+1} (2 a B (m+1)-A b (2 m+11)) \, _2F_1\left(-\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+11) \sqrt{\frac{b x^3}{a}+1}}","\frac{2 B \left(a+b x^3\right)^{3/2} (e x)^{m+1}}{b e (2 m+11)}-\frac{\sqrt{a+b x^3} (e x)^{m+1} (2 a B (m+1)-A b (2 m+11)) \, _2F_1\left(-\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+11) \sqrt{\frac{b x^3}{a}+1}}",1,"(2*B*(e*x)^(1 + m)*(a + b*x^3)^(3/2))/(b*e*(11 + 2*m)) - ((2*a*B*(1 + m) - A*b*(11 + 2*m))*(e*x)^(1 + m)*Sqrt[a + b*x^3]*Hypergeometric2F1[-1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(b*e*(1 + m)*(11 + 2*m)*Sqrt[1 + (b*x^3)/a])","A",3,3,24,0.1250,1,"{459, 365, 364}"
503,1,131,0,0.0708553,"\int \frac{(e x)^m \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[((e*x)^m*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{2 B \sqrt{a+b x^3} (e x)^{m+1}}{b e (2 m+5)}-\frac{\sqrt{\frac{b x^3}{a}+1} (e x)^{m+1} (2 a B (m+1)-A b (2 m+5)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+5) \sqrt{a+b x^3}}","\frac{2 B \sqrt{a+b x^3} (e x)^{m+1}}{b e (2 m+5)}-\frac{\sqrt{\frac{b x^3}{a}+1} (e x)^{m+1} (2 a B (m+1)-A b (2 m+5)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{b e (m+1) (2 m+5) \sqrt{a+b x^3}}",1,"(2*B*(e*x)^(1 + m)*Sqrt[a + b*x^3])/(b*e*(5 + 2*m)) - ((2*a*B*(1 + m) - A*b*(5 + 2*m))*(e*x)^(1 + m)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(b*e*(1 + m)*(5 + 2*m)*Sqrt[a + b*x^3])","A",3,3,24,0.1250,1,"{459, 365, 364}"
504,1,133,0,0.0771552,"\int \frac{(e x)^m \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[((e*x)^m*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{\sqrt{\frac{b x^3}{a}+1} (e x)^{m+1} (2 a B (m+1)+A (b-2 b m)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{3 a b e (m+1) \sqrt{a+b x^3}}+\frac{2 (e x)^{m+1} (A b-a B)}{3 a b e \sqrt{a+b x^3}}","\frac{\sqrt{\frac{b x^3}{a}+1} (e x)^{m+1} (2 a B (m+1)+A (b-2 b m)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{3 a b e (m+1) \sqrt{a+b x^3}}+\frac{2 (e x)^{m+1} (A b-a B)}{3 a b e \sqrt{a+b x^3}}",1,"(2*(A*b - a*B)*(e*x)^(1 + m))/(3*a*b*e*Sqrt[a + b*x^3]) + ((2*a*B*(1 + m) + A*(b - 2*b*m))*(e*x)^(1 + m)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[1/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(3*a*b*e*(1 + m)*Sqrt[a + b*x^3])","A",3,3,24,0.1250,1,"{457, 365, 364}"
505,1,133,0,0.0789417,"\int \frac{(e x)^m \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[((e*x)^m*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{\sqrt{\frac{b x^3}{a}+1} (e x)^{m+1} (2 a B (m+1)+A b (7-2 m)) \, _2F_1\left(\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{9 a^2 b e (m+1) \sqrt{a+b x^3}}+\frac{2 (e x)^{m+1} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}","\frac{\sqrt{\frac{b x^3}{a}+1} (e x)^{m+1} (2 a B (m+1)+A b (7-2 m)) \, _2F_1\left(\frac{3}{2},\frac{m+1}{3};\frac{m+4}{3};-\frac{b x^3}{a}\right)}{9 a^2 b e (m+1) \sqrt{a+b x^3}}+\frac{2 (e x)^{m+1} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*(e*x)^(1 + m))/(9*a*b*e*(a + b*x^3)^(3/2)) + ((A*b*(7 - 2*m) + 2*a*B*(1 + m))*(e*x)^(1 + m)*Sqrt[1 + (b*x^3)/a]*Hypergeometric2F1[3/2, (1 + m)/3, (4 + m)/3, -((b*x^3)/a)])/(9*a^2*b*e*(1 + m)*Sqrt[a + b*x^3])","A",3,3,24,0.1250,1,"{457, 365, 364}"
506,1,88,0,0.0933625,"\int \frac{x^5}{\sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[x^5/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{\sqrt{a+b x^3} \sqrt{c+d x^3}}{3 b d}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^3}}{\sqrt{b} \sqrt{c+d x^3}}\right)}{3 b^{3/2} d^{3/2}}","\frac{\sqrt{a+b x^3} \sqrt{c+d x^3}}{3 b d}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^3}}{\sqrt{b} \sqrt{c+d x^3}}\right)}{3 b^{3/2} d^{3/2}}",1,"(Sqrt[a + b*x^3]*Sqrt[c + d*x^3])/(3*b*d) - ((b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^3])/(Sqrt[b]*Sqrt[c + d*x^3])])/(3*b^(3/2)*d^(3/2))","A",5,5,26,0.1923,1,"{446, 80, 63, 217, 206}"
507,1,48,0,0.0594079,"\int \frac{x^2}{\sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[x^2/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^3}}{\sqrt{b} \sqrt{c+d x^3}}\right)}{3 \sqrt{b} \sqrt{d}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^3}}{\sqrt{b} \sqrt{c+d x^3}}\right)}{3 \sqrt{b} \sqrt{d}}",1,"(2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^3])/(Sqrt[b]*Sqrt[c + d*x^3])])/(3*Sqrt[b]*Sqrt[d])","A",4,4,26,0.1538,1,"{444, 63, 217, 206}"
508,1,48,0,0.0482415,"\int \frac{1}{x \sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[1/(x*Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^3}}{\sqrt{a} \sqrt{c+d x^3}}\right)}{3 \sqrt{a} \sqrt{c}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^3}}{\sqrt{a} \sqrt{c+d x^3}}\right)}{3 \sqrt{a} \sqrt{c}}",1,"(-2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^3])/(Sqrt[a]*Sqrt[c + d*x^3])])/(3*Sqrt[a]*Sqrt[c])","A",3,3,26,0.1154,1,"{446, 93, 208}"
509,1,91,0,0.0801235,"\int \frac{1}{x^4 \sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[1/(x^4*Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^3}}{\sqrt{a} \sqrt{c+d x^3}}\right)}{3 a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x^3} \sqrt{c+d x^3}}{3 a c x^3}","\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^3}}{\sqrt{a} \sqrt{c+d x^3}}\right)}{3 a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x^3} \sqrt{c+d x^3}}{3 a c x^3}",1,"-(Sqrt[a + b*x^3]*Sqrt[c + d*x^3])/(3*a*c*x^3) + ((b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^3])/(Sqrt[a]*Sqrt[c + d*x^3])])/(3*a^(3/2)*c^(3/2))","A",4,4,26,0.1538,1,"{446, 96, 93, 208}"
510,1,88,0,0.0973033,"\int \frac{x^4}{\sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[x^4/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{x^5 \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{5}{3};\frac{1}{2},\frac{1}{2};\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 \sqrt{a+b x^3} \sqrt{c+d x^3}}","\frac{x^5 \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{5}{3};\frac{1}{2},\frac{1}{2};\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 \sqrt{a+b x^3} \sqrt{c+d x^3}}",1,"(x^5*Sqrt[1 + (b*x^3)/a]*Sqrt[1 + (d*x^3)/c]*AppellF1[5/3, 1/2, 1/2, 8/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*Sqrt[a + b*x^3]*Sqrt[c + d*x^3])","A",3,2,26,0.07692,1,"{511, 510}"
511,1,88,0,0.1010982,"\int \frac{x^3}{\sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[x^3/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{x^4 \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};\frac{1}{2},\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 \sqrt{a+b x^3} \sqrt{c+d x^3}}","\frac{x^4 \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{4}{3};\frac{1}{2},\frac{1}{2};\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 \sqrt{a+b x^3} \sqrt{c+d x^3}}",1,"(x^4*Sqrt[1 + (b*x^3)/a]*Sqrt[1 + (d*x^3)/c]*AppellF1[4/3, 1/2, 1/2, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*Sqrt[a + b*x^3]*Sqrt[c + d*x^3])","A",3,2,26,0.07692,1,"{511, 510}"
512,1,88,0,0.0706296,"\int \frac{x}{\sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[x/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{x^2 \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 \sqrt{a+b x^3} \sqrt{c+d x^3}}","\frac{x^2 \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 \sqrt{a+b x^3} \sqrt{c+d x^3}}",1,"(x^2*Sqrt[1 + (b*x^3)/a]*Sqrt[1 + (d*x^3)/c]*AppellF1[2/3, 1/2, 1/2, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*Sqrt[a + b*x^3]*Sqrt[c + d*x^3])","A",3,2,24,0.08333,1,"{511, 510}"
513,1,83,0,0.046574,"\int \frac{1}{\sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[1/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","\frac{x \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{\sqrt{a+b x^3} \sqrt{c+d x^3}}","\frac{x \sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{\sqrt{a+b x^3} \sqrt{c+d x^3}}",1,"(x*Sqrt[1 + (b*x^3)/a]*Sqrt[1 + (d*x^3)/c]*AppellF1[1/3, 1/2, 1/2, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(Sqrt[a + b*x^3]*Sqrt[c + d*x^3])","A",3,2,23,0.08696,1,"{430, 429}"
514,1,86,0,0.097289,"\int \frac{1}{x^2 \sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[1/(x^2*Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{x \sqrt{a+b x^3} \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{1}{3};\frac{1}{2},\frac{1}{2};\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{x \sqrt{a+b x^3} \sqrt{c+d x^3}}",1,"-((Sqrt[1 + (b*x^3)/a]*Sqrt[1 + (d*x^3)/c]*AppellF1[-1/3, 1/2, 1/2, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(x*Sqrt[a + b*x^3]*Sqrt[c + d*x^3]))","A",3,2,26,0.07692,1,"{511, 510}"
515,1,88,0,0.0957892,"\int \frac{1}{x^3 \sqrt{a+b x^3} \sqrt{c+d x^3}} \, dx","Int[1/(x^3*Sqrt[a + b*x^3]*Sqrt[c + d*x^3]),x]","-\frac{\sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 x^2 \sqrt{a+b x^3} \sqrt{c+d x^3}}","-\frac{\sqrt{\frac{b x^3}{a}+1} \sqrt{\frac{d x^3}{c}+1} F_1\left(-\frac{2}{3};\frac{1}{2},\frac{1}{2};\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 x^2 \sqrt{a+b x^3} \sqrt{c+d x^3}}",1,"-(Sqrt[1 + (b*x^3)/a]*Sqrt[1 + (d*x^3)/c]*AppellF1[-2/3, 1/2, 1/2, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*x^2*Sqrt[a + b*x^3]*Sqrt[c + d*x^3])","A",3,2,26,0.07692,1,"{511, 510}"
516,1,161,0,0.112619,"\int (e x)^{7/2} \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[(e*x)^(7/2)*Sqrt[a + b*x^3]*(A + B*x^3),x]","-\frac{a^2 e^{7/2} (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{24 b^{5/2}}+\frac{a e^2 (e x)^{3/2} \sqrt{a+b x^3} (2 A b-a B)}{24 b^2}+\frac{(e x)^{9/2} \sqrt{a+b x^3} (2 A b-a B)}{12 b e}+\frac{B (e x)^{9/2} \left(a+b x^3\right)^{3/2}}{9 b e}","-\frac{a^2 e^{7/2} (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{24 b^{5/2}}+\frac{a e^2 (e x)^{3/2} \sqrt{a+b x^3} (2 A b-a B)}{24 b^2}+\frac{(e x)^{9/2} \sqrt{a+b x^3} (2 A b-a B)}{12 b e}+\frac{B (e x)^{9/2} \left(a+b x^3\right)^{3/2}}{9 b e}",1,"(a*(2*A*b - a*B)*e^2*(e*x)^(3/2)*Sqrt[a + b*x^3])/(24*b^2) + ((2*A*b - a*B)*(e*x)^(9/2)*Sqrt[a + b*x^3])/(12*b*e) + (B*(e*x)^(9/2)*(a + b*x^3)^(3/2))/(9*b*e) - (a^2*(2*A*b - a*B)*e^(7/2)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(24*b^(5/2))","A",7,7,26,0.2692,1,"{459, 279, 321, 329, 275, 217, 206}"
517,1,324,0,0.3197871,"\int (e x)^{5/2} \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[(e*x)^(5/2)*Sqrt[a + b*x^3]*(A + B*x^3),x]","-\frac{3^{3/4} a^{5/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (16 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 a e^2 \sqrt{e x} \sqrt{a+b x^3} (16 A b-7 a B)}{320 b^2}+\frac{(e x)^{7/2} \sqrt{a+b x^3} (16 A b-7 a B)}{80 b e}+\frac{B (e x)^{7/2} \left(a+b x^3\right)^{3/2}}{8 b e}","-\frac{3^{3/4} a^{5/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (16 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 a e^2 \sqrt{e x} \sqrt{a+b x^3} (16 A b-7 a B)}{320 b^2}+\frac{(e x)^{7/2} \sqrt{a+b x^3} (16 A b-7 a B)}{80 b e}+\frac{B (e x)^{7/2} \left(a+b x^3\right)^{3/2}}{8 b e}",1,"(3*a*(16*A*b - 7*a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^3])/(320*b^2) + ((16*A*b - 7*a*B)*(e*x)^(7/2)*Sqrt[a + b*x^3])/(80*b*e) + (B*(e*x)^(7/2)*(a + b*x^3)^(3/2))/(8*b*e) - (3^(3/4)*a^(5/3)*(16*A*b - 7*a*B)*e^2*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(640*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,26,0.1923,1,"{459, 279, 321, 329, 225}"
518,1,581,0,0.62115,"\int (e x)^{3/2} \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[(e*x)^(3/2)*Sqrt[a + b*x^3]*(A + B*x^3),x]","-\frac{3^{3/4} \left(1-\sqrt{3}\right) a^{4/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (14 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{224 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} a^{4/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (14 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{112 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \left(1+\sqrt{3}\right) a e \sqrt{e x} \sqrt{a+b x^3} (14 A b-5 a B)}{112 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{(e x)^{5/2} \sqrt{a+b x^3} (14 A b-5 a B)}{56 b e}+\frac{B (e x)^{5/2} \left(a+b x^3\right)^{3/2}}{7 b e}","-\frac{3^{3/4} \left(1-\sqrt{3}\right) a^{4/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (14 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{224 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} a^{4/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (14 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{112 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \left(1+\sqrt{3}\right) a e \sqrt{e x} \sqrt{a+b x^3} (14 A b-5 a B)}{112 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{(e x)^{5/2} \sqrt{a+b x^3} (14 A b-5 a B)}{56 b e}+\frac{B (e x)^{5/2} \left(a+b x^3\right)^{3/2}}{7 b e}",1,"((14*A*b - 5*a*B)*(e*x)^(5/2)*Sqrt[a + b*x^3])/(56*b*e) + (3*(1 + Sqrt[3])*a*(14*A*b - 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^3])/(112*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + (B*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(7*b*e) - (3*3^(1/4)*a^(4/3)*(14*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(112*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*(1 - Sqrt[3])*a^(4/3)*(14*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(224*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,26,0.2308,1,"{459, 279, 329, 308, 225, 1881}"
519,1,121,0,0.0893504,"\int \sqrt{e x} \sqrt{a+b x^3} \left(A+B x^3\right) \, dx","Int[Sqrt[e*x]*Sqrt[a + b*x^3]*(A + B*x^3),x]","\frac{a \sqrt{e} (4 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{12 b^{3/2}}+\frac{(e x)^{3/2} \sqrt{a+b x^3} (4 A b-a B)}{12 b e}+\frac{B (e x)^{3/2} \left(a+b x^3\right)^{3/2}}{6 b e}","\frac{a \sqrt{e} (4 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{12 b^{3/2}}+\frac{(e x)^{3/2} \sqrt{a+b x^3} (4 A b-a B)}{12 b e}+\frac{B (e x)^{3/2} \left(a+b x^3\right)^{3/2}}{6 b e}",1,"((4*A*b - a*B)*(e*x)^(3/2)*Sqrt[a + b*x^3])/(12*b*e) + (B*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(6*b*e) + (a*(4*A*b - a*B)*Sqrt[e]*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(12*b^(3/2))","A",6,6,26,0.2308,1,"{459, 279, 329, 275, 217, 206}"
520,1,286,0,0.2290956,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{\sqrt{e x}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/Sqrt[e*x],x]","\frac{3^{3/4} a^{2/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \sqrt{a+b x^3} (10 A b-a B)}{20 b e}+\frac{B \sqrt{e x} \left(a+b x^3\right)^{3/2}}{5 b e}","\frac{3^{3/4} a^{2/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \sqrt{a+b x^3} (10 A b-a B)}{20 b e}+\frac{B \sqrt{e x} \left(a+b x^3\right)^{3/2}}{5 b e}",1,"((10*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(20*b*e) + (B*Sqrt[e*x]*(a + b*x^3)^(3/2))/(5*b*e) + (3^(3/4)*a^(2/3)*(10*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(40*b*e*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{459, 279, 329, 225}"
521,1,580,0,0.5916889,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{(e x)^{3/2}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/(e*x)^(3/2),x]","-\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{a} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+8 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+8 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (a B+8 A b)}{8 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{(e x)^{5/2} \sqrt{a+b x^3} (a B+8 A b)}{4 a e^4}-\frac{2 A \left(a+b x^3\right)^{3/2}}{a e \sqrt{e x}}","-\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{a} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+8 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt[3]{a} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+8 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{3 \left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (a B+8 A b)}{8 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{(e x)^{5/2} \sqrt{a+b x^3} (a B+8 A b)}{4 a e^4}-\frac{2 A \left(a+b x^3\right)^{3/2}}{a e \sqrt{e x}}",1,"((8*A*b + a*B)*(e*x)^(5/2)*Sqrt[a + b*x^3])/(4*a*e^4) + (3*(1 + Sqrt[3])*(8*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(8*b^(2/3)*e^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) - (2*A*(a + b*x^3)^(3/2))/(a*e*Sqrt[e*x]) - (3*3^(1/4)*a^(1/3)*(8*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(8*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*(1 - Sqrt[3])*a^(1/3)*(8*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(16*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,26,0.2308,1,"{453, 279, 329, 308, 225, 1881}"
522,1,118,0,0.0844829,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{(e x)^{5/2}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/(e*x)^(5/2),x]","\frac{(e x)^{3/2} \sqrt{a+b x^3} (a B+2 A b)}{3 a e^4}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 \sqrt{b} e^{5/2}}-\frac{2 A \left(a+b x^3\right)^{3/2}}{3 a e (e x)^{3/2}}","\frac{(e x)^{3/2} \sqrt{a+b x^3} (a B+2 A b)}{3 a e^4}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 \sqrt{b} e^{5/2}}-\frac{2 A \left(a+b x^3\right)^{3/2}}{3 a e (e x)^{3/2}}",1,"((2*A*b + a*B)*(e*x)^(3/2)*Sqrt[a + b*x^3])/(3*a*e^4) - (2*A*(a + b*x^3)^(3/2))/(3*a*e*(e*x)^(3/2)) + ((2*A*b + a*B)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(3*Sqrt[b]*e^(5/2))","A",6,6,26,0.2308,1,"{453, 279, 329, 275, 217, 206}"
523,1,283,0,0.2272157,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{(e x)^{7/2}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/(e*x)^(7/2),x]","\frac{3^{3/4} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+4 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{20 \sqrt[3]{a} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \sqrt{a+b x^3} (5 a B+4 A b)}{10 a e^4}-\frac{2 A \left(a+b x^3\right)^{3/2}}{5 a e (e x)^{5/2}}","\frac{3^{3/4} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+4 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{20 \sqrt[3]{a} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \sqrt{a+b x^3} (5 a B+4 A b)}{10 a e^4}-\frac{2 A \left(a+b x^3\right)^{3/2}}{5 a e (e x)^{5/2}}",1,"((4*A*b + 5*a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(10*a*e^4) - (2*A*(a + b*x^3)^(3/2))/(5*a*e*(e*x)^(5/2)) + (3^(3/4)*(4*A*b + 5*a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(20*a^(1/3)*e^4*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{453, 279, 329, 225}"
524,1,564,0,0.5299738,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^{9/2}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^(9/2),x]","-\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt{x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (7 a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{14 a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt[3]{b} \sqrt{x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (7 a B+2 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7 a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (7 a B+2 A b)}{7 a \sqrt{x}}+\frac{3 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{x} \sqrt{a+b x^3} (7 a B+2 A b)}{7 a \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{2 A \left(a+b x^3\right)^{3/2}}{7 a x^{7/2}}","-\frac{3^{3/4} \left(1-\sqrt{3}\right) \sqrt[3]{b} \sqrt{x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (7 a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{14 a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{3 \sqrt[4]{3} \sqrt[3]{b} \sqrt{x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (7 a B+2 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{7 a^{2/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{a+b x^3} (7 a B+2 A b)}{7 a \sqrt{x}}+\frac{3 \left(1+\sqrt{3}\right) \sqrt[3]{b} \sqrt{x} \sqrt{a+b x^3} (7 a B+2 A b)}{7 a \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{2 A \left(a+b x^3\right)^{3/2}}{7 a x^{7/2}}",1,"(-2*(2*A*b + 7*a*B)*Sqrt[a + b*x^3])/(7*a*Sqrt[x]) + (3*(1 + Sqrt[3])*b^(1/3)*(2*A*b + 7*a*B)*Sqrt[x]*Sqrt[a + b*x^3])/(7*a*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) - (2*A*(a + b*x^3)^(3/2))/(7*a*x^(7/2)) - (3*3^(1/4)*b^(1/3)*(2*A*b + 7*a*B)*Sqrt[x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(7*a^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (3^(3/4)*(1 - Sqrt[3])*b^(1/3)*(2*A*b + 7*a*B)*Sqrt[x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(14*a^(2/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,24,0.2500,1,"{453, 277, 329, 308, 225, 1881}"
525,1,79,0,0.0458653,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^{11/2}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^(11/2),x]","-\frac{2 A \left(a+b x^3\right)^{3/2}}{9 a x^{9/2}}-\frac{2 B \sqrt{a+b x^3}}{3 x^{3/2}}+\frac{2}{3} \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)","-\frac{2 A \left(a+b x^3\right)^{3/2}}{9 a x^{9/2}}-\frac{2 B \sqrt{a+b x^3}}{3 x^{3/2}}+\frac{2}{3} \sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x^{3/2}}{\sqrt{a+b x^3}}\right)",1,"(-2*B*Sqrt[a + b*x^3])/(3*x^(3/2)) - (2*A*(a + b*x^3)^(3/2))/(9*a*x^(9/2)) + (2*Sqrt[b]*B*ArcTanh[(Sqrt[b]*x^(3/2))/Sqrt[a + b*x^3]])/3","A",6,6,24,0.2500,1,"{451, 277, 329, 275, 217, 206}"
526,1,269,0,0.1991477,"\int \frac{\sqrt{a+b x^3} \left(A+B x^3\right)}{x^{13/2}} \, dx","Int[(Sqrt[a + b*x^3]*(A + B*x^3))/x^(13/2),x]","-\frac{3^{3/4} b \sqrt{x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-11 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 a^{4/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (2 A b-11 a B)}{55 a x^{5/2}}-\frac{2 A \left(a+b x^3\right)^{3/2}}{11 a x^{11/2}}","-\frac{3^{3/4} b \sqrt{x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-11 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{55 a^{4/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{a+b x^3} (2 A b-11 a B)}{55 a x^{5/2}}-\frac{2 A \left(a+b x^3\right)^{3/2}}{11 a x^{11/2}}",1,"(2*(2*A*b - 11*a*B)*Sqrt[a + b*x^3])/(55*a*x^(5/2)) - (2*A*(a + b*x^3)^(3/2))/(11*a*x^(11/2)) - (3^(3/4)*b*(2*A*b - 11*a*B)*Sqrt[x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(55*a^(4/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,24,0.1667,1,"{453, 277, 329, 225}"
527,1,201,0,0.1385264,"\int (e x)^{7/2} \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[(e*x)^(7/2)*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{a^2 e^2 (e x)^{3/2} \sqrt{a+b x^3} (8 A b-3 a B)}{192 b^2}-\frac{a^3 e^{7/2} (8 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{192 b^{5/2}}+\frac{(e x)^{9/2} \left(a+b x^3\right)^{3/2} (8 A b-3 a B)}{72 b e}+\frac{a (e x)^{9/2} \sqrt{a+b x^3} (8 A b-3 a B)}{96 b e}+\frac{B (e x)^{9/2} \left(a+b x^3\right)^{5/2}}{12 b e}","\frac{a^2 e^2 (e x)^{3/2} \sqrt{a+b x^3} (8 A b-3 a B)}{192 b^2}-\frac{a^3 e^{7/2} (8 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{192 b^{5/2}}+\frac{(e x)^{9/2} \left(a+b x^3\right)^{3/2} (8 A b-3 a B)}{72 b e}+\frac{a (e x)^{9/2} \sqrt{a+b x^3} (8 A b-3 a B)}{96 b e}+\frac{B (e x)^{9/2} \left(a+b x^3\right)^{5/2}}{12 b e}",1,"(a^2*(8*A*b - 3*a*B)*e^2*(e*x)^(3/2)*Sqrt[a + b*x^3])/(192*b^2) + (a*(8*A*b - 3*a*B)*(e*x)^(9/2)*Sqrt[a + b*x^3])/(96*b*e) + ((8*A*b - 3*a*B)*(e*x)^(9/2)*(a + b*x^3)^(3/2))/(72*b*e) + (B*(e*x)^(9/2)*(a + b*x^3)^(5/2))/(12*b*e) - (a^3*(8*A*b - 3*a*B)*e^(7/2)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(192*b^(5/2))","A",8,7,26,0.2692,1,"{459, 279, 321, 329, 275, 217, 206}"
528,1,364,0,0.3093577,"\int (e x)^{5/2} \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[(e*x)^(5/2)*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{27 a^2 e^2 \sqrt{e x} \sqrt{a+b x^3} (22 A b-7 a B)}{7040 b^2}-\frac{9\ 3^{3/4} a^{8/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (22 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{14080 b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{(e x)^{7/2} \left(a+b x^3\right)^{3/2} (22 A b-7 a B)}{176 b e}+\frac{9 a (e x)^{7/2} \sqrt{a+b x^3} (22 A b-7 a B)}{1760 b e}+\frac{B (e x)^{7/2} \left(a+b x^3\right)^{5/2}}{11 b e}","\frac{27 a^2 e^2 \sqrt{e x} \sqrt{a+b x^3} (22 A b-7 a B)}{7040 b^2}-\frac{9\ 3^{3/4} a^{8/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (22 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{14080 b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{(e x)^{7/2} \left(a+b x^3\right)^{3/2} (22 A b-7 a B)}{176 b e}+\frac{9 a (e x)^{7/2} \sqrt{a+b x^3} (22 A b-7 a B)}{1760 b e}+\frac{B (e x)^{7/2} \left(a+b x^3\right)^{5/2}}{11 b e}",1,"(27*a^2*(22*A*b - 7*a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^3])/(7040*b^2) + (9*a*(22*A*b - 7*a*B)*(e*x)^(7/2)*Sqrt[a + b*x^3])/(1760*b*e) + ((22*A*b - 7*a*B)*(e*x)^(7/2)*(a + b*x^3)^(3/2))/(176*b*e) + (B*(e*x)^(7/2)*(a + b*x^3)^(5/2))/(11*b*e) - (9*3^(3/4)*a^(8/3)*(22*A*b - 7*a*B)*e^2*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(14080*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,5,26,0.1923,1,"{459, 279, 321, 329, 225}"
529,1,621,0,0.6605388,"\int (e x)^{3/2} \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[(e*x)^(3/2)*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{27 \left(1+\sqrt{3}\right) a^2 e \sqrt{e x} \sqrt{a+b x^3} (4 A b-a B)}{448 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{9\ 3^{3/4} \left(1-\sqrt{3}\right) a^{7/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{896 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} a^{7/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{448 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{3/2} (4 A b-a B)}{28 b e}+\frac{9 a (e x)^{5/2} \sqrt{a+b x^3} (4 A b-a B)}{224 b e}+\frac{B (e x)^{5/2} \left(a+b x^3\right)^{5/2}}{10 b e}","\frac{27 \left(1+\sqrt{3}\right) a^2 e \sqrt{e x} \sqrt{a+b x^3} (4 A b-a B)}{448 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{9\ 3^{3/4} \left(1-\sqrt{3}\right) a^{7/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{896 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} a^{7/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{448 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{3/2} (4 A b-a B)}{28 b e}+\frac{9 a (e x)^{5/2} \sqrt{a+b x^3} (4 A b-a B)}{224 b e}+\frac{B (e x)^{5/2} \left(a+b x^3\right)^{5/2}}{10 b e}",1,"(9*a*(4*A*b - a*B)*(e*x)^(5/2)*Sqrt[a + b*x^3])/(224*b*e) + (27*(1 + Sqrt[3])*a^2*(4*A*b - a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^3])/(448*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + ((4*A*b - a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(28*b*e) + (B*(e*x)^(5/2)*(a + b*x^3)^(5/2))/(10*b*e) - (27*3^(1/4)*a^(7/3)*(4*A*b - a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(448*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (9*3^(3/4)*(1 - Sqrt[3])*a^(7/3)*(4*A*b - a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(896*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,26,0.2308,1,"{459, 279, 329, 308, 225, 1881}"
530,1,161,0,0.1134348,"\int \sqrt{e x} \left(a+b x^3\right)^{3/2} \left(A+B x^3\right) \, dx","Int[Sqrt[e*x]*(a + b*x^3)^(3/2)*(A + B*x^3),x]","\frac{a^2 \sqrt{e} (6 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{24 b^{3/2}}+\frac{(e x)^{3/2} \left(a+b x^3\right)^{3/2} (6 A b-a B)}{36 b e}+\frac{a (e x)^{3/2} \sqrt{a+b x^3} (6 A b-a B)}{24 b e}+\frac{B (e x)^{3/2} \left(a+b x^3\right)^{5/2}}{9 b e}","\frac{a^2 \sqrt{e} (6 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{24 b^{3/2}}+\frac{(e x)^{3/2} \left(a+b x^3\right)^{3/2} (6 A b-a B)}{36 b e}+\frac{a (e x)^{3/2} \sqrt{a+b x^3} (6 A b-a B)}{24 b e}+\frac{B (e x)^{3/2} \left(a+b x^3\right)^{5/2}}{9 b e}",1,"(a*(6*A*b - a*B)*(e*x)^(3/2)*Sqrt[a + b*x^3])/(24*b*e) + ((6*A*b - a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(36*b*e) + (B*(e*x)^(3/2)*(a + b*x^3)^(5/2))/(9*b*e) + (a^2*(6*A*b - a*B)*Sqrt[e]*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(24*b^(3/2))","A",7,6,26,0.2308,1,"{459, 279, 329, 275, 217, 206}"
531,1,324,0,0.2556698,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{\sqrt{e x}} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/Sqrt[e*x],x]","\frac{9\ 3^{3/4} a^{5/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (16 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \left(a+b x^3\right)^{3/2} (16 A b-a B)}{80 b e}+\frac{9 a \sqrt{e x} \sqrt{a+b x^3} (16 A b-a B)}{320 b e}+\frac{B \sqrt{e x} \left(a+b x^3\right)^{5/2}}{8 b e}","\frac{9\ 3^{3/4} a^{5/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (16 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \left(a+b x^3\right)^{3/2} (16 A b-a B)}{80 b e}+\frac{9 a \sqrt{e x} \sqrt{a+b x^3} (16 A b-a B)}{320 b e}+\frac{B \sqrt{e x} \left(a+b x^3\right)^{5/2}}{8 b e}",1,"(9*a*(16*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(320*b*e) + ((16*A*b - a*B)*Sqrt[e*x]*(a + b*x^3)^(3/2))/(80*b*e) + (B*Sqrt[e*x]*(a + b*x^3)^(5/2))/(8*b*e) + (9*3^(3/4)*a^(5/3)*(16*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(640*b*e*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,26,0.1538,1,"{459, 279, 329, 225}"
532,1,614,0,0.6443032,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{(e x)^{3/2}} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/(e*x)^(3/2),x]","-\frac{9\ 3^{3/4} \left(1-\sqrt{3}\right) a^{4/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+14 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{224 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} a^{4/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+14 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{112 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 \left(1+\sqrt{3}\right) a \sqrt{e x} \sqrt{a+b x^3} (a B+14 A b)}{112 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{3/2} (a B+14 A b)}{7 a e^4}+\frac{9 (e x)^{5/2} \sqrt{a+b x^3} (a B+14 A b)}{56 e^4}-\frac{2 A \left(a+b x^3\right)^{5/2}}{a e \sqrt{e x}}","-\frac{9\ 3^{3/4} \left(1-\sqrt{3}\right) a^{4/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+14 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{224 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{27 \sqrt[4]{3} a^{4/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+14 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{112 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 \left(1+\sqrt{3}\right) a \sqrt{e x} \sqrt{a+b x^3} (a B+14 A b)}{112 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{3/2} (a B+14 A b)}{7 a e^4}+\frac{9 (e x)^{5/2} \sqrt{a+b x^3} (a B+14 A b)}{56 e^4}-\frac{2 A \left(a+b x^3\right)^{5/2}}{a e \sqrt{e x}}",1,"(9*(14*A*b + a*B)*(e*x)^(5/2)*Sqrt[a + b*x^3])/(56*e^4) + (27*(1 + Sqrt[3])*a*(14*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(112*b^(2/3)*e^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + ((14*A*b + a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(7*a*e^4) - (2*A*(a + b*x^3)^(5/2))/(a*e*Sqrt[e*x]) - (27*3^(1/4)*a^(4/3)*(14*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(112*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (9*3^(3/4)*(1 - Sqrt[3])*a^(4/3)*(14*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(224*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,26,0.2308,1,"{453, 279, 329, 308, 225, 1881}"
533,1,152,0,0.1040423,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{(e x)^{5/2}} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/(e*x)^(5/2),x]","\frac{(e x)^{3/2} \left(a+b x^3\right)^{3/2} (a B+4 A b)}{6 a e^4}+\frac{(e x)^{3/2} \sqrt{a+b x^3} (a B+4 A b)}{4 e^4}+\frac{a (a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{4 \sqrt{b} e^{5/2}}-\frac{2 A \left(a+b x^3\right)^{5/2}}{3 a e (e x)^{3/2}}","\frac{(e x)^{3/2} \left(a+b x^3\right)^{3/2} (a B+4 A b)}{6 a e^4}+\frac{(e x)^{3/2} \sqrt{a+b x^3} (a B+4 A b)}{4 e^4}+\frac{a (a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{4 \sqrt{b} e^{5/2}}-\frac{2 A \left(a+b x^3\right)^{5/2}}{3 a e (e x)^{3/2}}",1,"((4*A*b + a*B)*(e*x)^(3/2)*Sqrt[a + b*x^3])/(4*e^4) + ((4*A*b + a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(6*a*e^4) - (2*A*(a + b*x^3)^(5/2))/(3*a*e*(e*x)^(3/2)) + (a*(4*A*b + a*B)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(4*Sqrt[b]*e^(5/2))","A",7,6,26,0.2308,1,"{453, 279, 329, 275, 217, 206}"
534,1,314,0,0.246942,"\int \frac{\left(a+b x^3\right)^{3/2} \left(A+B x^3\right)}{(e x)^{7/2}} \, dx","Int[((a + b*x^3)^(3/2)*(A + B*x^3))/(e*x)^(7/2),x]","\frac{9\ 3^{3/4} a^{2/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \left(a+b x^3\right)^{3/2} (a B+2 A b)}{5 a e^4}+\frac{9 \sqrt{e x} \sqrt{a+b x^3} (a B+2 A b)}{20 e^4}-\frac{2 A \left(a+b x^3\right)^{5/2}}{5 a e (e x)^{5/2}}","\frac{9\ 3^{3/4} a^{2/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \left(a+b x^3\right)^{3/2} (a B+2 A b)}{5 a e^4}+\frac{9 \sqrt{e x} \sqrt{a+b x^3} (a B+2 A b)}{20 e^4}-\frac{2 A \left(a+b x^3\right)^{5/2}}{5 a e (e x)^{5/2}}",1,"(9*(2*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(20*e^4) + ((2*A*b + a*B)*Sqrt[e*x]*(a + b*x^3)^(3/2))/(5*a*e^4) - (2*A*(a + b*x^3)^(5/2))/(5*a*e*(e*x)^(5/2)) + (9*3^(3/4)*a^(2/3)*(2*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(40*e^4*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,26,0.1538,1,"{453, 279, 329, 225}"
535,1,241,0,0.1589722,"\int (e x)^{7/2} \left(a+b x^3\right)^{5/2} \left(A+B x^3\right) \, dx","Int[(e*x)^(7/2)*(a + b*x^3)^(5/2)*(A + B*x^3),x]","\frac{a^3 e^2 (e x)^{3/2} \sqrt{a+b x^3} (10 A b-3 a B)}{384 b^2}-\frac{a^4 e^{7/2} (10 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{384 b^{5/2}}+\frac{a^2 (e x)^{9/2} \sqrt{a+b x^3} (10 A b-3 a B)}{192 b e}+\frac{(e x)^{9/2} \left(a+b x^3\right)^{5/2} (10 A b-3 a B)}{120 b e}+\frac{a (e x)^{9/2} \left(a+b x^3\right)^{3/2} (10 A b-3 a B)}{144 b e}+\frac{B (e x)^{9/2} \left(a+b x^3\right)^{7/2}}{15 b e}","\frac{a^3 e^2 (e x)^{3/2} \sqrt{a+b x^3} (10 A b-3 a B)}{384 b^2}-\frac{a^4 e^{7/2} (10 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{384 b^{5/2}}+\frac{a^2 (e x)^{9/2} \sqrt{a+b x^3} (10 A b-3 a B)}{192 b e}+\frac{(e x)^{9/2} \left(a+b x^3\right)^{5/2} (10 A b-3 a B)}{120 b e}+\frac{a (e x)^{9/2} \left(a+b x^3\right)^{3/2} (10 A b-3 a B)}{144 b e}+\frac{B (e x)^{9/2} \left(a+b x^3\right)^{7/2}}{15 b e}",1,"(a^3*(10*A*b - 3*a*B)*e^2*(e*x)^(3/2)*Sqrt[a + b*x^3])/(384*b^2) + (a^2*(10*A*b - 3*a*B)*(e*x)^(9/2)*Sqrt[a + b*x^3])/(192*b*e) + (a*(10*A*b - 3*a*B)*(e*x)^(9/2)*(a + b*x^3)^(3/2))/(144*b*e) + ((10*A*b - 3*a*B)*(e*x)^(9/2)*(a + b*x^3)^(5/2))/(120*b*e) + (B*(e*x)^(9/2)*(a + b*x^3)^(7/2))/(15*b*e) - (a^4*(10*A*b - 3*a*B)*e^(7/2)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(384*b^(5/2))","A",9,7,26,0.2692,1,"{459, 279, 321, 329, 275, 217, 206}"
536,1,404,0,0.3437499,"\int (e x)^{5/2} \left(a+b x^3\right)^{5/2} \left(A+B x^3\right) \, dx","Int[(e*x)^(5/2)*(a + b*x^3)^(5/2)*(A + B*x^3),x]","\frac{81 a^3 e^2 \sqrt{e x} \sqrt{a+b x^3} (4 A b-a B)}{5632 b^2}-\frac{27\ 3^{3/4} a^{11/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{11264 b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a^2 (e x)^{7/2} \sqrt{a+b x^3} (4 A b-a B)}{1408 b e}+\frac{15 a (e x)^{7/2} \left(a+b x^3\right)^{3/2} (4 A b-a B)}{704 b e}+\frac{(e x)^{7/2} \left(a+b x^3\right)^{5/2} (4 A b-a B)}{44 b e}+\frac{B (e x)^{7/2} \left(a+b x^3\right)^{7/2}}{14 b e}","\frac{81 a^3 e^2 \sqrt{e x} \sqrt{a+b x^3} (4 A b-a B)}{5632 b^2}-\frac{27\ 3^{3/4} a^{11/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{11264 b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a^2 (e x)^{7/2} \sqrt{a+b x^3} (4 A b-a B)}{1408 b e}+\frac{15 a (e x)^{7/2} \left(a+b x^3\right)^{3/2} (4 A b-a B)}{704 b e}+\frac{(e x)^{7/2} \left(a+b x^3\right)^{5/2} (4 A b-a B)}{44 b e}+\frac{B (e x)^{7/2} \left(a+b x^3\right)^{7/2}}{14 b e}",1,"(81*a^3*(4*A*b - a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^3])/(5632*b^2) + (27*a^2*(4*A*b - a*B)*(e*x)^(7/2)*Sqrt[a + b*x^3])/(1408*b*e) + (15*a*(4*A*b - a*B)*(e*x)^(7/2)*(a + b*x^3)^(3/2))/(704*b*e) + ((4*A*b - a*B)*(e*x)^(7/2)*(a + b*x^3)^(5/2))/(44*b*e) + (B*(e*x)^(7/2)*(a + b*x^3)^(7/2))/(14*b*e) - (27*3^(3/4)*a^(11/3)*(4*A*b - a*B)*e^2*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(11264*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,5,26,0.1923,1,"{459, 279, 321, 329, 225}"
537,1,661,0,0.7079383,"\int (e x)^{3/2} \left(a+b x^3\right)^{5/2} \left(A+B x^3\right) \, dx","Int[(e*x)^(3/2)*(a + b*x^3)^(5/2)*(A + B*x^3),x]","\frac{81 \left(1+\sqrt{3}\right) a^3 e \sqrt{e x} \sqrt{a+b x^3} (26 A b-5 a B)}{11648 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) a^{10/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (26 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{23296 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{81 \sqrt[4]{3} a^{10/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (26 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{11648 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a^2 (e x)^{5/2} \sqrt{a+b x^3} (26 A b-5 a B)}{5824 b e}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{5/2} (26 A b-5 a B)}{260 b e}+\frac{3 a (e x)^{5/2} \left(a+b x^3\right)^{3/2} (26 A b-5 a B)}{728 b e}+\frac{B (e x)^{5/2} \left(a+b x^3\right)^{7/2}}{13 b e}","\frac{81 \left(1+\sqrt{3}\right) a^3 e \sqrt{e x} \sqrt{a+b x^3} (26 A b-5 a B)}{11648 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) a^{10/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (26 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{23296 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{81 \sqrt[4]{3} a^{10/3} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (26 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{11648 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a^2 (e x)^{5/2} \sqrt{a+b x^3} (26 A b-5 a B)}{5824 b e}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{5/2} (26 A b-5 a B)}{260 b e}+\frac{3 a (e x)^{5/2} \left(a+b x^3\right)^{3/2} (26 A b-5 a B)}{728 b e}+\frac{B (e x)^{5/2} \left(a+b x^3\right)^{7/2}}{13 b e}",1,"(27*a^2*(26*A*b - 5*a*B)*(e*x)^(5/2)*Sqrt[a + b*x^3])/(5824*b*e) + (81*(1 + Sqrt[3])*a^3*(26*A*b - 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^3])/(11648*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + (3*a*(26*A*b - 5*a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(728*b*e) + ((26*A*b - 5*a*B)*(e*x)^(5/2)*(a + b*x^3)^(5/2))/(260*b*e) + (B*(e*x)^(5/2)*(a + b*x^3)^(7/2))/(13*b*e) - (81*3^(1/4)*a^(10/3)*(26*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(11648*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (27*3^(3/4)*(1 - Sqrt[3])*a^(10/3)*(26*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(23296*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",8,6,26,0.2308,1,"{459, 279, 329, 308, 225, 1881}"
538,1,201,0,0.1271238,"\int \sqrt{e x} \left(a+b x^3\right)^{5/2} \left(A+B x^3\right) \, dx","Int[Sqrt[e*x]*(a + b*x^3)^(5/2)*(A + B*x^3),x]","\frac{5 a^3 \sqrt{e} (8 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{192 b^{3/2}}+\frac{5 a^2 (e x)^{3/2} \sqrt{a+b x^3} (8 A b-a B)}{192 b e}+\frac{(e x)^{3/2} \left(a+b x^3\right)^{5/2} (8 A b-a B)}{72 b e}+\frac{5 a (e x)^{3/2} \left(a+b x^3\right)^{3/2} (8 A b-a B)}{288 b e}+\frac{B (e x)^{3/2} \left(a+b x^3\right)^{7/2}}{12 b e}","\frac{5 a^3 \sqrt{e} (8 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{192 b^{3/2}}+\frac{5 a^2 (e x)^{3/2} \sqrt{a+b x^3} (8 A b-a B)}{192 b e}+\frac{(e x)^{3/2} \left(a+b x^3\right)^{5/2} (8 A b-a B)}{72 b e}+\frac{5 a (e x)^{3/2} \left(a+b x^3\right)^{3/2} (8 A b-a B)}{288 b e}+\frac{B (e x)^{3/2} \left(a+b x^3\right)^{7/2}}{12 b e}",1,"(5*a^2*(8*A*b - a*B)*(e*x)^(3/2)*Sqrt[a + b*x^3])/(192*b*e) + (5*a*(8*A*b - a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(288*b*e) + ((8*A*b - a*B)*(e*x)^(3/2)*(a + b*x^3)^(5/2))/(72*b*e) + (B*(e*x)^(3/2)*(a + b*x^3)^(7/2))/(12*b*e) + (5*a^3*(8*A*b - a*B)*Sqrt[e]*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(192*b^(3/2))","A",8,6,26,0.2308,1,"{459, 279, 329, 275, 217, 206}"
539,1,364,0,0.2837236,"\int \frac{\left(a+b x^3\right)^{5/2} \left(A+B x^3\right)}{\sqrt{e x}} \, dx","Int[((a + b*x^3)^(5/2)*(A + B*x^3))/Sqrt[e*x],x]","\frac{27\ 3^{3/4} a^{8/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (22 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2816 b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a^2 \sqrt{e x} \sqrt{a+b x^3} (22 A b-a B)}{1408 b e}+\frac{\sqrt{e x} \left(a+b x^3\right)^{5/2} (22 A b-a B)}{176 b e}+\frac{3 a \sqrt{e x} \left(a+b x^3\right)^{3/2} (22 A b-a B)}{352 b e}+\frac{B \sqrt{e x} \left(a+b x^3\right)^{7/2}}{11 b e}","\frac{27\ 3^{3/4} a^{8/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (22 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2816 b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{27 a^2 \sqrt{e x} \sqrt{a+b x^3} (22 A b-a B)}{1408 b e}+\frac{\sqrt{e x} \left(a+b x^3\right)^{5/2} (22 A b-a B)}{176 b e}+\frac{3 a \sqrt{e x} \left(a+b x^3\right)^{3/2} (22 A b-a B)}{352 b e}+\frac{B \sqrt{e x} \left(a+b x^3\right)^{7/2}}{11 b e}",1,"(27*a^2*(22*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(1408*b*e) + (3*a*(22*A*b - a*B)*Sqrt[e*x]*(a + b*x^3)^(3/2))/(352*b*e) + ((22*A*b - a*B)*Sqrt[e*x]*(a + b*x^3)^(5/2))/(176*b*e) + (B*Sqrt[e*x]*(a + b*x^3)^(7/2))/(11*b*e) + (27*3^(3/4)*a^(8/3)*(22*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(2816*b*e*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,4,26,0.1538,1,"{459, 279, 329, 225}"
540,1,650,0,0.6983794,"\int \frac{\left(a+b x^3\right)^{5/2} \left(A+B x^3\right)}{(e x)^{3/2}} \, dx","Int[((a + b*x^3)^(5/2)*(A + B*x^3))/(e*x)^(3/2),x]","\frac{81 \left(1+\sqrt{3}\right) a^2 \sqrt{e x} \sqrt{a+b x^3} (a B+20 A b)}{448 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) a^{7/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+20 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{896 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{81 \sqrt[4]{3} a^{7/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+20 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{448 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{5/2} (a B+20 A b)}{10 a e^4}+\frac{3 (e x)^{5/2} \left(a+b x^3\right)^{3/2} (a B+20 A b)}{28 e^4}+\frac{27 a (e x)^{5/2} \sqrt{a+b x^3} (a B+20 A b)}{224 e^4}-\frac{2 A \left(a+b x^3\right)^{7/2}}{a e \sqrt{e x}}","\frac{81 \left(1+\sqrt{3}\right) a^2 \sqrt{e x} \sqrt{a+b x^3} (a B+20 A b)}{448 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{27\ 3^{3/4} \left(1-\sqrt{3}\right) a^{7/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+20 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{896 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{81 \sqrt[4]{3} a^{7/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+20 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{448 b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{(e x)^{5/2} \left(a+b x^3\right)^{5/2} (a B+20 A b)}{10 a e^4}+\frac{3 (e x)^{5/2} \left(a+b x^3\right)^{3/2} (a B+20 A b)}{28 e^4}+\frac{27 a (e x)^{5/2} \sqrt{a+b x^3} (a B+20 A b)}{224 e^4}-\frac{2 A \left(a+b x^3\right)^{7/2}}{a e \sqrt{e x}}",1,"(27*a*(20*A*b + a*B)*(e*x)^(5/2)*Sqrt[a + b*x^3])/(224*e^4) + (81*(1 + Sqrt[3])*a^2*(20*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(448*b^(2/3)*e^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + (3*(20*A*b + a*B)*(e*x)^(5/2)*(a + b*x^3)^(3/2))/(28*e^4) + ((20*A*b + a*B)*(e*x)^(5/2)*(a + b*x^3)^(5/2))/(10*a*e^4) - (2*A*(a + b*x^3)^(7/2))/(a*e*Sqrt[e*x]) - (81*3^(1/4)*a^(7/3)*(20*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(448*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (27*3^(3/4)*(1 - Sqrt[3])*a^(7/3)*(20*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(896*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",8,6,26,0.2308,1,"{453, 279, 329, 308, 225, 1881}"
541,1,188,0,0.1283345,"\int \frac{\left(a+b x^3\right)^{5/2} \left(A+B x^3\right)}{(e x)^{5/2}} \, dx","Int[((a + b*x^3)^(5/2)*(A + B*x^3))/(e*x)^(5/2),x]","\frac{5 a^2 (a B+6 A b) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{24 \sqrt{b} e^{5/2}}+\frac{(e x)^{3/2} \left(a+b x^3\right)^{5/2} (a B+6 A b)}{9 a e^4}+\frac{5 (e x)^{3/2} \left(a+b x^3\right)^{3/2} (a B+6 A b)}{36 e^4}+\frac{5 a (e x)^{3/2} \sqrt{a+b x^3} (a B+6 A b)}{24 e^4}-\frac{2 A \left(a+b x^3\right)^{7/2}}{3 a e (e x)^{3/2}}","\frac{5 a^2 (a B+6 A b) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{24 \sqrt{b} e^{5/2}}+\frac{(e x)^{3/2} \left(a+b x^3\right)^{5/2} (a B+6 A b)}{9 a e^4}+\frac{5 (e x)^{3/2} \left(a+b x^3\right)^{3/2} (a B+6 A b)}{36 e^4}+\frac{5 a (e x)^{3/2} \sqrt{a+b x^3} (a B+6 A b)}{24 e^4}-\frac{2 A \left(a+b x^3\right)^{7/2}}{3 a e (e x)^{3/2}}",1,"(5*a*(6*A*b + a*B)*(e*x)^(3/2)*Sqrt[a + b*x^3])/(24*e^4) + (5*(6*A*b + a*B)*(e*x)^(3/2)*(a + b*x^3)^(3/2))/(36*e^4) + ((6*A*b + a*B)*(e*x)^(3/2)*(a + b*x^3)^(5/2))/(9*a*e^4) - (2*A*(a + b*x^3)^(7/2))/(3*a*e*(e*x)^(3/2)) + (5*a^2*(6*A*b + a*B)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(24*Sqrt[b]*e^(5/2))","A",8,6,26,0.2308,1,"{453, 279, 329, 275, 217, 206}"
542,1,352,0,0.2866745,"\int \frac{\left(a+b x^3\right)^{5/2} \left(A+B x^3\right)}{(e x)^{7/2}} \, dx","Int[((a + b*x^3)^(5/2)*(A + B*x^3))/(e*x)^(7/2),x]","\frac{27\ 3^{3/4} a^{5/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+16 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \left(a+b x^3\right)^{5/2} (5 a B+16 A b)}{40 a e^4}+\frac{3 \sqrt{e x} \left(a+b x^3\right)^{3/2} (5 a B+16 A b)}{80 e^4}+\frac{27 a \sqrt{e x} \sqrt{a+b x^3} (5 a B+16 A b)}{320 e^4}-\frac{2 A \left(a+b x^3\right)^{7/2}}{5 a e (e x)^{5/2}}","\frac{27\ 3^{3/4} a^{5/3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+16 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{640 e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\sqrt{e x} \left(a+b x^3\right)^{5/2} (5 a B+16 A b)}{40 a e^4}+\frac{3 \sqrt{e x} \left(a+b x^3\right)^{3/2} (5 a B+16 A b)}{80 e^4}+\frac{27 a \sqrt{e x} \sqrt{a+b x^3} (5 a B+16 A b)}{320 e^4}-\frac{2 A \left(a+b x^3\right)^{7/2}}{5 a e (e x)^{5/2}}",1,"(27*a*(16*A*b + 5*a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(320*e^4) + (3*(16*A*b + 5*a*B)*Sqrt[e*x]*(a + b*x^3)^(3/2))/(80*e^4) + ((16*A*b + 5*a*B)*Sqrt[e*x]*(a + b*x^3)^(5/2))/(40*a*e^4) - (2*A*(a + b*x^3)^(7/2))/(5*a*e*(e*x)^(5/2)) + (27*3^(3/4)*a^(5/3)*(16*A*b + 5*a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(640*e^4*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,4,26,0.1538,1,"{453, 279, 329, 225}"
543,1,121,0,0.0860604,"\int \frac{(e x)^{7/2} \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[((e*x)^(7/2)*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{e^2 (e x)^{3/2} \sqrt{a+b x^3} (4 A b-3 a B)}{12 b^2}-\frac{a e^{7/2} (4 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{12 b^{5/2}}+\frac{B (e x)^{9/2} \sqrt{a+b x^3}}{6 b e}","\frac{e^2 (e x)^{3/2} \sqrt{a+b x^3} (4 A b-3 a B)}{12 b^2}-\frac{a e^{7/2} (4 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{12 b^{5/2}}+\frac{B (e x)^{9/2} \sqrt{a+b x^3}}{6 b e}",1,"((4*A*b - 3*a*B)*e^2*(e*x)^(3/2)*Sqrt[a + b*x^3])/(12*b^2) + (B*(e*x)^(9/2)*Sqrt[a + b*x^3])/(6*b*e) - (a*(4*A*b - 3*a*B)*e^(7/2)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(12*b^(5/2))","A",6,6,26,0.2308,1,"{459, 321, 329, 275, 217, 206}"
544,1,286,0,0.2216296,"\int \frac{(e x)^{5/2} \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[((e*x)^(5/2)*(A + B*x^3))/Sqrt[a + b*x^3],x]","-\frac{a^{2/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 \sqrt[4]{3} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{e^2 \sqrt{e x} \sqrt{a+b x^3} (10 A b-7 a B)}{20 b^2}+\frac{B (e x)^{7/2} \sqrt{a+b x^3}}{5 b e}","-\frac{a^{2/3} e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{40 \sqrt[4]{3} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{e^2 \sqrt{e x} \sqrt{a+b x^3} (10 A b-7 a B)}{20 b^2}+\frac{B (e x)^{7/2} \sqrt{a+b x^3}}{5 b e}",1,"((10*A*b - 7*a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^3])/(20*b^2) + (B*(e*x)^(7/2)*Sqrt[a + b*x^3])/(5*b*e) - (a^(2/3)*(10*A*b - 7*a*B)*e^2*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(40*3^(1/4)*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{459, 321, 329, 225}"
545,1,543,0,0.5007641,"\int \frac{(e x)^{3/2} \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[((e*x)^(3/2)*(A + B*x^3))/Sqrt[a + b*x^3],x]","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (8 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt[3]{a} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (8 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(1+\sqrt{3}\right) e \sqrt{e x} \sqrt{a+b x^3} (8 A b-5 a B)}{8 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{B (e x)^{5/2} \sqrt{a+b x^3}}{4 b e}","-\frac{\left(1-\sqrt{3}\right) \sqrt[3]{a} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (8 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{16 \sqrt[4]{3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt[3]{a} e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (8 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{8 b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(1+\sqrt{3}\right) e \sqrt{e x} \sqrt{a+b x^3} (8 A b-5 a B)}{8 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{B (e x)^{5/2} \sqrt{a+b x^3}}{4 b e}",1,"(B*(e*x)^(5/2)*Sqrt[a + b*x^3])/(4*b*e) + ((1 + Sqrt[3])*(8*A*b - 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^3])/(8*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) - (3^(1/4)*a^(1/3)*(8*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(8*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - ((1 - Sqrt[3])*a^(1/3)*(8*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(16*3^(1/4)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,26,0.1923,1,"{459, 329, 308, 225, 1881}"
546,1,83,0,0.0673085,"\int \frac{\sqrt{e x} \left(A+B x^3\right)}{\sqrt{a+b x^3}} \, dx","Int[(Sqrt[e*x]*(A + B*x^3))/Sqrt[a + b*x^3],x]","\frac{\sqrt{e} (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{3/2}}+\frac{B (e x)^{3/2} \sqrt{a+b x^3}}{3 b e}","\frac{\sqrt{e} (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{3/2}}+\frac{B (e x)^{3/2} \sqrt{a+b x^3}}{3 b e}",1,"(B*(e*x)^(3/2)*Sqrt[a + b*x^3])/(3*b*e) + ((2*A*b - a*B)*Sqrt[e]*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(3*b^(3/2))","A",5,5,26,0.1923,1,"{459, 329, 275, 217, 206}"
547,1,249,0,0.1829858,"\int \frac{A+B x^3}{\sqrt{e x} \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/(Sqrt[e*x]*Sqrt[a + b*x^3]),x]","\frac{\sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[4]{3} \sqrt[3]{a} b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{B \sqrt{e x} \sqrt{a+b x^3}}{2 b e}","\frac{\sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{4 \sqrt[4]{3} \sqrt[3]{a} b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{B \sqrt{e x} \sqrt{a+b x^3}}{2 b e}",1,"(B*Sqrt[e*x]*Sqrt[a + b*x^3])/(2*b*e) + ((4*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(4*3^(1/4)*a^(1/3)*b*e*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,26,0.1154,1,"{459, 329, 225}"
548,1,542,0,0.5049858,"\int \frac{A+B x^3}{(e x)^{3/2} \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/((e*x)^(3/2)*Sqrt[a + b*x^3]),x]","-\frac{\left(1-\sqrt{3}\right) \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} a^{2/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{a^{2/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (a B+2 A b)}{a b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{2 A \sqrt{a+b x^3}}{a e \sqrt{e x}}","-\frac{\left(1-\sqrt{3}\right) \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{2 \sqrt[4]{3} a^{2/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\sqrt[4]{3} \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{a^{2/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{\left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (a B+2 A b)}{a b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{2 A \sqrt{a+b x^3}}{a e \sqrt{e x}}",1,"(-2*A*Sqrt[a + b*x^3])/(a*e*Sqrt[e*x]) + ((1 + Sqrt[3])*(2*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(a*b^(2/3)*e^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) - (3^(1/4)*(2*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(a^(2/3)*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - ((1 - Sqrt[3])*(2*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(2*3^(1/4)*a^(2/3)*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,26,0.1923,1,"{453, 329, 308, 225, 1881}"
549,1,75,0,0.0570957,"\int \frac{A+B x^3}{(e x)^{5/2} \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/((e*x)^(5/2)*Sqrt[a + b*x^3]),x]","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 \sqrt{b} e^{5/2}}-\frac{2 A \sqrt{a+b x^3}}{3 a e (e x)^{3/2}}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 \sqrt{b} e^{5/2}}-\frac{2 A \sqrt{a+b x^3}}{3 a e (e x)^{3/2}}",1,"(-2*A*Sqrt[a + b*x^3])/(3*a*e*(e*x)^(3/2)) + (2*B*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(3*Sqrt[b]*e^(5/2))","A",5,5,26,0.1923,1,"{451, 329, 275, 217, 206}"
550,1,246,0,0.1830945,"\int \frac{A+B x^3}{(e x)^{7/2} \sqrt{a+b x^3}} \, dx","Int[(A + B*x^3)/((e*x)^(7/2)*Sqrt[a + b*x^3]),x]","-\frac{\sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} a^{4/3} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 A \sqrt{a+b x^3}}{5 a e (e x)^{5/2}}","-\frac{\sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{5 \sqrt[4]{3} a^{4/3} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 A \sqrt{a+b x^3}}{5 a e (e x)^{5/2}}",1,"(-2*A*Sqrt[a + b*x^3])/(5*a*e*(e*x)^(5/2)) - ((2*A*b - 5*a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(5*3^(1/4)*a^(4/3)*e^4*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,26,0.1154,1,"{453, 329, 225}"
551,1,120,0,0.0864786,"\int \frac{(e x)^{7/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[((e*x)^(7/2)*(A + B*x^3))/(a + b*x^3)^(3/2),x]","-\frac{e^2 (e x)^{3/2} (2 A b-3 a B)}{3 b^2 \sqrt{a+b x^3}}+\frac{e^{7/2} (2 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{5/2}}+\frac{B (e x)^{9/2}}{3 b e \sqrt{a+b x^3}}","-\frac{e^2 (e x)^{3/2} (2 A b-3 a B)}{3 b^2 \sqrt{a+b x^3}}+\frac{e^{7/2} (2 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{5/2}}+\frac{B (e x)^{9/2}}{3 b e \sqrt{a+b x^3}}",1,"-((2*A*b - 3*a*B)*e^2*(e*x)^(3/2))/(3*b^2*Sqrt[a + b*x^3]) + (B*(e*x)^(9/2))/(3*b*e*Sqrt[a + b*x^3]) + ((2*A*b - 3*a*B)*e^(7/2)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(3*b^(5/2))","A",6,6,26,0.2308,1,"{459, 288, 329, 275, 217, 206}"
552,1,286,0,0.2213208,"\int \frac{(e x)^{5/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[((e*x)^(5/2)*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{12 \sqrt[4]{3} \sqrt[3]{a} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{e^2 \sqrt{e x} (4 A b-7 a B)}{6 b^2 \sqrt{a+b x^3}}+\frac{B (e x)^{7/2}}{2 b e \sqrt{a+b x^3}}","\frac{e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-7 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{12 \sqrt[4]{3} \sqrt[3]{a} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{e^2 \sqrt{e x} (4 A b-7 a B)}{6 b^2 \sqrt{a+b x^3}}+\frac{B (e x)^{7/2}}{2 b e \sqrt{a+b x^3}}",1,"-((4*A*b - 7*a*B)*e^2*Sqrt[e*x])/(6*b^2*Sqrt[a + b*x^3]) + (B*(e*x)^(7/2))/(2*b*e*Sqrt[a + b*x^3]) + ((4*A*b - 7*a*B)*e^2*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(12*3^(1/4)*a^(1/3)*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{459, 288, 329, 225}"
553,1,553,0,0.5025032,"\int \frac{(e x)^{3/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[((e*x)^(3/2)*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{\left(1-\sqrt{3}\right) e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6 \sqrt[4]{3} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3^{3/4} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(1+\sqrt{3}\right) e \sqrt{e x} \sqrt{a+b x^3} (2 A b-5 a B)}{3 a b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{2 (e x)^{5/2} (A b-a B)}{3 a b e \sqrt{a+b x^3}}","\frac{\left(1-\sqrt{3}\right) e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{6 \sqrt[4]{3} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (2 A b-5 a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3^{3/4} a^{2/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{\left(1+\sqrt{3}\right) e \sqrt{e x} \sqrt{a+b x^3} (2 A b-5 a B)}{3 a b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{2 (e x)^{5/2} (A b-a B)}{3 a b e \sqrt{a+b x^3}}",1,"(2*(A*b - a*B)*(e*x)^(5/2))/(3*a*b*e*Sqrt[a + b*x^3]) - ((1 + Sqrt[3])*(2*A*b - 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^3])/(3*a*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + ((2*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3^(3/4)*a^(2/3)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + ((1 - Sqrt[3])*(2*A*b - 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(6*3^(1/4)*a^(2/3)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,5,26,0.1923,1,"{457, 329, 308, 225, 1881}"
554,1,85,0,0.0623942,"\int \frac{\sqrt{e x} \left(A+B x^3\right)}{\left(a+b x^3\right)^{3/2}} \, dx","Int[(Sqrt[e*x]*(A + B*x^3))/(a + b*x^3)^(3/2),x]","\frac{2 (e x)^{3/2} (A b-a B)}{3 a b e \sqrt{a+b x^3}}+\frac{2 B \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{3/2}}","\frac{2 (e x)^{3/2} (A b-a B)}{3 a b e \sqrt{a+b x^3}}+\frac{2 B \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{3/2}}",1,"(2*(A*b - a*B)*(e*x)^(3/2))/(3*a*b*e*Sqrt[a + b*x^3]) + (2*B*Sqrt[e]*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(3*b^(3/2))","A",5,5,26,0.1923,1,"{452, 329, 275, 217, 206}"
555,1,258,0,0.188183,"\int \frac{A+B x^3}{\sqrt{e x} \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/(Sqrt[e*x]*(a + b*x^3)^(3/2)),x]","\frac{\sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3 \sqrt[4]{3} a^{4/3} b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{e x} (A b-a B)}{3 a b e \sqrt{a+b x^3}}","\frac{\sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3 \sqrt[4]{3} a^{4/3} b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{e x} (A b-a B)}{3 a b e \sqrt{a+b x^3}}",1,"(2*(A*b - a*B)*Sqrt[e*x])/(3*a*b*e*Sqrt[a + b*x^3]) + ((2*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3*3^(1/4)*a^(4/3)*b*e*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",3,3,26,0.1154,1,"{457, 329, 225}"
556,1,585,0,0.5707692,"\int \frac{A+B x^3}{(e x)^{3/2} \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(3/2)),x]","\frac{2 \left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (4 A b-a B)}{3 a^2 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{\left(1-\sqrt{3}\right) \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3 \sqrt[4]{3} a^{5/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3^{3/4} a^{5/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 (e x)^{5/2} (4 A b-a B)}{3 a^2 e^4 \sqrt{a+b x^3}}-\frac{2 A}{a e \sqrt{e x} \sqrt{a+b x^3}}","\frac{2 \left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (4 A b-a B)}{3 a^2 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{\left(1-\sqrt{3}\right) \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3 \sqrt[4]{3} a^{5/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (4 A b-a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{3^{3/4} a^{5/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 (e x)^{5/2} (4 A b-a B)}{3 a^2 e^4 \sqrt{a+b x^3}}-\frac{2 A}{a e \sqrt{e x} \sqrt{a+b x^3}}",1,"(-2*A)/(a*e*Sqrt[e*x]*Sqrt[a + b*x^3]) - (2*(4*A*b - a*B)*(e*x)^(5/2))/(3*a^2*e^4*Sqrt[a + b*x^3]) + (2*(1 + Sqrt[3])*(4*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(3*a^2*b^(2/3)*e^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) - (2*(4*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3^(3/4)*a^(5/3)*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - ((1 - Sqrt[3])*(4*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(3*3^(1/4)*a^(5/3)*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,26,0.2308,1,"{453, 290, 329, 308, 225, 1881}"
557,1,67,0,0.029186,"\int \frac{A+B x^3}{(e x)^{5/2} \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(3/2)),x]","-\frac{2 (e x)^{3/2} (2 A b-a B)}{3 a^2 e^4 \sqrt{a+b x^3}}-\frac{2 A}{3 a e (e x)^{3/2} \sqrt{a+b x^3}}","-\frac{2 (e x)^{3/2} (2 A b-a B)}{3 a^2 e^4 \sqrt{a+b x^3}}-\frac{2 A}{3 a e (e x)^{3/2} \sqrt{a+b x^3}}",1,"(-2*A)/(3*a*e*(e*x)^(3/2)*Sqrt[a + b*x^3]) - (2*(2*A*b - a*B)*(e*x)^(3/2))/(3*a^2*e^4*Sqrt[a + b*x^3])","A",2,2,26,0.07692,1,"{453, 264}"
558,1,283,0,0.2226521,"\int \frac{A+B x^3}{(e x)^{7/2} \left(a+b x^3\right)^{3/2}} \, dx","Int[(A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(3/2)),x]","-\frac{2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (8 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{15 \sqrt[4]{3} a^{7/3} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{e x} (8 A b-5 a B)}{15 a^2 e^4 \sqrt{a+b x^3}}-\frac{2 A}{5 a e (e x)^{5/2} \sqrt{a+b x^3}}","-\frac{2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (8 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{15 \sqrt[4]{3} a^{7/3} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 \sqrt{e x} (8 A b-5 a B)}{15 a^2 e^4 \sqrt{a+b x^3}}-\frac{2 A}{5 a e (e x)^{5/2} \sqrt{a+b x^3}}",1,"(-2*A)/(5*a*e*(e*x)^(5/2)*Sqrt[a + b*x^3]) - (2*(8*A*b - 5*a*B)*Sqrt[e*x])/(15*a^2*e^4*Sqrt[a + b*x^3]) - (2*(8*A*b - 5*a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(15*3^(1/4)*a^(7/3)*e^4*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{453, 290, 329, 225}"
559,1,114,0,0.0750009,"\int \frac{(e x)^{7/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[((e*x)^(7/2)*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{2 (e x)^{9/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}-\frac{2 B e^2 (e x)^{3/2}}{3 b^2 \sqrt{a+b x^3}}+\frac{2 B e^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{5/2}}","\frac{2 (e x)^{9/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}-\frac{2 B e^2 (e x)^{3/2}}{3 b^2 \sqrt{a+b x^3}}+\frac{2 B e^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} (e x)^{3/2}}{e^{3/2} \sqrt{a+b x^3}}\right)}{3 b^{5/2}}",1,"(2*(A*b - a*B)*(e*x)^(9/2))/(9*a*b*e*(a + b*x^3)^(3/2)) - (2*B*e^2*(e*x)^(3/2))/(3*b^2*Sqrt[a + b*x^3]) + (2*B*e^(7/2)*ArcTanh[(Sqrt[b]*(e*x)^(3/2))/(e^(3/2)*Sqrt[a + b*x^3])])/(3*b^(5/2))","A",6,6,26,0.2308,1,"{452, 288, 329, 275, 217, 206}"
560,1,299,0,0.2288177,"\int \frac{(e x)^{5/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[((e*x)^(5/2)*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (7 a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{4/3} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 e^2 \sqrt{e x} (7 a B+2 A b)}{27 a b^2 \sqrt{a+b x^3}}+\frac{2 (e x)^{7/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}","\frac{e^2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (7 a B+2 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{4/3} b^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{2 e^2 \sqrt{e x} (7 a B+2 A b)}{27 a b^2 \sqrt{a+b x^3}}+\frac{2 (e x)^{7/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*(e*x)^(7/2))/(9*a*b*e*(a + b*x^3)^(3/2)) - (2*(2*A*b + 7*a*B)*e^2*Sqrt[e*x])/(27*a*b^2*Sqrt[a + b*x^3]) + ((2*A*b + 7*a*B)*e^2*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(27*3^(1/4)*a^(4/3)*b^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{457, 288, 329, 225}"
561,1,596,0,0.5726808,"\int \frac{(e x)^{3/2} \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[((e*x)^(3/2)*(A + B*x^3))/(a + b*x^3)^(5/2),x]","-\frac{2 \left(1+\sqrt{3}\right) e \sqrt{e x} \sqrt{a+b x^3} (5 a B+4 A b)}{27 a^2 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{\left(1-\sqrt{3}\right) e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+4 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+4 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9\ 3^{3/4} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 (e x)^{5/2} (5 a B+4 A b)}{27 a^2 b e \sqrt{a+b x^3}}+\frac{2 (e x)^{5/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}","-\frac{2 \left(1+\sqrt{3}\right) e \sqrt{e x} \sqrt{a+b x^3} (5 a B+4 A b)}{27 a^2 b^{5/3} \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}+\frac{\left(1-\sqrt{3}\right) e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+4 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 e \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (5 a B+4 A b) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9\ 3^{3/4} a^{5/3} b^{5/3} \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 (e x)^{5/2} (5 a B+4 A b)}{27 a^2 b e \sqrt{a+b x^3}}+\frac{2 (e x)^{5/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*(e*x)^(5/2))/(9*a*b*e*(a + b*x^3)^(3/2)) + (2*(4*A*b + 5*a*B)*(e*x)^(5/2))/(27*a^2*b*e*Sqrt[a + b*x^3]) - (2*(1 + Sqrt[3])*(4*A*b + 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^3])/(27*a^2*b^(5/3)*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) + (2*(4*A*b + 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(9*3^(3/4)*a^(5/3)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) + ((1 - Sqrt[3])*(4*A*b + 5*a*B)*e*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(27*3^(1/4)*a^(5/3)*b^(5/3)*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",6,6,26,0.2308,1,"{457, 290, 329, 308, 225, 1881}"
562,1,79,0,0.0311775,"\int \frac{\sqrt{e x} \left(A+B x^3\right)}{\left(a+b x^3\right)^{5/2}} \, dx","Int[(Sqrt[e*x]*(A + B*x^3))/(a + b*x^3)^(5/2),x]","\frac{2 (e x)^{3/2} (a B+2 A b)}{9 a^2 b e \sqrt{a+b x^3}}+\frac{2 (e x)^{3/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}","\frac{2 (e x)^{3/2} (a B+2 A b)}{9 a^2 b e \sqrt{a+b x^3}}+\frac{2 (e x)^{3/2} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*(e*x)^(3/2))/(9*a*b*e*(a + b*x^3)^(3/2)) + (2*(2*A*b + a*B)*(e*x)^(3/2))/(9*a^2*b*e*Sqrt[a + b*x^3])","A",2,2,26,0.07692,1,"{457, 264}"
563,1,297,0,0.2220826,"\int \frac{A+B x^3}{\sqrt{e x} \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/(Sqrt[e*x]*(a + b*x^3)^(5/2)),x]","\frac{2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+8 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{7/3} b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{e x} (a B+8 A b)}{27 a^2 b e \sqrt{a+b x^3}}+\frac{2 \sqrt{e x} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}","\frac{2 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (a B+8 A b) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{7/3} b e \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}+\frac{2 \sqrt{e x} (a B+8 A b)}{27 a^2 b e \sqrt{a+b x^3}}+\frac{2 \sqrt{e x} (A b-a B)}{9 a b e \left(a+b x^3\right)^{3/2}}",1,"(2*(A*b - a*B)*Sqrt[e*x])/(9*a*b*e*(a + b*x^3)^(3/2)) + (2*(8*A*b + a*B)*Sqrt[e*x])/(27*a^2*b*e*Sqrt[a + b*x^3]) + (2*(8*A*b + a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(27*3^(1/4)*a^(7/3)*b*e*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",4,4,26,0.1538,1,"{457, 290, 329, 225}"
564,1,624,0,0.6386002,"\int \frac{A+B x^3}{(e x)^{3/2} \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/((e*x)^(3/2)*(a + b*x^3)^(5/2)),x]","\frac{8 \left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (10 A b-a B)}{27 a^3 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{4 \left(1-\sqrt{3}\right) \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{8/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9\ 3^{3/4} a^{8/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 (e x)^{5/2} (10 A b-a B)}{27 a^3 e^4 \sqrt{a+b x^3}}-\frac{2 (e x)^{5/2} (10 A b-a B)}{9 a^2 e^4 \left(a+b x^3\right)^{3/2}}-\frac{2 A}{a e \sqrt{e x} \left(a+b x^3\right)^{3/2}}","\frac{8 \left(1+\sqrt{3}\right) \sqrt{e x} \sqrt{a+b x^3} (10 A b-a B)}{27 a^3 b^{2/3} e^2 \left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)}-\frac{4 \left(1-\sqrt{3}\right) \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{27 \sqrt[4]{3} a^{8/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (10 A b-a B) E\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{9\ 3^{3/4} a^{8/3} b^{2/3} e^2 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{8 (e x)^{5/2} (10 A b-a B)}{27 a^3 e^4 \sqrt{a+b x^3}}-\frac{2 (e x)^{5/2} (10 A b-a B)}{9 a^2 e^4 \left(a+b x^3\right)^{3/2}}-\frac{2 A}{a e \sqrt{e x} \left(a+b x^3\right)^{3/2}}",1,"(-2*A)/(a*e*Sqrt[e*x]*(a + b*x^3)^(3/2)) - (2*(10*A*b - a*B)*(e*x)^(5/2))/(9*a^2*e^4*(a + b*x^3)^(3/2)) - (8*(10*A*b - a*B)*(e*x)^(5/2))/(27*a^3*e^4*Sqrt[a + b*x^3]) + (8*(1 + Sqrt[3])*(10*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^3])/(27*a^3*b^(2/3)*e^2*(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)) - (8*(10*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticE[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(9*3^(3/4)*a^(8/3)*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3]) - (4*(1 - Sqrt[3])*(10*A*b - a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(27*3^(1/4)*a^(8/3)*b^(2/3)*e^2*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",7,6,26,0.2308,1,"{453, 290, 329, 308, 225, 1881}"
565,1,104,0,0.0464514,"\int \frac{A+B x^3}{(e x)^{5/2} \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/((e*x)^(5/2)*(a + b*x^3)^(5/2)),x]","-\frac{4 (e x)^{3/2} (4 A b-a B)}{9 a^3 e^4 \sqrt{a+b x^3}}-\frac{2 (e x)^{3/2} (4 A b-a B)}{9 a^2 e^4 \left(a+b x^3\right)^{3/2}}-\frac{2 A}{3 a e (e x)^{3/2} \left(a+b x^3\right)^{3/2}}","-\frac{4 (e x)^{3/2} (4 A b-a B)}{9 a^3 e^4 \sqrt{a+b x^3}}-\frac{2 (e x)^{3/2} (4 A b-a B)}{9 a^2 e^4 \left(a+b x^3\right)^{3/2}}-\frac{2 A}{3 a e (e x)^{3/2} \left(a+b x^3\right)^{3/2}}",1,"(-2*A)/(3*a*e*(e*x)^(3/2)*(a + b*x^3)^(3/2)) - (2*(4*A*b - a*B)*(e*x)^(3/2))/(9*a^2*e^4*(a + b*x^3)^(3/2)) - (4*(4*A*b - a*B)*(e*x)^(3/2))/(9*a^3*e^4*Sqrt[a + b*x^3])","A",3,3,26,0.1154,1,"{453, 273, 264}"
566,1,320,0,0.2576916,"\int \frac{A+B x^3}{(e x)^{7/2} \left(a+b x^3\right)^{5/2}} \, dx","Int[(A + B*x^3)/((e*x)^(7/2)*(a + b*x^3)^(5/2)),x]","-\frac{16 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (14 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{135 \sqrt[4]{3} a^{10/3} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{16 \sqrt{e x} (14 A b-5 a B)}{135 a^3 e^4 \sqrt{a+b x^3}}-\frac{2 \sqrt{e x} (14 A b-5 a B)}{45 a^2 e^4 \left(a+b x^3\right)^{3/2}}-\frac{2 A}{5 a e (e x)^{5/2} \left(a+b x^3\right)^{3/2}}","-\frac{16 \sqrt{e x} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right) \sqrt{\frac{a^{2/3}-\sqrt[3]{a} \sqrt[3]{b} x+b^{2/3} x^2}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} (14 A b-5 a B) F\left(\cos ^{-1}\left(\frac{\left(1-\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}{\left(1+\sqrt{3}\right) \sqrt[3]{b} x+\sqrt[3]{a}}\right)|\frac{1}{4} \left(2+\sqrt{3}\right)\right)}{135 \sqrt[4]{3} a^{10/3} e^4 \sqrt{\frac{\sqrt[3]{b} x \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\left(\sqrt[3]{a}+\left(1+\sqrt{3}\right) \sqrt[3]{b} x\right)^2}} \sqrt{a+b x^3}}-\frac{16 \sqrt{e x} (14 A b-5 a B)}{135 a^3 e^4 \sqrt{a+b x^3}}-\frac{2 \sqrt{e x} (14 A b-5 a B)}{45 a^2 e^4 \left(a+b x^3\right)^{3/2}}-\frac{2 A}{5 a e (e x)^{5/2} \left(a+b x^3\right)^{3/2}}",1,"(-2*A)/(5*a*e*(e*x)^(5/2)*(a + b*x^3)^(3/2)) - (2*(14*A*b - 5*a*B)*Sqrt[e*x])/(45*a^2*e^4*(a + b*x^3)^(3/2)) - (16*(14*A*b - 5*a*B)*Sqrt[e*x])/(135*a^3*e^4*Sqrt[a + b*x^3]) - (16*(14*A*b - 5*a*B)*Sqrt[e*x]*(a^(1/3) + b^(1/3)*x)*Sqrt[(a^(2/3) - a^(1/3)*b^(1/3)*x + b^(2/3)*x^2)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*EllipticF[ArcCos[(a^(1/3) + (1 - Sqrt[3])*b^(1/3)*x)/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)], (2 + Sqrt[3])/4])/(135*3^(1/4)*a^(10/3)*e^4*Sqrt[(b^(1/3)*x*(a^(1/3) + b^(1/3)*x))/(a^(1/3) + (1 + Sqrt[3])*b^(1/3)*x)^2]*Sqrt[a + b*x^3])","A",5,4,26,0.1538,1,"{453, 290, 329, 225}"
567,1,220,0,0.235602,"\int \frac{x^{11} \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^11*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","-\frac{a^3 \sqrt[3]{a+b x^3}}{b^4 d}-\frac{a^2 \left(a+b x^3\right)^{4/3}}{4 b^4 d}+\frac{a^{10/3} \log \left(a-b x^3\right)}{3\ 2^{2/3} b^4 d}-\frac{a^{10/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^4 d}+\frac{\sqrt[3]{2} a^{10/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^4 d}+\frac{a \left(a+b x^3\right)^{7/3}}{7 b^4 d}-\frac{\left(a+b x^3\right)^{10/3}}{10 b^4 d}","-\frac{a^3 \sqrt[3]{a+b x^3}}{b^4 d}-\frac{a^2 \left(a+b x^3\right)^{4/3}}{4 b^4 d}+\frac{a^{10/3} \log \left(a-b x^3\right)}{3\ 2^{2/3} b^4 d}-\frac{a^{10/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^4 d}+\frac{\sqrt[3]{2} a^{10/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^4 d}+\frac{a \left(a+b x^3\right)^{7/3}}{7 b^4 d}-\frac{\left(a+b x^3\right)^{10/3}}{10 b^4 d}",1,"-((a^3*(a + b*x^3)^(1/3))/(b^4*d)) - (a^2*(a + b*x^3)^(4/3))/(4*b^4*d) + (a*(a + b*x^3)^(7/3))/(7*b^4*d) - (a + b*x^3)^(10/3)/(10*b^4*d) + (2^(1/3)*a^(10/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^4*d) + (a^(10/3)*Log[a - b*x^3])/(3*2^(2/3)*b^4*d) - (a^(10/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(2/3)*b^4*d)","A",8,7,28,0.2500,1,"{446, 88, 50, 57, 617, 204, 31}"
568,1,174,0,0.1784902,"\int \frac{x^8 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^8*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","-\frac{a^2 \sqrt[3]{a+b x^3}}{b^3 d}+\frac{a^{7/3} \log \left(a-b x^3\right)}{3\ 2^{2/3} b^3 d}-\frac{a^{7/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^3 d}+\frac{\sqrt[3]{2} a^{7/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^3 d}-\frac{\left(a+b x^3\right)^{7/3}}{7 b^3 d}","-\frac{a^2 \sqrt[3]{a+b x^3}}{b^3 d}+\frac{a^{7/3} \log \left(a-b x^3\right)}{3\ 2^{2/3} b^3 d}-\frac{a^{7/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^3 d}+\frac{\sqrt[3]{2} a^{7/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^3 d}-\frac{\left(a+b x^3\right)^{7/3}}{7 b^3 d}",1,"-((a^2*(a + b*x^3)^(1/3))/(b^3*d)) - (a + b*x^3)^(7/3)/(7*b^3*d) + (2^(1/3)*a^(7/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^3*d) + (a^(7/3)*Log[a - b*x^3])/(3*2^(2/3)*b^3*d) - (a^(7/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(2/3)*b^3*d)","A",8,7,28,0.2500,1,"{446, 88, 50, 57, 617, 204, 31}"
569,1,172,0,0.1485677,"\int \frac{x^5 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^5*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","\frac{a^{4/3} \log \left(a-b x^3\right)}{3\ 2^{2/3} b^2 d}-\frac{a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^2 d}+\frac{\sqrt[3]{2} a^{4/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^2 d}-\frac{a \sqrt[3]{a+b x^3}}{b^2 d}-\frac{\left(a+b x^3\right)^{4/3}}{4 b^2 d}","\frac{a^{4/3} \log \left(a-b x^3\right)}{3\ 2^{2/3} b^2 d}-\frac{a^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^2 d}+\frac{\sqrt[3]{2} a^{4/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^2 d}-\frac{a \sqrt[3]{a+b x^3}}{b^2 d}-\frac{\left(a+b x^3\right)^{4/3}}{4 b^2 d}",1,"-((a*(a + b*x^3)^(1/3))/(b^2*d)) - (a + b*x^3)^(4/3)/(4*b^2*d) + (2^(1/3)*a^(4/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^2*d) + (a^(4/3)*Log[a - b*x^3])/(3*2^(2/3)*b^2*d) - (a^(4/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(2/3)*b^2*d)","A",7,7,28,0.2500,1,"{446, 80, 50, 57, 617, 204, 31}"
570,1,150,0,0.1185227,"\int \frac{x^2 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^2*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","-\frac{\sqrt[3]{a+b x^3}}{b d}+\frac{\sqrt[3]{a} \log \left(a-b x^3\right)}{3\ 2^{2/3} b d}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b d}+\frac{\sqrt[3]{2} \sqrt[3]{a} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b d}","-\frac{\sqrt[3]{a+b x^3}}{b d}+\frac{\sqrt[3]{a} \log \left(a-b x^3\right)}{3\ 2^{2/3} b d}-\frac{\sqrt[3]{a} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b d}+\frac{\sqrt[3]{2} \sqrt[3]{a} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b d}",1,"-((a + b*x^3)^(1/3)/(b*d)) + (2^(1/3)*a^(1/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b*d) + (a^(1/3)*Log[a - b*x^3])/(3*2^(2/3)*b*d) - (a^(1/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(2/3)*b*d)","A",6,6,28,0.2143,1,"{444, 50, 57, 617, 204, 31}"
571,1,214,0,0.1738034,"\int \frac{\sqrt[3]{a+b x^3}}{x \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x*(a*d - b*d*x^3)),x]","\frac{\log \left(a-b x^3\right)}{3\ 2^{2/3} a^{2/3} d}+\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{2/3} d}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^{2/3} d}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} d}+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} d}-\frac{\log (x)}{2 a^{2/3} d}","\frac{\log \left(a-b x^3\right)}{3\ 2^{2/3} a^{2/3} d}+\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{2/3} d}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^{2/3} d}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} d}+\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} d}-\frac{\log (x)}{2 a^{2/3} d}",1,"-(ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*d)) + (2^(1/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(2/3)*d) - Log[x]/(2*a^(2/3)*d) + Log[a - b*x^3]/(3*2^(2/3)*a^(2/3)*d) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(2/3)*d) - Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)]/(2^(2/3)*a^(2/3)*d)","A",10,6,28,0.2143,1,"{446, 83, 57, 617, 204, 31}"
572,1,268,0,0.2472682,"\int \frac{\sqrt[3]{a+b x^3}}{x^4 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^4*(a*d - b*d*x^3)),x]","-\frac{\left(a+b x^3\right)^{4/3}}{3 a^2 d x^3}+\frac{b \sqrt[3]{a+b x^3}}{3 a^2 d}+\frac{b \log \left(a-b x^3\right)}{3\ 2^{2/3} a^{5/3} d}+\frac{2 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{3 a^{5/3} d}-\frac{b \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^{5/3} d}-\frac{4 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} d}+\frac{\sqrt[3]{2} b \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} d}-\frac{2 b \log (x)}{3 a^{5/3} d}","-\frac{\left(a+b x^3\right)^{4/3}}{3 a^2 d x^3}+\frac{b \sqrt[3]{a+b x^3}}{3 a^2 d}+\frac{b \log \left(a-b x^3\right)}{3\ 2^{2/3} a^{5/3} d}+\frac{2 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{3 a^{5/3} d}-\frac{b \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^{5/3} d}-\frac{4 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} d}+\frac{\sqrt[3]{2} b \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{5/3} d}-\frac{2 b \log (x)}{3 a^{5/3} d}",1,"(b*(a + b*x^3)^(1/3))/(3*a^2*d) - (a + b*x^3)^(4/3)/(3*a^2*d*x^3) - (4*b*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*d) + (2^(1/3)*b*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(5/3)*d) - (2*b*Log[x])/(3*a^(5/3)*d) + (b*Log[a - b*x^3])/(3*2^(2/3)*a^(5/3)*d) + (2*b*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(3*a^(5/3)*d) - (b*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(2/3)*a^(5/3)*d)","A",13,8,28,0.2857,1,"{446, 103, 156, 50, 57, 617, 204, 31}"
573,1,283,0,0.2643172,"\int \frac{\sqrt[3]{a+b x^3}}{x^7 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^7*(a*d - b*d*x^3)),x]","\frac{b^2 \log \left(a-b x^3\right)}{3\ 2^{2/3} a^{8/3} d}+\frac{11 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{8/3} d}-\frac{b^2 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^{8/3} d}-\frac{11 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} d}+\frac{\sqrt[3]{2} b^2 \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3} d}-\frac{11 b^2 \log (x)}{18 a^{8/3} d}-\frac{2 b \sqrt[3]{a+b x^3}}{9 a^2 d x^3}-\frac{\left(a+b x^3\right)^{4/3}}{6 a^2 d x^6}","\frac{b^2 \log \left(a-b x^3\right)}{3\ 2^{2/3} a^{8/3} d}+\frac{11 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{8/3} d}-\frac{b^2 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^{8/3} d}-\frac{11 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{8/3} d}+\frac{\sqrt[3]{2} b^2 \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{8/3} d}-\frac{11 b^2 \log (x)}{18 a^{8/3} d}-\frac{2 b \sqrt[3]{a+b x^3}}{9 a^2 d x^3}-\frac{\left(a+b x^3\right)^{4/3}}{6 a^2 d x^6}",1,"(-2*b*(a + b*x^3)^(1/3))/(9*a^2*d*x^3) - (a + b*x^3)^(4/3)/(6*a^2*d*x^6) - (11*b^2*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(8/3)*d) + (2^(1/3)*b^2*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(8/3)*d) - (11*b^2*Log[x])/(18*a^(8/3)*d) + (b^2*Log[a - b*x^3])/(3*2^(2/3)*a^(8/3)*d) + (11*b^2*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(18*a^(8/3)*d) - (b^2*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(2/3)*a^(8/3)*d)","A",12,8,28,0.2857,1,"{446, 103, 149, 156, 57, 617, 204, 31}"
574,1,66,0,0.0596524,"\int \frac{x^7 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^7*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","\frac{x^8 \sqrt[3]{a+b x^3} F_1\left(\frac{8}{3};-\frac{1}{3},1;\frac{11}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{8 a d \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a^2 \log \left(a d-b d x^3\right)}{3\ 2^{2/3} b^{8/3} d}+\frac{11 a^2 \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{18 b^{8/3} d}-\frac{a^2 \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^{8/3} d}+\frac{11 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{8/3} d}-\frac{\sqrt[3]{2} a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{8/3} d}-\frac{7 a x^2 \sqrt[3]{a+b x^3}}{18 b^2 d}-\frac{x^5 \sqrt[3]{a+b x^3}}{6 b d}",1,"(x^8*(a + b*x^3)^(1/3)*AppellF1[8/3, -1/3, 1, 11/3, -((b*x^3)/a), (b*x^3)/a])/(8*a*d*(1 + (b*x^3)/a)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
575,1,66,0,0.0625171,"\int \frac{x^4 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^4*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","\frac{x^5 \sqrt[3]{a+b x^3} F_1\left(\frac{5}{3};-\frac{1}{3},1;\frac{8}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{5 a d \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a \log \left(a d-b d x^3\right)}{3\ 2^{2/3} b^{5/3} d}+\frac{2 a \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{3 b^{5/3} d}-\frac{a \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^{5/3} d}+\frac{4 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3} d}-\frac{\sqrt[3]{2} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{5/3} d}-\frac{x^2 \sqrt[3]{a+b x^3}}{3 b d}",1,"(x^5*(a + b*x^3)^(1/3)*AppellF1[5/3, -1/3, 1, 8/3, -((b*x^3)/a), (b*x^3)/a])/(5*a*d*(1 + (b*x^3)/a)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
576,1,66,0,0.042767,"\int \frac{x \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","\frac{x^2 \sqrt[3]{a+b x^3} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{2 a d \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{\log \left(a d-b d x^3\right)}{3\ 2^{2/3} b^{2/3} d}+\frac{\log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 b^{2/3} d}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} b^{2/3} d}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d}-\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d}",1,"(x^2*(a + b*x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -((b*x^3)/a), (b*x^3)/a])/(2*a*d*(1 + (b*x^3)/a)^(1/3))","C",2,2,26,0.07692,0,"{511, 510}"
577,1,77,0,0.0700063,"\int \frac{\sqrt[3]{a+b x^3}}{x^2 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^2*(a*d - b*d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} \sqrt[3]{1-\frac{b x^3}{a}} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{2 b x^3}{a-b x^3}\right)}{a d x \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\sqrt[3]{a+b x^3}}{a d x}+\frac{\sqrt[3]{b} \log \left(a d-b d x^3\right)}{3\ 2^{2/3} a d}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a d}-\frac{\sqrt[3]{2} \sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a d}",1,"-(((a + b*x^3)^(1/3)*(1 - (b*x^3)/a)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, (-2*b*x^3)/(a - b*x^3)])/(a*d*x*(1 + (b*x^3)/a)^(1/3)))","C",2,2,28,0.07143,0,"{511, 510}"
578,1,117,0,0.4220166,"\int \frac{\sqrt[3]{a+b x^3}}{x^5 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^5*(a*d - b*d*x^3)),x]","-\frac{a^2-b x^3 \left(a+3 b x^3\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+3 b x^3 \left(a-b x^3\right) \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+4 a b x^3+3 b^2 x^6}{4 a^2 d x^4 \left(a+b x^3\right)^{2/3}}","\frac{b^{4/3} \log \left(a d-b d x^3\right)}{3\ 2^{2/3} a^2 d}-\frac{b^{4/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^2 d}-\frac{\sqrt[3]{2} b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^2 d}-\frac{5 b \sqrt[3]{a+b x^3}}{4 a^2 d x}-\frac{\sqrt[3]{a+b x^3}}{4 a d x^4}",1,"-(a^2 + 4*a*b*x^3 + 3*b^2*x^6 - b*x^3*(a + 3*b*x^3)*Hypergeometric2F1[2/3, 1, 5/3, (2*b*x^3)/(a + b*x^3)] + 3*b*x^3*(a - b*x^3)*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)])/(4*a^2*d*x^4*(a + b*x^3)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
579,1,244,0,19.7802382,"\int \frac{\sqrt[3]{a+b x^3}}{x^8 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^8*(a*d - b*d*x^3)),x]","-\frac{-9 b x^3 \left(a-b x^3\right)^2 \, _3F_2\left(\frac{2}{3},2,2;1,\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)-2 b x^3 \left(2 a^2+3 a b x^3+9 b^2 x^6\right) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+15 a^2 b x^3 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+10 a^2 b x^3+4 a^3-27 b^3 x^9 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+12 a b^2 x^6 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+24 a b^2 x^6+18 b^3 x^9}{28 a^3 d x^7 \left(a+b x^3\right)^{2/3}}","-\frac{8 b^2 \sqrt[3]{a+b x^3}}{7 a^3 d x}+\frac{b^{7/3} \log \left(a d-b d x^3\right)}{3\ 2^{2/3} a^3 d}-\frac{b^{7/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^3 d}-\frac{\sqrt[3]{2} b^{7/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^3 d}-\frac{2 b \sqrt[3]{a+b x^3}}{7 a^2 d x^4}-\frac{\sqrt[3]{a+b x^3}}{7 a d x^7}",1,"-(4*a^3 + 10*a^2*b*x^3 + 24*a*b^2*x^6 + 18*b^3*x^9 - 2*b*x^3*(2*a^2 + 3*a*b*x^3 + 9*b^2*x^6)*Hypergeometric2F1[2/3, 1, 5/3, (2*b*x^3)/(a + b*x^3)] + 15*a^2*b*x^3*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] + 12*a*b^2*x^6*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] - 27*b^3*x^9*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] - 9*b*x^3*(a - b*x^3)^2*HypergeometricPFQ[{2/3, 2, 2}, {1, 5/3}, (2*b*x^3)/(a + b*x^3)])/(28*a^3*d*x^7*(a + b*x^3)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
580,1,423,0,29.209014,"\int \frac{\sqrt[3]{a+b x^3}}{x^{11} \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^11*(a*d - b*d*x^3)),x]","-\frac{-54 b x^3 \left(a-b x^3\right)^2 \left(2 a+3 b x^3\right) \, _3F_2\left(\frac{2}{3},2,2;1,\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+27 b x^3 \left(a-b x^3\right)^3 \, _4F_3\left(\frac{2}{3},2,2,2;1,1,\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)-36 a^2 b^2 x^6 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+99 a^2 b^2 x^6 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+90 a^2 b^2 x^6-28 a^3 b x^3 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+117 a^3 b x^3 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+64 a^3 b x^3+28 a^4-162 b^4 x^{12} \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)-297 b^4 x^{12} \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)-54 a b^3 x^9 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+81 a b^3 x^9 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{2 b x^3}{b x^3+a}\right)+216 a b^3 x^9+162 b^4 x^{12}}{280 a^4 d x^{10} \left(a+b x^3\right)^{2/3}}","-\frac{169 b^3 \sqrt[3]{a+b x^3}}{140 a^4 d x}-\frac{37 b^2 \sqrt[3]{a+b x^3}}{140 a^3 d x^4}+\frac{b^{10/3} \log \left(a d-b d x^3\right)}{3\ 2^{2/3} a^4 d}-\frac{b^{10/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2^{2/3} a^4 d}-\frac{\sqrt[3]{2} b^{10/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^4 d}-\frac{11 b \sqrt[3]{a+b x^3}}{70 a^2 d x^7}-\frac{\sqrt[3]{a+b x^3}}{10 a d x^{10}}",1,"-(28*a^4 + 64*a^3*b*x^3 + 90*a^2*b^2*x^6 + 216*a*b^3*x^9 + 162*b^4*x^12 - 28*a^3*b*x^3*Hypergeometric2F1[2/3, 1, 5/3, (2*b*x^3)/(a + b*x^3)] - 36*a^2*b^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, (2*b*x^3)/(a + b*x^3)] - 54*a*b^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, (2*b*x^3)/(a + b*x^3)] - 162*b^4*x^12*Hypergeometric2F1[2/3, 1, 5/3, (2*b*x^3)/(a + b*x^3)] + 117*a^3*b*x^3*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] + 99*a^2*b^2*x^6*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] + 81*a*b^3*x^9*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] - 297*b^4*x^12*Hypergeometric2F1[2/3, 2, 5/3, (2*b*x^3)/(a + b*x^3)] - 54*b*x^3*(a - b*x^3)^2*(2*a + 3*b*x^3)*HypergeometricPFQ[{2/3, 2, 2}, {1, 5/3}, (2*b*x^3)/(a + b*x^3)] + 27*b*x^3*(a - b*x^3)^3*HypergeometricPFQ[{2/3, 2, 2, 2}, {1, 1, 5/3}, (2*b*x^3)/(a + b*x^3)])/(280*a^4*d*x^10*(a + b*x^3)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
581,1,66,0,0.0625733,"\int \frac{x^6 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^6*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","\frac{x^7 \sqrt[3]{a+b x^3} F_1\left(\frac{7}{3};-\frac{1}{3},1;\frac{10}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{7 a d \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{2 a^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 b^2 d \left(a+b x^3\right)^{2/3}}-\frac{a^{5/3} \log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3\ 2^{2/3} b^{7/3} d}+\frac{a^{5/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} b^{7/3} d}-\frac{\sqrt[3]{2} a^{5/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{7/3} d}+\frac{a^{5/3} \log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3} b^{7/3} d}-\frac{\sqrt[3]{2} a^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^{7/3} d}-\frac{a^{5/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} b^{7/3} d}-\frac{3 a x \sqrt[3]{a+b x^3}}{5 b^2 d}-\frac{x^4 \sqrt[3]{a+b x^3}}{5 b d}",1,"(x^7*(a + b*x^3)^(1/3)*AppellF1[7/3, -1/3, 1, 10/3, -((b*x^3)/a), (b*x^3)/a])/(7*a*d*(1 + (b*x^3)/a)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
582,1,66,0,0.0623486,"\int \frac{x^3 \sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(x^3*(a + b*x^3)^(1/3))/(a*d - b*d*x^3),x]","\frac{x^4 \sqrt[3]{a+b x^3} F_1\left(\frac{4}{3};-\frac{1}{3},1;\frac{7}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{4 a d \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{a^{2/3} \log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3\ 2^{2/3} b^{4/3} d}+\frac{a^{2/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} b^{4/3} d}-\frac{\sqrt[3]{2} a^{2/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{4/3} d}+\frac{a^{2/3} \log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3} b^{4/3} d}-\frac{\sqrt[3]{2} a^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} d}-\frac{a^{2/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} b^{4/3} d}-\frac{a x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 b d \left(a+b x^3\right)^{2/3}}-\frac{x \sqrt[3]{a+b x^3}}{2 b d}",1,"(x^4*(a + b*x^3)^(1/3)*AppellF1[4/3, -1/3, 1, 7/3, -((b*x^3)/a), (b*x^3)/a])/(4*a*d*(1 + (b*x^3)/a)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
583,1,61,0,0.0311958,"\int \frac{\sqrt[3]{a+b x^3}}{a d-b d x^3} \, dx","Int[(a + b*x^3)^(1/3)/(a*d - b*d*x^3),x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{a d \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3\ 2^{2/3} \sqrt[3]{a} \sqrt[3]{b} d}+\frac{\log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} \sqrt[3]{a} \sqrt[3]{b} d}-\frac{\sqrt[3]{2} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{a} \sqrt[3]{b} d}+\frac{\log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3} \sqrt[3]{a} \sqrt[3]{b} d}-\frac{\sqrt[3]{2} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{a} \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} \sqrt[3]{a} \sqrt[3]{b} d}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, -((b*x^3)/a), (b*x^3)/a])/(a*d*(1 + (b*x^3)/a)^(1/3))","C",2,2,25,0.08000,0,"{430, 429}"
584,1,66,0,0.0638079,"\int \frac{\sqrt[3]{a+b x^3}}{x^3 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^3*(a*d - b*d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} F_1\left(-\frac{2}{3};-\frac{1}{3},1;\frac{1}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{2 a d x^2 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{b^{2/3} \log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3\ 2^{2/3} a^{4/3} d}+\frac{b^{2/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} a^{4/3} d}-\frac{\sqrt[3]{2} b^{2/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 a^{4/3} d}+\frac{b^{2/3} \log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3} a^{4/3} d}-\frac{\sqrt[3]{2} b^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} a^{4/3} d}-\frac{b^{2/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a^{4/3} d}+\frac{b x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{2 a d \left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{2 a d x^2}",1,"-((a + b*x^3)^(1/3)*AppellF1[-2/3, -1/3, 1, 1/3, -((b*x^3)/a), (b*x^3)/a])/(2*a*d*x^2*(1 + (b*x^3)/a)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
585,1,66,0,0.067572,"\int \frac{\sqrt[3]{a+b x^3}}{x^6 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^6*(a*d - b*d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} F_1\left(-\frac{5}{3};-\frac{1}{3},1;-\frac{2}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{5 a d x^5 \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{2 b^2 x \left(\frac{b x^3}{a}+1\right)^{2/3} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};-\frac{b x^3}{a}\right)}{5 a^2 d \left(a+b x^3\right)^{2/3}}-\frac{b^{5/3} \log \left(2^{2/3}-\frac{\sqrt[3]{a}+\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3\ 2^{2/3} a^{7/3} d}+\frac{b^{5/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3\ 2^{2/3} a^{7/3} d}-\frac{\sqrt[3]{2} b^{5/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 a^{7/3} d}+\frac{b^{5/3} \log \left(\frac{\left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}+\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+2 \sqrt[3]{2}\right)}{6\ 2^{2/3} a^{7/3} d}-\frac{\sqrt[3]{2} b^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} a^{7/3} d}-\frac{b^{5/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3} a^{7/3} d}-\frac{3 b \sqrt[3]{a+b x^3}}{5 a^2 d x^2}-\frac{\sqrt[3]{a+b x^3}}{5 a d x^5}",1,"-((a + b*x^3)^(1/3)*AppellF1[-5/3, -1/3, 1, -2/3, -((b*x^3)/a), (b*x^3)/a])/(5*a*d*x^5*(1 + (b*x^3)/a)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
586,1,223,0,0.2503873,"\int \frac{x^{11} \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^11*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","-\frac{a^3 \left(a+b x^3\right)^{2/3}}{2 b^4 d}-\frac{a^2 \left(a+b x^3\right)^{5/3}}{5 b^4 d}+\frac{a^{11/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b^4 d}-\frac{a^{11/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^4 d}-\frac{2^{2/3} a^{11/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^4 d}+\frac{a \left(a+b x^3\right)^{8/3}}{8 b^4 d}-\frac{\left(a+b x^3\right)^{11/3}}{11 b^4 d}","-\frac{a^3 \left(a+b x^3\right)^{2/3}}{2 b^4 d}-\frac{a^2 \left(a+b x^3\right)^{5/3}}{5 b^4 d}+\frac{a^{11/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b^4 d}-\frac{a^{11/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^4 d}-\frac{2^{2/3} a^{11/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^4 d}+\frac{a \left(a+b x^3\right)^{8/3}}{8 b^4 d}-\frac{\left(a+b x^3\right)^{11/3}}{11 b^4 d}",1,"-(a^3*(a + b*x^3)^(2/3))/(2*b^4*d) - (a^2*(a + b*x^3)^(5/3))/(5*b^4*d) + (a*(a + b*x^3)^(8/3))/(8*b^4*d) - (a + b*x^3)^(11/3)/(11*b^4*d) - (2^(2/3)*a^(11/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^4*d) + (a^(11/3)*Log[a - b*x^3])/(3*2^(1/3)*b^4*d) - (a^(11/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(1/3)*b^4*d)","A",8,7,28,0.2500,1,"{446, 88, 50, 55, 617, 204, 31}"
587,1,177,0,0.1995331,"\int \frac{x^8 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^8*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","-\frac{a^2 \left(a+b x^3\right)^{2/3}}{2 b^3 d}+\frac{a^{8/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b^3 d}-\frac{a^{8/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^3 d}-\frac{2^{2/3} a^{8/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^3 d}-\frac{\left(a+b x^3\right)^{8/3}}{8 b^3 d}","-\frac{a^2 \left(a+b x^3\right)^{2/3}}{2 b^3 d}+\frac{a^{8/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b^3 d}-\frac{a^{8/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^3 d}-\frac{2^{2/3} a^{8/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^3 d}-\frac{\left(a+b x^3\right)^{8/3}}{8 b^3 d}",1,"-(a^2*(a + b*x^3)^(2/3))/(2*b^3*d) - (a + b*x^3)^(8/3)/(8*b^3*d) - (2^(2/3)*a^(8/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^3*d) + (a^(8/3)*Log[a - b*x^3])/(3*2^(1/3)*b^3*d) - (a^(8/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(1/3)*b^3*d)","A",8,7,28,0.2500,1,"{446, 88, 50, 55, 617, 204, 31}"
588,1,175,0,0.1564646,"\int \frac{x^5 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^5*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{a^{5/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b^2 d}-\frac{a^{5/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^2 d}-\frac{2^{2/3} a^{5/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^2 d}-\frac{a \left(a+b x^3\right)^{2/3}}{2 b^2 d}-\frac{\left(a+b x^3\right)^{5/3}}{5 b^2 d}","\frac{a^{5/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b^2 d}-\frac{a^{5/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^2 d}-\frac{2^{2/3} a^{5/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b^2 d}-\frac{a \left(a+b x^3\right)^{2/3}}{2 b^2 d}-\frac{\left(a+b x^3\right)^{5/3}}{5 b^2 d}",1,"-(a*(a + b*x^3)^(2/3))/(2*b^2*d) - (a + b*x^3)^(5/3)/(5*b^2*d) - (2^(2/3)*a^(5/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b^2*d) + (a^(5/3)*Log[a - b*x^3])/(3*2^(1/3)*b^2*d) - (a^(5/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(1/3)*b^2*d)","A",7,7,28,0.2500,1,"{446, 80, 50, 55, 617, 204, 31}"
589,1,153,0,0.1257549,"\int \frac{x^2 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^2*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{a^{2/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b d}-\frac{a^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b d}-\frac{2^{2/3} a^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b d}-\frac{\left(a+b x^3\right)^{2/3}}{2 b d}","\frac{a^{2/3} \log \left(a-b x^3\right)}{3 \sqrt[3]{2} b d}-\frac{a^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b d}-\frac{2^{2/3} a^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} b d}-\frac{\left(a+b x^3\right)^{2/3}}{2 b d}",1,"-(a + b*x^3)^(2/3)/(2*b*d) - (2^(2/3)*a^(2/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*b*d) + (a^(2/3)*Log[a - b*x^3])/(3*2^(1/3)*b*d) - (a^(2/3)*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(1/3)*b*d)","A",6,6,28,0.2143,1,"{444, 50, 55, 617, 204, 31}"
590,1,214,0,0.1820699,"\int \frac{\left(a+b x^3\right)^{2/3}}{x \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x*(a*d - b*d*x^3)),x]","\frac{\log \left(a-b x^3\right)}{3 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a} d}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} \sqrt[3]{a} d}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} d}-\frac{2^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} d}-\frac{\log (x)}{2 \sqrt[3]{a} d}","\frac{\log \left(a-b x^3\right)}{3 \sqrt[3]{2} \sqrt[3]{a} d}+\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a} d}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} \sqrt[3]{a} d}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} d}-\frac{2^{2/3} \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} d}-\frac{\log (x)}{2 \sqrt[3]{a} d}",1,"ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(1/3)*d) - (2^(2/3)*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(1/3)*d) - Log[x]/(2*a^(1/3)*d) + Log[a - b*x^3]/(3*2^(1/3)*a^(1/3)*d) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(1/3)*d) - Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)]/(2^(1/3)*a^(1/3)*d)","A",10,6,28,0.2143,1,"{446, 83, 55, 617, 204, 31}"
591,1,269,0,0.2633983,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^4 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^4*(a*d - b*d*x^3)),x]","-\frac{\left(a+b x^3\right)^{5/3}}{3 a^2 d x^3}+\frac{b \left(a+b x^3\right)^{2/3}}{3 a^2 d}+\frac{b \log \left(a-b x^3\right)}{3 \sqrt[3]{2} a^{4/3} d}+\frac{5 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{4/3} d}-\frac{b \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^{4/3} d}+\frac{5 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} d}-\frac{2^{2/3} b \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{5 b \log (x)}{6 a^{4/3} d}","-\frac{\left(a+b x^3\right)^{5/3}}{3 a^2 d x^3}+\frac{b \left(a+b x^3\right)^{2/3}}{3 a^2 d}+\frac{b \log \left(a-b x^3\right)}{3 \sqrt[3]{2} a^{4/3} d}+\frac{5 b \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{4/3} d}-\frac{b \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^{4/3} d}+\frac{5 b \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} d}-\frac{2^{2/3} b \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} d}-\frac{5 b \log (x)}{6 a^{4/3} d}",1,"(b*(a + b*x^3)^(2/3))/(3*a^2*d) - (a + b*x^3)^(5/3)/(3*a^2*d*x^3) + (5*b*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*d) - (2^(2/3)*b*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(4/3)*d) - (5*b*Log[x])/(6*a^(4/3)*d) + (b*Log[a - b*x^3])/(3*2^(1/3)*a^(4/3)*d) + (5*b*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(4/3)*d) - (b*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(1/3)*a^(4/3)*d)","A",13,8,28,0.2857,1,"{446, 103, 156, 50, 55, 617, 204, 31}"
592,1,284,0,0.2792634,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^7 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^7*(a*d - b*d*x^3)),x]","\frac{b^2 \log \left(a-b x^3\right)}{3 \sqrt[3]{2} a^{7/3} d}+\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{9 a^{7/3} d}-\frac{b^2 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^{7/3} d}+\frac{14 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} d}-\frac{2^{2/3} b^2 \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3} d}-\frac{7 b^2 \log (x)}{9 a^{7/3} d}-\frac{5 b \left(a+b x^3\right)^{2/3}}{18 a^2 d x^3}-\frac{\left(a+b x^3\right)^{5/3}}{6 a^2 d x^6}","\frac{b^2 \log \left(a-b x^3\right)}{3 \sqrt[3]{2} a^{7/3} d}+\frac{7 b^2 \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{9 a^{7/3} d}-\frac{b^2 \log \left(\sqrt[3]{2} \sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^{7/3} d}+\frac{14 b^2 \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{7/3} d}-\frac{2^{2/3} b^2 \tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{7/3} d}-\frac{7 b^2 \log (x)}{9 a^{7/3} d}-\frac{5 b \left(a+b x^3\right)^{2/3}}{18 a^2 d x^3}-\frac{\left(a+b x^3\right)^{5/3}}{6 a^2 d x^6}",1,"(-5*b*(a + b*x^3)^(2/3))/(18*a^2*d*x^3) - (a + b*x^3)^(5/3)/(6*a^2*d*x^6) + (14*b^2*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(7/3)*d) - (2^(2/3)*b^2*ArcTan[(a^(1/3) + 2^(2/3)*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*a^(7/3)*d) - (7*b^2*Log[x])/(9*a^(7/3)*d) + (b^2*Log[a - b*x^3])/(3*2^(1/3)*a^(7/3)*d) + (7*b^2*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(9*a^(7/3)*d) - (b^2*Log[2^(1/3)*a^(1/3) - (a + b*x^3)^(1/3)])/(2^(1/3)*a^(7/3)*d)","A",12,8,28,0.2857,1,"{446, 103, 149, 156, 55, 617, 204, 31}"
593,1,66,0,0.0632764,"\int \frac{x^6 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^6*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{x^7 \left(a+b x^3\right)^{2/3} F_1\left(\frac{7}{3};-\frac{2}{3},1;\frac{10}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{7 a d \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{a^2 \log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} b^{7/3} d}-\frac{a^2 \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^{7/3} d}+\frac{7 a^2 \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{9 b^{7/3} d}-\frac{14 a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{7/3} d}+\frac{2^{2/3} a^2 \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{7/3} d}-\frac{4 a x \left(a+b x^3\right)^{2/3}}{9 b^2 d}-\frac{x^4 \left(a+b x^3\right)^{2/3}}{6 b d}",1,"(x^7*(a + b*x^3)^(2/3)*AppellF1[7/3, -2/3, 1, 10/3, -((b*x^3)/a), (b*x^3)/a])/(7*a*d*(1 + (b*x^3)/a)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
594,1,66,0,0.0634338,"\int \frac{x^3 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^3*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{x^4 \left(a+b x^3\right)^{2/3} F_1\left(\frac{4}{3};-\frac{2}{3},1;\frac{7}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{4 a d \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{a \log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} b^{4/3} d}-\frac{a \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} b^{4/3} d}+\frac{5 a \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3} d}-\frac{5 a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3} d}+\frac{2^{2/3} a \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} d}-\frac{x \left(a+b x^3\right)^{2/3}}{3 b d}",1,"(x^4*(a + b*x^3)^(2/3)*AppellF1[4/3, -2/3, 1, 7/3, -((b*x^3)/a), (b*x^3)/a])/(4*a*d*(1 + (b*x^3)/a)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
595,1,61,0,0.0328836,"\int \frac{\left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(a + b*x^3)^(2/3)/(a*d - b*d*x^3),x]","\frac{x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{a d \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{\log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} \sqrt[3]{b} d}-\frac{\log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} \sqrt[3]{b} d}+\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b} d}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} d}+\frac{2^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} d}",1,"(x*(a + b*x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, -((b*x^3)/a), (b*x^3)/a])/(a*d*(1 + (b*x^3)/a)^(2/3))","C",2,2,25,0.08000,0,"{430, 429}"
596,1,79,0,0.0707691,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^3 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^3*(a*d - b*d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} \left(1-\frac{b x^3}{a}\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-\frac{2 b x^3}{a-b x^3}\right)}{2 a d x^2 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{b^{2/3} \log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} a d}-\frac{b^{2/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a d}+\frac{2^{2/3} b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a d}-\frac{\left(a+b x^3\right)^{2/3}}{2 a d x^2}",1,"-((a + b*x^3)^(2/3)*(1 - (b*x^3)/a)^(2/3)*Hypergeometric2F1[-2/3, -2/3, 1/3, (-2*b*x^3)/(a - b*x^3)])/(2*a*d*x^2*(1 + (b*x^3)/a)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
597,1,121,0,0.4292478,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^6 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^6*(a*d - b*d*x^3)),x]","-\frac{2 a^2-4 b x^3 \left(2 a+3 b x^3\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+12 b x^3 \left(a-b x^3\right) \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+5 a b x^3+3 b^2 x^6}{10 a^2 d x^5 \sqrt[3]{a+b x^3}}","\frac{b^{5/3} \log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} a^2 d}-\frac{b^{5/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^2 d}+\frac{2^{2/3} b^{5/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^2 d}-\frac{7 b \left(a+b x^3\right)^{2/3}}{10 a^2 d x^2}-\frac{\left(a+b x^3\right)^{2/3}}{5 a d x^5}",1,"-(2*a^2 + 5*a*b*x^3 + 3*b^2*x^6 - 4*b*x^3*(2*a + 3*b*x^3)*Hypergeometric2F1[1/3, 1, 4/3, (2*b*x^3)/(a + b*x^3)] + 12*b*x^3*(a - b*x^3)*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)])/(10*a^2*d*x^5*(a + b*x^3)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
598,1,244,0,10.6764468,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^9 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^9*(a*d - b*d*x^3)),x]","-\frac{-18 b x^3 \left(a-b x^3\right)^2 \, _3F_2\left(\frac{1}{3},2,2;1,\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)-4 b x^3 \left(5 a^2+6 a b x^3+9 b^2 x^6\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+42 a^2 b x^3 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+11 a^2 b x^3+5 a^3-54 b^3 x^9 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+12 a b^2 x^6 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+15 a b^2 x^6+9 b^3 x^9}{40 a^3 d x^8 \sqrt[3]{a+b x^3}}","-\frac{5 b^2 \left(a+b x^3\right)^{2/3}}{8 a^3 d x^2}+\frac{b^{8/3} \log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} a^3 d}-\frac{b^{8/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^3 d}+\frac{2^{2/3} b^{8/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^3 d}-\frac{b \left(a+b x^3\right)^{2/3}}{4 a^2 d x^5}-\frac{\left(a+b x^3\right)^{2/3}}{8 a d x^8}",1,"-(5*a^3 + 11*a^2*b*x^3 + 15*a*b^2*x^6 + 9*b^3*x^9 - 4*b*x^3*(5*a^2 + 6*a*b*x^3 + 9*b^2*x^6)*Hypergeometric2F1[1/3, 1, 4/3, (2*b*x^3)/(a + b*x^3)] + 42*a^2*b*x^3*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)] + 12*a*b^2*x^6*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)] - 54*b^3*x^9*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)] - 18*b*x^3*(a - b*x^3)^2*HypergeometricPFQ[{1/3, 2, 2}, {1, 4/3}, (2*b*x^3)/(a + b*x^3)])/(40*a^3*d*x^8*(a + b*x^3)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
599,1,391,0,17.6006052,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^{12} \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^12*(a*d - b*d*x^3)),x]","-\frac{-54 b x^3 \left(a-b x^3\right)^2 \left(5 a+6 b x^3\right) \, _3F_2\left(\frac{1}{3},2,2;1,\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+54 b x^3 \left(a-b x^3\right)^3 \, _4F_3\left(\frac{1}{3},2,2,2;1,1,\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)-180 a^2 b^2 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+198 a^2 b^2 x^6 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+99 a^2 b^2 x^6-160 a^3 b x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+396 a^3 b x^3 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+85 a^3 b x^3+40 a^4-324 b^4 x^{12} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)-594 b^4 x^{12} \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)-216 a b^3 x^9 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{2 b x^3}{b x^3+a}\right)+135 a b^3 x^9+81 b^4 x^{12}}{440 a^4 d x^{11} \sqrt[3]{a+b x^3}}","-\frac{293 b^3 \left(a+b x^3\right)^{2/3}}{440 a^4 d x^2}-\frac{49 b^2 \left(a+b x^3\right)^{2/3}}{220 a^3 d x^5}+\frac{b^{11/3} \log \left(a d-b d x^3\right)}{3 \sqrt[3]{2} a^4 d}-\frac{b^{11/3} \log \left(\sqrt[3]{2} \sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{\sqrt[3]{2} a^4 d}+\frac{2^{2/3} b^{11/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{2} \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} a^4 d}-\frac{13 b \left(a+b x^3\right)^{2/3}}{88 a^2 d x^8}-\frac{\left(a+b x^3\right)^{2/3}}{11 a d x^{11}}",1,"-(40*a^4 + 85*a^3*b*x^3 + 99*a^2*b^2*x^6 + 135*a*b^3*x^9 + 81*b^4*x^12 - 160*a^3*b*x^3*Hypergeometric2F1[1/3, 1, 4/3, (2*b*x^3)/(a + b*x^3)] - 180*a^2*b^2*x^6*Hypergeometric2F1[1/3, 1, 4/3, (2*b*x^3)/(a + b*x^3)] - 216*a*b^3*x^9*Hypergeometric2F1[1/3, 1, 4/3, (2*b*x^3)/(a + b*x^3)] - 324*b^4*x^12*Hypergeometric2F1[1/3, 1, 4/3, (2*b*x^3)/(a + b*x^3)] + 396*a^3*b*x^3*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)] + 198*a^2*b^2*x^6*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)] - 594*b^4*x^12*Hypergeometric2F1[1/3, 2, 4/3, (2*b*x^3)/(a + b*x^3)] - 54*b*x^3*(a - b*x^3)^2*(5*a + 6*b*x^3)*HypergeometricPFQ[{1/3, 2, 2}, {1, 4/3}, (2*b*x^3)/(a + b*x^3)] + 54*b*x^3*(a - b*x^3)^3*HypergeometricPFQ[{1/3, 2, 2, 2}, {1, 1, 4/3}, (2*b*x^3)/(a + b*x^3)])/(440*a^4*d*x^11*(a + b*x^3)^(1/3))","C",2,2,28,0.07143,0,"{511, 510}"
600,1,66,0,0.0658789,"\int \frac{x^7 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^7*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{x^8 \left(a+b x^3\right)^{2/3} F_1\left(\frac{8}{3};-\frac{2}{3},1;\frac{11}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{8 a d \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{19 a^2 x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{28 b^2 d \sqrt[3]{a+b x^3}}+\frac{a^{7/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{2} b^{8/3} d}-\frac{2^{2/3} a^{7/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{8/3} d}-\frac{a^{7/3} \log \left(\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{2^{2/3} \sqrt[3]{b} \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}\right)}{2 \sqrt[3]{2} b^{8/3} d}+\frac{2^{2/3} a^{7/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^{8/3} d}+\frac{a^{7/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} b^{8/3} d}+\frac{a^{7/3} \log \left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a}\right)}{6 \sqrt[3]{2} b^{8/3} d}-\frac{9 a x^2 \left(a+b x^3\right)^{2/3}}{28 b^2 d}-\frac{x^5 \left(a+b x^3\right)^{2/3}}{7 b d}",1,"(x^8*(a + b*x^3)^(2/3)*AppellF1[8/3, -2/3, 1, 11/3, -((b*x^3)/a), (b*x^3)/a])/(8*a*d*(1 + (b*x^3)/a)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
601,1,66,0,0.0655671,"\int \frac{x^4 \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x^4*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{x^5 \left(a+b x^3\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},1;\frac{8}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{5 a d \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{a^{4/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{2} b^{5/3} d}-\frac{2^{2/3} a^{4/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{5/3} d}-\frac{a^{4/3} \log \left(\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{2^{2/3} \sqrt[3]{b} \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}\right)}{2 \sqrt[3]{2} b^{5/3} d}+\frac{2^{2/3} a^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^{5/3} d}+\frac{a^{4/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} b^{5/3} d}+\frac{a^{4/3} \log \left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a}\right)}{6 \sqrt[3]{2} b^{5/3} d}-\frac{3 a x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{4 b d \sqrt[3]{a+b x^3}}-\frac{x^2 \left(a+b x^3\right)^{2/3}}{4 b d}",1,"(x^5*(a + b*x^3)^(2/3)*AppellF1[5/3, -2/3, 1, 8/3, -((b*x^3)/a), (b*x^3)/a])/(5*a*d*(1 + (b*x^3)/a)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
602,1,66,0,0.0465118,"\int \frac{x \left(a+b x^3\right)^{2/3}}{a d-b d x^3} \, dx","Int[(x*(a + b*x^3)^(2/3))/(a*d - b*d*x^3),x]","\frac{x^2 \left(a+b x^3\right)^{2/3} F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{2 a d \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{\sqrt[3]{a} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{2} b^{2/3} d}-\frac{2^{2/3} \sqrt[3]{a} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 b^{2/3} d}-\frac{\sqrt[3]{a} \log \left(\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{2^{2/3} \sqrt[3]{b} \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}\right)}{2 \sqrt[3]{2} b^{2/3} d}+\frac{2^{2/3} \sqrt[3]{a} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d}+\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} b^{2/3} d}+\frac{\sqrt[3]{a} \log \left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a}\right)}{6 \sqrt[3]{2} b^{2/3} d}-\frac{x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 d \sqrt[3]{a+b x^3}}",1,"(x^2*(a + b*x^3)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, -((b*x^3)/a), (b*x^3)/a])/(2*a*d*(1 + (b*x^3)/a)^(2/3))","C",2,2,26,0.07692,0,"{511, 510}"
603,1,64,0,0.069205,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^2 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^2*(a*d - b*d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} F_1\left(-\frac{1}{3};-\frac{2}{3},1;\frac{2}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{a d x \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{\sqrt[3]{b} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{2} a^{2/3} d}-\frac{2^{2/3} \sqrt[3]{b} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 a^{2/3} d}-\frac{\sqrt[3]{b} \log \left(\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{2^{2/3} \sqrt[3]{b} \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}\right)}{2 \sqrt[3]{2} a^{2/3} d}+\frac{2^{2/3} \sqrt[3]{b} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} a^{2/3} d}+\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a^{2/3} d}+\frac{\sqrt[3]{b} \log \left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a}\right)}{6 \sqrt[3]{2} a^{2/3} d}+\frac{b x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{2 a d \sqrt[3]{a+b x^3}}-\frac{\left(a+b x^3\right)^{2/3}}{a d x}",1,"-(((a + b*x^3)^(2/3)*AppellF1[-1/3, -2/3, 1, 2/3, -((b*x^3)/a), (b*x^3)/a])/(a*d*x*(1 + (b*x^3)/a)^(2/3)))","C",2,2,28,0.07143,0,"{511, 510}"
604,1,66,0,0.0689181,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^5 \left(a d-b d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^5*(a*d - b*d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} F_1\left(-\frac{4}{3};-\frac{2}{3},1;-\frac{1}{3};-\frac{b x^3}{a},\frac{b x^3}{a}\right)}{4 a d x^4 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{3 b^2 x^2 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};-\frac{b x^3}{a}\right)}{4 a^2 d \sqrt[3]{a+b x^3}}+\frac{b^{4/3} \log \left(\frac{2^{2/3} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)^2}{\left(a+b x^3\right)^{2/3}}-\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 \sqrt[3]{2} a^{5/3} d}-\frac{2^{2/3} b^{4/3} \log \left(\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1\right)}{3 a^{5/3} d}-\frac{b^{4/3} \log \left(\frac{\sqrt[3]{b} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a}}-\frac{2^{2/3} \sqrt[3]{b} \sqrt[3]{a+b x^3}}{\sqrt[3]{a}}\right)}{2 \sqrt[3]{2} a^{5/3} d}+\frac{2^{2/3} b^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}}{\sqrt{3}}\right)}{\sqrt{3} a^{5/3} d}+\frac{b^{4/3} \tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3} a^{5/3} d}+\frac{b^{4/3} \log \left(\frac{\left(\sqrt[3]{a}-\sqrt[3]{b} x\right)^2 \left(\sqrt[3]{a}+\sqrt[3]{b} x\right)}{a}\right)}{6 \sqrt[3]{2} a^{5/3} d}-\frac{3 b \left(a+b x^3\right)^{2/3}}{2 a^2 d x}-\frac{\left(a+b x^3\right)^{2/3}}{4 a d x^4}",1,"-((a + b*x^3)^(2/3)*AppellF1[-4/3, -2/3, 1, -1/3, -((b*x^3)/a), (b*x^3)/a])/(4*a*d*x^4*(1 + (b*x^3)/a)^(2/3))","C",2,2,28,0.07143,0,"{511, 510}"
605,1,127,0,0.0934224,"\int \frac{x^{14}}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^14/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{11} \left(1-x^3\right)^{11/3}-\frac{1}{4} \left(1-x^3\right)^{8/3}+\frac{2}{5} \left(1-x^3\right)^{5/3}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","\frac{1}{11} \left(1-x^3\right)^{11/3}-\frac{1}{4} \left(1-x^3\right)^{8/3}+\frac{2}{5} \left(1-x^3\right)^{5/3}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"(2*(1 - x^3)^(5/3))/5 - (1 - x^3)^(8/3)/4 + (1 - x^3)^(11/3)/11 + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(6*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",7,6,22,0.2727,1,"{446, 88, 55, 617, 204, 31}"
606,1,128,0,0.0879538,"\int \frac{x^{11}}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^11/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{1}{8} \left(1-x^3\right)^{8/3}+\frac{1}{5} \left(1-x^3\right)^{5/3}-\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{1}{8} \left(1-x^3\right)^{8/3}+\frac{1}{5} \left(1-x^3\right)^{5/3}-\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(1 - x^3)^(2/3)/2 + (1 - x^3)^(5/3)/5 - (1 - x^3)^(8/3)/8 - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[1 + x^3]/(6*2^(1/3)) - Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",7,6,22,0.2727,1,"{446, 88, 55, 617, 204, 31}"
607,1,97,0,0.0770901,"\int \frac{x^8}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^8/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{5} \left(1-x^3\right)^{5/3}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","\frac{1}{5} \left(1-x^3\right)^{5/3}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"(1 - x^3)^(5/3)/5 + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(6*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",7,6,22,0.2727,1,"{446, 88, 55, 617, 204, 31}"
608,1,98,0,0.0637919,"\int \frac{x^5}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^5/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(1 - x^3)^(2/3)/2 - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[1 + x^3]/(6*2^(1/3)) - Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",6,6,22,0.2727,1,"{446, 80, 55, 617, 204, 31}"
609,1,82,0,0.0588563,"\int \frac{x^2}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^2/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(6*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",5,5,22,0.2273,1,"{444, 55, 617, 204, 31}"
610,1,137,0,0.0910683,"\int \frac{1}{x \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x*(1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{\log (x)}{2}","\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{\log (x)}{2}",1,"ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[x]/2 + Log[1 + x^3]/(6*2^(1/3)) + Log[1 - (1 - x^3)^(1/3)]/2 - Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",10,7,22,0.3182,1,"{446, 86, 55, 618, 204, 31, 617}"
611,1,157,0,0.1034107,"\int \frac{1}{x^4 \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x^4*(1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\left(1-x^3\right)^{2/3}}{3 x^3}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{1}{3} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\log (x)}{3}","-\frac{\left(1-x^3\right)^{2/3}}{3 x^3}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{1}{3} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2 \sqrt[3]{2}}-\frac{2 \tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\log (x)}{3}",1,"-(1 - x^3)^(2/3)/(3*x^3) - (2*ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[x]/3 - Log[1 + x^3]/(6*2^(1/3)) - Log[1 - (1 - x^3)^(1/3)]/3 + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(1/3))","A",11,8,22,0.3636,1,"{446, 103, 156, 55, 618, 204, 31, 617}"
612,1,226,0,0.1492128,"\int \frac{x^6}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^6/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{1}{3} \left(1-x^3\right)^{2/3} x+\frac{1}{9} \log \left(\frac{x^2}{\left(1-x^3\right)^{2/3}}-\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{2}{9} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}+\frac{2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{1}{3} \left(1-x^3\right)^{2/3} x-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{1}{3} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{2 \tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(x*(1 - x^3)^(2/3))/3 + (2*ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]) - ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/9 - (2*Log[1 + x/(1 - x^3)^(1/3)])/9 - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",15,10,22,0.4545,1,"{494, 470, 522, 200, 31, 634, 618, 204, 628, 617}"
613,1,207,0,0.1049338,"\int \frac{x^3}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^3/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{1}{6} \log \left(\frac{x^2}{\left(1-x^3\right)^{2/3}}-\frac{x}{\sqrt[3]{1-x^3}}+1\right)+\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)+\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}+\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3]) + ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/6 + Log[1 + x/(1 - x^3)^(1/3)]/3 + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) - Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",14,9,22,0.4091,1,"{494, 481, 200, 31, 634, 618, 204, 628, 617}"
614,1,122,0,0.057282,"\int \frac{1}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/((1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3])) - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",7,7,19,0.3684,1,"{377, 200, 31, 634, 617, 204, 628}"
615,1,139,0,0.0715571,"\int \frac{1}{x^3 \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x^3*(1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\left(1-x^3\right)^{2/3}}{2 x^2}+\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{\left(1-x^3\right)^{2/3}}{2 x^2}+\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(1 - x^3)^(2/3)/(2*x^2) + ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) - Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",8,8,22,0.3636,1,"{494, 453, 200, 31, 634, 617, 204, 628}"
616,1,140,0,0.0882245,"\int \frac{1}{x^6 \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x^6*(1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\left(1-x^3\right)^{5/3}}{5 x^5}-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","\frac{\left(1-x^3\right)^{2/3}}{5 x^2}-\frac{\left(1-x^3\right)^{2/3}}{5 x^5}-\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(1 - x^3)^(5/3)/(5*x^5) - ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",9,8,22,0.3636,1,"{494, 461, 200, 31, 634, 617, 204, 628}"
617,1,175,0,0.0920679,"\int \frac{1}{x^9 \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x^9*(1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{\left(1-x^3\right)^{8/3}}{8 x^8}-\frac{\left(1-x^3\right)^{5/3}}{5 x^5}-\frac{\left(1-x^3\right)^{2/3}}{2 x^2}+\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}","-\frac{17 \left(1-x^3\right)^{2/3}}{40 x^2}+\frac{\left(1-x^3\right)^{2/3}}{20 x^5}-\frac{\left(1-x^3\right)^{2/3}}{8 x^8}+\frac{\log \left(x^3+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}",1,"-(1 - x^3)^(2/3)/(2*x^2) - (1 - x^3)^(5/3)/(5*x^5) - (1 - x^3)^(8/3)/(8*x^8) + ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(1/3)*Sqrt[3]) + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3)) - Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(1/3))","A",9,8,22,0.3636,1,"{494, 461, 200, 31, 634, 617, 204, 628}"
618,1,26,0,0.0167184,"\int \frac{x^7}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^7/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{8} x^8 F_1\left(\frac{8}{3};\frac{1}{3},1;\frac{11}{3};x^3,-x^3\right)","-\frac{1}{4} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\frac{1}{4} \left(1-x^3\right)^{2/3} x^2+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}",1,"(x^8*AppellF1[8/3, 1/3, 1, 11/3, x^3, -x^3])/8","C",1,1,22,0.04545,0,"{510}"
619,1,26,0,0.0162367,"\int \frac{x^4}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x^4/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{5} x^5 F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};x^3,-x^3\right)","\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}",1,"(x^5*AppellF1[5/3, 1/3, 1, 8/3, x^3, -x^3])/5","C",1,1,22,0.04545,0,"{510}"
620,1,26,0,0.0125221,"\int \frac{x}{\sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[x/((1 - x^3)^(1/3)*(1 + x^3)),x]","\frac{1}{2} x^2 F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};x^3,-x^3\right)","\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}",1,"(x^2*AppellF1[2/3, 1/3, 1, 5/3, x^3, -x^3])/2","C",1,1,20,0.05000,0,"{510}"
621,1,24,0,0.0172514,"\int \frac{1}{x^2 \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x^2*(1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{F_1\left(-\frac{1}{3};\frac{1}{3},1;\frac{2}{3};x^3,-x^3\right)}{x}","-\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\frac{\left(1-x^3\right)^{2/3}}{x}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}",1,"-(AppellF1[-1/3, 1/3, 1, 2/3, x^3, -x^3]/x)","C",1,1,22,0.04545,0,"{510}"
622,1,26,0,0.0181233,"\int \frac{1}{x^5 \sqrt[3]{1-x^3} \left(1+x^3\right)} \, dx","Int[1/(x^5*(1 - x^3)^(1/3)*(1 + x^3)),x]","-\frac{F_1\left(-\frac{4}{3};\frac{1}{3},1;-\frac{1}{3};x^3,-x^3\right)}{4 x^4}","\frac{1}{4} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{\left(1-x^3\right)^{2/3}}{2 x}-\frac{\left(1-x^3\right)^{2/3}}{4 x^4}+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{12 \sqrt[3]{2}}",1,"-AppellF1[-4/3, 1/3, 1, -1/3, x^3, -x^3]/(4*x^4)","C",1,1,22,0.04545,0,"{510}"
623,1,125,0,0.0949,"\int \frac{x^{11}}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^11/((1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{1}{7} \left(1-x^3\right)^{7/3}+\frac{1}{4} \left(1-x^3\right)^{4/3}-\sqrt[3]{1-x^3}+\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\frac{1}{7} \left(1-x^3\right)^{7/3}+\frac{1}{4} \left(1-x^3\right)^{4/3}-\sqrt[3]{1-x^3}+\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(1 - x^3)^(1/3) + (1 - x^3)^(4/3)/4 - (1 - x^3)^(7/3)/7 + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) + Log[1 + x^3]/(6*2^(2/3)) - Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(2/3))","A",7,6,22,0.2727,1,"{446, 88, 57, 617, 204, 31}"
624,1,98,0,0.0749959,"\int \frac{x^8}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^8/((1 - x^3)^(2/3)*(1 + x^3)),x]","\frac{1}{4} \left(1-x^3\right)^{4/3}-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","\frac{1}{4} \left(1-x^3\right)^{4/3}-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"(1 - x^3)^(4/3)/4 - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) - Log[1 + x^3]/(6*2^(2/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(2/3))","A",7,6,22,0.2727,1,"{446, 88, 57, 617, 204, 31}"
625,1,95,0,0.0617366,"\int \frac{x^5}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^5/((1 - x^3)^(2/3)*(1 + x^3)),x]","-\sqrt[3]{1-x^3}+\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\sqrt[3]{1-x^3}+\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(1 - x^3)^(1/3) + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) + Log[1 + x^3]/(6*2^(2/3)) - Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(2/3))","A",6,6,22,0.2727,1,"{446, 80, 57, 617, 204, 31}"
626,1,83,0,0.0555175,"\int \frac{x^2}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^2/((1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3])) - Log[1 + x^3]/(6*2^(2/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(2/3))","A",5,5,22,0.2273,1,"{444, 57, 617, 204, 31}"
627,1,137,0,0.0896032,"\int \frac{1}{x \left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[1/(x*(1 - x^3)^(2/3)*(1 + x^3)),x]","\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log (x)}{2}","\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\log (x)}{2}",1,"-(ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3]) + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) - Log[x]/2 + Log[1 + x^3]/(6*2^(2/3)) + Log[1 - (1 - x^3)^(1/3)]/2 - Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(2/3))","A",10,7,22,0.3182,1,"{446, 86, 57, 618, 204, 31, 617}"
628,1,158,0,0.1027881,"\int \frac{1}{x^4 \left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[1/(x^4*(1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{\sqrt[3]{1-x^3}}{3 x^3}-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{1}{6} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log (x)}{6}","-\frac{\sqrt[3]{1-x^3}}{3 x^3}-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{1}{6} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\log (x)}{6}",1,"-(1 - x^3)^(1/3)/(3*x^3) + ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) + Log[x]/6 - Log[1 + x^3]/(6*2^(2/3)) - Log[1 - (1 - x^3)^(1/3)]/6 + Log[2^(1/3) - (1 - x^3)^(1/3)]/(2*2^(2/3))","A",11,8,22,0.3636,1,"{446, 103, 156, 57, 618, 204, 31, 617}"
629,1,228,0,0.1629471,"\int \frac{x^7}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^7/((1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{1}{3} \sqrt[3]{1-x^3} x^2-\frac{1}{18} \log \left(\frac{x^2}{\left(1-x^3\right)^{2/3}}-\frac{x}{\sqrt[3]{1-x^3}}+1\right)+\frac{1}{9} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)+\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\frac{1}{3} \sqrt[3]{1-x^3} x^2+\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{1}{6} \log \left(-\sqrt[3]{1-x^3}-x\right)-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(x^2*(1 - x^3)^(1/3))/3 + ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) - ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) - Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/18 + Log[1 + x/(1 - x^3)^(1/3)]/9 + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(2/3)) - Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(2/3))","A",14,10,22,0.4545,1,"{494, 470, 584, 634, 618, 204, 628, 292, 31, 617}"
630,1,207,0,0.1031819,"\int \frac{x^4}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^4/((1 - x^3)^(2/3)*(1 + x^3)),x]","\frac{1}{6} \log \left(\frac{x^2}{\left(1-x^3\right)^{2/3}}-\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{1}{3} \log \left(\frac{x}{\sqrt[3]{1-x^3}}+1\right)-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{1}{2} \log \left(-\sqrt[3]{1-x^3}-x\right)+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(ArcTan[(1 - (2*x)/(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3]) + ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) + Log[1 + x^2/(1 - x^3)^(2/3) - x/(1 - x^3)^(1/3)]/6 - Log[1 + x/(1 - x^3)^(1/3)]/3 - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(2/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(2/3))","A",14,9,22,0.4091,1,"{494, 481, 292, 31, 634, 618, 204, 628, 617}"
631,1,122,0,0.0611541,"\int \frac{x}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x/((1 - x^3)^(2/3)*(1 + x^3)),x]","\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3])) + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(2/3)) - Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(2/3))","A",7,7,20,0.3500,1,"{494, 292, 31, 634, 617, 204, 628}"
632,1,137,0,0.0718635,"\int \frac{1}{x^2 \left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[1/(x^2*(1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{\sqrt[3]{1-x^3}}{x}-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","-\frac{\sqrt[3]{1-x^3}}{x}-\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-((1 - x^3)^(1/3)/x) + ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(2/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(2/3))","A",8,8,22,0.3636,1,"{494, 453, 292, 31, 634, 617, 204, 628}"
633,1,140,0,0.0844884,"\int \frac{1}{x^5 \left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[1/(x^5*(1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{\left(1-x^3\right)^{4/3}}{4 x^4}+\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}","\frac{\sqrt[3]{1-x^3}}{4 x}-\frac{\sqrt[3]{1-x^3}}{4 x^4}+\frac{\log \left(x^3+1\right)}{6\ 2^{2/3}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{2\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}",1,"-(1 - x^3)^(4/3)/(4*x^4) - ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2^(2/3)*Sqrt[3]) + Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(2/3)) - Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(3*2^(2/3))","A",9,8,22,0.3636,1,"{494, 461, 292, 31, 634, 617, 204, 628}"
634,1,26,0,0.0189698,"\int \frac{x^6}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^6/((1 - x^3)^(2/3)*(1 + x^3)),x]","\frac{1}{7} x^7 F_1\left(\frac{7}{3};\frac{2}{3},1;\frac{10}{3};x^3,-x^3\right)","-\frac{1}{2} \sqrt[3]{1-x^3} x+\frac{\log \left(2^{2/3}-\frac{1-x}{\sqrt[3]{1-x^3}}\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}-\frac{\log \left(\frac{(1-x)^2}{\left(1-x^3\right)^{2/3}}+\frac{2^{2/3} (1-x)}{\sqrt[3]{1-x^3}}+2 \sqrt[3]{2}\right)}{12\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3}}",1,"(x^7*AppellF1[7/3, 2/3, 1, 10/3, x^3, -x^3])/7","C",1,1,22,0.04545,0,"{510}"
635,1,26,0,0.0185345,"\int \frac{x^3}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[x^3/((1 - x^3)^(2/3)*(1 + x^3)),x]","\frac{1}{4} x^4 F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};x^3,-x^3\right)","\frac{1}{2} x \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};x^3\right)-\frac{\log \left(2^{2/3}-\frac{1-x}{\sqrt[3]{1-x^3}}\right)}{6\ 2^{2/3}}+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}+\frac{\log \left(\frac{(1-x)^2}{\left(1-x^3\right)^{2/3}}+\frac{2^{2/3} (1-x)}{\sqrt[3]{1-x^3}}+2 \sqrt[3]{2}\right)}{12\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3}}",1,"(x^4*AppellF1[4/3, 2/3, 1, 7/3, x^3, -x^3])/4","C",1,1,22,0.04545,0,"{510}"
636,1,21,0,0.0088603,"\int \frac{1}{\left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[1/((1 - x^3)^(2/3)*(1 + x^3)),x]","x F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};x^3,-x^3\right)","\frac{1}{2} x \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{4}{3};x^3\right)+\frac{\log \left(2^{2/3}-\frac{1-x}{\sqrt[3]{1-x^3}}\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}-\frac{\log \left(\frac{(1-x)^2}{\left(1-x^3\right)^{2/3}}+\frac{2^{2/3} (1-x)}{\sqrt[3]{1-x^3}}+2 \sqrt[3]{2}\right)}{12\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3}}",1,"x*AppellF1[1/3, 2/3, 1, 4/3, x^3, -x^3]","C",1,1,19,0.05263,0,"{429}"
637,1,26,0,0.0188149,"\int \frac{1}{x^3 \left(1-x^3\right)^{2/3} \left(1+x^3\right)} \, dx","Int[1/(x^3*(1 - x^3)^(2/3)*(1 + x^3)),x]","-\frac{F_1\left(-\frac{2}{3};\frac{2}{3},1;\frac{1}{3};x^3,-x^3\right)}{2 x^2}","-\frac{\sqrt[3]{1-x^3}}{2 x^2}-\frac{\log \left(2^{2/3}-\frac{1-x}{\sqrt[3]{1-x^3}}\right)}{6\ 2^{2/3}}+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6\ 2^{2/3}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{3\ 2^{2/3}}+\frac{\log \left(\frac{(1-x)^2}{\left(1-x^3\right)^{2/3}}+\frac{2^{2/3} (1-x)}{\sqrt[3]{1-x^3}}+2 \sqrt[3]{2}\right)}{12\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3}}",1,"-AppellF1[-2/3, 2/3, 1, 1/3, x^3, -x^3]/(2*x^2)","C",1,1,22,0.04545,0,"{510}"
638,1,141,0,0.1135761,"\int \frac{x^{14}}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^14/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{8} \left(1-x^3\right)^{8/3}-\frac{2}{5} \left(1-x^3\right)^{5/3}+\left(1-x^3\right)^{2/3}+\frac{1}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}","\frac{1}{8} \left(1-x^3\right)^{8/3}-\frac{2}{5} \left(1-x^3\right)^{5/3}+\left(1-x^3\right)^{2/3}+\frac{1}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"1/(2*(1 - x^3)^(1/3)) + (1 - x^3)^(2/3) - (2*(1 - x^3)^(5/3))/5 + (1 - x^3)^(8/3)/8 + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(12*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",11,9,22,0.4091,1,"{446, 87, 43, 627, 51, 55, 617, 204, 31}"
639,1,130,0,0.1012456,"\int \frac{x^{11}}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^11/((1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{1}{5} \left(1-x^3\right)^{5/3}+\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}","-\frac{1}{5} \left(1-x^3\right)^{5/3}+\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"1/(2*(1 - x^3)^(1/3)) + (1 - x^3)^(2/3)/2 - (1 - x^3)^(5/3)/5 - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) + Log[1 + x^3]/(12*2^(1/3)) - Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",11,9,22,0.4091,1,"{446, 87, 43, 783, 78, 55, 617, 204, 31}"
640,1,115,0,0.0901354,"\int \frac{x^8}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^8/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}","\frac{1}{2} \left(1-x^3\right)^{2/3}+\frac{1}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"1/(2*(1 - x^3)^(1/3)) + (1 - x^3)^(2/3)/2 + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(12*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",9,8,22,0.3636,1,"{446, 87, 627, 51, 55, 617, 204, 31}"
641,1,100,0,0.0683699,"\int \frac{x^5}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^5/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}","\frac{1}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"1/(2*(1 - x^3)^(1/3)) - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) + Log[1 + x^3]/(12*2^(1/3)) - Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",6,6,22,0.2727,1,"{446, 78, 55, 617, 204, 31}"
642,1,100,0,0.0683153,"\int \frac{x^2}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^2/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}","\frac{1}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"1/(2*(1 - x^3)^(1/3)) + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) - Log[1 + x^3]/(12*2^(1/3)) + Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",6,6,22,0.2727,1,"{444, 51, 55, 617, 204, 31}"
643,1,154,0,0.1107022,"\int \frac{1}{x \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x*(1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log (x)}{2}","\frac{1}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{1}{2} \log \left(1-\sqrt[3]{1-x^3}\right)-\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log (x)}{2}",1,"1/(2*(1 - x^3)^(1/3)) + ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/Sqrt[3] - ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) - Log[x]/2 + Log[1 + x^3]/(12*2^(1/3)) + Log[1 - (1 - x^3)^(1/3)]/2 - Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",11,8,22,0.3636,1,"{446, 85, 156, 55, 618, 204, 31, 617}"
644,1,175,0,0.1156593,"\int \frac{1}{x^4 \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x^4*(1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{1}{3 x^3 \sqrt[3]{1-x^3}}+\frac{5}{6 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{1}{6} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log (x)}{6}","-\frac{1}{3 x^3 \sqrt[3]{1-x^3}}+\frac{5}{6 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{1}{6} \log \left(1-\sqrt[3]{1-x^3}\right)+\frac{\log \left(\sqrt[3]{2}-\sqrt[3]{1-x^3}\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2^{2/3} \sqrt[3]{1-x^3}+1}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\log (x)}{6}",1,"5/(6*(1 - x^3)^(1/3)) - 1/(3*x^3*(1 - x^3)^(1/3)) + ArcTan[(1 + 2*(1 - x^3)^(1/3))/Sqrt[3]]/(3*Sqrt[3]) + ArcTan[(1 + 2^(2/3)*(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) - Log[x]/6 - Log[1 + x^3]/(12*2^(1/3)) + Log[1 - (1 - x^3)^(1/3)]/6 + Log[2^(1/3) - (1 - x^3)^(1/3)]/(4*2^(1/3))","A",13,9,22,0.4091,1,"{446, 103, 156, 51, 55, 618, 204, 31, 617}"
645,1,26,0,0.0178236,"\int \frac{x^9}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^9/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{10} x^{10} F_1\left(\frac{10}{3};\frac{4}{3},1;\frac{13}{3};x^3,-x^3\right)","\frac{x^4}{2 \sqrt[3]{1-x^3}}+\frac{5}{6} \left(1-x^3\right)^{2/3} x+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}-\frac{1}{6} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{3 \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"(x^10*AppellF1[10/3, 4/3, 1, 13/3, x^3, -x^3])/10","C",1,1,22,0.04545,0,"{510}"
646,1,26,0,0.0180263,"\int \frac{x^6}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^6/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{7} x^7 F_1\left(\frac{7}{3};\frac{4}{3},1;\frac{10}{3};x^3,-x^3\right)","\frac{x}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}-\frac{1}{2} \log \left(\sqrt[3]{1-x^3}+x\right)+\frac{\tan ^{-1}\left(\frac{1-\frac{2 x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{\sqrt{3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"(x^7*AppellF1[7/3, 4/3, 1, 10/3, x^3, -x^3])/7","C",1,1,22,0.04545,0,"{510}"
647,1,38,0,0.018378,"\int \frac{x^3}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^3/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{x^4 \, _2F_1\left(\frac{4}{3},\frac{4}{3};\frac{7}{3};\frac{2 x^3}{x^3+1}\right)}{4 \left(x^3+1\right)^{4/3}}","\frac{x}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"(x^4*Hypergeometric2F1[4/3, 4/3, 7/3, (2*x^3)/(1 + x^3)])/(4*(1 + x^3)^(4/3))","C",1,1,22,0.04545,0,"{510}"
648,1,140,0,0.0762032,"\int \frac{1}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{x}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(\frac{2^{2/3} x^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} x}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}","\frac{x}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"x/(2*(1 - x^3)^(1/3)) - ArcTan[(1 - (2*2^(1/3)*x)/(1 - x^3)^(1/3))/Sqrt[3]]/(2*2^(1/3)*Sqrt[3]) - Log[1 + (2^(2/3)*x^2)/(1 - x^3)^(2/3) - (2^(1/3)*x)/(1 - x^3)^(1/3)]/(12*2^(1/3)) + Log[1 + (2^(1/3)*x)/(1 - x^3)^(1/3)]/(6*2^(1/3))","A",8,8,19,0.4211,1,"{382, 377, 200, 31, 634, 617, 204, 628}"
649,1,204,0,8.1214113,"\int \frac{1}{x^3 \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x^3*(1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{-18 \left(x^3+1\right)^2 x^6 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-54 x^{12} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-84 x^9 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-30 x^6 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-7 \left(1-x^3\right)^2 \left(9 x^6+12 x^3+2\right) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)+63 x^{12}-42 x^9-91 x^6+56 x^3+14}{14 x^5 \left(1-x^3\right)^{7/3}}","-\frac{\left(1-x^3\right)^{2/3}}{x^2}+\frac{1}{2 x^2 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"-(14 + 56*x^3 - 91*x^6 - 42*x^9 + 63*x^12 - 7*(1 - x^3)^2*(2 + 12*x^3 + 9*x^6)*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 30*x^6*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] - 84*x^9*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] - 54*x^12*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] - 18*x^6*(1 + x^3)^2*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, (-2*x^3)/(1 - x^3)])/(14*x^5*(1 - x^3)^(7/3))","C",1,1,22,0.04545,0,"{510}"
650,1,397,0,8.318319,"\int \frac{1}{x^6 \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x^6*(1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{54 \left(x^3+1\right)^2 \left(6 x^3+1\right) x^6 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+54 \left(x^3+1\right)^3 x^6 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+567 x^{15} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)+594 x^{15} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-378 x^{12} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)+972 x^{12} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-819 x^9 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)+342 x^9 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+476 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-36 x^6 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+182 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-28 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-567 x^{15}+378 x^{12}+819 x^9-476 x^6-182 x^3+28}{70 x^8 \left(1-x^3\right)^{7/3}}","-\frac{4 \left(1-x^3\right)^{2/3}}{5 x^2}-\frac{7 \left(1-x^3\right)^{2/3}}{10 x^5}+\frac{1}{2 x^5 \sqrt[3]{1-x^3}}-\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"-(28 - 182*x^3 - 476*x^6 + 819*x^9 + 378*x^12 - 567*x^15 - 28*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] + 182*x^3*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] + 476*x^6*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 819*x^9*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 378*x^12*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] + 567*x^15*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 36*x^6*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] + 342*x^9*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] + 972*x^12*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] + 594*x^15*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] + 54*x^6*(1 + x^3)^2*(1 + 6*x^3)*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, (-2*x^3)/(1 - x^3)] + 54*x^6*(1 + x^3)^3*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, (-2*x^3)/(1 - x^3)])/(70*x^8*(1 - x^3)^(7/3))","C",1,1,22,0.04545,0,"{510}"
651,1,643,0,10.5945499,"\int \frac{1}{x^9 \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x^9*(1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{-81 x^{18} \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-324 x^{15} \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-486 x^{12} \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-324 x^9 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+27 \left(x^3+1\right)^2 \left(-105 x^6-18 x^3+7\right) x^6 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+54 \left(1-15 x^3\right) \left(x^3+1\right)^3 x^6 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-81 x^6 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-3402 x^{18} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-4050 x^{18} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+2268 x^{15} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-6696 x^{15} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+4914 x^{12} \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-2268 x^{12} \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-2856 x^9 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)+312 x^9 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)-1162 x^6 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-66 x^6 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};-\frac{2 x^3}{1-x^3}\right)+308 x^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)-70 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};-\frac{2 x^3}{1-x^3}\right)+3402 x^{18}-2268 x^{15}-4914 x^{12}+2856 x^9+1162 x^6-308 x^3+70}{280 x^{11} \left(1-x^3\right)^{7/3}}","-\frac{49 \left(1-x^3\right)^{2/3}}{40 x^2}-\frac{13 \left(1-x^3\right)^{2/3}}{20 x^5}-\frac{5 \left(1-x^3\right)^{2/3}}{8 x^8}+\frac{1}{2 x^8 \sqrt[3]{1-x^3}}+\frac{\log \left(x^3+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(-\sqrt[3]{1-x^3}-\sqrt[3]{2} x\right)}{4 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} x}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}",1,"-(70 - 308*x^3 + 1162*x^6 + 2856*x^9 - 4914*x^12 - 2268*x^15 + 3402*x^18 - 70*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] + 308*x^3*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 1162*x^6*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 2856*x^9*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] + 4914*x^12*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] + 2268*x^15*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 3402*x^18*Hypergeometric2F1[1/3, 1, 4/3, (-2*x^3)/(1 - x^3)] - 66*x^6*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] + 312*x^9*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] - 2268*x^12*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] - 6696*x^15*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] - 4050*x^18*Hypergeometric2F1[2, 7/3, 10/3, (-2*x^3)/(1 - x^3)] + 27*x^6*(1 + x^3)^2*(7 - 18*x^3 - 105*x^6)*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, (-2*x^3)/(1 - x^3)] + 54*x^6*(1 - 15*x^3)*(1 + x^3)^3*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, (-2*x^3)/(1 - x^3)] - 81*x^6*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, (-2*x^3)/(1 - x^3)] - 324*x^9*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, (-2*x^3)/(1 - x^3)] - 486*x^12*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, (-2*x^3)/(1 - x^3)] - 324*x^15*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, (-2*x^3)/(1 - x^3)] - 81*x^18*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, (-2*x^3)/(1 - x^3)])/(280*x^11*(1 - x^3)^(7/3))","C",1,1,22,0.04545,0,"{510}"
652,1,26,0,0.0188917,"\int \frac{x^{10}}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^10/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{11} x^{11} F_1\left(\frac{11}{3};\frac{4}{3},1;\frac{14}{3};x^3,-x^3\right)","-\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{x^5}{2 \sqrt[3]{1-x^3}}+\frac{3}{4} \left(1-x^3\right)^{2/3} x^2-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{8 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{24 \sqrt[3]{2}}",1,"(x^11*AppellF1[11/3, 4/3, 1, 14/3, x^3, -x^3])/11","C",1,1,22,0.04545,0,"{510}"
653,1,26,0,0.0183977,"\int \frac{x^7}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^7/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{8} x^8 F_1\left(\frac{8}{3};\frac{4}{3},1;\frac{11}{3};x^3,-x^3\right)","-\frac{3}{4} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{x^2}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{8 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{24 \sqrt[3]{2}}",1,"(x^8*AppellF1[8/3, 4/3, 1, 11/3, x^3, -x^3])/8","C",1,1,22,0.04545,0,"{510}"
654,1,26,0,0.0178863,"\int \frac{x^4}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x^4/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{5} x^5 F_1\left(\frac{5}{3};\frac{4}{3},1;\frac{8}{3};x^3,-x^3\right)","-\frac{1}{4} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{x^2}{2 \sqrt[3]{1-x^3}}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{8 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{24 \sqrt[3]{2}}",1,"(x^5*AppellF1[5/3, 4/3, 1, 8/3, x^3, -x^3])/5","C",1,1,22,0.04545,0,"{510}"
655,1,26,0,0.0130731,"\int \frac{x}{\left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[x/((1 - x^3)^(4/3)*(1 + x^3)),x]","\frac{1}{2} x^2 F_1\left(\frac{2}{3};\frac{4}{3},1;\frac{5}{3};x^3,-x^3\right)","-\frac{1}{4} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)+\frac{x^2}{2 \sqrt[3]{1-x^3}}+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{8 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{24 \sqrt[3]{2}}",1,"(x^2*AppellF1[2/3, 4/3, 1, 5/3, x^3, -x^3])/2","C",1,1,20,0.05000,0,"{510}"
656,1,24,0,0.0190919,"\int \frac{1}{x^2 \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x^2*(1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{F_1\left(-\frac{1}{3};\frac{4}{3},1;\frac{2}{3};x^3,-x^3\right)}{x}","-\frac{3}{4} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\frac{3 \left(1-x^3\right)^{2/3}}{2 x}+\frac{1}{2 \sqrt[3]{1-x^3} x}-\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}+\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}+\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{8 \sqrt[3]{2}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}-\frac{\log \left((1-x) (x+1)^2\right)}{24 \sqrt[3]{2}}",1,"-(AppellF1[-1/3, 4/3, 1, 2/3, x^3, -x^3]/x)","C",1,1,22,0.04545,0,"{510}"
657,1,26,0,0.0196007,"\int \frac{1}{x^5 \left(1-x^3\right)^{4/3} \left(1+x^3\right)} \, dx","Int[1/(x^5*(1 - x^3)^(4/3)*(1 + x^3)),x]","-\frac{F_1\left(-\frac{4}{3};\frac{4}{3},1;-\frac{1}{3};x^3,-x^3\right)}{4 x^4}","-\frac{1}{2} x^2 \, _2F_1\left(\frac{1}{3},\frac{2}{3};\frac{5}{3};x^3\right)-\frac{\left(1-x^3\right)^{2/3}}{x}-\frac{3 \left(1-x^3\right)^{2/3}}{4 x^4}+\frac{1}{2 \sqrt[3]{1-x^3} x^4}+\frac{\log \left(\frac{2^{2/3} (1-x)^2}{\left(1-x^3\right)^{2/3}}-\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{12 \sqrt[3]{2}}-\frac{\log \left(\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1\right)}{6 \sqrt[3]{2}}-\frac{\log \left(2^{2/3} \sqrt[3]{1-x^3}+x-1\right)}{8 \sqrt[3]{2}}+\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}}{\sqrt{3}}\right)}{2 \sqrt[3]{2} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{\frac{\sqrt[3]{2} (1-x)}{\sqrt[3]{1-x^3}}+1}{\sqrt{3}}\right)}{4 \sqrt[3]{2} \sqrt{3}}+\frac{\log \left((1-x) (x+1)^2\right)}{24 \sqrt[3]{2}}",1,"-AppellF1[-4/3, 4/3, 1, -1/3, x^3, -x^3]/(4*x^4)","C",1,1,22,0.04545,0,"{510}"
658,1,264,0,0.3861406,"\int \frac{x^{11} \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^11*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{\left(a+b x^3\right)^{4/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{4 b^3 d^3}-\frac{\left(a+b x^3\right)^{7/3} (2 a d+b c)}{7 b^3 d^2}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^3 d}-\frac{c^3 \sqrt[3]{a+b x^3}}{d^4}-\frac{c^3 \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{13/3}}+\frac{c^3 \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{13/3}}-\frac{c^3 \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{13/3}}","\frac{\left(a+b x^3\right)^{4/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{4 b^3 d^3}-\frac{\left(a+b x^3\right)^{7/3} (2 a d+b c)}{7 b^3 d^2}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^3 d}-\frac{c^3 \sqrt[3]{a+b x^3}}{d^4}-\frac{c^3 \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{13/3}}+\frac{c^3 \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{13/3}}-\frac{c^3 \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{13/3}}",1,"-((c^3*(a + b*x^3)^(1/3))/d^4) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(4/3))/(4*b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(7/3))/(7*b^3*d^2) + (a + b*x^3)^(10/3)/(10*b^3*d) - (c^3*(b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(13/3)) - (c^3*(b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*d^(13/3)) + (c^3*(b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(13/3))","A",8,7,24,0.2917,1,"{446, 88, 50, 58, 617, 204, 31}"
659,1,220,0,0.2585994,"\int \frac{x^8 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^8*(a + b*x^3)^(1/3))/(c + d*x^3),x]","-\frac{\left(a+b x^3\right)^{4/3} (a d+b c)}{4 b^2 d^2}+\frac{\left(a+b x^3\right)^{7/3}}{7 b^2 d}+\frac{c^2 \sqrt[3]{a+b x^3}}{d^3}+\frac{c^2 \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{10/3}}-\frac{c^2 \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{10/3}}+\frac{c^2 \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{10/3}}","-\frac{\left(a+b x^3\right)^{4/3} (a d+b c)}{4 b^2 d^2}+\frac{\left(a+b x^3\right)^{7/3}}{7 b^2 d}+\frac{c^2 \sqrt[3]{a+b x^3}}{d^3}+\frac{c^2 \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{10/3}}-\frac{c^2 \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{10/3}}+\frac{c^2 \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{10/3}}",1,"(c^2*(a + b*x^3)^(1/3))/d^3 - ((b*c + a*d)*(a + b*x^3)^(4/3))/(4*b^2*d^2) + (a + b*x^3)^(7/3)/(7*b^2*d) + (c^2*(b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(10/3)) + (c^2*(b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*d^(10/3)) - (c^2*(b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(10/3))","A",8,7,24,0.2917,1,"{446, 88, 50, 58, 617, 204, 31}"
660,1,186,0,0.2022189,"\int \frac{x^5 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^5*(a + b*x^3)^(1/3))/(c + d*x^3),x]","-\frac{c \sqrt[3]{a+b x^3}}{d^2}-\frac{c \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{7/3}}+\frac{c \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{7/3}}-\frac{c \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}+\frac{\left(a+b x^3\right)^{4/3}}{4 b d}","-\frac{c \sqrt[3]{a+b x^3}}{d^2}-\frac{c \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{7/3}}+\frac{c \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{7/3}}-\frac{c \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}+\frac{\left(a+b x^3\right)^{4/3}}{4 b d}",1,"-((c*(a + b*x^3)^(1/3))/d^2) + (a + b*x^3)^(4/3)/(4*b*d) - (c*(b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(7/3)) - (c*(b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*d^(7/3)) + (c*(b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(7/3))","A",7,7,24,0.2917,1,"{446, 80, 50, 58, 617, 204, 31}"
661,1,159,0,0.1547648,"\int \frac{x^2 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^2*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{\sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{4/3}}-\frac{\sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{4/3}}+\frac{\sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{4/3}}+\frac{\sqrt[3]{a+b x^3}}{d}","\frac{\sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^{4/3}}-\frac{\sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{4/3}}+\frac{\sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{4/3}}+\frac{\sqrt[3]{a+b x^3}}{d}",1,"(a + b*x^3)^(1/3)/d + ((b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(4/3)) + ((b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*d^(4/3)) - ((b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(4/3))","A",6,6,24,0.2500,1,"{444, 50, 58, 617, 204, 31}"
662,1,246,0,0.2341888,"\int \frac{\sqrt[3]{a+b x^3}}{x \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x*(c + d*x^3)),x]","-\frac{\sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c \sqrt[3]{d}}+\frac{\sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c \sqrt[3]{d}}-\frac{\sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c \sqrt[3]{d}}+\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 c}-\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} c}-\frac{\sqrt[3]{a} \log (x)}{2 c}","-\frac{\sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c \sqrt[3]{d}}+\frac{\sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c \sqrt[3]{d}}-\frac{\sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c \sqrt[3]{d}}+\frac{\sqrt[3]{a} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 c}-\frac{\sqrt[3]{a} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} c}-\frac{\sqrt[3]{a} \log (x)}{2 c}",1,"-((a^(1/3)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*c)) - ((b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*d^(1/3)) - (a^(1/3)*Log[x])/(2*c) - ((b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*c*d^(1/3)) + (a^(1/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(2*c) + ((b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c*d^(1/3))","A",10,7,24,0.2917,1,"{446, 83, 57, 617, 204, 31, 58}"
663,1,340,0,0.3837116,"\int \frac{\sqrt[3]{a+b x^3}}{x^4 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^4*(c + d*x^3)),x]","\frac{(b c-3 a d) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{2/3} c^2}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} c^2}-\frac{\log (x) (b c-3 a d)}{6 a^{2/3} c^2}+\frac{d^{2/3} \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^2}-\frac{d^{2/3} \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2}+\frac{d^{2/3} \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2}+\frac{d \sqrt[3]{a+b x^3}}{c^2}+\frac{\sqrt[3]{a+b x^3} (b c-3 a d)}{3 a c^2}-\frac{\left(a+b x^3\right)^{4/3}}{3 a c x^3}","\frac{(b c-3 a d) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{2/3} c^2}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{2/3} c^2}-\frac{\log (x) (b c-3 a d)}{6 a^{2/3} c^2}+\frac{d^{2/3} \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^2}-\frac{d^{2/3} \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2}+\frac{d^{2/3} \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2}+\frac{d \sqrt[3]{a+b x^3}}{c^2}+\frac{\sqrt[3]{a+b x^3} (b c-3 a d)}{3 a c^2}-\frac{\left(a+b x^3\right)^{4/3}}{3 a c x^3}",1,"(d*(a + b*x^3)^(1/3))/c^2 + ((b*c - 3*a*d)*(a + b*x^3)^(1/3))/(3*a*c^2) - (a + b*x^3)^(4/3)/(3*a*c*x^3) - ((b*c - 3*a*d)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(2/3)*c^2) + (d^(2/3)*(b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^2) - ((b*c - 3*a*d)*Log[x])/(6*a^(2/3)*c^2) + (d^(2/3)*(b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*c^2) + ((b*c - 3*a*d)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(2/3)*c^2) - (d^(2/3)*(b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^2)","A",13,9,24,0.3750,1,"{446, 103, 156, 50, 57, 617, 204, 31, 58}"
664,1,370,0,0.4886745,"\int \frac{\sqrt[3]{a+b x^3}}{x^7 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^7*(c + d*x^3)),x]","-\frac{\left(-9 a^2 d^2+3 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{5/3} c^3}+\frac{\left(-9 a^2 d^2+3 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} c^3}+\frac{\log (x) \left(-9 a^2 d^2+3 a b c d+b^2 c^2\right)}{18 a^{5/3} c^3}-\frac{d^{5/3} \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^3}+\frac{d^{5/3} \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^3}-\frac{d^{5/3} \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^3}+\frac{\sqrt[3]{a+b x^3} (3 a d+b c)}{9 a c^2 x^3}-\frac{\left(a+b x^3\right)^{4/3}}{6 a c x^6}","-\frac{\left(-9 a^2 d^2+3 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{5/3} c^3}+\frac{\left(-9 a^2 d^2+3 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{5/3} c^3}+\frac{\log (x) \left(-9 a^2 d^2+3 a b c d+b^2 c^2\right)}{18 a^{5/3} c^3}-\frac{d^{5/3} \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^3}+\frac{d^{5/3} \sqrt[3]{b c-a d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^3}-\frac{d^{5/3} \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^3}+\frac{\sqrt[3]{a+b x^3} (3 a d+b c)}{9 a c^2 x^3}-\frac{\left(a+b x^3\right)^{4/3}}{6 a c x^6}",1,"((b*c + 3*a*d)*(a + b*x^3)^(1/3))/(9*a*c^2*x^3) - (a + b*x^3)^(4/3)/(6*a*c*x^6) + ((b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(5/3)*c^3) - (d^(5/3)*(b*c - a*d)^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^3) + ((b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*Log[x])/(18*a^(5/3)*c^3) - (d^(5/3)*(b*c - a*d)^(1/3)*Log[c + d*x^3])/(6*c^3) - ((b^2*c^2 + 3*a*b*c*d - 9*a^2*d^2)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(18*a^(5/3)*c^3) + (d^(5/3)*(b*c - a*d)^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^3)","A",12,9,24,0.3750,1,"{446, 103, 149, 156, 57, 617, 204, 31, 58}"
665,1,64,0,0.0544801,"\int \frac{x^7 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^7*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{x^8 \sqrt[3]{a+b x^3} F_1\left(\frac{8}{3};-\frac{1}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 c \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\left(-a^2 d^2-3 a b c d+9 b^2 c^2\right) \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{18 b^{5/3} d^3}-\frac{\left(-a^2 d^2-3 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{5/3} d^3}-\frac{c^{5/3} \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^3}+\frac{c^{5/3} \sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^3}+\frac{c^{5/3} \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^3}-\frac{x^2 \sqrt[3]{a+b x^3} (6 b c-a d)}{18 b d^2}+\frac{x^5 \sqrt[3]{a+b x^3}}{6 d}",1,"(x^8*(a + b*x^3)^(1/3)*AppellF1[8/3, -1/3, 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)])/(8*c*(1 + (b*x^3)/a)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
666,1,64,0,0.0540282,"\int \frac{x^4 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^4*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{x^5 \sqrt[3]{a+b x^3} F_1\left(\frac{5}{3};-\frac{1}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{(3 b c-a d) \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{6 b^{2/3} d^2}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{2/3} d^2}+\frac{c^{2/3} \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 d^2}-\frac{c^{2/3} \sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^2}-\frac{c^{2/3} \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{x^2 \sqrt[3]{a+b x^3}}{3 d}",1,"(x^5*(a + b*x^3)^(1/3)*AppellF1[5/3, -1/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*c*(1 + (b*x^3)/a)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
667,1,64,0,0.0377606,"\int \frac{x \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{x^2 \sqrt[3]{a+b x^3} F_1\left(\frac{2}{3};-\frac{1}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 \sqrt[3]{c} d}+\frac{\sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{c} d}+\frac{\sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{c} d}-\frac{\sqrt[3]{b} \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 d}-\frac{\sqrt[3]{b} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d}",1,"(x^2*(a + b*x^3)^(1/3)*AppellF1[2/3, -1/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*(1 + (b*x^3)/a)^(1/3))","C",2,2,22,0.09091,0,"{511, 510}"
668,1,87,0,0.0636257,"\int \frac{\sqrt[3]{a+b x^3}}{x^2 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^2*(c + d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} \sqrt[3]{\frac{d x^3}{c}+1} \, _2F_1\left(-\frac{1}{3},-\frac{1}{3};\frac{2}{3};-\frac{c \left(\frac{b x^3}{a}-\frac{d x^3}{c}\right)}{d x^3+c}\right)}{c x \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{\sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^{4/3}}-\frac{\sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{4/3}}-\frac{\sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{4/3}}-\frac{\sqrt[3]{a+b x^3}}{c x}",1,"-(((a + b*x^3)^(1/3)*(1 + (d*x^3)/c)^(1/3)*Hypergeometric2F1[-1/3, -1/3, 2/3, -((c*((b*x^3)/a - (d*x^3)/c))/(c + d*x^3))])/(c*x*(1 + (b*x^3)/a)^(1/3)))","C",2,2,24,0.08333,0,"{511, 510}"
669,1,145,0,0.1328766,"\int \frac{\sqrt[3]{a+b x^3}}{x^5 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^5*(c + d*x^3)),x]","-\frac{x^3 \left(c-3 d x^3\right) (-(b c-a d)) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+3 x^3 \left(c+d x^3\right) (b c-a d) \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+2 c \left(a+b x^3\right) \left(c-3 d x^3\right)}{8 c^3 x^4 \left(a+b x^3\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} (b c-4 a d)}{4 a c^2 x}-\frac{d \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^{7/3}}+\frac{d \sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{7/3}}+\frac{d \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{7/3}}-\frac{\sqrt[3]{a+b x^3}}{4 c x^4}",1,"-(2*c*(a + b*x^3)*(c - 3*d*x^3) - (b*c - a*d)*x^3*(c - 3*d*x^3)*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 3*(b*c - a*d)*x^3*(c + d*x^3)*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(8*c^3*x^4*(a + b*x^3)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
670,1,451,0,0.9398772,"\int \frac{\sqrt[3]{a+b x^3}}{x^8 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^8*(c + d*x^3)),x]","-\frac{-9 x^3 \left(c+d x^3\right)^2 (b c-a d) \, _3F_2\left(\frac{2}{3},2,2;1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-2 x^3 \left(2 c^2-3 c d x^3+9 d^2 x^6\right) (b c-a d) \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-12 b c^2 d x^6 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+15 b c^3 x^3 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-15 a c^2 d x^3 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+27 a d^3 x^9 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-27 b c d^2 x^9 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+12 a c d^2 x^6 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-12 a c^2 d x^3+8 a c^3+36 a c d^2 x^6-12 b c^2 d x^6+8 b c^3 x^3+36 b c d^2 x^9}{56 c^4 x^7 \left(a+b x^3\right)^{2/3}}","\frac{\sqrt[3]{a+b x^3} \left(-28 a^2 d^2+7 a b c d+3 b^2 c^2\right)}{28 a^2 c^3 x}+\frac{d^2 \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^{10/3}}-\frac{d^2 \sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{10/3}}-\frac{d^2 \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{10/3}}-\frac{\sqrt[3]{a+b x^3} (b c-7 a d)}{28 a c^2 x^4}-\frac{\sqrt[3]{a+b x^3}}{7 c x^7}",1,"-(8*a*c^3 + 8*b*c^3*x^3 - 12*a*c^2*d*x^3 - 12*b*c^2*d*x^6 + 36*a*c*d^2*x^6 + 36*b*c*d^2*x^9 - 2*(b*c - a*d)*x^3*(2*c^2 - 3*c*d*x^3 + 9*d^2*x^6)*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 15*b*c^3*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 15*a*c^2*d*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 12*b*c^2*d*x^6*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 12*a*c*d^2*x^6*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 27*b*c*d^2*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*a*d^3*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 9*(b*c - a*d)*x^3*(c + d*x^3)^2*HypergeometricPFQ[{2/3, 2, 2}, {1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(56*c^4*x^7*(a + b*x^3)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
671,1,905,0,2.6418434,"\int \frac{\sqrt[3]{a+b x^3}}{x^{11} \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^11*(c + d*x^3)),x]","-\frac{-324 b c d^3 x^{12}-162 a d^4 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+162 b c d^3 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-297 a d^4 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+297 b c d^3 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-324 a c d^3 x^9+108 b c^2 d^2 x^9+54 a c d^3 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-54 b c^2 d^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-81 a c d^3 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+81 b c^2 d^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+108 a c^2 d^2 x^6-72 b c^3 d x^6-36 a c^2 d^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+36 b c^3 d \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+99 a c^2 d^2 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-99 b c^3 d \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+56 b c^4 x^3-72 a c^3 d x^3-28 b c^4 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+28 a c^3 d \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+117 b c^4 \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-117 a c^3 d \, _2F_1\left(\frac{2}{3},2;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-54 (b c-a d) \left(2 c-3 d x^3\right) \left(d x^3+c\right)^2 \, _3F_2\left(\frac{2}{3},2,2;1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+27 (b c-a d) \left(d x^3+c\right)^3 \, _4F_3\left(\frac{2}{3},2,2,2;1,1,\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+56 a c^4}{560 c^5 x^{10} \left(b x^3+a\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} \left(35 a^2 b c d^2-140 a^3 d^3+15 a b^2 c^2 d+9 b^3 c^3\right)}{140 a^3 c^4 x}+\frac{\sqrt[3]{a+b x^3} \left(-35 a^2 d^2+5 a b c d+3 b^2 c^2\right)}{140 a^2 c^3 x^4}-\frac{d^3 \sqrt[3]{b c-a d} \log \left(c+d x^3\right)}{6 c^{13/3}}+\frac{d^3 \sqrt[3]{b c-a d} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{13/3}}+\frac{d^3 \sqrt[3]{b c-a d} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{13/3}}-\frac{\sqrt[3]{a+b x^3} (b c-10 a d)}{70 a c^2 x^7}-\frac{\sqrt[3]{a+b x^3}}{10 c x^{10}}",1,"-(56*a*c^4 + 56*b*c^4*x^3 - 72*a*c^3*d*x^3 - 72*b*c^3*d*x^6 + 108*a*c^2*d^2*x^6 + 108*b*c^2*d^2*x^9 - 324*a*c*d^3*x^9 - 324*b*c*d^3*x^12 - 28*b*c^4*x^3*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 28*a*c^3*d*x^3*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 36*b*c^3*d*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 36*a*c^2*d^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 54*b*c^2*d^2*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*a*c*d^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*b*c*d^3*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 162*a*d^4*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 117*b*c^4*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 117*a*c^3*d*x^3*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 99*b*c^3*d*x^6*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 99*a*c^2*d^2*x^6*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*b*c^2*d^2*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 81*a*c*d^3*x^9*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 297*b*c*d^3*x^12*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 297*a*d^4*x^12*Hypergeometric2F1[2/3, 2, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 54*(b*c - a*d)*x^3*(2*c - 3*d*x^3)*(c + d*x^3)^2*HypergeometricPFQ[{2/3, 2, 2}, {1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*(b*c - a*d)*x^3*(c + d*x^3)^3*HypergeometricPFQ[{2/3, 2, 2, 2}, {1, 1, 5/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(560*c^5*x^10*(a + b*x^3)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
672,1,64,0,0.0509833,"\int \frac{x^6 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^6*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{x^7 \sqrt[3]{a+b x^3} F_1\left(\frac{7}{3};-\frac{1}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x^7 \sqrt[3]{a+b x^3} F_1\left(\frac{7}{3};-\frac{1}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(x^7*(a + b*x^3)^(1/3)*AppellF1[7/3, -1/3, 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)])/(7*c*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
673,1,64,0,0.0530495,"\int \frac{x^3 \sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(x^3*(a + b*x^3)^(1/3))/(c + d*x^3),x]","\frac{x^4 \sqrt[3]{a+b x^3} F_1\left(\frac{4}{3};-\frac{1}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x^4 \sqrt[3]{a+b x^3} F_1\left(\frac{4}{3};-\frac{1}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(x^4*(a + b*x^3)^(1/3)*AppellF1[4/3, -1/3, 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*c*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
674,1,59,0,0.025742,"\int \frac{\sqrt[3]{a+b x^3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(1/3)/(c + d*x^3),x]","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{1}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(x*(a + b*x^3)^(1/3)*AppellF1[1/3, -1/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
675,1,64,0,0.0531591,"\int \frac{\sqrt[3]{a+b x^3}}{x^3 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^3*(c + d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} F_1\left(-\frac{2}{3};-\frac{1}{3},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c x^2 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\sqrt[3]{a+b x^3} F_1\left(-\frac{2}{3};-\frac{1}{3},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c x^2 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"-((a + b*x^3)^(1/3)*AppellF1[-2/3, -1/3, 1, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*x^2*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
676,1,64,0,0.0544718,"\int \frac{\sqrt[3]{a+b x^3}}{x^6 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(1/3)/(x^6*(c + d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} F_1\left(-\frac{5}{3};-\frac{1}{3},1;-\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c x^5 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\sqrt[3]{a+b x^3} F_1\left(-\frac{5}{3};-\frac{1}{3},1;-\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c x^5 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"-((a + b*x^3)^(1/3)*AppellF1[-5/3, -1/3, 1, -2/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*c*x^5*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
677,1,266,0,0.3220752,"\int \frac{x^{11} \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^11*(a + b*x^3)^(2/3))/(c + d*x^3),x]","\frac{\left(a+b x^3\right)^{5/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{5 b^3 d^3}-\frac{\left(a+b x^3\right)^{8/3} (2 a d+b c)}{8 b^3 d^2}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^3 d}-\frac{c^3 \left(a+b x^3\right)^{2/3}}{2 d^4}+\frac{c^3 (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{14/3}}-\frac{c^3 (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{14/3}}-\frac{c^3 (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{14/3}}","\frac{\left(a+b x^3\right)^{5/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{5 b^3 d^3}-\frac{\left(a+b x^3\right)^{8/3} (2 a d+b c)}{8 b^3 d^2}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^3 d}-\frac{c^3 \left(a+b x^3\right)^{2/3}}{2 d^4}+\frac{c^3 (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{14/3}}-\frac{c^3 (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{14/3}}-\frac{c^3 (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{14/3}}",1,"-(c^3*(a + b*x^3)^(2/3))/(2*d^4) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(5/3))/(5*b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(8/3))/(8*b^3*d^2) + (a + b*x^3)^(11/3)/(11*b^3*d) - (c^3*(b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(14/3)) + (c^3*(b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*d^(14/3)) - (c^3*(b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(14/3))","A",8,7,24,0.2917,1,"{446, 88, 50, 56, 617, 204, 31}"
678,1,223,0,0.2593458,"\int \frac{x^8 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^8*(a + b*x^3)^(2/3))/(c + d*x^3),x]","-\frac{\left(a+b x^3\right)^{5/3} (a d+b c)}{5 b^2 d^2}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^2 d}+\frac{c^2 \left(a+b x^3\right)^{2/3}}{2 d^3}-\frac{c^2 (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{11/3}}+\frac{c^2 (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{11/3}}+\frac{c^2 (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{11/3}}","-\frac{\left(a+b x^3\right)^{5/3} (a d+b c)}{5 b^2 d^2}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^2 d}+\frac{c^2 \left(a+b x^3\right)^{2/3}}{2 d^3}-\frac{c^2 (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{11/3}}+\frac{c^2 (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{11/3}}+\frac{c^2 (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{11/3}}",1,"(c^2*(a + b*x^3)^(2/3))/(2*d^3) - ((b*c + a*d)*(a + b*x^3)^(5/3))/(5*b^2*d^2) + (a + b*x^3)^(8/3)/(8*b^2*d) + (c^2*(b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(11/3)) - (c^2*(b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*d^(11/3)) + (c^2*(b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(11/3))","A",8,7,24,0.2917,1,"{446, 88, 50, 56, 617, 204, 31}"
679,1,188,0,0.198692,"\int \frac{x^5 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^5*(a + b*x^3)^(2/3))/(c + d*x^3),x]","-\frac{c \left(a+b x^3\right)^{2/3}}{2 d^2}+\frac{c (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{8/3}}-\frac{c (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{8/3}}-\frac{c (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{8/3}}+\frac{\left(a+b x^3\right)^{5/3}}{5 b d}","-\frac{c \left(a+b x^3\right)^{2/3}}{2 d^2}+\frac{c (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{8/3}}-\frac{c (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{8/3}}-\frac{c (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{8/3}}+\frac{\left(a+b x^3\right)^{5/3}}{5 b d}",1,"-(c*(a + b*x^3)^(2/3))/(2*d^2) + (a + b*x^3)^(5/3)/(5*b*d) - (c*(b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(8/3)) + (c*(b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*d^(8/3)) - (c*(b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(8/3))","A",7,7,24,0.2917,1,"{446, 80, 50, 56, 617, 204, 31}"
680,1,162,0,0.1702455,"\int \frac{x^2 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^2*(a + b*x^3)^(2/3))/(c + d*x^3),x]","-\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{5/3}}+\frac{(b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{5/3}}+\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{5/3}}+\frac{\left(a+b x^3\right)^{2/3}}{2 d}","-\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^{5/3}}+\frac{(b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{5/3}}+\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{5/3}}+\frac{\left(a+b x^3\right)^{2/3}}{2 d}",1,"(a + b*x^3)^(2/3)/(2*d) + ((b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(5/3)) - ((b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*d^(5/3)) + ((b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(5/3))","A",6,6,24,0.2500,1,"{444, 50, 56, 617, 204, 31}"
681,1,245,0,0.2288953,"\int \frac{\left(a+b x^3\right)^{2/3}}{x \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x*(c + d*x^3)),x]","\frac{a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 c}+\frac{a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} c}-\frac{a^{2/3} \log (x)}{2 c}+\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c d^{2/3}}-\frac{(b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c d^{2/3}}-\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c d^{2/3}}","\frac{a^{2/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 c}+\frac{a^{2/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} c}-\frac{a^{2/3} \log (x)}{2 c}+\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c d^{2/3}}-\frac{(b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c d^{2/3}}-\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c d^{2/3}}",1,"(a^(2/3)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*c) - ((b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*d^(2/3)) - (a^(2/3)*Log[x])/(2*c) + ((b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*c*d^(2/3)) + (a^(2/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(2*c) - ((b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c*d^(2/3))","A",10,7,24,0.2917,1,"{446, 83, 55, 617, 204, 31, 56}"
682,1,347,0,0.3891233,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^4 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^4*(c + d*x^3)),x]","\frac{d \left(a+b x^3\right)^{2/3}}{2 c^2}+\frac{\left(a+b x^3\right)^{2/3} (2 b c-3 a d)}{6 a c^2}-\frac{\sqrt[3]{d} (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^2}+\frac{(2 b c-3 a d) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 \sqrt[3]{a} c^2}+\frac{\sqrt[3]{d} (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2}+\frac{(2 b c-3 a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} c^2}+\frac{\sqrt[3]{d} (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2}-\frac{\log (x) (2 b c-3 a d)}{6 \sqrt[3]{a} c^2}-\frac{\left(a+b x^3\right)^{5/3}}{3 a c x^3}","\frac{d \left(a+b x^3\right)^{2/3}}{2 c^2}+\frac{\left(a+b x^3\right)^{2/3} (2 b c-3 a d)}{6 a c^2}-\frac{\sqrt[3]{d} (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^2}+\frac{(2 b c-3 a d) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 \sqrt[3]{a} c^2}+\frac{\sqrt[3]{d} (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2}+\frac{(2 b c-3 a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} \sqrt[3]{a} c^2}+\frac{\sqrt[3]{d} (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2}-\frac{\log (x) (2 b c-3 a d)}{6 \sqrt[3]{a} c^2}-\frac{\left(a+b x^3\right)^{5/3}}{3 a c x^3}",1,"(d*(a + b*x^3)^(2/3))/(2*c^2) + ((2*b*c - 3*a*d)*(a + b*x^3)^(2/3))/(6*a*c^2) - (a + b*x^3)^(5/3)/(3*a*c*x^3) + ((2*b*c - 3*a*d)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(1/3)*c^2) + (d^(1/3)*(b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^2) - ((2*b*c - 3*a*d)*Log[x])/(6*a^(1/3)*c^2) - (d^(1/3)*(b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*c^2) + ((2*b*c - 3*a*d)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(1/3)*c^2) + (d^(1/3)*(b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^2)","A",13,9,24,0.3750,1,"{446, 103, 156, 50, 55, 617, 204, 31, 56}"
683,1,370,0,0.4963068,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^7 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^7*(c + d*x^3)),x]","-\frac{\left(-9 a^2 d^2+6 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{4/3} c^3}-\frac{\left(-9 a^2 d^2+6 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} c^3}+\frac{\log (x) \left(-9 a^2 d^2+6 a b c d+b^2 c^2\right)}{18 a^{4/3} c^3}+\frac{d^{4/3} (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^3}-\frac{d^{4/3} (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^3}-\frac{d^{4/3} (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^3}+\frac{\left(a+b x^3\right)^{2/3} (6 a d+b c)}{18 a c^2 x^3}-\frac{\left(a+b x^3\right)^{5/3}}{6 a c x^6}","-\frac{\left(-9 a^2 d^2+6 a b c d+b^2 c^2\right) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{4/3} c^3}-\frac{\left(-9 a^2 d^2+6 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{4/3} c^3}+\frac{\log (x) \left(-9 a^2 d^2+6 a b c d+b^2 c^2\right)}{18 a^{4/3} c^3}+\frac{d^{4/3} (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^3}-\frac{d^{4/3} (b c-a d)^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^3}-\frac{d^{4/3} (b c-a d)^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^3}+\frac{\left(a+b x^3\right)^{2/3} (6 a d+b c)}{18 a c^2 x^3}-\frac{\left(a+b x^3\right)^{5/3}}{6 a c x^6}",1,"((b*c + 6*a*d)*(a + b*x^3)^(2/3))/(18*a*c^2*x^3) - (a + b*x^3)^(5/3)/(6*a*c*x^6) - ((b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(4/3)*c^3) - (d^(4/3)*(b*c - a*d)^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^3) + ((b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*Log[x])/(18*a^(4/3)*c^3) + (d^(4/3)*(b*c - a*d)^(2/3)*Log[c + d*x^3])/(6*c^3) - ((b^2*c^2 + 6*a*b*c*d - 9*a^2*d^2)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(18*a^(4/3)*c^3) - (d^(4/3)*(b*c - a*d)^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^3)","A",12,9,24,0.3750,1,"{446, 103, 149, 156, 55, 617, 204, 31, 56}"
684,1,64,0,0.0558136,"\int \frac{x^6 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^6*(a + b*x^3)^(2/3))/(c + d*x^3),x]","\frac{x^7 \left(a+b x^3\right)^{2/3} F_1\left(\frac{7}{3};-\frac{2}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{\left(-a^2 d^2-6 a b c d+9 b^2 c^2\right) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{18 b^{4/3} d^3}+\frac{\left(-a^2 d^2-6 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{4/3} d^3}-\frac{c^{4/3} (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^3}+\frac{c^{4/3} (b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^3}-\frac{c^{4/3} (b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^3}-\frac{x \left(a+b x^3\right)^{2/3} (3 b c-a d)}{9 b d^2}+\frac{x^4 \left(a+b x^3\right)^{2/3}}{6 d}",1,"(x^7*(a + b*x^3)^(2/3)*AppellF1[7/3, -2/3, 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)])/(7*c*(1 + (b*x^3)/a)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
685,1,64,0,0.0591927,"\int \frac{x^3 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^3*(a + b*x^3)^(2/3))/(c + d*x^3),x]","\frac{x^4 \left(a+b x^3\right)^{2/3} F_1\left(\frac{4}{3};-\frac{2}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{\sqrt[3]{c} (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 d^2}-\frac{\sqrt[3]{c} (b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^2}+\frac{(3 b c-2 a d) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 \sqrt[3]{b} d^2}-\frac{(3 b c-2 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} \sqrt[3]{b} d^2}+\frac{\sqrt[3]{c} (b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2}+\frac{x \left(a+b x^3\right)^{2/3}}{3 d}",1,"(x^4*(a + b*x^3)^(2/3)*AppellF1[4/3, -2/3, 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*c*(1 + (b*x^3)/a)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
686,1,59,0,0.0273266,"\int \frac{\left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(2/3)/(c + d*x^3),x]","\frac{x \left(a+b x^3\right)^{2/3} F_1\left(\frac{1}{3};-\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{b^{2/3} \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 d}+\frac{b^{2/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d}-\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^{2/3} d}+\frac{(b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} d}-\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} d}",1,"(x*(a + b*x^3)^(2/3)*AppellF1[1/3, -2/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(2/3))","C",2,2,21,0.09524,0,"{430, 429}"
687,1,89,0,0.0627971,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^3 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^3*(c + d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} \left(\frac{d x^3}{c}+1\right)^{2/3} \, _2F_1\left(-\frac{2}{3},-\frac{2}{3};\frac{1}{3};-\frac{c \left(\frac{b x^3}{a}-\frac{d x^3}{c}\right)}{d x^3+c}\right)}{2 c x^2 \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{(b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^{5/3}}-\frac{(b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{5/3}}+\frac{(b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{5/3}}-\frac{\left(a+b x^3\right)^{2/3}}{2 c x^2}",1,"-((a + b*x^3)^(2/3)*(1 + (d*x^3)/c)^(2/3)*Hypergeometric2F1[-2/3, -2/3, 1/3, -((c*((b*x^3)/a - (d*x^3)/c))/(c + d*x^3))])/(2*c*x^2*(1 + (b*x^3)/a)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
688,1,148,0,0.134778,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^6 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^6*(c + d*x^3)),x]","-\frac{-2 x^3 \left(2 c-3 d x^3\right) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+6 x^3 \left(c+d x^3\right) (b c-a d) \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+c \left(a+b x^3\right) \left(2 c-3 d x^3\right)}{10 c^3 x^5 \sqrt[3]{a+b x^3}}","-\frac{\left(a+b x^3\right)^{2/3} (2 b c-5 a d)}{10 a c^2 x^2}-\frac{d (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^{8/3}}+\frac{d (b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{8/3}}-\frac{d (b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{8/3}}-\frac{\left(a+b x^3\right)^{2/3}}{5 c x^5}",1,"-(c*(a + b*x^3)*(2*c - 3*d*x^3) - 2*(b*c - a*d)*x^3*(2*c - 3*d*x^3)*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 6*(b*c - a*d)*x^3*(c + d*x^3)*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(10*c^3*x^5*(a + b*x^3)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
689,1,451,0,0.9709831,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^9 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^9*(c + d*x^3)),x]","-\frac{-9 x^3 \left(c+d x^3\right)^2 (b c-a d) \, _3F_2\left(\frac{1}{3},2,2;1,\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-2 x^3 \left(5 c^2-6 c d x^3+9 d^2 x^6\right) (b c-a d) \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-6 b c^2 d x^6 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+21 b c^3 x^3 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-21 a c^2 d x^3 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+27 a d^3 x^9 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-27 b c d^2 x^9 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+6 a c d^2 x^6 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-6 a c^2 d x^3+5 a c^3+9 a c d^2 x^6-6 b c^2 d x^6+5 b c^3 x^3+9 b c d^2 x^9}{40 c^4 x^8 \sqrt[3]{a+b x^3}}","\frac{\left(a+b x^3\right)^{2/3} \left(-20 a^2 d^2+8 a b c d+3 b^2 c^2\right)}{40 a^2 c^3 x^2}+\frac{d^2 (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^{11/3}}-\frac{d^2 (b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{11/3}}+\frac{d^2 (b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{11/3}}-\frac{\left(a+b x^3\right)^{2/3} (b c-4 a d)}{20 a c^2 x^5}-\frac{\left(a+b x^3\right)^{2/3}}{8 c x^8}",1,"-(5*a*c^3 + 5*b*c^3*x^3 - 6*a*c^2*d*x^3 - 6*b*c^2*d*x^6 + 9*a*c*d^2*x^6 + 9*b*c*d^2*x^9 - 2*(b*c - a*d)*x^3*(5*c^2 - 6*c*d*x^3 + 9*d^2*x^6)*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 21*b*c^3*x^3*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 21*a*c^2*d*x^3*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 6*b*c^2*d*x^6*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 6*a*c*d^2*x^6*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 27*b*c*d^2*x^9*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*a*d^3*x^9*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 9*(b*c - a*d)*x^3*(c + d*x^3)^2*HypergeometricPFQ[{1/3, 2, 2}, {1, 4/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(40*c^4*x^8*(a + b*x^3)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
690,1,819,0,2.6255301,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^{12} \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^12*(c + d*x^3)),x]","-\frac{-81 b c d^3 x^{12}-162 a d^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+162 b c d^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-297 a d^4 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+297 b c d^3 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-81 a c d^3 x^9+54 b c^2 d^2 x^9+108 a c d^3 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-108 b c^2 d^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+54 a c^2 d^2 x^6-45 b c^3 d x^6-90 a c^2 d^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+90 b c^3 d \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+99 a c^2 d^2 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-99 b c^3 d \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+40 b c^4 x^3-45 a c^3 d x^3-80 b c^4 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+80 a c^3 d \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+198 b c^4 \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-198 a c^3 d \, _2F_1\left(\frac{1}{3},2;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-27 (b c-a d) \left(5 c-6 d x^3\right) \left(d x^3+c\right)^2 \, _3F_2\left(\frac{1}{3},2,2;1,\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+27 (b c-a d) \left(d x^3+c\right)^3 \, _4F_3\left(\frac{1}{3},2,2,2;1,1,\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+40 a c^4}{440 c^5 x^{11} \sqrt[3]{b x^3+a}}","-\frac{\left(a+b x^3\right)^{2/3} \left(88 a^2 b c d^2-220 a^3 d^3+33 a b^2 c^2 d+18 b^3 c^3\right)}{440 a^3 c^4 x^2}+\frac{\left(a+b x^3\right)^{2/3} \left(-44 a^2 d^2+11 a b c d+6 b^2 c^2\right)}{220 a^2 c^3 x^5}-\frac{d^3 (b c-a d)^{2/3} \log \left(c+d x^3\right)}{6 c^{14/3}}+\frac{d^3 (b c-a d)^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{14/3}}-\frac{d^3 (b c-a d)^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{14/3}}-\frac{\left(a+b x^3\right)^{2/3} (2 b c-11 a d)}{88 a c^2 x^8}-\frac{\left(a+b x^3\right)^{2/3}}{11 c x^{11}}",1,"-(40*a*c^4 + 40*b*c^4*x^3 - 45*a*c^3*d*x^3 - 45*b*c^3*d*x^6 + 54*a*c^2*d^2*x^6 + 54*b*c^2*d^2*x^9 - 81*a*c*d^3*x^9 - 81*b*c*d^3*x^12 - 80*b*c^4*x^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 80*a*c^3*d*x^3*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 90*b*c^3*d*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 90*a*c^2*d^2*x^6*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 108*b*c^2*d^2*x^9*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 108*a*c*d^3*x^9*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*b*c*d^3*x^12*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 162*a*d^4*x^12*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 198*b*c^4*x^3*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 198*a*c^3*d*x^3*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 99*b*c^3*d*x^6*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 99*a*c^2*d^2*x^6*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 297*b*c*d^3*x^12*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 297*a*d^4*x^12*Hypergeometric2F1[1/3, 2, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 27*(b*c - a*d)*x^3*(5*c - 6*d*x^3)*(c + d*x^3)^2*HypergeometricPFQ[{1/3, 2, 2}, {1, 4/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*(b*c - a*d)*x^3*(c + d*x^3)^3*HypergeometricPFQ[{1/3, 2, 2, 2}, {1, 1, 4/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(440*c^5*x^11*(a + b*x^3)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
691,1,64,0,0.0579732,"\int \frac{x^7 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^7*(a + b*x^3)^(2/3))/(c + d*x^3),x]","\frac{x^8 \left(a+b x^3\right)^{2/3} F_1\left(\frac{8}{3};-\frac{2}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 c \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{x^8 \left(a+b x^3\right)^{2/3} F_1\left(\frac{8}{3};-\frac{2}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 c \left(\frac{b x^3}{a}+1\right)^{2/3}}",1,"(x^8*(a + b*x^3)^(2/3)*AppellF1[8/3, -2/3, 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)])/(8*c*(1 + (b*x^3)/a)^(2/3))","A",2,2,24,0.08333,1,"{511, 510}"
692,1,64,0,0.0561503,"\int \frac{x^4 \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x^4*(a + b*x^3)^(2/3))/(c + d*x^3),x]","\frac{x^5 \left(a+b x^3\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{x^5 \left(a+b x^3\right)^{2/3} F_1\left(\frac{5}{3};-\frac{2}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c \left(\frac{b x^3}{a}+1\right)^{2/3}}",1,"(x^5*(a + b*x^3)^(2/3)*AppellF1[5/3, -2/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*c*(1 + (b*x^3)/a)^(2/3))","A",2,2,24,0.08333,1,"{511, 510}"
693,1,64,0,0.0398454,"\int \frac{x \left(a+b x^3\right)^{2/3}}{c+d x^3} \, dx","Int[(x*(a + b*x^3)^(2/3))/(c + d*x^3),x]","\frac{x^2 \left(a+b x^3\right)^{2/3} F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c \left(\frac{b x^3}{a}+1\right)^{2/3}}","\frac{x^2 \left(a+b x^3\right)^{2/3} F_1\left(\frac{2}{3};-\frac{2}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c \left(\frac{b x^3}{a}+1\right)^{2/3}}",1,"(x^2*(a + b*x^3)^(2/3)*AppellF1[2/3, -2/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*(1 + (b*x^3)/a)^(2/3))","A",2,2,22,0.09091,1,"{511, 510}"
694,1,62,0,0.0601531,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^2 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^2*(c + d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} F_1\left(-\frac{1}{3};-\frac{2}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c x \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{\left(a+b x^3\right)^{2/3} F_1\left(-\frac{1}{3};-\frac{2}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c x \left(\frac{b x^3}{a}+1\right)^{2/3}}",1,"-(((a + b*x^3)^(2/3)*AppellF1[-1/3, -2/3, 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*x*(1 + (b*x^3)/a)^(2/3)))","A",2,2,24,0.08333,1,"{511, 510}"
695,1,64,0,0.0605682,"\int \frac{\left(a+b x^3\right)^{2/3}}{x^5 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(2/3)/(x^5*(c + d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} F_1\left(-\frac{4}{3};-\frac{2}{3},1;-\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c x^4 \left(\frac{b x^3}{a}+1\right)^{2/3}}","-\frac{\left(a+b x^3\right)^{2/3} F_1\left(-\frac{4}{3};-\frac{2}{3},1;-\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c x^4 \left(\frac{b x^3}{a}+1\right)^{2/3}}",1,"-((a + b*x^3)^(2/3)*AppellF1[-4/3, -2/3, 1, -1/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*c*x^4*(1 + (b*x^3)/a)^(2/3))","A",2,2,24,0.08333,1,"{511, 510}"
696,1,251,0,0.3626665,"\int \frac{x^8 \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x^8*(a + b*x^3)^(4/3))/(c + d*x^3),x]","-\frac{\left(a+b x^3\right)^{7/3} (a d+b c)}{7 b^2 d^2}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^2 d}+\frac{c^2 \left(a+b x^3\right)^{4/3}}{4 d^3}-\frac{c^2 \sqrt[3]{a+b x^3} (b c-a d)}{d^4}-\frac{c^2 (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^{13/3}}+\frac{c^2 (b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{13/3}}-\frac{c^2 (b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{13/3}}","-\frac{\left(a+b x^3\right)^{7/3} (a d+b c)}{7 b^2 d^2}+\frac{\left(a+b x^3\right)^{10/3}}{10 b^2 d}+\frac{c^2 \left(a+b x^3\right)^{4/3}}{4 d^3}-\frac{c^2 \sqrt[3]{a+b x^3} (b c-a d)}{d^4}-\frac{c^2 (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^{13/3}}+\frac{c^2 (b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{13/3}}-\frac{c^2 (b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{13/3}}",1,"-((c^2*(b*c - a*d)*(a + b*x^3)^(1/3))/d^4) + (c^2*(a + b*x^3)^(4/3))/(4*d^3) - ((b*c + a*d)*(a + b*x^3)^(7/3))/(7*b^2*d^2) + (a + b*x^3)^(10/3)/(10*b^2*d) - (c^2*(b*c - a*d)^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(13/3)) - (c^2*(b*c - a*d)^(4/3)*Log[c + d*x^3])/(6*d^(13/3)) + (c^2*(b*c - a*d)^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(13/3))","A",9,7,24,0.2917,1,"{446, 88, 50, 58, 617, 204, 31}"
697,1,211,0,0.2449957,"\int \frac{x^5 \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x^5*(a + b*x^3)^(4/3))/(c + d*x^3),x]","-\frac{c \left(a+b x^3\right)^{4/3}}{4 d^2}+\frac{c \sqrt[3]{a+b x^3} (b c-a d)}{d^3}+\frac{c (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^{10/3}}-\frac{c (b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{10/3}}+\frac{c (b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{10/3}}+\frac{\left(a+b x^3\right)^{7/3}}{7 b d}","-\frac{c \left(a+b x^3\right)^{4/3}}{4 d^2}+\frac{c \sqrt[3]{a+b x^3} (b c-a d)}{d^3}+\frac{c (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^{10/3}}-\frac{c (b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{10/3}}+\frac{c (b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{10/3}}+\frac{\left(a+b x^3\right)^{7/3}}{7 b d}",1,"(c*(b*c - a*d)*(a + b*x^3)^(1/3))/d^3 - (c*(a + b*x^3)^(4/3))/(4*d^2) + (a + b*x^3)^(7/3)/(7*b*d) + (c*(b*c - a*d)^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(10/3)) + (c*(b*c - a*d)^(4/3)*Log[c + d*x^3])/(6*d^(10/3)) - (c*(b*c - a*d)^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(10/3))","A",8,7,24,0.2917,1,"{446, 80, 50, 58, 617, 204, 31}"
698,1,187,0,0.2077139,"\int \frac{x^2 \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x^2*(a + b*x^3)^(4/3))/(c + d*x^3),x]","-\frac{\sqrt[3]{a+b x^3} (b c-a d)}{d^2}-\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^{7/3}}+\frac{(b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{7/3}}-\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}+\frac{\left(a+b x^3\right)^{4/3}}{4 d}","-\frac{\sqrt[3]{a+b x^3} (b c-a d)}{d^2}-\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^{7/3}}+\frac{(b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{7/3}}-\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3}}+\frac{\left(a+b x^3\right)^{4/3}}{4 d}",1,"-(((b*c - a*d)*(a + b*x^3)^(1/3))/d^2) + (a + b*x^3)^(4/3)/(4*d) - ((b*c - a*d)^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(7/3)) - ((b*c - a*d)^(4/3)*Log[c + d*x^3])/(6*d^(7/3)) + ((b*c - a*d)^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(7/3))","A",7,6,24,0.2500,1,"{444, 50, 58, 617, 204, 31}"
699,1,261,0,0.3043923,"\int \frac{\left(a+b x^3\right)^{4/3}}{x \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x*(c + d*x^3)),x]","\frac{a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 c}-\frac{a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} c}-\frac{a^{4/3} \log (x)}{2 c}+\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c d^{4/3}}-\frac{(b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c d^{4/3}}+\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c d^{4/3}}+\frac{b \sqrt[3]{a+b x^3}}{d}","\frac{a^{4/3} \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 c}-\frac{a^{4/3} \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} c}-\frac{a^{4/3} \log (x)}{2 c}+\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c d^{4/3}}-\frac{(b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c d^{4/3}}+\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c d^{4/3}}+\frac{b \sqrt[3]{a+b x^3}}{d}",1,"(b*(a + b*x^3)^(1/3))/d - (a^(4/3)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(Sqrt[3]*c) + ((b*c - a*d)^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*d^(4/3)) - (a^(4/3)*Log[x])/(2*c) + ((b*c - a*d)^(4/3)*Log[c + d*x^3])/(6*c*d^(4/3)) + (a^(4/3)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(2*c) - ((b*c - a*d)^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c*d^(4/3))","A",11,8,24,0.3333,1,"{446, 84, 156, 57, 617, 204, 31, 58}"
700,1,399,0,0.4835204,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^4 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^4*(c + d*x^3)),x]","\frac{d \left(a+b x^3\right)^{4/3}}{4 c^2}+\frac{\left(a+b x^3\right)^{4/3} (4 b c-3 a d)}{12 a c^2}+\frac{\sqrt[3]{a+b x^3} (4 b c-3 a d)}{3 c^2}-\frac{\sqrt[3]{a+b x^3} (b c-a d)}{c^2}-\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^2 \sqrt[3]{d}}+\frac{\sqrt[3]{a} (4 b c-3 a d) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 c^2}+\frac{(b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 \sqrt[3]{d}}-\frac{\sqrt[3]{a} (4 b c-3 a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} c^2}-\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 \sqrt[3]{d}}-\frac{\sqrt[3]{a} \log (x) (4 b c-3 a d)}{6 c^2}-\frac{\left(a+b x^3\right)^{7/3}}{3 a c x^3}","\frac{d \left(a+b x^3\right)^{4/3}}{4 c^2}+\frac{\left(a+b x^3\right)^{4/3} (4 b c-3 a d)}{12 a c^2}+\frac{\sqrt[3]{a+b x^3} (4 b c-3 a d)}{3 c^2}-\frac{\sqrt[3]{a+b x^3} (b c-a d)}{c^2}-\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^2 \sqrt[3]{d}}+\frac{\sqrt[3]{a} (4 b c-3 a d) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 c^2}+\frac{(b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 \sqrt[3]{d}}-\frac{\sqrt[3]{a} (4 b c-3 a d) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} c^2}-\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 \sqrt[3]{d}}-\frac{\sqrt[3]{a} \log (x) (4 b c-3 a d)}{6 c^2}-\frac{\left(a+b x^3\right)^{7/3}}{3 a c x^3}",1,"((4*b*c - 3*a*d)*(a + b*x^3)^(1/3))/(3*c^2) - ((b*c - a*d)*(a + b*x^3)^(1/3))/c^2 + (d*(a + b*x^3)^(4/3))/(4*c^2) + ((4*b*c - 3*a*d)*(a + b*x^3)^(4/3))/(12*a*c^2) - (a + b*x^3)^(7/3)/(3*a*c*x^3) - (a^(1/3)*(4*b*c - 3*a*d)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*c^2) - ((b*c - a*d)^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^2*d^(1/3)) - (a^(1/3)*(4*b*c - 3*a*d)*Log[x])/(6*c^2) - ((b*c - a*d)^(4/3)*Log[c + d*x^3])/(6*c^2*d^(1/3)) + (a^(1/3)*(4*b*c - 3*a*d)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*c^2) + ((b*c - a*d)^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^2*d^(1/3))","A",15,9,24,0.3750,1,"{446, 103, 156, 50, 57, 617, 204, 31, 58}"
701,1,440,0,0.6228636,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^7 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^7*(c + d*x^3)),x]","\frac{\sqrt[3]{a+b x^3} \left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right)}{9 a c^3}+\frac{\left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{2/3} c^3}-\frac{\left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{2/3} c^3}-\frac{\log (x) \left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right)}{18 a^{2/3} c^3}+\frac{d^{2/3} (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^3}-\frac{d^{2/3} (b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^3}+\frac{d^{2/3} (b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^3}-\frac{\left(a+b x^3\right)^{4/3} (b c-6 a d)}{18 a c^2 x^3}+\frac{d \sqrt[3]{a+b x^3} (b c-a d)}{c^3}-\frac{\left(a+b x^3\right)^{7/3}}{6 a c x^6}","\frac{\sqrt[3]{a+b x^3} \left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right)}{9 a c^3}+\frac{\left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{18 a^{2/3} c^3}-\frac{\left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{9 \sqrt{3} a^{2/3} c^3}-\frac{\log (x) \left(9 a^2 d^2-12 a b c d+2 b^2 c^2\right)}{18 a^{2/3} c^3}+\frac{d^{2/3} (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^3}-\frac{d^{2/3} (b c-a d)^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^3}+\frac{d^{2/3} (b c-a d)^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^3}-\frac{\left(a+b x^3\right)^{4/3} (b c-6 a d)}{18 a c^2 x^3}+\frac{d \sqrt[3]{a+b x^3} (b c-a d)}{c^3}-\frac{\left(a+b x^3\right)^{7/3}}{6 a c x^6}",1,"(d*(b*c - a*d)*(a + b*x^3)^(1/3))/c^3 + ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*(a + b*x^3)^(1/3))/(9*a*c^3) - ((b*c - 6*a*d)*(a + b*x^3)^(4/3))/(18*a*c^2*x^3) - (a + b*x^3)^(7/3)/(6*a*c*x^6) - ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(9*Sqrt[3]*a^(2/3)*c^3) + (d^(2/3)*(b*c - a*d)^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^3) - ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*Log[x])/(18*a^(2/3)*c^3) + (d^(2/3)*(b*c - a*d)^(4/3)*Log[c + d*x^3])/(6*c^3) + ((2*b^2*c^2 - 12*a*b*c*d + 9*a^2*d^2)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(18*a^(2/3)*c^3) - (d^(2/3)*(b*c - a*d)^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^3)","A",14,10,24,0.4167,1,"{446, 103, 149, 156, 50, 57, 617, 204, 31, 58}"
702,1,65,0,0.0590289,"\int \frac{x^4 \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x^4*(a + b*x^3)^(4/3))/(c + d*x^3),x]","\frac{a x^5 \sqrt[3]{a+b x^3} F_1\left(\frac{5}{3};-\frac{4}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\left(2 a^2 d^2-12 a b c d+9 b^2 c^2\right) \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{18 b^{2/3} d^3}-\frac{\left(2 a^2 d^2-12 a b c d+9 b^2 c^2\right) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{9 \sqrt{3} b^{2/3} d^3}-\frac{c^{2/3} (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 d^3}+\frac{c^{2/3} (b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^3}+\frac{c^{2/3} (b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^3}-\frac{x^2 \sqrt[3]{a+b x^3} (6 b c-7 a d)}{18 d^2}+\frac{b x^5 \sqrt[3]{a+b x^3}}{6 d}",1,"(a*x^5*(a + b*x^3)^(1/3)*AppellF1[5/3, -4/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*c*(1 + (b*x^3)/a)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
703,1,65,0,0.0439897,"\int \frac{x \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x*(a + b*x^3)^(4/3))/(c + d*x^3),x]","\frac{a x^2 \sqrt[3]{a+b x^3} F_1\left(\frac{2}{3};-\frac{4}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 \sqrt[3]{c} d^2}+\frac{\sqrt[3]{b} (3 b c-4 a d) \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{6 d^2}-\frac{(b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{c} d^2}+\frac{\sqrt[3]{b} (3 b c-4 a d) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} d^2}-\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{c} d^2}+\frac{b x^2 \sqrt[3]{a+b x^3}}{3 d}",1,"(a*x^2*(a + b*x^3)^(1/3)*AppellF1[2/3, -4/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*(1 + (b*x^3)/a)^(1/3))","C",2,2,22,0.09091,0,"{511, 510}"
704,1,63,0,0.0590058,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^2 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^2*(c + d*x^3)),x]","-\frac{a \sqrt[3]{a+b x^3} F_1\left(-\frac{1}{3};-\frac{4}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c x \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{b^{4/3} \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 d}-\frac{b^{4/3} \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d}-\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^{4/3} d}+\frac{(b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{4/3} d}+\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{4/3} d}-\frac{a \sqrt[3]{a+b x^3}}{c x}",1,"-((a*(a + b*x^3)^(1/3)*AppellF1[-1/3, -4/3, 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*x*(1 + (b*x^3)/a)^(1/3)))","C",2,2,24,0.08333,0,"{511, 510}"
705,1,90,0,0.0635623,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^5 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^5*(c + d*x^3)),x]","-\frac{a \sqrt[3]{a+b x^3} \left(\frac{d x^3}{c}+1\right)^{4/3} \, _2F_1\left(-\frac{4}{3},-\frac{4}{3};-\frac{1}{3};-\frac{c \left(\frac{b x^3}{a}-\frac{d x^3}{c}\right)}{d x^3+c}\right)}{4 c x^4 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{\sqrt[3]{a+b x^3} (5 b c-4 a d)}{4 c^2 x}+\frac{(b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^{7/3}}-\frac{(b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{7/3}}-\frac{(b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{7/3}}-\frac{a \sqrt[3]{a+b x^3}}{4 c x^4}",1,"-(a*(a + b*x^3)^(1/3)*(1 + (d*x^3)/c)^(4/3)*Hypergeometric2F1[-4/3, -4/3, -1/3, -((c*((b*x^3)/a - (d*x^3)/c))/(c + d*x^3))])/(4*c*x^4*(1 + (b*x^3)/a)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
706,1,169,0,0.5065862,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^8 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^8*(c + d*x^3)),x]","\frac{12 c x^3 \left(a+b x^3\right) \left(c+d x^3\right) (b c-a d) \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-\left(4 c-3 d x^3\right) \left(c \left(a+b x^3\right) \left(a \left(c-4 d x^3\right)+5 b c x^3\right)-2 x^6 (b c-a d)^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)\right)}{28 c^4 x^7 \left(a+b x^3\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} \left(28 a^2 d^2-35 a b c d+4 b^2 c^2\right)}{28 a c^3 x}-\frac{\sqrt[3]{a+b x^3} (8 b c-7 a d)}{28 c^2 x^4}-\frac{d (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^{10/3}}+\frac{d (b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{10/3}}+\frac{d (b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{10/3}}-\frac{a \sqrt[3]{a+b x^3}}{7 c x^7}",1,"(12*c*(b*c - a*d)*x^3*(a + b*x^3)*(c + d*x^3)*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - (4*c - 3*d*x^3)*(c*(a + b*x^3)*(5*b*c*x^3 + a*(c - 4*d*x^3)) - 2*(b*c - a*d)^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]))/(28*c^4*x^7*(a + b*x^3)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
707,1,260,0,1.8011436,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^{11} \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^11*(c + d*x^3)),x]","\frac{-18 c x^3 \left(a+b x^3\right) \left(c+d x^3\right)^2 (b c-a d) \, _3F_2\left(-\frac{1}{3},2,2;\frac{2}{3},1;\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+6 c x^3 \left(a+b x^3\right) \left(11 c^2+2 c d x^3-9 d^2 x^6\right) (b c-a d) \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-\left(14 c^2-12 c d x^3+9 d^2 x^6\right) \left(c \left(a+b x^3\right) \left(a \left(c-4 d x^3\right)+5 b c x^3\right)-2 x^6 (b c-a d)^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)\right)}{140 c^5 x^{10} \left(a+b x^3\right)^{2/3}}","\frac{\sqrt[3]{a+b x^3} \left(-175 a^2 b c d^2+140 a^3 d^3+20 a b^2 c^2 d+6 b^3 c^3\right)}{140 a^2 c^4 x}-\frac{\sqrt[3]{a+b x^3} \left(35 a^2 d^2-40 a b c d+2 b^2 c^2\right)}{140 a c^3 x^4}+\frac{d^2 (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^{13/3}}-\frac{d^2 (b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{13/3}}-\frac{d^2 (b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{13/3}}-\frac{\sqrt[3]{a+b x^3} (11 b c-10 a d)}{70 c^2 x^7}-\frac{a \sqrt[3]{a+b x^3}}{10 c x^{10}}",1,"(6*c*(b*c - a*d)*x^3*(a + b*x^3)*(11*c^2 + 2*c*d*x^3 - 9*d^2*x^6)*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - (14*c^2 - 12*c*d*x^3 + 9*d^2*x^6)*(c*(a + b*x^3)*(5*b*c*x^3 + a*(c - 4*d*x^3)) - 2*(b*c - a*d)^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))]) - 18*c*(b*c - a*d)*x^3*(a + b*x^3)*(c + d*x^3)^2*HypergeometricPFQ[{-1/3, 2, 2}, {2/3, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(140*c^5*x^10*(a + b*x^3)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
708,1,1446,0,4.3905679,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^{14} \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^14*(c + d*x^3)),x]","-\frac{324 a b c d^4 x^{15}-405 b^2 c^2 d^3 x^{15}+594 a b c d^4 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-594 b^2 c^2 d^3 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+162 a^2 d^5 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-324 a b c d^4 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+162 b^2 c^2 d^3 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+324 a^2 c d^4 x^{12}-918 a b c^2 d^3 x^{12}+540 b^2 c^3 d^2 x^{12}+594 a^2 c d^4 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-918 a b c^2 d^3 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+324 b^2 c^3 d^2 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-216 a^2 c d^4 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+432 a b c^2 d^3 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-216 b^2 c^3 d^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-513 a^2 c^2 d^3 x^9+1152 a b c^3 d^2 x^9-630 b^2 c^4 d x^9-324 a^2 c^2 d^3 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+234 a b c^3 d^2 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+90 b^2 c^4 d \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+252 a^2 c^2 d^3 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-504 a b c^3 d^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+252 b^2 c^4 d \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+700 b^2 c^5 x^6+612 a^2 c^3 d^2 x^6-1316 a b c^4 d x^6-828 b^2 c^5 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-90 a^2 c^3 d^2 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+918 a b c^4 d \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-280 b^2 c^5 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-280 a^2 c^3 d^2 \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+560 a b c^4 d \, _2F_1\left(\frac{2}{3},1;\frac{5}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+840 a b c^5 x^3-686 a^2 c^4 d x^3-828 a b c^5 \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+828 a^2 c^4 d \, _2F_1\left(-\frac{1}{3},2;\frac{2}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+54 c (b c-a d) \left(b x^3+a\right) \left(7 c-6 d x^3\right) \left(d x^3+c\right)^2 \, _3F_2\left(-\frac{1}{3},2,2;\frac{2}{3},1;\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3-54 c (b c-a d) \left(b x^3+a\right) \left(d x^3+c\right)^3 \, _4F_3\left(-\frac{1}{3},2,2,2;\frac{2}{3},1,1;\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+140 a^2 c^5}{1820 c^6 x^{13} \left(b x^3+a\right)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} \left(260 a^2 b^2 c^2 d^2-2275 a^3 b c d^3+1820 a^4 d^4+78 a b^3 c^3 d+36 b^4 c^4\right)}{1820 a^3 c^5 x}+\frac{\sqrt[3]{a+b x^3} \left(-520 a^2 b c d^2+455 a^3 d^3+26 a b^2 c^2 d+12 b^3 c^3\right)}{1820 a^2 c^4 x^4}-\frac{\sqrt[3]{a+b x^3} \left(130 a^2 d^2-143 a b c d+4 b^2 c^2\right)}{910 a c^3 x^7}-\frac{d^3 (b c-a d)^{4/3} \log \left(c+d x^3\right)}{6 c^{16/3}}+\frac{d^3 (b c-a d)^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{16/3}}+\frac{d^3 (b c-a d)^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{16/3}}-\frac{\sqrt[3]{a+b x^3} (14 b c-13 a d)}{130 c^2 x^{10}}-\frac{a \sqrt[3]{a+b x^3}}{13 c x^{13}}",1,"-(140*a^2*c^5 + 840*a*b*c^5*x^3 - 686*a^2*c^4*d*x^3 + 700*b^2*c^5*x^6 - 1316*a*b*c^4*d*x^6 + 612*a^2*c^3*d^2*x^6 - 630*b^2*c^4*d*x^9 + 1152*a*b*c^3*d^2*x^9 - 513*a^2*c^2*d^3*x^9 + 540*b^2*c^3*d^2*x^12 - 918*a*b*c^2*d^3*x^12 + 324*a^2*c*d^4*x^12 - 405*b^2*c^2*d^3*x^15 + 324*a*b*c*d^4*x^15 - 828*a*b*c^5*x^3*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 828*a^2*c^4*d*x^3*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 828*b^2*c^5*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 918*a*b*c^4*d*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 90*a^2*c^3*d^2*x^6*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 90*b^2*c^4*d*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 234*a*b*c^3*d^2*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324*a^2*c^2*d^3*x^9*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 324*b^2*c^3*d^2*x^12*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 918*a*b*c^2*d^3*x^12*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 594*a^2*c*d^4*x^12*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 594*b^2*c^2*d^3*x^15*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 594*a*b*c*d^4*x^15*Hypergeometric2F1[-1/3, 2, 2/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 280*b^2*c^5*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 560*a*b*c^4*d*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 280*a^2*c^3*d^2*x^6*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 252*b^2*c^4*d*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 504*a*b*c^3*d^2*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 252*a^2*c^2*d^3*x^9*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 216*b^2*c^3*d^2*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 432*a*b*c^2*d^3*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 216*a^2*c*d^4*x^12*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*b^2*c^2*d^3*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324*a*b*c*d^4*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*a^2*d^5*x^15*Hypergeometric2F1[2/3, 1, 5/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*c*(b*c - a*d)*x^3*(a + b*x^3)*(7*c - 6*d*x^3)*(c + d*x^3)^2*HypergeometricPFQ[{-1/3, 2, 2}, {2/3, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 54*c*(b*c - a*d)*x^3*(a + b*x^3)*(c + d*x^3)^3*HypergeometricPFQ[{-1/3, 2, 2, 2}, {2/3, 1, 1}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(1820*c^6*x^13*(a + b*x^3)^(2/3))","C",2,2,24,0.08333,0,"{511, 510}"
709,1,65,0,0.0559373,"\int \frac{x^6 \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x^6*(a + b*x^3)^(4/3))/(c + d*x^3),x]","\frac{a x^7 \sqrt[3]{a+b x^3} F_1\left(\frac{7}{3};-\frac{4}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a x^7 \sqrt[3]{a+b x^3} F_1\left(\frac{7}{3};-\frac{4}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*x^7*(a + b*x^3)^(1/3)*AppellF1[7/3, -4/3, 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)])/(7*c*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
710,1,65,0,0.0560588,"\int \frac{x^3 \left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(x^3*(a + b*x^3)^(4/3))/(c + d*x^3),x]","\frac{a x^4 \sqrt[3]{a+b x^3} F_1\left(\frac{4}{3};-\frac{4}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a x^4 \sqrt[3]{a+b x^3} F_1\left(\frac{4}{3};-\frac{4}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*x^4*(a + b*x^3)^(1/3)*AppellF1[4/3, -4/3, 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*c*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
711,1,60,0,0.0273729,"\int \frac{\left(a+b x^3\right)^{4/3}}{c+d x^3} \, dx","Int[(a + b*x^3)^(4/3)/(c + d*x^3),x]","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}","\frac{a x \sqrt[3]{a+b x^3} F_1\left(\frac{1}{3};-\frac{4}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \sqrt[3]{\frac{b x^3}{a}+1}}",1,"(a*x*(a + b*x^3)^(1/3)*AppellF1[1/3, -4/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(1 + (b*x^3)/a)^(1/3))","A",2,2,21,0.09524,1,"{430, 429}"
712,1,65,0,0.0570861,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^3 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^3*(c + d*x^3)),x]","-\frac{a \sqrt[3]{a+b x^3} F_1\left(-\frac{2}{3};-\frac{4}{3},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c x^2 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{a \sqrt[3]{a+b x^3} F_1\left(-\frac{2}{3};-\frac{4}{3},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c x^2 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"-(a*(a + b*x^3)^(1/3)*AppellF1[-2/3, -4/3, 1, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*x^2*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
713,1,65,0,0.0577736,"\int \frac{\left(a+b x^3\right)^{4/3}}{x^6 \left(c+d x^3\right)} \, dx","Int[(a + b*x^3)^(4/3)/(x^6*(c + d*x^3)),x]","-\frac{a \sqrt[3]{a+b x^3} F_1\left(-\frac{5}{3};-\frac{4}{3},1;-\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c x^5 \sqrt[3]{\frac{b x^3}{a}+1}}","-\frac{a \sqrt[3]{a+b x^3} F_1\left(-\frac{5}{3};-\frac{4}{3},1;-\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c x^5 \sqrt[3]{\frac{b x^3}{a}+1}}",1,"-(a*(a + b*x^3)^(1/3)*AppellF1[-5/3, -4/3, 1, -2/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*c*x^5*(1 + (b*x^3)/a)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
714,1,290,0,0.3167778,"\int \frac{x^{14}}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^14/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{\left(a+b x^3\right)^{5/3} \left(3 a^2 d^2+2 a b c d+b^2 c^2\right)}{5 b^4 d^3}-\frac{\left(a+b x^3\right)^{2/3} (a d+b c) \left(a^2 d^2+b^2 c^2\right)}{2 b^4 d^4}-\frac{\left(a+b x^3\right)^{8/3} (3 a d+b c)}{8 b^4 d^2}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^4 d}+\frac{c^4 \log \left(c+d x^3\right)}{6 d^{14/3} \sqrt[3]{b c-a d}}-\frac{c^4 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{14/3} \sqrt[3]{b c-a d}}-\frac{c^4 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{14/3} \sqrt[3]{b c-a d}}","\frac{\left(a+b x^3\right)^{5/3} \left(3 a^2 d^2+2 a b c d+b^2 c^2\right)}{5 b^4 d^3}-\frac{\left(a+b x^3\right)^{2/3} (a d+b c) \left(a^2 d^2+b^2 c^2\right)}{2 b^4 d^4}-\frac{\left(a+b x^3\right)^{8/3} (3 a d+b c)}{8 b^4 d^2}+\frac{\left(a+b x^3\right)^{11/3}}{11 b^4 d}+\frac{c^4 \log \left(c+d x^3\right)}{6 d^{14/3} \sqrt[3]{b c-a d}}-\frac{c^4 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{14/3} \sqrt[3]{b c-a d}}-\frac{c^4 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{14/3} \sqrt[3]{b c-a d}}",1,"-((b*c + a*d)*(b^2*c^2 + a^2*d^2)*(a + b*x^3)^(2/3))/(2*b^4*d^4) + ((b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*(a + b*x^3)^(5/3))/(5*b^4*d^3) - ((b*c + 3*a*d)*(a + b*x^3)^(8/3))/(8*b^4*d^2) + (a + b*x^3)^(11/3)/(11*b^4*d) - (c^4*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(14/3)*(b*c - a*d)^(1/3)) + (c^4*Log[c + d*x^3])/(6*d^(14/3)*(b*c - a*d)^(1/3)) - (c^4*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(14/3)*(b*c - a*d)^(1/3))","A",7,6,24,0.2500,1,"{446, 88, 56, 617, 204, 31}"
715,1,244,0,0.2434044,"\int \frac{x^{11}}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^11/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{\left(a+b x^3\right)^{2/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{2 b^3 d^3}-\frac{\left(a+b x^3\right)^{5/3} (2 a d+b c)}{5 b^3 d^2}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^3 d}-\frac{c^3 \log \left(c+d x^3\right)}{6 d^{11/3} \sqrt[3]{b c-a d}}+\frac{c^3 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{11/3} \sqrt[3]{b c-a d}}+\frac{c^3 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{11/3} \sqrt[3]{b c-a d}}","\frac{\left(a+b x^3\right)^{2/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{2 b^3 d^3}-\frac{\left(a+b x^3\right)^{5/3} (2 a d+b c)}{5 b^3 d^2}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^3 d}-\frac{c^3 \log \left(c+d x^3\right)}{6 d^{11/3} \sqrt[3]{b c-a d}}+\frac{c^3 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{11/3} \sqrt[3]{b c-a d}}+\frac{c^3 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{11/3} \sqrt[3]{b c-a d}}",1,"((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(2/3))/(2*b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(5/3))/(5*b^3*d^2) + (a + b*x^3)^(8/3)/(8*b^3*d) + (c^3*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(11/3)*(b*c - a*d)^(1/3)) - (c^3*Log[c + d*x^3])/(6*d^(11/3)*(b*c - a*d)^(1/3)) + (c^3*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(11/3)*(b*c - a*d)^(1/3))","A",7,6,24,0.2500,1,"{446, 88, 56, 617, 204, 31}"
716,1,203,0,0.2136499,"\int \frac{x^8}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^8/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} (a d+b c)}{2 b^2 d^2}+\frac{\left(a+b x^3\right)^{5/3}}{5 b^2 d}+\frac{c^2 \log \left(c+d x^3\right)}{6 d^{8/3} \sqrt[3]{b c-a d}}-\frac{c^2 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{8/3} \sqrt[3]{b c-a d}}-\frac{c^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{8/3} \sqrt[3]{b c-a d}}","-\frac{\left(a+b x^3\right)^{2/3} (a d+b c)}{2 b^2 d^2}+\frac{\left(a+b x^3\right)^{5/3}}{5 b^2 d}+\frac{c^2 \log \left(c+d x^3\right)}{6 d^{8/3} \sqrt[3]{b c-a d}}-\frac{c^2 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{8/3} \sqrt[3]{b c-a d}}-\frac{c^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{8/3} \sqrt[3]{b c-a d}}",1,"-((b*c + a*d)*(a + b*x^3)^(2/3))/(2*b^2*d^2) + (a + b*x^3)^(5/3)/(5*b^2*d) - (c^2*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(8/3)*(b*c - a*d)^(1/3)) + (c^2*Log[c + d*x^3])/(6*d^(8/3)*(b*c - a*d)^(1/3)) - (c^2*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(8/3)*(b*c - a*d)^(1/3))","A",7,6,24,0.2500,1,"{446, 88, 56, 617, 204, 31}"
717,1,168,0,0.1612124,"\int \frac{x^5}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^5/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{c \log \left(c+d x^3\right)}{6 d^{5/3} \sqrt[3]{b c-a d}}+\frac{c \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{5/3} \sqrt[3]{b c-a d}}+\frac{c \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{5/3} \sqrt[3]{b c-a d}}+\frac{\left(a+b x^3\right)^{2/3}}{2 b d}","-\frac{c \log \left(c+d x^3\right)}{6 d^{5/3} \sqrt[3]{b c-a d}}+\frac{c \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{5/3} \sqrt[3]{b c-a d}}+\frac{c \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{5/3} \sqrt[3]{b c-a d}}+\frac{\left(a+b x^3\right)^{2/3}}{2 b d}",1,"(a + b*x^3)^(2/3)/(2*b*d) + (c*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(5/3)*(b*c - a*d)^(1/3)) - (c*Log[c + d*x^3])/(6*d^(5/3)*(b*c - a*d)^(1/3)) + (c*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(5/3)*(b*c - a*d)^(1/3))","A",6,6,24,0.2500,1,"{446, 80, 56, 617, 204, 31}"
718,1,145,0,0.1252128,"\int \frac{x^2}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^2/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{\log \left(c+d x^3\right)}{6 d^{2/3} \sqrt[3]{b c-a d}}-\frac{\log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{2/3} \sqrt[3]{b c-a d}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{2/3} \sqrt[3]{b c-a d}}","\frac{\log \left(c+d x^3\right)}{6 d^{2/3} \sqrt[3]{b c-a d}}-\frac{\log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{2/3} \sqrt[3]{b c-a d}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{2/3} \sqrt[3]{b c-a d}}",1,"-(ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]]/(Sqrt[3]*d^(2/3)*(b*c - a*d)^(1/3))) + Log[c + d*x^3]/(6*d^(2/3)*(b*c - a*d)^(1/3)) - Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)]/(2*d^(2/3)*(b*c - a*d)^(1/3))","A",5,5,24,0.2083,1,"{444, 56, 617, 204, 31}"
719,1,244,0,0.2121113,"\int \frac{1}{x \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\sqrt[3]{d} \log \left(c+d x^3\right)}{6 c \sqrt[3]{b c-a d}}+\frac{\sqrt[3]{d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c \sqrt[3]{b c-a d}}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c \sqrt[3]{b c-a d}}+\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a} c}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} c}-\frac{\log (x)}{2 \sqrt[3]{a} c}","-\frac{\sqrt[3]{d} \log \left(c+d x^3\right)}{6 c \sqrt[3]{b c-a d}}+\frac{\sqrt[3]{d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c \sqrt[3]{b c-a d}}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c \sqrt[3]{b c-a d}}+\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{a} c}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} \sqrt[3]{a} c}-\frac{\log (x)}{2 \sqrt[3]{a} c}",1,"ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(1/3)*c) + (d^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*(b*c - a*d)^(1/3)) - Log[x]/(2*a^(1/3)*c) - (d^(1/3)*Log[c + d*x^3])/(6*c*(b*c - a*d)^(1/3)) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(1/3)*c) + (d^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c*(b*c - a*d)^(1/3))","A",10,7,24,0.2917,1,"{446, 86, 55, 617, 204, 31, 56}"
720,1,296,0,0.3141654,"\int \frac{1}{x^4 \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x^4*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{(3 a d+b c) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{4/3} c^2}-\frac{(3 a d+b c) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} c^2}+\frac{\log (x) (3 a d+b c)}{6 a^{4/3} c^2}+\frac{d^{4/3} \log \left(c+d x^3\right)}{6 c^2 \sqrt[3]{b c-a d}}-\frac{d^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 \sqrt[3]{b c-a d}}-\frac{d^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 \sqrt[3]{b c-a d}}-\frac{\left(a+b x^3\right)^{2/3}}{3 a c x^3}","-\frac{(3 a d+b c) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{4/3} c^2}-\frac{(3 a d+b c) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{4/3} c^2}+\frac{\log (x) (3 a d+b c)}{6 a^{4/3} c^2}+\frac{d^{4/3} \log \left(c+d x^3\right)}{6 c^2 \sqrt[3]{b c-a d}}-\frac{d^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 \sqrt[3]{b c-a d}}-\frac{d^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 \sqrt[3]{b c-a d}}-\frac{\left(a+b x^3\right)^{2/3}}{3 a c x^3}",1,"-(a + b*x^3)^(2/3)/(3*a*c*x^3) - ((b*c + 3*a*d)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(4/3)*c^2) - (d^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^2*(b*c - a*d)^(1/3)) + ((b*c + 3*a*d)*Log[x])/(6*a^(4/3)*c^2) + (d^(4/3)*Log[c + d*x^3])/(6*c^2*(b*c - a*d)^(1/3)) - ((b*c + 3*a*d)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(4/3)*c^2) - (d^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^2*(b*c - a*d)^(1/3))","A",11,8,24,0.3333,1,"{446, 103, 156, 55, 617, 204, 31, 56}"
721,1,394,0,0.5090681,"\int \frac{x^6}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^6/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{(a d+3 b c) \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{4/3} d^2}-\frac{(a d+3 b c) \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{18 b^{4/3} d^2}-\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3} d^2}-\frac{c^{4/3} \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 d^2 \sqrt[3]{b c-a d}}+\frac{c^{4/3} \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 d^2 \sqrt[3]{b c-a d}}+\frac{c^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^2 \sqrt[3]{b c-a d}}+\frac{x \left(a+b x^3\right)^{2/3}}{3 b d}","\frac{(a d+3 b c) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{4/3} d^2}-\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{4/3} d^2}+\frac{c^{4/3} \log \left(c+d x^3\right)}{6 d^2 \sqrt[3]{b c-a d}}-\frac{c^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^2 \sqrt[3]{b c-a d}}+\frac{c^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2 \sqrt[3]{b c-a d}}+\frac{x \left(a+b x^3\right)^{2/3}}{3 b d}",1,"(x*(a + b*x^3)^(2/3))/(3*b*d) - ((3*b*c + a*d)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(4/3)*d^2) + (c^(4/3)*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d^2*(b*c - a*d)^(1/3)) + ((3*b*c + a*d)*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(4/3)*d^2) - ((3*b*c + a*d)*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(18*b^(4/3)*d^2) - (c^(4/3)*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*d^2*(b*c - a*d)^(1/3)) + (c^(4/3)*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*d^2*(b*c - a*d)^(1/3))","A",15,9,24,0.3750,1,"{494, 470, 522, 200, 31, 634, 617, 204, 628}"
722,1,346,0,0.2912946,"\int \frac{x^3}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^3/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{\log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{6 \sqrt[3]{b} d}-\frac{\sqrt[3]{c} \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 d \sqrt[3]{b c-a d}}+\frac{\sqrt[3]{c} \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 d \sqrt[3]{b c-a d}}-\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d \sqrt[3]{b c-a d}}-\frac{\log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 \sqrt[3]{b} d}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} d}","-\frac{\sqrt[3]{c} \log \left(c+d x^3\right)}{6 d \sqrt[3]{b c-a d}}+\frac{\sqrt[3]{c} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d \sqrt[3]{b c-a d}}-\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d \sqrt[3]{b c-a d}}-\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 \sqrt[3]{b} d}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{b} d}",1,"ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(1/3)*d) - (c^(1/3)*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d*(b*c - a*d)^(1/3)) - Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*b^(1/3)*d) + Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*b^(1/3)*d) + (c^(1/3)*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*d*(b*c - a*d)^(1/3)) - (c^(1/3)*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*d*(b*c - a*d)^(1/3))","A",14,8,24,0.3333,1,"{494, 481, 200, 31, 634, 617, 204, 628}"
723,1,207,0,0.1272087,"\int \frac{1}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{2/3} \sqrt[3]{b c-a d}}+\frac{\log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{2/3} \sqrt[3]{b c-a d}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} \sqrt[3]{b c-a d}}","\frac{\log \left(c+d x^3\right)}{6 c^{2/3} \sqrt[3]{b c-a d}}-\frac{\log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} \sqrt[3]{b c-a d}}+\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} \sqrt[3]{b c-a d}}",1,"ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))]/(Sqrt[3]*c^(2/3)*(b*c - a*d)^(1/3)) - Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*c^(2/3)*(b*c - a*d)^(1/3)) + Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*c^(2/3)*(b*c - a*d)^(1/3))","A",7,7,21,0.3333,1,"{377, 200, 31, 634, 617, 204, 628}"
724,1,235,0,0.2261739,"\int \frac{1}{x^3 \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x^3*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{d \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{5/3} \sqrt[3]{b c-a d}}-\frac{d \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{5/3} \sqrt[3]{b c-a d}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{5/3} \sqrt[3]{b c-a d}}-\frac{\left(a+b x^3\right)^{2/3}}{2 a c x^2}","-\frac{d \log \left(c+d x^3\right)}{6 c^{5/3} \sqrt[3]{b c-a d}}+\frac{d \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{5/3} \sqrt[3]{b c-a d}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{5/3} \sqrt[3]{b c-a d}}-\frac{\left(a+b x^3\right)^{2/3}}{2 a c x^2}",1,"-(a + b*x^3)^(2/3)/(2*a*c*x^2) - (d*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(5/3)*(b*c - a*d)^(1/3)) + (d*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(5/3)*(b*c - a*d)^(1/3)) - (d*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(5/3)*(b*c - a*d)^(1/3))","A",8,8,24,0.3333,1,"{494, 453, 200, 31, 634, 617, 204, 628}"
725,1,271,0,0.2862119,"\int \frac{1}{x^6 \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x^6*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{\left(a+b x^3\right)^{2/3} (a d+b c)}{2 a^2 c^2 x^2}-\frac{\left(a+b x^3\right)^{5/3}}{5 a^2 c x^5}-\frac{d^2 \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{8/3} \sqrt[3]{b c-a d}}+\frac{d^2 \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{8/3} \sqrt[3]{b c-a d}}+\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{8/3} \sqrt[3]{b c-a d}}","\frac{\left(a+b x^3\right)^{2/3} (5 a d+3 b c)}{10 a^2 c^2 x^2}+\frac{d^2 \log \left(c+d x^3\right)}{6 c^{8/3} \sqrt[3]{b c-a d}}-\frac{d^2 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{8/3} \sqrt[3]{b c-a d}}+\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{8/3} \sqrt[3]{b c-a d}}-\frac{\left(a+b x^3\right)^{2/3}}{5 a c x^5}",1,"((b*c + a*d)*(a + b*x^3)^(2/3))/(2*a^2*c^2*x^2) - (a + b*x^3)^(5/3)/(5*a^2*c*x^5) + (d^2*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(8/3)*(b*c - a*d)^(1/3)) - (d^2*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(8/3)*(b*c - a*d)^(1/3)) + (d^2*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(8/3)*(b*c - a*d)^(1/3))","A",9,8,24,0.3333,1,"{494, 461, 200, 31, 634, 617, 204, 628}"
726,1,317,0,0.3245427,"\int \frac{1}{x^9 \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x^9*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\left(a+b x^3\right)^{2/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{2 a^3 c^3 x^2}+\frac{\left(a+b x^3\right)^{5/3} (a d+2 b c)}{5 a^3 c^2 x^5}-\frac{\left(a+b x^3\right)^{8/3}}{8 a^3 c x^8}+\frac{d^3 \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{11/3} \sqrt[3]{b c-a d}}-\frac{d^3 \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{11/3} \sqrt[3]{b c-a d}}-\frac{d^3 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{11/3} \sqrt[3]{b c-a d}}","-\frac{\left(a+b x^3\right)^{2/3} \left(20 a^2 d^2+12 a b c d+9 b^2 c^2\right)}{40 a^3 c^3 x^2}+\frac{\left(a+b x^3\right)^{2/3} (4 a d+3 b c)}{20 a^2 c^2 x^5}-\frac{d^3 \log \left(c+d x^3\right)}{6 c^{11/3} \sqrt[3]{b c-a d}}+\frac{d^3 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{11/3} \sqrt[3]{b c-a d}}-\frac{d^3 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{11/3} \sqrt[3]{b c-a d}}-\frac{\left(a+b x^3\right)^{2/3}}{8 a c x^8}",1,"-((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(2/3))/(2*a^3*c^3*x^2) + ((2*b*c + a*d)*(a + b*x^3)^(5/3))/(5*a^3*c^2*x^5) - (a + b*x^3)^(8/3)/(8*a^3*c*x^8) - (d^3*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(11/3)*(b*c - a*d)^(1/3)) + (d^3*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(11/3)*(b*c - a*d)^(1/3)) - (d^3*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(11/3)*(b*c - a*d)^(1/3))","A",9,8,24,0.3333,1,"{494, 461, 200, 31, 634, 617, 204, 628}"
727,1,64,0,0.0526605,"\int \frac{x^7}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^7/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{x^8 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{8}{3};\frac{1}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 c \sqrt[3]{a+b x^3}}","\frac{x^8 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{8}{3};\frac{1}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 c \sqrt[3]{a+b x^3}}",1,"(x^8*(1 + (b*x^3)/a)^(1/3)*AppellF1[8/3, 1/3, 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)])/(8*c*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
728,1,64,0,0.0529023,"\int \frac{x^4}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x^4/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{x^5 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c \sqrt[3]{a+b x^3}}","\frac{x^5 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{5}{3};\frac{1}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 c \sqrt[3]{a+b x^3}}",1,"(x^5*(1 + (b*x^3)/a)^(1/3)*AppellF1[5/3, 1/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*c*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
729,1,64,0,0.0395461,"\int \frac{x}{\sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[x/((a + b*x^3)^(1/3)*(c + d*x^3)),x]","\frac{x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c \sqrt[3]{a+b x^3}}","\frac{x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{1}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c \sqrt[3]{a+b x^3}}",1,"(x^2*(1 + (b*x^3)/a)^(1/3)*AppellF1[2/3, 1/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*(a + b*x^3)^(1/3))","A",2,2,22,0.09091,1,"{511, 510}"
730,1,62,0,0.0547463,"\int \frac{1}{x^2 \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x^2*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{1}{3};\frac{1}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c x \sqrt[3]{a+b x^3}}","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{1}{3};\frac{1}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c x \sqrt[3]{a+b x^3}}",1,"-(((1 + (b*x^3)/a)^(1/3)*AppellF1[-1/3, 1/3, 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*x*(a + b*x^3)^(1/3)))","A",2,2,24,0.08333,1,"{511, 510}"
731,1,64,0,0.0544019,"\int \frac{1}{x^5 \sqrt[3]{a+b x^3} \left(c+d x^3\right)} \, dx","Int[1/(x^5*(a + b*x^3)^(1/3)*(c + d*x^3)),x]","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{4}{3};\frac{1}{3},1;-\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c x^4 \sqrt[3]{a+b x^3}}","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{4}{3};\frac{1}{3},1;-\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c x^4 \sqrt[3]{a+b x^3}}",1,"-((1 + (b*x^3)/a)^(1/3)*AppellF1[-4/3, 1/3, 1, -1/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*c*x^4*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
732,1,241,0,0.2630864,"\int \frac{x^{11}}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^11/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{\sqrt[3]{a+b x^3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{b^3 d^3}-\frac{\left(a+b x^3\right)^{4/3} (2 a d+b c)}{4 b^3 d^2}+\frac{\left(a+b x^3\right)^{7/3}}{7 b^3 d}+\frac{c^3 \log \left(c+d x^3\right)}{6 d^{10/3} (b c-a d)^{2/3}}-\frac{c^3 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{10/3} (b c-a d)^{2/3}}+\frac{c^3 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{10/3} (b c-a d)^{2/3}}","\frac{\sqrt[3]{a+b x^3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{b^3 d^3}-\frac{\left(a+b x^3\right)^{4/3} (2 a d+b c)}{4 b^3 d^2}+\frac{\left(a+b x^3\right)^{7/3}}{7 b^3 d}+\frac{c^3 \log \left(c+d x^3\right)}{6 d^{10/3} (b c-a d)^{2/3}}-\frac{c^3 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{10/3} (b c-a d)^{2/3}}+\frac{c^3 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{10/3} (b c-a d)^{2/3}}",1,"((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(1/3))/(b^3*d^3) - ((b*c + 2*a*d)*(a + b*x^3)^(4/3))/(4*b^3*d^2) + (a + b*x^3)^(7/3)/(7*b^3*d) + (c^3*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(10/3)*(b*c - a*d)^(2/3)) + (c^3*Log[c + d*x^3])/(6*d^(10/3)*(b*c - a*d)^(2/3)) - (c^3*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(10/3)*(b*c - a*d)^(2/3))","A",7,6,24,0.2500,1,"{446, 88, 58, 617, 204, 31}"
733,1,201,0,0.2119124,"\int \frac{x^8}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^8/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","-\frac{\sqrt[3]{a+b x^3} (a d+b c)}{b^2 d^2}+\frac{\left(a+b x^3\right)^{4/3}}{4 b^2 d}-\frac{c^2 \log \left(c+d x^3\right)}{6 d^{7/3} (b c-a d)^{2/3}}+\frac{c^2 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{7/3} (b c-a d)^{2/3}}-\frac{c^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3} (b c-a d)^{2/3}}","-\frac{\sqrt[3]{a+b x^3} (a d+b c)}{b^2 d^2}+\frac{\left(a+b x^3\right)^{4/3}}{4 b^2 d}-\frac{c^2 \log \left(c+d x^3\right)}{6 d^{7/3} (b c-a d)^{2/3}}+\frac{c^2 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{7/3} (b c-a d)^{2/3}}-\frac{c^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{7/3} (b c-a d)^{2/3}}",1,"-(((b*c + a*d)*(a + b*x^3)^(1/3))/(b^2*d^2)) + (a + b*x^3)^(4/3)/(4*b^2*d) - (c^2*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(7/3)*(b*c - a*d)^(2/3)) - (c^2*Log[c + d*x^3])/(6*d^(7/3)*(b*c - a*d)^(2/3)) + (c^2*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(7/3)*(b*c - a*d)^(2/3))","A",7,6,24,0.2500,1,"{446, 88, 58, 617, 204, 31}"
734,1,165,0,0.155348,"\int \frac{x^5}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^5/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{c \log \left(c+d x^3\right)}{6 d^{4/3} (b c-a d)^{2/3}}-\frac{c \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{4/3} (b c-a d)^{2/3}}+\frac{c \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{4/3} (b c-a d)^{2/3}}+\frac{\sqrt[3]{a+b x^3}}{b d}","\frac{c \log \left(c+d x^3\right)}{6 d^{4/3} (b c-a d)^{2/3}}-\frac{c \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{4/3} (b c-a d)^{2/3}}+\frac{c \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{4/3} (b c-a d)^{2/3}}+\frac{\sqrt[3]{a+b x^3}}{b d}",1,"(a + b*x^3)^(1/3)/(b*d) + (c*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(4/3)*(b*c - a*d)^(2/3)) + (c*Log[c + d*x^3])/(6*d^(4/3)*(b*c - a*d)^(2/3)) - (c*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(4/3)*(b*c - a*d)^(2/3))","A",6,6,24,0.2500,1,"{446, 80, 58, 617, 204, 31}"
735,1,145,0,0.1235712,"\int \frac{x^2}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^2/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","-\frac{\log \left(c+d x^3\right)}{6 \sqrt[3]{d} (b c-a d)^{2/3}}+\frac{\log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{d} (b c-a d)^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{d} (b c-a d)^{2/3}}","-\frac{\log \left(c+d x^3\right)}{6 \sqrt[3]{d} (b c-a d)^{2/3}}+\frac{\log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{d} (b c-a d)^{2/3}}-\frac{\tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{d} (b c-a d)^{2/3}}",1,"-(ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]]/(Sqrt[3]*d^(1/3)*(b*c - a*d)^(2/3))) - Log[c + d*x^3]/(6*d^(1/3)*(b*c - a*d)^(2/3)) + Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)]/(2*d^(1/3)*(b*c - a*d)^(2/3))","A",5,5,24,0.2083,1,"{444, 58, 617, 204, 31}"
736,1,245,0,0.2105221,"\int \frac{1}{x \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/(x*(a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{2/3} c}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} c}-\frac{\log (x)}{2 a^{2/3} c}+\frac{d^{2/3} \log \left(c+d x^3\right)}{6 c (b c-a d)^{2/3}}-\frac{d^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c (b c-a d)^{2/3}}+\frac{d^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c (b c-a d)^{2/3}}","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{2/3} c}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{2/3} c}-\frac{\log (x)}{2 a^{2/3} c}+\frac{d^{2/3} \log \left(c+d x^3\right)}{6 c (b c-a d)^{2/3}}-\frac{d^{2/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c (b c-a d)^{2/3}}+\frac{d^{2/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c (b c-a d)^{2/3}}",1,"-(ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(2/3)*c)) + (d^(2/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*(b*c - a*d)^(2/3)) - Log[x]/(2*a^(2/3)*c) + (d^(2/3)*Log[c + d*x^3])/(6*c*(b*c - a*d)^(2/3)) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(2/3)*c) - (d^(2/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c*(b*c - a*d)^(2/3))","A",10,7,24,0.2917,1,"{446, 86, 57, 617, 204, 31, 58}"
737,1,299,0,0.3167019,"\int \frac{1}{x^4 \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/(x^4*(a + b*x^3)^(2/3)*(c + d*x^3)),x]","-\frac{(3 a d+2 b c) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{5/3} c^2}+\frac{(3 a d+2 b c) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} c^2}+\frac{\log (x) (3 a d+2 b c)}{6 a^{5/3} c^2}-\frac{d^{5/3} \log \left(c+d x^3\right)}{6 c^2 (b c-a d)^{2/3}}+\frac{d^{5/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 (b c-a d)^{2/3}}-\frac{d^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 (b c-a d)^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{3 a c x^3}","-\frac{(3 a d+2 b c) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{5/3} c^2}+\frac{(3 a d+2 b c) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{5/3} c^2}+\frac{\log (x) (3 a d+2 b c)}{6 a^{5/3} c^2}-\frac{d^{5/3} \log \left(c+d x^3\right)}{6 c^2 (b c-a d)^{2/3}}+\frac{d^{5/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 (b c-a d)^{2/3}}-\frac{d^{5/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 (b c-a d)^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{3 a c x^3}",1,"-(a + b*x^3)^(1/3)/(3*a*c*x^3) + ((2*b*c + 3*a*d)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(5/3)*c^2) - (d^(5/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^2*(b*c - a*d)^(2/3)) + ((2*b*c + 3*a*d)*Log[x])/(6*a^(5/3)*c^2) - (d^(5/3)*Log[c + d*x^3])/(6*c^2*(b*c - a*d)^(2/3)) - ((2*b*c + 3*a*d)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(5/3)*c^2) + (d^(5/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^2*(b*c - a*d)^(2/3))","A",11,8,24,0.3333,1,"{446, 103, 156, 57, 617, 204, 31, 58}"
738,1,400,0,0.5015081,"\int \frac{x^7}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^7/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{(2 a d+3 b c) \log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{9 b^{5/3} d^2}-\frac{(2 a d+3 b c) \log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{18 b^{5/3} d^2}+\frac{(2 a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3} d^2}-\frac{c^{5/3} \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 d^2 (b c-a d)^{2/3}}+\frac{c^{5/3} \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 d^2 (b c-a d)^{2/3}}-\frac{c^{5/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d^2 (b c-a d)^{2/3}}+\frac{x^2 \sqrt[3]{a+b x^3}}{3 b d}","\frac{(2 a d+3 b c) \log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{6 b^{5/3} d^2}+\frac{(2 a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{5/3} d^2}+\frac{c^{5/3} \log \left(c+d x^3\right)}{6 d^2 (b c-a d)^{2/3}}-\frac{c^{5/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^2 (b c-a d)^{2/3}}-\frac{c^{5/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2 (b c-a d)^{2/3}}+\frac{x^2 \sqrt[3]{a+b x^3}}{3 b d}",1,"(x^2*(a + b*x^3)^(1/3))/(3*b*d) + ((3*b*c + 2*a*d)*ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]])/(3*Sqrt[3]*b^(5/3)*d^2) - (c^(5/3)*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d^2*(b*c - a*d)^(2/3)) + ((3*b*c + 2*a*d)*Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(9*b^(5/3)*d^2) - ((3*b*c + 2*a*d)*Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)])/(18*b^(5/3)*d^2) - (c^(5/3)*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*d^2*(b*c - a*d)^(2/3)) + (c^(5/3)*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*d^2*(b*c - a*d)^(2/3))","A",16,9,24,0.3750,1,"{494, 470, 584, 292, 31, 634, 617, 204, 628}"
739,1,346,0,0.3082441,"\int \frac{x^4}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^4/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","-\frac{\log \left(1-\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}\right)}{3 b^{2/3} d}+\frac{\log \left(\frac{b^{2/3} x^2}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1\right)}{6 b^{2/3} d}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d}+\frac{c^{2/3} \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 d (b c-a d)^{2/3}}-\frac{c^{2/3} \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 d (b c-a d)^{2/3}}+\frac{c^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} d (b c-a d)^{2/3}}","-\frac{\log \left(\sqrt[3]{b} x-\sqrt[3]{a+b x^3}\right)}{2 b^{2/3} d}-\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{2/3} d}-\frac{c^{2/3} \log \left(c+d x^3\right)}{6 d (b c-a d)^{2/3}}+\frac{c^{2/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d (b c-a d)^{2/3}}+\frac{c^{2/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d (b c-a d)^{2/3}}",1,"-(ArcTan[(1 + (2*b^(1/3)*x)/(a + b*x^3)^(1/3))/Sqrt[3]]/(Sqrt[3]*b^(2/3)*d)) + (c^(2/3)*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*d*(b*c - a*d)^(2/3)) - Log[1 - (b^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*b^(2/3)*d) + Log[1 + (b^(2/3)*x^2)/(a + b*x^3)^(2/3) + (b^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*b^(2/3)*d) + (c^(2/3)*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*d*(b*c - a*d)^(2/3)) - (c^(2/3)*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*d*(b*c - a*d)^(2/3))","A",14,8,24,0.3333,1,"{494, 481, 292, 31, 634, 617, 204, 628}"
740,1,208,0,0.1402444,"\int \frac{x}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{\log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 \sqrt[3]{c} (b c-a d)^{2/3}}-\frac{\log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 \sqrt[3]{c} (b c-a d)^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} \sqrt[3]{c} (b c-a d)^{2/3}}","\frac{\log \left(c+d x^3\right)}{6 \sqrt[3]{c} (b c-a d)^{2/3}}-\frac{\log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 \sqrt[3]{c} (b c-a d)^{2/3}}-\frac{\tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} \sqrt[3]{c} (b c-a d)^{2/3}}",1,"-(ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))]/(Sqrt[3]*c^(1/3)*(b*c - a*d)^(2/3))) - Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)]/(3*c^(1/3)*(b*c - a*d)^(2/3)) + Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)]/(6*c^(1/3)*(b*c - a*d)^(2/3))","A",7,7,22,0.3182,1,"{494, 292, 31, 634, 617, 204, 628}"
741,1,232,0,0.2206902,"\int \frac{1}{x^2 \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/(x^2*(a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{d \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{4/3} (b c-a d)^{2/3}}-\frac{d \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{4/3} (b c-a d)^{2/3}}+\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{4/3} (b c-a d)^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{a c x}","-\frac{d \log \left(c+d x^3\right)}{6 c^{4/3} (b c-a d)^{2/3}}+\frac{d \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{4/3} (b c-a d)^{2/3}}+\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{4/3} (b c-a d)^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{a c x}",1,"-((a + b*x^3)^(1/3)/(a*c*x)) + (d*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(4/3)*(b*c - a*d)^(2/3)) + (d*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(4/3)*(b*c - a*d)^(2/3)) - (d*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(4/3)*(b*c - a*d)^(2/3))","A",8,8,24,0.3333,1,"{494, 453, 292, 31, 634, 617, 204, 628}"
742,1,269,0,0.296604,"\int \frac{1}{x^5 \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/(x^5*(a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{\sqrt[3]{a+b x^3} (a d+b c)}{a^2 c^2 x}-\frac{\left(a+b x^3\right)^{4/3}}{4 a^2 c x^4}-\frac{d^2 \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{7/3} (b c-a d)^{2/3}}+\frac{d^2 \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{7/3} (b c-a d)^{2/3}}-\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{7/3} (b c-a d)^{2/3}}","\frac{\sqrt[3]{a+b x^3} (4 a d+3 b c)}{4 a^2 c^2 x}+\frac{d^2 \log \left(c+d x^3\right)}{6 c^{7/3} (b c-a d)^{2/3}}-\frac{d^2 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{7/3} (b c-a d)^{2/3}}-\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{7/3} (b c-a d)^{2/3}}-\frac{\sqrt[3]{a+b x^3}}{4 a c x^4}",1,"((b*c + a*d)*(a + b*x^3)^(1/3))/(a^2*c^2*x) - (a + b*x^3)^(4/3)/(4*a^2*c*x^4) - (d^2*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(7/3)*(b*c - a*d)^(2/3)) - (d^2*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(7/3)*(b*c - a*d)^(2/3)) + (d^2*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(7/3)*(b*c - a*d)^(2/3))","A",9,8,24,0.3333,1,"{494, 461, 292, 31, 634, 617, 204, 628}"
743,1,64,0,0.0575557,"\int \frac{x^6}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^6/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{x^7 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{7}{3};\frac{2}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \left(a+b x^3\right)^{2/3}}","\frac{x^7 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{7}{3};\frac{2}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 c \left(a+b x^3\right)^{2/3}}",1,"(x^7*(1 + (b*x^3)/a)^(2/3)*AppellF1[7/3, 2/3, 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)])/(7*c*(a + b*x^3)^(2/3))","A",2,2,24,0.08333,1,"{511, 510}"
744,1,64,0,0.0612628,"\int \frac{x^3}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[x^3/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \left(a+b x^3\right)^{2/3}}","\frac{x^4 \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{4}{3};\frac{2}{3},1;\frac{7}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 c \left(a+b x^3\right)^{2/3}}",1,"(x^4*(1 + (b*x^3)/a)^(2/3)*AppellF1[4/3, 2/3, 1, 7/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*c*(a + b*x^3)^(2/3))","A",2,2,24,0.08333,1,"{511, 510}"
745,1,59,0,0.0310665,"\int \frac{1}{\left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(2/3)*(c + d*x^3)),x]","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(a+b x^3\right)^{2/3}}","\frac{x \left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(\frac{1}{3};\frac{2}{3},1;\frac{4}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{c \left(a+b x^3\right)^{2/3}}",1,"(x*(1 + (b*x^3)/a)^(2/3)*AppellF1[1/3, 2/3, 1, 4/3, -((b*x^3)/a), -((d*x^3)/c)])/(c*(a + b*x^3)^(2/3))","A",2,2,21,0.09524,1,"{430, 429}"
746,1,64,0,0.062456,"\int \frac{1}{x^3 \left(a+b x^3\right)^{2/3} \left(c+d x^3\right)} \, dx","Int[1/(x^3*(a + b*x^3)^(2/3)*(c + d*x^3)),x]","-\frac{\left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(-\frac{2}{3};\frac{2}{3},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c x^2 \left(a+b x^3\right)^{2/3}}","-\frac{\left(\frac{b x^3}{a}+1\right)^{2/3} F_1\left(-\frac{2}{3};\frac{2}{3},1;\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 c x^2 \left(a+b x^3\right)^{2/3}}",1,"-((1 + (b*x^3)/a)^(2/3)*AppellF1[-2/3, 2/3, 1, 1/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*c*x^2*(a + b*x^3)^(2/3))","A",2,2,24,0.08333,1,"{511, 510}"
747,1,347,0,0.4405893,"\int \frac{x^{14}}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^14/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{\left(a+b x^3\right)^{2/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{2 b^4 d^3}-\frac{a^4}{b^4 \sqrt[3]{a+b x^3} (b c-a d)}+\frac{a^2 \left(a+b x^3\right)^{2/3}}{2 b^4 d}+\frac{a \left(a+b x^3\right)^{2/3} (a d+b c)}{2 b^4 d^2}-\frac{\left(a+b x^3\right)^{5/3} (a d+b c)}{5 b^4 d^2}-\frac{2 a \left(a+b x^3\right)^{5/3}}{5 b^4 d}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^4 d}-\frac{c^4 \log \left(c+d x^3\right)}{6 d^{11/3} (b c-a d)^{4/3}}+\frac{c^4 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{11/3} (b c-a d)^{4/3}}+\frac{c^4 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{11/3} (b c-a d)^{4/3}}","\frac{\left(a+b x^3\right)^{2/3} \left(a^2 d^2+a b c d+b^2 c^2\right)}{2 b^4 d^3}-\frac{a^4}{b^4 \sqrt[3]{a+b x^3} (b c-a d)}+\frac{a^2 \left(a+b x^3\right)^{2/3}}{2 b^4 d}+\frac{a \left(a+b x^3\right)^{2/3} (a d+b c)}{2 b^4 d^2}-\frac{\left(a+b x^3\right)^{5/3} (a d+b c)}{5 b^4 d^2}-\frac{2 a \left(a+b x^3\right)^{5/3}}{5 b^4 d}+\frac{\left(a+b x^3\right)^{8/3}}{8 b^4 d}-\frac{c^4 \log \left(c+d x^3\right)}{6 d^{11/3} (b c-a d)^{4/3}}+\frac{c^4 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{11/3} (b c-a d)^{4/3}}+\frac{c^4 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{11/3} (b c-a d)^{4/3}}",1,"-(a^4/(b^4*(b*c - a*d)*(a + b*x^3)^(1/3))) + (a^2*(a + b*x^3)^(2/3))/(2*b^4*d) + (a*(b*c + a*d)*(a + b*x^3)^(2/3))/(2*b^4*d^2) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*(a + b*x^3)^(2/3))/(2*b^4*d^3) - (2*a*(a + b*x^3)^(5/3))/(5*b^4*d) - ((b*c + a*d)*(a + b*x^3)^(5/3))/(5*b^4*d^2) + (a + b*x^3)^(8/3)/(8*b^4*d) + (c^4*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(11/3)*(b*c - a*d)^(4/3)) - (c^4*Log[c + d*x^3])/(6*d^(11/3)*(b*c - a*d)^(4/3)) + (c^4*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(11/3)*(b*c - a*d)^(4/3))","A",11,7,24,0.2917,1,"{446, 87, 43, 56, 617, 204, 31}"
748,1,253,0,0.3401685,"\int \frac{x^{11}}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^11/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{a^3}{b^3 \sqrt[3]{a+b x^3} (b c-a d)}-\frac{\left(a+b x^3\right)^{2/3} (a d+b c)}{2 b^3 d^2}-\frac{a \left(a+b x^3\right)^{2/3}}{2 b^3 d}+\frac{\left(a+b x^3\right)^{5/3}}{5 b^3 d}+\frac{c^3 \log \left(c+d x^3\right)}{6 d^{8/3} (b c-a d)^{4/3}}-\frac{c^3 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{8/3} (b c-a d)^{4/3}}-\frac{c^3 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{8/3} (b c-a d)^{4/3}}","\frac{a^3}{b^3 \sqrt[3]{a+b x^3} (b c-a d)}-\frac{\left(a+b x^3\right)^{2/3} (a d+b c)}{2 b^3 d^2}-\frac{a \left(a+b x^3\right)^{2/3}}{2 b^3 d}+\frac{\left(a+b x^3\right)^{5/3}}{5 b^3 d}+\frac{c^3 \log \left(c+d x^3\right)}{6 d^{8/3} (b c-a d)^{4/3}}-\frac{c^3 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{8/3} (b c-a d)^{4/3}}-\frac{c^3 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{8/3} (b c-a d)^{4/3}}",1,"a^3/(b^3*(b*c - a*d)*(a + b*x^3)^(1/3)) - (a*(a + b*x^3)^(2/3))/(2*b^3*d) - ((b*c + a*d)*(a + b*x^3)^(2/3))/(2*b^3*d^2) + (a + b*x^3)^(5/3)/(5*b^3*d) - (c^3*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(8/3)*(b*c - a*d)^(4/3)) + (c^3*Log[c + d*x^3])/(6*d^(8/3)*(b*c - a*d)^(4/3)) - (c^3*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(8/3)*(b*c - a*d)^(4/3))","A",9,7,24,0.2917,1,"{446, 87, 43, 56, 617, 204, 31}"
749,1,203,0,0.2415947,"\int \frac{x^8}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^8/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","-\frac{a^2}{b^2 \sqrt[3]{a+b x^3} (b c-a d)}+\frac{\left(a+b x^3\right)^{2/3}}{2 b^2 d}-\frac{c^2 \log \left(c+d x^3\right)}{6 d^{5/3} (b c-a d)^{4/3}}+\frac{c^2 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{5/3} (b c-a d)^{4/3}}+\frac{c^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{5/3} (b c-a d)^{4/3}}","-\frac{a^2}{b^2 \sqrt[3]{a+b x^3} (b c-a d)}+\frac{\left(a+b x^3\right)^{2/3}}{2 b^2 d}-\frac{c^2 \log \left(c+d x^3\right)}{6 d^{5/3} (b c-a d)^{4/3}}+\frac{c^2 \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{5/3} (b c-a d)^{4/3}}+\frac{c^2 \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{5/3} (b c-a d)^{4/3}}",1,"-(a^2/(b^2*(b*c - a*d)*(a + b*x^3)^(1/3))) + (a + b*x^3)^(2/3)/(2*b^2*d) + (c^2*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(5/3)*(b*c - a*d)^(4/3)) - (c^2*Log[c + d*x^3])/(6*d^(5/3)*(b*c - a*d)^(4/3)) + (c^2*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(5/3)*(b*c - a*d)^(4/3))","A",7,6,24,0.2500,1,"{446, 87, 56, 617, 204, 31}"
750,1,174,0,0.1711188,"\int \frac{x^5}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^5/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{c \log \left(c+d x^3\right)}{6 d^{2/3} (b c-a d)^{4/3}}-\frac{c \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{2/3} (b c-a d)^{4/3}}-\frac{c \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{2/3} (b c-a d)^{4/3}}+\frac{a}{b \sqrt[3]{a+b x^3} (b c-a d)}","\frac{c \log \left(c+d x^3\right)}{6 d^{2/3} (b c-a d)^{4/3}}-\frac{c \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 d^{2/3} (b c-a d)^{4/3}}-\frac{c \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} d^{2/3} (b c-a d)^{4/3}}+\frac{a}{b \sqrt[3]{a+b x^3} (b c-a d)}",1,"a/(b*(b*c - a*d)*(a + b*x^3)^(1/3)) - (c*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*d^(2/3)*(b*c - a*d)^(4/3)) + (c*Log[c + d*x^3])/(6*d^(2/3)*(b*c - a*d)^(4/3)) - (c*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*d^(2/3)*(b*c - a*d)^(4/3))","A",6,6,24,0.2500,1,"{446, 78, 56, 617, 204, 31}"
751,1,167,0,0.1654782,"\int \frac{x^2}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^2/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","-\frac{1}{\sqrt[3]{a+b x^3} (b c-a d)}-\frac{\sqrt[3]{d} \log \left(c+d x^3\right)}{6 (b c-a d)^{4/3}}+\frac{\sqrt[3]{d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 (b c-a d)^{4/3}}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} (b c-a d)^{4/3}}","-\frac{1}{\sqrt[3]{a+b x^3} (b c-a d)}-\frac{\sqrt[3]{d} \log \left(c+d x^3\right)}{6 (b c-a d)^{4/3}}+\frac{\sqrt[3]{d} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 (b c-a d)^{4/3}}+\frac{\sqrt[3]{d} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} (b c-a d)^{4/3}}",1,"-(1/((b*c - a*d)*(a + b*x^3)^(1/3))) + (d^(1/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*(b*c - a*d)^(4/3)) - (d^(1/3)*Log[c + d*x^3])/(6*(b*c - a*d)^(4/3)) + (d^(1/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*(b*c - a*d)^(4/3))","A",6,6,24,0.2500,1,"{444, 51, 56, 617, 204, 31}"
752,1,271,0,0.3163292,"\int \frac{1}{x \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{4/3} c}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} c}-\frac{\log (x)}{2 a^{4/3} c}+\frac{d^{4/3} \log \left(c+d x^3\right)}{6 c (b c-a d)^{4/3}}-\frac{d^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c (b c-a d)^{4/3}}-\frac{d^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c (b c-a d)^{4/3}}+\frac{b}{a \sqrt[3]{a+b x^3} (b c-a d)}","\frac{\log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{2 a^{4/3} c}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{\sqrt{3} a^{4/3} c}-\frac{\log (x)}{2 a^{4/3} c}+\frac{d^{4/3} \log \left(c+d x^3\right)}{6 c (b c-a d)^{4/3}}-\frac{d^{4/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c (b c-a d)^{4/3}}-\frac{d^{4/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c (b c-a d)^{4/3}}+\frac{b}{a \sqrt[3]{a+b x^3} (b c-a d)}",1,"b/(a*(b*c - a*d)*(a + b*x^3)^(1/3)) + ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))]/(Sqrt[3]*a^(4/3)*c) - (d^(4/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c*(b*c - a*d)^(4/3)) - Log[x]/(2*a^(4/3)*c) + (d^(4/3)*Log[c + d*x^3])/(6*c*(b*c - a*d)^(4/3)) + Log[a^(1/3) - (a + b*x^3)^(1/3)]/(2*a^(4/3)*c) - (d^(4/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c*(b*c - a*d)^(4/3))","A",11,8,24,0.3333,1,"{446, 85, 156, 55, 617, 204, 31, 56}"
753,1,357,0,0.3938914,"\int \frac{1}{x^4 \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x^4*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","-\frac{3 a d+4 b c}{3 a^2 c^2 \sqrt[3]{a+b x^3}}-\frac{(3 a d+4 b c) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{7/3} c^2}-\frac{(3 a d+4 b c) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} c^2}+\frac{\log (x) (3 a d+4 b c)}{6 a^{7/3} c^2}-\frac{d^2}{c^2 \sqrt[3]{a+b x^3} (b c-a d)}-\frac{d^{7/3} \log \left(c+d x^3\right)}{6 c^2 (b c-a d)^{4/3}}+\frac{d^{7/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 (b c-a d)^{4/3}}+\frac{d^{7/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 (b c-a d)^{4/3}}-\frac{1}{3 a c x^3 \sqrt[3]{a+b x^3}}","-\frac{3 a d+4 b c}{3 a^2 c^2 \sqrt[3]{a+b x^3}}-\frac{(3 a d+4 b c) \log \left(\sqrt[3]{a}-\sqrt[3]{a+b x^3}\right)}{6 a^{7/3} c^2}-\frac{(3 a d+4 b c) \tan ^{-1}\left(\frac{2 \sqrt[3]{a+b x^3}+\sqrt[3]{a}}{\sqrt{3} \sqrt[3]{a}}\right)}{3 \sqrt{3} a^{7/3} c^2}+\frac{\log (x) (3 a d+4 b c)}{6 a^{7/3} c^2}-\frac{d^2}{c^2 \sqrt[3]{a+b x^3} (b c-a d)}-\frac{d^{7/3} \log \left(c+d x^3\right)}{6 c^2 (b c-a d)^{4/3}}+\frac{d^{7/3} \log \left(\sqrt[3]{b c-a d}+\sqrt[3]{d} \sqrt[3]{a+b x^3}\right)}{2 c^2 (b c-a d)^{4/3}}+\frac{d^{7/3} \tan ^{-1}\left(\frac{1-\frac{2 \sqrt[3]{d} \sqrt[3]{a+b x^3}}{\sqrt[3]{b c-a d}}}{\sqrt{3}}\right)}{\sqrt{3} c^2 (b c-a d)^{4/3}}-\frac{1}{3 a c x^3 \sqrt[3]{a+b x^3}}",1,"-(d^2/(c^2*(b*c - a*d)*(a + b*x^3)^(1/3))) - (4*b*c + 3*a*d)/(3*a^2*c^2*(a + b*x^3)^(1/3)) - 1/(3*a*c*x^3*(a + b*x^3)^(1/3)) - ((4*b*c + 3*a*d)*ArcTan[(a^(1/3) + 2*(a + b*x^3)^(1/3))/(Sqrt[3]*a^(1/3))])/(3*Sqrt[3]*a^(7/3)*c^2) + (d^(7/3)*ArcTan[(1 - (2*d^(1/3)*(a + b*x^3)^(1/3))/(b*c - a*d)^(1/3))/Sqrt[3]])/(Sqrt[3]*c^2*(b*c - a*d)^(4/3)) + ((4*b*c + 3*a*d)*Log[x])/(6*a^(7/3)*c^2) - (d^(7/3)*Log[c + d*x^3])/(6*c^2*(b*c - a*d)^(4/3)) - ((4*b*c + 3*a*d)*Log[a^(1/3) - (a + b*x^3)^(1/3)])/(6*a^(7/3)*c^2) + (d^(7/3)*Log[(b*c - a*d)^(1/3) + d^(1/3)*(a + b*x^3)^(1/3)])/(2*c^2*(b*c - a*d)^(4/3))","A",13,9,24,0.3750,1,"{446, 103, 156, 51, 55, 617, 204, 31, 56}"
754,1,67,0,0.0603097,"\int \frac{x^9}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^9/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^{10} \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{10}{3};\frac{4}{3},1;\frac{13}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{10 a c \sqrt[3]{a+b x^3}}","\frac{(4 a d+3 b c) \log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{6 b^{7/3} d^2}-\frac{(4 a d+3 b c) \tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{3 \sqrt{3} b^{7/3} d^2}+\frac{x \left(a+b x^3\right)^{2/3} (b c-4 a d)}{3 b^2 d (b c-a d)}+\frac{c^{7/3} \log \left(c+d x^3\right)}{6 d^2 (b c-a d)^{4/3}}-\frac{c^{7/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d^2 (b c-a d)^{4/3}}+\frac{c^{7/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d^2 (b c-a d)^{4/3}}+\frac{a x^4}{b \sqrt[3]{a+b x^3} (b c-a d)}",1,"(x^10*(1 + (b*x^3)/a)^(1/3)*AppellF1[10/3, 4/3, 1, 13/3, -((b*x^3)/a), -((d*x^3)/c)])/(10*a*c*(a + b*x^3)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
755,1,67,0,0.0589555,"\int \frac{x^6}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^6/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^7 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{7}{3};\frac{4}{3},1;\frac{10}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{7 a c \sqrt[3]{a+b x^3}}","-\frac{\log \left(\sqrt[3]{a+b x^3}-\sqrt[3]{b} x\right)}{2 b^{4/3} d}+\frac{\tan ^{-1}\left(\frac{\frac{2 \sqrt[3]{b} x}{\sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} b^{4/3} d}-\frac{c^{4/3} \log \left(c+d x^3\right)}{6 d (b c-a d)^{4/3}}+\frac{c^{4/3} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 d (b c-a d)^{4/3}}-\frac{c^{4/3} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} d (b c-a d)^{4/3}}+\frac{a x}{b \sqrt[3]{a+b x^3} (b c-a d)}",1,"(x^7*(1 + (b*x^3)/a)^(1/3)*AppellF1[7/3, 4/3, 1, 10/3, -((b*x^3)/a), -((d*x^3)/c)])/(7*a*c*(a + b*x^3)^(1/3))","C",2,2,24,0.08333,0,"{511, 510}"
756,1,92,0,0.0654884,"\int \frac{x^3}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^3/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^4 \sqrt[3]{\frac{b x^3}{a}+1} \, _2F_1\left(\frac{4}{3},\frac{4}{3};\frac{7}{3};-\frac{c \left(\frac{b x^3}{a}-\frac{d x^3}{c}\right)}{d x^3+c}\right)}{4 a c \sqrt[3]{a+b x^3} \left(\frac{d x^3}{c}+1\right)^{4/3}}","-\frac{x}{\sqrt[3]{a+b x^3} (b c-a d)}+\frac{\sqrt[3]{c} \log \left(c+d x^3\right)}{6 (b c-a d)^{4/3}}-\frac{\sqrt[3]{c} \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 (b c-a d)^{4/3}}+\frac{\sqrt[3]{c} \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} (b c-a d)^{4/3}}",1,"(x^4*(1 + (b*x^3)/a)^(1/3)*Hypergeometric2F1[4/3, 4/3, 7/3, -((c*((b*x^3)/a - (d*x^3)/c))/(c + d*x^3))])/(4*a*c*(a + b*x^3)^(1/3)*(1 + (d*x^3)/c)^(4/3))","C",2,2,24,0.08333,0,"{511, 510}"
757,1,238,0,0.1957804,"\int \frac{1}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{d \log \left(\sqrt[3]{c}-\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}\right)}{3 c^{2/3} (b c-a d)^{4/3}}-\frac{d \log \left(\frac{x^2 (b c-a d)^{2/3}}{\left(a+b x^3\right)^{2/3}}+\frac{\sqrt[3]{c} x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+c^{2/3}\right)}{6 c^{2/3} (b c-a d)^{4/3}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{a+b x^3}}+\sqrt[3]{c}}{\sqrt{3} \sqrt[3]{c}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^{4/3}}+\frac{b x}{a \sqrt[3]{a+b x^3} (b c-a d)}","-\frac{d \log \left(c+d x^3\right)}{6 c^{2/3} (b c-a d)^{4/3}}+\frac{d \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{2/3} (b c-a d)^{4/3}}-\frac{d \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{2/3} (b c-a d)^{4/3}}+\frac{b x}{a \sqrt[3]{a+b x^3} (b c-a d)}",1,"(b*x)/(a*(b*c - a*d)*(a + b*x^3)^(1/3)) - (d*ArcTan[(c^(1/3) + (2*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3))/(Sqrt[3]*c^(1/3))])/(Sqrt[3]*c^(2/3)*(b*c - a*d)^(4/3)) + (d*Log[c^(1/3) - ((b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(3*c^(2/3)*(b*c - a*d)^(4/3)) - (d*Log[c^(2/3) + ((b*c - a*d)^(2/3)*x^2)/(a + b*x^3)^(2/3) + (c^(1/3)*(b*c - a*d)^(1/3)*x)/(a + b*x^3)^(1/3)])/(6*c^(2/3)*(b*c - a*d)^(4/3))","A",8,8,21,0.3810,1,"{382, 377, 200, 31, 634, 617, 204, 628}"
758,1,542,0,1.2874327,"\int \frac{1}{x^3 \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x^3*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{-9 c^2 x^6 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-9 d^2 x^{12} (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-18 c d x^9 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-126 c^2 d^2 x^6 \left(a+b x^3\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+126 c^2 d^2 x^6 \left(a+b x^3\right)^2-15 c^2 x^6 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-168 c^3 d x^3 \left(a+b x^3\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-28 c^4 \left(a+b x^3\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)+168 c^3 d x^3 \left(a+b x^3\right)^2+28 c^4 \left(a+b x^3\right)^2-27 d^2 x^{12} (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)-42 c d x^9 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{14 c^4 x^5 \left(a+b x^3\right)^{7/3} (b c-a d)}","-\frac{\left(a+b x^3\right)^{2/3} (3 b c-a d)}{2 a^2 c x^2 (b c-a d)}+\frac{d^2 \log \left(c+d x^3\right)}{6 c^{5/3} (b c-a d)^{4/3}}-\frac{d^2 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{5/3} (b c-a d)^{4/3}}+\frac{d^2 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{5/3} (b c-a d)^{4/3}}+\frac{b}{a x^2 \sqrt[3]{a+b x^3} (b c-a d)}",1,"(28*c^4*(a + b*x^3)^2 + 168*c^3*d*x^3*(a + b*x^3)^2 + 126*c^2*d^2*x^6*(a + b*x^3)^2 - 28*c^4*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 168*c^3*d*x^3*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 126*c^2*d^2*x^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 15*c^2*(b*c - a*d)^2*x^6*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 42*c*d*(b*c - a*d)^2*x^9*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 27*d^2*(b*c - a*d)^2*x^12*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 9*c^2*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 18*c*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 9*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(14*c^4*(b*c - a*d)*x^5*(a + b*x^3)^(7/3))","C",2,2,24,0.08333,0,"{511, 510}"
759,1,950,0,3.8574889,"\int \frac{1}{x^6 \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x^6*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{297 d^3 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+162 d^3 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+27 d^3 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+486 c d^2 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+351 c d^2 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+81 c d^2 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-1134 c^2 d^3 \left(b x^3+a\right)^2 x^9+1134 c^2 d^3 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+171 c^2 d (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+216 c^2 d (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+81 c^2 d (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-1512 c^3 d^2 \left(b x^3+a\right)^2 x^6+1512 c^3 d^2 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-18 c^3 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+27 c^3 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+27 c^3 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-252 c^4 d \left(b x^3+a\right)^2 x^3+252 c^4 d \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+56 c^5 \left(b x^3+a\right)^2-56 c^5 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{70 c^5 (b c-a d) x^8 \left(b x^3+a\right)^{7/3}}","\frac{\left(a+b x^3\right)^{2/3} \left(-5 a^2 d^2-3 a b c d+18 b^2 c^2\right)}{10 a^3 c^2 x^2 (b c-a d)}-\frac{\left(a+b x^3\right)^{2/3} (6 b c-a d)}{5 a^2 c x^5 (b c-a d)}-\frac{d^3 \log \left(c+d x^3\right)}{6 c^{8/3} (b c-a d)^{4/3}}+\frac{d^3 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{8/3} (b c-a d)^{4/3}}-\frac{d^3 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{8/3} (b c-a d)^{4/3}}+\frac{b}{a x^5 \sqrt[3]{a+b x^3} (b c-a d)}",1,"(56*c^5*(a + b*x^3)^2 - 252*c^4*d*x^3*(a + b*x^3)^2 - 1512*c^3*d^2*x^6*(a + b*x^3)^2 - 1134*c^2*d^3*x^9*(a + b*x^3)^2 - 56*c^5*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 252*c^4*d*x^3*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1512*c^3*d^2*x^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 1134*c^2*d^3*x^9*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 18*c^3*(b*c - a*d)^2*x^6*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 171*c^2*d*(b*c - a*d)^2*x^9*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 486*c*d^2*(b*c - a*d)^2*x^12*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 297*d^3*(b*c - a*d)^2*x^15*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*c^3*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 216*c^2*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 351*c*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 162*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*c^3*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*c^2*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 81*c*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 27*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(70*c^5*(b*c - a*d)*x^8*(a + b*x^3)^(7/3))","C",2,2,24,0.08333,0,"{511, 510}"
760,1,1486,0,8.2954908,"\int \frac{1}{x^9 \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x^9*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{-4050 d^4 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-2835 d^4 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-810 d^4 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-81 d^4 (b c-a d)^2 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{18}-6696 c d^3 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-6156 c d^3 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-2376 c d^3 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}-324 c d^3 (b c-a d)^2 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{15}+13608 c^2 d^4 \left(b x^3+a\right)^2 x^{12}-13608 c^2 d^4 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-2268 c^2 d^2 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-3618 c^2 d^2 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-2268 c^2 d^2 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}-486 c^2 d^2 (b c-a d)^2 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^{12}+18144 c^3 d^3 \left(b x^3+a\right)^2 x^9-18144 c^3 d^3 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+312 c^3 d (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-108 c^3 d (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-648 c^3 d (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9-324 c^3 d (b c-a d)^2 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^9+3024 c^4 d^2 \left(b x^3+a\right)^2 x^6-3024 c^4 d^2 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-66 c^4 (b c-a d)^2 \, _2F_1\left(2,\frac{7}{3};\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+189 c^4 (b c-a d)^2 \, _3F_2\left(2,2,\frac{7}{3};1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6+54 c^4 (b c-a d)^2 \, _4F_3\left(2,2,2,\frac{7}{3};1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-81 c^4 (b c-a d)^2 \, _5F_4\left(2,2,2,2,\frac{7}{3};1,1,1,\frac{10}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^6-672 c^5 d \left(b x^3+a\right)^2 x^3+672 c^5 d \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right) x^3+280 c^6 \left(b x^3+a\right)^2-280 c^6 \left(b x^3+a\right)^2 \, _2F_1\left(\frac{1}{3},1;\frac{4}{3};\frac{(b c-a d) x^3}{c \left(b x^3+a\right)}\right)}{560 c^6 (b c-a d) x^{11} \left(b x^3+a\right)^{7/3}}","-\frac{\left(a+b x^3\right)^{2/3} \left(-12 a^2 b c d^2-20 a^3 d^3-9 a b^2 c^2 d+81 b^3 c^3\right)}{40 a^4 c^3 x^2 (b c-a d)}+\frac{\left(a+b x^3\right)^{2/3} (9 b c-4 a d) (a d+3 b c)}{20 a^3 c^2 x^5 (b c-a d)}-\frac{\left(a+b x^3\right)^{2/3} (9 b c-a d)}{8 a^2 c x^8 (b c-a d)}+\frac{d^4 \log \left(c+d x^3\right)}{6 c^{11/3} (b c-a d)^{4/3}}-\frac{d^4 \log \left(\frac{x \sqrt[3]{b c-a d}}{\sqrt[3]{c}}-\sqrt[3]{a+b x^3}\right)}{2 c^{11/3} (b c-a d)^{4/3}}+\frac{d^4 \tan ^{-1}\left(\frac{\frac{2 x \sqrt[3]{b c-a d}}{\sqrt[3]{c} \sqrt[3]{a+b x^3}}+1}{\sqrt{3}}\right)}{\sqrt{3} c^{11/3} (b c-a d)^{4/3}}+\frac{b}{a x^8 \sqrt[3]{a+b x^3} (b c-a d)}",1,"(280*c^6*(a + b*x^3)^2 - 672*c^5*d*x^3*(a + b*x^3)^2 + 3024*c^4*d^2*x^6*(a + b*x^3)^2 + 18144*c^3*d^3*x^9*(a + b*x^3)^2 + 13608*c^2*d^4*x^12*(a + b*x^3)^2 - 280*c^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 672*c^5*d*x^3*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 3024*c^4*d^2*x^6*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 18144*c^3*d^3*x^9*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 13608*c^2*d^4*x^12*(a + b*x^3)^2*Hypergeometric2F1[1/3, 1, 4/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 66*c^4*(b*c - a*d)^2*x^6*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 312*c^3*d*(b*c - a*d)^2*x^9*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2268*c^2*d^2*(b*c - a*d)^2*x^12*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 6696*c*d^3*(b*c - a*d)^2*x^15*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 4050*d^4*(b*c - a*d)^2*x^18*Hypergeometric2F1[2, 7/3, 10/3, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 189*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 108*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 3618*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 6156*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2835*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 7/3}, {1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] + 54*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 648*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2268*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 2376*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 810*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 2, 7/3}, {1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 81*c^4*(b*c - a*d)^2*x^6*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324*c^3*d*(b*c - a*d)^2*x^9*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 486*c^2*d^2*(b*c - a*d)^2*x^12*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 324*c*d^3*(b*c - a*d)^2*x^15*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))] - 81*d^4*(b*c - a*d)^2*x^18*HypergeometricPFQ[{2, 2, 2, 2, 7/3}, {1, 1, 1, 10/3}, ((b*c - a*d)*x^3)/(c*(a + b*x^3))])/(560*c^6*(b*c - a*d)*x^11*(a + b*x^3)^(7/3))","C",2,2,24,0.08333,0,"{511, 510}"
761,1,67,0,0.0577278,"\int \frac{x^{10}}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^10/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^{11} \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{11}{3};\frac{4}{3},1;\frac{14}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{11 a c \sqrt[3]{a+b x^3}}","\frac{x^{11} \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{11}{3};\frac{4}{3},1;\frac{14}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{11 a c \sqrt[3]{a+b x^3}}",1,"(x^11*(1 + (b*x^3)/a)^(1/3)*AppellF1[11/3, 4/3, 1, 14/3, -((b*x^3)/a), -((d*x^3)/c)])/(11*a*c*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
762,1,67,0,0.0567504,"\int \frac{x^7}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^7/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^8 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{8}{3};\frac{4}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 a c \sqrt[3]{a+b x^3}}","\frac{x^8 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{8}{3};\frac{4}{3},1;\frac{11}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{8 a c \sqrt[3]{a+b x^3}}",1,"(x^8*(1 + (b*x^3)/a)^(1/3)*AppellF1[8/3, 4/3, 1, 11/3, -((b*x^3)/a), -((d*x^3)/c)])/(8*a*c*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
763,1,67,0,0.0556653,"\int \frac{x^4}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x^4/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^5 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{5}{3};\frac{4}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 a c \sqrt[3]{a+b x^3}}","\frac{x^5 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{5}{3};\frac{4}{3},1;\frac{8}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{5 a c \sqrt[3]{a+b x^3}}",1,"(x^5*(1 + (b*x^3)/a)^(1/3)*AppellF1[5/3, 4/3, 1, 8/3, -((b*x^3)/a), -((d*x^3)/c)])/(5*a*c*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
764,1,67,0,0.0405861,"\int \frac{x}{\left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[x/((a + b*x^3)^(4/3)*(c + d*x^3)),x]","\frac{x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{4}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a c \sqrt[3]{a+b x^3}}","\frac{x^2 \sqrt[3]{\frac{b x^3}{a}+1} F_1\left(\frac{2}{3};\frac{4}{3},1;\frac{5}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{2 a c \sqrt[3]{a+b x^3}}",1,"(x^2*(1 + (b*x^3)/a)^(1/3)*AppellF1[2/3, 4/3, 1, 5/3, -((b*x^3)/a), -((d*x^3)/c)])/(2*a*c*(a + b*x^3)^(1/3))","A",2,2,22,0.09091,1,"{511, 510}"
765,1,65,0,0.0594091,"\int \frac{1}{x^2 \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x^2*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{1}{3};\frac{4}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c x \sqrt[3]{a+b x^3}}","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{1}{3};\frac{4}{3},1;\frac{2}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{a c x \sqrt[3]{a+b x^3}}",1,"-(((1 + (b*x^3)/a)^(1/3)*AppellF1[-1/3, 4/3, 1, 2/3, -((b*x^3)/a), -((d*x^3)/c)])/(a*c*x*(a + b*x^3)^(1/3)))","A",2,2,24,0.08333,1,"{511, 510}"
766,1,67,0,0.0583748,"\int \frac{1}{x^5 \left(a+b x^3\right)^{4/3} \left(c+d x^3\right)} \, dx","Int[1/(x^5*(a + b*x^3)^(4/3)*(c + d*x^3)),x]","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{4}{3};\frac{4}{3},1;-\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a c x^4 \sqrt[3]{a+b x^3}}","-\frac{\sqrt[3]{\frac{b x^3}{a}+1} F_1\left(-\frac{4}{3};\frac{4}{3},1;-\frac{1}{3};-\frac{b x^3}{a},-\frac{d x^3}{c}\right)}{4 a c x^4 \sqrt[3]{a+b x^3}}",1,"-((1 + (b*x^3)/a)^(1/3)*AppellF1[-4/3, 4/3, 1, -1/3, -((b*x^3)/a), -((d*x^3)/c)])/(4*a*c*x^4*(a + b*x^3)^(1/3))","A",2,2,24,0.08333,1,"{511, 510}"
767,1,90,0,0.0955465,"\int \frac{x^{15}}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^15/((a + b*x^4)*(c + d*x^4)),x]","-\frac{a^3 \log \left(a+b x^4\right)}{4 b^3 (b c-a d)}-\frac{x^4 (a d+b c)}{4 b^2 d^2}+\frac{c^3 \log \left(c+d x^4\right)}{4 d^3 (b c-a d)}+\frac{x^8}{8 b d}","-\frac{a^3 \log \left(a+b x^4\right)}{4 b^3 (b c-a d)}-\frac{x^4 (a d+b c)}{4 b^2 d^2}+\frac{c^3 \log \left(c+d x^4\right)}{4 d^3 (b c-a d)}+\frac{x^8}{8 b d}",1,"-((b*c + a*d)*x^4)/(4*b^2*d^2) + x^8/(8*b*d) - (a^3*Log[a + b*x^4])/(4*b^3*(b*c - a*d)) + (c^3*Log[c + d*x^4])/(4*d^3*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
768,1,70,0,0.0637166,"\int \frac{x^{11}}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^11/((a + b*x^4)*(c + d*x^4)),x]","\frac{a^2 \log \left(a+b x^4\right)}{4 b^2 (b c-a d)}-\frac{c^2 \log \left(c+d x^4\right)}{4 d^2 (b c-a d)}+\frac{x^4}{4 b d}","\frac{a^2 \log \left(a+b x^4\right)}{4 b^2 (b c-a d)}-\frac{c^2 \log \left(c+d x^4\right)}{4 d^2 (b c-a d)}+\frac{x^4}{4 b d}",1,"x^4/(4*b*d) + (a^2*Log[a + b*x^4])/(4*b^2*(b*c - a*d)) - (c^2*Log[c + d*x^4])/(4*d^2*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
769,1,53,0,0.0499208,"\int \frac{x^7}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^7/((a + b*x^4)*(c + d*x^4)),x]","\frac{c \log \left(c+d x^4\right)}{4 d (b c-a d)}-\frac{a \log \left(a+b x^4\right)}{4 b (b c-a d)}","\frac{c \log \left(c+d x^4\right)}{4 d (b c-a d)}-\frac{a \log \left(a+b x^4\right)}{4 b (b c-a d)}",1,"-(a*Log[a + b*x^4])/(4*b*(b*c - a*d)) + (c*Log[c + d*x^4])/(4*d*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
770,1,45,0,0.0314069,"\int \frac{x^3}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^3/((a + b*x^4)*(c + d*x^4)),x]","\frac{\log \left(a+b x^4\right)}{4 (b c-a d)}-\frac{\log \left(c+d x^4\right)}{4 (b c-a d)}","\frac{\log \left(a+b x^4\right)}{4 (b c-a d)}-\frac{\log \left(c+d x^4\right)}{4 (b c-a d)}",1,"Log[a + b*x^4]/(4*(b*c - a*d)) - Log[c + d*x^4]/(4*(b*c - a*d))","A",4,3,22,0.1364,1,"{444, 36, 31}"
771,1,62,0,0.0637304,"\int \frac{1}{x \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x*(a + b*x^4)*(c + d*x^4)),x]","-\frac{b \log \left(a+b x^4\right)}{4 a (b c-a d)}+\frac{d \log \left(c+d x^4\right)}{4 c (b c-a d)}+\frac{\log (x)}{a c}","-\frac{b \log \left(a+b x^4\right)}{4 a (b c-a d)}+\frac{d \log \left(c+d x^4\right)}{4 c (b c-a d)}+\frac{\log (x)}{a c}",1,"Log[x]/(a*c) - (b*Log[a + b*x^4])/(4*a*(b*c - a*d)) + (d*Log[c + d*x^4])/(4*c*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
772,1,87,0,0.0899582,"\int \frac{1}{x^5 \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x^5*(a + b*x^4)*(c + d*x^4)),x]","\frac{b^2 \log \left(a+b x^4\right)}{4 a^2 (b c-a d)}-\frac{\log (x) (a d+b c)}{a^2 c^2}-\frac{d^2 \log \left(c+d x^4\right)}{4 c^2 (b c-a d)}-\frac{1}{4 a c x^4}","\frac{b^2 \log \left(a+b x^4\right)}{4 a^2 (b c-a d)}-\frac{\log (x) (a d+b c)}{a^2 c^2}-\frac{d^2 \log \left(c+d x^4\right)}{4 c^2 (b c-a d)}-\frac{1}{4 a c x^4}",1,"-1/(4*a*c*x^4) - ((b*c + a*d)*Log[x])/(a^2*c^2) + (b^2*Log[a + b*x^4])/(4*a^2*(b*c - a*d)) - (d^2*Log[c + d*x^4])/(4*c^2*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
773,1,112,0,0.2730422,"\int \frac{x^{13}}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^13/((a + b*x^4)*(c + d*x^4)),x]","-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{5/2} (b c-a d)}-\frac{x^2 (a d+b c)}{2 b^2 d^2}+\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 d^{5/2} (b c-a d)}+\frac{x^6}{6 b d}","-\frac{a^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{5/2} (b c-a d)}-\frac{x^2 (a d+b c)}{2 b^2 d^2}+\frac{c^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 d^{5/2} (b c-a d)}+\frac{x^6}{6 b d}",1,"-((b*c + a*d)*x^2)/(2*b^2*d^2) + x^6/(6*b*d) - (a^(5/2)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*b^(5/2)*(b*c - a*d)) + (c^(5/2)*ArcTan[(Sqrt[d]*x^2)/Sqrt[c]])/(2*d^(5/2)*(b*c - a*d))","A",6,5,22,0.2273,1,"{465, 479, 582, 522, 205}"
774,1,92,0,0.1184312,"\int \frac{x^9}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^9/((a + b*x^4)*(c + d*x^4)),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{3/2} (b c-a d)}-\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 d^{3/2} (b c-a d)}+\frac{x^2}{2 b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 b^{3/2} (b c-a d)}-\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 d^{3/2} (b c-a d)}+\frac{x^2}{2 b d}",1,"x^2/(2*b*d) + (a^(3/2)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*b^(3/2)*(b*c - a*d)) - (c^(3/2)*ArcTan[(Sqrt[d]*x^2)/Sqrt[c]])/(2*d^(3/2)*(b*c - a*d))","A",5,4,22,0.1818,1,"{465, 479, 522, 205}"
775,1,79,0,0.0621678,"\int \frac{x^5}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^5/((a + b*x^4)*(c + d*x^4)),x]","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 \sqrt{d} (b c-a d)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{b} (b c-a d)}","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 \sqrt{d} (b c-a d)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{b} (b c-a d)}",1,"-(Sqrt[a]*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[b]*(b*c - a*d)) + (Sqrt[c]*ArcTan[(Sqrt[d]*x^2)/Sqrt[c]])/(2*Sqrt[d]*(b*c - a*d))","A",4,3,22,0.1364,1,"{465, 481, 205}"
776,1,79,0,0.0480111,"\int \frac{x}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x/((a + b*x^4)*(c + d*x^4)),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} (b c-a d)}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 \sqrt{c} (b c-a d)}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 \sqrt{a} (b c-a d)}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 \sqrt{c} (b c-a d)}",1,"(Sqrt[b]*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*Sqrt[a]*(b*c - a*d)) - (Sqrt[d]*ArcTan[(Sqrt[d]*x^2)/Sqrt[c]])/(2*Sqrt[c]*(b*c - a*d))","A",4,3,20,0.1500,1,"{465, 391, 205}"
777,1,92,0,0.1219414,"\int \frac{1}{x^3 \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x^3*(a + b*x^4)*(c + d*x^4)),x]","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 c^{3/2} (b c-a d)}-\frac{1}{2 a c x^2}","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 c^{3/2} (b c-a d)}-\frac{1}{2 a c x^2}",1,"-1/(2*a*c*x^2) - (b^(3/2)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*a^(3/2)*(b*c - a*d)) + (d^(3/2)*ArcTan[(Sqrt[d]*x^2)/Sqrt[c]])/(2*c^(3/2)*(b*c - a*d))","A",5,4,22,0.1818,1,"{465, 480, 522, 205}"
778,1,112,0,0.218099,"\int \frac{1}{x^7 \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x^7*(a + b*x^4)*(c + d*x^4)),x]","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 c^{5/2} (b c-a d)}-\frac{1}{6 a c x^6}","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x^2}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c}}\right)}{2 c^{5/2} (b c-a d)}-\frac{1}{6 a c x^6}",1,"-1/(6*a*c*x^6) + (b*c + a*d)/(2*a^2*c^2*x^2) + (b^(5/2)*ArcTan[(Sqrt[b]*x^2)/Sqrt[a]])/(2*a^(5/2)*(b*c - a*d)) - (d^(5/2)*ArcTan[(Sqrt[d]*x^2)/Sqrt[c]])/(2*c^(5/2)*(b*c - a*d))","A",6,5,22,0.2273,1,"{465, 480, 583, 522, 205}"
779,1,457,0,0.4426114,"\int \frac{x^8}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^8/((a + b*x^4)*(c + d*x^4)),x]","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{5/4} (b c-a d)}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}+\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{5/4} (b c-a d)}+\frac{c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}+\frac{x}{b d}","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{5/4} (b c-a d)}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}+\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{5/4} (b c-a d)}+\frac{c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}+\frac{x}{b d}",1,"x/(b*d) - (a^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(5/4)*(b*c - a*d)) + (a^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(5/4)*(b*c - a*d)) + (c^(5/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*d^(5/4)*(b*c - a*d)) - (c^(5/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*d^(5/4)*(b*c - a*d)) - (a^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(5/4)*(b*c - a*d)) + (a^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(5/4)*(b*c - a*d)) + (c^(5/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*d^(5/4)*(b*c - a*d)) - (c^(5/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*d^(5/4)*(b*c - a*d))","A",20,8,22,0.3636,1,"{479, 522, 211, 1165, 628, 1162, 617, 204}"
780,1,449,0,0.2847637,"\int \frac{x^6}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^6/((a + b*x^4)*(c + d*x^4)),x]","-\frac{a^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}+\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}+\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}","-\frac{a^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}+\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}+\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}",1,"(a^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(3/4)*(b*c - a*d)) - (a^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(3/4)*(b*c - a*d)) - (c^(3/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*d^(3/4)*(b*c - a*d)) + (c^(3/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*d^(3/4)*(b*c - a*d)) - (a^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(3/4)*(b*c - a*d)) + (a^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(3/4)*(b*c - a*d)) + (c^(3/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*d^(3/4)*(b*c - a*d)) - (c^(3/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*d^(3/4)*(b*c - a*d))","A",19,7,22,0.3182,1,"{481, 297, 1162, 617, 204, 1165, 628}"
781,1,449,0,0.2742678,"\int \frac{x^4}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^4/((a + b*x^4)*(c + d*x^4)),x]","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}",1,"(a^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(1/4)*(b*c - a*d)) - (a^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*b^(1/4)*(b*c - a*d)) - (c^(1/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*d^(1/4)*(b*c - a*d)) + (c^(1/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*d^(1/4)*(b*c - a*d)) + (a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(1/4)*(b*c - a*d)) - (a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*b^(1/4)*(b*c - a*d)) - (c^(1/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*d^(1/4)*(b*c - a*d)) + (c^(1/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*d^(1/4)*(b*c - a*d))","A",19,7,22,0.3182,1,"{481, 211, 1165, 628, 1162, 617, 204}"
782,1,449,0,0.2700486,"\int \frac{x^2}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[x^2/((a + b*x^4)*(c + d*x^4)),x]","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)}+\frac{\sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)}+\frac{\sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}",1,"-(b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)) + (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)) + (d^(1/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(1/4)*(b*c - a*d)) - (d^(1/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(1/4)*(b*c - a*d)) + (b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(1/4)*(b*c - a*d)) - (b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(1/4)*(b*c - a*d)) - (d^(1/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(1/4)*(b*c - a*d)) + (d^(1/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(1/4)*(b*c - a*d))","A",19,7,22,0.3182,1,"{482, 297, 1162, 617, 204, 1165, 628}"
783,1,449,0,0.2591827,"\int \frac{1}{\left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/((a + b*x^4)*(c + d*x^4)),x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}-\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{d^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}+\frac{d^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{3/4} (b c-a d)}-\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{d^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{3/4} (b c-a d)}+\frac{d^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}",1,"-(b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (d^(3/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (d^(3/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (d^(3/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (d^(3/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d))","A",19,7,19,0.3684,1,"{391, 211, 1165, 628, 1162, 617, 204}"
784,1,460,0,0.4450536,"\int \frac{1}{x^2 \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x^2*(a + b*x^4)*(c + d*x^4)),x]","-\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}+\frac{d^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}+\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}-\frac{1}{a c x}","-\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}+\frac{d^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}+\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}-\frac{1}{a c x}",1,"-(1/(a*c*x)) + (b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)) - (b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)) - (d^(5/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(5/4)*(b*c - a*d)) + (d^(5/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(5/4)*(b*c - a*d)) - (b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)) + (b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)) + (d^(5/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(5/4)*(b*c - a*d)) - (d^(5/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(5/4)*(b*c - a*d))","A",21,8,22,0.3636,1,"{480, 584, 297, 1162, 617, 204, 1165, 628}"
785,1,462,0,0.4320138,"\int \frac{1}{x^4 \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x^4*(a + b*x^4)*(c + d*x^4)),x]","\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{7/4} (b c-a d)}+\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}-\frac{d^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{7/4} (b c-a d)}-\frac{d^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}-\frac{1}{3 a c x^3}","\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{7/4} (b c-a d)}+\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}-\frac{d^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{7/4} (b c-a d)}-\frac{d^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}-\frac{1}{3 a c x^3}",1,"-1/(3*a*c*x^3) + (b^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)) - (b^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)) - (d^(7/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(7/4)*(b*c - a*d)) + (d^(7/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(7/4)*(b*c - a*d)) + (b^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(7/4)*(b*c - a*d)) - (b^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(7/4)*(b*c - a*d)) - (d^(7/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(7/4)*(b*c - a*d)) + (d^(7/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(7/4)*(b*c - a*d))","A",20,8,22,0.3636,1,"{480, 522, 211, 1165, 628, 1162, 617, 204}"
786,1,479,0,0.5965419,"\int \frac{1}{x^6 \left(a+b x^4\right) \left(c+d x^4\right)} \, dx","Int[1/(x^6*(a + b*x^4)*(c + d*x^4)),x]","\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}+\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}-\frac{d^{9/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}-\frac{d^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}-\frac{1}{5 a c x^5}","\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} x+\sqrt{a}+\sqrt{b} x^2\right)}{4 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}+\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} x}{\sqrt[4]{a}}+1\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}-\frac{d^{9/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} x+\sqrt{c}+\sqrt{d} x^2\right)}{4 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}-\frac{d^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} x}{\sqrt[4]{c}}+1\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}-\frac{1}{5 a c x^5}",1,"-1/(5*a*c*x^5) + (b*c + a*d)/(a^2*c^2*x) - (b^(9/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)) + (b^(9/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*x)/a^(1/4)])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)) + (d^(9/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(9/4)*(b*c - a*d)) - (d^(9/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*x)/c^(1/4)])/(2*Sqrt[2]*c^(9/4)*(b*c - a*d)) + (b^(9/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(9/4)*(b*c - a*d)) - (b^(9/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*x + Sqrt[b]*x^2])/(4*Sqrt[2]*a^(9/4)*(b*c - a*d)) - (d^(9/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(9/4)*(b*c - a*d)) + (d^(9/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*x + Sqrt[d]*x^2])/(4*Sqrt[2]*c^(9/4)*(b*c - a*d))","A",22,9,22,0.4091,1,"{480, 583, 584, 297, 1162, 617, 204, 1165, 628}"
787,1,93,0,0.0824442,"\int \frac{x^7 \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x^7*Sqrt[c + d*x^4])/(a + b*x^4),x]","-\frac{a \sqrt{c+d x^4}}{2 b^2}+\frac{a \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{5/2}}+\frac{\left(c+d x^4\right)^{3/2}}{6 b d}","-\frac{a \sqrt{c+d x^4}}{2 b^2}+\frac{a \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{5/2}}+\frac{\left(c+d x^4\right)^{3/2}}{6 b d}",1,"-(a*Sqrt[c + d*x^4])/(2*b^2) + (c + d*x^4)^(3/2)/(6*b*d) + (a*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*b^(5/2))","A",5,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
788,1,120,0,0.1542384,"\int \frac{x^5 \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x^5*Sqrt[c + d*x^4])/(a + b*x^4),x]","-\frac{\sqrt{a} \sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 b^2}+\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{4 b^2 \sqrt{d}}+\frac{x^2 \sqrt{c+d x^4}}{4 b}","-\frac{\sqrt{a} \sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 b^2}+\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{4 b^2 \sqrt{d}}+\frac{x^2 \sqrt{c+d x^4}}{4 b}",1,"(x^2*Sqrt[c + d*x^4])/(4*b) - (Sqrt[a]*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*b^2) + ((b*c - 2*a*d)*ArcTanh[(Sqrt[d]*x^2)/Sqrt[c + d*x^4]])/(4*b^2*Sqrt[d])","A",7,7,24,0.2917,1,"{465, 478, 523, 217, 206, 377, 205}"
789,1,70,0,0.0610729,"\int \frac{x^3 \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x^3*Sqrt[c + d*x^4])/(a + b*x^4),x]","\frac{\sqrt{c+d x^4}}{2 b}-\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{3/2}}","\frac{\sqrt{c+d x^4}}{2 b}-\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{3/2}}",1,"Sqrt[c + d*x^4]/(2*b) - (Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*b^(3/2))","A",4,4,24,0.1667,1,"{444, 50, 63, 208}"
790,1,91,0,0.0763402,"\int \frac{x \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x*Sqrt[c + d*x^4])/(a + b*x^4),x]","\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 \sqrt{a} b}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{2 b}","\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 \sqrt{a} b}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{2 b}",1,"(Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*Sqrt[a]*b) + (Sqrt[d]*ArcTanh[(Sqrt[d]*x^2)/Sqrt[c + d*x^4]])/(2*b)","A",6,6,22,0.2727,1,"{465, 402, 217, 206, 377, 205}"
791,1,85,0,0.0746659,"\int \frac{\sqrt{c+d x^4}}{x \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(x*(a + b*x^4)),x]","\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a \sqrt{b}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{2 a}","\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a \sqrt{b}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{2 a}",1,"-(Sqrt[c]*ArcTanh[Sqrt[c + d*x^4]/Sqrt[c]])/(2*a) + (Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*a*Sqrt[b])","A",6,4,24,0.1667,1,"{446, 83, 63, 208}"
792,1,76,0,0.0862588,"\int \frac{\sqrt{c+d x^4}}{x^3 \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(x^3*(a + b*x^4)),x]","-\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{3/2}}-\frac{\sqrt{c+d x^4}}{2 a x^2}","-\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{3/2}}-\frac{\sqrt{c+d x^4}}{2 a x^2}",1,"-Sqrt[c + d*x^4]/(2*a*x^2) - (Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*a^(3/2))","A",5,5,24,0.2083,1,"{465, 475, 12, 377, 205}"
793,1,115,0,0.1237268,"\int \frac{\sqrt{c+d x^4}}{x^5 \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(x^5*(a + b*x^4)),x]","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{4 a^2 \sqrt{c}}-\frac{\sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a^2}-\frac{\sqrt{c+d x^4}}{4 a x^4}","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{4 a^2 \sqrt{c}}-\frac{\sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a^2}-\frac{\sqrt{c+d x^4}}{4 a x^4}",1,"-Sqrt[c + d*x^4]/(4*a*x^4) + ((2*b*c - a*d)*ArcTanh[Sqrt[c + d*x^4]/Sqrt[c]])/(4*a^2*Sqrt[c]) - (Sqrt[b]*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*a^2)","A",7,5,24,0.2083,1,"{446, 99, 156, 63, 208}"
794,1,110,0,0.1597596,"\int \frac{\sqrt{c+d x^4}}{x^7 \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(x^7*(a + b*x^4)),x]","\frac{\sqrt{c+d x^4} (3 b c-a d)}{6 a^2 c x^2}+\frac{b \sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{5/2}}-\frac{\sqrt{c+d x^4}}{6 a x^6}","\frac{\sqrt{c+d x^4} (3 b c-a d)}{6 a^2 c x^2}+\frac{b \sqrt{b c-a d} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{5/2}}-\frac{\sqrt{c+d x^4}}{6 a x^6}",1,"-Sqrt[c + d*x^4]/(6*a*x^6) + ((3*b*c - a*d)*Sqrt[c + d*x^4])/(6*a^2*c*x^2) + (b*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*a^(5/2))","A",6,6,24,0.2500,1,"{465, 475, 583, 12, 377, 205}"
795,1,1067,0,1.85504,"\int \frac{x^6 \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x^6*Sqrt[c + d*x^4])/(a + b*x^4),x]","\frac{\sqrt{d x^4+c} x^3}{5 b}+\frac{(2 b c-5 a d) \sqrt{d x^4+c} x}{5 b^2 \sqrt{d} \left(\sqrt{d} x^2+\sqrt{c}\right)}+\frac{(-a)^{3/4} \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{9/4}}+\frac{(-a)^{3/4} \sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{9/4}}-\frac{\sqrt[4]{c} (2 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{5 b^2 d^{3/4} \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} (2 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{10 b^2 d^{3/4} \sqrt{d x^4+c}}+\frac{a \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{a \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{-a} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{-a} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}","\frac{\sqrt{d x^4+c} x^3}{5 b}+\frac{(2 b c-5 a d) \sqrt{d x^4+c} x}{5 b^2 \sqrt{d} \left(\sqrt{d} x^2+\sqrt{c}\right)}-\frac{a \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 b^2}-\frac{a \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 b^2}-\frac{\sqrt[4]{c} (2 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{5 b^2 d^{3/4} \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} \left(b^2 c^2+a b d c-5 a^2 d^2\right) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{5 b^2 d^{3/4} (b c+a d) \sqrt{d x^4+c}}+\frac{a \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{5/2} \sqrt[4]{c} \left(\sqrt{-a} \sqrt{b} \sqrt{c}-a \sqrt{d}\right) \sqrt[4]{d} \sqrt{d x^4+c}}-\frac{a \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\sqrt{c} \left(\sqrt{b}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{c}}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{5/2} \sqrt[4]{c} \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \sqrt{d x^4+c}}",1,"(x^3*Sqrt[c + d*x^4])/(5*b) + ((2*b*c - 5*a*d)*x*Sqrt[c + d*x^4])/(5*b^2*Sqrt[d]*(Sqrt[c] + Sqrt[d]*x^2)) + ((-a)^(3/4)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(9/4)) + ((-a)^(3/4)*Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(9/4)) - (c^(1/4)*(2*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(5*b^2*d^(3/4)*Sqrt[c + d*x^4]) + (c^(1/4)*(2*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(10*b^2*d^(3/4)*Sqrt[c + d*x^4]) + (a*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (a*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (Sqrt[-a]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^(5/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (Sqrt[-a]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^(5/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",13,8,24,0.3333,0,"{478, 584, 305, 220, 1196, 490, 1217, 1707}"
796,1,904,0,1.2478982,"\int \frac{x^4 \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x^4*Sqrt[c + d*x^4])/(a + b*x^4),x]","-\frac{(b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{-a} \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{-a} \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{7/4}}+\frac{\sqrt[4]{-a} \sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{7/4}}+\frac{(2 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{6 b^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{d x^4+c}}-\frac{a \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{x \sqrt{d x^4+c}}{3 b}","-\frac{(b c-a d) \tan ^{-1}\left(\frac{x \sqrt{\frac{\sqrt{-a} \left(\frac{b c}{a}-d\right)}{\sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 b^2 \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 b^2 \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) (b c-a d) \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) (b c-a d) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)}+\frac{c^{3/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} (b c-2 a d) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{3 b \sqrt[4]{d} \sqrt{c+d x^4} (a d+b c)}+\frac{x \sqrt{c+d x^4}}{3 b}",1,"(x*Sqrt[c + d*x^4])/(3*b) - ((-a)^(1/4)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(7/4)) + ((-a)^(1/4)*Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(7/4)) + ((2*b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(6*b^2*c^(1/4)*d^(1/4)*Sqrt[c + d*x^4]) - (a*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (Sqrt[-a]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",10,6,24,0.2500,0,"{478, 523, 220, 409, 1217, 1707}"
797,1,1012,0,1.037877,"\int \frac{x^2 \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(x^2*Sqrt[c + d*x^4])/(a + b*x^4),x]","-\frac{(b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 \sqrt[4]{-a} b^{5/4}}+\frac{\sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 \sqrt[4]{-a} b^{5/4}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{b \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{d} x \sqrt{d x^4+c}}{b \left(\sqrt{d} x^2+\sqrt{c}\right)}","-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) (b c-a d) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{b} \sqrt{c}-a \sqrt{d}\right)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) (b c-a d) \Pi \left(-\frac{\sqrt{c} \left(\sqrt{b}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{c}}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{b} \sqrt{c}+a \sqrt{d}\right)}+\frac{a \sqrt[4]{c} d^{5/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{b \sqrt{c+d x^4} (a d+b c)}+\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{x \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 b}+\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 b}+\frac{\sqrt{d} x \sqrt{c+d x^4}}{b \left(\sqrt{c}+\sqrt{d} x^2\right)}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{b \sqrt{c+d x^4}}",1,"(Sqrt[d]*x*Sqrt[c + d*x^4])/(b*(Sqrt[c] + Sqrt[d]*x^2)) + (Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(1/4)*b^(5/4)) + (Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(1/4)*b^(5/4)) - (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(b*Sqrt[c + d*x^4]) + (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(2*b*Sqrt[c + d*x^4]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*Sqrt[-a]*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*Sqrt[-a]*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",11,7,24,0.2917,0,"{491, 305, 220, 1196, 490, 1217, 1707}"
798,1,881,0,0.9782004,"\int \frac{\sqrt{c+d x^4}}{a+b x^4} \, dx","Int[Sqrt[c + d*x^4]/(a + b*x^4),x]","\frac{(b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 a b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{4 \sqrt{-a} b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{3/4} b^{3/4}}+\frac{\sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{3/4} b^{3/4}}+\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b \sqrt[4]{c} \sqrt{d x^4+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}","\frac{c^{3/4} d^{3/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{\sqrt{c+d x^4} (a d+b c)}+\frac{(b c-a d) \tan ^{-1}\left(\frac{x \sqrt{\frac{\sqrt{-a} \left(\frac{b c}{a}-d\right)}{\sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a b \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}+\frac{(b c-a d) \tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a b \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) (b c-a d) \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a b \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) (b c-a d) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a b \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)}",1,"-(Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(3/4)*b^(3/4)) + (Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(3/4)*b^(3/4)) + (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(2*b*c^(1/4)*Sqrt[c + d*x^4]) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*Sqrt[-a]*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a*b*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a*b*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",9,5,21,0.2381,0,"{406, 220, 409, 1217, 1707}"
799,1,1031,0,1.5064705,"\int \frac{\sqrt{c+d x^4}}{x^2 \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(x^2*(a + b*x^4)),x]","-\frac{(b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{5/4} \sqrt[4]{b}}+\frac{\sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{5/4} \sqrt[4]{b}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{a \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 a \sqrt{d x^4+c}}+\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{d x^4+c}}{a x}+\frac{\sqrt{d} x \sqrt{d x^4+c}}{a \left(\sqrt{d} x^2+\sqrt{c}\right)}","\frac{b \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) c^{5/4}}{a (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \sqrt[4]{c}}{a \sqrt{d x^4+c}}-\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 a}-\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 a}-\frac{\sqrt{d x^4+c}}{a x}+\frac{\sqrt{d} x \sqrt{d x^4+c}}{a \left(\sqrt{d} x^2+\sqrt{c}\right)}-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt{b} \left(\sqrt{d} a^2+(-a)^{3/2} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \sqrt{d x^4+c} \sqrt[4]{c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\sqrt{c} \left(\sqrt{b}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{c}}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt{b} \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \sqrt{d x^4+c} \sqrt[4]{c}}",1,"-(Sqrt[c + d*x^4]/(a*x)) + (Sqrt[d]*x*Sqrt[c + d*x^4])/(a*(Sqrt[c] + Sqrt[d]*x^2)) + (Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(5/4)*b^(1/4)) + (Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(5/4)*b^(1/4)) - (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(a*Sqrt[c + d*x^4]) + (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(2*a*Sqrt[c + d*x^4]) + ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*(-a)^(3/2)*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*(-a)^(3/2)*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",13,8,24,0.3333,0,"{475, 584, 305, 220, 1196, 490, 1217, 1707}"
800,1,893,0,1.1904603,"\int \frac{\sqrt{c+d x^4}}{x^4 \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(x^4*(a + b*x^4)),x]","-\frac{(b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{4 (-a)^{3/2} \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{b} \sqrt{b c-a d} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{7/4}}+\frac{\sqrt[4]{b} \sqrt{a d-b c} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{7/4}}-\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{6 a \sqrt[4]{c} \sqrt{d x^4+c}}-\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{d x^4+c}}{3 a x^3}","-\frac{(b c-a d) \tan ^{-1}\left(\frac{x \sqrt{\frac{\sqrt{-a} \left(\frac{b c}{a}-d\right)}{\sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a^2 \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{(b c-a d) \tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a^2 \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) (b c-a d) \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) (b c-a d) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)}-\frac{d^{3/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} (2 b c-a d) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{3 a \sqrt[4]{c} \sqrt{c+d x^4} (a d+b c)}-\frac{\sqrt{c+d x^4}}{3 a x^3}",1,"-Sqrt[c + d*x^4]/(3*a*x^3) - (b^(1/4)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(7/4)) + (b^(1/4)*Sqrt[-(b*c) + a*d]*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(7/4)) - (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(6*a*c^(1/4)*Sqrt[c + d*x^4]) - (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*(-a)^(3/2)*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",10,6,24,0.2500,0,"{475, 523, 220, 409, 1217, 1707}"
801,1,71,0,0.11706,"\int \frac{(e x)^{3/2} \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[((e*x)^(3/2)*Sqrt[c + d*x^4])/(a + b*x^4),x]","\frac{2 (e x)^{5/2} \sqrt{c+d x^4} F_1\left(\frac{5}{8};1,-\frac{1}{2};\frac{13}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{5 a e \sqrt{\frac{d x^4}{c}+1}}","\frac{2 (e x)^{5/2} \sqrt{c+d x^4} F_1\left(\frac{5}{8};1,-\frac{1}{2};\frac{13}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{5 a e \sqrt{\frac{d x^4}{c}+1}}",1,"(2*(e*x)^(5/2)*Sqrt[c + d*x^4]*AppellF1[5/8, 1, -1/2, 13/8, -((b*x^4)/a), -((d*x^4)/c)])/(5*a*e*Sqrt[1 + (d*x^4)/c])","A",3,3,28,0.1071,1,"{466, 511, 510}"
802,1,71,0,0.1144217,"\int \frac{\sqrt{e x} \sqrt{c+d x^4}}{a+b x^4} \, dx","Int[(Sqrt[e*x]*Sqrt[c + d*x^4])/(a + b*x^4),x]","\frac{2 (e x)^{3/2} \sqrt{c+d x^4} F_1\left(\frac{3}{8};1,-\frac{1}{2};\frac{11}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{3 a e \sqrt{\frac{d x^4}{c}+1}}","\frac{2 (e x)^{3/2} \sqrt{c+d x^4} F_1\left(\frac{3}{8};1,-\frac{1}{2};\frac{11}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{3 a e \sqrt{\frac{d x^4}{c}+1}}",1,"(2*(e*x)^(3/2)*Sqrt[c + d*x^4]*AppellF1[3/8, 1, -1/2, 11/8, -((b*x^4)/a), -((d*x^4)/c)])/(3*a*e*Sqrt[1 + (d*x^4)/c])","A",3,3,28,0.1071,1,"{466, 511, 510}"
803,1,69,0,0.0729746,"\int \frac{\sqrt{c+d x^4}}{\sqrt{e x} \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/(Sqrt[e*x]*(a + b*x^4)),x]","\frac{2 \sqrt{e x} \sqrt{c+d x^4} F_1\left(\frac{1}{8};1,-\frac{1}{2};\frac{9}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a e \sqrt{\frac{d x^4}{c}+1}}","\frac{2 \sqrt{e x} \sqrt{c+d x^4} F_1\left(\frac{1}{8};1,-\frac{1}{2};\frac{9}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a e \sqrt{\frac{d x^4}{c}+1}}",1,"(2*Sqrt[e*x]*Sqrt[c + d*x^4]*AppellF1[1/8, 1, -1/2, 9/8, -((b*x^4)/a), -((d*x^4)/c)])/(a*e*Sqrt[1 + (d*x^4)/c])","A",3,3,28,0.1071,1,"{466, 430, 429}"
804,1,69,0,0.1186794,"\int \frac{\sqrt{c+d x^4}}{(e x)^{3/2} \left(a+b x^4\right)} \, dx","Int[Sqrt[c + d*x^4]/((e*x)^(3/2)*(a + b*x^4)),x]","-\frac{2 \sqrt{c+d x^4} F_1\left(-\frac{1}{8};1,-\frac{1}{2};\frac{7}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a e \sqrt{e x} \sqrt{\frac{d x^4}{c}+1}}","-\frac{2 \sqrt{c+d x^4} F_1\left(-\frac{1}{8};1,-\frac{1}{2};\frac{7}{8};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a e \sqrt{e x} \sqrt{\frac{d x^4}{c}+1}}",1,"(-2*Sqrt[c + d*x^4]*AppellF1[-1/8, 1, -1/2, 7/8, -((b*x^4)/a), -((d*x^4)/c)])/(a*e*Sqrt[e*x]*Sqrt[1 + (d*x^4)/c])","A",3,3,28,0.1071,1,"{466, 511, 510}"
805,1,104,0,0.1117932,"\int \frac{x^{11}}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^11/((a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^4} (a d+b c)}{2 b^2 d^2}+\frac{\left(c+d x^4\right)^{3/2}}{6 b d^2}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^4} (a d+b c)}{2 b^2 d^2}+\frac{\left(c+d x^4\right)^{3/2}}{6 b d^2}",1,"-((b*c + a*d)*Sqrt[c + d*x^4])/(2*b^2*d^2) + (c + d*x^4)^(3/2)/(6*b*d^2) - (a^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*b^(5/2)*Sqrt[b*c - a*d])","A",5,4,24,0.1667,1,"{446, 88, 63, 208}"
806,1,74,0,0.0648049,"\int \frac{x^7}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^7/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^4}}{2 b d}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^4}}{2 b d}",1,"Sqrt[c + d*x^4]/(2*b*d) + (a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*b^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{446, 80, 63, 208}"
807,1,51,0,0.0485695,"\int \frac{x^3}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^3/((a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 \sqrt{b} \sqrt{b c-a d}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 \sqrt{b} \sqrt{b c-a d}}",1,"-ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]]/(2*Sqrt[b]*Sqrt[b*c - a*d])","A",3,3,24,0.1250,1,"{444, 63, 208}"
808,1,85,0,0.0731661,"\int \frac{1}{x \left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/(x*(a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{2 a \sqrt{c}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{2 a \sqrt{c}}",1,"-ArcTanh[Sqrt[c + d*x^4]/Sqrt[c]]/(2*a*Sqrt[c]) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*a*Sqrt[b*c - a*d])","A",6,4,24,0.1667,1,"{446, 86, 63, 208}"
809,1,117,0,0.1199909,"\int \frac{1}{x^5 \left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/(x^5*(a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{4 a^2 c^{3/2}}-\frac{\sqrt{c+d x^4}}{4 a c x^4}","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{2 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{4 a^2 c^{3/2}}-\frac{\sqrt{c+d x^4}}{4 a c x^4}",1,"-Sqrt[c + d*x^4]/(4*a*c*x^4) + ((2*b*c + a*d)*ArcTanh[Sqrt[c + d*x^4]/Sqrt[c]])/(4*a^2*c^(3/2)) - (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(2*a^2*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
810,1,123,0,0.1491093,"\int \frac{x^9}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^9/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{4 b^2 d^{3/2}}+\frac{x^2 \sqrt{c+d x^4}}{4 b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{4 b^2 d^{3/2}}+\frac{x^2 \sqrt{c+d x^4}}{4 b d}",1,"(x^2*Sqrt[c + d*x^4])/(4*b*d) + (a^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*b^2*Sqrt[b*c - a*d]) - ((b*c + 2*a*d)*ArcTanh[(Sqrt[d]*x^2)/Sqrt[c + d*x^4]])/(4*b^2*d^(3/2))","A",7,7,24,0.2917,1,"{465, 479, 523, 217, 206, 377, 205}"
811,1,91,0,0.0874657,"\int \frac{x^5}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^5/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{2 b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 b \sqrt{b c-a d}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{2 b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 b \sqrt{b c-a d}}",1,"-(Sqrt[a]*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*b*Sqrt[b*c - a*d]) + ArcTanh[(Sqrt[d]*x^2)/Sqrt[c + d*x^4]]/(2*b*Sqrt[d])","A",6,6,24,0.2500,1,"{465, 483, 217, 206, 377, 205}"
812,1,54,0,0.0436755,"\int \frac{x}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{\tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 \sqrt{a} \sqrt{b c-a d}}","\frac{\tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 \sqrt{a} \sqrt{b c-a d}}",1,"ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])]/(2*Sqrt[a]*Sqrt[b*c - a*d])","A",3,3,22,0.1364,1,"{465, 377, 205}"
813,1,80,0,0.0880034,"\int \frac{1}{x^3 \left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/(x^3*(a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{b \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^4}}{2 a c x^2}","-\frac{b \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^4}}{2 a c x^2}",1,"-Sqrt[c + d*x^4]/(2*a*c*x^2) - (b*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*a^(3/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{465, 480, 12, 377, 205}"
814,1,115,0,0.1635564,"\int \frac{1}{x^7 \left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/(x^7*(a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{b^2 \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^4} (2 a d+3 b c)}{6 a^2 c^2 x^2}-\frac{\sqrt{c+d x^4}}{6 a c x^6}","\frac{b^2 \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{2 a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^4} (2 a d+3 b c)}{6 a^2 c^2 x^2}-\frac{\sqrt{c+d x^4}}{6 a c x^6}",1,"-Sqrt[c + d*x^4]/(6*a*c*x^6) + ((3*b*c + 2*a*d)*Sqrt[c + d*x^4])/(6*a^2*c^2*x^2) + (b^2*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(2*a^(5/2)*Sqrt[b*c - a*d])","A",6,6,24,0.2500,1,"{465, 480, 583, 12, 377, 205}"
815,1,872,0,1.0190273,"\int \frac{x^8}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^8/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a^2}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{(-a)^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{7/4} \sqrt{b c-a d}}-\frac{(-a)^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{7/4} \sqrt{a d-b c}}-\frac{(b c+3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{6 b^2 \sqrt[4]{c} d^{5/4} \sqrt{d x^4+c}}+\frac{x \sqrt{d x^4+c}}{3 b d}","\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a^2}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a}{4 b^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) a}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{(-a)^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{7/4} \sqrt{b c-a d}}-\frac{(-a)^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{7/4} \sqrt{a d-b c}}-\frac{(b c+3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{6 b^2 \sqrt[4]{c} d^{5/4} \sqrt{d x^4+c}}+\frac{x \sqrt{d x^4+c}}{3 b d}",1,"(x*Sqrt[c + d*x^4])/(3*b*d) - ((-a)^(5/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(7/4)*Sqrt[b*c - a*d]) - ((-a)^(5/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(7/4)*Sqrt[-(b*c) + a*d]) + (a^2*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (a*(Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((b*c + 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(6*b^2*c^(1/4)*d^(5/4)*Sqrt[c + d*x^4]) + (a*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (a*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",10,6,24,0.2500,1,"{479, 523, 220, 409, 1217, 1707}"
816,1,837,0,0.6815986,"\int \frac{x^4}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^4/((a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{\left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{-a} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{-a} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{3/4} \sqrt{a d-b c}}+\frac{\left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b \sqrt[4]{c} \sqrt[4]{d} \sqrt{d x^4+c}}-\frac{a \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}","\frac{c^{3/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{d} \sqrt{c+d x^4} (a d+b c)}-\frac{\tan ^{-1}\left(\frac{x \sqrt{\frac{\sqrt{-a} \left(\frac{b c}{a}-d\right)}{\sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 b \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{\tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 b \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)}",1,"-((-a)^(1/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(3/4)*Sqrt[b*c - a*d]) - ((-a)^(1/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(3/4)*Sqrt[-(b*c) + a*d]) + ((Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(2*b*c^(1/4)*d^(1/4)*Sqrt[c + d*x^4]) - (a*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",9,5,24,0.2083,0,"{483, 220, 409, 1217, 1707}"
817,1,742,0,0.6015648,"\int \frac{1}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/((a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^4}}\right)}{4 (-a)^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{x \sqrt{a d-b c}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^4}}\right)}{4 (-a)^{3/4} \sqrt{a d-b c}}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} \sqrt{c+d x^4} (a d+b c)}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{b} \sqrt{c}+a \sqrt{d}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} \sqrt{c+d x^4} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} (a d+b c)}","\frac{d^{3/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{c} \sqrt{c+d x^4} (a d+b c)}+\frac{\tan ^{-1}\left(\frac{x \sqrt{\frac{\sqrt{-a} \left(\frac{b c}{a}-d\right)}{\sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}+\frac{\tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)}",1,"-(b^(1/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(3/4)*Sqrt[b*c - a*d]) - (b^(1/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(3/4)*Sqrt[-(b*c) + a*d]) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",7,4,21,0.1905,0,"{409, 1217, 220, 1707}"
818,1,864,0,0.991279,"\int \frac{1}{x^4 \left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/(x^4*(a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{b \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{7/4} \sqrt{b c-a d}}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{7/4} \sqrt{a d-b c}}-\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{6 a c^{5/4} \sqrt{d x^4+c}}-\frac{b \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{b \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{d x^4+c}}{3 a c x^3}","-\frac{b \tan ^{-1}\left(\frac{x \sqrt{\frac{\sqrt{-a} \left(\frac{b c}{a}-d\right)}{\sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a^2 \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{b \tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 a^2 \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}-\frac{b \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}-\frac{b \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)}-\frac{d^{3/4} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} (a d+4 b c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{6 a c^{5/4} \sqrt{c+d x^4} (a d+b c)}-\frac{\sqrt{c+d x^4}}{3 a c x^3}",1,"-Sqrt[c + d*x^4]/(3*a*c*x^3) - (b^(5/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(7/4)*Sqrt[b*c - a*d]) - (b^(5/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(7/4)*Sqrt[-(b*c) + a*d]) - (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(6*a*c^(5/4)*Sqrt[c + d*x^4]) - (b*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (b*(Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (b*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (b*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",10,6,24,0.2500,0,"{480, 523, 220, 409, 1217, 1707}"
819,1,982,0,0.9629569,"\int \frac{x^6}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^6/((a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{\sqrt{-a} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{(-a)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{5/4} \sqrt{b c-a d}}-\frac{(-a)^{3/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 b^{5/4} \sqrt{a d-b c}}-\frac{\sqrt[4]{c} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{b d^{3/4} \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b d^{3/4} \sqrt{d x^4+c}}+\frac{a \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{a \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{-a} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{x \sqrt{d x^4+c}}{b \sqrt{d} \left(\sqrt{d} x^2+\sqrt{c}\right)}","\frac{\sqrt{d x^4+c} x}{b \sqrt{d} \left(\sqrt{d} x^2+\sqrt{c}\right)}-\frac{a \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 b (b c-a d)}-\frac{a \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 b (b c-a d)}-\frac{\sqrt[4]{c} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{b d^{3/4} \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} (b c+2 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b d^{3/4} (b c+a d) \sqrt{d x^4+c}}+\frac{a \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{3/2} \sqrt[4]{c} \left(\sqrt{-a} \sqrt{b} \sqrt{c}-a \sqrt{d}\right) \sqrt[4]{d} \sqrt{d x^4+c}}-\frac{a \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\sqrt{c} \left(\sqrt{b}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{c}}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^{3/2} \sqrt[4]{c} \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \sqrt{d x^4+c}}",1,"(x*Sqrt[c + d*x^4])/(b*Sqrt[d]*(Sqrt[c] + Sqrt[d]*x^2)) + ((-a)^(3/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(5/4)*Sqrt[b*c - a*d]) - ((-a)^(3/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*b^(5/4)*Sqrt[-(b*c) + a*d]) - (c^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(b*d^(3/4)*Sqrt[c + d*x^4]) + (c^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(2*b*d^(3/4)*Sqrt[c + d*x^4]) + (a*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (a*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (Sqrt[-a]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (Sqrt[-a]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",11,7,24,0.2917,0,"{483, 305, 220, 1196, 490, 1217, 1707}"
820,1,756,0,0.7095625,"\int \frac{x^2}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[x^2/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^4}}\right)}{4 \sqrt[4]{-a} \sqrt[4]{b} \sqrt{b c-a d}}-\frac{\tan ^{-1}\left(\frac{x \sqrt{a d-b c}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^4}}\right)}{4 \sqrt[4]{-a} \sqrt[4]{b} \sqrt{a d-b c}}-\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} \sqrt{c+d x^4} (a d+b c)}-\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 \sqrt[4]{c} \sqrt{c+d x^4} (a d+b c)}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt{-a} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt{-a} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} (a d+b c)}","\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{x \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 (b c-a d)}+\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{x \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}}}{\sqrt{c+d x^4}}\right)}{4 (b c-a d)}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 \sqrt{c+d x^4} (a d+b c)}-\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right) \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{b} \sqrt{c}-a \sqrt{d}\right)}+\frac{\left(\sqrt{c}+\sqrt{d} x^2\right) \sqrt{\frac{c+d x^4}{\left(\sqrt{c}+\sqrt{d} x^2\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right) \Pi \left(-\frac{\sqrt{c} \left(\sqrt{b}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{c}}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^4} \left(\sqrt{-a} \sqrt{b} \sqrt{c}+a \sqrt{d}\right)}",1,"ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])]/(4*(-a)^(1/4)*b^(1/4)*Sqrt[b*c - a*d]) - ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])]/(4*(-a)^(1/4)*b^(1/4)*Sqrt[-(b*c) + a*d]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*Sqrt[-a]*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*Sqrt[-a]*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",7,4,24,0.1667,0,"{490, 1217, 220, 1707}"
821,1,1007,0,1.3085332,"\int \frac{1}{x^2 \left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[1/(x^2*(a + b*x^4)*Sqrt[c + d*x^4]),x]","-\frac{\sqrt{b} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{8 (-a)^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{5/4} \sqrt{b c-a d}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{4 (-a)^{5/4} \sqrt{a d-b c}}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{a c^{3/4} \sqrt{d x^4+c}}+\frac{\sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 a c^{3/4} \sqrt{d x^4+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a \sqrt[4]{c} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 (-a)^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{d x^4+c}}{a c x}+\frac{\sqrt{d} x \sqrt{d x^4+c}}{a c \left(\sqrt{d} x^2+\sqrt{c}\right)}","\frac{\sqrt{d} \sqrt{d x^4+c} x}{a c \left(\sqrt{d} x^2+\sqrt{c}\right)}-\frac{b \sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{-\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 a (b c-a d)}-\frac{b \sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} \tan ^{-1}\left(\frac{\sqrt{\frac{b c-a d}{\sqrt{-a} \sqrt{b}}} x}{\sqrt{d x^4+c}}\right)}{4 a (b c-a d)}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{a c^{3/4} \sqrt{d x^4+c}}+\frac{\sqrt[4]{d} (2 b c+a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 a c^{3/4} (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt{b} \left(\frac{\sqrt{b} \sqrt[4]{c}}{\sqrt[4]{d}}-\frac{\sqrt{-a} \sqrt[4]{d}}{\sqrt[4]{c}}\right) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \left(\sqrt{-a} \sqrt{b} \sqrt{c}-a \sqrt{d}\right) \sqrt{d x^4+c}}-\frac{\sqrt{b} \left(\frac{\sqrt[4]{d} \sqrt{-a}}{\sqrt[4]{c}}+\frac{\sqrt{b} \sqrt[4]{c}}{\sqrt[4]{d}}\right) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\sqrt{c} \left(\sqrt{b}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{c}}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt{d x^4+c}}-\frac{\sqrt{d x^4+c}}{a c x}",1,"-(Sqrt[c + d*x^4]/(a*c*x)) + (Sqrt[d]*x*Sqrt[c + d*x^4])/(a*c*(Sqrt[c] + Sqrt[d]*x^2)) + (b^(3/4)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(5/4)*Sqrt[b*c - a*d]) - (b^(3/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(4*(-a)^(5/4)*Sqrt[-(b*c) + a*d]) - (d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(a*c^(3/4)*Sqrt[c + d*x^4]) + (d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(2*a*c^(3/4)*Sqrt[c + d*x^4]) + (b*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (b*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) + (Sqrt[b]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4]) - (Sqrt[b]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^4])","A",13,8,24,0.3333,0,"{480, 584, 305, 220, 1196, 490, 1217, 1707}"
822,1,175,0,0.1733866,"\int \frac{x^{15}}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^15/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{\sqrt{c+d x^4} \left(-15 a^2 d^2-b d x^4 (2 b c-5 a d)+8 a b c d+4 b^2 c^2\right)}{12 b^3 d^2 (b c-a d)}-\frac{a^2 (6 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 b^{7/2} (b c-a d)^{3/2}}+\frac{a x^8 \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}","-\frac{\sqrt{c+d x^4} \left(-15 a^2 d^2-b d x^4 (2 b c-5 a d)+8 a b c d+4 b^2 c^2\right)}{12 b^3 d^2 (b c-a d)}-\frac{a^2 (6 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 b^{7/2} (b c-a d)^{3/2}}+\frac{a x^8 \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}",1,"(a*x^8*Sqrt[c + d*x^4])/(4*b*(b*c - a*d)*(a + b*x^4)) - (Sqrt[c + d*x^4]*(4*b^2*c^2 + 8*a*b*c*d - 15*a^2*d^2 - b*d*(2*b*c - 5*a*d)*x^4))/(12*b^3*d^2*(b*c - a*d)) - (a^2*(6*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(4*b^(7/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{446, 98, 147, 63, 208}"
823,1,123,0,0.1463279,"\int \frac{x^{11}}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^11/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{a^2 \sqrt{c+d x^4}}{4 b^2 \left(a+b x^4\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^4}}{2 b^2 d}","-\frac{a^2 \sqrt{c+d x^4}}{4 b^2 \left(a+b x^4\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^4}}{2 b^2 d}",1,"Sqrt[c + d*x^4]/(2*b^2*d) - (a^2*Sqrt[c + d*x^4])/(4*b^2*(b*c - a*d)*(a + b*x^4)) + (a*(4*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(4*b^(5/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{446, 89, 80, 63, 208}"
824,1,99,0,0.0867293,"\int \frac{x^7}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^7/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{a \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} (b c-a d)^{3/2}}","\frac{a \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} (b c-a d)^{3/2}}",1,"(a*Sqrt[c + d*x^4])/(4*b*(b*c - a*d)*(a + b*x^4)) - ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(4*b^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
825,1,87,0,0.0735342,"\int \frac{x^3}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^3/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^4}}{4 \left(a+b x^4\right) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^4}}{4 \left(a+b x^4\right) (b c-a d)}",1,"-Sqrt[c + d*x^4]/(4*(b*c - a*d)*(a + b*x^4)) + (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(4*Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{444, 51, 63, 208}"
826,1,132,0,0.1415087,"\int \frac{1}{x \left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/(x*(a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{2 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^4}}{4 a \left(a+b x^4\right) (b c-a d)}","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{2 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^4}}{4 a \left(a+b x^4\right) (b c-a d)}",1,"(b*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*(a + b*x^4)) - ArcTanh[Sqrt[c + d*x^4]/Sqrt[c]]/(2*a^2*Sqrt[c]) + (Sqrt[b]*(2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(4*a^2*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
827,1,185,0,0.2508425,"\int \frac{1}{x^5 \left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/(x^5*(a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{4 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^4} (2 b c-a d)}{4 a^2 c \left(a+b x^4\right) (b c-a d)}-\frac{\sqrt{c+d x^4}}{4 a c x^4 \left(a+b x^4\right)}","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^4}}{\sqrt{b c-a d}}\right)}{4 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^4}}{\sqrt{c}}\right)}{4 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^4} (2 b c-a d)}{4 a^2 c \left(a+b x^4\right) (b c-a d)}-\frac{\sqrt{c+d x^4}}{4 a c x^4 \left(a+b x^4\right)}",1,"-(b*(2*b*c - a*d)*Sqrt[c + d*x^4])/(4*a^2*c*(b*c - a*d)*(a + b*x^4)) - Sqrt[c + d*x^4]/(4*a*c*x^4*(a + b*x^4)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x^4]/Sqrt[c]])/(4*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^4])/Sqrt[b*c - a*d]])/(4*a^3*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 151, 156, 63, 208}"
828,1,191,0,0.3654624,"\int \frac{x^{13}}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^13/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{a^{3/2} (5 b c-4 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 b^3 (b c-a d)^{3/2}}-\frac{(4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{4 b^3 d^{3/2}}+\frac{x^2 \sqrt{c+d x^4} (b c-2 a d)}{4 b^2 d (b c-a d)}+\frac{a x^6 \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}","\frac{a^{3/2} (5 b c-4 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 b^3 (b c-a d)^{3/2}}-\frac{(4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{4 b^3 d^{3/2}}+\frac{x^2 \sqrt{c+d x^4} (b c-2 a d)}{4 b^2 d (b c-a d)}+\frac{a x^6 \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}",1,"((b*c - 2*a*d)*x^2*Sqrt[c + d*x^4])/(4*b^2*d*(b*c - a*d)) + (a*x^6*Sqrt[c + d*x^4])/(4*b*(b*c - a*d)*(a + b*x^4)) + (a^(3/2)*(5*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(4*b^3*(b*c - a*d)^(3/2)) - ((b*c + 4*a*d)*ArcTanh[(Sqrt[d]*x^2)/Sqrt[c + d*x^4]])/(4*b^3*d^(3/2))","A",8,8,24,0.3333,1,"{465, 470, 582, 523, 217, 206, 377, 205}"
829,1,141,0,0.1622047,"\int \frac{x^9}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^9/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 b^2 (b c-a d)^{3/2}}+\frac{a x^2 \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{2 b^2 \sqrt{d}}","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 b^2 (b c-a d)^{3/2}}+\frac{a x^2 \sqrt{c+d x^4}}{4 b \left(a+b x^4\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^2}{\sqrt{c+d x^4}}\right)}{2 b^2 \sqrt{d}}",1,"(a*x^2*Sqrt[c + d*x^4])/(4*b*(b*c - a*d)*(a + b*x^4)) - (Sqrt[a]*(3*b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(4*b^2*(b*c - a*d)^(3/2)) + ArcTanh[(Sqrt[d]*x^2)/Sqrt[c + d*x^4]]/(2*b^2*Sqrt[d])","A",7,7,24,0.2917,1,"{465, 470, 523, 217, 206, 377, 205}"
830,1,93,0,0.0915647,"\int \frac{x^5}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^5/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{c \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 \sqrt{a} (b c-a d)^{3/2}}-\frac{x^2 \sqrt{c+d x^4}}{4 \left(a+b x^4\right) (b c-a d)}","\frac{c \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 \sqrt{a} (b c-a d)^{3/2}}-\frac{x^2 \sqrt{c+d x^4}}{4 \left(a+b x^4\right) (b c-a d)}",1,"-(x^2*Sqrt[c + d*x^4])/(4*(b*c - a*d)*(a + b*x^4)) + (c*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(4*Sqrt[a]*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{465, 471, 12, 377, 205}"
831,1,104,0,0.0941179,"\int \frac{x}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 a^{3/2} (b c-a d)^{3/2}}+\frac{b x^2 \sqrt{c+d x^4}}{4 a \left(a+b x^4\right) (b c-a d)}","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 a^{3/2} (b c-a d)^{3/2}}+\frac{b x^2 \sqrt{c+d x^4}}{4 a \left(a+b x^4\right) (b c-a d)}",1,"(b*x^2*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*(a + b*x^4)) + ((b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(4*a^(3/2)*(b*c - a*d)^(3/2))","A",4,4,22,0.1818,1,"{465, 382, 377, 205}"
832,1,149,0,0.1987447,"\int \frac{1}{x^3 \left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/(x^3*(a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{\sqrt{c+d x^4} (3 b c-2 a d)}{4 a^2 c x^2 (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^4}}{4 a x^2 \left(a+b x^4\right) (b c-a d)}","-\frac{\sqrt{c+d x^4} (3 b c-2 a d)}{4 a^2 c x^2 (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^4}}{4 a x^2 \left(a+b x^4\right) (b c-a d)}",1,"-((3*b*c - 2*a*d)*Sqrt[c + d*x^4])/(4*a^2*c*(b*c - a*d)*x^2) + (b*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*x^2*(a + b*x^4)) - (b*(3*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(4*a^(5/2)*(b*c - a*d)^(3/2))","A",6,6,24,0.2500,1,"{465, 472, 583, 12, 377, 205}"
833,1,208,0,0.3280086,"\int \frac{1}{x^7 \left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/(x^7*(a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{\sqrt{c+d x^4} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{12 a^3 c^2 x^2 (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^4} (5 b c-2 a d)}{12 a^2 c x^6 (b c-a d)}+\frac{b \sqrt{c+d x^4}}{4 a x^6 \left(a+b x^4\right) (b c-a d)}","\frac{\sqrt{c+d x^4} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{12 a^3 c^2 x^2 (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^4}}\right)}{4 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^4} (5 b c-2 a d)}{12 a^2 c x^6 (b c-a d)}+\frac{b \sqrt{c+d x^4}}{4 a x^6 \left(a+b x^4\right) (b c-a d)}",1,"-((5*b*c - 2*a*d)*Sqrt[c + d*x^4])/(12*a^2*c*(b*c - a*d)*x^6) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*Sqrt[c + d*x^4])/(12*a^3*c^2*(b*c - a*d)*x^2) + (b*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*x^6*(a + b*x^4)) + (b^2*(5*b*c - 6*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/(Sqrt[a]*Sqrt[c + d*x^4])])/(4*a^(7/2)*(b*c - a*d)^(3/2))","A",7,6,24,0.2500,1,"{465, 472, 583, 12, 377, 205}"
834,1,996,0,1.3081161,"\int \frac{x^8}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^8/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{(5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{-a} \sqrt[4]{d} (5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{16 b^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{-a} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 b^{7/4} (b c-a d)^{3/2}}+\frac{\sqrt[4]{-a} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 b^{7/4} (a d-b c)^{3/2}}+\frac{(4 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^4+c}}-\frac{a \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{a x \sqrt{d x^4+c}}{4 b (b c-a d) \left(b x^4+a\right)}","-\frac{(5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{-a} \sqrt[4]{d} (5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{16 b^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{-a} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 b^{7/4} (b c-a d)^{3/2}}+\frac{\sqrt[4]{-a} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 b^{7/4} (a d-b c)^{3/2}}+\frac{(4 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^4+c}}-\frac{a \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (5 b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{a x \sqrt{d x^4+c}}{4 b (b c-a d) \left(b x^4+a\right)}",1,"(a*x*Sqrt[c + d*x^4])/(4*b*(b*c - a*d)*(a + b*x^4)) - ((-a)^(1/4)*(5*b*c - 3*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*b^(7/4)*(b*c - a*d)^(3/2)) + ((-a)^(1/4)*(5*b*c - 3*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*b^(7/4)*(-(b*c) + a*d)^(3/2)) + ((4*b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4]) - (a*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(5*b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*b^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - (Sqrt[-a]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(5*b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*b^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(5*b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(5*b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*b^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4])","A",10,6,24,0.2500,1,"{470, 523, 220, 409, 1217, 1707}"
835,1,908,0,0.9063659,"\int \frac{x^4}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^4/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{\left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^4+c}}-\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{3/4} b^{3/4} (b c-a d)^{3/2}}+\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{3/4} b^{3/4} (a d-b c)^{3/2}}-\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a b \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^4+c}}-\frac{x \sqrt{d x^4+c}}{4 (b c-a d) \left(b x^4+a\right)}","\frac{\left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^4+c}}-\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{3/4} b^{3/4} (b c-a d)^{3/2}}+\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{3/4} b^{3/4} (a d-b c)^{3/2}}-\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a b \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^4+c}}-\frac{x \sqrt{d x^4+c}}{4 (b c-a d) \left(b x^4+a\right)}",1,"-(x*Sqrt[c + d*x^4])/(4*(b*c - a*d)*(a + b*x^4)) - ((b*c + a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(3/4)*b^(3/4)*(b*c - a*d)^(3/2)) + ((b*c + a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(3/4)*b^(3/4)*(-(b*c) + a*d)^(3/2)) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*b*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + ((Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*a*b*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4]) - (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4])","A",10,6,24,0.2500,1,"{471, 523, 220, 409, 1217, 1707}"
836,1,983,0,1.0326537,"\int \frac{1}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{(3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{16 (-a)^{3/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{7/4} (b c-a d)^{3/2}}-\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{7/4} (a d-b c)^{3/2}}+\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b x \sqrt{d x^4+c}}{4 a (b c-a d) \left(b x^4+a\right)}","\frac{(3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{16 (-a)^{3/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{7/4} (b c-a d)^{3/2}}-\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{7/4} (a d-b c)^{3/2}}+\frac{d^{3/4} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c-a d) \sqrt{d x^4+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-5 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b x \sqrt{d x^4+c}}{4 a (b c-a d) \left(b x^4+a\right)}",1,"(b*x*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*(a + b*x^4)) + (b^(1/4)*(3*b*c - 5*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(7/4)*(b*c - a*d)^(3/2)) - (b^(1/4)*(3*b*c - 5*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(7/4)*(-(b*c) + a*d)^(3/2)) + (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*(-a)^(3/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4])","A",10,6,21,0.2857,1,"{414, 523, 220, 409, 1217, 1707}"
837,1,1046,0,1.5571285,"\int \frac{1}{x^4 \left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/(x^4*(a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{b (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{16 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{11/4} (b c-a d)^{3/2}}-\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{11/4} (a d-b c)^{3/2}}-\frac{d^{3/4} (7 b c-4 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{24 a^2 c^{5/4} (b c-a d) \sqrt{d x^4+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b \sqrt{d x^4+c}}{4 a (b c-a d) x^3 \left(b x^4+a\right)}-\frac{(7 b c-4 a d) \sqrt{d x^4+c}}{12 a^2 c (b c-a d) x^3}","-\frac{b (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{16 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{11/4} (b c-a d)^{3/2}}-\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{11/4} (a d-b c)^{3/2}}-\frac{d^{3/4} (7 b c-4 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{24 a^2 c^{5/4} (b c-a d) \sqrt{d x^4+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (7 b c-9 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b \sqrt{d x^4+c}}{4 a (b c-a d) x^3 \left(b x^4+a\right)}-\frac{(7 b c-4 a d) \sqrt{d x^4+c}}{12 a^2 c (b c-a d) x^3}",1,"-((7*b*c - 4*a*d)*Sqrt[c + d*x^4])/(12*a^2*c*(b*c - a*d)*x^3) + (b*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*x^3*(a + b*x^4)) + (b^(5/4)*(7*b*c - 9*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(11/4)*(b*c - a*d)^(3/2)) - (b^(5/4)*(7*b*c - 9*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(11/4)*(-(b*c) + a*d)^(3/2)) - (d^(3/4)*(7*b*c - 4*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(24*a^2*c^(5/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + (b*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - (b*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])*d^(1/4)*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - (b*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - (b*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4])","A",11,7,24,0.2917,1,"{472, 583, 523, 220, 409, 1217, 1707}"
838,1,1146,0,1.5628404,"\int \frac{x^6}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^6/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","-\frac{\sqrt{d x^4+c} x^3}{4 (b c-a d) \left(b x^4+a\right)}+\frac{\sqrt{d} \sqrt{d x^4+c} x}{4 b (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right)}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 \sqrt[4]{-a} b^{5/4} (b c-a d)^{3/2}}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 \sqrt[4]{-a} b^{5/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b (b c-a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b (b c-a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}","-\frac{\sqrt{d x^4+c} x^3}{4 (b c-a d) \left(b x^4+a\right)}+\frac{\sqrt{d} \sqrt{d x^4+c} x}{4 b (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right)}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 \sqrt[4]{-a} b^{5/4} (b c-a d)^{3/2}}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 \sqrt[4]{-a} b^{5/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b (b c-a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b (b c-a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}",1,"(Sqrt[d]*x*Sqrt[c + d*x^4])/(4*b*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)) - (x^3*Sqrt[c + d*x^4])/(4*(b*c - a*d)*(a + b*x^4)) + ((3*b*c - a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(1/4)*b^(5/4)*(b*c - a*d)^(3/2)) + ((3*b*c - a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(1/4)*b^(5/4)*(-(b*c) + a*d)^(3/2)) - (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*b*(b*c - a*d)*Sqrt[c + d*x^4]) + (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*b*(b*c - a*d)*Sqrt[c + d*x^4]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*Sqrt[-a]*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*Sqrt[-a]*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4])","A",13,8,24,0.3333,1,"{471, 584, 305, 220, 1196, 490, 1217, 1707}"
839,1,1144,0,1.4407038,"\int \frac{x^2}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[x^2/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{b \sqrt{d x^4+c} x^3}{4 a (b c-a d) \left(b x^4+a\right)}-\frac{\sqrt{d} \sqrt{d x^4+c} x}{4 a (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right)}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{5/4} \sqrt[4]{b} (b c-a d)^{3/2}}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{5/4} \sqrt[4]{b} (a d-b c)^{3/2}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a (b c-a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a (b c-a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}","\frac{b \sqrt{d x^4+c} x^3}{4 a (b c-a d) \left(b x^4+a\right)}-\frac{\sqrt{d} \sqrt{d x^4+c} x}{4 a (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right)}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{5/4} \sqrt[4]{b} (b c-a d)^{3/2}}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{5/4} \sqrt[4]{b} (a d-b c)^{3/2}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a (b c-a d) \sqrt{d x^4+c}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a (b c-a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}",1,"-(Sqrt[d]*x*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)) + (b*x^3*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*(a + b*x^4)) - ((b*c - 3*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(5/4)*b^(1/4)*(b*c - a*d)^(3/2)) - ((b*c - 3*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(5/4)*b^(1/4)*(-(b*c) + a*d)^(3/2)) + (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a*(b*c - a*d)*Sqrt[c + d*x^4]) - (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a*(b*c - a*d)*Sqrt[c + d*x^4]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*(-a)^(3/2)*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*(-a)^(3/2)*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4])","A",13,8,24,0.3333,1,"{472, 584, 305, 220, 1196, 490, 1217, 1707}"
840,1,1225,0,1.8982346,"\int \frac{1}{x^2 \left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[1/(x^2*(a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{\sqrt{b} (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{9/4} (b c-a d)^{3/2}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{9/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a^2 c^{3/4} (b c-a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 c^{3/4} (b c-a d) \sqrt{d x^4+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{(5 b c-4 a d) \sqrt{d x^4+c}}{4 a^2 c (b c-a d) x}+\frac{\sqrt{d} (5 b c-4 a d) x \sqrt{d x^4+c}}{4 a^2 c (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right)}+\frac{b \sqrt{d x^4+c}}{4 a (b c-a d) x \left(b x^4+a\right)}","\frac{\sqrt{b} (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{32 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{9/4} (b c-a d)^{3/2}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^4+c}}\right)}{16 (-a)^{9/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a^2 c^{3/4} (b c-a d) \sqrt{d x^4+c}}+\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 c^{3/4} (b c-a d) \sqrt{d x^4+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (5 b c-7 a d) \left(\sqrt{d} x^2+\sqrt{c}\right) \sqrt{\frac{d x^4+c}{\left(\sqrt{d} x^2+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^4+c}}-\frac{(5 b c-4 a d) \sqrt{d x^4+c}}{4 a^2 c (b c-a d) x}+\frac{\sqrt{d} (5 b c-4 a d) x \sqrt{d x^4+c}}{4 a^2 c (b c-a d) \left(\sqrt{d} x^2+\sqrt{c}\right)}+\frac{b \sqrt{d x^4+c}}{4 a (b c-a d) x \left(b x^4+a\right)}",1,"-((5*b*c - 4*a*d)*Sqrt[c + d*x^4])/(4*a^2*c*(b*c - a*d)*x) + (Sqrt[d]*(5*b*c - 4*a*d)*x*Sqrt[c + d*x^4])/(4*a^2*c*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^2)) + (b*Sqrt[c + d*x^4])/(4*a*(b*c - a*d)*x*(a + b*x^4)) - (b^(3/4)*(5*b*c - 7*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(9/4)*(b*c - a*d)^(3/2)) - (b^(3/4)*(5*b*c - 7*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^4])])/(16*(-a)^(9/4)*(-(b*c) + a*d)^(3/2)) - (d^(1/4)*(5*b*c - 4*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticE[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(4*a^2*c^(3/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + (d^(1/4)*(5*b*c - 4*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(8*a^2*c^(3/4)*(b*c - a*d)*Sqrt[c + d*x^4]) + (b*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + (b*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticF[2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(16*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) - (Sqrt[b]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4]) + (Sqrt[b]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^2)*Sqrt[(c + d*x^4)/(Sqrt[c] + Sqrt[d]*x^2)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x)/c^(1/4)], 1/2])/(32*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^4])","A",14,9,24,0.3750,1,"{472, 583, 584, 305, 220, 1196, 490, 1217, 1707}"
841,1,194,0,0.2120914,"\int \frac{(e x)^m \left(a+b x^4\right)^2}{\sqrt{c+d x^4}} \, dx","Int[((e*x)^m*(a + b*x^4)^2)/Sqrt[c + d*x^4],x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \left(\frac{a^2 d^2 (m+7)}{m+1}+\frac{b c (b c (m+5)-2 a d (m+7))}{m+3}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{d^2 e (m+7) \sqrt{c+d x^4}}-\frac{b \sqrt{c+d x^4} (e x)^{m+1} (b c (m+5)-2 a d (m+7))}{d^2 e (m+3) (m+7)}+\frac{b^2 \sqrt{c+d x^4} (e x)^{m+5}}{d e^5 (m+7)}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \left(a^2 d^2 (m+3) (m+7)+b c (m+1) (b c (m+5)-2 a d (m+7))\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{d^2 e (m+1) (m+3) (m+7) \sqrt{c+d x^4}}-\frac{b \sqrt{c+d x^4} (e x)^{m+1} (b c (m+5)-2 a d (m+7))}{d^2 e (m+3) (m+7)}+\frac{b^2 \sqrt{c+d x^4} (e x)^{m+5}}{d e^5 (m+7)}",1,"-((b*(b*c*(5 + m) - 2*a*d*(7 + m))*(e*x)^(1 + m)*Sqrt[c + d*x^4])/(d^2*e*(3 + m)*(7 + m))) + (b^2*(e*x)^(5 + m)*Sqrt[c + d*x^4])/(d*e^5*(7 + m)) + (((a^2*d^2*(7 + m))/(1 + m) + (b*c*(b*c*(5 + m) - 2*a*d*(7 + m)))/(3 + m))*(e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*Hypergeometric2F1[1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)])/(d^2*e*(7 + m)*Sqrt[c + d*x^4])","A",4,4,26,0.1538,1,"{464, 459, 365, 364}"
842,1,115,0,0.0590184,"\int \frac{(e x)^m \left(a+b x^4\right)}{\sqrt{c+d x^4}} \, dx","Int[((e*x)^m*(a + b*x^4))/Sqrt[c + d*x^4],x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \left(\frac{a}{m+1}-\frac{b c}{d (m+3)}\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{e \sqrt{c+d x^4}}+\frac{b \sqrt{c+d x^4} (e x)^{m+1}}{d e (m+3)}","\frac{b \sqrt{c+d x^4} (e x)^{m+1}}{d e (m+3)}-\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} (b c (m+1)-a d (m+3)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{d e (m+1) (m+3) \sqrt{c+d x^4}}",1,"(b*(e*x)^(1 + m)*Sqrt[c + d*x^4])/(d*e*(3 + m)) + ((a/(1 + m) - (b*c)/(d*(3 + m)))*(e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*Hypergeometric2F1[1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)])/(e*Sqrt[c + d*x^4])","A",3,3,24,0.1250,1,"{459, 365, 364}"
843,1,68,0,0.0194269,"\int \frac{(e x)^m}{\sqrt{c+d x^4}} \, dx","Int[(e*x)^m/Sqrt[c + d*x^4],x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*Hypergeometric2F1[1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)])/(e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,17,0.1176,1,"{365, 364}"
844,1,81,0,0.0552466,"\int \frac{(e x)^m}{\left(a+b x^4\right) \sqrt{c+d x^4}} \, dx","Int[(e*x)^m/((a + b*x^4)*Sqrt[c + d*x^4]),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};1,\frac{1}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};1,\frac{1}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*AppellF1[(1 + m)/4, 1, 1/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)])/(a*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,26,0.07692,1,"{511, 510}"
845,1,81,0,0.0563393,"\int \frac{(e x)^m}{\left(a+b x^4\right)^2 \sqrt{c+d x^4}} \, dx","Int[(e*x)^m/((a + b*x^4)^2*Sqrt[c + d*x^4]),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};2,\frac{1}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^2 e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};2,\frac{1}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^2 e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*AppellF1[(1 + m)/4, 2, 1/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)])/(a^2*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,26,0.07692,1,"{511, 510}"
846,1,81,0,0.0564448,"\int \frac{(e x)^m}{\left(a+b x^4\right)^3 \sqrt{c+d x^4}} \, dx","Int[(e*x)^m/((a + b*x^4)^3*Sqrt[c + d*x^4]),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};3,\frac{1}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^3 e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};3,\frac{1}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^3 e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*AppellF1[(1 + m)/4, 3, 1/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)])/(a^3*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,26,0.07692,1,"{511, 510}"
847,1,198,0,0.1784903,"\int \frac{(e x)^m \left(a+b x^4\right)^2}{\left(c+d x^4\right)^{3/2}} \, dx","Int[((e*x)^m*(a + b*x^4)^2)/(c + d*x^4)^(3/2),x]","-\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \left(2 b^2 c^2 (m+1)-(m+3) \left(2 a^2 d^2-(m+1) (b c-a d)^2\right)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{2 c d^2 e (m+1) (m+3) \sqrt{c+d x^4}}+\frac{(e x)^{m+1} (b c-a d)^2}{2 c d^2 e \sqrt{c+d x^4}}+\frac{b^2 \sqrt{c+d x^4} (e x)^{m+1}}{d^2 e (m+3)}","-\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \left(2 b^2 c^2 (m+1)-(m+3) \left(2 a^2 d^2-(m+1) (b c-a d)^2\right)\right) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{2 c d^2 e (m+1) (m+3) \sqrt{c+d x^4}}+\frac{(e x)^{m+1} (b c-a d)^2}{2 c d^2 e \sqrt{c+d x^4}}+\frac{b^2 \sqrt{c+d x^4} (e x)^{m+1}}{d^2 e (m+3)}",1,"((b*c - a*d)^2*(e*x)^(1 + m))/(2*c*d^2*e*Sqrt[c + d*x^4]) + (b^2*(e*x)^(1 + m)*Sqrt[c + d*x^4])/(d^2*e*(3 + m)) - ((2*b^2*c^2*(1 + m) - (3 + m)*(2*a^2*d^2 - (b*c - a*d)^2*(1 + m)))*(e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*Hypergeometric2F1[1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)])/(2*c*d^2*e*(1 + m)*(3 + m)*Sqrt[c + d*x^4])","A",4,4,26,0.1538,1,"{463, 459, 365, 364}"
848,1,132,0,0.0599819,"\int \frac{(e x)^m \left(a+b x^4\right)}{\left(c+d x^4\right)^{3/2}} \, dx","Int[((e*x)^m*(a + b*x^4))/(c + d*x^4)^(3/2),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} (a d (1-m)+b c (m+1)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{2 c d e (m+1) \sqrt{c+d x^4}}-\frac{(e x)^{m+1} (b c-a d)}{2 c d e \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} (a d (1-m)+b c (m+1)) \, _2F_1\left(\frac{1}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{2 c d e (m+1) \sqrt{c+d x^4}}-\frac{(e x)^{m+1} (b c-a d)}{2 c d e \sqrt{c+d x^4}}",1,"-((b*c - a*d)*(e*x)^(1 + m))/(2*c*d*e*Sqrt[c + d*x^4]) + ((a*d*(1 - m) + b*c*(1 + m))*(e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*Hypergeometric2F1[1/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)])/(2*c*d*e*(1 + m)*Sqrt[c + d*x^4])","A",3,3,24,0.1250,1,"{457, 365, 364}"
849,1,71,0,0.0231556,"\int \frac{(e x)^m}{\left(c+d x^4\right)^{3/2}} \, dx","Int[(e*x)^m/(c + d*x^4)^(3/2),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{c e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{4};\frac{m+5}{4};-\frac{d x^4}{c}\right)}{c e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*Hypergeometric2F1[3/2, (1 + m)/4, (5 + m)/4, -((d*x^4)/c)])/(c*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,17,0.1176,1,"{365, 364}"
850,1,84,0,0.0601804,"\int \frac{(e x)^m}{\left(a+b x^4\right) \left(c+d x^4\right)^{3/2}} \, dx","Int[(e*x)^m/((a + b*x^4)*(c + d*x^4)^(3/2)),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};1,\frac{3}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a c e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};1,\frac{3}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a c e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*AppellF1[(1 + m)/4, 1, 3/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)])/(a*c*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,26,0.07692,1,"{511, 510}"
851,1,84,0,0.0603985,"\int \frac{(e x)^m}{\left(a+b x^4\right)^2 \left(c+d x^4\right)^{3/2}} \, dx","Int[(e*x)^m/((a + b*x^4)^2*(c + d*x^4)^(3/2)),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};2,\frac{3}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^2 c e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};2,\frac{3}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^2 c e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*AppellF1[(1 + m)/4, 2, 3/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)])/(a^2*c*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,26,0.07692,1,"{511, 510}"
852,1,84,0,0.0618125,"\int \frac{(e x)^m}{\left(a+b x^4\right)^3 \left(c+d x^4\right)^{3/2}} \, dx","Int[(e*x)^m/((a + b*x^4)^3*(c + d*x^4)^(3/2)),x]","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};3,\frac{3}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^3 c e (m+1) \sqrt{c+d x^4}}","\frac{\sqrt{\frac{d x^4}{c}+1} (e x)^{m+1} F_1\left(\frac{m+1}{4};3,\frac{3}{2};\frac{m+5}{4};-\frac{b x^4}{a},-\frac{d x^4}{c}\right)}{a^3 c e (m+1) \sqrt{c+d x^4}}",1,"((e*x)^(1 + m)*Sqrt[1 + (d*x^4)/c]*AppellF1[(1 + m)/4, 3, 3/2, (5 + m)/4, -((b*x^4)/a), -((d*x^4)/c)])/(a^3*c*e*(1 + m)*Sqrt[c + d*x^4])","A",2,2,26,0.07692,1,"{511, 510}"
853,1,104,0,0.1071556,"\int \frac{x^{17}}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^17/((a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^6} (a d+b c)}{3 b^2 d^2}+\frac{\left(c+d x^6\right)^{3/2}}{9 b d^2}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^6} (a d+b c)}{3 b^2 d^2}+\frac{\left(c+d x^6\right)^{3/2}}{9 b d^2}",1,"-((b*c + a*d)*Sqrt[c + d*x^6])/(3*b^2*d^2) + (c + d*x^6)^(3/2)/(9*b*d^2) - (a^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(3*b^(5/2)*Sqrt[b*c - a*d])","A",5,4,24,0.1667,1,"{446, 88, 63, 208}"
854,1,74,0,0.0632217,"\int \frac{x^{11}}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^11/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^6}}{3 b d}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^6}}{3 b d}",1,"Sqrt[c + d*x^6]/(3*b*d) + (a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(3*b^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{446, 80, 63, 208}"
855,1,51,0,0.0459977,"\int \frac{x^5}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^5/((a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} \sqrt{b c-a d}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 \sqrt{b} \sqrt{b c-a d}}",1,"-ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]]/(3*Sqrt[b]*Sqrt[b*c - a*d])","A",3,3,24,0.1250,1,"{444, 63, 208}"
856,1,85,0,0.0741793,"\int \frac{1}{x \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x*(a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{3 a \sqrt{c}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{3 a \sqrt{c}}",1,"-ArcTanh[Sqrt[c + d*x^6]/Sqrt[c]]/(3*a*Sqrt[c]) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(3*a*Sqrt[b*c - a*d])","A",6,4,24,0.1667,1,"{446, 86, 63, 208}"
857,1,117,0,0.1187524,"\int \frac{1}{x^7 \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x^7*(a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{6 a^2 c^{3/2}}-\frac{\sqrt{c+d x^6}}{6 a c x^6}","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{3 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{6 a^2 c^{3/2}}-\frac{\sqrt{c+d x^6}}{6 a c x^6}",1,"-Sqrt[c + d*x^6]/(6*a*c*x^6) + ((2*b*c + a*d)*ArcTanh[Sqrt[c + d*x^6]/Sqrt[c]])/(6*a^2*c^(3/2)) - (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(3*a^2*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
858,1,123,0,0.1533337,"\int \frac{x^{14}}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^14/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^3}{\sqrt{c+d x^6}}\right)}{6 b^2 d^{3/2}}+\frac{x^3 \sqrt{c+d x^6}}{6 b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^3}{\sqrt{c+d x^6}}\right)}{6 b^2 d^{3/2}}+\frac{x^3 \sqrt{c+d x^6}}{6 b d}",1,"(x^3*Sqrt[c + d*x^6])/(6*b*d) + (a^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(3*b^2*Sqrt[b*c - a*d]) - ((b*c + 2*a*d)*ArcTanh[(Sqrt[d]*x^3)/Sqrt[c + d*x^6]])/(6*b^2*d^(3/2))","A",7,7,24,0.2917,1,"{465, 479, 523, 217, 206, 377, 205}"
859,1,91,0,0.0873107,"\int \frac{x^8}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^8/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^3}{\sqrt{c+d x^6}}\right)}{3 b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 b \sqrt{b c-a d}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^3}{\sqrt{c+d x^6}}\right)}{3 b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 b \sqrt{b c-a d}}",1,"-(Sqrt[a]*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(3*b*Sqrt[b*c - a*d]) + ArcTanh[(Sqrt[d]*x^3)/Sqrt[c + d*x^6]]/(3*b*Sqrt[d])","A",6,6,24,0.2500,1,"{465, 483, 217, 206, 377, 205}"
860,1,54,0,0.0487174,"\int \frac{x^2}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^2/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{\tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 \sqrt{a} \sqrt{b c-a d}}","\frac{\tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 \sqrt{a} \sqrt{b c-a d}}",1,"ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])]/(3*Sqrt[a]*Sqrt[b*c - a*d])","A",3,3,24,0.1250,1,"{465, 377, 205}"
861,1,80,0,0.0887366,"\int \frac{1}{x^4 \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x^4*(a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{b \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^6}}{3 a c x^3}","-\frac{b \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^6}}{3 a c x^3}",1,"-Sqrt[c + d*x^6]/(3*a*c*x^3) - (b*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(3*a^(3/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{465, 480, 12, 377, 205}"
862,1,115,0,0.162659,"\int \frac{1}{x^{10} \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x^10*(a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{b^2 \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^6} (2 a d+3 b c)}{9 a^2 c^2 x^3}-\frac{\sqrt{c+d x^6}}{9 a c x^9}","\frac{b^2 \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{3 a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^6} (2 a d+3 b c)}{9 a^2 c^2 x^3}-\frac{\sqrt{c+d x^6}}{9 a c x^9}",1,"-Sqrt[c + d*x^6]/(9*a*c*x^9) + ((3*b*c + 2*a*d)*Sqrt[c + d*x^6])/(9*a^2*c^2*x^3) + (b^2*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(3*a^(5/2)*Sqrt[b*c - a*d])","A",6,6,24,0.2500,1,"{465, 480, 583, 12, 377, 205}"
863,1,64,0,0.0517917,"\int \frac{x^4}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^4/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{x^5 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{5}{6};1,\frac{1}{2};\frac{11}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{5 a \sqrt{c+d x^6}}","\frac{x^5 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{5}{6};1,\frac{1}{2};\frac{11}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{5 a \sqrt{c+d x^6}}",1,"(x^5*Sqrt[1 + (d*x^6)/c]*AppellF1[5/6, 1, 1/2, 11/6, -((b*x^6)/a), -((d*x^6)/c)])/(5*a*Sqrt[c + d*x^6])","A",2,2,24,0.08333,1,"{511, 510}"
864,1,64,0,0.0714221,"\int \frac{x^3}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x^3/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{x^4 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a \sqrt{c+d x^6}}","\frac{x^4 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{2}{3};1,\frac{1}{2};\frac{5}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a \sqrt{c+d x^6}}",1,"(x^4*Sqrt[1 + (d*x^6)/c]*AppellF1[2/3, 1, 1/2, 5/3, -((b*x^6)/a), -((d*x^6)/c)])/(4*a*Sqrt[c + d*x^6])","A",3,3,24,0.1250,1,"{465, 511, 510}"
865,1,64,0,0.0544657,"\int \frac{x}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[x/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{x^2 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a \sqrt{c+d x^6}}","\frac{x^2 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{3};1,\frac{1}{2};\frac{4}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a \sqrt{c+d x^6}}",1,"(x^2*Sqrt[1 + (d*x^6)/c]*AppellF1[1/3, 1, 1/2, 4/3, -((b*x^6)/a), -((d*x^6)/c)])/(2*a*Sqrt[c + d*x^6])","A",3,3,22,0.1364,1,"{465, 430, 429}"
866,1,59,0,0.0248053,"\int \frac{1}{\left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/((a + b*x^6)*Sqrt[c + d*x^6]),x]","\frac{x \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{6};1,\frac{1}{2};\frac{7}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a \sqrt{c+d x^6}}","\frac{x \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{6};1,\frac{1}{2};\frac{7}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a \sqrt{c+d x^6}}",1,"(x*Sqrt[1 + (d*x^6)/c]*AppellF1[1/6, 1, 1/2, 7/6, -((b*x^6)/a), -((d*x^6)/c)])/(a*Sqrt[c + d*x^6])","A",2,2,21,0.09524,1,"{430, 429}"
867,1,62,0,0.0503759,"\int \frac{1}{x^2 \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x^2*(a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{6};1,\frac{1}{2};\frac{5}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a x \sqrt{c+d x^6}}","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{6};1,\frac{1}{2};\frac{5}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a x \sqrt{c+d x^6}}",1,"-((Sqrt[1 + (d*x^6)/c]*AppellF1[-1/6, 1, 1/2, 5/6, -((b*x^6)/a), -((d*x^6)/c)])/(a*x*Sqrt[c + d*x^6]))","A",2,2,24,0.08333,1,"{511, 510}"
868,1,64,0,0.0868468,"\int \frac{1}{x^3 \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x^3*(a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a x^2 \sqrt{c+d x^6}}","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{3};1,\frac{1}{2};\frac{2}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a x^2 \sqrt{c+d x^6}}",1,"-(Sqrt[1 + (d*x^6)/c]*AppellF1[-1/3, 1, 1/2, 2/3, -((b*x^6)/a), -((d*x^6)/c)])/(2*a*x^2*Sqrt[c + d*x^6])","A",3,3,24,0.1250,1,"{465, 511, 510}"
869,1,64,0,0.0838677,"\int \frac{1}{x^5 \left(a+b x^6\right) \sqrt{c+d x^6}} \, dx","Int[1/(x^5*(a + b*x^6)*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a x^4 \sqrt{c+d x^6}}","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{2}{3};1,\frac{1}{2};\frac{1}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a x^4 \sqrt{c+d x^6}}",1,"-(Sqrt[1 + (d*x^6)/c]*AppellF1[-2/3, 1, 1/2, 1/3, -((b*x^6)/a), -((d*x^6)/c)])/(4*a*x^4*Sqrt[c + d*x^6])","A",3,3,24,0.1250,1,"{465, 511, 510}"
870,1,123,0,0.1395816,"\int \frac{x^{17}}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^17/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{a^2 \sqrt{c+d x^6}}{6 b^2 \left(a+b x^6\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 b^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^6}}{3 b^2 d}","-\frac{a^2 \sqrt{c+d x^6}}{6 b^2 \left(a+b x^6\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 b^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^6}}{3 b^2 d}",1,"Sqrt[c + d*x^6]/(3*b^2*d) - (a^2*Sqrt[c + d*x^6])/(6*b^2*(b*c - a*d)*(a + b*x^6)) + (a*(4*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(6*b^(5/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{446, 89, 80, 63, 208}"
871,1,99,0,0.0803535,"\int \frac{x^{11}}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^11/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{a \sqrt{c+d x^6}}{6 b \left(a+b x^6\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 b^{3/2} (b c-a d)^{3/2}}","\frac{a \sqrt{c+d x^6}}{6 b \left(a+b x^6\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 b^{3/2} (b c-a d)^{3/2}}",1,"(a*Sqrt[c + d*x^6])/(6*b*(b*c - a*d)*(a + b*x^6)) - ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(6*b^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
872,1,87,0,0.0685971,"\int \frac{x^5}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^5/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^6}}{6 \left(a+b x^6\right) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^6}}{6 \left(a+b x^6\right) (b c-a d)}",1,"-Sqrt[c + d*x^6]/(6*(b*c - a*d)*(a + b*x^6)) + (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(6*Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{444, 51, 63, 208}"
873,1,132,0,0.1272383,"\int \frac{1}{x \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{3 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^6}}{6 a \left(a+b x^6\right) (b c-a d)}","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{3 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^6}}{6 a \left(a+b x^6\right) (b c-a d)}",1,"(b*Sqrt[c + d*x^6])/(6*a*(b*c - a*d)*(a + b*x^6)) - ArcTanh[Sqrt[c + d*x^6]/Sqrt[c]]/(3*a^2*Sqrt[c]) + (Sqrt[b]*(2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(6*a^2*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
874,1,185,0,0.2276786,"\int \frac{1}{x^7 \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x^7*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{6 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^6} (2 b c-a d)}{6 a^2 c \left(a+b x^6\right) (b c-a d)}-\frac{\sqrt{c+d x^6}}{6 a c x^6 \left(a+b x^6\right)}","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^6}}{\sqrt{b c-a d}}\right)}{6 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^6}}{\sqrt{c}}\right)}{6 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^6} (2 b c-a d)}{6 a^2 c \left(a+b x^6\right) (b c-a d)}-\frac{\sqrt{c+d x^6}}{6 a c x^6 \left(a+b x^6\right)}",1,"-(b*(2*b*c - a*d)*Sqrt[c + d*x^6])/(6*a^2*c*(b*c - a*d)*(a + b*x^6)) - Sqrt[c + d*x^6]/(6*a*c*x^6*(a + b*x^6)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x^6]/Sqrt[c]])/(6*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^6])/Sqrt[b*c - a*d]])/(6*a^3*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 151, 156, 63, 208}"
875,1,141,0,0.1575836,"\int \frac{x^{14}}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^14/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 b^2 (b c-a d)^{3/2}}+\frac{a x^3 \sqrt{c+d x^6}}{6 b \left(a+b x^6\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^3}{\sqrt{c+d x^6}}\right)}{3 b^2 \sqrt{d}}","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 b^2 (b c-a d)^{3/2}}+\frac{a x^3 \sqrt{c+d x^6}}{6 b \left(a+b x^6\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^3}{\sqrt{c+d x^6}}\right)}{3 b^2 \sqrt{d}}",1,"(a*x^3*Sqrt[c + d*x^6])/(6*b*(b*c - a*d)*(a + b*x^6)) - (Sqrt[a]*(3*b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(6*b^2*(b*c - a*d)^(3/2)) + ArcTanh[(Sqrt[d]*x^3)/Sqrt[c + d*x^6]]/(3*b^2*Sqrt[d])","A",7,7,24,0.2917,1,"{465, 470, 523, 217, 206, 377, 205}"
876,1,93,0,0.09026,"\int \frac{x^8}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^8/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{c \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 \sqrt{a} (b c-a d)^{3/2}}-\frac{x^3 \sqrt{c+d x^6}}{6 \left(a+b x^6\right) (b c-a d)}","\frac{c \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 \sqrt{a} (b c-a d)^{3/2}}-\frac{x^3 \sqrt{c+d x^6}}{6 \left(a+b x^6\right) (b c-a d)}",1,"-(x^3*Sqrt[c + d*x^6])/(6*(b*c - a*d)*(a + b*x^6)) + (c*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(6*Sqrt[a]*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{465, 471, 12, 377, 205}"
877,1,104,0,0.0981687,"\int \frac{x^2}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^2/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 a^{3/2} (b c-a d)^{3/2}}+\frac{b x^3 \sqrt{c+d x^6}}{6 a \left(a+b x^6\right) (b c-a d)}","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 a^{3/2} (b c-a d)^{3/2}}+\frac{b x^3 \sqrt{c+d x^6}}{6 a \left(a+b x^6\right) (b c-a d)}",1,"(b*x^3*Sqrt[c + d*x^6])/(6*a*(b*c - a*d)*(a + b*x^6)) + ((b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(6*a^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{465, 382, 377, 205}"
878,1,149,0,0.1939361,"\int \frac{1}{x^4 \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x^4*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{c+d x^6} (3 b c-2 a d)}{6 a^2 c x^3 (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^6}}{6 a x^3 \left(a+b x^6\right) (b c-a d)}","-\frac{\sqrt{c+d x^6} (3 b c-2 a d)}{6 a^2 c x^3 (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^6}}{6 a x^3 \left(a+b x^6\right) (b c-a d)}",1,"-((3*b*c - 2*a*d)*Sqrt[c + d*x^6])/(6*a^2*c*(b*c - a*d)*x^3) + (b*Sqrt[c + d*x^6])/(6*a*(b*c - a*d)*x^3*(a + b*x^6)) - (b*(3*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(6*a^(5/2)*(b*c - a*d)^(3/2))","A",6,6,24,0.2500,1,"{465, 472, 583, 12, 377, 205}"
879,1,208,0,0.3080146,"\int \frac{1}{x^{10} \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x^10*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{\sqrt{c+d x^6} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{18 a^3 c^2 x^3 (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^6} (5 b c-2 a d)}{18 a^2 c x^9 (b c-a d)}+\frac{b \sqrt{c+d x^6}}{6 a x^9 \left(a+b x^6\right) (b c-a d)}","\frac{\sqrt{c+d x^6} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{18 a^3 c^2 x^3 (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x^3 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^6}}\right)}{6 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^6} (5 b c-2 a d)}{18 a^2 c x^9 (b c-a d)}+\frac{b \sqrt{c+d x^6}}{6 a x^9 \left(a+b x^6\right) (b c-a d)}",1,"-((5*b*c - 2*a*d)*Sqrt[c + d*x^6])/(18*a^2*c*(b*c - a*d)*x^9) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*Sqrt[c + d*x^6])/(18*a^3*c^2*(b*c - a*d)*x^3) + (b*Sqrt[c + d*x^6])/(6*a*(b*c - a*d)*x^9*(a + b*x^6)) + (b^2*(5*b*c - 6*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^3)/(Sqrt[a]*Sqrt[c + d*x^6])])/(6*a^(7/2)*(b*c - a*d)^(3/2))","A",7,6,24,0.2500,1,"{465, 472, 583, 12, 377, 205}"
880,1,64,0,0.0512849,"\int \frac{x^4}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^4/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{x^5 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{5}{6};2,\frac{1}{2};\frac{11}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{5 a^2 \sqrt{c+d x^6}}","\frac{x^5 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{5}{6};2,\frac{1}{2};\frac{11}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{5 a^2 \sqrt{c+d x^6}}",1,"(x^5*Sqrt[1 + (d*x^6)/c]*AppellF1[5/6, 2, 1/2, 11/6, -((b*x^6)/a), -((d*x^6)/c)])/(5*a^2*Sqrt[c + d*x^6])","A",2,2,24,0.08333,1,"{511, 510}"
881,1,64,0,0.0730317,"\int \frac{x^3}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x^3/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{x^4 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{2}{3};2,\frac{1}{2};\frac{5}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a^2 \sqrt{c+d x^6}}","\frac{x^4 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{2}{3};2,\frac{1}{2};\frac{5}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a^2 \sqrt{c+d x^6}}",1,"(x^4*Sqrt[1 + (d*x^6)/c]*AppellF1[2/3, 2, 1/2, 5/3, -((b*x^6)/a), -((d*x^6)/c)])/(4*a^2*Sqrt[c + d*x^6])","A",3,3,24,0.1250,1,"{465, 511, 510}"
882,1,64,0,0.0540988,"\int \frac{x}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[x/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{x^2 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{3};2,\frac{1}{2};\frac{4}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a^2 \sqrt{c+d x^6}}","\frac{x^2 \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{3};2,\frac{1}{2};\frac{4}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a^2 \sqrt{c+d x^6}}",1,"(x^2*Sqrt[1 + (d*x^6)/c]*AppellF1[1/3, 2, 1/2, 4/3, -((b*x^6)/a), -((d*x^6)/c)])/(2*a^2*Sqrt[c + d*x^6])","A",3,3,22,0.1364,1,"{465, 430, 429}"
883,1,59,0,0.02523,"\int \frac{1}{\left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/((a + b*x^6)^2*Sqrt[c + d*x^6]),x]","\frac{x \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{6};2,\frac{1}{2};\frac{7}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a^2 \sqrt{c+d x^6}}","\frac{x \sqrt{\frac{d x^6}{c}+1} F_1\left(\frac{1}{6};2,\frac{1}{2};\frac{7}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a^2 \sqrt{c+d x^6}}",1,"(x*Sqrt[1 + (d*x^6)/c]*AppellF1[1/6, 2, 1/2, 7/6, -((b*x^6)/a), -((d*x^6)/c)])/(a^2*Sqrt[c + d*x^6])","A",2,2,21,0.09524,1,"{430, 429}"
884,1,62,0,0.0524712,"\int \frac{1}{x^2 \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x^2*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{6};2,\frac{1}{2};\frac{5}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a^2 x \sqrt{c+d x^6}}","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{6};2,\frac{1}{2};\frac{5}{6};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{a^2 x \sqrt{c+d x^6}}",1,"-((Sqrt[1 + (d*x^6)/c]*AppellF1[-1/6, 2, 1/2, 5/6, -((b*x^6)/a), -((d*x^6)/c)])/(a^2*x*Sqrt[c + d*x^6]))","A",2,2,24,0.08333,1,"{511, 510}"
885,1,64,0,0.0875388,"\int \frac{1}{x^3 \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x^3*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{3};2,\frac{1}{2};\frac{2}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a^2 x^2 \sqrt{c+d x^6}}","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{1}{3};2,\frac{1}{2};\frac{2}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{2 a^2 x^2 \sqrt{c+d x^6}}",1,"-(Sqrt[1 + (d*x^6)/c]*AppellF1[-1/3, 2, 1/2, 2/3, -((b*x^6)/a), -((d*x^6)/c)])/(2*a^2*x^2*Sqrt[c + d*x^6])","A",3,3,24,0.1250,1,"{465, 511, 510}"
886,1,64,0,0.082107,"\int \frac{1}{x^5 \left(a+b x^6\right)^2 \sqrt{c+d x^6}} \, dx","Int[1/(x^5*(a + b*x^6)^2*Sqrt[c + d*x^6]),x]","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{2}{3};2,\frac{1}{2};\frac{1}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a^2 x^4 \sqrt{c+d x^6}}","-\frac{\sqrt{\frac{d x^6}{c}+1} F_1\left(-\frac{2}{3};2,\frac{1}{2};\frac{1}{3};-\frac{b x^6}{a},-\frac{d x^6}{c}\right)}{4 a^2 x^4 \sqrt{c+d x^6}}",1,"-(Sqrt[1 + (d*x^6)/c]*AppellF1[-2/3, 2, 1/2, 1/3, -((b*x^6)/a), -((d*x^6)/c)])/(4*a^2*x^4*Sqrt[c + d*x^6])","A",3,3,24,0.1250,1,"{465, 511, 510}"
887,1,104,0,0.0985776,"\int \frac{x^{23}}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^23/((a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^8} (a d+b c)}{4 b^2 d^2}+\frac{\left(c+d x^8\right)^{3/2}}{12 b d^2}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^8} (a d+b c)}{4 b^2 d^2}+\frac{\left(c+d x^8\right)^{3/2}}{12 b d^2}",1,"-((b*c + a*d)*Sqrt[c + d*x^8])/(4*b^2*d^2) + (c + d*x^8)^(3/2)/(12*b*d^2) - (a^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(4*b^(5/2)*Sqrt[b*c - a*d])","A",5,4,24,0.1667,1,"{446, 88, 63, 208}"
888,1,74,0,0.0610699,"\int \frac{x^{15}}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^15/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^8}}{4 b d}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^8}}{4 b d}",1,"Sqrt[c + d*x^8]/(4*b*d) + (a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(4*b^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{446, 80, 63, 208}"
889,1,51,0,0.0468158,"\int \frac{x^7}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^7/((a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} \sqrt{b c-a d}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 \sqrt{b} \sqrt{b c-a d}}",1,"-ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]]/(4*Sqrt[b]*Sqrt[b*c - a*d])","A",3,3,24,0.1250,1,"{444, 63, 208}"
890,1,85,0,0.0792753,"\int \frac{1}{x \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x*(a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{4 a \sqrt{c}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{4 a \sqrt{c}}",1,"-ArcTanh[Sqrt[c + d*x^8]/Sqrt[c]]/(4*a*Sqrt[c]) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(4*a*Sqrt[b*c - a*d])","A",6,4,24,0.1667,1,"{446, 86, 63, 208}"
891,1,117,0,0.1127174,"\int \frac{1}{x^9 \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^9*(a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{8 a^2 c^{3/2}}-\frac{\sqrt{c+d x^8}}{8 a c x^8}","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{4 a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{8 a^2 c^{3/2}}-\frac{\sqrt{c+d x^8}}{8 a c x^8}",1,"-Sqrt[c + d*x^8]/(8*a*c*x^8) + ((2*b*c + a*d)*ArcTanh[Sqrt[c + d*x^8]/Sqrt[c]])/(8*a^2*c^(3/2)) - (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(4*a^2*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
892,1,123,0,0.1306211,"\int \frac{x^{19}}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^19/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^4}{\sqrt{c+d x^8}}\right)}{8 b^2 d^{3/2}}+\frac{x^4 \sqrt{c+d x^8}}{8 b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x^4}{\sqrt{c+d x^8}}\right)}{8 b^2 d^{3/2}}+\frac{x^4 \sqrt{c+d x^8}}{8 b d}",1,"(x^4*Sqrt[c + d*x^8])/(8*b*d) + (a^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(4*b^2*Sqrt[b*c - a*d]) - ((b*c + 2*a*d)*ArcTanh[(Sqrt[d]*x^4)/Sqrt[c + d*x^8]])/(8*b^2*d^(3/2))","A",7,7,24,0.2917,1,"{465, 479, 523, 217, 206, 377, 205}"
893,1,91,0,0.1101153,"\int \frac{x^{11}}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^11/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^4}{\sqrt{c+d x^8}}\right)}{4 b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 b \sqrt{b c-a d}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^4}{\sqrt{c+d x^8}}\right)}{4 b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 b \sqrt{b c-a d}}",1,"-(Sqrt[a]*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(4*b*Sqrt[b*c - a*d]) + ArcTanh[(Sqrt[d]*x^4)/Sqrt[c + d*x^8]]/(4*b*Sqrt[d])","A",6,6,24,0.2500,1,"{465, 483, 217, 206, 377, 205}"
894,1,54,0,0.0546701,"\int \frac{x^3}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^3/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{\tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 \sqrt{a} \sqrt{b c-a d}}","\frac{\tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 \sqrt{a} \sqrt{b c-a d}}",1,"ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])]/(4*Sqrt[a]*Sqrt[b*c - a*d])","A",3,3,24,0.1250,1,"{465, 377, 205}"
895,1,80,0,0.0873839,"\int \frac{1}{x^5 \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^5*(a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{b \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^8}}{4 a c x^4}","-\frac{b \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^8}}{4 a c x^4}",1,"-Sqrt[c + d*x^8]/(4*a*c*x^4) - (b*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(4*a^(3/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{465, 480, 12, 377, 205}"
896,1,115,0,0.1610499,"\int \frac{1}{x^{13} \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^13*(a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{b^2 \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^8} (2 a d+3 b c)}{12 a^2 c^2 x^4}-\frac{\sqrt{c+d x^8}}{12 a c x^{12}}","\frac{b^2 \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{4 a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^8} (2 a d+3 b c)}{12 a^2 c^2 x^4}-\frac{\sqrt{c+d x^8}}{12 a c x^{12}}",1,"-Sqrt[c + d*x^8]/(12*a*c*x^12) + ((3*b*c + 2*a*d)*Sqrt[c + d*x^8])/(12*a^2*c^2*x^4) + (b^2*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(4*a^(5/2)*Sqrt[b*c - a*d])","A",6,6,24,0.2500,1,"{465, 480, 583, 12, 377, 205}"
897,1,851,0,1.1013148,"\int \frac{x^9}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^9/((a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}-\frac{\sqrt[4]{-a} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{-a} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{3/4} \sqrt{a d-b c}}+\frac{\left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} \sqrt[4]{d} \sqrt{d x^8+c}}-\frac{a \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}","-\frac{\left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}-\frac{\sqrt[4]{-a} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{-a} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{3/4} \sqrt{a d-b c}}+\frac{\left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b \sqrt[4]{c} \sqrt[4]{d} \sqrt{d x^8+c}}-\frac{a \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}",1,"-((-a)^(1/4)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*b^(3/4)*Sqrt[b*c - a*d]) - ((-a)^(1/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*b^(3/4)*Sqrt[-(b*c) + a*d]) + ((Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(4*b*c^(1/4)*d^(1/4)*Sqrt[c + d*x^8]) - (a*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*b*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*b*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8])","A",10,6,24,0.2500,1,"{465, 483, 220, 409, 1217, 1707}"
898,1,754,0,0.7655453,"\int \frac{x}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x/((a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 (-a)^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{x^2 \sqrt{a d-b c}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 (-a)^{3/4} \sqrt{a d-b c}}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{-a} \sqrt{b} \sqrt{c}+a \sqrt{d}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}","-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 (-a)^{3/4} \sqrt{b c-a d}}-\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{x^2 \sqrt{a d-b c}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 (-a)^{3/4} \sqrt{a d-b c}}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{-a} \sqrt{b} \sqrt{c}+a \sqrt{d}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}",1,"-(b^(1/4)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*(-a)^(3/4)*Sqrt[b*c - a*d]) - (b^(1/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*(-a)^(3/4)*Sqrt[-(b*c) + a*d]) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8])","A",8,5,22,0.2273,1,"{465, 409, 1217, 220, 1707}"
899,1,878,0,1.2215886,"\int \frac{1}{x^7 \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^7*(a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{b \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{7/4} \sqrt{b c-a d}}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{7/4} \sqrt{a d-b c}}-\frac{d^{3/4} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{12 a c^{5/4} \sqrt{d x^8+c}}-\frac{b \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}-\frac{\sqrt{d x^8+c}}{6 a c x^6}","-\frac{b \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{7/4} \sqrt{b c-a d}}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{7/4} \sqrt{a d-b c}}-\frac{d^{3/4} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{12 a c^{5/4} \sqrt{d x^8+c}}-\frac{b \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}-\frac{\sqrt{d x^8+c}}{6 a c x^6}",1,"-Sqrt[c + d*x^8]/(6*a*c*x^6) - (b^(5/4)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*(-a)^(7/4)*Sqrt[b*c - a*d]) - (b^(5/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*(-a)^(7/4)*Sqrt[-(b*c) + a*d]) - (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(12*a*c^(5/4)*Sqrt[c + d*x^8]) - (b*((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - (b*(Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a^2*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - (b*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - (b*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a^2*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8])","A",11,7,24,0.2917,1,"{465, 480, 523, 220, 409, 1217, 1707}"
900,1,1005,0,1.3633301,"\int \frac{x^{13}}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^13/((a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{-a} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{(-a)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{5/4} \sqrt{b c-a d}}-\frac{(-a)^{3/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{5/4} \sqrt{a d-b c}}-\frac{\sqrt[4]{c} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b d^{3/4} \sqrt{d x^8+c}}+\frac{\sqrt[4]{c} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b d^{3/4} \sqrt{d x^8+c}}+\frac{a \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{a \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{-a} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{x^2 \sqrt{d x^8+c}}{2 b \sqrt{d} \left(\sqrt{d} x^4+\sqrt{c}\right)}","-\frac{\sqrt{-a} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{(-a)^{3/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{5/4} \sqrt{b c-a d}}-\frac{(-a)^{3/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 b^{5/4} \sqrt{a d-b c}}-\frac{\sqrt[4]{c} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 b d^{3/4} \sqrt{d x^8+c}}+\frac{\sqrt[4]{c} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 b d^{3/4} \sqrt{d x^8+c}}+\frac{a \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{a \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{-a} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{x^2 \sqrt{d x^8+c}}{2 b \sqrt{d} \left(\sqrt{d} x^4+\sqrt{c}\right)}",1,"(x^2*Sqrt[c + d*x^8])/(2*b*Sqrt[d]*(Sqrt[c] + Sqrt[d]*x^4)) + ((-a)^(3/4)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*b^(5/4)*Sqrt[b*c - a*d]) - ((-a)^(3/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*b^(5/4)*Sqrt[-(b*c) + a*d]) - (c^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticE[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(2*b*d^(3/4)*Sqrt[c + d*x^8]) + (c^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(4*b*d^(3/4)*Sqrt[c + d*x^8]) + (a*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + (a*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*b*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + (Sqrt[-a]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - (Sqrt[-a]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*b^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8])","A",12,8,24,0.3333,1,"{465, 483, 305, 220, 1196, 490, 1217, 1707}"
901,1,768,0,0.9350994,"\int \frac{x^5}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^5/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{\tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 \sqrt[4]{-a} \sqrt[4]{b} \sqrt{b c-a d}}-\frac{\tan ^{-1}\left(\frac{x^2 \sqrt{a d-b c}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 \sqrt[4]{-a} \sqrt[4]{b} \sqrt{a d-b c}}-\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}-\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}-\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 \sqrt{-a} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 \sqrt{-a} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}","\frac{\tan ^{-1}\left(\frac{x^2 \sqrt{b c-a d}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 \sqrt[4]{-a} \sqrt[4]{b} \sqrt{b c-a d}}-\frac{\tan ^{-1}\left(\frac{x^2 \sqrt{a d-b c}}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{c+d x^8}}\right)}{8 \sqrt[4]{-a} \sqrt[4]{b} \sqrt{a d-b c}}-\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}-\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}+\sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 \sqrt[4]{c} \sqrt{c+d x^8} (a d+b c)}-\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 \sqrt{-a} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}+\frac{\left(\sqrt{c}+\sqrt{d} x^4\right) \sqrt{\frac{c+d x^8}{\left(\sqrt{c}+\sqrt{d} x^4\right)^2}} \left(\sqrt{-a} \sqrt{d}+\sqrt{b} \sqrt{c}\right)^2 \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 \sqrt{-a} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} \sqrt{c+d x^8} (a d+b c)}",1,"ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])]/(8*(-a)^(1/4)*b^(1/4)*Sqrt[b*c - a*d]) - ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])]/(8*(-a)^(1/4)*b^(1/4)*Sqrt[-(b*c) + a*d]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*Sqrt[-a]*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*Sqrt[-a]*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8])","A",8,5,24,0.2083,1,"{465, 490, 1217, 220, 1707}"
902,1,1032,0,1.6116773,"\int \frac{1}{x^3 \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^3*(a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{b} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 (-a)^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{5/4} \sqrt{b c-a d}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{5/4} \sqrt{a d-b c}}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 a c^{3/4} \sqrt{d x^8+c}}+\frac{\sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a c^{3/4} \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 (-a)^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{d} x^2 \sqrt{d x^8+c}}{2 a c \left(\sqrt{d} x^4+\sqrt{c}\right)}-\frac{\sqrt{d x^8+c}}{2 a c x^2}","-\frac{\sqrt{b} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{16 (-a)^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{5/4} \sqrt{b c-a d}}-\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{8 (-a)^{5/4} \sqrt{a d-b c}}-\frac{\sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{2 a c^{3/4} \sqrt{d x^8+c}}+\frac{\sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{4 a c^{3/4} \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a \sqrt[4]{c} (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 (-a)^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{d} x^2 \sqrt{d x^8+c}}{2 a c \left(\sqrt{d} x^4+\sqrt{c}\right)}-\frac{\sqrt{d x^8+c}}{2 a c x^2}",1,"-Sqrt[c + d*x^8]/(2*a*c*x^2) + (Sqrt[d]*x^2*Sqrt[c + d*x^8])/(2*a*c*(Sqrt[c] + Sqrt[d]*x^4)) + (b^(3/4)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*(-a)^(5/4)*Sqrt[b*c - a*d]) - (b^(3/4)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(8*(-a)^(5/4)*Sqrt[-(b*c) + a*d]) - (d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticE[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(2*a*c^(3/4)*Sqrt[c + d*x^8]) + (d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(4*a*c^(3/4)*Sqrt[c + d*x^8]) + (b*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + (b*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a*c^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) + (Sqrt[b]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8]) - (Sqrt[b]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*(-a)^(3/2)*c^(1/4)*d^(1/4)*(b*c + a*d)*Sqrt[c + d*x^8])","A",14,9,24,0.3750,1,"{465, 480, 584, 305, 220, 1196, 490, 1217, 1707}"
903,1,64,0,0.051597,"\int \frac{x^4}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^4/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{x^5 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{5}{8};1,\frac{1}{2};\frac{13}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{5 a \sqrt{c+d x^8}}","\frac{x^5 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{5}{8};1,\frac{1}{2};\frac{13}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{5 a \sqrt{c+d x^8}}",1,"(x^5*Sqrt[1 + (d*x^8)/c]*AppellF1[5/8, 1, 1/2, 13/8, -((b*x^8)/a), -((d*x^8)/c)])/(5*a*Sqrt[c + d*x^8])","A",2,2,24,0.08333,1,"{511, 510}"
904,1,64,0,0.053032,"\int \frac{x^2}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[x^2/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{x^3 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{3}{8};1,\frac{1}{2};\frac{11}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a \sqrt{c+d x^8}}","\frac{x^3 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{3}{8};1,\frac{1}{2};\frac{11}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a \sqrt{c+d x^8}}",1,"(x^3*Sqrt[1 + (d*x^8)/c]*AppellF1[3/8, 1, 1/2, 11/8, -((b*x^8)/a), -((d*x^8)/c)])/(3*a*Sqrt[c + d*x^8])","A",2,2,24,0.08333,1,"{511, 510}"
905,1,59,0,0.0272912,"\int \frac{1}{\left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/((a + b*x^8)*Sqrt[c + d*x^8]),x]","\frac{x \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{1}{8};1,\frac{1}{2};\frac{9}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a \sqrt{c+d x^8}}","\frac{x \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{1}{8};1,\frac{1}{2};\frac{9}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a \sqrt{c+d x^8}}",1,"(x*Sqrt[1 + (d*x^8)/c]*AppellF1[1/8, 1, 1/2, 9/8, -((b*x^8)/a), -((d*x^8)/c)])/(a*Sqrt[c + d*x^8])","A",2,2,21,0.09524,1,"{430, 429}"
906,1,62,0,0.0586223,"\int \frac{1}{x^2 \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^2*(a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{1}{8};1,\frac{1}{2};\frac{7}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a x \sqrt{c+d x^8}}","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{1}{8};1,\frac{1}{2};\frac{7}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a x \sqrt{c+d x^8}}",1,"-((Sqrt[1 + (d*x^8)/c]*AppellF1[-1/8, 1, 1/2, 7/8, -((b*x^8)/a), -((d*x^8)/c)])/(a*x*Sqrt[c + d*x^8]))","A",2,2,24,0.08333,1,"{511, 510}"
907,1,64,0,0.05565,"\int \frac{1}{x^4 \left(a+b x^8\right) \sqrt{c+d x^8}} \, dx","Int[1/(x^4*(a + b*x^8)*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{3}{8};1,\frac{1}{2};\frac{5}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a x^3 \sqrt{c+d x^8}}","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{3}{8};1,\frac{1}{2};\frac{5}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a x^3 \sqrt{c+d x^8}}",1,"-(Sqrt[1 + (d*x^8)/c]*AppellF1[-3/8, 1, 1/2, 5/8, -((b*x^8)/a), -((d*x^8)/c)])/(3*a*x^3*Sqrt[c + d*x^8])","A",2,2,24,0.08333,1,"{511, 510}"
908,1,123,0,0.1424709,"\int \frac{x^{23}}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^23/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{a^2 \sqrt{c+d x^8}}{8 b^2 \left(a+b x^8\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 b^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^8}}{4 b^2 d}","-\frac{a^2 \sqrt{c+d x^8}}{8 b^2 \left(a+b x^8\right) (b c-a d)}+\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 b^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^8}}{4 b^2 d}",1,"Sqrt[c + d*x^8]/(4*b^2*d) - (a^2*Sqrt[c + d*x^8])/(8*b^2*(b*c - a*d)*(a + b*x^8)) + (a*(4*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(8*b^(5/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{446, 89, 80, 63, 208}"
909,1,99,0,0.0829682,"\int \frac{x^{15}}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^15/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{a \sqrt{c+d x^8}}{8 b \left(a+b x^8\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 b^{3/2} (b c-a d)^{3/2}}","\frac{a \sqrt{c+d x^8}}{8 b \left(a+b x^8\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 b^{3/2} (b c-a d)^{3/2}}",1,"(a*Sqrt[c + d*x^8])/(8*b*(b*c - a*d)*(a + b*x^8)) - ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(8*b^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
910,1,87,0,0.0733321,"\int \frac{x^7}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^7/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^8}}{8 \left(a+b x^8\right) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^8}}{8 \left(a+b x^8\right) (b c-a d)}",1,"-Sqrt[c + d*x^8]/(8*(b*c - a*d)*(a + b*x^8)) + (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(8*Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{444, 51, 63, 208}"
911,1,132,0,0.1372627,"\int \frac{1}{x \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{4 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^8}}{8 a \left(a+b x^8\right) (b c-a d)}","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{4 a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^8}}{8 a \left(a+b x^8\right) (b c-a d)}",1,"(b*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*(a + b*x^8)) - ArcTanh[Sqrt[c + d*x^8]/Sqrt[c]]/(4*a^2*Sqrt[c]) + (Sqrt[b]*(2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(8*a^2*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
912,1,185,0,0.2293783,"\int \frac{1}{x^9 \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^9*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{8 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^8} (2 b c-a d)}{8 a^2 c \left(a+b x^8\right) (b c-a d)}-\frac{\sqrt{c+d x^8}}{8 a c x^8 \left(a+b x^8\right)}","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^8}}{\sqrt{b c-a d}}\right)}{8 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^8}}{\sqrt{c}}\right)}{8 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^8} (2 b c-a d)}{8 a^2 c \left(a+b x^8\right) (b c-a d)}-\frac{\sqrt{c+d x^8}}{8 a c x^8 \left(a+b x^8\right)}",1,"-(b*(2*b*c - a*d)*Sqrt[c + d*x^8])/(8*a^2*c*(b*c - a*d)*(a + b*x^8)) - Sqrt[c + d*x^8]/(8*a*c*x^8*(a + b*x^8)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x^8]/Sqrt[c]])/(8*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^8])/Sqrt[b*c - a*d]])/(8*a^3*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 151, 156, 63, 208}"
913,1,141,0,0.1599606,"\int \frac{x^{19}}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^19/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 b^2 (b c-a d)^{3/2}}+\frac{a x^4 \sqrt{c+d x^8}}{8 b \left(a+b x^8\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^4}{\sqrt{c+d x^8}}\right)}{4 b^2 \sqrt{d}}","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 b^2 (b c-a d)^{3/2}}+\frac{a x^4 \sqrt{c+d x^8}}{8 b \left(a+b x^8\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x^4}{\sqrt{c+d x^8}}\right)}{4 b^2 \sqrt{d}}",1,"(a*x^4*Sqrt[c + d*x^8])/(8*b*(b*c - a*d)*(a + b*x^8)) - (Sqrt[a]*(3*b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(8*b^2*(b*c - a*d)^(3/2)) + ArcTanh[(Sqrt[d]*x^4)/Sqrt[c + d*x^8]]/(4*b^2*Sqrt[d])","A",7,7,24,0.2917,1,"{465, 470, 523, 217, 206, 377, 205}"
914,1,93,0,0.0856842,"\int \frac{x^{11}}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^11/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{c \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 \sqrt{a} (b c-a d)^{3/2}}-\frac{x^4 \sqrt{c+d x^8}}{8 \left(a+b x^8\right) (b c-a d)}","\frac{c \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 \sqrt{a} (b c-a d)^{3/2}}-\frac{x^4 \sqrt{c+d x^8}}{8 \left(a+b x^8\right) (b c-a d)}",1,"-(x^4*Sqrt[c + d*x^8])/(8*(b*c - a*d)*(a + b*x^8)) + (c*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(8*Sqrt[a]*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{465, 471, 12, 377, 205}"
915,1,104,0,0.090251,"\int \frac{x^3}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^3/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 a^{3/2} (b c-a d)^{3/2}}+\frac{b x^4 \sqrt{c+d x^8}}{8 a \left(a+b x^8\right) (b c-a d)}","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 a^{3/2} (b c-a d)^{3/2}}+\frac{b x^4 \sqrt{c+d x^8}}{8 a \left(a+b x^8\right) (b c-a d)}",1,"(b*x^4*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*(a + b*x^8)) + ((b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(8*a^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{465, 382, 377, 205}"
916,1,149,0,0.1848417,"\int \frac{1}{x^5 \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^5*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{c+d x^8} (3 b c-2 a d)}{8 a^2 c x^4 (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^8}}{8 a x^4 \left(a+b x^8\right) (b c-a d)}","-\frac{\sqrt{c+d x^8} (3 b c-2 a d)}{8 a^2 c x^4 (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^8}}{8 a x^4 \left(a+b x^8\right) (b c-a d)}",1,"-((3*b*c - 2*a*d)*Sqrt[c + d*x^8])/(8*a^2*c*(b*c - a*d)*x^4) + (b*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*x^4*(a + b*x^8)) - (b*(3*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(8*a^(5/2)*(b*c - a*d)^(3/2))","A",6,6,24,0.2500,1,"{465, 472, 583, 12, 377, 205}"
917,1,208,0,0.2974865,"\int \frac{1}{x^{13} \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^13*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{\sqrt{c+d x^8} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{24 a^3 c^2 x^4 (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^8} (5 b c-2 a d)}{24 a^2 c x^{12} (b c-a d)}+\frac{b \sqrt{c+d x^8}}{8 a x^{12} \left(a+b x^8\right) (b c-a d)}","\frac{\sqrt{c+d x^8} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{24 a^3 c^2 x^4 (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x^4 \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^8}}\right)}{8 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^8} (5 b c-2 a d)}{24 a^2 c x^{12} (b c-a d)}+\frac{b \sqrt{c+d x^8}}{8 a x^{12} \left(a+b x^8\right) (b c-a d)}",1,"-((5*b*c - 2*a*d)*Sqrt[c + d*x^8])/(24*a^2*c*(b*c - a*d)*x^12) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*Sqrt[c + d*x^8])/(24*a^3*c^2*(b*c - a*d)*x^4) + (b*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*x^12*(a + b*x^8)) + (b^2*(5*b*c - 6*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^4)/(Sqrt[a]*Sqrt[c + d*x^8])])/(8*a^(7/2)*(b*c - a*d)^(3/2))","A",7,6,24,0.2500,1,"{465, 472, 583, 12, 377, 205}"
918,1,924,0,1.2876979,"\int \frac{x^9}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^9/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{\left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^8+c}}-\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{3/4} b^{3/4} (b c-a d)^{3/2}}+\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{3/4} b^{3/4} (a d-b c)^{3/2}}-\frac{d^{3/4} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a b \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^8+c}}-\frac{x^2 \sqrt{d x^8+c}}{8 (b c-a d) \left(b x^8+a\right)}","\frac{\left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^8+c}}-\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{3/4} b^{3/4} (b c-a d)^{3/2}}+\frac{(b c+a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{3/4} b^{3/4} (a d-b c)^{3/2}}-\frac{d^{3/4} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{d} a+\sqrt{-a} \sqrt{b} \sqrt{c}\right) \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a b \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 a b \sqrt[4]{c} \sqrt[4]{d} (b c-a d) \sqrt{d x^8+c}}-\frac{x^2 \sqrt{d x^8+c}}{8 (b c-a d) \left(b x^8+a\right)}",1,"-(x^2*Sqrt[c + d*x^8])/(8*(b*c - a*d)*(a + b*x^8)) - ((b*c + a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(3/4)*b^(3/4)*(b*c - a*d)^(3/2)) + ((b*c + a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(3/4)*b^(3/4)*(-(b*c) + a*d)^(3/2)) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*b*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + ((Sqrt[-a]*Sqrt[b]*Sqrt[c] + a*Sqrt[d])*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*a*b*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^8]) - (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*b*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*a*b*c^(1/4)*d^(1/4)*(b*c - a*d)*Sqrt[c + d*x^8])","A",11,7,24,0.2917,1,"{465, 471, 523, 220, 409, 1217, 1707}"
919,1,999,0,1.4063803,"\int \frac{x}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{(3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{32 (-a)^{3/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{7/4} (b c-a d)^{3/2}}-\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{7/4} (a d-b c)^{3/2}}+\frac{d^{3/4} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b x^2 \sqrt{d x^8+c}}{8 a (b c-a d) \left(b x^8+a\right)}","\frac{(3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{32 (-a)^{3/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{7/4} (b c-a d)^{3/2}}-\frac{\sqrt[4]{b} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{7/4} (a d-b c)^{3/2}}+\frac{d^{3/4} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a \sqrt[4]{c} (b c-a d) \sqrt{d x^8+c}}+\frac{\left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{-a}}+\sqrt{d}\right) \sqrt[4]{d} (3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-5 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 a^2 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b x^2 \sqrt{d x^8+c}}{8 a (b c-a d) \left(b x^8+a\right)}",1,"(b*x^2*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*(a + b*x^8)) + (b^(1/4)*(3*b*c - 5*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(7/4)*(b*c - a*d)^(3/2)) - (b^(1/4)*(3*b*c - 5*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(7/4)*(-(b*c) + a*d)^(3/2)) + (d^(3/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a*c^(1/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + (((Sqrt[b]*Sqrt[c])/Sqrt[-a] + Sqrt[d])*d^(1/4)*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*(-a)^(3/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(3*b*c - 5*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*a^2*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8])","A",11,7,22,0.3182,1,"{465, 414, 523, 220, 409, 1217, 1707}"
920,1,1060,0,1.9825249,"\int \frac{1}{x^7 \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^7*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{b (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{32 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{11/4} (b c-a d)^{3/2}}-\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{11/4} (a d-b c)^{3/2}}-\frac{d^{3/4} (7 b c-4 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{48 a^2 c^{5/4} (b c-a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b \sqrt{d x^8+c}}{8 a (b c-a d) x^6 \left(b x^8+a\right)}-\frac{(7 b c-4 a d) \sqrt{d x^8+c}}{24 a^2 c (b c-a d) x^6}","-\frac{b (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)}{32 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{11/4} (b c-a d)^{3/2}}-\frac{b^{5/4} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{11/4} (a d-b c)^{3/2}}-\frac{d^{3/4} (7 b c-4 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{48 a^2 c^{5/4} (b c-a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right) \sqrt[4]{d} (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 (-a)^{5/2} \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{b \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (7 b c-9 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 a^3 \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b \sqrt{d x^8+c}}{8 a (b c-a d) x^6 \left(b x^8+a\right)}-\frac{(7 b c-4 a d) \sqrt{d x^8+c}}{24 a^2 c (b c-a d) x^6}",1,"-((7*b*c - 4*a*d)*Sqrt[c + d*x^8])/(24*a^2*c*(b*c - a*d)*x^6) + (b*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*x^6*(a + b*x^8)) + (b^(5/4)*(7*b*c - 9*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(11/4)*(b*c - a*d)^(3/2)) - (b^(5/4)*(7*b*c - 9*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(11/4)*(-(b*c) + a*d)^(3/2)) - (d^(3/4)*(7*b*c - 4*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(48*a^2*c^(5/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + (b*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])*d^(1/4)*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - (b*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])*d^(1/4)*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*(-a)^(5/2)*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - (b*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - (b*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(7*b*c - 9*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*a^3*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8])","A",12,8,24,0.3333,1,"{465, 472, 583, 523, 220, 409, 1217, 1707}"
921,1,1164,0,1.9355314,"\int \frac{x^{13}}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^13/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{d x^8+c} x^6}{8 (b c-a d) \left(b x^8+a\right)}+\frac{\sqrt{d} \sqrt{d x^8+c} x^2}{8 b (b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right)}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 \sqrt[4]{-a} b^{5/4} (b c-a d)^{3/2}}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 \sqrt[4]{-a} b^{5/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b (b c-a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b (b c-a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}","-\frac{\sqrt{d x^8+c} x^6}{8 (b c-a d) \left(b x^8+a\right)}+\frac{\sqrt{d} \sqrt{d x^8+c} x^2}{8 b (b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right)}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 \sqrt[4]{-a} b^{5/4} (b c-a d)^{3/2}}+\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 \sqrt[4]{-a} b^{5/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 b (b c-a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 b (b c-a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 b \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (3 b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 \sqrt{-a} b^{3/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}",1,"(Sqrt[d]*x^2*Sqrt[c + d*x^8])/(8*b*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)) - (x^6*Sqrt[c + d*x^8])/(8*(b*c - a*d)*(a + b*x^8)) + ((3*b*c - a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(1/4)*b^(5/4)*(b*c - a*d)^(3/2)) + ((3*b*c - a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(1/4)*b^(5/4)*(-(b*c) + a*d)^(3/2)) - (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticE[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*b*(b*c - a*d)*Sqrt[c + d*x^8]) + (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*b*(b*c - a*d)*Sqrt[c + d*x^8]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*b*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*Sqrt[-a]*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(3*b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*Sqrt[-a]*b^(3/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8])","A",14,9,24,0.3750,1,"{465, 471, 584, 305, 220, 1196, 490, 1217, 1707}"
922,1,1162,0,1.9097303,"\int \frac{x^5}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^5/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{b \sqrt{d x^8+c} x^6}{8 a (b c-a d) \left(b x^8+a\right)}-\frac{\sqrt{d} \sqrt{d x^8+c} x^2}{8 a (b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right)}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{5/4} \sqrt[4]{b} (b c-a d)^{3/2}}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{5/4} \sqrt[4]{b} (a d-b c)^{3/2}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a (b c-a d) \sqrt{d x^8+c}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a (b c-a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}","\frac{b \sqrt{d x^8+c} x^6}{8 a (b c-a d) \left(b x^8+a\right)}-\frac{\sqrt{d} \sqrt{d x^8+c} x^2}{8 a (b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right)}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{5/4} \sqrt[4]{b} (b c-a d)^{3/2}}-\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{5/4} \sqrt[4]{b} (a d-b c)^{3/2}}+\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a (b c-a d) \sqrt{d x^8+c}}-\frac{\sqrt[4]{c} \sqrt[4]{d} \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a (b c-a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2 (b c-3 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 (-a)^{3/2} \sqrt{b} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}",1,"-(Sqrt[d]*x^2*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)) + (b*x^6*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*(a + b*x^8)) - ((b*c - 3*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(5/4)*b^(1/4)*(b*c - a*d)^(3/2)) - ((b*c - 3*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(5/4)*b^(1/4)*(-(b*c) + a*d)^(3/2)) + (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticE[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a*(b*c - a*d)*Sqrt[c + d*x^8]) - (c^(1/4)*d^(1/4)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a*(b*c - a*d)*Sqrt[c + d*x^8]) - ((Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*a*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - ((Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*(-a)^(3/2)*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + ((Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(b*c - 3*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*(-a)^(3/2)*Sqrt[b]*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8])","A",14,9,24,0.3750,1,"{465, 472, 584, 305, 220, 1196, 490, 1217, 1707}"
923,1,1243,0,2.3838373,"\int \frac{1}{x^3 \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^3*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{\sqrt{b} (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{9/4} (b c-a d)^{3/2}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{9/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 c^{3/4} (b c-a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 c^{3/4} (b c-a d) \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{d} (5 b c-4 a d) x^2 \sqrt{d x^8+c}}{8 a^2 c (b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right)}+\frac{b \sqrt{d x^8+c}}{8 a (b c-a d) x^2 \left(b x^8+a\right)}-\frac{(5 b c-4 a d) \sqrt{d x^8+c}}{8 a^2 c (b c-a d) x^2}","\frac{\sqrt{b} (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(\frac{\left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right) \left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{64 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b c-a d} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{9/4} (b c-a d)^{3/2}}-\frac{b^{3/4} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{a d-b c} x^2}{\sqrt[4]{-a} \sqrt[4]{b} \sqrt{d x^8+c}}\right)}{32 (-a)^{9/4} (a d-b c)^{3/2}}-\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{8 a^2 c^{3/4} (b c-a d) \sqrt{d x^8+c}}+\frac{\sqrt[4]{d} (5 b c-4 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{16 a^2 c^{3/4} (b c-a d) \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}-\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{b \left(\sqrt{c}+\frac{\sqrt{-a} \sqrt{d}}{\sqrt{b}}\right) \sqrt[4]{d} (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{32 a^2 \sqrt[4]{c} (b c-a d) (b c+a d) \sqrt{d x^8+c}}-\frac{\sqrt{b} \left(\sqrt{b} \sqrt{c}+\sqrt{-a} \sqrt{d}\right)^2 (5 b c-7 a d) \left(\sqrt{d} x^4+\sqrt{c}\right) \sqrt{\frac{d x^8+c}{\left(\sqrt{d} x^4+\sqrt{c}\right)^2}} \Pi \left(-\frac{\left(\sqrt{b} \sqrt{c}-\sqrt{-a} \sqrt{d}\right)^2}{4 \sqrt{-a} \sqrt{b} \sqrt{c} \sqrt{d}};2 \tan ^{-1}\left(\frac{\sqrt[4]{d} x^2}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{64 (-a)^{5/2} \sqrt[4]{c} \sqrt[4]{d} (b c-a d) (b c+a d) \sqrt{d x^8+c}}+\frac{\sqrt{d} (5 b c-4 a d) x^2 \sqrt{d x^8+c}}{8 a^2 c (b c-a d) \left(\sqrt{d} x^4+\sqrt{c}\right)}+\frac{b \sqrt{d x^8+c}}{8 a (b c-a d) x^2 \left(b x^8+a\right)}-\frac{(5 b c-4 a d) \sqrt{d x^8+c}}{8 a^2 c (b c-a d) x^2}",1,"-((5*b*c - 4*a*d)*Sqrt[c + d*x^8])/(8*a^2*c*(b*c - a*d)*x^2) + (Sqrt[d]*(5*b*c - 4*a*d)*x^2*Sqrt[c + d*x^8])/(8*a^2*c*(b*c - a*d)*(Sqrt[c] + Sqrt[d]*x^4)) + (b*Sqrt[c + d*x^8])/(8*a*(b*c - a*d)*x^2*(a + b*x^8)) - (b^(3/4)*(5*b*c - 7*a*d)*ArcTan[(Sqrt[b*c - a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(9/4)*(b*c - a*d)^(3/2)) - (b^(3/4)*(5*b*c - 7*a*d)*ArcTan[(Sqrt[-(b*c) + a*d]*x^2)/((-a)^(1/4)*b^(1/4)*Sqrt[c + d*x^8])])/(32*(-a)^(9/4)*(-(b*c) + a*d)^(3/2)) - (d^(1/4)*(5*b*c - 4*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticE[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(8*a^2*c^(3/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + (d^(1/4)*(5*b*c - 4*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(16*a^2*c^(3/4)*(b*c - a*d)*Sqrt[c + d*x^8]) + (b*(Sqrt[c] - (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + (b*(Sqrt[c] + (Sqrt[-a]*Sqrt[d])/Sqrt[b])*d^(1/4)*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticF[2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(32*a^2*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) - (Sqrt[b]*(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[-(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8]) + (Sqrt[b]*(Sqrt[b]*Sqrt[c] - Sqrt[-a]*Sqrt[d])^2*(5*b*c - 7*a*d)*(Sqrt[c] + Sqrt[d]*x^4)*Sqrt[(c + d*x^8)/(Sqrt[c] + Sqrt[d]*x^4)^2]*EllipticPi[(Sqrt[b]*Sqrt[c] + Sqrt[-a]*Sqrt[d])^2/(4*Sqrt[-a]*Sqrt[b]*Sqrt[c]*Sqrt[d]), 2*ArcTan[(d^(1/4)*x^2)/c^(1/4)], 1/2])/(64*(-a)^(5/2)*c^(1/4)*d^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[c + d*x^8])","A",15,10,24,0.4167,1,"{465, 472, 583, 584, 305, 220, 1196, 490, 1217, 1707}"
924,1,64,0,0.05191,"\int \frac{x^4}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^4/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{x^5 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{5}{8};2,\frac{1}{2};\frac{13}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{5 a^2 \sqrt{c+d x^8}}","\frac{x^5 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{5}{8};2,\frac{1}{2};\frac{13}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{5 a^2 \sqrt{c+d x^8}}",1,"(x^5*Sqrt[1 + (d*x^8)/c]*AppellF1[5/8, 2, 1/2, 13/8, -((b*x^8)/a), -((d*x^8)/c)])/(5*a^2*Sqrt[c + d*x^8])","A",2,2,24,0.08333,1,"{511, 510}"
925,1,64,0,0.0530837,"\int \frac{x^2}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[x^2/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{x^3 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{3}{8};2,\frac{1}{2};\frac{11}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a^2 \sqrt{c+d x^8}}","\frac{x^3 \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{3}{8};2,\frac{1}{2};\frac{11}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a^2 \sqrt{c+d x^8}}",1,"(x^3*Sqrt[1 + (d*x^8)/c]*AppellF1[3/8, 2, 1/2, 11/8, -((b*x^8)/a), -((d*x^8)/c)])/(3*a^2*Sqrt[c + d*x^8])","A",2,2,24,0.08333,1,"{511, 510}"
926,1,59,0,0.0270407,"\int \frac{1}{\left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/((a + b*x^8)^2*Sqrt[c + d*x^8]),x]","\frac{x \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{1}{8};2,\frac{1}{2};\frac{9}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a^2 \sqrt{c+d x^8}}","\frac{x \sqrt{\frac{d x^8}{c}+1} F_1\left(\frac{1}{8};2,\frac{1}{2};\frac{9}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a^2 \sqrt{c+d x^8}}",1,"(x*Sqrt[1 + (d*x^8)/c]*AppellF1[1/8, 2, 1/2, 9/8, -((b*x^8)/a), -((d*x^8)/c)])/(a^2*Sqrt[c + d*x^8])","A",2,2,21,0.09524,1,"{430, 429}"
927,1,62,0,0.0544516,"\int \frac{1}{x^2 \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^2*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{1}{8};2,\frac{1}{2};\frac{7}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a^2 x \sqrt{c+d x^8}}","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{1}{8};2,\frac{1}{2};\frac{7}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{a^2 x \sqrt{c+d x^8}}",1,"-((Sqrt[1 + (d*x^8)/c]*AppellF1[-1/8, 2, 1/2, 7/8, -((b*x^8)/a), -((d*x^8)/c)])/(a^2*x*Sqrt[c + d*x^8]))","A",2,2,24,0.08333,1,"{511, 510}"
928,1,64,0,0.0561598,"\int \frac{1}{x^4 \left(a+b x^8\right)^2 \sqrt{c+d x^8}} \, dx","Int[1/(x^4*(a + b*x^8)^2*Sqrt[c + d*x^8]),x]","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{3}{8};2,\frac{1}{2};\frac{5}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a^2 x^3 \sqrt{c+d x^8}}","-\frac{\sqrt{\frac{d x^8}{c}+1} F_1\left(-\frac{3}{8};2,\frac{1}{2};\frac{5}{8};-\frac{b x^8}{a},-\frac{d x^8}{c}\right)}{3 a^2 x^3 \sqrt{c+d x^8}}",1,"-(Sqrt[1 + (d*x^8)/c]*AppellF1[-3/8, 2, 1/2, 5/8, -((b*x^8)/a), -((d*x^8)/c)])/(3*a^2*x^3*Sqrt[c + d*x^8])","A",2,2,24,0.08333,1,"{511, 510}"
929,1,123,0,0.0942834,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^5 \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^5,x]","-\frac{d^2 (2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{16 c^{5/2}}+\frac{d x^2 \sqrt{c+\frac{d}{x^2}} (2 b c-a d)}{16 c^2}+\frac{x^4 \sqrt{c+\frac{d}{x^2}} (2 b c-a d)}{8 c}+\frac{a x^6 \left(c+\frac{d}{x^2}\right)^{3/2}}{6 c}","-\frac{d^2 (2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{16 c^{5/2}}+\frac{d x^2 \sqrt{c+\frac{d}{x^2}} (2 b c-a d)}{16 c^2}+\frac{x^4 \sqrt{c+\frac{d}{x^2}} (2 b c-a d)}{8 c}+\frac{a x^6 \left(c+\frac{d}{x^2}\right)^{3/2}}{6 c}",1,"(d*(2*b*c - a*d)*Sqrt[c + d/x^2]*x^2)/(16*c^2) + ((2*b*c - a*d)*Sqrt[c + d/x^2]*x^4)/(8*c) + (a*(c + d/x^2)^(3/2)*x^6)/(6*c) - (d^2*(2*b*c - a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(16*c^(5/2))","A",6,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
930,1,90,0,0.0678375,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^3 \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^3,x]","\frac{d (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 c^{3/2}}+\frac{x^2 \sqrt{c+\frac{d}{x^2}} (4 b c-a d)}{8 c}+\frac{a x^4 \left(c+\frac{d}{x^2}\right)^{3/2}}{4 c}","\frac{d (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 c^{3/2}}+\frac{x^2 \sqrt{c+\frac{d}{x^2}} (4 b c-a d)}{8 c}+\frac{a x^4 \left(c+\frac{d}{x^2}\right)^{3/2}}{4 c}",1,"((4*b*c - a*d)*Sqrt[c + d/x^2]*x^2)/(8*c) + (a*(c + d/x^2)^(3/2)*x^4)/(4*c) + (d*(4*b*c - a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(8*c^(3/2))","A",5,5,22,0.2273,1,"{446, 78, 47, 63, 208}"
931,1,84,0,0.0579218,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x,x]","-\frac{\sqrt{c+\frac{d}{x^2}} (a d+2 b c)}{2 c}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2 \sqrt{c}}+\frac{a x^2 \left(c+\frac{d}{x^2}\right)^{3/2}}{2 c}","-\frac{\sqrt{c+\frac{d}{x^2}} (a d+2 b c)}{2 c}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2 \sqrt{c}}+\frac{a x^2 \left(c+\frac{d}{x^2}\right)^{3/2}}{2 c}",1,"-((2*b*c + a*d)*Sqrt[c + d/x^2])/(2*c) + (a*(c + d/x^2)^(3/2)*x^2)/(2*c) + ((2*b*c + a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(2*Sqrt[c])","A",5,5,20,0.2500,1,"{446, 78, 50, 63, 208}"
932,1,59,0,0.0431102,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x,x]","-a \sqrt{c+\frac{d}{x^2}}+a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{3 d}","-a \sqrt{c+\frac{d}{x^2}}+a \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{3 d}",1,"-(a*Sqrt[c + d/x^2]) - (b*(c + d/x^2)^(3/2))/(3*d) + a*Sqrt[c]*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]]","A",5,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
933,1,46,0,0.0373817,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x^3} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x^3,x]","\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^2}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d^2}","\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^2}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d^2}",1,"((b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^2) - (b*(c + d/x^2)^(5/2))/(5*d^2)","A",3,2,22,0.09091,1,"{444, 43}"
934,1,74,0,0.0587087,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x^5} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x^5,x]","\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (2 b c-a d)}{5 d^3}-\frac{c \left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^3}","\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (2 b c-a d)}{5 d^3}-\frac{c \left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^3}",1,"-(c*(b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^3) + ((2*b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^3) - (b*(c + d/x^2)^(7/2))/(7*d^3)","A",3,2,22,0.09091,1,"{446, 77}"
935,1,104,0,0.0790056,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x^7} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x^7,x]","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^4}+\frac{\left(c+\frac{d}{x^2}\right)^{7/2} (3 b c-a d)}{7 d^4}-\frac{c \left(c+\frac{d}{x^2}\right)^{5/2} (3 b c-2 a d)}{5 d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{9/2}}{9 d^4}","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^4}+\frac{\left(c+\frac{d}{x^2}\right)^{7/2} (3 b c-a d)}{7 d^4}-\frac{c \left(c+\frac{d}{x^2}\right)^{5/2} (3 b c-2 a d)}{5 d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{9/2}}{9 d^4}",1,"(c^2*(b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^4) - (c*(3*b*c - 2*a*d)*(c + d/x^2)^(5/2))/(5*d^4) + ((3*b*c - a*d)*(c + d/x^2)^(7/2))/(7*d^4) - (b*(c + d/x^2)^(9/2))/(9*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
936,1,134,0,0.1017586,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x^9} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x^9,x]","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{5/2} (4 b c-3 a d)}{5 d^5}-\frac{c^3 \left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^5}+\frac{\left(c+\frac{d}{x^2}\right)^{9/2} (4 b c-a d)}{9 d^5}-\frac{3 c \left(c+\frac{d}{x^2}\right)^{7/2} (2 b c-a d)}{7 d^5}-\frac{b \left(c+\frac{d}{x^2}\right)^{11/2}}{11 d^5}","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{5/2} (4 b c-3 a d)}{5 d^5}-\frac{c^3 \left(c+\frac{d}{x^2}\right)^{3/2} (b c-a d)}{3 d^5}+\frac{\left(c+\frac{d}{x^2}\right)^{9/2} (4 b c-a d)}{9 d^5}-\frac{3 c \left(c+\frac{d}{x^2}\right)^{7/2} (2 b c-a d)}{7 d^5}-\frac{b \left(c+\frac{d}{x^2}\right)^{11/2}}{11 d^5}",1,"-(c^3*(b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^5) + (c^2*(4*b*c - 3*a*d)*(c + d/x^2)^(5/2))/(5*d^5) - (3*c*(2*b*c - a*d)*(c + d/x^2)^(7/2))/(7*d^5) + ((4*b*c - a*d)*(c + d/x^2)^(9/2))/(9*d^5) - (b*(c + d/x^2)^(11/2))/(11*d^5)","A",3,2,22,0.09091,1,"{446, 77}"
937,1,150,0,0.0725086,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^{10} \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^10,x]","\frac{8 d^2 x^5 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{1155 c^4}-\frac{16 d^3 x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{3465 c^5}+\frac{x^9 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{99 c^2}-\frac{2 d x^7 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{231 c^3}+\frac{a x^{11} \left(c+\frac{d}{x^2}\right)^{3/2}}{11 c}","\frac{8 d^2 x^5 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{1155 c^4}-\frac{16 d^3 x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{3465 c^5}+\frac{x^9 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{99 c^2}-\frac{2 d x^7 \left(c+\frac{d}{x^2}\right)^{3/2} (11 b c-8 a d)}{231 c^3}+\frac{a x^{11} \left(c+\frac{d}{x^2}\right)^{3/2}}{11 c}",1,"(-16*d^3*(11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^3)/(3465*c^5) + (8*d^2*(11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^5)/(1155*c^4) - (2*d*(11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^7)/(231*c^3) + ((11*b*c - 8*a*d)*(c + d/x^2)^(3/2)*x^9)/(99*c^2) + (a*(c + d/x^2)^(3/2)*x^11)/(11*c)","A",5,3,22,0.1364,1,"{453, 271, 264}"
938,1,117,0,0.0616844,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^8 \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^8,x]","\frac{8 d^2 x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{315 c^4}+\frac{x^7 \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{21 c^2}-\frac{4 d x^5 \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{105 c^3}+\frac{a x^9 \left(c+\frac{d}{x^2}\right)^{3/2}}{9 c}","\frac{8 d^2 x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{315 c^4}+\frac{x^7 \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{21 c^2}-\frac{4 d x^5 \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{105 c^3}+\frac{a x^9 \left(c+\frac{d}{x^2}\right)^{3/2}}{9 c}",1,"(8*d^2*(3*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^3)/(315*c^4) - (4*d*(3*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^5)/(105*c^3) + ((3*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^7)/(21*c^2) + (a*(c + d/x^2)^(3/2)*x^9)/(9*c)","A",4,3,22,0.1364,1,"{453, 271, 264}"
939,1,84,0,0.0398965,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^6 \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^6,x]","\frac{x^5 \left(c+\frac{d}{x^2}\right)^{3/2} (7 b c-4 a d)}{35 c^2}-\frac{2 d x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (7 b c-4 a d)}{105 c^3}+\frac{a x^7 \left(c+\frac{d}{x^2}\right)^{3/2}}{7 c}","\frac{x^5 \left(c+\frac{d}{x^2}\right)^{3/2} (7 b c-4 a d)}{35 c^2}-\frac{2 d x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (7 b c-4 a d)}{105 c^3}+\frac{a x^7 \left(c+\frac{d}{x^2}\right)^{3/2}}{7 c}",1,"(-2*d*(7*b*c - 4*a*d)*(c + d/x^2)^(3/2)*x^3)/(105*c^3) + ((7*b*c - 4*a*d)*(c + d/x^2)^(3/2)*x^5)/(35*c^2) + (a*(c + d/x^2)^(3/2)*x^7)/(7*c)","A",3,3,22,0.1364,1,"{453, 271, 264}"
940,1,53,0,0.024704,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^4 \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^4,x]","\frac{x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (5 b c-2 a d)}{15 c^2}+\frac{a x^5 \left(c+\frac{d}{x^2}\right)^{3/2}}{5 c}","\frac{x^3 \left(c+\frac{d}{x^2}\right)^{3/2} (5 b c-2 a d)}{15 c^2}+\frac{a x^5 \left(c+\frac{d}{x^2}\right)^{3/2}}{5 c}",1,"((5*b*c - 2*a*d)*(c + d/x^2)^(3/2)*x^3)/(15*c^2) + (a*(c + d/x^2)^(3/2)*x^5)/(5*c)","A",2,2,22,0.09091,1,"{453, 264}"
941,1,66,0,0.0366468,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} x^2 \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2]*x^2,x]","\frac{a x^3 \left(c+\frac{d}{x^2}\right)^{3/2}}{3 c}+b x \sqrt{c+\frac{d}{x^2}}-b \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)","\frac{a x^3 \left(c+\frac{d}{x^2}\right)^{3/2}}{3 c}+b x \sqrt{c+\frac{d}{x^2}}-b \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)",1,"b*Sqrt[c + d/x^2]*x + (a*(c + d/x^2)^(3/2)*x^3)/(3*c) - b*Sqrt[d]*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)]","A",5,5,22,0.2273,1,"{451, 242, 277, 217, 206}"
942,1,85,0,0.0463275,"\int \left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}} \, dx","Int[(a + b/x^2)*Sqrt[c + d/x^2],x]","-\frac{\sqrt{c+\frac{d}{x^2}} (2 a d+b c)}{2 c x}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{2 \sqrt{d}}+\frac{a x \left(c+\frac{d}{x^2}\right)^{3/2}}{c}","-\frac{\sqrt{c+\frac{d}{x^2}} (2 a d+b c)}{2 c x}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{2 \sqrt{d}}+\frac{a x \left(c+\frac{d}{x^2}\right)^{3/2}}{c}",1,"-((b*c + 2*a*d)*Sqrt[c + d/x^2])/(2*c*x) + (a*(c + d/x^2)^(3/2)*x)/c - ((b*c + 2*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(2*Sqrt[d])","A",5,5,19,0.2632,1,"{375, 453, 195, 217, 206}"
943,1,91,0,0.0507795,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x^2} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x^2,x]","\frac{c (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 d^{3/2}}+\frac{\sqrt{c+\frac{d}{x^2}} (b c-4 a d)}{8 d x}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{4 d x}","\frac{c (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 d^{3/2}}+\frac{\sqrt{c+\frac{d}{x^2}} (b c-4 a d)}{8 d x}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{4 d x}",1,"((b*c - 4*a*d)*Sqrt[c + d/x^2])/(8*d*x) - (b*(c + d/x^2)^(3/2))/(4*d*x) + (c*(b*c - 4*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(8*d^(3/2))","A",5,5,22,0.2273,1,"{459, 335, 195, 217, 206}"
944,1,123,0,0.0805208,"\int \frac{\left(a+\frac{b}{x^2}\right) \sqrt{c+\frac{d}{x^2}}}{x^4} \, dx","Int[((a + b/x^2)*Sqrt[c + d/x^2])/x^4,x]","-\frac{c^2 (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{16 d^{5/2}}+\frac{c \sqrt{c+\frac{d}{x^2}} (b c-2 a d)}{16 d^2 x}+\frac{\sqrt{c+\frac{d}{x^2}} (b c-2 a d)}{8 d x^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{6 d x^3}","-\frac{c^2 (b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{16 d^{5/2}}+\frac{c \sqrt{c+\frac{d}{x^2}} (b c-2 a d)}{16 d^2 x}+\frac{\sqrt{c+\frac{d}{x^2}} (b c-2 a d)}{8 d x^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{6 d x^3}",1,"((b*c - 2*a*d)*Sqrt[c + d/x^2])/(8*d*x^3) - (b*(c + d/x^2)^(3/2))/(6*d*x^3) + (c*(b*c - 2*a*d)*Sqrt[c + d/x^2])/(16*d^2*x) - (c^2*(b*c - 2*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(16*d^(5/2))","A",6,6,22,0.2727,1,"{459, 335, 279, 321, 217, 206}"
945,1,123,0,0.0901921,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^5 \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^5,x]","\frac{d^2 (6 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{16 c^{3/2}}+\frac{x^4 \left(c+\frac{d}{x^2}\right)^{3/2} (6 b c-a d)}{24 c}+\frac{d x^2 \sqrt{c+\frac{d}{x^2}} (6 b c-a d)}{16 c}+\frac{a x^6 \left(c+\frac{d}{x^2}\right)^{5/2}}{6 c}","\frac{d^2 (6 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{16 c^{3/2}}+\frac{x^4 \left(c+\frac{d}{x^2}\right)^{3/2} (6 b c-a d)}{24 c}+\frac{d x^2 \sqrt{c+\frac{d}{x^2}} (6 b c-a d)}{16 c}+\frac{a x^6 \left(c+\frac{d}{x^2}\right)^{5/2}}{6 c}",1,"(d*(6*b*c - a*d)*Sqrt[c + d/x^2]*x^2)/(16*c) + ((6*b*c - a*d)*(c + d/x^2)^(3/2)*x^4)/(24*c) + (a*(c + d/x^2)^(5/2)*x^6)/(6*c) + (d^2*(6*b*c - a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(16*c^(3/2))","A",6,5,22,0.2273,1,"{446, 78, 47, 63, 208}"
946,1,115,0,0.0844772,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^3 \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^3,x]","\frac{x^2 \left(c+\frac{d}{x^2}\right)^{3/2} (a d+4 b c)}{8 c}-\frac{3 d \sqrt{c+\frac{d}{x^2}} (a d+4 b c)}{8 c}+\frac{3 d (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 \sqrt{c}}+\frac{a x^4 \left(c+\frac{d}{x^2}\right)^{5/2}}{4 c}","\frac{x^2 \left(c+\frac{d}{x^2}\right)^{3/2} (a d+4 b c)}{8 c}-\frac{3 d \sqrt{c+\frac{d}{x^2}} (a d+4 b c)}{8 c}+\frac{3 d (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 \sqrt{c}}+\frac{a x^4 \left(c+\frac{d}{x^2}\right)^{5/2}}{4 c}",1,"(-3*d*(4*b*c + a*d)*Sqrt[c + d/x^2])/(8*c) + ((4*b*c + a*d)*(c + d/x^2)^(3/2)*x^2)/(8*c) + (a*(c + d/x^2)^(5/2)*x^4)/(4*c) + (3*d*(4*b*c + a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(8*Sqrt[c])","A",6,6,22,0.2727,1,"{446, 78, 47, 50, 63, 208}"
947,1,110,0,0.0727332,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x,x]","-\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (3 a d+2 b c)}{6 c}-\frac{1}{2} \sqrt{c+\frac{d}{x^2}} (3 a d+2 b c)+\frac{1}{2} \sqrt{c} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)+\frac{a x^2 \left(c+\frac{d}{x^2}\right)^{5/2}}{2 c}","-\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (3 a d+2 b c)}{6 c}-\frac{1}{2} \sqrt{c+\frac{d}{x^2}} (3 a d+2 b c)+\frac{1}{2} \sqrt{c} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)+\frac{a x^2 \left(c+\frac{d}{x^2}\right)^{5/2}}{2 c}",1,"-((2*b*c + 3*a*d)*Sqrt[c + d/x^2])/2 - ((2*b*c + 3*a*d)*(c + d/x^2)^(3/2))/(6*c) + (a*(c + d/x^2)^(5/2)*x^2)/(2*c) + (Sqrt[c]*(2*b*c + 3*a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/2","A",6,5,20,0.2500,1,"{446, 78, 50, 63, 208}"
948,1,76,0,0.0541351,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x,x]","a c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-\frac{1}{3} a \left(c+\frac{d}{x^2}\right)^{3/2}-a c \sqrt{c+\frac{d}{x^2}}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d}","a c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)-\frac{1}{3} a \left(c+\frac{d}{x^2}\right)^{3/2}-a c \sqrt{c+\frac{d}{x^2}}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d}",1,"-(a*c*Sqrt[c + d/x^2]) - (a*(c + d/x^2)^(3/2))/3 - (b*(c + d/x^2)^(5/2))/(5*d) + a*c^(3/2)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]]","A",6,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
949,1,46,0,0.0364029,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x^3} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x^3,x]","\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^2}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^2}","\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^2}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^2}",1,"((b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^2) - (b*(c + d/x^2)^(7/2))/(7*d^2)","A",3,2,22,0.09091,1,"{444, 43}"
950,1,74,0,0.0557358,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x^5} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x^5,x]","\frac{\left(c+\frac{d}{x^2}\right)^{7/2} (2 b c-a d)}{7 d^3}-\frac{c \left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{9/2}}{9 d^3}","\frac{\left(c+\frac{d}{x^2}\right)^{7/2} (2 b c-a d)}{7 d^3}-\frac{c \left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{9/2}}{9 d^3}",1,"-(c*(b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^3) + ((2*b*c - a*d)*(c + d/x^2)^(7/2))/(7*d^3) - (b*(c + d/x^2)^(9/2))/(9*d^3)","A",3,2,22,0.09091,1,"{446, 77}"
951,1,104,0,0.0720556,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x^7} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x^7,x]","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^4}+\frac{\left(c+\frac{d}{x^2}\right)^{9/2} (3 b c-a d)}{9 d^4}-\frac{c \left(c+\frac{d}{x^2}\right)^{7/2} (3 b c-2 a d)}{7 d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{11/2}}{11 d^4}","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^4}+\frac{\left(c+\frac{d}{x^2}\right)^{9/2} (3 b c-a d)}{9 d^4}-\frac{c \left(c+\frac{d}{x^2}\right)^{7/2} (3 b c-2 a d)}{7 d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{11/2}}{11 d^4}",1,"(c^2*(b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^4) - (c*(3*b*c - 2*a*d)*(c + d/x^2)^(7/2))/(7*d^4) + ((3*b*c - a*d)*(c + d/x^2)^(9/2))/(9*d^4) - (b*(c + d/x^2)^(11/2))/(11*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
952,1,134,0,0.0960258,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x^9} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x^9,x]","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{7/2} (4 b c-3 a d)}{7 d^5}-\frac{c^3 \left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^5}+\frac{\left(c+\frac{d}{x^2}\right)^{11/2} (4 b c-a d)}{11 d^5}-\frac{c \left(c+\frac{d}{x^2}\right)^{9/2} (2 b c-a d)}{3 d^5}-\frac{b \left(c+\frac{d}{x^2}\right)^{13/2}}{13 d^5}","\frac{c^2 \left(c+\frac{d}{x^2}\right)^{7/2} (4 b c-3 a d)}{7 d^5}-\frac{c^3 \left(c+\frac{d}{x^2}\right)^{5/2} (b c-a d)}{5 d^5}+\frac{\left(c+\frac{d}{x^2}\right)^{11/2} (4 b c-a d)}{11 d^5}-\frac{c \left(c+\frac{d}{x^2}\right)^{9/2} (2 b c-a d)}{3 d^5}-\frac{b \left(c+\frac{d}{x^2}\right)^{13/2}}{13 d^5}",1,"-(c^3*(b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^5) + (c^2*(4*b*c - 3*a*d)*(c + d/x^2)^(7/2))/(7*d^5) - (c*(2*b*c - a*d)*(c + d/x^2)^(9/2))/(3*d^5) + ((4*b*c - a*d)*(c + d/x^2)^(11/2))/(11*d^5) - (b*(c + d/x^2)^(13/2))/(13*d^5)","A",3,2,22,0.09091,1,"{446, 77}"
953,1,150,0,0.0717679,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^{12} \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^12,x]","\frac{8 d^2 x^7 \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{3003 c^4}-\frac{16 d^3 x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{15015 c^5}+\frac{x^{11} \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{143 c^2}-\frac{2 d x^9 \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{429 c^3}+\frac{a x^{13} \left(c+\frac{d}{x^2}\right)^{5/2}}{13 c}","\frac{8 d^2 x^7 \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{3003 c^4}-\frac{16 d^3 x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{15015 c^5}+\frac{x^{11} \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{143 c^2}-\frac{2 d x^9 \left(c+\frac{d}{x^2}\right)^{5/2} (13 b c-8 a d)}{429 c^3}+\frac{a x^{13} \left(c+\frac{d}{x^2}\right)^{5/2}}{13 c}",1,"(-16*d^3*(13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^5)/(15015*c^5) + (8*d^2*(13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^7)/(3003*c^4) - (2*d*(13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^9)/(429*c^3) + ((13*b*c - 8*a*d)*(c + d/x^2)^(5/2)*x^11)/(143*c^2) + (a*(c + d/x^2)^(5/2)*x^13)/(13*c)","A",5,3,22,0.1364,1,"{453, 271, 264}"
954,1,117,0,0.0569717,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^{10} \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^10,x]","\frac{8 d^2 x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (11 b c-6 a d)}{3465 c^4}+\frac{x^9 \left(c+\frac{d}{x^2}\right)^{5/2} (11 b c-6 a d)}{99 c^2}-\frac{4 d x^7 \left(c+\frac{d}{x^2}\right)^{5/2} (11 b c-6 a d)}{693 c^3}+\frac{a x^{11} \left(c+\frac{d}{x^2}\right)^{5/2}}{11 c}","\frac{8 d^2 x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (11 b c-6 a d)}{3465 c^4}+\frac{x^9 \left(c+\frac{d}{x^2}\right)^{5/2} (11 b c-6 a d)}{99 c^2}-\frac{4 d x^7 \left(c+\frac{d}{x^2}\right)^{5/2} (11 b c-6 a d)}{693 c^3}+\frac{a x^{11} \left(c+\frac{d}{x^2}\right)^{5/2}}{11 c}",1,"(8*d^2*(11*b*c - 6*a*d)*(c + d/x^2)^(5/2)*x^5)/(3465*c^4) - (4*d*(11*b*c - 6*a*d)*(c + d/x^2)^(5/2)*x^7)/(693*c^3) + ((11*b*c - 6*a*d)*(c + d/x^2)^(5/2)*x^9)/(99*c^2) + (a*(c + d/x^2)^(5/2)*x^11)/(11*c)","A",4,3,22,0.1364,1,"{453, 271, 264}"
955,1,84,0,0.0415588,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^8 \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^8,x]","\frac{x^7 \left(c+\frac{d}{x^2}\right)^{5/2} (9 b c-4 a d)}{63 c^2}-\frac{2 d x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (9 b c-4 a d)}{315 c^3}+\frac{a x^9 \left(c+\frac{d}{x^2}\right)^{5/2}}{9 c}","\frac{x^7 \left(c+\frac{d}{x^2}\right)^{5/2} (9 b c-4 a d)}{63 c^2}-\frac{2 d x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (9 b c-4 a d)}{315 c^3}+\frac{a x^9 \left(c+\frac{d}{x^2}\right)^{5/2}}{9 c}",1,"(-2*d*(9*b*c - 4*a*d)*(c + d/x^2)^(5/2)*x^5)/(315*c^3) + ((9*b*c - 4*a*d)*(c + d/x^2)^(5/2)*x^7)/(63*c^2) + (a*(c + d/x^2)^(5/2)*x^9)/(9*c)","A",3,3,22,0.1364,1,"{453, 271, 264}"
956,1,53,0,0.0253675,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^6 \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^6,x]","\frac{x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (7 b c-2 a d)}{35 c^2}+\frac{a x^7 \left(c+\frac{d}{x^2}\right)^{5/2}}{7 c}","\frac{x^5 \left(c+\frac{d}{x^2}\right)^{5/2} (7 b c-2 a d)}{35 c^2}+\frac{a x^7 \left(c+\frac{d}{x^2}\right)^{5/2}}{7 c}",1,"((7*b*c - 2*a*d)*(c + d/x^2)^(5/2)*x^5)/(35*c^2) + (a*(c + d/x^2)^(5/2)*x^7)/(7*c)","A",2,2,22,0.09091,1,"{453, 264}"
957,1,86,0,0.05509,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^4 \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^4,x]","\frac{a x^5 \left(c+\frac{d}{x^2}\right)^{5/2}}{5 c}-b d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)+\frac{1}{3} b x^3 \left(c+\frac{d}{x^2}\right)^{3/2}+b d x \sqrt{c+\frac{d}{x^2}}","\frac{a x^5 \left(c+\frac{d}{x^2}\right)^{5/2}}{5 c}-b d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)+\frac{1}{3} b x^3 \left(c+\frac{d}{x^2}\right)^{3/2}+b d x \sqrt{c+\frac{d}{x^2}}",1,"b*d*Sqrt[c + d/x^2]*x + (b*(c + d/x^2)^(3/2)*x^3)/3 + (a*(c + d/x^2)^(5/2)*x^5)/(5*c) - b*d^(3/2)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)]","A",6,5,22,0.2273,1,"{451, 335, 277, 217, 206}"
958,1,121,0,0.0575027,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} x^2 \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2)*x^2,x]","\frac{x \left(c+\frac{d}{x^2}\right)^{3/2} (2 a d+3 b c)}{3 c}-\frac{d \sqrt{c+\frac{d}{x^2}} (2 a d+3 b c)}{2 c x}-\frac{1}{2} \sqrt{d} (2 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)+\frac{a x^3 \left(c+\frac{d}{x^2}\right)^{5/2}}{3 c}","\frac{x \left(c+\frac{d}{x^2}\right)^{3/2} (2 a d+3 b c)}{3 c}-\frac{d \sqrt{c+\frac{d}{x^2}} (2 a d+3 b c)}{2 c x}-\frac{1}{2} \sqrt{d} (2 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)+\frac{a x^3 \left(c+\frac{d}{x^2}\right)^{5/2}}{3 c}",1,"-(d*(3*b*c + 2*a*d)*Sqrt[c + d/x^2])/(2*c*x) + ((3*b*c + 2*a*d)*(c + d/x^2)^(3/2)*x)/(3*c) + (a*(c + d/x^2)^(5/2)*x^3)/(3*c) - (Sqrt[d]*(3*b*c + 2*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/2","A",6,6,22,0.2727,1,"{453, 242, 277, 195, 217, 206}"
959,1,112,0,0.0623911,"\int \left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2} \, dx","Int[(a + b/x^2)*(c + d/x^2)^(3/2),x]","-\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (4 a d+b c)}{4 c x}-\frac{3 \sqrt{c+\frac{d}{x^2}} (4 a d+b c)}{8 x}-\frac{3 c (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 \sqrt{d}}+\frac{a x \left(c+\frac{d}{x^2}\right)^{5/2}}{c}","-\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (4 a d+b c)}{4 c x}-\frac{3 \sqrt{c+\frac{d}{x^2}} (4 a d+b c)}{8 x}-\frac{3 c (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 \sqrt{d}}+\frac{a x \left(c+\frac{d}{x^2}\right)^{5/2}}{c}",1,"(-3*(b*c + 4*a*d)*Sqrt[c + d/x^2])/(8*x) - ((b*c + 4*a*d)*(c + d/x^2)^(3/2))/(4*c*x) + (a*(c + d/x^2)^(5/2)*x)/c - (3*c*(b*c + 4*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(8*Sqrt[d])","A",6,5,19,0.2632,1,"{375, 453, 195, 217, 206}"
960,1,123,0,0.0638926,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x^2} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x^2,x]","\frac{c^2 (b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{16 d^{3/2}}+\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (b c-6 a d)}{24 d x}+\frac{c \sqrt{c+\frac{d}{x^2}} (b c-6 a d)}{16 d x}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{6 d x}","\frac{c^2 (b c-6 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{16 d^{3/2}}+\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (b c-6 a d)}{24 d x}+\frac{c \sqrt{c+\frac{d}{x^2}} (b c-6 a d)}{16 d x}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{6 d x}",1,"(c*(b*c - 6*a*d)*Sqrt[c + d/x^2])/(16*d*x) + ((b*c - 6*a*d)*(c + d/x^2)^(3/2))/(24*d*x) - (b*(c + d/x^2)^(5/2))/(6*d*x) + (c^2*(b*c - 6*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(16*d^(3/2))","A",6,5,22,0.2273,1,"{459, 335, 195, 217, 206}"
961,1,159,0,0.0887293,"\int \frac{\left(a+\frac{b}{x^2}\right) \left(c+\frac{d}{x^2}\right)^{3/2}}{x^4} \, dx","Int[((a + b/x^2)*(c + d/x^2)^(3/2))/x^4,x]","\frac{c^2 \sqrt{c+\frac{d}{x^2}} (3 b c-8 a d)}{128 d^2 x}-\frac{c^3 (3 b c-8 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{128 d^{5/2}}+\frac{c \sqrt{c+\frac{d}{x^2}} (3 b c-8 a d)}{64 d x^3}+\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-8 a d)}{48 d x^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{8 d x^3}","\frac{c^2 \sqrt{c+\frac{d}{x^2}} (3 b c-8 a d)}{128 d^2 x}-\frac{c^3 (3 b c-8 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{128 d^{5/2}}+\frac{c \sqrt{c+\frac{d}{x^2}} (3 b c-8 a d)}{64 d x^3}+\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-8 a d)}{48 d x^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{8 d x^3}",1,"(c*(3*b*c - 8*a*d)*Sqrt[c + d/x^2])/(64*d*x^3) + ((3*b*c - 8*a*d)*(c + d/x^2)^(3/2))/(48*d*x^3) - (b*(c + d/x^2)^(5/2))/(8*d*x^3) + (c^2*(3*b*c - 8*a*d)*Sqrt[c + d/x^2])/(128*d^2*x) - (c^3*(3*b*c - 8*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(128*d^(5/2))","A",7,6,22,0.2727,1,"{459, 335, 279, 321, 217, 206}"
962,1,90,0,0.0673245,"\int \frac{\left(a+\frac{b}{x^2}\right) x^3}{\sqrt{c+\frac{d}{x^2}}} \, dx","Int[((a + b/x^2)*x^3)/Sqrt[c + d/x^2],x]","\frac{x^2 \sqrt{c+\frac{d}{x^2}} (4 b c-3 a d)}{8 c^2}-\frac{d (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 c^{5/2}}+\frac{a x^4 \sqrt{c+\frac{d}{x^2}}}{4 c}","\frac{x^2 \sqrt{c+\frac{d}{x^2}} (4 b c-3 a d)}{8 c^2}-\frac{d (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 c^{5/2}}+\frac{a x^4 \sqrt{c+\frac{d}{x^2}}}{4 c}",1,"((4*b*c - 3*a*d)*Sqrt[c + d/x^2]*x^2)/(8*c^2) + (a*Sqrt[c + d/x^2]*x^4)/(4*c) - (d*(4*b*c - 3*a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(8*c^(5/2))","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
963,1,59,0,0.0402656,"\int \frac{\left(a+\frac{b}{x^2}\right) x}{\sqrt{c+\frac{d}{x^2}}} \, dx","Int[((a + b/x^2)*x)/Sqrt[c + d/x^2],x]","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2 c^{3/2}}+\frac{a x^2 \sqrt{c+\frac{d}{x^2}}}{2 c}","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2 c^{3/2}}+\frac{a x^2 \sqrt{c+\frac{d}{x^2}}}{2 c}",1,"(a*Sqrt[c + d/x^2]*x^2)/(2*c) + ((2*b*c - a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(2*c^(3/2))","A",4,4,20,0.2000,1,"{446, 78, 63, 208}"
964,1,43,0,0.033241,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}} x} \, dx","Int[(a + b/x^2)/(Sqrt[c + d/x^2]*x),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{\sqrt{c}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{d}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{\sqrt{c}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{d}",1,"-((b*Sqrt[c + d/x^2])/d) + (a*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/Sqrt[c]","A",4,4,22,0.1818,1,"{446, 80, 63, 208}"
965,1,43,0,0.0356831,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}} x^3} \, dx","Int[(a + b/x^2)/(Sqrt[c + d/x^2]*x^3),x]","\frac{\sqrt{c+\frac{d}{x^2}} (b c-a d)}{d^2}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{3 d^2}","\frac{\sqrt{c+\frac{d}{x^2}} (b c-a d)}{d^2}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{3 d^2}",1,"((b*c - a*d)*Sqrt[c + d/x^2])/d^2 - (b*(c + d/x^2)^(3/2))/(3*d^2)","A",3,2,22,0.09091,1,"{444, 43}"
966,1,72,0,0.0516449,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}} x^5} \, dx","Int[(a + b/x^2)/(Sqrt[c + d/x^2]*x^5),x]","\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (2 b c-a d)}{3 d^3}-\frac{c \sqrt{c+\frac{d}{x^2}} (b c-a d)}{d^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d^3}","\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (2 b c-a d)}{3 d^3}-\frac{c \sqrt{c+\frac{d}{x^2}} (b c-a d)}{d^3}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d^3}",1,"-((c*(b*c - a*d)*Sqrt[c + d/x^2])/d^3) + ((2*b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^3) - (b*(c + d/x^2)^(5/2))/(5*d^3)","A",3,2,22,0.09091,1,"{446, 77}"
967,1,101,0,0.0693012,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}} x^7} \, dx","Int[(a + b/x^2)/(Sqrt[c + d/x^2]*x^7),x]","\frac{c^2 \sqrt{c+\frac{d}{x^2}} (b c-a d)}{d^4}+\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (3 b c-a d)}{5 d^4}-\frac{c \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{3 d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^4}","\frac{c^2 \sqrt{c+\frac{d}{x^2}} (b c-a d)}{d^4}+\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (3 b c-a d)}{5 d^4}-\frac{c \left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-2 a d)}{3 d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^4}",1,"(c^2*(b*c - a*d)*Sqrt[c + d/x^2])/d^4 - (c*(3*b*c - 2*a*d)*(c + d/x^2)^(3/2))/(3*d^4) + ((3*b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^4) - (b*(c + d/x^2)^(7/2))/(7*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
968,1,82,0,0.0333523,"\int \frac{\left(a+\frac{b}{x^2}\right) x^4}{\sqrt{c+\frac{d}{x^2}}} \, dx","Int[((a + b/x^2)*x^4)/Sqrt[c + d/x^2],x]","\frac{x^3 \sqrt{c+\frac{d}{x^2}} (5 b c-4 a d)}{15 c^2}-\frac{2 d x \sqrt{c+\frac{d}{x^2}} (5 b c-4 a d)}{15 c^3}+\frac{a x^5 \sqrt{c+\frac{d}{x^2}}}{5 c}","\frac{x^3 \sqrt{c+\frac{d}{x^2}} (5 b c-4 a d)}{15 c^2}-\frac{2 d x \sqrt{c+\frac{d}{x^2}} (5 b c-4 a d)}{15 c^3}+\frac{a x^5 \sqrt{c+\frac{d}{x^2}}}{5 c}",1,"(-2*d*(5*b*c - 4*a*d)*Sqrt[c + d/x^2]*x)/(15*c^3) + ((5*b*c - 4*a*d)*Sqrt[c + d/x^2]*x^3)/(15*c^2) + (a*Sqrt[c + d/x^2]*x^5)/(5*c)","A",3,3,22,0.1364,1,"{453, 271, 191}"
969,1,51,0,0.0202861,"\int \frac{\left(a+\frac{b}{x^2}\right) x^2}{\sqrt{c+\frac{d}{x^2}}} \, dx","Int[((a + b/x^2)*x^2)/Sqrt[c + d/x^2],x]","\frac{x \sqrt{c+\frac{d}{x^2}} (3 b c-2 a d)}{3 c^2}+\frac{a x^3 \sqrt{c+\frac{d}{x^2}}}{3 c}","\frac{x \sqrt{c+\frac{d}{x^2}} (3 b c-2 a d)}{3 c^2}+\frac{a x^3 \sqrt{c+\frac{d}{x^2}}}{3 c}",1,"((3*b*c - 2*a*d)*Sqrt[c + d/x^2]*x)/(3*c^2) + (a*Sqrt[c + d/x^2]*x^3)/(3*c)","A",2,2,22,0.09091,1,"{453, 191}"
970,1,47,0,0.0292151,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}}} \, dx","Int[(a + b/x^2)/Sqrt[c + d/x^2],x]","\frac{a x \sqrt{c+\frac{d}{x^2}}}{c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{\sqrt{d}}","\frac{a x \sqrt{c+\frac{d}{x^2}}}{c}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{\sqrt{d}}",1,"(a*Sqrt[c + d/x^2]*x)/c - (b*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/Sqrt[d]","A",4,4,19,0.2105,1,"{375, 451, 217, 206}"
971,1,61,0,0.0375054,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}} x^2} \, dx","Int[(a + b/x^2)/(Sqrt[c + d/x^2]*x^2),x]","\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{2 d^{3/2}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{2 d x}","\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{2 d^{3/2}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{2 d x}",1,"-(b*Sqrt[c + d/x^2])/(2*d*x) + ((b*c - 2*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(2*d^(3/2))","A",4,4,22,0.1818,1,"{459, 335, 217, 206}"
972,1,93,0,0.0502702,"\int \frac{a+\frac{b}{x^2}}{\sqrt{c+\frac{d}{x^2}} x^4} \, dx","Int[(a + b/x^2)/(Sqrt[c + d/x^2]*x^4),x]","\frac{\sqrt{c+\frac{d}{x^2}} (3 b c-4 a d)}{8 d^2 x}-\frac{c (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 d^{5/2}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{4 d x^3}","\frac{\sqrt{c+\frac{d}{x^2}} (3 b c-4 a d)}{8 d^2 x}-\frac{c (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 d^{5/2}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{4 d x^3}",1,"-(b*Sqrt[c + d/x^2])/(4*d*x^3) + ((3*b*c - 4*a*d)*Sqrt[c + d/x^2])/(8*d^2*x) - (c*(3*b*c - 4*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(8*d^(5/2))","A",5,5,22,0.2273,1,"{459, 335, 321, 217, 206}"
973,1,120,0,0.0848099,"\int \frac{\left(a+\frac{b}{x^2}\right) x^3}{\left(c+\frac{d}{x^2}\right)^{3/2}} \, dx","Int[((a + b/x^2)*x^3)/(c + d/x^2)^(3/2),x]","\frac{3 x^2 \sqrt{c+\frac{d}{x^2}} (4 b c-5 a d)}{8 c^3}-\frac{x^2 (4 b c-5 a d)}{4 c^2 \sqrt{c+\frac{d}{x^2}}}-\frac{3 d (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 c^{7/2}}+\frac{a x^4}{4 c \sqrt{c+\frac{d}{x^2}}}","\frac{x^2 (4 b c-5 a d)}{8 c^2 \sqrt{c+\frac{d}{x^2}}}+\frac{3 d (4 b c-5 a d)}{8 c^3 \sqrt{c+\frac{d}{x^2}}}-\frac{3 d (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{8 c^{7/2}}+\frac{a x^4}{4 c \sqrt{c+\frac{d}{x^2}}}",1,"-((4*b*c - 5*a*d)*x^2)/(4*c^2*Sqrt[c + d/x^2]) + (3*(4*b*c - 5*a*d)*Sqrt[c + d/x^2]*x^2)/(8*c^3) + (a*x^4)/(4*c*Sqrt[c + d/x^2]) - (3*d*(4*b*c - 5*a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(8*c^(7/2))","A",6,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
974,1,86,0,0.0583173,"\int \frac{\left(a+\frac{b}{x^2}\right) x}{\left(c+\frac{d}{x^2}\right)^{3/2}} \, dx","Int[((a + b/x^2)*x)/(c + d/x^2)^(3/2),x]","-\frac{2 b c-3 a d}{2 c^2 \sqrt{c+\frac{d}{x^2}}}+\frac{(2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2 c^{5/2}}+\frac{a x^2}{2 c \sqrt{c+\frac{d}{x^2}}}","-\frac{2 b c-3 a d}{2 c^2 \sqrt{c+\frac{d}{x^2}}}+\frac{(2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{2 c^{5/2}}+\frac{a x^2}{2 c \sqrt{c+\frac{d}{x^2}}}",1,"-(2*b*c - 3*a*d)/(2*c^2*Sqrt[c + d/x^2]) + (a*x^2)/(2*c*Sqrt[c + d/x^2]) + ((2*b*c - 3*a*d)*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/(2*c^(5/2))","A",5,5,20,0.2500,1,"{446, 78, 51, 63, 208}"
975,1,52,0,0.0400453,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x),x]","\frac{b c-a d}{c d \sqrt{c+\frac{d}{x^2}}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{c^{3/2}}","\frac{b c-a d}{c d \sqrt{c+\frac{d}{x^2}}}+\frac{a \tanh ^{-1}\left(\frac{\sqrt{c+\frac{d}{x^2}}}{\sqrt{c}}\right)}{c^{3/2}}",1,"(b*c - a*d)/(c*d*Sqrt[c + d/x^2]) + (a*ArcTanh[Sqrt[c + d/x^2]/Sqrt[c]])/c^(3/2)","A",4,4,22,0.1818,1,"{446, 78, 63, 208}"
976,1,42,0,0.0354627,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^3} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^3),x]","-\frac{b c-a d}{d^2 \sqrt{c+\frac{d}{x^2}}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{d^2}","-\frac{b c-a d}{d^2 \sqrt{c+\frac{d}{x^2}}}-\frac{b \sqrt{c+\frac{d}{x^2}}}{d^2}",1,"-((b*c - a*d)/(d^2*Sqrt[c + d/x^2])) - (b*Sqrt[c + d/x^2])/d^2","A",3,2,22,0.09091,1,"{444, 43}"
977,1,68,0,0.0521264,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^5} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^5),x]","\frac{\sqrt{c+\frac{d}{x^2}} (2 b c-a d)}{d^3}+\frac{c (b c-a d)}{d^3 \sqrt{c+\frac{d}{x^2}}}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{3 d^3}","\frac{\sqrt{c+\frac{d}{x^2}} (2 b c-a d)}{d^3}+\frac{c (b c-a d)}{d^3 \sqrt{c+\frac{d}{x^2}}}-\frac{b \left(c+\frac{d}{x^2}\right)^{3/2}}{3 d^3}",1,"(c*(b*c - a*d))/(d^3*Sqrt[c + d/x^2]) + ((2*b*c - a*d)*Sqrt[c + d/x^2])/d^3 - (b*(c + d/x^2)^(3/2))/(3*d^3)","A",3,2,22,0.09091,1,"{446, 77}"
978,1,100,0,0.0710595,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^7} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^7),x]","-\frac{c^2 (b c-a d)}{d^4 \sqrt{c+\frac{d}{x^2}}}+\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-a d)}{3 d^4}-\frac{c \sqrt{c+\frac{d}{x^2}} (3 b c-2 a d)}{d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d^4}","-\frac{c^2 (b c-a d)}{d^4 \sqrt{c+\frac{d}{x^2}}}+\frac{\left(c+\frac{d}{x^2}\right)^{3/2} (3 b c-a d)}{3 d^4}-\frac{c \sqrt{c+\frac{d}{x^2}} (3 b c-2 a d)}{d^4}-\frac{b \left(c+\frac{d}{x^2}\right)^{5/2}}{5 d^4}",1,"-((c^2*(b*c - a*d))/(d^4*Sqrt[c + d/x^2])) - (c*(3*b*c - 2*a*d)*Sqrt[c + d/x^2])/d^4 + ((3*b*c - a*d)*(c + d/x^2)^(3/2))/(3*d^4) - (b*(c + d/x^2)^(5/2))/(5*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
979,1,126,0,0.0889519,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^9} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^9),x]","\frac{c^2 \sqrt{c+\frac{d}{x^2}} (4 b c-3 a d)}{d^5}+\frac{c^3 (b c-a d)}{d^5 \sqrt{c+\frac{d}{x^2}}}+\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (4 b c-a d)}{5 d^5}-\frac{c \left(c+\frac{d}{x^2}\right)^{3/2} (2 b c-a d)}{d^5}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^5}","\frac{c^2 \sqrt{c+\frac{d}{x^2}} (4 b c-3 a d)}{d^5}+\frac{c^3 (b c-a d)}{d^5 \sqrt{c+\frac{d}{x^2}}}+\frac{\left(c+\frac{d}{x^2}\right)^{5/2} (4 b c-a d)}{5 d^5}-\frac{c \left(c+\frac{d}{x^2}\right)^{3/2} (2 b c-a d)}{d^5}-\frac{b \left(c+\frac{d}{x^2}\right)^{7/2}}{7 d^5}",1,"(c^3*(b*c - a*d))/(d^5*Sqrt[c + d/x^2]) + (c^2*(4*b*c - 3*a*d)*Sqrt[c + d/x^2])/d^5 - (c*(2*b*c - a*d)*(c + d/x^2)^(3/2))/d^5 + ((4*b*c - a*d)*(c + d/x^2)^(5/2))/(5*d^5) - (b*(c + d/x^2)^(7/2))/(7*d^5)","A",3,2,22,0.09091,1,"{446, 77}"
980,1,111,0,0.0488855,"\int \frac{\left(a+\frac{b}{x^2}\right) x^4}{\left(c+\frac{d}{x^2}\right)^{3/2}} \, dx","Int[((a + b/x^2)*x^4)/(c + d/x^2)^(3/2),x]","\frac{x^3 (5 b c-6 a d)}{15 c^2 \sqrt{c+\frac{d}{x^2}}}-\frac{8 d x \sqrt{c+\frac{d}{x^2}} (5 b c-6 a d)}{15 c^4}+\frac{4 d x (5 b c-6 a d)}{15 c^3 \sqrt{c+\frac{d}{x^2}}}+\frac{a x^5}{5 c \sqrt{c+\frac{d}{x^2}}}","\frac{x^3 (5 b c-6 a d)}{15 c^2 \sqrt{c+\frac{d}{x^2}}}-\frac{8 d x \sqrt{c+\frac{d}{x^2}} (5 b c-6 a d)}{15 c^4}+\frac{4 d x (5 b c-6 a d)}{15 c^3 \sqrt{c+\frac{d}{x^2}}}+\frac{a x^5}{5 c \sqrt{c+\frac{d}{x^2}}}",1,"(4*d*(5*b*c - 6*a*d)*x)/(15*c^3*Sqrt[c + d/x^2]) - (8*d*(5*b*c - 6*a*d)*Sqrt[c + d/x^2]*x)/(15*c^4) + ((5*b*c - 6*a*d)*x^3)/(15*c^2*Sqrt[c + d/x^2]) + (a*x^5)/(5*c*Sqrt[c + d/x^2])","A",4,4,22,0.1818,1,"{453, 271, 192, 191}"
981,1,79,0,0.0301135,"\int \frac{\left(a+\frac{b}{x^2}\right) x^2}{\left(c+\frac{d}{x^2}\right)^{3/2}} \, dx","Int[((a + b/x^2)*x^2)/(c + d/x^2)^(3/2),x]","\frac{2 x \sqrt{c+\frac{d}{x^2}} (3 b c-4 a d)}{3 c^3}-\frac{x (3 b c-4 a d)}{3 c^2 \sqrt{c+\frac{d}{x^2}}}+\frac{a x^3}{3 c \sqrt{c+\frac{d}{x^2}}}","\frac{2 x \sqrt{c+\frac{d}{x^2}} (3 b c-4 a d)}{3 c^3}-\frac{x (3 b c-4 a d)}{3 c^2 \sqrt{c+\frac{d}{x^2}}}+\frac{a x^3}{3 c \sqrt{c+\frac{d}{x^2}}}",1,"-((3*b*c - 4*a*d)*x)/(3*c^2*Sqrt[c + d/x^2]) + (2*(3*b*c - 4*a*d)*Sqrt[c + d/x^2]*x)/(3*c^3) + (a*x^3)/(3*c*Sqrt[c + d/x^2])","A",3,3,22,0.1364,1,"{453, 192, 191}"
982,1,45,0,0.0299469,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2}} \, dx","Int[(a + b/x^2)/(c + d/x^2)^(3/2),x]","\frac{a x}{c \sqrt{c+\frac{d}{x^2}}}-\frac{b c-2 a d}{c^2 x \sqrt{c+\frac{d}{x^2}}}","\frac{a x}{c \sqrt{c+\frac{d}{x^2}}}-\frac{b c-2 a d}{c^2 x \sqrt{c+\frac{d}{x^2}}}",1,"-((b*c - 2*a*d)/(c^2*Sqrt[c + d/x^2]*x)) + (a*x)/(c*Sqrt[c + d/x^2])","A",3,3,19,0.1579,1,"{375, 453, 191}"
983,1,59,0,0.0340979,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^2} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^2),x]","\frac{b c-a d}{c d x \sqrt{c+\frac{d}{x^2}}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{d^{3/2}}","\frac{b c-a d}{c d x \sqrt{c+\frac{d}{x^2}}}-\frac{b \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{d^{3/2}}",1,"(b*c - a*d)/(c*d*Sqrt[c + d/x^2]*x) - (b*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/d^(3/2)","A",4,4,22,0.1818,1,"{452, 335, 217, 206}"
984,1,92,0,0.050077,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^4} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^4),x]","-\frac{3 b c-2 a d}{2 d^2 x \sqrt{c+\frac{d}{x^2}}}+\frac{(3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{2 d^{5/2}}-\frac{b}{2 d x^3 \sqrt{c+\frac{d}{x^2}}}","-\frac{3 b c-2 a d}{2 d^2 x \sqrt{c+\frac{d}{x^2}}}+\frac{(3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{2 d^{5/2}}-\frac{b}{2 d x^3 \sqrt{c+\frac{d}{x^2}}}",1,"-b/(2*d*Sqrt[c + d/x^2]*x^3) - (3*b*c - 2*a*d)/(2*d^2*Sqrt[c + d/x^2]*x) + ((3*b*c - 2*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(2*d^(5/2))","A",5,5,22,0.2273,1,"{459, 335, 288, 217, 206}"
985,1,123,0,0.0689806,"\int \frac{a+\frac{b}{x^2}}{\left(c+\frac{d}{x^2}\right)^{3/2} x^6} \, dx","Int[(a + b/x^2)/((c + d/x^2)^(3/2)*x^6),x]","\frac{3 \sqrt{c+\frac{d}{x^2}} (5 b c-4 a d)}{8 d^3 x}-\frac{5 b c-4 a d}{4 d^2 x^3 \sqrt{c+\frac{d}{x^2}}}-\frac{3 c (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 d^{7/2}}-\frac{b}{4 d x^5 \sqrt{c+\frac{d}{x^2}}}","\frac{3 \sqrt{c+\frac{d}{x^2}} (5 b c-4 a d)}{8 d^3 x}-\frac{5 b c-4 a d}{4 d^2 x^3 \sqrt{c+\frac{d}{x^2}}}-\frac{3 c (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d}}{x \sqrt{c+\frac{d}{x^2}}}\right)}{8 d^{7/2}}-\frac{b}{4 d x^5 \sqrt{c+\frac{d}{x^2}}}",1,"-b/(4*d*Sqrt[c + d/x^2]*x^5) - (5*b*c - 4*a*d)/(4*d^2*Sqrt[c + d/x^2]*x^3) + (3*(5*b*c - 4*a*d)*Sqrt[c + d/x^2])/(8*d^3*x) - (3*c*(5*b*c - 4*a*d)*ArcTanh[Sqrt[d]/(Sqrt[c + d/x^2]*x)])/(8*d^(7/2))","A",6,6,22,0.2727,1,"{459, 335, 288, 321, 217, 206}"
986,1,101,0,0.1159098,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q (e x)^m \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^m,x]","\frac{x (e x)^m \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{1}{2} (-m-1);-p,-q;\frac{1-m}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{m+1}","\frac{(e x)^{m+1} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{1}{2} (-m-1);-p,-q;\frac{1-m}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{e (m+1)}",1,"((a + b/x^2)^p*(c + d/x^2)^q*x*(e*x)^m*AppellF1[(-1 - m)/2, -p, -q, (1 - m)/2, -(b/(a*x^2)), -(d/(c*x^2))])/((1 + m)*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,24,0.1250,1,"{497, 511, 510}"
987,1,84,0,0.0885412,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q x^4 \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*x^4,x]","\frac{1}{5} x^5 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{5}{2};-p,-q;-\frac{3}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)","\frac{1}{5} x^5 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{5}{2};-p,-q;-\frac{3}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)",1,"((a + b/x^2)^p*(c + d/x^2)^q*x^5*AppellF1[-5/2, -p, -q, -3/2, -(b/(a*x^2)), -(d/(c*x^2))])/(5*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,22,0.1364,1,"{495, 511, 510}"
988,1,100,0,0.0830878,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q x^3 \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*x^3,x]","\frac{b^2 \left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,3;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d},\frac{a+\frac{b}{x^2}}{a}\right)}{2 a^3 (p+1)}","\frac{b^2 \left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,3;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d},\frac{a+\frac{b}{x^2}}{a}\right)}{2 a^3 (p+1)}",1,"(b^2*(a + b/x^2)^(1 + p)*(c + d/x^2)^q*AppellF1[1 + p, -q, 3, 2 + p, -((d*(a + b/x^2))/(b*c - a*d)), (a + b/x^2)/a])/(2*a^3*(1 + p)*((b*(c + d/x^2))/(b*c - a*d))^q)","A",3,3,22,0.1364,1,"{446, 137, 136}"
989,1,84,0,0.0906104,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q x^2 \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*x^2,x]","\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{3}{2};-p,-q;-\frac{1}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)","\frac{1}{3} x^3 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{3}{2};-p,-q;-\frac{1}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)",1,"((a + b/x^2)^p*(c + d/x^2)^q*x^3*AppellF1[-3/2, -p, -q, -1/2, -(b/(a*x^2)), -(d/(c*x^2))])/(3*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,22,0.1364,1,"{495, 511, 510}"
990,1,98,0,0.068031,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q x \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*x,x]","-\frac{b \left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,2;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d},\frac{a+\frac{b}{x^2}}{a}\right)}{2 a^2 (p+1)}","-\frac{b \left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,2;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d},\frac{a+\frac{b}{x^2}}{a}\right)}{2 a^2 (p+1)}",1,"-(b*(a + b/x^2)^(1 + p)*(c + d/x^2)^q*AppellF1[1 + p, -q, 2, 2 + p, -((d*(a + b/x^2))/(b*c - a*d)), (a + b/x^2)/a])/(2*a^2*(1 + p)*((b*(c + d/x^2))/(b*c - a*d))^q)","A",3,3,20,0.1500,1,"{446, 137, 136}"
991,1,79,0,0.0806013,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q,x]","x \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{1}{2};-p,-q;\frac{1}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)","x \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{1}{2};-p,-q;\frac{1}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)",1,"((a + b/x^2)^p*(c + d/x^2)^q*x*AppellF1[-1/2, -p, -q, 1/2, -(b/(a*x^2)), -(d/(c*x^2))])/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,19,0.1579,1,"{375, 511, 510}"
992,1,97,0,0.0704423,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{x} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/x,x]","\frac{\left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,1;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d},\frac{a+\frac{b}{x^2}}{a}\right)}{2 a (p+1)}","\frac{\left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,1;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d},\frac{a+\frac{b}{x^2}}{a}\right)}{2 a (p+1)}",1,"((a + b/x^2)^(1 + p)*(c + d/x^2)^q*AppellF1[1 + p, -q, 1, 2 + p, -((d*(a + b/x^2))/(b*c - a*d)), (a + b/x^2)/a])/(2*a*(1 + p)*((b*(c + d/x^2))/(b*c - a*d))^q)","A",3,3,22,0.1364,1,"{446, 137, 136}"
993,1,82,0,0.0624714,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{x^2} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/x^2,x]","-\frac{\left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{x}","-\frac{\left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{x}",1,"-(((a + b/x^2)^p*(c + d/x^2)^q*AppellF1[1/2, -p, -q, 3/2, -(b/(a*x^2)), -(d/(c*x^2))])/((1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*x))","A",4,3,22,0.1364,1,"{495, 430, 429}"
994,1,85,0,0.0618262,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{x^3} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/x^3,x]","-\frac{\left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d}\right)}{2 b (p+1)}","-\frac{\left(a+\frac{b}{x^2}\right)^{p+1} \left(c+\frac{d}{x^2}\right)^q \left(\frac{b \left(c+\frac{d}{x^2}\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(a+\frac{b}{x^2}\right)}{b c-a d}\right)}{2 b (p+1)}",1,"-((a + b/x^2)^(1 + p)*(c + d/x^2)^q*Hypergeometric2F1[1 + p, -q, 2 + p, -((d*(a + b/x^2))/(b*c - a*d))])/(2*b*(1 + p)*((b*(c + d/x^2))/(b*c - a*d))^q)","A",3,3,22,0.1364,1,"{444, 70, 69}"
995,1,84,0,0.0922017,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{x^4} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/x^4,x]","-\frac{\left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{3 x^3}","-\frac{\left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{3 x^3}",1,"-((a + b/x^2)^p*(c + d/x^2)^q*AppellF1[3/2, -p, -q, 5/2, -(b/(a*x^2)), -(d/(c*x^2))])/(3*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*x^3)","A",4,3,22,0.1364,1,"{495, 511, 510}"
996,1,91,0,0.1245297,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q (e x)^{5/2} \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(5/2),x]","\frac{2 (e x)^{7/2} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{7}{4};-p,-q;-\frac{3}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{7 e}","\frac{2 (e x)^{7/2} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{7}{4};-p,-q;-\frac{3}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{7 e}",1,"(2*(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(7/2)*AppellF1[-7/4, -p, -q, -3/4, -(b/(a*x^2)), -(d/(c*x^2))])/(7*e*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,26,0.1154,1,"{496, 511, 510}"
997,1,91,0,0.121727,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q (e x)^{3/2} \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(3/2),x]","\frac{2 (e x)^{5/2} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{5}{4};-p,-q;-\frac{1}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{5 e}","\frac{2 (e x)^{5/2} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{5}{4};-p,-q;-\frac{1}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{5 e}",1,"(2*(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(5/2)*AppellF1[-5/4, -p, -q, -1/4, -(b/(a*x^2)), -(d/(c*x^2))])/(5*e*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,26,0.1154,1,"{496, 511, 510}"
998,1,91,0,0.1203507,"\int \left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q \sqrt{e x} \, dx","Int[(a + b/x^2)^p*(c + d/x^2)^q*Sqrt[e*x],x]","\frac{2 (e x)^{3/2} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{3}{4};-p,-q;\frac{1}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{3 e}","\frac{2 (e x)^{3/2} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{3}{4};-p,-q;\frac{1}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{3 e}",1,"(2*(a + b/x^2)^p*(c + d/x^2)^q*(e*x)^(3/2)*AppellF1[-3/4, -p, -q, 1/4, -(b/(a*x^2)), -(d/(c*x^2))])/(3*e*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,26,0.1154,1,"{496, 511, 510}"
999,1,89,0,0.1259501,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{\sqrt{e x}} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/Sqrt[e*x],x]","\frac{2 \sqrt{e x} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{1}{4};-p,-q;\frac{3}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{e}","\frac{2 \sqrt{e x} \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(-\frac{1}{4};-p,-q;\frac{3}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{e}",1,"(2*(a + b/x^2)^p*(c + d/x^2)^q*Sqrt[e*x]*AppellF1[-1/4, -p, -q, 3/4, -(b/(a*x^2)), -(d/(c*x^2))])/(e*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q)","A",4,3,26,0.1154,1,"{496, 511, 510}"
1000,1,89,0,0.089408,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{(e x)^{3/2}} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/(e*x)^(3/2),x]","-\frac{2 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{1}{4};-p,-q;\frac{5}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{e \sqrt{e x}}","-\frac{2 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{1}{4};-p,-q;\frac{5}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{e \sqrt{e x}}",1,"(-2*(a + b/x^2)^p*(c + d/x^2)^q*AppellF1[1/4, -p, -q, 5/4, -(b/(a*x^2)), -(d/(c*x^2))])/(e*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*Sqrt[e*x])","A",4,3,26,0.1154,1,"{496, 430, 429}"
1001,1,91,0,0.1204709,"\int \frac{\left(a+\frac{b}{x^2}\right)^p \left(c+\frac{d}{x^2}\right)^q}{(e x)^{5/2}} \, dx","Int[((a + b/x^2)^p*(c + d/x^2)^q)/(e*x)^(5/2),x]","-\frac{2 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{3}{4};-p,-q;\frac{7}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{3 e (e x)^{3/2}}","-\frac{2 \left(a+\frac{b}{x^2}\right)^p \left(\frac{b}{a x^2}+1\right)^{-p} \left(c+\frac{d}{x^2}\right)^q \left(\frac{d}{c x^2}+1\right)^{-q} F_1\left(\frac{3}{4};-p,-q;\frac{7}{4};-\frac{b}{a x^2},-\frac{d}{c x^2}\right)}{3 e (e x)^{3/2}}",1,"(-2*(a + b/x^2)^p*(c + d/x^2)^q*AppellF1[3/4, -p, -q, 7/4, -(b/(a*x^2)), -(d/(c*x^2))])/(3*e*(1 + b/(a*x^2))^p*(1 + d/(c*x^2))^q*(e*x)^(3/2))","A",4,3,26,0.1154,1,"{496, 511, 510}"
1002,1,135,0,0.0607087,"\int \sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} x^{5/2} \, dx","Int[Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(5/2),x]","\frac{1}{4} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{7/2}-\frac{1}{24} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{5}{96} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}-\frac{5}{64} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{5}{64} \cosh ^{-1}\left(\sqrt{x}\right)","\frac{1}{4} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{7/2}-\frac{1}{24} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{5}{96} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}-\frac{5}{64} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{5}{64} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(-5*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/64 - (5*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/96 - (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(5/2))/24 + (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(7/2))/4 - (5*ArcCosh[Sqrt[x]])/64","A",6,4,28,0.1429,1,"{280, 323, 330, 52}"
1003,1,104,0,0.0485153,"\int \sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} x^{3/2} \, dx","Int[Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2),x]","\frac{1}{3} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{1}{12} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}-\frac{1}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{1}{8} \cosh ^{-1}\left(\sqrt{x}\right)","\frac{1}{3} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}-\frac{1}{12} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}-\frac{1}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{1}{8} \cosh ^{-1}\left(\sqrt{x}\right)",1,"-(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/8 - (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/12 + (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(5/2))/3 - ArcCosh[Sqrt[x]]/8","A",5,4,28,0.1429,1,"{280, 323, 330, 52}"
1004,1,73,0,0.0324258,"\int \sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} \sqrt{x} \, dx","Int[Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x],x]","\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}-\frac{1}{4} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{1}{4} \cosh ^{-1}\left(\sqrt{x}\right)","\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}-\frac{1}{4} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\frac{1}{4} \cosh ^{-1}\left(\sqrt{x}\right)",1,"-(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/4 + (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/2 - ArcCosh[Sqrt[x]]/4","A",4,4,28,0.1429,1,"{280, 323, 330, 52}"
1005,1,37,0,0.0208203,"\int \frac{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}}{\sqrt{x}} \, dx","Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/Sqrt[x],x]","\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\cosh ^{-1}\left(\sqrt{x}\right)","\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}-\cosh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x] - ArcCosh[Sqrt[x]]","A",3,3,28,0.1071,1,"{280, 330, 52}"
1006,1,67,0,0.0307674,"\int \frac{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}}{x^{3/2}} \, dx","Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(3/2),x]","\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{\sqrt{x}}-2 \sqrt{\sqrt{x}-1} \sqrt{x} \sqrt{\sqrt{x}+1}+2 \cosh ^{-1}\left(\sqrt{x}\right)","\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{\sqrt{x}}-2 \sqrt{\sqrt{x}-1} \sqrt{x} \sqrt{\sqrt{x}+1}+2 \cosh ^{-1}\left(\sqrt{x}\right)",1,"(2*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/Sqrt[x] - 2*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x] + 2*ArcCosh[Sqrt[x]]","A",4,4,28,0.1429,1,"{327, 280, 330, 52}"
1007,1,31,0,0.0093252,"\int \frac{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}}{x^{5/2}} \, dx","Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(5/2),x]","\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{3 x^{3/2}}","\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{3 x^{3/2}}",1,"(2*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(3*x^(3/2))","A",1,1,28,0.03571,1,"{265}"
1008,1,63,0,0.0203429,"\int \frac{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}}{x^{7/2}} \, dx","Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(7/2),x]","\frac{4 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{15 x^{3/2}}+\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{5 x^{5/2}}","\frac{4 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{15 x^{3/2}}+\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{5 x^{5/2}}",1,"(2*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(5*x^(5/2)) + (4*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(15*x^(3/2))","A",2,2,28,0.07143,1,"{272, 265}"
1009,1,94,0,0.0312135,"\int \frac{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}}{x^{9/2}} \, dx","Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(9/2),x]","\frac{16 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{105 x^{3/2}}+\frac{8 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{35 x^{5/2}}+\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{7 x^{7/2}}","\frac{16 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{105 x^{3/2}}+\frac{8 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{35 x^{5/2}}+\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{7 x^{7/2}}",1,"(2*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(7*x^(7/2)) + (8*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(35*x^(5/2)) + (16*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(105*x^(3/2))","A",3,2,28,0.07143,1,"{272, 265}"
1010,1,125,0,0.041845,"\int \frac{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}}{x^{11/2}} \, dx","Int[(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/x^(11/2),x]","\frac{32 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{315 x^{3/2}}+\frac{16 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{105 x^{5/2}}+\frac{4 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{21 x^{7/2}}+\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{9 x^{9/2}}","\frac{32 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{315 x^{3/2}}+\frac{16 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{105 x^{5/2}}+\frac{4 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{21 x^{7/2}}+\frac{2 \left(\sqrt{x}-1\right)^{3/2} \left(\sqrt{x}+1\right)^{3/2}}{9 x^{9/2}}",1,"(2*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(9*x^(9/2)) + (4*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(21*x^(7/2)) + (16*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(105*x^(5/2)) + (32*(-1 + Sqrt[x])^(3/2)*(1 + Sqrt[x])^(3/2))/(315*x^(3/2))","A",4,2,28,0.07143,1,"{272, 265}"
1011,1,104,0,0.0452857,"\int \frac{x^{5/2}}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}} \, dx","Int[x^(5/2)/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]),x]","\frac{1}{3} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}+\frac{5}{12} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{5}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+\frac{5}{8} \cosh ^{-1}\left(\sqrt{x}\right)","\frac{1}{3} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{5/2}+\frac{5}{12} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{5}{8} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+\frac{5}{8} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(5*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/8 + (5*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/12 + (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(5/2))/3 + (5*ArcCosh[Sqrt[x]])/8","A",5,3,28,0.1071,1,"{323, 330, 52}"
1012,1,73,0,0.0324438,"\int \frac{x^{3/2}}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}} \, dx","Int[x^(3/2)/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]),x]","\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{3}{4} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+\frac{3}{4} \cosh ^{-1}\left(\sqrt{x}\right)","\frac{1}{2} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} x^{3/2}+\frac{3}{4} \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+\frac{3}{4} \cosh ^{-1}\left(\sqrt{x}\right)",1,"(3*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x])/4 + (Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2))/2 + (3*ArcCosh[Sqrt[x]])/4","A",4,3,28,0.1071,1,"{323, 330, 52}"
1013,1,35,0,0.0206963,"\int \frac{\sqrt{x}}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}}} \, dx","Int[Sqrt[x]/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]),x]","\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+\cosh ^{-1}\left(\sqrt{x}\right)","\sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1} \sqrt{x}+\cosh ^{-1}\left(\sqrt{x}\right)",1,"Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x] + ArcCosh[Sqrt[x]]","A",3,3,28,0.1071,1,"{323, 330, 52}"
1014,1,8,0,0.0106923,"\int \frac{1}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} \sqrt{x}} \, dx","Int[1/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*Sqrt[x]),x]","2 \cosh ^{-1}\left(\sqrt{x}\right)","2 \cosh ^{-1}\left(\sqrt{x}\right)",1,"2*ArcCosh[Sqrt[x]]","A",2,2,28,0.07143,1,"{330, 52}"
1015,1,29,0,0.0098801,"\int \frac{1}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} x^{3/2}} \, dx","Int[1/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(3/2)),x]","\frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{\sqrt{x}}","\frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{\sqrt{x}}",1,"(2*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/Sqrt[x]","A",1,1,28,0.03571,1,"{265}"
1016,1,63,0,0.0201345,"\int \frac{1}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} x^{5/2}} \, dx","Int[1/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(5/2)),x]","\frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 x^{3/2}}+\frac{4 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 \sqrt{x}}","\frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 x^{3/2}}+\frac{4 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{3 \sqrt{x}}",1,"(2*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(3*x^(3/2)) + (4*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(3*Sqrt[x])","A",2,2,28,0.07143,1,"{272, 265}"
1017,1,94,0,0.0333635,"\int \frac{1}{\sqrt{-1+\sqrt{x}} \sqrt{1+\sqrt{x}} x^{7/2}} \, dx","Int[1/(Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]]*x^(7/2)),x]","\frac{8 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{15 x^{3/2}}+\frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{5 x^{5/2}}+\frac{16 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{15 \sqrt{x}}","\frac{8 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{15 x^{3/2}}+\frac{2 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{5 x^{5/2}}+\frac{16 \sqrt{\sqrt{x}-1} \sqrt{\sqrt{x}+1}}{15 \sqrt{x}}",1,"(2*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(5*x^(5/2)) + (8*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(15*x^(3/2)) + (16*Sqrt[-1 + Sqrt[x]]*Sqrt[1 + Sqrt[x]])/(15*Sqrt[x])","A",3,2,28,0.07143,1,"{272, 265}"
1018,1,78,0,0.0414691,"\int x^2 \left(-a+b x^n\right)^p \left(a+b x^n\right)^p \, dx","Int[x^2*(-a + b*x^n)^p*(a + b*x^n)^p,x]","\frac{1}{3} x^3 \left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{3}{2 n},-p;1+\frac{3}{2 n};\frac{b^2 x^{2 n}}{a^2}\right)","\frac{1}{3} x^3 \left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{3}{2 n},-p;1+\frac{3}{2 n};\frac{b^2 x^{2 n}}{a^2}\right)",1,"(x^3*(-a + b*x^n)^p*(a + b*x^n)^p*Hypergeometric2F1[3/(2*n), -p, 1 + 3/(2*n), (b^2*x^(2*n))/a^2])/(3*(1 - (b^2*x^(2*n))/a^2)^p)","A",3,3,24,0.1250,1,"{366, 365, 364}"
1019,1,70,0,0.0307147,"\int x \left(-a+b x^n\right)^p \left(a+b x^n\right)^p \, dx","Int[x*(-a + b*x^n)^p*(a + b*x^n)^p,x]","\frac{1}{2} x^2 \left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};\frac{b^2 x^{2 n}}{a^2}\right)","\frac{1}{2} x^2 \left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{n},-p;1+\frac{1}{n};\frac{b^2 x^{2 n}}{a^2}\right)",1,"(x^2*(-a + b*x^n)^p*(a + b*x^n)^p*Hypergeometric2F1[n^(-1), -p, 1 + n^(-1), (b^2*x^(2*n))/a^2])/(2*(1 - (b^2*x^(2*n))/a^2)^p)","A",3,3,22,0.1364,1,"{366, 365, 364}"
1020,1,73,0,0.0273191,"\int \left(-a+b x^n\right)^p \left(a+b x^n\right)^p \, dx","Int[(-a + b*x^n)^p*(a + b*x^n)^p,x]","x \left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{2 n},-p;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)","x \left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(\frac{1}{2 n},-p;\frac{1}{2} \left(2+\frac{1}{n}\right);\frac{b^2 x^{2 n}}{a^2}\right)",1,"(x*(-a + b*x^n)^p*(a + b*x^n)^p*Hypergeometric2F1[1/(2*n), -p, (2 + n^(-1))/2, (b^2*x^(2*n))/a^2])/(1 - (b^2*x^(2*n))/a^2)^p","A",3,3,21,0.1429,1,"{253, 246, 245}"
1021,1,72,0,0.0671256,"\int \frac{\left(-a+b x^n\right)^p \left(a+b x^n\right)^p}{x} \, dx","Int[((-a + b*x^n)^p*(a + b*x^n)^p)/x,x]","-\frac{\left(a^2-b^2 x^{2 n}\right) \left(b x^n-a\right)^p \left(a+b x^n\right)^p \, _2F_1\left(1,p+1;p+2;1-\frac{b^2 x^{2 n}}{a^2}\right)}{2 a^2 n (p+1)}","-\frac{\left(a^2-b^2 x^{2 n}\right) \left(b x^n-a\right)^p \left(a+b x^n\right)^p \, _2F_1\left(1,p+1;p+2;1-\frac{b^2 x^{2 n}}{a^2}\right)}{2 a^2 n (p+1)}",1,"-((-a + b*x^n)^p*(a + b*x^n)^p*(a^2 - b^2*x^(2*n))*Hypergeometric2F1[1, 1 + p, 2 + p, 1 - (b^2*x^(2*n))/a^2])/(2*a^2*n*(1 + p))","A",4,4,24,0.1667,1,"{267, 126, 266, 65}"
1022,1,76,0,0.0520478,"\int \frac{\left(-a+b x^n\right)^p \left(a+b x^n\right)^p}{x^2} \, dx","Int[((-a + b*x^n)^p*(a + b*x^n)^p)/x^2,x]","-\frac{\left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2 n},-p;1-\frac{1}{2 n};\frac{b^2 x^{2 n}}{a^2}\right)}{x}","-\frac{\left(b x^n-a\right)^p \left(a+b x^n\right)^p \left(1-\frac{b^2 x^{2 n}}{a^2}\right)^{-p} \, _2F_1\left(-\frac{1}{2 n},-p;1-\frac{1}{2 n};\frac{b^2 x^{2 n}}{a^2}\right)}{x}",1,"-(((-a + b*x^n)^p*(a + b*x^n)^p*Hypergeometric2F1[-1/(2*n), -p, 1 - 1/(2*n), (b^2*x^(2*n))/a^2])/(x*(1 - (b^2*x^(2*n))/a^2)^p))","A",3,3,24,0.1250,1,"{366, 365, 364}"
1023,1,15,0,0.0137918,"\int \frac{1+x^6}{x \left(1-x^6\right)} \, dx","Int[(1 + x^6)/(x*(1 - x^6)),x]","\log (x)-\frac{1}{3} \log \left(1-x^6\right)","\log (x)-\frac{1}{3} \log \left(1-x^6\right)",1,"Log[x] - Log[1 - x^6]/3","A",3,2,18,0.1111,1,"{446, 72}"
1024,1,22,0,0.0148312,"\int (e x)^m \left(a+b x^n\right)^p \left(a (1+m)+b (1+m+n+n p) x^n\right) \, dx","Int[(e*x)^m*(a + b*x^n)^p*(a*(1 + m) + b*(1 + m + n + n*p)*x^n),x]","\frac{(e x)^{m+1} \left(a+b x^n\right)^{p+1}}{e}","\frac{(e x)^{m+1} \left(a+b x^n\right)^{p+1}}{e}",1,"((e*x)^(1 + m)*(a + b*x^n)^(1 + p))/e","A",1,1,33,0.03030,1,"{449}"
1025,1,114,0,0.0624926,"\int \frac{(e x)^m}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[(e*x)^m/((a + b*x^n)*(c + d*x^n)),x]","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)}","\frac{b (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a e (m+1) (b c-a d)}-\frac{d (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)}",1,"(b*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a*(b*c - a*d)*e*(1 + m)) - (d*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*(b*c - a*d)*e*(1 + m))","A",3,2,24,0.08333,1,"{508, 364}"
1026,1,89,0,0.0418385,"\int \frac{x^2}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[x^2/((a + b*x^n)*(c + d*x^n)),x]","\frac{b x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a (b c-a d)}-\frac{d x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{d x^n}{c}\right)}{3 c (b c-a d)}","\frac{b x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a (b c-a d)}-\frac{d x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{d x^n}{c}\right)}{3 c (b c-a d)}",1,"(b*x^3*Hypergeometric2F1[1, 3/n, (3 + n)/n, -((b*x^n)/a)])/(3*a*(b*c - a*d)) - (d*x^3*Hypergeometric2F1[1, 3/n, (3 + n)/n, -((d*x^n)/c)])/(3*c*(b*c - a*d))","A",3,2,22,0.09091,1,"{508, 364}"
1027,1,89,0,0.033347,"\int \frac{x}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[x/((a + b*x^n)*(c + d*x^n)),x]","\frac{b x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a (b c-a d)}-\frac{d x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{d x^n}{c}\right)}{2 c (b c-a d)}","\frac{b x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a (b c-a d)}-\frac{d x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{d x^n}{c}\right)}{2 c (b c-a d)}",1,"(b*x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a*(b*c - a*d)) - (d*x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, -((d*x^n)/c)])/(2*c*(b*c - a*d))","A",3,2,20,0.1000,1,"{508, 364}"
1028,1,72,0,0.0231652,"\int \frac{1}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[1/((a + b*x^n)*(c + d*x^n)),x]","\frac{b x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)}-\frac{d x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)}","\frac{b x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a (b c-a d)}-\frac{d x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)}",1,"(b*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a*(b*c - a*d)) - (d*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c*(b*c - a*d))","A",3,2,19,0.1053,1,"{391, 245}"
1029,1,63,0,0.0678896,"\int \frac{1}{x \left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[1/(x*(a + b*x^n)*(c + d*x^n)),x]","-\frac{b \log \left(a+b x^n\right)}{a n (b c-a d)}+\frac{d \log \left(c+d x^n\right)}{c n (b c-a d)}+\frac{\log (x)}{a c}","-\frac{b \log \left(a+b x^n\right)}{a n (b c-a d)}+\frac{d \log \left(c+d x^n\right)}{c n (b c-a d)}+\frac{\log (x)}{a c}",1,"Log[x]/(a*c) - (b*Log[a + b*x^n])/(a*(b*c - a*d)*n) + (d*Log[c + d*x^n])/(c*(b*c - a*d)*n)","A",3,2,22,0.09091,1,"{446, 72}"
1030,1,90,0,0.0430339,"\int \frac{1}{x^2 \left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[1/(x^2*(a + b*x^n)*(c + d*x^n)),x]","\frac{d \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{d x^n}{c}\right)}{c x (b c-a d)}-\frac{b \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x (b c-a d)}","\frac{d \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{d x^n}{c}\right)}{c x (b c-a d)}-\frac{b \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a x (b c-a d)}",1,"-((b*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(a*(b*c - a*d)*x)) + (d*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), -((d*x^n)/c)])/(c*(b*c - a*d)*x)","A",3,2,22,0.09091,1,"{508, 364}"
1031,1,95,0,0.0428551,"\int \frac{1}{x^3 \left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[1/(x^3*(a + b*x^n)*(c + d*x^n)),x]","\frac{d \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{d x^n}{c}\right)}{2 c x^2 (b c-a d)}-\frac{b \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 (b c-a d)}","\frac{d \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{d x^n}{c}\right)}{2 c x^2 (b c-a d)}-\frac{b \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a x^2 (b c-a d)}",1,"-(b*Hypergeometric2F1[1, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*a*(b*c - a*d)*x^2) + (d*Hypergeometric2F1[1, -2/n, -((2 - n)/n), -((d*x^n)/c)])/(2*c*(b*c - a*d)*x^2)","A",3,2,22,0.09091,1,"{508, 364}"
1032,1,175,0,0.288443,"\int \frac{(e x)^m}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[(e*x)^m/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{b (e x)^{m+1} (a d (m-2 n+1)-b c (m-n+1)) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^2 e (m+1) n (b c-a d)^2}+\frac{d^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)^2}+\frac{b (e x)^{m+1}}{a e n (b c-a d) \left(a+b x^n\right)}","\frac{b (e x)^{m+1} (a d (m-2 n+1)-b c (m-n+1)) \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{b x^n}{a}\right)}{a^2 e (m+1) n (b c-a d)^2}+\frac{d^2 (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{n};\frac{m+n+1}{n};-\frac{d x^n}{c}\right)}{c e (m+1) (b c-a d)^2}+\frac{b (e x)^{m+1}}{a e n (b c-a d) \left(a+b x^n\right)}",1,"(b*(e*x)^(1 + m))/(a*(b*c - a*d)*e*n*(a + b*x^n)) + (b*(a*d*(1 + m - 2*n) - b*c*(1 + m - n))*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((b*x^n)/a)])/(a^2*(b*c - a*d)^2*e*(1 + m)*n) + (d^2*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/n, (1 + m + n)/n, -((d*x^n)/c)])/(c*(b*c - a*d)^2*e*(1 + m))","A",5,3,24,0.1250,1,"{504, 597, 364}"
1033,1,142,0,0.2242735,"\int \frac{x^2}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[x^2/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{b x^3 (a d (3-2 n)-b c (3-n)) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a^2 n (b c-a d)^2}+\frac{d^2 x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{d x^n}{c}\right)}{3 c (b c-a d)^2}+\frac{b x^3}{a n (b c-a d) \left(a+b x^n\right)}","\frac{b x^3 (a d (3-2 n)-b c (3-n)) \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{b x^n}{a}\right)}{3 a^2 n (b c-a d)^2}+\frac{d^2 x^3 \, _2F_1\left(1,\frac{3}{n};\frac{n+3}{n};-\frac{d x^n}{c}\right)}{3 c (b c-a d)^2}+\frac{b x^3}{a n (b c-a d) \left(a+b x^n\right)}",1,"(b*x^3)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(a*d*(3 - 2*n) - b*c*(3 - n))*x^3*Hypergeometric2F1[1, 3/n, (3 + n)/n, -((b*x^n)/a)])/(3*a^2*(b*c - a*d)^2*n) + (d^2*x^3*Hypergeometric2F1[1, 3/n, (3 + n)/n, -((d*x^n)/c)])/(3*c*(b*c - a*d)^2)","A",5,3,22,0.1364,1,"{504, 597, 364}"
1034,1,143,0,0.1815163,"\int \frac{x}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[x/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{b x^2 (2 a d (1-n)-b c (2-n)) \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^2 n (b c-a d)^2}+\frac{d^2 x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{d x^n}{c}\right)}{2 c (b c-a d)^2}+\frac{b x^2}{a n (b c-a d) \left(a+b x^n\right)}","\frac{b x^2 (2 a d (1-n)-b c (2-n)) \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{b x^n}{a}\right)}{2 a^2 n (b c-a d)^2}+\frac{d^2 x^2 \, _2F_1\left(1,\frac{2}{n};\frac{n+2}{n};-\frac{d x^n}{c}\right)}{2 c (b c-a d)^2}+\frac{b x^2}{a n (b c-a d) \left(a+b x^n\right)}",1,"(b*x^2)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(2*a*d*(1 - n) - b*c*(2 - n))*x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, -((b*x^n)/a)])/(2*a^2*(b*c - a*d)^2*n) + (d^2*x^2*Hypergeometric2F1[1, 2/n, (2 + n)/n, -((d*x^n)/c)])/(2*c*(b*c - a*d)^2)","A",5,3,20,0.1500,1,"{504, 597, 364}"
1035,1,122,0,0.1376923,"\int \frac{1}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[1/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{b x (a d (1-2 n)-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^2}+\frac{d^2 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)^2}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right)}","\frac{b x (a d (1-2 n)-b c (1-n)) \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{b x^n}{a}\right)}{a^2 n (b c-a d)^2}+\frac{d^2 x \, _2F_1\left(1,\frac{1}{n};1+\frac{1}{n};-\frac{d x^n}{c}\right)}{c (b c-a d)^2}+\frac{b x}{a n (b c-a d) \left(a+b x^n\right)}",1,"(b*x)/(a*(b*c - a*d)*n*(a + b*x^n)) + (b*(a*d*(1 - 2*n) - b*c*(1 - n))*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((b*x^n)/a)])/(a^2*(b*c - a*d)^2*n) + (d^2*x*Hypergeometric2F1[1, n^(-1), 1 + n^(-1), -((d*x^n)/c)])/(c*(b*c - a*d)^2)","A",4,3,19,0.1579,1,"{414, 522, 245}"
1036,1,101,0,0.1050122,"\int \frac{1}{x \left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[1/(x*(a + b*x^n)^2*(c + d*x^n)),x]","-\frac{b (b c-2 a d) \log \left(a+b x^n\right)}{a^2 n (b c-a d)^2}+\frac{\log (x)}{a^2 c}-\frac{d^2 \log \left(c+d x^n\right)}{c n (b c-a d)^2}+\frac{b}{a n (b c-a d) \left(a+b x^n\right)}","-\frac{b (b c-2 a d) \log \left(a+b x^n\right)}{a^2 n (b c-a d)^2}+\frac{\log (x)}{a^2 c}-\frac{d^2 \log \left(c+d x^n\right)}{c n (b c-a d)^2}+\frac{b}{a n (b c-a d) \left(a+b x^n\right)}",1,"b/(a*(b*c - a*d)*n*(a + b*x^n)) + Log[x]/(a^2*c) - (b*(b*c - 2*a*d)*Log[a + b*x^n])/(a^2*(b*c - a*d)^2*n) - (d^2*Log[c + d*x^n])/(c*(b*c - a*d)^2*n)","A",3,2,22,0.09091,1,"{446, 72}"
1037,1,142,0,0.2140418,"\int \frac{1}{x^2 \left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[1/(x^2*(a + b*x^n)^2*(c + d*x^n)),x]","-\frac{b (b c (n+1)-a d (2 n+1)) \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^2 n x (b c-a d)^2}-\frac{d^2 \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{d x^n}{c}\right)}{c x (b c-a d)^2}+\frac{b}{a n x (b c-a d) \left(a+b x^n\right)}","-\frac{b (b c (n+1)-a d (2 n+1)) \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{b x^n}{a}\right)}{a^2 n x (b c-a d)^2}-\frac{d^2 \, _2F_1\left(1,-\frac{1}{n};-\frac{1-n}{n};-\frac{d x^n}{c}\right)}{c x (b c-a d)^2}+\frac{b}{a n x (b c-a d) \left(a+b x^n\right)}",1,"b/(a*(b*c - a*d)*n*x*(a + b*x^n)) - (b*(b*c*(1 + n) - a*d*(1 + 2*n))*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), -((b*x^n)/a)])/(a^2*(b*c - a*d)^2*n*x) - (d^2*Hypergeometric2F1[1, -n^(-1), -((1 - n)/n), -((d*x^n)/c)])/(c*(b*c - a*d)^2*x)","A",5,3,22,0.1364,1,"{504, 597, 364}"
1038,1,145,0,0.2137295,"\int \frac{1}{x^3 \left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[1/(x^3*(a + b*x^n)^2*(c + d*x^n)),x]","\frac{b (2 a d (n+1)-b c (n+2)) \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^2 n x^2 (b c-a d)^2}-\frac{d^2 \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{d x^n}{c}\right)}{2 c x^2 (b c-a d)^2}+\frac{b}{a n x^2 (b c-a d) \left(a+b x^n\right)}","\frac{b (2 a d (n+1)-b c (n+2)) \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{b x^n}{a}\right)}{2 a^2 n x^2 (b c-a d)^2}-\frac{d^2 \, _2F_1\left(1,-\frac{2}{n};-\frac{2-n}{n};-\frac{d x^n}{c}\right)}{2 c x^2 (b c-a d)^2}+\frac{b}{a n x^2 (b c-a d) \left(a+b x^n\right)}",1,"b/(a*(b*c - a*d)*n*x^2*(a + b*x^n)) + (b*(2*a*d*(1 + n) - b*c*(2 + n))*Hypergeometric2F1[1, -2/n, -((2 - n)/n), -((b*x^n)/a)])/(2*a^2*(b*c - a*d)^2*n*x^2) - (d^2*Hypergeometric2F1[1, -2/n, -((2 - n)/n), -((d*x^n)/c)])/(2*c*(b*c - a*d)^2*x^2)","A",5,3,22,0.1364,1,"{504, 597, 364}"
1039,1,130,0,0.138426,"\int \frac{x^{-1+2 n} \left(a+b x^n\right)^3}{c+d x^n} \, dx","Int[(x^(-1 + 2*n)*(a + b*x^n)^3)/(c + d*x^n),x]","\frac{b x^{2 n} \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{2 d^3 n}-\frac{b^2 x^{3 n} (b c-3 a d)}{3 d^2 n}-\frac{x^n (b c-a d)^3}{d^4 n}+\frac{c (b c-a d)^3 \log \left(c+d x^n\right)}{d^5 n}+\frac{b^3 x^{4 n}}{4 d n}","\frac{b x^{2 n} \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{2 d^3 n}-\frac{b^2 x^{3 n} (b c-3 a d)}{3 d^2 n}-\frac{x^n (b c-a d)^3}{d^4 n}+\frac{c (b c-a d)^3 \log \left(c+d x^n\right)}{d^5 n}+\frac{b^3 x^{4 n}}{4 d n}",1,"-(((b*c - a*d)^3*x^n)/(d^4*n)) + (b*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*x^(2*n))/(2*d^3*n) - (b^2*(b*c - 3*a*d)*x^(3*n))/(3*d^2*n) + (b^3*x^(4*n))/(4*d*n) + (c*(b*c - a*d)^3*Log[c + d*x^n])/(d^5*n)","A",3,2,26,0.07692,1,"{446, 77}"
1040,1,90,0,0.0893512,"\int \frac{x^{-1+2 n} \left(a+b x^n\right)^2}{c+d x^n} \, dx","Int[(x^(-1 + 2*n)*(a + b*x^n)^2)/(c + d*x^n),x]","\frac{x^n (b c-a d)^2}{d^3 n}-\frac{b x^{2 n} (b c-2 a d)}{2 d^2 n}-\frac{c (b c-a d)^2 \log \left(c+d x^n\right)}{d^4 n}+\frac{b^2 x^{3 n}}{3 d n}","\frac{x^n (b c-a d)^2}{d^3 n}-\frac{b x^{2 n} (b c-2 a d)}{2 d^2 n}-\frac{c (b c-a d)^2 \log \left(c+d x^n\right)}{d^4 n}+\frac{b^2 x^{3 n}}{3 d n}",1,"((b*c - a*d)^2*x^n)/(d^3*n) - (b*(b*c - 2*a*d)*x^(2*n))/(2*d^2*n) + (b^2*x^(3*n))/(3*d*n) - (c*(b*c - a*d)^2*Log[c + d*x^n])/(d^4*n)","A",3,2,26,0.07692,1,"{446, 77}"
1041,1,60,0,0.0540822,"\int \frac{x^{-1+2 n} \left(a+b x^n\right)}{c+d x^n} \, dx","Int[(x^(-1 + 2*n)*(a + b*x^n))/(c + d*x^n),x]","-\frac{x^n (b c-a d)}{d^2 n}+\frac{c (b c-a d) \log \left(c+d x^n\right)}{d^3 n}+\frac{b x^{2 n}}{2 d n}","-\frac{x^n (b c-a d)}{d^2 n}+\frac{c (b c-a d) \log \left(c+d x^n\right)}{d^3 n}+\frac{b x^{2 n}}{2 d n}",1,"-(((b*c - a*d)*x^n)/(d^2*n)) + (b*x^(2*n))/(2*d*n) + (c*(b*c - a*d)*Log[c + d*x^n])/(d^3*n)","A",3,2,24,0.08333,1,"{446, 77}"
1042,1,54,0,0.0543653,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[x^(-1 + 2*n)/((a + b*x^n)*(c + d*x^n)),x]","\frac{c \log \left(c+d x^n\right)}{d n (b c-a d)}-\frac{a \log \left(a+b x^n\right)}{b n (b c-a d)}","\frac{c \log \left(c+d x^n\right)}{d n (b c-a d)}-\frac{a \log \left(a+b x^n\right)}{b n (b c-a d)}",1,"-((a*Log[a + b*x^n])/(b*(b*c - a*d)*n)) + (c*Log[c + d*x^n])/(d*(b*c - a*d)*n)","A",3,2,26,0.07692,1,"{446, 72}"
1043,1,75,0,0.0624375,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[x^(-1 + 2*n)/((a + b*x^n)^2*(c + d*x^n)),x]","\frac{a}{b n (b c-a d) \left(a+b x^n\right)}+\frac{c \log \left(a+b x^n\right)}{n (b c-a d)^2}-\frac{c \log \left(c+d x^n\right)}{n (b c-a d)^2}","\frac{a}{b n (b c-a d) \left(a+b x^n\right)}+\frac{c \log \left(a+b x^n\right)}{n (b c-a d)^2}-\frac{c \log \left(c+d x^n\right)}{n (b c-a d)^2}",1,"a/(b*(b*c - a*d)*n*(a + b*x^n)) + (c*Log[a + b*x^n])/((b*c - a*d)^2*n) - (c*Log[c + d*x^n])/((b*c - a*d)^2*n)","A",3,2,26,0.07692,1,"{446, 77}"
1044,1,105,0,0.0899089,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^3 \left(c+d x^n\right)} \, dx","Int[x^(-1 + 2*n)/((a + b*x^n)^3*(c + d*x^n)),x]","\frac{a}{2 b n (b c-a d) \left(a+b x^n\right)^2}-\frac{c}{n (b c-a d)^2 \left(a+b x^n\right)}-\frac{c d \log \left(a+b x^n\right)}{n (b c-a d)^3}+\frac{c d \log \left(c+d x^n\right)}{n (b c-a d)^3}","\frac{a}{2 b n (b c-a d) \left(a+b x^n\right)^2}-\frac{c}{n (b c-a d)^2 \left(a+b x^n\right)}-\frac{c d \log \left(a+b x^n\right)}{n (b c-a d)^3}+\frac{c d \log \left(c+d x^n\right)}{n (b c-a d)^3}",1,"a/(2*b*(b*c - a*d)*n*(a + b*x^n)^2) - c/((b*c - a*d)^2*n*(a + b*x^n)) - (c*d*Log[a + b*x^n])/((b*c - a*d)^3*n) + (c*d*Log[c + d*x^n])/((b*c - a*d)^3*n)","A",3,2,26,0.07692,1,"{446, 77}"
1045,1,158,0,0.1507637,"\int \frac{x^{-1+3 n} \left(a+b x^n\right)^3}{c+d x^n} \, dx","Int[(x^(-1 + 3*n)*(a + b*x^n)^3)/(c + d*x^n),x]","\frac{b x^{3 n} \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{3 d^3 n}-\frac{b^2 x^{4 n} (b c-3 a d)}{4 d^2 n}-\frac{c^2 (b c-a d)^3 \log \left(c+d x^n\right)}{d^6 n}+\frac{c x^n (b c-a d)^3}{d^5 n}-\frac{x^{2 n} (b c-a d)^3}{2 d^4 n}+\frac{b^3 x^{5 n}}{5 d n}","\frac{b x^{3 n} \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{3 d^3 n}-\frac{b^2 x^{4 n} (b c-3 a d)}{4 d^2 n}-\frac{c^2 (b c-a d)^3 \log \left(c+d x^n\right)}{d^6 n}+\frac{c x^n (b c-a d)^3}{d^5 n}-\frac{x^{2 n} (b c-a d)^3}{2 d^4 n}+\frac{b^3 x^{5 n}}{5 d n}",1,"(c*(b*c - a*d)^3*x^n)/(d^5*n) - ((b*c - a*d)^3*x^(2*n))/(2*d^4*n) + (b*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2)*x^(3*n))/(3*d^3*n) - (b^2*(b*c - 3*a*d)*x^(4*n))/(4*d^2*n) + (b^3*x^(5*n))/(5*d*n) - (c^2*(b*c - a*d)^3*Log[c + d*x^n])/(d^6*n)","A",3,2,26,0.07692,1,"{446, 88}"
1046,1,118,0,0.115469,"\int \frac{x^{-1+3 n} \left(a+b x^n\right)^2}{c+d x^n} \, dx","Int[(x^(-1 + 3*n)*(a + b*x^n)^2)/(c + d*x^n),x]","\frac{c^2 (b c-a d)^2 \log \left(c+d x^n\right)}{d^5 n}-\frac{c x^n (b c-a d)^2}{d^4 n}+\frac{x^{2 n} (b c-a d)^2}{2 d^3 n}-\frac{b x^{3 n} (b c-2 a d)}{3 d^2 n}+\frac{b^2 x^{4 n}}{4 d n}","\frac{c^2 (b c-a d)^2 \log \left(c+d x^n\right)}{d^5 n}-\frac{c x^n (b c-a d)^2}{d^4 n}+\frac{x^{2 n} (b c-a d)^2}{2 d^3 n}-\frac{b x^{3 n} (b c-2 a d)}{3 d^2 n}+\frac{b^2 x^{4 n}}{4 d n}",1,"-((c*(b*c - a*d)^2*x^n)/(d^4*n)) + ((b*c - a*d)^2*x^(2*n))/(2*d^3*n) - (b*(b*c - 2*a*d)*x^(3*n))/(3*d^2*n) + (b^2*x^(4*n))/(4*d*n) + (c^2*(b*c - a*d)^2*Log[c + d*x^n])/(d^5*n)","A",3,2,26,0.07692,1,"{446, 88}"
1047,1,86,0,0.0755024,"\int \frac{x^{-1+3 n} \left(a+b x^n\right)}{c+d x^n} \, dx","Int[(x^(-1 + 3*n)*(a + b*x^n))/(c + d*x^n),x]","-\frac{c^2 (b c-a d) \log \left(c+d x^n\right)}{d^4 n}+\frac{c x^n (b c-a d)}{d^3 n}-\frac{x^{2 n} (b c-a d)}{2 d^2 n}+\frac{b x^{3 n}}{3 d n}","-\frac{c^2 (b c-a d) \log \left(c+d x^n\right)}{d^4 n}+\frac{c x^n (b c-a d)}{d^3 n}-\frac{x^{2 n} (b c-a d)}{2 d^2 n}+\frac{b x^{3 n}}{3 d n}",1,"(c*(b*c - a*d)*x^n)/(d^3*n) - ((b*c - a*d)*x^(2*n))/(2*d^2*n) + (b*x^(3*n))/(3*d*n) - (c^2*(b*c - a*d)*Log[c + d*x^n])/(d^4*n)","A",3,2,24,0.08333,1,"{446, 77}"
1048,1,71,0,0.0691811,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right) \left(c+d x^n\right)} \, dx","Int[x^(-1 + 3*n)/((a + b*x^n)*(c + d*x^n)),x]","\frac{a^2 \log \left(a+b x^n\right)}{b^2 n (b c-a d)}-\frac{c^2 \log \left(c+d x^n\right)}{d^2 n (b c-a d)}+\frac{x^n}{b d n}","\frac{a^2 \log \left(a+b x^n\right)}{b^2 n (b c-a d)}-\frac{c^2 \log \left(c+d x^n\right)}{d^2 n (b c-a d)}+\frac{x^n}{b d n}",1,"x^n/(b*d*n) + (a^2*Log[a + b*x^n])/(b^2*(b*c - a*d)*n) - (c^2*Log[c + d*x^n])/(d^2*(b*c - a*d)*n)","A",3,2,26,0.07692,1,"{446, 72}"
1049,1,95,0,0.0903976,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^2 \left(c+d x^n\right)} \, dx","Int[x^(-1 + 3*n)/((a + b*x^n)^2*(c + d*x^n)),x]","-\frac{a^2}{b^2 n (b c-a d) \left(a+b x^n\right)}-\frac{a (2 b c-a d) \log \left(a+b x^n\right)}{b^2 n (b c-a d)^2}+\frac{c^2 \log \left(c+d x^n\right)}{d n (b c-a d)^2}","-\frac{a^2}{b^2 n (b c-a d) \left(a+b x^n\right)}-\frac{a (2 b c-a d) \log \left(a+b x^n\right)}{b^2 n (b c-a d)^2}+\frac{c^2 \log \left(c+d x^n\right)}{d n (b c-a d)^2}",1,"-(a^2/(b^2*(b*c - a*d)*n*(a + b*x^n))) - (a*(2*b*c - a*d)*Log[a + b*x^n])/(b^2*(b*c - a*d)^2*n) + (c^2*Log[c + d*x^n])/(d*(b*c - a*d)^2*n)","A",3,2,26,0.07692,1,"{446, 88}"
1050,1,120,0,0.1053519,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^3 \left(c+d x^n\right)} \, dx","Int[x^(-1 + 3*n)/((a + b*x^n)^3*(c + d*x^n)),x]","-\frac{a^2}{2 b^2 n (b c-a d) \left(a+b x^n\right)^2}+\frac{a (2 b c-a d)}{b^2 n (b c-a d)^2 \left(a+b x^n\right)}+\frac{c^2 \log \left(a+b x^n\right)}{n (b c-a d)^3}-\frac{c^2 \log \left(c+d x^n\right)}{n (b c-a d)^3}","-\frac{a^2}{2 b^2 n (b c-a d) \left(a+b x^n\right)^2}+\frac{a (2 b c-a d)}{b^2 n (b c-a d)^2 \left(a+b x^n\right)}+\frac{c^2 \log \left(a+b x^n\right)}{n (b c-a d)^3}-\frac{c^2 \log \left(c+d x^n\right)}{n (b c-a d)^3}",1,"-a^2/(2*b^2*(b*c - a*d)*n*(a + b*x^n)^2) + (a*(2*b*c - a*d))/(b^2*(b*c - a*d)^2*n*(a + b*x^n)) + (c^2*Log[a + b*x^n])/((b*c - a*d)^3*n) - (c^2*Log[c + d*x^n])/((b*c - a*d)^3*n)","A",3,2,26,0.07692,1,"{446, 88}"
1051,1,14,0,0.0018061,"\int x^{13} (b+c x)^{13} (b+2 c x) \, dx","Int[x^13*(b + c*x)^13*(b + 2*c*x),x]","\frac{1}{14} x^{14} (b+c x)^{14}","\frac{1}{14} x^{14} (b+c x)^{14}",1,"(x^14*(b + c*x)^14)/14","A",1,1,17,0.05882,1,"{74}"
1052,1,16,0,0.0413561,"\int x^{27} \left(b+c x^2\right)^{13} \left(b+2 c x^2\right) \, dx","Int[x^27*(b + c*x^2)^13*(b + 2*c*x^2),x]","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}","\frac{1}{28} x^{28} \left(b+c x^2\right)^{14}",1,"(x^28*(b + c*x^2)^14)/28","A",2,2,21,0.09524,1,"{446, 74}"
1053,1,16,0,0.0363611,"\int x^{41} \left(b+c x^3\right)^{13} \left(b+2 c x^3\right) \, dx","Int[x^41*(b + c*x^3)^13*(b + 2*c*x^3),x]","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}","\frac{1}{42} x^{42} \left(b+c x^3\right)^{14}",1,"(x^42*(b + c*x^3)^14)/42","A",2,2,21,0.09524,1,"{446, 74}"
1054,1,21,0,0.0160322,"\int x^{-1+14 n} \left(b+c x^n\right)^{13} \left(b+2 c x^n\right) \, dx","Int[x^(-1 + 14*n)*(b + c*x^n)^13*(b + 2*c*x^n),x]","\frac{x^{14 n} \left(b+c x^n\right)^{14}}{14 n}","\frac{x^{14 n} \left(b+c x^n\right)^{14}}{14 n}",1,"(x^(14*n)*(b + c*x^n)^14)/(14*n)","A",2,2,25,0.08000,1,"{446, 74}"
1055,1,13,0,0.0138087,"\int x^{-1+m} \left(a+b x^n\right)^{-1+p} \left(a m+b (m+n p) x^n\right) \, dx","Int[x^(-1 + m)*(a + b*x^n)^(-1 + p)*(a*m + b*(m + n*p)*x^n),x]","x^m \left(a+b x^n\right)^p","x^m \left(a+b x^n\right)^p",1,"x^m*(a + b*x^n)^p","A",1,1,31,0.03226,1,"{449}"
1056,1,9,0,0.0056778,"\int \frac{b+2 c x}{x (b+c x)} \, dx","Int[(b + 2*c*x)/(x*(b + c*x)),x]","\log (b+c x)+\log (x)","\log (x (b+c x))",1,"Log[x] + Log[b + c*x]","A",2,1,17,0.05882,1,"{72}"
1057,1,15,0,0.0151964,"\int \frac{b+2 c x^2}{x \left(b+c x^2\right)} \, dx","Int[(b + 2*c*x^2)/(x*(b + c*x^2)),x]","\frac{1}{2} \log \left(b+c x^2\right)+\log (x)","\frac{1}{2} \log \left(b+c x^2\right)+\log (x)",1,"Log[x] + Log[b + c*x^2]/2","A",3,2,21,0.09524,1,"{446, 72}"
1058,1,15,0,0.0144698,"\int \frac{b+2 c x^3}{x \left(b+c x^3\right)} \, dx","Int[(b + 2*c*x^3)/(x*(b + c*x^3)),x]","\frac{1}{3} \log \left(b+c x^3\right)+\log (x)","\frac{1}{3} \log \left(b+c x^3\right)+\log (x)",1,"Log[x] + Log[b + c*x^3]/3","A",3,2,21,0.09524,1,"{446, 72}"
1059,1,15,0,0.0153942,"\int \frac{b+2 c x^n}{x \left(b+c x^n\right)} \, dx","Int[(b + 2*c*x^n)/(x*(b + c*x^n)),x]","\frac{\log \left(b+c x^n\right)}{n}+\log (x)","\frac{\log \left(b+c x^n\right)}{n}+\log (x)",1,"Log[x] + Log[b + c*x^n]/n","A",3,2,21,0.09524,1,"{446, 72}"
1060,1,14,0,0.002028,"\int \frac{b+2 c x}{x^8 (b+c x)^8} \, dx","Int[(b + 2*c*x)/(x^8*(b + c*x)^8),x]","-\frac{1}{7 x^7 (b+c x)^7}","-\frac{1}{7 x^7 (b+c x)^7}",1,"-1/(7*x^7*(b + c*x)^7)","A",1,1,17,0.05882,1,"{74}"
1061,1,16,0,0.0135677,"\int \frac{b+2 c x^2}{x^{15} \left(b+c x^2\right)^8} \, dx","Int[(b + 2*c*x^2)/(x^15*(b + c*x^2)^8),x]","-\frac{1}{14 x^{14} \left(b+c x^2\right)^7}","-\frac{1}{14 x^{14} \left(b+c x^2\right)^7}",1,"-1/(14*x^14*(b + c*x^2)^7)","A",2,2,21,0.09524,1,"{446, 74}"
1062,1,16,0,0.0129464,"\int \frac{b+2 c x^3}{x^{22} \left(b+c x^3\right)^8} \, dx","Int[(b + 2*c*x^3)/(x^22*(b + c*x^3)^8),x]","-\frac{1}{21 x^{21} \left(b+c x^3\right)^7}","-\frac{1}{21 x^{21} \left(b+c x^3\right)^7}",1,"-1/(21*x^21*(b + c*x^3)^7)","A",2,2,21,0.09524,1,"{446, 74}"
1063,1,21,0,0.0132773,"\int \frac{x^{-1-7 n} \left(b+2 c x^n\right)}{\left(b+c x^n\right)^8} \, dx","Int[(x^(-1 - 7*n)*(b + 2*c*x^n))/(b + c*x^n)^8,x]","-\frac{x^{-7 n}}{7 n \left(b+c x^n\right)^7}","-\frac{x^{-7 n}}{7 n \left(b+c x^n\right)^7}",1,"-1/(7*n*x^(7*n)*(b + c*x^n)^7)","A",2,2,25,0.08000,1,"{446, 74}"
1064,1,52,0,0.027784,"\int \frac{x^{31} \sqrt{1+x^{16}}}{1-x^{16}} \, dx","Int[(x^31*Sqrt[1 + x^16])/(1 - x^16),x]","-\frac{1}{24} \left(x^{16}+1\right)^{3/2}-\frac{\sqrt{x^{16}+1}}{8}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x^{16}+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}","-\frac{1}{24} \left(x^{16}+1\right)^{3/2}-\frac{\sqrt{x^{16}+1}}{8}+\frac{\tanh ^{-1}\left(\frac{\sqrt{x^{16}+1}}{\sqrt{2}}\right)}{4 \sqrt{2}}",1,"-Sqrt[1 + x^16]/8 - (1 + x^16)^(3/2)/24 + ArcTanh[Sqrt[1 + x^16]/Sqrt[2]]/(4*Sqrt[2])","A",5,5,22,0.2273,1,"{446, 80, 50, 63, 206}"
1065,1,93,0,0.0863921,"\int \frac{\sqrt{c+\frac{d}{x}}}{\sqrt{a+\frac{b}{x}} x} \, dx","Int[Sqrt[c + d/x]/(Sqrt[a + b/x]*x),x]","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{b}}","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+\frac{b}{x}}}{\sqrt{a} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{a}}-\frac{2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+\frac{b}{x}}}{\sqrt{b} \sqrt{c+\frac{d}{x}}}\right)}{\sqrt{b}}",1,"(2*Sqrt[c]*ArcTanh[(Sqrt[c]*Sqrt[a + b/x])/(Sqrt[a]*Sqrt[c + d/x])])/Sqrt[a] - (2*Sqrt[d]*ArcTanh[(Sqrt[d]*Sqrt[a + b/x])/(Sqrt[b]*Sqrt[c + d/x])])/Sqrt[b]","A",7,7,26,0.2692,1,"{446, 105, 63, 217, 206, 93, 208}"
1066,1,252,0,0.2339383,"\int \frac{x^{-1+2 n} \left(a+b x^n\right)^{5/2}}{\sqrt{c+d x^n}} \, dx","Int[(x^(-1 + 2*n)*(a + b*x^n)^(5/2))/Sqrt[c + d*x^n],x]","\frac{5 (b c-a d)^3 (a d+7 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{64 b^{3/2} d^{9/2} n}-\frac{(a d+7 b c) \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{24 b d^2 n}+\frac{5 (b c-a d) (a d+7 b c) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{96 b d^3 n}-\frac{5 (b c-a d)^2 (a d+7 b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{64 b d^4 n}+\frac{\left(a+b x^n\right)^{7/2} \sqrt{c+d x^n}}{4 b d n}","\frac{5 (b c-a d)^3 (a d+7 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{64 b^{3/2} d^{9/2} n}-\frac{(a d+7 b c) \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{24 b d^2 n}+\frac{5 (b c-a d) (a d+7 b c) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{96 b d^3 n}-\frac{5 (b c-a d)^2 (a d+7 b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{64 b d^4 n}+\frac{\left(a+b x^n\right)^{7/2} \sqrt{c+d x^n}}{4 b d n}",1,"(-5*(b*c - a*d)^2*(7*b*c + a*d)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(64*b*d^4*n) + (5*(b*c - a*d)*(7*b*c + a*d)*(a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(96*b*d^3*n) - ((7*b*c + a*d)*(a + b*x^n)^(5/2)*Sqrt[c + d*x^n])/(24*b*d^2*n) + ((a + b*x^n)^(7/2)*Sqrt[c + d*x^n])/(4*b*d*n) + (5*(b*c - a*d)^3*(7*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(64*b^(3/2)*d^(9/2)*n)","A",8,6,30,0.2000,1,"{446, 80, 50, 63, 217, 206}"
1067,1,199,0,0.1642624,"\int \frac{x^{-1+2 n} \left(a+b x^n\right)^{3/2}}{\sqrt{c+d x^n}} \, dx","Int[(x^(-1 + 2*n)*(a + b*x^n)^(3/2))/Sqrt[c + d*x^n],x]","-\frac{(b c-a d)^2 (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{8 b^{3/2} d^{7/2} n}-\frac{(a d+5 b c) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{12 b d^2 n}+\frac{(b c-a d) (a d+5 b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{8 b d^3 n}+\frac{\left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{3 b d n}","-\frac{(b c-a d)^2 (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{8 b^{3/2} d^{7/2} n}-\frac{(a d+5 b c) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{12 b d^2 n}+\frac{(b c-a d) (a d+5 b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{8 b d^3 n}+\frac{\left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{3 b d n}",1,"((b*c - a*d)*(5*b*c + a*d)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(8*b*d^3*n) - ((5*b*c + a*d)*(a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(12*b*d^2*n) + ((a + b*x^n)^(5/2)*Sqrt[c + d*x^n])/(3*b*d*n) - ((b*c - a*d)^2*(5*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(8*b^(3/2)*d^(7/2)*n)","A",7,6,30,0.2000,1,"{446, 80, 50, 63, 217, 206}"
1068,1,146,0,0.1209631,"\int \frac{x^{-1+2 n} \sqrt{a+b x^n}}{\sqrt{c+d x^n}} \, dx","Int[(x^(-1 + 2*n)*Sqrt[a + b*x^n])/Sqrt[c + d*x^n],x]","\frac{(b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{4 b^{3/2} d^{5/2} n}-\frac{(a d+3 b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{4 b d^2 n}+\frac{\left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{2 b d n}","\frac{(b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{4 b^{3/2} d^{5/2} n}-\frac{(a d+3 b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{4 b d^2 n}+\frac{\left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{2 b d n}",1,"-((3*b*c + a*d)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(4*b*d^2*n) + ((a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(2*b*d*n) + ((b*c - a*d)*(3*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(4*b^(3/2)*d^(5/2)*n)","A",6,6,30,0.2000,1,"{446, 80, 50, 63, 217, 206}"
1069,1,89,0,0.0875472,"\int \frac{x^{-1+2 n}}{\sqrt{a+b x^n} \sqrt{c+d x^n}} \, dx","Int[x^(-1 + 2*n)/(Sqrt[a + b*x^n]*Sqrt[c + d*x^n]),x]","\frac{\sqrt{a+b x^n} \sqrt{c+d x^n}}{b d n}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{3/2} d^{3/2} n}","\frac{\sqrt{a+b x^n} \sqrt{c+d x^n}}{b d n}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{3/2} d^{3/2} n}",1,"(Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(b*d*n) - ((b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(b^(3/2)*d^(3/2)*n)","A",5,5,30,0.1667,1,"{446, 80, 63, 217, 206}"
1070,1,91,0,0.0888679,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}} \, dx","Int[x^(-1 + 2*n)/((a + b*x^n)^(3/2)*Sqrt[c + d*x^n]),x]","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{3/2} \sqrt{d} n}+\frac{2 a \sqrt{c+d x^n}}{b n (b c-a d) \sqrt{a+b x^n}}","\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{3/2} \sqrt{d} n}+\frac{2 a \sqrt{c+d x^n}}{b n (b c-a d) \sqrt{a+b x^n}}",1,"(2*a*Sqrt[c + d*x^n])/(b*(b*c - a*d)*n*Sqrt[a + b*x^n]) + (2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(b^(3/2)*Sqrt[d]*n)","A",5,5,30,0.1667,1,"{446, 78, 63, 217, 206}"
1071,1,95,0,0.0654474,"\int \frac{x^{-1+2 n}}{\left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}} \, dx","Int[x^(-1 + 2*n)/((a + b*x^n)^(5/2)*Sqrt[c + d*x^n]),x]","\frac{2 a \sqrt{c+d x^n}}{3 b n (b c-a d) \left(a+b x^n\right)^{3/2}}-\frac{2 (3 b c-a d) \sqrt{c+d x^n}}{3 b n (b c-a d)^2 \sqrt{a+b x^n}}","\frac{2 a \sqrt{c+d x^n}}{3 b n (b c-a d) \left(a+b x^n\right)^{3/2}}-\frac{2 (3 b c-a d) \sqrt{c+d x^n}}{3 b n (b c-a d)^2 \sqrt{a+b x^n}}",1,"(2*a*Sqrt[c + d*x^n])/(3*b*(b*c - a*d)*n*(a + b*x^n)^(3/2)) - (2*(3*b*c - a*d)*Sqrt[c + d*x^n])/(3*b*(b*c - a*d)^2*n*Sqrt[a + b*x^n])","A",3,3,30,0.1000,1,"{446, 78, 37}"
1072,1,358,0,0.4046925,"\int \frac{x^{-1+3 n} \left(a+b x^n\right)^{5/2}}{\sqrt{c+d x^n}} \, dx","Int[(x^(-1 + 3*n)*(a + b*x^n)^(5/2))/Sqrt[c + d*x^n],x]","\frac{\left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{240 b^2 d^3 n}-\frac{(b c-a d) \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{192 b^2 d^4 n}+\frac{(b c-a d)^2 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \sqrt{a+b x^n} \sqrt{c+d x^n}}{128 b^2 d^5 n}-\frac{(b c-a d)^3 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{128 b^{5/2} d^{11/2} n}-\frac{3 (a d+3 b c) \left(a+b x^n\right)^{7/2} \sqrt{c+d x^n}}{40 b^2 d^2 n}+\frac{x^n \left(a+b x^n\right)^{7/2} \sqrt{c+d x^n}}{5 b d n}","\frac{\left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{240 b^2 d^3 n}-\frac{(b c-a d) \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{192 b^2 d^4 n}+\frac{(b c-a d)^2 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \sqrt{a+b x^n} \sqrt{c+d x^n}}{128 b^2 d^5 n}-\frac{(b c-a d)^3 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{128 b^{5/2} d^{11/2} n}-\frac{3 (a d+3 b c) \left(a+b x^n\right)^{7/2} \sqrt{c+d x^n}}{40 b^2 d^2 n}+\frac{x^n \left(a+b x^n\right)^{7/2} \sqrt{c+d x^n}}{5 b d n}",1,"((b*c - a*d)^2*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(128*b^2*d^5*n) - ((b*c - a*d)*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(192*b^2*d^4*n) + ((63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x^n)^(5/2)*Sqrt[c + d*x^n])/(240*b^2*d^3*n) - (3*(3*b*c + a*d)*(a + b*x^n)^(7/2)*Sqrt[c + d*x^n])/(40*b^2*d^2*n) + (x^n*(a + b*x^n)^(7/2)*Sqrt[c + d*x^n])/(5*b*d*n) - ((b*c - a*d)^3*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(128*b^(5/2)*d^(11/2)*n)","A",9,7,30,0.2333,1,"{446, 90, 80, 50, 63, 217, 206}"
1073,1,291,0,0.3158573,"\int \frac{x^{-1+3 n} \left(a+b x^n\right)^{3/2}}{\sqrt{c+d x^n}} \, dx","Int[(x^(-1 + 3*n)*(a + b*x^n)^(3/2))/Sqrt[c + d*x^n],x]","\frac{\left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{96 b^2 d^3 n}-\frac{(b c-a d) \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \sqrt{a+b x^n} \sqrt{c+d x^n}}{64 b^2 d^4 n}+\frac{(b c-a d)^2 \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{64 b^{5/2} d^{9/2} n}-\frac{(3 a d+7 b c) \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{24 b^2 d^2 n}+\frac{x^n \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{4 b d n}","\frac{\left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{96 b^2 d^3 n}-\frac{(b c-a d) \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \sqrt{a+b x^n} \sqrt{c+d x^n}}{64 b^2 d^4 n}+\frac{(b c-a d)^2 \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{64 b^{5/2} d^{9/2} n}-\frac{(3 a d+7 b c) \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{24 b^2 d^2 n}+\frac{x^n \left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}}{4 b d n}",1,"-((b*c - a*d)*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(64*b^2*d^4*n) + ((35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*(a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(96*b^2*d^3*n) - ((7*b*c + 3*a*d)*(a + b*x^n)^(5/2)*Sqrt[c + d*x^n])/(24*b^2*d^2*n) + (x^n*(a + b*x^n)^(5/2)*Sqrt[c + d*x^n])/(4*b*d*n) + ((b*c - a*d)^2*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(64*b^(5/2)*d^(9/2)*n)","A",8,7,30,0.2333,1,"{446, 90, 80, 50, 63, 217, 206}"
1074,1,221,0,0.2451181,"\int \frac{x^{-1+3 n} \sqrt{a+b x^n}}{\sqrt{c+d x^n}} \, dx","Int[(x^(-1 + 3*n)*Sqrt[a + b*x^n])/Sqrt[c + d*x^n],x]","\frac{\left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \sqrt{a+b x^n} \sqrt{c+d x^n}}{8 b^2 d^3 n}-\frac{(b c-a d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{8 b^{5/2} d^{7/2} n}-\frac{(3 a d+5 b c) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{12 b^2 d^2 n}+\frac{x^n \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{3 b d n}","\frac{\left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \sqrt{a+b x^n} \sqrt{c+d x^n}}{8 b^2 d^3 n}-\frac{(b c-a d) \left(a^2 d^2+2 a b c d+5 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{8 b^{5/2} d^{7/2} n}-\frac{(3 a d+5 b c) \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{12 b^2 d^2 n}+\frac{x^n \left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}}{3 b d n}",1,"((5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(8*b^2*d^3*n) - ((5*b*c + 3*a*d)*(a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(12*b^2*d^2*n) + (x^n*(a + b*x^n)^(3/2)*Sqrt[c + d*x^n])/(3*b*d*n) - ((b*c - a*d)*(5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(8*b^(5/2)*d^(7/2)*n)","A",7,7,30,0.2333,1,"{446, 90, 80, 50, 63, 217, 206}"
1075,1,150,0,0.1516727,"\int \frac{x^{-1+3 n}}{\sqrt{a+b x^n} \sqrt{c+d x^n}} \, dx","Int[x^(-1 + 3*n)/(Sqrt[a + b*x^n]*Sqrt[c + d*x^n]),x]","-\frac{3 (a d+b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{4 b^2 d^2 n}-\frac{\left(4 a b c d-3 (a d+b c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{4 b^{5/2} d^{5/2} n}+\frac{x^n \sqrt{a+b x^n} \sqrt{c+d x^n}}{2 b d n}","-\frac{3 (a d+b c) \sqrt{a+b x^n} \sqrt{c+d x^n}}{4 b^2 d^2 n}-\frac{\left(4 a b c d-3 (a d+b c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{4 b^{5/2} d^{5/2} n}+\frac{x^n \sqrt{a+b x^n} \sqrt{c+d x^n}}{2 b d n}",1,"(-3*(b*c + a*d)*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(4*b^2*d^2*n) + (x^n*Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(2*b*d*n) - ((4*a*b*c*d - 3*(b*c + a*d)^2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(4*b^(5/2)*d^(5/2)*n)","A",6,6,30,0.2000,1,"{446, 90, 80, 63, 217, 206}"
1076,1,133,0,0.1605746,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^{3/2} \sqrt{c+d x^n}} \, dx","Int[x^(-1 + 3*n)/((a + b*x^n)^(3/2)*Sqrt[c + d*x^n]),x]","-\frac{2 a^2 \sqrt{c+d x^n}}{b^2 n (b c-a d) \sqrt{a+b x^n}}-\frac{(3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{5/2} d^{3/2} n}+\frac{\sqrt{a+b x^n} \sqrt{c+d x^n}}{b^2 d n}","-\frac{2 a^2 \sqrt{c+d x^n}}{b^2 n (b c-a d) \sqrt{a+b x^n}}-\frac{(3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{5/2} d^{3/2} n}+\frac{\sqrt{a+b x^n} \sqrt{c+d x^n}}{b^2 d n}",1,"(-2*a^2*Sqrt[c + d*x^n])/(b^2*(b*c - a*d)*n*Sqrt[a + b*x^n]) + (Sqrt[a + b*x^n]*Sqrt[c + d*x^n])/(b^2*d*n) - ((b*c + 3*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(b^(5/2)*d^(3/2)*n)","A",6,6,30,0.2000,1,"{446, 89, 80, 63, 217, 206}"
1077,1,147,0,0.1420428,"\int \frac{x^{-1+3 n}}{\left(a+b x^n\right)^{5/2} \sqrt{c+d x^n}} \, dx","Int[x^(-1 + 3*n)/((a + b*x^n)^(5/2)*Sqrt[c + d*x^n]),x]","-\frac{2 a^2 \sqrt{c+d x^n}}{3 b^2 n (b c-a d) \left(a+b x^n\right)^{3/2}}+\frac{4 a (3 b c-2 a d) \sqrt{c+d x^n}}{3 b^2 n (b c-a d)^2 \sqrt{a+b x^n}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{5/2} \sqrt{d} n}","-\frac{2 a^2 \sqrt{c+d x^n}}{3 b^2 n (b c-a d) \left(a+b x^n\right)^{3/2}}+\frac{4 a (3 b c-2 a d) \sqrt{c+d x^n}}{3 b^2 n (b c-a d)^2 \sqrt{a+b x^n}}+\frac{2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^n}}{\sqrt{b} \sqrt{c+d x^n}}\right)}{b^{5/2} \sqrt{d} n}",1,"(-2*a^2*Sqrt[c + d*x^n])/(3*b^2*(b*c - a*d)*n*(a + b*x^n)^(3/2)) + (4*a*(3*b*c - 2*a*d)*Sqrt[c + d*x^n])/(3*b^2*(b*c - a*d)^2*n*Sqrt[a + b*x^n]) + (2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^n])/(Sqrt[b]*Sqrt[c + d*x^n])])/(b^(5/2)*Sqrt[d]*n)","A",6,6,30,0.2000,1,"{446, 89, 78, 63, 217, 206}"
1078,1,20,0,0.003549,"\int x^p (b+c x)^p (b+2 c x) \, dx","Int[x^p*(b + c*x)^p*(b + 2*c*x),x]","\frac{x^{p+1} (b+c x)^{p+1}}{p+1}","\frac{x^{p+1} (b+c x)^{p+1}}{p+1}",1,"(x^(1 + p)*(b + c*x)^(1 + p))/(1 + p)","A",1,1,17,0.05882,1,"{74}"
1079,1,27,0,0.0089422,"\int x^{-1+2 (1+p)} \left(b+c x^2\right)^p \left(b+2 c x^2\right) \, dx","Int[x^(-1 + 2*(1 + p))*(b + c*x^2)^p*(b + 2*c*x^2),x]","\frac{x^{2 (p+1)} \left(b+c x^2\right)^{p+1}}{2 (p+1)}","\frac{x^{2 (p+1)} \left(b+c x^2\right)^{p+1}}{2 (p+1)}",1,"(x^(2*(1 + p))*(b + c*x^2)^(1 + p))/(2*(1 + p))","A",1,1,27,0.03704,1,"{449}"
1080,1,27,0,0.0088568,"\int x^{-1+3 (1+p)} \left(b+c x^3\right)^p \left(b+2 c x^3\right) \, dx","Int[x^(-1 + 3*(1 + p))*(b + c*x^3)^p*(b + 2*c*x^3),x]","\frac{x^{3 (p+1)} \left(b+c x^3\right)^{p+1}}{3 (p+1)}","\frac{x^{3 (p+1)} \left(b+c x^3\right)^{p+1}}{3 (p+1)}",1,"(x^(3*(1 + p))*(b + c*x^3)^(1 + p))/(3*(1 + p))","A",1,1,27,0.03704,1,"{449}"
1081,1,27,0,0.0124291,"\int x^{-1+n (1+p)} \left(b+c x^n\right)^p \left(b+2 c x^n\right) \, dx","Int[x^(-1 + n*(1 + p))*(b + c*x^n)^p*(b + 2*c*x^n),x]","\frac{x^{n (p+1)} \left(b+c x^n\right)^{p+1}}{n (p+1)}","\frac{x^{n (p+1)} \left(b+c x^n\right)^{p+1}}{n (p+1)}",1,"(x^(n*(1 + p))*(b + c*x^n)^(1 + p))/(n*(1 + p))","A",1,1,27,0.03704,1,"{449}"