1,1,33,0,0.0195923,"\int x^2 \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[x^2*(a + b*x^2)*(A + B*x^2),x]","\frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7","\frac{1}{5} x^5 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{7} b B x^7",1,"(a*A*x^3)/3 + ((A*b + a*B)*x^5)/5 + (b*B*x^7)/7","A",2,1,18,0.05556,1,"{448}"
2,1,33,0,0.0316592,"\int x \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[x*(a + b*x^2)*(A + B*x^2),x]","\frac{1}{4} x^4 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{6} b B x^6","\frac{1}{4} x^4 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{6} b B x^6",1,"(a*A*x^2)/2 + ((A*b + a*B)*x^4)/4 + (b*B*x^6)/6","A",3,2,16,0.1250,1,"{444, 43}"
3,1,28,0,0.0125876,"\int \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[(a + b*x^2)*(A + B*x^2),x]","\frac{1}{3} x^3 (a B+A b)+a A x+\frac{1}{5} b B x^5","\frac{1}{3} x^3 (a B+A b)+a A x+\frac{1}{5} b B x^5",1,"a*A*x + ((A*b + a*B)*x^3)/3 + (b*B*x^5)/5","A",2,1,15,0.06667,1,"{373}"
4,1,29,0,0.0208088,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x,x]","\frac{1}{2} x^2 (a B+A b)+a A \log (x)+\frac{1}{4} b B x^4","\frac{1}{2} x^2 (a B+A b)+a A \log (x)+\frac{1}{4} b B x^4",1,"((A*b + a*B)*x^2)/2 + (b*B*x^4)/4 + a*A*Log[x]","A",3,2,18,0.1111,1,"{446, 76}"
5,1,26,0,0.0164823,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^2} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^2,x]","x (a B+A b)-\frac{a A}{x}+\frac{1}{3} b B x^3","x (a B+A b)-\frac{a A}{x}+\frac{1}{3} b B x^3",1,"-((a*A)/x) + (A*b + a*B)*x + (b*B*x^3)/3","A",2,1,18,0.05556,1,"{448}"
6,1,29,0,0.0202266,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^3} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^3,x]","\log (x) (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{2} b B x^2","\log (x) (a B+A b)-\frac{a A}{2 x^2}+\frac{1}{2} b B x^2",1,"-(a*A)/(2*x^2) + (b*B*x^2)/2 + (A*b + a*B)*Log[x]","A",3,2,18,0.1111,1,"{446, 76}"
7,1,26,0,0.015107,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^4} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^4,x]","-\frac{a B+A b}{x}-\frac{a A}{3 x^3}+b B x","-\frac{a B+A b}{x}-\frac{a A}{3 x^3}+b B x",1,"-(a*A)/(3*x^3) - (A*b + a*B)/x + b*B*x","A",2,1,18,0.05556,1,"{448}"
8,1,29,0,0.0203407,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^5} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^5,x]","-\frac{a B+A b}{2 x^2}-\frac{a A}{4 x^4}+b B \log (x)","-\frac{a B+A b}{2 x^2}-\frac{a A}{4 x^4}+b B \log (x)",1,"-(a*A)/(4*x^4) - (A*b + a*B)/(2*x^2) + b*B*Log[x]","A",3,2,18,0.1111,1,"{446, 76}"
9,1,31,0,0.015195,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^6} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^6,x]","-\frac{a B+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{b B}{x}","-\frac{a B+A b}{3 x^3}-\frac{a A}{5 x^5}-\frac{b B}{x}",1,"-(a*A)/(5*x^5) - (A*b + a*B)/(3*x^3) - (b*B)/x","A",2,1,18,0.05556,1,"{448}"
10,1,33,0,0.021635,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^7} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^7,x]","-\frac{a B+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{b B}{2 x^2}","-\frac{a B+A b}{4 x^4}-\frac{a A}{6 x^6}-\frac{b B}{2 x^2}",1,"-(a*A)/(6*x^6) - (A*b + a*B)/(4*x^4) - (b*B)/(2*x^2)","A",3,2,18,0.1111,1,"{446, 76}"
11,1,55,0,0.0361749,"\int x^2 \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[x^2*(a + b*x^2)^2*(A + B*x^2),x]","\frac{1}{3} a^2 A x^3+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{9} b^2 B x^9","\frac{1}{3} a^2 A x^3+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{9} b^2 B x^9",1,"(a^2*A*x^3)/3 + (a*(2*A*b + a*B)*x^5)/5 + (b*(A*b + 2*a*B)*x^7)/7 + (b^2*B*x^9)/9","A",2,1,20,0.05000,1,"{448}"
12,1,42,0,0.0643204,"\int x \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[x*(a + b*x^2)^2*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^3 (A b-a B)}{6 b^2}+\frac{B \left(a+b x^2\right)^4}{8 b^2}","\frac{\left(a+b x^2\right)^3 (A b-a B)}{6 b^2}+\frac{B \left(a+b x^2\right)^4}{8 b^2}",1,"((A*b - a*B)*(a + b*x^2)^3)/(6*b^2) + (B*(a + b*x^2)^4)/(8*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
13,1,50,0,0.0223412,"\int \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[(a + b*x^2)^2*(A + B*x^2),x]","a^2 A x+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{7} b^2 B x^7","a^2 A x+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{7} b^2 B x^7",1,"a^2*A*x + (a*(2*A*b + a*B)*x^3)/3 + (b*(A*b + 2*a*B)*x^5)/5 + (b^2*B*x^7)/7","A",2,1,17,0.05882,1,"{373}"
14,1,43,0,0.0315544,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x,x]","a^2 A \log (x)+a A b x^2+\frac{B \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} A b^2 x^4","a^2 A \log (x)+a A b x^2+\frac{B \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} A b^2 x^4",1,"a*A*b*x^2 + (A*b^2*x^4)/4 + (B*(a + b*x^2)^3)/(6*b) + a^2*A*Log[x]","A",4,3,20,0.1500,1,"{446, 80, 43}"
15,1,48,0,0.026731,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^2} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^2,x]","-\frac{a^2 A}{x}+\frac{1}{3} b x^3 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{5} b^2 B x^5","-\frac{a^2 A}{x}+\frac{1}{3} b x^3 (2 a B+A b)+a x (a B+2 A b)+\frac{1}{5} b^2 B x^5",1,"-((a^2*A)/x) + a*(2*A*b + a*B)*x + (b*(A*b + 2*a*B)*x^3)/3 + (b^2*B*x^5)/5","A",2,1,20,0.05000,1,"{448}"
16,1,51,0,0.0456132,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^3} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^3,x]","-\frac{a^2 A}{2 x^2}+\frac{1}{2} b x^2 (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{4} b^2 B x^4","-\frac{a^2 A}{2 x^2}+\frac{1}{2} b x^2 (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{4} b^2 B x^4",1,"-(a^2*A)/(2*x^2) + (b*(A*b + 2*a*B)*x^2)/2 + (b^2*B*x^4)/4 + a*(2*A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
17,1,48,0,0.029933,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^4} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^4,x]","-\frac{a^2 A}{3 x^3}+b x (2 a B+A b)-\frac{a (a B+2 A b)}{x}+\frac{1}{3} b^2 B x^3","-\frac{a^2 A}{3 x^3}+b x (2 a B+A b)-\frac{a (a B+2 A b)}{x}+\frac{1}{3} b^2 B x^3",1,"-(a^2*A)/(3*x^3) - (a*(2*A*b + a*B))/x + b*(A*b + 2*a*B)*x + (b^2*B*x^3)/3","A",2,1,20,0.05000,1,"{448}"
18,1,51,0,0.0383888,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^5} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^5,x]","-\frac{a^2 A}{4 x^4}-\frac{a (a B+2 A b)}{2 x^2}+b \log (x) (2 a B+A b)+\frac{1}{2} b^2 B x^2","-\frac{a^2 A}{4 x^4}-\frac{a (a B+2 A b)}{2 x^2}+b \log (x) (2 a B+A b)+\frac{1}{2} b^2 B x^2",1,"-(a^2*A)/(4*x^4) - (a*(2*A*b + a*B))/(2*x^2) + (b^2*B*x^2)/2 + b*(A*b + 2*a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
19,1,48,0,0.0280537,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^6} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^6,x]","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{3 x^3}-\frac{b (2 a B+A b)}{x}+b^2 B x","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{3 x^3}-\frac{b (2 a B+A b)}{x}+b^2 B x",1,"-(a^2*A)/(5*x^5) - (a*(2*A*b + a*B))/(3*x^3) - (b*(A*b + 2*a*B))/x + b^2*B*x","A",2,1,20,0.05000,1,"{448}"
20,1,51,0,0.0367519,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^7} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^7,x]","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B \log (x)","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{2 x^2}+b^2 B \log (x)",1,"-(a^2*A)/(6*x^6) - (a*(2*A*b + a*B))/(4*x^4) - (b*(A*b + 2*a*B))/(2*x^2) + b^2*B*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
21,1,53,0,0.0274398,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^8} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^8,x]","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{x}","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{x}",1,"-(a^2*A)/(7*x^7) - (a*(2*A*b + a*B))/(5*x^5) - (b*(A*b + 2*a*B))/(3*x^3) - (b^2*B)/x","A",2,1,20,0.05000,1,"{448}"
22,1,48,0,0.0311508,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^9} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^9,x]","\frac{\left(a+b x^2\right)^3 (A b-4 a B)}{24 a^2 x^6}-\frac{A \left(a+b x^2\right)^3}{8 a x^8}","\frac{\left(a+b x^2\right)^3 (A b-4 a B)}{24 a^2 x^6}-\frac{A \left(a+b x^2\right)^3}{8 a x^8}",1,"-(A*(a + b*x^2)^3)/(8*a*x^8) + ((A*b - 4*a*B)*(a + b*x^2)^3)/(24*a^2*x^6)","A",3,3,20,0.1500,1,"{446, 78, 37}"
23,1,117,0,0.1525466,"\int x^9 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^9*(a + b*x^2)^5*(A + B*x^2),x]","\frac{5}{8} a^2 b^2 x^{16} (a B+A b)+\frac{5}{14} a^3 b x^{14} (a B+2 A b)+\frac{1}{12} a^4 x^{12} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{18} a b^3 x^{18} (2 a B+A b)+\frac{1}{22} b^5 B x^{22}","\frac{5}{8} a^2 b^2 x^{16} (a B+A b)+\frac{5}{14} a^3 b x^{14} (a B+2 A b)+\frac{1}{12} a^4 x^{12} (a B+5 A b)+\frac{1}{10} a^5 A x^{10}+\frac{1}{20} b^4 x^{20} (5 a B+A b)+\frac{5}{18} a b^3 x^{18} (2 a B+A b)+\frac{1}{22} b^5 B x^{22}",1,"(a^5*A*x^10)/10 + (a^4*(5*A*b + a*B)*x^12)/12 + (5*a^3*b*(2*A*b + a*B)*x^14)/14 + (5*a^2*b^2*(A*b + a*B)*x^16)/8 + (5*a*b^3*(A*b + 2*a*B)*x^18)/18 + (b^4*(A*b + 5*a*B)*x^20)/20 + (b^5*B*x^22)/22","A",3,2,20,0.1000,1,"{446, 76}"
24,1,117,0,0.092316,"\int x^8 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^8*(a + b*x^2)^5*(A + B*x^2),x]","\frac{2}{3} a^2 b^2 x^{15} (a B+A b)+\frac{5}{13} a^3 b x^{13} (a B+2 A b)+\frac{1}{11} a^4 x^{11} (a B+5 A b)+\frac{1}{9} a^5 A x^9+\frac{1}{19} b^4 x^{19} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{21} b^5 B x^{21}","\frac{2}{3} a^2 b^2 x^{15} (a B+A b)+\frac{5}{13} a^3 b x^{13} (a B+2 A b)+\frac{1}{11} a^4 x^{11} (a B+5 A b)+\frac{1}{9} a^5 A x^9+\frac{1}{19} b^4 x^{19} (5 a B+A b)+\frac{5}{17} a b^3 x^{17} (2 a B+A b)+\frac{1}{21} b^5 B x^{21}",1,"(a^5*A*x^9)/9 + (a^4*(5*A*b + a*B)*x^11)/11 + (5*a^3*b*(2*A*b + a*B)*x^13)/13 + (2*a^2*b^2*(A*b + a*B)*x^15)/3 + (5*a*b^3*(A*b + 2*a*B)*x^17)/17 + (b^4*(A*b + 5*a*B)*x^19)/19 + (b^5*B*x^21)/21","A",2,1,20,0.05000,1,"{448}"
25,1,122,0,0.2800257,"\int x^7 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^7*(a + b*x^2)^5*(A + B*x^2),x]","\frac{a^2 \left(a+b x^2\right)^7 (3 A b-4 a B)}{14 b^5}-\frac{a^3 \left(a+b x^2\right)^6 (A b-a B)}{12 b^5}+\frac{\left(a+b x^2\right)^9 (A b-4 a B)}{18 b^5}-\frac{3 a \left(a+b x^2\right)^8 (A b-2 a B)}{16 b^5}+\frac{B \left(a+b x^2\right)^{10}}{20 b^5}","\frac{a^2 \left(a+b x^2\right)^7 (3 A b-4 a B)}{14 b^5}-\frac{a^3 \left(a+b x^2\right)^6 (A b-a B)}{12 b^5}+\frac{\left(a+b x^2\right)^9 (A b-4 a B)}{18 b^5}-\frac{3 a \left(a+b x^2\right)^8 (A b-2 a B)}{16 b^5}+\frac{B \left(a+b x^2\right)^{10}}{20 b^5}",1,"-(a^3*(A*b - a*B)*(a + b*x^2)^6)/(12*b^5) + (a^2*(3*A*b - 4*a*B)*(a + b*x^2)^7)/(14*b^5) - (3*a*(A*b - 2*a*B)*(a + b*x^2)^8)/(16*b^5) + ((A*b - 4*a*B)*(a + b*x^2)^9)/(18*b^5) + (B*(a + b*x^2)^10)/(20*b^5)","A",3,2,20,0.1000,1,"{446, 76}"
26,1,117,0,0.0700851,"\int x^6 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^6*(a + b*x^2)^5*(A + B*x^2),x]","\frac{10}{13} a^2 b^2 x^{13} (a B+A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{1}{9} a^4 x^9 (a B+5 A b)+\frac{1}{7} a^5 A x^7+\frac{1}{17} b^4 x^{17} (5 a B+A b)+\frac{1}{3} a b^3 x^{15} (2 a B+A b)+\frac{1}{19} b^5 B x^{19}","\frac{10}{13} a^2 b^2 x^{13} (a B+A b)+\frac{5}{11} a^3 b x^{11} (a B+2 A b)+\frac{1}{9} a^4 x^9 (a B+5 A b)+\frac{1}{7} a^5 A x^7+\frac{1}{17} b^4 x^{17} (5 a B+A b)+\frac{1}{3} a b^3 x^{15} (2 a B+A b)+\frac{1}{19} b^5 B x^{19}",1,"(a^5*A*x^7)/7 + (a^4*(5*A*b + a*B)*x^9)/9 + (5*a^3*b*(2*A*b + a*B)*x^11)/11 + (10*a^2*b^2*(A*b + a*B)*x^13)/13 + (a*b^3*(A*b + 2*a*B)*x^15)/3 + (b^4*(A*b + 5*a*B)*x^17)/17 + (b^5*B*x^19)/19","A",2,1,20,0.05000,1,"{448}"
27,1,95,0,0.2133307,"\int x^5 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^5*(a + b*x^2)^5*(A + B*x^2),x]","\frac{a^2 \left(a+b x^2\right)^6 (A b-a B)}{12 b^4}+\frac{\left(a+b x^2\right)^8 (A b-3 a B)}{16 b^4}-\frac{a \left(a+b x^2\right)^7 (2 A b-3 a B)}{14 b^4}+\frac{B \left(a+b x^2\right)^9}{18 b^4}","\frac{a^2 \left(a+b x^2\right)^6 (A b-a B)}{12 b^4}+\frac{\left(a+b x^2\right)^8 (A b-3 a B)}{16 b^4}-\frac{a \left(a+b x^2\right)^7 (2 A b-3 a B)}{14 b^4}+\frac{B \left(a+b x^2\right)^9}{18 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x^2)^6)/(12*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x^2)^7)/(14*b^4) + ((A*b - 3*a*B)*(a + b*x^2)^8)/(16*b^4) + (B*(a + b*x^2)^9)/(18*b^4)","A",3,2,20,0.1000,1,"{446, 76}"
28,1,117,0,0.0701615,"\int x^4 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^4*(a + b*x^2)^5*(A + B*x^2),x]","\frac{10}{11} a^2 b^2 x^{11} (a B+A b)+\frac{5}{9} a^3 b x^9 (a B+2 A b)+\frac{1}{7} a^4 x^7 (a B+5 A b)+\frac{1}{5} a^5 A x^5+\frac{1}{15} b^4 x^{15} (5 a B+A b)+\frac{5}{13} a b^3 x^{13} (2 a B+A b)+\frac{1}{17} b^5 B x^{17}","\frac{10}{11} a^2 b^2 x^{11} (a B+A b)+\frac{5}{9} a^3 b x^9 (a B+2 A b)+\frac{1}{7} a^4 x^7 (a B+5 A b)+\frac{1}{5} a^5 A x^5+\frac{1}{15} b^4 x^{15} (5 a B+A b)+\frac{5}{13} a b^3 x^{13} (2 a B+A b)+\frac{1}{17} b^5 B x^{17}",1,"(a^5*A*x^5)/5 + (a^4*(5*A*b + a*B)*x^7)/7 + (5*a^3*b*(2*A*b + a*B)*x^9)/9 + (10*a^2*b^2*(A*b + a*B)*x^11)/11 + (5*a*b^3*(A*b + 2*a*B)*x^13)/13 + (b^4*(A*b + 5*a*B)*x^15)/15 + (b^5*B*x^17)/17","A",2,1,20,0.05000,1,"{448}"
29,1,67,0,0.1431356,"\int x^3 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^3*(a + b*x^2)^5*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^7 (A b-2 a B)}{14 b^3}-\frac{a \left(a+b x^2\right)^6 (A b-a B)}{12 b^3}+\frac{B \left(a+b x^2\right)^8}{16 b^3}","\frac{\left(a+b x^2\right)^7 (A b-2 a B)}{14 b^3}-\frac{a \left(a+b x^2\right)^6 (A b-a B)}{12 b^3}+\frac{B \left(a+b x^2\right)^8}{16 b^3}",1,"-(a*(A*b - a*B)*(a + b*x^2)^6)/(12*b^3) + ((A*b - 2*a*B)*(a + b*x^2)^7)/(14*b^3) + (B*(a + b*x^2)^8)/(16*b^3)","A",3,2,20,0.1000,1,"{446, 76}"
30,1,117,0,0.0664618,"\int x^2 \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x^2*(a + b*x^2)^5*(A + B*x^2),x]","\frac{10}{9} a^2 b^2 x^9 (a B+A b)+\frac{5}{7} a^3 b x^7 (a B+2 A b)+\frac{1}{5} a^4 x^5 (a B+5 A b)+\frac{1}{3} a^5 A x^3+\frac{1}{13} b^4 x^{13} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{15} b^5 B x^{15}","\frac{10}{9} a^2 b^2 x^9 (a B+A b)+\frac{5}{7} a^3 b x^7 (a B+2 A b)+\frac{1}{5} a^4 x^5 (a B+5 A b)+\frac{1}{3} a^5 A x^3+\frac{1}{13} b^4 x^{13} (5 a B+A b)+\frac{5}{11} a b^3 x^{11} (2 a B+A b)+\frac{1}{15} b^5 B x^{15}",1,"(a^5*A*x^3)/3 + (a^4*(5*A*b + a*B)*x^5)/5 + (5*a^3*b*(2*A*b + a*B)*x^7)/7 + (10*a^2*b^2*(A*b + a*B)*x^9)/9 + (5*a*b^3*(A*b + 2*a*B)*x^11)/11 + (b^4*(A*b + 5*a*B)*x^13)/13 + (b^5*B*x^15)/15","A",2,1,20,0.05000,1,"{448}"
31,1,42,0,0.0661224,"\int x \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[x*(a + b*x^2)^5*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^6 (A b-a B)}{12 b^2}+\frac{B \left(a+b x^2\right)^7}{14 b^2}","\frac{\left(a+b x^2\right)^6 (A b-a B)}{12 b^2}+\frac{B \left(a+b x^2\right)^7}{14 b^2}",1,"((A*b - a*B)*(a + b*x^2)^6)/(12*b^2) + (B*(a + b*x^2)^7)/(14*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
32,1,109,0,0.0600984,"\int \left(a+b x^2\right)^5 \left(A+B x^2\right) \, dx","Int[(a + b*x^2)^5*(A + B*x^2),x]","\frac{10}{7} a^2 b^2 x^7 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{3} a^4 x^3 (a B+5 A b)+a^5 A x+\frac{1}{11} b^4 x^{11} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{13} b^5 B x^{13}","\frac{10}{7} a^2 b^2 x^7 (a B+A b)+a^3 b x^5 (a B+2 A b)+\frac{1}{3} a^4 x^3 (a B+5 A b)+a^5 A x+\frac{1}{11} b^4 x^{11} (5 a B+A b)+\frac{5}{9} a b^3 x^9 (2 a B+A b)+\frac{1}{13} b^5 B x^{13}",1,"a^5*A*x + (a^4*(5*A*b + a*B)*x^3)/3 + a^3*b*(2*A*b + a*B)*x^5 + (10*a^2*b^2*(A*b + a*B)*x^7)/7 + (5*a*b^3*(A*b + 2*a*B)*x^9)/9 + (b^4*(A*b + 5*a*B)*x^11)/11 + (b^5*B*x^13)/13","A",2,1,17,0.05882,1,"{373}"
33,1,88,0,0.0645913,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x,x]","\frac{5}{3} a^2 A b^3 x^6+\frac{5}{2} a^3 A b^2 x^4+\frac{5}{2} a^4 A b x^2+a^5 A \log (x)+\frac{5}{8} a A b^4 x^8+\frac{B \left(a+b x^2\right)^6}{12 b}+\frac{1}{10} A b^5 x^{10}","\frac{5}{3} a^2 A b^3 x^6+\frac{5}{2} a^3 A b^2 x^4+\frac{5}{2} a^4 A b x^2+a^5 A \log (x)+\frac{5}{8} a A b^4 x^8+\frac{B \left(a+b x^2\right)^6}{12 b}+\frac{1}{10} A b^5 x^{10}",1,"(5*a^4*A*b*x^2)/2 + (5*a^3*A*b^2*x^4)/2 + (5*a^2*A*b^3*x^6)/3 + (5*a*A*b^4*x^8)/8 + (A*b^5*x^10)/10 + (B*(a + b*x^2)^6)/(12*b) + a^5*A*Log[x]","A",4,3,20,0.1500,1,"{446, 80, 43}"
34,1,108,0,0.0619118,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^2} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^2,x]","2 a^2 b^2 x^5 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+a^4 x (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{11} b^5 B x^{11}","2 a^2 b^2 x^5 (a B+A b)+\frac{5}{3} a^3 b x^3 (a B+2 A b)+a^4 x (a B+5 A b)-\frac{a^5 A}{x}+\frac{1}{9} b^4 x^9 (5 a B+A b)+\frac{5}{7} a b^3 x^7 (2 a B+A b)+\frac{1}{11} b^5 B x^{11}",1,"-((a^5*A)/x) + a^4*(5*A*b + a*B)*x + (5*a^3*b*(2*A*b + a*B)*x^3)/3 + 2*a^2*b^2*(A*b + a*B)*x^5 + (5*a*b^3*(A*b + 2*a*B)*x^7)/7 + (b^4*(A*b + 5*a*B)*x^9)/9 + (b^5*B*x^11)/11","A",2,1,20,0.05000,1,"{448}"
35,1,113,0,0.1127831,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^3} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^3,x]","\frac{5}{2} a^2 b^2 x^4 (a B+A b)+\frac{5}{2} a^3 b x^2 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac{a^5 A}{2 x^2}+\frac{1}{8} b^4 x^8 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{10} b^5 B x^{10}","\frac{5}{2} a^2 b^2 x^4 (a B+A b)+\frac{5}{2} a^3 b x^2 (a B+2 A b)+a^4 \log (x) (a B+5 A b)-\frac{a^5 A}{2 x^2}+\frac{1}{8} b^4 x^8 (5 a B+A b)+\frac{5}{6} a b^3 x^6 (2 a B+A b)+\frac{1}{10} b^5 B x^{10}",1,"-(a^5*A)/(2*x^2) + (5*a^3*b*(2*A*b + a*B)*x^2)/2 + (5*a^2*b^2*(A*b + a*B)*x^4)/2 + (5*a*b^3*(A*b + 2*a*B)*x^6)/6 + (b^4*(A*b + 5*a*B)*x^8)/8 + (b^5*B*x^10)/10 + a^4*(5*A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
36,1,108,0,0.0610051,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^4} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^4,x]","\frac{10}{3} a^2 b^2 x^3 (a B+A b)+5 a^3 b x (a B+2 A b)-\frac{a^4 (a B+5 A b)}{x}-\frac{a^5 A}{3 x^3}+\frac{1}{7} b^4 x^7 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac{1}{9} b^5 B x^9","\frac{10}{3} a^2 b^2 x^3 (a B+A b)+5 a^3 b x (a B+2 A b)-\frac{a^4 (a B+5 A b)}{x}-\frac{a^5 A}{3 x^3}+\frac{1}{7} b^4 x^7 (5 a B+A b)+a b^3 x^5 (2 a B+A b)+\frac{1}{9} b^5 B x^9",1,"-(a^5*A)/(3*x^3) - (a^4*(5*A*b + a*B))/x + 5*a^3*b*(2*A*b + a*B)*x + (10*a^2*b^2*(A*b + a*B)*x^3)/3 + a*b^3*(A*b + 2*a*B)*x^5 + (b^4*(A*b + 5*a*B)*x^7)/7 + (b^5*B*x^9)/9","A",2,1,20,0.05000,1,"{448}"
37,1,112,0,0.1043404,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^5} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^5,x]","5 a^2 b^2 x^2 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b \log (x) (a B+2 A b)-\frac{a^5 A}{4 x^4}+\frac{1}{6} b^4 x^6 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{8} b^5 B x^8","5 a^2 b^2 x^2 (a B+A b)-\frac{a^4 (a B+5 A b)}{2 x^2}+5 a^3 b \log (x) (a B+2 A b)-\frac{a^5 A}{4 x^4}+\frac{1}{6} b^4 x^6 (5 a B+A b)+\frac{5}{4} a b^3 x^4 (2 a B+A b)+\frac{1}{8} b^5 B x^8",1,"-(a^5*A)/(4*x^4) - (a^4*(5*A*b + a*B))/(2*x^2) + 5*a^2*b^2*(A*b + a*B)*x^2 + (5*a*b^3*(A*b + 2*a*B)*x^4)/4 + (b^4*(A*b + 5*a*B)*x^6)/6 + (b^5*B*x^8)/8 + 5*a^3*b*(2*A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
38,1,111,0,0.0623546,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^6} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^6,x]","10 a^2 b^2 x (a B+A b)-\frac{a^4 (a B+5 A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{x}-\frac{a^5 A}{5 x^5}+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{7} b^5 B x^7","10 a^2 b^2 x (a B+A b)-\frac{a^4 (a B+5 A b)}{3 x^3}-\frac{5 a^3 b (a B+2 A b)}{x}-\frac{a^5 A}{5 x^5}+\frac{1}{5} b^4 x^5 (5 a B+A b)+\frac{5}{3} a b^3 x^3 (2 a B+A b)+\frac{1}{7} b^5 B x^7",1,"-(a^5*A)/(5*x^5) - (a^4*(5*A*b + a*B))/(3*x^3) - (5*a^3*b*(2*A*b + a*B))/x + 10*a^2*b^2*(A*b + a*B)*x + (5*a*b^3*(A*b + 2*a*B)*x^3)/3 + (b^4*(A*b + 5*a*B)*x^5)/5 + (b^5*B*x^7)/7","A",2,1,20,0.05000,1,"{448}"
39,1,114,0,0.1005598,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^7} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^7,x]","10 a^2 b^2 \log (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)}{4 x^4}-\frac{a^5 A}{6 x^6}+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{6} b^5 B x^6","10 a^2 b^2 \log (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)}{4 x^4}-\frac{a^5 A}{6 x^6}+\frac{1}{4} b^4 x^4 (5 a B+A b)+\frac{5}{2} a b^3 x^2 (2 a B+A b)+\frac{1}{6} b^5 B x^6",1,"-(a^5*A)/(6*x^6) - (a^4*(5*A*b + a*B))/(4*x^4) - (5*a^3*b*(2*A*b + a*B))/(2*x^2) + (5*a*b^3*(A*b + 2*a*B)*x^2)/2 + (b^4*(A*b + 5*a*B)*x^4)/4 + (b^5*B*x^6)/6 + 10*a^2*b^2*(A*b + a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
40,1,111,0,0.0617063,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^8} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^8,x]","-\frac{10 a^2 b^2 (a B+A b)}{x}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{a^5 A}{7 x^7}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac{1}{5} b^5 B x^5","-\frac{10 a^2 b^2 (a B+A b)}{x}-\frac{a^4 (a B+5 A b)}{5 x^5}-\frac{5 a^3 b (a B+2 A b)}{3 x^3}-\frac{a^5 A}{7 x^7}+\frac{1}{3} b^4 x^3 (5 a B+A b)+5 a b^3 x (2 a B+A b)+\frac{1}{5} b^5 B x^5",1,"-(a^5*A)/(7*x^7) - (a^4*(5*A*b + a*B))/(5*x^5) - (5*a^3*b*(2*A*b + a*B))/(3*x^3) - (10*a^2*b^2*(A*b + a*B))/x + 5*a*b^3*(A*b + 2*a*B)*x + (b^4*(A*b + 5*a*B)*x^3)/3 + (b^5*B*x^5)/5","A",2,1,20,0.05000,1,"{448}"
41,1,112,0,0.0965514,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^9} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^9,x]","-\frac{5 a^2 b^2 (a B+A b)}{x^2}-\frac{a^4 (a B+5 A b)}{6 x^6}-\frac{5 a^3 b (a B+2 A b)}{4 x^4}-\frac{a^5 A}{8 x^8}+\frac{1}{2} b^4 x^2 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{4} b^5 B x^4","-\frac{5 a^2 b^2 (a B+A b)}{x^2}-\frac{a^4 (a B+5 A b)}{6 x^6}-\frac{5 a^3 b (a B+2 A b)}{4 x^4}-\frac{a^5 A}{8 x^8}+\frac{1}{2} b^4 x^2 (5 a B+A b)+5 a b^3 \log (x) (2 a B+A b)+\frac{1}{4} b^5 B x^4",1,"-(a^5*A)/(8*x^8) - (a^4*(5*A*b + a*B))/(6*x^6) - (5*a^3*b*(2*A*b + a*B))/(4*x^4) - (5*a^2*b^2*(A*b + a*B))/x^2 + (b^4*(A*b + 5*a*B)*x^2)/2 + (b^5*B*x^4)/4 + 5*a*b^3*(A*b + 2*a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
42,1,108,0,0.0663631,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{10}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^10,x]","-\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^3 b (a B+2 A b)}{x^5}-\frac{a^5 A}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{x}+b^4 x (5 a B+A b)+\frac{1}{3} b^5 B x^3","-\frac{10 a^2 b^2 (a B+A b)}{3 x^3}-\frac{a^4 (a B+5 A b)}{7 x^7}-\frac{a^3 b (a B+2 A b)}{x^5}-\frac{a^5 A}{9 x^9}-\frac{5 a b^3 (2 a B+A b)}{x}+b^4 x (5 a B+A b)+\frac{1}{3} b^5 B x^3",1,"-(a^5*A)/(9*x^9) - (a^4*(5*A*b + a*B))/(7*x^7) - (a^3*b*(2*A*b + a*B))/x^5 - (10*a^2*b^2*(A*b + a*B))/(3*x^3) - (5*a*b^3*(A*b + 2*a*B))/x + b^4*(A*b + 5*a*B)*x + (b^5*B*x^3)/3","A",2,1,20,0.05000,1,"{448}"
43,1,113,0,0.0893554,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{11}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^11,x]","-\frac{5 a^2 b^2 (a B+A b)}{2 x^4}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{a^5 A}{10 x^{10}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 \log (x) (5 a B+A b)+\frac{1}{2} b^5 B x^2","-\frac{5 a^2 b^2 (a B+A b)}{2 x^4}-\frac{a^4 (a B+5 A b)}{8 x^8}-\frac{5 a^3 b (a B+2 A b)}{6 x^6}-\frac{a^5 A}{10 x^{10}}-\frac{5 a b^3 (2 a B+A b)}{2 x^2}+b^4 \log (x) (5 a B+A b)+\frac{1}{2} b^5 B x^2",1,"-(a^5*A)/(10*x^10) - (a^4*(5*A*b + a*B))/(8*x^8) - (5*a^3*b*(2*A*b + a*B))/(6*x^6) - (5*a^2*b^2*(A*b + a*B))/(2*x^4) - (5*a*b^3*(A*b + 2*a*B))/(2*x^2) + (b^5*B*x^2)/2 + b^4*(A*b + 5*a*B)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
44,1,108,0,0.0621864,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{12}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^12,x]","-\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{a^5 A}{11 x^{11}}-\frac{5 a b^3 (2 a B+A b)}{3 x^3}-\frac{b^4 (5 a B+A b)}{x}+b^5 B x","-\frac{2 a^2 b^2 (a B+A b)}{x^5}-\frac{a^4 (a B+5 A b)}{9 x^9}-\frac{5 a^3 b (a B+2 A b)}{7 x^7}-\frac{a^5 A}{11 x^{11}}-\frac{5 a b^3 (2 a B+A b)}{3 x^3}-\frac{b^4 (5 a B+A b)}{x}+b^5 B x",1,"-(a^5*A)/(11*x^11) - (a^4*(5*A*b + a*B))/(9*x^9) - (5*a^3*b*(2*A*b + a*B))/(7*x^7) - (2*a^2*b^2*(A*b + a*B))/x^5 - (5*a*b^3*(A*b + 2*a*B))/(3*x^3) - (b^4*(A*b + 5*a*B))/x + b^5*B*x","A",2,1,20,0.05000,1,"{448}"
45,1,91,0,0.055555,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{13}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^13,x]","-\frac{5 a^2 b^3 B}{2 x^4}-\frac{5 a^3 b^2 B}{3 x^6}-\frac{5 a^4 b B}{8 x^8}-\frac{a^5 B}{10 x^{10}}-\frac{A \left(a+b x^2\right)^6}{12 a x^{12}}-\frac{5 a b^4 B}{2 x^2}+b^5 B \log (x)","-\frac{5 a^2 b^3 B}{2 x^4}-\frac{5 a^3 b^2 B}{3 x^6}-\frac{5 a^4 b B}{8 x^8}-\frac{a^5 B}{10 x^{10}}-\frac{A \left(a+b x^2\right)^6}{12 a x^{12}}-\frac{5 a b^4 B}{2 x^2}+b^5 B \log (x)",1,"-(a^5*B)/(10*x^10) - (5*a^4*b*B)/(8*x^8) - (5*a^3*b^2*B)/(3*x^6) - (5*a^2*b^3*B)/(2*x^4) - (5*a*b^4*B)/(2*x^2) - (A*(a + b*x^2)^6)/(12*a*x^12) + b^5*B*Log[x]","A",4,3,20,0.1500,1,"{446, 78, 43}"
46,1,113,0,0.062222,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{14}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^14,x]","-\frac{10 a^2 b^2 (a B+A b)}{7 x^7}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{a^5 A}{13 x^{13}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{3 x^3}-\frac{b^5 B}{x}","-\frac{10 a^2 b^2 (a B+A b)}{7 x^7}-\frac{a^4 (a B+5 A b)}{11 x^{11}}-\frac{5 a^3 b (a B+2 A b)}{9 x^9}-\frac{a^5 A}{13 x^{13}}-\frac{a b^3 (2 a B+A b)}{x^5}-\frac{b^4 (5 a B+A b)}{3 x^3}-\frac{b^5 B}{x}",1,"-(a^5*A)/(13*x^13) - (a^4*(5*A*b + a*B))/(11*x^11) - (5*a^3*b*(2*A*b + a*B))/(9*x^9) - (10*a^2*b^2*(A*b + a*B))/(7*x^7) - (a*b^3*(A*b + 2*a*B))/x^5 - (b^4*(A*b + 5*a*B))/(3*x^3) - (b^5*B)/x","A",2,1,20,0.05000,1,"{448}"
47,1,48,0,0.0296584,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{15}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^15,x]","\frac{\left(a+b x^2\right)^6 (A b-7 a B)}{84 a^2 x^{12}}-\frac{A \left(a+b x^2\right)^6}{14 a x^{14}}","\frac{\left(a+b x^2\right)^6 (A b-7 a B)}{84 a^2 x^{12}}-\frac{A \left(a+b x^2\right)^6}{14 a x^{14}}",1,"-(A*(a + b*x^2)^6)/(14*a*x^14) + ((A*b - 7*a*B)*(a + b*x^2)^6)/(84*a^2*x^12)","A",3,3,20,0.1500,1,"{446, 78, 37}"
48,1,117,0,0.058662,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{16}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^16,x]","-\frac{10 a^2 b^2 (a B+A b)}{9 x^9}-\frac{a^4 (a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{15 x^{15}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{b^5 B}{3 x^3}","-\frac{10 a^2 b^2 (a B+A b)}{9 x^9}-\frac{a^4 (a B+5 A b)}{13 x^{13}}-\frac{5 a^3 b (a B+2 A b)}{11 x^{11}}-\frac{a^5 A}{15 x^{15}}-\frac{5 a b^3 (2 a B+A b)}{7 x^7}-\frac{b^4 (5 a B+A b)}{5 x^5}-\frac{b^5 B}{3 x^3}",1,"-(a^5*A)/(15*x^15) - (a^4*(5*A*b + a*B))/(13*x^13) - (5*a^3*b*(2*A*b + a*B))/(11*x^11) - (10*a^2*b^2*(A*b + a*B))/(9*x^9) - (5*a*b^3*(A*b + 2*a*B))/(7*x^7) - (b^4*(A*b + 5*a*B))/(5*x^5) - (b^5*B)/(3*x^3)","A",2,1,20,0.05000,1,"{448}"
49,1,76,0,0.0513359,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{17}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^17,x]","-\frac{b \left(a+b x^2\right)^6 (A b-4 a B)}{336 a^3 x^{12}}+\frac{\left(a+b x^2\right)^6 (A b-4 a B)}{56 a^2 x^{14}}-\frac{A \left(a+b x^2\right)^6}{16 a x^{16}}","-\frac{b \left(a+b x^2\right)^6 (A b-4 a B)}{336 a^3 x^{12}}+\frac{\left(a+b x^2\right)^6 (A b-4 a B)}{56 a^2 x^{14}}-\frac{A \left(a+b x^2\right)^6}{16 a x^{16}}",1,"-(A*(a + b*x^2)^6)/(16*a*x^16) + ((A*b - 4*a*B)*(a + b*x^2)^6)/(56*a^2*x^14) - (b*(A*b - 4*a*B)*(a + b*x^2)^6)/(336*a^3*x^12)","A",4,4,20,0.2000,1,"{446, 78, 45, 37}"
50,1,117,0,0.0593107,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{18}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^18,x]","-\frac{10 a^2 b^2 (a B+A b)}{11 x^{11}}-\frac{a^4 (a B+5 A b)}{15 x^{15}}-\frac{5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac{a^5 A}{17 x^{17}}-\frac{5 a b^3 (2 a B+A b)}{9 x^9}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{5 x^5}","-\frac{10 a^2 b^2 (a B+A b)}{11 x^{11}}-\frac{a^4 (a B+5 A b)}{15 x^{15}}-\frac{5 a^3 b (a B+2 A b)}{13 x^{13}}-\frac{a^5 A}{17 x^{17}}-\frac{5 a b^3 (2 a B+A b)}{9 x^9}-\frac{b^4 (5 a B+A b)}{7 x^7}-\frac{b^5 B}{5 x^5}",1,"-(a^5*A)/(17*x^17) - (a^4*(5*A*b + a*B))/(15*x^15) - (5*a^3*b*(2*A*b + a*B))/(13*x^13) - (10*a^2*b^2*(A*b + a*B))/(11*x^11) - (5*a*b^3*(A*b + 2*a*B))/(9*x^9) - (b^4*(A*b + 5*a*B))/(7*x^7) - (b^5*B)/(5*x^5)","A",2,1,20,0.05000,1,"{448}"
51,1,117,0,0.0838325,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{19}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^19,x]","-\frac{5 a^2 b^2 (a B+A b)}{6 x^{12}}-\frac{a^4 (a B+5 A b)}{16 x^{16}}-\frac{5 a^3 b (a B+2 A b)}{14 x^{14}}-\frac{a^5 A}{18 x^{18}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{8 x^8}-\frac{b^5 B}{6 x^6}","-\frac{5 a^2 b^2 (a B+A b)}{6 x^{12}}-\frac{a^4 (a B+5 A b)}{16 x^{16}}-\frac{5 a^3 b (a B+2 A b)}{14 x^{14}}-\frac{a^5 A}{18 x^{18}}-\frac{a b^3 (2 a B+A b)}{2 x^{10}}-\frac{b^4 (5 a B+A b)}{8 x^8}-\frac{b^5 B}{6 x^6}",1,"-(a^5*A)/(18*x^18) - (a^4*(5*A*b + a*B))/(16*x^16) - (5*a^3*b*(2*A*b + a*B))/(14*x^14) - (5*a^2*b^2*(A*b + a*B))/(6*x^12) - (a*b^3*(A*b + 2*a*B))/(2*x^10) - (b^4*(A*b + 5*a*B))/(8*x^8) - (b^5*B)/(6*x^6)","A",3,2,20,0.1000,1,"{446, 76}"
52,1,117,0,0.0586581,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{20}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^20,x]","-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{b^5 B}{7 x^7}","-\frac{10 a^2 b^2 (a B+A b)}{13 x^{13}}-\frac{a^4 (a B+5 A b)}{17 x^{17}}-\frac{a^3 b (a B+2 A b)}{3 x^{15}}-\frac{a^5 A}{19 x^{19}}-\frac{5 a b^3 (2 a B+A b)}{11 x^{11}}-\frac{b^4 (5 a B+A b)}{9 x^9}-\frac{b^5 B}{7 x^7}",1,"-(a^5*A)/(19*x^19) - (a^4*(5*A*b + a*B))/(17*x^17) - (a^3*b*(2*A*b + a*B))/(3*x^15) - (10*a^2*b^2*(A*b + a*B))/(13*x^13) - (5*a*b^3*(A*b + 2*a*B))/(11*x^11) - (b^4*(A*b + 5*a*B))/(9*x^9) - (b^5*B)/(7*x^7)","A",2,1,20,0.05000,1,"{448}"
53,1,117,0,0.0825582,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{21}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^21,x]","-\frac{5 a^2 b^2 (a B+A b)}{7 x^{14}}-\frac{a^4 (a B+5 A b)}{18 x^{18}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{20 x^{20}}-\frac{5 a b^3 (2 a B+A b)}{12 x^{12}}-\frac{b^4 (5 a B+A b)}{10 x^{10}}-\frac{b^5 B}{8 x^8}","-\frac{5 a^2 b^2 (a B+A b)}{7 x^{14}}-\frac{a^4 (a B+5 A b)}{18 x^{18}}-\frac{5 a^3 b (a B+2 A b)}{16 x^{16}}-\frac{a^5 A}{20 x^{20}}-\frac{5 a b^3 (2 a B+A b)}{12 x^{12}}-\frac{b^4 (5 a B+A b)}{10 x^{10}}-\frac{b^5 B}{8 x^8}",1,"-(a^5*A)/(20*x^20) - (a^4*(5*A*b + a*B))/(18*x^18) - (5*a^3*b*(2*A*b + a*B))/(16*x^16) - (5*a^2*b^2*(A*b + a*B))/(7*x^14) - (5*a*b^3*(A*b + 2*a*B))/(12*x^12) - (b^4*(A*b + 5*a*B))/(10*x^10) - (b^5*B)/(8*x^8)","A",3,2,20,0.1000,1,"{446, 76}"
54,1,117,0,0.0620889,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{22}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^22,x]","-\frac{2 a^2 b^2 (a B+A b)}{3 x^{15}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{17 x^{17}}-\frac{a^5 A}{21 x^{21}}-\frac{5 a b^3 (2 a B+A b)}{13 x^{13}}-\frac{b^4 (5 a B+A b)}{11 x^{11}}-\frac{b^5 B}{9 x^9}","-\frac{2 a^2 b^2 (a B+A b)}{3 x^{15}}-\frac{a^4 (a B+5 A b)}{19 x^{19}}-\frac{5 a^3 b (a B+2 A b)}{17 x^{17}}-\frac{a^5 A}{21 x^{21}}-\frac{5 a b^3 (2 a B+A b)}{13 x^{13}}-\frac{b^4 (5 a B+A b)}{11 x^{11}}-\frac{b^5 B}{9 x^9}",1,"-(a^5*A)/(21*x^21) - (a^4*(5*A*b + a*B))/(19*x^19) - (5*a^3*b*(2*A*b + a*B))/(17*x^17) - (2*a^2*b^2*(A*b + a*B))/(3*x^15) - (5*a*b^3*(A*b + 2*a*B))/(13*x^13) - (b^4*(A*b + 5*a*B))/(11*x^11) - (b^5*B)/(9*x^9)","A",2,1,20,0.05000,1,"{448}"
55,1,117,0,0.0848973,"\int \frac{\left(a+b x^2\right)^5 \left(A+B x^2\right)}{x^{23}} \, dx","Int[((a + b*x^2)^5*(A + B*x^2))/x^23,x]","-\frac{5 a^2 b^2 (a B+A b)}{8 x^{16}}-\frac{a^4 (a B+5 A b)}{20 x^{20}}-\frac{5 a^3 b (a B+2 A b)}{18 x^{18}}-\frac{a^5 A}{22 x^{22}}-\frac{5 a b^3 (2 a B+A b)}{14 x^{14}}-\frac{b^4 (5 a B+A b)}{12 x^{12}}-\frac{b^5 B}{10 x^{10}}","-\frac{5 a^2 b^2 (a B+A b)}{8 x^{16}}-\frac{a^4 (a B+5 A b)}{20 x^{20}}-\frac{5 a^3 b (a B+2 A b)}{18 x^{18}}-\frac{a^5 A}{22 x^{22}}-\frac{5 a b^3 (2 a B+A b)}{14 x^{14}}-\frac{b^4 (5 a B+A b)}{12 x^{12}}-\frac{b^5 B}{10 x^{10}}",1,"-(a^5*A)/(22*x^22) - (a^4*(5*A*b + a*B))/(20*x^20) - (5*a^3*b*(2*A*b + a*B))/(18*x^18) - (5*a^2*b^2*(A*b + a*B))/(8*x^16) - (5*a*b^3*(A*b + 2*a*B))/(14*x^14) - (b^4*(A*b + 5*a*B))/(12*x^12) - (b^5*B)/(10*x^10)","A",3,2,20,0.1000,1,"{446, 76}"
56,1,98,0,0.0605939,"\int \frac{x^6 \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2),x]","\frac{a^2 x (A b-a B)}{b^4}-\frac{a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{x^5 (A b-a B)}{5 b^2}-\frac{a x^3 (A b-a B)}{3 b^3}+\frac{B x^7}{7 b}","\frac{a^2 x (A b-a B)}{b^4}-\frac{a^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{x^5 (A b-a B)}{5 b^2}-\frac{a x^3 (A b-a B)}{3 b^3}+\frac{B x^7}{7 b}",1,"(a^2*(A*b - a*B)*x)/b^4 - (a*(A*b - a*B)*x^3)/(3*b^3) + ((A*b - a*B)*x^5)/(5*b^2) + (B*x^7)/(7*b) - (a^(5/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(9/2)","A",4,3,20,0.1500,1,"{459, 302, 205}"
57,1,75,0,0.0869095,"\int \frac{x^5 \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2),x]","\frac{a^2 (A b-a B) \log \left(a+b x^2\right)}{2 b^4}+\frac{x^4 (A b-a B)}{4 b^2}-\frac{a x^2 (A b-a B)}{2 b^3}+\frac{B x^6}{6 b}","\frac{a^2 (A b-a B) \log \left(a+b x^2\right)}{2 b^4}+\frac{x^4 (A b-a B)}{4 b^2}-\frac{a x^2 (A b-a B)}{2 b^3}+\frac{B x^6}{6 b}",1,"-(a*(A*b - a*B)*x^2)/(2*b^3) + ((A*b - a*B)*x^4)/(4*b^2) + (B*x^6)/(6*b) + (a^2*(A*b - a*B)*Log[a + b*x^2])/(2*b^4)","A",3,2,20,0.1000,1,"{446, 77}"
58,1,77,0,0.0501443,"\int \frac{x^4 \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2),x]","\frac{a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^3 (A b-a B)}{3 b^2}-\frac{a x (A b-a B)}{b^3}+\frac{B x^5}{5 b}","\frac{a^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^3 (A b-a B)}{3 b^2}-\frac{a x (A b-a B)}{b^3}+\frac{B x^5}{5 b}",1,"-((a*(A*b - a*B)*x)/b^3) + ((A*b - a*B)*x^3)/(3*b^2) + (B*x^5)/(5*b) + (a^(3/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2)","A",4,3,20,0.1500,1,"{459, 302, 205}"
59,1,54,0,0.0555315,"\int \frac{x^3 \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2),x]","\frac{x^2 (A b-a B)}{2 b^2}-\frac{a (A b-a B) \log \left(a+b x^2\right)}{2 b^3}+\frac{B x^4}{4 b}","\frac{x^2 (A b-a B)}{2 b^2}-\frac{a (A b-a B) \log \left(a+b x^2\right)}{2 b^3}+\frac{B x^4}{4 b}",1,"((A*b - a*B)*x^2)/(2*b^2) + (B*x^4)/(4*b) - (a*(A*b - a*B)*Log[a + b*x^2])/(2*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
60,1,58,0,0.035743,"\int \frac{x^2 \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2),x]","\frac{x (A b-a B)}{b^2}-\frac{\sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{B x^3}{3 b}","\frac{x (A b-a B)}{b^2}-\frac{\sqrt{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{B x^3}{3 b}",1,"((A*b - a*B)*x)/b^2 + (B*x^3)/(3*b) - (Sqrt[a]*(A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2)","A",3,3,20,0.1500,1,"{459, 321, 205}"
61,1,35,0,0.0299063,"\int \frac{x \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2),x]","\frac{(A b-a B) \log \left(a+b x^2\right)}{2 b^2}+\frac{B x^2}{2 b}","\frac{(A b-a B) \log \left(a+b x^2\right)}{2 b^2}+\frac{B x^2}{2 b}",1,"(B*x^2)/(2*b) + ((A*b - a*B)*Log[a + b*x^2])/(2*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
62,1,39,0,0.0168032,"\int \frac{A+B x^2}{a+b x^2} \, dx","Int[(A + B*x^2)/(a + b*x^2),x]","\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{B x}{b}","\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{B x}{b}",1,"(B*x)/b + ((A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(3/2))","A",2,2,17,0.1176,1,"{388, 205}"
63,1,34,0,0.0335423,"\int \frac{A+B x^2}{x \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2)),x]","\frac{A \log (x)}{a}-\frac{(A b-a B) \log \left(a+b x^2\right)}{2 a b}","\frac{A \log (x)}{a}-\frac{(A b-a B) \log \left(a+b x^2\right)}{2 a b}",1,"(A*Log[x])/a - ((A*b - a*B)*Log[a + b*x^2])/(2*a*b)","A",3,2,20,0.1000,1,"{446, 72}"
64,1,43,0,0.0209988,"\int \frac{A+B x^2}{x^2 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2)),x]","-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{A}{a x}","-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{A}{a x}",1,"-(A/(a*x)) - ((A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[b])","A",2,2,20,0.1000,1,"{453, 205}"
65,1,50,0,0.0476906,"\int \frac{A+B x^2}{x^3 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2)),x]","\frac{(A b-a B) \log \left(a+b x^2\right)}{2 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{2 a x^2}","\frac{(A b-a B) \log \left(a+b x^2\right)}{2 a^2}-\frac{\log (x) (A b-a B)}{a^2}-\frac{A}{2 a x^2}",1,"-A/(2*a*x^2) - ((A*b - a*B)*Log[x])/a^2 + ((A*b - a*B)*Log[a + b*x^2])/(2*a^2)","A",3,2,20,0.1000,1,"{446, 77}"
66,1,59,0,0.0393545,"\int \frac{A+B x^2}{x^4 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2)),x]","\frac{A b-a B}{a^2 x}+\frac{\sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}-\frac{A}{3 a x^3}","\frac{A b-a B}{a^2 x}+\frac{\sqrt{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}-\frac{A}{3 a x^3}",1,"-A/(3*a*x^3) + (A*b - a*B)/(a^2*x) + (Sqrt[b]*(A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(5/2)","A",3,3,20,0.1500,1,"{453, 325, 205}"
67,1,69,0,0.0602773,"\int \frac{A+B x^2}{x^5 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^5*(a + b*x^2)),x]","\frac{A b-a B}{2 a^2 x^2}-\frac{b (A b-a B) \log \left(a+b x^2\right)}{2 a^3}+\frac{b \log (x) (A b-a B)}{a^3}-\frac{A}{4 a x^4}","\frac{A b-a B}{2 a^2 x^2}-\frac{b (A b-a B) \log \left(a+b x^2\right)}{2 a^3}+\frac{b \log (x) (A b-a B)}{a^3}-\frac{A}{4 a x^4}",1,"-A/(4*a*x^4) + (A*b - a*B)/(2*a^2*x^2) + (b*(A*b - a*B)*Log[x])/a^3 - (b*(A*b - a*B)*Log[a + b*x^2])/(2*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
68,1,80,0,0.0500374,"\int \frac{A+B x^2}{x^6 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^6*(a + b*x^2)),x]","-\frac{b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2}}+\frac{A b-a B}{3 a^2 x^3}-\frac{b (A b-a B)}{a^3 x}-\frac{A}{5 a x^5}","-\frac{b^{3/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2}}+\frac{A b-a B}{3 a^2 x^3}-\frac{b (A b-a B)}{a^3 x}-\frac{A}{5 a x^5}",1,"-A/(5*a*x^5) + (A*b - a*B)/(3*a^2*x^3) - (b*(A*b - a*B))/(a^3*x) - (b^(3/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(7/2)","A",4,3,20,0.1500,1,"{453, 325, 205}"
69,1,93,0,0.0823365,"\int \frac{A+B x^2}{x^7 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^7*(a + b*x^2)),x]","\frac{b^2 (A b-a B) \log \left(a+b x^2\right)}{2 a^4}-\frac{b^2 \log (x) (A b-a B)}{a^4}-\frac{b (A b-a B)}{2 a^3 x^2}+\frac{A b-a B}{4 a^2 x^4}-\frac{A}{6 a x^6}","\frac{b^2 (A b-a B) \log \left(a+b x^2\right)}{2 a^4}-\frac{b^2 \log (x) (A b-a B)}{a^4}-\frac{b (A b-a B)}{2 a^3 x^2}+\frac{A b-a B}{4 a^2 x^4}-\frac{A}{6 a x^6}",1,"-A/(6*a*x^6) + (A*b - a*B)/(4*a^2*x^4) - (b*(A*b - a*B))/(2*a^3*x^2) - (b^2*(A*b - a*B)*Log[x])/a^4 + (b^2*(A*b - a*B)*Log[a + b*x^2])/(2*a^4)","A",3,2,20,0.1000,1,"{446, 77}"
70,1,99,0,0.0681236,"\int \frac{A+B x^2}{x^8 \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^8*(a + b*x^2)),x]","\frac{b^2 (A b-a B)}{a^4 x}+\frac{b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{9/2}}-\frac{b (A b-a B)}{3 a^3 x^3}+\frac{A b-a B}{5 a^2 x^5}-\frac{A}{7 a x^7}","\frac{b^2 (A b-a B)}{a^4 x}+\frac{b^{5/2} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{9/2}}-\frac{b (A b-a B)}{3 a^3 x^3}+\frac{A b-a B}{5 a^2 x^5}-\frac{A}{7 a x^7}",1,"-A/(7*a*x^7) + (A*b - a*B)/(5*a^2*x^5) - (b*(A*b - a*B))/(3*a^3*x^3) + (b^2*(A*b - a*B))/(a^4*x) + (b^(5/2)*(A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(9/2)","A",5,3,20,0.1500,1,"{453, 325, 205}"
71,1,126,0,0.1691301,"\int \frac{x^9 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^9*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{a^2 x^2 (3 A b-4 a B)}{2 b^5}-\frac{a^4 (A b-a B)}{2 b^6 \left(a+b x^2\right)}-\frac{a^3 (4 A b-5 a B) \log \left(a+b x^2\right)}{2 b^6}+\frac{x^6 (A b-2 a B)}{6 b^3}-\frac{a x^4 (2 A b-3 a B)}{4 b^4}+\frac{B x^8}{8 b^2}","\frac{a^2 x^2 (3 A b-4 a B)}{2 b^5}-\frac{a^4 (A b-a B)}{2 b^6 \left(a+b x^2\right)}-\frac{a^3 (4 A b-5 a B) \log \left(a+b x^2\right)}{2 b^6}+\frac{x^6 (A b-2 a B)}{6 b^3}-\frac{a x^4 (2 A b-3 a B)}{4 b^4}+\frac{B x^8}{8 b^2}",1,"(a^2*(3*A*b - 4*a*B)*x^2)/(2*b^5) - (a*(2*A*b - 3*a*B)*x^4)/(4*b^4) + ((A*b - 2*a*B)*x^6)/(6*b^3) + (B*x^8)/(8*b^2) - (a^4*(A*b - a*B))/(2*b^6*(a + b*x^2)) - (a^3*(4*A*b - 5*a*B)*Log[a + b*x^2])/(2*b^6)","A",3,2,20,0.1000,1,"{446, 77}"
72,1,131,0,0.1504824,"\int \frac{x^8 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^8*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{a^3 x (A b-a B)}{2 b^5 \left(a+b x^2\right)}+\frac{a^2 x (3 A b-4 a B)}{b^5}-\frac{a^{5/2} (7 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}+\frac{x^5 (A b-2 a B)}{5 b^3}-\frac{a x^3 (2 A b-3 a B)}{3 b^4}+\frac{B x^7}{7 b^2}","\frac{a^3 x (A b-a B)}{2 b^5 \left(a+b x^2\right)}+\frac{a^2 x (3 A b-4 a B)}{b^5}-\frac{a^{5/2} (7 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}+\frac{x^5 (A b-2 a B)}{5 b^3}-\frac{a x^3 (2 A b-3 a B)}{3 b^4}+\frac{B x^7}{7 b^2}",1,"(a^2*(3*A*b - 4*a*B)*x)/b^5 - (a*(2*A*b - 3*a*B)*x^3)/(3*b^4) + ((A*b - 2*a*B)*x^5)/(5*b^3) + (B*x^7)/(7*b^2) + (a^3*(A*b - a*B)*x)/(2*b^5*(a + b*x^2)) - (a^(5/2)*(7*A*b - 9*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(11/2))","A",4,3,20,0.1500,1,"{455, 1810, 205}"
73,1,104,0,0.1264273,"\int \frac{x^7 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^7*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{a^3 (A b-a B)}{2 b^5 \left(a+b x^2\right)}+\frac{a^2 (3 A b-4 a B) \log \left(a+b x^2\right)}{2 b^5}+\frac{x^4 (A b-2 a B)}{4 b^3}-\frac{a x^2 (2 A b-3 a B)}{2 b^4}+\frac{B x^6}{6 b^2}","\frac{a^3 (A b-a B)}{2 b^5 \left(a+b x^2\right)}+\frac{a^2 (3 A b-4 a B) \log \left(a+b x^2\right)}{2 b^5}+\frac{x^4 (A b-2 a B)}{4 b^3}-\frac{a x^2 (2 A b-3 a B)}{2 b^4}+\frac{B x^6}{6 b^2}",1,"-(a*(2*A*b - 3*a*B)*x^2)/(2*b^4) + ((A*b - 2*a*B)*x^4)/(4*b^3) + (B*x^6)/(6*b^2) + (a^3*(A*b - a*B))/(2*b^5*(a + b*x^2)) + (a^2*(3*A*b - 4*a*B)*Log[a + b*x^2])/(2*b^5)","A",3,2,20,0.1000,1,"{446, 77}"
74,1,110,0,0.1137945,"\int \frac{x^6 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2)^2,x]","-\frac{a^2 x (A b-a B)}{2 b^4 \left(a+b x^2\right)}+\frac{a^{3/2} (5 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}+\frac{x^3 (A b-2 a B)}{3 b^3}-\frac{a x (2 A b-3 a B)}{b^4}+\frac{B x^5}{5 b^2}","-\frac{a^2 x (A b-a B)}{2 b^4 \left(a+b x^2\right)}+\frac{a^{3/2} (5 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}+\frac{x^3 (A b-2 a B)}{3 b^3}-\frac{a x (2 A b-3 a B)}{b^4}+\frac{B x^5}{5 b^2}",1,"-((a*(2*A*b - 3*a*B)*x)/b^4) + ((A*b - 2*a*B)*x^3)/(3*b^3) + (B*x^5)/(5*b^2) - (a^2*(A*b - a*B)*x)/(2*b^4*(a + b*x^2)) + (a^(3/2)*(5*A*b - 7*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(9/2))","A",4,3,20,0.1500,1,"{455, 1810, 205}"
75,1,82,0,0.0873322,"\int \frac{x^5 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2)^2,x]","-\frac{a^2 (A b-a B)}{2 b^4 \left(a+b x^2\right)}+\frac{x^2 (A b-2 a B)}{2 b^3}-\frac{a (2 A b-3 a B) \log \left(a+b x^2\right)}{2 b^4}+\frac{B x^4}{4 b^2}","-\frac{a^2 (A b-a B)}{2 b^4 \left(a+b x^2\right)}+\frac{x^2 (A b-2 a B)}{2 b^3}-\frac{a (2 A b-3 a B) \log \left(a+b x^2\right)}{2 b^4}+\frac{B x^4}{4 b^2}",1,"((A*b - 2*a*B)*x^2)/(2*b^3) + (B*x^4)/(4*b^2) - (a^2*(A*b - a*B))/(2*b^4*(a + b*x^2)) - (a*(2*A*b - 3*a*B)*Log[a + b*x^2])/(2*b^4)","A",3,2,20,0.1000,1,"{446, 77}"
76,1,87,0,0.0702195,"\int \frac{x^4 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{a x (A b-a B)}{2 b^3 \left(a+b x^2\right)}+\frac{x (A b-2 a B)}{b^3}-\frac{\sqrt{a} (3 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}+\frac{B x^3}{3 b^2}","\frac{a x (A b-a B)}{2 b^3 \left(a+b x^2\right)}+\frac{x (A b-2 a B)}{b^3}-\frac{\sqrt{a} (3 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}+\frac{B x^3}{3 b^2}",1,"((A*b - 2*a*B)*x)/b^3 + (B*x^3)/(3*b^2) + (a*(A*b - a*B)*x)/(2*b^3*(a + b*x^2)) - (Sqrt[a]*(3*A*b - 5*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2))","A",4,3,20,0.1500,1,"{455, 1153, 205}"
77,1,60,0,0.0576699,"\int \frac{x^3 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{a (A b-a B)}{2 b^3 \left(a+b x^2\right)}+\frac{(A b-2 a B) \log \left(a+b x^2\right)}{2 b^3}+\frac{B x^2}{2 b^2}","\frac{a (A b-a B)}{2 b^3 \left(a+b x^2\right)}+\frac{(A b-2 a B) \log \left(a+b x^2\right)}{2 b^3}+\frac{B x^2}{2 b^2}",1,"(B*x^2)/(2*b^2) + (a*(A*b - a*B))/(2*b^3*(a + b*x^2)) + ((A*b - 2*a*B)*Log[a + b*x^2])/(2*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
78,1,67,0,0.0504237,"\int \frac{x^2 \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2)^2,x]","-\frac{x (A b-a B)}{2 b^2 \left(a+b x^2\right)}+\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}+\frac{B x}{b^2}","-\frac{x (A b-a B)}{2 b^2 \left(a+b x^2\right)}+\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}+\frac{B x}{b^2}",1,"(B*x)/b^2 - ((A*b - a*B)*x)/(2*b^2*(a + b*x^2)) + ((A*b - 3*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(5/2))","A",3,3,20,0.1500,1,"{455, 388, 205}"
79,1,41,0,0.0363941,"\int \frac{x \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{B \log \left(a+b x^2\right)}{2 b^2}-\frac{A b-a B}{2 b^2 \left(a+b x^2\right)}","\frac{B \log \left(a+b x^2\right)}{2 b^2}-\frac{A b-a B}{2 b^2 \left(a+b x^2\right)}",1,"-(A*b - a*B)/(2*b^2*(a + b*x^2)) + (B*Log[a + b*x^2])/(2*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
80,1,63,0,0.0220863,"\int \frac{A+B x^2}{\left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(a + b*x^2)^2,x]","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}+\frac{x (A b-a B)}{2 a b \left(a+b x^2\right)}","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}+\frac{x (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"((A*b - a*B)*x)/(2*a*b*(a + b*x^2)) + ((A*b + a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(3/2))","A",2,2,17,0.1176,1,"{385, 205}"
81,1,51,0,0.0448555,"\int \frac{A+B x^2}{x \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2)^2),x]","-\frac{A \log \left(a+b x^2\right)}{2 a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{2 a b \left(a+b x^2\right)}","-\frac{A \log \left(a+b x^2\right)}{2 a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{2 a b \left(a+b x^2\right)}",1,"(A*b - a*B)/(2*a*b*(a + b*x^2)) + (A*Log[x])/a^2 - (A*Log[a + b*x^2])/(2*a^2)","A",3,2,20,0.1000,1,"{446, 77}"
82,1,71,0,0.0511968,"\int \frac{A+B x^2}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2)^2),x]","-\frac{x (A b-a B)}{2 a^2 \left(a+b x^2\right)}-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{A}{a^2 x}","-\frac{x (A b-a B)}{2 a^2 \left(a+b x^2\right)}-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{A}{a^2 x}",1,"-(A/(a^2*x)) - ((A*b - a*B)*x)/(2*a^2*(a + b*x^2)) - ((3*A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*Sqrt[b])","A",3,3,20,0.1500,1,"{456, 453, 205}"
83,1,76,0,0.0745697,"\int \frac{A+B x^2}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2)^2),x]","-\frac{A b-a B}{2 a^2 \left(a+b x^2\right)}+\frac{(2 A b-a B) \log \left(a+b x^2\right)}{2 a^3}-\frac{\log (x) (2 A b-a B)}{a^3}-\frac{A}{2 a^2 x^2}","-\frac{A b-a B}{2 a^2 \left(a+b x^2\right)}+\frac{(2 A b-a B) \log \left(a+b x^2\right)}{2 a^3}-\frac{\log (x) (2 A b-a B)}{a^3}-\frac{A}{2 a^2 x^2}",1,"-A/(2*a^2*x^2) - (A*b - a*B)/(2*a^2*(a + b*x^2)) - ((2*A*b - a*B)*Log[x])/a^3 + ((2*A*b - a*B)*Log[a + b*x^2])/(2*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
84,1,90,0,0.1057569,"\int \frac{A+B x^2}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2)^2),x]","\frac{b x (A b-a B)}{2 a^3 \left(a+b x^2\right)}+\frac{2 A b-a B}{a^3 x}+\frac{\sqrt{b} (5 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{A}{3 a^2 x^3}","\frac{b x (A b-a B)}{2 a^3 \left(a+b x^2\right)}+\frac{2 A b-a B}{a^3 x}+\frac{\sqrt{b} (5 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{A}{3 a^2 x^3}",1,"-A/(3*a^2*x^3) + (2*A*b - a*B)/(a^3*x) + (b*(A*b - a*B)*x)/(2*a^3*(a + b*x^2)) + (Sqrt[b]*(5*A*b - 3*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",4,3,20,0.1500,1,"{456, 1261, 205}"
85,1,97,0,0.0950933,"\int \frac{A+B x^2}{x^5 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^5*(a + b*x^2)^2),x]","\frac{b (A b-a B)}{2 a^3 \left(a+b x^2\right)}+\frac{2 A b-a B}{2 a^3 x^2}-\frac{b (3 A b-2 a B) \log \left(a+b x^2\right)}{2 a^4}+\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{A}{4 a^2 x^4}","\frac{b (A b-a B)}{2 a^3 \left(a+b x^2\right)}+\frac{2 A b-a B}{2 a^3 x^2}-\frac{b (3 A b-2 a B) \log \left(a+b x^2\right)}{2 a^4}+\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{A}{4 a^2 x^4}",1,"-A/(4*a^2*x^4) + (2*A*b - a*B)/(2*a^3*x^2) + (b*(A*b - a*B))/(2*a^3*(a + b*x^2)) + (b*(3*A*b - 2*a*B)*Log[x])/a^4 - (b*(3*A*b - 2*a*B)*Log[a + b*x^2])/(2*a^4)","A",3,2,20,0.1000,1,"{446, 77}"
86,1,113,0,0.1864401,"\int \frac{A+B x^2}{x^6 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^6*(a + b*x^2)^2),x]","-\frac{b^2 x (A b-a B)}{2 a^4 \left(a+b x^2\right)}-\frac{b^{3/2} (7 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}+\frac{2 A b-a B}{3 a^3 x^3}-\frac{b (3 A b-2 a B)}{a^4 x}-\frac{A}{5 a^2 x^5}","-\frac{b^2 x (A b-a B)}{2 a^4 \left(a+b x^2\right)}-\frac{b^{3/2} (7 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2}}+\frac{2 A b-a B}{3 a^3 x^3}-\frac{b (3 A b-2 a B)}{a^4 x}-\frac{A}{5 a^2 x^5}",1,"-A/(5*a^2*x^5) + (2*A*b - a*B)/(3*a^3*x^3) - (b*(3*A*b - 2*a*B))/(a^4*x) - (b^2*(A*b - a*B)*x)/(2*a^4*(a + b*x^2)) - (b^(3/2)*(7*A*b - 5*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(9/2))","A",4,3,20,0.1500,1,"{456, 1802, 205}"
87,1,124,0,0.1295391,"\int \frac{A+B x^2}{x^7 \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^7*(a + b*x^2)^2),x]","-\frac{b^2 (A b-a B)}{2 a^4 \left(a+b x^2\right)}+\frac{b^2 (4 A b-3 a B) \log \left(a+b x^2\right)}{2 a^5}-\frac{b^2 \log (x) (4 A b-3 a B)}{a^5}-\frac{b (3 A b-2 a B)}{2 a^4 x^2}+\frac{2 A b-a B}{4 a^3 x^4}-\frac{A}{6 a^2 x^6}","-\frac{b^2 (A b-a B)}{2 a^4 \left(a+b x^2\right)}+\frac{b^2 (4 A b-3 a B) \log \left(a+b x^2\right)}{2 a^5}-\frac{b^2 \log (x) (4 A b-3 a B)}{a^5}-\frac{b (3 A b-2 a B)}{2 a^4 x^2}+\frac{2 A b-a B}{4 a^3 x^4}-\frac{A}{6 a^2 x^6}",1,"-A/(6*a^2*x^6) + (2*A*b - a*B)/(4*a^3*x^4) - (b*(3*A*b - 2*a*B))/(2*a^4*x^2) - (b^2*(A*b - a*B))/(2*a^4*(a + b*x^2)) - (b^2*(4*A*b - 3*a*B)*Log[x])/a^5 + (b^2*(4*A*b - 3*a*B)*Log[a + b*x^2])/(2*a^5)","A",3,2,20,0.1000,1,"{446, 77}"
88,1,150,0,0.230432,"\int \frac{x^{11} \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^11*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{a^2 x^2 (3 A b-5 a B)}{b^6}-\frac{a^4 (5 A b-6 a B)}{2 b^7 \left(a+b x^2\right)}+\frac{a^5 (A b-a B)}{4 b^7 \left(a+b x^2\right)^2}-\frac{5 a^3 (2 A b-3 a B) \log \left(a+b x^2\right)}{2 b^7}+\frac{x^6 (A b-3 a B)}{6 b^4}-\frac{3 a x^4 (A b-2 a B)}{4 b^5}+\frac{B x^8}{8 b^3}","\frac{a^2 x^2 (3 A b-5 a B)}{b^6}-\frac{a^4 (5 A b-6 a B)}{2 b^7 \left(a+b x^2\right)}+\frac{a^5 (A b-a B)}{4 b^7 \left(a+b x^2\right)^2}-\frac{5 a^3 (2 A b-3 a B) \log \left(a+b x^2\right)}{2 b^7}+\frac{x^6 (A b-3 a B)}{6 b^4}-\frac{3 a x^4 (A b-2 a B)}{4 b^5}+\frac{B x^8}{8 b^3}",1,"(a^2*(3*A*b - 5*a*B)*x^2)/b^6 - (3*a*(A*b - 2*a*B)*x^4)/(4*b^5) + ((A*b - 3*a*B)*x^6)/(6*b^4) + (B*x^8)/(8*b^3) + (a^5*(A*b - a*B))/(4*b^7*(a + b*x^2)^2) - (a^4*(5*A*b - 6*a*B))/(2*b^7*(a + b*x^2)) - (5*a^3*(2*A*b - 3*a*B)*Log[a + b*x^2])/(2*b^7)","A",3,2,20,0.1000,1,"{446, 77}"
89,1,128,0,0.1655596,"\int \frac{x^9 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^9*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{a^3 (4 A b-5 a B)}{2 b^6 \left(a+b x^2\right)}-\frac{a^4 (A b-a B)}{4 b^6 \left(a+b x^2\right)^2}+\frac{a^2 (3 A b-5 a B) \log \left(a+b x^2\right)}{b^6}+\frac{x^4 (A b-3 a B)}{4 b^4}-\frac{3 a x^2 (A b-2 a B)}{2 b^5}+\frac{B x^6}{6 b^3}","\frac{a^3 (4 A b-5 a B)}{2 b^6 \left(a+b x^2\right)}-\frac{a^4 (A b-a B)}{4 b^6 \left(a+b x^2\right)^2}+\frac{a^2 (3 A b-5 a B) \log \left(a+b x^2\right)}{b^6}+\frac{x^4 (A b-3 a B)}{4 b^4}-\frac{3 a x^2 (A b-2 a B)}{2 b^5}+\frac{B x^6}{6 b^3}",1,"(-3*a*(A*b - 2*a*B)*x^2)/(2*b^5) + ((A*b - 3*a*B)*x^4)/(4*b^4) + (B*x^6)/(6*b^3) - (a^4*(A*b - a*B))/(4*b^6*(a + b*x^2)^2) + (a^3*(4*A*b - 5*a*B))/(2*b^6*(a + b*x^2)) + (a^2*(3*A*b - 5*a*B)*Log[a + b*x^2])/b^6","A",3,2,20,0.1000,1,"{446, 77}"
90,1,109,0,0.1212353,"\int \frac{x^7 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^7*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{a^2 (3 A b-4 a B)}{2 b^5 \left(a+b x^2\right)}+\frac{a^3 (A b-a B)}{4 b^5 \left(a+b x^2\right)^2}+\frac{x^2 (A b-3 a B)}{2 b^4}-\frac{3 a (A b-2 a B) \log \left(a+b x^2\right)}{2 b^5}+\frac{B x^4}{4 b^3}","-\frac{a^2 (3 A b-4 a B)}{2 b^5 \left(a+b x^2\right)}+\frac{a^3 (A b-a B)}{4 b^5 \left(a+b x^2\right)^2}+\frac{x^2 (A b-3 a B)}{2 b^4}-\frac{3 a (A b-2 a B) \log \left(a+b x^2\right)}{2 b^5}+\frac{B x^4}{4 b^3}",1,"((A*b - 3*a*B)*x^2)/(2*b^4) + (B*x^4)/(4*b^3) + (a^3*(A*b - a*B))/(4*b^5*(a + b*x^2)^2) - (a^2*(3*A*b - 4*a*B))/(2*b^5*(a + b*x^2)) - (3*a*(A*b - 2*a*B)*Log[a + b*x^2])/(2*b^5)","A",3,2,20,0.1000,1,"{446, 77}"
91,1,88,0,0.09024,"\int \frac{x^5 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{a^2 (A b-a B)}{4 b^4 \left(a+b x^2\right)^2}+\frac{a (2 A b-3 a B)}{2 b^4 \left(a+b x^2\right)}+\frac{(A b-3 a B) \log \left(a+b x^2\right)}{2 b^4}+\frac{B x^2}{2 b^3}","-\frac{a^2 (A b-a B)}{4 b^4 \left(a+b x^2\right)^2}+\frac{a (2 A b-3 a B)}{2 b^4 \left(a+b x^2\right)}+\frac{(A b-3 a B) \log \left(a+b x^2\right)}{2 b^4}+\frac{B x^2}{2 b^3}",1,"(B*x^2)/(2*b^3) - (a^2*(A*b - a*B))/(4*b^4*(a + b*x^2)^2) + (a*(2*A*b - 3*a*B))/(2*b^4*(a + b*x^2)) + ((A*b - 3*a*B)*Log[a + b*x^2])/(2*b^4)","A",3,2,20,0.1000,1,"{446, 77}"
92,1,66,0,0.06588,"\int \frac{x^3 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{A b-2 a B}{2 b^3 \left(a+b x^2\right)}+\frac{a (A b-a B)}{4 b^3 \left(a+b x^2\right)^2}+\frac{B \log \left(a+b x^2\right)}{2 b^3}","-\frac{A b-2 a B}{2 b^3 \left(a+b x^2\right)}+\frac{a (A b-a B)}{4 b^3 \left(a+b x^2\right)^2}+\frac{B \log \left(a+b x^2\right)}{2 b^3}",1,"(a*(A*b - a*B))/(4*b^3*(a + b*x^2)^2) - (A*b - 2*a*B)/(2*b^3*(a + b*x^2)) + (B*Log[a + b*x^2])/(2*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
93,1,32,0,0.0195665,"\int \frac{x \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{\left(A+B x^2\right)^2}{4 \left(a+b x^2\right)^2 (A b-a B)}","-\frac{\left(A+B x^2\right)^2}{4 \left(a+b x^2\right)^2 (A b-a B)}",1,"-(A + B*x^2)^2/(4*(A*b - a*B)*(a + b*x^2)^2)","A",2,2,18,0.1111,1,"{444, 37}"
94,1,68,0,0.0604057,"\int \frac{A+B x^2}{x \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2)^3),x]","\frac{A}{2 a^2 \left(a+b x^2\right)}-\frac{A \log \left(a+b x^2\right)}{2 a^3}+\frac{A \log (x)}{a^3}+\frac{A b-a B}{4 a b \left(a+b x^2\right)^2}","\frac{A}{2 a^2 \left(a+b x^2\right)}-\frac{A \log \left(a+b x^2\right)}{2 a^3}+\frac{A \log (x)}{a^3}+\frac{A b-a B}{4 a b \left(a+b x^2\right)^2}",1,"(A*b - a*B)/(4*a*b*(a + b*x^2)^2) + A/(2*a^2*(a + b*x^2)) + (A*Log[x])/a^3 - (A*Log[a + b*x^2])/(2*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
95,1,101,0,0.1048975,"\int \frac{A+B x^2}{x^3 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2)^3),x]","-\frac{2 A b-a B}{2 a^3 \left(a+b x^2\right)}-\frac{A b-a B}{4 a^2 \left(a+b x^2\right)^2}+\frac{(3 A b-a B) \log \left(a+b x^2\right)}{2 a^4}-\frac{\log (x) (3 A b-a B)}{a^4}-\frac{A}{2 a^3 x^2}","-\frac{2 A b-a B}{2 a^3 \left(a+b x^2\right)}-\frac{A b-a B}{4 a^2 \left(a+b x^2\right)^2}+\frac{(3 A b-a B) \log \left(a+b x^2\right)}{2 a^4}-\frac{\log (x) (3 A b-a B)}{a^4}-\frac{A}{2 a^3 x^2}",1,"-A/(2*a^3*x^2) - (A*b - a*B)/(4*a^2*(a + b*x^2)^2) - (2*A*b - a*B)/(2*a^3*(a + b*x^2)) - ((3*A*b - a*B)*Log[x])/a^4 + ((3*A*b - a*B)*Log[a + b*x^2])/(2*a^4)","A",3,2,20,0.1000,1,"{446, 77}"
96,1,124,0,0.1297326,"\int \frac{A+B x^2}{x^5 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^5*(a + b*x^2)^3),x]","\frac{b (3 A b-2 a B)}{2 a^4 \left(a+b x^2\right)}+\frac{3 A b-a B}{2 a^4 x^2}+\frac{b (A b-a B)}{4 a^3 \left(a+b x^2\right)^2}-\frac{3 b (2 A b-a B) \log \left(a+b x^2\right)}{2 a^5}+\frac{3 b \log (x) (2 A b-a B)}{a^5}-\frac{A}{4 a^3 x^4}","\frac{b (3 A b-2 a B)}{2 a^4 \left(a+b x^2\right)}+\frac{3 A b-a B}{2 a^4 x^2}+\frac{b (A b-a B)}{4 a^3 \left(a+b x^2\right)^2}-\frac{3 b (2 A b-a B) \log \left(a+b x^2\right)}{2 a^5}+\frac{3 b \log (x) (2 A b-a B)}{a^5}-\frac{A}{4 a^3 x^4}",1,"-A/(4*a^3*x^4) + (3*A*b - a*B)/(2*a^4*x^2) + (b*(A*b - a*B))/(4*a^3*(a + b*x^2)^2) + (b*(3*A*b - 2*a*B))/(2*a^4*(a + b*x^2)) + (3*b*(2*A*b - a*B)*Log[x])/a^5 - (3*b*(2*A*b - a*B)*Log[a + b*x^2])/(2*a^5)","A",3,2,20,0.1000,1,"{446, 77}"
97,1,149,0,0.1660513,"\int \frac{A+B x^2}{x^7 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^7*(a + b*x^2)^3),x]","-\frac{b^2 (4 A b-3 a B)}{2 a^5 \left(a+b x^2\right)}-\frac{b^2 (A b-a B)}{4 a^4 \left(a+b x^2\right)^2}+\frac{b^2 (5 A b-3 a B) \log \left(a+b x^2\right)}{a^6}-\frac{2 b^2 \log (x) (5 A b-3 a B)}{a^6}-\frac{3 b (2 A b-a B)}{2 a^5 x^2}+\frac{3 A b-a B}{4 a^4 x^4}-\frac{A}{6 a^3 x^6}","-\frac{b^2 (4 A b-3 a B)}{2 a^5 \left(a+b x^2\right)}-\frac{b^2 (A b-a B)}{4 a^4 \left(a+b x^2\right)^2}+\frac{b^2 (5 A b-3 a B) \log \left(a+b x^2\right)}{a^6}-\frac{2 b^2 \log (x) (5 A b-3 a B)}{a^6}-\frac{3 b (2 A b-a B)}{2 a^5 x^2}+\frac{3 A b-a B}{4 a^4 x^4}-\frac{A}{6 a^3 x^6}",1,"-A/(6*a^3*x^6) + (3*A*b - a*B)/(4*a^4*x^4) - (3*b*(2*A*b - a*B))/(2*a^5*x^2) - (b^2*(A*b - a*B))/(4*a^4*(a + b*x^2)^2) - (b^2*(4*A*b - 3*a*B))/(2*a^5*(a + b*x^2)) - (2*b^2*(5*A*b - 3*a*B)*Log[x])/a^6 + (b^2*(5*A*b - 3*a*B)*Log[a + b*x^2])/a^6","A",3,2,20,0.1000,1,"{446, 77}"
98,1,158,0,0.2831526,"\int \frac{x^{10} \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^10*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{a^3 x (17 A b-21 a B)}{8 b^6 \left(a+b x^2\right)}-\frac{a^4 x (A b-a B)}{4 b^6 \left(a+b x^2\right)^2}+\frac{2 a^2 x (3 A b-5 a B)}{b^6}-\frac{9 a^{5/2} (7 A b-11 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{13/2}}+\frac{x^5 (A b-3 a B)}{5 b^4}-\frac{a x^3 (A b-2 a B)}{b^5}+\frac{B x^7}{7 b^3}","\frac{a^3 x (17 A b-21 a B)}{8 b^6 \left(a+b x^2\right)}-\frac{a^4 x (A b-a B)}{4 b^6 \left(a+b x^2\right)^2}+\frac{2 a^2 x (3 A b-5 a B)}{b^6}-\frac{9 a^{5/2} (7 A b-11 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{13/2}}+\frac{x^5 (A b-3 a B)}{5 b^4}-\frac{a x^3 (A b-2 a B)}{b^5}+\frac{B x^7}{7 b^3}",1,"(2*a^2*(3*A*b - 5*a*B)*x)/b^6 - (a*(A*b - 2*a*B)*x^3)/b^5 + ((A*b - 3*a*B)*x^5)/(5*b^4) + (B*x^7)/(7*b^3) - (a^4*(A*b - a*B)*x)/(4*b^6*(a + b*x^2)^2) + (a^3*(17*A*b - 21*a*B)*x)/(8*b^6*(a + b*x^2)) - (9*a^(5/2)*(7*A*b - 11*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(13/2))","A",5,4,20,0.2000,1,"{455, 1814, 1810, 205}"
99,1,138,0,0.2178754,"\int \frac{x^8 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^8*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{a^2 x (13 A b-17 a B)}{8 b^5 \left(a+b x^2\right)}+\frac{a^3 x (A b-a B)}{4 b^5 \left(a+b x^2\right)^2}+\frac{7 a^{3/2} (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{11/2}}+\frac{x^3 (A b-3 a B)}{3 b^4}-\frac{3 a x (A b-2 a B)}{b^5}+\frac{B x^5}{5 b^3}","-\frac{a^2 x (13 A b-17 a B)}{8 b^5 \left(a+b x^2\right)}+\frac{a^3 x (A b-a B)}{4 b^5 \left(a+b x^2\right)^2}+\frac{7 a^{3/2} (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{11/2}}+\frac{x^3 (A b-3 a B)}{3 b^4}-\frac{3 a x (A b-2 a B)}{b^5}+\frac{B x^5}{5 b^3}",1,"(-3*a*(A*b - 2*a*B)*x)/b^5 + ((A*b - 3*a*B)*x^3)/(3*b^4) + (B*x^5)/(5*b^3) + (a^3*(A*b - a*B)*x)/(4*b^5*(a + b*x^2)^2) - (a^2*(13*A*b - 17*a*B)*x)/(8*b^5*(a + b*x^2)) + (7*a^(3/2)*(5*A*b - 9*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(11/2))","A",5,4,20,0.2000,1,"{455, 1814, 1810, 205}"
100,1,116,0,0.1515086,"\int \frac{x^6 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{a^2 x (A b-a B)}{4 b^4 \left(a+b x^2\right)^2}+\frac{a x (9 A b-13 a B)}{8 b^4 \left(a+b x^2\right)}+\frac{x (A b-3 a B)}{b^4}-\frac{5 \sqrt{a} (3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{9/2}}+\frac{B x^3}{3 b^3}","-\frac{a^2 x (A b-a B)}{4 b^4 \left(a+b x^2\right)^2}+\frac{a x (9 A b-13 a B)}{8 b^4 \left(a+b x^2\right)}+\frac{x (A b-3 a B)}{b^4}-\frac{5 \sqrt{a} (3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 b^{9/2}}+\frac{B x^3}{3 b^3}",1,"((A*b - 3*a*B)*x)/b^4 + (B*x^3)/(3*b^3) - (a^2*(A*b - a*B)*x)/(4*b^4*(a + b*x^2)^2) + (a*(9*A*b - 13*a*B)*x)/(8*b^4*(a + b*x^2)) - (5*Sqrt[a]*(3*A*b - 7*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*b^(9/2))","A",5,4,20,0.2000,1,"{455, 1814, 1153, 205}"
101,1,94,0,0.0862616,"\int \frac{x^4 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{x (5 A b-9 a B)}{8 b^3 \left(a+b x^2\right)}+\frac{a x (A b-a B)}{4 b^3 \left(a+b x^2\right)^2}+\frac{3 (A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{7/2}}+\frac{B x}{b^3}","-\frac{x (5 A b-9 a B)}{8 b^3 \left(a+b x^2\right)}+\frac{a x (A b-a B)}{4 b^3 \left(a+b x^2\right)^2}+\frac{3 (A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 \sqrt{a} b^{7/2}}+\frac{B x}{b^3}",1,"(B*x)/b^3 + (a*(A*b - a*B)*x)/(4*b^3*(a + b*x^2)^2) - ((5*A*b - 9*a*B)*x)/(8*b^3*(a + b*x^2)) + (3*(A*b - 5*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*Sqrt[a]*b^(7/2))","A",4,4,20,0.2000,1,"{455, 1157, 388, 205}"
102,1,89,0,0.0619753,"\int \frac{x^2 \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2}}+\frac{x (A b-5 a B)}{8 a b^2 \left(a+b x^2\right)}-\frac{x (A b-a B)}{4 b^2 \left(a+b x^2\right)^2}","\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{3/2} b^{5/2}}+\frac{x (A b-5 a B)}{8 a b^2 \left(a+b x^2\right)}-\frac{x (A b-a B)}{4 b^2 \left(a+b x^2\right)^2}",1,"-((A*b - a*B)*x)/(4*b^2*(a + b*x^2)^2) + ((A*b - 5*a*B)*x)/(8*a*b^2*(a + b*x^2)) + ((A*b + 3*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(3/2)*b^(5/2))","A",3,3,20,0.1500,1,"{455, 385, 205}"
103,1,92,0,0.0324289,"\int \frac{A+B x^2}{\left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(a + b*x^2)^3,x]","\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2}}+\frac{x (a B+3 A b)}{8 a^2 b \left(a+b x^2\right)}+\frac{x (A b-a B)}{4 a b \left(a+b x^2\right)^2}","\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{5/2} b^{3/2}}+\frac{x (a B+3 A b)}{8 a^2 b \left(a+b x^2\right)}+\frac{x (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"((A*b - a*B)*x)/(4*a*b*(a + b*x^2)^2) + ((3*A*b + a*B)*x)/(8*a^2*b*(a + b*x^2)) + ((3*A*b + a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(5/2)*b^(3/2))","A",3,3,17,0.1765,1,"{385, 199, 205}"
104,1,97,0,0.1002561,"\int \frac{A+B x^2}{x^2 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2)^3),x]","-\frac{x (7 A b-3 a B)}{8 a^3 \left(a+b x^2\right)}-\frac{x (A b-a B)}{4 a^2 \left(a+b x^2\right)^2}-\frac{3 (5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b}}-\frac{A}{a^3 x}","-\frac{x (7 A b-3 a B)}{8 a^3 \left(a+b x^2\right)}-\frac{x (A b-a B)}{4 a^2 \left(a+b x^2\right)^2}-\frac{3 (5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{7/2} \sqrt{b}}-\frac{A}{a^3 x}",1,"-(A/(a^3*x)) - ((A*b - a*B)*x)/(4*a^2*(a + b*x^2)^2) - ((7*A*b - 3*a*B)*x)/(8*a^3*(a + b*x^2)) - (3*(5*A*b - a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(7/2)*Sqrt[b])","A",4,3,20,0.1500,1,"{456, 453, 205}"
105,1,117,0,0.1652636,"\int \frac{A+B x^2}{x^4 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2)^3),x]","\frac{b x (11 A b-7 a B)}{8 a^4 \left(a+b x^2\right)}+\frac{b x (A b-a B)}{4 a^3 \left(a+b x^2\right)^2}+\frac{3 A b-a B}{a^4 x}+\frac{5 \sqrt{b} (7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{A}{3 a^3 x^3}","\frac{b x (11 A b-7 a B)}{8 a^4 \left(a+b x^2\right)}+\frac{b x (A b-a B)}{4 a^3 \left(a+b x^2\right)^2}+\frac{3 A b-a B}{a^4 x}+\frac{5 \sqrt{b} (7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{A}{3 a^3 x^3}",1,"-A/(3*a^3*x^3) + (3*A*b - a*B)/(a^4*x) + (b*(A*b - a*B)*x)/(4*a^3*(a + b*x^2)^2) + (b*(11*A*b - 7*a*B)*x)/(8*a^4*(a + b*x^2)) + (5*Sqrt[b]*(7*A*b - 3*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(9/2))","A",5,4,20,0.2000,1,"{456, 1259, 1261, 205}"
106,1,142,0,0.3296768,"\int \frac{A+B x^2}{x^6 \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^6*(a + b*x^2)^3),x]","-\frac{b^2 x (15 A b-11 a B)}{8 a^5 \left(a+b x^2\right)}-\frac{b^2 x (A b-a B)}{4 a^4 \left(a+b x^2\right)^2}-\frac{7 b^{3/2} (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{11/2}}+\frac{3 A b-a B}{3 a^4 x^3}-\frac{3 b (2 A b-a B)}{a^5 x}-\frac{A}{5 a^3 x^5}","-\frac{b^2 x (15 A b-11 a B)}{8 a^5 \left(a+b x^2\right)}-\frac{b^2 x (A b-a B)}{4 a^4 \left(a+b x^2\right)^2}-\frac{7 b^{3/2} (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{8 a^{11/2}}+\frac{3 A b-a B}{3 a^4 x^3}-\frac{3 b (2 A b-a B)}{a^5 x}-\frac{A}{5 a^3 x^5}",1,"-A/(5*a^3*x^5) + (3*A*b - a*B)/(3*a^4*x^3) - (3*b*(2*A*b - a*B))/(a^5*x) - (b^2*(A*b - a*B)*x)/(4*a^4*(a + b*x^2)^2) - (b^2*(15*A*b - 11*a*B)*x)/(8*a^5*(a + b*x^2)) - (7*b^(3/2)*(9*A*b - 5*a*B)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(8*a^(11/2))","A",5,4,20,0.2000,1,"{456, 1805, 1802, 205}"
107,1,12,0,0.0063076,"\int \frac{a+b x^2}{1+x^2} \, dx","Int[(a + b*x^2)/(1 + x^2),x]","(a-b) \tan ^{-1}(x)+b x","(a-b) \tan ^{-1}(x)+b x",1,"b*x + (a - b)*ArcTan[x]","A",2,2,15,0.1333,1,"{388, 203}"
108,1,11,0,0.0066391,"\int \frac{a+b x^2}{1-x^2} \, dx","Int[(a + b*x^2)/(1 - x^2),x]","(a+b) \tanh ^{-1}(x)-b x","(a+b) \tanh ^{-1}(x)-b x",1,"-(b*x) + (a + b)*ArcTanh[x]","A",2,2,17,0.1176,1,"{388, 206}"
109,1,11,0,0.0028755,"\int \frac{1+x^2}{\left(-1+x^2\right)^2} \, dx","Int[(1 + x^2)/(-1 + x^2)^2,x]","\frac{x}{1-x^2}","\frac{x}{1-x^2}",1,"x/(1 - x^2)","A",1,1,13,0.07692,1,"{383}"
110,1,9,0,0.0030811,"\int \frac{1-x^2}{\left(1+x^2\right)^2} \, dx","Int[(1 - x^2)/(1 + x^2)^2,x]","\frac{x}{x^2+1}","\frac{x}{x^2+1}",1,"x/(1 + x^2)","A",1,1,15,0.06667,1,"{383}"
111,1,19,0,0.0043252,"\int \frac{3+2 x^2}{\left(1+x^2\right)^2} \, dx","Int[(3 + 2*x^2)/(1 + x^2)^2,x]","\frac{x}{2 \left(x^2+1\right)}+\frac{5}{2} \tan ^{-1}(x)","\frac{x}{2 \left(x^2+1\right)}+\frac{5}{2} \tan ^{-1}(x)",1,"x/(2*(1 + x^2)) + (5*ArcTan[x])/2","A",2,2,15,0.1333,1,"{385, 203}"
112,1,19,0,0.0040069,"\int \frac{-2+x^2}{\left(1+x^2\right)^2} \, dx","Int[(-2 + x^2)/(1 + x^2)^2,x]","-\frac{3 x}{2 \left(x^2+1\right)}-\frac{1}{2} \tan ^{-1}(x)","-\frac{3 x}{2 \left(x^2+1\right)}-\frac{1}{2} \tan ^{-1}(x)",1,"(-3*x)/(2*(1 + x^2)) - ArcTan[x]/2","A",2,2,13,0.1538,1,"{385, 203}"
113,1,14,0,0.0040127,"\int \frac{3+x^2}{\left(1+x^2\right)^2} \, dx","Int[(3 + x^2)/(1 + x^2)^2,x]","\frac{x}{x^2+1}+2 \tan ^{-1}(x)","\frac{x}{x^2+1}+2 \tan ^{-1}(x)",1,"x/(1 + x^2) + 2*ArcTan[x]","A",2,2,13,0.1538,1,"{385, 203}"
114,1,12,0,0.0043831,"\int \frac{a+b x^2}{\left(-a+b x^2\right)^2} \, dx","Int[(a + b*x^2)/(-a + b*x^2)^2,x]","\frac{x}{a-b x^2}","\frac{x}{a-b x^2}",1,"x/(a - b*x^2)","A",1,1,19,0.05263,1,"{383}"
115,1,12,0,0.004321,"\int \frac{a+b x^2}{\left(a-b x^2\right)^2} \, dx","Int[(a + b*x^2)/(a - b*x^2)^2,x]","\frac{x}{a-b x^2}","\frac{x}{a-b x^2}",1,"x/(a - b*x^2)","A",1,1,18,0.05556,1,"{383}"
116,1,39,0,0.018227,"\int \frac{A+B x^2}{a-b x^2} \, dx","Int[(A + B*x^2)/(a - b*x^2),x]","\frac{(a B+A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}-\frac{B x}{b}","\frac{(a B+A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}-\frac{B x}{b}",1,"-((B*x)/b) + ((A*b + a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(3/2))","A",2,2,18,0.1111,1,"{388, 208}"
117,1,35,0,0.0068099,"\int \frac{1+x^2}{\left(16+x^2\right)^3} \, dx","Int[(1 + x^2)/(16 + x^2)^3,x]","\frac{19 x}{2048 \left(x^2+16\right)}-\frac{15 x}{64 \left(x^2+16\right)^2}+\frac{19 \tan ^{-1}\left(\frac{x}{4}\right)}{8192}","\frac{19 x}{2048 \left(x^2+16\right)}-\frac{15 x}{64 \left(x^2+16\right)^2}+\frac{19 \tan ^{-1}\left(\frac{x}{4}\right)}{8192}",1,"(-15*x)/(64*(16 + x^2)^2) + (19*x)/(2048*(16 + x^2)) + (19*ArcTan[x/4])/8192","A",3,3,13,0.2308,1,"{385, 199, 203}"
118,1,14,0,0.0083808,"\int \frac{1+2 x^2}{x^5 \left(1+x^2\right)^3} \, dx","Int[(1 + 2*x^2)/(x^5*(1 + x^2)^3),x]","-\frac{1}{4 x^4 \left(x^2+1\right)^2}","-\frac{1}{4 x^4 \left(x^2+1\right)^2}",1,"-1/(4*x^4*(1 + x^2)^2)","A",2,2,18,0.1111,1,"{446, 74}"
119,1,1,0,0.0004407,"\int \frac{\left(1-x^2\right)^2}{\left(-1+x^2\right)^2} \, dx","Int[(1 - x^2)^2/(-1 + x^2)^2,x]","x","x",1,"x","A",2,2,17,0.1176,1,"{21, 8}"
120,1,8,0,0.0015319,"\int \frac{x^3 \left(a c+b c x^2\right)}{a+b x^2} \, dx","Int[(x^3*(a*c + b*c*x^2))/(a + b*x^2),x]","\frac{c x^4}{4}","\frac{c x^4}{4}",1,"(c*x^4)/4","A",2,2,23,0.08696,1,"{21, 30}"
121,1,8,0,0.0014441,"\int \frac{x^2 \left(a c+b c x^2\right)}{a+b x^2} \, dx","Int[(x^2*(a*c + b*c*x^2))/(a + b*x^2),x]","\frac{c x^3}{3}","\frac{c x^3}{3}",1,"(c*x^3)/3","A",2,2,23,0.08696,1,"{21, 30}"
122,1,8,0,0.0015419,"\int \frac{x \left(a c+b c x^2\right)}{a+b x^2} \, dx","Int[(x*(a*c + b*c*x^2))/(a + b*x^2),x]","\frac{c x^2}{2}","\frac{c x^2}{2}",1,"(c*x^2)/2","A",2,2,21,0.09524,1,"{21, 30}"
123,1,3,0,0.0009539,"\int \frac{a c+b c x^2}{a+b x^2} \, dx","Int[(a*c + b*c*x^2)/(a + b*x^2),x]","c x","c x",1,"c*x","A",2,2,20,0.1000,1,"{21, 8}"
124,1,4,0,0.0010773,"\int \frac{a c+b c x^2}{x \left(a+b x^2\right)} \, dx","Int[(a*c + b*c*x^2)/(x*(a + b*x^2)),x]","c \log (x)","c \log (x)",1,"c*Log[x]","A",2,2,23,0.08696,1,"{21, 29}"
125,1,6,0,0.0014597,"\int \frac{a c+b c x^2}{x^2 \left(a+b x^2\right)} \, dx","Int[(a*c + b*c*x^2)/(x^2*(a + b*x^2)),x]","-\frac{c}{x}","-\frac{c}{x}",1,"-(c/x)","A",2,2,23,0.08696,1,"{21, 30}"
126,1,8,0,0.0014944,"\int \frac{a c+b c x^2}{x^3 \left(a+b x^2\right)} \, dx","Int[(a*c + b*c*x^2)/(x^3*(a + b*x^2)),x]","-\frac{c}{2 x^2}","-\frac{c}{2 x^2}",1,"-c/(2*x^2)","A",2,2,23,0.08696,1,"{21, 30}"
127,1,29,0,0.0213888,"\int \frac{x^3 \left(a c+b c x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(a*c + b*c*x^2))/(a + b*x^2)^2,x]","\frac{c x^2}{2 b}-\frac{a c \log \left(a+b x^2\right)}{2 b^2}","\frac{c x^2}{2 b}-\frac{a c \log \left(a+b x^2\right)}{2 b^2}",1,"(c*x^2)/(2*b) - (a*c*Log[a + b*x^2])/(2*b^2)","A",4,3,23,0.1304,1,"{21, 266, 43}"
128,1,33,0,0.01463,"\int \frac{x^2 \left(a c+b c x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(a*c + b*c*x^2))/(a + b*x^2)^2,x]","\frac{c x}{b}-\frac{\sqrt{a} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}","\frac{c x}{b}-\frac{\sqrt{a} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2}}",1,"(c*x)/b - (Sqrt[a]*c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(3/2)","A",3,3,23,0.1304,1,"{21, 321, 205}"
129,1,16,0,0.0045227,"\int \frac{x \left(a c+b c x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x*(a*c + b*c*x^2))/(a + b*x^2)^2,x]","\frac{c \log \left(a+b x^2\right)}{2 b}","\frac{c \log \left(a+b x^2\right)}{2 b}",1,"(c*Log[a + b*x^2])/(2*b)","A",2,2,21,0.09524,1,"{21, 260}"
130,1,25,0,0.0082619,"\int \frac{a c+b c x^2}{\left(a+b x^2\right)^2} \, dx","Int[(a*c + b*c*x^2)/(a + b*x^2)^2,x]","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b}}",1,"(c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b])","A",2,2,20,0.1000,1,"{21, 205}"
131,1,24,0,0.0130802,"\int \frac{a c+b c x^2}{x \left(a+b x^2\right)^2} \, dx","Int[(a*c + b*c*x^2)/(x*(a + b*x^2)^2),x]","\frac{c \log (x)}{a}-\frac{c \log \left(a+b x^2\right)}{2 a}","\frac{c \log (x)}{a}-\frac{c \log \left(a+b x^2\right)}{2 a}",1,"(c*Log[x])/a - (c*Log[a + b*x^2])/(2*a)","A",5,5,23,0.2174,1,"{21, 266, 36, 29, 31}"
132,1,36,0,0.0145887,"\int \frac{a c+b c x^2}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(a*c + b*c*x^2)/(x^2*(a + b*x^2)^2),x]","-\frac{\sqrt{b} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{c}{a x}","-\frac{\sqrt{b} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{c}{a x}",1,"-(c/(a*x)) - (Sqrt[b]*c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(3/2)","A",3,3,23,0.1304,1,"{21, 325, 205}"
133,1,38,0,0.0237782,"\int \frac{a c+b c x^2}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(a*c + b*c*x^2)/(x^3*(a + b*x^2)^2),x]","\frac{b c \log \left(a+b x^2\right)}{2 a^2}-\frac{b c \log (x)}{a^2}-\frac{c}{2 a x^2}","\frac{b c \log \left(a+b x^2\right)}{2 a^2}-\frac{b c \log (x)}{a^2}-\frac{c}{2 a x^2}",1,"-c/(2*a*x^2) - (b*c*Log[x])/a^2 + (b*c*Log[a + b*x^2])/(2*a^2)","A",4,3,23,0.1304,1,"{21, 266, 44}"
134,1,35,0,0.0268245,"\int \frac{x^3 \left(a c+b c x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^3*(a*c + b*c*x^2))/(a + b*x^2)^3,x]","\frac{a c}{2 b^2 \left(a+b x^2\right)}+\frac{c \log \left(a+b x^2\right)}{2 b^2}","\frac{a c}{2 b^2 \left(a+b x^2\right)}+\frac{c \log \left(a+b x^2\right)}{2 b^2}",1,"(a*c)/(2*b^2*(a + b*x^2)) + (c*Log[a + b*x^2])/(2*b^2)","A",4,3,23,0.1304,1,"{21, 266, 43}"
135,1,47,0,0.0153651,"\int \frac{x^2 \left(a c+b c x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^2*(a*c + b*c*x^2))/(a + b*x^2)^3,x]","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{c x}{2 b \left(a+b x^2\right)}","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{3/2}}-\frac{c x}{2 b \left(a+b x^2\right)}",1,"-(c*x)/(2*b*(a + b*x^2)) + (c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(3/2))","A",3,3,23,0.1304,1,"{21, 288, 205}"
136,1,17,0,0.0044847,"\int \frac{x \left(a c+b c x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x*(a*c + b*c*x^2))/(a + b*x^2)^3,x]","-\frac{c}{2 b \left(a+b x^2\right)}","-\frac{c}{2 b \left(a+b x^2\right)}",1,"-c/(2*b*(a + b*x^2))","A",2,2,21,0.09524,1,"{21, 261}"
137,1,47,0,0.0133698,"\int \frac{a c+b c x^2}{\left(a+b x^2\right)^3} \, dx","Int[(a*c + b*c*x^2)/(a + b*x^2)^3,x]","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{c x}{2 a \left(a+b x^2\right)}","\frac{c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{b}}+\frac{c x}{2 a \left(a+b x^2\right)}",1,"(c*x)/(2*a*(a + b*x^2)) + (c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[b])","A",3,3,20,0.1500,1,"{21, 199, 205}"
138,1,41,0,0.0301275,"\int \frac{a c+b c x^2}{x \left(a+b x^2\right)^3} \, dx","Int[(a*c + b*c*x^2)/(x*(a + b*x^2)^3),x]","-\frac{c \log \left(a+b x^2\right)}{2 a^2}+\frac{c \log (x)}{a^2}+\frac{c}{2 a \left(a+b x^2\right)}","-\frac{c \log \left(a+b x^2\right)}{2 a^2}+\frac{c \log (x)}{a^2}+\frac{c}{2 a \left(a+b x^2\right)}",1,"c/(2*a*(a + b*x^2)) + (c*Log[x])/a^2 - (c*Log[a + b*x^2])/(2*a^2)","A",4,3,23,0.1304,1,"{21, 266, 44}"
139,1,60,0,0.0220548,"\int \frac{a c+b c x^2}{x^2 \left(a+b x^2\right)^3} \, dx","Int[(a*c + b*c*x^2)/(x^2*(a + b*x^2)^3),x]","-\frac{3 \sqrt{b} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3 c}{2 a^2 x}+\frac{c}{2 a x \left(a+b x^2\right)}","-\frac{3 \sqrt{b} c \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{3 c}{2 a^2 x}+\frac{c}{2 a x \left(a+b x^2\right)}",1,"(-3*c)/(2*a^2*x) + c/(2*a*x*(a + b*x^2)) - (3*Sqrt[b]*c*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2))","A",4,4,23,0.1739,1,"{21, 290, 325, 205}"
140,1,53,0,0.0410684,"\int \frac{a c+b c x^2}{x^3 \left(a+b x^2\right)^3} \, dx","Int[(a*c + b*c*x^2)/(x^3*(a + b*x^2)^3),x]","-\frac{b c}{2 a^2 \left(a+b x^2\right)}+\frac{b c \log \left(a+b x^2\right)}{a^3}-\frac{2 b c \log (x)}{a^3}-\frac{c}{2 a^2 x^2}","-\frac{b c}{2 a^2 \left(a+b x^2\right)}+\frac{b c \log \left(a+b x^2\right)}{a^3}-\frac{2 b c \log (x)}{a^3}-\frac{c}{2 a^2 x^2}",1,"-c/(2*a^2*x^2) - (b*c)/(2*a^2*(a + b*x^2)) - (2*b*c*Log[x])/a^3 + (b*c*Log[a + b*x^2])/a^3","A",4,3,23,0.1304,1,"{21, 266, 44}"
141,1,55,0,0.0346943,"\int x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^4*(a + b*x^2)^2*(c + d*x^2),x]","\frac{1}{5} a^2 c x^5+\frac{1}{9} b x^9 (2 a d+b c)+\frac{1}{7} a x^7 (a d+2 b c)+\frac{1}{11} b^2 d x^{11}","\frac{1}{5} a^2 c x^5+\frac{1}{9} b x^9 (2 a d+b c)+\frac{1}{7} a x^7 (a d+2 b c)+\frac{1}{11} b^2 d x^{11}",1,"(a^2*c*x^5)/5 + (a*(2*b*c + a*d)*x^7)/7 + (b*(b*c + 2*a*d)*x^9)/9 + (b^2*d*x^11)/11","A",2,1,20,0.05000,1,"{448}"
142,1,55,0,0.0610322,"\int x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^3*(a + b*x^2)^2*(c + d*x^2),x]","\frac{1}{4} a^2 c x^4+\frac{1}{8} b x^8 (2 a d+b c)+\frac{1}{6} a x^6 (a d+2 b c)+\frac{1}{10} b^2 d x^{10}","\frac{1}{4} a^2 c x^4+\frac{1}{8} b x^8 (2 a d+b c)+\frac{1}{6} a x^6 (a d+2 b c)+\frac{1}{10} b^2 d x^{10}",1,"(a^2*c*x^4)/4 + (a*(2*b*c + a*d)*x^6)/6 + (b*(b*c + 2*a*d)*x^8)/8 + (b^2*d*x^10)/10","A",3,2,20,0.1000,1,"{446, 76}"
143,1,55,0,0.0296691,"\int x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^2*(a + b*x^2)^2*(c + d*x^2),x]","\frac{1}{3} a^2 c x^3+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{9} b^2 d x^9","\frac{1}{3} a^2 c x^3+\frac{1}{7} b x^7 (2 a d+b c)+\frac{1}{5} a x^5 (a d+2 b c)+\frac{1}{9} b^2 d x^9",1,"(a^2*c*x^3)/3 + (a*(2*b*c + a*d)*x^5)/5 + (b*(b*c + 2*a*d)*x^7)/7 + (b^2*d*x^9)/9","A",2,1,20,0.05000,1,"{448}"
144,1,42,0,0.0592418,"\int x \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x*(a + b*x^2)^2*(c + d*x^2),x]","\frac{\left(a+b x^2\right)^3 (b c-a d)}{6 b^2}+\frac{d \left(a+b x^2\right)^4}{8 b^2}","\frac{\left(a+b x^2\right)^3 (b c-a d)}{6 b^2}+\frac{d \left(a+b x^2\right)^4}{8 b^2}",1,"((b*c - a*d)*(a + b*x^2)^3)/(6*b^2) + (d*(a + b*x^2)^4)/(8*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
145,1,50,0,0.0250865,"\int \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[(a + b*x^2)^2*(c + d*x^2),x]","a^2 c x+\frac{1}{5} b x^5 (2 a d+b c)+\frac{1}{3} a x^3 (a d+2 b c)+\frac{1}{7} b^2 d x^7","a^2 c x+\frac{1}{5} b x^5 (2 a d+b c)+\frac{1}{3} a x^3 (a d+2 b c)+\frac{1}{7} b^2 d x^7",1,"a^2*c*x + (a*(2*b*c + a*d)*x^3)/3 + (b*(b*c + 2*a*d)*x^5)/5 + (b^2*d*x^7)/7","A",2,1,17,0.05882,1,"{373}"
146,1,43,0,0.0312346,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x,x]","a^2 c \log (x)+a b c x^2+\frac{d \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} b^2 c x^4","a^2 c \log (x)+a b c x^2+\frac{d \left(a+b x^2\right)^3}{6 b}+\frac{1}{4} b^2 c x^4",1,"a*b*c*x^2 + (b^2*c*x^4)/4 + (d*(a + b*x^2)^3)/(6*b) + a^2*c*Log[x]","A",4,3,20,0.1500,1,"{446, 80, 43}"
147,1,48,0,0.0256699,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x^2} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x^2,x]","-\frac{a^2 c}{x}+\frac{1}{3} b x^3 (2 a d+b c)+a x (a d+2 b c)+\frac{1}{5} b^2 d x^5","-\frac{a^2 c}{x}+\frac{1}{3} b x^3 (2 a d+b c)+a x (a d+2 b c)+\frac{1}{5} b^2 d x^5",1,"-((a^2*c)/x) + a*(2*b*c + a*d)*x + (b*(b*c + 2*a*d)*x^3)/3 + (b^2*d*x^5)/5","A",2,1,20,0.05000,1,"{448}"
148,1,51,0,0.0421537,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x^3} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x^3,x]","-\frac{a^2 c}{2 x^2}+\frac{1}{2} b x^2 (2 a d+b c)+a \log (x) (a d+2 b c)+\frac{1}{4} b^2 d x^4","-\frac{a^2 c}{2 x^2}+\frac{1}{2} b x^2 (2 a d+b c)+a \log (x) (a d+2 b c)+\frac{1}{4} b^2 d x^4",1,"-(a^2*c)/(2*x^2) + (b*(b*c + 2*a*d)*x^2)/2 + (b^2*d*x^4)/4 + a*(2*b*c + a*d)*Log[x]","A",3,2,20,0.1000,1,"{446, 76}"
149,1,48,0,0.0278166,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x^4} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x^4,x]","-\frac{a^2 c}{3 x^3}+b x (2 a d+b c)-\frac{a (a d+2 b c)}{x}+\frac{1}{3} b^2 d x^3","-\frac{a^2 c}{3 x^3}+b x (2 a d+b c)-\frac{a (a d+2 b c)}{x}+\frac{1}{3} b^2 d x^3",1,"-(a^2*c)/(3*x^3) - (a*(2*b*c + a*d))/x + b*(b*c + 2*a*d)*x + (b^2*d*x^3)/3","A",2,1,20,0.05000,1,"{448}"
150,1,87,0,0.0618824,"\int x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^4*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{1}{9} x^9 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{1}{5} a^2 c^2 x^5+\frac{2}{11} b d x^{11} (a d+b c)+\frac{2}{7} a c x^7 (a d+b c)+\frac{1}{13} b^2 d^2 x^{13}","\frac{1}{9} x^9 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{1}{5} a^2 c^2 x^5+\frac{2}{11} b d x^{11} (a d+b c)+\frac{2}{7} a c x^7 (a d+b c)+\frac{1}{13} b^2 d^2 x^{13}",1,"(a^2*c^2*x^5)/5 + (2*a*c*(b*c + a*d)*x^7)/7 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^9)/9 + (2*b*d*(b*c + a*d)*x^11)/11 + (b^2*d^2*x^13)/13","A",2,1,22,0.04545,1,"{448}"
151,1,87,0,0.1056196,"\int x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^3*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{1}{8} x^8 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{1}{4} a^2 c^2 x^4+\frac{1}{5} b d x^{10} (a d+b c)+\frac{1}{3} a c x^6 (a d+b c)+\frac{1}{12} b^2 d^2 x^{12}","\frac{1}{8} x^8 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{1}{4} a^2 c^2 x^4+\frac{1}{5} b d x^{10} (a d+b c)+\frac{1}{3} a c x^6 (a d+b c)+\frac{1}{12} b^2 d^2 x^{12}",1,"(a^2*c^2*x^4)/4 + (a*c*(b*c + a*d)*x^6)/3 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^8)/8 + (b*d*(b*c + a*d)*x^10)/5 + (b^2*d^2*x^12)/12","A",3,2,22,0.09091,1,"{446, 77}"
152,1,87,0,0.052869,"\int x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^2*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{1}{7} x^7 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{1}{3} a^2 c^2 x^3+\frac{2}{9} b d x^9 (a d+b c)+\frac{2}{5} a c x^5 (a d+b c)+\frac{1}{11} b^2 d^2 x^{11}","\frac{1}{7} x^7 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{1}{3} a^2 c^2 x^3+\frac{2}{9} b d x^9 (a d+b c)+\frac{2}{5} a c x^5 (a d+b c)+\frac{1}{11} b^2 d^2 x^{11}",1,"(a^2*c^2*x^3)/3 + (2*a*c*(b*c + a*d)*x^5)/5 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^7)/7 + (2*b*d*(b*c + a*d)*x^9)/9 + (b^2*d^2*x^11)/11","A",2,1,22,0.04545,1,"{448}"
153,1,71,0,0.1054956,"\int x \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{d \left(a+b x^2\right)^4 (b c-a d)}{4 b^3}+\frac{\left(a+b x^2\right)^3 (b c-a d)^2}{6 b^3}+\frac{d^2 \left(a+b x^2\right)^5}{10 b^3}","\frac{d \left(a+b x^2\right)^4 (b c-a d)}{4 b^3}+\frac{\left(a+b x^2\right)^3 (b c-a d)^2}{6 b^3}+\frac{d^2 \left(a+b x^2\right)^5}{10 b^3}",1,"((b*c - a*d)^2*(a + b*x^2)^3)/(6*b^3) + (d*(b*c - a*d)*(a + b*x^2)^4)/(4*b^3) + (d^2*(a + b*x^2)^5)/(10*b^3)","A",3,2,20,0.1000,1,"{444, 43}"
154,1,82,0,0.0387515,"\int \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{1}{5} x^5 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{2}{7} b d x^7 (a d+b c)+\frac{2}{3} a c x^3 (a d+b c)+\frac{1}{9} b^2 d^2 x^9","\frac{1}{5} x^5 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 x+\frac{2}{7} b d x^7 (a d+b c)+\frac{2}{3} a c x^3 (a d+b c)+\frac{1}{9} b^2 d^2 x^9",1,"a^2*c^2*x + (2*a*c*(b*c + a*d)*x^3)/3 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^5)/5 + (2*b*d*(b*c + a*d)*x^7)/7 + (b^2*d^2*x^9)/9","A",2,1,19,0.05263,1,"{373}"
155,1,80,0,0.0750831,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x,x]","\frac{1}{4} x^4 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 \log (x)+\frac{1}{3} b d x^6 (a d+b c)+a c x^2 (a d+b c)+\frac{1}{8} b^2 d^2 x^8","\frac{1}{4} x^4 \left(a^2 d^2+4 a b c d+b^2 c^2\right)+a^2 c^2 \log (x)+\frac{1}{3} b d x^6 (a d+b c)+a c x^2 (a d+b c)+\frac{1}{8} b^2 d^2 x^8",1,"a*c*(b*c + a*d)*x^2 + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^4)/4 + (b*d*(b*c + a*d)*x^6)/3 + (b^2*d^2*x^8)/8 + a^2*c^2*Log[x]","A",3,2,22,0.09091,1,"{446, 88}"
156,1,81,0,0.0426554,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x^2} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x^2,x]","\frac{1}{3} x^3 \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{a^2 c^2}{x}+\frac{2}{5} b d x^5 (a d+b c)+2 a c x (a d+b c)+\frac{1}{7} b^2 d^2 x^7","\frac{1}{3} x^3 \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{a^2 c^2}{x}+\frac{2}{5} b d x^5 (a d+b c)+2 a c x (a d+b c)+\frac{1}{7} b^2 d^2 x^7",1,"-((a^2*c^2)/x) + 2*a*c*(b*c + a*d)*x + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^3)/3 + (2*b*d*(b*c + a*d)*x^5)/5 + (b^2*d^2*x^7)/7","A",2,1,22,0.04545,1,"{448}"
157,1,84,0,0.078103,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x^3} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x^3,x]","\frac{1}{2} x^2 \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{a^2 c^2}{2 x^2}+\frac{1}{2} b d x^4 (a d+b c)+2 a c \log (x) (a d+b c)+\frac{1}{6} b^2 d^2 x^6","\frac{1}{2} x^2 \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{a^2 c^2}{2 x^2}+\frac{1}{2} b d x^4 (a d+b c)+2 a c \log (x) (a d+b c)+\frac{1}{6} b^2 d^2 x^6",1,"-(a^2*c^2)/(2*x^2) + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^2)/2 + (b*d*(b*c + a*d)*x^4)/2 + (b^2*d^2*x^6)/6 + 2*a*c*(b*c + a*d)*Log[x]","A",3,2,22,0.09091,1,"{446, 88}"
158,1,80,0,0.0527717,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x^4} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x^4,x]","x \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{a^2 c^2}{3 x^3}+\frac{2}{3} b d x^3 (a d+b c)-\frac{2 a c (a d+b c)}{x}+\frac{1}{5} b^2 d^2 x^5","x \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{a^2 c^2}{3 x^3}+\frac{2}{3} b d x^3 (a d+b c)-\frac{2 a c (a d+b c)}{x}+\frac{1}{5} b^2 d^2 x^5",1,"-(a^2*c^2)/(3*x^3) - (2*a*c*(b*c + a*d))/x + (b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x + (2*b*d*(b*c + a*d)*x^3)/3 + (b^2*d^2*x^5)/5","A",2,1,22,0.04545,1,"{448}"
159,1,127,0,0.0880314,"\int x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^4*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{1}{11} d x^{11} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{9} c x^9 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{1}{5} a^2 c^3 x^5+\frac{1}{7} a c^2 x^7 (3 a d+2 b c)+\frac{1}{13} b d^2 x^{13} (2 a d+3 b c)+\frac{1}{15} b^2 d^3 x^{15}","\frac{1}{11} d x^{11} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{9} c x^9 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{1}{5} a^2 c^3 x^5+\frac{1}{7} a c^2 x^7 (3 a d+2 b c)+\frac{1}{13} b d^2 x^{13} (2 a d+3 b c)+\frac{1}{15} b^2 d^3 x^{15}",1,"(a^2*c^3*x^5)/5 + (a*c^2*(2*b*c + 3*a*d)*x^7)/7 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^9)/9 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^11)/11 + (b*d^2*(3*b*c + 2*a*d)*x^13)/13 + (b^2*d^3*x^15)/15","A",2,1,22,0.04545,1,"{448}"
160,1,106,0,0.2248567,"\int x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^3*(a + b*x^2)^2*(c + d*x^2)^3,x]","-\frac{b \left(c+d x^2\right)^6 (3 b c-2 a d)}{12 d^4}+\frac{\left(c+d x^2\right)^5 (b c-a d) (3 b c-a d)}{10 d^4}-\frac{c \left(c+d x^2\right)^4 (b c-a d)^2}{8 d^4}+\frac{b^2 \left(c+d x^2\right)^7}{14 d^4}","-\frac{b \left(c+d x^2\right)^6 (3 b c-2 a d)}{12 d^4}+\frac{\left(c+d x^2\right)^5 (b c-a d) (3 b c-a d)}{10 d^4}-\frac{c \left(c+d x^2\right)^4 (b c-a d)^2}{8 d^4}+\frac{b^2 \left(c+d x^2\right)^7}{14 d^4}",1,"-(c*(b*c - a*d)^2*(c + d*x^2)^4)/(8*d^4) + ((b*c - a*d)*(3*b*c - a*d)*(c + d*x^2)^5)/(10*d^4) - (b*(3*b*c - 2*a*d)*(c + d*x^2)^6)/(12*d^4) + (b^2*(c + d*x^2)^7)/(14*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
161,1,127,0,0.0716647,"\int x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^2*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{1}{9} d x^9 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{7} c x^7 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{1}{3} a^2 c^3 x^3+\frac{1}{5} a c^2 x^5 (3 a d+2 b c)+\frac{1}{11} b d^2 x^{11} (2 a d+3 b c)+\frac{1}{13} b^2 d^3 x^{13}","\frac{1}{9} d x^9 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{7} c x^7 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{1}{3} a^2 c^3 x^3+\frac{1}{5} a c^2 x^5 (3 a d+2 b c)+\frac{1}{11} b d^2 x^{11} (2 a d+3 b c)+\frac{1}{13} b^2 d^3 x^{13}",1,"(a^2*c^3*x^3)/3 + (a*c^2*(2*b*c + 3*a*d)*x^5)/5 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^7)/7 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^9)/9 + (b*d^2*(3*b*c + 2*a*d)*x^11)/11 + (b^2*d^3*x^13)/13","A",2,1,22,0.04545,1,"{448}"
162,1,71,0,0.1183063,"\int x \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x*(a + b*x^2)^2*(c + d*x^2)^3,x]","-\frac{b \left(c+d x^2\right)^5 (b c-a d)}{5 d^3}+\frac{\left(c+d x^2\right)^4 (b c-a d)^2}{8 d^3}+\frac{b^2 \left(c+d x^2\right)^6}{12 d^3}","-\frac{b \left(c+d x^2\right)^5 (b c-a d)}{5 d^3}+\frac{\left(c+d x^2\right)^4 (b c-a d)^2}{8 d^3}+\frac{b^2 \left(c+d x^2\right)^6}{12 d^3}",1,"((b*c - a*d)^2*(c + d*x^2)^4)/(8*d^3) - (b*(b*c - a*d)*(c + d*x^2)^5)/(5*d^3) + (b^2*(c + d*x^2)^6)/(12*d^3)","A",3,2,20,0.1000,1,"{444, 43}"
163,1,122,0,0.0538846,"\int \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{1}{7} d x^7 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{5} c x^5 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{3} a c^2 x^3 (3 a d+2 b c)+\frac{1}{9} b d^2 x^9 (2 a d+3 b c)+\frac{1}{11} b^2 d^3 x^{11}","\frac{1}{7} d x^7 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{5} c x^5 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 x+\frac{1}{3} a c^2 x^3 (3 a d+2 b c)+\frac{1}{9} b d^2 x^9 (2 a d+3 b c)+\frac{1}{11} b^2 d^3 x^{11}",1,"a^2*c^3*x + (a*c^2*(2*b*c + 3*a*d)*x^3)/3 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^5)/5 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^7)/7 + (b*d^2*(3*b*c + 2*a*d)*x^9)/9 + (b^2*d^3*x^11)/11","A",2,1,19,0.05263,1,"{373}"
164,1,123,0,0.1038827,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x,x]","\frac{1}{6} d x^6 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{4} c x^4 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 \log (x)+\frac{1}{2} a c^2 x^2 (3 a d+2 b c)+\frac{1}{8} b d^2 x^8 (2 a d+3 b c)+\frac{1}{10} b^2 d^3 x^{10}","\frac{1}{6} d x^6 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{4} c x^4 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+a^2 c^3 \log (x)+\frac{1}{2} a c^2 x^2 (3 a d+2 b c)+\frac{1}{8} b d^2 x^8 (2 a d+3 b c)+\frac{1}{10} b^2 d^3 x^{10}",1,"(a*c^2*(2*b*c + 3*a*d)*x^2)/2 + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^4)/4 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^6)/6 + (b*d^2*(3*b*c + 2*a*d)*x^8)/8 + (b^2*d^3*x^10)/10 + a^2*c^3*Log[x]","A",3,2,22,0.09091,1,"{446, 88}"
165,1,120,0,0.0564373,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x^2} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x^2,x]","\frac{1}{5} d x^5 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{3} c x^3 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{a^2 c^3}{x}+a c^2 x (3 a d+2 b c)+\frac{1}{7} b d^2 x^7 (2 a d+3 b c)+\frac{1}{9} b^2 d^3 x^9","\frac{1}{5} d x^5 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{3} c x^3 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{a^2 c^3}{x}+a c^2 x (3 a d+2 b c)+\frac{1}{7} b d^2 x^7 (2 a d+3 b c)+\frac{1}{9} b^2 d^3 x^9",1,"-((a^2*c^3)/x) + a*c^2*(2*b*c + 3*a*d)*x + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^3)/3 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^5)/5 + (b*d^2*(3*b*c + 2*a*d)*x^7)/7 + (b^2*d^3*x^9)/9","A",2,1,22,0.04545,1,"{448}"
166,1,123,0,0.1008733,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x^3} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x^3,x]","\frac{1}{4} d x^4 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{2} c x^2 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{a^2 c^3}{2 x^2}+a c^2 \log (x) (3 a d+2 b c)+\frac{1}{6} b d^2 x^6 (2 a d+3 b c)+\frac{1}{8} b^2 d^3 x^8","\frac{1}{4} d x^4 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{1}{2} c x^2 \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{a^2 c^3}{2 x^2}+a c^2 \log (x) (3 a d+2 b c)+\frac{1}{6} b d^2 x^6 (2 a d+3 b c)+\frac{1}{8} b^2 d^3 x^8",1,"-(a^2*c^3)/(2*x^2) + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^2)/2 + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^4)/4 + (b*d^2*(3*b*c + 2*a*d)*x^6)/6 + (b^2*d^3*x^8)/8 + a*c^2*(2*b*c + 3*a*d)*Log[x]","A",3,2,22,0.09091,1,"{446, 88}"
167,1,120,0,0.0601588,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x^4} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x^4,x]","\frac{1}{3} d x^3 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+c x \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{a^2 c^3}{3 x^3}-\frac{a c^2 (3 a d+2 b c)}{x}+\frac{1}{5} b d^2 x^5 (2 a d+3 b c)+\frac{1}{7} b^2 d^3 x^7","\frac{1}{3} d x^3 \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+c x \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{a^2 c^3}{3 x^3}-\frac{a c^2 (3 a d+2 b c)}{x}+\frac{1}{5} b d^2 x^5 (2 a d+3 b c)+\frac{1}{7} b^2 d^3 x^7",1,"-(a^2*c^3)/(3*x^3) - (a*c^2*(2*b*c + 3*a*d))/x + c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^3)/3 + (b*d^2*(3*b*c + 2*a*d)*x^5)/5 + (b^2*d^3*x^7)/7","A",2,1,22,0.04545,1,"{448}"
168,1,104,0,0.0737845,"\int \frac{x^4 \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^4*(a + b*x^2)^2)/(c + d*x^2),x]","\frac{c^{3/2} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{d^{9/2}}-\frac{b x^5 (b c-2 a d)}{5 d^2}+\frac{x^3 (b c-a d)^2}{3 d^3}-\frac{c x (b c-a d)^2}{d^4}+\frac{b^2 x^7}{7 d}","\frac{c^{3/2} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{d^{9/2}}-\frac{b x^5 (b c-2 a d)}{5 d^2}+\frac{x^3 (b c-a d)^2}{3 d^3}-\frac{c x (b c-a d)^2}{d^4}+\frac{b^2 x^7}{7 d}",1,"-((c*(b*c - a*d)^2*x)/d^4) + ((b*c - a*d)^2*x^3)/(3*d^3) - (b*(b*c - 2*a*d)*x^5)/(5*d^2) + (b^2*x^7)/(7*d) + (c^(3/2)*(b*c - a*d)^2*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/d^(9/2)","A",3,2,22,0.09091,1,"{461, 205}"
169,1,79,0,0.0842049,"\int \frac{x^3 \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^3*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{b x^4 (b c-2 a d)}{4 d^2}+\frac{x^2 (b c-a d)^2}{2 d^3}-\frac{c (b c-a d)^2 \log \left(c+d x^2\right)}{2 d^4}+\frac{b^2 x^6}{6 d}","-\frac{b x^4 (b c-2 a d)}{4 d^2}+\frac{x^2 (b c-a d)^2}{2 d^3}-\frac{c (b c-a d)^2 \log \left(c+d x^2\right)}{2 d^4}+\frac{b^2 x^6}{6 d}",1,"((b*c - a*d)^2*x^2)/(2*d^3) - (b*(b*c - 2*a*d)*x^4)/(4*d^2) + (b^2*x^6)/(6*d) - (c*(b*c - a*d)^2*Log[c + d*x^2])/(2*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
170,1,83,0,0.0644815,"\int \frac{x^2 \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^2*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{b x^3 (b c-2 a d)}{3 d^2}+\frac{x (b c-a d)^2}{d^3}-\frac{\sqrt{c} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{d^{7/2}}+\frac{b^2 x^5}{5 d}","-\frac{b x^3 (b c-2 a d)}{3 d^2}+\frac{x (b c-a d)^2}{d^3}-\frac{\sqrt{c} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{d^{7/2}}+\frac{b^2 x^5}{5 d}",1,"((b*c - a*d)^2*x)/d^3 - (b*(b*c - 2*a*d)*x^3)/(3*d^2) + (b^2*x^5)/(5*d) - (Sqrt[c]*(b*c - a*d)^2*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/d^(7/2)","A",3,2,22,0.09091,1,"{461, 205}"
171,1,61,0,0.0489539,"\int \frac{x \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{b x^2 (b c-a d)}{2 d^2}+\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 d^3}+\frac{\left(a+b x^2\right)^2}{4 d}","-\frac{b x^2 (b c-a d)}{2 d^2}+\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 d^3}+\frac{\left(a+b x^2\right)^2}{4 d}",1,"-(b*(b*c - a*d)*x^2)/(2*d^2) + (a + b*x^2)^2/(4*d) + ((b*c - a*d)^2*Log[c + d*x^2])/(2*d^3)","A",3,2,20,0.1000,1,"{444, 43}"
172,1,63,0,0.0392406,"\int \frac{\left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(a + b*x^2)^2/(c + d*x^2),x]","-\frac{b x (b c-2 a d)}{d^2}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{c} d^{5/2}}+\frac{b^2 x^3}{3 d}","-\frac{b x (b c-2 a d)}{d^2}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{c} d^{5/2}}+\frac{b^2 x^3}{3 d}",1,"-((b*(b*c - 2*a*d)*x)/d^2) + (b^2*x^3)/(3*d) + ((b*c - a*d)^2*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(Sqrt[c]*d^(5/2))","A",3,2,19,0.1053,1,"{390, 205}"
173,1,51,0,0.0463171,"\int \frac{\left(a+b x^2\right)^2}{x \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x*(c + d*x^2)),x]","\frac{a^2 \log (x)}{c}-\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 c d^2}+\frac{b^2 x^2}{2 d}","\frac{a^2 \log (x)}{c}-\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 c d^2}+\frac{b^2 x^2}{2 d}",1,"(b^2*x^2)/(2*d) + (a^2*Log[x])/c - ((b*c - a*d)^2*Log[c + d*x^2])/(2*c*d^2)","A",3,2,22,0.09091,1,"{446, 72}"
174,1,55,0,0.0488449,"\int \frac{\left(a+b x^2\right)^2}{x^2 \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^2*(c + d*x^2)),x]","-\frac{a^2}{c x}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{3/2} d^{3/2}}+\frac{b^2 x}{d}","-\frac{a^2}{c x}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{3/2} d^{3/2}}+\frac{b^2 x}{d}",1,"-(a^2/(c*x)) + (b^2*x)/d - ((b*c - a*d)^2*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*d^(3/2))","A",3,2,22,0.09091,1,"{461, 205}"
175,1,58,0,0.0576856,"\int \frac{\left(a+b x^2\right)^2}{x^3 \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^3*(c + d*x^2)),x]","-\frac{a^2}{2 c x^2}+\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 c^2 d}+\frac{a \log (x) (2 b c-a d)}{c^2}","-\frac{a^2}{2 c x^2}+\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 c^2 d}+\frac{a \log (x) (2 b c-a d)}{c^2}",1,"-a^2/(2*c*x^2) + (a*(2*b*c - a*d)*Log[x])/c^2 + ((b*c - a*d)^2*Log[c + d*x^2])/(2*c^2*d)","A",3,2,22,0.09091,1,"{446, 88}"
176,1,66,0,0.0547288,"\int \frac{\left(a+b x^2\right)^2}{x^4 \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^4*(c + d*x^2)),x]","-\frac{a^2}{3 c x^3}-\frac{a (2 b c-a d)}{c^2 x}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{5/2} \sqrt{d}}","-\frac{a^2}{3 c x^3}-\frac{a (2 b c-a d)}{c^2 x}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{5/2} \sqrt{d}}",1,"-a^2/(3*c*x^3) - (a*(2*b*c - a*d))/(c^2*x) + ((b*c - a*d)^2*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*Sqrt[d])","A",3,2,22,0.09091,1,"{461, 205}"
177,1,75,0,0.0672466,"\int \frac{\left(a+b x^2\right)^2}{x^5 \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^5*(c + d*x^2)),x]","-\frac{a^2}{4 c x^4}-\frac{a (2 b c-a d)}{2 c^2 x^2}-\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 c^3}+\frac{\log (x) (b c-a d)^2}{c^3}","-\frac{a^2}{4 c x^4}-\frac{a (2 b c-a d)}{2 c^2 x^2}-\frac{(b c-a d)^2 \log \left(c+d x^2\right)}{2 c^3}+\frac{\log (x) (b c-a d)^2}{c^3}",1,"-a^2/(4*c*x^4) - (a*(2*b*c - a*d))/(2*c^2*x^2) + ((b*c - a*d)^2*Log[x])/c^3 - ((b*c - a*d)^2*Log[c + d*x^2])/(2*c^3)","A",3,2,22,0.09091,1,"{446, 88}"
178,1,87,0,0.0649296,"\int \frac{\left(a+b x^2\right)^2}{x^6 \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^6*(c + d*x^2)),x]","-\frac{a^2}{5 c x^5}-\frac{a (2 b c-a d)}{3 c^2 x^3}-\frac{(b c-a d)^2}{c^3 x}-\frac{\sqrt{d} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{7/2}}","-\frac{a^2}{5 c x^5}-\frac{a (2 b c-a d)}{3 c^2 x^3}-\frac{(b c-a d)^2}{c^3 x}-\frac{\sqrt{d} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{7/2}}",1,"-a^2/(5*c*x^5) - (a*(2*b*c - a*d))/(3*c^2*x^3) - (b*c - a*d)^2/(c^3*x) - (Sqrt[d]*(b*c - a*d)^2*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/c^(7/2)","A",3,2,22,0.09091,1,"{461, 205}"
179,1,98,0,0.0833537,"\int \frac{\left(a+b x^2\right)^2}{x^7 \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^7*(c + d*x^2)),x]","-\frac{a^2}{6 c x^6}-\frac{a (2 b c-a d)}{4 c^2 x^4}-\frac{(b c-a d)^2}{2 c^3 x^2}+\frac{d (b c-a d)^2 \log \left(c+d x^2\right)}{2 c^4}-\frac{d \log (x) (b c-a d)^2}{c^4}","-\frac{a^2}{6 c x^6}-\frac{a (2 b c-a d)}{4 c^2 x^4}-\frac{(b c-a d)^2}{2 c^3 x^2}+\frac{d (b c-a d)^2 \log \left(c+d x^2\right)}{2 c^4}-\frac{d \log (x) (b c-a d)^2}{c^4}",1,"-a^2/(6*c*x^6) - (a*(2*b*c - a*d))/(4*c^2*x^4) - (b*c - a*d)^2/(2*c^3*x^2) - (d*(b*c - a*d)^2*Log[x])/c^4 + (d*(b*c - a*d)^2*Log[c + d*x^2])/(2*c^4)","A",3,2,22,0.09091,1,"{446, 88}"
180,1,145,0,0.1346564,"\int \frac{x^4 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^4*(a + b*x^2)^2)/(c + d*x^2)^2,x]","\frac{x^5 (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x^3 (7 b c-3 a d) (b c-a d)}{6 c d^3}+\frac{x (7 b c-3 a d) (b c-a d)}{2 d^4}-\frac{\sqrt{c} (7 b c-3 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 d^{9/2}}+\frac{b^2 x^5}{5 d^2}","\frac{x^5 (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x^3 (7 b c-3 a d) (b c-a d)}{6 c d^3}+\frac{x (7 b c-3 a d) (b c-a d)}{2 d^4}-\frac{\sqrt{c} (7 b c-3 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 d^{9/2}}+\frac{b^2 x^5}{5 d^2}",1,"((7*b*c - 3*a*d)*(b*c - a*d)*x)/(2*d^4) - ((7*b*c - 3*a*d)*(b*c - a*d)*x^3)/(6*c*d^3) + (b^2*x^5)/(5*d^2) + ((b*c - a*d)^2*x^5)/(2*c*d^2*(c + d*x^2)) - (Sqrt[c]*(7*b*c - 3*a*d)*(b*c - a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*d^(9/2))","A",5,4,22,0.1818,1,"{463, 459, 302, 205}"
181,1,90,0,0.0975002,"\int \frac{x^3 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^3*(a + b*x^2)^2)/(c + d*x^2)^2,x]","-\frac{b x^2 (b c-a d)}{d^3}+\frac{c (b c-a d)^2}{2 d^4 \left(c+d x^2\right)}+\frac{(b c-a d) (3 b c-a d) \log \left(c+d x^2\right)}{2 d^4}+\frac{b^2 x^4}{4 d^2}","-\frac{b x^2 (b c-a d)}{d^3}+\frac{c (b c-a d)^2}{2 d^4 \left(c+d x^2\right)}+\frac{(b c-a d) (3 b c-a d) \log \left(c+d x^2\right)}{2 d^4}+\frac{b^2 x^4}{4 d^2}",1,"-((b*(b*c - a*d)*x^2)/d^3) + (b^2*x^4)/(4*d^2) + (c*(b*c - a*d)^2)/(2*d^4*(c + d*x^2)) + ((b*c - a*d)*(3*b*c - a*d)*Log[c + d*x^2])/(2*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
182,1,118,0,0.110162,"\int \frac{x^2 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^2*(a + b*x^2)^2)/(c + d*x^2)^2,x]","\frac{x^3 (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x (b c-a d) (5 b c-a d)}{2 c d^3}+\frac{(b c-a d) (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} d^{7/2}}+\frac{b^2 x^3}{3 d^2}","\frac{x^3 (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x (b c-a d) (5 b c-a d)}{2 c d^3}+\frac{(b c-a d) (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} d^{7/2}}+\frac{b^2 x^3}{3 d^2}",1,"-((b*c - a*d)*(5*b*c - a*d)*x)/(2*c*d^3) + (b^2*x^3)/(3*d^2) + ((b*c - a*d)^2*x^3)/(2*c*d^2*(c + d*x^2)) + ((b*c - a*d)*(5*b*c - a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*Sqrt[c]*d^(7/2))","A",4,4,22,0.1818,1,"{463, 459, 321, 205}"
183,1,62,0,0.058084,"\int \frac{x \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x*(a + b*x^2)^2)/(c + d*x^2)^2,x]","-\frac{(b c-a d)^2}{2 d^3 \left(c+d x^2\right)}-\frac{b (b c-a d) \log \left(c+d x^2\right)}{d^3}+\frac{b^2 x^2}{2 d^2}","-\frac{(b c-a d)^2}{2 d^3 \left(c+d x^2\right)}-\frac{b (b c-a d) \log \left(c+d x^2\right)}{d^3}+\frac{b^2 x^2}{2 d^2}",1,"(b^2*x^2)/(2*d^2) - (b*c - a*d)^2/(2*d^3*(c + d*x^2)) - (b*(b*c - a*d)*Log[c + d*x^2])/d^3","A",3,2,20,0.1000,1,"{444, 43}"
184,1,82,0,0.1072159,"\int \frac{\left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(c + d*x^2)^2,x]","-\frac{(b c-a d) (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} d^{5/2}}+\frac{x (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{b^2 x}{d^2}","-\frac{(b c-a d) (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} d^{5/2}}+\frac{x (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{b^2 x}{d^2}",1,"(b^2*x)/d^2 + ((b*c - a*d)^2*x)/(2*c*d^2*(c + d*x^2)) - ((b*c - a*d)*(3*b*c + a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(3/2)*d^(5/2))","A",4,3,19,0.1579,1,"{390, 385, 205}"
185,1,67,0,0.0635326,"\int \frac{\left(a+b x^2\right)^2}{x \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x*(c + d*x^2)^2),x]","-\frac{1}{2} \left(\frac{a^2}{c^2}-\frac{b^2}{d^2}\right) \log \left(c+d x^2\right)+\frac{a^2 \log (x)}{c^2}+\frac{(b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}","-\frac{1}{2} \left(\frac{a^2}{c^2}-\frac{b^2}{d^2}\right) \log \left(c+d x^2\right)+\frac{a^2 \log (x)}{c^2}+\frac{(b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}",1,"(b*c - a*d)^2/(2*c*d^2*(c + d*x^2)) + (a^2*Log[x])/c^2 - ((a^2/c^2 - b^2/d^2)*Log[c + d*x^2])/2","A",3,2,22,0.09091,1,"{446, 88}"
186,1,106,0,0.0756784,"\int \frac{\left(a+b x^2\right)^2}{x^2 \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x^2*(c + d*x^2)^2),x]","-\frac{x \left(3 a^2 d^2-2 a b c d+b^2 c^2\right)}{2 c^2 d \left(c+d x^2\right)}-\frac{a^2}{c x \left(c+d x^2\right)}+\frac{(b c-a d) (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{5/2} d^{3/2}}","-\frac{x \left(3 a^2 d^2-2 a b c d+b^2 c^2\right)}{2 c^2 d \left(c+d x^2\right)}-\frac{a^2}{c x \left(c+d x^2\right)}+\frac{(b c-a d) (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{5/2} d^{3/2}}",1,"-(a^2/(c*x*(c + d*x^2))) - ((b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*x)/(2*c^2*d*(c + d*x^2)) + ((b*c - a*d)*(b*c + 3*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(5/2)*d^(3/2))","A",3,3,22,0.1364,1,"{462, 385, 205}"
187,1,81,0,0.0789378,"\int \frac{\left(a+b x^2\right)^2}{x^3 \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x^3*(c + d*x^2)^2),x]","-\frac{a^2}{2 c^2 x^2}-\frac{(b c-a d)^2}{2 c^2 d \left(c+d x^2\right)}-\frac{a (b c-a d) \log \left(c+d x^2\right)}{c^3}+\frac{2 a \log (x) (b c-a d)}{c^3}","-\frac{a^2}{2 c^2 x^2}-\frac{(b c-a d)^2}{2 c^2 d \left(c+d x^2\right)}-\frac{a (b c-a d) \log \left(c+d x^2\right)}{c^3}+\frac{2 a \log (x) (b c-a d)}{c^3}",1,"-a^2/(2*c^2*x^2) - (b*c - a*d)^2/(2*c^2*d*(c + d*x^2)) + (2*a*(b*c - a*d)*Log[x])/c^3 - (a*(b*c - a*d)*Log[c + d*x^2])/c^3","A",3,2,22,0.09091,1,"{446, 88}"
188,1,126,0,0.1346785,"\int \frac{\left(a+b x^2\right)^2}{x^4 \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x^4*(c + d*x^2)^2),x]","\frac{x \left(5 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{6 c^3 \left(c+d x^2\right)}-\frac{a^2}{3 c x^3 \left(c+d x^2\right)}-\frac{a (6 b c-5 a d)}{3 c^3 x}+\frac{(b c-5 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{7/2} \sqrt{d}}","\frac{x \left(5 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{6 c^3 \left(c+d x^2\right)}-\frac{a^2}{3 c x^3 \left(c+d x^2\right)}-\frac{a (6 b c-5 a d)}{3 c^3 x}+\frac{(b c-5 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{7/2} \sqrt{d}}",1,"-(a*(6*b*c - 5*a*d))/(3*c^3*x) - a^2/(3*c*x^3*(c + d*x^2)) + ((3*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*x)/(6*c^3*(c + d*x^2)) + ((b*c - 5*a*d)*(b*c - a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(7/2)*Sqrt[d])","A",4,4,22,0.1818,1,"{462, 456, 453, 205}"
189,1,163,0,0.1577006,"\int \frac{x^4 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^4*(a + b*x^2)^2)/(c + d*x^2)^3,x]","-\frac{x \left(a^2 d^2-10 a b c d+13 b^2 c^2\right)}{4 c d^4}+\frac{\left(3 a^2 d^2-30 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 \sqrt{c} d^{9/2}}+\frac{x^5 (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}-\frac{x (b c-a d) (9 b c-a d)}{8 d^4 \left(c+d x^2\right)}+\frac{b^2 x^3}{3 d^3}","-\frac{x \left(a^2 d^2-10 a b c d+13 b^2 c^2\right)}{4 c d^4}+\frac{\left(3 a^2 d^2-30 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 \sqrt{c} d^{9/2}}+\frac{x^5 (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}-\frac{x (b c-a d) (9 b c-a d)}{8 d^4 \left(c+d x^2\right)}+\frac{b^2 x^3}{3 d^3}",1,"-((13*b^2*c^2 - 10*a*b*c*d + a^2*d^2)*x)/(4*c*d^4) + (b^2*x^3)/(3*d^3) + ((b*c - a*d)^2*x^5)/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(9*b*c - a*d)*x)/(8*d^4*(c + d*x^2)) + ((35*b^2*c^2 - 30*a*b*c*d + 3*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*Sqrt[c]*d^(9/2))","A",5,4,22,0.1818,1,"{463, 455, 1153, 205}"
190,1,99,0,0.1000782,"\int \frac{x^3 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^3*(a + b*x^2)^2)/(c + d*x^2)^3,x]","\frac{c (b c-a d)^2}{4 d^4 \left(c+d x^2\right)^2}-\frac{(3 b c-a d) (b c-a d)}{2 d^4 \left(c+d x^2\right)}-\frac{b (3 b c-2 a d) \log \left(c+d x^2\right)}{2 d^4}+\frac{b^2 x^2}{2 d^3}","\frac{c (b c-a d)^2}{4 d^4 \left(c+d x^2\right)^2}-\frac{(3 b c-a d) (b c-a d)}{2 d^4 \left(c+d x^2\right)}-\frac{b (3 b c-2 a d) \log \left(c+d x^2\right)}{2 d^4}+\frac{b^2 x^2}{2 d^3}",1,"(b^2*x^2)/(2*d^3) + (c*(b*c - a*d)^2)/(4*d^4*(c + d*x^2)^2) - ((b*c - a*d)*(3*b*c - a*d))/(2*d^4*(c + d*x^2)) - (b*(3*b*c - 2*a*d)*Log[c + d*x^2])/(2*d^4)","A",3,2,22,0.09091,1,"{446, 77}"
191,1,127,0,0.1247171,"\int \frac{x^2 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^2*(a + b*x^2)^2)/(c + d*x^2)^3,x]","-\frac{\left(-a^2 d^2-6 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{3/2} d^{7/2}}+\frac{x^3 (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}+\frac{x (b c-a d) (a d+7 b c)}{8 c d^3 \left(c+d x^2\right)}+\frac{b^2 x}{d^3}","-\frac{\left(-a^2 d^2-6 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{3/2} d^{7/2}}+\frac{x^3 (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}+\frac{x (b c-a d) (a d+7 b c)}{8 c d^3 \left(c+d x^2\right)}+\frac{b^2 x}{d^3}",1,"(b^2*x)/d^3 + ((b*c - a*d)^2*x^3)/(4*c*d^2*(c + d*x^2)^2) + ((b*c - a*d)*(7*b*c + a*d)*x)/(8*c*d^3*(c + d*x^2)) - ((15*b^2*c^2 - 6*a*b*c*d - a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(3/2)*d^(7/2))","A",4,4,22,0.1818,1,"{463, 455, 388, 205}"
192,1,67,0,0.0681163,"\int \frac{x \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x*(a + b*x^2)^2)/(c + d*x^2)^3,x]","\frac{b (b c-a d)}{d^3 \left(c+d x^2\right)}-\frac{(b c-a d)^2}{4 d^3 \left(c+d x^2\right)^2}+\frac{b^2 \log \left(c+d x^2\right)}{2 d^3}","\frac{b (b c-a d)}{d^3 \left(c+d x^2\right)}-\frac{(b c-a d)^2}{4 d^3 \left(c+d x^2\right)^2}+\frac{b^2 \log \left(c+d x^2\right)}{2 d^3}",1,"-(b*c - a*d)^2/(4*d^3*(c + d*x^2)^2) + (b*(b*c - a*d))/(d^3*(c + d*x^2)) + (b^2*Log[c + d*x^2])/(2*d^3)","A",3,2,20,0.1000,1,"{444, 43}"
193,1,116,0,0.0765431,"\int \frac{\left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(c + d*x^2)^3,x]","\frac{3 x \left(\frac{a^2}{c^2}-\frac{b^2}{d^2}\right)}{8 \left(c+d x^2\right)}+\frac{\left(3 a^2 d^2+2 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} d^{5/2}}-\frac{x \left(a+b x^2\right) (b c-a d)}{4 c d \left(c+d x^2\right)^2}","\frac{3 x \left(\frac{a^2}{c^2}-\frac{b^2}{d^2}\right)}{8 \left(c+d x^2\right)}+\frac{\left(3 a^2 d^2+2 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} d^{5/2}}-\frac{x \left(a+b x^2\right) (b c-a d)}{4 c d \left(c+d x^2\right)^2}",1,"-((b*c - a*d)*x*(a + b*x^2))/(4*c*d*(c + d*x^2)^2) + (3*(a^2/c^2 - b^2/d^2)*x)/(8*(c + d*x^2)) + ((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(5/2)*d^(5/2))","A",3,3,19,0.1579,1,"{413, 385, 205}"
194,1,86,0,0.0829324,"\int \frac{\left(a+b x^2\right)^2}{x \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x*(c + d*x^2)^3),x]","\frac{\frac{a^2}{c^2}-\frac{b^2}{d^2}}{2 \left(c+d x^2\right)}-\frac{a^2 \log \left(c+d x^2\right)}{2 c^3}+\frac{a^2 \log (x)}{c^3}+\frac{(b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","\frac{\frac{a^2}{c^2}-\frac{b^2}{d^2}}{2 \left(c+d x^2\right)}-\frac{a^2 \log \left(c+d x^2\right)}{2 c^3}+\frac{a^2 \log (x)}{c^3}+\frac{(b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"(b*c - a*d)^2/(4*c*d^2*(c + d*x^2)^2) + (a^2/c^2 - b^2/d^2)/(2*(c + d*x^2)) + (a^2*Log[x])/c^3 - (a^2*Log[c + d*x^2])/(2*c^3)","A",3,2,22,0.09091,1,"{446, 88}"
195,1,151,0,0.1088405,"\int \frac{\left(a+b x^2\right)^2}{x^2 \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x^2*(c + d*x^2)^3),x]","-\frac{x \left(5 a^2 d^2-2 a b c d+b^2 c^2\right)}{4 c^2 d \left(c+d x^2\right)^2}-\frac{a^2}{c x \left(c+d x^2\right)^2}+\frac{\left(3 a d (2 b c-5 a d)+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{7/2} d^{3/2}}+\frac{x \left(\frac{3 a (2 b c-5 a d)}{c^2}+\frac{b^2}{d}\right)}{8 c \left(c+d x^2\right)}","-\frac{x \left(5 a^2 d^2-2 a b c d+b^2 c^2\right)}{4 c^2 d \left(c+d x^2\right)^2}-\frac{a^2}{c x \left(c+d x^2\right)^2}+\frac{\left(3 a d (2 b c-5 a d)+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{7/2} d^{3/2}}+\frac{x \left(3 a d (2 b c-5 a d)+b^2 c^2\right)}{8 c^3 d \left(c+d x^2\right)}",1,"-(a^2/(c*x*(c + d*x^2)^2)) - ((b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*x)/(4*c^2*d*(c + d*x^2)^2) + ((b^2/d + (3*a*(2*b*c - 5*a*d))/c^2)*x)/(8*c*(c + d*x^2)) + ((b^2*c^2 + 3*a*d*(2*b*c - 5*a*d))*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(7/2)*d^(3/2))","A",4,4,22,0.1818,1,"{462, 385, 199, 205}"
196,1,106,0,0.1142063,"\int \frac{\left(a+b x^2\right)^2}{x^3 \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x^3*(c + d*x^2)^3),x]","-\frac{a^2}{2 c^3 x^2}+\frac{a (b c-a d)}{c^3 \left(c+d x^2\right)}-\frac{(b c-a d)^2}{4 c^2 d \left(c+d x^2\right)^2}-\frac{a (2 b c-3 a d) \log \left(c+d x^2\right)}{2 c^4}+\frac{a \log (x) (2 b c-3 a d)}{c^4}","-\frac{a^2}{2 c^3 x^2}+\frac{a (b c-a d)}{c^3 \left(c+d x^2\right)}-\frac{(b c-a d)^2}{4 c^2 d \left(c+d x^2\right)^2}-\frac{a (2 b c-3 a d) \log \left(c+d x^2\right)}{2 c^4}+\frac{a \log (x) (2 b c-3 a d)}{c^4}",1,"-a^2/(2*c^3*x^2) - (b*c - a*d)^2/(4*c^2*d*(c + d*x^2)^2) + (a*(b*c - a*d))/(c^3*(c + d*x^2)) + (a*(2*b*c - 3*a*d)*Log[x])/c^4 - (a*(2*b*c - 3*a*d)*Log[c + d*x^2])/(2*c^4)","A",3,2,22,0.09091,1,"{446, 88}"
197,1,161,0,0.1914234,"\int \frac{\left(a+b x^2\right)^2}{x^4 \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x^4*(c + d*x^2)^3),x]","\frac{x \left(7 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{12 c^3 \left(c+d x^2\right)^2}+\frac{\left(35 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{9/2} \sqrt{d}}-\frac{a^2}{3 c x^3 \left(c+d x^2\right)^2}+\frac{x (3 b c-7 a d)^2}{24 c^4 \left(c+d x^2\right)}-\frac{a (6 b c-7 a d)}{3 c^4 x}","\frac{x \left(7 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{12 c^3 \left(c+d x^2\right)^2}+\frac{\left(35 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{9/2} \sqrt{d}}-\frac{a^2}{3 c x^3 \left(c+d x^2\right)^2}+\frac{x (3 b c-7 a d)^2}{24 c^4 \left(c+d x^2\right)}-\frac{a (6 b c-7 a d)}{3 c^4 x}",1,"-(a*(6*b*c - 7*a*d))/(3*c^4*x) - a^2/(3*c*x^3*(c + d*x^2)^2) + ((3*b^2*c^2 - 6*a*b*c*d + 7*a^2*d^2)*x)/(12*c^3*(c + d*x^2)^2) + ((3*b*c - 7*a*d)^2*x)/(24*c^4*(c + d*x^2)) + ((3*b^2*c^2 - 30*a*b*c*d + 35*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(9/2)*Sqrt[d])","A",5,4,22,0.1818,1,"{462, 456, 453, 205}"
198,1,75,0,0.0852302,"\int \frac{x^5 \left(c+d x^2\right)}{a+b x^2} \, dx","Int[(x^5*(c + d*x^2))/(a + b*x^2),x]","\frac{a^2 (b c-a d) \log \left(a+b x^2\right)}{2 b^4}+\frac{x^4 (b c-a d)}{4 b^2}-\frac{a x^2 (b c-a d)}{2 b^3}+\frac{d x^6}{6 b}","\frac{a^2 (b c-a d) \log \left(a+b x^2\right)}{2 b^4}+\frac{x^4 (b c-a d)}{4 b^2}-\frac{a x^2 (b c-a d)}{2 b^3}+\frac{d x^6}{6 b}",1,"-(a*(b*c - a*d)*x^2)/(2*b^3) + ((b*c - a*d)*x^4)/(4*b^2) + (d*x^6)/(6*b) + (a^2*(b*c - a*d)*Log[a + b*x^2])/(2*b^4)","A",3,2,20,0.1000,1,"{446, 77}"
199,1,77,0,0.0516394,"\int \frac{x^4 \left(c+d x^2\right)}{a+b x^2} \, dx","Int[(x^4*(c + d*x^2))/(a + b*x^2),x]","\frac{a^{3/2} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^3 (b c-a d)}{3 b^2}-\frac{a x (b c-a d)}{b^3}+\frac{d x^5}{5 b}","\frac{a^{3/2} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^3 (b c-a d)}{3 b^2}-\frac{a x (b c-a d)}{b^3}+\frac{d x^5}{5 b}",1,"-((a*(b*c - a*d)*x)/b^3) + ((b*c - a*d)*x^3)/(3*b^2) + (d*x^5)/(5*b) + (a^(3/2)*(b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2)","A",4,3,20,0.1500,1,"{459, 302, 205}"
200,1,54,0,0.0559814,"\int \frac{x^3 \left(c+d x^2\right)}{a+b x^2} \, dx","Int[(x^3*(c + d*x^2))/(a + b*x^2),x]","\frac{x^2 (b c-a d)}{2 b^2}-\frac{a (b c-a d) \log \left(a+b x^2\right)}{2 b^3}+\frac{d x^4}{4 b}","\frac{x^2 (b c-a d)}{2 b^2}-\frac{a (b c-a d) \log \left(a+b x^2\right)}{2 b^3}+\frac{d x^4}{4 b}",1,"((b*c - a*d)*x^2)/(2*b^2) + (d*x^4)/(4*b) - (a*(b*c - a*d)*Log[a + b*x^2])/(2*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
201,1,58,0,0.034077,"\int \frac{x^2 \left(c+d x^2\right)}{a+b x^2} \, dx","Int[(x^2*(c + d*x^2))/(a + b*x^2),x]","\frac{x (b c-a d)}{b^2}-\frac{\sqrt{a} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{d x^3}{3 b}","\frac{x (b c-a d)}{b^2}-\frac{\sqrt{a} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2}}+\frac{d x^3}{3 b}",1,"((b*c - a*d)*x)/b^2 + (d*x^3)/(3*b) - (Sqrt[a]*(b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(5/2)","A",3,3,20,0.1500,1,"{459, 321, 205}"
202,1,35,0,0.0311675,"\int \frac{x \left(c+d x^2\right)}{a+b x^2} \, dx","Int[(x*(c + d*x^2))/(a + b*x^2),x]","\frac{(b c-a d) \log \left(a+b x^2\right)}{2 b^2}+\frac{d x^2}{2 b}","\frac{(b c-a d) \log \left(a+b x^2\right)}{2 b^2}+\frac{d x^2}{2 b}",1,"(d*x^2)/(2*b) + ((b*c - a*d)*Log[a + b*x^2])/(2*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
203,1,39,0,0.014759,"\int \frac{c+d x^2}{a+b x^2} \, dx","Int[(c + d*x^2)/(a + b*x^2),x]","\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{d x}{b}","\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2}}+\frac{d x}{b}",1,"(d*x)/b + ((b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(3/2))","A",2,2,17,0.1176,1,"{388, 205}"
204,1,34,0,0.0314507,"\int \frac{c+d x^2}{x \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)/(x*(a + b*x^2)),x]","\frac{c \log (x)}{a}-\frac{(b c-a d) \log \left(a+b x^2\right)}{2 a b}","\frac{c \log (x)}{a}-\frac{(b c-a d) \log \left(a+b x^2\right)}{2 a b}",1,"(c*Log[x])/a - ((b*c - a*d)*Log[a + b*x^2])/(2*a*b)","A",3,2,20,0.1000,1,"{446, 72}"
205,1,43,0,0.0203093,"\int \frac{c+d x^2}{x^2 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)/(x^2*(a + b*x^2)),x]","-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{c}{a x}","-\frac{(b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b}}-\frac{c}{a x}",1,"-(c/(a*x)) - ((b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[b])","A",2,2,20,0.1000,1,"{453, 205}"
206,1,50,0,0.045265,"\int \frac{c+d x^2}{x^3 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)/(x^3*(a + b*x^2)),x]","\frac{(b c-a d) \log \left(a+b x^2\right)}{2 a^2}-\frac{\log (x) (b c-a d)}{a^2}-\frac{c}{2 a x^2}","\frac{(b c-a d) \log \left(a+b x^2\right)}{2 a^2}-\frac{\log (x) (b c-a d)}{a^2}-\frac{c}{2 a x^2}",1,"-c/(2*a*x^2) - ((b*c - a*d)*Log[x])/a^2 + ((b*c - a*d)*Log[a + b*x^2])/(2*a^2)","A",3,2,20,0.1000,1,"{446, 77}"
207,1,59,0,0.0359807,"\int \frac{c+d x^2}{x^4 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)/(x^4*(a + b*x^2)),x]","\frac{b c-a d}{a^2 x}+\frac{\sqrt{b} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}-\frac{c}{3 a x^3}","\frac{b c-a d}{a^2 x}+\frac{\sqrt{b} (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2}}-\frac{c}{3 a x^3}",1,"-c/(3*a*x^3) + (b*c - a*d)/(a^2*x) + (Sqrt[b]*(b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/a^(5/2)","A",3,3,20,0.1500,1,"{453, 325, 205}"
208,1,103,0,0.1221495,"\int \frac{x^5 \left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(x^5*(c + d*x^2)^2)/(a + b*x^2),x]","\frac{a^2 (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^5}+\frac{d x^6 (2 b c-a d)}{6 b^2}+\frac{x^4 (b c-a d)^2}{4 b^3}-\frac{a x^2 (b c-a d)^2}{2 b^4}+\frac{d^2 x^8}{8 b}","\frac{a^2 (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^5}+\frac{d x^6 (2 b c-a d)}{6 b^2}+\frac{x^4 (b c-a d)^2}{4 b^3}-\frac{a x^2 (b c-a d)^2}{2 b^4}+\frac{d^2 x^8}{8 b}",1,"-(a*(b*c - a*d)^2*x^2)/(2*b^4) + ((b*c - a*d)^2*x^4)/(4*b^3) + (d*(2*b*c - a*d)*x^6)/(6*b^2) + (d^2*x^8)/(8*b) + (a^2*(b*c - a*d)^2*Log[a + b*x^2])/(2*b^5)","A",3,2,22,0.09091,1,"{446, 88}"
209,1,105,0,0.069337,"\int \frac{x^4 \left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(x^4*(c + d*x^2)^2)/(a + b*x^2),x]","\frac{a^{3/2} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{d x^5 (2 b c-a d)}{5 b^2}+\frac{x^3 (b c-a d)^2}{3 b^3}-\frac{a x (b c-a d)^2}{b^4}+\frac{d^2 x^7}{7 b}","\frac{a^{3/2} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{d x^5 (2 b c-a d)}{5 b^2}+\frac{x^3 (b c-a d)^2}{3 b^3}-\frac{a x (b c-a d)^2}{b^4}+\frac{d^2 x^7}{7 b}",1,"-((a*(b*c - a*d)^2*x)/b^4) + ((b*c - a*d)^2*x^3)/(3*b^3) + (d*(2*b*c - a*d)*x^5)/(5*b^2) + (d^2*x^7)/(7*b) + (a^(3/2)*(b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(9/2)","A",3,2,22,0.09091,1,"{461, 205}"
210,1,80,0,0.0863416,"\int \frac{x^3 \left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(x^3*(c + d*x^2)^2)/(a + b*x^2),x]","\frac{d x^4 (2 b c-a d)}{4 b^2}+\frac{x^2 (b c-a d)^2}{2 b^3}-\frac{a (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^4}+\frac{d^2 x^6}{6 b}","\frac{d x^4 (2 b c-a d)}{4 b^2}+\frac{x^2 (b c-a d)^2}{2 b^3}-\frac{a (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^4}+\frac{d^2 x^6}{6 b}",1,"((b*c - a*d)^2*x^2)/(2*b^3) + (d*(2*b*c - a*d)*x^4)/(4*b^2) + (d^2*x^6)/(6*b) - (a*(b*c - a*d)^2*Log[a + b*x^2])/(2*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
211,1,84,0,0.064104,"\int \frac{x^2 \left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(x^2*(c + d*x^2)^2)/(a + b*x^2),x]","\frac{d x^3 (2 b c-a d)}{3 b^2}+\frac{x (b c-a d)^2}{b^3}-\frac{\sqrt{a} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{d^2 x^5}{5 b}","\frac{d x^3 (2 b c-a d)}{3 b^2}+\frac{x (b c-a d)^2}{b^3}-\frac{\sqrt{a} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{7/2}}+\frac{d^2 x^5}{5 b}",1,"((b*c - a*d)^2*x)/b^3 + (d*(2*b*c - a*d)*x^3)/(3*b^2) + (d^2*x^5)/(5*b) - (Sqrt[a]*(b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(7/2)","A",3,2,22,0.09091,1,"{461, 205}"
212,1,61,0,0.0489202,"\int \frac{x \left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(x*(c + d*x^2)^2)/(a + b*x^2),x]","\frac{d x^2 (b c-a d)}{2 b^2}+\frac{(b c-a d)^2 \log \left(a+b x^2\right)}{2 b^3}+\frac{\left(c+d x^2\right)^2}{4 b}","\frac{d x^2 (b c-a d)}{2 b^2}+\frac{(b c-a d)^2 \log \left(a+b x^2\right)}{2 b^3}+\frac{\left(c+d x^2\right)^2}{4 b}",1,"(d*(b*c - a*d)*x^2)/(2*b^2) + (c + d*x^2)^2/(4*b) + ((b*c - a*d)^2*Log[a + b*x^2])/(2*b^3)","A",3,2,20,0.1000,1,"{444, 43}"
213,1,63,0,0.0422312,"\int \frac{\left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(c + d*x^2)^2/(a + b*x^2),x]","\frac{d x (2 b c-a d)}{b^2}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{d^2 x^3}{3 b}","\frac{d x (2 b c-a d)}{b^2}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{d^2 x^3}{3 b}",1,"(d*(2*b*c - a*d)*x)/b^2 + (d^2*x^3)/(3*b) + ((b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(5/2))","A",3,2,19,0.1053,1,"{390, 205}"
214,1,51,0,0.0482164,"\int \frac{\left(c+d x^2\right)^2}{x \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^2/(x*(a + b*x^2)),x]","-\frac{(b c-a d)^2 \log \left(a+b x^2\right)}{2 a b^2}+\frac{c^2 \log (x)}{a}+\frac{d^2 x^2}{2 b}","-\frac{(b c-a d)^2 \log \left(a+b x^2\right)}{2 a b^2}+\frac{c^2 \log (x)}{a}+\frac{d^2 x^2}{2 b}",1,"(d^2*x^2)/(2*b) + (c^2*Log[x])/a - ((b*c - a*d)^2*Log[a + b*x^2])/(2*a*b^2)","A",3,2,22,0.09091,1,"{446, 72}"
215,1,55,0,0.0498151,"\int \frac{\left(c+d x^2\right)^2}{x^2 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^2/(x^2*(a + b*x^2)),x]","-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} b^{3/2}}-\frac{c^2}{a x}+\frac{d^2 x}{b}","-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} b^{3/2}}-\frac{c^2}{a x}+\frac{d^2 x}{b}",1,"-(c^2/(a*x)) + (d^2*x)/b - ((b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*b^(3/2))","A",3,2,22,0.09091,1,"{461, 205}"
216,1,58,0,0.0577754,"\int \frac{\left(c+d x^2\right)^2}{x^3 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^2/(x^3*(a + b*x^2)),x]","\frac{(b c-a d)^2 \log \left(a+b x^2\right)}{2 a^2 b}-\frac{c \log (x) (b c-2 a d)}{a^2}-\frac{c^2}{2 a x^2}","\frac{(b c-a d)^2 \log \left(a+b x^2\right)}{2 a^2 b}-\frac{c \log (x) (b c-2 a d)}{a^2}-\frac{c^2}{2 a x^2}",1,"-c^2/(2*a*x^2) - (c*(b*c - 2*a*d)*Log[x])/a^2 + ((b*c - a*d)^2*Log[a + b*x^2])/(2*a^2*b)","A",3,2,22,0.09091,1,"{446, 88}"
217,1,64,0,0.0546262,"\int \frac{\left(c+d x^2\right)^2}{x^4 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^2/(x^4*(a + b*x^2)),x]","\frac{c (b c-2 a d)}{a^2 x}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b}}-\frac{c^2}{3 a x^3}","\frac{c (b c-2 a d)}{a^2 x}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b}}-\frac{c^2}{3 a x^3}",1,"-c^2/(3*a*x^3) + (c*(b*c - 2*a*d))/(a^2*x) + ((b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*Sqrt[b])","A",3,2,22,0.09091,1,"{461, 205}"
218,1,138,0,0.1783585,"\int \frac{x^5 \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^5*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{d x^6 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{6 b^3}+\frac{a^2 (b c-a d)^3 \log \left(a+b x^2\right)}{2 b^6}+\frac{d^2 x^8 (3 b c-a d)}{8 b^2}+\frac{x^4 (b c-a d)^3}{4 b^4}-\frac{a x^2 (b c-a d)^3}{2 b^5}+\frac{d^3 x^{10}}{10 b}","\frac{d x^6 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{6 b^3}+\frac{a^2 (b c-a d)^3 \log \left(a+b x^2\right)}{2 b^6}+\frac{d^2 x^8 (3 b c-a d)}{8 b^2}+\frac{x^4 (b c-a d)^3}{4 b^4}-\frac{a x^2 (b c-a d)^3}{2 b^5}+\frac{d^3 x^{10}}{10 b}",1,"-(a*(b*c - a*d)^3*x^2)/(2*b^5) + ((b*c - a*d)^3*x^4)/(4*b^4) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^6)/(6*b^3) + (d^2*(3*b*c - a*d)*x^8)/(8*b^2) + (d^3*x^10)/(10*b) + (a^2*(b*c - a*d)^3*Log[a + b*x^2])/(2*b^6)","A",3,2,22,0.09091,1,"{446, 88}"
219,1,140,0,0.0971003,"\int \frac{x^4 \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^4*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{d x^5 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{5 b^3}+\frac{a^{3/2} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{11/2}}+\frac{d^2 x^7 (3 b c-a d)}{7 b^2}+\frac{x^3 (b c-a d)^3}{3 b^4}-\frac{a x (b c-a d)^3}{b^5}+\frac{d^3 x^9}{9 b}","\frac{d x^5 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{5 b^3}+\frac{a^{3/2} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{11/2}}+\frac{d^2 x^7 (3 b c-a d)}{7 b^2}+\frac{x^3 (b c-a d)^3}{3 b^4}-\frac{a x (b c-a d)^3}{b^5}+\frac{d^3 x^9}{9 b}",1,"-((a*(b*c - a*d)^3*x)/b^5) + ((b*c - a*d)^3*x^3)/(3*b^4) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^5)/(5*b^3) + (d^2*(3*b*c - a*d)*x^7)/(7*b^2) + (d^3*x^9)/(9*b) + (a^(3/2)*(b*c - a*d)^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(11/2)","A",3,2,22,0.09091,1,"{461, 205}"
220,1,115,0,0.1247934,"\int \frac{x^3 \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^3*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{d x^4 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{4 b^3}+\frac{d^2 x^6 (3 b c-a d)}{6 b^2}+\frac{x^2 (b c-a d)^3}{2 b^4}-\frac{a (b c-a d)^3 \log \left(a+b x^2\right)}{2 b^5}+\frac{d^3 x^8}{8 b}","\frac{d x^4 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{4 b^3}+\frac{d^2 x^6 (3 b c-a d)}{6 b^2}+\frac{x^2 (b c-a d)^3}{2 b^4}-\frac{a (b c-a d)^3 \log \left(a+b x^2\right)}{2 b^5}+\frac{d^3 x^8}{8 b}",1,"((b*c - a*d)^3*x^2)/(2*b^4) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^4)/(4*b^3) + (d^2*(3*b*c - a*d)*x^6)/(6*b^2) + (d^3*x^8)/(8*b) - (a*(b*c - a*d)^3*Log[a + b*x^2])/(2*b^5)","A",3,2,22,0.09091,1,"{446, 77}"
221,1,119,0,0.0847938,"\int \frac{x^2 \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^2*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{d x^3 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{3 b^3}+\frac{d^2 x^5 (3 b c-a d)}{5 b^2}+\frac{x (b c-a d)^3}{b^4}-\frac{\sqrt{a} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{d^3 x^7}{7 b}","\frac{d x^3 \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{3 b^3}+\frac{d^2 x^5 (3 b c-a d)}{5 b^2}+\frac{x (b c-a d)^3}{b^4}-\frac{\sqrt{a} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{9/2}}+\frac{d^3 x^7}{7 b}",1,"((b*c - a*d)^3*x)/b^4 + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^3)/(3*b^3) + (d^2*(3*b*c - a*d)*x^5)/(5*b^2) + (d^3*x^7)/(7*b) - (Sqrt[a]*(b*c - a*d)^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/b^(9/2)","A",3,2,22,0.09091,1,"{461, 205}"
222,1,87,0,0.0811352,"\int \frac{x \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{d x^2 (b c-a d)^2}{2 b^3}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{4 b^2}+\frac{(b c-a d)^3 \log \left(a+b x^2\right)}{2 b^4}+\frac{\left(c+d x^2\right)^3}{6 b}","\frac{d x^2 (b c-a d)^2}{2 b^3}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{4 b^2}+\frac{(b c-a d)^3 \log \left(a+b x^2\right)}{2 b^4}+\frac{\left(c+d x^2\right)^3}{6 b}",1,"(d*(b*c - a*d)^2*x^2)/(2*b^3) + ((b*c - a*d)*(c + d*x^2)^2)/(4*b^2) + (c + d*x^2)^3/(6*b) + ((b*c - a*d)^3*Log[a + b*x^2])/(2*b^4)","A",3,2,20,0.1000,1,"{444, 43}"
223,1,98,0,0.0555838,"\int \frac{\left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(c + d*x^2)^3/(a + b*x^2),x]","\frac{d x \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}+\frac{d^2 x^3 (3 b c-a d)}{3 b^2}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}+\frac{d^3 x^5}{5 b}","\frac{d x \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}+\frac{d^2 x^3 (3 b c-a d)}{3 b^2}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} b^{7/2}}+\frac{d^3 x^5}{5 b}",1,"(d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x)/b^3 + (d^2*(3*b*c - a*d)*x^3)/(3*b^2) + (d^3*x^5)/(5*b) + ((b*c - a*d)^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*b^(7/2))","A",3,2,19,0.1053,1,"{390, 205}"
224,1,73,0,0.0772613,"\int \frac{\left(c+d x^2\right)^3}{x \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x*(a + b*x^2)),x]","\frac{d^2 x^2 (3 b c-a d)}{2 b^2}-\frac{(b c-a d)^3 \log \left(a+b x^2\right)}{2 a b^3}+\frac{c^3 \log (x)}{a}+\frac{d^3 x^4}{4 b}","\frac{d^2 x^2 (3 b c-a d)}{2 b^2}-\frac{(b c-a d)^3 \log \left(a+b x^2\right)}{2 a b^3}+\frac{c^3 \log (x)}{a}+\frac{d^3 x^4}{4 b}",1,"(d^2*(3*b*c - a*d)*x^2)/(2*b^2) + (d^3*x^4)/(4*b) + (c^3*Log[x])/a - ((b*c - a*d)^3*Log[a + b*x^2])/(2*a*b^3)","A",3,2,22,0.09091,1,"{446, 72}"
225,1,77,0,0.064137,"\int \frac{\left(c+d x^2\right)^3}{x^2 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^2*(a + b*x^2)),x]","-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} b^{5/2}}+\frac{d^2 x (3 b c-a d)}{b^2}-\frac{c^3}{a x}+\frac{d^3 x^3}{3 b}","-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} b^{5/2}}+\frac{d^2 x (3 b c-a d)}{b^2}-\frac{c^3}{a x}+\frac{d^3 x^3}{3 b}",1,"-(c^3/(a*x)) + (d^2*(3*b*c - a*d)*x)/b^2 + (d^3*x^3)/(3*b) - ((b*c - a*d)^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*b^(5/2))","A",3,2,22,0.09091,1,"{461, 205}"
226,1,73,0,0.0759506,"\int \frac{\left(c+d x^2\right)^3}{x^3 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^3*(a + b*x^2)),x]","\frac{(b c-a d)^3 \log \left(a+b x^2\right)}{2 a^2 b^2}-\frac{c^2 \log (x) (b c-3 a d)}{a^2}-\frac{c^3}{2 a x^2}+\frac{d^3 x^2}{2 b}","\frac{(b c-a d)^3 \log \left(a+b x^2\right)}{2 a^2 b^2}-\frac{c^2 \log (x) (b c-3 a d)}{a^2}-\frac{c^3}{2 a x^2}+\frac{d^3 x^2}{2 b}",1,"-c^3/(2*a*x^2) + (d^3*x^2)/(2*b) - (c^2*(b*c - 3*a*d)*Log[x])/a^2 + ((b*c - a*d)^3*Log[a + b*x^2])/(2*a^2*b^2)","A",3,2,22,0.09091,1,"{446, 88}"
227,1,74,0,0.0657843,"\int \frac{\left(c+d x^2\right)^3}{x^4 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^4*(a + b*x^2)),x]","\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} b^{3/2}}+\frac{c^2 (b c-3 a d)}{a^2 x}-\frac{c^3}{3 a x^3}+\frac{d^3 x}{b}","\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} b^{3/2}}+\frac{c^2 (b c-3 a d)}{a^2 x}-\frac{c^3}{3 a x^3}+\frac{d^3 x}{b}",1,"-c^3/(3*a*x^3) + (c^2*(b*c - 3*a*d))/(a^2*x) + (d^3*x)/b + ((b*c - a*d)^3*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*b^(3/2))","A",3,2,22,0.09091,1,"{461, 205}"
228,1,70,0,0.0668481,"\int \frac{x^5}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^5/((a + b*x^2)*(c + d*x^2)),x]","\frac{a^2 \log \left(a+b x^2\right)}{2 b^2 (b c-a d)}-\frac{c^2 \log \left(c+d x^2\right)}{2 d^2 (b c-a d)}+\frac{x^2}{2 b d}","\frac{a^2 \log \left(a+b x^2\right)}{2 b^2 (b c-a d)}-\frac{c^2 \log \left(c+d x^2\right)}{2 d^2 (b c-a d)}+\frac{x^2}{2 b d}",1,"x^2/(2*b*d) + (a^2*Log[a + b*x^2])/(2*b^2*(b*c - a*d)) - (c^2*Log[c + d*x^2])/(2*d^2*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
229,1,78,0,0.0834722,"\int \frac{x^4}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^4/((a + b*x^2)*(c + d*x^2)),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2} (b c-a d)}-\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{d^{3/2} (b c-a d)}+\frac{x}{b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2} (b c-a d)}-\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{d^{3/2} (b c-a d)}+\frac{x}{b d}",1,"x/(b*d) + (a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b^(3/2)*(b*c - a*d)) - (c^(3/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(d^(3/2)*(b*c - a*d))","A",4,3,22,0.1364,1,"{479, 522, 205}"
230,1,53,0,0.0490427,"\int \frac{x^3}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^3/((a + b*x^2)*(c + d*x^2)),x]","\frac{c \log \left(c+d x^2\right)}{2 d (b c-a d)}-\frac{a \log \left(a+b x^2\right)}{2 b (b c-a d)}","\frac{c \log \left(c+d x^2\right)}{2 d (b c-a d)}-\frac{a \log \left(a+b x^2\right)}{2 b (b c-a d)}",1,"-(a*Log[a + b*x^2])/(2*b*(b*c - a*d)) + (c*Log[c + d*x^2])/(2*d*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
231,1,70,0,0.0340432,"\int \frac{x^2}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^2/((a + b*x^2)*(c + d*x^2)),x]","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{d} (b c-a d)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} (b c-a d)}","\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{d} (b c-a d)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} (b c-a d)}",1,"-((Sqrt[a]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*(b*c - a*d))) + (Sqrt[c]*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(Sqrt[d]*(b*c - a*d))","A",3,2,22,0.09091,1,"{481, 205}"
232,1,45,0,0.0262701,"\int \frac{x}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x/((a + b*x^2)*(c + d*x^2)),x]","\frac{\log \left(a+b x^2\right)}{2 (b c-a d)}-\frac{\log \left(c+d x^2\right)}{2 (b c-a d)}","\frac{\log \left(a+b x^2\right)}{2 (b c-a d)}-\frac{\log \left(c+d x^2\right)}{2 (b c-a d)}",1,"Log[a + b*x^2]/(2*(b*c - a*d)) - Log[c + d*x^2]/(2*(b*c - a*d))","A",4,3,20,0.1500,1,"{444, 36, 31}"
233,1,70,0,0.0268952,"\int \frac{1}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/((a + b*x^2)*(c + d*x^2)),x]","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} (b c-a d)}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{c} (b c-a d)}","\frac{\sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} (b c-a d)}-\frac{\sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{c} (b c-a d)}",1,"(Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*(b*c - a*d)) - (Sqrt[d]*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(Sqrt[c]*(b*c - a*d))","A",3,2,19,0.1053,1,"{391, 205}"
234,1,62,0,0.0611619,"\int \frac{1}{x \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x*(a + b*x^2)*(c + d*x^2)),x]","-\frac{b \log \left(a+b x^2\right)}{2 a (b c-a d)}+\frac{d \log \left(c+d x^2\right)}{2 c (b c-a d)}+\frac{\log (x)}{a c}","-\frac{b \log \left(a+b x^2\right)}{2 a (b c-a d)}+\frac{d \log \left(c+d x^2\right)}{2 c (b c-a d)}+\frac{\log (x)}{a c}",1,"Log[x]/(a*c) - (b*Log[a + b*x^2])/(2*a*(b*c - a*d)) + (d*Log[c + d*x^2])/(2*c*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
235,1,81,0,0.0855364,"\int \frac{1}{x^2 \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^2*(a + b*x^2)*(c + d*x^2)),x]","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} (b c-a d)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{3/2} (b c-a d)}-\frac{1}{a c x}","-\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} (b c-a d)}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{3/2} (b c-a d)}-\frac{1}{a c x}",1,"-(1/(a*c*x)) - (b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*(b*c - a*d)) + (d^(3/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*(b*c - a*d))","A",4,3,22,0.1364,1,"{480, 522, 205}"
236,1,87,0,0.0905256,"\int \frac{1}{x^3 \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^3*(a + b*x^2)*(c + d*x^2)),x]","\frac{b^2 \log \left(a+b x^2\right)}{2 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^2\right)}{2 c^2 (b c-a d)}-\frac{1}{2 a c x^2}","\frac{b^2 \log \left(a+b x^2\right)}{2 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^2\right)}{2 c^2 (b c-a d)}-\frac{1}{2 a c x^2}",1,"-1/(2*a*c*x^2) - ((b*c + a*d)*Log[x])/(a^2*c^2) + (b^2*Log[a + b*x^2])/(2*a^2*(b*c - a*d)) - (d^2*Log[c + d*x^2])/(2*c^2*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
237,1,100,0,0.1769158,"\int \frac{1}{x^4 \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^4*(a + b*x^2)*(c + d*x^2)),x]","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{5/2} (b c-a d)}-\frac{1}{3 a c x^3}","\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} (b c-a d)}+\frac{a d+b c}{a^2 c^2 x}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{5/2} (b c-a d)}-\frac{1}{3 a c x^3}",1,"-1/(3*a*c*x^3) + (b*c + a*d)/(a^2*c^2*x) + (b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*(b*c - a*d)) - (d^(5/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*(b*c - a*d))","A",5,4,22,0.1818,1,"{480, 583, 522, 205}"
238,1,119,0,0.1274458,"\int \frac{1}{x^5 \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^5*(a + b*x^2)*(c + d*x^2)),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^2\right)}{2 a^3 (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}+\frac{d^3 \log \left(c+d x^2\right)}{2 c^3 (b c-a d)}-\frac{1}{4 a c x^4}","\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^2\right)}{2 a^3 (b c-a d)}+\frac{a d+b c}{2 a^2 c^2 x^2}+\frac{d^3 \log \left(c+d x^2\right)}{2 c^3 (b c-a d)}-\frac{1}{4 a c x^4}",1,"-1/(4*a*c*x^4) + (b*c + a*d)/(2*a^2*c^2*x^2) + ((b^2*c^2 + a*b*c*d + a^2*d^2)*Log[x])/(a^3*c^3) - (b^3*Log[a + b*x^2])/(2*a^3*(b*c - a*d)) + (d^3*Log[c + d*x^2])/(2*c^3*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
239,1,134,0,0.2270017,"\int \frac{1}{x^6 \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^6*(a + b*x^2)*(c + d*x^2)),x]","-\frac{a^2 d^2+a b c d+b^2 c^2}{a^3 c^3 x}-\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2} (b c-a d)}+\frac{a d+b c}{3 a^2 c^2 x^3}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{7/2} (b c-a d)}-\frac{1}{5 a c x^5}","-\frac{a^2 d^2+a b c d+b^2 c^2}{a^3 c^3 x}-\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{7/2} (b c-a d)}+\frac{a d+b c}{3 a^2 c^2 x^3}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{7/2} (b c-a d)}-\frac{1}{5 a c x^5}",1,"-1/(5*a*c*x^5) + (b*c + a*d)/(3*a^2*c^2*x^3) - (b^2*c^2 + a*b*c*d + a^2*d^2)/(a^3*c^3*x) - (b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(7/2)*(b*c - a*d)) + (d^(7/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(7/2)*(b*c - a*d))","A",6,4,22,0.1818,1,"{480, 583, 522, 205}"
240,1,155,0,0.1690093,"\int \frac{1}{x^7 \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^7*(a + b*x^2)*(c + d*x^2)),x]","-\frac{a^2 d^2+a b c d+b^2 c^2}{2 a^3 c^3 x^2}-\frac{\log (x) (a d+b c) \left(a^2 d^2+b^2 c^2\right)}{a^4 c^4}+\frac{b^4 \log \left(a+b x^2\right)}{2 a^4 (b c-a d)}+\frac{a d+b c}{4 a^2 c^2 x^4}-\frac{d^4 \log \left(c+d x^2\right)}{2 c^4 (b c-a d)}-\frac{1}{6 a c x^6}","-\frac{a^2 d^2+a b c d+b^2 c^2}{2 a^3 c^3 x^2}-\frac{\log (x) (a d+b c) \left(a^2 d^2+b^2 c^2\right)}{a^4 c^4}+\frac{b^4 \log \left(a+b x^2\right)}{2 a^4 (b c-a d)}+\frac{a d+b c}{4 a^2 c^2 x^4}-\frac{d^4 \log \left(c+d x^2\right)}{2 c^4 (b c-a d)}-\frac{1}{6 a c x^6}",1,"-1/(6*a*c*x^6) + (b*c + a*d)/(4*a^2*c^2*x^4) - (b^2*c^2 + a*b*c*d + a^2*d^2)/(2*a^3*c^3*x^2) - ((b*c + a*d)*(b^2*c^2 + a^2*d^2)*Log[x])/(a^4*c^4) + (b^4*Log[a + b*x^2])/(2*a^4*(b*c - a*d)) - (d^4*Log[c + d*x^2])/(2*c^4*(b*c - a*d))","A",3,2,22,0.09091,1,"{446, 72}"
241,1,93,0,0.0865865,"\int \frac{x^5}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x^5/((a + b*x^2)^2*(c + d*x^2)),x]","-\frac{a^2}{2 b^2 \left(a+b x^2\right) (b c-a d)}-\frac{a (2 b c-a d) \log \left(a+b x^2\right)}{2 b^2 (b c-a d)^2}+\frac{c^2 \log \left(c+d x^2\right)}{2 d (b c-a d)^2}","-\frac{a^2}{2 b^2 \left(a+b x^2\right) (b c-a d)}-\frac{a (2 b c-a d) \log \left(a+b x^2\right)}{2 b^2 (b c-a d)^2}+\frac{c^2 \log \left(c+d x^2\right)}{2 d (b c-a d)^2}",1,"-a^2/(2*b^2*(b*c - a*d)*(a + b*x^2)) - (a*(2*b*c - a*d)*Log[a + b*x^2])/(2*b^2*(b*c - a*d)^2) + (c^2*Log[c + d*x^2])/(2*d*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 88}"
242,1,108,0,0.0846266,"\int \frac{x^4}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^4/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} (b c-a d)^2}+\frac{\sqrt{c} (b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 d^{3/2} (b c-a d)^2}-\frac{c x}{2 d \left(c+d x^2\right) (b c-a d)}","\frac{a^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{b} (b c-a d)^2}+\frac{\sqrt{c} (b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 d^{3/2} (b c-a d)^2}-\frac{c x}{2 d \left(c+d x^2\right) (b c-a d)}",1,"-(c*x)/(2*d*(b*c - a*d)*(c + d*x^2)) + (a^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[b]*(b*c - a*d)^2) + (Sqrt[c]*(b*c - 3*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*d^(3/2)*(b*c - a*d)^2)","A",4,3,22,0.1364,1,"{470, 522, 205}"
243,1,74,0,0.0642443,"\int \frac{x^3}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^3/((a + b*x^2)*(c + d*x^2)^2),x]","-\frac{c}{2 d \left(c+d x^2\right) (b c-a d)}-\frac{a \log \left(a+b x^2\right)}{2 (b c-a d)^2}+\frac{a \log \left(c+d x^2\right)}{2 (b c-a d)^2}","-\frac{c}{2 d \left(c+d x^2\right) (b c-a d)}-\frac{a \log \left(a+b x^2\right)}{2 (b c-a d)^2}+\frac{a \log \left(c+d x^2\right)}{2 (b c-a d)^2}",1,"-c/(2*d*(b*c - a*d)*(c + d*x^2)) - (a*Log[a + b*x^2])/(2*(b*c - a*d)^2) + (a*Log[c + d*x^2])/(2*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 77}"
244,1,104,0,0.0631776,"\int \frac{x^2}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^2/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{x}{2 \left(c+d x^2\right) (b c-a d)}-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{(b c-a d)^2}+\frac{(a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d} (b c-a d)^2}","\frac{x}{2 \left(c+d x^2\right) (b c-a d)}-\frac{\sqrt{a} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{(b c-a d)^2}+\frac{(a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} \sqrt{d} (b c-a d)^2}",1,"x/(2*(b*c - a*d)*(c + d*x^2)) - (Sqrt[a]*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b*c - a*d)^2 + ((b*c + a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*Sqrt[c]*Sqrt[d]*(b*c - a*d)^2)","A",4,3,22,0.1364,1,"{471, 522, 205}"
245,1,70,0,0.0541384,"\int \frac{x}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{1}{2 \left(c+d x^2\right) (b c-a d)}+\frac{b \log \left(a+b x^2\right)}{2 (b c-a d)^2}-\frac{b \log \left(c+d x^2\right)}{2 (b c-a d)^2}","\frac{1}{2 \left(c+d x^2\right) (b c-a d)}+\frac{b \log \left(a+b x^2\right)}{2 (b c-a d)^2}-\frac{b \log \left(c+d x^2\right)}{2 (b c-a d)^2}",1,"1/(2*(b*c - a*d)*(c + d*x^2)) + (b*Log[a + b*x^2])/(2*(b*c - a*d)^2) - (b*Log[c + d*x^2])/(2*(b*c - a*d)^2)","A",3,2,20,0.1000,1,"{444, 44}"
246,1,109,0,0.0790209,"\int \frac{1}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} (b c-a d)^2}-\frac{\sqrt{d} (3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} (b c-a d)^2}-\frac{d x}{2 c \left(c+d x^2\right) (b c-a d)}","\frac{b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} (b c-a d)^2}-\frac{\sqrt{d} (3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} (b c-a d)^2}-\frac{d x}{2 c \left(c+d x^2\right) (b c-a d)}",1,"-(d*x)/(2*c*(b*c - a*d)*(c + d*x^2)) + (b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*(b*c - a*d)^2) - (Sqrt[d]*(3*b*c - a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(3/2)*(b*c - a*d)^2)","A",4,3,19,0.1579,1,"{414, 522, 205}"
247,1,100,0,0.1013407,"\int \frac{1}{x \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x*(a + b*x^2)*(c + d*x^2)^2),x]","-\frac{b^2 \log \left(a+b x^2\right)}{2 a (b c-a d)^2}+\frac{d (2 b c-a d) \log \left(c+d x^2\right)}{2 c^2 (b c-a d)^2}-\frac{d}{2 c \left(c+d x^2\right) (b c-a d)}+\frac{\log (x)}{a c^2}","-\frac{b^2 \log \left(a+b x^2\right)}{2 a (b c-a d)^2}+\frac{d (2 b c-a d) \log \left(c+d x^2\right)}{2 c^2 (b c-a d)^2}-\frac{d}{2 c \left(c+d x^2\right) (b c-a d)}+\frac{\log (x)}{a c^2}",1,"-d/(2*c*(b*c - a*d)*(c + d*x^2)) + Log[x]/(a*c^2) - (b^2*Log[a + b*x^2])/(2*a*(b*c - a*d)^2) + (d*(2*b*c - a*d)*Log[c + d*x^2])/(2*c^2*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 72}"
248,1,144,0,0.1983737,"\int \frac{1}{x^2 \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x^2*(a + b*x^2)*(c + d*x^2)^2),x]","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} (b c-a d)^2}+\frac{d^{3/2} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{5/2} (b c-a d)^2}-\frac{2 b c-3 a d}{2 a c^2 x (b c-a d)}-\frac{d}{2 c x \left(c+d x^2\right) (b c-a d)}","-\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} (b c-a d)^2}+\frac{d^{3/2} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{5/2} (b c-a d)^2}-\frac{2 b c-3 a d}{2 a c^2 x (b c-a d)}-\frac{d}{2 c x \left(c+d x^2\right) (b c-a d)}",1,"-(2*b*c - 3*a*d)/(2*a*c^2*(b*c - a*d)*x) - d/(2*c*(b*c - a*d)*x*(c + d*x^2)) - (b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*(b*c - a*d)^2) + (d^(3/2)*(5*b*c - 3*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(5/2)*(b*c - a*d)^2)","A",5,4,22,0.1818,1,"{472, 583, 522, 205}"
249,1,126,0,0.1444646,"\int \frac{1}{x^3 \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x^3*(a + b*x^2)*(c + d*x^2)^2),x]","\frac{b^3 \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^2}-\frac{\log (x) (2 a d+b c)}{a^2 c^3}+\frac{d^2}{2 c^2 \left(c+d x^2\right) (b c-a d)}-\frac{d^2 (3 b c-2 a d) \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^2}-\frac{1}{2 a c^2 x^2}","\frac{b^3 \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^2}-\frac{\log (x) (2 a d+b c)}{a^2 c^3}+\frac{d^2}{2 c^2 \left(c+d x^2\right) (b c-a d)}-\frac{d^2 (3 b c-2 a d) \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^2}-\frac{1}{2 a c^2 x^2}",1,"-1/(2*a*c^2*x^2) + d^2/(2*c^2*(b*c - a*d)*(c + d*x^2)) - ((b*c + 2*a*d)*Log[x])/(a^2*c^3) + (b^3*Log[a + b*x^2])/(2*a^2*(b*c - a*d)^2) - (d^2*(3*b*c - 2*a*d)*Log[c + d*x^2])/(2*c^3*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 88}"
250,1,189,0,0.2720609,"\int \frac{1}{x^4 \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x^4*(a + b*x^2)*(c + d*x^2)^2),x]","\frac{-5 a^2 d^2+2 a b c d+2 b^2 c^2}{2 a^2 c^3 x (b c-a d)}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} (b c-a d)^2}-\frac{d^{5/2} (7 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{7/2} (b c-a d)^2}-\frac{2 b c-5 a d}{6 a c^2 x^3 (b c-a d)}-\frac{d}{2 c x^3 \left(c+d x^2\right) (b c-a d)}","\frac{-5 a^2 d^2+2 a b c d+2 b^2 c^2}{2 a^2 c^3 x (b c-a d)}+\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} (b c-a d)^2}-\frac{d^{5/2} (7 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{7/2} (b c-a d)^2}-\frac{2 b c-5 a d}{6 a c^2 x^3 (b c-a d)}-\frac{d}{2 c x^3 \left(c+d x^2\right) (b c-a d)}",1,"-(2*b*c - 5*a*d)/(6*a*c^2*(b*c - a*d)*x^3) + (2*b^2*c^2 + 2*a*b*c*d - 5*a^2*d^2)/(2*a^2*c^3*(b*c - a*d)*x) - d/(2*c*(b*c - a*d)*x^3*(c + d*x^2)) + (b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*(b*c - a*d)^2) - (d^(5/2)*(7*b*c - 5*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(7/2)*(b*c - a*d)^2)","A",6,4,22,0.1818,1,"{472, 583, 522, 205}"
251,1,116,0,0.113149,"\int \frac{x^5}{\left(a+b x^2\right)^3 \left(c+d x^2\right)} \, dx","Int[x^5/((a + b*x^2)^3*(c + d*x^2)),x]","-\frac{a^2}{4 b^2 \left(a+b x^2\right)^2 (b c-a d)}+\frac{a (2 b c-a d)}{2 b^2 \left(a+b x^2\right) (b c-a d)^2}+\frac{c^2 \log \left(a+b x^2\right)}{2 (b c-a d)^3}-\frac{c^2 \log \left(c+d x^2\right)}{2 (b c-a d)^3}","-\frac{a^2}{4 b^2 \left(a+b x^2\right)^2 (b c-a d)}+\frac{a (2 b c-a d)}{2 b^2 \left(a+b x^2\right) (b c-a d)^2}+\frac{c^2 \log \left(a+b x^2\right)}{2 (b c-a d)^3}-\frac{c^2 \log \left(c+d x^2\right)}{2 (b c-a d)^3}",1,"-a^2/(4*b^2*(b*c - a*d)*(a + b*x^2)^2) + (a*(2*b*c - a*d))/(2*b^2*(b*c - a*d)^2*(a + b*x^2)) + (c^2*Log[a + b*x^2])/(2*(b*c - a*d)^3) - (c^2*Log[c + d*x^2])/(2*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 88}"
252,1,157,0,0.1720412,"\int \frac{x^4}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x^4/((a + b*x^2)*(c + d*x^2)^3),x]","\frac{\left(-3 a^2 d^2-6 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 \sqrt{c} d^{3/2} (b c-a d)^3}+\frac{a^{3/2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{(b c-a d)^3}+\frac{x (b c-5 a d)}{8 d \left(c+d x^2\right) (b c-a d)^2}-\frac{c x}{4 d \left(c+d x^2\right)^2 (b c-a d)}","\frac{\left(-3 a^2 d^2-6 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 \sqrt{c} d^{3/2} (b c-a d)^3}+\frac{a^{3/2} \sqrt{b} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{(b c-a d)^3}+\frac{x (b c-5 a d)}{8 d \left(c+d x^2\right) (b c-a d)^2}-\frac{c x}{4 d \left(c+d x^2\right)^2 (b c-a d)}",1,"-(c*x)/(4*d*(b*c - a*d)*(c + d*x^2)^2) + ((b*c - 5*a*d)*x)/(8*d*(b*c - a*d)^2*(c + d*x^2)) + (a^(3/2)*Sqrt[b]*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b*c - a*d)^3 + ((b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*Sqrt[c]*d^(3/2)*(b*c - a*d)^3)","A",5,4,22,0.1818,1,"{470, 527, 522, 205}"
253,1,100,0,0.0924123,"\int \frac{x^3}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x^3/((a + b*x^2)*(c + d*x^2)^3),x]","-\frac{a}{2 \left(c+d x^2\right) (b c-a d)^2}-\frac{c}{4 d \left(c+d x^2\right)^2 (b c-a d)}-\frac{a b \log \left(a+b x^2\right)}{2 (b c-a d)^3}+\frac{a b \log \left(c+d x^2\right)}{2 (b c-a d)^3}","-\frac{a}{2 \left(c+d x^2\right) (b c-a d)^2}-\frac{c}{4 d \left(c+d x^2\right)^2 (b c-a d)}-\frac{a b \log \left(a+b x^2\right)}{2 (b c-a d)^3}+\frac{a b \log \left(c+d x^2\right)}{2 (b c-a d)^3}",1,"-c/(4*d*(b*c - a*d)*(c + d*x^2)^2) - a/(2*(b*c - a*d)^2*(c + d*x^2)) - (a*b*Log[a + b*x^2])/(2*(b*c - a*d)^3) + (a*b*Log[c + d*x^2])/(2*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 77}"
254,1,155,0,0.1402161,"\int \frac{x^2}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x^2/((a + b*x^2)*(c + d*x^2)^3),x]","\frac{\left(-a^2 d^2+6 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{3/2} \sqrt{d} (b c-a d)^3}-\frac{\sqrt{a} b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{(b c-a d)^3}+\frac{x (a d+3 b c)}{8 c \left(c+d x^2\right) (b c-a d)^2}+\frac{x}{4 \left(c+d x^2\right)^2 (b c-a d)}","\frac{\left(-a^2 d^2+6 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{3/2} \sqrt{d} (b c-a d)^3}-\frac{\sqrt{a} b^{3/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{(b c-a d)^3}+\frac{x (a d+3 b c)}{8 c \left(c+d x^2\right) (b c-a d)^2}+\frac{x}{4 \left(c+d x^2\right)^2 (b c-a d)}",1,"x/(4*(b*c - a*d)*(c + d*x^2)^2) + ((3*b*c + a*d)*x)/(8*c*(b*c - a*d)^2*(c + d*x^2)) - (Sqrt[a]*b^(3/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b*c - a*d)^3 + ((3*b^2*c^2 + 6*a*b*c*d - a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(3/2)*Sqrt[d]*(b*c - a*d)^3)","A",5,4,22,0.1818,1,"{471, 527, 522, 205}"
255,1,98,0,0.0749927,"\int \frac{x}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x/((a + b*x^2)*(c + d*x^2)^3),x]","\frac{b^2 \log \left(a+b x^2\right)}{2 (b c-a d)^3}-\frac{b^2 \log \left(c+d x^2\right)}{2 (b c-a d)^3}+\frac{b}{2 \left(c+d x^2\right) (b c-a d)^2}+\frac{1}{4 \left(c+d x^2\right)^2 (b c-a d)}","\frac{b^2 \log \left(a+b x^2\right)}{2 (b c-a d)^3}-\frac{b^2 \log \left(c+d x^2\right)}{2 (b c-a d)^3}+\frac{b}{2 \left(c+d x^2\right) (b c-a d)^2}+\frac{1}{4 \left(c+d x^2\right)^2 (b c-a d)}",1,"1/(4*(b*c - a*d)*(c + d*x^2)^2) + b/(2*(b*c - a*d)^2*(c + d*x^2)) + (b^2*Log[a + b*x^2])/(2*(b*c - a*d)^3) - (b^2*Log[c + d*x^2])/(2*(b*c - a*d)^3)","A",3,2,20,0.1000,1,"{444, 44}"
256,1,160,0,0.1888464,"\int \frac{1}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/((a + b*x^2)*(c + d*x^2)^3),x]","-\frac{\sqrt{d} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} (b c-a d)^3}+\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} (b c-a d)^3}-\frac{d x (7 b c-3 a d)}{8 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d x}{4 c \left(c+d x^2\right)^2 (b c-a d)}","-\frac{\sqrt{d} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} (b c-a d)^3}+\frac{b^{5/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} (b c-a d)^3}-\frac{d x (7 b c-3 a d)}{8 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d x}{4 c \left(c+d x^2\right)^2 (b c-a d)}",1,"-(d*x)/(4*c*(b*c - a*d)*(c + d*x^2)^2) - (d*(7*b*c - 3*a*d)*x)/(8*c^2*(b*c - a*d)^2*(c + d*x^2)) + (b^(5/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*(b*c - a*d)^3) - (Sqrt[d]*(15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(5/2)*(b*c - a*d)^3)","A",5,4,19,0.2105,1,"{414, 527, 522, 205}"
257,1,149,0,0.1523683,"\int \frac{1}{x \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x*(a + b*x^2)*(c + d*x^2)^3),x]","\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^3}-\frac{b^3 \log \left(a+b x^2\right)}{2 a (b c-a d)^3}-\frac{d (2 b c-a d)}{2 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c \left(c+d x^2\right)^2 (b c-a d)}+\frac{\log (x)}{a c^3}","\frac{d \left(a^2 d^2-3 a b c d+3 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^3}-\frac{b^3 \log \left(a+b x^2\right)}{2 a (b c-a d)^3}-\frac{d (2 b c-a d)}{2 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c \left(c+d x^2\right)^2 (b c-a d)}+\frac{\log (x)}{a c^3}",1,"-d/(4*c*(b*c - a*d)*(c + d*x^2)^2) - (d*(2*b*c - a*d))/(2*c^2*(b*c - a*d)^2*(c + d*x^2)) + Log[x]/(a*c^3) - (b^3*Log[a + b*x^2])/(2*a*(b*c - a*d)^3) + (d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Log[c + d*x^2])/(2*c^3*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 72}"
258,1,211,0,0.3092683,"\int \frac{1}{x^2 \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x^2*(a + b*x^2)*(c + d*x^2)^3),x]","-\frac{15 a^2 d^2-27 a b c d+8 b^2 c^2}{8 a c^3 x (b c-a d)^2}+\frac{d^{3/2} \left(15 a^2 d^2-42 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{7/2} (b c-a d)^3}-\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} (b c-a d)^3}-\frac{d (9 b c-5 a d)}{8 c^2 x \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x \left(c+d x^2\right)^2 (b c-a d)}","-\frac{15 a^2 d^2-27 a b c d+8 b^2 c^2}{8 a c^3 x (b c-a d)^2}+\frac{d^{3/2} \left(15 a^2 d^2-42 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{7/2} (b c-a d)^3}-\frac{b^{7/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} (b c-a d)^3}-\frac{d (9 b c-5 a d)}{8 c^2 x \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x \left(c+d x^2\right)^2 (b c-a d)}",1,"-(8*b^2*c^2 - 27*a*b*c*d + 15*a^2*d^2)/(8*a*c^3*(b*c - a*d)^2*x) - d/(4*c*(b*c - a*d)*x*(c + d*x^2)^2) - (d*(9*b*c - 5*a*d))/(8*c^2*(b*c - a*d)^2*x*(c + d*x^2)) - (b^(7/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*(b*c - a*d)^3) + (d^(3/2)*(35*b^2*c^2 - 42*a*b*c*d + 15*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(7/2)*(b*c - a*d)^3)","A",6,5,22,0.2273,1,"{472, 579, 583, 522, 205}"
259,1,178,0,0.2134169,"\int \frac{1}{x^3 \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x^3*(a + b*x^2)*(c + d*x^2)^3),x]","-\frac{d^2 \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^4 (b c-a d)^3}+\frac{b^4 \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^3}-\frac{\log (x) (3 a d+b c)}{a^2 c^4}+\frac{d^2 (3 b c-2 a d)}{2 c^3 \left(c+d x^2\right) (b c-a d)^2}+\frac{d^2}{4 c^2 \left(c+d x^2\right)^2 (b c-a d)}-\frac{1}{2 a c^3 x^2}","-\frac{d^2 \left(3 a^2 d^2-8 a b c d+6 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^4 (b c-a d)^3}+\frac{b^4 \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^3}-\frac{\log (x) (3 a d+b c)}{a^2 c^4}+\frac{d^2 (3 b c-2 a d)}{2 c^3 \left(c+d x^2\right) (b c-a d)^2}+\frac{d^2}{4 c^2 \left(c+d x^2\right)^2 (b c-a d)}-\frac{1}{2 a c^3 x^2}",1,"-1/(2*a*c^3*x^2) + d^2/(4*c^2*(b*c - a*d)*(c + d*x^2)^2) + (d^2*(3*b*c - 2*a*d))/(2*c^3*(b*c - a*d)^2*(c + d*x^2)) - ((b*c + 3*a*d)*Log[x])/(a^2*c^4) + (b^4*Log[a + b*x^2])/(2*a^2*(b*c - a*d)^3) - (d^2*(6*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*Log[c + d*x^2])/(2*c^4*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 88}"
260,1,270,0,0.4337256,"\int \frac{1}{x^4 \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x^4*(a + b*x^2)*(c + d*x^2)^3),x]","-\frac{35 a^2 d^2-55 a b c d+8 b^2 c^2}{24 a c^3 x^3 (b c-a d)^2}+\frac{-55 a^2 b c d^2+35 a^3 d^3+8 a b^2 c^2 d+8 b^3 c^3}{8 a^2 c^4 x (b c-a d)^2}-\frac{d^{5/2} \left(35 a^2 d^2-90 a b c d+63 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{9/2} (b c-a d)^3}+\frac{b^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} (b c-a d)^3}-\frac{d (11 b c-7 a d)}{8 c^2 x^3 \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x^3 \left(c+d x^2\right)^2 (b c-a d)}","-\frac{35 a^2 d^2-55 a b c d+8 b^2 c^2}{24 a c^3 x^3 (b c-a d)^2}+\frac{-55 a^2 b c d^2+35 a^3 d^3+8 a b^2 c^2 d+8 b^3 c^3}{8 a^2 c^4 x (b c-a d)^2}-\frac{d^{5/2} \left(35 a^2 d^2-90 a b c d+63 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{9/2} (b c-a d)^3}+\frac{b^{9/2} \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} (b c-a d)^3}-\frac{d (11 b c-7 a d)}{8 c^2 x^3 \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x^3 \left(c+d x^2\right)^2 (b c-a d)}",1,"-(8*b^2*c^2 - 55*a*b*c*d + 35*a^2*d^2)/(24*a*c^3*(b*c - a*d)^2*x^3) + (8*b^3*c^3 + 8*a*b^2*c^2*d - 55*a^2*b*c*d^2 + 35*a^3*d^3)/(8*a^2*c^4*(b*c - a*d)^2*x) - d/(4*c*(b*c - a*d)*x^3*(c + d*x^2)^2) - (d*(11*b*c - 7*a*d))/(8*c^2*(b*c - a*d)^2*x^3*(c + d*x^2)) + (b^(9/2)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*(b*c - a*d)^3) - (d^(5/2)*(63*b^2*c^2 - 90*a*b*c*d + 35*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(9/2)*(b*c - a*d)^3)","A",7,5,22,0.2273,1,"{472, 579, 583, 522, 205}"
261,1,21,0,0.0126227,"\int \frac{x}{\left(1+x^2\right) \left(4+x^2\right)} \, dx","Int[x/((1 + x^2)*(4 + x^2)),x]","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{6} \log \left(x^2+4\right)","\frac{1}{6} \log \left(x^2+1\right)-\frac{1}{6} \log \left(x^2+4\right)",1,"Log[1 + x^2]/6 - Log[4 + x^2]/6","A",4,3,16,0.1875,1,"{444, 36, 31}"
262,1,87,0,0.071397,"\int \frac{x^4 \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(c + d*x^2))/(a + b*x^2)^2,x]","\frac{a x (b c-a d)}{2 b^3 \left(a+b x^2\right)}+\frac{x (b c-2 a d)}{b^3}-\frac{\sqrt{a} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}+\frac{d x^3}{3 b^2}","\frac{a x (b c-a d)}{2 b^3 \left(a+b x^2\right)}+\frac{x (b c-2 a d)}{b^3}-\frac{\sqrt{a} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{7/2}}+\frac{d x^3}{3 b^2}",1,"((b*c - 2*a*d)*x)/b^3 + (d*x^3)/(3*b^2) + (a*(b*c - a*d)*x)/(2*b^3*(a + b*x^2)) - (Sqrt[a]*(3*b*c - 5*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(7/2))","A",4,3,20,0.1500,1,"{455, 1153, 205}"
263,1,60,0,0.0604614,"\int \frac{x^3 \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(c + d*x^2))/(a + b*x^2)^2,x]","\frac{a (b c-a d)}{2 b^3 \left(a+b x^2\right)}+\frac{(b c-2 a d) \log \left(a+b x^2\right)}{2 b^3}+\frac{d x^2}{2 b^2}","\frac{a (b c-a d)}{2 b^3 \left(a+b x^2\right)}+\frac{(b c-2 a d) \log \left(a+b x^2\right)}{2 b^3}+\frac{d x^2}{2 b^2}",1,"(d*x^2)/(2*b^2) + (a*(b*c - a*d))/(2*b^3*(a + b*x^2)) + ((b*c - 2*a*d)*Log[a + b*x^2])/(2*b^3)","A",3,2,20,0.1000,1,"{446, 77}"
264,1,67,0,0.0507307,"\int \frac{x^2 \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(c + d*x^2))/(a + b*x^2)^2,x]","-\frac{x (b c-a d)}{2 b^2 \left(a+b x^2\right)}+\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}+\frac{d x}{b^2}","-\frac{x (b c-a d)}{2 b^2 \left(a+b x^2\right)}+\frac{(b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{5/2}}+\frac{d x}{b^2}",1,"(d*x)/b^2 - ((b*c - a*d)*x)/(2*b^2*(a + b*x^2)) + ((b*c - 3*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(5/2))","A",3,3,20,0.1500,1,"{455, 388, 205}"
265,1,41,0,0.0358749,"\int \frac{x \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x*(c + d*x^2))/(a + b*x^2)^2,x]","\frac{d \log \left(a+b x^2\right)}{2 b^2}-\frac{b c-a d}{2 b^2 \left(a+b x^2\right)}","\frac{d \log \left(a+b x^2\right)}{2 b^2}-\frac{b c-a d}{2 b^2 \left(a+b x^2\right)}",1,"-(b*c - a*d)/(2*b^2*(a + b*x^2)) + (d*Log[a + b*x^2])/(2*b^2)","A",3,2,18,0.1111,1,"{444, 43}"
266,1,63,0,0.0222988,"\int \frac{c+d x^2}{\left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)/(a + b*x^2)^2,x]","\frac{(a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}+\frac{x (b c-a d)}{2 a b \left(a+b x^2\right)}","\frac{(a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{3/2}}+\frac{x (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"((b*c - a*d)*x)/(2*a*b*(a + b*x^2)) + ((b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(3/2))","A",2,2,17,0.1176,1,"{385, 205}"
267,1,51,0,0.0441073,"\int \frac{c+d x^2}{x \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)/(x*(a + b*x^2)^2),x]","-\frac{c \log \left(a+b x^2\right)}{2 a^2}+\frac{c \log (x)}{a^2}+\frac{b c-a d}{2 a b \left(a+b x^2\right)}","-\frac{c \log \left(a+b x^2\right)}{2 a^2}+\frac{c \log (x)}{a^2}+\frac{b c-a d}{2 a b \left(a+b x^2\right)}",1,"(b*c - a*d)/(2*a*b*(a + b*x^2)) + (c*Log[x])/a^2 - (c*Log[a + b*x^2])/(2*a^2)","A",3,2,20,0.1000,1,"{446, 77}"
268,1,71,0,0.0529184,"\int \frac{c+d x^2}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)/(x^2*(a + b*x^2)^2),x]","-\frac{x (b c-a d)}{2 a^2 \left(a+b x^2\right)}-\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{c}{a^2 x}","-\frac{x (b c-a d)}{2 a^2 \left(a+b x^2\right)}-\frac{(3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} \sqrt{b}}-\frac{c}{a^2 x}",1,"-(c/(a^2*x)) - ((b*c - a*d)*x)/(2*a^2*(a + b*x^2)) - ((3*b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*Sqrt[b])","A",3,3,20,0.1500,1,"{456, 453, 205}"
269,1,76,0,0.0740186,"\int \frac{c+d x^2}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)/(x^3*(a + b*x^2)^2),x]","-\frac{b c-a d}{2 a^2 \left(a+b x^2\right)}+\frac{(2 b c-a d) \log \left(a+b x^2\right)}{2 a^3}-\frac{\log (x) (2 b c-a d)}{a^3}-\frac{c}{2 a^2 x^2}","-\frac{b c-a d}{2 a^2 \left(a+b x^2\right)}+\frac{(2 b c-a d) \log \left(a+b x^2\right)}{2 a^3}-\frac{\log (x) (2 b c-a d)}{a^3}-\frac{c}{2 a^2 x^2}",1,"-c/(2*a^2*x^2) - (b*c - a*d)/(2*a^2*(a + b*x^2)) - ((2*b*c - a*d)*Log[x])/a^3 + ((2*b*c - a*d)*Log[a + b*x^2])/(2*a^3)","A",3,2,20,0.1000,1,"{446, 77}"
270,1,90,0,0.1063812,"\int \frac{c+d x^2}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)/(x^4*(a + b*x^2)^2),x]","\frac{b x (b c-a d)}{2 a^3 \left(a+b x^2\right)}+\frac{2 b c-a d}{a^3 x}+\frac{\sqrt{b} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{c}{3 a^2 x^3}","\frac{b x (b c-a d)}{2 a^3 \left(a+b x^2\right)}+\frac{2 b c-a d}{a^3 x}+\frac{\sqrt{b} (5 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{c}{3 a^2 x^3}",1,"-c/(3*a^2*x^3) + (2*b*c - a*d)/(a^3*x) + (b*(b*c - a*d)*x)/(2*a^3*(a + b*x^2)) + (Sqrt[b]*(5*b*c - 3*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2))","A",4,3,20,0.1500,1,"{456, 1261, 205}"
271,1,145,0,0.1321204,"\int \frac{x^4 \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(c + d*x^2)^2)/(a + b*x^2)^2,x]","\frac{x^5 (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}-\frac{x^3 (3 b c-7 a d) (b c-a d)}{6 a b^3}+\frac{x (3 b c-7 a d) (b c-a d)}{2 b^4}-\frac{\sqrt{a} (3 b c-7 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}+\frac{d^2 x^5}{5 b^2}","\frac{x^5 (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}-\frac{x^3 (3 b c-7 a d) (b c-a d)}{6 a b^3}+\frac{x (3 b c-7 a d) (b c-a d)}{2 b^4}-\frac{\sqrt{a} (3 b c-7 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{9/2}}+\frac{d^2 x^5}{5 b^2}",1,"((3*b*c - 7*a*d)*(b*c - a*d)*x)/(2*b^4) - ((3*b*c - 7*a*d)*(b*c - a*d)*x^3)/(6*a*b^3) + (d^2*x^5)/(5*b^2) + ((b*c - a*d)^2*x^5)/(2*a*b^2*(a + b*x^2)) - (Sqrt[a]*(3*b*c - 7*a*d)*(b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(9/2))","A",5,4,22,0.1818,1,"{463, 459, 302, 205}"
272,1,88,0,0.1058007,"\int \frac{x^3 \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(c + d*x^2)^2)/(a + b*x^2)^2,x]","\frac{d x^2 (b c-a d)}{b^3}+\frac{a (b c-a d)^2}{2 b^4 \left(a+b x^2\right)}+\frac{(b c-3 a d) (b c-a d) \log \left(a+b x^2\right)}{2 b^4}+\frac{d^2 x^4}{4 b^2}","\frac{d x^2 (b c-a d)}{b^3}+\frac{a (b c-a d)^2}{2 b^4 \left(a+b x^2\right)}+\frac{(b c-3 a d) (b c-a d) \log \left(a+b x^2\right)}{2 b^4}+\frac{d^2 x^4}{4 b^2}",1,"(d*(b*c - a*d)*x^2)/b^3 + (d^2*x^4)/(4*b^2) + (a*(b*c - a*d)^2)/(2*b^4*(a + b*x^2)) + ((b*c - 3*a*d)*(b*c - a*d)*Log[a + b*x^2])/(2*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
273,1,116,0,0.1114115,"\int \frac{x^2 \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(c + d*x^2)^2)/(a + b*x^2)^2,x]","\frac{x^3 (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}-\frac{x (b c-5 a d) (b c-a d)}{2 a b^3}+\frac{(b c-5 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{7/2}}+\frac{d^2 x^3}{3 b^2}","\frac{x^3 (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}-\frac{x (b c-5 a d) (b c-a d)}{2 a b^3}+\frac{(b c-5 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{7/2}}+\frac{d^2 x^3}{3 b^2}",1,"-((b*c - 5*a*d)*(b*c - a*d)*x)/(2*a*b^3) + (d^2*x^3)/(3*b^2) + ((b*c - a*d)^2*x^3)/(2*a*b^2*(a + b*x^2)) + ((b*c - 5*a*d)*(b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(7/2))","A",4,4,22,0.1818,1,"{463, 459, 321, 205}"
274,1,61,0,0.0580752,"\int \frac{x \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","Int[(x*(c + d*x^2)^2)/(a + b*x^2)^2,x]","-\frac{(b c-a d)^2}{2 b^3 \left(a+b x^2\right)}+\frac{d (b c-a d) \log \left(a+b x^2\right)}{b^3}+\frac{d^2 x^2}{2 b^2}","-\frac{(b c-a d)^2}{2 b^3 \left(a+b x^2\right)}+\frac{d (b c-a d) \log \left(a+b x^2\right)}{b^3}+\frac{d^2 x^2}{2 b^2}",1,"(d^2*x^2)/(2*b^2) - (b*c - a*d)^2/(2*b^3*(a + b*x^2)) + (d*(b*c - a*d)*Log[a + b*x^2])/b^3","A",3,2,20,0.1000,1,"{444, 43}"
275,1,82,0,0.0991134,"\int \frac{\left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^2/(a + b*x^2)^2,x]","\frac{(b c-a d) (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{5/2}}+\frac{x (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}+\frac{d^2 x}{b^2}","\frac{(b c-a d) (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{5/2}}+\frac{x (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}+\frac{d^2 x}{b^2}",1,"(d^2*x)/b^2 + ((b*c - a*d)^2*x)/(2*a*b^2*(a + b*x^2)) + ((b*c - a*d)*(b*c + 3*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(5/2))","A",4,3,19,0.1579,1,"{390, 385, 205}"
276,1,67,0,0.0646807,"\int \frac{\left(c+d x^2\right)^2}{x \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^2/(x*(a + b*x^2)^2),x]","-\frac{1}{2} \left(\frac{c^2}{a^2}-\frac{d^2}{b^2}\right) \log \left(a+b x^2\right)+\frac{c^2 \log (x)}{a^2}+\frac{(b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}","-\frac{1}{2} \left(\frac{c^2}{a^2}-\frac{d^2}{b^2}\right) \log \left(a+b x^2\right)+\frac{c^2 \log (x)}{a^2}+\frac{(b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}",1,"(b*c - a*d)^2/(2*a*b^2*(a + b*x^2)) + (c^2*Log[x])/a^2 - ((c^2/a^2 - d^2/b^2)*Log[a + b*x^2])/2","A",3,2,22,0.09091,1,"{446, 88}"
277,1,103,0,0.0777147,"\int \frac{\left(c+d x^2\right)^2}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^2/(x^2*(a + b*x^2)^2),x]","-\frac{(b c-a d) (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} b^{3/2}}-\frac{x \left(\frac{3 b c^2}{a}+\frac{a d^2}{b}-2 c d\right)}{2 a \left(a+b x^2\right)}-\frac{c^2}{a x \left(a+b x^2\right)}","-\frac{(b c-a d) (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} b^{3/2}}-\frac{x \left(\frac{3 b c^2}{a}+\frac{a d^2}{b}-2 c d\right)}{2 a \left(a+b x^2\right)}-\frac{c^2}{a x \left(a+b x^2\right)}",1,"-(c^2/(a*x*(a + b*x^2))) - (((3*b*c^2)/a - 2*c*d + (a*d^2)/b)*x)/(2*a*(a + b*x^2)) - ((b*c - a*d)*(3*b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*b^(3/2))","A",3,3,22,0.1364,1,"{462, 385, 205}"
278,1,80,0,0.0814483,"\int \frac{\left(c+d x^2\right)^2}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^2/(x^3*(a + b*x^2)^2),x]","-\frac{(b c-a d)^2}{2 a^2 b \left(a+b x^2\right)}+\frac{c (b c-a d) \log \left(a+b x^2\right)}{a^3}-\frac{2 c \log (x) (b c-a d)}{a^3}-\frac{c^2}{2 a^2 x^2}","-\frac{(b c-a d)^2}{2 a^2 b \left(a+b x^2\right)}+\frac{c (b c-a d) \log \left(a+b x^2\right)}{a^3}-\frac{2 c \log (x) (b c-a d)}{a^3}-\frac{c^2}{2 a^2 x^2}",1,"-c^2/(2*a^2*x^2) - (b*c - a*d)^2/(2*a^2*b*(a + b*x^2)) - (2*c*(b*c - a*d)*Log[x])/a^3 + (c*(b*c - a*d)*Log[a + b*x^2])/a^3","A",3,2,22,0.09091,1,"{446, 88}"
279,1,125,0,0.1427638,"\int \frac{\left(c+d x^2\right)^2}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^2/(x^4*(a + b*x^2)^2),x]","\frac{x \left(\frac{b c (5 b c-6 a d)}{a^2}+3 d^2\right)}{6 a \left(a+b x^2\right)}+\frac{c (5 b c-6 a d)}{3 a^3 x}+\frac{(b c-a d) (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} \sqrt{b}}-\frac{c^2}{3 a x^3 \left(a+b x^2\right)}","\frac{x \left(3 a^2 d^2-6 a b c d+5 b^2 c^2\right)}{6 a^3 \left(a+b x^2\right)}+\frac{c (5 b c-6 a d)}{3 a^3 x}+\frac{(b c-a d) (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} \sqrt{b}}-\frac{c^2}{3 a x^3 \left(a+b x^2\right)}",1,"(c*(5*b*c - 6*a*d))/(3*a^3*x) - c^2/(3*a*x^3*(a + b*x^2)) + ((3*d^2 + (b*c*(5*b*c - 6*a*d))/a^2)*x)/(6*a*(a + b*x^2)) + ((b*c - a*d)*(5*b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2)*Sqrt[b])","A",4,4,22,0.1818,1,"{462, 456, 453, 205}"
280,1,169,0,0.1561722,"\int \frac{x^4 \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d x^3 \left(3 a^2 d^2-7 a b c d+5 b^2 c^2\right)}{2 b^4}+\frac{3 d^2 x^5 (7 b c-3 a d)}{10 b^3}+\frac{3 x (b c-3 a d) (b c-a d)^2}{2 b^5}-\frac{3 \sqrt{a} (b c-3 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{x^3 \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{9 d^3 x^7}{14 b^2}","\frac{d x^3 \left(3 a^2 d^2-7 a b c d+5 b^2 c^2\right)}{2 b^4}+\frac{3 d^2 x^5 (7 b c-3 a d)}{10 b^3}+\frac{3 x (b c-3 a d) (b c-a d)^2}{2 b^5}-\frac{3 \sqrt{a} (b c-3 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{11/2}}-\frac{x^3 \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{9 d^3 x^7}{14 b^2}",1,"(3*(b*c - 3*a*d)*(b*c - a*d)^2*x)/(2*b^5) + (d*(5*b^2*c^2 - 7*a*b*c*d + 3*a^2*d^2)*x^3)/(2*b^4) + (3*d^2*(7*b*c - 3*a*d)*x^5)/(10*b^3) + (9*d^3*x^7)/(14*b^2) - (x^3*(c + d*x^2)^3)/(2*b*(a + b*x^2)) - (3*Sqrt[a]*(b*c - 3*a*d)*(b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(11/2))","A",4,3,22,0.1364,1,"{467, 570, 205}"
281,1,117,0,0.1484029,"\int \frac{x^3 \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d^2 x^4 (3 b c-2 a d)}{4 b^3}+\frac{3 d x^2 (b c-a d)^2}{2 b^4}+\frac{a (b c-a d)^3}{2 b^5 \left(a+b x^2\right)}+\frac{(b c-4 a d) (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^5}+\frac{d^3 x^6}{6 b^2}","\frac{d^2 x^4 (3 b c-2 a d)}{4 b^3}+\frac{3 d x^2 (b c-a d)^2}{2 b^4}+\frac{a (b c-a d)^3}{2 b^5 \left(a+b x^2\right)}+\frac{(b c-4 a d) (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^5}+\frac{d^3 x^6}{6 b^2}",1,"(3*d*(b*c - a*d)^2*x^2)/(2*b^4) + (d^2*(3*b*c - 2*a*d)*x^4)/(4*b^3) + (d^3*x^6)/(6*b^2) + (a*(b*c - a*d)^3)/(2*b^5*(a + b*x^2)) + ((b*c - 4*a*d)*(b*c - a*d)^2*Log[a + b*x^2])/(2*b^5)","A",3,2,22,0.09091,1,"{446, 77}"
282,1,147,0,0.1901672,"\int \frac{x^2 \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d x \left(105 a^2 d^2-190 a b c d+81 b^2 c^2\right)}{30 b^4}+\frac{d x \left(c+d x^2\right) (33 b c-35 a d)}{30 b^3}+\frac{(b c-7 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{9/2}}-\frac{x \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{7 d x \left(c+d x^2\right)^2}{10 b^2}","\frac{d x \left(105 a^2 d^2-190 a b c d+81 b^2 c^2\right)}{30 b^4}+\frac{d x \left(c+d x^2\right) (33 b c-35 a d)}{30 b^3}+\frac{(b c-7 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} b^{9/2}}-\frac{x \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{7 d x \left(c+d x^2\right)^2}{10 b^2}",1,"(d*(81*b^2*c^2 - 190*a*b*c*d + 105*a^2*d^2)*x)/(30*b^4) + (d*(33*b*c - 35*a*d)*x*(c + d*x^2))/(30*b^3) + (7*d*x*(c + d*x^2)^2)/(10*b^2) - (x*(c + d*x^2)^3)/(2*b*(a + b*x^2)) + ((b*c - 7*a*d)*(b*c - a*d)^2*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*b^(9/2))","A",5,4,22,0.1818,1,"{467, 528, 388, 205}"
283,1,88,0,0.0933621,"\int \frac{x \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d^2 x^2 (3 b c-2 a d)}{2 b^3}-\frac{(b c-a d)^3}{2 b^4 \left(a+b x^2\right)}+\frac{3 d (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^4}+\frac{d^3 x^4}{4 b^2}","\frac{d^2 x^2 (3 b c-2 a d)}{2 b^3}-\frac{(b c-a d)^3}{2 b^4 \left(a+b x^2\right)}+\frac{3 d (b c-a d)^2 \log \left(a+b x^2\right)}{2 b^4}+\frac{d^3 x^4}{4 b^2}",1,"(d^2*(3*b*c - 2*a*d)*x^2)/(2*b^3) + (d^3*x^4)/(4*b^2) - (b*c - a*d)^3/(2*b^4*(a + b*x^2)) + (3*d*(b*c - a*d)^2*Log[a + b*x^2])/(2*b^4)","A",3,2,20,0.1000,1,"{444, 43}"
284,1,106,0,0.0910083,"\int \frac{\left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(a + b*x^2)^2,x]","\frac{(5 a d+b c) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{7/2}}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{x (b c-a d)^3}{2 a b^3 \left(a+b x^2\right)}+\frac{d^3 x^3}{3 b^2}","\frac{(5 a d+b c) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} b^{7/2}}+\frac{d^2 x (3 b c-2 a d)}{b^3}+\frac{x (b c-a d)^3}{2 a b^3 \left(a+b x^2\right)}+\frac{d^3 x^3}{3 b^2}",1,"(d^2*(3*b*c - 2*a*d)*x)/b^3 + (d^3*x^3)/(3*b^2) + ((b*c - a*d)^3*x)/(2*a*b^3*(a + b*x^2)) + ((b*c - a*d)^2*(b*c + 5*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*b^(7/2))","A",4,3,19,0.1579,1,"{390, 385, 205}"
285,1,88,0,0.0844912,"\int \frac{\left(c+d x^2\right)^3}{x \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x*(a + b*x^2)^2),x]","-\frac{(b c-a d)^2 (2 a d+b c) \log \left(a+b x^2\right)}{2 a^2 b^3}+\frac{c^3 \log (x)}{a^2}+\frac{(b c-a d)^3}{2 a b^3 \left(a+b x^2\right)}+\frac{d^3 x^2}{2 b^2}","-\frac{(b c-a d)^2 (2 a d+b c) \log \left(a+b x^2\right)}{2 a^2 b^3}+\frac{c^3 \log (x)}{a^2}+\frac{(b c-a d)^3}{2 a b^3 \left(a+b x^2\right)}+\frac{d^3 x^2}{2 b^2}",1,"(d^3*x^2)/(2*b^2) + (b*c - a*d)^3/(2*a*b^3*(a + b*x^2)) + (c^3*Log[x])/a^2 - ((b*c - a*d)^2*(b*c + 2*a*d)*Log[a + b*x^2])/(2*a^2*b^3)","A",3,2,22,0.09091,1,"{446, 88}"
286,1,131,0,0.1331653,"\int \frac{\left(c+d x^2\right)^3}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^2*(a + b*x^2)^2),x]","-\frac{3 (b c-a d)^2 (a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} b^{5/2}}-\frac{c^2 (3 b c-a d)}{2 a^2 b x}-\frac{d^2 x (b c-3 a d)}{2 a b^2}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x \left(a+b x^2\right)}","-\frac{3 (b c-a d)^2 (a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} b^{5/2}}-\frac{c^2 (3 b c-a d)}{2 a^2 b x}-\frac{d^2 x (b c-3 a d)}{2 a b^2}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x \left(a+b x^2\right)}",1,"-(c^2*(3*b*c - a*d))/(2*a^2*b*x) - (d^2*(b*c - 3*a*d)*x)/(2*a*b^2) + ((b*c - a*d)*(c + d*x^2)^2)/(2*a*b*x*(a + b*x^2)) - (3*(b*c - a*d)^2*(b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*b^(5/2))","A",4,3,22,0.1364,1,"{468, 570, 205}"
287,1,98,0,0.105636,"\int \frac{\left(c+d x^2\right)^3}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^3*(a + b*x^2)^2),x]","-\frac{(b c-a d)^3}{2 a^2 b^2 \left(a+b x^2\right)}+\frac{(b c-a d)^2 (a d+2 b c) \log \left(a+b x^2\right)}{2 a^3 b^2}-\frac{c^2 \log (x) (2 b c-3 a d)}{a^3}-\frac{c^3}{2 a^2 x^2}","-\frac{(b c-a d)^3}{2 a^2 b^2 \left(a+b x^2\right)}+\frac{(b c-a d)^2 (a d+2 b c) \log \left(a+b x^2\right)}{2 a^3 b^2}-\frac{c^2 \log (x) (2 b c-3 a d)}{a^3}-\frac{c^3}{2 a^2 x^2}",1,"-c^3/(2*a^2*x^2) - (b*c - a*d)^3/(2*a^2*b^2*(a + b*x^2)) - (c^2*(2*b*c - 3*a*d)*Log[x])/a^3 + ((b*c - a*d)^2*(2*b*c + a*d)*Log[a + b*x^2])/(2*a^3*b^2)","A",3,2,22,0.09091,1,"{446, 88}"
288,1,147,0,0.1409736,"\int \frac{\left(c+d x^2\right)^3}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^4*(a + b*x^2)^2),x]","\frac{c \left(2 a^2 d^2-9 a b c d+5 b^2 c^2\right)}{2 a^3 b x}+\frac{(b c-a d)^2 (a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} b^{3/2}}-\frac{c^2 (5 b c-3 a d)}{6 a^2 b x^3}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^3 \left(a+b x^2\right)}","\frac{c \left(2 a^2 d^2-9 a b c d+5 b^2 c^2\right)}{2 a^3 b x}+\frac{(b c-a d)^2 (a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} b^{3/2}}-\frac{c^2 (5 b c-3 a d)}{6 a^2 b x^3}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^3 \left(a+b x^2\right)}",1,"-(c^2*(5*b*c - 3*a*d))/(6*a^2*b*x^3) + (c*(5*b^2*c^2 - 9*a*b*c*d + 2*a^2*d^2))/(2*a^3*b*x) + ((b*c - a*d)*(c + d*x^2)^2)/(2*a*b*x^3*(a + b*x^2)) + ((b*c - a*d)^2*(5*b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2)*b^(3/2))","A",4,3,22,0.1364,1,"{468, 570, 205}"
289,1,109,0,0.0854561,"\int \frac{x^4}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x^4/((a + b*x^2)^2*(c + d*x^2)),x]","-\frac{\sqrt{a} (3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{3/2} (b c-a d)^2}+\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{d} (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) (b c-a d)}","-\frac{\sqrt{a} (3 b c-a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 b^{3/2} (b c-a d)^2}+\frac{c^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{d} (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) (b c-a d)}",1,"(a*x)/(2*b*(b*c - a*d)*(a + b*x^2)) - (Sqrt[a]*(3*b*c - a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*b^(3/2)*(b*c - a*d)^2) + (c^(3/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(Sqrt[d]*(b*c - a*d)^2)","A",4,3,22,0.1364,1,"{470, 522, 205}"
290,1,74,0,0.0653426,"\int \frac{x^3}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x^3/((a + b*x^2)^2*(c + d*x^2)),x]","\frac{a}{2 b \left(a+b x^2\right) (b c-a d)}+\frac{c \log \left(a+b x^2\right)}{2 (b c-a d)^2}-\frac{c \log \left(c+d x^2\right)}{2 (b c-a d)^2}","\frac{a}{2 b \left(a+b x^2\right) (b c-a d)}+\frac{c \log \left(a+b x^2\right)}{2 (b c-a d)^2}-\frac{c \log \left(c+d x^2\right)}{2 (b c-a d)^2}",1,"a/(2*b*(b*c - a*d)*(a + b*x^2)) + (c*Log[a + b*x^2])/(2*(b*c - a*d)^2) - (c*Log[c + d*x^2])/(2*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 77}"
291,1,104,0,0.0646264,"\int \frac{x^2}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x^2/((a + b*x^2)^2*(c + d*x^2)),x]","-\frac{x}{2 \left(a+b x^2\right) (b c-a d)}+\frac{(a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} (b c-a d)^2}-\frac{\sqrt{c} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{(b c-a d)^2}","-\frac{x}{2 \left(a+b x^2\right) (b c-a d)}+\frac{(a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} \sqrt{b} (b c-a d)^2}-\frac{\sqrt{c} \sqrt{d} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{(b c-a d)^2}",1,"-x/(2*(b*c - a*d)*(a + b*x^2)) + ((b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*Sqrt[b]*(b*c - a*d)^2) - (Sqrt[c]*Sqrt[d]*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(b*c - a*d)^2","A",4,3,22,0.1364,1,"{471, 522, 205}"
292,1,70,0,0.0516852,"\int \frac{x}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x/((a + b*x^2)^2*(c + d*x^2)),x]","-\frac{1}{2 \left(a+b x^2\right) (b c-a d)}-\frac{d \log \left(a+b x^2\right)}{2 (b c-a d)^2}+\frac{d \log \left(c+d x^2\right)}{2 (b c-a d)^2}","-\frac{1}{2 \left(a+b x^2\right) (b c-a d)}-\frac{d \log \left(a+b x^2\right)}{2 (b c-a d)^2}+\frac{d \log \left(c+d x^2\right)}{2 (b c-a d)^2}",1,"-1/(2*(b*c - a*d)*(a + b*x^2)) - (d*Log[a + b*x^2])/(2*(b*c - a*d)^2) + (d*Log[c + d*x^2])/(2*(b*c - a*d)^2)","A",3,2,20,0.1000,1,"{444, 44}"
293,1,108,0,0.0804604,"\int \frac{1}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/((a + b*x^2)^2*(c + d*x^2)),x]","\frac{\sqrt{b} (b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)^2}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{c} (b c-a d)^2}+\frac{b x}{2 a \left(a+b x^2\right) (b c-a d)}","\frac{\sqrt{b} (b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)^2}+\frac{d^{3/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{\sqrt{c} (b c-a d)^2}+\frac{b x}{2 a \left(a+b x^2\right) (b c-a d)}",1,"(b*x)/(2*a*(b*c - a*d)*(a + b*x^2)) + (Sqrt[b]*(b*c - 3*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*(b*c - a*d)^2) + (d^(3/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(Sqrt[c]*(b*c - a*d)^2)","A",4,3,19,0.1579,1,"{414, 522, 205}"
294,1,99,0,0.105449,"\int \frac{1}{x \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x*(a + b*x^2)^2*(c + d*x^2)),x]","-\frac{b (b c-2 a d) \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^2}+\frac{\log (x)}{a^2 c}-\frac{d^2 \log \left(c+d x^2\right)}{2 c (b c-a d)^2}+\frac{b}{2 a \left(a+b x^2\right) (b c-a d)}","-\frac{b (b c-2 a d) \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^2}+\frac{\log (x)}{a^2 c}-\frac{d^2 \log \left(c+d x^2\right)}{2 c (b c-a d)^2}+\frac{b}{2 a \left(a+b x^2\right) (b c-a d)}",1,"b/(2*a*(b*c - a*d)*(a + b*x^2)) + Log[x]/(a^2*c) - (b*(b*c - 2*a*d)*Log[a + b*x^2])/(2*a^2*(b*c - a*d)^2) - (d^2*Log[c + d*x^2])/(2*c*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 72}"
295,1,144,0,0.2062785,"\int \frac{1}{x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x^2*(a + b*x^2)^2*(c + d*x^2)),x]","-\frac{b^{3/2} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)^2}-\frac{3 b c-2 a d}{2 a^2 c x (b c-a d)}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{3/2} (b c-a d)^2}+\frac{b}{2 a x \left(a+b x^2\right) (b c-a d)}","-\frac{b^{3/2} (3 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)^2}-\frac{3 b c-2 a d}{2 a^2 c x (b c-a d)}-\frac{d^{5/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{3/2} (b c-a d)^2}+\frac{b}{2 a x \left(a+b x^2\right) (b c-a d)}",1,"-(3*b*c - 2*a*d)/(2*a^2*c*(b*c - a*d)*x) + b/(2*a*(b*c - a*d)*x*(a + b*x^2)) - (b^(3/2)*(3*b*c - 5*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*(b*c - a*d)^2) - (d^(5/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(3/2)*(b*c - a*d)^2)","A",5,4,22,0.1818,1,"{472, 583, 522, 205}"
296,1,126,0,0.1458188,"\int \frac{1}{x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x^3*(a + b*x^2)^2*(c + d*x^2)),x]","-\frac{b^2}{2 a^2 \left(a+b x^2\right) (b c-a d)}+\frac{b^2 (2 b c-3 a d) \log \left(a+b x^2\right)}{2 a^3 (b c-a d)^2}-\frac{\log (x) (a d+2 b c)}{a^3 c^2}-\frac{1}{2 a^2 c x^2}+\frac{d^3 \log \left(c+d x^2\right)}{2 c^2 (b c-a d)^2}","-\frac{b^2}{2 a^2 \left(a+b x^2\right) (b c-a d)}+\frac{b^2 (2 b c-3 a d) \log \left(a+b x^2\right)}{2 a^3 (b c-a d)^2}-\frac{\log (x) (a d+2 b c)}{a^3 c^2}-\frac{1}{2 a^2 c x^2}+\frac{d^3 \log \left(c+d x^2\right)}{2 c^2 (b c-a d)^2}",1,"-1/(2*a^2*c*x^2) - b^2/(2*a^2*(b*c - a*d)*(a + b*x^2)) - ((2*b*c + a*d)*Log[x])/(a^3*c^2) + (b^2*(2*b*c - 3*a*d)*Log[a + b*x^2])/(2*a^3*(b*c - a*d)^2) + (d^3*Log[c + d*x^2])/(2*c^2*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 88}"
297,1,189,0,0.2774815,"\int \frac{1}{x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x^4*(a + b*x^2)^2*(c + d*x^2)),x]","\frac{-2 a^2 d^2-2 a b c d+5 b^2 c^2}{2 a^3 c^2 x (b c-a d)}+\frac{b^{5/2} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} (b c-a d)^2}-\frac{5 b c-2 a d}{6 a^2 c x^3 (b c-a d)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{5/2} (b c-a d)^2}+\frac{b}{2 a x^3 \left(a+b x^2\right) (b c-a d)}","\frac{-2 a^2 d^2-2 a b c d+5 b^2 c^2}{2 a^3 c^2 x (b c-a d)}+\frac{b^{5/2} (5 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} (b c-a d)^2}-\frac{5 b c-2 a d}{6 a^2 c x^3 (b c-a d)}+\frac{d^{7/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{5/2} (b c-a d)^2}+\frac{b}{2 a x^3 \left(a+b x^2\right) (b c-a d)}",1,"-(5*b*c - 2*a*d)/(6*a^2*c*(b*c - a*d)*x^3) + (5*b^2*c^2 - 2*a*b*c*d - 2*a^2*d^2)/(2*a^3*c^2*(b*c - a*d)*x) + b/(2*a*(b*c - a*d)*x^3*(a + b*x^2)) + (b^(5/2)*(5*b*c - 7*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2)*(b*c - a*d)^2) + (d^(7/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(5/2)*(b*c - a*d)^2)","A",6,4,22,0.1818,1,"{472, 583, 522, 205}"
298,1,160,0,0.1935241,"\int \frac{1}{x^5 \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x^5*(a + b*x^2)^2*(c + d*x^2)),x]","\frac{\log (x) \left(a^2 d^2+2 a b c d+3 b^2 c^2\right)}{a^4 c^3}+\frac{b^3}{2 a^3 \left(a+b x^2\right) (b c-a d)}-\frac{b^3 (3 b c-4 a d) \log \left(a+b x^2\right)}{2 a^4 (b c-a d)^2}+\frac{a d+2 b c}{2 a^3 c^2 x^2}-\frac{1}{4 a^2 c x^4}-\frac{d^4 \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^2}","\frac{\log (x) \left(a^2 d^2+2 a b c d+3 b^2 c^2\right)}{a^4 c^3}+\frac{b^3}{2 a^3 \left(a+b x^2\right) (b c-a d)}-\frac{b^3 (3 b c-4 a d) \log \left(a+b x^2\right)}{2 a^4 (b c-a d)^2}+\frac{a d+2 b c}{2 a^3 c^2 x^2}-\frac{1}{4 a^2 c x^4}-\frac{d^4 \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^2}",1,"-1/(4*a^2*c*x^4) + (2*b*c + a*d)/(2*a^3*c^2*x^2) + b^3/(2*a^3*(b*c - a*d)*(a + b*x^2)) + ((3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Log[x])/(a^4*c^3) - (b^3*(3*b*c - 4*a*d)*Log[a + b*x^2])/(2*a^4*(b*c - a*d)^2) - (d^4*Log[c + d*x^2])/(2*c^3*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 88}"
299,1,250,0,0.4087621,"\int \frac{1}{x^6 \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x^6*(a + b*x^2)^2*(c + d*x^2)),x]","\frac{-2 a^2 d^2-2 a b c d+7 b^2 c^2}{6 a^3 c^2 x^3 (b c-a d)}-\frac{-2 a^2 b c d^2-2 a^3 d^3-2 a b^2 c^2 d+7 b^3 c^3}{2 a^4 c^3 x (b c-a d)}-\frac{b^{7/2} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2} (b c-a d)^2}-\frac{7 b c-2 a d}{10 a^2 c x^5 (b c-a d)}-\frac{d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{7/2} (b c-a d)^2}+\frac{b}{2 a x^5 \left(a+b x^2\right) (b c-a d)}","\frac{-2 a^2 d^2-2 a b c d+7 b^2 c^2}{6 a^3 c^2 x^3 (b c-a d)}-\frac{-2 a^2 b c d^2-2 a^3 d^3-2 a b^2 c^2 d+7 b^3 c^3}{2 a^4 c^3 x (b c-a d)}-\frac{b^{7/2} (7 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{9/2} (b c-a d)^2}-\frac{7 b c-2 a d}{10 a^2 c x^5 (b c-a d)}-\frac{d^{9/2} \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{c^{7/2} (b c-a d)^2}+\frac{b}{2 a x^5 \left(a+b x^2\right) (b c-a d)}",1,"-(7*b*c - 2*a*d)/(10*a^2*c*(b*c - a*d)*x^5) + (7*b^2*c^2 - 2*a*b*c*d - 2*a^2*d^2)/(6*a^3*c^2*(b*c - a*d)*x^3) - (7*b^3*c^3 - 2*a*b^2*c^2*d - 2*a^2*b*c*d^2 - 2*a^3*d^3)/(2*a^4*c^3*(b*c - a*d)*x) + b/(2*a*(b*c - a*d)*x^5*(a + b*x^2)) - (b^(7/2)*(7*b*c - 9*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(9/2)*(b*c - a*d)^2) - (d^(9/2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(c^(7/2)*(b*c - a*d)^2)","A",7,4,22,0.1818,1,"{472, 583, 522, 205}"
300,1,210,0,0.2487916,"\int \frac{1}{x^7 \left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[1/(x^7*(a + b*x^2)^2*(c + d*x^2)),x]","-\frac{a^2 d^2+2 a b c d+3 b^2 c^2}{2 a^4 c^3 x^2}-\frac{\log (x) \left(2 a^2 b c d^2+a^3 d^3+3 a b^2 c^2 d+4 b^3 c^3\right)}{a^5 c^4}-\frac{b^4}{2 a^4 \left(a+b x^2\right) (b c-a d)}+\frac{b^4 (4 b c-5 a d) \log \left(a+b x^2\right)}{2 a^5 (b c-a d)^2}+\frac{a d+2 b c}{4 a^3 c^2 x^4}-\frac{1}{6 a^2 c x^6}+\frac{d^5 \log \left(c+d x^2\right)}{2 c^4 (b c-a d)^2}","-\frac{a^2 d^2+2 a b c d+3 b^2 c^2}{2 a^4 c^3 x^2}-\frac{\log (x) \left(2 a^2 b c d^2+a^3 d^3+3 a b^2 c^2 d+4 b^3 c^3\right)}{a^5 c^4}-\frac{b^4}{2 a^4 \left(a+b x^2\right) (b c-a d)}+\frac{b^4 (4 b c-5 a d) \log \left(a+b x^2\right)}{2 a^5 (b c-a d)^2}+\frac{a d+2 b c}{4 a^3 c^2 x^4}-\frac{1}{6 a^2 c x^6}+\frac{d^5 \log \left(c+d x^2\right)}{2 c^4 (b c-a d)^2}",1,"-1/(6*a^2*c*x^6) + (2*b*c + a*d)/(4*a^3*c^2*x^4) - (3*b^2*c^2 + 2*a*b*c*d + a^2*d^2)/(2*a^4*c^3*x^2) - b^4/(2*a^4*(b*c - a*d)*(a + b*x^2)) - ((4*b^3*c^3 + 3*a*b^2*c^2*d + 2*a^2*b*c*d^2 + a^3*d^3)*Log[x])/(a^5*c^4) + (b^4*(4*b*c - 5*a*d)*Log[a + b*x^2])/(2*a^5*(b*c - a*d)^2) + (d^5*Log[c + d*x^2])/(2*c^4*(b*c - a*d)^2)","A",3,2,22,0.09091,1,"{446, 88}"
301,1,162,0,0.1638333,"\int \frac{x^4}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^4/((a + b*x^2)^2*(c + d*x^2)^2),x]","\frac{x (a d+b c)}{2 b \left(c+d x^2\right) (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}-\frac{\sqrt{a} (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{b} (b c-a d)^3}+\frac{\sqrt{c} (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{d} (b c-a d)^3}","\frac{x (a d+b c)}{2 b \left(c+d x^2\right) (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}-\frac{\sqrt{a} (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{b} (b c-a d)^3}+\frac{\sqrt{c} (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{d} (b c-a d)^3}",1,"((b*c + a*d)*x)/(2*b*(b*c - a*d)^2*(c + d*x^2)) + (a*x)/(2*b*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) - (Sqrt[a]*(3*b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[b]*(b*c - a*d)^3) + (Sqrt[c]*(b*c + 3*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*Sqrt[d]*(b*c - a*d)^3)","A",5,4,22,0.1818,1,"{470, 527, 522, 205}"
302,1,107,0,0.1077651,"\int \frac{x^3}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^3/((a + b*x^2)^2*(c + d*x^2)^2),x]","\frac{a}{2 \left(a+b x^2\right) (b c-a d)^2}+\frac{c}{2 \left(c+d x^2\right) (b c-a d)^2}+\frac{(a d+b c) \log \left(a+b x^2\right)}{2 (b c-a d)^3}-\frac{(a d+b c) \log \left(c+d x^2\right)}{2 (b c-a d)^3}","\frac{a}{2 \left(a+b x^2\right) (b c-a d)^2}+\frac{c}{2 \left(c+d x^2\right) (b c-a d)^2}+\frac{(a d+b c) \log \left(a+b x^2\right)}{2 (b c-a d)^3}-\frac{(a d+b c) \log \left(c+d x^2\right)}{2 (b c-a d)^3}",1,"a/(2*(b*c - a*d)^2*(a + b*x^2)) + c/(2*(b*c - a*d)^2*(c + d*x^2)) + ((b*c + a*d)*Log[a + b*x^2])/(2*(b*c - a*d)^3) - ((b*c + a*d)*Log[c + d*x^2])/(2*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 77}"
303,1,147,0,0.1335623,"\int \frac{x^2}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^2/((a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{x}{2 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}-\frac{d x}{\left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt{b} (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} (b c-a d)^3}-\frac{\sqrt{d} (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} (b c-a d)^3}","-\frac{x}{2 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}-\frac{d x}{\left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt{b} (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} (b c-a d)^3}-\frac{\sqrt{d} (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 \sqrt{c} (b c-a d)^3}",1,"-((d*x)/((b*c - a*d)^2*(c + d*x^2))) - x/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) + (Sqrt[b]*(b*c + 3*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*(b*c - a*d)^3) - (Sqrt[d]*(3*b*c + a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*Sqrt[c]*(b*c - a*d)^3)","A",5,4,22,0.1818,1,"{471, 527, 522, 205}"
304,1,92,0,0.0792166,"\int \frac{x}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x/((a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{b}{2 \left(a+b x^2\right) (b c-a d)^2}-\frac{d}{2 \left(c+d x^2\right) (b c-a d)^2}-\frac{b d \log \left(a+b x^2\right)}{(b c-a d)^3}+\frac{b d \log \left(c+d x^2\right)}{(b c-a d)^3}","-\frac{b}{2 \left(a+b x^2\right) (b c-a d)^2}-\frac{d}{2 \left(c+d x^2\right) (b c-a d)^2}-\frac{b d \log \left(a+b x^2\right)}{(b c-a d)^3}+\frac{b d \log \left(c+d x^2\right)}{(b c-a d)^3}",1,"-b/(2*(b*c - a*d)^2*(a + b*x^2)) - d/(2*(b*c - a*d)^2*(c + d*x^2)) - (b*d*Log[a + b*x^2])/(b*c - a*d)^3 + (b*d*Log[c + d*x^2])/(b*c - a*d)^3","A",3,2,20,0.1000,1,"{444, 44}"
305,1,167,0,0.1982044,"\int \frac{1}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/((a + b*x^2)^2*(c + d*x^2)^2),x]","\frac{b^{3/2} (b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)^3}+\frac{d^{3/2} (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} (b c-a d)^3}+\frac{b x}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d x (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}","\frac{b^{3/2} (b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)^3}+\frac{d^{3/2} (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{3/2} (b c-a d)^3}+\frac{b x}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d x (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}",1,"(d*(b*c + a*d)*x)/(2*a*c*(b*c - a*d)^2*(c + d*x^2)) + (b*x)/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) + (b^(3/2)*(b*c - 5*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*(b*c - a*d)^3) + (d^(3/2)*(5*b*c - a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(3/2)*(b*c - a*d)^3)","A",5,4,19,0.2105,1,"{414, 527, 522, 205}"
306,1,141,0,0.1685804,"\int \frac{1}{x \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{b^2 (b c-3 a d) \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^3}+\frac{\log (x)}{a^2 c^2}+\frac{b^2}{2 a \left(a+b x^2\right) (b c-a d)^2}-\frac{d^2 (3 b c-a d) \log \left(c+d x^2\right)}{2 c^2 (b c-a d)^3}+\frac{d^2}{2 c \left(c+d x^2\right) (b c-a d)^2}","-\frac{b^2 (b c-3 a d) \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^3}+\frac{\log (x)}{a^2 c^2}+\frac{b^2}{2 a \left(a+b x^2\right) (b c-a d)^2}-\frac{d^2 (3 b c-a d) \log \left(c+d x^2\right)}{2 c^2 (b c-a d)^3}+\frac{d^2}{2 c \left(c+d x^2\right) (b c-a d)^2}",1,"b^2/(2*a*(b*c - a*d)^2*(a + b*x^2)) + d^2/(2*c*(b*c - a*d)^2*(c + d*x^2)) + Log[x]/(a^2*c^2) - (b^2*(b*c - 3*a*d)*Log[a + b*x^2])/(2*a^2*(b*c - a*d)^3) - (d^2*(3*b*c - a*d)*Log[c + d*x^2])/(2*c^2*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 88}"
307,1,218,0,0.3113063,"\int \frac{1}{x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x^2*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{3 a^2 d^2-4 a b c d+3 b^2 c^2}{2 a^2 c^2 x (b c-a d)^2}-\frac{b^{5/2} (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)^3}-\frac{d^{5/2} (7 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{5/2} (b c-a d)^3}+\frac{b}{2 a x \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x \left(c+d x^2\right) (b c-a d)^2}","-\frac{3 a^2 d^2-4 a b c d+3 b^2 c^2}{2 a^2 c^2 x (b c-a d)^2}-\frac{b^{5/2} (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)^3}-\frac{d^{5/2} (7 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{5/2} (b c-a d)^3}+\frac{b}{2 a x \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x \left(c+d x^2\right) (b c-a d)^2}",1,"-(3*b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)/(2*a^2*c^2*(b*c - a*d)^2*x) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*x*(c + d*x^2)) + b/(2*a*(b*c - a*d)*x*(a + b*x^2)*(c + d*x^2)) - (b^(5/2)*(3*b*c - 7*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*(b*c - a*d)^3) - (d^(5/2)*(7*b*c - 3*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(5/2)*(b*c - a*d)^3)","A",6,5,22,0.2273,1,"{472, 579, 583, 522, 205}"
308,1,156,0,0.2089597,"\int \frac{1}{x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x^3*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{b^3}{2 a^2 \left(a+b x^2\right) (b c-a d)^2}+\frac{b^3 (b c-2 a d) \log \left(a+b x^2\right)}{a^3 (b c-a d)^3}-\frac{2 \log (x) (a d+b c)}{a^3 c^3}-\frac{1}{2 a^2 c^2 x^2}-\frac{d^3}{2 c^2 \left(c+d x^2\right) (b c-a d)^2}+\frac{d^3 (2 b c-a d) \log \left(c+d x^2\right)}{c^3 (b c-a d)^3}","-\frac{b^3}{2 a^2 \left(a+b x^2\right) (b c-a d)^2}+\frac{b^3 (b c-2 a d) \log \left(a+b x^2\right)}{a^3 (b c-a d)^3}-\frac{2 \log (x) (a d+b c)}{a^3 c^3}-\frac{1}{2 a^2 c^2 x^2}-\frac{d^3}{2 c^2 \left(c+d x^2\right) (b c-a d)^2}+\frac{d^3 (2 b c-a d) \log \left(c+d x^2\right)}{c^3 (b c-a d)^3}",1,"-1/(2*a^2*c^2*x^2) - b^3/(2*a^2*(b*c - a*d)^2*(a + b*x^2)) - d^3/(2*c^2*(b*c - a*d)^2*(c + d*x^2)) - (2*(b*c + a*d)*Log[x])/(a^3*c^3) + (b^3*(b*c - 2*a*d)*Log[a + b*x^2])/(a^3*(b*c - a*d)^3) + (d^3*(2*b*c - a*d)*Log[c + d*x^2])/(c^3*(b*c - a*d)^3)","A",3,2,22,0.09091,1,"{446, 88}"
309,1,271,0,0.4482716,"\int \frac{1}{x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x^4*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{5 a^2 d^2-4 a b c d+5 b^2 c^2}{6 a^2 c^2 x^3 (b c-a d)^2}+\frac{(a d+b c) \left(5 a^2 d^2-9 a b c d+5 b^2 c^2\right)}{2 a^3 c^3 x (b c-a d)^2}+\frac{b^{7/2} (5 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} (b c-a d)^3}+\frac{d^{7/2} (9 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{7/2} (b c-a d)^3}+\frac{b}{2 a x^3 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x^3 \left(c+d x^2\right) (b c-a d)^2}","-\frac{5 a^2 d^2-4 a b c d+5 b^2 c^2}{6 a^2 c^2 x^3 (b c-a d)^2}+\frac{(a d+b c) \left(5 a^2 d^2-9 a b c d+5 b^2 c^2\right)}{2 a^3 c^3 x (b c-a d)^2}+\frac{b^{7/2} (5 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} (b c-a d)^3}+\frac{d^{7/2} (9 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{2 c^{7/2} (b c-a d)^3}+\frac{b}{2 a x^3 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x^3 \left(c+d x^2\right) (b c-a d)^2}",1,"-(5*b^2*c^2 - 4*a*b*c*d + 5*a^2*d^2)/(6*a^2*c^2*(b*c - a*d)^2*x^3) + ((b*c + a*d)*(5*b^2*c^2 - 9*a*b*c*d + 5*a^2*d^2))/(2*a^3*c^3*(b*c - a*d)^2*x) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*x^3*(c + d*x^2)) + b/(2*a*(b*c - a*d)*x^3*(a + b*x^2)*(c + d*x^2)) + (b^(7/2)*(5*b*c - 9*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2)*(b*c - a*d)^3) + (d^(7/2)*(9*b*c - 5*a*d)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(2*c^(7/2)*(b*c - a*d)^3)","A",7,5,22,0.2273,1,"{472, 579, 583, 522, 205}"
310,1,207,0,0.2769688,"\int \frac{x^4}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^4/((a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{3 \left(a^2 d^2+6 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 \sqrt{c} \sqrt{d} (b c-a d)^4}+\frac{3 x (3 a d+b c)}{8 \left(c+d x^2\right) (b c-a d)^3}+\frac{x (2 a d+b c)}{4 b \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}-\frac{3 \sqrt{a} \sqrt{b} (a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 (b c-a d)^4}","\frac{3 \left(a^2 d^2+6 a b c d+b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 \sqrt{c} \sqrt{d} (b c-a d)^4}+\frac{3 x (3 a d+b c)}{8 \left(c+d x^2\right) (b c-a d)^3}+\frac{x (2 a d+b c)}{4 b \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}-\frac{3 \sqrt{a} \sqrt{b} (a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 (b c-a d)^4}",1,"((b*c + 2*a*d)*x)/(4*b*(b*c - a*d)^2*(c + d*x^2)^2) + (a*x)/(2*b*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) + (3*(b*c + 3*a*d)*x)/(8*(b*c - a*d)^3*(c + d*x^2)) - (3*Sqrt[a]*Sqrt[b]*(b*c + a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*(b*c - a*d)^4) + (3*(b^2*c^2 + 6*a*b*c*d + a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*Sqrt[c]*Sqrt[d]*(b*c - a*d)^4)","A",6,4,22,0.1818,1,"{470, 527, 522, 205}"
311,1,142,0,0.1525563,"\int \frac{x^3}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^3/((a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{a b}{2 \left(a+b x^2\right) (b c-a d)^3}+\frac{a d+b c}{2 \left(c+d x^2\right) (b c-a d)^3}+\frac{c}{4 \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{b (2 a d+b c) \log \left(a+b x^2\right)}{2 (b c-a d)^4}-\frac{b (2 a d+b c) \log \left(c+d x^2\right)}{2 (b c-a d)^4}","\frac{a b}{2 \left(a+b x^2\right) (b c-a d)^3}+\frac{a d+b c}{2 \left(c+d x^2\right) (b c-a d)^3}+\frac{c}{4 \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{b (2 a d+b c) \log \left(a+b x^2\right)}{2 (b c-a d)^4}-\frac{b (2 a d+b c) \log \left(c+d x^2\right)}{2 (b c-a d)^4}",1,"(a*b)/(2*(b*c - a*d)^3*(a + b*x^2)) + c/(4*(b*c - a*d)^2*(c + d*x^2)^2) + (b*c + a*d)/(2*(b*c - a*d)^3*(c + d*x^2)) + (b*(b*c + 2*a*d)*Log[a + b*x^2])/(2*(b*c - a*d)^4) - (b*(b*c + 2*a*d)*Log[c + d*x^2])/(2*(b*c - a*d)^4)","A",3,2,22,0.09091,1,"{446, 77}"
312,1,200,0,0.2524238,"\int \frac{x^2}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^2/((a + b*x^2)^2*(c + d*x^2)^3),x]","-\frac{\sqrt{d} \left(-a^2 d^2+10 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{3/2} (b c-a d)^4}+\frac{b^{3/2} (5 a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} (b c-a d)^4}-\frac{d x (a d+11 b c)}{8 c \left(c+d x^2\right) (b c-a d)^3}-\frac{3 d x}{4 \left(c+d x^2\right)^2 (b c-a d)^2}-\frac{x}{2 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}","-\frac{\sqrt{d} \left(-a^2 d^2+10 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{3/2} (b c-a d)^4}+\frac{b^{3/2} (5 a d+b c) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 \sqrt{a} (b c-a d)^4}-\frac{d x (a d+11 b c)}{8 c \left(c+d x^2\right) (b c-a d)^3}-\frac{3 d x}{4 \left(c+d x^2\right)^2 (b c-a d)^2}-\frac{x}{2 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}",1,"(-3*d*x)/(4*(b*c - a*d)^2*(c + d*x^2)^2) - x/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) - (d*(11*b*c + a*d)*x)/(8*c*(b*c - a*d)^3*(c + d*x^2)) + (b^(3/2)*(b*c + 5*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*Sqrt[a]*(b*c - a*d)^4) - (Sqrt[d]*(15*b^2*c^2 + 10*a*b*c*d - a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(3/2)*(b*c - a*d)^4)","A",6,4,22,0.1818,1,"{471, 527, 522, 205}"
313,1,126,0,0.1092234,"\int \frac{x}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x/((a + b*x^2)^2*(c + d*x^2)^3),x]","-\frac{b^2}{2 \left(a+b x^2\right) (b c-a d)^3}-\frac{3 b^2 d \log \left(a+b x^2\right)}{2 (b c-a d)^4}+\frac{3 b^2 d \log \left(c+d x^2\right)}{2 (b c-a d)^4}-\frac{b d}{\left(c+d x^2\right) (b c-a d)^3}-\frac{d}{4 \left(c+d x^2\right)^2 (b c-a d)^2}","-\frac{b^2}{2 \left(a+b x^2\right) (b c-a d)^3}-\frac{3 b^2 d \log \left(a+b x^2\right)}{2 (b c-a d)^4}+\frac{3 b^2 d \log \left(c+d x^2\right)}{2 (b c-a d)^4}-\frac{b d}{\left(c+d x^2\right) (b c-a d)^3}-\frac{d}{4 \left(c+d x^2\right)^2 (b c-a d)^2}",1,"-b^2/(2*(b*c - a*d)^3*(a + b*x^2)) - d/(4*(b*c - a*d)^2*(c + d*x^2)^2) - (b*d)/((b*c - a*d)^3*(c + d*x^2)) - (3*b^2*d*Log[a + b*x^2])/(2*(b*c - a*d)^4) + (3*b^2*d*Log[c + d*x^2])/(2*(b*c - a*d)^4)","A",3,2,20,0.1000,1,"{444, 44}"
314,1,230,0,0.3014246,"\int \frac{1}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/((a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d^{3/2} \left(3 a^2 d^2-14 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} (b c-a d)^4}+\frac{b^{5/2} (b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)^4}+\frac{d x (4 b c-a d) (3 a d+b c)}{8 a c^2 \left(c+d x^2\right) (b c-a d)^3}+\frac{b x}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d x (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}","\frac{d^{3/2} \left(3 a^2 d^2-14 a b c d+35 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{5/2} (b c-a d)^4}+\frac{b^{5/2} (b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{3/2} (b c-a d)^4}+\frac{d x (4 b c-a d) (3 a d+b c)}{8 a c^2 \left(c+d x^2\right) (b c-a d)^3}+\frac{b x}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d x (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}",1,"(d*(2*b*c + a*d)*x)/(4*a*c*(b*c - a*d)^2*(c + d*x^2)^2) + (b*x)/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) + (d*(4*b*c - a*d)*(b*c + 3*a*d)*x)/(8*a*c^2*(b*c - a*d)^3*(c + d*x^2)) + (b^(5/2)*(b*c - 7*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(3/2)*(b*c - a*d)^4) + (d^(3/2)*(35*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(5/2)*(b*c - a*d)^4)","A",6,4,19,0.2105,1,"{414, 527, 522, 205}"
315,1,192,0,0.2406506,"\int \frac{1}{x \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x*(a + b*x^2)^2*(c + d*x^2)^3),x]","-\frac{d^2 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^4}-\frac{b^3 (b c-4 a d) \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^4}+\frac{\log (x)}{a^2 c^3}+\frac{b^3}{2 a \left(a+b x^2\right) (b c-a d)^3}+\frac{d^2 (3 b c-a d)}{2 c^2 \left(c+d x^2\right) (b c-a d)^3}+\frac{d^2}{4 c \left(c+d x^2\right)^2 (b c-a d)^2}","-\frac{d^2 \left(a^2 d^2-4 a b c d+6 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^3 (b c-a d)^4}-\frac{b^3 (b c-4 a d) \log \left(a+b x^2\right)}{2 a^2 (b c-a d)^4}+\frac{\log (x)}{a^2 c^3}+\frac{b^3}{2 a \left(a+b x^2\right) (b c-a d)^3}+\frac{d^2 (3 b c-a d)}{2 c^2 \left(c+d x^2\right) (b c-a d)^3}+\frac{d^2}{4 c \left(c+d x^2\right)^2 (b c-a d)^2}",1,"b^3/(2*a*(b*c - a*d)^3*(a + b*x^2)) + d^2/(4*c*(b*c - a*d)^2*(c + d*x^2)^2) + (d^2*(3*b*c - a*d))/(2*c^2*(b*c - a*d)^3*(c + d*x^2)) + Log[x]/(a^2*c^3) - (b^3*(b*c - 4*a*d)*Log[a + b*x^2])/(2*a^2*(b*c - a*d)^4) - (d^2*(6*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Log[c + d*x^2])/(2*c^3*(b*c - a*d)^4)","A",3,2,22,0.09091,1,"{446, 88}"
316,1,297,0,0.4965677,"\int \frac{1}{x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x^2*(a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d \left(-5 a^2 d^2+13 a b c d+4 b^2 c^2\right)}{8 a c^2 x \left(c+d x^2\right) (b c-a d)^3}-\frac{3 (2 b c-a d) \left(5 a^2 d^2-3 a b c d+2 b^2 c^2\right)}{8 a^2 c^3 x (b c-a d)^3}-\frac{3 d^{5/2} \left(5 a^2 d^2-18 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{7/2} (b c-a d)^4}-\frac{3 b^{7/2} (b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)^4}+\frac{b}{2 a x \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d (a d+2 b c)}{4 a c x \left(c+d x^2\right)^2 (b c-a d)^2}","\frac{d \left(-5 a^2 d^2+13 a b c d+4 b^2 c^2\right)}{8 a c^2 x \left(c+d x^2\right) (b c-a d)^3}-\frac{3 (2 b c-a d) \left(5 a^2 d^2-3 a b c d+2 b^2 c^2\right)}{8 a^2 c^3 x (b c-a d)^3}-\frac{3 d^{5/2} \left(5 a^2 d^2-18 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{7/2} (b c-a d)^4}-\frac{3 b^{7/2} (b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{5/2} (b c-a d)^4}+\frac{b}{2 a x \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d (a d+2 b c)}{4 a c x \left(c+d x^2\right)^2 (b c-a d)^2}",1,"(-3*(2*b*c - a*d)*(2*b^2*c^2 - 3*a*b*c*d + 5*a^2*d^2))/(8*a^2*c^3*(b*c - a*d)^3*x) + (d*(2*b*c + a*d))/(4*a*c*(b*c - a*d)^2*x*(c + d*x^2)^2) + b/(2*a*(b*c - a*d)*x*(a + b*x^2)*(c + d*x^2)^2) + (d*(4*b^2*c^2 + 13*a*b*c*d - 5*a^2*d^2))/(8*a*c^2*(b*c - a*d)^3*x*(c + d*x^2)) - (3*b^(7/2)*(b*c - 3*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(5/2)*(b*c - a*d)^4) - (3*d^(5/2)*(21*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(7/2)*(b*c - a*d)^4)","A",7,5,22,0.2273,1,"{472, 579, 583, 522, 205}"
317,1,215,0,0.2943293,"\int \frac{1}{x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x^3*(a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d^3 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^4 (b c-a d)^4}-\frac{b^4}{2 a^2 \left(a+b x^2\right) (b c-a d)^3}+\frac{b^4 (2 b c-5 a d) \log \left(a+b x^2\right)}{2 a^3 (b c-a d)^4}-\frac{\log (x) (3 a d+2 b c)}{a^3 c^4}-\frac{1}{2 a^2 c^3 x^2}-\frac{d^3 (2 b c-a d)}{c^3 \left(c+d x^2\right) (b c-a d)^3}-\frac{d^3}{4 c^2 \left(c+d x^2\right)^2 (b c-a d)^2}","\frac{d^3 \left(3 a^2 d^2-10 a b c d+10 b^2 c^2\right) \log \left(c+d x^2\right)}{2 c^4 (b c-a d)^4}-\frac{b^4}{2 a^2 \left(a+b x^2\right) (b c-a d)^3}+\frac{b^4 (2 b c-5 a d) \log \left(a+b x^2\right)}{2 a^3 (b c-a d)^4}-\frac{\log (x) (3 a d+2 b c)}{a^3 c^4}-\frac{1}{2 a^2 c^3 x^2}-\frac{d^3 (2 b c-a d)}{c^3 \left(c+d x^2\right) (b c-a d)^3}-\frac{d^3}{4 c^2 \left(c+d x^2\right)^2 (b c-a d)^2}",1,"-1/(2*a^2*c^3*x^2) - b^4/(2*a^2*(b*c - a*d)^3*(a + b*x^2)) - d^3/(4*c^2*(b*c - a*d)^2*(c + d*x^2)^2) - (d^3*(2*b*c - a*d))/(c^3*(b*c - a*d)^3*(c + d*x^2)) - ((2*b*c + 3*a*d)*Log[x])/(a^3*c^4) + (b^4*(2*b*c - 5*a*d)*Log[a + b*x^2])/(2*a^3*(b*c - a*d)^4) + (d^3*(10*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*Log[c + d*x^2])/(2*c^4*(b*c - a*d)^4)","A",3,2,22,0.09091,1,"{446, 88}"
318,1,377,0,0.6860396,"\int \frac{1}{x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x^4*(a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d \left(-7 a^2 d^2+15 a b c d+4 b^2 c^2\right)}{8 a c^2 x^3 \left(c+d x^2\right) (b c-a d)^3}-\frac{75 a^2 b c d^2-35 a^3 d^3-24 a b^2 c^2 d+20 b^3 c^3}{24 a^2 c^3 x^3 (b c-a d)^3}+\frac{-24 a^2 b^2 c^2 d^2+75 a^3 b c d^3-35 a^4 d^4-24 a b^3 c^3 d+20 b^4 c^4}{8 a^3 c^4 x (b c-a d)^3}+\frac{d^{7/2} \left(35 a^2 d^2-110 a b c d+99 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{9/2} (b c-a d)^4}+\frac{b^{9/2} (5 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} (b c-a d)^4}+\frac{b}{2 a x^3 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d (a d+2 b c)}{4 a c x^3 \left(c+d x^2\right)^2 (b c-a d)^2}","\frac{d \left(-7 a^2 d^2+15 a b c d+4 b^2 c^2\right)}{8 a c^2 x^3 \left(c+d x^2\right) (b c-a d)^3}-\frac{75 a^2 b c d^2-35 a^3 d^3-24 a b^2 c^2 d+20 b^3 c^3}{24 a^2 c^3 x^3 (b c-a d)^3}+\frac{-24 a^2 b^2 c^2 d^2+75 a^3 b c d^3-35 a^4 d^4-24 a b^3 c^3 d+20 b^4 c^4}{8 a^3 c^4 x (b c-a d)^3}+\frac{d^{7/2} \left(35 a^2 d^2-110 a b c d+99 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)}{8 c^{9/2} (b c-a d)^4}+\frac{b^{9/2} (5 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{2 a^{7/2} (b c-a d)^4}+\frac{b}{2 a x^3 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d (a d+2 b c)}{4 a c x^3 \left(c+d x^2\right)^2 (b c-a d)^2}",1,"-(20*b^3*c^3 - 24*a*b^2*c^2*d + 75*a^2*b*c*d^2 - 35*a^3*d^3)/(24*a^2*c^3*(b*c - a*d)^3*x^3) + (20*b^4*c^4 - 24*a*b^3*c^3*d - 24*a^2*b^2*c^2*d^2 + 75*a^3*b*c*d^3 - 35*a^4*d^4)/(8*a^3*c^4*(b*c - a*d)^3*x) + (d*(2*b*c + a*d))/(4*a*c*(b*c - a*d)^2*x^3*(c + d*x^2)^2) + b/(2*a*(b*c - a*d)*x^3*(a + b*x^2)*(c + d*x^2)^2) + (d*(4*b^2*c^2 + 15*a*b*c*d - 7*a^2*d^2))/(8*a*c^2*(b*c - a*d)^3*x^3*(c + d*x^2)) + (b^(9/2)*(5*b*c - 11*a*d)*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(2*a^(7/2)*(b*c - a*d)^4) + (d^(7/2)*(99*b^2*c^2 - 110*a*b*c*d + 35*a^2*d^2)*ArcTan[(Sqrt[d]*x)/Sqrt[c]])/(8*c^(9/2)*(b*c - a*d)^4)","A",8,5,22,0.2273,1,"{472, 579, 583, 522, 205}"
319,1,96,0,0.0651068,"\int x^m \left(a+b x^2\right)^3 \left(A+B x^2\right) \, dx","Int[x^m*(a + b*x^2)^3*(A + B*x^2),x]","\frac{a^2 x^{m+3} (a B+3 A b)}{m+3}+\frac{a^3 A x^{m+1}}{m+1}+\frac{b^2 x^{m+7} (3 a B+A b)}{m+7}+\frac{3 a b x^{m+5} (a B+A b)}{m+5}+\frac{b^3 B x^{m+9}}{m+9}","\frac{a^2 x^{m+3} (a B+3 A b)}{m+3}+\frac{a^3 A x^{m+1}}{m+1}+\frac{b^2 x^{m+7} (3 a B+A b)}{m+7}+\frac{3 a b x^{m+5} (a B+A b)}{m+5}+\frac{b^3 B x^{m+9}}{m+9}",1,"(a^3*A*x^(1 + m))/(1 + m) + (a^2*(3*A*b + a*B)*x^(3 + m))/(3 + m) + (3*a*b*(A*b + a*B)*x^(5 + m))/(5 + m) + (b^2*(A*b + 3*a*B)*x^(7 + m))/(7 + m) + (b^3*B*x^(9 + m))/(9 + m)","A",2,1,20,0.05000,1,"{448}"
320,1,71,0,0.0421679,"\int x^m \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[x^m*(a + b*x^2)^2*(A + B*x^2),x]","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+3} (a B+2 A b)}{m+3}+\frac{b x^{m+5} (2 a B+A b)}{m+5}+\frac{b^2 B x^{m+7}}{m+7}","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+3} (a B+2 A b)}{m+3}+\frac{b x^{m+5} (2 a B+A b)}{m+5}+\frac{b^2 B x^{m+7}}{m+7}",1,"(a^2*A*x^(1 + m))/(1 + m) + (a*(2*A*b + a*B)*x^(3 + m))/(3 + m) + (b*(A*b + 2*a*B)*x^(5 + m))/(5 + m) + (b^2*B*x^(7 + m))/(7 + m)","A",2,1,20,0.05000,1,"{448}"
321,1,45,0,0.0214541,"\int x^m \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[x^m*(a + b*x^2)*(A + B*x^2),x]","\frac{x^{m+3} (a B+A b)}{m+3}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+5}}{m+5}","\frac{x^{m+3} (a B+A b)}{m+3}+\frac{a A x^{m+1}}{m+1}+\frac{b B x^{m+5}}{m+5}",1,"(a*A*x^(1 + m))/(1 + m) + ((A*b + a*B)*x^(3 + m))/(3 + m) + (b*B*x^(5 + m))/(5 + m)","A",2,1,18,0.05556,1,"{448}"
322,1,66,0,0.0330978,"\int \frac{x^m \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^m*(A + B*x^2))/(a + b*x^2),x]","\frac{x^{m+1} (A b-a B) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{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}{2};\frac{m+3}{2};-\frac{b x^2}{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)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b*(1 + m))","A",2,2,20,0.1000,1,"{459, 364}"
323,1,93,0,0.0439417,"\int \frac{x^m \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^m*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{x^{m+1} (a B (m+1)+A (b-b m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b (m+1)}+\frac{x^{m+1} (A b-a B)}{2 a b \left(a+b x^2\right)}","\frac{x^{m+1} (a B (m+1)+A (b-b m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b (m+1)}+\frac{x^{m+1} (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"((A*b - a*B)*x^(1 + m))/(2*a*b*(a + b*x^2)) + ((a*B*(1 + m) + A*(b - b*m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*b*(1 + m))","A",2,2,20,0.1000,1,"{457, 364}"
324,1,93,0,0.0415536,"\int \frac{x^m \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^m*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{x^{m+1} (a B (m+1)+A b (3-m)) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{4 a^3 b (m+1)}+\frac{x^{m+1} (A b-a B)}{4 a b \left(a+b x^2\right)^2}","\frac{x^{m+1} (a B (m+1)+A b (3-m)) \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{4 a^3 b (m+1)}+\frac{x^{m+1} (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"((A*b - a*B)*x^(1 + m))/(4*a*b*(a + b*x^2)^2) + ((A*b*(3 - m) + a*B*(1 + m))*x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(4*a^3*b*(1 + m))","A",2,2,20,0.1000,1,"{457, 364}"
325,1,151,0,0.0885689,"\int x^m \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^m*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{c x^{m+5} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)}{m+5}+\frac{d x^{m+7} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)}{m+7}+\frac{a^2 c^3 x^{m+1}}{m+1}+\frac{a c^2 x^{m+3} (3 a d+2 b c)}{m+3}+\frac{b d^2 x^{m+9} (2 a d+3 b c)}{m+9}+\frac{b^2 d^3 x^{m+11}}{m+11}","\frac{c x^{m+5} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)}{m+5}+\frac{d x^{m+7} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)}{m+7}+\frac{a^2 c^3 x^{m+1}}{m+1}+\frac{a c^2 x^{m+3} (3 a d+2 b c)}{m+3}+\frac{b d^2 x^{m+9} (2 a d+3 b c)}{m+9}+\frac{b^2 d^3 x^{m+11}}{m+11}",1,"(a^2*c^3*x^(1 + m))/(1 + m) + (a*c^2*(2*b*c + 3*a*d)*x^(3 + m))/(3 + m) + (c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(5 + m))/(5 + m) + (d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(7 + m))/(7 + m) + (b*d^2*(3*b*c + 2*a*d)*x^(9 + m))/(9 + m) + (b^2*d^3*x^(11 + m))/(11 + m)","A",2,1,22,0.04545,1,"{448}"
326,1,109,0,0.0622496,"\int x^m \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^m*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{x^{m+5} \left(a^2 d^2+4 a b c d+b^2 c^2\right)}{m+5}+\frac{a^2 c^2 x^{m+1}}{m+1}+\frac{2 a c x^{m+3} (a d+b c)}{m+3}+\frac{2 b d x^{m+7} (a d+b c)}{m+7}+\frac{b^2 d^2 x^{m+9}}{m+9}","\frac{x^{m+5} \left(a^2 d^2+4 a b c d+b^2 c^2\right)}{m+5}+\frac{a^2 c^2 x^{m+1}}{m+1}+\frac{2 a c x^{m+3} (a d+b c)}{m+3}+\frac{2 b d x^{m+7} (a d+b c)}{m+7}+\frac{b^2 d^2 x^{m+9}}{m+9}",1,"(a^2*c^2*x^(1 + m))/(1 + m) + (2*a*c*(b*c + a*d)*x^(3 + m))/(3 + m) + ((b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(5 + m))/(5 + m) + (2*b*d*(b*c + a*d)*x^(7 + m))/(7 + m) + (b^2*d^2*x^(9 + m))/(9 + m)","A",2,1,22,0.04545,1,"{448}"
327,1,71,0,0.0374977,"\int x^m \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^m*(a + b*x^2)^2*(c + d*x^2),x]","\frac{a^2 c x^{m+1}}{m+1}+\frac{a x^{m+3} (a d+2 b c)}{m+3}+\frac{b x^{m+5} (2 a d+b c)}{m+5}+\frac{b^2 d x^{m+7}}{m+7}","\frac{a^2 c x^{m+1}}{m+1}+\frac{a x^{m+3} (a d+2 b c)}{m+3}+\frac{b x^{m+5} (2 a d+b c)}{m+5}+\frac{b^2 d x^{m+7}}{m+7}",1,"(a^2*c*x^(1 + m))/(1 + m) + (a*(2*b*c + a*d)*x^(3 + m))/(3 + m) + (b*(b*c + 2*a*d)*x^(5 + m))/(5 + m) + (b^2*d*x^(7 + m))/(7 + m)","A",2,1,20,0.05000,1,"{448}"
328,1,94,0,0.0597319,"\int \frac{x^m \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^m*(a + b*x^2)^2)/(c + d*x^2),x]","\frac{x^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d^2 (m+1)}-\frac{b x^{m+1} (b c-2 a d)}{d^2 (m+1)}+\frac{b^2 x^{m+3}}{d (m+3)}","\frac{x^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c d^2 (m+1)}-\frac{b x^{m+1} (b c-2 a d)}{d^2 (m+1)}+\frac{b^2 x^{m+3}}{d (m+3)}",1,"-((b*(b*c - 2*a*d)*x^(1 + m))/(d^2*(1 + m))) + (b^2*x^(3 + m))/(d*(3 + m)) + ((b*c - a*d)^2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(c*d^2*(1 + m))","A",3,2,22,0.09091,1,"{461, 364}"
329,1,120,0,0.103223,"\int \frac{x^m \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^m*(a + b*x^2)^2)/(c + d*x^2)^2,x]","-\frac{x^{m+1} (b c-a d) (a d (1-m)+b c (m+3)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{2 c^2 d^2 (m+1)}+\frac{x^{m+1} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{b^2 x^{m+1}}{d^2 (m+1)}","-\frac{x^{m+1} (b c-a d) (a d (1-m)+b c (m+3)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{2 c^2 d^2 (m+1)}+\frac{x^{m+1} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{b^2 x^{m+1}}{d^2 (m+1)}",1,"(b^2*x^(1 + m))/(d^2*(1 + m)) + ((b*c - a*d)^2*x^(1 + m))/(2*c*d^2*(c + d*x^2)) - ((b*c - a*d)*(a*d*(1 - m) + b*c*(3 + m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(2*c^2*d^2*(1 + m))","A",3,3,22,0.1364,1,"{463, 459, 364}"
330,1,166,0,0.1535982,"\int \frac{x^m \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^m*(a + b*x^2)^2)/(c + d*x^2)^3,x]","\frac{x^{m+1} \left(\frac{(1-m) \left(4 a^2 d^2-(m+1) (b c-a d)^2\right)}{c^2 (m+1)}+4 b^2\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{8 c d^2}-\frac{x^{m+1} (b c-a d) (a d (3-m)+b c (m+5))}{8 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{m+1} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","\frac{x^{m+1} \left(a^2 d^2 \left(m^2-4 m+3\right)+2 a b c d \left(1-m^2\right)+b^2 c^2 \left(m^2+4 m+3\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{8 c^3 d^2 (m+1)}-\frac{x^{m+1} (b c-a d) (a d (3-m)+b c (m+5))}{8 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{m+1} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"((b*c - a*d)^2*x^(1 + m))/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(a*d*(3 - m) + b*c*(5 + m))*x^(1 + m))/(8*c^2*d^2*(c + d*x^2)) + ((4*b^2 + ((1 - m)*(4*a^2*d^2 - (b*c - a*d)^2*(1 + m)))/(c^2*(1 + m)))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(8*c*d^2)","A",3,3,22,0.1364,1,"{463, 457, 364}"
331,1,133,0,0.0860909,"\int \frac{x^m \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^m*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{d x^{m+1} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3 (m+1)}+\frac{d^2 x^{m+3} (3 b c-a d)}{b^2 (m+3)}+\frac{x^{m+1} (b c-a d)^3 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^3 (m+1)}+\frac{d^3 x^{m+5}}{b (m+5)}","\frac{d x^{m+1} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3 (m+1)}+\frac{d^2 x^{m+3} (3 b c-a d)}{b^2 (m+3)}+\frac{x^{m+1} (b c-a d)^3 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^3 (m+1)}+\frac{d^3 x^{m+5}}{b (m+5)}",1,"(d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^(1 + m))/(b^3*(1 + m)) + (d^2*(3*b*c - a*d)*x^(3 + m))/(b^2*(3 + m)) + (d^3*x^(5 + m))/(b*(5 + m)) + ((b*c - a*d)^3*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b^3*(1 + m))","A",3,2,22,0.09091,1,"{461, 364}"
332,1,94,0,0.0576673,"\int \frac{x^m \left(c+d x^2\right)^2}{a+b x^2} \, dx","Int[(x^m*(c + d*x^2)^2)/(a + b*x^2),x]","\frac{x^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^2 (m+1)}+\frac{d x^{m+1} (2 b c-a d)}{b^2 (m+1)}+\frac{d^2 x^{m+3}}{b (m+3)}","\frac{x^{m+1} (b c-a d)^2 \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b^2 (m+1)}+\frac{d x^{m+1} (2 b c-a d)}{b^2 (m+1)}+\frac{d^2 x^{m+3}}{b (m+3)}",1,"(d*(2*b*c - a*d)*x^(1 + m))/(b^2*(1 + m)) + (d^2*x^(3 + m))/(b*(3 + m)) + ((b*c - a*d)^2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b^2*(1 + m))","A",3,2,22,0.09091,1,"{461, 364}"
333,1,66,0,0.0311237,"\int \frac{x^m \left(c+d x^2\right)}{a+b x^2} \, dx","Int[(x^m*(c + d*x^2))/(a + b*x^2),x]","\frac{x^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b (m+1)}+\frac{d x^{m+1}}{b (m+1)}","\frac{x^{m+1} (b c-a d) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a b (m+1)}+\frac{d x^{m+1}}{b (m+1)}",1,"(d*x^(1 + m))/(b*(1 + m)) + ((b*c - a*d)*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*b*(1 + m))","A",2,2,20,0.1000,1,"{459, 364}"
334,1,102,0,0.0437234,"\int \frac{x^m}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^m/((a + b*x^2)*(c + d*x^2)),x]","\frac{b x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1) (b c-a d)}-\frac{d x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)}","\frac{b x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{a (m+1) (b c-a d)}-\frac{d x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)}",1,"(b*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(a*(b*c - a*d)*(1 + m)) - (d*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(c*(b*c - a*d)*(1 + m))","A",3,2,22,0.09091,1,"{482, 364}"
335,1,156,0,0.1899392,"\int \frac{x^m}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x^m/((a + b*x^2)^2*(c + d*x^2)),x]","\frac{b x^{m+1} (b c (1-m)-a d (3-m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^2}+\frac{d^2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) (b c-a d)}","\frac{b x^{m+1} (b c (1-m)-a d (3-m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^2}+\frac{d^2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) (b c-a d)}",1,"(b*x^(1 + m))/(2*a*(b*c - a*d)*(a + b*x^2)) + (b*(b*c*(1 - m) - a*d*(3 - m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*(b*c - a*d)^2*(1 + m)) + (d^2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(c*(b*c - a*d)^2*(1 + m))","A",5,3,22,0.1364,1,"{472, 584, 364}"
336,1,234,0,0.3738125,"\int \frac{x^m}{\left(a+b x^2\right)^3 \left(c+d x^2\right)} \, dx","Int[x^m/((a + b*x^2)^3*(c + d*x^2)),x]","\frac{b x^{m+1} \left(a^2 d^2 \left(m^2-8 m+15\right)-2 a b c d \left(m^2-6 m+5\right)+b^2 c^2 \left(m^2-4 m+3\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{8 a^3 (m+1) (b c-a d)^3}+\frac{b x^{m+1} (b c (3-m)-a d (7-m))}{8 a^2 \left(a+b x^2\right) (b c-a d)^2}-\frac{d^3 x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)^3}+\frac{b x^{m+1}}{4 a \left(a+b x^2\right)^2 (b c-a d)}","\frac{b x^{m+1} \left(a^2 d^2 \left(m^2-8 m+15\right)-2 a b c d \left(m^2-6 m+5\right)+b^2 c^2 \left(m^2-4 m+3\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{8 a^3 (m+1) (b c-a d)^3}+\frac{b x^{m+1} (b c (3-m)-a d (7-m))}{8 a^2 \left(a+b x^2\right) (b c-a d)^2}-\frac{d^3 x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)^3}+\frac{b x^{m+1}}{4 a \left(a+b x^2\right)^2 (b c-a d)}",1,"(b*x^(1 + m))/(4*a*(b*c - a*d)*(a + b*x^2)^2) + (b*(b*c*(3 - m) - a*d*(7 - m))*x^(1 + m))/(8*a^2*(b*c - a*d)^2*(a + b*x^2)) + (b*(a^2*d^2*(15 - 8*m + m^2) - 2*a*b*c*d*(5 - 6*m + m^2) + b^2*c^2*(3 - 4*m + m^2))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(8*a^3*(b*c - a*d)^3*(1 + m)) - (d^3*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(c*(b*c - a*d)^3*(1 + m))","A",6,4,22,0.1818,1,"{472, 579, 584, 364}"
337,1,201,0,0.2242485,"\int \frac{x^m \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^m*(c + d*x^2)^3)/(a + b*x^2)^2,x]","-\frac{d x^{m+1} \left(a^2 d^2 (m+5)-3 a b c d (m+3)+2 b^2 c^2 (m+1)\right)}{2 a b^3 (m+1)}+\frac{x^{m+1} (b c-a d)^2 (a d (m+5)+b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b^3 (m+1)}-\frac{d^2 x^{m+3} (b c (m+3)-a d (m+5))}{2 a b^2 (m+3)}+\frac{x^{m+1} \left(c+d x^2\right)^2 (b c-a d)}{2 a b \left(a+b x^2\right)}","-\frac{d x^{m+1} \left(a^2 d^2 (m+5)-3 a b c d (m+3)+2 b^2 c^2 (m+1)\right)}{2 a b^3 (m+1)}+\frac{x^{m+1} (b c-a d)^2 (a d (m+5)+b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b^3 (m+1)}-\frac{d^2 x^{m+3} (b c (m+3)-a d (m+5))}{2 a b^2 (m+3)}+\frac{x^{m+1} \left(c+d x^2\right)^2 (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"-(d*(2*b^2*c^2*(1 + m) - 3*a*b*c*d*(3 + m) + a^2*d^2*(5 + m))*x^(1 + m))/(2*a*b^3*(1 + m)) - (d^2*(b*c*(3 + m) - a*d*(5 + m))*x^(3 + m))/(2*a*b^2*(3 + m)) + ((b*c - a*d)*x^(1 + m)*(c + d*x^2)^2)/(2*a*b*(a + b*x^2)) + ((b*c - a*d)^2*(a*d*(5 + m) + b*(c - c*m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*b^3*(1 + m))","A",4,3,22,0.1364,1,"{468, 570, 364}"
338,1,120,0,0.1057252,"\int \frac{x^m \left(c+d x^2\right)^2}{\left(a+b x^2\right)^2} \, dx","Int[(x^m*(c + d*x^2)^2)/(a + b*x^2)^2,x]","\frac{x^{m+1} (b c-a d) (a d (m+3)+b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b^2 (m+1)}+\frac{x^{m+1} (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}+\frac{d^2 x^{m+1}}{b^2 (m+1)}","\frac{x^{m+1} (b c-a d) (a d (m+3)+b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b^2 (m+1)}+\frac{x^{m+1} (b c-a d)^2}{2 a b^2 \left(a+b x^2\right)}+\frac{d^2 x^{m+1}}{b^2 (m+1)}",1,"(d^2*x^(1 + m))/(b^2*(1 + m)) + ((b*c - a*d)^2*x^(1 + m))/(2*a*b^2*(a + b*x^2)) + ((b*c - a*d)*(a*d*(3 + m) + b*(c - c*m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*b^2*(1 + m))","A",3,3,22,0.1364,1,"{463, 459, 364}"
339,1,93,0,0.042393,"\int \frac{x^m \left(c+d x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^m*(c + d*x^2))/(a + b*x^2)^2,x]","\frac{x^{m+1} (a d (m+1)+b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b (m+1)}+\frac{x^{m+1} (b c-a d)}{2 a b \left(a+b x^2\right)}","\frac{x^{m+1} (a d (m+1)+b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 b (m+1)}+\frac{x^{m+1} (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"((b*c - a*d)*x^(1 + m))/(2*a*b*(a + b*x^2)) + ((a*d*(1 + m) + b*(c - c*m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*b*(1 + m))","A",2,2,20,0.1000,1,"{457, 364}"
340,1,156,0,0.1606393,"\int \frac{x^m}{\left(a+b x^2\right)^2 \left(c+d x^2\right)} \, dx","Int[x^m/((a + b*x^2)^2*(c + d*x^2)),x]","\frac{b x^{m+1} (b c (1-m)-a d (3-m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^2}+\frac{d^2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) (b c-a d)}","\frac{b x^{m+1} (b c (1-m)-a d (3-m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^2}+\frac{d^2 x^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{c (m+1) (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) (b c-a d)}",1,"(b*x^(1 + m))/(2*a*(b*c - a*d)*(a + b*x^2)) + (b*(b*c*(1 - m) - a*d*(3 - m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*(b*c - a*d)^2*(1 + m)) + (d^2*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(c*(b*c - a*d)^2*(1 + m))","A",5,3,22,0.1364,1,"{472, 584, 364}"
341,1,230,0,0.3880532,"\int \frac{x^m}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^m/((a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{b^2 x^{m+1} (a d (5-m)-b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^3}-\frac{d^2 x^{m+1} (a d (1-m)-b c (5-m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{2 c^2 (m+1) (b c-a d)^3}+\frac{d x^{m+1} (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}","-\frac{b^2 x^{m+1} (a d (5-m)-b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^3}-\frac{d^2 x^{m+1} (a d (1-m)-b c (5-m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{2 c^2 (m+1) (b c-a d)^3}+\frac{d x^{m+1} (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}",1,"(d*(b*c + a*d)*x^(1 + m))/(2*a*c*(b*c - a*d)^2*(c + d*x^2)) + (b*x^(1 + m))/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) - (b^2*(a*d*(5 - m) - b*(c - c*m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*(b*c - a*d)^3*(1 + m)) - (d^2*(a*d*(1 - m) - b*c*(5 - m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(2*c^2*(b*c - a*d)^3*(1 + m))","A",6,4,22,0.1818,1,"{472, 579, 584, 364}"
342,1,325,0,0.6137019,"\int \frac{x^m}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^m/((a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d^2 x^{m+1} \left(a^2 d^2 \left(m^2-4 m+3\right)-2 a b c d \left(m^2-8 m+7\right)+b^2 c^2 \left(m^2-12 m+35\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{8 c^3 (m+1) (b c-a d)^4}+\frac{d x^{m+1} \left(-a^2 d^2 (3-m)+a b c d (11-m)+4 b^2 c^2\right)}{8 a c^2 \left(c+d x^2\right) (b c-a d)^3}-\frac{b^3 x^{m+1} (a d (7-m)-b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^4}+\frac{d x^{m+1} (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}","\frac{d^2 x^{m+1} \left(a^2 d^2 \left(m^2-4 m+3\right)-2 a b c d \left(m^2-8 m+7\right)+b^2 c^2 \left(m^2-12 m+35\right)\right) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{d x^2}{c}\right)}{8 c^3 (m+1) (b c-a d)^4}+\frac{d x^{m+1} \left(-a^2 d^2 (3-m)+a b c d (11-m)+4 b^2 c^2\right)}{8 a c^2 \left(c+d x^2\right) (b c-a d)^3}-\frac{b^3 x^{m+1} (a d (7-m)-b (c-c m)) \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{b x^2}{a}\right)}{2 a^2 (m+1) (b c-a d)^4}+\frac{d x^{m+1} (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}+\frac{b x^{m+1}}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}",1,"(d*(2*b*c + a*d)*x^(1 + m))/(4*a*c*(b*c - a*d)^2*(c + d*x^2)^2) + (b*x^(1 + m))/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) + (d*(4*b^2*c^2 - a^2*d^2*(3 - m) + a*b*c*d*(11 - m))*x^(1 + m))/(8*a*c^2*(b*c - a*d)^3*(c + d*x^2)) - (b^3*(a*d*(7 - m) - b*(c - c*m))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((b*x^2)/a)])/(2*a^2*(b*c - a*d)^4*(1 + m)) + (d^2*(b^2*c^2*(35 - 12*m + m^2) - 2*a*b*c*d*(7 - 8*m + m^2) + a^2*d^2*(3 - 4*m + m^2))*x^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((d*x^2)/c)])/(8*c^3*(b*c - a*d)^4*(1 + m))","A",7,4,22,0.1818,1,"{472, 579, 584, 364}"
343,1,39,0,0.0159898,"\int x^{7/2} \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[x^(7/2)*(a + b*x^2)*(A + B*x^2),x]","\frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{17} b B x^{17/2}","\frac{2}{13} x^{13/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{17} b B x^{17/2}",1,"(2*a*A*x^(9/2))/9 + (2*(A*b + a*B)*x^(13/2))/13 + (2*b*B*x^(17/2))/17","A",2,1,20,0.05000,1,"{448}"
344,1,39,0,0.0159631,"\int x^{5/2} \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[x^(5/2)*(a + b*x^2)*(A + B*x^2),x]","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{15} b B x^{15/2}","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{15} b B x^{15/2}",1,"(2*a*A*x^(7/2))/7 + (2*(A*b + a*B)*x^(11/2))/11 + (2*b*B*x^(15/2))/15","A",2,1,20,0.05000,1,"{448}"
345,1,39,0,0.015995,"\int x^{3/2} \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[x^(3/2)*(a + b*x^2)*(A + B*x^2),x]","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{13} b B x^{13/2}","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{13} b B x^{13/2}",1,"(2*a*A*x^(5/2))/5 + (2*(A*b + a*B)*x^(9/2))/9 + (2*b*B*x^(13/2))/13","A",2,1,20,0.05000,1,"{448}"
346,1,39,0,0.0153497,"\int \sqrt{x} \left(a+b x^2\right) \left(A+B x^2\right) \, dx","Int[Sqrt[x]*(a + b*x^2)*(A + B*x^2),x]","\frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{11} b B x^{11/2}","\frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{11} b B x^{11/2}",1,"(2*a*A*x^(3/2))/3 + (2*(A*b + a*B)*x^(7/2))/7 + (2*b*B*x^(11/2))/11","A",2,1,20,0.05000,1,"{448}"
347,1,37,0,0.0153744,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{\sqrt{x}} \, dx","Int[((a + b*x^2)*(A + B*x^2))/Sqrt[x],x]","\frac{2}{5} x^{5/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{9} b B x^{9/2}","\frac{2}{5} x^{5/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{9} b B x^{9/2}",1,"2*a*A*Sqrt[x] + (2*(A*b + a*B)*x^(5/2))/5 + (2*b*B*x^(9/2))/9","A",2,1,20,0.05000,1,"{448}"
348,1,37,0,0.015213,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^{3/2}} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^(3/2),x]","\frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{7} b B x^{7/2}","\frac{2}{3} x^{3/2} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{7} b B x^{7/2}",1,"(-2*a*A)/Sqrt[x] + (2*(A*b + a*B)*x^(3/2))/3 + (2*b*B*x^(7/2))/7","A",2,1,20,0.05000,1,"{448}"
349,1,37,0,0.016267,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^{5/2}} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^(5/2),x]","2 \sqrt{x} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{5} b B x^{5/2}","2 \sqrt{x} (a B+A b)-\frac{2 a A}{3 x^{3/2}}+\frac{2}{5} b B x^{5/2}",1,"(-2*a*A)/(3*x^(3/2)) + 2*(A*b + a*B)*Sqrt[x] + (2*b*B*x^(5/2))/5","A",2,1,20,0.05000,1,"{448}"
350,1,37,0,0.0156172,"\int \frac{\left(a+b x^2\right) \left(A+B x^2\right)}{x^{7/2}} \, dx","Int[((a + b*x^2)*(A + B*x^2))/x^(7/2),x]","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{5 x^{5/2}}+\frac{2}{3} b B x^{3/2}","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{5 x^{5/2}}+\frac{2}{3} b B x^{3/2}",1,"(-2*a*A)/(5*x^(5/2)) - (2*(A*b + a*B))/Sqrt[x] + (2*b*B*x^(3/2))/3","A",2,1,20,0.05000,1,"{448}"
351,1,63,0,0.0299327,"\int x^{7/2} \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[x^(7/2)*(a + b*x^2)^2*(A + B*x^2),x]","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{17} b x^{17/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{21} b^2 B x^{21/2}","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{17} b x^{17/2} (2 a B+A b)+\frac{2}{13} a x^{13/2} (a B+2 A b)+\frac{2}{21} b^2 B x^{21/2}",1,"(2*a^2*A*x^(9/2))/9 + (2*a*(2*A*b + a*B)*x^(13/2))/13 + (2*b*(A*b + 2*a*B)*x^(17/2))/17 + (2*b^2*B*x^(21/2))/21","A",2,1,22,0.04545,1,"{448}"
352,1,63,0,0.0299246,"\int x^{5/2} \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[x^(5/2)*(a + b*x^2)^2*(A + B*x^2),x]","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{15} b x^{15/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{19} b^2 B x^{19/2}","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{15} b x^{15/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{19} b^2 B x^{19/2}",1,"(2*a^2*A*x^(7/2))/7 + (2*a*(2*A*b + a*B)*x^(11/2))/11 + (2*b*(A*b + 2*a*B)*x^(15/2))/15 + (2*b^2*B*x^(19/2))/19","A",2,1,22,0.04545,1,"{448}"
353,1,63,0,0.0301834,"\int x^{3/2} \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[x^(3/2)*(a + b*x^2)^2*(A + B*x^2),x]","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2}","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{17} b^2 B x^{17/2}",1,"(2*a^2*A*x^(5/2))/5 + (2*a*(2*A*b + a*B)*x^(9/2))/9 + (2*b*(A*b + 2*a*B)*x^(13/2))/13 + (2*b^2*B*x^(17/2))/17","A",2,1,22,0.04545,1,"{448}"
354,1,63,0,0.0293406,"\int \sqrt{x} \left(a+b x^2\right)^2 \left(A+B x^2\right) \, dx","Int[Sqrt[x]*(a + b*x^2)^2*(A + B*x^2),x]","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}",1,"(2*a^2*A*x^(3/2))/3 + (2*a*(2*A*b + a*B)*x^(7/2))/7 + (2*b*(A*b + 2*a*B)*x^(11/2))/11 + (2*b^2*B*x^(15/2))/15","A",2,1,22,0.04545,1,"{448}"
355,1,61,0,0.0322777,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{\sqrt{x}} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/Sqrt[x],x]","2 a^2 A \sqrt{x}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}","2 a^2 A \sqrt{x}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}",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^(9/2))/9 + (2*b^2*B*x^(13/2))/13","A",2,1,22,0.04545,1,"{448}"
356,1,61,0,0.030532,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^{3/2}} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^(3/2),x]","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{7} b x^{7/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{11} b^2 B x^{11/2}","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{7} b x^{7/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{11} b^2 B x^{11/2}",1,"(-2*a^2*A)/Sqrt[x] + (2*a*(2*A*b + a*B)*x^(3/2))/3 + (2*b*(A*b + 2*a*B)*x^(7/2))/7 + (2*b^2*B*x^(11/2))/11","A",2,1,22,0.04545,1,"{448}"
357,1,61,0,0.0288711,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^{5/2}} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^(5/2),x]","-\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{5} b x^{5/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{9} b^2 B x^{9/2}","-\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{5} b x^{5/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{9} b^2 B x^{9/2}",1,"(-2*a^2*A)/(3*x^(3/2)) + 2*a*(2*A*b + a*B)*Sqrt[x] + (2*b*(A*b + 2*a*B)*x^(5/2))/5 + (2*b^2*B*x^(9/2))/9","A",2,1,22,0.04545,1,"{448}"
358,1,61,0,0.0287255,"\int \frac{\left(a+b x^2\right)^2 \left(A+B x^2\right)}{x^{7/2}} \, dx","Int[((a + b*x^2)^2*(A + B*x^2))/x^(7/2),x]","-\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{3} b x^{3/2} (2 a B+A b)-\frac{2 a (a B+2 A b)}{\sqrt{x}}+\frac{2}{7} b^2 B x^{7/2}","-\frac{2 a^2 A}{5 x^{5/2}}+\frac{2}{3} b x^{3/2} (2 a B+A b)-\frac{2 a (a B+2 A b)}{\sqrt{x}}+\frac{2}{7} b^2 B x^{7/2}",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^(3/2))/3 + (2*b^2*B*x^(7/2))/7","A",2,1,22,0.04545,1,"{448}"
359,1,85,0,0.0420046,"\int x^{7/2} \left(a+b x^2\right)^3 \left(A+B x^2\right) \, dx","Int[x^(7/2)*(a + b*x^2)^3*(A + B*x^2),x]","\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{21} b^2 x^{21/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{25} b^3 B x^{25/2}","\frac{2}{13} a^2 x^{13/2} (a B+3 A b)+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{21} b^2 x^{21/2} (3 a B+A b)+\frac{6}{17} a b x^{17/2} (a B+A b)+\frac{2}{25} b^3 B x^{25/2}",1,"(2*a^3*A*x^(9/2))/9 + (2*a^2*(3*A*b + a*B)*x^(13/2))/13 + (6*a*b*(A*b + a*B)*x^(17/2))/17 + (2*b^2*(A*b + 3*a*B)*x^(21/2))/21 + (2*b^3*B*x^(25/2))/25","A",2,1,22,0.04545,1,"{448}"
360,1,85,0,0.040575,"\int x^{5/2} \left(a+b x^2\right)^3 \left(A+B x^2\right) \, dx","Int[x^(5/2)*(a + b*x^2)^3*(A + B*x^2),x]","\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{7} a^3 A x^{7/2}+\frac{2}{19} b^2 x^{19/2} (3 a B+A b)+\frac{2}{5} a b x^{15/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2}","\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{7} a^3 A x^{7/2}+\frac{2}{19} b^2 x^{19/2} (3 a B+A b)+\frac{2}{5} a b x^{15/2} (a B+A b)+\frac{2}{23} b^3 B x^{23/2}",1,"(2*a^3*A*x^(7/2))/7 + (2*a^2*(3*A*b + a*B)*x^(11/2))/11 + (2*a*b*(A*b + a*B)*x^(15/2))/5 + (2*b^2*(A*b + 3*a*B)*x^(19/2))/19 + (2*b^3*B*x^(23/2))/23","A",2,1,22,0.04545,1,"{448}"
361,1,85,0,0.0403044,"\int x^{3/2} \left(a+b x^2\right)^3 \left(A+B x^2\right) \, dx","Int[x^(3/2)*(a + b*x^2)^3*(A + B*x^2),x]","\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{13} a b x^{13/2} (a B+A b)+\frac{2}{21} b^3 B x^{21/2}","\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{17} b^2 x^{17/2} (3 a B+A b)+\frac{6}{13} a b x^{13/2} (a B+A b)+\frac{2}{21} b^3 B x^{21/2}",1,"(2*a^3*A*x^(5/2))/5 + (2*a^2*(3*A*b + a*B)*x^(9/2))/9 + (6*a*b*(A*b + a*B)*x^(13/2))/13 + (2*b^2*(A*b + 3*a*B)*x^(17/2))/17 + (2*b^3*B*x^(21/2))/21","A",2,1,22,0.04545,1,"{448}"
362,1,85,0,0.0412365,"\int \sqrt{x} \left(a+b x^2\right)^3 \left(A+B x^2\right) \, dx","Int[Sqrt[x]*(a + b*x^2)^3*(A + B*x^2),x]","\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{19} b^3 B x^{19/2}","\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{15} b^2 x^{15/2} (3 a B+A b)+\frac{6}{11} a b x^{11/2} (a B+A b)+\frac{2}{19} b^3 B x^{19/2}",1,"(2*a^3*A*x^(3/2))/3 + (2*a^2*(3*A*b + a*B)*x^(7/2))/7 + (6*a*b*(A*b + a*B)*x^(11/2))/11 + (2*b^2*(A*b + 3*a*B)*x^(15/2))/15 + (2*b^3*B*x^(19/2))/19","A",2,1,22,0.04545,1,"{448}"
363,1,83,0,0.0403782,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x^2\right)}{\sqrt{x}} \, dx","Int[((a + b*x^2)^3*(A + B*x^2))/Sqrt[x],x]","\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+2 a^3 A \sqrt{x}+\frac{2}{13} b^2 x^{13/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{17} b^3 B x^{17/2}","\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+2 a^3 A \sqrt{x}+\frac{2}{13} b^2 x^{13/2} (3 a B+A b)+\frac{2}{3} a b x^{9/2} (a B+A b)+\frac{2}{17} b^3 B x^{17/2}",1,"2*a^3*A*Sqrt[x] + (2*a^2*(3*A*b + a*B)*x^(5/2))/5 + (2*a*b*(A*b + a*B)*x^(9/2))/3 + (2*b^2*(A*b + 3*a*B)*x^(13/2))/13 + (2*b^3*B*x^(17/2))/17","A",2,1,22,0.04545,1,"{448}"
364,1,83,0,0.0437627,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x^2\right)}{x^{3/2}} \, dx","Int[((a + b*x^2)^3*(A + B*x^2))/x^(3/2),x]","\frac{2}{3} a^2 x^{3/2} (a B+3 A b)-\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{11} b^2 x^{11/2} (3 a B+A b)+\frac{6}{7} a b x^{7/2} (a B+A b)+\frac{2}{15} b^3 B x^{15/2}","\frac{2}{3} a^2 x^{3/2} (a B+3 A b)-\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{11} b^2 x^{11/2} (3 a B+A b)+\frac{6}{7} a b x^{7/2} (a B+A b)+\frac{2}{15} b^3 B x^{15/2}",1,"(-2*a^3*A)/Sqrt[x] + (2*a^2*(3*A*b + a*B)*x^(3/2))/3 + (6*a*b*(A*b + a*B)*x^(7/2))/7 + (2*b^2*(A*b + 3*a*B)*x^(11/2))/11 + (2*b^3*B*x^(15/2))/15","A",2,1,22,0.04545,1,"{448}"
365,1,83,0,0.0432517,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x^2\right)}{x^{5/2}} \, dx","Int[((a + b*x^2)^3*(A + B*x^2))/x^(5/2),x]","2 a^2 \sqrt{x} (a B+3 A b)-\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{9} b^2 x^{9/2} (3 a B+A b)+\frac{6}{5} a b x^{5/2} (a B+A b)+\frac{2}{13} b^3 B x^{13/2}","2 a^2 \sqrt{x} (a B+3 A b)-\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{9} b^2 x^{9/2} (3 a B+A b)+\frac{6}{5} a b x^{5/2} (a B+A b)+\frac{2}{13} b^3 B x^{13/2}",1,"(-2*a^3*A)/(3*x^(3/2)) + 2*a^2*(3*A*b + a*B)*Sqrt[x] + (6*a*b*(A*b + a*B)*x^(5/2))/5 + (2*b^2*(A*b + 3*a*B)*x^(9/2))/9 + (2*b^3*B*x^(13/2))/13","A",2,1,22,0.04545,1,"{448}"
366,1,81,0,0.0427194,"\int \frac{\left(a+b x^2\right)^3 \left(A+B x^2\right)}{x^{7/2}} \, dx","Int[((a + b*x^2)^3*(A + B*x^2))/x^(7/2),x]","-\frac{2 a^2 (a B+3 A b)}{\sqrt{x}}-\frac{2 a^3 A}{5 x^{5/2}}+\frac{2}{7} b^2 x^{7/2} (3 a B+A b)+2 a b x^{3/2} (a B+A b)+\frac{2}{11} b^3 B x^{11/2}","-\frac{2 a^2 (a B+3 A b)}{\sqrt{x}}-\frac{2 a^3 A}{5 x^{5/2}}+\frac{2}{7} b^2 x^{7/2} (3 a B+A b)+2 a b x^{3/2} (a B+A b)+\frac{2}{11} b^3 B x^{11/2}",1,"(-2*a^3*A)/(5*x^(5/2)) - (2*a^2*(3*A*b + a*B))/Sqrt[x] + 2*a*b*(A*b + a*B)*x^(3/2) + (2*b^2*(A*b + 3*a*B)*x^(7/2))/7 + (2*b^3*B*x^(11/2))/11","A",2,1,22,0.04545,1,"{448}"
367,1,276,0,0.2587582,"\int \frac{x^{7/2} \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^(7/2)*(A + B*x^2))/(a + b*x^2),x]","-\frac{a^{5/4} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{13/4}}+\frac{a^{5/4} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{13/4}}-\frac{a^{5/4} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{13/4}}+\frac{a^{5/4} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{13/4}}+\frac{2 x^{5/2} (A b-a B)}{5 b^2}-\frac{2 a \sqrt{x} (A b-a B)}{b^3}+\frac{2 B x^{9/2}}{9 b}","-\frac{a^{5/4} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{13/4}}+\frac{a^{5/4} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{13/4}}-\frac{a^{5/4} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{13/4}}+\frac{a^{5/4} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{13/4}}+\frac{2 x^{5/2} (A b-a B)}{5 b^2}-\frac{2 a \sqrt{x} (A b-a B)}{b^3}+\frac{2 B x^{9/2}}{9 b}",1,"(-2*a*(A*b - a*B)*Sqrt[x])/b^3 + (2*(A*b - a*B)*x^(5/2))/(5*b^2) + (2*B*x^(9/2))/(9*b) - (a^(5/4)*(A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(13/4)) + (a^(5/4)*(A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(13/4)) - (a^(5/4)*(A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(13/4)) + (a^(5/4)*(A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(13/4))","A",13,9,22,0.4091,1,"{459, 321, 329, 211, 1165, 628, 1162, 617, 204}"
368,1,257,0,0.2053985,"\int \frac{x^{5/2} \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^(5/2)*(A + B*x^2))/(a + b*x^2),x]","-\frac{a^{3/4} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{a^{3/4} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{a^{3/4} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{11/4}}-\frac{a^{3/4} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{11/4}}+\frac{2 x^{3/2} (A b-a B)}{3 b^2}+\frac{2 B x^{7/2}}{7 b}","-\frac{a^{3/4} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{a^{3/4} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{a^{3/4} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{11/4}}-\frac{a^{3/4} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{11/4}}+\frac{2 x^{3/2} (A b-a B)}{3 b^2}+\frac{2 B x^{7/2}}{7 b}",1,"(2*(A*b - a*B)*x^(3/2))/(3*b^2) + (2*B*x^(7/2))/(7*b) + (a^(3/4)*(A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(11/4)) - (a^(3/4)*(A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(11/4)) - (a^(3/4)*(A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(11/4)) + (a^(3/4)*(A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(11/4))","A",12,9,22,0.4091,1,"{459, 321, 329, 297, 1162, 617, 204, 1165, 628}"
369,1,255,0,0.2024825,"\int \frac{x^{3/2} \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(x^(3/2)*(A + B*x^2))/(a + b*x^2),x]","\frac{2 \sqrt{x} (A b-a B)}{b^2}+\frac{\sqrt[4]{a} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{\sqrt[4]{a} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{\sqrt[4]{a} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{9/4}}-\frac{\sqrt[4]{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{9/4}}+\frac{2 B x^{5/2}}{5 b}","\frac{2 \sqrt{x} (A b-a B)}{b^2}+\frac{\sqrt[4]{a} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}-\frac{\sqrt[4]{a} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{\sqrt[4]{a} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{9/4}}-\frac{\sqrt[4]{a} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{9/4}}+\frac{2 B x^{5/2}}{5 b}",1,"(2*(A*b - a*B)*Sqrt[x])/b^2 + (2*B*x^(5/2))/(5*b) + (a^(1/4)*(A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(9/4)) - (a^(1/4)*(A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(9/4)) + (a^(1/4)*(A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(9/4)) - (a^(1/4)*(A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(9/4))","A",12,9,22,0.4091,1,"{459, 321, 329, 211, 1165, 628, 1162, 617, 204}"
370,1,237,0,0.1783352,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{a+b x^2} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(a + b*x^2),x]","\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{2 B x^{3/2}}{3 b}","\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{7/4}}-\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{7/4}}+\frac{2 B x^{3/2}}{3 b}",1,"(2*B*x^(3/2))/(3*b) - ((A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*b^(7/4)) + ((A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*b^(7/4)) + ((A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*b^(7/4)) - ((A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*b^(7/4))","A",11,8,22,0.3636,1,"{459, 329, 297, 1162, 617, 204, 1165, 628}"
371,1,235,0,0.1760652,"\int \frac{A+B x^2}{\sqrt{x} \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(a + b*x^2)),x]","-\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}-\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} b^{5/4}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} b^{5/4}}+\frac{2 B \sqrt{x}}{b}","-\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}+\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{5/4}}-\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} b^{5/4}}+\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} b^{5/4}}+\frac{2 B \sqrt{x}}{b}",1,"(2*B*Sqrt[x])/b - ((A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*b^(5/4)) + ((A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*b^(5/4)) - ((A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*b^(5/4)) + ((A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*b^(5/4))","A",11,8,22,0.3636,1,"{459, 329, 211, 1165, 628, 1162, 617, 204}"
372,1,235,0,0.1805863,"\int \frac{A+B x^2}{x^{3/2} \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^(3/2)*(a + b*x^2)),x]","-\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{3/4}}+\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{3/4}}+\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} b^{3/4}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} b^{3/4}}-\frac{2 A}{a \sqrt{x}}","-\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{3/4}}+\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{3/4}}+\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} b^{3/4}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} b^{3/4}}-\frac{2 A}{a \sqrt{x}}",1,"(-2*A)/(a*Sqrt[x]) + ((A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*b^(3/4)) - ((A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*b^(3/4)) - ((A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*b^(3/4)) + ((A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*b^(3/4))","A",11,8,22,0.3636,1,"{453, 329, 297, 1162, 617, 204, 1165, 628}"
373,1,237,0,0.1769352,"\int \frac{A+B x^2}{x^{5/2} \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^(5/2)*(a + b*x^2)),x]","\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{2 A}{3 a x^{3/2}}","\frac{(A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{(A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} \sqrt[4]{b}}+\frac{(A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{(A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} \sqrt[4]{b}}-\frac{2 A}{3 a x^{3/2}}",1,"(-2*A)/(3*a*x^(3/2)) + ((A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*b^(1/4)) - ((A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*b^(1/4)) + ((A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*b^(1/4)) - ((A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*b^(1/4))","A",11,8,22,0.3636,1,"{453, 329, 211, 1165, 628, 1162, 617, 204}"
374,1,255,0,0.2057793,"\int \frac{A+B x^2}{x^{7/2} \left(a+b x^2\right)} \, dx","Int[(A + B*x^2)/(x^(7/2)*(a + b*x^2)),x]","\frac{2 (A b-a B)}{a^2 \sqrt{x}}+\frac{\sqrt[4]{b} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{\sqrt[4]{b} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{\sqrt[4]{b} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4}}+\frac{\sqrt[4]{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4}}-\frac{2 A}{5 a x^{5/2}}","\frac{2 (A b-a B)}{a^2 \sqrt{x}}+\frac{\sqrt[4]{b} (A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{\sqrt[4]{b} (A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{\sqrt[4]{b} (A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4}}+\frac{\sqrt[4]{b} (A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4}}-\frac{2 A}{5 a x^{5/2}}",1,"(-2*A)/(5*a*x^(5/2)) + (2*(A*b - a*B))/(a^2*Sqrt[x]) - (b^(1/4)*(A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)) + (b^(1/4)*(A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)) + (b^(1/4)*(A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)) - (b^(1/4)*(A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4))","A",12,9,22,0.4091,1,"{453, 325, 329, 297, 1162, 617, 204, 1165, 628}"
375,1,310,0,0.2430828,"\int \frac{x^{7/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^(7/2)*(A + B*x^2))/(a + b*x^2)^2,x]","-\frac{x^{5/2} (5 A b-9 a B)}{10 a b^2}+\frac{\sqrt{x} (5 A b-9 a B)}{2 b^3}+\frac{\sqrt[4]{a} (5 A b-9 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{\sqrt[4]{a} (5 A b-9 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{\sqrt[4]{a} (5 A b-9 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{13/4}}-\frac{\sqrt[4]{a} (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{13/4}}+\frac{x^{9/2} (A b-a B)}{2 a b \left(a+b x^2\right)}","-\frac{x^{5/2} (5 A b-9 a B)}{10 a b^2}+\frac{\sqrt{x} (5 A b-9 a B)}{2 b^3}+\frac{\sqrt[4]{a} (5 A b-9 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{13/4}}-\frac{\sqrt[4]{a} (5 A b-9 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{\sqrt[4]{a} (5 A b-9 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{13/4}}-\frac{\sqrt[4]{a} (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{13/4}}+\frac{x^{9/2} (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"((5*A*b - 9*a*B)*Sqrt[x])/(2*b^3) - ((5*A*b - 9*a*B)*x^(5/2))/(10*a*b^2) + ((A*b - a*B)*x^(9/2))/(2*a*b*(a + b*x^2)) + (a^(1/4)*(5*A*b - 9*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(13/4)) - (a^(1/4)*(5*A*b - 9*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(13/4)) + (a^(1/4)*(5*A*b - 9*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(13/4)) - (a^(1/4)*(5*A*b - 9*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(13/4))","A",13,9,22,0.4091,1,"{457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
376,1,289,0,0.2185904,"\int \frac{x^{5/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^(5/2)*(A + B*x^2))/(a + b*x^2)^2,x]","-\frac{x^{3/2} (3 A b-7 a B)}{6 a b^2}+\frac{(3 A b-7 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{11/4}}-\frac{(3 A b-7 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{11/4}}-\frac{(3 A b-7 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{11/4}}+\frac{(3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{11/4}}+\frac{x^{7/2} (A b-a B)}{2 a b \left(a+b x^2\right)}","-\frac{x^{3/2} (3 A b-7 a B)}{6 a b^2}+\frac{(3 A b-7 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{11/4}}-\frac{(3 A b-7 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{11/4}}-\frac{(3 A b-7 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{11/4}}+\frac{(3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{11/4}}+\frac{x^{7/2} (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"-((3*A*b - 7*a*B)*x^(3/2))/(6*a*b^2) + ((A*b - a*B)*x^(7/2))/(2*a*b*(a + b*x^2)) - ((3*A*b - 7*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*b^(11/4)) + ((3*A*b - 7*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*b^(11/4)) + ((3*A*b - 7*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*b^(11/4)) - ((3*A*b - 7*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*b^(11/4))","A",12,9,22,0.4091,1,"{457, 321, 329, 297, 1162, 617, 204, 1165, 628}"
377,1,284,0,0.2086113,"\int \frac{x^{3/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(x^(3/2)*(A + B*x^2))/(a + b*x^2)^2,x]","-\frac{(A b-5 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(A b-5 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{9/4}}-\frac{(A b-5 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}-\frac{\sqrt{x} (A b-5 a B)}{2 a b^2}+\frac{x^{5/2} (A b-a B)}{2 a b \left(a+b x^2\right)}","-\frac{(A b-5 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(A b-5 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{9/4}}-\frac{(A b-5 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}+\frac{(A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} b^{9/4}}-\frac{\sqrt{x} (A b-5 a B)}{2 a b^2}+\frac{x^{5/2} (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"-((A*b - 5*a*B)*Sqrt[x])/(2*a*b^2) + ((A*b - a*B)*x^(5/2))/(2*a*b*(a + b*x^2)) - ((A*b - 5*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*b^(9/4)) + ((A*b - 5*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*b^(9/4)) - ((A*b - 5*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*b^(9/4)) + ((A*b - 5*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*b^(9/4))","A",12,9,22,0.4091,1,"{457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
378,1,261,0,0.1815852,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{\left(a+b x^2\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(a + b*x^2)^2,x]","\frac{(3 a B+A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{7/4}}-\frac{(3 a B+A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{7/4}}-\frac{(3 a B+A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} b^{7/4}}+\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} b^{7/4}}+\frac{x^{3/2} (A b-a B)}{2 a b \left(a+b x^2\right)}","\frac{(3 a B+A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{7/4}}-\frac{(3 a B+A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{7/4}}-\frac{(3 a B+A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} b^{7/4}}+\frac{(3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} b^{7/4}}+\frac{x^{3/2} (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"((A*b - a*B)*x^(3/2))/(2*a*b*(a + b*x^2)) - ((A*b + 3*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*b^(7/4)) + ((A*b + 3*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*b^(7/4)) + ((A*b + 3*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*b^(7/4)) - ((A*b + 3*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*b^(7/4))","A",11,8,22,0.3636,1,"{457, 329, 297, 1162, 617, 204, 1165, 628}"
379,1,261,0,0.1809237,"\int \frac{A+B x^2}{\sqrt{x} \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(a + b*x^2)^2),x]","-\frac{(a B+3 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a B+3 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}-\frac{(a B+3 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\sqrt{x} (A b-a B)}{2 a b \left(a+b x^2\right)}","-\frac{(a B+3 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a B+3 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{5/4}}-\frac{(a B+3 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} b^{5/4}}+\frac{(a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} b^{5/4}}+\frac{\sqrt{x} (A b-a B)}{2 a b \left(a+b x^2\right)}",1,"((A*b - a*B)*Sqrt[x])/(2*a*b*(a + b*x^2)) - ((3*A*b + a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*A*b + a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*b^(5/4)) - ((3*A*b + a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*b^(5/4)) + ((3*A*b + a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*b^(5/4))","A",11,8,22,0.3636,1,"{457, 329, 211, 1165, 628, 1162, 617, 204}"
380,1,289,0,0.2117438,"\int \frac{A+B x^2}{x^{3/2} \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^(3/2)*(a + b*x^2)^2),x]","-\frac{(5 A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{3/4}}+\frac{(5 A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{3/4}}+\frac{(5 A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} b^{3/4}}-\frac{(5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 A b-a B}{2 a^2 b \sqrt{x}}+\frac{A b-a B}{2 a b \sqrt{x} \left(a+b x^2\right)}","-\frac{(5 A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{3/4}}+\frac{(5 A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{3/4}}+\frac{(5 A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} b^{3/4}}-\frac{(5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} b^{3/4}}-\frac{5 A b-a B}{2 a^2 b \sqrt{x}}+\frac{A b-a B}{2 a b \sqrt{x} \left(a+b x^2\right)}",1,"-(5*A*b - a*B)/(2*a^2*b*Sqrt[x]) + (A*b - a*B)/(2*a*b*Sqrt[x]*(a + b*x^2)) + ((5*A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*b^(3/4)) - ((5*A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*b^(3/4)) - ((5*A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*b^(3/4)) + ((5*A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*b^(3/4))","A",12,9,22,0.4091,1,"{457, 325, 329, 297, 1162, 617, 204, 1165, 628}"
381,1,289,0,0.213974,"\int \frac{A+B x^2}{x^{5/2} \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^(5/2)*(a + b*x^2)^2),x]","-\frac{7 A b-3 a B}{6 a^2 b x^{3/2}}+\frac{(7 A b-3 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{(7 A b-3 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{(7 A b-3 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{(7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{A b-a B}{2 a b x^{3/2} \left(a+b x^2\right)}","-\frac{7 A b-3 a B}{6 a^2 b x^{3/2}}+\frac{(7 A b-3 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{(7 A b-3 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{(7 A b-3 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4} \sqrt[4]{b}}-\frac{(7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4} \sqrt[4]{b}}+\frac{A b-a B}{2 a b x^{3/2} \left(a+b x^2\right)}",1,"-(7*A*b - 3*a*B)/(6*a^2*b*x^(3/2)) + (A*b - a*B)/(2*a*b*x^(3/2)*(a + b*x^2)) + ((7*A*b - 3*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*b^(1/4)) - ((7*A*b - 3*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*b^(1/4)) + ((7*A*b - 3*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*b^(1/4)) - ((7*A*b - 3*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*b^(1/4))","A",12,9,22,0.4091,1,"{457, 325, 329, 211, 1165, 628, 1162, 617, 204}"
382,1,310,0,0.2369506,"\int \frac{A+B x^2}{x^{7/2} \left(a+b x^2\right)^2} \, dx","Int[(A + B*x^2)/(x^(7/2)*(a + b*x^2)^2),x]","-\frac{9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac{9 A b-5 a B}{2 a^3 \sqrt{x}}+\frac{\sqrt[4]{b} (9 A b-5 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{\sqrt[4]{b} (9 A b-5 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{\sqrt[4]{b} (9 A b-5 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4}}+\frac{\sqrt[4]{b} (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4}}+\frac{A b-a B}{2 a b x^{5/2} \left(a+b x^2\right)}","-\frac{9 A b-5 a B}{10 a^2 b x^{5/2}}+\frac{9 A b-5 a B}{2 a^3 \sqrt{x}}+\frac{\sqrt[4]{b} (9 A b-5 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{\sqrt[4]{b} (9 A b-5 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4}}-\frac{\sqrt[4]{b} (9 A b-5 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4}}+\frac{\sqrt[4]{b} (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4}}+\frac{A b-a B}{2 a b x^{5/2} \left(a+b x^2\right)}",1,"-(9*A*b - 5*a*B)/(10*a^2*b*x^(5/2)) + (9*A*b - 5*a*B)/(2*a^3*Sqrt[x]) + (A*b - a*B)/(2*a*b*x^(5/2)*(a + b*x^2)) - (b^(1/4)*(9*A*b - 5*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)) + (b^(1/4)*(9*A*b - 5*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)) + (b^(1/4)*(9*A*b - 5*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)) - (b^(1/4)*(9*A*b - 5*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4))","A",13,9,22,0.4091,1,"{457, 325, 329, 297, 1162, 617, 204, 1165, 628}"
383,1,316,0,0.2397008,"\int \frac{x^{7/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^(7/2)*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{5 (A b-9 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{13/4}}+\frac{5 (A b-9 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{13/4}}-\frac{5 (A b-9 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{3/4} b^{13/4}}+\frac{5 (A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{3/4} b^{13/4}}+\frac{x^{5/2} (A b-9 a B)}{16 a b^2 \left(a+b x^2\right)}-\frac{5 \sqrt{x} (A b-9 a B)}{16 a b^3}+\frac{x^{9/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}","-\frac{5 (A b-9 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{13/4}}+\frac{5 (A b-9 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{3/4} b^{13/4}}-\frac{5 (A b-9 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{3/4} b^{13/4}}+\frac{5 (A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{3/4} b^{13/4}}+\frac{x^{5/2} (A b-9 a B)}{16 a b^2 \left(a+b x^2\right)}-\frac{5 \sqrt{x} (A b-9 a B)}{16 a b^3}+\frac{x^{9/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"(-5*(A*b - 9*a*B)*Sqrt[x])/(16*a*b^3) + ((A*b - a*B)*x^(9/2))/(4*a*b*(a + b*x^2)^2) + ((A*b - 9*a*B)*x^(5/2))/(16*a*b^2*(a + b*x^2)) - (5*(A*b - 9*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(3/4)*b^(13/4)) + (5*(A*b - 9*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(3/4)*b^(13/4)) - (5*(A*b - 9*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(3/4)*b^(13/4)) + (5*(A*b - 9*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(3/4)*b^(13/4))","A",13,10,22,0.4545,1,"{457, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
384,1,293,0,0.2158873,"\int \frac{x^{5/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^(5/2)*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{3 (7 a B+A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{11/4}}-\frac{3 (7 a B+A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{11/4}}-\frac{3 (7 a B+A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{5/4} b^{11/4}}+\frac{3 (7 a B+A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{5/4} b^{11/4}}-\frac{x^{3/2} (7 a B+A b)}{16 a b^2 \left(a+b x^2\right)}+\frac{x^{7/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}","\frac{3 (7 a B+A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{11/4}}-\frac{3 (7 a B+A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{5/4} b^{11/4}}-\frac{3 (7 a B+A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{5/4} b^{11/4}}+\frac{3 (7 a B+A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{5/4} b^{11/4}}-\frac{x^{3/2} (7 a B+A b)}{16 a b^2 \left(a+b x^2\right)}+\frac{x^{7/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"((A*b - a*B)*x^(7/2))/(4*a*b*(a + b*x^2)^2) - ((A*b + 7*a*B)*x^(3/2))/(16*a*b^2*(a + b*x^2)) - (3*(A*b + 7*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(5/4)*b^(11/4)) + (3*(A*b + 7*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(5/4)*b^(11/4)) + (3*(A*b + 7*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(5/4)*b^(11/4)) - (3*(A*b + 7*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(5/4)*b^(11/4))","A",12,9,22,0.4091,1,"{457, 288, 329, 297, 1162, 617, 204, 1165, 628}"
385,1,298,0,0.2119354,"\int \frac{x^{3/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(x^(3/2)*(A + B*x^2))/(a + b*x^2)^3,x]","-\frac{(5 a B+3 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(5 a B+3 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{9/4}}-\frac{(5 a B+3 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(5 a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{7/4} b^{9/4}}-\frac{\sqrt{x} (5 a B+3 A b)}{16 a b^2 \left(a+b x^2\right)}+\frac{x^{5/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}","-\frac{(5 a B+3 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(5 a B+3 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{7/4} b^{9/4}}-\frac{(5 a B+3 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(5 a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{7/4} b^{9/4}}-\frac{\sqrt{x} (5 a B+3 A b)}{16 a b^2 \left(a+b x^2\right)}+\frac{x^{5/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"((A*b - a*B)*x^(5/2))/(4*a*b*(a + b*x^2)^2) - ((3*A*b + 5*a*B)*Sqrt[x])/(16*a*b^2*(a + b*x^2)) - ((3*A*b + 5*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(7/4)*b^(9/4)) + ((3*A*b + 5*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(7/4)*b^(9/4)) - ((3*A*b + 5*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(7/4)*b^(9/4)) + ((3*A*b + 5*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(7/4)*b^(9/4))","A",12,9,22,0.4091,1,"{457, 288, 329, 211, 1165, 628, 1162, 617, 204}"
386,1,298,0,0.2161978,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{\left(a+b x^2\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(a + b*x^2)^3,x]","\frac{(3 a B+5 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(3 a B+5 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(3 a B+5 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{9/4} b^{7/4}}+\frac{(3 a B+5 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{9/4} b^{7/4}}+\frac{x^{3/2} (3 a B+5 A b)}{16 a^2 b \left(a+b x^2\right)}+\frac{x^{3/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}","\frac{(3 a B+5 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(3 a B+5 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(3 a B+5 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{9/4} b^{7/4}}+\frac{(3 a B+5 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{9/4} b^{7/4}}+\frac{x^{3/2} (3 a B+5 A b)}{16 a^2 b \left(a+b x^2\right)}+\frac{x^{3/2} (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"((A*b - a*B)*x^(3/2))/(4*a*b*(a + b*x^2)^2) + ((5*A*b + 3*a*B)*x^(3/2))/(16*a^2*b*(a + b*x^2)) - ((5*A*b + 3*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(9/4)*b^(7/4)) + ((5*A*b + 3*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(9/4)*b^(7/4)) + ((5*A*b + 3*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(9/4)*b^(7/4)) - ((5*A*b + 3*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(9/4)*b^(7/4))","A",12,9,22,0.4091,1,"{457, 290, 329, 297, 1162, 617, 204, 1165, 628}"
387,1,293,0,0.2124559,"\int \frac{A+B x^2}{\sqrt{x} \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(a + b*x^2)^3),x]","-\frac{3 (a B+7 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{3 (a B+7 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}-\frac{3 (a B+7 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{11/4} b^{5/4}}+\frac{3 (a B+7 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\sqrt{x} (a B+7 A b)}{16 a^2 b \left(a+b x^2\right)}+\frac{\sqrt{x} (A b-a B)}{4 a b \left(a+b x^2\right)^2}","-\frac{3 (a B+7 A b) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}+\frac{3 (a B+7 A b) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{11/4} b^{5/4}}-\frac{3 (a B+7 A b) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{11/4} b^{5/4}}+\frac{3 (a B+7 A b) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{11/4} b^{5/4}}+\frac{\sqrt{x} (a B+7 A b)}{16 a^2 b \left(a+b x^2\right)}+\frac{\sqrt{x} (A b-a B)}{4 a b \left(a+b x^2\right)^2}",1,"((A*b - a*B)*Sqrt[x])/(4*a*b*(a + b*x^2)^2) + ((7*A*b + a*B)*Sqrt[x])/(16*a^2*b*(a + b*x^2)) - (3*(7*A*b + a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(11/4)*b^(5/4)) + (3*(7*A*b + a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(11/4)*b^(5/4)) - (3*(7*A*b + a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(11/4)*b^(5/4)) + (3*(7*A*b + a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(11/4)*b^(5/4))","A",12,9,22,0.4091,1,"{457, 290, 329, 211, 1165, 628, 1162, 617, 204}"
388,1,322,0,0.2338064,"\int \frac{A+B x^2}{x^{3/2} \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^(3/2)*(a + b*x^2)^3),x]","-\frac{5 (9 A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4} b^{3/4}}+\frac{5 (9 A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4} b^{3/4}}+\frac{5 (9 A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{13/4} b^{3/4}}-\frac{5 (9 A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{13/4} b^{3/4}}+\frac{9 A b-a B}{16 a^2 b \sqrt{x} \left(a+b x^2\right)}-\frac{5 (9 A b-a B)}{16 a^3 b \sqrt{x}}+\frac{A b-a B}{4 a b \sqrt{x} \left(a+b x^2\right)^2}","-\frac{5 (9 A b-a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4} b^{3/4}}+\frac{5 (9 A b-a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{13/4} b^{3/4}}+\frac{5 (9 A b-a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{13/4} b^{3/4}}-\frac{5 (9 A b-a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{13/4} b^{3/4}}+\frac{9 A b-a B}{16 a^2 b \sqrt{x} \left(a+b x^2\right)}-\frac{5 (9 A b-a B)}{16 a^3 b \sqrt{x}}+\frac{A b-a B}{4 a b \sqrt{x} \left(a+b x^2\right)^2}",1,"(-5*(9*A*b - a*B))/(16*a^3*b*Sqrt[x]) + (A*b - a*B)/(4*a*b*Sqrt[x]*(a + b*x^2)^2) + (9*A*b - a*B)/(16*a^2*b*Sqrt[x]*(a + b*x^2)) + (5*(9*A*b - a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(13/4)*b^(3/4)) - (5*(9*A*b - a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(13/4)*b^(3/4)) - (5*(9*A*b - a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(13/4)*b^(3/4)) + (5*(9*A*b - a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(13/4)*b^(3/4))","A",13,10,22,0.4545,1,"{457, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
389,1,322,0,0.2369543,"\int \frac{A+B x^2}{x^{5/2} \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^(5/2)*(a + b*x^2)^3),x]","\frac{11 A b-3 a B}{16 a^2 b x^{3/2} \left(a+b x^2\right)}-\frac{7 (11 A b-3 a B)}{48 a^3 b x^{3/2}}+\frac{7 (11 A b-3 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{7 (11 A b-3 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{7 (11 A b-3 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{7 (11 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{A b-a B}{4 a b x^{3/2} \left(a+b x^2\right)^2}","\frac{11 A b-3 a B}{16 a^2 b x^{3/2} \left(a+b x^2\right)}-\frac{7 (11 A b-3 a B)}{48 a^3 b x^{3/2}}+\frac{7 (11 A b-3 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{7 (11 A b-3 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{7 (11 A b-3 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{7 (11 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{A b-a B}{4 a b x^{3/2} \left(a+b x^2\right)^2}",1,"(-7*(11*A*b - 3*a*B))/(48*a^3*b*x^(3/2)) + (A*b - a*B)/(4*a*b*x^(3/2)*(a + b*x^2)^2) + (11*A*b - 3*a*B)/(16*a^2*b*x^(3/2)*(a + b*x^2)) + (7*(11*A*b - 3*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(15/4)*b^(1/4)) - (7*(11*A*b - 3*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(15/4)*b^(1/4)) + (7*(11*A*b - 3*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(15/4)*b^(1/4)) - (7*(11*A*b - 3*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(15/4)*b^(1/4))","A",13,10,22,0.4545,1,"{457, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
390,1,343,0,0.2615802,"\int \frac{A+B x^2}{x^{7/2} \left(a+b x^2\right)^3} \, dx","Int[(A + B*x^2)/(x^(7/2)*(a + b*x^2)^3),x]","\frac{13 A b-5 a B}{16 a^2 b x^{5/2} \left(a+b x^2\right)}-\frac{9 (13 A b-5 a B)}{80 a^3 b x^{5/2}}+\frac{9 (13 A b-5 a B)}{16 a^4 \sqrt{x}}+\frac{9 \sqrt[4]{b} (13 A b-5 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{9 \sqrt[4]{b} (13 A b-5 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{9 \sqrt[4]{b} (13 A b-5 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{17/4}}+\frac{9 \sqrt[4]{b} (13 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{17/4}}+\frac{A b-a B}{4 a b x^{5/2} \left(a+b x^2\right)^2}","\frac{13 A b-5 a B}{16 a^2 b x^{5/2} \left(a+b x^2\right)}-\frac{9 (13 A b-5 a B)}{80 a^3 b x^{5/2}}+\frac{9 (13 A b-5 a B)}{16 a^4 \sqrt{x}}+\frac{9 \sqrt[4]{b} (13 A b-5 a B) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{9 \sqrt[4]{b} (13 A b-5 a B) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{64 \sqrt{2} a^{17/4}}-\frac{9 \sqrt[4]{b} (13 A b-5 a B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{17/4}}+\frac{9 \sqrt[4]{b} (13 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{17/4}}+\frac{A b-a B}{4 a b x^{5/2} \left(a+b x^2\right)^2}",1,"(-9*(13*A*b - 5*a*B))/(80*a^3*b*x^(5/2)) + (9*(13*A*b - 5*a*B))/(16*a^4*Sqrt[x]) + (A*b - a*B)/(4*a*b*x^(5/2)*(a + b*x^2)^2) + (13*A*b - 5*a*B)/(16*a^2*b*x^(5/2)*(a + b*x^2)) - (9*b^(1/4)*(13*A*b - 5*a*B)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(17/4)) + (9*b^(1/4)*(13*A*b - 5*a*B)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(17/4)) + (9*b^(1/4)*(13*A*b - 5*a*B)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(17/4)) - (9*b^(1/4)*(13*A*b - 5*a*B)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(64*Sqrt[2]*a^(17/4))","A",14,10,22,0.4545,1,"{457, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
391,1,63,0,0.0327075,"\int x^{7/2} \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^(7/2)*(a + b*x^2)^2*(c + d*x^2),x]","\frac{2}{9} a^2 c x^{9/2}+\frac{2}{17} b x^{17/2} (2 a d+b c)+\frac{2}{13} a x^{13/2} (a d+2 b c)+\frac{2}{21} b^2 d x^{21/2}","\frac{2}{9} a^2 c x^{9/2}+\frac{2}{17} b x^{17/2} (2 a d+b c)+\frac{2}{13} a x^{13/2} (a d+2 b c)+\frac{2}{21} b^2 d x^{21/2}",1,"(2*a^2*c*x^(9/2))/9 + (2*a*(2*b*c + a*d)*x^(13/2))/13 + (2*b*(b*c + 2*a*d)*x^(17/2))/17 + (2*b^2*d*x^(21/2))/21","A",2,1,22,0.04545,1,"{448}"
392,1,63,0,0.0292791,"\int x^{5/2} \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^(5/2)*(a + b*x^2)^2*(c + d*x^2),x]","\frac{2}{7} a^2 c x^{7/2}+\frac{2}{15} b x^{15/2} (2 a d+b c)+\frac{2}{11} a x^{11/2} (a d+2 b c)+\frac{2}{19} b^2 d x^{19/2}","\frac{2}{7} a^2 c x^{7/2}+\frac{2}{15} b x^{15/2} (2 a d+b c)+\frac{2}{11} a x^{11/2} (a d+2 b c)+\frac{2}{19} b^2 d x^{19/2}",1,"(2*a^2*c*x^(7/2))/7 + (2*a*(2*b*c + a*d)*x^(11/2))/11 + (2*b*(b*c + 2*a*d)*x^(15/2))/15 + (2*b^2*d*x^(19/2))/19","A",2,1,22,0.04545,1,"{448}"
393,1,63,0,0.0298885,"\int x^{3/2} \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[x^(3/2)*(a + b*x^2)^2*(c + d*x^2),x]","\frac{2}{5} a^2 c x^{5/2}+\frac{2}{13} b x^{13/2} (2 a d+b c)+\frac{2}{9} a x^{9/2} (a d+2 b c)+\frac{2}{17} b^2 d x^{17/2}","\frac{2}{5} a^2 c x^{5/2}+\frac{2}{13} b x^{13/2} (2 a d+b c)+\frac{2}{9} a x^{9/2} (a d+2 b c)+\frac{2}{17} b^2 d x^{17/2}",1,"(2*a^2*c*x^(5/2))/5 + (2*a*(2*b*c + a*d)*x^(9/2))/9 + (2*b*(b*c + 2*a*d)*x^(13/2))/13 + (2*b^2*d*x^(17/2))/17","A",2,1,22,0.04545,1,"{448}"
394,1,63,0,0.0285362,"\int \sqrt{x} \left(a+b x^2\right)^2 \left(c+d x^2\right) \, dx","Int[Sqrt[x]*(a + b*x^2)^2*(c + d*x^2),x]","\frac{2}{3} a^2 c x^{3/2}+\frac{2}{11} b x^{11/2} (2 a d+b c)+\frac{2}{7} a x^{7/2} (a d+2 b c)+\frac{2}{15} b^2 d x^{15/2}","\frac{2}{3} a^2 c x^{3/2}+\frac{2}{11} b x^{11/2} (2 a d+b c)+\frac{2}{7} a x^{7/2} (a d+2 b c)+\frac{2}{15} b^2 d x^{15/2}",1,"(2*a^2*c*x^(3/2))/3 + (2*a*(2*b*c + a*d)*x^(7/2))/7 + (2*b*(b*c + 2*a*d)*x^(11/2))/11 + (2*b^2*d*x^(15/2))/15","A",2,1,22,0.04545,1,"{448}"
395,1,61,0,0.0290469,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{\sqrt{x}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/Sqrt[x],x]","2 a^2 c \sqrt{x}+\frac{2}{9} b x^{9/2} (2 a d+b c)+\frac{2}{5} a x^{5/2} (a d+2 b c)+\frac{2}{13} b^2 d x^{13/2}","2 a^2 c \sqrt{x}+\frac{2}{9} b x^{9/2} (2 a d+b c)+\frac{2}{5} a x^{5/2} (a d+2 b c)+\frac{2}{13} b^2 d x^{13/2}",1,"2*a^2*c*Sqrt[x] + (2*a*(2*b*c + a*d)*x^(5/2))/5 + (2*b*(b*c + 2*a*d)*x^(9/2))/9 + (2*b^2*d*x^(13/2))/13","A",2,1,22,0.04545,1,"{448}"
396,1,61,0,0.030651,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x^{3/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x^(3/2),x]","-\frac{2 a^2 c}{\sqrt{x}}+\frac{2}{7} b x^{7/2} (2 a d+b c)+\frac{2}{3} a x^{3/2} (a d+2 b c)+\frac{2}{11} b^2 d x^{11/2}","-\frac{2 a^2 c}{\sqrt{x}}+\frac{2}{7} b x^{7/2} (2 a d+b c)+\frac{2}{3} a x^{3/2} (a d+2 b c)+\frac{2}{11} b^2 d x^{11/2}",1,"(-2*a^2*c)/Sqrt[x] + (2*a*(2*b*c + a*d)*x^(3/2))/3 + (2*b*(b*c + 2*a*d)*x^(7/2))/7 + (2*b^2*d*x^(11/2))/11","A",2,1,22,0.04545,1,"{448}"
397,1,61,0,0.0288909,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x^{5/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x^(5/2),x]","-\frac{2 a^2 c}{3 x^{3/2}}+\frac{2}{5} b x^{5/2} (2 a d+b c)+2 a \sqrt{x} (a d+2 b c)+\frac{2}{9} b^2 d x^{9/2}","-\frac{2 a^2 c}{3 x^{3/2}}+\frac{2}{5} b x^{5/2} (2 a d+b c)+2 a \sqrt{x} (a d+2 b c)+\frac{2}{9} b^2 d x^{9/2}",1,"(-2*a^2*c)/(3*x^(3/2)) + 2*a*(2*b*c + a*d)*Sqrt[x] + (2*b*(b*c + 2*a*d)*x^(5/2))/5 + (2*b^2*d*x^(9/2))/9","A",2,1,22,0.04545,1,"{448}"
398,1,61,0,0.0294659,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)}{x^{7/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2))/x^(7/2),x]","-\frac{2 a^2 c}{5 x^{5/2}}+\frac{2}{3} b x^{3/2} (2 a d+b c)-\frac{2 a (a d+2 b c)}{\sqrt{x}}+\frac{2}{7} b^2 d x^{7/2}","-\frac{2 a^2 c}{5 x^{5/2}}+\frac{2}{3} b x^{3/2} (2 a d+b c)-\frac{2 a (a d+2 b c)}{\sqrt{x}}+\frac{2}{7} b^2 d x^{7/2}",1,"(-2*a^2*c)/(5*x^(5/2)) - (2*a*(2*b*c + a*d))/Sqrt[x] + (2*b*(b*c + 2*a*d)*x^(3/2))/3 + (2*b^2*d*x^(7/2))/7","A",2,1,22,0.04545,1,"{448}"
399,1,97,0,0.0494179,"\int x^{7/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{2}{17} x^{17/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{9} a^2 c^2 x^{9/2}+\frac{4}{21} b d x^{21/2} (a d+b c)+\frac{4}{13} a c x^{13/2} (a d+b c)+\frac{2}{25} b^2 d^2 x^{25/2}","\frac{2}{17} x^{17/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{9} a^2 c^2 x^{9/2}+\frac{4}{21} b d x^{21/2} (a d+b c)+\frac{4}{13} a c x^{13/2} (a d+b c)+\frac{2}{25} b^2 d^2 x^{25/2}",1,"(2*a^2*c^2*x^(9/2))/9 + (4*a*c*(b*c + a*d)*x^(13/2))/13 + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(17/2))/17 + (4*b*d*(b*c + a*d)*x^(21/2))/21 + (2*b^2*d^2*x^(25/2))/25","A",2,1,24,0.04167,1,"{448}"
400,1,97,0,0.0459392,"\int x^{5/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{2}{15} x^{15/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{7} a^2 c^2 x^{7/2}+\frac{4}{19} b d x^{19/2} (a d+b c)+\frac{4}{11} a c x^{11/2} (a d+b c)+\frac{2}{23} b^2 d^2 x^{23/2}","\frac{2}{15} x^{15/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{7} a^2 c^2 x^{7/2}+\frac{4}{19} b d x^{19/2} (a d+b c)+\frac{4}{11} a c x^{11/2} (a d+b c)+\frac{2}{23} b^2 d^2 x^{23/2}",1,"(2*a^2*c^2*x^(7/2))/7 + (4*a*c*(b*c + a*d)*x^(11/2))/11 + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(15/2))/15 + (4*b*d*(b*c + a*d)*x^(19/2))/19 + (2*b^2*d^2*x^(23/2))/23","A",2,1,24,0.04167,1,"{448}"
401,1,97,0,0.0497726,"\int x^{3/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{2}{13} x^{13/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{5} a^2 c^2 x^{5/2}+\frac{4}{17} b d x^{17/2} (a d+b c)+\frac{4}{9} a c x^{9/2} (a d+b c)+\frac{2}{21} b^2 d^2 x^{21/2}","\frac{2}{13} x^{13/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{5} a^2 c^2 x^{5/2}+\frac{4}{17} b d x^{17/2} (a d+b c)+\frac{4}{9} a c x^{9/2} (a d+b c)+\frac{2}{21} b^2 d^2 x^{21/2}",1,"(2*a^2*c^2*x^(5/2))/5 + (4*a*c*(b*c + a*d)*x^(9/2))/9 + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(13/2))/13 + (4*b*d*(b*c + a*d)*x^(17/2))/17 + (2*b^2*d^2*x^(21/2))/21","A",2,1,24,0.04167,1,"{448}"
402,1,97,0,0.0465173,"\int \sqrt{x} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2 \, dx","Int[Sqrt[x]*(a + b*x^2)^2*(c + d*x^2)^2,x]","\frac{2}{11} x^{11/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{3} a^2 c^2 x^{3/2}+\frac{4}{15} b d x^{15/2} (a d+b c)+\frac{4}{7} a c x^{7/2} (a d+b c)+\frac{2}{19} b^2 d^2 x^{19/2}","\frac{2}{11} x^{11/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+\frac{2}{3} a^2 c^2 x^{3/2}+\frac{4}{15} b d x^{15/2} (a d+b c)+\frac{4}{7} a c x^{7/2} (a d+b c)+\frac{2}{19} b^2 d^2 x^{19/2}",1,"(2*a^2*c^2*x^(3/2))/3 + (4*a*c*(b*c + a*d)*x^(7/2))/7 + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(11/2))/11 + (4*b*d*(b*c + a*d)*x^(15/2))/15 + (2*b^2*d^2*x^(19/2))/19","A",2,1,24,0.04167,1,"{448}"
403,1,95,0,0.0459258,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{\sqrt{x}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/Sqrt[x],x]","\frac{2}{9} x^{9/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+2 a^2 c^2 \sqrt{x}+\frac{4}{13} b d x^{13/2} (a d+b c)+\frac{4}{5} a c x^{5/2} (a d+b c)+\frac{2}{17} b^2 d^2 x^{17/2}","\frac{2}{9} x^{9/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)+2 a^2 c^2 \sqrt{x}+\frac{4}{13} b d x^{13/2} (a d+b c)+\frac{4}{5} a c x^{5/2} (a d+b c)+\frac{2}{17} b^2 d^2 x^{17/2}",1,"2*a^2*c^2*Sqrt[x] + (4*a*c*(b*c + a*d)*x^(5/2))/5 + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(9/2))/9 + (4*b*d*(b*c + a*d)*x^(13/2))/13 + (2*b^2*d^2*x^(17/2))/17","A",2,1,24,0.04167,1,"{448}"
404,1,95,0,0.0475267,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x^{3/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x^(3/2),x]","\frac{2}{7} x^{7/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{2 a^2 c^2}{\sqrt{x}}+\frac{4}{11} b d x^{11/2} (a d+b c)+\frac{4}{3} a c x^{3/2} (a d+b c)+\frac{2}{15} b^2 d^2 x^{15/2}","\frac{2}{7} x^{7/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{2 a^2 c^2}{\sqrt{x}}+\frac{4}{11} b d x^{11/2} (a d+b c)+\frac{4}{3} a c x^{3/2} (a d+b c)+\frac{2}{15} b^2 d^2 x^{15/2}",1,"(-2*a^2*c^2)/Sqrt[x] + (4*a*c*(b*c + a*d)*x^(3/2))/3 + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(7/2))/7 + (4*b*d*(b*c + a*d)*x^(11/2))/11 + (2*b^2*d^2*x^(15/2))/15","A",2,1,24,0.04167,1,"{448}"
405,1,95,0,0.0466474,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x^{5/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x^(5/2),x]","\frac{2}{5} x^{5/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{2 a^2 c^2}{3 x^{3/2}}+\frac{4}{9} b d x^{9/2} (a d+b c)+4 a c \sqrt{x} (a d+b c)+\frac{2}{13} b^2 d^2 x^{13/2}","\frac{2}{5} x^{5/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{2 a^2 c^2}{3 x^{3/2}}+\frac{4}{9} b d x^{9/2} (a d+b c)+4 a c \sqrt{x} (a d+b c)+\frac{2}{13} b^2 d^2 x^{13/2}",1,"(-2*a^2*c^2)/(3*x^(3/2)) + 4*a*c*(b*c + a*d)*Sqrt[x] + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(5/2))/5 + (4*b*d*(b*c + a*d)*x^(9/2))/9 + (2*b^2*d^2*x^(13/2))/13","A",2,1,24,0.04167,1,"{448}"
406,1,95,0,0.0471844,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2}{x^{7/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^2)/x^(7/2),x]","\frac{2}{3} x^{3/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{2 a^2 c^2}{5 x^{5/2}}+\frac{4}{7} b d x^{7/2} (a d+b c)-\frac{4 a c (a d+b c)}{\sqrt{x}}+\frac{2}{11} b^2 d^2 x^{11/2}","\frac{2}{3} x^{3/2} \left(a^2 d^2+4 a b c d+b^2 c^2\right)-\frac{2 a^2 c^2}{5 x^{5/2}}+\frac{4}{7} b d x^{7/2} (a d+b c)-\frac{4 a c (a d+b c)}{\sqrt{x}}+\frac{2}{11} b^2 d^2 x^{11/2}",1,"(-2*a^2*c^2)/(5*x^(5/2)) - (4*a*c*(b*c + a*d))/Sqrt[x] + (2*(b^2*c^2 + 4*a*b*c*d + a^2*d^2)*x^(3/2))/3 + (4*b*d*(b*c + a*d)*x^(7/2))/7 + (2*b^2*d^2*x^(11/2))/11","A",2,1,24,0.04167,1,"{448}"
407,1,139,0,0.064872,"\int x^{7/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{2}{21} d x^{21/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{17} c x^{17/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{9} a^2 c^3 x^{9/2}+\frac{2}{13} a c^2 x^{13/2} (3 a d+2 b c)+\frac{2}{25} b d^2 x^{25/2} (2 a d+3 b c)+\frac{2}{29} b^2 d^3 x^{29/2}","\frac{2}{21} d x^{21/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{17} c x^{17/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{9} a^2 c^3 x^{9/2}+\frac{2}{13} a c^2 x^{13/2} (3 a d+2 b c)+\frac{2}{25} b d^2 x^{25/2} (2 a d+3 b c)+\frac{2}{29} b^2 d^3 x^{29/2}",1,"(2*a^2*c^3*x^(9/2))/9 + (2*a*c^2*(2*b*c + 3*a*d)*x^(13/2))/13 + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(17/2))/17 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(21/2))/21 + (2*b*d^2*(3*b*c + 2*a*d)*x^(25/2))/25 + (2*b^2*d^3*x^(29/2))/29","A",2,1,24,0.04167,1,"{448}"
408,1,139,0,0.0647248,"\int x^{5/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{2}{19} d x^{19/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{15} c x^{15/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{7} a^2 c^3 x^{7/2}+\frac{2}{11} a c^2 x^{11/2} (3 a d+2 b c)+\frac{2}{23} b d^2 x^{23/2} (2 a d+3 b c)+\frac{2}{27} b^2 d^3 x^{27/2}","\frac{2}{19} d x^{19/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{15} c x^{15/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{7} a^2 c^3 x^{7/2}+\frac{2}{11} a c^2 x^{11/2} (3 a d+2 b c)+\frac{2}{23} b d^2 x^{23/2} (2 a d+3 b c)+\frac{2}{27} b^2 d^3 x^{27/2}",1,"(2*a^2*c^3*x^(7/2))/7 + (2*a*c^2*(2*b*c + 3*a*d)*x^(11/2))/11 + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(15/2))/15 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(19/2))/19 + (2*b*d^2*(3*b*c + 2*a*d)*x^(23/2))/23 + (2*b^2*d^3*x^(27/2))/27","A",2,1,24,0.04167,1,"{448}"
409,1,139,0,0.0632243,"\int x^{3/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{2}{17} d x^{17/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{13} c x^{13/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{5} a^2 c^3 x^{5/2}+\frac{2}{9} a c^2 x^{9/2} (3 a d+2 b c)+\frac{2}{21} b d^2 x^{21/2} (2 a d+3 b c)+\frac{2}{25} b^2 d^3 x^{25/2}","\frac{2}{17} d x^{17/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{13} c x^{13/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{5} a^2 c^3 x^{5/2}+\frac{2}{9} a c^2 x^{9/2} (3 a d+2 b c)+\frac{2}{21} b d^2 x^{21/2} (2 a d+3 b c)+\frac{2}{25} b^2 d^3 x^{25/2}",1,"(2*a^2*c^3*x^(5/2))/5 + (2*a*c^2*(2*b*c + 3*a*d)*x^(9/2))/9 + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(13/2))/13 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(17/2))/17 + (2*b*d^2*(3*b*c + 2*a*d)*x^(21/2))/21 + (2*b^2*d^3*x^(25/2))/25","A",2,1,24,0.04167,1,"{448}"
410,1,139,0,0.0635255,"\int \sqrt{x} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3 \, dx","Int[Sqrt[x]*(a + b*x^2)^2*(c + d*x^2)^3,x]","\frac{2}{15} d x^{15/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{11} c x^{11/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{3} a^2 c^3 x^{3/2}+\frac{2}{7} a c^2 x^{7/2} (3 a d+2 b c)+\frac{2}{19} b d^2 x^{19/2} (2 a d+3 b c)+\frac{2}{23} b^2 d^3 x^{23/2}","\frac{2}{15} d x^{15/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{11} c x^{11/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+\frac{2}{3} a^2 c^3 x^{3/2}+\frac{2}{7} a c^2 x^{7/2} (3 a d+2 b c)+\frac{2}{19} b d^2 x^{19/2} (2 a d+3 b c)+\frac{2}{23} b^2 d^3 x^{23/2}",1,"(2*a^2*c^3*x^(3/2))/3 + (2*a*c^2*(2*b*c + 3*a*d)*x^(7/2))/7 + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(11/2))/11 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(15/2))/15 + (2*b*d^2*(3*b*c + 2*a*d)*x^(19/2))/19 + (2*b^2*d^3*x^(23/2))/23","A",2,1,24,0.04167,1,"{448}"
411,1,137,0,0.0647974,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{\sqrt{x}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/Sqrt[x],x]","\frac{2}{13} d x^{13/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{9} c x^{9/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+2 a^2 c^3 \sqrt{x}+\frac{2}{5} a c^2 x^{5/2} (3 a d+2 b c)+\frac{2}{17} b d^2 x^{17/2} (2 a d+3 b c)+\frac{2}{21} b^2 d^3 x^{21/2}","\frac{2}{13} d x^{13/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{9} c x^{9/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)+2 a^2 c^3 \sqrt{x}+\frac{2}{5} a c^2 x^{5/2} (3 a d+2 b c)+\frac{2}{17} b d^2 x^{17/2} (2 a d+3 b c)+\frac{2}{21} b^2 d^3 x^{21/2}",1,"2*a^2*c^3*Sqrt[x] + (2*a*c^2*(2*b*c + 3*a*d)*x^(5/2))/5 + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(9/2))/9 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(13/2))/13 + (2*b*d^2*(3*b*c + 2*a*d)*x^(17/2))/17 + (2*b^2*d^3*x^(21/2))/21","A",2,1,24,0.04167,1,"{448}"
412,1,137,0,0.0638812,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x^{3/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x^(3/2),x]","\frac{2}{11} d x^{11/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{7} c x^{7/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{2 a^2 c^3}{\sqrt{x}}+\frac{2}{3} a c^2 x^{3/2} (3 a d+2 b c)+\frac{2}{15} b d^2 x^{15/2} (2 a d+3 b c)+\frac{2}{19} b^2 d^3 x^{19/2}","\frac{2}{11} d x^{11/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{7} c x^{7/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{2 a^2 c^3}{\sqrt{x}}+\frac{2}{3} a c^2 x^{3/2} (3 a d+2 b c)+\frac{2}{15} b d^2 x^{15/2} (2 a d+3 b c)+\frac{2}{19} b^2 d^3 x^{19/2}",1,"(-2*a^2*c^3)/Sqrt[x] + (2*a*c^2*(2*b*c + 3*a*d)*x^(3/2))/3 + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(7/2))/7 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(11/2))/11 + (2*b*d^2*(3*b*c + 2*a*d)*x^(15/2))/15 + (2*b^2*d^3*x^(19/2))/19","A",2,1,24,0.04167,1,"{448}"
413,1,137,0,0.0644083,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x^{5/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x^(5/2),x]","\frac{2}{9} d x^{9/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{5} c x^{5/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{2 a^2 c^3}{3 x^{3/2}}+2 a c^2 \sqrt{x} (3 a d+2 b c)+\frac{2}{13} b d^2 x^{13/2} (2 a d+3 b c)+\frac{2}{17} b^2 d^3 x^{17/2}","\frac{2}{9} d x^{9/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{5} c x^{5/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{2 a^2 c^3}{3 x^{3/2}}+2 a c^2 \sqrt{x} (3 a d+2 b c)+\frac{2}{13} b d^2 x^{13/2} (2 a d+3 b c)+\frac{2}{17} b^2 d^3 x^{17/2}",1,"(-2*a^2*c^3)/(3*x^(3/2)) + 2*a*c^2*(2*b*c + 3*a*d)*Sqrt[x] + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(5/2))/5 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(9/2))/9 + (2*b*d^2*(3*b*c + 2*a*d)*x^(13/2))/13 + (2*b^2*d^3*x^(17/2))/17","A",2,1,24,0.04167,1,"{448}"
414,1,137,0,0.0627778,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3}{x^{7/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^3)/x^(7/2),x]","\frac{2}{7} d x^{7/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{3} c x^{3/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{2 a^2 c^3}{5 x^{5/2}}-\frac{2 a c^2 (3 a d+2 b c)}{\sqrt{x}}+\frac{2}{11} b d^2 x^{11/2} (2 a d+3 b c)+\frac{2}{15} b^2 d^3 x^{15/2}","\frac{2}{7} d x^{7/2} \left(a^2 d^2+6 a b c d+3 b^2 c^2\right)+\frac{2}{3} c x^{3/2} \left(3 a^2 d^2+6 a b c d+b^2 c^2\right)-\frac{2 a^2 c^3}{5 x^{5/2}}-\frac{2 a c^2 (3 a d+2 b c)}{\sqrt{x}}+\frac{2}{11} b d^2 x^{11/2} (2 a d+3 b c)+\frac{2}{15} b^2 d^3 x^{15/2}",1,"(-2*a^2*c^3)/(5*x^(5/2)) - (2*a*c^2*(2*b*c + 3*a*d))/Sqrt[x] + (2*c*(b^2*c^2 + 6*a*b*c*d + 3*a^2*d^2)*x^(3/2))/3 + (2*d*(3*b^2*c^2 + 6*a*b*c*d + a^2*d^2)*x^(7/2))/7 + (2*b*d^2*(3*b*c + 2*a*d)*x^(11/2))/11 + (2*b^2*d^3*x^(15/2))/15","A",2,1,24,0.04167,1,"{448}"
415,1,311,0,0.3125517,"\int \frac{x^{7/2} \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^(7/2)*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{c^{5/4} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{17/4}}+\frac{c^{5/4} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{17/4}}-\frac{c^{5/4} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{17/4}}+\frac{c^{5/4} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{17/4}}-\frac{2 b x^{9/2} (b c-2 a d)}{9 d^2}+\frac{2 x^{5/2} (b c-a d)^2}{5 d^3}-\frac{2 c \sqrt{x} (b c-a d)^2}{d^4}+\frac{2 b^2 x^{13/2}}{13 d}","-\frac{c^{5/4} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{17/4}}+\frac{c^{5/4} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{17/4}}-\frac{c^{5/4} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{17/4}}+\frac{c^{5/4} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{17/4}}-\frac{2 b x^{9/2} (b c-2 a d)}{9 d^2}+\frac{2 x^{5/2} (b c-a d)^2}{5 d^3}-\frac{2 c \sqrt{x} (b c-a d)^2}{d^4}+\frac{2 b^2 x^{13/2}}{13 d}",1,"(-2*c*(b*c - a*d)^2*Sqrt[x])/d^4 + (2*(b*c - a*d)^2*x^(5/2))/(5*d^3) - (2*b*(b*c - 2*a*d)*x^(9/2))/(9*d^2) + (2*b^2*x^(13/2))/(13*d) - (c^(5/4)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(17/4)) + (c^(5/4)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(17/4)) - (c^(5/4)*(b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(17/4)) + (c^(5/4)*(b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(17/4))","A",14,9,24,0.3750,1,"{461, 321, 329, 211, 1165, 628, 1162, 617, 204}"
416,1,290,0,0.2540766,"\int \frac{x^{5/2} \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^(5/2)*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{c^{3/4} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{15/4}}+\frac{c^{3/4} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{15/4}}+\frac{c^{3/4} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{15/4}}-\frac{c^{3/4} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{15/4}}-\frac{2 b x^{7/2} (b c-2 a d)}{7 d^2}+\frac{2 x^{3/2} (b c-a d)^2}{3 d^3}+\frac{2 b^2 x^{11/2}}{11 d}","-\frac{c^{3/4} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{15/4}}+\frac{c^{3/4} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{15/4}}+\frac{c^{3/4} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{15/4}}-\frac{c^{3/4} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{15/4}}-\frac{2 b x^{7/2} (b c-2 a d)}{7 d^2}+\frac{2 x^{3/2} (b c-a d)^2}{3 d^3}+\frac{2 b^2 x^{11/2}}{11 d}",1,"(2*(b*c - a*d)^2*x^(3/2))/(3*d^3) - (2*b*(b*c - 2*a*d)*x^(7/2))/(7*d^2) + (2*b^2*x^(11/2))/(11*d) + (c^(3/4)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(15/4)) - (c^(3/4)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(15/4)) - (c^(3/4)*(b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(15/4)) + (c^(3/4)*(b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(15/4))","A",13,9,24,0.3750,1,"{461, 321, 329, 297, 1162, 617, 204, 1165, 628}"
417,1,288,0,0.2399186,"\int \frac{x^{3/2} \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(x^(3/2)*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{2 b x^{5/2} (b c-2 a d)}{5 d^2}+\frac{2 \sqrt{x} (b c-a d)^2}{d^3}+\frac{\sqrt[4]{c} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{13/4}}-\frac{\sqrt[4]{c} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{13/4}}+\frac{\sqrt[4]{c} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{13/4}}-\frac{\sqrt[4]{c} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{13/4}}+\frac{2 b^2 x^{9/2}}{9 d}","-\frac{2 b x^{5/2} (b c-2 a d)}{5 d^2}+\frac{2 \sqrt{x} (b c-a d)^2}{d^3}+\frac{\sqrt[4]{c} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{13/4}}-\frac{\sqrt[4]{c} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{13/4}}+\frac{\sqrt[4]{c} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{13/4}}-\frac{\sqrt[4]{c} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{13/4}}+\frac{2 b^2 x^{9/2}}{9 d}",1,"(2*(b*c - a*d)^2*Sqrt[x])/d^3 - (2*b*(b*c - 2*a*d)*x^(5/2))/(5*d^2) + (2*b^2*x^(9/2))/(9*d) + (c^(1/4)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(13/4)) - (c^(1/4)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(13/4)) + (c^(1/4)*(b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(13/4)) - (c^(1/4)*(b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(13/4))","A",13,9,24,0.3750,1,"{461, 321, 329, 211, 1165, 628, 1162, 617, 204}"
418,1,268,0,0.2330373,"\int \frac{\sqrt{x} \left(a+b x^2\right)^2}{c+d x^2} \, dx","Int[(Sqrt[x]*(a + b*x^2)^2)/(c + d*x^2),x]","-\frac{2 b x^{3/2} (b c-2 a d)}{3 d^2}+\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} d^{11/4}}-\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} d^{11/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} \sqrt[4]{c} d^{11/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} \sqrt[4]{c} d^{11/4}}+\frac{2 b^2 x^{7/2}}{7 d}","-\frac{2 b x^{3/2} (b c-2 a d)}{3 d^2}+\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} d^{11/4}}-\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} d^{11/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} \sqrt[4]{c} d^{11/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} \sqrt[4]{c} d^{11/4}}+\frac{2 b^2 x^{7/2}}{7 d}",1,"(-2*b*(b*c - 2*a*d)*x^(3/2))/(3*d^2) + (2*b^2*x^(7/2))/(7*d) - ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(1/4)*d^(11/4)) + ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(1/4)*d^(11/4)) + ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(1/4)*d^(11/4)) - ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(1/4)*d^(11/4))","A",12,8,24,0.3333,1,"{461, 329, 297, 1162, 617, 204, 1165, 628}"
419,1,266,0,0.2119481,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{x} \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(Sqrt[x]*(c + d*x^2)),x]","-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{3/4} d^{9/4}}-\frac{2 b \sqrt{x} (b c-2 a d)}{d^2}+\frac{2 b^2 x^{5/2}}{5 d}","-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} d^{9/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{3/4} d^{9/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{3/4} d^{9/4}}-\frac{2 b \sqrt{x} (b c-2 a d)}{d^2}+\frac{2 b^2 x^{5/2}}{5 d}",1,"(-2*b*(b*c - 2*a*d)*Sqrt[x])/d^2 + (2*b^2*x^(5/2))/(5*d) - ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(3/4)*d^(9/4)) + ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(3/4)*d^(9/4)) - ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(3/4)*d^(9/4)) + ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(3/4)*d^(9/4))","A",12,8,24,0.3333,1,"{461, 329, 211, 1165, 628, 1162, 617, 204}"
420,1,260,0,0.2663507,"\int \frac{\left(a+b x^2\right)^2}{x^{3/2} \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^(3/2)*(c + d*x^2)),x]","-\frac{2 a^2}{c \sqrt{x}}-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} d^{7/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} d^{7/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{5/4} d^{7/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{5/4} d^{7/4}}+\frac{2 b^2 x^{3/2}}{3 d}","-\frac{2 a^2}{c \sqrt{x}}-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} d^{7/4}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} d^{7/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{5/4} d^{7/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{5/4} d^{7/4}}+\frac{2 b^2 x^{3/2}}{3 d}",1,"(-2*a^2)/(c*Sqrt[x]) + (2*b^2*x^(3/2))/(3*d) + ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(5/4)*d^(7/4)) - ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(5/4)*d^(7/4)) - ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(5/4)*d^(7/4)) + ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(5/4)*d^(7/4))","A",12,9,24,0.3750,1,"{462, 459, 329, 297, 1162, 617, 204, 1165, 628}"
421,1,260,0,0.2649034,"\int \frac{\left(a+b x^2\right)^2}{x^{5/2} \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^(5/2)*(c + d*x^2)),x]","-\frac{2 a^2}{3 c x^{3/2}}+\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} d^{5/4}}-\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} d^{5/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{7/4} d^{5/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{7/4} d^{5/4}}+\frac{2 b^2 \sqrt{x}}{d}","-\frac{2 a^2}{3 c x^{3/2}}+\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} d^{5/4}}-\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} d^{5/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{7/4} d^{5/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{7/4} d^{5/4}}+\frac{2 b^2 \sqrt{x}}{d}",1,"(-2*a^2)/(3*c*x^(3/2)) + (2*b^2*Sqrt[x])/d + ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(7/4)*d^(5/4)) - ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(7/4)*d^(5/4)) + ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(7/4)*d^(5/4)) - ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(7/4)*d^(5/4))","A",12,9,24,0.3750,1,"{462, 459, 329, 211, 1165, 628, 1162, 617, 204}"
422,1,267,0,0.280172,"\int \frac{\left(a+b x^2\right)^2}{x^{7/2} \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^(7/2)*(c + d*x^2)),x]","-\frac{2 a^2}{5 c x^{5/2}}+\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} d^{3/4}}-\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} d^{3/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{9/4} d^{3/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{9/4} d^{3/4}}-\frac{2 a (2 b c-a d)}{c^2 \sqrt{x}}","-\frac{2 a^2}{5 c x^{5/2}}+\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} d^{3/4}}-\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} d^{3/4}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{9/4} d^{3/4}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{9/4} d^{3/4}}-\frac{2 a (2 b c-a d)}{c^2 \sqrt{x}}",1,"(-2*a^2)/(5*c*x^(5/2)) - (2*a*(2*b*c - a*d))/(c^2*Sqrt[x]) - ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(9/4)*d^(3/4)) + ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(9/4)*d^(3/4)) + ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(9/4)*d^(3/4)) - ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(9/4)*d^(3/4))","A",12,9,24,0.3750,1,"{462, 453, 329, 297, 1162, 617, 204, 1165, 628}"
423,1,269,0,0.2755322,"\int \frac{\left(a+b x^2\right)^2}{x^{9/2} \left(c+d x^2\right)} \, dx","Int[(a + b*x^2)^2/(x^(9/2)*(c + d*x^2)),x]","-\frac{2 a^2}{7 c x^{7/2}}-\frac{2 a (2 b c-a d)}{3 c^2 x^{3/2}}-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{11/4} \sqrt[4]{d}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{11/4} \sqrt[4]{d}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{11/4} \sqrt[4]{d}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{11/4} \sqrt[4]{d}}","-\frac{2 a^2}{7 c x^{7/2}}-\frac{2 a (2 b c-a d)}{3 c^2 x^{3/2}}-\frac{(b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{11/4} \sqrt[4]{d}}+\frac{(b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{11/4} \sqrt[4]{d}}-\frac{(b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{11/4} \sqrt[4]{d}}+\frac{(b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{11/4} \sqrt[4]{d}}",1,"(-2*a^2)/(7*c*x^(7/2)) - (2*a*(2*b*c - a*d))/(3*c^2*x^(3/2)) - ((b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(11/4)*d^(1/4)) + ((b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(11/4)*d^(1/4)) - ((b*c - a*d)^2*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(11/4)*d^(1/4)) + ((b*c - a*d)^2*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(11/4)*d^(1/4))","A",12,9,24,0.3750,1,"{462, 453, 329, 211, 1165, 628, 1162, 617, 204}"
424,1,288,0,0.316244,"\int \frac{\left(c+d x^2\right)^2}{x^{11/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^2/(x^(11/2)*(a + b*x^2)),x]","\frac{2 c (b c-2 a d)}{5 a^2 x^{5/2}}-\frac{2 (b c-a d)^2}{a^3 \sqrt{x}}-\frac{\sqrt[4]{b} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4}}+\frac{\sqrt[4]{b} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4}}+\frac{\sqrt[4]{b} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{13/4}}-\frac{\sqrt[4]{b} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{13/4}}-\frac{2 c^2}{9 a x^{9/2}}","\frac{2 c (b c-2 a d)}{5 a^2 x^{5/2}}-\frac{2 (b c-a d)^2}{a^3 \sqrt{x}}-\frac{\sqrt[4]{b} (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4}}+\frac{\sqrt[4]{b} (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4}}+\frac{\sqrt[4]{b} (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{13/4}}-\frac{\sqrt[4]{b} (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{13/4}}-\frac{2 c^2}{9 a x^{9/2}}",1,"(-2*c^2)/(9*a*x^(9/2)) + (2*c*(b*c - 2*a*d))/(5*a^2*x^(5/2)) - (2*(b*c - a*d)^2)/(a^3*Sqrt[x]) + (b^(1/4)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(13/4)) - (b^(1/4)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(13/4)) - (b^(1/4)*(b*c - a*d)^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(13/4)) + (b^(1/4)*(b*c - a*d)^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(13/4))","A",13,10,24,0.4167,1,"{462, 453, 325, 329, 297, 1162, 617, 204, 1165, 628}"
425,1,375,0,0.4370067,"\int \frac{x^{7/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x]","\frac{x^{9/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x^{5/2} (13 b c-5 a d) (b c-a d)}{10 c d^3}+\frac{\sqrt{x} (13 b c-5 a d) (b c-a d)}{2 d^4}+\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{17/4}}-\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{17/4}}+\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{17/4}}-\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{17/4}}+\frac{2 b^2 x^{9/2}}{9 d^2}","\frac{x^{9/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x^{5/2} (13 b c-5 a d) (b c-a d)}{10 c d^3}+\frac{\sqrt{x} (13 b c-5 a d) (b c-a d)}{2 d^4}+\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{17/4}}-\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{17/4}}+\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{17/4}}-\frac{\sqrt[4]{c} (13 b c-5 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{17/4}}+\frac{2 b^2 x^{9/2}}{9 d^2}",1,"((13*b*c - 5*a*d)*(b*c - a*d)*Sqrt[x])/(2*d^4) - ((13*b*c - 5*a*d)*(b*c - a*d)*x^(5/2))/(10*c*d^3) + (2*b^2*x^(9/2))/(9*d^2) + ((b*c - a*d)^2*x^(9/2))/(2*c*d^2*(c + d*x^2)) + (c^(1/4)*(13*b*c - 5*a*d)*(b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(17/4)) - (c^(1/4)*(13*b*c - 5*a*d)*(b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(17/4)) + (c^(1/4)*(13*b*c - 5*a*d)*(b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(17/4)) - (c^(1/4)*(13*b*c - 5*a*d)*(b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(17/4))","A",14,10,24,0.4167,1,"{463, 459, 321, 329, 211, 1165, 628, 1162, 617, 204}"
426,1,346,0,0.3174224,"\int \frac{x^{5/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x]","\frac{x^{7/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x^{3/2} (11 b c-3 a d) (b c-a d)}{6 c d^3}+\frac{(11 b c-3 a d) (b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{15/4}}-\frac{(11 b c-3 a d) (b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{15/4}}-\frac{(11 b c-3 a d) (b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{c} d^{15/4}}+\frac{(11 b c-3 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{c} d^{15/4}}+\frac{2 b^2 x^{7/2}}{7 d^2}","\frac{x^{7/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{x^{3/2} (11 b c-3 a d) (b c-a d)}{6 c d^3}+\frac{(11 b c-3 a d) (b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{15/4}}-\frac{(11 b c-3 a d) (b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{15/4}}-\frac{(11 b c-3 a d) (b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{c} d^{15/4}}+\frac{(11 b c-3 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{c} d^{15/4}}+\frac{2 b^2 x^{7/2}}{7 d^2}",1,"-((11*b*c - 3*a*d)*(b*c - a*d)*x^(3/2))/(6*c*d^3) + (2*b^2*x^(7/2))/(7*d^2) + ((b*c - a*d)^2*x^(7/2))/(2*c*d^2*(c + d*x^2)) - ((11*b*c - 3*a*d)*(b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(1/4)*d^(15/4)) + ((11*b*c - 3*a*d)*(b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(1/4)*d^(15/4)) + ((11*b*c - 3*a*d)*(b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(1/4)*d^(15/4)) - ((11*b*c - 3*a*d)*(b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(1/4)*d^(15/4))","A",13,10,24,0.4167,1,"{463, 459, 321, 329, 297, 1162, 617, 204, 1165, 628}"
427,1,346,0,0.3288875,"\int \frac{x^{3/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(x^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^2,x]","-\frac{(b c-a d) (9 b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} d^{13/4}}+\frac{(b c-a d) (9 b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} d^{13/4}}-\frac{(b c-a d) (9 b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{3/4} d^{13/4}}+\frac{(b c-a d) (9 b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{3/4} d^{13/4}}+\frac{x^{5/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{\sqrt{x} (b c-a d) (9 b c-a d)}{2 c d^3}+\frac{2 b^2 x^{5/2}}{5 d^2}","-\frac{(b c-a d) (9 b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} d^{13/4}}+\frac{(b c-a d) (9 b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} d^{13/4}}-\frac{(b c-a d) (9 b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{3/4} d^{13/4}}+\frac{(b c-a d) (9 b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{3/4} d^{13/4}}+\frac{x^{5/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}-\frac{\sqrt{x} (b c-a d) (9 b c-a d)}{2 c d^3}+\frac{2 b^2 x^{5/2}}{5 d^2}",1,"-((b*c - a*d)*(9*b*c - a*d)*Sqrt[x])/(2*c*d^3) + (2*b^2*x^(5/2))/(5*d^2) + ((b*c - a*d)^2*x^(5/2))/(2*c*d^2*(c + d*x^2)) - ((b*c - a*d)*(9*b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(3/4)*d^(13/4)) + ((b*c - a*d)*(9*b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(3/4)*d^(13/4)) - ((b*c - a*d)*(9*b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(3/4)*d^(13/4)) + ((b*c - a*d)*(9*b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(3/4)*d^(13/4))","A",13,10,24,0.4167,1,"{463, 459, 321, 329, 211, 1165, 628, 1162, 617, 204}"
428,1,310,0,0.2817985,"\int \frac{\sqrt{x} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^2} \, dx","Int[(Sqrt[x]*(a + b*x^2)^2)/(c + d*x^2)^2,x]","-\frac{(b c-a d) (a d+7 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} d^{11/4}}+\frac{(b c-a d) (a d+7 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} d^{11/4}}+\frac{(b c-a d) (a d+7 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{5/4} d^{11/4}}-\frac{(b c-a d) (a d+7 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{5/4} d^{11/4}}+\frac{x^{3/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{2 b^2 x^{3/2}}{3 d^2}","-\frac{(b c-a d) (a d+7 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} d^{11/4}}+\frac{(b c-a d) (a d+7 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} d^{11/4}}+\frac{(b c-a d) (a d+7 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{5/4} d^{11/4}}-\frac{(b c-a d) (a d+7 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{5/4} d^{11/4}}+\frac{x^{3/2} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{2 b^2 x^{3/2}}{3 d^2}",1,"(2*b^2*x^(3/2))/(3*d^2) + ((b*c - a*d)^2*x^(3/2))/(2*c*d^2*(c + d*x^2)) + ((b*c - a*d)*(7*b*c + a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(5/4)*d^(11/4)) - ((b*c - a*d)*(7*b*c + a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(5/4)*d^(11/4)) - ((b*c - a*d)*(7*b*c + a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(5/4)*d^(11/4)) + ((b*c - a*d)*(7*b*c + a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(5/4)*d^(11/4))","A",12,9,24,0.3750,1,"{463, 459, 329, 297, 1162, 617, 204, 1165, 628}"
429,1,312,0,0.3423702,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{x} \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(Sqrt[x]*(c + d*x^2)^2),x]","\frac{(b c-a d) (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}+\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{7/4} d^{9/4}}+\frac{\sqrt{x} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{2 b^2 \sqrt{x}}{d^2}","\frac{(b c-a d) (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} d^{9/4}}+\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{7/4} d^{9/4}}-\frac{(b c-a d) (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{7/4} d^{9/4}}+\frac{\sqrt{x} (b c-a d)^2}{2 c d^2 \left(c+d x^2\right)}+\frac{2 b^2 \sqrt{x}}{d^2}",1,"(2*b^2*Sqrt[x])/d^2 + ((b*c - a*d)^2*Sqrt[x])/(2*c*d^2*(c + d*x^2)) + ((b*c - a*d)*(5*b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(7/4)*d^(9/4)) - ((b*c - a*d)*(5*b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(7/4)*d^(9/4)) + ((b*c - a*d)*(5*b*c + 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(7/4)*d^(9/4)) - ((b*c - a*d)*(5*b*c + 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(7/4)*d^(9/4))","A",12,9,24,0.3750,1,"{463, 459, 329, 211, 1165, 628, 1162, 617, 204}"
430,1,333,0,0.3275283,"\int \frac{\left(a+b x^2\right)^2}{x^{3/2} \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x^(3/2)*(c + d*x^2)^2),x]","-\frac{x^{3/2} \left(5 a^2 d^2-2 a b c d+b^2 c^2\right)}{2 c^2 d \left(c+d x^2\right)}-\frac{2 a^2}{c \sqrt{x} \left(c+d x^2\right)}+\frac{(b c-a d) (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} d^{7/4}}-\frac{(b c-a d) (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} d^{7/4}}-\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{9/4} d^{7/4}}+\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{9/4} d^{7/4}}","-\frac{x^{3/2} \left(5 a^2 d^2-2 a b c d+b^2 c^2\right)}{2 c^2 d \left(c+d x^2\right)}-\frac{2 a^2}{c \sqrt{x} \left(c+d x^2\right)}+\frac{(b c-a d) (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} d^{7/4}}-\frac{(b c-a d) (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} d^{7/4}}-\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{9/4} d^{7/4}}+\frac{(b c-a d) (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{9/4} d^{7/4}}",1,"(-2*a^2)/(c*Sqrt[x]*(c + d*x^2)) - ((b^2*c^2 - 2*a*b*c*d + 5*a^2*d^2)*x^(3/2))/(2*c^2*d*(c + d*x^2)) - ((b*c - a*d)*(3*b*c + 5*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(9/4)*d^(7/4)) + ((b*c - a*d)*(3*b*c + 5*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(9/4)*d^(7/4)) + ((b*c - a*d)*(3*b*c + 5*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(9/4)*d^(7/4)) - ((b*c - a*d)*(3*b*c + 5*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(9/4)*d^(7/4))","A",12,9,24,0.3750,1,"{462, 457, 329, 297, 1162, 617, 204, 1165, 628}"
431,1,332,0,0.3433465,"\int \frac{\left(a+b x^2\right)^2}{x^{5/2} \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x^(5/2)*(c + d*x^2)^2),x]","-\frac{\sqrt{x} \left(7 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{6 c^2 d \left(c+d x^2\right)}-\frac{2 a^2}{3 c x^{3/2} \left(c+d x^2\right)}-\frac{(b c-a d) (7 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} d^{5/4}}+\frac{(b c-a d) (7 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} d^{5/4}}-\frac{(b c-a d) (7 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{11/4} d^{5/4}}+\frac{(b c-a d) (7 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{11/4} d^{5/4}}","-\frac{\sqrt{x} \left(7 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{6 c^2 d \left(c+d x^2\right)}-\frac{2 a^2}{3 c x^{3/2} \left(c+d x^2\right)}-\frac{(b c-a d) (7 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} d^{5/4}}+\frac{(b c-a d) (7 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} d^{5/4}}-\frac{(b c-a d) (7 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{11/4} d^{5/4}}+\frac{(b c-a d) (7 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{11/4} d^{5/4}}",1,"(-2*a^2)/(3*c*x^(3/2)*(c + d*x^2)) - ((3*b^2*c^2 - 6*a*b*c*d + 7*a^2*d^2)*Sqrt[x])/(6*c^2*d*(c + d*x^2)) - ((b*c - a*d)*(b*c + 7*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*d^(5/4)) + ((b*c - a*d)*(b*c + 7*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*d^(5/4)) - ((b*c - a*d)*(b*c + 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*d^(5/4)) + ((b*c - a*d)*(b*c + 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*d^(5/4))","A",12,9,24,0.3750,1,"{462, 457, 329, 211, 1165, 628, 1162, 617, 204}"
432,1,363,0,0.3771619,"\int \frac{\left(a+b x^2\right)^2}{x^{7/2} \left(c+d x^2\right)^2} \, dx","Int[(a + b*x^2)^2/(x^(7/2)*(c + d*x^2)^2),x]","-\frac{9 a^2 d^2-10 a b c d+5 b^2 c^2}{10 c^2 d \sqrt{x} \left(c+d x^2\right)}-\frac{2 a^2}{5 c x^{5/2} \left(c+d x^2\right)}+\frac{(b c-9 a d) (b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} d^{3/4}}-\frac{(b c-9 a d) (b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} d^{3/4}}-\frac{(b c-9 a d) (b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{13/4} d^{3/4}}+\frac{(b c-9 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{13/4} d^{3/4}}+\frac{(b c-9 a d) (b c-a d)}{2 c^3 d \sqrt{x}}","-\frac{9 a^2 d^2-10 a b c d+5 b^2 c^2}{10 c^2 d \sqrt{x} \left(c+d x^2\right)}-\frac{2 a^2}{5 c x^{5/2} \left(c+d x^2\right)}+\frac{(b c-9 a d) (b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} d^{3/4}}-\frac{(b c-9 a d) (b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} d^{3/4}}-\frac{(b c-9 a d) (b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{13/4} d^{3/4}}+\frac{(b c-9 a d) (b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{13/4} d^{3/4}}+\frac{(b c-9 a d) (b c-a d)}{2 c^3 d \sqrt{x}}",1,"((b*c - 9*a*d)*(b*c - a*d))/(2*c^3*d*Sqrt[x]) - (2*a^2)/(5*c*x^(5/2)*(c + d*x^2)) - (5*b^2*c^2 - 10*a*b*c*d + 9*a^2*d^2)/(10*c^2*d*Sqrt[x]*(c + d*x^2)) - ((b*c - 9*a*d)*(b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*d^(3/4)) + ((b*c - 9*a*d)*(b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*d^(3/4)) + ((b*c - 9*a*d)*(b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*d^(3/4)) - ((b*c - 9*a*d)*(b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*d^(3/4))","A",13,10,24,0.4167,1,"{462, 457, 325, 329, 297, 1162, 617, 204, 1165, 628}"
433,1,440,0,0.3809125,"\int \frac{x^{7/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x]","\frac{x^{5/2} \left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right)}{80 c^2 d^3}-\frac{\sqrt{x} \left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right)}{16 c d^4}-\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{17/4}}+\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{17/4}}-\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{3/4} d^{17/4}}+\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{3/4} d^{17/4}}-\frac{x^{9/2} (b c-a d) (17 b c-a d)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{9/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","\frac{x^{5/2} \left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right)}{80 c^2 d^3}-\frac{\sqrt{x} \left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right)}{16 c d^4}-\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{17/4}}+\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{17/4}}-\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{3/4} d^{17/4}}+\frac{\left(5 a^2 d^2-90 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{3/4} d^{17/4}}-\frac{x^{9/2} (b c-a d) (17 b c-a d)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{9/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"-((117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*Sqrt[x])/(16*c*d^4) + ((117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*x^(5/2))/(80*c^2*d^3) + ((b*c - a*d)^2*x^(9/2))/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(17*b*c - a*d)*x^(9/2))/(16*c^2*d^2*(c + d*x^2)) - ((117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(3/4)*d^(17/4)) + ((117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(3/4)*d^(17/4)) - ((117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(3/4)*d^(17/4)) + ((117*b^2*c^2 - 90*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(3/4)*d^(17/4))","A",14,10,24,0.4167,1,"{463, 457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
434,1,401,0,0.3433863,"\int \frac{x^{5/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x]","-\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{15/4}}+\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{15/4}}+\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{5/4} d^{15/4}}-\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{5/4} d^{15/4}}-\frac{x^{3/2} \left(\frac{3 a^2 d}{c}+42 a b-\frac{77 b^2 c}{d}\right)}{48 c d^2}-\frac{x^{7/2} (b c-a d) (a d+15 b c)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{7/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","-\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{15/4}}+\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{15/4}}+\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{5/4} d^{15/4}}-\frac{\left(-3 a^2 d^2-42 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{5/4} d^{15/4}}-\frac{x^{3/2} \left(\frac{3 a^2 d}{c}+42 a b-\frac{77 b^2 c}{d}\right)}{48 c d^2}-\frac{x^{7/2} (b c-a d) (a d+15 b c)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{7/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"-((42*a*b - (77*b^2*c)/d + (3*a^2*d)/c)*x^(3/2))/(48*c*d^2) + ((b*c - a*d)^2*x^(7/2))/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(15*b*c + a*d)*x^(7/2))/(16*c^2*d^2*(c + d*x^2)) + ((77*b^2*c^2 - 42*a*b*c*d - 3*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(5/4)*d^(15/4)) - ((77*b^2*c^2 - 42*a*b*c*d - 3*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(5/4)*d^(15/4)) - ((77*b^2*c^2 - 42*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(5/4)*d^(15/4)) + ((77*b^2*c^2 - 42*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(5/4)*d^(15/4))","A",13,10,24,0.4167,1,"{463, 457, 321, 329, 297, 1162, 617, 204, 1165, 628}"
435,1,402,0,0.3296274,"\int \frac{x^{3/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(x^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^3,x]","\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} d^{13/4}}-\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} d^{13/4}}+\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{7/4} d^{13/4}}-\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{7/4} d^{13/4}}-\frac{\sqrt{x} \left(\frac{3 a^2 d}{c}+10 a b-\frac{45 b^2 c}{d}\right)}{16 c d^2}-\frac{x^{5/2} (b c-a d) (3 a d+13 b c)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{5/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} d^{13/4}}-\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} d^{13/4}}+\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{7/4} d^{13/4}}-\frac{\left(-3 a^2 d^2-10 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{7/4} d^{13/4}}-\frac{\sqrt{x} \left(\frac{3 a^2 d}{c}+10 a b-\frac{45 b^2 c}{d}\right)}{16 c d^2}-\frac{x^{5/2} (b c-a d) (3 a d+13 b c)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{5/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"-((10*a*b - (45*b^2*c)/d + (3*a^2*d)/c)*Sqrt[x])/(16*c*d^2) + ((b*c - a*d)^2*x^(5/2))/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(13*b*c + 3*a*d)*x^(5/2))/(16*c^2*d^2*(c + d*x^2)) + ((45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*d^(13/4)) - ((45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*d^(13/4)) + ((45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*d^(13/4)) - ((45*b^2*c^2 - 10*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*d^(13/4))","A",13,10,24,0.4167,1,"{463, 457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
436,1,364,0,0.2925968,"\int \frac{\sqrt{x} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^3} \, dx","Int[(Sqrt[x]*(a + b*x^2)^2)/(c + d*x^2)^3,x]","\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} d^{11/4}}-\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} d^{11/4}}-\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{9/4} d^{11/4}}+\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{9/4} d^{11/4}}-\frac{x^{3/2} (5 a d+11 b c) (b c-a d)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{3/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} d^{11/4}}-\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} d^{11/4}}-\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{9/4} d^{11/4}}+\frac{\left(5 a^2 d^2+6 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{9/4} d^{11/4}}-\frac{x^{3/2} (5 a d+11 b c) (b c-a d)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{x^{3/2} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"((b*c - a*d)^2*x^(3/2))/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(11*b*c + 5*a*d)*x^(3/2))/(16*c^2*d^2*(c + d*x^2)) - ((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*d^(11/4)) + ((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*d^(11/4)) + ((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*d^(11/4)) - ((21*b^2*c^2 + 6*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*d^(11/4))","A",12,9,24,0.3750,1,"{463, 457, 329, 297, 1162, 617, 204, 1165, 628}"
437,1,364,0,0.2970394,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{x} \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(Sqrt[x]*(c + d*x^2)^3),x]","-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{11/4} d^{9/4}}-\frac{\sqrt{x} (7 a d+9 b c) (b c-a d)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{\sqrt{x} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}","-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} d^{9/4}}-\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{11/4} d^{9/4}}+\frac{\left(21 a^2 d^2+6 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{11/4} d^{9/4}}-\frac{\sqrt{x} (7 a d+9 b c) (b c-a d)}{16 c^2 d^2 \left(c+d x^2\right)}+\frac{\sqrt{x} (b c-a d)^2}{4 c d^2 \left(c+d x^2\right)^2}",1,"((b*c - a*d)^2*Sqrt[x])/(4*c*d^2*(c + d*x^2)^2) - ((b*c - a*d)*(9*b*c + 7*a*d)*Sqrt[x])/(16*c^2*d^2*(c + d*x^2)) - ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(11/4)*d^(9/4)) + ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(11/4)*d^(9/4)) - ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(11/4)*d^(9/4)) + ((5*b^2*c^2 + 6*a*b*c*d + 21*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(11/4)*d^(9/4))","A",12,9,24,0.3750,1,"{463, 457, 329, 211, 1165, 628, 1162, 617, 204}"
438,1,398,0,0.3945203,"\int \frac{\left(a+b x^2\right)^2}{x^{3/2} \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x^(3/2)*(c + d*x^2)^3),x]","-\frac{x^{3/2} \left(9 a^2 d^2-2 a b c d+b^2 c^2\right)}{4 c^2 d \left(c+d x^2\right)^2}-\frac{2 a^2}{c \sqrt{x} \left(c+d x^2\right)^2}+\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} d^{7/4}}-\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} d^{7/4}}-\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{13/4} d^{7/4}}+\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{13/4} d^{7/4}}+\frac{x^{3/2} \left(\frac{5 a (2 b c-9 a d)}{c^2}+\frac{3 b^2}{d}\right)}{16 c \left(c+d x^2\right)}","-\frac{x^{3/2} \left(9 a^2 d^2-2 a b c d+b^2 c^2\right)}{4 c^2 d \left(c+d x^2\right)^2}-\frac{2 a^2}{c \sqrt{x} \left(c+d x^2\right)^2}+\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} d^{7/4}}-\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} d^{7/4}}-\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{13/4} d^{7/4}}+\frac{\left(5 a d (2 b c-9 a d)+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{13/4} d^{7/4}}+\frac{x^{3/2} \left(5 a d (2 b c-9 a d)+3 b^2 c^2\right)}{16 c^3 d \left(c+d x^2\right)}",1,"(-2*a^2)/(c*Sqrt[x]*(c + d*x^2)^2) - ((b^2*c^2 - 2*a*b*c*d + 9*a^2*d^2)*x^(3/2))/(4*c^2*d*(c + d*x^2)^2) + (((3*b^2)/d + (5*a*(2*b*c - 9*a*d))/c^2)*x^(3/2))/(16*c*(c + d*x^2)) - ((3*b^2*c^2 + 5*a*d*(2*b*c - 9*a*d))*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(13/4)*d^(7/4)) + ((3*b^2*c^2 + 5*a*d*(2*b*c - 9*a*d))*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(13/4)*d^(7/4)) + ((3*b^2*c^2 + 5*a*d*(2*b*c - 9*a*d))*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(13/4)*d^(7/4)) - ((3*b^2*c^2 + 5*a*d*(2*b*c - 9*a*d))*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(13/4)*d^(7/4))","A",13,10,24,0.4167,1,"{462, 457, 290, 329, 297, 1162, 617, 204, 1165, 628}"
439,1,401,0,0.4055643,"\int \frac{\left(a+b x^2\right)^2}{x^{5/2} \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x^(5/2)*(c + d*x^2)^3),x]","-\frac{\sqrt{x} \left(11 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{12 c^2 d \left(c+d x^2\right)^2}-\frac{2 a^2}{3 c x^{3/2} \left(c+d x^2\right)^2}-\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} d^{5/4}}+\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} d^{5/4}}-\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{15/4} d^{5/4}}+\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{15/4} d^{5/4}}+\frac{\sqrt{x} \left(\frac{7 a (6 b c-11 a d)}{c^2}+\frac{3 b^2}{d}\right)}{48 c \left(c+d x^2\right)}","-\frac{\sqrt{x} \left(11 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{12 c^2 d \left(c+d x^2\right)^2}-\frac{2 a^2}{3 c x^{3/2} \left(c+d x^2\right)^2}-\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} d^{5/4}}+\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} d^{5/4}}-\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{15/4} d^{5/4}}+\frac{\left(7 a d (6 b c-11 a d)+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{15/4} d^{5/4}}+\frac{\sqrt{x} \left(7 a d (6 b c-11 a d)+3 b^2 c^2\right)}{48 c^3 d \left(c+d x^2\right)}",1,"(-2*a^2)/(3*c*x^(3/2)*(c + d*x^2)^2) - ((3*b^2*c^2 - 6*a*b*c*d + 11*a^2*d^2)*Sqrt[x])/(12*c^2*d*(c + d*x^2)^2) + (((3*b^2)/d + (7*a*(6*b*c - 11*a*d))/c^2)*Sqrt[x])/(48*c*(c + d*x^2)) - ((3*b^2*c^2 + 7*a*d*(6*b*c - 11*a*d))*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(15/4)*d^(5/4)) + ((3*b^2*c^2 + 7*a*d*(6*b*c - 11*a*d))*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(15/4)*d^(5/4)) - ((3*b^2*c^2 + 7*a*d*(6*b*c - 11*a*d))*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(15/4)*d^(5/4)) + ((3*b^2*c^2 + 7*a*d*(6*b*c - 11*a*d))*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(15/4)*d^(5/4))","A",13,10,24,0.4167,1,"{462, 457, 290, 329, 211, 1165, 628, 1162, 617, 204}"
440,1,438,0,0.4502072,"\int \frac{\left(a+b x^2\right)^2}{x^{7/2} \left(c+d x^2\right)^3} \, dx","Int[(a + b*x^2)^2/(x^(7/2)*(c + d*x^2)^3),x]","-\frac{13 a^2 d^2-10 a b c d+5 b^2 c^2}{20 c^2 d \sqrt{x} \left(c+d x^2\right)^2}-\frac{2 a^2}{5 c x^{5/2} \left(c+d x^2\right)^2}+\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} d^{3/4}}-\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} d^{3/4}}-\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{17/4} d^{3/4}}+\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{17/4} d^{3/4}}-\frac{\frac{5 b^2}{d}-\frac{9 a (10 b c-13 a d)}{c^2}}{80 c \sqrt{x} \left(c+d x^2\right)}+\frac{5 b^2 c^2-9 a d (10 b c-13 a d)}{16 c^4 d \sqrt{x}}","-\frac{13 a^2 d^2-10 a b c d+5 b^2 c^2}{20 c^2 d \sqrt{x} \left(c+d x^2\right)^2}-\frac{2 a^2}{5 c x^{5/2} \left(c+d x^2\right)^2}+\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} d^{3/4}}-\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} d^{3/4}}-\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{17/4} d^{3/4}}+\frac{\left(5 b^2 c^2-9 a d (10 b c-13 a d)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{17/4} d^{3/4}}-\frac{5 b^2 c^2-9 a d (10 b c-13 a d)}{80 c^3 d \sqrt{x} \left(c+d x^2\right)}+\frac{5 b^2 c^2-9 a d (10 b c-13 a d)}{16 c^4 d \sqrt{x}}",1,"(5*b^2*c^2 - 9*a*d*(10*b*c - 13*a*d))/(16*c^4*d*Sqrt[x]) - (2*a^2)/(5*c*x^(5/2)*(c + d*x^2)^2) - (5*b^2*c^2 - 10*a*b*c*d + 13*a^2*d^2)/(20*c^2*d*Sqrt[x]*(c + d*x^2)^2) - ((5*b^2)/d - (9*a*(10*b*c - 13*a*d))/c^2)/(80*c*Sqrt[x]*(c + d*x^2)) - ((5*b^2*c^2 - 9*a*d*(10*b*c - 13*a*d))*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*d^(3/4)) + ((5*b^2*c^2 - 9*a*d*(10*b*c - 13*a*d))*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*d^(3/4)) + ((5*b^2*c^2 - 9*a*d*(10*b*c - 13*a*d))*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*d^(3/4)) - ((5*b^2*c^2 - 9*a*d*(10*b*c - 13*a*d))*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*d^(3/4))","A",14,11,24,0.4583,1,"{462, 457, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
441,1,328,0,0.2934914,"\int \frac{x^{5/2} \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^(5/2)*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{2 d x^{7/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{7 b^3}-\frac{a^{3/4} (b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{19/4}}+\frac{a^{3/4} (b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{19/4}}+\frac{a^{3/4} (b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{19/4}}-\frac{a^{3/4} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{19/4}}+\frac{2 d^2 x^{11/2} (3 b c-a d)}{11 b^2}+\frac{2 x^{3/2} (b c-a d)^3}{3 b^4}+\frac{2 d^3 x^{15/2}}{15 b}","\frac{2 d x^{7/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{7 b^3}-\frac{a^{3/4} (b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{19/4}}+\frac{a^{3/4} (b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{19/4}}+\frac{a^{3/4} (b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{19/4}}-\frac{a^{3/4} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{19/4}}+\frac{2 d^2 x^{11/2} (3 b c-a d)}{11 b^2}+\frac{2 x^{3/2} (b c-a d)^3}{3 b^4}+\frac{2 d^3 x^{15/2}}{15 b}",1,"(2*(b*c - a*d)^3*x^(3/2))/(3*b^4) + (2*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^(7/2))/(7*b^3) + (2*d^2*(3*b*c - a*d)*x^(11/2))/(11*b^2) + (2*d^3*x^(15/2))/(15*b) + (a^(3/4)*(b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(19/4)) - (a^(3/4)*(b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(19/4)) - (a^(3/4)*(b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(19/4)) + (a^(3/4)*(b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(19/4))","A",13,9,24,0.3750,1,"{461, 321, 329, 297, 1162, 617, 204, 1165, 628}"
442,1,326,0,0.2766605,"\int \frac{x^{3/2} \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(x^(3/2)*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{2 d x^{5/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{5 b^3}+\frac{2 d^2 x^{9/2} (3 b c-a d)}{9 b^2}+\frac{2 \sqrt{x} (b c-a d)^3}{b^4}+\frac{\sqrt[4]{a} (b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{17/4}}-\frac{\sqrt[4]{a} (b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{17/4}}+\frac{\sqrt[4]{a} (b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{17/4}}-\frac{\sqrt[4]{a} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{17/4}}+\frac{2 d^3 x^{13/2}}{13 b}","\frac{2 d x^{5/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{5 b^3}+\frac{2 d^2 x^{9/2} (3 b c-a d)}{9 b^2}+\frac{2 \sqrt{x} (b c-a d)^3}{b^4}+\frac{\sqrt[4]{a} (b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{17/4}}-\frac{\sqrt[4]{a} (b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{17/4}}+\frac{\sqrt[4]{a} (b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{17/4}}-\frac{\sqrt[4]{a} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{17/4}}+\frac{2 d^3 x^{13/2}}{13 b}",1,"(2*(b*c - a*d)^3*Sqrt[x])/b^4 + (2*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^(5/2))/(5*b^3) + (2*d^2*(3*b*c - a*d)*x^(9/2))/(9*b^2) + (2*d^3*x^(13/2))/(13*b) + (a^(1/4)*(b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(17/4)) - (a^(1/4)*(b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(17/4)) + (a^(1/4)*(b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(17/4)) - (a^(1/4)*(b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(17/4))","A",13,9,24,0.3750,1,"{461, 321, 329, 211, 1165, 628, 1162, 617, 204}"
443,1,306,0,0.2454344,"\int \frac{\sqrt{x} \left(c+d x^2\right)^3}{a+b x^2} \, dx","Int[(Sqrt[x]*(c + d*x^2)^3)/(a + b*x^2),x]","\frac{2 d x^{3/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{3 b^3}+\frac{2 d^2 x^{7/2} (3 b c-a d)}{7 b^2}+\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{15/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{15/4}}+\frac{2 d^3 x^{11/2}}{11 b}","\frac{2 d x^{3/2} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{3 b^3}+\frac{2 d^2 x^{7/2} (3 b c-a d)}{7 b^2}+\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} b^{15/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{15/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} b^{15/4}}+\frac{2 d^3 x^{11/2}}{11 b}",1,"(2*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*x^(3/2))/(3*b^3) + (2*d^2*(3*b*c - a*d)*x^(7/2))/(7*b^2) + (2*d^3*x^(11/2))/(11*b) - ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*b^(15/4)) + ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*b^(15/4)) + ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*b^(15/4)) - ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*b^(15/4))","A",12,8,24,0.3333,1,"{461, 329, 297, 1162, 617, 204, 1165, 628}"
444,1,304,0,0.2492369,"\int \frac{\left(c+d x^2\right)^3}{\sqrt{x} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(Sqrt[x]*(a + b*x^2)),x]","\frac{2 d \sqrt{x} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} b^{13/4}}+\frac{2 d^2 x^{5/2} (3 b c-a d)}{5 b^2}+\frac{2 d^3 x^{9/2}}{9 b}","\frac{2 d \sqrt{x} \left(a^2 d^2-3 a b c d+3 b^2 c^2\right)}{b^3}-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} b^{13/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} b^{13/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} b^{13/4}}+\frac{2 d^2 x^{5/2} (3 b c-a d)}{5 b^2}+\frac{2 d^3 x^{9/2}}{9 b}",1,"(2*d*(3*b^2*c^2 - 3*a*b*c*d + a^2*d^2)*Sqrt[x])/b^3 + (2*d^2*(3*b*c - a*d)*x^(5/2))/(5*b^2) + (2*d^3*x^(9/2))/(9*b) - ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*b^(13/4)) + ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*b^(13/4)) - ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*b^(13/4)) + ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*b^(13/4))","A",12,8,24,0.3333,1,"{461, 329, 211, 1165, 628, 1162, 617, 204}"
445,1,284,0,0.2902173,"\int \frac{\left(c+d x^2\right)^3}{x^{3/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(3/2)*(a + b*x^2)),x]","-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{11/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{11/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} b^{11/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} b^{11/4}}+\frac{2 d^2 x^{3/2} (3 b c-a d)}{3 b^2}-\frac{2 c^3}{a \sqrt{x}}+\frac{2 d^3 x^{7/2}}{7 b}","-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{11/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} b^{11/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} b^{11/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} b^{11/4}}+\frac{2 d^2 x^{3/2} (3 b c-a d)}{3 b^2}-\frac{2 c^3}{a \sqrt{x}}+\frac{2 d^3 x^{7/2}}{7 b}",1,"(-2*c^3)/(a*Sqrt[x]) + (2*d^2*(3*b*c - a*d)*x^(3/2))/(3*b^2) + (2*d^3*x^(7/2))/(7*b) + ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*b^(11/4)) - ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*b^(11/4)) - ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*b^(11/4)) + ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*b^(11/4))","A",12,8,24,0.3333,1,"{466, 461, 297, 1162, 617, 204, 1165, 628}"
446,1,284,0,0.2669195,"\int \frac{\left(c+d x^2\right)^3}{x^{5/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(5/2)*(a + b*x^2)),x]","\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} b^{9/4}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} b^{9/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} b^{9/4}}+\frac{2 d^2 \sqrt{x} (3 b c-a d)}{b^2}-\frac{2 c^3}{3 a x^{3/2}}+\frac{2 d^3 x^{5/2}}{5 b}","\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} b^{9/4}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} b^{9/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} b^{9/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} b^{9/4}}+\frac{2 d^2 \sqrt{x} (3 b c-a d)}{b^2}-\frac{2 c^3}{3 a x^{3/2}}+\frac{2 d^3 x^{5/2}}{5 b}",1,"(-2*c^3)/(3*a*x^(3/2)) + (2*d^2*(3*b*c - a*d)*Sqrt[x])/b^2 + (2*d^3*x^(5/2))/(5*b) + ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*b^(9/4)) - ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*b^(9/4)) + ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*b^(9/4)) - ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*b^(9/4))","A",12,8,24,0.3333,1,"{466, 461, 211, 1165, 628, 1162, 617, 204}"
447,1,283,0,0.2752808,"\int \frac{\left(c+d x^2\right)^3}{x^{7/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(7/2)*(a + b*x^2)),x]","\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} b^{7/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} b^{7/4}}+\frac{2 c^2 (b c-3 a d)}{a^2 \sqrt{x}}-\frac{2 c^3}{5 a x^{5/2}}+\frac{2 d^3 x^{3/2}}{3 b}","\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} b^{7/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} b^{7/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} b^{7/4}}+\frac{2 c^2 (b c-3 a d)}{a^2 \sqrt{x}}-\frac{2 c^3}{5 a x^{5/2}}+\frac{2 d^3 x^{3/2}}{3 b}",1,"(-2*c^3)/(5*a*x^(5/2)) + (2*c^2*(b*c - 3*a*d))/(a^2*Sqrt[x]) + (2*d^3*x^(3/2))/(3*b) - ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*b^(7/4)) + ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*b^(7/4)) + ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*b^(7/4)) - ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*b^(7/4))","A",12,8,24,0.3333,1,"{466, 461, 297, 1162, 617, 204, 1165, 628}"
448,1,283,0,0.2581359,"\int \frac{\left(c+d x^2\right)^3}{x^{9/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(9/2)*(a + b*x^2)),x]","-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{11/4} b^{5/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{11/4} b^{5/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{11/4} b^{5/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{11/4} b^{5/4}}+\frac{2 c^2 (b c-3 a d)}{3 a^2 x^{3/2}}-\frac{2 c^3}{7 a x^{7/2}}+\frac{2 d^3 \sqrt{x}}{b}","-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{11/4} b^{5/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{11/4} b^{5/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{11/4} b^{5/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{11/4} b^{5/4}}+\frac{2 c^2 (b c-3 a d)}{3 a^2 x^{3/2}}-\frac{2 c^3}{7 a x^{7/2}}+\frac{2 d^3 \sqrt{x}}{b}",1,"(-2*c^3)/(7*a*x^(7/2)) + (2*c^2*(b*c - 3*a*d))/(3*a^2*x^(3/2)) + (2*d^3*Sqrt[x])/b - ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(11/4)*b^(5/4)) + ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(11/4)*b^(5/4)) - ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(11/4)*b^(5/4)) + ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(11/4)*b^(5/4))","A",12,8,24,0.3333,1,"{466, 461, 211, 1165, 628, 1162, 617, 204}"
449,1,303,0,0.2906927,"\int \frac{\left(c+d x^2\right)^3}{x^{11/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(11/2)*(a + b*x^2)),x]","-\frac{2 c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{a^3 \sqrt{x}}-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4} b^{3/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4} b^{3/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{13/4} b^{3/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{13/4} b^{3/4}}+\frac{2 c^2 (b c-3 a d)}{5 a^2 x^{5/2}}-\frac{2 c^3}{9 a x^{9/2}}","-\frac{2 c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{a^3 \sqrt{x}}-\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4} b^{3/4}}+\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{13/4} b^{3/4}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{13/4} b^{3/4}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{13/4} b^{3/4}}+\frac{2 c^2 (b c-3 a d)}{5 a^2 x^{5/2}}-\frac{2 c^3}{9 a x^{9/2}}",1,"(-2*c^3)/(9*a*x^(9/2)) + (2*c^2*(b*c - 3*a*d))/(5*a^2*x^(5/2)) - (2*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2))/(a^3*Sqrt[x]) + ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(13/4)*b^(3/4)) - ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(13/4)*b^(3/4)) - ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(13/4)*b^(3/4)) + ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(13/4)*b^(3/4))","A",12,8,24,0.3333,1,"{466, 461, 297, 1162, 617, 204, 1165, 628}"
450,1,305,0,0.2676109,"\int \frac{\left(c+d x^2\right)^3}{x^{13/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(13/2)*(a + b*x^2)),x]","-\frac{2 c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{3 a^3 x^{3/2}}+\frac{2 c^2 (b c-3 a d)}{7 a^2 x^{7/2}}+\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{2 c^3}{11 a x^{11/2}}","-\frac{2 c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{3 a^3 x^{3/2}}+\frac{2 c^2 (b c-3 a d)}{7 a^2 x^{7/2}}+\frac{(b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{(b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{15/4} \sqrt[4]{b}}+\frac{(b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{(b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{15/4} \sqrt[4]{b}}-\frac{2 c^3}{11 a x^{11/2}}",1,"(-2*c^3)/(11*a*x^(11/2)) + (2*c^2*(b*c - 3*a*d))/(7*a^2*x^(7/2)) - (2*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2))/(3*a^3*x^(3/2)) + ((b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(15/4)*b^(1/4)) - ((b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(15/4)*b^(1/4)) + ((b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(15/4)*b^(1/4)) - ((b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(15/4)*b^(1/4))","A",12,8,24,0.3333,1,"{466, 461, 211, 1165, 628, 1162, 617, 204}"
451,1,325,0,0.305925,"\int \frac{\left(c+d x^2\right)^3}{x^{15/2} \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^3/(x^(15/2)*(a + b*x^2)),x]","-\frac{2 c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{5 a^3 x^{5/2}}+\frac{2 c^2 (b c-3 a d)}{9 a^2 x^{9/2}}+\frac{2 (b c-a d)^3}{a^4 \sqrt{x}}+\frac{\sqrt[4]{b} (b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{17/4}}-\frac{\sqrt[4]{b} (b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{17/4}}-\frac{\sqrt[4]{b} (b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{17/4}}+\frac{\sqrt[4]{b} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{17/4}}-\frac{2 c^3}{13 a x^{13/2}}","-\frac{2 c \left(3 a^2 d^2-3 a b c d+b^2 c^2\right)}{5 a^3 x^{5/2}}+\frac{2 c^2 (b c-3 a d)}{9 a^2 x^{9/2}}+\frac{2 (b c-a d)^3}{a^4 \sqrt{x}}+\frac{\sqrt[4]{b} (b c-a d)^3 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{17/4}}-\frac{\sqrt[4]{b} (b c-a d)^3 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{17/4}}-\frac{\sqrt[4]{b} (b c-a d)^3 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{17/4}}+\frac{\sqrt[4]{b} (b c-a d)^3 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{17/4}}-\frac{2 c^3}{13 a x^{13/2}}",1,"(-2*c^3)/(13*a*x^(13/2)) + (2*c^2*(b*c - 3*a*d))/(9*a^2*x^(9/2)) - (2*c*(b^2*c^2 - 3*a*b*c*d + 3*a^2*d^2))/(5*a^3*x^(5/2)) + (2*(b*c - a*d)^3)/(a^4*Sqrt[x]) - (b^(1/4)*(b*c - a*d)^3*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(17/4)) + (b^(1/4)*(b*c - a*d)^3*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(17/4)) + (b^(1/4)*(b*c - a*d)^3*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(17/4)) - (b^(1/4)*(b*c - a*d)^3*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(17/4))","A",12,8,24,0.3333,1,"{466, 461, 297, 1162, 617, 204, 1165, 628}"
452,1,409,0,0.4672703,"\int \frac{x^{7/2} \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^(7/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d x^{5/2} \left(17 a^2 d^2-39 a b c d+27 b^2 c^2\right)}{10 b^4}+\frac{d^2 x^{9/2} (39 b c-17 a d)}{18 b^3}+\frac{\sqrt{x} (5 b c-17 a d) (b c-a d)^2}{2 b^5}+\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{21/4}}-\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{21/4}}+\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{21/4}}-\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{21/4}}-\frac{x^{5/2} \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{17 d^3 x^{13/2}}{26 b^2}","\frac{d x^{5/2} \left(17 a^2 d^2-39 a b c d+27 b^2 c^2\right)}{10 b^4}+\frac{d^2 x^{9/2} (39 b c-17 a d)}{18 b^3}+\frac{\sqrt{x} (5 b c-17 a d) (b c-a d)^2}{2 b^5}+\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{21/4}}-\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} b^{21/4}}+\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} b^{21/4}}-\frac{\sqrt[4]{a} (5 b c-17 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} b^{21/4}}-\frac{x^{5/2} \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{17 d^3 x^{13/2}}{26 b^2}",1,"((5*b*c - 17*a*d)*(b*c - a*d)^2*Sqrt[x])/(2*b^5) + (d*(27*b^2*c^2 - 39*a*b*c*d + 17*a^2*d^2)*x^(5/2))/(10*b^4) + (d^2*(39*b*c - 17*a*d)*x^(9/2))/(18*b^3) + (17*d^3*x^(13/2))/(26*b^2) - (x^(5/2)*(c + d*x^2)^3)/(2*b*(a + b*x^2)) + (a^(1/4)*(5*b*c - 17*a*d)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(21/4)) - (a^(1/4)*(5*b*c - 17*a*d)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(21/4)) + (a^(1/4)*(5*b*c - 17*a*d)*(b*c - a*d)^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(21/4)) - (a^(1/4)*(5*b*c - 17*a*d)*(b*c - a*d)^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(21/4))","A",13,9,24,0.3750,1,"{466, 467, 570, 211, 1165, 628, 1162, 617, 204}"
453,1,374,0,0.4149846,"\int \frac{x^{5/2} \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^(5/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d x^{3/2} \left(5 a^2 d^2-11 a b c d+7 b^2 c^2\right)}{2 b^4}+\frac{3 d^2 x^{7/2} (11 b c-5 a d)}{14 b^3}+\frac{3 (b c-5 a d) (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{19/4}}-\frac{3 (b c-5 a d) (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{19/4}}-\frac{3 (b c-5 a d) (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{19/4}}+\frac{3 (b c-5 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{19/4}}-\frac{x^{3/2} \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{15 d^3 x^{11/2}}{22 b^2}","\frac{d x^{3/2} \left(5 a^2 d^2-11 a b c d+7 b^2 c^2\right)}{2 b^4}+\frac{3 d^2 x^{7/2} (11 b c-5 a d)}{14 b^3}+\frac{3 (b c-5 a d) (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{19/4}}-\frac{3 (b c-5 a d) (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} b^{19/4}}-\frac{3 (b c-5 a d) (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} b^{19/4}}+\frac{3 (b c-5 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} b^{19/4}}-\frac{x^{3/2} \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{15 d^3 x^{11/2}}{22 b^2}",1,"(d*(7*b^2*c^2 - 11*a*b*c*d + 5*a^2*d^2)*x^(3/2))/(2*b^4) + (3*d^2*(11*b*c - 5*a*d)*x^(7/2))/(14*b^3) + (15*d^3*x^(11/2))/(22*b^2) - (x^(3/2)*(c + d*x^2)^3)/(2*b*(a + b*x^2)) - (3*(b*c - 5*a*d)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*b^(19/4)) + (3*(b*c - 5*a*d)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*b^(19/4)) + (3*(b*c - 5*a*d)*(b*c - a*d)^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*b^(19/4)) - (3*(b*c - 5*a*d)*(b*c - a*d)^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*b^(19/4))","A",13,9,24,0.3750,1,"{466, 467, 570, 297, 1162, 617, 204, 1165, 628}"
454,1,386,0,0.5292803,"\int \frac{x^{3/2} \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(x^(3/2)*(c + d*x^2)^3)/(a + b*x^2)^2,x]","\frac{d \sqrt{x} \left(585 a^2 d^2-1098 a b c d+497 b^2 c^2\right)}{90 b^4}-\frac{(b c-13 a d) (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-13 a d) (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{17/4}}-\frac{(b c-13 a d) (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-13 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}+\frac{d \sqrt{x} \left(c+d x^2\right) (113 b c-117 a d)}{90 b^3}-\frac{\sqrt{x} \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{13 d \sqrt{x} \left(c+d x^2\right)^2}{18 b^2}","\frac{d \sqrt{x} \left(585 a^2 d^2-1098 a b c d+497 b^2 c^2\right)}{90 b^4}-\frac{(b c-13 a d) (b c-a d)^2 \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-13 a d) (b c-a d)^2 \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} b^{17/4}}-\frac{(b c-13 a d) (b c-a d)^2 \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}+\frac{(b c-13 a d) (b c-a d)^2 \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} b^{17/4}}+\frac{d \sqrt{x} \left(c+d x^2\right) (113 b c-117 a d)}{90 b^3}-\frac{\sqrt{x} \left(c+d x^2\right)^3}{2 b \left(a+b x^2\right)}+\frac{13 d \sqrt{x} \left(c+d x^2\right)^2}{18 b^2}",1,"(d*(497*b^2*c^2 - 1098*a*b*c*d + 585*a^2*d^2)*Sqrt[x])/(90*b^4) + (d*(113*b*c - 117*a*d)*Sqrt[x]*(c + d*x^2))/(90*b^3) + (13*d*Sqrt[x]*(c + d*x^2)^2)/(18*b^2) - (Sqrt[x]*(c + d*x^2)^3)/(2*b*(a + b*x^2)) - ((b*c - 13*a*d)*(b*c - a*d)^2*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*b^(17/4)) + ((b*c - 13*a*d)*(b*c - a*d)^2*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*b^(17/4)) - ((b*c - 13*a*d)*(b*c - a*d)^2*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*b^(17/4)) + ((b*c - 13*a*d)*(b*c - a*d)^2*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*b^(17/4))","A",14,10,24,0.4167,1,"{466, 467, 528, 388, 211, 1165, 628, 1162, 617, 204}"
455,1,376,0,0.4258694,"\int \frac{\sqrt{x} \left(c+d x^2\right)^3}{\left(a+b x^2\right)^2} \, dx","Int[(Sqrt[x]*(c + d*x^2)^3)/(a + b*x^2)^2,x]","-\frac{d x^{3/2} \left(11 a^2 d^2-21 a b c d+6 b^2 c^2\right)}{6 a b^3}+\frac{(b c-a d)^2 (11 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{15/4}}-\frac{(b c-a d)^2 (11 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{15/4}}-\frac{(b c-a d)^2 (11 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} b^{15/4}}+\frac{(b c-a d)^2 (11 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} b^{15/4}}-\frac{d^2 x^{7/2} (7 b c-11 a d)}{14 a b^2}+\frac{x^{3/2} \left(c+d x^2\right)^2 (b c-a d)}{2 a b \left(a+b x^2\right)}","-\frac{d x^{3/2} \left(11 a^2 d^2-21 a b c d+6 b^2 c^2\right)}{6 a b^3}+\frac{(b c-a d)^2 (11 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{15/4}}-\frac{(b c-a d)^2 (11 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} b^{15/4}}-\frac{(b c-a d)^2 (11 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} b^{15/4}}+\frac{(b c-a d)^2 (11 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} b^{15/4}}-\frac{d^2 x^{7/2} (7 b c-11 a d)}{14 a b^2}+\frac{x^{3/2} \left(c+d x^2\right)^2 (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"-(d*(6*b^2*c^2 - 21*a*b*c*d + 11*a^2*d^2)*x^(3/2))/(6*a*b^3) - (d^2*(7*b*c - 11*a*d)*x^(7/2))/(14*a*b^2) + ((b*c - a*d)*x^(3/2)*(c + d*x^2)^2)/(2*a*b*(a + b*x^2)) - ((b*c - a*d)^2*(b*c + 11*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*b^(15/4)) + ((b*c - a*d)^2*(b*c + 11*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*b^(15/4)) + ((b*c - a*d)^2*(b*c + 11*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*b^(15/4)) - ((b*c - a*d)^2*(b*c + 11*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*b^(15/4))","A",13,9,24,0.3750,1,"{466, 468, 570, 297, 1162, 617, 204, 1165, 628}"
456,1,340,0,0.3883113,"\int \frac{\left(c+d x^2\right)^3}{\sqrt{x} \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(Sqrt[x]*(a + b*x^2)^2),x]","-\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}-\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} b^{13/4}}+\frac{2 d^2 \sqrt{x} (3 b c-2 a d)}{b^3}+\frac{\sqrt{x} (b c-a d)^3}{2 a b^3 \left(a+b x^2\right)}+\frac{2 d^3 x^{5/2}}{5 b^2}","-\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} b^{13/4}}-\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} b^{13/4}}+\frac{3 (b c-a d)^2 (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} b^{13/4}}+\frac{2 d^2 \sqrt{x} (3 b c-2 a d)}{b^3}+\frac{\sqrt{x} (b c-a d)^3}{2 a b^3 \left(a+b x^2\right)}+\frac{2 d^3 x^{5/2}}{5 b^2}",1,"(2*d^2*(3*b*c - 2*a*d)*Sqrt[x])/b^3 + (2*d^3*x^(5/2))/(5*b^2) + ((b*c - a*d)^3*Sqrt[x])/(2*a*b^3*(a + b*x^2)) - (3*(b*c - a*d)^2*(b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*b^(13/4)) + (3*(b*c - a*d)^2*(b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*b^(13/4)) - (3*(b*c - a*d)^2*(b*c + 3*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*b^(13/4)) + (3*(b*c - a*d)^2*(b*c + 3*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*b^(13/4))","A",13,9,24,0.3750,1,"{466, 390, 385, 211, 1165, 628, 1162, 617, 204}"
457,1,368,0,0.4312879,"\int \frac{\left(c+d x^2\right)^3}{x^{3/2} \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^(3/2)*(a + b*x^2)^2),x]","-\frac{(b c-a d)^2 (7 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{11/4}}+\frac{(b c-a d)^2 (7 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{11/4}}+\frac{(b c-a d)^2 (7 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} b^{11/4}}-\frac{(b c-a d)^2 (7 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} b^{11/4}}-\frac{c^2 (5 b c-a d)}{2 a^2 b \sqrt{x}}-\frac{d^2 x^{3/2} (3 b c-7 a d)}{6 a b^2}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b \sqrt{x} \left(a+b x^2\right)}","-\frac{(b c-a d)^2 (7 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{11/4}}+\frac{(b c-a d)^2 (7 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} b^{11/4}}+\frac{(b c-a d)^2 (7 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} b^{11/4}}-\frac{(b c-a d)^2 (7 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} b^{11/4}}-\frac{c^2 (5 b c-a d)}{2 a^2 b \sqrt{x}}-\frac{d^2 x^{3/2} (3 b c-7 a d)}{6 a b^2}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b \sqrt{x} \left(a+b x^2\right)}",1,"-(c^2*(5*b*c - a*d))/(2*a^2*b*Sqrt[x]) - (d^2*(3*b*c - 7*a*d)*x^(3/2))/(6*a*b^2) + ((b*c - a*d)*(c + d*x^2)^2)/(2*a*b*Sqrt[x]*(a + b*x^2)) + ((b*c - a*d)^2*(5*b*c + 7*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*b^(11/4)) - ((b*c - a*d)^2*(5*b*c + 7*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*b^(11/4)) - ((b*c - a*d)^2*(5*b*c + 7*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*b^(11/4)) + ((b*c - a*d)^2*(5*b*c + 7*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*b^(11/4))","A",13,9,24,0.3750,1,"{466, 468, 570, 297, 1162, 617, 204, 1165, 628}"
458,1,367,0,0.4109478,"\int \frac{\left(c+d x^2\right)^3}{x^{5/2} \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^(5/2)*(a + b*x^2)^2),x]","\frac{(b c-a d)^2 (5 a d+7 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} b^{9/4}}-\frac{(b c-a d)^2 (5 a d+7 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} b^{9/4}}+\frac{(b c-a d)^2 (5 a d+7 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4} b^{9/4}}-\frac{(b c-a d)^2 (5 a d+7 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4} b^{9/4}}-\frac{c^2 (7 b c-3 a d)}{6 a^2 b x^{3/2}}-\frac{d^2 \sqrt{x} (b c-5 a d)}{2 a b^2}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^{3/2} \left(a+b x^2\right)}","\frac{(b c-a d)^2 (5 a d+7 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} b^{9/4}}-\frac{(b c-a d)^2 (5 a d+7 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} b^{9/4}}+\frac{(b c-a d)^2 (5 a d+7 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4} b^{9/4}}-\frac{(b c-a d)^2 (5 a d+7 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4} b^{9/4}}-\frac{c^2 (7 b c-3 a d)}{6 a^2 b x^{3/2}}-\frac{d^2 \sqrt{x} (b c-5 a d)}{2 a b^2}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^{3/2} \left(a+b x^2\right)}",1,"-(c^2*(7*b*c - 3*a*d))/(6*a^2*b*x^(3/2)) - (d^2*(b*c - 5*a*d)*Sqrt[x])/(2*a*b^2) + ((b*c - a*d)*(c + d*x^2)^2)/(2*a*b*x^(3/2)*(a + b*x^2)) + ((b*c - a*d)^2*(7*b*c + 5*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*b^(9/4)) - ((b*c - a*d)^2*(7*b*c + 5*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*b^(9/4)) + ((b*c - a*d)^2*(7*b*c + 5*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*b^(9/4)) - ((b*c - a*d)^2*(7*b*c + 5*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*b^(9/4))","A",13,9,24,0.3750,1,"{466, 468, 570, 211, 1165, 628, 1162, 617, 204}"
459,1,376,0,0.4293712,"\int \frac{\left(c+d x^2\right)^3}{x^{7/2} \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^(7/2)*(a + b*x^2)^2),x]","\frac{c \left(2 a^2 d^2-15 a b c d+9 b^2 c^2\right)}{2 a^3 b \sqrt{x}}+\frac{3 (b c-a d)^2 (a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} b^{7/4}}-\frac{3 (b c-a d)^2 (a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} b^{7/4}}-\frac{3 (b c-a d)^2 (a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4} b^{7/4}}+\frac{3 (b c-a d)^2 (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4} b^{7/4}}-\frac{c^2 (9 b c-5 a d)}{10 a^2 b x^{5/2}}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^{5/2} \left(a+b x^2\right)}","\frac{c \left(2 a^2 d^2-15 a b c d+9 b^2 c^2\right)}{2 a^3 b \sqrt{x}}+\frac{3 (b c-a d)^2 (a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} b^{7/4}}-\frac{3 (b c-a d)^2 (a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} b^{7/4}}-\frac{3 (b c-a d)^2 (a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4} b^{7/4}}+\frac{3 (b c-a d)^2 (a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4} b^{7/4}}-\frac{c^2 (9 b c-5 a d)}{10 a^2 b x^{5/2}}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^{5/2} \left(a+b x^2\right)}",1,"-(c^2*(9*b*c - 5*a*d))/(10*a^2*b*x^(5/2)) + (c*(9*b^2*c^2 - 15*a*b*c*d + 2*a^2*d^2))/(2*a^3*b*Sqrt[x]) + ((b*c - a*d)*(c + d*x^2)^2)/(2*a*b*x^(5/2)*(a + b*x^2)) - (3*(b*c - a*d)^2*(3*b*c + a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*b^(7/4)) + (3*(b*c - a*d)^2*(3*b*c + a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*b^(7/4)) + (3*(b*c - a*d)^2*(3*b*c + a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*b^(7/4)) - (3*(b*c - a*d)^2*(3*b*c + a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*b^(7/4))","A",13,9,24,0.3750,1,"{466, 468, 570, 297, 1162, 617, 204, 1165, 628}"
460,1,376,0,0.4157586,"\int \frac{\left(c+d x^2\right)^3}{x^{9/2} \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^3/(x^(9/2)*(a + b*x^2)^2),x]","\frac{c \left(6 a^2 d^2-21 a b c d+11 b^2 c^2\right)}{6 a^3 b x^{3/2}}-\frac{(b c-a d)^2 (a d+11 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{15/4} b^{5/4}}+\frac{(b c-a d)^2 (a d+11 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{15/4} b^{5/4}}-\frac{(b c-a d)^2 (a d+11 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{15/4} b^{5/4}}+\frac{(b c-a d)^2 (a d+11 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{15/4} b^{5/4}}-\frac{c^2 (11 b c-7 a d)}{14 a^2 b x^{7/2}}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^{7/2} \left(a+b x^2\right)}","\frac{c \left(6 a^2 d^2-21 a b c d+11 b^2 c^2\right)}{6 a^3 b x^{3/2}}-\frac{(b c-a d)^2 (a d+11 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{15/4} b^{5/4}}+\frac{(b c-a d)^2 (a d+11 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{15/4} b^{5/4}}-\frac{(b c-a d)^2 (a d+11 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{15/4} b^{5/4}}+\frac{(b c-a d)^2 (a d+11 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{15/4} b^{5/4}}-\frac{c^2 (11 b c-7 a d)}{14 a^2 b x^{7/2}}+\frac{\left(c+d x^2\right)^2 (b c-a d)}{2 a b x^{7/2} \left(a+b x^2\right)}",1,"-(c^2*(11*b*c - 7*a*d))/(14*a^2*b*x^(7/2)) + (c*(11*b^2*c^2 - 21*a*b*c*d + 6*a^2*d^2))/(6*a^3*b*x^(3/2)) + ((b*c - a*d)*(c + d*x^2)^2)/(2*a*b*x^(7/2)*(a + b*x^2)) - ((b*c - a*d)^2*(11*b*c + a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(15/4)*b^(5/4)) + ((b*c - a*d)^2*(11*b*c + a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(15/4)*b^(5/4)) - ((b*c - a*d)^2*(11*b*c + a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(15/4)*b^(5/4)) + ((b*c - a*d)^2*(11*b*c + a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(15/4)*b^(5/4))","A",13,9,24,0.3750,1,"{466, 468, 570, 211, 1165, 628, 1162, 617, 204}"
461,1,478,0,0.5573872,"\int \frac{x^{9/2}}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^(9/2)/((a + b*x^2)*(c + d*x^2)),x]","\frac{a^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4} (b c-a d)}-\frac{a^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4} (b c-a d)}-\frac{a^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{7/4} (b c-a d)}+\frac{a^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{7/4} (b c-a d)}-\frac{c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{7/4} (b c-a d)}+\frac{c^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{7/4} (b c-a d)}+\frac{c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{7/4} (b c-a d)}-\frac{c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{7/4} (b c-a d)}+\frac{2 x^{3/2}}{3 b d}","\frac{a^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4} (b c-a d)}-\frac{a^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{7/4} (b c-a d)}-\frac{a^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{7/4} (b c-a d)}+\frac{a^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{7/4} (b c-a d)}-\frac{c^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{7/4} (b c-a d)}+\frac{c^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{7/4} (b c-a d)}+\frac{c^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{7/4} (b c-a d)}-\frac{c^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{7/4} (b c-a d)}+\frac{2 x^{3/2}}{3 b d}",1,"(2*x^(3/2))/(3*b*d) - (a^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(7/4)*(b*c - a*d)) + (a^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(7/4)*(b*c - a*d)) + (c^(7/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(7/4)*(b*c - a*d)) - (c^(7/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(7/4)*(b*c - a*d)) + (a^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(7/4)*(b*c - a*d)) - (a^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(7/4)*(b*c - a*d)) - (c^(7/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(7/4)*(b*c - a*d)) + (c^(7/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(7/4)*(b*c - a*d))","A",22,9,24,0.3750,1,"{466, 479, 584, 297, 1162, 617, 204, 1165, 628}"
462,1,476,0,0.4890763,"\int \frac{x^{7/2}}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^(7/2)/((a + b*x^2)*(c + d*x^2)),x]","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{5/4} (b c-a d)}+\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}+\frac{c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{5/4} (b c-a d)}+\frac{2 \sqrt{x}}{b d}","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{5/4} (b c-a d)}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{5/4} (b c-a d)}+\frac{c^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{5/4} (b c-a d)}+\frac{c^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{5/4} (b c-a d)}-\frac{c^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{5/4} (b c-a d)}+\frac{2 \sqrt{x}}{b d}",1,"(2*Sqrt[x])/(b*d) - (a^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(5/4)*(b*c - a*d)) + (a^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(5/4)*(b*c - a*d)) + (c^(5/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(5/4)*(b*c - a*d)) - (c^(5/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(5/4)*(b*c - a*d)) - (a^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(5/4)*(b*c - a*d)) + (a^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(5/4)*(b*c - a*d)) + (c^(5/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(5/4)*(b*c - a*d)) - (c^(5/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(5/4)*(b*c - a*d))","A",21,9,24,0.3750,1,"{466, 479, 522, 211, 1165, 628, 1162, 617, 204}"
463,1,463,0,0.3588549,"\int \frac{x^{5/2}}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^(5/2)/((a + b*x^2)*(c + d*x^2)),x]","-\frac{a^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{3/4} (b c-a d)}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{3/4} (b c-a d)}+\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{3/4} (b c-a d)}+\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{3/4} (b c-a d)}","-\frac{a^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)}+\frac{a^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{3/4} (b c-a d)}-\frac{a^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{3/4} (b c-a d)}+\frac{c^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} d^{3/4} (b c-a d)}-\frac{c^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} d^{3/4} (b c-a d)}+\frac{c^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} d^{3/4} (b c-a d)}",1,"(a^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(3/4)*(b*c - a*d)) - (a^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(3/4)*(b*c - a*d)) - (c^(3/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(3/4)*(b*c - a*d)) + (c^(3/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(3/4)*(b*c - a*d)) - (a^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(3/4)*(b*c - a*d)) + (a^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(3/4)*(b*c - a*d)) + (c^(3/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(3/4)*(b*c - a*d)) - (c^(3/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(3/4)*(b*c - a*d))","A",20,8,24,0.3333,1,"{466, 481, 297, 1162, 617, 204, 1165, 628}"
464,1,463,0,0.362682,"\int \frac{x^{3/2}}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[x^(3/2)/((a + b*x^2)*(c + d*x^2)),x]","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} \sqrt[4]{d} (b c-a d)}","\frac{\sqrt[4]{a} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{a} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{a} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)}-\frac{\sqrt[4]{c} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} \sqrt[4]{d} (b c-a d)}+\frac{\sqrt[4]{c} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} \sqrt[4]{d} (b c-a d)}",1,"(a^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(1/4)*(b*c - a*d)) - (a^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(1/4)*(b*c - a*d)) - (c^(1/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(1/4)*(b*c - a*d)) + (c^(1/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*d^(1/4)*(b*c - a*d)) + (a^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(1/4)*(b*c - a*d)) - (a^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(1/4)*(b*c - a*d)) - (c^(1/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(1/4)*(b*c - a*d)) + (c^(1/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*d^(1/4)*(b*c - a*d))","A",20,8,24,0.3333,1,"{466, 481, 211, 1165, 628, 1162, 617, 204}"
465,1,463,0,0.3575688,"\int \frac{\sqrt{x}}{\left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[Sqrt[x]/((a + b*x^2)*(c + d*x^2)),x]","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}+\frac{\sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} \sqrt[4]{c} (b c-a d)}","\frac{\sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)}-\frac{\sqrt[4]{d} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}+\frac{\sqrt[4]{d} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)}+\frac{\sqrt[4]{d} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} \sqrt[4]{c} (b c-a d)}-\frac{\sqrt[4]{d} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} \sqrt[4]{c} (b c-a d)}",1,"-((b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*(b*c - a*d))) + (b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*(b*c - a*d)) + (d^(1/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(1/4)*(b*c - a*d)) - (d^(1/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(1/4)*(b*c - a*d)) + (b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)) - (b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)) - (d^(1/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(1/4)*(b*c - a*d)) + (d^(1/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(1/4)*(b*c - a*d))","A",20,8,24,0.3333,1,"{466, 482, 297, 1162, 617, 204, 1165, 628}"
466,1,463,0,0.347413,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)*(c + d*x^2)),x]","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}-\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} (b c-a d)}+\frac{d^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}+\frac{d^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{3/4} (b c-a d)}","-\frac{b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)}-\frac{b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} (b c-a d)}+\frac{b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} (b c-a d)}+\frac{d^{3/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{3/4} (b c-a d)}+\frac{d^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{3/4} (b c-a d)}-\frac{d^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{3/4} (b c-a d)}",1,"-((b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*(b*c - a*d))) + (b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*(b*c - a*d)) + (d^(3/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(3/4)*(b*c - a*d)) - (d^(3/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(3/4)*(b*c - a*d)) - (b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)) + (d^(3/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d)) - (d^(3/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(3/4)*(b*c - a*d))","A",20,8,24,0.3333,1,"{466, 391, 211, 1165, 628, 1162, 617, 204}"
467,1,476,0,0.5353492,"\int \frac{1}{x^{3/2} \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^(3/2)*(a + b*x^2)*(c + d*x^2)),x]","-\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} (b c-a d)}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} (b c-a d)}+\frac{d^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{5/4} (b c-a d)}+\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{5/4} (b c-a d)}-\frac{2}{a c \sqrt{x}}","-\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)}+\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} (b c-a d)}-\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} (b c-a d)}+\frac{d^{5/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{5/4} (b c-a d)}-\frac{d^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{5/4} (b c-a d)}+\frac{d^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{5/4} (b c-a d)}-\frac{2}{a c \sqrt{x}}",1,"-2/(a*c*Sqrt[x]) + (b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*(b*c - a*d)) - (b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*(b*c - a*d)) - (d^(5/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(5/4)*(b*c - a*d)) + (d^(5/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(5/4)*(b*c - a*d)) - (b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)) + (b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)) + (d^(5/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(5/4)*(b*c - a*d)) - (d^(5/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(5/4)*(b*c - a*d))","A",22,9,24,0.3750,1,"{466, 480, 584, 297, 1162, 617, 204, 1165, 628}"
468,1,478,0,0.4813072,"\int \frac{1}{x^{5/2} \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^(5/2)*(a + b*x^2)*(c + d*x^2)),x]","\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}+\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} (b c-a d)}-\frac{d^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}-\frac{d^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{7/4} (b c-a d)}-\frac{2}{3 a c x^{3/2}}","\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)}+\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} (b c-a d)}-\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} (b c-a d)}-\frac{d^{7/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{7/4} (b c-a d)}-\frac{d^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{7/4} (b c-a d)}+\frac{d^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{7/4} (b c-a d)}-\frac{2}{3 a c x^{3/2}}",1,"-2/(3*a*c*x^(3/2)) + (b^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*(b*c - a*d)) - (b^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*(b*c - a*d)) - (d^(7/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(7/4)*(b*c - a*d)) + (d^(7/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(7/4)*(b*c - a*d)) + (b^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)) - (b^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)) - (d^(7/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(7/4)*(b*c - a*d)) + (d^(7/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(7/4)*(b*c - a*d))","A",21,9,24,0.3750,1,"{466, 480, 522, 211, 1165, 628, 1162, 617, 204}"
469,1,498,0,0.687037,"\int \frac{1}{x^{7/2} \left(a+b x^2\right) \left(c+d x^2\right)} \, dx","Int[1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)),x]","\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} (b c-a d)}+\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} (b c-a d)}+\frac{2 (a d+b c)}{a^2 c^2 \sqrt{x}}-\frac{d^{9/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{9/4} (b c-a d)}-\frac{d^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{9/4} (b c-a d)}-\frac{2}{5 a c x^{5/2}}","\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)}-\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} (b c-a d)}+\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} (b c-a d)}+\frac{2 (a d+b c)}{a^2 c^2 \sqrt{x}}-\frac{d^{9/4} \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{2 \sqrt{2} c^{9/4} (b c-a d)}+\frac{d^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{\sqrt{2} c^{9/4} (b c-a d)}-\frac{d^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{\sqrt{2} c^{9/4} (b c-a d)}-\frac{2}{5 a c x^{5/2}}",1,"-2/(5*a*c*x^(5/2)) + (2*(b*c + a*d))/(a^2*c^2*Sqrt[x]) - (b^(9/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)) + (b^(9/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)) + (d^(9/4)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(9/4)*(b*c - a*d)) - (d^(9/4)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(Sqrt[2]*c^(9/4)*(b*c - a*d)) + (b^(9/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)) - (b^(9/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)) - (d^(9/4)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(9/4)*(b*c - a*d)) + (d^(9/4)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(2*Sqrt[2]*c^(9/4)*(b*c - a*d))","A",23,10,24,0.4167,1,"{466, 480, 583, 584, 297, 1162, 617, 204, 1165, 628}"
470,1,570,0,0.8459095,"\int \frac{x^{11/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^(11/2)/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{a^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)^2}-\frac{a^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)^2}+\frac{a^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{5/4} (b c-a d)^2}-\frac{a^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{5/4} (b c-a d)^2}+\frac{c^{5/4} (5 b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{9/4} (b c-a d)^2}-\frac{c^{5/4} (5 b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{9/4} (b c-a d)^2}+\frac{c^{5/4} (5 b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{9/4} (b c-a d)^2}-\frac{c^{5/4} (5 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{9/4} (b c-a d)^2}+\frac{\sqrt{x} (5 b c-4 a d)}{2 b d^2 (b c-a d)}-\frac{c x^{5/2}}{2 d \left(c+d x^2\right) (b c-a d)}","\frac{a^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)^2}-\frac{a^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{5/4} (b c-a d)^2}+\frac{a^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{5/4} (b c-a d)^2}-\frac{a^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{5/4} (b c-a d)^2}+\frac{c^{5/4} (5 b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{9/4} (b c-a d)^2}-\frac{c^{5/4} (5 b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{9/4} (b c-a d)^2}+\frac{c^{5/4} (5 b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{9/4} (b c-a d)^2}-\frac{c^{5/4} (5 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{9/4} (b c-a d)^2}+\frac{\sqrt{x} (5 b c-4 a d)}{2 b d^2 (b c-a d)}-\frac{c x^{5/2}}{2 d \left(c+d x^2\right) (b c-a d)}",1,"((5*b*c - 4*a*d)*Sqrt[x])/(2*b*d^2*(b*c - a*d)) - (c*x^(5/2))/(2*d*(b*c - a*d)*(c + d*x^2)) + (a^(9/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(5/4)*(b*c - a*d)^2) - (a^(9/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(5/4)*(b*c - a*d)^2) + (c^(5/4)*(5*b*c - 9*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(9/4)*(b*c - a*d)^2) - (c^(5/4)*(5*b*c - 9*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(9/4)*(b*c - a*d)^2) + (a^(9/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(5/4)*(b*c - a*d)^2) - (a^(9/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(5/4)*(b*c - a*d)^2) + (c^(5/4)*(5*b*c - 9*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(9/4)*(b*c - a*d)^2) - (c^(5/4)*(5*b*c - 9*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(9/4)*(b*c - a*d)^2)","A",22,10,24,0.4167,1,"{466, 470, 582, 522, 211, 1165, 628, 1162, 617, 204}"
471,1,536,0,0.5922079,"\int \frac{x^{9/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^(9/2)/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{a^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)^2}-\frac{a^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)^2}-\frac{a^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{3/4} (b c-a d)^2}+\frac{a^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{3/4} (b c-a d)^2}+\frac{c^{3/4} (3 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{7/4} (b c-a d)^2}-\frac{c^{3/4} (3 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{7/4} (b c-a d)^2}-\frac{c^{3/4} (3 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{7/4} (b c-a d)^2}+\frac{c^{3/4} (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{7/4} (b c-a d)^2}-\frac{c x^{3/2}}{2 d \left(c+d x^2\right) (b c-a d)}","\frac{a^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)^2}-\frac{a^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} b^{3/4} (b c-a d)^2}-\frac{a^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} b^{3/4} (b c-a d)^2}+\frac{a^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} b^{3/4} (b c-a d)^2}+\frac{c^{3/4} (3 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{7/4} (b c-a d)^2}-\frac{c^{3/4} (3 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{7/4} (b c-a d)^2}-\frac{c^{3/4} (3 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{7/4} (b c-a d)^2}+\frac{c^{3/4} (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{7/4} (b c-a d)^2}-\frac{c x^{3/2}}{2 d \left(c+d x^2\right) (b c-a d)}",1,"-(c*x^(3/2))/(2*d*(b*c - a*d)*(c + d*x^2)) - (a^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(3/4)*(b*c - a*d)^2) + (a^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(3/4)*(b*c - a*d)^2) - (c^(3/4)*(3*b*c - 7*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(7/4)*(b*c - a*d)^2) + (c^(3/4)*(3*b*c - 7*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(7/4)*(b*c - a*d)^2) + (a^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(3/4)*(b*c - a*d)^2) - (a^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(3/4)*(b*c - a*d)^2) + (c^(3/4)*(3*b*c - 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(7/4)*(b*c - a*d)^2) - (c^(3/4)*(3*b*c - 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(7/4)*(b*c - a*d)^2)","A",22,9,24,0.3750,1,"{466, 470, 584, 297, 1162, 617, 204, 1165, 628}"
472,1,532,0,0.5290848,"\int \frac{x^{7/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^(7/2)/((a + b*x^2)*(c + d*x^2)^2),x]","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)^2}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)^2}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)^2}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)^2}-\frac{\sqrt[4]{c} (b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{c} (b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{5/4} (b c-a d)^2}-\frac{\sqrt[4]{c} (b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{c} (b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{5/4} (b c-a d)^2}-\frac{c \sqrt{x}}{2 d \left(c+d x^2\right) (b c-a d)}","-\frac{a^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)^2}+\frac{a^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{b} (b c-a d)^2}-\frac{a^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)^2}+\frac{a^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{b} (b c-a d)^2}-\frac{\sqrt[4]{c} (b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{c} (b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} d^{5/4} (b c-a d)^2}-\frac{\sqrt[4]{c} (b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} d^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{c} (b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} d^{5/4} (b c-a d)^2}-\frac{c \sqrt{x}}{2 d \left(c+d x^2\right) (b c-a d)}",1,"-(c*Sqrt[x])/(2*d*(b*c - a*d)*(c + d*x^2)) - (a^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(1/4)*(b*c - a*d)^2) + (a^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*b^(1/4)*(b*c - a*d)^2) - (c^(1/4)*(b*c - 5*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(5/4)*(b*c - a*d)^2) + (c^(1/4)*(b*c - 5*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(5/4)*(b*c - a*d)^2) - (a^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(1/4)*(b*c - a*d)^2) + (a^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*b^(1/4)*(b*c - a*d)^2) - (c^(1/4)*(b*c - 5*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(5/4)*(b*c - a*d)^2) + (c^(1/4)*(b*c - 5*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(5/4)*(b*c - a*d)^2)","A",21,9,24,0.3750,1,"{466, 470, 522, 211, 1165, 628, 1162, 617, 204}"
473,1,528,0,0.5911024,"\int \frac{x^{5/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^(5/2)/((a + b*x^2)*(c + d*x^2)^2),x]","-\frac{a^{3/4} \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}+\frac{a^{3/4} \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}+\frac{a^{3/4} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^2}-\frac{a^{3/4} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^2}+\frac{(3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}-\frac{(3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}-\frac{(3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}+\frac{(3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}+\frac{x^{3/2}}{2 \left(c+d x^2\right) (b c-a d)}","-\frac{a^{3/4} \sqrt[4]{b} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}+\frac{a^{3/4} \sqrt[4]{b} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}+\frac{a^{3/4} \sqrt[4]{b} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^2}-\frac{a^{3/4} \sqrt[4]{b} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^2}+\frac{(3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}-\frac{(3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}-\frac{(3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}+\frac{(3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{c} d^{3/4} (b c-a d)^2}+\frac{x^{3/2}}{2 \left(c+d x^2\right) (b c-a d)}",1,"x^(3/2)/(2*(b*c - a*d)*(c + d*x^2)) + (a^(3/4)*b^(1/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^2) - (a^(3/4)*b^(1/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^2) - ((b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(1/4)*d^(3/4)*(b*c - a*d)^2) + ((b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(1/4)*d^(3/4)*(b*c - a*d)^2) - (a^(3/4)*b^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^2) + (a^(3/4)*b^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^2) + ((b*c + 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(1/4)*d^(3/4)*(b*c - a*d)^2) - ((b*c + 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(1/4)*d^(3/4)*(b*c - a*d)^2)","A",22,9,24,0.3750,1,"{466, 471, 584, 297, 1162, 617, 204, 1165, 628}"
474,1,528,0,0.4753226,"\int \frac{x^{3/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[x^(3/2)/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{\sqrt[4]{a} b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}-\frac{\sqrt[4]{a} b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}+\frac{\sqrt[4]{a} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^2}-\frac{\sqrt[4]{a} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^2}-\frac{(a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}+\frac{(a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}-\frac{(a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}+\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}+\frac{\sqrt{x}}{2 \left(c+d x^2\right) (b c-a d)}","\frac{\sqrt[4]{a} b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}-\frac{\sqrt[4]{a} b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^2}+\frac{\sqrt[4]{a} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^2}-\frac{\sqrt[4]{a} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^2}-\frac{(a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}+\frac{(a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}-\frac{(a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}+\frac{(a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^2}+\frac{\sqrt{x}}{2 \left(c+d x^2\right) (b c-a d)}",1,"Sqrt[x]/(2*(b*c - a*d)*(c + d*x^2)) + (a^(1/4)*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^2) - (a^(1/4)*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^2) - ((3*b*c + a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^2) + ((3*b*c + a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^2) + (a^(1/4)*b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^2) - (a^(1/4)*b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^2) - ((3*b*c + a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^2) + ((3*b*c + a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^2)","A",21,9,24,0.3750,1,"{466, 471, 522, 211, 1165, 628, 1162, 617, 204}"
475,1,536,0,0.5978175,"\int \frac{\sqrt{x}}{\left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[Sqrt[x]/((a + b*x^2)*(c + d*x^2)^2),x]","\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^2}-\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^2}-\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^2}+\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^2}-\frac{\sqrt[4]{d} (5 b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{d} (5 b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{d} (5 b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^2}-\frac{\sqrt[4]{d} (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^2}-\frac{d x^{3/2}}{2 c \left(c+d x^2\right) (b c-a d)}","\frac{b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^2}-\frac{b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^2}-\frac{b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^2}+\frac{b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^2}-\frac{\sqrt[4]{d} (5 b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{d} (5 b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^2}+\frac{\sqrt[4]{d} (5 b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^2}-\frac{\sqrt[4]{d} (5 b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^2}-\frac{d x^{3/2}}{2 c \left(c+d x^2\right) (b c-a d)}",1,"-(d*x^(3/2))/(2*c*(b*c - a*d)*(c + d*x^2)) - (b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*(b*c - a*d)^2) + (b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*(b*c - a*d)^2) + (d^(1/4)*(5*b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(5/4)*(b*c - a*d)^2) - (d^(1/4)*(5*b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(5/4)*(b*c - a*d)^2) + (b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)^2) - (b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)^2) - (d^(1/4)*(5*b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(5/4)*(b*c - a*d)^2) + (d^(1/4)*(5*b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(5/4)*(b*c - a*d)^2)","A",22,9,24,0.3750,1,"{466, 472, 584, 297, 1162, 617, 204, 1165, 628}"
476,1,536,0,0.532762,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)*(c + d*x^2)^2),x]","-\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}-\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d \sqrt{x}}{2 c \left(c+d x^2\right) (b c-a d)}","-\frac{b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^2}-\frac{b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} (b c-a d)^2}+\frac{b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^2}+\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d^{3/4} (7 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^2}-\frac{d \sqrt{x}}{2 c \left(c+d x^2\right) (b c-a d)}",1,"-(d*Sqrt[x])/(2*c*(b*c - a*d)*(c + d*x^2)) - (b^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (b^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (d^(3/4)*(7*b*c - 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(7/4)*(b*c - a*d)^2) - (d^(3/4)*(7*b*c - 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(7/4)*(b*c - a*d)^2) - (b^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (b^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)^2) + (d^(3/4)*(7*b*c - 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^2) - (d^(3/4)*(7*b*c - 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^2)","A",21,9,24,0.3750,1,"{466, 414, 522, 211, 1165, 628, 1162, 617, 204}"
477,1,570,0,0.7500908,"\int \frac{1}{x^{3/2} \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x^(3/2)*(a + b*x^2)*(c + d*x^2)^2),x]","-\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^2}+\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^2}+\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} (b c-a d)^2}-\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} (b c-a d)^2}+\frac{d^{5/4} (9 b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^2}-\frac{d^{5/4} (9 b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^2}-\frac{d^{5/4} (9 b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^2}+\frac{d^{5/4} (9 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^2}-\frac{4 b c-5 a d}{2 a c^2 \sqrt{x} (b c-a d)}-\frac{d}{2 c \sqrt{x} \left(c+d x^2\right) (b c-a d)}","-\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^2}+\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^2}+\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} (b c-a d)^2}-\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} (b c-a d)^2}+\frac{d^{5/4} (9 b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^2}-\frac{d^{5/4} (9 b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^2}-\frac{d^{5/4} (9 b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^2}+\frac{d^{5/4} (9 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^2}-\frac{4 b c-5 a d}{2 a c^2 \sqrt{x} (b c-a d)}-\frac{d}{2 c \sqrt{x} \left(c+d x^2\right) (b c-a d)}",1,"-(4*b*c - 5*a*d)/(2*a*c^2*(b*c - a*d)*Sqrt[x]) - d/(2*c*(b*c - a*d)*Sqrt[x]*(c + d*x^2)) + (b^(9/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*(b*c - a*d)^2) - (b^(9/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*(b*c - a*d)^2) - (d^(5/4)*(9*b*c - 5*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(9/4)*(b*c - a*d)^2) + (d^(5/4)*(9*b*c - 5*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(9/4)*(b*c - a*d)^2) - (b^(9/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)^2) + (b^(9/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)^2) + (d^(5/4)*(9*b*c - 5*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(9/4)*(b*c - a*d)^2) - (d^(5/4)*(9*b*c - 5*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(9/4)*(b*c - a*d)^2)","A",23,10,24,0.4167,1,"{466, 472, 583, 584, 297, 1162, 617, 204, 1165, 628}"
478,1,570,0,0.8232192,"\int \frac{1}{x^{5/2} \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x^(5/2)*(a + b*x^2)*(c + d*x^2)^2),x]","\frac{b^{11/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^2}-\frac{b^{11/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^2}+\frac{b^{11/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} (b c-a d)^2}-\frac{b^{11/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} (b c-a d)^2}-\frac{d^{7/4} (11 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^2}+\frac{d^{7/4} (11 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^2}-\frac{d^{7/4} (11 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^2}+\frac{d^{7/4} (11 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^2}-\frac{4 b c-7 a d}{6 a c^2 x^{3/2} (b c-a d)}-\frac{d}{2 c x^{3/2} \left(c+d x^2\right) (b c-a d)}","\frac{b^{11/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^2}-\frac{b^{11/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^2}+\frac{b^{11/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} (b c-a d)^2}-\frac{b^{11/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} (b c-a d)^2}-\frac{d^{7/4} (11 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^2}+\frac{d^{7/4} (11 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^2}-\frac{d^{7/4} (11 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^2}+\frac{d^{7/4} (11 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^2}-\frac{4 b c-7 a d}{6 a c^2 x^{3/2} (b c-a d)}-\frac{d}{2 c x^{3/2} \left(c+d x^2\right) (b c-a d)}",1,"-(4*b*c - 7*a*d)/(6*a*c^2*(b*c - a*d)*x^(3/2)) - d/(2*c*(b*c - a*d)*x^(3/2)*(c + d*x^2)) + (b^(11/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*(b*c - a*d)^2) - (b^(11/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*(b*c - a*d)^2) - (d^(7/4)*(11*b*c - 7*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*(b*c - a*d)^2) + (d^(7/4)*(11*b*c - 7*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*(b*c - a*d)^2) + (b^(11/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)^2) - (b^(11/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)^2) - (d^(7/4)*(11*b*c - 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*(b*c - a*d)^2) + (d^(7/4)*(11*b*c - 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*(b*c - a*d)^2)","A",22,10,24,0.4167,1,"{466, 472, 583, 522, 211, 1165, 628, 1162, 617, 204}"
479,1,618,0,0.9620105,"\int \frac{1}{x^{7/2} \left(a+b x^2\right) \left(c+d x^2\right)^2} \, dx","Int[1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^2),x]","\frac{-9 a^2 d^2+4 a b c d+4 b^2 c^2}{2 a^2 c^3 \sqrt{x} (b c-a d)}+\frac{b^{13/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^2}-\frac{b^{13/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^2}-\frac{b^{13/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} (b c-a d)^2}+\frac{b^{13/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} (b c-a d)^2}-\frac{d^{9/4} (13 b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^2}+\frac{d^{9/4} (13 b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^2}+\frac{d^{9/4} (13 b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^2}-\frac{d^{9/4} (13 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^2}-\frac{4 b c-9 a d}{10 a c^2 x^{5/2} (b c-a d)}-\frac{d}{2 c x^{5/2} \left(c+d x^2\right) (b c-a d)}","\frac{-9 a^2 d^2+4 a b c d+4 b^2 c^2}{2 a^2 c^3 \sqrt{x} (b c-a d)}+\frac{b^{13/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^2}-\frac{b^{13/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^2}-\frac{b^{13/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} (b c-a d)^2}+\frac{b^{13/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} (b c-a d)^2}-\frac{d^{9/4} (13 b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^2}+\frac{d^{9/4} (13 b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^2}+\frac{d^{9/4} (13 b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^2}-\frac{d^{9/4} (13 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^2}-\frac{4 b c-9 a d}{10 a c^2 x^{5/2} (b c-a d)}-\frac{d}{2 c x^{5/2} \left(c+d x^2\right) (b c-a d)}",1,"-(4*b*c - 9*a*d)/(10*a*c^2*(b*c - a*d)*x^(5/2)) + (4*b^2*c^2 + 4*a*b*c*d - 9*a^2*d^2)/(2*a^2*c^3*(b*c - a*d)*Sqrt[x]) - d/(2*c*(b*c - a*d)*x^(5/2)*(c + d*x^2)) - (b^(13/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^2) + (b^(13/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^2) + (d^(9/4)*(13*b*c - 9*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*(b*c - a*d)^2) - (d^(9/4)*(13*b*c - 9*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*(b*c - a*d)^2) + (b^(13/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^2) - (b^(13/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^2) - (d^(9/4)*(13*b*c - 9*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(b*c - a*d)^2) + (d^(9/4)*(13*b*c - 9*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(b*c - a*d)^2)","A",24,10,24,0.4167,1,"{466, 472, 583, 584, 297, 1162, 617, 204, 1165, 628}"
480,1,631,0,0.8140702,"\int \frac{x^{7/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x^(7/2)/((a + b*x^2)*(c + d*x^2)^3),x]","-\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}+\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}-\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}+\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}-\frac{a^{5/4} b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{a^{5/4} b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}-\frac{a^{5/4} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^3}+\frac{a^{5/4} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^3}+\frac{\sqrt{x} (b c-9 a d)}{16 d \left(c+d x^2\right) (b c-a d)^2}-\frac{c \sqrt{x}}{4 d \left(c+d x^2\right)^2 (b c-a d)}","-\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}+\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}-\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}+\frac{\left(-5 a^2 d^2-30 a b c d+3 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{3/4} d^{5/4} (b c-a d)^3}-\frac{a^{5/4} b^{3/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{a^{5/4} b^{3/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}-\frac{a^{5/4} b^{3/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^3}+\frac{a^{5/4} b^{3/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^3}+\frac{\sqrt{x} (b c-9 a d)}{16 d \left(c+d x^2\right) (b c-a d)^2}-\frac{c \sqrt{x}}{4 d \left(c+d x^2\right)^2 (b c-a d)}",1,"-(c*Sqrt[x])/(4*d*(b*c - a*d)*(c + d*x^2)^2) + ((b*c - 9*a*d)*Sqrt[x])/(16*d*(b*c - a*d)^2*(c + d*x^2)) - (a^(5/4)*b^(3/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^3) + (a^(5/4)*b^(3/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^3) - ((3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(3/4)*d^(5/4)*(b*c - a*d)^3) + ((3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(3/4)*d^(5/4)*(b*c - a*d)^3) - (a^(5/4)*b^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^3) + (a^(5/4)*b^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^3) - ((3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(3/4)*d^(5/4)*(b*c - a*d)^3) + ((3*b^2*c^2 - 30*a*b*c*d - 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(3/4)*d^(5/4)*(b*c - a*d)^3)","A",22,10,24,0.4167,1,"{466, 470, 527, 522, 211, 1165, 628, 1162, 617, 204}"
481,1,628,0,0.7612701,"\int \frac{x^{5/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x^(5/2)/((a + b*x^2)*(c + d*x^2)^3),x]","\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}-\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}-\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}+\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}-\frac{a^{3/4} b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{a^{3/4} b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{a^{3/4} b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^3}-\frac{a^{3/4} b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^3}+\frac{x^{3/2} (3 a d+5 b c)}{16 c \left(c+d x^2\right) (b c-a d)^2}+\frac{x^{3/2}}{4 \left(c+d x^2\right)^2 (b c-a d)}","\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}-\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}-\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}+\frac{\left(-3 a^2 d^2+30 a b c d+5 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{5/4} d^{3/4} (b c-a d)^3}-\frac{a^{3/4} b^{5/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{a^{3/4} b^{5/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{a^{3/4} b^{5/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^3}-\frac{a^{3/4} b^{5/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^3}+\frac{x^{3/2} (3 a d+5 b c)}{16 c \left(c+d x^2\right) (b c-a d)^2}+\frac{x^{3/2}}{4 \left(c+d x^2\right)^2 (b c-a d)}",1,"x^(3/2)/(4*(b*c - a*d)*(c + d*x^2)^2) + ((5*b*c + 3*a*d)*x^(3/2))/(16*c*(b*c - a*d)^2*(c + d*x^2)) + (a^(3/4)*b^(5/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^3) - (a^(3/4)*b^(5/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^3) - ((5*b^2*c^2 + 30*a*b*c*d - 3*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(5/4)*d^(3/4)*(b*c - a*d)^3) + ((5*b^2*c^2 + 30*a*b*c*d - 3*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(5/4)*d^(3/4)*(b*c - a*d)^3) - (a^(3/4)*b^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^3) + (a^(3/4)*b^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^3) + ((5*b^2*c^2 + 30*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(5/4)*d^(3/4)*(b*c - a*d)^3) - ((5*b^2*c^2 + 30*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(5/4)*d^(3/4)*(b*c - a*d)^3)","A",23,10,24,0.4167,1,"{466, 471, 579, 584, 297, 1162, 617, 204, 1165, 628}"
482,1,627,0,0.7101889,"\int \frac{x^{3/2}}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[x^(3/2)/((a + b*x^2)*(c + d*x^2)^3),x]","-\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}+\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}-\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}+\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{a} b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}-\frac{\sqrt[4]{a} b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{\sqrt[4]{a} b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^3}-\frac{\sqrt[4]{a} b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^3}+\frac{\sqrt{x} (a d+7 b c)}{16 c \left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt{x}}{4 \left(c+d x^2\right)^2 (b c-a d)}","-\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}+\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}-\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}+\frac{\left(-3 a^2 d^2+14 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{7/4} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{a} b^{7/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}-\frac{\sqrt[4]{a} b^{7/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} (b c-a d)^3}+\frac{\sqrt[4]{a} b^{7/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} (b c-a d)^3}-\frac{\sqrt[4]{a} b^{7/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} (b c-a d)^3}+\frac{\sqrt{x} (a d+7 b c)}{16 c \left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt{x}}{4 \left(c+d x^2\right)^2 (b c-a d)}",1,"Sqrt[x]/(4*(b*c - a*d)*(c + d*x^2)^2) + ((7*b*c + a*d)*Sqrt[x])/(16*c*(b*c - a*d)^2*(c + d*x^2)) + (a^(1/4)*b^(7/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^3) - (a^(1/4)*b^(7/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*(b*c - a*d)^3) - ((21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*d^(1/4)*(b*c - a*d)^3) + ((21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*d^(1/4)*(b*c - a*d)^3) + (a^(1/4)*b^(7/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^3) - (a^(1/4)*b^(7/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*(b*c - a*d)^3) - ((21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*d^(1/4)*(b*c - a*d)^3) + ((21*b^2*c^2 + 14*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*d^(1/4)*(b*c - a*d)^3)","A",22,10,24,0.4167,1,"{466, 471, 527, 522, 211, 1165, 628, 1162, 617, 204}"
483,1,633,0,0.8172309,"\int \frac{\sqrt{x}}{\left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[Sqrt[x]/((a + b*x^2)*(c + d*x^2)^3),x]","-\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^3}-\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^3}+\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{d x^{3/2} (13 b c-5 a d)}{16 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d x^{3/2}}{4 c \left(c+d x^2\right)^2 (b c-a d)}","-\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^3}-\frac{\sqrt[4]{d} \left(5 a^2 d^2-18 a b c d+45 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{b^{9/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{b^{9/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{b^{9/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^3}+\frac{b^{9/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{d x^{3/2} (13 b c-5 a d)}{16 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d x^{3/2}}{4 c \left(c+d x^2\right)^2 (b c-a d)}",1,"-(d*x^(3/2))/(4*c*(b*c - a*d)*(c + d*x^2)^2) - (d*(13*b*c - 5*a*d)*x^(3/2))/(16*c^2*(b*c - a*d)^2*(c + d*x^2)) - (b^(9/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*(b*c - a*d)^3) + (b^(9/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*(b*c - a*d)^3) + (d^(1/4)*(45*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)^3) - (d^(1/4)*(45*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)^3) + (b^(9/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)^3) - (b^(9/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(1/4)*(b*c - a*d)^3) - (d^(1/4)*(45*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(b*c - a*d)^3) + (d^(1/4)*(45*b^2*c^2 - 18*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(b*c - a*d)^3)","A",23,10,24,0.4167,1,"{466, 472, 579, 584, 297, 1162, 617, 204, 1165, 628}"
484,1,633,0,0.8318152,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)*(c + d*x^2)^3),x]","\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^3}+\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{b^{11/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{11/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^3}-\frac{b^{11/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{11/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} (b c-a d)^3}-\frac{d \sqrt{x} (15 b c-7 a d)}{16 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d \sqrt{x}}{4 c \left(c+d x^2\right)^2 (b c-a d)}","\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^3}+\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{3/4} \left(21 a^2 d^2-66 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{b^{11/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{11/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{3/4} (b c-a d)^3}-\frac{b^{11/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{11/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} (b c-a d)^3}-\frac{d \sqrt{x} (15 b c-7 a d)}{16 c^2 \left(c+d x^2\right) (b c-a d)^2}-\frac{d \sqrt{x}}{4 c \left(c+d x^2\right)^2 (b c-a d)}",1,"-(d*Sqrt[x])/(4*c*(b*c - a*d)*(c + d*x^2)^2) - (d*(15*b*c - 7*a*d)*Sqrt[x])/(16*c^2*(b*c - a*d)^2*(c + d*x^2)) - (b^(11/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (b^(11/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (d^(3/4)*(77*b^2*c^2 - 66*a*b*c*d + 21*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) - (d^(3/4)*(77*b^2*c^2 - 66*a*b*c*d + 21*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) - (b^(11/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (b^(11/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (d^(3/4)*(77*b^2*c^2 - 66*a*b*c*d + 21*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) - (d^(3/4)*(77*b^2*c^2 - 66*a*b*c*d + 21*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(11/4)*(b*c - a*d)^3)","A",22,10,24,0.4167,1,"{466, 414, 527, 522, 211, 1165, 628, 1162, 617, 204}"
485,1,681,0,1.0064529,"\int \frac{1}{x^{3/2} \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x^(3/2)*(a + b*x^2)*(c + d*x^2)^3),x]","-\frac{45 a^2 d^2-85 a b c d+32 b^2 c^2}{16 a c^3 \sqrt{x} (b c-a d)^2}+\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^3}+\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{b^{13/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{b^{13/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{b^{13/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} (b c-a d)^3}-\frac{b^{13/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} (b c-a d)^3}-\frac{d (17 b c-9 a d)}{16 c^2 \sqrt{x} \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c \sqrt{x} \left(c+d x^2\right)^2 (b c-a d)}","-\frac{45 a^2 d^2-85 a b c d+32 b^2 c^2}{16 a c^3 \sqrt{x} (b c-a d)^2}+\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^3}+\frac{d^{5/4} \left(45 a^2 d^2-130 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{b^{13/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{b^{13/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{b^{13/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} (b c-a d)^3}-\frac{b^{13/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} (b c-a d)^3}-\frac{d (17 b c-9 a d)}{16 c^2 \sqrt{x} \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c \sqrt{x} \left(c+d x^2\right)^2 (b c-a d)}",1,"-(32*b^2*c^2 - 85*a*b*c*d + 45*a^2*d^2)/(16*a*c^3*(b*c - a*d)^2*Sqrt[x]) - d/(4*c*(b*c - a*d)*Sqrt[x]*(c + d*x^2)^2) - (d*(17*b*c - 9*a*d))/(16*c^2*(b*c - a*d)^2*Sqrt[x]*(c + d*x^2)) + (b^(13/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*(b*c - a*d)^3) - (b^(13/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*(b*c - a*d)^3) - (d^(5/4)*(117*b^2*c^2 - 130*a*b*c*d + 45*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) + (d^(5/4)*(117*b^2*c^2 - 130*a*b*c*d + 45*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) - (b^(13/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)^3) + (b^(13/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(5/4)*(b*c - a*d)^3) + (d^(5/4)*(117*b^2*c^2 - 130*a*b*c*d + 45*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) - (d^(5/4)*(117*b^2*c^2 - 130*a*b*c*d + 45*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(13/4)*(b*c - a*d)^3)","A",24,11,24,0.4583,1,"{466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628}"
486,1,681,0,0.927946,"\int \frac{1}{x^{5/2} \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x^(5/2)*(a + b*x^2)*(c + d*x^2)^3),x]","-\frac{77 a^2 d^2-133 a b c d+32 b^2 c^2}{48 a c^3 x^{3/2} (b c-a d)^2}-\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^3}+\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^3}-\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^3}+\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^3}+\frac{b^{15/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{15/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{15/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{15/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} (b c-a d)^3}-\frac{d (19 b c-11 a d)}{16 c^2 x^{3/2} \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x^{3/2} \left(c+d x^2\right)^2 (b c-a d)}","-\frac{77 a^2 d^2-133 a b c d+32 b^2 c^2}{48 a c^3 x^{3/2} (b c-a d)^2}-\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^3}+\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^3}-\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^3}+\frac{d^{7/4} \left(77 a^2 d^2-210 a b c d+165 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^3}+\frac{b^{15/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{15/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{15/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{15/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4} (b c-a d)^3}-\frac{d (19 b c-11 a d)}{16 c^2 x^{3/2} \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x^{3/2} \left(c+d x^2\right)^2 (b c-a d)}",1,"-(32*b^2*c^2 - 133*a*b*c*d + 77*a^2*d^2)/(48*a*c^3*(b*c - a*d)^2*x^(3/2)) - d/(4*c*(b*c - a*d)*x^(3/2)*(c + d*x^2)^2) - (d*(19*b*c - 11*a*d))/(16*c^2*(b*c - a*d)^2*x^(3/2)*(c + d*x^2)) + (b^(15/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (b^(15/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (d^(7/4)*(165*b^2*c^2 - 210*a*b*c*d + 77*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(15/4)*(b*c - a*d)^3) + (d^(7/4)*(165*b^2*c^2 - 210*a*b*c*d + 77*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(15/4)*(b*c - a*d)^3) + (b^(15/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (b^(15/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (d^(7/4)*(165*b^2*c^2 - 210*a*b*c*d + 77*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(15/4)*(b*c - a*d)^3) + (d^(7/4)*(165*b^2*c^2 - 210*a*b*c*d + 77*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(15/4)*(b*c - a*d)^3)","A",23,11,24,0.4583,1,"{466, 472, 579, 583, 522, 211, 1165, 628, 1162, 617, 204}"
487,1,743,0,1.2331052,"\int \frac{1}{x^{7/2} \left(a+b x^2\right) \left(c+d x^2\right)^3} \, dx","Int[1/(x^(7/2)*(a + b*x^2)*(c + d*x^2)^3),x]","-\frac{117 a^2 d^2-189 a b c d+32 b^2 c^2}{80 a c^3 x^{5/2} (b c-a d)^2}+\frac{-189 a^2 b c d^2+117 a^3 d^3+32 a b^2 c^2 d+32 b^3 c^3}{16 a^2 c^4 \sqrt{x} (b c-a d)^2}-\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^3}+\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^3}+\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^3}-\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^3}+\frac{b^{17/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{b^{17/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{b^{17/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} (b c-a d)^3}+\frac{b^{17/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} (b c-a d)^3}-\frac{d (21 b c-13 a d)}{16 c^2 x^{5/2} \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x^{5/2} \left(c+d x^2\right)^2 (b c-a d)}","-\frac{117 a^2 d^2-189 a b c d+32 b^2 c^2}{80 a c^3 x^{5/2} (b c-a d)^2}+\frac{-189 a^2 b c d^2+117 a^3 d^3+32 a b^2 c^2 d+32 b^3 c^3}{16 a^2 c^4 \sqrt{x} (b c-a d)^2}-\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^3}+\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^3}+\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^3}-\frac{d^{9/4} \left(117 a^2 d^2-306 a b c d+221 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^3}+\frac{b^{17/4} \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{b^{17/4} \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{2 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{b^{17/4} \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4} (b c-a d)^3}+\frac{b^{17/4} \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4} (b c-a d)^3}-\frac{d (21 b c-13 a d)}{16 c^2 x^{5/2} \left(c+d x^2\right) (b c-a d)^2}-\frac{d}{4 c x^{5/2} \left(c+d x^2\right)^2 (b c-a d)}",1,"-(32*b^2*c^2 - 189*a*b*c*d + 117*a^2*d^2)/(80*a*c^3*(b*c - a*d)^2*x^(5/2)) + (32*b^3*c^3 + 32*a*b^2*c^2*d - 189*a^2*b*c*d^2 + 117*a^3*d^3)/(16*a^2*c^4*(b*c - a*d)^2*Sqrt[x]) - d/(4*c*(b*c - a*d)*x^(5/2)*(c + d*x^2)^2) - (d*(21*b*c - 13*a*d))/(16*c^2*(b*c - a*d)^2*x^(5/2)*(c + d*x^2)) - (b^(17/4)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (b^(17/4)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*(b*c - a*d)^3) - (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*(b*c - a*d)^3) + (b^(17/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (b^(17/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(2*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*(b*c - a*d)^3) + (d^(9/4)*(221*b^2*c^2 - 306*a*b*c*d + 117*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*(b*c - a*d)^3)","A",25,11,24,0.4583,1,"{466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628}"
488,1,624,0,0.7571919,"\int \frac{x^{7/2}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^(7/2)/((a + b*x^2)^2*(c + d*x^2)^2),x]","\frac{a \sqrt{x}}{2 b \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{\sqrt{x} (a d+b c)}{2 b \left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt[4]{a} (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{a} (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{c} (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{c} (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{a} (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{a} (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{c} (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{c} (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}","\frac{a \sqrt{x}}{2 b \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{\sqrt{x} (a d+b c)}{2 b \left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt[4]{a} (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{a} (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{c} (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{c} (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{a} (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{a} (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{b} (b c-a d)^3}-\frac{\sqrt[4]{c} (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}+\frac{\sqrt[4]{c} (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{d} (b c-a d)^3}",1,"((b*c + a*d)*Sqrt[x])/(2*b*(b*c - a*d)^2*(c + d*x^2)) + (a*Sqrt[x])/(2*b*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) + (a^(1/4)*(5*b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(1/4)*(b*c - a*d)^3) - (a^(1/4)*(5*b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*b^(1/4)*(b*c - a*d)^3) - (c^(1/4)*(3*b*c + 5*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(1/4)*(b*c - a*d)^3) + (c^(1/4)*(3*b*c + 5*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*d^(1/4)*(b*c - a*d)^3) + (a^(1/4)*(5*b*c + 3*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(1/4)*(b*c - a*d)^3) - (a^(1/4)*(5*b*c + 3*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*b^(1/4)*(b*c - a*d)^3) - (c^(1/4)*(3*b*c + 5*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(1/4)*(b*c - a*d)^3) + (c^(1/4)*(3*b*c + 5*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*d^(1/4)*(b*c - a*d)^3)","A",22,10,24,0.4167,1,"{466, 470, 527, 522, 211, 1165, 628, 1162, 617, 204}"
489,1,609,0,0.7960885,"\int \frac{x^{5/2}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^(5/2)/((a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{x^{3/2}}{2 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}-\frac{d x^{3/2}}{\left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt[4]{b} (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{\sqrt[4]{b} (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{\sqrt[4]{d} (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}+\frac{\sqrt[4]{d} (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}-\frac{\sqrt[4]{b} (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}+\frac{\sqrt[4]{b} (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}+\frac{\sqrt[4]{d} (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}-\frac{\sqrt[4]{d} (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}","-\frac{x^{3/2}}{2 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}-\frac{d x^{3/2}}{\left(c+d x^2\right) (b c-a d)^2}+\frac{\sqrt[4]{b} (5 a d+3 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{\sqrt[4]{b} (5 a d+3 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}-\frac{\sqrt[4]{d} (3 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}+\frac{\sqrt[4]{d} (3 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}-\frac{\sqrt[4]{b} (5 a d+3 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}+\frac{\sqrt[4]{b} (5 a d+3 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^3}+\frac{\sqrt[4]{d} (3 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}-\frac{\sqrt[4]{d} (3 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} \sqrt[4]{c} (b c-a d)^3}",1,"-((d*x^(3/2))/((b*c - a*d)^2*(c + d*x^2))) - x^(3/2)/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) - (b^(1/4)*(3*b*c + 5*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*(b*c - a*d)^3) + (b^(1/4)*(3*b*c + 5*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*(b*c - a*d)^3) + (d^(1/4)*(5*b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(1/4)*(b*c - a*d)^3) - (d^(1/4)*(5*b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(1/4)*(b*c - a*d)^3) + (b^(1/4)*(3*b*c + 5*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*(b*c - a*d)^3) - (b^(1/4)*(3*b*c + 5*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*(b*c - a*d)^3) - (d^(1/4)*(5*b*c + 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(1/4)*(b*c - a*d)^3) + (d^(1/4)*(5*b*c + 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(1/4)*(b*c - a*d)^3)","A",23,10,24,0.4167,1,"{466, 471, 579, 584, 297, 1162, 617, 204, 1165, 628}"
490,1,601,0,0.6909092,"\int \frac{x^{3/2}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{b^{3/4} (7 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{3/4} (7 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^3}-\frac{b^{3/4} (7 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{3/4} (7 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{d^{3/4} (a d+7 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} (b c-a d)^3}-\frac{d^{3/4} (a d+7 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} (b c-a d)^3}+\frac{d^{3/4} (a d+7 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^3}-\frac{d^{3/4} (a d+7 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^3}-\frac{d \sqrt{x}}{\left(c+d x^2\right) (b c-a d)^2}-\frac{\sqrt{x}}{2 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}","-\frac{b^{3/4} (7 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{3/4} (7 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^3}-\frac{b^{3/4} (7 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{b^{3/4} (7 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^3}+\frac{d^{3/4} (a d+7 b c) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} (b c-a d)^3}-\frac{d^{3/4} (a d+7 b c) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{3/4} (b c-a d)^3}+\frac{d^{3/4} (a d+7 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^3}-\frac{d^{3/4} (a d+7 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{3/4} (b c-a d)^3}-\frac{d \sqrt{x}}{\left(c+d x^2\right) (b c-a d)^2}-\frac{\sqrt{x}}{2 \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}",1,"-((d*Sqrt[x])/((b*c - a*d)^2*(c + d*x^2))) - Sqrt[x]/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) - (b^(3/4)*(b*c + 7*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (b^(3/4)*(b*c + 7*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (d^(3/4)*(7*b*c + a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d)^3) - (d^(3/4)*(7*b*c + a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(3/4)*(b*c - a*d)^3) - (b^(3/4)*(b*c + 7*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (b^(3/4)*(b*c + 7*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*(b*c - a*d)^3) + (d^(3/4)*(7*b*c + a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(3/4)*(b*c - a*d)^3) - (d^(3/4)*(7*b*c + a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(3/4)*(b*c - a*d)^3)","A",22,10,24,0.4167,1,"{466, 471, 527, 522, 211, 1165, 628, 1162, 617, 204}"
491,1,624,0,0.8580005,"\int \frac{\sqrt{x}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[Sqrt[x]/((a + b*x^2)^2*(c + d*x^2)^2),x]","\frac{b^{5/4} (b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^3}-\frac{b^{5/4} (b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^3}-\frac{b^{5/4} (b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{b^{5/4} (b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{d^{5/4} (9 b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^3}-\frac{d^{5/4} (9 b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^3}-\frac{d^{5/4} (9 b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^3}+\frac{d^{5/4} (9 b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^3}+\frac{d x^{3/2} (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}+\frac{b x^{3/2}}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}","\frac{b^{5/4} (b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^3}-\frac{b^{5/4} (b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^3}-\frac{b^{5/4} (b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{b^{5/4} (b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^3}+\frac{d^{5/4} (9 b c-a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^3}-\frac{d^{5/4} (9 b c-a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{5/4} (b c-a d)^3}-\frac{d^{5/4} (9 b c-a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^3}+\frac{d^{5/4} (9 b c-a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{5/4} (b c-a d)^3}+\frac{d x^{3/2} (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}+\frac{b x^{3/2}}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}",1,"(d*(b*c + a*d)*x^(3/2))/(2*a*c*(b*c - a*d)^2*(c + d*x^2)) + (b*x^(3/2))/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) - (b^(5/4)*(b*c - 9*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^3) + (b^(5/4)*(b*c - 9*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^3) - (d^(5/4)*(9*b*c - a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(5/4)*(b*c - a*d)^3) + (d^(5/4)*(9*b*c - a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(5/4)*(b*c - a*d)^3) + (b^(5/4)*(b*c - 9*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^3) - (b^(5/4)*(b*c - 9*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^3) + (d^(5/4)*(9*b*c - a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(5/4)*(b*c - a*d)^3) - (d^(5/4)*(9*b*c - a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(5/4)*(b*c - a*d)^3)","A",23,10,24,0.4167,1,"{466, 472, 579, 584, 297, 1162, 617, 204, 1165, 628}"
492,1,628,0,0.861671,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{b^{7/4} (3 b c-11 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{b \sqrt{x}}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d \sqrt{x} (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}","-\frac{b^{7/4} (3 b c-11 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^3}+\frac{b^{7/4} (3 b c-11 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{7/4} (b c-a d)^3}-\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{d^{7/4} (11 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{7/4} (b c-a d)^3}+\frac{b \sqrt{x}}{2 a \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d \sqrt{x} (a d+b c)}{2 a c \left(c+d x^2\right) (b c-a d)^2}",1,"(d*(b*c + a*d)*Sqrt[x])/(2*a*c*(b*c - a*d)^2*(c + d*x^2)) + (b*Sqrt[x])/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)) - (b^(7/4)*(3*b*c - 11*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) + (b^(7/4)*(3*b*c - 11*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (d^(7/4)*(11*b*c - 3*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(7/4)*(b*c - a*d)^3) + (d^(7/4)*(11*b*c - 3*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(7/4)*(b*c - a*d)^3) - (b^(7/4)*(3*b*c - 11*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) + (b^(7/4)*(3*b*c - 11*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^3) - (d^(7/4)*(11*b*c - 3*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^3) + (d^(7/4)*(11*b*c - 3*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(7/4)*(b*c - a*d)^3)","A",22,10,24,0.4167,1,"{466, 414, 527, 522, 211, 1165, 628, 1162, 617, 204}"
493,1,676,0,1.0559358,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{5 a^2 d^2-8 a b c d+5 b^2 c^2}{2 a^2 c^2 \sqrt{x} (b c-a d)^2}-\frac{b^{9/4} (5 b c-13 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} (b c-a d)^3}+\frac{b^{9/4} (5 b c-13 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} (b c-a d)^3}+\frac{b^{9/4} (5 b c-13 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{b^{9/4} (5 b c-13 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{d^{9/4} (13 b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{d^{9/4} (13 b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{d^{9/4} (13 b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^3}-\frac{d^{9/4} (13 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{b}{2 a \sqrt{x} \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c \sqrt{x} \left(c+d x^2\right) (b c-a d)^2}","-\frac{5 a^2 d^2-8 a b c d+5 b^2 c^2}{2 a^2 c^2 \sqrt{x} (b c-a d)^2}-\frac{b^{9/4} (5 b c-13 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} (b c-a d)^3}+\frac{b^{9/4} (5 b c-13 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{9/4} (b c-a d)^3}+\frac{b^{9/4} (5 b c-13 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{b^{9/4} (5 b c-13 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} (b c-a d)^3}-\frac{d^{9/4} (13 b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{d^{9/4} (13 b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{d^{9/4} (13 b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^3}-\frac{d^{9/4} (13 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{9/4} (b c-a d)^3}+\frac{b}{2 a \sqrt{x} \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c \sqrt{x} \left(c+d x^2\right) (b c-a d)^2}",1,"-(5*b^2*c^2 - 8*a*b*c*d + 5*a^2*d^2)/(2*a^2*c^2*(b*c - a*d)^2*Sqrt[x]) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*Sqrt[x]*(c + d*x^2)) + b/(2*a*(b*c - a*d)*Sqrt[x]*(a + b*x^2)*(c + d*x^2)) + (b^(9/4)*(5*b*c - 13*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (b^(9/4)*(5*b*c - 13*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (d^(9/4)*(13*b*c - 5*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(9/4)*(b*c - a*d)^3) - (d^(9/4)*(13*b*c - 5*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(9/4)*(b*c - a*d)^3) - (b^(9/4)*(5*b*c - 13*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) + (b^(9/4)*(5*b*c - 13*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*(b*c - a*d)^3) - (d^(9/4)*(13*b*c - 5*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(9/4)*(b*c - a*d)^3) + (d^(9/4)*(13*b*c - 5*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(9/4)*(b*c - a*d)^3)","A",24,11,24,0.4583,1,"{466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628}"
494,1,676,0,0.9665713,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{7 a^2 d^2-8 a b c d+7 b^2 c^2}{6 a^2 c^2 x^{3/2} (b c-a d)^2}+\frac{b^{11/4} (7 b c-15 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} (b c-a d)^3}-\frac{b^{11/4} (7 b c-15 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} (b c-a d)^3}+\frac{b^{11/4} (7 b c-15 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4} (b c-a d)^3}-\frac{b^{11/4} (7 b c-15 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4} (b c-a d)^3}+\frac{d^{11/4} (15 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{11/4} (15 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^3}+\frac{d^{11/4} (15 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{11/4} (15 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^3}+\frac{b}{2 a x^{3/2} \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x^{3/2} \left(c+d x^2\right) (b c-a d)^2}","-\frac{7 a^2 d^2-8 a b c d+7 b^2 c^2}{6 a^2 c^2 x^{3/2} (b c-a d)^2}+\frac{b^{11/4} (7 b c-15 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} (b c-a d)^3}-\frac{b^{11/4} (7 b c-15 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{11/4} (b c-a d)^3}+\frac{b^{11/4} (7 b c-15 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4} (b c-a d)^3}-\frac{b^{11/4} (7 b c-15 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4} (b c-a d)^3}+\frac{d^{11/4} (15 b c-7 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{11/4} (15 b c-7 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{11/4} (b c-a d)^3}+\frac{d^{11/4} (15 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^3}-\frac{d^{11/4} (15 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{11/4} (b c-a d)^3}+\frac{b}{2 a x^{3/2} \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x^{3/2} \left(c+d x^2\right) (b c-a d)^2}",1,"-(7*b^2*c^2 - 8*a*b*c*d + 7*a^2*d^2)/(6*a^2*c^2*(b*c - a*d)^2*x^(3/2)) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*x^(3/2)*(c + d*x^2)) + b/(2*a*(b*c - a*d)*x^(3/2)*(a + b*x^2)*(c + d*x^2)) + (b^(11/4)*(7*b*c - 15*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) - (b^(11/4)*(7*b*c - 15*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) + (d^(11/4)*(15*b*c - 7*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) - (d^(11/4)*(15*b*c - 7*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) + (b^(11/4)*(7*b*c - 15*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) - (b^(11/4)*(7*b*c - 15*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c - a*d)^3) + (d^(11/4)*(15*b*c - 7*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*(b*c - a*d)^3) - (d^(11/4)*(15*b*c - 7*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(11/4)*(b*c - a*d)^3)","A",23,11,24,0.4583,1,"{466, 472, 579, 583, 522, 211, 1165, 628, 1162, 617, 204}"
495,1,731,0,1.2761459,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^2} \, dx","Int[1/(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^2),x]","-\frac{9 a^2 d^2-8 a b c d+9 b^2 c^2}{10 a^2 c^2 x^{5/2} (b c-a d)^2}+\frac{(a d+b c) \left(9 a^2 d^2-17 a b c d+9 b^2 c^2\right)}{2 a^3 c^3 \sqrt{x} (b c-a d)^2}+\frac{b^{13/4} (9 b c-17 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} (b c-a d)^3}-\frac{b^{13/4} (9 b c-17 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} (b c-a d)^3}-\frac{b^{13/4} (9 b c-17 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4} (b c-a d)^3}+\frac{b^{13/4} (9 b c-17 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4} (b c-a d)^3}+\frac{d^{13/4} (17 b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{13/4} (17 b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{13/4} (17 b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^3}+\frac{d^{13/4} (17 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^3}+\frac{b}{2 a x^{5/2} \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x^{5/2} \left(c+d x^2\right) (b c-a d)^2}","-\frac{9 a^2 d^2-8 a b c d+9 b^2 c^2}{10 a^2 c^2 x^{5/2} (b c-a d)^2}+\frac{(a d+b c) \left(9 a^2 d^2-17 a b c d+9 b^2 c^2\right)}{2 a^3 c^3 \sqrt{x} (b c-a d)^2}+\frac{b^{13/4} (9 b c-17 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} (b c-a d)^3}-\frac{b^{13/4} (9 b c-17 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{13/4} (b c-a d)^3}-\frac{b^{13/4} (9 b c-17 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{13/4} (b c-a d)^3}+\frac{b^{13/4} (9 b c-17 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{13/4} (b c-a d)^3}+\frac{d^{13/4} (17 b c-9 a d) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{13/4} (17 b c-9 a d) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{8 \sqrt{2} c^{13/4} (b c-a d)^3}-\frac{d^{13/4} (17 b c-9 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^3}+\frac{d^{13/4} (17 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{4 \sqrt{2} c^{13/4} (b c-a d)^3}+\frac{b}{2 a x^{5/2} \left(a+b x^2\right) \left(c+d x^2\right) (b c-a d)}+\frac{d (a d+b c)}{2 a c x^{5/2} \left(c+d x^2\right) (b c-a d)^2}",1,"-(9*b^2*c^2 - 8*a*b*c*d + 9*a^2*d^2)/(10*a^2*c^2*(b*c - a*d)^2*x^(5/2)) + ((b*c + a*d)*(9*b^2*c^2 - 17*a*b*c*d + 9*a^2*d^2))/(2*a^3*c^3*(b*c - a*d)^2*Sqrt[x]) + (d*(b*c + a*d))/(2*a*c*(b*c - a*d)^2*x^(5/2)*(c + d*x^2)) + b/(2*a*(b*c - a*d)*x^(5/2)*(a + b*x^2)*(c + d*x^2)) - (b^(13/4)*(9*b*c - 17*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) + (b^(13/4)*(9*b*c - 17*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (d^(13/4)*(17*b*c - 9*a*d)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) + (d^(13/4)*(17*b*c - 9*a*d)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(4*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) + (b^(13/4)*(9*b*c - 17*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) - (b^(13/4)*(9*b*c - 17*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^3) + (d^(13/4)*(17*b*c - 9*a*d)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(b*c - a*d)^3) - (d^(13/4)*(17*b*c - 9*a*d)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(8*Sqrt[2]*c^(13/4)*(b*c - a*d)^3)","A",25,11,24,0.4583,1,"{466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628}"
496,1,718,0,1.0415547,"\int \frac{x^{7/2}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^(7/2)/((a + b*x^2)^2*(c + d*x^2)^3),x]","-\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}+\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}-\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}+\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}+\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} (b c-a d)^4}-\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} (b c-a d)^4}+\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} (b c-a d)^4}-\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} (b c-a d)^4}+\frac{a \sqrt{x}}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{\sqrt{x} (17 a d+7 b c)}{16 \left(c+d x^2\right) (b c-a d)^3}+\frac{\sqrt{x} (2 a d+b c)}{4 b \left(c+d x^2\right)^2 (b c-a d)^2}","-\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}+\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}-\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}+\frac{\left(5 a^2 d^2+70 a b c d+21 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{3/4} \sqrt[4]{d} (b c-a d)^4}+\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} (b c-a d)^4}-\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} (b c-a d)^4}+\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} (b c-a d)^4}-\frac{\sqrt[4]{a} b^{3/4} (7 a d+5 b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} (b c-a d)^4}+\frac{a \sqrt{x}}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{\sqrt{x} (17 a d+7 b c)}{16 \left(c+d x^2\right) (b c-a d)^3}+\frac{\sqrt{x} (2 a d+b c)}{4 b \left(c+d x^2\right)^2 (b c-a d)^2}",1,"((b*c + 2*a*d)*Sqrt[x])/(4*b*(b*c - a*d)^2*(c + d*x^2)^2) + (a*Sqrt[x])/(2*b*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) + ((7*b*c + 17*a*d)*Sqrt[x])/(16*(b*c - a*d)^3*(c + d*x^2)) + (a^(1/4)*b^(3/4)*(5*b*c + 7*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*(b*c - a*d)^4) - (a^(1/4)*b^(3/4)*(5*b*c + 7*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*(b*c - a*d)^4) - ((21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^4) + ((21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^4) + (a^(1/4)*b^(3/4)*(5*b*c + 7*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*(b*c - a*d)^4) - (a^(1/4)*b^(3/4)*(5*b*c + 7*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*(b*c - a*d)^4) - ((21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^4) + ((21*b^2*c^2 + 70*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(3/4)*d^(1/4)*(b*c - a*d)^4)","A",23,10,24,0.4167,1,"{466, 470, 527, 522, 211, 1165, 628, 1162, 617, 204}"
497,1,703,0,1.0200635,"\int \frac{x^{5/2}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^(5/2)/((a + b*x^2)^2*(c + d*x^2)^3),x]","-\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} (b c-a d)^4}+\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} (b c-a d)^4}+\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{5/4} (b c-a d)^4}-\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{5/4} (b c-a d)^4}+\frac{3 b^{5/4} (3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}-\frac{3 b^{5/4} (3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}-\frac{3 b^{5/4} (3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}+\frac{3 b^{5/4} (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}-\frac{3 d x^{3/2} (a d+7 b c)}{16 c \left(c+d x^2\right) (b c-a d)^3}-\frac{x^{3/2}}{2 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}-\frac{3 d x^{3/2}}{4 \left(c+d x^2\right)^2 (b c-a d)^2}","-\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} (b c-a d)^4}+\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{5/4} (b c-a d)^4}+\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{5/4} (b c-a d)^4}-\frac{3 \sqrt[4]{d} \left(-a^2 d^2+18 a b c d+15 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{5/4} (b c-a d)^4}+\frac{3 b^{5/4} (3 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}-\frac{3 b^{5/4} (3 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}-\frac{3 b^{5/4} (3 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}+\frac{3 b^{5/4} (3 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} (b c-a d)^4}-\frac{3 d x^{3/2} (a d+7 b c)}{16 c \left(c+d x^2\right) (b c-a d)^3}-\frac{x^{3/2}}{2 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}-\frac{3 d x^{3/2}}{4 \left(c+d x^2\right)^2 (b c-a d)^2}",1,"(-3*d*x^(3/2))/(4*(b*c - a*d)^2*(c + d*x^2)^2) - x^(3/2)/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) - (3*d*(7*b*c + a*d)*x^(3/2))/(16*c*(b*c - a*d)^3*(c + d*x^2)) - (3*b^(5/4)*(b*c + 3*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*(b*c - a*d)^4) + (3*b^(5/4)*(b*c + 3*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*(b*c - a*d)^4) + (3*d^(1/4)*(15*b^2*c^2 + 18*a*b*c*d - a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(5/4)*(b*c - a*d)^4) - (3*d^(1/4)*(15*b^2*c^2 + 18*a*b*c*d - a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(5/4)*(b*c - a*d)^4) + (3*b^(5/4)*(b*c + 3*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*(b*c - a*d)^4) - (3*b^(5/4)*(b*c + 3*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(1/4)*(b*c - a*d)^4) - (3*d^(1/4)*(15*b^2*c^2 + 18*a*b*c*d - a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(5/4)*(b*c - a*d)^4) + (3*d^(1/4)*(15*b^2*c^2 + 18*a*b*c*d - a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(5/4)*(b*c - a*d)^4)","A",24,10,24,0.4167,1,"{466, 471, 579, 584, 297, 1162, 617, 204, 1165, 628}"
498,1,703,0,1.005415,"\int \frac{x^{3/2}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[x^(3/2)/((a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} (b c-a d)^4}-\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} (b c-a d)^4}+\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{7/4} (b c-a d)^4}-\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{7/4} (b c-a d)^4}-\frac{b^{7/4} (11 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^4}+\frac{b^{7/4} (11 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^4}-\frac{b^{7/4} (11 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^4}+\frac{b^{7/4} (11 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^4}-\frac{d \sqrt{x} (a d+23 b c)}{16 c \left(c+d x^2\right) (b c-a d)^3}-\frac{3 d \sqrt{x}}{4 \left(c+d x^2\right)^2 (b c-a d)^2}-\frac{\sqrt{x}}{2 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}","\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} (b c-a d)^4}-\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{7/4} (b c-a d)^4}+\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{7/4} (b c-a d)^4}-\frac{d^{3/4} \left(-3 a^2 d^2+22 a b c d+77 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{7/4} (b c-a d)^4}-\frac{b^{7/4} (11 a d+b c) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^4}+\frac{b^{7/4} (11 a d+b c) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{3/4} (b c-a d)^4}-\frac{b^{7/4} (11 a d+b c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^4}+\frac{b^{7/4} (11 a d+b c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} (b c-a d)^4}-\frac{d \sqrt{x} (a d+23 b c)}{16 c \left(c+d x^2\right) (b c-a d)^3}-\frac{3 d \sqrt{x}}{4 \left(c+d x^2\right)^2 (b c-a d)^2}-\frac{\sqrt{x}}{2 \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}",1,"(-3*d*Sqrt[x])/(4*(b*c - a*d)^2*(c + d*x^2)^2) - Sqrt[x]/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) - (d*(23*b*c + a*d)*Sqrt[x])/(16*c*(b*c - a*d)^3*(c + d*x^2)) - (b^(7/4)*(b*c + 11*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (b^(7/4)*(b*c + 11*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*(b*c - a*d)^4) - (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(7/4)*(b*c - a*d)^4) - (b^(7/4)*(b*c + 11*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (b^(7/4)*(b*c + 11*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(3/4)*(b*c - a*d)^4) + (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*(b*c - a*d)^4) - (d^(3/4)*(77*b^2*c^2 + 22*a*b*c*d - 3*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(7/4)*(b*c - a*d)^4)","A",23,10,24,0.4167,1,"{466, 471, 527, 522, 211, 1165, 628, 1162, 617, 204}"
499,1,739,0,1.158523,"\int \frac{\sqrt{x}}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[Sqrt[x]/((a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d x^{3/2} \left(-5 a^2 d^2+21 a b c d+8 b^2 c^2\right)}{16 a c^2 \left(c+d x^2\right) (b c-a d)^3}+\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^4}-\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^4}-\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^4}+\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^4}+\frac{b^{9/4} (b c-13 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^4}-\frac{b^{9/4} (b c-13 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^4}-\frac{b^{9/4} (b c-13 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^4}+\frac{b^{9/4} (b c-13 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^4}+\frac{b x^{3/2}}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d x^{3/2} (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}","\frac{d x^{3/2} \left(-5 a^2 d^2+21 a b c d+8 b^2 c^2\right)}{16 a c^2 \left(c+d x^2\right) (b c-a d)^3}+\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^4}-\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{9/4} (b c-a d)^4}-\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^4}+\frac{d^{5/4} \left(5 a^2 d^2-26 a b c d+117 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{9/4} (b c-a d)^4}+\frac{b^{9/4} (b c-13 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^4}-\frac{b^{9/4} (b c-13 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{5/4} (b c-a d)^4}-\frac{b^{9/4} (b c-13 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^4}+\frac{b^{9/4} (b c-13 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} (b c-a d)^4}+\frac{b x^{3/2}}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d x^{3/2} (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}",1,"(d*(2*b*c + a*d)*x^(3/2))/(4*a*c*(b*c - a*d)^2*(c + d*x^2)^2) + (b*x^(3/2))/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) + (d*(8*b^2*c^2 + 21*a*b*c*d - 5*a^2*d^2)*x^(3/2))/(16*a*c^2*(b*c - a*d)^3*(c + d*x^2)) - (b^(9/4)*(b*c - 13*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (b^(9/4)*(b*c - 13*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) - (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)^4) + (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(9/4)*(b*c - a*d)^4) + (b^(9/4)*(b*c - 13*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) - (b^(9/4)*(b*c - 13*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(5/4)*(b*c - a*d)^4) + (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(b*c - a*d)^4) - (d^(5/4)*(117*b^2*c^2 - 26*a*b*c*d + 5*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(9/4)*(b*c - a*d)^4)","A",24,10,24,0.4167,1,"{466, 472, 579, 584, 297, 1162, 617, 204, 1165, 628}"
500,1,739,0,0.9777572,"\int \frac{1}{\sqrt{x} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(Sqrt[x]*(a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{d \sqrt{x} \left(-7 a^2 d^2+23 a b c d+8 b^2 c^2\right)}{16 a c^2 \left(c+d x^2\right) (b c-a d)^3}-\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^4}+\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^4}-\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^4}+\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^4}-\frac{3 b^{11/4} (b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^4}+\frac{3 b^{11/4} (b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^4}-\frac{3 b^{11/4} (b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^4}+\frac{3 b^{11/4} (b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^4}+\frac{b \sqrt{x}}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d \sqrt{x} (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}","\frac{d \sqrt{x} \left(-7 a^2 d^2+23 a b c d+8 b^2 c^2\right)}{16 a c^2 \left(c+d x^2\right) (b c-a d)^3}-\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \log \left(-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^4}+\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \log \left(\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}+\sqrt{d} x\right)}{64 \sqrt{2} c^{11/4} (b c-a d)^4}-\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^4}+\frac{3 d^{7/4} \left(7 a^2 d^2-30 a b c d+55 b^2 c^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{11/4} (b c-a d)^4}-\frac{3 b^{11/4} (b c-5 a d) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^4}+\frac{3 b^{11/4} (b c-5 a d) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}+\sqrt{b} x\right)}{8 \sqrt{2} a^{7/4} (b c-a d)^4}-\frac{3 b^{11/4} (b c-5 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^4}+\frac{3 b^{11/4} (b c-5 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} (b c-a d)^4}+\frac{b \sqrt{x}}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^2 (b c-a d)}+\frac{d \sqrt{x} (a d+2 b c)}{4 a c \left(c+d x^2\right)^2 (b c-a d)^2}",1,"(d*(2*b*c + a*d)*Sqrt[x])/(4*a*c*(b*c - a*d)^2*(c + d*x^2)^2) + (b*Sqrt[x])/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^2) + (d*(8*b^2*c^2 + 23*a*b*c*d - 7*a^2*d^2)*Sqrt[x])/(16*a*c^2*(b*c - a*d)^3*(c + d*x^2)) - (3*b^(11/4)*(b*c - 5*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*(b*c - a*d)^4) + (3*b^(11/4)*(b*c - 5*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*(b*c - a*d)^4) - (3*d^(7/4)*(55*b^2*c^2 - 30*a*b*c*d + 7*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(11/4)*(b*c - a*d)^4) + (3*d^(7/4)*(55*b^2*c^2 - 30*a*b*c*d + 7*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(11/4)*(b*c - a*d)^4) - (3*b^(11/4)*(b*c - 5*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^4) + (3*b^(11/4)*(b*c - 5*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(7/4)*(b*c - a*d)^4) - (3*d^(7/4)*(55*b^2*c^2 - 30*a*b*c*d + 7*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(11/4)*(b*c - a*d)^4) + (3*d^(7/4)*(55*b^2*c^2 - 30*a*b*c*d + 7*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(11/4)*(b*c - a*d)^4)","A",23,10,24,0.4167,1,"{466, 414, 527, 522, 211, 1165, 628, 1162, 617, 204}"
501,1,805,0,1.3995961,"\int \frac{1}{x^{3/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x^(3/2)*(a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{(5 b c-17 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right) b^{13/4}}{4 \sqrt{2} a^{9/4} (b c-a d)^4}-\frac{(5 b c-17 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right) b^{13/4}}{4 \sqrt{2} a^{9/4} (b c-a d)^4}-\frac{(5 b c-17 a d) \log \left(\sqrt{b} x-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{13/4}}{8 \sqrt{2} a^{9/4} (b c-a d)^4}+\frac{(5 b c-17 a d) \log \left(\sqrt{b} x+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{13/4}}{8 \sqrt{2} a^{9/4} (b c-a d)^4}+\frac{b}{2 a (b c-a d) \sqrt{x} \left(b x^2+a\right) \left(d x^2+c\right)^2}+\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^4}-\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^4}-\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \log \left(\sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^4}+\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \log \left(\sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^4}-\frac{40 b^3 c^3-96 a b^2 d c^2+125 a^2 b d^2 c-45 a^3 d^3}{16 a^2 c^3 (b c-a d)^3 \sqrt{x}}+\frac{d \left(8 b^2 c^2+25 a b d c-9 a^2 d^2\right)}{16 a c^2 (b c-a d)^3 \sqrt{x} \left(d x^2+c\right)}+\frac{d (2 b c+a d)}{4 a c (b c-a d)^2 \sqrt{x} \left(d x^2+c\right)^2}","\frac{(5 b c-17 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right) b^{13/4}}{4 \sqrt{2} a^{9/4} (b c-a d)^4}-\frac{(5 b c-17 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right) b^{13/4}}{4 \sqrt{2} a^{9/4} (b c-a d)^4}-\frac{(5 b c-17 a d) \log \left(\sqrt{b} x-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{13/4}}{8 \sqrt{2} a^{9/4} (b c-a d)^4}+\frac{(5 b c-17 a d) \log \left(\sqrt{b} x+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{13/4}}{8 \sqrt{2} a^{9/4} (b c-a d)^4}+\frac{b}{2 a (b c-a d) \sqrt{x} \left(b x^2+a\right) \left(d x^2+c\right)^2}+\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^4}-\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{13/4} (b c-a d)^4}-\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \log \left(\sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^4}+\frac{d^{9/4} \left(221 b^2 c^2-170 a b d c+45 a^2 d^2\right) \log \left(\sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{13/4} (b c-a d)^4}-\frac{40 b^3 c^3-96 a b^2 d c^2+125 a^2 b d^2 c-45 a^3 d^3}{16 a^2 c^3 (b c-a d)^3 \sqrt{x}}+\frac{d \left(8 b^2 c^2+25 a b d c-9 a^2 d^2\right)}{16 a c^2 (b c-a d)^3 \sqrt{x} \left(d x^2+c\right)}+\frac{d (2 b c+a d)}{4 a c (b c-a d)^2 \sqrt{x} \left(d x^2+c\right)^2}",1,"-(40*b^3*c^3 - 96*a*b^2*c^2*d + 125*a^2*b*c*d^2 - 45*a^3*d^3)/(16*a^2*c^3*(b*c - a*d)^3*Sqrt[x]) + (d*(2*b*c + a*d))/(4*a*c*(b*c - a*d)^2*Sqrt[x]*(c + d*x^2)^2) + b/(2*a*(b*c - a*d)*Sqrt[x]*(a + b*x^2)*(c + d*x^2)^2) + (d*(8*b^2*c^2 + 25*a*b*c*d - 9*a^2*d^2))/(16*a*c^2*(b*c - a*d)^3*Sqrt[x]*(c + d*x^2)) + (b^(13/4)*(5*b*c - 17*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*(b*c - a*d)^4) - (b^(13/4)*(5*b*c - 17*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*(b*c - a*d)^4) + (d^(9/4)*(221*b^2*c^2 - 170*a*b*c*d + 45*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(13/4)*(b*c - a*d)^4) - (d^(9/4)*(221*b^2*c^2 - 170*a*b*c*d + 45*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(13/4)*(b*c - a*d)^4) - (b^(13/4)*(5*b*c - 17*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*(b*c - a*d)^4) + (b^(13/4)*(5*b*c - 17*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(9/4)*(b*c - a*d)^4) - (d^(9/4)*(221*b^2*c^2 - 170*a*b*c*d + 45*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(13/4)*(b*c - a*d)^4) + (d^(9/4)*(221*b^2*c^2 - 170*a*b*c*d + 45*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(13/4)*(b*c - a*d)^4)","A",25,11,24,0.4583,1,"{466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628}"
502,1,805,0,1.3218861,"\int \frac{1}{x^{5/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x^(5/2)*(a + b*x^2)^2*(c + d*x^2)^3),x]","\frac{(7 b c-19 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right) b^{15/4}}{4 \sqrt{2} a^{11/4} (b c-a d)^4}-\frac{(7 b c-19 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right) b^{15/4}}{4 \sqrt{2} a^{11/4} (b c-a d)^4}+\frac{(7 b c-19 a d) \log \left(\sqrt{b} x-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{15/4}}{8 \sqrt{2} a^{11/4} (b c-a d)^4}-\frac{(7 b c-19 a d) \log \left(\sqrt{b} x+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{15/4}}{8 \sqrt{2} a^{11/4} (b c-a d)^4}+\frac{b}{2 a (b c-a d) x^{3/2} \left(b x^2+a\right) \left(d x^2+c\right)^2}+\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^4}-\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^4}+\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \log \left(\sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^4}-\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \log \left(\sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^4}+\frac{d \left(8 b^2 c^2+27 a b d c-11 a^2 d^2\right)}{16 a c^2 (b c-a d)^3 x^{3/2} \left(d x^2+c\right)}-\frac{56 b^3 c^3-96 a b^2 d c^2+189 a^2 b d^2 c-77 a^3 d^3}{48 a^2 c^3 (b c-a d)^3 x^{3/2}}+\frac{d (2 b c+a d)}{4 a c (b c-a d)^2 x^{3/2} \left(d x^2+c\right)^2}","\frac{(7 b c-19 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right) b^{15/4}}{4 \sqrt{2} a^{11/4} (b c-a d)^4}-\frac{(7 b c-19 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right) b^{15/4}}{4 \sqrt{2} a^{11/4} (b c-a d)^4}+\frac{(7 b c-19 a d) \log \left(\sqrt{b} x-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{15/4}}{8 \sqrt{2} a^{11/4} (b c-a d)^4}-\frac{(7 b c-19 a d) \log \left(\sqrt{b} x+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{15/4}}{8 \sqrt{2} a^{11/4} (b c-a d)^4}+\frac{b}{2 a (b c-a d) x^{3/2} \left(b x^2+a\right) \left(d x^2+c\right)^2}+\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^4}-\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{15/4} (b c-a d)^4}+\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \log \left(\sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^4}-\frac{d^{11/4} \left(285 b^2 c^2-266 a b d c+77 a^2 d^2\right) \log \left(\sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{15/4} (b c-a d)^4}+\frac{d \left(8 b^2 c^2+27 a b d c-11 a^2 d^2\right)}{16 a c^2 (b c-a d)^3 x^{3/2} \left(d x^2+c\right)}-\frac{56 b^3 c^3-96 a b^2 d c^2+189 a^2 b d^2 c-77 a^3 d^3}{48 a^2 c^3 (b c-a d)^3 x^{3/2}}+\frac{d (2 b c+a d)}{4 a c (b c-a d)^2 x^{3/2} \left(d x^2+c\right)^2}",1,"-(56*b^3*c^3 - 96*a*b^2*c^2*d + 189*a^2*b*c*d^2 - 77*a^3*d^3)/(48*a^2*c^3*(b*c - a*d)^3*x^(3/2)) + (d*(2*b*c + a*d))/(4*a*c*(b*c - a*d)^2*x^(3/2)*(c + d*x^2)^2) + b/(2*a*(b*c - a*d)*x^(3/2)*(a + b*x^2)*(c + d*x^2)^2) + (d*(8*b^2*c^2 + 27*a*b*c*d - 11*a^2*d^2))/(16*a*c^2*(b*c - a*d)^3*x^(3/2)*(c + d*x^2)) + (b^(15/4)*(7*b*c - 19*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^4) - (b^(15/4)*(7*b*c - 19*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)*(b*c - a*d)^4) + (d^(11/4)*(285*b^2*c^2 - 266*a*b*c*d + 77*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(15/4)*(b*c - a*d)^4) - (d^(11/4)*(285*b^2*c^2 - 266*a*b*c*d + 77*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(15/4)*(b*c - a*d)^4) + (b^(15/4)*(7*b*c - 19*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c - a*d)^4) - (b^(15/4)*(7*b*c - 19*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(11/4)*(b*c - a*d)^4) + (d^(11/4)*(285*b^2*c^2 - 266*a*b*c*d + 77*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(15/4)*(b*c - a*d)^4) - (d^(11/4)*(285*b^2*c^2 - 266*a*b*c*d + 77*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(15/4)*(b*c - a*d)^4)","A",24,11,24,0.4583,1,"{466, 472, 579, 583, 522, 211, 1165, 628, 1162, 617, 204}"
503,1,881,0,1.6910892,"\int \frac{1}{x^{7/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^3} \, dx","Int[1/(x^(7/2)*(a + b*x^2)^2*(c + d*x^2)^3),x]","-\frac{3 (3 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right) b^{17/4}}{4 \sqrt{2} a^{13/4} (b c-a d)^4}+\frac{3 (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right) b^{17/4}}{4 \sqrt{2} a^{13/4} (b c-a d)^4}+\frac{3 (3 b c-7 a d) \log \left(\sqrt{b} x-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{17/4}}{8 \sqrt{2} a^{13/4} (b c-a d)^4}-\frac{3 (3 b c-7 a d) \log \left(\sqrt{b} x+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{17/4}}{8 \sqrt{2} a^{13/4} (b c-a d)^4}+\frac{b}{2 a (b c-a d) x^{5/2} \left(b x^2+a\right) \left(d x^2+c\right)^2}-\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^4}+\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^4}+\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \log \left(\sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^4}-\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \log \left(\sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^4}+\frac{3 \left(24 b^4 c^4-32 a b^3 d c^3-32 a^2 b^2 d^2 c^2+87 a^3 b d^3 c-39 a^4 d^4\right)}{16 a^3 c^4 (b c-a d)^3 \sqrt{x}}+\frac{d \left(8 b^2 c^2+29 a b d c-13 a^2 d^2\right)}{16 a c^2 (b c-a d)^3 x^{5/2} \left(d x^2+c\right)}+\frac{d (2 b c+a d)}{4 a c (b c-a d)^2 x^{5/2} \left(d x^2+c\right)^2}-\frac{3 \left(24 b^3 c^3-32 a b^2 d c^2+87 a^2 b d^2 c-39 a^3 d^3\right)}{80 a^2 c^3 (b c-a d)^3 x^{5/2}}","-\frac{3 (3 b c-7 a d) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right) b^{17/4}}{4 \sqrt{2} a^{13/4} (b c-a d)^4}+\frac{3 (3 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}+1\right) b^{17/4}}{4 \sqrt{2} a^{13/4} (b c-a d)^4}+\frac{3 (3 b c-7 a d) \log \left(\sqrt{b} x-\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{17/4}}{8 \sqrt{2} a^{13/4} (b c-a d)^4}-\frac{3 (3 b c-7 a d) \log \left(\sqrt{b} x+\sqrt{2} \sqrt[4]{a} \sqrt[4]{b} \sqrt{x}+\sqrt{a}\right) b^{17/4}}{8 \sqrt{2} a^{13/4} (b c-a d)^4}+\frac{b}{2 a (b c-a d) x^{5/2} \left(b x^2+a\right) \left(d x^2+c\right)^2}-\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^4}+\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}+1\right)}{32 \sqrt{2} c^{17/4} (b c-a d)^4}+\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \log \left(\sqrt{d} x-\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^4}-\frac{3 d^{13/4} \left(119 b^2 c^2-126 a b d c+39 a^2 d^2\right) \log \left(\sqrt{d} x+\sqrt{2} \sqrt[4]{c} \sqrt[4]{d} \sqrt{x}+\sqrt{c}\right)}{64 \sqrt{2} c^{17/4} (b c-a d)^4}+\frac{3 \left(24 b^4 c^4-32 a b^3 d c^3-32 a^2 b^2 d^2 c^2+87 a^3 b d^3 c-39 a^4 d^4\right)}{16 a^3 c^4 (b c-a d)^3 \sqrt{x}}+\frac{d \left(8 b^2 c^2+29 a b d c-13 a^2 d^2\right)}{16 a c^2 (b c-a d)^3 x^{5/2} \left(d x^2+c\right)}+\frac{d (2 b c+a d)}{4 a c (b c-a d)^2 x^{5/2} \left(d x^2+c\right)^2}-\frac{3 \left(24 b^3 c^3-32 a b^2 d c^2+87 a^2 b d^2 c-39 a^3 d^3\right)}{80 a^2 c^3 (b c-a d)^3 x^{5/2}}",1,"(-3*(24*b^3*c^3 - 32*a*b^2*c^2*d + 87*a^2*b*c*d^2 - 39*a^3*d^3))/(80*a^2*c^3*(b*c - a*d)^3*x^(5/2)) + (3*(24*b^4*c^4 - 32*a*b^3*c^3*d - 32*a^2*b^2*c^2*d^2 + 87*a^3*b*c*d^3 - 39*a^4*d^4))/(16*a^3*c^4*(b*c - a*d)^3*Sqrt[x]) + (d*(2*b*c + a*d))/(4*a*c*(b*c - a*d)^2*x^(5/2)*(c + d*x^2)^2) + b/(2*a*(b*c - a*d)*x^(5/2)*(a + b*x^2)*(c + d*x^2)^2) + (d*(8*b^2*c^2 + 29*a*b*c*d - 13*a^2*d^2))/(16*a*c^2*(b*c - a*d)^3*x^(5/2)*(c + d*x^2)) - (3*b^(17/4)*(3*b*c - 7*a*d)*ArcTan[1 - (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^4) + (3*b^(17/4)*(3*b*c - 7*a*d)*ArcTan[1 + (Sqrt[2]*b^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(13/4)*(b*c - a*d)^4) - (3*d^(13/4)*(119*b^2*c^2 - 126*a*b*c*d + 39*a^2*d^2)*ArcTan[1 - (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*(b*c - a*d)^4) + (3*d^(13/4)*(119*b^2*c^2 - 126*a*b*c*d + 39*a^2*d^2)*ArcTan[1 + (Sqrt[2]*d^(1/4)*Sqrt[x])/c^(1/4)])/(32*Sqrt[2]*c^(17/4)*(b*c - a*d)^4) + (3*b^(17/4)*(3*b*c - 7*a*d)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^4) - (3*b^(17/4)*(3*b*c - 7*a*d)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*b^(1/4)*Sqrt[x] + Sqrt[b]*x])/(8*Sqrt[2]*a^(13/4)*(b*c - a*d)^4) + (3*d^(13/4)*(119*b^2*c^2 - 126*a*b*c*d + 39*a^2*d^2)*Log[Sqrt[c] - Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*(b*c - a*d)^4) - (3*d^(13/4)*(119*b^2*c^2 - 126*a*b*c*d + 39*a^2*d^2)*Log[Sqrt[c] + Sqrt[2]*c^(1/4)*d^(1/4)*Sqrt[x] + Sqrt[d]*x])/(64*Sqrt[2]*c^(17/4)*(b*c - a*d)^4)","A",26,11,24,0.4583,1,"{466, 472, 579, 583, 584, 297, 1162, 617, 204, 1165, 628}"
504,1,103,0,0.0873286,"\int x^5 \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[x^5*Sqrt[a + b*x^2]*(A + B*x^2),x]","\frac{a^2 \left(a+b x^2\right)^{3/2} (A b-a B)}{3 b^4}+\frac{\left(a+b x^2\right)^{7/2} (A b-3 a B)}{7 b^4}-\frac{a \left(a+b x^2\right)^{5/2} (2 A b-3 a B)}{5 b^4}+\frac{B \left(a+b x^2\right)^{9/2}}{9 b^4}","\frac{a^2 \left(a+b x^2\right)^{3/2} (A b-a B)}{3 b^4}+\frac{\left(a+b x^2\right)^{7/2} (A b-3 a B)}{7 b^4}-\frac{a \left(a+b x^2\right)^{5/2} (2 A b-3 a B)}{5 b^4}+\frac{B \left(a+b x^2\right)^{9/2}}{9 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x^2)^(3/2))/(3*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x^2)^(5/2))/(5*b^4) + ((A*b - 3*a*B)*(a + b*x^2)^(7/2))/(7*b^4) + (B*(a + b*x^2)^(9/2))/(9*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
505,1,155,0,0.07237,"\int x^4 \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[x^4*Sqrt[a + b*x^2]*(A + B*x^2),x]","-\frac{a^2 x \sqrt{a+b x^2} (8 A b-5 a B)}{128 b^3}+\frac{a^3 (8 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{7/2}}+\frac{a x^3 \sqrt{a+b x^2} (8 A b-5 a B)}{192 b^2}+\frac{x^5 \sqrt{a+b x^2} (8 A b-5 a B)}{48 b}+\frac{B x^5 \left(a+b x^2\right)^{3/2}}{8 b}","-\frac{a^2 x \sqrt{a+b x^2} (8 A b-5 a B)}{128 b^3}+\frac{a^3 (8 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{7/2}}+\frac{a x^3 \sqrt{a+b x^2} (8 A b-5 a B)}{192 b^2}+\frac{x^5 \sqrt{a+b x^2} (8 A b-5 a B)}{48 b}+\frac{B x^5 \left(a+b x^2\right)^{3/2}}{8 b}",1,"-(a^2*(8*A*b - 5*a*B)*x*Sqrt[a + b*x^2])/(128*b^3) + (a*(8*A*b - 5*a*B)*x^3*Sqrt[a + b*x^2])/(192*b^2) + ((8*A*b - 5*a*B)*x^5*Sqrt[a + b*x^2])/(48*b) + (B*x^5*(a + b*x^2)^(3/2))/(8*b) + (a^3*(8*A*b - 5*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(7/2))","A",6,5,22,0.2273,1,"{459, 279, 321, 217, 206}"
506,1,73,0,0.061788,"\int x^3 \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[x^3*Sqrt[a + b*x^2]*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^{5/2} (A b-2 a B)}{5 b^3}-\frac{a \left(a+b x^2\right)^{3/2} (A b-a B)}{3 b^3}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b^3}","\frac{\left(a+b x^2\right)^{5/2} (A b-2 a B)}{5 b^3}-\frac{a \left(a+b x^2\right)^{3/2} (A b-a B)}{3 b^3}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b^3}",1,"-(a*(A*b - a*B)*(a + b*x^2)^(3/2))/(3*b^3) + ((A*b - 2*a*B)*(a + b*x^2)^(5/2))/(5*b^3) + (B*(a + b*x^2)^(7/2))/(7*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
507,1,122,0,0.0591792,"\int x^2 \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[x^2*Sqrt[a + b*x^2]*(A + B*x^2),x]","-\frac{a^2 (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}+\frac{a x \sqrt{a+b x^2} (2 A b-a B)}{16 b^2}+\frac{x^3 \sqrt{a+b x^2} (2 A b-a B)}{8 b}+\frac{B x^3 \left(a+b x^2\right)^{3/2}}{6 b}","-\frac{a^2 (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{5/2}}+\frac{a x \sqrt{a+b x^2} (2 A b-a B)}{16 b^2}+\frac{x^3 \sqrt{a+b x^2} (2 A b-a B)}{8 b}+\frac{B x^3 \left(a+b x^2\right)^{3/2}}{6 b}",1,"(a*(2*A*b - a*B)*x*Sqrt[a + b*x^2])/(16*b^2) + ((2*A*b - a*B)*x^3*Sqrt[a + b*x^2])/(8*b) + (B*x^3*(a + b*x^2)^(3/2))/(6*b) - (a^2*(2*A*b - a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(5/2))","A",5,5,22,0.2273,1,"{459, 279, 321, 217, 206}"
508,1,46,0,0.0362037,"\int x \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[x*Sqrt[a + b*x^2]*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^{3/2} (A b-a B)}{3 b^2}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^2}","\frac{\left(a+b x^2\right)^{3/2} (A b-a B)}{3 b^2}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^2}",1,"((A*b - a*B)*(a + b*x^2)^(3/2))/(3*b^2) + (B*(a + b*x^2)^(5/2))/(5*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
509,1,87,0,0.028411,"\int \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[Sqrt[a + b*x^2]*(A + B*x^2),x]","\frac{a (4 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{x \sqrt{a+b x^2} (4 A b-a B)}{8 b}+\frac{B x \left(a+b x^2\right)^{3/2}}{4 b}","\frac{a (4 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{3/2}}+\frac{x \sqrt{a+b x^2} (4 A b-a B)}{8 b}+\frac{B x \left(a+b x^2\right)^{3/2}}{4 b}",1,"((4*A*b - a*B)*x*Sqrt[a + b*x^2])/(8*b) + (B*x*(a + b*x^2)^(3/2))/(4*b) + (a*(4*A*b - a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(3/2))","A",4,4,19,0.2105,1,"{388, 195, 217, 206}"
510,1,59,0,0.0442799,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x,x]","A \sqrt{a+b x^2}-\sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{B \left(a+b x^2\right)^{3/2}}{3 b}","A \sqrt{a+b x^2}-\sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{B \left(a+b x^2\right)^{3/2}}{3 b}",1,"A*Sqrt[a + b*x^2] + (B*(a + b*x^2)^(3/2))/(3*b) - Sqrt[a]*A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",5,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
511,1,84,0,0.0333191,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^2} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^2,x]","\frac{x \sqrt{a+b x^2} (a B+2 A b)}{2 a}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}-\frac{A \left(a+b x^2\right)^{3/2}}{a x}","\frac{x \sqrt{a+b x^2} (a B+2 A b)}{2 a}+\frac{(a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 \sqrt{b}}-\frac{A \left(a+b x^2\right)^{3/2}}{a x}",1,"((2*A*b + a*B)*x*Sqrt[a + b*x^2])/(2*a) - (A*(a + b*x^2)^(3/2))/(a*x) + ((2*A*b + a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*Sqrt[b])","A",4,4,22,0.1818,1,"{453, 195, 217, 206}"
512,1,84,0,0.0629452,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^3} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^3,x]","\frac{\sqrt{a+b x^2} (2 a B+A b)}{2 a}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{A \left(a+b x^2\right)^{3/2}}{2 a x^2}","\frac{\sqrt{a+b x^2} (2 a B+A b)}{2 a}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}-\frac{A \left(a+b x^2\right)^{3/2}}{2 a x^2}",1,"((A*b + 2*a*B)*Sqrt[a + b*x^2])/(2*a) - (A*(a + b*x^2)^(3/2))/(2*a*x^2) - ((A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*Sqrt[a])","A",5,5,22,0.2273,1,"{446, 78, 50, 63, 208}"
513,1,66,0,0.0249793,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^4} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^4,x]","-\frac{A \left(a+b x^2\right)^{3/2}}{3 a x^3}-\frac{B \sqrt{a+b x^2}}{x}+\sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)","-\frac{A \left(a+b x^2\right)^{3/2}}{3 a x^3}-\frac{B \sqrt{a+b x^2}}{x}+\sqrt{b} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)",1,"-((B*Sqrt[a + b*x^2])/x) - (A*(a + b*x^2)^(3/2))/(3*a*x^3) + Sqrt[b]*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",4,4,22,0.1818,1,"{451, 277, 217, 206}"
514,1,88,0,0.0688513,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^5} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^5,x]","\frac{b (A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{\sqrt{a+b x^2} (A b-4 a B)}{8 a x^2}-\frac{A \left(a+b x^2\right)^{3/2}}{4 a x^4}","\frac{b (A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{\sqrt{a+b x^2} (A b-4 a B)}{8 a x^2}-\frac{A \left(a+b x^2\right)^{3/2}}{4 a x^4}",1,"((A*b - 4*a*B)*Sqrt[a + b*x^2])/(8*a*x^2) - (A*(a + b*x^2)^(3/2))/(4*a*x^4) + (b*(A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(3/2))","A",5,5,22,0.2273,1,"{446, 78, 47, 63, 208}"
515,1,53,0,0.0211285,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^6} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^6,x]","\frac{\left(a+b x^2\right)^{3/2} (2 A b-5 a B)}{15 a^2 x^3}-\frac{A \left(a+b x^2\right)^{3/2}}{5 a x^5}","\frac{\left(a+b x^2\right)^{3/2} (2 A b-5 a B)}{15 a^2 x^3}-\frac{A \left(a+b x^2\right)^{3/2}}{5 a x^5}",1,"-(A*(a + b*x^2)^(3/2))/(5*a*x^5) + ((2*A*b - 5*a*B)*(a + b*x^2)^(3/2))/(15*a^2*x^3)","A",2,2,22,0.09091,1,"{453, 264}"
516,1,120,0,0.0936198,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^7} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^7,x]","-\frac{b^2 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}+\frac{b \sqrt{a+b x^2} (A b-2 a B)}{16 a^2 x^2}+\frac{\sqrt{a+b x^2} (A b-2 a B)}{8 a x^4}-\frac{A \left(a+b x^2\right)^{3/2}}{6 a x^6}","-\frac{b^2 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}+\frac{b \sqrt{a+b x^2} (A b-2 a B)}{16 a^2 x^2}+\frac{\sqrt{a+b x^2} (A b-2 a B)}{8 a x^4}-\frac{A \left(a+b x^2\right)^{3/2}}{6 a x^6}",1,"((A*b - 2*a*B)*Sqrt[a + b*x^2])/(8*a*x^4) + (b*(A*b - 2*a*B)*Sqrt[a + b*x^2])/(16*a^2*x^2) - (A*(a + b*x^2)^(3/2))/(6*a*x^6) - (b^2*(A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(5/2))","A",6,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
517,1,84,0,0.0336299,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^8} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^8,x]","-\frac{2 b \left(a+b x^2\right)^{3/2} (4 A b-7 a B)}{105 a^3 x^3}+\frac{\left(a+b x^2\right)^{3/2} (4 A b-7 a B)}{35 a^2 x^5}-\frac{A \left(a+b x^2\right)^{3/2}}{7 a x^7}","-\frac{2 b \left(a+b x^2\right)^{3/2} (4 A b-7 a B)}{105 a^3 x^3}+\frac{\left(a+b x^2\right)^{3/2} (4 A b-7 a B)}{35 a^2 x^5}-\frac{A \left(a+b x^2\right)^{3/2}}{7 a x^7}",1,"-(A*(a + b*x^2)^(3/2))/(7*a*x^7) + ((4*A*b - 7*a*B)*(a + b*x^2)^(3/2))/(35*a^2*x^5) - (2*b*(4*A*b - 7*a*B)*(a + b*x^2)^(3/2))/(105*a^3*x^3)","A",3,3,22,0.1364,1,"{453, 271, 264}"
518,1,156,0,0.1199131,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^9} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^9,x]","-\frac{b^2 \sqrt{a+b x^2} (5 A b-8 a B)}{128 a^3 x^2}+\frac{b^3 (5 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{7/2}}+\frac{b \sqrt{a+b x^2} (5 A b-8 a B)}{192 a^2 x^4}+\frac{\sqrt{a+b x^2} (5 A b-8 a B)}{48 a x^6}-\frac{A \left(a+b x^2\right)^{3/2}}{8 a x^8}","-\frac{b^2 \sqrt{a+b x^2} (5 A b-8 a B)}{128 a^3 x^2}+\frac{b^3 (5 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{7/2}}+\frac{b \sqrt{a+b x^2} (5 A b-8 a B)}{192 a^2 x^4}+\frac{\sqrt{a+b x^2} (5 A b-8 a B)}{48 a x^6}-\frac{A \left(a+b x^2\right)^{3/2}}{8 a x^8}",1,"((5*A*b - 8*a*B)*Sqrt[a + b*x^2])/(48*a*x^6) + (b*(5*A*b - 8*a*B)*Sqrt[a + b*x^2])/(192*a^2*x^4) - (b^2*(5*A*b - 8*a*B)*Sqrt[a + b*x^2])/(128*a^3*x^2) - (A*(a + b*x^2)^(3/2))/(8*a*x^8) + (b^3*(5*A*b - 8*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(7/2))","A",7,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
519,1,117,0,0.0554634,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^{10}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^10,x]","\frac{8 b^2 \left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{315 a^4 x^3}-\frac{4 b \left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{105 a^3 x^5}+\frac{\left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{21 a^2 x^7}-\frac{A \left(a+b x^2\right)^{3/2}}{9 a x^9}","\frac{8 b^2 \left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{315 a^4 x^3}-\frac{4 b \left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{105 a^3 x^5}+\frac{\left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{21 a^2 x^7}-\frac{A \left(a+b x^2\right)^{3/2}}{9 a x^9}",1,"-(A*(a + b*x^2)^(3/2))/(9*a*x^9) + ((2*A*b - 3*a*B)*(a + b*x^2)^(3/2))/(21*a^2*x^7) - (4*b*(2*A*b - 3*a*B)*(a + b*x^2)^(3/2))/(105*a^3*x^5) + (8*b^2*(2*A*b - 3*a*B)*(a + b*x^2)^(3/2))/(315*a^4*x^3)","A",4,3,22,0.1364,1,"{453, 271, 264}"
520,1,189,0,0.1468026,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^{11}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^11,x]","\frac{b^3 \sqrt{a+b x^2} (7 A b-10 a B)}{256 a^4 x^2}-\frac{b^2 \sqrt{a+b x^2} (7 A b-10 a B)}{384 a^3 x^4}-\frac{b^4 (7 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{9/2}}+\frac{b \sqrt{a+b x^2} (7 A b-10 a B)}{480 a^2 x^6}+\frac{\sqrt{a+b x^2} (7 A b-10 a B)}{80 a x^8}-\frac{A \left(a+b x^2\right)^{3/2}}{10 a x^{10}}","\frac{b^3 \sqrt{a+b x^2} (7 A b-10 a B)}{256 a^4 x^2}-\frac{b^2 \sqrt{a+b x^2} (7 A b-10 a B)}{384 a^3 x^4}-\frac{b^4 (7 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{9/2}}+\frac{b \sqrt{a+b x^2} (7 A b-10 a B)}{480 a^2 x^6}+\frac{\sqrt{a+b x^2} (7 A b-10 a B)}{80 a x^8}-\frac{A \left(a+b x^2\right)^{3/2}}{10 a x^{10}}",1,"((7*A*b - 10*a*B)*Sqrt[a + b*x^2])/(80*a*x^8) + (b*(7*A*b - 10*a*B)*Sqrt[a + b*x^2])/(480*a^2*x^6) - (b^2*(7*A*b - 10*a*B)*Sqrt[a + b*x^2])/(384*a^3*x^4) + (b^3*(7*A*b - 10*a*B)*Sqrt[a + b*x^2])/(256*a^4*x^2) - (A*(a + b*x^2)^(3/2))/(10*a*x^10) - (b^4*(7*A*b - 10*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*a^(9/2))","A",8,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
521,1,103,0,0.0773654,"\int x^5 \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[x^5*(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{a^2 \left(a+b x^2\right)^{5/2} (A b-a B)}{5 b^4}+\frac{\left(a+b x^2\right)^{9/2} (A b-3 a B)}{9 b^4}-\frac{a \left(a+b x^2\right)^{7/2} (2 A b-3 a B)}{7 b^4}+\frac{B \left(a+b x^2\right)^{11/2}}{11 b^4}","\frac{a^2 \left(a+b x^2\right)^{5/2} (A b-a B)}{5 b^4}+\frac{\left(a+b x^2\right)^{9/2} (A b-3 a B)}{9 b^4}-\frac{a \left(a+b x^2\right)^{7/2} (2 A b-3 a B)}{7 b^4}+\frac{B \left(a+b x^2\right)^{11/2}}{11 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x^2)^(5/2))/(5*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x^2)^(7/2))/(7*b^4) + ((A*b - 3*a*B)*(a + b*x^2)^(9/2))/(9*b^4) + (B*(a + b*x^2)^(11/2))/(11*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
522,1,188,0,0.0963296,"\int x^4 \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[x^4*(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{a^2 x^3 \sqrt{a+b x^2} (2 A b-a B)}{128 b^2}-\frac{3 a^3 x \sqrt{a+b x^2} (2 A b-a B)}{256 b^3}+\frac{3 a^4 (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{7/2}}+\frac{x^5 \left(a+b x^2\right)^{3/2} (2 A b-a B)}{16 b}+\frac{a x^5 \sqrt{a+b x^2} (2 A b-a B)}{32 b}+\frac{B x^5 \left(a+b x^2\right)^{5/2}}{10 b}","\frac{a^2 x^3 \sqrt{a+b x^2} (2 A b-a B)}{128 b^2}-\frac{3 a^3 x \sqrt{a+b x^2} (2 A b-a B)}{256 b^3}+\frac{3 a^4 (2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{7/2}}+\frac{x^5 \left(a+b x^2\right)^{3/2} (2 A b-a B)}{16 b}+\frac{a x^5 \sqrt{a+b x^2} (2 A b-a B)}{32 b}+\frac{B x^5 \left(a+b x^2\right)^{5/2}}{10 b}",1,"(-3*a^3*(2*A*b - a*B)*x*Sqrt[a + b*x^2])/(256*b^3) + (a^2*(2*A*b - a*B)*x^3*Sqrt[a + b*x^2])/(128*b^2) + (a*(2*A*b - a*B)*x^5*Sqrt[a + b*x^2])/(32*b) + ((2*A*b - a*B)*x^5*(a + b*x^2)^(3/2))/(16*b) + (B*x^5*(a + b*x^2)^(5/2))/(10*b) + (3*a^4*(2*A*b - a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*b^(7/2))","A",7,5,22,0.2273,1,"{459, 279, 321, 217, 206}"
523,1,73,0,0.0592361,"\int x^3 \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[x^3*(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^{7/2} (A b-2 a B)}{7 b^3}-\frac{a \left(a+b x^2\right)^{5/2} (A b-a B)}{5 b^3}+\frac{B \left(a+b x^2\right)^{9/2}}{9 b^3}","\frac{\left(a+b x^2\right)^{7/2} (A b-2 a B)}{7 b^3}-\frac{a \left(a+b x^2\right)^{5/2} (A b-a B)}{5 b^3}+\frac{B \left(a+b x^2\right)^{9/2}}{9 b^3}",1,"-(a*(A*b - a*B)*(a + b*x^2)^(5/2))/(5*b^3) + ((A*b - 2*a*B)*(a + b*x^2)^(7/2))/(7*b^3) + (B*(a + b*x^2)^(9/2))/(9*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
524,1,155,0,0.0673113,"\int x^2 \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[x^2*(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{a^2 x \sqrt{a+b x^2} (8 A b-3 a B)}{128 b^2}-\frac{a^3 (8 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}+\frac{a x^3 \sqrt{a+b x^2} (8 A b-3 a B)}{64 b}+\frac{x^3 \left(a+b x^2\right)^{3/2} (8 A b-3 a B)}{48 b}+\frac{B x^3 \left(a+b x^2\right)^{5/2}}{8 b}","\frac{a^2 x \sqrt{a+b x^2} (8 A b-3 a B)}{128 b^2}-\frac{a^3 (8 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{5/2}}+\frac{a x^3 \sqrt{a+b x^2} (8 A b-3 a B)}{64 b}+\frac{x^3 \left(a+b x^2\right)^{3/2} (8 A b-3 a B)}{48 b}+\frac{B x^3 \left(a+b x^2\right)^{5/2}}{8 b}",1,"(a^2*(8*A*b - 3*a*B)*x*Sqrt[a + b*x^2])/(128*b^2) + (a*(8*A*b - 3*a*B)*x^3*Sqrt[a + b*x^2])/(64*b) + ((8*A*b - 3*a*B)*x^3*(a + b*x^2)^(3/2))/(48*b) + (B*x^3*(a + b*x^2)^(5/2))/(8*b) - (a^3*(8*A*b - 3*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(5/2))","A",6,5,22,0.2273,1,"{459, 279, 321, 217, 206}"
525,1,46,0,0.0324109,"\int x \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[x*(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^{5/2} (A b-a B)}{5 b^2}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b^2}","\frac{\left(a+b x^2\right)^{5/2} (A b-a B)}{5 b^2}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b^2}",1,"((A*b - a*B)*(a + b*x^2)^(5/2))/(5*b^2) + (B*(a + b*x^2)^(7/2))/(7*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
526,1,118,0,0.040886,"\int \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{a^2 (6 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}+\frac{x \left(a+b x^2\right)^{3/2} (6 A b-a B)}{24 b}+\frac{a x \sqrt{a+b x^2} (6 A b-a B)}{16 b}+\frac{B x \left(a+b x^2\right)^{5/2}}{6 b}","\frac{a^2 (6 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{3/2}}+\frac{x \left(a+b x^2\right)^{3/2} (6 A b-a B)}{24 b}+\frac{a x \sqrt{a+b x^2} (6 A b-a B)}{16 b}+\frac{B x \left(a+b x^2\right)^{5/2}}{6 b}",1,"(a*(6*A*b - a*B)*x*Sqrt[a + b*x^2])/(16*b) + ((6*A*b - a*B)*x*(a + b*x^2)^(3/2))/(24*b) + (B*x*(a + b*x^2)^(5/2))/(6*b) + (a^2*(6*A*b - a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(3/2))","A",5,4,19,0.2105,1,"{388, 195, 217, 206}"
527,1,76,0,0.0533293,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x,x]","-a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{1}{3} A \left(a+b x^2\right)^{3/2}+a A \sqrt{a+b x^2}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b}","-a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{1}{3} A \left(a+b x^2\right)^{3/2}+a A \sqrt{a+b x^2}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b}",1,"a*A*Sqrt[a + b*x^2] + (A*(a + b*x^2)^(3/2))/3 + (B*(a + b*x^2)^(5/2))/(5*b) - a^(3/2)*A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",6,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
528,1,109,0,0.0411167,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^2} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^2,x]","\frac{x \left(a+b x^2\right)^{3/2} (a B+4 A b)}{4 a}+\frac{3}{8} x \sqrt{a+b x^2} (a B+4 A b)+\frac{3 a (a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}-\frac{A \left(a+b x^2\right)^{5/2}}{a x}","\frac{x \left(a+b x^2\right)^{3/2} (a B+4 A b)}{4 a}+\frac{3}{8} x \sqrt{a+b x^2} (a B+4 A b)+\frac{3 a (a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 \sqrt{b}}-\frac{A \left(a+b x^2\right)^{5/2}}{a x}",1,"(3*(4*A*b + a*B)*x*Sqrt[a + b*x^2])/8 + ((4*A*b + a*B)*x*(a + b*x^2)^(3/2))/(4*a) - (A*(a + b*x^2)^(5/2))/(a*x) + (3*a*(4*A*b + a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*Sqrt[b])","A",5,4,22,0.1818,1,"{453, 195, 217, 206}"
529,1,110,0,0.0801891,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^3} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^3,x]","\frac{\left(a+b x^2\right)^{3/2} (2 a B+3 A b)}{6 a}+\frac{1}{2} \sqrt{a+b x^2} (2 a B+3 A b)-\frac{1}{2} \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{A \left(a+b x^2\right)^{5/2}}{2 a x^2}","\frac{\left(a+b x^2\right)^{3/2} (2 a B+3 A b)}{6 a}+\frac{1}{2} \sqrt{a+b x^2} (2 a B+3 A b)-\frac{1}{2} \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{A \left(a+b x^2\right)^{5/2}}{2 a x^2}",1,"((3*A*b + 2*a*B)*Sqrt[a + b*x^2])/2 + ((3*A*b + 2*a*B)*(a + b*x^2)^(3/2))/(6*a) - (A*(a + b*x^2)^(5/2))/(2*a*x^2) - (Sqrt[a]*(3*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",6,5,22,0.2273,1,"{446, 78, 50, 63, 208}"
530,1,119,0,0.0472946,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^4} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^4,x]","-\frac{\left(a+b x^2\right)^{3/2} (3 a B+2 A b)}{3 a x}+\frac{b x \sqrt{a+b x^2} (3 a B+2 A b)}{2 a}+\frac{1}{2} \sqrt{b} (3 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{A \left(a+b x^2\right)^{5/2}}{3 a x^3}","-\frac{\left(a+b x^2\right)^{3/2} (3 a B+2 A b)}{3 a x}+\frac{b x \sqrt{a+b x^2} (3 a B+2 A b)}{2 a}+\frac{1}{2} \sqrt{b} (3 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{A \left(a+b x^2\right)^{5/2}}{3 a x^3}",1,"(b*(2*A*b + 3*a*B)*x*Sqrt[a + b*x^2])/(2*a) - ((2*A*b + 3*a*B)*(a + b*x^2)^(3/2))/(3*a*x) - (A*(a + b*x^2)^(5/2))/(3*a*x^3) + (Sqrt[b]*(2*A*b + 3*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",5,5,22,0.2273,1,"{453, 277, 195, 217, 206}"
531,1,115,0,0.0839492,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^5} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^5,x]","-\frac{\left(a+b x^2\right)^{3/2} (4 a B+A b)}{8 a x^2}+\frac{3 b \sqrt{a+b x^2} (4 a B+A b)}{8 a}-\frac{3 b (4 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{A \left(a+b x^2\right)^{5/2}}{4 a x^4}","-\frac{\left(a+b x^2\right)^{3/2} (4 a B+A b)}{8 a x^2}+\frac{3 b \sqrt{a+b x^2} (4 a B+A b)}{8 a}-\frac{3 b (4 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{A \left(a+b x^2\right)^{5/2}}{4 a x^4}",1,"(3*b*(A*b + 4*a*B)*Sqrt[a + b*x^2])/(8*a) - ((A*b + 4*a*B)*(a + b*x^2)^(3/2))/(8*a*x^2) - (A*(a + b*x^2)^(5/2))/(4*a*x^4) - (3*b*(A*b + 4*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*Sqrt[a])","A",6,6,22,0.2727,1,"{446, 78, 47, 50, 63, 208}"
532,1,86,0,0.0346065,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^6} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^6,x]","-\frac{A \left(a+b x^2\right)^{5/2}}{5 a x^5}+b^{3/2} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{B \left(a+b x^2\right)^{3/2}}{3 x^3}-\frac{b B \sqrt{a+b x^2}}{x}","-\frac{A \left(a+b x^2\right)^{5/2}}{5 a x^5}+b^{3/2} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{B \left(a+b x^2\right)^{3/2}}{3 x^3}-\frac{b B \sqrt{a+b x^2}}{x}",1,"-((b*B*Sqrt[a + b*x^2])/x) - (B*(a + b*x^2)^(3/2))/(3*x^3) - (A*(a + b*x^2)^(5/2))/(5*a*x^5) + b^(3/2)*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",5,4,22,0.1818,1,"{451, 277, 217, 206}"
533,1,120,0,0.0961466,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^7} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^7,x]","\frac{b^2 (A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}+\frac{\left(a+b x^2\right)^{3/2} (A b-6 a B)}{24 a x^4}+\frac{b \sqrt{a+b x^2} (A b-6 a B)}{16 a x^2}-\frac{A \left(a+b x^2\right)^{5/2}}{6 a x^6}","\frac{b^2 (A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}+\frac{\left(a+b x^2\right)^{3/2} (A b-6 a B)}{24 a x^4}+\frac{b \sqrt{a+b x^2} (A b-6 a B)}{16 a x^2}-\frac{A \left(a+b x^2\right)^{5/2}}{6 a x^6}",1,"(b*(A*b - 6*a*B)*Sqrt[a + b*x^2])/(16*a*x^2) + ((A*b - 6*a*B)*(a + b*x^2)^(3/2))/(24*a*x^4) - (A*(a + b*x^2)^(5/2))/(6*a*x^6) + (b^2*(A*b - 6*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(3/2))","A",6,5,22,0.2273,1,"{446, 78, 47, 63, 208}"
534,1,53,0,0.0221359,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^8} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^8,x]","\frac{\left(a+b x^2\right)^{5/2} (2 A b-7 a B)}{35 a^2 x^5}-\frac{A \left(a+b x^2\right)^{5/2}}{7 a x^7}","\frac{\left(a+b x^2\right)^{5/2} (2 A b-7 a B)}{35 a^2 x^5}-\frac{A \left(a+b x^2\right)^{5/2}}{7 a x^7}",1,"-(A*(a + b*x^2)^(5/2))/(7*a*x^7) + ((2*A*b - 7*a*B)*(a + b*x^2)^(5/2))/(35*a^2*x^5)","A",2,2,22,0.09091,1,"{453, 264}"
535,1,156,0,0.1230871,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^9} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^9,x]","\frac{b^2 \sqrt{a+b x^2} (3 A b-8 a B)}{128 a^2 x^2}-\frac{b^3 (3 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{5/2}}+\frac{b \sqrt{a+b x^2} (3 A b-8 a B)}{64 a x^4}+\frac{\left(a+b x^2\right)^{3/2} (3 A b-8 a B)}{48 a x^6}-\frac{A \left(a+b x^2\right)^{5/2}}{8 a x^8}","\frac{b^2 \sqrt{a+b x^2} (3 A b-8 a B)}{128 a^2 x^2}-\frac{b^3 (3 A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{5/2}}+\frac{b \sqrt{a+b x^2} (3 A b-8 a B)}{64 a x^4}+\frac{\left(a+b x^2\right)^{3/2} (3 A b-8 a B)}{48 a x^6}-\frac{A \left(a+b x^2\right)^{5/2}}{8 a x^8}",1,"(b*(3*A*b - 8*a*B)*Sqrt[a + b*x^2])/(64*a*x^4) + (b^2*(3*A*b - 8*a*B)*Sqrt[a + b*x^2])/(128*a^2*x^2) + ((3*A*b - 8*a*B)*(a + b*x^2)^(3/2))/(48*a*x^6) - (A*(a + b*x^2)^(5/2))/(8*a*x^8) - (b^3*(3*A*b - 8*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(5/2))","A",7,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
536,1,84,0,0.0361016,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^{10}} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^10,x]","-\frac{2 b \left(a+b x^2\right)^{5/2} (4 A b-9 a B)}{315 a^3 x^5}+\frac{\left(a+b x^2\right)^{5/2} (4 A b-9 a B)}{63 a^2 x^7}-\frac{A \left(a+b x^2\right)^{5/2}}{9 a x^9}","-\frac{2 b \left(a+b x^2\right)^{5/2} (4 A b-9 a B)}{315 a^3 x^5}+\frac{\left(a+b x^2\right)^{5/2} (4 A b-9 a B)}{63 a^2 x^7}-\frac{A \left(a+b x^2\right)^{5/2}}{9 a x^9}",1,"-(A*(a + b*x^2)^(5/2))/(9*a*x^9) + ((4*A*b - 9*a*B)*(a + b*x^2)^(5/2))/(63*a^2*x^7) - (2*b*(4*A*b - 9*a*B)*(a + b*x^2)^(5/2))/(315*a^3*x^5)","A",3,3,22,0.1364,1,"{453, 271, 264}"
537,1,184,0,0.1455622,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{x^{11}} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/x^11,x]","-\frac{3 b^3 \sqrt{a+b x^2} (A b-2 a B)}{256 a^3 x^2}+\frac{b^2 \sqrt{a+b x^2} (A b-2 a B)}{128 a^2 x^4}+\frac{3 b^4 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{7/2}}+\frac{b \sqrt{a+b x^2} (A b-2 a B)}{32 a x^6}+\frac{\left(a+b x^2\right)^{3/2} (A b-2 a B)}{16 a x^8}-\frac{A \left(a+b x^2\right)^{5/2}}{10 a x^{10}}","-\frac{3 b^3 \sqrt{a+b x^2} (A b-2 a B)}{256 a^3 x^2}+\frac{b^2 \sqrt{a+b x^2} (A b-2 a B)}{128 a^2 x^4}+\frac{3 b^4 (A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{7/2}}+\frac{b \sqrt{a+b x^2} (A b-2 a B)}{32 a x^6}+\frac{\left(a+b x^2\right)^{3/2} (A b-2 a B)}{16 a x^8}-\frac{A \left(a+b x^2\right)^{5/2}}{10 a x^{10}}",1,"(b*(A*b - 2*a*B)*Sqrt[a + b*x^2])/(32*a*x^6) + (b^2*(A*b - 2*a*B)*Sqrt[a + b*x^2])/(128*a^2*x^4) - (3*b^3*(A*b - 2*a*B)*Sqrt[a + b*x^2])/(256*a^3*x^2) + ((A*b - 2*a*B)*(a + b*x^2)^(3/2))/(16*a*x^8) - (A*(a + b*x^2)^(5/2))/(10*a*x^10) + (3*b^4*(A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*a^(7/2))","A",8,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
538,1,103,0,0.0763276,"\int x^5 \left(a+b x^2\right)^{5/2} \left(A+B x^2\right) \, dx","Int[x^5*(a + b*x^2)^(5/2)*(A + B*x^2),x]","\frac{a^2 \left(a+b x^2\right)^{7/2} (A b-a B)}{7 b^4}+\frac{\left(a+b x^2\right)^{11/2} (A b-3 a B)}{11 b^4}-\frac{a \left(a+b x^2\right)^{9/2} (2 A b-3 a B)}{9 b^4}+\frac{B \left(a+b x^2\right)^{13/2}}{13 b^4}","\frac{a^2 \left(a+b x^2\right)^{7/2} (A b-a B)}{7 b^4}+\frac{\left(a+b x^2\right)^{11/2} (A b-3 a B)}{11 b^4}-\frac{a \left(a+b x^2\right)^{9/2} (2 A b-3 a B)}{9 b^4}+\frac{B \left(a+b x^2\right)^{13/2}}{13 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x^2)^(7/2))/(7*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x^2)^(9/2))/(9*b^4) + ((A*b - 3*a*B)*(a + b*x^2)^(11/2))/(11*b^4) + (B*(a + b*x^2)^(13/2))/(13*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
539,1,221,0,0.1027895,"\int x^4 \left(a+b x^2\right)^{5/2} \left(A+B x^2\right) \, dx","Int[x^4*(a + b*x^2)^(5/2)*(A + B*x^2),x]","-\frac{a^4 x \sqrt{a+b x^2} (12 A b-5 a B)}{1024 b^3}+\frac{a^3 x^3 \sqrt{a+b x^2} (12 A b-5 a B)}{1536 b^2}+\frac{a^5 (12 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{1024 b^{7/2}}+\frac{a^2 x^5 \sqrt{a+b x^2} (12 A b-5 a B)}{384 b}+\frac{a x^5 \left(a+b x^2\right)^{3/2} (12 A b-5 a B)}{192 b}+\frac{x^5 \left(a+b x^2\right)^{5/2} (12 A b-5 a B)}{120 b}+\frac{B x^5 \left(a+b x^2\right)^{7/2}}{12 b}","-\frac{a^4 x \sqrt{a+b x^2} (12 A b-5 a B)}{1024 b^3}+\frac{a^3 x^3 \sqrt{a+b x^2} (12 A b-5 a B)}{1536 b^2}+\frac{a^5 (12 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{1024 b^{7/2}}+\frac{a^2 x^5 \sqrt{a+b x^2} (12 A b-5 a B)}{384 b}+\frac{a x^5 \left(a+b x^2\right)^{3/2} (12 A b-5 a B)}{192 b}+\frac{x^5 \left(a+b x^2\right)^{5/2} (12 A b-5 a B)}{120 b}+\frac{B x^5 \left(a+b x^2\right)^{7/2}}{12 b}",1,"-(a^4*(12*A*b - 5*a*B)*x*Sqrt[a + b*x^2])/(1024*b^3) + (a^3*(12*A*b - 5*a*B)*x^3*Sqrt[a + b*x^2])/(1536*b^2) + (a^2*(12*A*b - 5*a*B)*x^5*Sqrt[a + b*x^2])/(384*b) + (a*(12*A*b - 5*a*B)*x^5*(a + b*x^2)^(3/2))/(192*b) + ((12*A*b - 5*a*B)*x^5*(a + b*x^2)^(5/2))/(120*b) + (B*x^5*(a + b*x^2)^(7/2))/(12*b) + (a^5*(12*A*b - 5*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(1024*b^(7/2))","A",8,5,22,0.2273,1,"{459, 279, 321, 217, 206}"
540,1,73,0,0.0556794,"\int x^3 \left(a+b x^2\right)^{5/2} \left(A+B x^2\right) \, dx","Int[x^3*(a + b*x^2)^(5/2)*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^{9/2} (A b-2 a B)}{9 b^3}-\frac{a \left(a+b x^2\right)^{7/2} (A b-a B)}{7 b^3}+\frac{B \left(a+b x^2\right)^{11/2}}{11 b^3}","\frac{\left(a+b x^2\right)^{9/2} (A b-2 a B)}{9 b^3}-\frac{a \left(a+b x^2\right)^{7/2} (A b-a B)}{7 b^3}+\frac{B \left(a+b x^2\right)^{11/2}}{11 b^3}",1,"-(a*(A*b - a*B)*(a + b*x^2)^(7/2))/(7*b^3) + ((A*b - 2*a*B)*(a + b*x^2)^(9/2))/(9*b^3) + (B*(a + b*x^2)^(11/2))/(11*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
541,1,188,0,0.08813,"\int x^2 \left(a+b x^2\right)^{5/2} \left(A+B x^2\right) \, dx","Int[x^2*(a + b*x^2)^(5/2)*(A + B*x^2),x]","\frac{a^3 x \sqrt{a+b x^2} (10 A b-3 a B)}{256 b^2}-\frac{a^4 (10 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}+\frac{a^2 x^3 \sqrt{a+b x^2} (10 A b-3 a B)}{128 b}+\frac{a x^3 \left(a+b x^2\right)^{3/2} (10 A b-3 a B)}{96 b}+\frac{x^3 \left(a+b x^2\right)^{5/2} (10 A b-3 a B)}{80 b}+\frac{B x^3 \left(a+b x^2\right)^{7/2}}{10 b}","\frac{a^3 x \sqrt{a+b x^2} (10 A b-3 a B)}{256 b^2}-\frac{a^4 (10 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{256 b^{5/2}}+\frac{a^2 x^3 \sqrt{a+b x^2} (10 A b-3 a B)}{128 b}+\frac{a x^3 \left(a+b x^2\right)^{3/2} (10 A b-3 a B)}{96 b}+\frac{x^3 \left(a+b x^2\right)^{5/2} (10 A b-3 a B)}{80 b}+\frac{B x^3 \left(a+b x^2\right)^{7/2}}{10 b}",1,"(a^3*(10*A*b - 3*a*B)*x*Sqrt[a + b*x^2])/(256*b^2) + (a^2*(10*A*b - 3*a*B)*x^3*Sqrt[a + b*x^2])/(128*b) + (a*(10*A*b - 3*a*B)*x^3*(a + b*x^2)^(3/2))/(96*b) + ((10*A*b - 3*a*B)*x^3*(a + b*x^2)^(5/2))/(80*b) + (B*x^3*(a + b*x^2)^(7/2))/(10*b) - (a^4*(10*A*b - 3*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(256*b^(5/2))","A",7,5,22,0.2273,1,"{459, 279, 321, 217, 206}"
542,1,46,0,0.0345383,"\int x \left(a+b x^2\right)^{5/2} \left(A+B x^2\right) \, dx","Int[x*(a + b*x^2)^(5/2)*(A + B*x^2),x]","\frac{\left(a+b x^2\right)^{7/2} (A b-a B)}{7 b^2}+\frac{B \left(a+b x^2\right)^{9/2}}{9 b^2}","\frac{\left(a+b x^2\right)^{7/2} (A b-a B)}{7 b^2}+\frac{B \left(a+b x^2\right)^{9/2}}{9 b^2}",1,"((A*b - a*B)*(a + b*x^2)^(7/2))/(7*b^2) + (B*(a + b*x^2)^(9/2))/(9*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
543,1,149,0,0.0541756,"\int \left(a+b x^2\right)^{5/2} \left(A+B x^2\right) \, dx","Int[(a + b*x^2)^(5/2)*(A + B*x^2),x]","\frac{5 a^3 (8 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}+\frac{5 a^2 x \sqrt{a+b x^2} (8 A b-a B)}{128 b}+\frac{x \left(a+b x^2\right)^{5/2} (8 A b-a B)}{48 b}+\frac{5 a x \left(a+b x^2\right)^{3/2} (8 A b-a B)}{192 b}+\frac{B x \left(a+b x^2\right)^{7/2}}{8 b}","\frac{5 a^3 (8 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{128 b^{3/2}}+\frac{5 a^2 x \sqrt{a+b x^2} (8 A b-a B)}{128 b}+\frac{x \left(a+b x^2\right)^{5/2} (8 A b-a B)}{48 b}+\frac{5 a x \left(a+b x^2\right)^{3/2} (8 A b-a B)}{192 b}+\frac{B x \left(a+b x^2\right)^{7/2}}{8 b}",1,"(5*a^2*(8*A*b - a*B)*x*Sqrt[a + b*x^2])/(128*b) + (5*a*(8*A*b - a*B)*x*(a + b*x^2)^(3/2))/(192*b) + ((8*A*b - a*B)*x*(a + b*x^2)^(5/2))/(48*b) + (B*x*(a + b*x^2)^(7/2))/(8*b) + (5*a^3*(8*A*b - a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(128*b^(3/2))","A",6,4,19,0.2105,1,"{388, 195, 217, 206}"
544,1,95,0,0.0643206,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x,x]","a^2 A \sqrt{a+b x^2}-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{1}{5} A \left(a+b x^2\right)^{5/2}+\frac{1}{3} a A \left(a+b x^2\right)^{3/2}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b}","a^2 A \sqrt{a+b x^2}-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{1}{5} A \left(a+b x^2\right)^{5/2}+\frac{1}{3} a A \left(a+b x^2\right)^{3/2}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b}",1,"a^2*A*Sqrt[a + b*x^2] + (a*A*(a + b*x^2)^(3/2))/3 + (A*(a + b*x^2)^(5/2))/5 + (B*(a + b*x^2)^(7/2))/(7*b) - a^(5/2)*A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]]","A",7,5,22,0.2273,1,"{446, 80, 50, 63, 208}"
545,1,136,0,0.0532958,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^2} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^2,x]","\frac{5 a^2 (a B+6 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{x \left(a+b x^2\right)^{5/2} (a B+6 A b)}{6 a}+\frac{5}{24} x \left(a+b x^2\right)^{3/2} (a B+6 A b)+\frac{5}{16} a x \sqrt{a+b x^2} (a B+6 A b)-\frac{A \left(a+b x^2\right)^{7/2}}{a x}","\frac{5 a^2 (a B+6 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 \sqrt{b}}+\frac{x \left(a+b x^2\right)^{5/2} (a B+6 A b)}{6 a}+\frac{5}{24} x \left(a+b x^2\right)^{3/2} (a B+6 A b)+\frac{5}{16} a x \sqrt{a+b x^2} (a B+6 A b)-\frac{A \left(a+b x^2\right)^{7/2}}{a x}",1,"(5*a*(6*A*b + a*B)*x*Sqrt[a + b*x^2])/16 + (5*(6*A*b + a*B)*x*(a + b*x^2)^(3/2))/24 + ((6*A*b + a*B)*x*(a + b*x^2)^(5/2))/(6*a) - (A*(a + b*x^2)^(7/2))/(a*x) + (5*a^2*(6*A*b + a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*Sqrt[b])","A",6,4,22,0.1818,1,"{453, 195, 217, 206}"
546,1,135,0,0.1003379,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^3} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^3,x]","-\frac{1}{2} a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{\left(a+b x^2\right)^{5/2} (2 a B+5 A b)}{10 a}+\frac{1}{6} \left(a+b x^2\right)^{3/2} (2 a B+5 A b)+\frac{1}{2} a \sqrt{a+b x^2} (2 a B+5 A b)-\frac{A \left(a+b x^2\right)^{7/2}}{2 a x^2}","-\frac{1}{2} a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)+\frac{\left(a+b x^2\right)^{5/2} (2 a B+5 A b)}{10 a}+\frac{1}{6} \left(a+b x^2\right)^{3/2} (2 a B+5 A b)+\frac{1}{2} a \sqrt{a+b x^2} (2 a B+5 A b)-\frac{A \left(a+b x^2\right)^{7/2}}{2 a x^2}",1,"(a*(5*A*b + 2*a*B)*Sqrt[a + b*x^2])/2 + ((5*A*b + 2*a*B)*(a + b*x^2)^(3/2))/6 + ((5*A*b + 2*a*B)*(a + b*x^2)^(5/2))/(10*a) - (A*(a + b*x^2)^(7/2))/(2*a*x^2) - (a^(3/2)*(5*A*b + 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/2","A",7,5,22,0.2273,1,"{446, 78, 50, 63, 208}"
547,1,146,0,0.0600457,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^4} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^4,x]","-\frac{\left(a+b x^2\right)^{5/2} (3 a B+4 A b)}{3 a x}+\frac{5 b x \left(a+b x^2\right)^{3/2} (3 a B+4 A b)}{12 a}+\frac{5}{8} b x \sqrt{a+b x^2} (3 a B+4 A b)+\frac{5}{8} a \sqrt{b} (3 a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{A \left(a+b x^2\right)^{7/2}}{3 a x^3}","-\frac{\left(a+b x^2\right)^{5/2} (3 a B+4 A b)}{3 a x}+\frac{5 b x \left(a+b x^2\right)^{3/2} (3 a B+4 A b)}{12 a}+\frac{5}{8} b x \sqrt{a+b x^2} (3 a B+4 A b)+\frac{5}{8} a \sqrt{b} (3 a B+4 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{A \left(a+b x^2\right)^{7/2}}{3 a x^3}",1,"(5*b*(4*A*b + 3*a*B)*x*Sqrt[a + b*x^2])/8 + (5*b*(4*A*b + 3*a*B)*x*(a + b*x^2)^(3/2))/(12*a) - ((4*A*b + 3*a*B)*(a + b*x^2)^(5/2))/(3*a*x) - (A*(a + b*x^2)^(7/2))/(3*a*x^3) + (5*a*Sqrt[b]*(4*A*b + 3*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/8","A",6,5,22,0.2273,1,"{453, 277, 195, 217, 206}"
548,1,143,0,0.1011503,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^5} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^5,x]","-\frac{\left(a+b x^2\right)^{5/2} (4 a B+3 A b)}{8 a x^2}+\frac{5 b \left(a+b x^2\right)^{3/2} (4 a B+3 A b)}{24 a}+\frac{5}{8} b \sqrt{a+b x^2} (4 a B+3 A b)-\frac{5}{8} \sqrt{a} b (4 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{A \left(a+b x^2\right)^{7/2}}{4 a x^4}","-\frac{\left(a+b x^2\right)^{5/2} (4 a B+3 A b)}{8 a x^2}+\frac{5 b \left(a+b x^2\right)^{3/2} (4 a B+3 A b)}{24 a}+\frac{5}{8} b \sqrt{a+b x^2} (4 a B+3 A b)-\frac{5}{8} \sqrt{a} b (4 a B+3 A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)-\frac{A \left(a+b x^2\right)^{7/2}}{4 a x^4}",1,"(5*b*(3*A*b + 4*a*B)*Sqrt[a + b*x^2])/8 + (5*b*(3*A*b + 4*a*B)*(a + b*x^2)^(3/2))/(24*a) - ((3*A*b + 4*a*B)*(a + b*x^2)^(5/2))/(8*a*x^2) - (A*(a + b*x^2)^(7/2))/(4*a*x^4) - (5*Sqrt[a]*b*(3*A*b + 4*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/8","A",7,6,22,0.2727,1,"{446, 78, 47, 50, 63, 208}"
549,1,152,0,0.0624304,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^6} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^6,x]","\frac{b^2 x \sqrt{a+b x^2} (5 a B+2 A b)}{2 a}+\frac{1}{2} b^{3/2} (5 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2} (5 a B+2 A b)}{15 a x^3}-\frac{b \left(a+b x^2\right)^{3/2} (5 a B+2 A b)}{3 a x}-\frac{A \left(a+b x^2\right)^{7/2}}{5 a x^5}","\frac{b^2 x \sqrt{a+b x^2} (5 a B+2 A b)}{2 a}+\frac{1}{2} b^{3/2} (5 a B+2 A b) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{\left(a+b x^2\right)^{5/2} (5 a B+2 A b)}{15 a x^3}-\frac{b \left(a+b x^2\right)^{3/2} (5 a B+2 A b)}{3 a x}-\frac{A \left(a+b x^2\right)^{7/2}}{5 a x^5}",1,"(b^2*(2*A*b + 5*a*B)*x*Sqrt[a + b*x^2])/(2*a) - (b*(2*A*b + 5*a*B)*(a + b*x^2)^(3/2))/(3*a*x) - ((2*A*b + 5*a*B)*(a + b*x^2)^(5/2))/(15*a*x^3) - (A*(a + b*x^2)^(7/2))/(5*a*x^5) + (b^(3/2)*(2*A*b + 5*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/2","A",6,5,22,0.2273,1,"{453, 277, 195, 217, 206}"
550,1,149,0,0.1103621,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^7} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^7,x]","\frac{5 b^2 \sqrt{a+b x^2} (6 a B+A b)}{16 a}-\frac{5 b^2 (6 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{\left(a+b x^2\right)^{5/2} (6 a B+A b)}{24 a x^4}-\frac{5 b \left(a+b x^2\right)^{3/2} (6 a B+A b)}{48 a x^2}-\frac{A \left(a+b x^2\right)^{7/2}}{6 a x^6}","\frac{5 b^2 \sqrt{a+b x^2} (6 a B+A b)}{16 a}-\frac{5 b^2 (6 a B+A b) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{\left(a+b x^2\right)^{5/2} (6 a B+A b)}{24 a x^4}-\frac{5 b \left(a+b x^2\right)^{3/2} (6 a B+A b)}{48 a x^2}-\frac{A \left(a+b x^2\right)^{7/2}}{6 a x^6}",1,"(5*b^2*(A*b + 6*a*B)*Sqrt[a + b*x^2])/(16*a) - (5*b*(A*b + 6*a*B)*(a + b*x^2)^(3/2))/(48*a*x^2) - ((A*b + 6*a*B)*(a + b*x^2)^(5/2))/(24*a*x^4) - (A*(a + b*x^2)^(7/2))/(6*a*x^6) - (5*b^2*(A*b + 6*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*Sqrt[a])","A",7,6,22,0.2727,1,"{446, 78, 47, 50, 63, 208}"
551,1,108,0,0.0459612,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^8} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^8,x]","-\frac{A \left(a+b x^2\right)^{7/2}}{7 a x^7}-\frac{b^2 B \sqrt{a+b x^2}}{x}+b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{B \left(a+b x^2\right)^{5/2}}{5 x^5}-\frac{b B \left(a+b x^2\right)^{3/2}}{3 x^3}","-\frac{A \left(a+b x^2\right)^{7/2}}{7 a x^7}-\frac{b^2 B \sqrt{a+b x^2}}{x}+b^{5/2} B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)-\frac{B \left(a+b x^2\right)^{5/2}}{5 x^5}-\frac{b B \left(a+b x^2\right)^{3/2}}{3 x^3}",1,"-((b^2*B*Sqrt[a + b*x^2])/x) - (b*B*(a + b*x^2)^(3/2))/(3*x^3) - (B*(a + b*x^2)^(5/2))/(5*x^5) - (A*(a + b*x^2)^(7/2))/(7*a*x^7) + b^(5/2)*B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]]","A",6,4,22,0.1818,1,"{451, 277, 217, 206}"
552,1,152,0,0.11766,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^9} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^9,x]","\frac{5 b^3 (A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}+\frac{5 b^2 \sqrt{a+b x^2} (A b-8 a B)}{128 a x^2}+\frac{\left(a+b x^2\right)^{5/2} (A b-8 a B)}{48 a x^6}+\frac{5 b \left(a+b x^2\right)^{3/2} (A b-8 a B)}{192 a x^4}-\frac{A \left(a+b x^2\right)^{7/2}}{8 a x^8}","\frac{5 b^3 (A b-8 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}+\frac{5 b^2 \sqrt{a+b x^2} (A b-8 a B)}{128 a x^2}+\frac{\left(a+b x^2\right)^{5/2} (A b-8 a B)}{48 a x^6}+\frac{5 b \left(a+b x^2\right)^{3/2} (A b-8 a B)}{192 a x^4}-\frac{A \left(a+b x^2\right)^{7/2}}{8 a x^8}",1,"(5*b^2*(A*b - 8*a*B)*Sqrt[a + b*x^2])/(128*a*x^2) + (5*b*(A*b - 8*a*B)*(a + b*x^2)^(3/2))/(192*a*x^4) + ((A*b - 8*a*B)*(a + b*x^2)^(5/2))/(48*a*x^6) - (A*(a + b*x^2)^(7/2))/(8*a*x^8) + (5*b^3*(A*b - 8*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(128*a^(3/2))","A",7,5,22,0.2273,1,"{446, 78, 47, 63, 208}"
553,1,53,0,0.0215579,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^{10}} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^10,x]","\frac{\left(a+b x^2\right)^{7/2} (2 A b-9 a B)}{63 a^2 x^7}-\frac{A \left(a+b x^2\right)^{7/2}}{9 a x^9}","\frac{\left(a+b x^2\right)^{7/2} (2 A b-9 a B)}{63 a^2 x^7}-\frac{A \left(a+b x^2\right)^{7/2}}{9 a x^9}",1,"-(A*(a + b*x^2)^(7/2))/(9*a*x^9) + ((2*A*b - 9*a*B)*(a + b*x^2)^(7/2))/(63*a^2*x^7)","A",2,2,22,0.09091,1,"{453, 264}"
554,1,189,0,0.1480229,"\int \frac{\left(a+b x^2\right)^{5/2} \left(A+B x^2\right)}{x^{11}} \, dx","Int[((a + b*x^2)^(5/2)*(A + B*x^2))/x^11,x]","\frac{b^3 \sqrt{a+b x^2} (3 A b-10 a B)}{256 a^2 x^2}-\frac{b^4 (3 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{5/2}}+\frac{b^2 \sqrt{a+b x^2} (3 A b-10 a B)}{128 a x^4}+\frac{b \left(a+b x^2\right)^{3/2} (3 A b-10 a B)}{96 a x^6}+\frac{\left(a+b x^2\right)^{5/2} (3 A b-10 a B)}{80 a x^8}-\frac{A \left(a+b x^2\right)^{7/2}}{10 a x^{10}}","\frac{b^3 \sqrt{a+b x^2} (3 A b-10 a B)}{256 a^2 x^2}-\frac{b^4 (3 A b-10 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{256 a^{5/2}}+\frac{b^2 \sqrt{a+b x^2} (3 A b-10 a B)}{128 a x^4}+\frac{b \left(a+b x^2\right)^{3/2} (3 A b-10 a B)}{96 a x^6}+\frac{\left(a+b x^2\right)^{5/2} (3 A b-10 a B)}{80 a x^8}-\frac{A \left(a+b x^2\right)^{7/2}}{10 a x^{10}}",1,"(b^2*(3*A*b - 10*a*B)*Sqrt[a + b*x^2])/(128*a*x^4) + (b^3*(3*A*b - 10*a*B)*Sqrt[a + b*x^2])/(256*a^2*x^2) + (b*(3*A*b - 10*a*B)*(a + b*x^2)^(3/2))/(96*a*x^6) + ((3*A*b - 10*a*B)*(a + b*x^2)^(5/2))/(80*a*x^8) - (A*(a + b*x^2)^(7/2))/(10*a*x^10) - (b^4*(3*A*b - 10*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(256*a^(5/2))","A",8,6,22,0.2727,1,"{446, 78, 47, 51, 63, 208}"
555,1,100,0,0.0760649,"\int \frac{x^5 \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^5*(A + B*x^2))/Sqrt[a + b*x^2],x]","\frac{a^2 \sqrt{a+b x^2} (A b-a B)}{b^4}+\frac{\left(a+b x^2\right)^{5/2} (A b-3 a B)}{5 b^4}-\frac{a \left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{3 b^4}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b^4}","\frac{a^2 \sqrt{a+b x^2} (A b-a B)}{b^4}+\frac{\left(a+b x^2\right)^{5/2} (A b-3 a B)}{5 b^4}-\frac{a \left(a+b x^2\right)^{3/2} (2 A b-3 a B)}{3 b^4}+\frac{B \left(a+b x^2\right)^{7/2}}{7 b^4}",1,"(a^2*(A*b - a*B)*Sqrt[a + b*x^2])/b^4 - (a*(2*A*b - 3*a*B)*(a + b*x^2)^(3/2))/(3*b^4) + ((A*b - 3*a*B)*(a + b*x^2)^(5/2))/(5*b^4) + (B*(a + b*x^2)^(7/2))/(7*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
556,1,122,0,0.0529656,"\int \frac{x^4 \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^4*(A + B*x^2))/Sqrt[a + b*x^2],x]","\frac{a^2 (6 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{7/2}}+\frac{x^3 \sqrt{a+b x^2} (6 A b-5 a B)}{24 b^2}-\frac{a x \sqrt{a+b x^2} (6 A b-5 a B)}{16 b^3}+\frac{B x^5 \sqrt{a+b x^2}}{6 b}","\frac{a^2 (6 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{7/2}}+\frac{x^3 \sqrt{a+b x^2} (6 A b-5 a B)}{24 b^2}-\frac{a x \sqrt{a+b x^2} (6 A b-5 a B)}{16 b^3}+\frac{B x^5 \sqrt{a+b x^2}}{6 b}",1,"-(a*(6*A*b - 5*a*B)*x*Sqrt[a + b*x^2])/(16*b^3) + ((6*A*b - 5*a*B)*x^3*Sqrt[a + b*x^2])/(24*b^2) + (B*x^5*Sqrt[a + b*x^2])/(6*b) + (a^2*(6*A*b - 5*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(7/2))","A",5,4,22,0.1818,1,"{459, 321, 217, 206}"
557,1,71,0,0.0549245,"\int \frac{x^3 \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^3*(A + B*x^2))/Sqrt[a + b*x^2],x]","\frac{\left(a+b x^2\right)^{3/2} (A b-2 a B)}{3 b^3}-\frac{a \sqrt{a+b x^2} (A b-a B)}{b^3}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^3}","\frac{\left(a+b x^2\right)^{3/2} (A b-2 a B)}{3 b^3}-\frac{a \sqrt{a+b x^2} (A b-a B)}{b^3}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^3}",1,"-((a*(A*b - a*B)*Sqrt[a + b*x^2])/b^3) + ((A*b - 2*a*B)*(a + b*x^2)^(3/2))/(3*b^3) + (B*(a + b*x^2)^(5/2))/(5*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
558,1,89,0,0.035899,"\int \frac{x^2 \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(x^2*(A + B*x^2))/Sqrt[a + b*x^2],x]","\frac{x \sqrt{a+b x^2} (4 A b-3 a B)}{8 b^2}-\frac{a (4 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}+\frac{B x^3 \sqrt{a+b x^2}}{4 b}","\frac{x \sqrt{a+b x^2} (4 A b-3 a B)}{8 b^2}-\frac{a (4 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{5/2}}+\frac{B x^3 \sqrt{a+b x^2}}{4 b}",1,"((4*A*b - 3*a*B)*x*Sqrt[a + b*x^2])/(8*b^2) + (B*x^3*Sqrt[a + b*x^2])/(4*b) - (a*(4*A*b - 3*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(5/2))","A",4,4,22,0.1818,1,"{459, 321, 217, 206}"
559,1,43,0,0.0335874,"\int \frac{x \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(x*(A + B*x^2))/Sqrt[a + b*x^2],x]","\frac{\sqrt{a+b x^2} (A b-a B)}{b^2}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b^2}","\frac{\sqrt{a+b x^2} (A b-a B)}{b^2}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b^2}",1,"((A*b - a*B)*Sqrt[a + b*x^2])/b^2 + (B*(a + b*x^2)^(3/2))/(3*b^2)","A",3,2,20,0.1000,1,"{444, 43}"
560,1,58,0,0.017414,"\int \frac{A+B x^2}{\sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/Sqrt[a + b*x^2],x]","\frac{(2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}+\frac{B x \sqrt{a+b x^2}}{2 b}","\frac{(2 A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{3/2}}+\frac{B x \sqrt{a+b x^2}}{2 b}",1,"(B*x*Sqrt[a + b*x^2])/(2*b) + ((2*A*b - a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(3/2))","A",3,3,19,0.1579,1,"{388, 217, 206}"
561,1,43,0,0.0331544,"\int \frac{A+B x^2}{x \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x*Sqrt[a + b*x^2]),x]","\frac{B \sqrt{a+b x^2}}{b}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{B \sqrt{a+b x^2}}{b}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(B*Sqrt[a + b*x^2])/b - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/Sqrt[a]","A",4,4,22,0.1818,1,"{446, 80, 63, 208}"
562,1,47,0,0.0176591,"\int \frac{A+B x^2}{x^2 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^2*Sqrt[a + b*x^2]),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}-\frac{A \sqrt{a+b x^2}}{a x}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{\sqrt{b}}-\frac{A \sqrt{a+b x^2}}{a x}",1,"-((A*Sqrt[a + b*x^2])/(a*x)) + (B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/Sqrt[b]","A",3,3,22,0.1364,1,"{451, 217, 206}"
563,1,58,0,0.0458618,"\int \frac{A+B x^2}{x^3 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^3*Sqrt[a + b*x^2]),x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+b x^2}}{2 a x^2}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+b x^2}}{2 a x^2}",1,"-(A*Sqrt[a + b*x^2])/(2*a*x^2) + ((A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(3/2))","A",4,4,22,0.1818,1,"{446, 78, 63, 208}"
564,1,53,0,0.0197902,"\int \frac{A+B x^2}{x^4 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^4*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} (2 A b-3 a B)}{3 a^2 x}-\frac{A \sqrt{a+b x^2}}{3 a x^3}","\frac{\sqrt{a+b x^2} (2 A b-3 a B)}{3 a^2 x}-\frac{A \sqrt{a+b x^2}}{3 a x^3}",1,"-(A*Sqrt[a + b*x^2])/(3*a*x^3) + ((2*A*b - 3*a*B)*Sqrt[a + b*x^2])/(3*a^2*x)","A",2,2,22,0.09091,1,"{453, 264}"
565,1,90,0,0.0678825,"\int \frac{A+B x^2}{x^5 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^5*Sqrt[a + b*x^2]),x]","\frac{\sqrt{a+b x^2} (3 A b-4 a B)}{8 a^2 x^2}-\frac{b (3 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{A \sqrt{a+b x^2}}{4 a x^4}","\frac{\sqrt{a+b x^2} (3 A b-4 a B)}{8 a^2 x^2}-\frac{b (3 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}-\frac{A \sqrt{a+b x^2}}{4 a x^4}",1,"-(A*Sqrt[a + b*x^2])/(4*a*x^4) + ((3*A*b - 4*a*B)*Sqrt[a + b*x^2])/(8*a^2*x^2) - (b*(3*A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(5/2))","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
566,1,84,0,0.0346146,"\int \frac{A+B x^2}{x^6 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^6*Sqrt[a + b*x^2]),x]","-\frac{2 b \sqrt{a+b x^2} (4 A b-5 a B)}{15 a^3 x}+\frac{\sqrt{a+b x^2} (4 A b-5 a B)}{15 a^2 x^3}-\frac{A \sqrt{a+b x^2}}{5 a x^5}","-\frac{2 b \sqrt{a+b x^2} (4 A b-5 a B)}{15 a^3 x}+\frac{\sqrt{a+b x^2} (4 A b-5 a B)}{15 a^2 x^3}-\frac{A \sqrt{a+b x^2}}{5 a x^5}",1,"-(A*Sqrt[a + b*x^2])/(5*a*x^5) + ((4*A*b - 5*a*B)*Sqrt[a + b*x^2])/(15*a^2*x^3) - (2*b*(4*A*b - 5*a*B)*Sqrt[a + b*x^2])/(15*a^3*x)","A",3,3,22,0.1364,1,"{453, 271, 264}"
567,1,123,0,0.094098,"\int \frac{A+B x^2}{x^7 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^7*Sqrt[a + b*x^2]),x]","\frac{b^2 (5 A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{7/2}}-\frac{b \sqrt{a+b x^2} (5 A b-6 a B)}{16 a^3 x^2}+\frac{\sqrt{a+b x^2} (5 A b-6 a B)}{24 a^2 x^4}-\frac{A \sqrt{a+b x^2}}{6 a x^6}","\frac{b^2 (5 A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{7/2}}-\frac{b \sqrt{a+b x^2} (5 A b-6 a B)}{16 a^3 x^2}+\frac{\sqrt{a+b x^2} (5 A b-6 a B)}{24 a^2 x^4}-\frac{A \sqrt{a+b x^2}}{6 a x^6}",1,"-(A*Sqrt[a + b*x^2])/(6*a*x^6) + ((5*A*b - 6*a*B)*Sqrt[a + b*x^2])/(24*a^2*x^4) - (b*(5*A*b - 6*a*B)*Sqrt[a + b*x^2])/(16*a^3*x^2) + (b^2*(5*A*b - 6*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(7/2))","A",6,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
568,1,117,0,0.0473258,"\int \frac{A+B x^2}{x^8 \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(x^8*Sqrt[a + b*x^2]),x]","\frac{8 b^2 \sqrt{a+b x^2} (6 A b-7 a B)}{105 a^4 x}-\frac{4 b \sqrt{a+b x^2} (6 A b-7 a B)}{105 a^3 x^3}+\frac{\sqrt{a+b x^2} (6 A b-7 a B)}{35 a^2 x^5}-\frac{A \sqrt{a+b x^2}}{7 a x^7}","\frac{8 b^2 \sqrt{a+b x^2} (6 A b-7 a B)}{105 a^4 x}-\frac{4 b \sqrt{a+b x^2} (6 A b-7 a B)}{105 a^3 x^3}+\frac{\sqrt{a+b x^2} (6 A b-7 a B)}{35 a^2 x^5}-\frac{A \sqrt{a+b x^2}}{7 a x^7}",1,"-(A*Sqrt[a + b*x^2])/(7*a*x^7) + ((6*A*b - 7*a*B)*Sqrt[a + b*x^2])/(35*a^2*x^5) - (4*b*(6*A*b - 7*a*B)*Sqrt[a + b*x^2])/(105*a^3*x^3) + (8*b^2*(6*A*b - 7*a*B)*Sqrt[a + b*x^2])/(105*a^4*x)","A",4,3,22,0.1364,1,"{453, 271, 264}"
569,1,152,0,0.0676372,"\int \frac{x^6 \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2)^(3/2),x]","\frac{5 a^2 (6 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{9/2}}-\frac{x^5 (6 A b-7 a B)}{6 b^2 \sqrt{a+b x^2}}+\frac{5 x^3 \sqrt{a+b x^2} (6 A b-7 a B)}{24 b^3}-\frac{5 a x \sqrt{a+b x^2} (6 A b-7 a B)}{16 b^4}+\frac{B x^7}{6 b \sqrt{a+b x^2}}","\frac{5 a^2 (6 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{16 b^{9/2}}-\frac{x^5 (6 A b-7 a B)}{6 b^2 \sqrt{a+b x^2}}+\frac{5 x^3 \sqrt{a+b x^2} (6 A b-7 a B)}{24 b^3}-\frac{5 a x \sqrt{a+b x^2} (6 A b-7 a B)}{16 b^4}+\frac{B x^7}{6 b \sqrt{a+b x^2}}",1,"-((6*A*b - 7*a*B)*x^5)/(6*b^2*Sqrt[a + b*x^2]) + (B*x^7)/(6*b*Sqrt[a + b*x^2]) - (5*a*(6*A*b - 7*a*B)*x*Sqrt[a + b*x^2])/(16*b^4) + (5*(6*A*b - 7*a*B)*x^3*Sqrt[a + b*x^2])/(24*b^3) + (5*a^2*(6*A*b - 7*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(16*b^(9/2))","A",6,5,22,0.2273,1,"{459, 288, 321, 217, 206}"
570,1,99,0,0.0761042,"\int \frac{x^5 \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2)^(3/2),x]","-\frac{a^2 (A b-a B)}{b^4 \sqrt{a+b x^2}}+\frac{\left(a+b x^2\right)^{3/2} (A b-3 a B)}{3 b^4}-\frac{a \sqrt{a+b x^2} (2 A b-3 a B)}{b^4}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^4}","-\frac{a^2 (A b-a B)}{b^4 \sqrt{a+b x^2}}+\frac{\left(a+b x^2\right)^{3/2} (A b-3 a B)}{3 b^4}-\frac{a \sqrt{a+b x^2} (2 A b-3 a B)}{b^4}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^4}",1,"-((a^2*(A*b - a*B))/(b^4*Sqrt[a + b*x^2])) - (a*(2*A*b - 3*a*B)*Sqrt[a + b*x^2])/b^4 + ((A*b - 3*a*B)*(a + b*x^2)^(3/2))/(3*b^4) + (B*(a + b*x^2)^(5/2))/(5*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
571,1,119,0,0.0505837,"\int \frac{x^4 \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2)^(3/2),x]","-\frac{x^3 (4 A b-5 a B)}{4 b^2 \sqrt{a+b x^2}}+\frac{3 x \sqrt{a+b x^2} (4 A b-5 a B)}{8 b^3}-\frac{3 a (4 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{7/2}}+\frac{B x^5}{4 b \sqrt{a+b x^2}}","-\frac{x^3 (4 A b-5 a B)}{4 b^2 \sqrt{a+b x^2}}+\frac{3 x \sqrt{a+b x^2} (4 A b-5 a B)}{8 b^3}-\frac{3 a (4 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{7/2}}+\frac{B x^5}{4 b \sqrt{a+b x^2}}",1,"-((4*A*b - 5*a*B)*x^3)/(4*b^2*Sqrt[a + b*x^2]) + (B*x^5)/(4*b*Sqrt[a + b*x^2]) + (3*(4*A*b - 5*a*B)*x*Sqrt[a + b*x^2])/(8*b^3) - (3*a*(4*A*b - 5*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(7/2))","A",5,5,22,0.2273,1,"{459, 288, 321, 217, 206}"
572,1,67,0,0.0555836,"\int \frac{x^3 \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2)^(3/2),x]","\frac{\sqrt{a+b x^2} (A b-2 a B)}{b^3}+\frac{a (A b-a B)}{b^3 \sqrt{a+b x^2}}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b^3}","\frac{\sqrt{a+b x^2} (A b-2 a B)}{b^3}+\frac{a (A b-a B)}{b^3 \sqrt{a+b x^2}}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b^3}",1,"(a*(A*b - a*B))/(b^3*Sqrt[a + b*x^2]) + ((A*b - 2*a*B)*Sqrt[a + b*x^2])/b^3 + (B*(a + b*x^2)^(3/2))/(3*b^3)","A",3,2,22,0.09091,1,"{446, 77}"
573,1,83,0,0.0568336,"\int \frac{x^2 \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2)^(3/2),x]","-\frac{x (A b-a B)}{b^2 \sqrt{a+b x^2}}+\frac{(2 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}+\frac{B x \sqrt{a+b x^2}}{2 b^2}","-\frac{x (A b-a B)}{b^2 \sqrt{a+b x^2}}+\frac{(2 A b-3 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{5/2}}+\frac{B x \sqrt{a+b x^2}}{2 b^2}",1,"-(((A*b - a*B)*x)/(b^2*Sqrt[a + b*x^2])) + (B*x*Sqrt[a + b*x^2])/(2*b^2) + ((2*A*b - 3*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(5/2))","A",4,4,22,0.1818,1,"{455, 388, 217, 206}"
574,1,41,0,0.0321411,"\int \frac{x \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2)^(3/2),x]","\frac{B \sqrt{a+b x^2}}{b^2}-\frac{A b-a B}{b^2 \sqrt{a+b x^2}}","\frac{B \sqrt{a+b x^2}}{b^2}-\frac{A b-a B}{b^2 \sqrt{a+b x^2}}",1,"-((A*b - a*B)/(b^2*Sqrt[a + b*x^2])) + (B*Sqrt[a + b*x^2])/b^2","A",3,2,20,0.1000,1,"{444, 43}"
575,1,54,0,0.0178983,"\int \frac{A+B x^2}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(a + b*x^2)^(3/2),x]","\frac{x (A b-a B)}{a b \sqrt{a+b x^2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}","\frac{x (A b-a B)}{a b \sqrt{a+b x^2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{3/2}}",1,"((A*b - a*B)*x)/(a*b*Sqrt[a + b*x^2]) + (B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(3/2)","A",3,3,19,0.1579,1,"{385, 217, 206}"
576,1,53,0,0.0387111,"\int \frac{A+B x^2}{x \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2)^(3/2)),x]","\frac{A b-a B}{a b \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{A b-a B}{a b \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(A*b - a*B)/(a*b*Sqrt[a + b*x^2]) - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(3/2)","A",4,4,22,0.1818,1,"{446, 78, 63, 208}"
577,1,47,0,0.0188691,"\int \frac{A+B x^2}{x^2 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2)^(3/2)),x]","-\frac{x (2 A b-a B)}{a^2 \sqrt{a+b x^2}}-\frac{A}{a x \sqrt{a+b x^2}}","-\frac{x (2 A b-a B)}{a^2 \sqrt{a+b x^2}}-\frac{A}{a x \sqrt{a+b x^2}}",1,"-(A/(a*x*Sqrt[a + b*x^2])) - ((2*A*b - a*B)*x)/(a^2*Sqrt[a + b*x^2])","A",2,2,22,0.09091,1,"{453, 191}"
578,1,86,0,0.0671464,"\int \frac{A+B x^2}{x^3 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2)^(3/2)),x]","-\frac{3 A b-2 a B}{2 a^2 \sqrt{a+b x^2}}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{A}{2 a x^2 \sqrt{a+b x^2}}","-\frac{3 A b-2 a B}{2 a^2 \sqrt{a+b x^2}}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{A}{2 a x^2 \sqrt{a+b x^2}}",1,"-(3*A*b - 2*a*B)/(2*a^2*Sqrt[a + b*x^2]) - A/(2*a*x^2*Sqrt[a + b*x^2]) + ((3*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(5/2))","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
579,1,82,0,0.0311549,"\int \frac{A+B x^2}{x^4 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2)^(3/2)),x]","\frac{2 b x (4 A b-3 a B)}{3 a^3 \sqrt{a+b x^2}}+\frac{4 A b-3 a B}{3 a^2 x \sqrt{a+b x^2}}-\frac{A}{3 a x^3 \sqrt{a+b x^2}}","\frac{2 b x (4 A b-3 a B)}{3 a^3 \sqrt{a+b x^2}}+\frac{4 A b-3 a B}{3 a^2 x \sqrt{a+b x^2}}-\frac{A}{3 a x^3 \sqrt{a+b x^2}}",1,"-A/(3*a*x^3*Sqrt[a + b*x^2]) + (4*A*b - 3*a*B)/(3*a^2*x*Sqrt[a + b*x^2]) + (2*b*(4*A*b - 3*a*B)*x)/(3*a^3*Sqrt[a + b*x^2])","A",3,3,22,0.1364,1,"{453, 271, 191}"
580,1,120,0,0.0882975,"\int \frac{A+B x^2}{x^5 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^5*(a + b*x^2)^(3/2)),x]","\frac{3 \sqrt{a+b x^2} (5 A b-4 a B)}{8 a^3 x^2}-\frac{5 A b-4 a B}{4 a^2 x^2 \sqrt{a+b x^2}}-\frac{3 b (5 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{A}{4 a x^4 \sqrt{a+b x^2}}","\frac{3 b (5 A b-4 a B)}{8 a^3 \sqrt{a+b x^2}}+\frac{5 A b-4 a B}{8 a^2 x^2 \sqrt{a+b x^2}}-\frac{3 b (5 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{7/2}}-\frac{A}{4 a x^4 \sqrt{a+b x^2}}",1,"-A/(4*a*x^4*Sqrt[a + b*x^2]) - (5*A*b - 4*a*B)/(4*a^2*x^2*Sqrt[a + b*x^2]) + (3*(5*A*b - 4*a*B)*Sqrt[a + b*x^2])/(8*a^3*x^2) - (3*b*(5*A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(7/2))","A",6,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
581,1,115,0,0.0447022,"\int \frac{A+B x^2}{x^6 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^6*(a + b*x^2)^(3/2)),x]","-\frac{8 b^2 x (6 A b-5 a B)}{15 a^4 \sqrt{a+b x^2}}-\frac{4 b (6 A b-5 a B)}{15 a^3 x \sqrt{a+b x^2}}+\frac{6 A b-5 a B}{15 a^2 x^3 \sqrt{a+b x^2}}-\frac{A}{5 a x^5 \sqrt{a+b x^2}}","-\frac{8 b^2 x (6 A b-5 a B)}{15 a^4 \sqrt{a+b x^2}}-\frac{4 b (6 A b-5 a B)}{15 a^3 x \sqrt{a+b x^2}}+\frac{6 A b-5 a B}{15 a^2 x^3 \sqrt{a+b x^2}}-\frac{A}{5 a x^5 \sqrt{a+b x^2}}",1,"-A/(5*a*x^5*Sqrt[a + b*x^2]) + (6*A*b - 5*a*B)/(15*a^2*x^3*Sqrt[a + b*x^2]) - (4*b*(6*A*b - 5*a*B))/(15*a^3*x*Sqrt[a + b*x^2]) - (8*b^2*(6*A*b - 5*a*B)*x)/(15*a^4*Sqrt[a + b*x^2])","A",4,3,22,0.1364,1,"{453, 271, 191}"
582,1,153,0,0.1169511,"\int \frac{A+B x^2}{x^7 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^7*(a + b*x^2)^(3/2)),x]","\frac{5 b^2 (7 A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{9/2}}-\frac{5 b \sqrt{a+b x^2} (7 A b-6 a B)}{16 a^4 x^2}+\frac{5 \sqrt{a+b x^2} (7 A b-6 a B)}{24 a^3 x^4}-\frac{7 A b-6 a B}{6 a^2 x^4 \sqrt{a+b x^2}}-\frac{A}{6 a x^6 \sqrt{a+b x^2}}","-\frac{5 b^2 (7 A b-6 a B)}{16 a^4 \sqrt{a+b x^2}}+\frac{5 b^2 (7 A b-6 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{16 a^{9/2}}-\frac{5 b (7 A b-6 a B)}{48 a^3 x^2 \sqrt{a+b x^2}}+\frac{7 A b-6 a B}{24 a^2 x^4 \sqrt{a+b x^2}}-\frac{A}{6 a x^6 \sqrt{a+b x^2}}",1,"-A/(6*a*x^6*Sqrt[a + b*x^2]) - (7*A*b - 6*a*B)/(6*a^2*x^4*Sqrt[a + b*x^2]) + (5*(7*A*b - 6*a*B)*Sqrt[a + b*x^2])/(24*a^3*x^4) - (5*b*(7*A*b - 6*a*B)*Sqrt[a + b*x^2])/(16*a^4*x^2) + (5*b^2*(7*A*b - 6*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(16*a^(9/2))","A",7,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
583,1,148,0,0.0612387,"\int \frac{A+B x^2}{x^8 \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^8*(a + b*x^2)^(3/2)),x]","\frac{16 b^3 x (8 A b-7 a B)}{35 a^5 \sqrt{a+b x^2}}+\frac{8 b^2 (8 A b-7 a B)}{35 a^4 x \sqrt{a+b x^2}}-\frac{2 b (8 A b-7 a B)}{35 a^3 x^3 \sqrt{a+b x^2}}+\frac{8 A b-7 a B}{35 a^2 x^5 \sqrt{a+b x^2}}-\frac{A}{7 a x^7 \sqrt{a+b x^2}}","\frac{16 b^3 x (8 A b-7 a B)}{35 a^5 \sqrt{a+b x^2}}+\frac{8 b^2 (8 A b-7 a B)}{35 a^4 x \sqrt{a+b x^2}}-\frac{2 b (8 A b-7 a B)}{35 a^3 x^3 \sqrt{a+b x^2}}+\frac{8 A b-7 a B}{35 a^2 x^5 \sqrt{a+b x^2}}-\frac{A}{7 a x^7 \sqrt{a+b x^2}}",1,"-A/(7*a*x^7*Sqrt[a + b*x^2]) + (8*A*b - 7*a*B)/(35*a^2*x^5*Sqrt[a + b*x^2]) - (2*b*(8*A*b - 7*a*B))/(35*a^3*x^3*Sqrt[a + b*x^2]) + (8*b^2*(8*A*b - 7*a*B))/(35*a^4*x*Sqrt[a + b*x^2]) + (16*b^3*(8*A*b - 7*a*B)*x)/(35*a^5*Sqrt[a + b*x^2])","A",5,3,22,0.1364,1,"{453, 271, 191}"
584,1,128,0,0.1015291,"\int \frac{x^7 \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^7*(A + B*x^2))/(a + b*x^2)^(5/2),x]","\frac{a^3 (A b-a B)}{3 b^5 \left(a+b x^2\right)^{3/2}}-\frac{a^2 (3 A b-4 a B)}{b^5 \sqrt{a+b x^2}}-\frac{3 a \sqrt{a+b x^2} (A b-2 a B)}{b^5}+\frac{\left(a+b x^2\right)^{3/2} (A b-4 a B)}{3 b^5}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^5}","\frac{a^3 (A b-a B)}{3 b^5 \left(a+b x^2\right)^{3/2}}-\frac{a^2 (3 A b-4 a B)}{b^5 \sqrt{a+b x^2}}-\frac{3 a \sqrt{a+b x^2} (A b-2 a B)}{b^5}+\frac{\left(a+b x^2\right)^{3/2} (A b-4 a B)}{3 b^5}+\frac{B \left(a+b x^2\right)^{5/2}}{5 b^5}",1,"(a^3*(A*b - a*B))/(3*b^5*(a + b*x^2)^(3/2)) - (a^2*(3*A*b - 4*a*B))/(b^5*Sqrt[a + b*x^2]) - (3*a*(A*b - 2*a*B)*Sqrt[a + b*x^2])/b^5 + ((A*b - 4*a*B)*(a + b*x^2)^(3/2))/(3*b^5) + (B*(a + b*x^2)^(5/2))/(5*b^5)","A",3,2,22,0.09091,1,"{446, 77}"
585,1,149,0,0.0620309,"\int \frac{x^6 \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^6*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{x^5 (4 A b-7 a B)}{12 b^2 \left(a+b x^2\right)^{3/2}}-\frac{5 x^3 (4 A b-7 a B)}{12 b^3 \sqrt{a+b x^2}}+\frac{5 x \sqrt{a+b x^2} (4 A b-7 a B)}{8 b^4}-\frac{5 a (4 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{9/2}}+\frac{B x^7}{4 b \left(a+b x^2\right)^{3/2}}","-\frac{x^5 (4 A b-7 a B)}{12 b^2 \left(a+b x^2\right)^{3/2}}-\frac{5 x^3 (4 A b-7 a B)}{12 b^3 \sqrt{a+b x^2}}+\frac{5 x \sqrt{a+b x^2} (4 A b-7 a B)}{8 b^4}-\frac{5 a (4 A b-7 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{8 b^{9/2}}+\frac{B x^7}{4 b \left(a+b x^2\right)^{3/2}}",1,"-((4*A*b - 7*a*B)*x^5)/(12*b^2*(a + b*x^2)^(3/2)) + (B*x^7)/(4*b*(a + b*x^2)^(3/2)) - (5*(4*A*b - 7*a*B)*x^3)/(12*b^3*Sqrt[a + b*x^2]) + (5*(4*A*b - 7*a*B)*x*Sqrt[a + b*x^2])/(8*b^4) - (5*a*(4*A*b - 7*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(8*b^(9/2))","A",6,5,22,0.2273,1,"{459, 288, 321, 217, 206}"
586,1,97,0,0.0759132,"\int \frac{x^5 \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^5*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{a^2 (A b-a B)}{3 b^4 \left(a+b x^2\right)^{3/2}}+\frac{a (2 A b-3 a B)}{b^4 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2} (A b-3 a B)}{b^4}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b^4}","-\frac{a^2 (A b-a B)}{3 b^4 \left(a+b x^2\right)^{3/2}}+\frac{a (2 A b-3 a B)}{b^4 \sqrt{a+b x^2}}+\frac{\sqrt{a+b x^2} (A b-3 a B)}{b^4}+\frac{B \left(a+b x^2\right)^{3/2}}{3 b^4}",1,"-(a^2*(A*b - a*B))/(3*b^4*(a + b*x^2)^(3/2)) + (a*(2*A*b - 3*a*B))/(b^4*Sqrt[a + b*x^2]) + ((A*b - 3*a*B)*Sqrt[a + b*x^2])/b^4 + (B*(a + b*x^2)^(3/2))/(3*b^4)","A",3,2,22,0.09091,1,"{446, 77}"
587,1,114,0,0.0900452,"\int \frac{x^4 \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^4*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{x (4 A b-7 a B)}{3 b^3 \sqrt{a+b x^2}}+\frac{a x (A b-a B)}{3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{(2 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{7/2}}+\frac{B x \sqrt{a+b x^2}}{2 b^3}","-\frac{x (4 A b-7 a B)}{3 b^3 \sqrt{a+b x^2}}+\frac{a x (A b-a B)}{3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{(2 A b-5 a B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{2 b^{7/2}}+\frac{B x \sqrt{a+b x^2}}{2 b^3}",1,"(a*(A*b - a*B)*x)/(3*b^3*(a + b*x^2)^(3/2)) - ((4*A*b - 7*a*B)*x)/(3*b^3*Sqrt[a + b*x^2]) + (B*x*Sqrt[a + b*x^2])/(2*b^3) + ((2*A*b - 5*a*B)*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/(2*b^(7/2))","A",5,5,22,0.2273,1,"{455, 1157, 388, 217, 206}"
588,1,68,0,0.0535126,"\int \frac{x^3 \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^3*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{A b-2 a B}{b^3 \sqrt{a+b x^2}}+\frac{a (A b-a B)}{3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{B \sqrt{a+b x^2}}{b^3}","-\frac{A b-2 a B}{b^3 \sqrt{a+b x^2}}+\frac{a (A b-a B)}{3 b^3 \left(a+b x^2\right)^{3/2}}+\frac{B \sqrt{a+b x^2}}{b^3}",1,"(a*(A*b - a*B))/(3*b^3*(a + b*x^2)^(3/2)) - (A*b - 2*a*B)/(b^3*Sqrt[a + b*x^2]) + (B*Sqrt[a + b*x^2])/b^3","A",3,2,22,0.09091,1,"{446, 77}"
589,1,77,0,0.0303405,"\int \frac{x^2 \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x^2*(A + B*x^2))/(a + b*x^2)^(5/2),x]","\frac{x^3 (A b-a B)}{3 a b \left(a+b x^2\right)^{3/2}}-\frac{B x}{b^2 \sqrt{a+b x^2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}","\frac{x^3 (A b-a B)}{3 a b \left(a+b x^2\right)^{3/2}}-\frac{B x}{b^2 \sqrt{a+b x^2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a+b x^2}}\right)}{b^{5/2}}",1,"((A*b - a*B)*x^3)/(3*a*b*(a + b*x^2)^(3/2)) - (B*x)/(b^2*Sqrt[a + b*x^2]) + (B*ArcTanh[(Sqrt[b]*x)/Sqrt[a + b*x^2]])/b^(5/2)","A",4,4,22,0.1818,1,"{452, 288, 217, 206}"
590,1,44,0,0.0329654,"\int \frac{x \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(x*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{A b-a B}{3 b^2 \left(a+b x^2\right)^{3/2}}-\frac{B}{b^2 \sqrt{a+b x^2}}","-\frac{A b-a B}{3 b^2 \left(a+b x^2\right)^{3/2}}-\frac{B}{b^2 \sqrt{a+b x^2}}",1,"-(A*b - a*B)/(3*b^2*(a + b*x^2)^(3/2)) - B/(b^2*Sqrt[a + b*x^2])","A",3,2,20,0.1000,1,"{444, 43}"
591,1,47,0,0.0098935,"\int \frac{A+B x^2}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(a + b*x^2)^(5/2),x]","\frac{2 A x}{3 a^2 \sqrt{a+b x^2}}+\frac{x \left(A+B x^2\right)}{3 a \left(a+b x^2\right)^{3/2}}","\frac{2 A x}{3 a^2 \sqrt{a+b x^2}}+\frac{x \left(A+B x^2\right)}{3 a \left(a+b x^2\right)^{3/2}}",1,"(2*A*x)/(3*a^2*Sqrt[a + b*x^2]) + (x*(A + B*x^2))/(3*a*(a + b*x^2)^(3/2))","A",2,2,19,0.1053,1,"{378, 191}"
592,1,72,0,0.0492278,"\int \frac{A+B x^2}{x \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(x*(a + b*x^2)^(5/2)),x]","\frac{A}{a^2 \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A b-a B}{3 a b \left(a+b x^2\right)^{3/2}}","\frac{A}{a^2 \sqrt{a+b x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A b-a B}{3 a b \left(a+b x^2\right)^{3/2}}",1,"(A*b - a*B)/(3*a*b*(a + b*x^2)^(3/2)) + A/(a^2*Sqrt[a + b*x^2]) - (A*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/a^(5/2)","A",5,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
593,1,77,0,0.0265301,"\int \frac{A+B x^2}{x^2 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(x^2*(a + b*x^2)^(5/2)),x]","-\frac{2 x (4 A b-a B)}{3 a^3 \sqrt{a+b x^2}}-\frac{x (4 A b-a B)}{3 a^2 \left(a+b x^2\right)^{3/2}}-\frac{A}{a x \left(a+b x^2\right)^{3/2}}","-\frac{2 x (4 A b-a B)}{3 a^3 \sqrt{a+b x^2}}-\frac{x (4 A b-a B)}{3 a^2 \left(a+b x^2\right)^{3/2}}-\frac{A}{a x \left(a+b x^2\right)^{3/2}}",1,"-(A/(a*x*(a + b*x^2)^(3/2))) - ((4*A*b - a*B)*x)/(3*a^2*(a + b*x^2)^(3/2)) - (2*(4*A*b - a*B)*x)/(3*a^3*Sqrt[a + b*x^2])","A",3,3,22,0.1364,1,"{453, 192, 191}"
594,1,113,0,0.0865613,"\int \frac{A+B x^2}{x^3 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(x^3*(a + b*x^2)^(5/2)),x]","-\frac{5 A b-2 a B}{2 a^3 \sqrt{a+b x^2}}-\frac{5 A b-2 a B}{6 a^2 \left(a+b x^2\right)^{3/2}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{A}{2 a x^2 \left(a+b x^2\right)^{3/2}}","-\frac{5 A b-2 a B}{2 a^3 \sqrt{a+b x^2}}-\frac{5 A b-2 a B}{6 a^2 \left(a+b x^2\right)^{3/2}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{A}{2 a x^2 \left(a+b x^2\right)^{3/2}}",1,"-(5*A*b - 2*a*B)/(6*a^2*(a + b*x^2)^(3/2)) - A/(2*a*x^2*(a + b*x^2)^(3/2)) - (5*A*b - 2*a*B)/(2*a^3*Sqrt[a + b*x^2]) + ((5*A*b - 2*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(2*a^(7/2))","A",6,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
595,1,108,0,0.0487297,"\int \frac{A+B x^2}{x^4 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(x^4*(a + b*x^2)^(5/2)),x]","\frac{8 b x (2 A b-a B)}{3 a^4 \sqrt{a+b x^2}}+\frac{4 b x (2 A b-a B)}{3 a^3 \left(a+b x^2\right)^{3/2}}+\frac{2 A b-a B}{a^2 x \left(a+b x^2\right)^{3/2}}-\frac{A}{3 a x^3 \left(a+b x^2\right)^{3/2}}","\frac{8 b x (2 A b-a B)}{3 a^4 \sqrt{a+b x^2}}+\frac{4 b x (2 A b-a B)}{3 a^3 \left(a+b x^2\right)^{3/2}}+\frac{2 A b-a B}{a^2 x \left(a+b x^2\right)^{3/2}}-\frac{A}{3 a x^3 \left(a+b x^2\right)^{3/2}}",1,"-A/(3*a*x^3*(a + b*x^2)^(3/2)) + (2*A*b - a*B)/(a^2*x*(a + b*x^2)^(3/2)) + (4*b*(2*A*b - a*B)*x)/(3*a^3*(a + b*x^2)^(3/2)) + (8*b*(2*A*b - a*B)*x)/(3*a^4*Sqrt[a + b*x^2])","A",4,4,22,0.1818,1,"{453, 271, 192, 191}"
596,1,150,0,0.1103516,"\int \frac{A+B x^2}{x^5 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(x^5*(a + b*x^2)^(5/2)),x]","\frac{5 \sqrt{a+b x^2} (7 A b-4 a B)}{8 a^4 x^2}-\frac{5 (7 A b-4 a B)}{12 a^3 x^2 \sqrt{a+b x^2}}-\frac{7 A b-4 a B}{12 a^2 x^2 \left(a+b x^2\right)^{3/2}}-\frac{5 b (7 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{A}{4 a x^4 \left(a+b x^2\right)^{3/2}}","\frac{5 b (7 A b-4 a B)}{8 a^4 \sqrt{a+b x^2}}+\frac{5 b (7 A b-4 a B)}{24 a^3 \left(a+b x^2\right)^{3/2}}+\frac{7 A b-4 a B}{8 a^2 x^2 \left(a+b x^2\right)^{3/2}}-\frac{5 b (7 A b-4 a B) \tanh ^{-1}\left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{8 a^{9/2}}-\frac{A}{4 a x^4 \left(a+b x^2\right)^{3/2}}",1,"-A/(4*a*x^4*(a + b*x^2)^(3/2)) - (7*A*b - 4*a*B)/(12*a^2*x^2*(a + b*x^2)^(3/2)) - (5*(7*A*b - 4*a*B))/(12*a^3*x^2*Sqrt[a + b*x^2]) + (5*(7*A*b - 4*a*B)*Sqrt[a + b*x^2])/(8*a^4*x^2) - (5*b*(7*A*b - 4*a*B)*ArcTanh[Sqrt[a + b*x^2]/Sqrt[a]])/(8*a^(9/2))","A",7,5,22,0.2273,1,"{446, 78, 51, 63, 208}"
597,1,146,0,0.0568177,"\int \frac{A+B x^2}{x^6 \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(x^6*(a + b*x^2)^(5/2)),x]","-\frac{16 b^2 x (8 A b-5 a B)}{15 a^5 \sqrt{a+b x^2}}-\frac{8 b^2 x (8 A b-5 a B)}{15 a^4 \left(a+b x^2\right)^{3/2}}-\frac{2 b (8 A b-5 a B)}{5 a^3 x \left(a+b x^2\right)^{3/2}}+\frac{8 A b-5 a B}{15 a^2 x^3 \left(a+b x^2\right)^{3/2}}-\frac{A}{5 a x^5 \left(a+b x^2\right)^{3/2}}","-\frac{16 b^2 x (8 A b-5 a B)}{15 a^5 \sqrt{a+b x^2}}-\frac{8 b^2 x (8 A b-5 a B)}{15 a^4 \left(a+b x^2\right)^{3/2}}-\frac{2 b (8 A b-5 a B)}{5 a^3 x \left(a+b x^2\right)^{3/2}}+\frac{8 A b-5 a B}{15 a^2 x^3 \left(a+b x^2\right)^{3/2}}-\frac{A}{5 a x^5 \left(a+b x^2\right)^{3/2}}",1,"-A/(5*a*x^5*(a + b*x^2)^(3/2)) + (8*A*b - 5*a*B)/(15*a^2*x^3*(a + b*x^2)^(3/2)) - (2*b*(8*A*b - 5*a*B))/(5*a^3*x*(a + b*x^2)^(3/2)) - (8*b^2*(8*A*b - 5*a*B)*x)/(15*a^4*(a + b*x^2)^(3/2)) - (16*b^2*(8*A*b - 5*a*B)*x)/(15*a^5*Sqrt[a + b*x^2])","A",5,4,22,0.1818,1,"{453, 271, 192, 191}"
598,1,157,0,0.1291356,"\int x^5 \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[x^5*(a + b*x^2)^2*Sqrt[c + d*x^2],x]","\frac{\left(c+d x^2\right)^{7/2} \left(a^2 d^2-6 a b c d+6 b^2 c^2\right)}{7 d^5}+\frac{c^2 \left(c+d x^2\right)^{3/2} (b c-a d)^2}{3 d^5}-\frac{2 b \left(c+d x^2\right)^{9/2} (2 b c-a d)}{9 d^5}-\frac{2 c \left(c+d x^2\right)^{5/2} (b c-a d) (2 b c-a d)}{5 d^5}+\frac{b^2 \left(c+d x^2\right)^{11/2}}{11 d^5}","\frac{\left(c+d x^2\right)^{7/2} \left(a^2 d^2-6 a b c d+6 b^2 c^2\right)}{7 d^5}+\frac{c^2 \left(c+d x^2\right)^{3/2} (b c-a d)^2}{3 d^5}-\frac{2 b \left(c+d x^2\right)^{9/2} (2 b c-a d)}{9 d^5}-\frac{2 c \left(c+d x^2\right)^{5/2} (b c-a d) (2 b c-a d)}{5 d^5}+\frac{b^2 \left(c+d x^2\right)^{11/2}}{11 d^5}",1,"(c^2*(b*c - a*d)^2*(c + d*x^2)^(3/2))/(3*d^5) - (2*c*(b*c - a*d)*(2*b*c - a*d)*(c + d*x^2)^(5/2))/(5*d^5) + ((6*b^2*c^2 - 6*a*b*c*d + a^2*d^2)*(c + d*x^2)^(7/2))/(7*d^5) - (2*b*(2*b*c - a*d)*(c + d*x^2)^(9/2))/(9*d^5) + (b^2*(c + d*x^2)^(11/2))/(11*d^5)","A",3,2,24,0.08333,1,"{446, 88}"
599,1,114,0,0.0959832,"\int x^3 \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[x^3*(a + b*x^2)^2*Sqrt[c + d*x^2],x]","-\frac{b \left(c+d x^2\right)^{7/2} (3 b c-2 a d)}{7 d^4}+\frac{\left(c+d x^2\right)^{5/2} (b c-a d) (3 b c-a d)}{5 d^4}-\frac{c \left(c+d x^2\right)^{3/2} (b c-a d)^2}{3 d^4}+\frac{b^2 \left(c+d x^2\right)^{9/2}}{9 d^4}","-\frac{b \left(c+d x^2\right)^{7/2} (3 b c-2 a d)}{7 d^4}+\frac{\left(c+d x^2\right)^{5/2} (b c-a d) (3 b c-a d)}{5 d^4}-\frac{c \left(c+d x^2\right)^{3/2} (b c-a d)^2}{3 d^4}+\frac{b^2 \left(c+d x^2\right)^{9/2}}{9 d^4}",1,"-(c*(b*c - a*d)^2*(c + d*x^2)^(3/2))/(3*d^4) + ((b*c - a*d)*(3*b*c - a*d)*(c + d*x^2)^(5/2))/(5*d^4) - (b*(3*b*c - 2*a*d)*(c + d*x^2)^(7/2))/(7*d^4) + (b^2*(c + d*x^2)^(9/2))/(9*d^4)","A",3,2,24,0.08333,1,"{446, 77}"
600,1,77,0,0.0595577,"\int x \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[x*(a + b*x^2)^2*Sqrt[c + d*x^2],x]","-\frac{2 b \left(c+d x^2\right)^{5/2} (b c-a d)}{5 d^3}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)^2}{3 d^3}+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d^3}","-\frac{2 b \left(c+d x^2\right)^{5/2} (b c-a d)}{5 d^3}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)^2}{3 d^3}+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d^3}",1,"((b*c - a*d)^2*(c + d*x^2)^(3/2))/(3*d^3) - (2*b*(b*c - a*d)*(c + d*x^2)^(5/2))/(5*d^3) + (b^2*(c + d*x^2)^(7/2))/(7*d^3)","A",3,2,22,0.09091,1,"{444, 43}"
601,1,92,0,0.0841289,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x,x]","a^2 \sqrt{c+d x^2}-a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)-\frac{b \left(c+d x^2\right)^{3/2} (b c-2 a d)}{3 d^2}+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d^2}","a^2 \sqrt{c+d x^2}-a^2 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)-\frac{b \left(c+d x^2\right)^{3/2} (b c-2 a d)}{3 d^2}+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d^2}",1,"a^2*Sqrt[c + d*x^2] - (b*(b*c - 2*a*d)*(c + d*x^2)^(3/2))/(3*d^2) + (b^2*(c + d*x^2)^(5/2))/(5*d^2) - a^2*Sqrt[c]*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]","A",6,5,24,0.2083,1,"{446, 88, 50, 63, 208}"
602,1,109,0,0.0873646,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^3} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^3,x]","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{2 c x^2}+\frac{a \sqrt{c+d x^2} (a d+4 b c)}{2 c}-\frac{a (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 \sqrt{c}}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{2 c x^2}+\frac{a \sqrt{c+d x^2} (a d+4 b c)}{2 c}-\frac{a (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 \sqrt{c}}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d}",1,"(a*(4*b*c + a*d)*Sqrt[c + d*x^2])/(2*c) + (b^2*(c + d*x^2)^(3/2))/(3*d) - (a^2*(c + d*x^2)^(3/2))/(2*c*x^2) - (a*(4*b*c + a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*Sqrt[c])","A",6,6,24,0.2500,1,"{446, 89, 80, 50, 63, 208}"
603,1,140,0,0.1599064,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^5} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^5,x]","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{4 c x^4}+\frac{1}{8} \sqrt{c+d x^2} \left(\frac{a d (8 b c-a d)}{c^2}+8 b^2\right)-\frac{\left(a d (8 b c-a d)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{3/2}}-\frac{a \left(c+d x^2\right)^{3/2} (8 b c-a d)}{8 c^2 x^2}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{4 c x^4}+\frac{\sqrt{c+d x^2} \left(a d (8 b c-a d)+8 b^2 c^2\right)}{8 c^2}-\frac{\left(a d (8 b c-a d)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{3/2}}-\frac{a \left(c+d x^2\right)^{3/2} (8 b c-a d)}{8 c^2 x^2}",1,"((8*b^2 + (a*d*(8*b*c - a*d))/c^2)*Sqrt[c + d*x^2])/8 - (a^2*(c + d*x^2)^(3/2))/(4*c*x^4) - (a*(8*b*c - a*d)*(c + d*x^2)^(3/2))/(8*c^2*x^2) - ((8*b^2*c^2 + a*d*(8*b*c - a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(8*c^(3/2))","A",6,6,24,0.2500,1,"{446, 89, 78, 50, 63, 208}"
604,1,149,0,0.1488486,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^7} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^7,x]","-\frac{\sqrt{c+d x^2} \left(a^2 d^2-4 a b c d+8 b^2 c^2\right)}{16 c^2 x^2}-\frac{d \left(a^2 d^2-4 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{5/2}}-\frac{a^2 \left(c+d x^2\right)^{3/2}}{6 c x^6}-\frac{a \left(c+d x^2\right)^{3/2} (4 b c-a d)}{8 c^2 x^4}","-\frac{\sqrt{c+d x^2} \left(a^2 d^2-4 a b c d+8 b^2 c^2\right)}{16 c^2 x^2}-\frac{d \left(a^2 d^2-4 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{5/2}}-\frac{a^2 \left(c+d x^2\right)^{3/2}}{6 c x^6}-\frac{a \left(c+d x^2\right)^{3/2} (4 b c-a d)}{8 c^2 x^4}",1,"-((8*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*Sqrt[c + d*x^2])/(16*c^2*x^2) - (a^2*(c + d*x^2)^(3/2))/(6*c*x^6) - (a*(4*b*c - a*d)*(c + d*x^2)^(3/2))/(8*c^2*x^4) - (d*(8*b^2*c^2 - 4*a*b*c*d + a^2*d^2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(16*c^(5/2))","A",6,6,24,0.2500,1,"{446, 89, 78, 47, 63, 208}"
605,1,188,0,0.1860785,"\int x^2 \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[x^2*(a + b*x^2)^2*Sqrt[c + d*x^2],x]","-\frac{c^2 \left(16 a^2 d^2+b c (5 b c-16 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{7/2}}+\frac{1}{64} x^3 \sqrt{c+d x^2} \left(16 a^2+\frac{b c (5 b c-16 a d)}{d^2}\right)+\frac{c x \sqrt{c+d x^2} \left(16 a^2 d^2+b c (5 b c-16 a d)\right)}{128 d^3}-\frac{b x^3 \left(c+d x^2\right)^{3/2} (5 b c-16 a d)}{48 d^2}+\frac{b^2 x^5 \left(c+d x^2\right)^{3/2}}{8 d}","-\frac{c^2 \left(16 a^2 d^2+b c (5 b c-16 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{7/2}}+\frac{x^3 \sqrt{c+d x^2} \left(16 a^2 d^2+b c (5 b c-16 a d)\right)}{64 d^2}+\frac{c x \sqrt{c+d x^2} \left(16 a^2 d^2+b c (5 b c-16 a d)\right)}{128 d^3}-\frac{b x^3 \left(c+d x^2\right)^{3/2} (5 b c-16 a d)}{48 d^2}+\frac{b^2 x^5 \left(c+d x^2\right)^{3/2}}{8 d}",1,"(c*(16*a^2*d^2 + b*c*(5*b*c - 16*a*d))*x*Sqrt[c + d*x^2])/(128*d^3) + ((16*a^2 + (b*c*(5*b*c - 16*a*d))/d^2)*x^3*Sqrt[c + d*x^2])/64 - (b*(5*b*c - 16*a*d)*x^3*(c + d*x^2)^(3/2))/(48*d^2) + (b^2*x^5*(c + d*x^2)^(3/2))/(8*d) - (c^2*(16*a^2*d^2 + b*c*(5*b*c - 16*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(128*d^(7/2))","A",6,6,24,0.2500,1,"{464, 459, 279, 321, 217, 206}"
606,1,149,0,0.0951957,"\int \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[(a + b*x^2)^2*Sqrt[c + d*x^2],x]","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-4 a b c d+b^2 c^2\right)}{16 d^2}+\frac{c \left(8 a^2 d^2-4 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{5/2}}-\frac{b x \left(c+d x^2\right)^{3/2} (3 b c-8 a d)}{24 d^2}+\frac{b x \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}}{6 d}","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-4 a b c d+b^2 c^2\right)}{16 d^2}+\frac{c \left(8 a^2 d^2-4 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{5/2}}-\frac{b x \left(c+d x^2\right)^{3/2} (3 b c-8 a d)}{24 d^2}+\frac{b x \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}}{6 d}",1,"((b^2*c^2 - 4*a*b*c*d + 8*a^2*d^2)*x*Sqrt[c + d*x^2])/(16*d^2) - (b*(3*b*c - 8*a*d)*x*(c + d*x^2)^(3/2))/(24*d^2) + (b*x*(a + b*x^2)*(c + d*x^2)^(3/2))/(6*d) + (c*(b^2*c^2 - 4*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*d^(5/2))","A",5,5,21,0.2381,1,"{416, 388, 195, 217, 206}"
607,1,130,0,0.086252,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^2} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^2,x]","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{c x}-\frac{\left(b^2 c^2-8 a d (a d+b c)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{3/2}}-\frac{1}{8} x \sqrt{c+d x^2} \left(\frac{b^2 c}{d}-\frac{8 a (a d+b c)}{c}\right)+\frac{b^2 x \left(c+d x^2\right)^{3/2}}{4 d}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{c x}-\frac{\left(b^2 c^2-8 a d (a d+b c)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{3/2}}-\frac{x \sqrt{c+d x^2} \left(b^2 c^2-8 a d (a d+b c)\right)}{8 c d}+\frac{b^2 x \left(c+d x^2\right)^{3/2}}{4 d}",1,"-(((b^2*c)/d - (8*a*(b*c + a*d))/c)*x*Sqrt[c + d*x^2])/8 - (a^2*(c + d*x^2)^(3/2))/(c*x) + (b^2*x*(c + d*x^2)^(3/2))/(4*d) - ((b^2*c^2 - 8*a*d*(b*c + a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*d^(3/2))","A",5,5,24,0.2083,1,"{462, 388, 195, 217, 206}"
608,1,111,0,0.0654748,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^4} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^4,x]","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{3 c x^3}-\frac{2 a b \left(c+d x^2\right)^{3/2}}{c x}+\frac{b x \sqrt{c+d x^2} (4 a d+b c)}{2 c}+\frac{b (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 \sqrt{d}}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{3 c x^3}-\frac{2 a b \left(c+d x^2\right)^{3/2}}{c x}+\frac{b x \sqrt{c+d x^2} (4 a d+b c)}{2 c}+\frac{b (4 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 \sqrt{d}}",1,"(b*(b*c + 4*a*d)*x*Sqrt[c + d*x^2])/(2*c) - (a^2*(c + d*x^2)^(3/2))/(3*c*x^3) - (2*a*b*(c + d*x^2)^(3/2))/(c*x) + (b*(b*c + 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*Sqrt[d])","A",5,5,24,0.2083,1,"{462, 453, 195, 217, 206}"
609,1,103,0,0.0580408,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^6} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^6,x]","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{5 c x^5}-\frac{2 a \left(c+d x^2\right)^{3/2} (5 b c-a d)}{15 c^2 x^3}-\frac{b^2 \sqrt{c+d x^2}}{x}+b^2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{5 c x^5}-\frac{2 a \left(c+d x^2\right)^{3/2} (5 b c-a d)}{15 c^2 x^3}-\frac{b^2 \sqrt{c+d x^2}}{x}+b^2 \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)",1,"-((b^2*Sqrt[c + d*x^2])/x) - (a^2*(c + d*x^2)^(3/2))/(5*c*x^5) - (2*a*(5*b*c - a*d)*(c + d*x^2)^(3/2))/(15*c^2*x^3) + b^2*Sqrt[d]*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]]","A",5,5,24,0.2083,1,"{462, 451, 277, 217, 206}"
610,1,100,0,0.0747952,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^8} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^8,x]","-\frac{\left(c+d x^2\right)^{3/2} \left(8 a^2 d^2-28 a b c d+35 b^2 c^2\right)}{105 c^3 x^3}-\frac{a^2 \left(c+d x^2\right)^{3/2}}{7 c x^7}-\frac{2 a \left(c+d x^2\right)^{3/2} (7 b c-2 a d)}{35 c^2 x^5}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{7 c x^7}-\frac{\left(c+d x^2\right)^{3/2} \left(35 b^2 c^2-4 a d (7 b c-2 a d)\right)}{105 c^3 x^3}-\frac{2 a \left(c+d x^2\right)^{3/2} (7 b c-2 a d)}{35 c^2 x^5}",1,"-(a^2*(c + d*x^2)^(3/2))/(7*c*x^7) - (2*a*(7*b*c - 2*a*d)*(c + d*x^2)^(3/2))/(35*c^2*x^5) - ((35*b^2*c^2 - 28*a*b*c*d + 8*a^2*d^2)*(c + d*x^2)^(3/2))/(105*c^3*x^3)","A",3,3,24,0.1250,1,"{462, 453, 264}"
611,1,144,0,0.1317673,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^{10}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^10,x]","-\frac{\left(c+d x^2\right)^{3/2} \left(8 a^2 d^2-24 a b c d+21 b^2 c^2\right)}{105 c^3 x^5}-\frac{a^2 \left(c+d x^2\right)^{3/2}}{9 c x^9}+\frac{2 d \left(c+d x^2\right)^{3/2} \left(21 b^2 c^2-8 a d (3 b c-a d)\right)}{315 c^4 x^3}-\frac{2 a \left(c+d x^2\right)^{3/2} (3 b c-a d)}{21 c^2 x^7}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{9 c x^9}+\frac{2 d \left(c+d x^2\right)^{3/2} \left(21 b^2 c^2-8 a d (3 b c-a d)\right)}{315 c^4 x^3}-\frac{\left(c+d x^2\right)^{3/2} \left(21 b^2 c^2-8 a d (3 b c-a d)\right)}{105 c^3 x^5}-\frac{2 a \left(c+d x^2\right)^{3/2} (3 b c-a d)}{21 c^2 x^7}",1,"-(a^2*(c + d*x^2)^(3/2))/(9*c*x^9) - (2*a*(3*b*c - a*d)*(c + d*x^2)^(3/2))/(21*c^2*x^7) - ((21*b^2*c^2 - 24*a*b*c*d + 8*a^2*d^2)*(c + d*x^2)^(3/2))/(105*c^3*x^5) + (2*d*(21*b^2*c^2 - 8*a*d*(3*b*c - a*d))*(c + d*x^2)^(3/2))/(315*c^4*x^3)","A",4,4,24,0.1667,1,"{462, 453, 271, 264}"
612,1,190,0,0.1707573,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^{12}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^12,x]","-\frac{\left(c+d x^2\right)^{3/2} \left(16 a^2 d^2-44 a b c d+33 b^2 c^2\right)}{231 c^3 x^7}-\frac{a^2 \left(c+d x^2\right)^{3/2}}{11 c x^{11}}-\frac{8 d^2 \left(c+d x^2\right)^{3/2} \left(33 b^2 c^2-4 a d (11 b c-4 a d)\right)}{3465 c^5 x^3}+\frac{4 d \left(c+d x^2\right)^{3/2} \left(33 b^2 c^2-4 a d (11 b c-4 a d)\right)}{1155 c^4 x^5}-\frac{2 a \left(c+d x^2\right)^{3/2} (11 b c-4 a d)}{99 c^2 x^9}","-\frac{a^2 \left(c+d x^2\right)^{3/2}}{11 c x^{11}}-\frac{8 d^2 \left(c+d x^2\right)^{3/2} \left(33 b^2 c^2-4 a d (11 b c-4 a d)\right)}{3465 c^5 x^3}+\frac{4 d \left(c+d x^2\right)^{3/2} \left(33 b^2 c^2-4 a d (11 b c-4 a d)\right)}{1155 c^4 x^5}-\frac{\left(c+d x^2\right)^{3/2} \left(33 b^2 c^2-4 a d (11 b c-4 a d)\right)}{231 c^3 x^7}-\frac{2 a \left(c+d x^2\right)^{3/2} (11 b c-4 a d)}{99 c^2 x^9}",1,"-(a^2*(c + d*x^2)^(3/2))/(11*c*x^11) - (2*a*(11*b*c - 4*a*d)*(c + d*x^2)^(3/2))/(99*c^2*x^9) - ((33*b^2*c^2 - 44*a*b*c*d + 16*a^2*d^2)*(c + d*x^2)^(3/2))/(231*c^3*x^7) + (4*d*(33*b^2*c^2 - 4*a*d*(11*b*c - 4*a*d))*(c + d*x^2)^(3/2))/(1155*c^4*x^5) - (8*d^2*(33*b^2*c^2 - 4*a*d*(11*b*c - 4*a*d))*(c + d*x^2)^(3/2))/(3465*c^5*x^3)","A",5,4,24,0.1667,1,"{462, 453, 271, 264}"
613,1,278,0,0.2661615,"\int x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[x^4*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","\frac{c^2 x^3 \sqrt{c+d x^2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{1536 d^3}-\frac{c^3 x \sqrt{c+d x^2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{1024 d^4}+\frac{c^4 \left(24 a^2 d^2+b c (7 b c-24 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{1024 d^{9/2}}+\frac{1}{192} x^5 \left(c+d x^2\right)^{3/2} \left(24 a^2+\frac{b c (7 b c-24 a d)}{d^2}\right)+\frac{c x^5 \sqrt{c+d x^2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{384 d^2}-\frac{b x^5 \left(c+d x^2\right)^{5/2} (7 b c-24 a d)}{120 d^2}+\frac{b^2 x^7 \left(c+d x^2\right)^{5/2}}{12 d}","\frac{c^2 x^3 \sqrt{c+d x^2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{1536 d^3}-\frac{c^3 x \sqrt{c+d x^2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{1024 d^4}+\frac{c^4 \left(24 a^2 d^2+b c (7 b c-24 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{1024 d^{9/2}}+\frac{x^5 \left(c+d x^2\right)^{3/2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{192 d^2}+\frac{c x^5 \sqrt{c+d x^2} \left(24 a^2 d^2+b c (7 b c-24 a d)\right)}{384 d^2}-\frac{b x^5 \left(c+d x^2\right)^{5/2} (7 b c-24 a d)}{120 d^2}+\frac{b^2 x^7 \left(c+d x^2\right)^{5/2}}{12 d}",1,"-(c^3*(24*a^2*d^2 + b*c*(7*b*c - 24*a*d))*x*Sqrt[c + d*x^2])/(1024*d^4) + (c^2*(24*a^2*d^2 + b*c*(7*b*c - 24*a*d))*x^3*Sqrt[c + d*x^2])/(1536*d^3) + (c*(24*a^2*d^2 + b*c*(7*b*c - 24*a*d))*x^5*Sqrt[c + d*x^2])/(384*d^2) + ((24*a^2 + (b*c*(7*b*c - 24*a*d))/d^2)*x^5*(c + d*x^2)^(3/2))/192 - (b*(7*b*c - 24*a*d)*x^5*(c + d*x^2)^(5/2))/(120*d^2) + (b^2*x^7*(c + d*x^2)^(5/2))/(12*d) + (c^4*(24*a^2*d^2 + b*c*(7*b*c - 24*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(1024*d^(9/2))","A",8,6,24,0.2500,1,"{464, 459, 279, 321, 217, 206}"
614,1,114,0,0.0896447,"\int x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[x^3*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","-\frac{b \left(c+d x^2\right)^{9/2} (3 b c-2 a d)}{9 d^4}+\frac{\left(c+d x^2\right)^{7/2} (b c-a d) (3 b c-a d)}{7 d^4}-\frac{c \left(c+d x^2\right)^{5/2} (b c-a d)^2}{5 d^4}+\frac{b^2 \left(c+d x^2\right)^{11/2}}{11 d^4}","-\frac{b \left(c+d x^2\right)^{9/2} (3 b c-2 a d)}{9 d^4}+\frac{\left(c+d x^2\right)^{7/2} (b c-a d) (3 b c-a d)}{7 d^4}-\frac{c \left(c+d x^2\right)^{5/2} (b c-a d)^2}{5 d^4}+\frac{b^2 \left(c+d x^2\right)^{11/2}}{11 d^4}",1,"-(c*(b*c - a*d)^2*(c + d*x^2)^(5/2))/(5*d^4) + ((b*c - a*d)*(3*b*c - a*d)*(c + d*x^2)^(7/2))/(7*d^4) - (b*(3*b*c - 2*a*d)*(c + d*x^2)^(9/2))/(9*d^4) + (b^2*(c + d*x^2)^(11/2))/(11*d^4)","A",3,2,24,0.08333,1,"{446, 77}"
615,1,232,0,0.2175667,"\int x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[x^2*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","\frac{c^2 x \sqrt{c+d x^2} \left(16 a^2 d^2+3 b c (b c-4 a d)\right)}{256 d^3}-\frac{c^3 \left(16 a^2 d^2+3 b c (b c-4 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{256 d^{7/2}}+\frac{1}{96} x^3 \left(c+d x^2\right)^{3/2} \left(16 a^2+\frac{3 b c (b c-4 a d)}{d^2}\right)+\frac{c x^3 \sqrt{c+d x^2} \left(16 a^2 d^2+3 b c (b c-4 a d)\right)}{128 d^2}-\frac{b x^3 \left(c+d x^2\right)^{5/2} (b c-4 a d)}{16 d^2}+\frac{b^2 x^5 \left(c+d x^2\right)^{5/2}}{10 d}","\frac{c^2 x \sqrt{c+d x^2} \left(16 a^2 d^2+3 b c (b c-4 a d)\right)}{256 d^3}-\frac{c^3 \left(16 a^2 d^2+3 b c (b c-4 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{256 d^{7/2}}+\frac{x^3 \left(c+d x^2\right)^{3/2} \left(16 a^2 d^2+3 b c (b c-4 a d)\right)}{96 d^2}+\frac{c x^3 \sqrt{c+d x^2} \left(16 a^2 d^2+3 b c (b c-4 a d)\right)}{128 d^2}-\frac{b x^3 \left(c+d x^2\right)^{5/2} (b c-4 a d)}{16 d^2}+\frac{b^2 x^5 \left(c+d x^2\right)^{5/2}}{10 d}",1,"(c^2*(16*a^2*d^2 + 3*b*c*(b*c - 4*a*d))*x*Sqrt[c + d*x^2])/(256*d^3) + (c*(16*a^2*d^2 + 3*b*c*(b*c - 4*a*d))*x^3*Sqrt[c + d*x^2])/(128*d^2) + ((16*a^2 + (3*b*c*(b*c - 4*a*d))/d^2)*x^3*(c + d*x^2)^(3/2))/96 - (b*(b*c - 4*a*d)*x^3*(c + d*x^2)^(5/2))/(16*d^2) + (b^2*x^5*(c + d*x^2)^(5/2))/(10*d) - (c^3*(16*a^2*d^2 + 3*b*c*(b*c - 4*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(256*d^(7/2))","A",7,6,24,0.2500,1,"{464, 459, 279, 321, 217, 206}"
616,1,77,0,0.0599617,"\int x \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[x*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","-\frac{2 b \left(c+d x^2\right)^{7/2} (b c-a d)}{7 d^3}+\frac{\left(c+d x^2\right)^{5/2} (b c-a d)^2}{5 d^3}+\frac{b^2 \left(c+d x^2\right)^{9/2}}{9 d^3}","-\frac{2 b \left(c+d x^2\right)^{7/2} (b c-a d)}{7 d^3}+\frac{\left(c+d x^2\right)^{5/2} (b c-a d)^2}{5 d^3}+\frac{b^2 \left(c+d x^2\right)^{9/2}}{9 d^3}",1,"((b*c - a*d)^2*(c + d*x^2)^(5/2))/(5*d^3) - (2*b*(b*c - a*d)*(c + d*x^2)^(7/2))/(7*d^3) + (b^2*(c + d*x^2)^(9/2))/(9*d^3)","A",3,2,22,0.09091,1,"{444, 43}"
617,1,196,0,0.1240544,"\int \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","\frac{x \left(c+d x^2\right)^{3/2} \left(48 a^2 d^2-16 a b c d+3 b^2 c^2\right)}{192 d^2}+\frac{c x \sqrt{c+d x^2} \left(48 a^2 d^2-16 a b c d+3 b^2 c^2\right)}{128 d^2}+\frac{c^2 \left(48 a^2 d^2-16 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{5/2}}-\frac{b x \left(c+d x^2\right)^{5/2} (3 b c-10 a d)}{48 d^2}+\frac{b x \left(a+b x^2\right) \left(c+d x^2\right)^{5/2}}{8 d}","\frac{x \left(c+d x^2\right)^{3/2} \left(48 a^2 d^2-16 a b c d+3 b^2 c^2\right)}{192 d^2}+\frac{c x \sqrt{c+d x^2} \left(48 a^2 d^2-16 a b c d+3 b^2 c^2\right)}{128 d^2}+\frac{c^2 \left(48 a^2 d^2-16 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{5/2}}-\frac{b x \left(c+d x^2\right)^{5/2} (3 b c-10 a d)}{48 d^2}+\frac{b x \left(a+b x^2\right) \left(c+d x^2\right)^{5/2}}{8 d}",1,"(c*(3*b^2*c^2 - 16*a*b*c*d + 48*a^2*d^2)*x*Sqrt[c + d*x^2])/(128*d^2) + ((3*b^2*c^2 - 16*a*b*c*d + 48*a^2*d^2)*x*(c + d*x^2)^(3/2))/(192*d^2) - (b*(3*b*c - 10*a*d)*x*(c + d*x^2)^(5/2))/(48*d^2) + (b*x*(a + b*x^2)*(c + d*x^2)^(5/2))/(8*d) + (c^2*(3*b^2*c^2 - 16*a*b*c*d + 48*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(128*d^(5/2))","A",6,5,21,0.2381,1,"{416, 388, 195, 217, 206}"
618,1,111,0,0.0936338,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x,x]","-a^2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{1}{3} a^2 \left(c+d x^2\right)^{3/2}+a^2 c \sqrt{c+d x^2}-\frac{b \left(c+d x^2\right)^{5/2} (b c-2 a d)}{5 d^2}+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d^2}","-a^2 c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{1}{3} a^2 \left(c+d x^2\right)^{3/2}+a^2 c \sqrt{c+d x^2}-\frac{b \left(c+d x^2\right)^{5/2} (b c-2 a d)}{5 d^2}+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d^2}",1,"a^2*c*Sqrt[c + d*x^2] + (a^2*(c + d*x^2)^(3/2))/3 - (b*(b*c - 2*a*d)*(c + d*x^2)^(5/2))/(5*d^2) + (b^2*(c + d*x^2)^(7/2))/(7*d^2) - a^2*c^(3/2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]","A",7,5,24,0.2083,1,"{446, 88, 50, 63, 208}"
619,1,172,0,0.1185548,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x^2} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^2,x]","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{c x}-\frac{c \left(b^2 c^2-12 a d (2 a d+b c)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{3/2}}-\frac{x \sqrt{c+d x^2} \left(b^2 c^2-12 a d (2 a d+b c)\right)}{16 d}-\frac{1}{24} x \left(c+d x^2\right)^{3/2} \left(\frac{b^2 c}{d}-\frac{12 a (2 a d+b c)}{c}\right)+\frac{b^2 x \left(c+d x^2\right)^{5/2}}{6 d}","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{c x}-\frac{c \left(b^2 c^2-12 a d (2 a d+b c)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{3/2}}-\frac{x \left(c+d x^2\right)^{3/2} \left(b^2 c^2-12 a d (2 a d+b c)\right)}{24 c d}-\frac{x \sqrt{c+d x^2} \left(b^2 c^2-12 a d (2 a d+b c)\right)}{16 d}+\frac{b^2 x \left(c+d x^2\right)^{5/2}}{6 d}",1,"-((b^2*c^2 - 12*a*d*(b*c + 2*a*d))*x*Sqrt[c + d*x^2])/(16*d) - (((b^2*c)/d - (12*a*(b*c + 2*a*d))/c)*x*(c + d*x^2)^(3/2))/24 - (a^2*(c + d*x^2)^(5/2))/(c*x) + (b^2*x*(c + d*x^2)^(5/2))/(6*d) - (c*(b^2*c^2 - 12*a*d*(b*c + 2*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*d^(3/2))","A",6,5,24,0.2083,1,"{462, 388, 195, 217, 206}"
620,1,136,0,0.1087648,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x^3} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^3,x]","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{2 c x^2}+\frac{a \left(c+d x^2\right)^{3/2} (3 a d+4 b c)}{6 c}+\frac{1}{2} a \sqrt{c+d x^2} (3 a d+4 b c)-\frac{1}{2} a \sqrt{c} (3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d}","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{2 c x^2}+\frac{a \left(c+d x^2\right)^{3/2} (3 a d+4 b c)}{6 c}+\frac{1}{2} a \sqrt{c+d x^2} (3 a d+4 b c)-\frac{1}{2} a \sqrt{c} (3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d}",1,"(a*(4*b*c + 3*a*d)*Sqrt[c + d*x^2])/2 + (a*(4*b*c + 3*a*d)*(c + d*x^2)^(3/2))/(6*c) + (b^2*(c + d*x^2)^(5/2))/(5*d) - (a^2*(c + d*x^2)^(5/2))/(2*c*x^2) - (a*Sqrt[c]*(4*b*c + 3*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/2","A",7,6,24,0.2500,1,"{446, 89, 80, 50, 63, 208}"
621,1,181,0,0.1298459,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x^4} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^4,x]","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{3 c x^3}+\frac{1}{12} x \left(c+d x^2\right)^{3/2} \left(\frac{8 a d (a d+3 b c)}{c^2}+3 b^2\right)+\frac{x \sqrt{c+d x^2} \left(8 a d (a d+3 b c)+3 b^2 c^2\right)}{8 c}+\frac{\left(8 a d (a d+3 b c)+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 \sqrt{d}}-\frac{2 a \left(c+d x^2\right)^{5/2} (a d+3 b c)}{3 c^2 x}","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{3 c x^3}+\frac{x \left(c+d x^2\right)^{3/2} \left(8 a d (a d+3 b c)+3 b^2 c^2\right)}{12 c^2}+\frac{x \sqrt{c+d x^2} \left(8 a d (a d+3 b c)+3 b^2 c^2\right)}{8 c}+\frac{\left(8 a d (a d+3 b c)+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 \sqrt{d}}-\frac{2 a \left(c+d x^2\right)^{5/2} (a d+3 b c)}{3 c^2 x}",1,"((3*b^2*c^2 + 8*a*d*(3*b*c + a*d))*x*Sqrt[c + d*x^2])/(8*c) + ((3*b^2 + (8*a*d*(3*b*c + a*d))/c^2)*x*(c + d*x^2)^(3/2))/12 - (a^2*(c + d*x^2)^(5/2))/(3*c*x^3) - (2*a*(3*b*c + a*d)*(c + d*x^2)^(5/2))/(3*c^2*x) + ((3*b^2*c^2 + 8*a*d*(3*b*c + a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*Sqrt[d])","A",6,5,24,0.2083,1,"{462, 453, 195, 217, 206}"
622,1,178,0,0.2070479,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x^5} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^5,x]","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{4 c x^4}+\frac{1}{24} \left(c+d x^2\right)^{3/2} \left(\frac{3 a d (a d+8 b c)}{c^2}+8 b^2\right)+\frac{\sqrt{c+d x^2} \left(3 a d (a d+8 b c)+8 b^2 c^2\right)}{8 c}-\frac{\left(3 a d (a d+8 b c)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 \sqrt{c}}-\frac{a \left(c+d x^2\right)^{5/2} (a d+8 b c)}{8 c^2 x^2}","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{4 c x^4}+\frac{\left(c+d x^2\right)^{3/2} \left(3 a d (a d+8 b c)+8 b^2 c^2\right)}{24 c^2}+\frac{\sqrt{c+d x^2} \left(3 a d (a d+8 b c)+8 b^2 c^2\right)}{8 c}-\frac{\left(3 a d (a d+8 b c)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 \sqrt{c}}-\frac{a \left(c+d x^2\right)^{5/2} (a d+8 b c)}{8 c^2 x^2}",1,"((8*b^2*c^2 + 3*a*d*(8*b*c + a*d))*Sqrt[c + d*x^2])/(8*c) + ((8*b^2 + (3*a*d*(8*b*c + a*d))/c^2)*(c + d*x^2)^(3/2))/24 - (a^2*(c + d*x^2)^(5/2))/(4*c*x^4) - (a*(8*b*c + a*d)*(c + d*x^2)^(5/2))/(8*c^2*x^2) - ((8*b^2*c^2 + 3*a*d*(8*b*c + a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(8*Sqrt[c])","A",7,6,24,0.2500,1,"{446, 89, 78, 50, 63, 208}"
623,1,147,0,0.0897115,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x^6} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^6,x]","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{5 c x^5}-\frac{2 a b \left(c+d x^2\right)^{5/2}}{3 c x^3}-\frac{b \left(c+d x^2\right)^{3/2} (4 a d+3 b c)}{3 c x}+\frac{b d x \sqrt{c+d x^2} (4 a d+3 b c)}{2 c}+\frac{1}{2} b \sqrt{d} (4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{5 c x^5}-\frac{2 a b \left(c+d x^2\right)^{5/2}}{3 c x^3}-\frac{b \left(c+d x^2\right)^{3/2} (4 a d+3 b c)}{3 c x}+\frac{b d x \sqrt{c+d x^2} (4 a d+3 b c)}{2 c}+\frac{1}{2} b \sqrt{d} (4 a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)",1,"(b*d*(3*b*c + 4*a*d)*x*Sqrt[c + d*x^2])/(2*c) - (b*(3*b*c + 4*a*d)*(c + d*x^2)^(3/2))/(3*c*x) - (a^2*(c + d*x^2)^(5/2))/(5*c*x^5) - (2*a*b*(c + d*x^2)^(5/2))/(3*c*x^3) + (b*Sqrt[d]*(3*b*c + 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/2","A",6,6,24,0.2500,1,"{462, 453, 277, 195, 217, 206}"
624,1,184,0,0.2220788,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{x^7} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/x^7,x]","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{6 c x^6}-\frac{\left(c+d x^2\right)^{3/2} \left(\frac{a d (12 b c-a d)}{c^2}+24 b^2\right)}{48 x^2}+\frac{d \sqrt{c+d x^2} \left(a d (12 b c-a d)+24 b^2 c^2\right)}{16 c^2}-\frac{d \left(a d (12 b c-a d)+24 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{3/2}}-\frac{a \left(c+d x^2\right)^{5/2} (12 b c-a d)}{24 c^2 x^4}","-\frac{a^2 \left(c+d x^2\right)^{5/2}}{6 c x^6}-\frac{\left(c+d x^2\right)^{3/2} \left(a d (12 b c-a d)+24 b^2 c^2\right)}{48 c^2 x^2}+\frac{d \sqrt{c+d x^2} \left(a d (12 b c-a d)+24 b^2 c^2\right)}{16 c^2}-\frac{d \left(a d (12 b c-a d)+24 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{3/2}}-\frac{a \left(c+d x^2\right)^{5/2} (12 b c-a d)}{24 c^2 x^4}",1,"(d*(24*b^2*c^2 + a*d*(12*b*c - a*d))*Sqrt[c + d*x^2])/(16*c^2) - ((24*b^2 + (a*d*(12*b*c - a*d))/c^2)*(c + d*x^2)^(3/2))/(48*x^2) - (a^2*(c + d*x^2)^(5/2))/(6*c*x^6) - (a*(12*b*c - a*d)*(c + d*x^2)^(5/2))/(24*c^2*x^4) - (d*(24*b^2*c^2 + a*d*(12*b*c - a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(16*c^(3/2))","A",7,7,24,0.2917,1,"{446, 89, 78, 47, 50, 63, 208}"
625,1,114,0,0.0897296,"\int x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2} \, dx","Int[x^3*(a + b*x^2)^2*(c + d*x^2)^(5/2),x]","-\frac{b \left(c+d x^2\right)^{11/2} (3 b c-2 a d)}{11 d^4}+\frac{\left(c+d x^2\right)^{9/2} (b c-a d) (3 b c-a d)}{9 d^4}-\frac{c \left(c+d x^2\right)^{7/2} (b c-a d)^2}{7 d^4}+\frac{b^2 \left(c+d x^2\right)^{13/2}}{13 d^4}","-\frac{b \left(c+d x^2\right)^{11/2} (3 b c-2 a d)}{11 d^4}+\frac{\left(c+d x^2\right)^{9/2} (b c-a d) (3 b c-a d)}{9 d^4}-\frac{c \left(c+d x^2\right)^{7/2} (b c-a d)^2}{7 d^4}+\frac{b^2 \left(c+d x^2\right)^{13/2}}{13 d^4}",1,"-(c*(b*c - a*d)^2*(c + d*x^2)^(7/2))/(7*d^4) + ((b*c - a*d)*(3*b*c - a*d)*(c + d*x^2)^(9/2))/(9*d^4) - (b*(3*b*c - 2*a*d)*(c + d*x^2)^(11/2))/(11*d^4) + (b^2*(c + d*x^2)^(13/2))/(13*d^4)","A",3,2,24,0.08333,1,"{446, 77}"
626,1,278,0,0.2576782,"\int x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2} \, dx","Int[x^2*(a + b*x^2)^2*(c + d*x^2)^(5/2),x]","\frac{c^2 x^3 \sqrt{c+d x^2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{512 d^2}+\frac{c^3 x \sqrt{c+d x^2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{1024 d^3}-\frac{c^4 \left(40 a^2 d^2+b c (5 b c-24 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{1024 d^{7/2}}+\frac{1}{320} x^3 \left(c+d x^2\right)^{5/2} \left(40 a^2+\frac{b c (5 b c-24 a d)}{d^2}\right)+\frac{c x^3 \left(c+d x^2\right)^{3/2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{384 d^2}-\frac{b x^3 \left(c+d x^2\right)^{7/2} (5 b c-24 a d)}{120 d^2}+\frac{b^2 x^5 \left(c+d x^2\right)^{7/2}}{12 d}","\frac{c^2 x^3 \sqrt{c+d x^2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{512 d^2}+\frac{c^3 x \sqrt{c+d x^2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{1024 d^3}-\frac{c^4 \left(40 a^2 d^2+b c (5 b c-24 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{1024 d^{7/2}}+\frac{x^3 \left(c+d x^2\right)^{5/2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{320 d^2}+\frac{c x^3 \left(c+d x^2\right)^{3/2} \left(40 a^2 d^2+b c (5 b c-24 a d)\right)}{384 d^2}-\frac{b x^3 \left(c+d x^2\right)^{7/2} (5 b c-24 a d)}{120 d^2}+\frac{b^2 x^5 \left(c+d x^2\right)^{7/2}}{12 d}",1,"(c^3*(40*a^2*d^2 + b*c*(5*b*c - 24*a*d))*x*Sqrt[c + d*x^2])/(1024*d^3) + (c^2*(40*a^2*d^2 + b*c*(5*b*c - 24*a*d))*x^3*Sqrt[c + d*x^2])/(512*d^2) + (c*(40*a^2*d^2 + b*c*(5*b*c - 24*a*d))*x^3*(c + d*x^2)^(3/2))/(384*d^2) + ((40*a^2 + (b*c*(5*b*c - 24*a*d))/d^2)*x^3*(c + d*x^2)^(5/2))/320 - (b*(5*b*c - 24*a*d)*x^3*(c + d*x^2)^(7/2))/(120*d^2) + (b^2*x^5*(c + d*x^2)^(7/2))/(12*d) - (c^4*(40*a^2*d^2 + b*c*(5*b*c - 24*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(1024*d^(7/2))","A",8,6,24,0.2500,1,"{464, 459, 279, 321, 217, 206}"
627,1,77,0,0.059001,"\int x \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2} \, dx","Int[x*(a + b*x^2)^2*(c + d*x^2)^(5/2),x]","-\frac{2 b \left(c+d x^2\right)^{9/2} (b c-a d)}{9 d^3}+\frac{\left(c+d x^2\right)^{7/2} (b c-a d)^2}{7 d^3}+\frac{b^2 \left(c+d x^2\right)^{11/2}}{11 d^3}","-\frac{2 b \left(c+d x^2\right)^{9/2} (b c-a d)}{9 d^3}+\frac{\left(c+d x^2\right)^{7/2} (b c-a d)^2}{7 d^3}+\frac{b^2 \left(c+d x^2\right)^{11/2}}{11 d^3}",1,"((b*c - a*d)^2*(c + d*x^2)^(7/2))/(7*d^3) - (2*b*(b*c - a*d)*(c + d*x^2)^(9/2))/(9*d^3) + (b^2*(c + d*x^2)^(11/2))/(11*d^3)","A",3,2,22,0.09091,1,"{444, 43}"
628,1,240,0,0.1523932,"\int \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2} \, dx","Int[(a + b*x^2)^2*(c + d*x^2)^(5/2),x]","\frac{x \left(c+d x^2\right)^{5/2} \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right)}{480 d^2}+\frac{c x \left(c+d x^2\right)^{3/2} \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right)}{384 d^2}+\frac{c^2 x \sqrt{c+d x^2} \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right)}{256 d^2}+\frac{c^3 \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{256 d^{5/2}}-\frac{3 b x \left(c+d x^2\right)^{7/2} (b c-4 a d)}{80 d^2}+\frac{b x \left(a+b x^2\right) \left(c+d x^2\right)^{7/2}}{10 d}","\frac{x \left(c+d x^2\right)^{5/2} \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right)}{480 d^2}+\frac{c x \left(c+d x^2\right)^{3/2} \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right)}{384 d^2}+\frac{c^2 x \sqrt{c+d x^2} \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right)}{256 d^2}+\frac{c^3 \left(80 a^2 d^2-20 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{256 d^{5/2}}-\frac{3 b x \left(c+d x^2\right)^{7/2} (b c-4 a d)}{80 d^2}+\frac{b x \left(a+b x^2\right) \left(c+d x^2\right)^{7/2}}{10 d}",1,"(c^2*(3*b^2*c^2 - 20*a*b*c*d + 80*a^2*d^2)*x*Sqrt[c + d*x^2])/(256*d^2) + (c*(3*b^2*c^2 - 20*a*b*c*d + 80*a^2*d^2)*x*(c + d*x^2)^(3/2))/(384*d^2) + ((3*b^2*c^2 - 20*a*b*c*d + 80*a^2*d^2)*x*(c + d*x^2)^(5/2))/(480*d^2) - (3*b*(b*c - 4*a*d)*x*(c + d*x^2)^(7/2))/(80*d^2) + (b*x*(a + b*x^2)*(c + d*x^2)^(7/2))/(10*d) + (c^3*(3*b^2*c^2 - 20*a*b*c*d + 80*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(256*d^(5/2))","A",7,5,21,0.2381,1,"{416, 388, 195, 217, 206}"
629,1,132,0,0.1106413,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x,x]","a^2 c^2 \sqrt{c+d x^2}-a^2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{1}{5} a^2 \left(c+d x^2\right)^{5/2}+\frac{1}{3} a^2 c \left(c+d x^2\right)^{3/2}-\frac{b \left(c+d x^2\right)^{7/2} (b c-2 a d)}{7 d^2}+\frac{b^2 \left(c+d x^2\right)^{9/2}}{9 d^2}","a^2 c^2 \sqrt{c+d x^2}-a^2 c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{1}{5} a^2 \left(c+d x^2\right)^{5/2}+\frac{1}{3} a^2 c \left(c+d x^2\right)^{3/2}-\frac{b \left(c+d x^2\right)^{7/2} (b c-2 a d)}{7 d^2}+\frac{b^2 \left(c+d x^2\right)^{9/2}}{9 d^2}",1,"a^2*c^2*Sqrt[c + d*x^2] + (a^2*c*(c + d*x^2)^(3/2))/3 + (a^2*(c + d*x^2)^(5/2))/5 - (b*(b*c - 2*a*d)*(c + d*x^2)^(7/2))/(7*d^2) + (b^2*(c + d*x^2)^(9/2))/(9*d^2) - a^2*c^(5/2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]","A",8,5,24,0.2083,1,"{446, 88, 50, 63, 208}"
630,1,214,0,0.1414559,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x^2} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^2,x]","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{c x}-\frac{5 c^2 \left(b^2 c^2-16 a d (3 a d+b c)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{3/2}}-\frac{5 x \left(c+d x^2\right)^{3/2} \left(b^2 c^2-16 a d (3 a d+b c)\right)}{192 d}-\frac{5 c x \sqrt{c+d x^2} \left(b^2 c^2-16 a d (3 a d+b c)\right)}{128 d}-\frac{1}{48} x \left(c+d x^2\right)^{5/2} \left(\frac{b^2 c}{d}-\frac{16 a (3 a d+b c)}{c}\right)+\frac{b^2 x \left(c+d x^2\right)^{7/2}}{8 d}","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{c x}-\frac{5 c^2 \left(b^2 c^2-16 a d (3 a d+b c)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{3/2}}-\frac{x \left(c+d x^2\right)^{5/2} \left(b^2 c^2-16 a d (3 a d+b c)\right)}{48 c d}-\frac{5 x \left(c+d x^2\right)^{3/2} \left(b^2 c^2-16 a d (3 a d+b c)\right)}{192 d}-\frac{5 c x \sqrt{c+d x^2} \left(b^2 c^2-16 a d (3 a d+b c)\right)}{128 d}+\frac{b^2 x \left(c+d x^2\right)^{7/2}}{8 d}",1,"(-5*c*(b^2*c^2 - 16*a*d*(b*c + 3*a*d))*x*Sqrt[c + d*x^2])/(128*d) - (5*(b^2*c^2 - 16*a*d*(b*c + 3*a*d))*x*(c + d*x^2)^(3/2))/(192*d) - (((b^2*c)/d - (16*a*(b*c + 3*a*d))/c)*x*(c + d*x^2)^(5/2))/48 - (a^2*(c + d*x^2)^(7/2))/(c*x) + (b^2*x*(c + d*x^2)^(7/2))/(8*d) - (5*c^2*(b^2*c^2 - 16*a*d*(b*c + 3*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(128*d^(3/2))","A",7,5,24,0.2083,1,"{462, 388, 195, 217, 206}"
631,1,162,0,0.132013,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x^3} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^3,x]","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{2 c x^2}-\frac{1}{2} a c^{3/2} (5 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{a \left(c+d x^2\right)^{5/2} (5 a d+4 b c)}{10 c}+\frac{1}{6} a \left(c+d x^2\right)^{3/2} (5 a d+4 b c)+\frac{1}{2} a c \sqrt{c+d x^2} (5 a d+4 b c)+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d}","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{2 c x^2}-\frac{1}{2} a c^{3/2} (5 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)+\frac{a \left(c+d x^2\right)^{5/2} (5 a d+4 b c)}{10 c}+\frac{1}{6} a \left(c+d x^2\right)^{3/2} (5 a d+4 b c)+\frac{1}{2} a c \sqrt{c+d x^2} (5 a d+4 b c)+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d}",1,"(a*c*(4*b*c + 5*a*d)*Sqrt[c + d*x^2])/2 + (a*(4*b*c + 5*a*d)*(c + d*x^2)^(3/2))/6 + (a*(4*b*c + 5*a*d)*(c + d*x^2)^(5/2))/(10*c) + (b^2*(c + d*x^2)^(7/2))/(7*d) - (a^2*(c + d*x^2)^(7/2))/(2*c*x^2) - (a*c^(3/2)*(4*b*c + 5*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/2","A",8,6,24,0.2500,1,"{446, 89, 80, 50, 63, 208}"
632,1,219,0,0.1749194,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x^4} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^4,x]","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{3 c x^3}+\frac{1}{6} x \left(c+d x^2\right)^{5/2} \left(\frac{4 a d (2 a d+3 b c)}{c^2}+b^2\right)+\frac{5 x \left(c+d x^2\right)^{3/2} \left(4 a d (2 a d+3 b c)+b^2 c^2\right)}{24 c}+\frac{5}{16} x \sqrt{c+d x^2} \left(4 a d (2 a d+3 b c)+b^2 c^2\right)+\frac{5 c \left(4 a d (2 a d+3 b c)+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 \sqrt{d}}-\frac{2 a \left(c+d x^2\right)^{7/2} (2 a d+3 b c)}{3 c^2 x}","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{3 c x^3}+\frac{x \left(c+d x^2\right)^{5/2} \left(4 a d (2 a d+3 b c)+b^2 c^2\right)}{6 c^2}+\frac{5 x \left(c+d x^2\right)^{3/2} \left(4 a d (2 a d+3 b c)+b^2 c^2\right)}{24 c}+\frac{5}{16} x \sqrt{c+d x^2} \left(4 a d (2 a d+3 b c)+b^2 c^2\right)+\frac{5 c \left(4 a d (2 a d+3 b c)+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 \sqrt{d}}-\frac{2 a \left(c+d x^2\right)^{7/2} (2 a d+3 b c)}{3 c^2 x}",1,"(5*(b^2*c^2 + 4*a*d*(3*b*c + 2*a*d))*x*Sqrt[c + d*x^2])/16 + (5*(b^2*c^2 + 4*a*d*(3*b*c + 2*a*d))*x*(c + d*x^2)^(3/2))/(24*c) + ((b^2 + (4*a*d*(3*b*c + 2*a*d))/c^2)*x*(c + d*x^2)^(5/2))/6 - (a^2*(c + d*x^2)^(7/2))/(3*c*x^3) - (2*a*(3*b*c + 2*a*d)*(c + d*x^2)^(7/2))/(3*c^2*x) + (5*c*(b^2*c^2 + 4*a*d*(3*b*c + 2*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*Sqrt[d])","A",7,5,24,0.2083,1,"{462, 453, 195, 217, 206}"
633,1,219,0,0.2533532,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x^5} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^5,x]","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{4 c x^4}+\frac{1}{40} \left(c+d x^2\right)^{5/2} \left(\frac{5 a d (3 a d+8 b c)}{c^2}+8 b^2\right)+\frac{\left(c+d x^2\right)^{3/2} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right)}{24 c}+\frac{1}{8} \sqrt{c+d x^2} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right)-\frac{1}{8} \sqrt{c} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)-\frac{a \left(c+d x^2\right)^{7/2} (3 a d+8 b c)}{8 c^2 x^2}","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{4 c x^4}+\frac{\left(c+d x^2\right)^{5/2} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right)}{40 c^2}+\frac{\left(c+d x^2\right)^{3/2} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right)}{24 c}+\frac{1}{8} \sqrt{c+d x^2} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right)-\frac{1}{8} \sqrt{c} \left(5 a d (3 a d+8 b c)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)-\frac{a \left(c+d x^2\right)^{7/2} (3 a d+8 b c)}{8 c^2 x^2}",1,"((8*b^2*c^2 + 5*a*d*(8*b*c + 3*a*d))*Sqrt[c + d*x^2])/8 + ((8*b^2*c^2 + 5*a*d*(8*b*c + 3*a*d))*(c + d*x^2)^(3/2))/(24*c) + ((8*b^2 + (5*a*d*(8*b*c + 3*a*d))/c^2)*(c + d*x^2)^(5/2))/40 - (a^2*(c + d*x^2)^(7/2))/(4*c*x^4) - (a*(8*b*c + 3*a*d)*(c + d*x^2)^(7/2))/(8*c^2*x^2) - (Sqrt[c]*(8*b^2*c^2 + 5*a*d*(8*b*c + 3*a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/8","A",8,6,24,0.2500,1,"{446, 89, 78, 50, 63, 208}"
634,1,225,0,0.160411,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x^6} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^6,x]","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{5 c x^5}-\frac{\left(c+d x^2\right)^{5/2} \left(\frac{8 a d (a d+5 b c)}{c^2}+15 b^2\right)}{15 x}+\frac{d x \left(c+d x^2\right)^{3/2} \left(8 a d (a d+5 b c)+15 b^2 c^2\right)}{12 c^2}+\frac{d x \sqrt{c+d x^2} \left(8 a d (a d+5 b c)+15 b^2 c^2\right)}{8 c}+\frac{1}{8} \sqrt{d} \left(8 a d (a d+5 b c)+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)-\frac{2 a \left(c+d x^2\right)^{7/2} (a d+5 b c)}{15 c^2 x^3}","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{5 c x^5}-\frac{\left(c+d x^2\right)^{5/2} \left(8 a d (a d+5 b c)+15 b^2 c^2\right)}{15 c^2 x}+\frac{d x \left(c+d x^2\right)^{3/2} \left(8 a d (a d+5 b c)+15 b^2 c^2\right)}{12 c^2}+\frac{d x \sqrt{c+d x^2} \left(8 a d (a d+5 b c)+15 b^2 c^2\right)}{8 c}+\frac{1}{8} \sqrt{d} \left(8 a d (a d+5 b c)+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)-\frac{2 a \left(c+d x^2\right)^{7/2} (a d+5 b c)}{15 c^2 x^3}",1,"(d*(15*b^2*c^2 + 8*a*d*(5*b*c + a*d))*x*Sqrt[c + d*x^2])/(8*c) + (d*(15*b^2*c^2 + 8*a*d*(5*b*c + a*d))*x*(c + d*x^2)^(3/2))/(12*c^2) - ((15*b^2 + (8*a*d*(5*b*c + a*d))/c^2)*(c + d*x^2)^(5/2))/(15*x) - (a^2*(c + d*x^2)^(7/2))/(5*c*x^5) - (2*a*(5*b*c + a*d)*(c + d*x^2)^(7/2))/(15*c^2*x^3) + (Sqrt[d]*(15*b^2*c^2 + 8*a*d*(5*b*c + a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/8","A",7,6,24,0.2500,1,"{462, 453, 277, 195, 217, 206}"
635,1,219,0,0.2521576,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}}{x^7} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(5/2))/x^7,x]","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{6 c x^6}-\frac{\left(c+d x^2\right)^{5/2} \left(\frac{a d (a d+12 b c)}{c^2}+8 b^2\right)}{16 x^2}+\frac{5 d \left(c+d x^2\right)^{3/2} \left(a d (a d+12 b c)+8 b^2 c^2\right)}{48 c^2}+\frac{5 d \sqrt{c+d x^2} \left(a d (a d+12 b c)+8 b^2 c^2\right)}{16 c}-\frac{5 d \left(a d (a d+12 b c)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 \sqrt{c}}-\frac{a \left(c+d x^2\right)^{7/2} (a d+12 b c)}{24 c^2 x^4}","-\frac{a^2 \left(c+d x^2\right)^{7/2}}{6 c x^6}-\frac{\left(c+d x^2\right)^{5/2} \left(a d (a d+12 b c)+8 b^2 c^2\right)}{16 c^2 x^2}+\frac{5 d \left(c+d x^2\right)^{3/2} \left(a d (a d+12 b c)+8 b^2 c^2\right)}{48 c^2}+\frac{5 d \sqrt{c+d x^2} \left(a d (a d+12 b c)+8 b^2 c^2\right)}{16 c}-\frac{5 d \left(a d (a d+12 b c)+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 \sqrt{c}}-\frac{a \left(c+d x^2\right)^{7/2} (a d+12 b c)}{24 c^2 x^4}",1,"(5*d*(8*b^2*c^2 + a*d*(12*b*c + a*d))*Sqrt[c + d*x^2])/(16*c) + (5*d*(8*b^2*c^2 + a*d*(12*b*c + a*d))*(c + d*x^2)^(3/2))/(48*c^2) - ((8*b^2 + (a*d*(12*b*c + a*d))/c^2)*(c + d*x^2)^(5/2))/(16*x^2) - (a^2*(c + d*x^2)^(7/2))/(6*c*x^6) - (a*(12*b*c + a*d)*(c + d*x^2)^(7/2))/(24*c^2*x^4) - (5*d*(8*b^2*c^2 + a*d*(12*b*c + a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(16*Sqrt[c])","A",8,7,24,0.2917,1,"{446, 89, 78, 47, 50, 63, 208}"
636,1,194,0,0.1545548,"\int \frac{x^4 \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[(x^4*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","\frac{c^2 \left(48 a^2 d^2+5 b c (7 b c-16 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{9/2}}+\frac{x^3 \sqrt{c+d x^2} \left(48 a^2+\frac{5 b c (7 b c-16 a d)}{d^2}\right)}{192 d}-\frac{c x \sqrt{c+d x^2} \left(48 a^2 d^2+5 b c (7 b c-16 a d)\right)}{128 d^4}-\frac{b x^5 \sqrt{c+d x^2} (7 b c-16 a d)}{48 d^2}+\frac{b^2 x^7 \sqrt{c+d x^2}}{8 d}","\frac{c^2 \left(48 a^2 d^2+5 b c (7 b c-16 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 d^{9/2}}+\frac{x^3 \sqrt{c+d x^2} \left(48 a^2 d^2+5 b c (7 b c-16 a d)\right)}{192 d^3}-\frac{c x \sqrt{c+d x^2} \left(48 a^2 d^2+5 b c (7 b c-16 a d)\right)}{128 d^4}-\frac{b x^5 \sqrt{c+d x^2} (7 b c-16 a d)}{48 d^2}+\frac{b^2 x^7 \sqrt{c+d x^2}}{8 d}",1,"-(c*(48*a^2*d^2 + 5*b*c*(7*b*c - 16*a*d))*x*Sqrt[c + d*x^2])/(128*d^4) + ((48*a^2 + (5*b*c*(7*b*c - 16*a*d))/d^2)*x^3*Sqrt[c + d*x^2])/(192*d) - (b*(7*b*c - 16*a*d)*x^5*Sqrt[c + d*x^2])/(48*d^2) + (b^2*x^7*Sqrt[c + d*x^2])/(8*d) + (c^2*(48*a^2*d^2 + 5*b*c*(7*b*c - 16*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(128*d^(9/2))","A",6,5,24,0.2083,1,"{464, 459, 321, 217, 206}"
637,1,112,0,0.0889361,"\int \frac{x^3 \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[(x^3*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","-\frac{b \left(c+d x^2\right)^{5/2} (3 b c-2 a d)}{5 d^4}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d) (3 b c-a d)}{3 d^4}-\frac{c \sqrt{c+d x^2} (b c-a d)^2}{d^4}+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d^4}","-\frac{b \left(c+d x^2\right)^{5/2} (3 b c-2 a d)}{5 d^4}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d) (3 b c-a d)}{3 d^4}-\frac{c \sqrt{c+d x^2} (b c-a d)^2}{d^4}+\frac{b^2 \left(c+d x^2\right)^{7/2}}{7 d^4}",1,"-((c*(b*c - a*d)^2*Sqrt[c + d*x^2])/d^4) + ((b*c - a*d)*(3*b*c - a*d)*(c + d*x^2)^(3/2))/(3*d^4) - (b*(3*b*c - 2*a*d)*(c + d*x^2)^(5/2))/(5*d^4) + (b^2*(c + d*x^2)^(7/2))/(7*d^4)","A",3,2,24,0.08333,1,"{446, 77}"
638,1,146,0,0.1401982,"\int \frac{x^2 \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[(x^2*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","\frac{x \sqrt{c+d x^2} \left(8 a^2+\frac{b c (5 b c-12 a d)}{d^2}\right)}{16 d}-\frac{c \left(8 a^2 d^2+b c (5 b c-12 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{7/2}}-\frac{b x^3 \sqrt{c+d x^2} (5 b c-12 a d)}{24 d^2}+\frac{b^2 x^5 \sqrt{c+d x^2}}{6 d}","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2+b c (5 b c-12 a d)\right)}{16 d^3}-\frac{c \left(8 a^2 d^2+b c (5 b c-12 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{7/2}}-\frac{b x^3 \sqrt{c+d x^2} (5 b c-12 a d)}{24 d^2}+\frac{b^2 x^5 \sqrt{c+d x^2}}{6 d}",1,"((8*a^2 + (b*c*(5*b*c - 12*a*d))/d^2)*x*Sqrt[c + d*x^2])/(16*d) - (b*(5*b*c - 12*a*d)*x^3*Sqrt[c + d*x^2])/(24*d^2) + (b^2*x^5*Sqrt[c + d*x^2])/(6*d) - (c*(8*a^2*d^2 + b*c*(5*b*c - 12*a*d))*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*d^(7/2))","A",5,5,24,0.2083,1,"{464, 459, 321, 217, 206}"
639,1,74,0,0.0535002,"\int \frac{x \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[(x*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","-\frac{2 b \left(c+d x^2\right)^{3/2} (b c-a d)}{3 d^3}+\frac{\sqrt{c+d x^2} (b c-a d)^2}{d^3}+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d^3}","-\frac{2 b \left(c+d x^2\right)^{3/2} (b c-a d)}{3 d^3}+\frac{\sqrt{c+d x^2} (b c-a d)^2}{d^3}+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d^3}",1,"((b*c - a*d)^2*Sqrt[c + d*x^2])/d^3 - (2*b*(b*c - a*d)*(c + d*x^2)^(3/2))/(3*d^3) + (b^2*(c + d*x^2)^(5/2))/(5*d^3)","A",3,2,22,0.09091,1,"{444, 43}"
640,1,107,0,0.0594074,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/Sqrt[c + d*x^2],x]","\frac{\left(8 a^2 d^2-8 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{5/2}}-\frac{3 b x \sqrt{c+d x^2} (b c-2 a d)}{8 d^2}+\frac{b x \left(a+b x^2\right) \sqrt{c+d x^2}}{4 d}","\frac{\left(8 a^2 d^2-8 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{5/2}}-\frac{3 b x \sqrt{c+d x^2} (b c-2 a d)}{8 d^2}+\frac{b x \left(a+b x^2\right) \sqrt{c+d x^2}}{4 d}",1,"(-3*b*(b*c - 2*a*d)*x*Sqrt[c + d*x^2])/(8*d^2) + (b*x*(a + b*x^2)*Sqrt[c + d*x^2])/(4*d) + ((3*b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*d^(5/2))","A",4,4,21,0.1905,1,"{416, 388, 217, 206}"
641,1,75,0,0.0706001,"\int \frac{\left(a+b x^2\right)^2}{x \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x*Sqrt[c + d*x^2]),x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{\sqrt{c}}-\frac{b \sqrt{c+d x^2} (b c-2 a d)}{d^2}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d^2}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{\sqrt{c}}-\frac{b \sqrt{c+d x^2} (b c-2 a d)}{d^2}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d^2}",1,"-((b*(b*c - 2*a*d)*Sqrt[c + d*x^2])/d^2) + (b^2*(c + d*x^2)^(3/2))/(3*d^2) - (a^2*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/Sqrt[c]","A",5,4,24,0.1667,1,"{446, 88, 63, 208}"
642,1,82,0,0.045298,"\int \frac{\left(a+b x^2\right)^2}{x^2 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x^2*Sqrt[c + d*x^2]),x]","-\frac{a^2 \sqrt{c+d x^2}}{c x}-\frac{b (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 d^{3/2}}+\frac{b^2 x \sqrt{c+d x^2}}{2 d}","-\frac{a^2 \sqrt{c+d x^2}}{c x}-\frac{b (b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 d^{3/2}}+\frac{b^2 x \sqrt{c+d x^2}}{2 d}",1,"-((a^2*Sqrt[c + d*x^2])/(c*x)) + (b^2*x*Sqrt[c + d*x^2])/(2*d) - (b*(b*c - 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*d^(3/2))","A",4,4,24,0.1667,1,"{462, 388, 217, 206}"
643,1,80,0,0.0676449,"\int \frac{\left(a+b x^2\right)^2}{x^3 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x^3*Sqrt[c + d*x^2]),x]","-\frac{a^2 \sqrt{c+d x^2}}{2 c x^2}-\frac{a (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 c^{3/2}}+\frac{b^2 \sqrt{c+d x^2}}{d}","-\frac{a^2 \sqrt{c+d x^2}}{2 c x^2}-\frac{a (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 c^{3/2}}+\frac{b^2 \sqrt{c+d x^2}}{d}",1,"(b^2*Sqrt[c + d*x^2])/d - (a^2*Sqrt[c + d*x^2])/(2*c*x^2) - (a*(4*b*c - a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*c^(3/2))","A",5,5,24,0.2083,1,"{446, 89, 80, 63, 208}"
644,1,84,0,0.0496488,"\int \frac{\left(a+b x^2\right)^2}{x^4 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x^4*Sqrt[c + d*x^2]),x]","-\frac{a^2 \sqrt{c+d x^2}}{3 c x^3}-\frac{2 a \sqrt{c+d x^2} (3 b c-a d)}{3 c^2 x}+\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{\sqrt{d}}","-\frac{a^2 \sqrt{c+d x^2}}{3 c x^3}-\frac{2 a \sqrt{c+d x^2} (3 b c-a d)}{3 c^2 x}+\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{\sqrt{d}}",1,"-(a^2*Sqrt[c + d*x^2])/(3*c*x^3) - (2*a*(3*b*c - a*d)*Sqrt[c + d*x^2])/(3*c^2*x) + (b^2*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/Sqrt[d]","A",4,4,24,0.1667,1,"{462, 451, 217, 206}"
645,1,106,0,0.1057927,"\int \frac{\left(a+b x^2\right)^2}{x^5 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x^5*Sqrt[c + d*x^2]),x]","-\frac{\left(3 a^2 d^2-8 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{5/2}}-\frac{a^2 \sqrt{c+d x^2}}{4 c x^4}-\frac{a \sqrt{c+d x^2} (8 b c-3 a d)}{8 c^2 x^2}","-\frac{\left(3 a^2 d^2-8 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{5/2}}-\frac{a^2 \sqrt{c+d x^2}}{4 c x^4}-\frac{a \sqrt{c+d x^2} (8 b c-3 a d)}{8 c^2 x^2}",1,"-(a^2*Sqrt[c + d*x^2])/(4*c*x^4) - (a*(8*b*c - 3*a*d)*Sqrt[c + d*x^2])/(8*c^2*x^2) - ((8*b^2*c^2 - 8*a*b*c*d + 3*a^2*d^2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(8*c^(5/2))","A",5,5,24,0.2083,1,"{446, 89, 78, 63, 208}"
646,1,100,0,0.0717884,"\int \frac{\left(a+b x^2\right)^2}{x^6 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x^6*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{c+d x^2} \left(8 a^2 d^2-20 a b c d+15 b^2 c^2\right)}{15 c^3 x}-\frac{a^2 \sqrt{c+d x^2}}{5 c x^5}-\frac{2 a \sqrt{c+d x^2} (5 b c-2 a d)}{15 c^2 x^3}","-\frac{a^2 \sqrt{c+d x^2}}{5 c x^5}-\frac{\sqrt{c+d x^2} \left(15 b^2 c^2-4 a d (5 b c-2 a d)\right)}{15 c^3 x}-\frac{2 a \sqrt{c+d x^2} (5 b c-2 a d)}{15 c^2 x^3}",1,"-(a^2*Sqrt[c + d*x^2])/(5*c*x^5) - (2*a*(5*b*c - 2*a*d)*Sqrt[c + d*x^2])/(15*c^2*x^3) - ((15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*Sqrt[c + d*x^2])/(15*c^3*x)","A",3,3,24,0.1250,1,"{462, 453, 264}"
647,1,151,0,0.1612907,"\int \frac{\left(a+b x^2\right)^2}{x^7 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(x^7*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{c+d x^2} \left(5 a^2 d^2-12 a b c d+8 b^2 c^2\right)}{16 c^3 x^2}+\frac{d \left(5 a^2 d^2-12 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{7/2}}-\frac{a^2 \sqrt{c+d x^2}}{6 c x^6}-\frac{a \sqrt{c+d x^2} (12 b c-5 a d)}{24 c^2 x^4}","-\frac{\sqrt{c+d x^2} \left(5 a^2 d^2-12 a b c d+8 b^2 c^2\right)}{16 c^3 x^2}+\frac{d \left(5 a^2 d^2-12 a b c d+8 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{7/2}}-\frac{a^2 \sqrt{c+d x^2}}{6 c x^6}-\frac{a \sqrt{c+d x^2} (12 b c-5 a d)}{24 c^2 x^4}",1,"-(a^2*Sqrt[c + d*x^2])/(6*c*x^6) - (a*(12*b*c - 5*a*d)*Sqrt[c + d*x^2])/(24*c^2*x^4) - ((8*b^2*c^2 - 12*a*b*c*d + 5*a^2*d^2)*Sqrt[c + d*x^2])/(16*c^3*x^2) + (d*(8*b^2*c^2 - 12*a*b*c*d + 5*a^2*d^2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(16*c^(7/2))","A",6,6,24,0.2500,1,"{446, 89, 78, 51, 63, 208}"
648,1,197,0,0.1494787,"\int \frac{x^4 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[(x^4*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","-\frac{x^3 \sqrt{c+d x^2} \left(24 a^2 d^2-60 a b c d+35 b^2 c^2\right)}{24 c d^3}+\frac{x \sqrt{c+d x^2} \left(24 a^2 d^2-60 a b c d+35 b^2 c^2\right)}{16 d^4}-\frac{c \left(24 a^2 d^2-60 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{9/2}}+\frac{x^5 (b c-a d)^2}{c d^2 \sqrt{c+d x^2}}+\frac{b^2 x^5 \sqrt{c+d x^2}}{6 d^2}","-\frac{x^3 \sqrt{c+d x^2} \left(24 a^2 d^2-60 a b c d+35 b^2 c^2\right)}{24 c d^3}+\frac{x \sqrt{c+d x^2} \left(24 a^2 d^2-60 a b c d+35 b^2 c^2\right)}{16 d^4}-\frac{c \left(24 a^2 d^2-60 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 d^{9/2}}+\frac{x^5 (b c-a d)^2}{c d^2 \sqrt{c+d x^2}}+\frac{b^2 x^5 \sqrt{c+d x^2}}{6 d^2}",1,"((b*c - a*d)^2*x^5)/(c*d^2*Sqrt[c + d*x^2]) + ((35*b^2*c^2 - 60*a*b*c*d + 24*a^2*d^2)*x*Sqrt[c + d*x^2])/(16*d^4) - ((35*b^2*c^2 - 60*a*b*c*d + 24*a^2*d^2)*x^3*Sqrt[c + d*x^2])/(24*c*d^3) + (b^2*x^5*Sqrt[c + d*x^2])/(6*d^2) - (c*(35*b^2*c^2 - 60*a*b*c*d + 24*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*d^(9/2))","A",6,5,24,0.2083,1,"{463, 459, 321, 217, 206}"
649,1,108,0,0.0859802,"\int \frac{x^3 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[(x^3*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","-\frac{b \left(c+d x^2\right)^{3/2} (3 b c-2 a d)}{3 d^4}+\frac{\sqrt{c+d x^2} (b c-a d) (3 b c-a d)}{d^4}+\frac{c (b c-a d)^2}{d^4 \sqrt{c+d x^2}}+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d^4}","-\frac{b \left(c+d x^2\right)^{3/2} (3 b c-2 a d)}{3 d^4}+\frac{\sqrt{c+d x^2} (b c-a d) (3 b c-a d)}{d^4}+\frac{c (b c-a d)^2}{d^4 \sqrt{c+d x^2}}+\frac{b^2 \left(c+d x^2\right)^{5/2}}{5 d^4}",1,"(c*(b*c - a*d)^2)/(d^4*Sqrt[c + d*x^2]) + ((b*c - a*d)*(3*b*c - a*d)*Sqrt[c + d*x^2])/d^4 - (b*(3*b*c - 2*a*d)*(c + d*x^2)^(3/2))/(3*d^4) + (b^2*(c + d*x^2)^(5/2))/(5*d^4)","A",3,2,24,0.08333,1,"{446, 77}"
650,1,152,0,0.1170519,"\int \frac{x^2 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[(x^2*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","-\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-24 a b c d+15 b^2 c^2\right)}{8 c d^3}+\frac{\left(8 a^2 d^2-24 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{7/2}}+\frac{x^3 (b c-a d)^2}{c d^2 \sqrt{c+d x^2}}+\frac{b^2 x^3 \sqrt{c+d x^2}}{4 d^2}","-\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-24 a b c d+15 b^2 c^2\right)}{8 c d^3}+\frac{\left(8 a^2 d^2-24 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{7/2}}+\frac{x^3 (b c-a d)^2}{c d^2 \sqrt{c+d x^2}}+\frac{b^2 x^3 \sqrt{c+d x^2}}{4 d^2}",1,"((b*c - a*d)^2*x^3)/(c*d^2*Sqrt[c + d*x^2]) - ((15*b^2*c^2 - 24*a*b*c*d + 8*a^2*d^2)*x*Sqrt[c + d*x^2])/(8*c*d^3) + (b^2*x^3*Sqrt[c + d*x^2])/(4*d^2) + ((15*b^2*c^2 - 24*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*d^(7/2))","A",5,5,24,0.2083,1,"{463, 459, 321, 217, 206}"
651,1,73,0,0.0556265,"\int \frac{x \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[(x*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","-\frac{2 b \sqrt{c+d x^2} (b c-a d)}{d^3}-\frac{(b c-a d)^2}{d^3 \sqrt{c+d x^2}}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d^3}","-\frac{2 b \sqrt{c+d x^2} (b c-a d)}{d^3}-\frac{(b c-a d)^2}{d^3 \sqrt{c+d x^2}}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d^3}",1,"-((b*c - a*d)^2/(d^3*Sqrt[c + d*x^2])) - (2*b*(b*c - a*d)*Sqrt[c + d*x^2])/d^3 + (b^2*(c + d*x^2)^(3/2))/(3*d^3)","A",3,2,22,0.09091,1,"{444, 43}"
652,1,106,0,0.0539976,"\int \frac{\left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(c + d*x^2)^(3/2),x]","\frac{b x \sqrt{c+d x^2} (3 b c-2 a d)}{2 c d^2}-\frac{b (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 d^{5/2}}-\frac{x \left(a+b x^2\right) (b c-a d)}{c d \sqrt{c+d x^2}}","\frac{b x \sqrt{c+d x^2} (3 b c-2 a d)}{2 c d^2}-\frac{b (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 d^{5/2}}-\frac{x \left(a+b x^2\right) (b c-a d)}{c d \sqrt{c+d x^2}}",1,"-(((b*c - a*d)*x*(a + b*x^2))/(c*d*Sqrt[c + d*x^2])) + (b*(3*b*c - 2*a*d)*x*Sqrt[c + d*x^2])/(2*c*d^2) - (b*(3*b*c - 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*d^(5/2))","A",4,4,21,0.1905,1,"{413, 388, 217, 206}"
653,1,75,0,0.0750599,"\int \frac{\left(a+b x^2\right)^2}{x \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x*(c + d*x^2)^(3/2)),x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{c^{3/2}}+\frac{(b c-a d)^2}{c d^2 \sqrt{c+d x^2}}+\frac{b^2 \sqrt{c+d x^2}}{d^2}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{c^{3/2}}+\frac{(b c-a d)^2}{c d^2 \sqrt{c+d x^2}}+\frac{b^2 \sqrt{c+d x^2}}{d^2}",1,"(b*c - a*d)^2/(c*d^2*Sqrt[c + d*x^2]) + (b^2*Sqrt[c + d*x^2])/d^2 - (a^2*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/c^(3/2)","A",5,4,24,0.1667,1,"{446, 87, 63, 208}"
654,1,87,0,0.0634586,"\int \frac{\left(a+b x^2\right)^2}{x^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x^2*(c + d*x^2)^(3/2)),x]","-\frac{a^2}{c x \sqrt{c+d x^2}}-\frac{x \left(\frac{b^2}{d}-\frac{2 a (b c-a d)}{c^2}\right)}{\sqrt{c+d x^2}}+\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{d^{3/2}}","-\frac{a^2}{c x \sqrt{c+d x^2}}-\frac{x \left(b^2 c^2-2 a d (b c-a d)\right)}{c^2 d \sqrt{c+d x^2}}+\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{d^{3/2}}",1,"-(a^2/(c*x*Sqrt[c + d*x^2])) - ((b^2/d - (2*a*(b*c - a*d))/c^2)*x)/Sqrt[c + d*x^2] + (b^2*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/d^(3/2)","A",4,4,24,0.1667,1,"{462, 385, 217, 206}"
655,1,103,0,0.0976093,"\int \frac{\left(a+b x^2\right)^2}{x^3 \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x^3*(c + d*x^2)^(3/2)),x]","\frac{-\frac{3 a^2 d}{c}+4 a b-\frac{2 b^2 c}{d}}{2 c \sqrt{c+d x^2}}-\frac{a^2}{2 c x^2 \sqrt{c+d x^2}}-\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 c^{5/2}}","\frac{-\frac{3 a^2 d}{c}+4 a b-\frac{2 b^2 c}{d}}{2 c \sqrt{c+d x^2}}-\frac{a^2}{2 c x^2 \sqrt{c+d x^2}}-\frac{a (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 c^{5/2}}",1,"(4*a*b - (2*b^2*c)/d - (3*a^2*d)/c)/(2*c*Sqrt[c + d*x^2]) - a^2/(2*c*x^2*Sqrt[c + d*x^2]) - (a*(4*b*c - 3*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*c^(5/2))","A",5,5,24,0.2083,1,"{446, 89, 78, 63, 208}"
656,1,98,0,0.0720084,"\int \frac{\left(a+b x^2\right)^2}{x^4 \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x^4*(c + d*x^2)^(3/2)),x]","\frac{x \left(8 a^2 d^2-12 a b c d+3 b^2 c^2\right)}{3 c^3 \sqrt{c+d x^2}}-\frac{a^2}{3 c x^3 \sqrt{c+d x^2}}-\frac{2 a (3 b c-2 a d)}{3 c^2 x \sqrt{c+d x^2}}","-\frac{a^2}{3 c x^3 \sqrt{c+d x^2}}+\frac{x \left(3 b^2 c^2-4 a d (3 b c-2 a d)\right)}{3 c^3 \sqrt{c+d x^2}}-\frac{2 a (3 b c-2 a d)}{3 c^2 x \sqrt{c+d x^2}}",1,"-a^2/(3*c*x^3*Sqrt[c + d*x^2]) - (2*a*(3*b*c - 2*a*d))/(3*c^2*x*Sqrt[c + d*x^2]) + ((3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*x)/(3*c^3*Sqrt[c + d*x^2])","A",3,3,24,0.1250,1,"{462, 453, 191}"
657,1,145,0,0.1671866,"\int \frac{\left(a+b x^2\right)^2}{x^5 \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x^5*(c + d*x^2)^(3/2)),x]","-\frac{a^2}{4 c x^4 \sqrt{c+d x^2}}+\frac{8 b^2-\frac{3 a d (8 b c-5 a d)}{c^2}}{8 c \sqrt{c+d x^2}}-\frac{\left(8 b^2 c^2-3 a d (8 b c-5 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{7/2}}-\frac{a (8 b c-5 a d)}{8 c^2 x^2 \sqrt{c+d x^2}}","-\frac{a^2}{4 c x^4 \sqrt{c+d x^2}}+\frac{8 b^2 c^2-3 a d (8 b c-5 a d)}{8 c^3 \sqrt{c+d x^2}}-\frac{\left(8 b^2 c^2-3 a d (8 b c-5 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{7/2}}-\frac{a (8 b c-5 a d)}{8 c^2 x^2 \sqrt{c+d x^2}}",1,"(8*b^2 - (3*a*d*(8*b*c - 5*a*d))/c^2)/(8*c*Sqrt[c + d*x^2]) - a^2/(4*c*x^4*Sqrt[c + d*x^2]) - (a*(8*b*c - 5*a*d))/(8*c^2*x^2*Sqrt[c + d*x^2]) - ((8*b^2*c^2 - 3*a*d*(8*b*c - 5*a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(8*c^(7/2))","A",6,6,24,0.2500,1,"{446, 89, 78, 51, 63, 208}"
658,1,141,0,0.1138815,"\int \frac{\left(a+b x^2\right)^2}{x^6 \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x^6*(c + d*x^2)^(3/2)),x]","-\frac{a^2}{5 c x^5 \sqrt{c+d x^2}}-\frac{2 d x \left(15 b^2 c^2-8 a d (5 b c-3 a d)\right)}{15 c^4 \sqrt{c+d x^2}}-\frac{15 b^2-\frac{8 a d (5 b c-3 a d)}{c^2}}{15 c x \sqrt{c+d x^2}}-\frac{2 a (5 b c-3 a d)}{15 c^2 x^3 \sqrt{c+d x^2}}","-\frac{a^2}{5 c x^5 \sqrt{c+d x^2}}-\frac{2 d x \left(15 b^2 c^2-8 a d (5 b c-3 a d)\right)}{15 c^4 \sqrt{c+d x^2}}-\frac{15 b^2 c^2-8 a d (5 b c-3 a d)}{15 c^3 x \sqrt{c+d x^2}}-\frac{2 a (5 b c-3 a d)}{15 c^2 x^3 \sqrt{c+d x^2}}",1,"-a^2/(5*c*x^5*Sqrt[c + d*x^2]) - (2*a*(5*b*c - 3*a*d))/(15*c^2*x^3*Sqrt[c + d*x^2]) - (15*b^2 - (8*a*d*(5*b*c - 3*a*d))/c^2)/(15*c*x*Sqrt[c + d*x^2]) - (2*d*(15*b^2*c^2 - 8*a*d*(5*b*c - 3*a*d))*x)/(15*c^4*Sqrt[c + d*x^2])","A",4,4,24,0.1667,1,"{462, 453, 271, 191}"
659,1,193,0,0.2180866,"\int \frac{\left(a+b x^2\right)^2}{x^7 \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(x^7*(c + d*x^2)^(3/2)),x]","\frac{35 a^2 d^2-60 a b c d+24 b^2 c^2}{24 c^3 x^2 \sqrt{c+d x^2}}-\frac{a^2}{6 c x^6 \sqrt{c+d x^2}}-\frac{\sqrt{c+d x^2} \left(24 b^2 c^2-5 a d (12 b c-7 a d)\right)}{16 c^4 x^2}+\frac{d \left(24 b^2 c^2-5 a d (12 b c-7 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{9/2}}-\frac{a (12 b c-7 a d)}{24 c^2 x^4 \sqrt{c+d x^2}}","-\frac{a^2}{6 c x^6 \sqrt{c+d x^2}}-\frac{d \left(24 b^2 c^2-5 a d (12 b c-7 a d)\right)}{16 c^4 \sqrt{c+d x^2}}-\frac{24 b^2 c^2-5 a d (12 b c-7 a d)}{48 c^3 x^2 \sqrt{c+d x^2}}+\frac{d \left(24 b^2 c^2-5 a d (12 b c-7 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{16 c^{9/2}}-\frac{a (12 b c-7 a d)}{24 c^2 x^4 \sqrt{c+d x^2}}",1,"-a^2/(6*c*x^6*Sqrt[c + d*x^2]) - (a*(12*b*c - 7*a*d))/(24*c^2*x^4*Sqrt[c + d*x^2]) + (24*b^2*c^2 - 60*a*b*c*d + 35*a^2*d^2)/(24*c^3*x^2*Sqrt[c + d*x^2]) - ((24*b^2*c^2 - 5*a*d*(12*b*c - 7*a*d))*Sqrt[c + d*x^2])/(16*c^4*x^2) + (d*(24*b^2*c^2 - 5*a*d*(12*b*c - 7*a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(16*c^(9/2))","A",7,6,24,0.2500,1,"{446, 89, 78, 51, 63, 208}"
660,1,202,0,0.1546852,"\int \frac{x^4 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[(x^4*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","\frac{x^3 \left(8 a^2 d^2-40 a b c d+35 b^2 c^2\right)}{12 c d^3 \sqrt{c+d x^2}}-\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-40 a b c d+35 b^2 c^2\right)}{8 c d^4}+\frac{\left(8 a^2 d^2-40 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{9/2}}+\frac{x^5 (b c-a d)^2}{3 c d^2 \left(c+d x^2\right)^{3/2}}+\frac{b^2 x^5}{4 d^2 \sqrt{c+d x^2}}","\frac{x^3 \left(8 a^2 d^2-40 a b c d+35 b^2 c^2\right)}{12 c d^3 \sqrt{c+d x^2}}-\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-40 a b c d+35 b^2 c^2\right)}{8 c d^4}+\frac{\left(8 a^2 d^2-40 a b c d+35 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 d^{9/2}}+\frac{x^5 (b c-a d)^2}{3 c d^2 \left(c+d x^2\right)^{3/2}}+\frac{b^2 x^5}{4 d^2 \sqrt{c+d x^2}}",1,"((b*c - a*d)^2*x^5)/(3*c*d^2*(c + d*x^2)^(3/2)) + ((35*b^2*c^2 - 40*a*b*c*d + 8*a^2*d^2)*x^3)/(12*c*d^3*Sqrt[c + d*x^2]) + (b^2*x^5)/(4*d^2*Sqrt[c + d*x^2]) - ((35*b^2*c^2 - 40*a*b*c*d + 8*a^2*d^2)*x*Sqrt[c + d*x^2])/(8*c*d^4) + ((35*b^2*c^2 - 40*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*d^(9/2))","A",6,6,24,0.2500,1,"{463, 459, 288, 321, 217, 206}"
661,1,110,0,0.0895646,"\int \frac{x^3 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[(x^3*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","-\frac{b \sqrt{c+d x^2} (3 b c-2 a d)}{d^4}-\frac{(b c-a d) (3 b c-a d)}{d^4 \sqrt{c+d x^2}}+\frac{c (b c-a d)^2}{3 d^4 \left(c+d x^2\right)^{3/2}}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d^4}","-\frac{b \sqrt{c+d x^2} (3 b c-2 a d)}{d^4}-\frac{(b c-a d) (3 b c-a d)}{d^4 \sqrt{c+d x^2}}+\frac{c (b c-a d)^2}{3 d^4 \left(c+d x^2\right)^{3/2}}+\frac{b^2 \left(c+d x^2\right)^{3/2}}{3 d^4}",1,"(c*(b*c - a*d)^2)/(3*d^4*(c + d*x^2)^(3/2)) - ((b*c - a*d)*(3*b*c - a*d))/(d^4*Sqrt[c + d*x^2]) - (b*(3*b*c - 2*a*d)*Sqrt[c + d*x^2])/d^4 + (b^2*(c + d*x^2)^(3/2))/(3*d^4)","A",3,2,24,0.08333,1,"{446, 77}"
662,1,121,0,0.108313,"\int \frac{x^2 \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[(x^2*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","\frac{x^3 (b c-a d)^2}{3 c d^2 \left(c+d x^2\right)^{3/2}}+\frac{2 b x (b c-a d)}{d^3 \sqrt{c+d x^2}}-\frac{b (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 d^{7/2}}+\frac{b^2 x \sqrt{c+d x^2}}{2 d^3}","\frac{x^3 (b c-a d)^2}{3 c d^2 \left(c+d x^2\right)^{3/2}}+\frac{2 b x (b c-a d)}{d^3 \sqrt{c+d x^2}}-\frac{b (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 d^{7/2}}+\frac{b^2 x \sqrt{c+d x^2}}{2 d^3}",1,"((b*c - a*d)^2*x^3)/(3*c*d^2*(c + d*x^2)^(3/2)) + (2*b*(b*c - a*d)*x)/(d^3*Sqrt[c + d*x^2]) + (b^2*x*Sqrt[c + d*x^2])/(2*d^3) - (b*(5*b*c - 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*d^(7/2))","A",5,5,24,0.2083,1,"{463, 455, 388, 217, 206}"
663,1,72,0,0.0581318,"\int \frac{x \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[(x*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","\frac{2 b (b c-a d)}{d^3 \sqrt{c+d x^2}}-\frac{(b c-a d)^2}{3 d^3 \left(c+d x^2\right)^{3/2}}+\frac{b^2 \sqrt{c+d x^2}}{d^3}","\frac{2 b (b c-a d)}{d^3 \sqrt{c+d x^2}}-\frac{(b c-a d)^2}{3 d^3 \left(c+d x^2\right)^{3/2}}+\frac{b^2 \sqrt{c+d x^2}}{d^3}",1,"-(b*c - a*d)^2/(3*d^3*(c + d*x^2)^(3/2)) + (2*b*(b*c - a*d))/(d^3*Sqrt[c + d*x^2]) + (b^2*Sqrt[c + d*x^2])/d^3","A",3,2,22,0.09091,1,"{444, 43}"
664,1,105,0,0.0497085,"\int \frac{\left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(c + d*x^2)^(5/2),x]","-\frac{x (b c-a d) (2 a d+3 b c)}{3 c^2 d^2 \sqrt{c+d x^2}}-\frac{x \left(a+b x^2\right) (b c-a d)}{3 c d \left(c+d x^2\right)^{3/2}}+\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{d^{5/2}}","-\frac{x (b c-a d) (2 a d+3 b c)}{3 c^2 d^2 \sqrt{c+d x^2}}-\frac{x \left(a+b x^2\right) (b c-a d)}{3 c d \left(c+d x^2\right)^{3/2}}+\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{d^{5/2}}",1,"-((b*c - a*d)*x*(a + b*x^2))/(3*c*d*(c + d*x^2)^(3/2)) - ((b*c - a*d)*(3*b*c + 2*a*d)*x)/(3*c^2*d^2*Sqrt[c + d*x^2]) + (b^2*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/d^(5/2)","A",4,4,21,0.1905,1,"{413, 385, 217, 206}"
665,1,88,0,0.0920913,"\int \frac{\left(a+b x^2\right)^2}{x \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(x*(c + d*x^2)^(5/2)),x]","\frac{\frac{a^2}{c^2}-\frac{b^2}{d^2}}{\sqrt{c+d x^2}}-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{c^{5/2}}+\frac{(b c-a d)^2}{3 c d^2 \left(c+d x^2\right)^{3/2}}","\frac{\frac{a^2}{c^2}-\frac{b^2}{d^2}}{\sqrt{c+d x^2}}-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{c^{5/2}}+\frac{(b c-a d)^2}{3 c d^2 \left(c+d x^2\right)^{3/2}}",1,"(b*c - a*d)^2/(3*c*d^2*(c + d*x^2)^(3/2)) + (a^2/c^2 - b^2/d^2)/Sqrt[c + d*x^2] - (a^2*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/c^(5/2)","A",5,4,24,0.1667,1,"{446, 87, 63, 208}"
666,1,90,0,0.0457317,"\int \frac{\left(a+b x^2\right)^2}{x^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(x^2*(c + d*x^2)^(5/2)),x]","-\frac{a^2}{c x \left(c+d x^2\right)^{3/2}}+\frac{x \left(2 a (b c-2 a d)+b^2 c x^2\right)}{3 c^2 \left(c+d x^2\right)^{3/2}}+\frac{4 a x (b c-2 a d)}{3 c^3 \sqrt{c+d x^2}}","-\frac{a^2}{c x \left(c+d x^2\right)^{3/2}}+\frac{x \left(2 a (b c-2 a d)+b^2 c x^2\right)}{3 c^2 \left(c+d x^2\right)^{3/2}}+\frac{4 a x (b c-2 a d)}{3 c^3 \sqrt{c+d x^2}}",1,"-(a^2/(c*x*(c + d*x^2)^(3/2))) + (x*(2*a*(b*c - 2*a*d) + b^2*c*x^2))/(3*c^2*(c + d*x^2)^(3/2)) + (4*a*(b*c - 2*a*d)*x)/(3*c^3*Sqrt[c + d*x^2])","A",3,3,24,0.1250,1,"{462, 378, 191}"
667,1,131,0,0.1171711,"\int \frac{\left(a+b x^2\right)^2}{x^3 \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(x^3*(c + d*x^2)^(5/2)),x]","\frac{-\frac{5 a^2 d}{c}+4 a b-\frac{2 b^2 c}{d}}{6 c \left(c+d x^2\right)^{3/2}}-\frac{a^2}{2 c x^2 \left(c+d x^2\right)^{3/2}}+\frac{a (4 b c-5 a d)}{2 c^3 \sqrt{c+d x^2}}-\frac{a (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 c^{7/2}}","\frac{-\frac{5 a^2 d}{c}+4 a b-\frac{2 b^2 c}{d}}{6 c \left(c+d x^2\right)^{3/2}}-\frac{a^2}{2 c x^2 \left(c+d x^2\right)^{3/2}}+\frac{a (4 b c-5 a d)}{2 c^3 \sqrt{c+d x^2}}-\frac{a (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 c^{7/2}}",1,"(4*a*b - (2*b^2*c)/d - (5*a^2*d)/c)/(6*c*(c + d*x^2)^(3/2)) - a^2/(2*c*x^2*(c + d*x^2)^(3/2)) + (a*(4*b*c - 5*a*d))/(2*c^3*Sqrt[c + d*x^2]) - (a*(4*b*c - 5*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*c^(7/2))","A",6,6,24,0.2500,1,"{446, 89, 78, 51, 63, 208}"
668,1,130,0,0.1248135,"\int \frac{\left(a+b x^2\right)^2}{x^4 \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(x^4*(c + d*x^2)^(5/2)),x]","-\frac{a^2}{3 c x^3 \left(c+d x^2\right)^{3/2}}+\frac{2 x \left(b^2 c^2-8 a d (b c-a d)\right)}{3 c^4 \sqrt{c+d x^2}}+\frac{x \left(b^2-\frac{8 a d (b c-a d)}{c^2}\right)}{3 c \left(c+d x^2\right)^{3/2}}-\frac{2 a (b c-a d)}{c^2 x \left(c+d x^2\right)^{3/2}}","-\frac{a^2}{3 c x^3 \left(c+d x^2\right)^{3/2}}+\frac{2 x \left(b^2 c^2-8 a d (b c-a d)\right)}{3 c^4 \sqrt{c+d x^2}}+\frac{x \left(b^2 c^2-8 a d (b c-a d)\right)}{3 c^3 \left(c+d x^2\right)^{3/2}}-\frac{2 a (b c-a d)}{c^2 x \left(c+d x^2\right)^{3/2}}",1,"-a^2/(3*c*x^3*(c + d*x^2)^(3/2)) - (2*a*(b*c - a*d))/(c^2*x*(c + d*x^2)^(3/2)) + ((b^2 - (8*a*d*(b*c - a*d))/c^2)*x)/(3*c*(c + d*x^2)^(3/2)) + (2*(b^2*c^2 - 8*a*d*(b*c - a*d))*x)/(3*c^4*Sqrt[c + d*x^2])","A",4,4,24,0.1667,1,"{462, 453, 192, 191}"
669,1,185,0,0.2155231,"\int \frac{\left(a+b x^2\right)^2}{x^5 \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(x^5*(c + d*x^2)^(5/2)),x]","-\frac{a^2}{4 c x^4 \left(c+d x^2\right)^{3/2}}+\frac{8 b^2 c^2-5 a d (8 b c-7 a d)}{8 c^4 \sqrt{c+d x^2}}+\frac{8 b^2-\frac{5 a d (8 b c-7 a d)}{c^2}}{24 c \left(c+d x^2\right)^{3/2}}-\frac{\left(8 b^2 c^2-5 a d (8 b c-7 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{9/2}}-\frac{a (8 b c-7 a d)}{8 c^2 x^2 \left(c+d x^2\right)^{3/2}}","-\frac{a^2}{4 c x^4 \left(c+d x^2\right)^{3/2}}+\frac{8 b^2 c^2-5 a d (8 b c-7 a d)}{8 c^4 \sqrt{c+d x^2}}+\frac{8 b^2 c^2-5 a d (8 b c-7 a d)}{24 c^3 \left(c+d x^2\right)^{3/2}}-\frac{\left(8 b^2 c^2-5 a d (8 b c-7 a d)\right) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{8 c^{9/2}}-\frac{a (8 b c-7 a d)}{8 c^2 x^2 \left(c+d x^2\right)^{3/2}}",1,"(8*b^2 - (5*a*d*(8*b*c - 7*a*d))/c^2)/(24*c*(c + d*x^2)^(3/2)) - a^2/(4*c*x^4*(c + d*x^2)^(3/2)) - (a*(8*b*c - 7*a*d))/(8*c^2*x^2*(c + d*x^2)^(3/2)) + (8*b^2*c^2 - 5*a*d*(8*b*c - 7*a*d))/(8*c^4*Sqrt[c + d*x^2]) - ((8*b^2*c^2 - 5*a*d*(8*b*c - 7*a*d))*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(8*c^(9/2))","A",7,6,24,0.2500,1,"{446, 89, 78, 51, 63, 208}"
670,1,183,0,0.1659872,"\int \frac{\left(a+b x^2\right)^2}{x^6 \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(x^6*(c + d*x^2)^(5/2)),x]","-\frac{a^2}{5 c x^5 \left(c+d x^2\right)^{3/2}}-\frac{8 d x \left(5 b^2 c^2-4 a d (5 b c-4 a d)\right)}{15 c^5 \sqrt{c+d x^2}}-\frac{4 d x \left(5 b^2 c^2-4 a d (5 b c-4 a d)\right)}{15 c^4 \left(c+d x^2\right)^{3/2}}-\frac{5 b^2-\frac{4 a d (5 b c-4 a d)}{c^2}}{5 c x \left(c+d x^2\right)^{3/2}}-\frac{2 a (5 b c-4 a d)}{15 c^2 x^3 \left(c+d x^2\right)^{3/2}}","-\frac{a^2}{5 c x^5 \left(c+d x^2\right)^{3/2}}-\frac{8 d x \left(5 b^2 c^2-4 a d (5 b c-4 a d)\right)}{15 c^5 \sqrt{c+d x^2}}-\frac{4 d x \left(5 b^2 c^2-4 a d (5 b c-4 a d)\right)}{15 c^4 \left(c+d x^2\right)^{3/2}}-\frac{5 b^2 c^2-4 a d (5 b c-4 a d)}{5 c^3 x \left(c+d x^2\right)^{3/2}}-\frac{2 a (5 b c-4 a d)}{15 c^2 x^3 \left(c+d x^2\right)^{3/2}}",1,"-a^2/(5*c*x^5*(c + d*x^2)^(3/2)) - (2*a*(5*b*c - 4*a*d))/(15*c^2*x^3*(c + d*x^2)^(3/2)) - (5*b^2 - (4*a*d*(5*b*c - 4*a*d))/c^2)/(5*c*x*(c + d*x^2)^(3/2)) - (4*d*(5*b^2*c^2 - 4*a*d*(5*b*c - 4*a*d))*x)/(15*c^4*(c + d*x^2)^(3/2)) - (8*d*(5*b^2*c^2 - 4*a*d*(5*b*c - 4*a*d))*x)/(15*c^5*Sqrt[c + d*x^2])","A",5,5,24,0.2083,1,"{462, 453, 271, 192, 191}"
671,1,72,0,0.0256232,"\int \frac{x^5}{\sqrt{d x^2} \left(a+b x^2\right)} \, dx","Int[x^5/(Sqrt[d*x^2]*(a + b*x^2)),x]","\frac{a^{3/2} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2} \sqrt{d x^2}}-\frac{a x^2}{b^2 \sqrt{d x^2}}+\frac{x^4}{3 b \sqrt{d x^2}}","\frac{a^{3/2} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{5/2} \sqrt{d x^2}}-\frac{a x^2}{b^2 \sqrt{d x^2}}+\frac{x^4}{3 b \sqrt{d x^2}}",1,"-((a*x^2)/(b^2*Sqrt[d*x^2])) + x^4/(3*b*Sqrt[d*x^2]) + (a^(3/2)*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b^(5/2)*Sqrt[d*x^2])","A",4,3,22,0.1364,1,"{15, 302, 205}"
672,1,52,0,0.0157799,"\int \frac{x^3}{\sqrt{d x^2} \left(a+b x^2\right)} \, dx","Int[x^3/(Sqrt[d*x^2]*(a + b*x^2)),x]","\frac{x^2}{b \sqrt{d x^2}}-\frac{\sqrt{a} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2} \sqrt{d x^2}}","\frac{x^2}{b \sqrt{d x^2}}-\frac{\sqrt{a} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{b^{3/2} \sqrt{d x^2}}",1,"x^2/(b*Sqrt[d*x^2]) - (Sqrt[a]*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(b^(3/2)*Sqrt[d*x^2])","A",3,3,22,0.1364,1,"{15, 321, 205}"
673,1,34,0,0.0082262,"\int \frac{x}{\sqrt{d x^2} \left(a+b x^2\right)} \, dx","Int[x/(Sqrt[d*x^2]*(a + b*x^2)),x]","\frac{x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \sqrt{d x^2}}","\frac{x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{b} \sqrt{d x^2}}",1,"(x*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[b]*Sqrt[d*x^2])","A",2,2,20,0.1000,1,"{15, 205}"
674,1,50,0,0.0165593,"\int \frac{1}{x \sqrt{d x^2} \left(a+b x^2\right)} \, dx","Int[1/(x*Sqrt[d*x^2]*(a + b*x^2)),x]","-\frac{\sqrt{b} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{d x^2}}-\frac{1}{a \sqrt{d x^2}}","-\frac{\sqrt{b} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{3/2} \sqrt{d x^2}}-\frac{1}{a \sqrt{d x^2}}",1,"-(1/(a*Sqrt[d*x^2])) - (Sqrt[b]*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(3/2)*Sqrt[d*x^2])","A",3,3,22,0.1364,1,"{15, 325, 205}"
675,1,68,0,0.0240175,"\int \frac{1}{x^3 \sqrt{d x^2} \left(a+b x^2\right)} \, dx","Int[1/(x^3*Sqrt[d*x^2]*(a + b*x^2)),x]","\frac{b^{3/2} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{d x^2}}+\frac{b}{a^2 \sqrt{d x^2}}-\frac{1}{3 a x^2 \sqrt{d x^2}}","\frac{b^{3/2} x \tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)}{a^{5/2} \sqrt{d x^2}}+\frac{b}{a^2 \sqrt{d x^2}}-\frac{1}{3 a x^2 \sqrt{d x^2}}",1,"b/(a^2*Sqrt[d*x^2]) - 1/(3*a*x^2*Sqrt[d*x^2]) + (b^(3/2)*x*ArcTan[(Sqrt[b]*x)/Sqrt[a]])/(a^(5/2)*Sqrt[d*x^2])","A",4,3,22,0.1364,1,"{15, 325, 205}"
676,1,157,0,0.2311555,"\int \frac{x^4 \sqrt{c+d x^2}}{a+b x^2} \, dx","Int[(x^4*Sqrt[c + d*x^2])/(a + b*x^2),x]","-\frac{\left(-8 a^2 d^2+4 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^3 d^{3/2}}+\frac{a^{3/2} \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^3}+\frac{x \sqrt{c+d x^2} (b c-4 a d)}{8 b^2 d}+\frac{x^3 \sqrt{c+d x^2}}{4 b}","-\frac{\left(-8 a^2 d^2+4 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^3 d^{3/2}}+\frac{a^{3/2} \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^3}+\frac{x \sqrt{c+d x^2} (b c-4 a d)}{8 b^2 d}+\frac{x^3 \sqrt{c+d x^2}}{4 b}",1,"((b*c - 4*a*d)*x*Sqrt[c + d*x^2])/(8*b^2*d) + (x^3*Sqrt[c + d*x^2])/(4*b) + (a^(3/2)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/b^3 - ((b^2*c^2 + 4*a*b*c*d - 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*b^3*d^(3/2))","A",7,7,24,0.2917,1,"{478, 582, 523, 217, 206, 377, 205}"
677,1,88,0,0.0812728,"\int \frac{x^3 \sqrt{c+d x^2}}{a+b x^2} \, dx","Int[(x^3*Sqrt[c + d*x^2])/(a + b*x^2),x]","-\frac{a \sqrt{c+d x^2}}{b^2}+\frac{a \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{5/2}}+\frac{\left(c+d x^2\right)^{3/2}}{3 b d}","-\frac{a \sqrt{c+d x^2}}{b^2}+\frac{a \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{5/2}}+\frac{\left(c+d x^2\right)^{3/2}}{3 b d}",1,"-((a*Sqrt[c + d*x^2])/b^2) + (c + d*x^2)^(3/2)/(3*b*d) + (a*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/b^(5/2)","A",5,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
678,1,112,0,0.0962023,"\int \frac{x^2 \sqrt{c+d x^2}}{a+b x^2} \, dx","Int[(x^2*Sqrt[c + d*x^2])/(a + b*x^2),x]","-\frac{\sqrt{a} \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^2}+\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2 \sqrt{d}}+\frac{x \sqrt{c+d x^2}}{2 b}","-\frac{\sqrt{a} \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^2}+\frac{(b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2 \sqrt{d}}+\frac{x \sqrt{c+d x^2}}{2 b}",1,"(x*Sqrt[c + d*x^2])/(2*b) - (Sqrt[a]*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/b^2 + ((b*c - 2*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^2*Sqrt[d])","A",6,6,24,0.2500,1,"{478, 523, 217, 206, 377, 205}"
679,1,65,0,0.0544701,"\int \frac{x \sqrt{c+d x^2}}{a+b x^2} \, dx","Int[(x*Sqrt[c + d*x^2])/(a + b*x^2),x]","\frac{\sqrt{c+d x^2}}{b}-\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{3/2}}","\frac{\sqrt{c+d x^2}}{b}-\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{3/2}}",1,"Sqrt[c + d*x^2]/b - (Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/b^(3/2)","A",4,4,22,0.1818,1,"{444, 50, 63, 208}"
680,1,81,0,0.0443272,"\int \frac{\sqrt{c+d x^2}}{a+b x^2} \, dx","Int[Sqrt[c + d*x^2]/(a + b*x^2),x]","\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} b}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b}","\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} b}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b}",1,"(Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(Sqrt[a]*b) + (Sqrt[d]*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/b","A",5,5,21,0.2381,1,"{402, 217, 206, 377, 205}"
681,1,80,0,0.0733895,"\int \frac{\sqrt{c+d x^2}}{x \left(a+b x^2\right)} \, dx","Int[Sqrt[c + d*x^2]/(x*(a + b*x^2)),x]","\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a \sqrt{b}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a}","\frac{\sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a \sqrt{b}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a}",1,"-((Sqrt[c]*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/a) + (Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a*Sqrt[b])","A",6,4,24,0.1667,1,"{446, 83, 63, 208}"
682,1,70,0,0.0506841,"\int \frac{\sqrt{c+d x^2}}{x^2 \left(a+b x^2\right)} \, dx","Int[Sqrt[c + d*x^2]/(x^2*(a + b*x^2)),x]","-\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2}}-\frac{\sqrt{c+d x^2}}{a x}","-\frac{\sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2}}-\frac{\sqrt{c+d x^2}}{a x}",1,"-(Sqrt[c + d*x^2]/(a*x)) - (Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/a^(3/2)","A",4,4,24,0.1667,1,"{475, 12, 377, 205}"
683,1,113,0,0.1204636,"\int \frac{\sqrt{c+d x^2}}{x^3 \left(a+b x^2\right)} \, dx","Int[Sqrt[c + d*x^2]/(x^3*(a + b*x^2)),x]","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 \sqrt{c}}-\frac{\sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2}-\frac{\sqrt{c+d x^2}}{2 a x^2}","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 \sqrt{c}}-\frac{\sqrt{b} \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2}-\frac{\sqrt{c+d x^2}}{2 a x^2}",1,"-Sqrt[c + d*x^2]/(2*a*x^2) + ((2*b*c - a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^2*Sqrt[c]) - (Sqrt[b]*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/a^2","A",7,5,24,0.2083,1,"{446, 99, 156, 63, 208}"
684,1,105,0,0.1196219,"\int \frac{\sqrt{c+d x^2}}{x^4 \left(a+b x^2\right)} \, dx","Int[Sqrt[c + d*x^2]/(x^4*(a + b*x^2)),x]","\frac{\sqrt{c+d x^2} (3 b c-a d)}{3 a^2 c x}+\frac{b \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2}}-\frac{\sqrt{c+d x^2}}{3 a x^3}","\frac{\sqrt{c+d x^2} (3 b c-a d)}{3 a^2 c x}+\frac{b \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2}}-\frac{\sqrt{c+d x^2}}{3 a x^3}",1,"-Sqrt[c + d*x^2]/(3*a*x^3) + ((3*b*c - a*d)*Sqrt[c + d*x^2])/(3*a^2*c*x) + (b*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/a^(5/2)","A",5,5,24,0.2083,1,"{475, 583, 12, 377, 205}"
685,1,210,0,0.4027024,"\int \frac{x^4 \left(c+d x^2\right)^{3/2}}{a+b x^2} \, dx","Int[(x^4*(c + d*x^2)^(3/2))/(a + b*x^2),x]","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-10 a b c d+b^2 c^2\right)}{16 b^3 d}-\frac{(b c-2 a d) \left(-8 a^2 d^2+8 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 b^4 d^{3/2}}+\frac{a^{3/2} (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^4}+\frac{x^3 \sqrt{c+d x^2} (7 b c-6 a d)}{24 b^2}+\frac{d x^5 \sqrt{c+d x^2}}{6 b}","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-10 a b c d+b^2 c^2\right)}{16 b^3 d}-\frac{(b c-2 a d) \left(-8 a^2 d^2+8 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 b^4 d^{3/2}}+\frac{a^{3/2} (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^4}+\frac{x^3 \sqrt{c+d x^2} (7 b c-6 a d)}{24 b^2}+\frac{d x^5 \sqrt{c+d x^2}}{6 b}",1,"((b^2*c^2 - 10*a*b*c*d + 8*a^2*d^2)*x*Sqrt[c + d*x^2])/(16*b^3*d) + ((7*b*c - 6*a*d)*x^3*Sqrt[c + d*x^2])/(24*b^2) + (d*x^5*Sqrt[c + d*x^2])/(6*b) + (a^(3/2)*(b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/b^4 - ((b*c - 2*a*d)*(b^2*c^2 + 8*a*b*c*d - 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*b^4*d^(3/2))","A",8,7,24,0.2917,1,"{477, 582, 523, 217, 206, 377, 205}"
686,1,115,0,0.1055788,"\int \frac{x^3 \left(c+d x^2\right)^{3/2}}{a+b x^2} \, dx","Int[(x^3*(c + d*x^2)^(3/2))/(a + b*x^2),x]","-\frac{a \left(c+d x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{c+d x^2} (b c-a d)}{b^3}+\frac{a (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{\left(c+d x^2\right)^{5/2}}{5 b d}","-\frac{a \left(c+d x^2\right)^{3/2}}{3 b^2}-\frac{a \sqrt{c+d x^2} (b c-a d)}{b^3}+\frac{a (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{\left(c+d x^2\right)^{5/2}}{5 b d}",1,"-((a*(b*c - a*d)*Sqrt[c + d*x^2])/b^3) - (a*(c + d*x^2)^(3/2))/(3*b^2) + (c + d*x^2)^(5/2)/(5*b*d) + (a*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/b^(7/2)","A",6,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
687,1,158,0,0.2519821,"\int \frac{x^2 \left(c+d x^2\right)^{3/2}}{a+b x^2} \, dx","Int[(x^2*(c + d*x^2)^(3/2))/(a + b*x^2),x]","\frac{\left(8 a^2 d^2-12 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^3 \sqrt{d}}+\frac{x \sqrt{c+d x^2} (5 b c-4 a d)}{8 b^2}-\frac{\sqrt{a} (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^3}+\frac{d x^3 \sqrt{c+d x^2}}{4 b}","\frac{\left(8 a^2 d^2-12 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^3 \sqrt{d}}+\frac{x \sqrt{c+d x^2} (5 b c-4 a d)}{8 b^2}-\frac{\sqrt{a} (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^3}+\frac{d x^3 \sqrt{c+d x^2}}{4 b}",1,"((5*b*c - 4*a*d)*x*Sqrt[c + d*x^2])/(8*b^2) + (d*x^3*Sqrt[c + d*x^2])/(4*b) - (Sqrt[a]*(b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/b^3 + ((3*b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*b^3*Sqrt[d])","A",7,7,24,0.2917,1,"{477, 582, 523, 217, 206, 377, 205}"
688,1,91,0,0.076083,"\int \frac{x \left(c+d x^2\right)^{3/2}}{a+b x^2} \, dx","Int[(x*(c + d*x^2)^(3/2))/(a + b*x^2),x]","\frac{\sqrt{c+d x^2} (b c-a d)}{b^2}-\frac{(b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{5/2}}+\frac{\left(c+d x^2\right)^{3/2}}{3 b}","\frac{\sqrt{c+d x^2} (b c-a d)}{b^2}-\frac{(b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{5/2}}+\frac{\left(c+d x^2\right)^{3/2}}{3 b}",1,"((b*c - a*d)*Sqrt[c + d*x^2])/b^2 + (c + d*x^2)^(3/2)/(3*b) - ((b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/b^(5/2)","A",5,4,22,0.1818,1,"{444, 50, 63, 208}"
689,1,113,0,0.0955573,"\int \frac{\left(c+d x^2\right)^{3/2}}{a+b x^2} \, dx","Int[(c + d*x^2)^(3/2)/(a + b*x^2),x]","\frac{(b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} b^2}+\frac{\sqrt{d} (3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2}+\frac{d x \sqrt{c+d x^2}}{2 b}","\frac{(b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} b^2}+\frac{\sqrt{d} (3 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2}+\frac{d x \sqrt{c+d x^2}}{2 b}",1,"(d*x*Sqrt[c + d*x^2])/(2*b) + ((b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(Sqrt[a]*b^2) + (Sqrt[d]*(3*b*c - 2*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^2)","A",6,6,21,0.2857,1,"{416, 523, 217, 206, 377, 205}"
690,1,96,0,0.1067066,"\int \frac{\left(c+d x^2\right)^{3/2}}{x \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(3/2)/(x*(a + b*x^2)),x]","\frac{(b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a b^{3/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a}+\frac{d \sqrt{c+d x^2}}{b}","\frac{(b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a b^{3/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a}+\frac{d \sqrt{c+d x^2}}{b}",1,"(d*Sqrt[c + d*x^2])/b - (c^(3/2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/a + ((b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a*b^(3/2))","A",7,5,24,0.2083,1,"{446, 84, 156, 63, 208}"
691,1,102,0,0.0914889,"\int \frac{\left(c+d x^2\right)^{3/2}}{x^2 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(3/2)/(x^2*(a + b*x^2)),x]","-\frac{(b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} b}-\frac{c \sqrt{c+d x^2}}{a x}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b}","-\frac{(b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} b}-\frac{c \sqrt{c+d x^2}}{a x}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b}",1,"-((c*Sqrt[c + d*x^2])/(a*x)) - ((b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(3/2)*b) + (d^(3/2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/b","A",6,6,24,0.2500,1,"{474, 523, 217, 206, 377, 205}"
692,1,114,0,0.1406288,"\int \frac{\left(c+d x^2\right)^{3/2}}{x^3 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(3/2)/(x^3*(a + b*x^2)),x]","-\frac{(b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 \sqrt{b}}+\frac{\sqrt{c} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2}-\frac{c \sqrt{c+d x^2}}{2 a x^2}","-\frac{(b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 \sqrt{b}}+\frac{\sqrt{c} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2}-\frac{c \sqrt{c+d x^2}}{2 a x^2}",1,"-(c*Sqrt[c + d*x^2])/(2*a*x^2) + (Sqrt[c]*(2*b*c - 3*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^2) - ((b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a^2*Sqrt[b])","A",7,5,24,0.2083,1,"{446, 98, 156, 63, 208}"
693,1,102,0,0.126267,"\int \frac{\left(c+d x^2\right)^{3/2}}{x^4 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(3/2)/(x^4*(a + b*x^2)),x]","\frac{\sqrt{c+d x^2} (3 b c-4 a d)}{3 a^2 x}+\frac{(b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2}}-\frac{c \sqrt{c+d x^2}}{3 a x^3}","\frac{\sqrt{c+d x^2} (3 b c-4 a d)}{3 a^2 x}+\frac{(b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2}}-\frac{c \sqrt{c+d x^2}}{3 a x^3}",1,"-(c*Sqrt[c + d*x^2])/(3*a*x^3) + ((3*b*c - 4*a*d)*Sqrt[c + d*x^2])/(3*a^2*x) + ((b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/a^(5/2)","A",5,5,24,0.2083,1,"{474, 583, 12, 377, 205}"
694,1,291,0,0.5745236,"\int \frac{x^4 \left(c+d x^2\right)^{5/2}}{a+b x^2} \, dx","Int[(x^4*(c + d*x^2)^(5/2))/(a + b*x^2),x]","\frac{x^3 \sqrt{c+d x^2} \left(48 a^2 d^2-104 a b c d+59 b^2 c^2\right)}{192 b^3}+\frac{x \sqrt{c+d x^2} \left(144 a^2 b c d^2-64 a^3 d^3-88 a b^2 c^2 d+5 b^3 c^3\right)}{128 b^4 d}-\frac{\left(-240 a^2 b^2 c^2 d^2+320 a^3 b c d^3-128 a^4 d^4+40 a b^3 c^3 d+5 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 b^5 d^{3/2}}+\frac{a^{3/2} (b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^5}+\frac{d x^5 \sqrt{c+d x^2} (11 b c-8 a d)}{48 b^2}+\frac{d x^5 \left(c+d x^2\right)^{3/2}}{8 b}","\frac{x^3 \sqrt{c+d x^2} \left(48 a^2 d^2-104 a b c d+59 b^2 c^2\right)}{192 b^3}+\frac{x \sqrt{c+d x^2} \left(144 a^2 b c d^2-64 a^3 d^3-88 a b^2 c^2 d+5 b^3 c^3\right)}{128 b^4 d}-\frac{\left(-240 a^2 b^2 c^2 d^2+320 a^3 b c d^3-128 a^4 d^4+40 a b^3 c^3 d+5 b^4 c^4\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{128 b^5 d^{3/2}}+\frac{a^{3/2} (b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^5}+\frac{d x^5 \sqrt{c+d x^2} (11 b c-8 a d)}{48 b^2}+\frac{d x^5 \left(c+d x^2\right)^{3/2}}{8 b}",1,"((5*b^3*c^3 - 88*a*b^2*c^2*d + 144*a^2*b*c*d^2 - 64*a^3*d^3)*x*Sqrt[c + d*x^2])/(128*b^4*d) + ((59*b^2*c^2 - 104*a*b*c*d + 48*a^2*d^2)*x^3*Sqrt[c + d*x^2])/(192*b^3) + (d*(11*b*c - 8*a*d)*x^5*Sqrt[c + d*x^2])/(48*b^2) + (d*x^5*(c + d*x^2)^(3/2))/(8*b) + (a^(3/2)*(b*c - a*d)^(5/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/b^5 - ((5*b^4*c^4 + 40*a*b^3*c^3*d - 240*a^2*b^2*c^2*d^2 + 320*a^3*b*c*d^3 - 128*a^4*d^4)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(128*b^5*d^(3/2))","A",9,8,24,0.3333,1,"{477, 581, 582, 523, 217, 206, 377, 205}"
695,1,144,0,0.1500298,"\int \frac{x^3 \left(c+d x^2\right)^{5/2}}{a+b x^2} \, dx","Int[(x^3*(c + d*x^2)^(5/2))/(a + b*x^2),x]","-\frac{a \left(c+d x^2\right)^{5/2}}{5 b^2}-\frac{a \left(c+d x^2\right)^{3/2} (b c-a d)}{3 b^3}-\frac{a \sqrt{c+d x^2} (b c-a d)^2}{b^4}+\frac{a (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{9/2}}+\frac{\left(c+d x^2\right)^{7/2}}{7 b d}","-\frac{a \left(c+d x^2\right)^{5/2}}{5 b^2}-\frac{a \left(c+d x^2\right)^{3/2} (b c-a d)}{3 b^3}-\frac{a \sqrt{c+d x^2} (b c-a d)^2}{b^4}+\frac{a (b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{9/2}}+\frac{\left(c+d x^2\right)^{7/2}}{7 b d}",1,"-((a*(b*c - a*d)^2*Sqrt[c + d*x^2])/b^4) - (a*(b*c - a*d)*(c + d*x^2)^(3/2))/(3*b^3) - (a*(c + d*x^2)^(5/2))/(5*b^2) + (c + d*x^2)^(7/2)/(7*b*d) + (a*(b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/b^(9/2)","A",7,5,24,0.2083,1,"{446, 80, 50, 63, 208}"
696,1,217,0,0.3921159,"\int \frac{x^2 \left(c+d x^2\right)^{5/2}}{a+b x^2} \, dx","Int[(x^2*(c + d*x^2)^(5/2))/(a + b*x^2),x]","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-18 a b c d+11 b^2 c^2\right)}{16 b^3}+\frac{\left(40 a^2 b c d^2-16 a^3 d^3-30 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 b^4 \sqrt{d}}+\frac{d x^3 \sqrt{c+d x^2} (3 b c-2 a d)}{8 b^2}-\frac{\sqrt{a} (b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^4}+\frac{d x^3 \left(c+d x^2\right)^{3/2}}{6 b}","\frac{x \sqrt{c+d x^2} \left(8 a^2 d^2-18 a b c d+11 b^2 c^2\right)}{16 b^3}+\frac{\left(40 a^2 b c d^2-16 a^3 d^3-30 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 b^4 \sqrt{d}}+\frac{d x^3 \sqrt{c+d x^2} (3 b c-2 a d)}{8 b^2}-\frac{\sqrt{a} (b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^4}+\frac{d x^3 \left(c+d x^2\right)^{3/2}}{6 b}",1,"((11*b^2*c^2 - 18*a*b*c*d + 8*a^2*d^2)*x*Sqrt[c + d*x^2])/(16*b^3) + (d*(3*b*c - 2*a*d)*x^3*Sqrt[c + d*x^2])/(8*b^2) + (d*x^3*(c + d*x^2)^(3/2))/(6*b) - (Sqrt[a]*(b*c - a*d)^(5/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/b^4 + ((5*b^3*c^3 - 30*a*b^2*c^2*d + 40*a^2*b*c*d^2 - 16*a^3*d^3)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*b^4*Sqrt[d])","A",8,8,24,0.3333,1,"{477, 581, 582, 523, 217, 206, 377, 205}"
697,1,119,0,0.1067652,"\int \frac{x \left(c+d x^2\right)^{5/2}}{a+b x^2} \, dx","Int[(x*(c + d*x^2)^(5/2))/(a + b*x^2),x]","\frac{\sqrt{c+d x^2} (b c-a d)^2}{b^3}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{3 b^2}-\frac{(b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{\left(c+d x^2\right)^{5/2}}{5 b}","\frac{\sqrt{c+d x^2} (b c-a d)^2}{b^3}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{3 b^2}-\frac{(b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{7/2}}+\frac{\left(c+d x^2\right)^{5/2}}{5 b}",1,"((b*c - a*d)^2*Sqrt[c + d*x^2])/b^3 + ((b*c - a*d)*(c + d*x^2)^(3/2))/(3*b^2) + (c + d*x^2)^(5/2)/(5*b) - ((b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/b^(7/2)","A",6,4,22,0.1818,1,"{444, 50, 63, 208}"
698,1,156,0,0.179535,"\int \frac{\left(c+d x^2\right)^{5/2}}{a+b x^2} \, dx","Int[(c + d*x^2)^(5/2)/(a + b*x^2),x]","\frac{\sqrt{d} \left(8 a^2 d^2-20 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^3}+\frac{d x \sqrt{c+d x^2} (7 b c-4 a d)}{8 b^2}+\frac{(b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} b^3}+\frac{d x \left(c+d x^2\right)^{3/2}}{4 b}","\frac{\sqrt{d} \left(8 a^2 d^2-20 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^3}+\frac{d x \sqrt{c+d x^2} (7 b c-4 a d)}{8 b^2}+\frac{(b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} b^3}+\frac{d x \left(c+d x^2\right)^{3/2}}{4 b}",1,"(d*(7*b*c - 4*a*d)*x*Sqrt[c + d*x^2])/(8*b^2) + (d*x*(c + d*x^2)^(3/2))/(4*b) + ((b*c - a*d)^(5/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(Sqrt[a]*b^3) + (Sqrt[d]*(15*b^2*c^2 - 20*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*b^3)","A",7,7,21,0.3333,1,"{416, 528, 523, 217, 206, 377, 205}"
699,1,124,0,0.1905225,"\int \frac{\left(c+d x^2\right)^{5/2}}{x \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(5/2)/(x*(a + b*x^2)),x]","\frac{d \sqrt{c+d x^2} (2 b c-a d)}{b^2}+\frac{(b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a b^{5/2}}-\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a}+\frac{d \left(c+d x^2\right)^{3/2}}{3 b}","\frac{d \sqrt{c+d x^2} (2 b c-a d)}{b^2}+\frac{(b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a b^{5/2}}-\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a}+\frac{d \left(c+d x^2\right)^{3/2}}{3 b}",1,"(d*(2*b*c - a*d)*Sqrt[c + d*x^2])/b^2 + (d*(c + d*x^2)^(3/2))/(3*b) - (c^(5/2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/a + ((b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a*b^(5/2))","A",8,6,24,0.2500,1,"{446, 84, 154, 156, 63, 208}"
700,1,145,0,0.1973593,"\int \frac{\left(c+d x^2\right)^{5/2}}{x^2 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(5/2)/(x^2*(a + b*x^2)),x]","-\frac{(b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} b^2}+\frac{d^{3/2} (5 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2}+\frac{d x \sqrt{c+d x^2} (a d+2 b c)}{2 a b}-\frac{c \left(c+d x^2\right)^{3/2}}{a x}","-\frac{(b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} b^2}+\frac{d^{3/2} (5 b c-2 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2}+\frac{d x \sqrt{c+d x^2} (a d+2 b c)}{2 a b}-\frac{c \left(c+d x^2\right)^{3/2}}{a x}",1,"(d*(2*b*c + a*d)*x*Sqrt[c + d*x^2])/(2*a*b) - (c*(c + d*x^2)^(3/2))/(a*x) - ((b*c - a*d)^(5/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(3/2)*b^2) + (d^(3/2)*(5*b*c - 2*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^2)","A",7,7,24,0.2917,1,"{474, 528, 523, 217, 206, 377, 205}"
701,1,144,0,0.2435892,"\int \frac{\left(c+d x^2\right)^{5/2}}{x^3 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(5/2)/(x^3*(a + b*x^2)),x]","-\frac{(b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 b^{3/2}}+\frac{c^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2}+\frac{d \sqrt{c+d x^2} (2 a d+b c)}{2 a b}-\frac{c \left(c+d x^2\right)^{3/2}}{2 a x^2}","-\frac{(b c-a d)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 b^{3/2}}+\frac{c^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2}+\frac{d \sqrt{c+d x^2} (2 a d+b c)}{2 a b}-\frac{c \left(c+d x^2\right)^{3/2}}{2 a x^2}",1,"(d*(b*c + 2*a*d)*Sqrt[c + d*x^2])/(2*a*b) - (c*(c + d*x^2)^(3/2))/(2*a*x^2) + (c^(3/2)*(2*b*c - 5*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^2) - ((b*c - a*d)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a^2*b^(3/2))","A",8,6,24,0.2500,1,"{446, 98, 154, 156, 63, 208}"
702,1,130,0,0.1783617,"\int \frac{\left(c+d x^2\right)^{5/2}}{x^4 \left(a+b x^2\right)} \, dx","Int[(c + d*x^2)^(5/2)/(x^4*(a + b*x^2)),x]","\frac{c \sqrt{c+d x^2} (b c-2 a d)}{a^2 x}+\frac{(b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} b}-\frac{c \left(c+d x^2\right)^{3/2}}{3 a x^3}+\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b}","\frac{c \sqrt{c+d x^2} (b c-2 a d)}{a^2 x}+\frac{(b c-a d)^{5/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} b}-\frac{c \left(c+d x^2\right)^{3/2}}{3 a x^3}+\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b}",1,"(c*(b*c - 2*a*d)*Sqrt[c + d*x^2])/(a^2*x) - (c*(c + d*x^2)^(3/2))/(3*a*x^3) + ((b*c - a*d)^(5/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(5/2)*b) + (d^(5/2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/b","A",7,7,24,0.2917,1,"{474, 580, 523, 217, 206, 377, 205}"
703,1,100,0,0.1062965,"\int \frac{x^5}{\left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[x^5/((a + b*x^2)*Sqrt[c + d*x^2]),x]","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^2} (a d+b c)}{b^2 d^2}+\frac{\left(c+d x^2\right)^{3/2}}{3 b d^2}","-\frac{a^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{5/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^2} (a d+b c)}{b^2 d^2}+\frac{\left(c+d x^2\right)^{3/2}}{3 b d^2}",1,"-(((b*c + a*d)*Sqrt[c + d*x^2])/(b^2*d^2)) + (c + d*x^2)^(3/2)/(3*b*d^2) - (a^2*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(b^(5/2)*Sqrt[b*c - a*d])","A",5,4,24,0.1667,1,"{446, 88, 63, 208}"
704,1,68,0,0.0639165,"\int \frac{x^3}{\left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[x^3/((a + b*x^2)*Sqrt[c + d*x^2]),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^2}}{b d}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{b^{3/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^2}}{b d}",1,"Sqrt[c + d*x^2]/(b*d) + (a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(b^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{446, 80, 63, 208}"
705,1,49,0,0.0427684,"\int \frac{x}{\left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[x/((a + b*x^2)*Sqrt[c + d*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{\sqrt{b} \sqrt{b c-a d}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{\sqrt{b} \sqrt{b c-a d}}",1,"-(ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]]/(Sqrt[b]*Sqrt[b*c - a*d]))","A",3,3,22,0.1364,1,"{444, 63, 208}"
706,1,80,0,0.0737381,"\int \frac{1}{x \left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[1/(x*(a + b*x^2)*Sqrt[c + d*x^2]),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a \sqrt{c}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a \sqrt{b c-a d}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a \sqrt{c}}",1,"-(ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]/(a*Sqrt[c])) + (Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a*Sqrt[b*c - a*d])","A",6,4,24,0.1667,1,"{446, 86, 63, 208}"
707,1,115,0,0.115032,"\int \frac{1}{x^3 \left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[1/(x^3*(a + b*x^2)*Sqrt[c + d*x^2]),x]","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 c^{3/2}}-\frac{\sqrt{c+d x^2}}{2 a c x^2}","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 \sqrt{b c-a d}}+\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 c^{3/2}}-\frac{\sqrt{c+d x^2}}{2 a c x^2}",1,"-Sqrt[c + d*x^2]/(2*a*c*x^2) + ((2*b*c + a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^2*c^(3/2)) - (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a^2*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
708,1,114,0,0.0939242,"\int \frac{x^4}{\left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[x^4/((a + b*x^2)*Sqrt[c + d*x^2]),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2 d^{3/2}}+\frac{x \sqrt{c+d x^2}}{2 b d}","\frac{a^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b^2 \sqrt{b c-a d}}-\frac{(2 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^2 d^{3/2}}+\frac{x \sqrt{c+d x^2}}{2 b d}",1,"(x*Sqrt[c + d*x^2])/(2*b*d) + (a^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(b^2*Sqrt[b*c - a*d]) - ((b*c + 2*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^2*d^(3/2))","A",6,6,24,0.2500,1,"{479, 523, 217, 206, 377, 205}"
709,1,82,0,0.0497784,"\int \frac{x^2}{\left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[x^2/((a + b*x^2)*Sqrt[c + d*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b \sqrt{b c-a d}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b \sqrt{d}}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b \sqrt{b c-a d}}",1,"-((Sqrt[a]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(b*Sqrt[b*c - a*d])) + ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]]/(b*Sqrt[d])","A",5,5,24,0.2083,1,"{483, 217, 206, 377, 205}"
710,1,49,0,0.019298,"\int \frac{1}{\left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[1/((a + b*x^2)*Sqrt[c + d*x^2]),x]","\frac{\tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} \sqrt{b c-a d}}","\frac{\tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} \sqrt{b c-a d}}",1,"ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])]/(Sqrt[a]*Sqrt[b*c - a*d])","A",2,2,21,0.09524,1,"{377, 205}"
711,1,74,0,0.0533914,"\int \frac{1}{x^2 \left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[1/(x^2*(a + b*x^2)*Sqrt[c + d*x^2]),x]","-\frac{b \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^2}}{a c x}","-\frac{b \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^2}}{a c x}",1,"-(Sqrt[c + d*x^2]/(a*c*x)) - (b*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(3/2)*Sqrt[b*c - a*d])","A",4,4,24,0.1667,1,"{480, 12, 377, 205}"
712,1,110,0,0.1227262,"\int \frac{1}{x^4 \left(a+b x^2\right) \sqrt{c+d x^2}} \, dx","Int[1/(x^4*(a + b*x^2)*Sqrt[c + d*x^2]),x]","\frac{b^2 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^2} (2 a d+3 b c)}{3 a^2 c^2 x}-\frac{\sqrt{c+d x^2}}{3 a c x^3}","\frac{b^2 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} \sqrt{b c-a d}}+\frac{\sqrt{c+d x^2} (2 a d+3 b c)}{3 a^2 c^2 x}-\frac{\sqrt{c+d x^2}}{3 a c x^3}",1,"-Sqrt[c + d*x^2]/(3*a*c*x^3) + ((3*b*c + 2*a*d)*Sqrt[c + d*x^2])/(3*a^2*c^2*x) + (b^2*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(5/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{480, 583, 12, 377, 205}"
713,1,109,0,0.1005274,"\int \frac{x^4}{\left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[x^4/((a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b (b c-a d)^{3/2}}-\frac{c x}{d \sqrt{c+d x^2} (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b d^{3/2}}","\frac{a^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{b (b c-a d)^{3/2}}-\frac{c x}{d \sqrt{c+d x^2} (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b d^{3/2}}",1,"-((c*x)/(d*(b*c - a*d)*Sqrt[c + d*x^2])) + (a^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(b*(b*c - a*d)^(3/2)) + ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]]/(b*d^(3/2))","A",6,6,24,0.2500,1,"{470, 523, 217, 206, 377, 205}"
714,1,77,0,0.0717906,"\int \frac{x^3}{\left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[x^3/((a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{\sqrt{b} (b c-a d)^{3/2}}-\frac{c}{d \sqrt{c+d x^2} (b c-a d)}","\frac{a \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{\sqrt{b} (b c-a d)^{3/2}}-\frac{c}{d \sqrt{c+d x^2} (b c-a d)}",1,"-(c/(d*(b*c - a*d)*Sqrt[c + d*x^2])) + (a*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
715,1,74,0,0.049263,"\int \frac{x^2}{\left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[x^2/((a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{x}{\sqrt{c+d x^2} (b c-a d)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{(b c-a d)^{3/2}}","\frac{x}{\sqrt{c+d x^2} (b c-a d)}-\frac{\sqrt{a} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{(b c-a d)^{3/2}}",1,"x/((b*c - a*d)*Sqrt[c + d*x^2]) - (Sqrt[a]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(b*c - a*d)^(3/2)","A",4,4,24,0.1667,1,"{471, 12, 377, 205}"
716,1,72,0,0.0563638,"\int \frac{x}{\left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[x/((a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{1}{\sqrt{c+d x^2} (b c-a d)}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{3/2}}","\frac{1}{\sqrt{c+d x^2} (b c-a d)}-\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{3/2}}",1,"1/((b*c - a*d)*Sqrt[c + d*x^2]) - (Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(b*c - a*d)^(3/2)","A",4,4,22,0.1818,1,"{444, 51, 63, 208}"
717,1,79,0,0.0369599,"\int \frac{1}{\left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[1/((a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{b \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} (b c-a d)^{3/2}}-\frac{d x}{c \sqrt{c+d x^2} (b c-a d)}","\frac{b \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} (b c-a d)^{3/2}}-\frac{d x}{c \sqrt{c+d x^2} (b c-a d)}",1,"-((d*x)/(c*(b*c - a*d)*Sqrt[c + d*x^2])) + (b*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(Sqrt[a]*(b*c - a*d)^(3/2))","A",3,3,21,0.1429,1,"{382, 377, 205}"
718,1,107,0,0.1121663,"\int \frac{1}{x \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a (b c-a d)^{3/2}}-\frac{d}{c \sqrt{c+d x^2} (b c-a d)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a c^{3/2}}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a (b c-a d)^{3/2}}-\frac{d}{c \sqrt{c+d x^2} (b c-a d)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a c^{3/2}}",1,"-(d/(c*(b*c - a*d)*Sqrt[c + d*x^2])) - ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]/(a*c^(3/2)) + (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 85, 156, 63, 208}"
719,1,124,0,0.116737,"\int \frac{1}{x^2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^2)*(c + d*x^2)^(3/2)),x]","-\frac{b^2 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^2} (b c-2 a d)}{a c^2 x (b c-a d)}-\frac{d}{c x \sqrt{c+d x^2} (b c-a d)}","-\frac{b^2 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^2} (b c-2 a d)}{a c^2 x (b c-a d)}-\frac{d}{c x \sqrt{c+d x^2} (b c-a d)}",1,"-(d/(c*(b*c - a*d)*x*Sqrt[c + d*x^2])) - ((b*c - 2*a*d)*Sqrt[c + d*x^2])/(a*c^2*(b*c - a*d)*x) - (b^2*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(3/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{472, 583, 12, 377, 205}"
720,1,156,0,0.2162355,"\int \frac{1}{x^3 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^2)*(c + d*x^2)^(3/2)),x]","-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 (b c-a d)^{3/2}}+\frac{(3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 c^{5/2}}-\frac{d (b c-3 a d)}{2 a c^2 \sqrt{c+d x^2} (b c-a d)}-\frac{1}{2 a c x^2 \sqrt{c+d x^2}}","-\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 (b c-a d)^{3/2}}+\frac{(3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 c^{5/2}}-\frac{d (b c-3 a d)}{2 a c^2 \sqrt{c+d x^2} (b c-a d)}-\frac{1}{2 a c x^2 \sqrt{c+d x^2}}",1,"-(d*(b*c - 3*a*d))/(2*a*c^2*(b*c - a*d)*Sqrt[c + d*x^2]) - 1/(2*a*c*x^2*Sqrt[c + d*x^2]) + ((2*b*c + 3*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^2*c^(5/2)) - (b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a^2*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 152, 156, 63, 208}"
721,1,176,0,0.218351,"\int \frac{1}{x^4 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^2)*(c + d*x^2)^(3/2)),x]","\frac{b^3 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^2} (3 b c-4 a d) (2 a d+b c)}{3 a^2 c^3 x (b c-a d)}-\frac{\sqrt{c+d x^2} (b c-4 a d)}{3 a c^2 x^3 (b c-a d)}-\frac{d}{c x^3 \sqrt{c+d x^2} (b c-a d)}","\frac{b^3 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} (b c-a d)^{3/2}}+\frac{\sqrt{c+d x^2} (3 b c-4 a d) (2 a d+b c)}{3 a^2 c^3 x (b c-a d)}-\frac{\sqrt{c+d x^2} (b c-4 a d)}{3 a c^2 x^3 (b c-a d)}-\frac{d}{c x^3 \sqrt{c+d x^2} (b c-a d)}",1,"-(d/(c*(b*c - a*d)*x^3*Sqrt[c + d*x^2])) - ((b*c - 4*a*d)*Sqrt[c + d*x^2])/(3*a*c^2*(b*c - a*d)*x^3) + ((3*b*c - 4*a*d)*(b*c + 2*a*d)*Sqrt[c + d*x^2])/(3*a^2*c^3*(b*c - a*d)*x) + (b^3*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(5/2)*(b*c - a*d)^(3/2))","A",6,5,24,0.2083,1,"{472, 583, 12, 377, 205}"
722,1,117,0,0.1127865,"\int \frac{x^4}{\left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[x^4/((a + b*x^2)*(c + d*x^2)^(5/2)),x]","\frac{a^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{(b c-a d)^{5/2}}+\frac{x (b c-4 a d)}{3 d \sqrt{c+d x^2} (b c-a d)^2}-\frac{c x}{3 d \left(c+d x^2\right)^{3/2} (b c-a d)}","\frac{a^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{(b c-a d)^{5/2}}+\frac{x (b c-4 a d)}{3 d \sqrt{c+d x^2} (b c-a d)^2}-\frac{c x}{3 d \left(c+d x^2\right)^{3/2} (b c-a d)}",1,"-(c*x)/(3*d*(b*c - a*d)*(c + d*x^2)^(3/2)) + ((b*c - 4*a*d)*x)/(3*d*(b*c - a*d)^2*Sqrt[c + d*x^2]) + (a^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(b*c - a*d)^(5/2)","A",5,5,24,0.2083,1,"{470, 527, 12, 377, 205}"
723,1,103,0,0.0920235,"\int \frac{x^3}{\left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[x^3/((a + b*x^2)*(c + d*x^2)^(5/2)),x]","-\frac{a}{\sqrt{c+d x^2} (b c-a d)^2}-\frac{c}{3 d \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}","-\frac{a}{\sqrt{c+d x^2} (b c-a d)^2}-\frac{c}{3 d \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{a \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}",1,"-c/(3*d*(b*c - a*d)*(c + d*x^2)^(3/2)) - a/((b*c - a*d)^2*Sqrt[c + d*x^2]) + (a*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(b*c - a*d)^(5/2)","A",5,5,24,0.2083,1,"{446, 78, 51, 63, 208}"
724,1,115,0,0.0875847,"\int \frac{x^2}{\left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[x^2/((a + b*x^2)*(c + d*x^2)^(5/2)),x]","\frac{x (a d+2 b c)}{3 c \sqrt{c+d x^2} (b c-a d)^2}+\frac{x}{3 \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{\sqrt{a} b \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{(b c-a d)^{5/2}}","\frac{x (a d+2 b c)}{3 c \sqrt{c+d x^2} (b c-a d)^2}+\frac{x}{3 \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{\sqrt{a} b \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{(b c-a d)^{5/2}}",1,"x/(3*(b*c - a*d)*(c + d*x^2)^(3/2)) + ((2*b*c + a*d)*x)/(3*c*(b*c - a*d)^2*Sqrt[c + d*x^2]) - (Sqrt[a]*b*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(b*c - a*d)^(5/2)","A",5,5,24,0.2083,1,"{471, 527, 12, 377, 205}"
725,1,98,0,0.0848251,"\int \frac{x}{\left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[x/((a + b*x^2)*(c + d*x^2)^(5/2)),x]","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}+\frac{b}{\sqrt{c+d x^2} (b c-a d)^2}+\frac{1}{3 \left(c+d x^2\right)^{3/2} (b c-a d)}","-\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{(b c-a d)^{5/2}}+\frac{b}{\sqrt{c+d x^2} (b c-a d)^2}+\frac{1}{3 \left(c+d x^2\right)^{3/2} (b c-a d)}",1,"1/(3*(b*c - a*d)*(c + d*x^2)^(3/2)) + b/((b*c - a*d)^2*Sqrt[c + d*x^2]) - (b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(b*c - a*d)^(5/2)","A",5,4,22,0.1818,1,"{444, 51, 63, 208}"
726,1,122,0,0.100544,"\int \frac{1}{\left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[1/((a + b*x^2)*(c + d*x^2)^(5/2)),x]","\frac{b^2 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} (b c-a d)^{5/2}}-\frac{d x (5 b c-2 a d)}{3 c^2 \sqrt{c+d x^2} (b c-a d)^2}-\frac{d x}{3 c \left(c+d x^2\right)^{3/2} (b c-a d)}","\frac{b^2 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} (b c-a d)^{5/2}}-\frac{d x (5 b c-2 a d)}{3 c^2 \sqrt{c+d x^2} (b c-a d)^2}-\frac{d x}{3 c \left(c+d x^2\right)^{3/2} (b c-a d)}",1,"-(d*x)/(3*c*(b*c - a*d)*(c + d*x^2)^(3/2)) - (d*(5*b*c - 2*a*d)*x)/(3*c^2*(b*c - a*d)^2*Sqrt[c + d*x^2]) + (b^2*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(Sqrt[a]*(b*c - a*d)^(5/2))","A",5,5,21,0.2381,1,"{414, 527, 12, 377, 205}"
727,1,145,0,0.1849832,"\int \frac{1}{x \left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x*(a + b*x^2)*(c + d*x^2)^(5/2)),x]","\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a (b c-a d)^{5/2}}-\frac{d (2 b c-a d)}{c^2 \sqrt{c+d x^2} (b c-a d)^2}-\frac{d}{3 c \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a c^{5/2}}","\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a (b c-a d)^{5/2}}-\frac{d (2 b c-a d)}{c^2 \sqrt{c+d x^2} (b c-a d)^2}-\frac{d}{3 c \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a c^{5/2}}",1,"-d/(3*c*(b*c - a*d)*(c + d*x^2)^(3/2)) - (d*(2*b*c - a*d))/(c^2*(b*c - a*d)^2*Sqrt[c + d*x^2]) - ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]/(a*c^(5/2)) + (b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a*(b*c - a*d)^(5/2))","A",8,6,24,0.2500,1,"{446, 85, 152, 156, 63, 208}"
728,1,178,0,0.2360138,"\int \frac{1}{x^2 \left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x^2*(a + b*x^2)*(c + d*x^2)^(5/2)),x]","-\frac{b^3 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} (b c-a d)^{5/2}}-\frac{\sqrt{c+d x^2} (b c-4 a d) (3 b c-2 a d)}{3 a c^3 x (b c-a d)^2}-\frac{d (7 b c-4 a d)}{3 c^2 x \sqrt{c+d x^2} (b c-a d)^2}-\frac{d}{3 c x \left(c+d x^2\right)^{3/2} (b c-a d)}","-\frac{b^3 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{3/2} (b c-a d)^{5/2}}-\frac{\sqrt{c+d x^2} (b c-4 a d) (3 b c-2 a d)}{3 a c^3 x (b c-a d)^2}-\frac{d (7 b c-4 a d)}{3 c^2 x \sqrt{c+d x^2} (b c-a d)^2}-\frac{d}{3 c x \left(c+d x^2\right)^{3/2} (b c-a d)}",1,"-d/(3*c*(b*c - a*d)*x*(c + d*x^2)^(3/2)) - (d*(7*b*c - 4*a*d))/(3*c^2*(b*c - a*d)^2*x*Sqrt[c + d*x^2]) - ((b*c - 4*a*d)*(3*b*c - 2*a*d)*Sqrt[c + d*x^2])/(3*a*c^3*(b*c - a*d)^2*x) - (b^3*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(3/2)*(b*c - a*d)^(5/2))","A",6,6,24,0.2500,1,"{472, 579, 583, 12, 377, 205}"
729,1,211,0,0.3222598,"\int \frac{1}{x^3 \left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x^3*(a + b*x^2)*(c + d*x^2)^(5/2)),x]","-\frac{d \left(5 a^2 d^2-8 a b c d+b^2 c^2\right)}{2 a c^3 \sqrt{c+d x^2} (b c-a d)^2}-\frac{b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 (b c-a d)^{5/2}}+\frac{(5 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 c^{7/2}}-\frac{d (3 b c-5 a d)}{6 a c^2 \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{1}{2 a c x^2 \left(c+d x^2\right)^{3/2}}","-\frac{d \left(5 a^2 d^2-8 a b c d+b^2 c^2\right)}{2 a c^3 \sqrt{c+d x^2} (b c-a d)^2}-\frac{b^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{a^2 (b c-a d)^{5/2}}+\frac{(5 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^2 c^{7/2}}-\frac{d (3 b c-5 a d)}{6 a c^2 \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{1}{2 a c x^2 \left(c+d x^2\right)^{3/2}}",1,"-(d*(3*b*c - 5*a*d))/(6*a*c^2*(b*c - a*d)*(c + d*x^2)^(3/2)) - 1/(2*a*c*x^2*(c + d*x^2)^(3/2)) - (d*(b^2*c^2 - 8*a*b*c*d + 5*a^2*d^2))/(2*a*c^3*(b*c - a*d)^2*Sqrt[c + d*x^2]) + ((2*b*c + 5*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^2*c^(7/2)) - (b^(7/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(a^2*(b*c - a*d)^(5/2))","A",9,6,24,0.2500,1,"{446, 103, 152, 156, 63, 208}"
730,1,245,0,0.3609262,"\int \frac{1}{x^4 \left(a+b x^2\right) \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x^4*(a + b*x^2)*(c + d*x^2)^(5/2)),x]","\frac{\sqrt{c+d x^2} (b c-2 a d) \left(-8 a^2 d^2+8 a b c d+3 b^2 c^2\right)}{3 a^2 c^4 x (b c-a d)^2}-\frac{\sqrt{c+d x^2} \left(8 a^2 d^2-12 a b c d+b^2 c^2\right)}{3 a c^3 x^3 (b c-a d)^2}+\frac{b^4 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} (b c-a d)^{5/2}}-\frac{d (3 b c-2 a d)}{c^2 x^3 \sqrt{c+d x^2} (b c-a d)^2}-\frac{d}{3 c x^3 \left(c+d x^2\right)^{3/2} (b c-a d)}","\frac{\sqrt{c+d x^2} (b c-2 a d) \left(-8 a^2 d^2+8 a b c d+3 b^2 c^2\right)}{3 a^2 c^4 x (b c-a d)^2}-\frac{\sqrt{c+d x^2} \left(8 a^2 d^2-12 a b c d+b^2 c^2\right)}{3 a c^3 x^3 (b c-a d)^2}+\frac{b^4 \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{a^{5/2} (b c-a d)^{5/2}}-\frac{d (3 b c-2 a d)}{c^2 x^3 \sqrt{c+d x^2} (b c-a d)^2}-\frac{d}{3 c x^3 \left(c+d x^2\right)^{3/2} (b c-a d)}",1,"-d/(3*c*(b*c - a*d)*x^3*(c + d*x^2)^(3/2)) - (d*(3*b*c - 2*a*d))/(c^2*(b*c - a*d)^2*x^3*Sqrt[c + d*x^2]) - ((b^2*c^2 - 12*a*b*c*d + 8*a^2*d^2)*Sqrt[c + d*x^2])/(3*a*c^3*(b*c - a*d)^2*x^3) + ((b*c - 2*a*d)*(3*b^2*c^2 + 8*a*b*c*d - 8*a^2*d^2)*Sqrt[c + d*x^2])/(3*a^2*c^4*(b*c - a*d)^2*x) + (b^4*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(a^(5/2)*(b*c - a*d)^(5/2))","A",7,6,24,0.2500,1,"{472, 579, 583, 12, 377, 205}"
731,1,150,0,0.168776,"\int \frac{x^4 \sqrt{c+d x^2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*Sqrt[c + d*x^2])/(a + b*x^2)^2,x]","-\frac{\sqrt{a} (3 b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^3 \sqrt{b c-a d}}+\frac{(b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^3 \sqrt{d}}-\frac{x^3 \sqrt{c+d x^2}}{2 b \left(a+b x^2\right)}+\frac{x \sqrt{c+d x^2}}{b^2}","-\frac{\sqrt{a} (3 b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^3 \sqrt{b c-a d}}+\frac{(b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^3 \sqrt{d}}-\frac{x^3 \sqrt{c+d x^2}}{2 b \left(a+b x^2\right)}+\frac{x \sqrt{c+d x^2}}{b^2}",1,"(x*Sqrt[c + d*x^2])/b^2 - (x^3*Sqrt[c + d*x^2])/(2*b*(a + b*x^2)) - (Sqrt[a]*(3*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*b^3*Sqrt[b*c - a*d]) + ((b*c - 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^3*Sqrt[d])","A",7,7,24,0.2917,1,"{467, 582, 523, 217, 206, 377, 205}"
732,1,136,0,0.1106548,"\int \frac{x^3 \sqrt{c+d x^2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*Sqrt[c + d*x^2])/(a + b*x^2)^2,x]","\frac{\sqrt{c+d x^2} (2 b c-3 a d)}{2 b^2 (b c-a d)}-\frac{(2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{5/2} \sqrt{b c-a d}}+\frac{a \left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right) (b c-a d)}","\frac{\sqrt{c+d x^2} (2 b c-3 a d)}{2 b^2 (b c-a d)}-\frac{(2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{5/2} \sqrt{b c-a d}}+\frac{a \left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right) (b c-a d)}",1,"((2*b*c - 3*a*d)*Sqrt[c + d*x^2])/(2*b^2*(b*c - a*d)) + (a*(c + d*x^2)^(3/2))/(2*b*(b*c - a*d)*(a + b*x^2)) - ((2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(5/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
733,1,120,0,0.0833367,"\int \frac{x^2 \sqrt{c+d x^2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*Sqrt[c + d*x^2])/(a + b*x^2)^2,x]","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} b^2 \sqrt{b c-a d}}-\frac{x \sqrt{c+d x^2}}{2 b \left(a+b x^2\right)}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2}","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} b^2 \sqrt{b c-a d}}-\frac{x \sqrt{c+d x^2}}{2 b \left(a+b x^2\right)}+\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2}",1,"-(x*Sqrt[c + d*x^2])/(2*b*(a + b*x^2)) + ((b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*b^2*Sqrt[b*c - a*d]) + (Sqrt[d]*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/b^2","A",6,6,24,0.2500,1,"{467, 523, 217, 206, 377, 205}"
734,1,80,0,0.0620141,"\int \frac{x \sqrt{c+d x^2}}{\left(a+b x^2\right)^2} \, dx","Int[(x*Sqrt[c + d*x^2])/(a + b*x^2)^2,x]","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^2}}{2 b \left(a+b x^2\right)}","-\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{3/2} \sqrt{b c-a d}}-\frac{\sqrt{c+d x^2}}{2 b \left(a+b x^2\right)}",1,"-Sqrt[c + d*x^2]/(2*b*(a + b*x^2)) - (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(3/2)*Sqrt[b*c - a*d])","A",4,4,22,0.1818,1,"{444, 47, 63, 208}"
735,1,82,0,0.0345822,"\int \frac{\sqrt{c+d x^2}}{\left(a+b x^2\right)^2} \, dx","Int[Sqrt[c + d*x^2]/(a + b*x^2)^2,x]","\frac{c \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} \sqrt{b c-a d}}+\frac{x \sqrt{c+d x^2}}{2 a \left(a+b x^2\right)}","\frac{c \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} \sqrt{b c-a d}}+\frac{x \sqrt{c+d x^2}}{2 a \left(a+b x^2\right)}",1,"(x*Sqrt[c + d*x^2])/(2*a*(a + b*x^2)) + (c*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*Sqrt[b*c - a*d])","A",3,3,21,0.1429,1,"{378, 377, 205}"
736,1,119,0,0.1117462,"\int \frac{\sqrt{c+d x^2}}{x \left(a+b x^2\right)^2} \, dx","Int[Sqrt[c + d*x^2]/(x*(a + b*x^2)^2),x]","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 \sqrt{b} \sqrt{b c-a d}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x^2}}{2 a \left(a+b x^2\right)}","\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 \sqrt{b} \sqrt{b c-a d}}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x^2}}{2 a \left(a+b x^2\right)}",1,"Sqrt[c + d*x^2]/(2*a*(a + b*x^2)) - (Sqrt[c]*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/a^2 + ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^2*Sqrt[b]*Sqrt[b*c - a*d])","A",7,5,24,0.2083,1,"{446, 99, 156, 63, 208}"
737,1,113,0,0.1101859,"\int \frac{\sqrt{c+d x^2}}{x^2 \left(a+b x^2\right)^2} \, dx","Int[Sqrt[c + d*x^2]/(x^2*(a + b*x^2)^2),x]","-\frac{(3 b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} \sqrt{b c-a d}}-\frac{3 \sqrt{c+d x^2}}{2 a^2 x}+\frac{\sqrt{c+d x^2}}{2 a x \left(a+b x^2\right)}","-\frac{(3 b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} \sqrt{b c-a d}}-\frac{3 \sqrt{c+d x^2}}{2 a^2 x}+\frac{\sqrt{c+d x^2}}{2 a x \left(a+b x^2\right)}",1,"(-3*Sqrt[c + d*x^2])/(2*a^2*x) + Sqrt[c + d*x^2]/(2*a*x*(a + b*x^2)) - ((3*b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(5/2)*Sqrt[b*c - a*d])","A",5,5,24,0.2083,1,"{469, 583, 12, 377, 205}"
738,1,159,0,0.2089624,"\int \frac{\sqrt{c+d x^2}}{x^3 \left(a+b x^2\right)^2} \, dx","Int[Sqrt[c + d*x^2]/(x^3*(a + b*x^2)^2),x]","-\frac{b \sqrt{c+d x^2}}{a^2 \left(a+b x^2\right)}-\frac{\sqrt{b} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 \sqrt{b c-a d}}+\frac{(4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 \sqrt{c}}-\frac{\sqrt{c+d x^2}}{2 a x^2 \left(a+b x^2\right)}","-\frac{b \sqrt{c+d x^2}}{a^2 \left(a+b x^2\right)}-\frac{\sqrt{b} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 \sqrt{b c-a d}}+\frac{(4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 \sqrt{c}}-\frac{\sqrt{c+d x^2}}{2 a x^2 \left(a+b x^2\right)}",1,"-((b*Sqrt[c + d*x^2])/(a^2*(a + b*x^2))) - Sqrt[c + d*x^2]/(2*a*x^2*(a + b*x^2)) + ((4*b*c - a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^3*Sqrt[c]) - (Sqrt[b]*(4*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^3*Sqrt[b*c - a*d])","A",8,6,24,0.2500,1,"{446, 99, 151, 156, 63, 208}"
739,1,147,0,0.2026421,"\int \frac{\sqrt{c+d x^2}}{x^4 \left(a+b x^2\right)^2} \, dx","Int[Sqrt[c + d*x^2]/(x^4*(a + b*x^2)^2),x]","\frac{\sqrt{c+d x^2} (15 b c-2 a d)}{6 a^3 c x}+\frac{b (5 b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} \sqrt{b c-a d}}-\frac{5 \sqrt{c+d x^2}}{6 a^2 x^3}+\frac{\sqrt{c+d x^2}}{2 a x^3 \left(a+b x^2\right)}","\frac{\sqrt{c+d x^2} (15 b c-2 a d)}{6 a^3 c x}+\frac{b (5 b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} \sqrt{b c-a d}}-\frac{5 \sqrt{c+d x^2}}{6 a^2 x^3}+\frac{\sqrt{c+d x^2}}{2 a x^3 \left(a+b x^2\right)}",1,"(-5*Sqrt[c + d*x^2])/(6*a^2*x^3) + ((15*b*c - 2*a*d)*Sqrt[c + d*x^2])/(6*a^3*c*x) + Sqrt[c + d*x^2]/(2*a*x^3*(a + b*x^2)) + (b*(5*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(7/2)*Sqrt[b*c - a*d])","A",6,5,24,0.2083,1,"{469, 583, 12, 377, 205}"
740,1,197,0,0.3376453,"\int \frac{x^4 \left(c+d x^2\right)^{3/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x]","\frac{3 \left(8 a^2 d^2-8 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^4 \sqrt{d}}+\frac{3 x \sqrt{c+d x^2} (3 b c-4 a d)}{8 b^3}-\frac{3 \sqrt{a} (b c-2 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^4}-\frac{x^3 \left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right)}+\frac{3 d x^3 \sqrt{c+d x^2}}{4 b^2}","\frac{3 \left(8 a^2 d^2-8 a b c d+b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^4 \sqrt{d}}+\frac{3 x \sqrt{c+d x^2} (3 b c-4 a d)}{8 b^3}-\frac{3 \sqrt{a} (b c-2 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^4}-\frac{x^3 \left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right)}+\frac{3 d x^3 \sqrt{c+d x^2}}{4 b^2}",1,"(3*(3*b*c - 4*a*d)*x*Sqrt[c + d*x^2])/(8*b^3) + (3*d*x^3*Sqrt[c + d*x^2])/(4*b^2) - (x^3*(c + d*x^2)^(3/2))/(2*b*(a + b*x^2)) - (3*Sqrt[a]*(b*c - 2*a*d)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*b^4) + (3*(b^2*c^2 - 8*a*b*c*d + 8*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*b^4*Sqrt[d])","A",8,8,24,0.3333,1,"{467, 581, 582, 523, 217, 206, 377, 205}"
741,1,163,0,0.1357379,"\int \frac{x^3 \left(c+d x^2\right)^{3/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x]","\frac{\left(c+d x^2\right)^{3/2} (2 b c-5 a d)}{6 b^2 (b c-a d)}+\frac{\sqrt{c+d x^2} (2 b c-5 a d)}{2 b^3}-\frac{(2 b c-5 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{7/2}}+\frac{a \left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right) (b c-a d)}","\frac{\left(c+d x^2\right)^{3/2} (2 b c-5 a d)}{6 b^2 (b c-a d)}+\frac{\sqrt{c+d x^2} (2 b c-5 a d)}{2 b^3}-\frac{(2 b c-5 a d) \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{7/2}}+\frac{a \left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right) (b c-a d)}",1,"((2*b*c - 5*a*d)*Sqrt[c + d*x^2])/(2*b^3) + ((2*b*c - 5*a*d)*(c + d*x^2)^(3/2))/(6*b^2*(b*c - a*d)) + (a*(c + d*x^2)^(5/2))/(2*b*(b*c - a*d)*(a + b*x^2)) - ((2*b*c - 5*a*d)*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(7/2))","A",6,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
742,1,149,0,0.1639715,"\int \frac{x^2 \left(c+d x^2\right)^{3/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x]","\frac{(b c-4 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} b^3}+\frac{\sqrt{d} (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^3}-\frac{x \left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right)}+\frac{d x \sqrt{c+d x^2}}{b^2}","\frac{(b c-4 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} b^3}+\frac{\sqrt{d} (3 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^3}-\frac{x \left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right)}+\frac{d x \sqrt{c+d x^2}}{b^2}",1,"(d*x*Sqrt[c + d*x^2])/b^2 - (x*(c + d*x^2)^(3/2))/(2*b*(a + b*x^2)) + ((b*c - 4*a*d)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*b^3) + (Sqrt[d]*(3*b*c - 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^3)","A",7,7,24,0.2917,1,"{467, 528, 523, 217, 206, 377, 205}"
743,1,99,0,0.0774449,"\int \frac{x \left(c+d x^2\right)^{3/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x*(c + d*x^2)^(3/2))/(a + b*x^2)^2,x]","-\frac{3 d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{5/2}}-\frac{\left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right)}+\frac{3 d \sqrt{c+d x^2}}{2 b^2}","-\frac{3 d \sqrt{b c-a d} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{5/2}}-\frac{\left(c+d x^2\right)^{3/2}}{2 b \left(a+b x^2\right)}+\frac{3 d \sqrt{c+d x^2}}{2 b^2}",1,"(3*d*Sqrt[c + d*x^2])/(2*b^2) - (c + d*x^2)^(3/2)/(2*b*(a + b*x^2)) - (3*d*Sqrt[b*c - a*d]*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(5/2))","A",5,5,22,0.2273,1,"{444, 47, 50, 63, 208}"
744,1,131,0,0.0887277,"\int \frac{\left(c+d x^2\right)^{3/2}}{\left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(3/2)/(a + b*x^2)^2,x]","\frac{\sqrt{b c-a d} (2 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} b^2}+\frac{x \sqrt{c+d x^2} (b c-a d)}{2 a b \left(a+b x^2\right)}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2}","\frac{\sqrt{b c-a d} (2 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} b^2}+\frac{x \sqrt{c+d x^2} (b c-a d)}{2 a b \left(a+b x^2\right)}+\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2}",1,"((b*c - a*d)*x*Sqrt[c + d*x^2])/(2*a*b*(a + b*x^2)) + (Sqrt[b*c - a*d]*(b*c + 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*b^2) + (d^(3/2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/b^2","A",6,6,21,0.2857,1,"{413, 523, 217, 206, 377, 205}"
745,1,129,0,0.1423034,"\int \frac{\left(c+d x^2\right)^{3/2}}{x \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(3/2)/(x*(a + b*x^2)^2),x]","\frac{\sqrt{b c-a d} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 b^{3/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x^2} (b c-a d)}{2 a b \left(a+b x^2\right)}","\frac{\sqrt{b c-a d} (a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 b^{3/2}}-\frac{c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2}+\frac{\sqrt{c+d x^2} (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"((b*c - a*d)*Sqrt[c + d*x^2])/(2*a*b*(a + b*x^2)) - (c^(3/2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/a^2 + (Sqrt[b*c - a*d]*(2*b*c + a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^2*b^(3/2))","A",7,5,24,0.2083,1,"{446, 98, 156, 63, 208}"
746,1,128,0,0.1243164,"\int \frac{\left(c+d x^2\right)^{3/2}}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(3/2)/(x^2*(a + b*x^2)^2),x]","-\frac{\sqrt{c+d x^2} (3 b c-a d)}{2 a^2 b x}-\frac{3 c \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2}}+\frac{\sqrt{c+d x^2} (b c-a d)}{2 a b x \left(a+b x^2\right)}","-\frac{\sqrt{c+d x^2} (3 b c-a d)}{2 a^2 b x}-\frac{3 c \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2}}+\frac{\sqrt{c+d x^2} (b c-a d)}{2 a b x \left(a+b x^2\right)}",1,"-((3*b*c - a*d)*Sqrt[c + d*x^2])/(2*a^2*b*x) + ((b*c - a*d)*Sqrt[c + d*x^2])/(2*a*b*x*(a + b*x^2)) - (3*c*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(5/2))","A",5,5,24,0.2083,1,"{468, 583, 12, 377, 205}"
747,1,170,0,0.2552234,"\int \frac{\left(c+d x^2\right)^{3/2}}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(3/2)/(x^3*(a + b*x^2)^2),x]","-\frac{\sqrt{c+d x^2} (2 b c-a d)}{2 a^2 \left(a+b x^2\right)}+\frac{\sqrt{c} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3}-\frac{\sqrt{b c-a d} (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 \sqrt{b}}-\frac{c \sqrt{c+d x^2}}{2 a x^2 \left(a+b x^2\right)}","-\frac{\sqrt{c+d x^2} (2 b c-a d)}{2 a^2 \left(a+b x^2\right)}+\frac{\sqrt{c} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3}-\frac{\sqrt{b c-a d} (4 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 \sqrt{b}}-\frac{c \sqrt{c+d x^2}}{2 a x^2 \left(a+b x^2\right)}",1,"-((2*b*c - a*d)*Sqrt[c + d*x^2])/(2*a^2*(a + b*x^2)) - (c*Sqrt[c + d*x^2])/(2*a*x^2*(a + b*x^2)) + (Sqrt[c]*(4*b*c - 3*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^3) - (Sqrt[b*c - a*d]*(4*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^3*Sqrt[b])","A",8,6,24,0.2500,1,"{446, 98, 151, 156, 63, 208}"
748,1,166,0,0.2395633,"\int \frac{\left(c+d x^2\right)^{3/2}}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(3/2)/(x^4*(a + b*x^2)^2),x]","\frac{\sqrt{c+d x^2} (15 b c-11 a d)}{6 a^3 x}-\frac{\sqrt{c+d x^2} (5 b c-3 a d)}{6 a^2 b x^3}+\frac{(5 b c-2 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2}}+\frac{\sqrt{c+d x^2} (b c-a d)}{2 a b x^3 \left(a+b x^2\right)}","\frac{\sqrt{c+d x^2} (15 b c-11 a d)}{6 a^3 x}-\frac{\sqrt{c+d x^2} (5 b c-3 a d)}{6 a^2 b x^3}+\frac{(5 b c-2 a d) \sqrt{b c-a d} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2}}+\frac{\sqrt{c+d x^2} (b c-a d)}{2 a b x^3 \left(a+b x^2\right)}",1,"-((5*b*c - 3*a*d)*Sqrt[c + d*x^2])/(6*a^2*b*x^3) + ((15*b*c - 11*a*d)*Sqrt[c + d*x^2])/(6*a^3*x) + ((b*c - a*d)*Sqrt[c + d*x^2])/(2*a*b*x^3*(a + b*x^2)) + ((5*b*c - 2*a*d)*Sqrt[b*c - a*d]*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(7/2))","A",6,5,24,0.2083,1,"{468, 583, 12, 377, 205}"
749,1,258,0,0.4483746,"\int \frac{x^4 \left(c+d x^2\right)^{5/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^4*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x]","\frac{x \sqrt{c+d x^2} \left(32 a^2 d^2-52 a b c d+19 b^2 c^2\right)}{16 b^4}+\frac{\left(120 a^2 b c d^2-64 a^3 d^3-60 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 b^5 \sqrt{d}}+\frac{d x^3 \sqrt{c+d x^2} (7 b c-8 a d)}{8 b^3}-\frac{\sqrt{a} (3 b c-8 a d) (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^5}-\frac{x^3 \left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{2 d x^3 \left(c+d x^2\right)^{3/2}}{3 b^2}","\frac{x \sqrt{c+d x^2} \left(32 a^2 d^2-52 a b c d+19 b^2 c^2\right)}{16 b^4}+\frac{\left(120 a^2 b c d^2-64 a^3 d^3-60 a b^2 c^2 d+5 b^3 c^3\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{16 b^5 \sqrt{d}}+\frac{d x^3 \sqrt{c+d x^2} (7 b c-8 a d)}{8 b^3}-\frac{\sqrt{a} (3 b c-8 a d) (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^5}-\frac{x^3 \left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{2 d x^3 \left(c+d x^2\right)^{3/2}}{3 b^2}",1,"((19*b^2*c^2 - 52*a*b*c*d + 32*a^2*d^2)*x*Sqrt[c + d*x^2])/(16*b^4) + (d*(7*b*c - 8*a*d)*x^3*Sqrt[c + d*x^2])/(8*b^3) + (2*d*x^3*(c + d*x^2)^(3/2))/(3*b^2) - (x^3*(c + d*x^2)^(5/2))/(2*b*(a + b*x^2)) - (Sqrt[a]*(3*b*c - 8*a*d)*(b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*b^5) + ((5*b^3*c^3 - 60*a*b^2*c^2*d + 120*a^2*b*c*d^2 - 64*a^3*d^3)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(16*b^5*Sqrt[d])","A",9,8,24,0.3333,1,"{467, 581, 582, 523, 217, 206, 377, 205}"
750,1,198,0,0.1832705,"\int \frac{x^3 \left(c+d x^2\right)^{5/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^3*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x]","\frac{\left(c+d x^2\right)^{5/2} (2 b c-7 a d)}{10 b^2 (b c-a d)}+\frac{\left(c+d x^2\right)^{3/2} (2 b c-7 a d)}{6 b^3}+\frac{\sqrt{c+d x^2} (2 b c-7 a d) (b c-a d)}{2 b^4}-\frac{(2 b c-7 a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{9/2}}+\frac{a \left(c+d x^2\right)^{7/2}}{2 b \left(a+b x^2\right) (b c-a d)}","\frac{\left(c+d x^2\right)^{5/2} (2 b c-7 a d)}{10 b^2 (b c-a d)}+\frac{\left(c+d x^2\right)^{3/2} (2 b c-7 a d)}{6 b^3}+\frac{\sqrt{c+d x^2} (2 b c-7 a d) (b c-a d)}{2 b^4}-\frac{(2 b c-7 a d) (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{9/2}}+\frac{a \left(c+d x^2\right)^{7/2}}{2 b \left(a+b x^2\right) (b c-a d)}",1,"((2*b*c - 7*a*d)*(b*c - a*d)*Sqrt[c + d*x^2])/(2*b^4) + ((2*b*c - 7*a*d)*(c + d*x^2)^(3/2))/(6*b^3) + ((2*b*c - 7*a*d)*(c + d*x^2)^(5/2))/(10*b^2*(b*c - a*d)) + (a*(c + d*x^2)^(7/2))/(2*b*(b*c - a*d)*(a + b*x^2)) - ((2*b*c - 7*a*d)*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(9/2))","A",7,5,24,0.2083,1,"{446, 78, 50, 63, 208}"
751,1,195,0,0.2441473,"\int \frac{x^2 \left(c+d x^2\right)^{5/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x^2*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x]","\frac{\sqrt{d} \left(24 a^2 d^2-40 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^4}+\frac{d x \sqrt{c+d x^2} (11 b c-12 a d)}{8 b^3}+\frac{(b c-6 a d) (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} b^4}-\frac{x \left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{3 d x \left(c+d x^2\right)^{3/2}}{4 b^2}","\frac{\sqrt{d} \left(24 a^2 d^2-40 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{8 b^4}+\frac{d x \sqrt{c+d x^2} (11 b c-12 a d)}{8 b^3}+\frac{(b c-6 a d) (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} b^4}-\frac{x \left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{3 d x \left(c+d x^2\right)^{3/2}}{4 b^2}",1,"(d*(11*b*c - 12*a*d)*x*Sqrt[c + d*x^2])/(8*b^3) + (3*d*x*(c + d*x^2)^(3/2))/(4*b^2) - (x*(c + d*x^2)^(5/2))/(2*b*(a + b*x^2)) + ((b*c - 6*a*d)*(b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*b^4) + (Sqrt[d]*(15*b^2*c^2 - 40*a*b*c*d + 24*a^2*d^2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(8*b^4)","A",8,7,24,0.2917,1,"{467, 528, 523, 217, 206, 377, 205}"
752,1,126,0,0.1028014,"\int \frac{x \left(c+d x^2\right)^{5/2}}{\left(a+b x^2\right)^2} \, dx","Int[(x*(c + d*x^2)^(5/2))/(a + b*x^2)^2,x]","\frac{5 d \sqrt{c+d x^2} (b c-a d)}{2 b^3}-\frac{5 d (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{7/2}}-\frac{\left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{5 d \left(c+d x^2\right)^{3/2}}{6 b^2}","\frac{5 d \sqrt{c+d x^2} (b c-a d)}{2 b^3}-\frac{5 d (b c-a d)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{7/2}}-\frac{\left(c+d x^2\right)^{5/2}}{2 b \left(a+b x^2\right)}+\frac{5 d \left(c+d x^2\right)^{3/2}}{6 b^2}",1,"(5*d*(b*c - a*d)*Sqrt[c + d*x^2])/(2*b^3) + (5*d*(c + d*x^2)^(3/2))/(6*b^2) - (c + d*x^2)^(5/2)/(2*b*(a + b*x^2)) - (5*d*(b*c - a*d)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(7/2))","A",6,5,22,0.2273,1,"{444, 47, 50, 63, 208}"
753,1,174,0,0.2193403,"\int \frac{\left(c+d x^2\right)^{5/2}}{\left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(5/2)/(a + b*x^2)^2,x]","\frac{(b c-a d)^{3/2} (4 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} b^3}+\frac{d^{3/2} (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^3}-\frac{d x \sqrt{c+d x^2} (b c-2 a d)}{2 a b^2}+\frac{x \left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b \left(a+b x^2\right)}","\frac{(b c-a d)^{3/2} (4 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} b^3}+\frac{d^{3/2} (5 b c-4 a d) \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{2 b^3}-\frac{d x \sqrt{c+d x^2} (b c-2 a d)}{2 a b^2}+\frac{x \left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"-(d*(b*c - 2*a*d)*x*Sqrt[c + d*x^2])/(2*a*b^2) + ((b*c - a*d)*x*(c + d*x^2)^(3/2))/(2*a*b*(a + b*x^2)) + ((b*c - a*d)^(3/2)*(b*c + 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*b^3) + (d^(3/2)*(5*b*c - 4*a*d)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/(2*b^3)","A",7,7,21,0.3333,1,"{413, 528, 523, 217, 206, 377, 205}"
754,1,160,0,0.218048,"\int \frac{\left(c+d x^2\right)^{5/2}}{x \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(5/2)/(x*(a + b*x^2)^2),x]","\frac{(b c-a d)^{3/2} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 b^{5/2}}-\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2}-\frac{d \sqrt{c+d x^2} (b c-3 a d)}{2 a b^2}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b \left(a+b x^2\right)}","\frac{(b c-a d)^{3/2} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 b^{5/2}}-\frac{c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2}-\frac{d \sqrt{c+d x^2} (b c-3 a d)}{2 a b^2}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b \left(a+b x^2\right)}",1,"-(d*(b*c - 3*a*d)*Sqrt[c + d*x^2])/(2*a*b^2) + ((b*c - a*d)*(c + d*x^2)^(3/2))/(2*a*b*(a + b*x^2)) - (c^(5/2)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/a^2 + ((b*c - a*d)^(3/2)*(2*b*c + 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^2*b^(5/2))","A",8,6,24,0.2500,1,"{446, 98, 154, 156, 63, 208}"
755,1,168,0,0.1887477,"\int \frac{\left(c+d x^2\right)^{5/2}}{x^2 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(5/2)/(x^2*(a + b*x^2)^2),x]","-\frac{(b c-a d)^{3/2} (2 a d+3 b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} b^2}-\frac{c \sqrt{c+d x^2} (3 b c-a d)}{2 a^2 b x}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b x \left(a+b x^2\right)}+\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2}","-\frac{(b c-a d)^{3/2} (2 a d+3 b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} b^2}-\frac{c \sqrt{c+d x^2} (3 b c-a d)}{2 a^2 b x}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b x \left(a+b x^2\right)}+\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2}",1,"-(c*(3*b*c - a*d)*Sqrt[c + d*x^2])/(2*a^2*b*x) + ((b*c - a*d)*(c + d*x^2)^(3/2))/(2*a*b*x*(a + b*x^2)) - ((b*c - a*d)^(3/2)*(3*b*c + 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(5/2)*b^2) + (d^(5/2)*ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]])/b^2","A",7,7,24,0.2917,1,"{468, 580, 523, 217, 206, 377, 205}"
756,1,180,0,0.2699852,"\int \frac{\left(c+d x^2\right)^{5/2}}{x^3 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(5/2)/(x^3*(a + b*x^2)^2),x]","-\frac{(b c-a d)^{3/2} (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 b^{3/2}}+\frac{c^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3}-\frac{\sqrt{c+d x^2} (b c-a d) (2 b c-a d)}{2 a^2 b \left(a+b x^2\right)}-\frac{c \left(c+d x^2\right)^{3/2}}{2 a x^2 \left(a+b x^2\right)}","-\frac{(b c-a d)^{3/2} (a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 b^{3/2}}+\frac{c^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3}-\frac{\sqrt{c+d x^2} (b c-a d) (2 b c-a d)}{2 a^2 b \left(a+b x^2\right)}-\frac{c \left(c+d x^2\right)^{3/2}}{2 a x^2 \left(a+b x^2\right)}",1,"-((b*c - a*d)*(2*b*c - a*d)*Sqrt[c + d*x^2])/(2*a^2*b*(a + b*x^2)) - (c*(c + d*x^2)^(3/2))/(2*a*x^2*(a + b*x^2)) + (c^(3/2)*(4*b*c - 5*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^3) - ((b*c - a*d)^(3/2)*(4*b*c + a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^3*b^(3/2))","A",8,6,24,0.2500,1,"{446, 98, 149, 156, 63, 208}"
757,1,176,0,0.2474349,"\int \frac{\left(c+d x^2\right)^{5/2}}{x^4 \left(a+b x^2\right)^2} \, dx","Int[(c + d*x^2)^(5/2)/(x^4*(a + b*x^2)^2),x]","\frac{\sqrt{c+d x^2} \left(3 a^2 d^2-20 a b c d+15 b^2 c^2\right)}{6 a^3 b x}-\frac{c \sqrt{c+d x^2} (5 b c-3 a d)}{6 a^2 b x^3}+\frac{5 c (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2}}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b x^3 \left(a+b x^2\right)}","\frac{\sqrt{c+d x^2} \left(3 a^2 d^2-20 a b c d+15 b^2 c^2\right)}{6 a^3 b x}-\frac{c \sqrt{c+d x^2} (5 b c-3 a d)}{6 a^2 b x^3}+\frac{5 c (b c-a d)^{3/2} \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2}}+\frac{\left(c+d x^2\right)^{3/2} (b c-a d)}{2 a b x^3 \left(a+b x^2\right)}",1,"-(c*(5*b*c - 3*a*d)*Sqrt[c + d*x^2])/(6*a^2*b*x^3) + ((15*b^2*c^2 - 20*a*b*c*d + 3*a^2*d^2)*Sqrt[c + d*x^2])/(6*a^3*b*x) + ((b*c - a*d)*(c + d*x^2)^(3/2))/(2*a*b*x^3*(a + b*x^2)) + (5*c*(b*c - a*d)^(3/2)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(7/2))","A",6,6,24,0.2500,1,"{468, 580, 583, 12, 377, 205}"
758,1,132,0,0.1116551,"\int \frac{x^4}{\left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[x^4/((a + b*x^2)^2*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^2 (b c-a d)^{3/2}}+\frac{a x \sqrt{c+d x^2}}{2 b \left(a+b x^2\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2 \sqrt{d}}","-\frac{\sqrt{a} (3 b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 b^2 (b c-a d)^{3/2}}+\frac{a x \sqrt{c+d x^2}}{2 b \left(a+b x^2\right) (b c-a d)}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c+d x^2}}\right)}{b^2 \sqrt{d}}",1,"(a*x*Sqrt[c + d*x^2])/(2*b*(b*c - a*d)*(a + b*x^2)) - (Sqrt[a]*(3*b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*b^2*(b*c - a*d)^(3/2)) + ArcTanh[(Sqrt[d]*x)/Sqrt[c + d*x^2]]/(b^2*Sqrt[d])","A",6,6,24,0.2500,1,"{470, 523, 217, 206, 377, 205}"
759,1,99,0,0.084961,"\int \frac{x^3}{\left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[x^3/((a + b*x^2)^2*Sqrt[c + d*x^2]),x]","\frac{a \sqrt{c+d x^2}}{2 b \left(a+b x^2\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{3/2} (b c-a d)^{3/2}}","\frac{a \sqrt{c+d x^2}}{2 b \left(a+b x^2\right) (b c-a d)}-\frac{(2 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 b^{3/2} (b c-a d)^{3/2}}",1,"(a*Sqrt[c + d*x^2])/(2*b*(b*c - a*d)*(a + b*x^2)) - ((2*b*c - a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*b^(3/2)*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{446, 78, 63, 208}"
760,1,89,0,0.0533037,"\int \frac{x^2}{\left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[x^2/((a + b*x^2)^2*Sqrt[c + d*x^2]),x]","\frac{c \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} (b c-a d)^{3/2}}-\frac{x \sqrt{c+d x^2}}{2 \left(a+b x^2\right) (b c-a d)}","\frac{c \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} (b c-a d)^{3/2}}-\frac{x \sqrt{c+d x^2}}{2 \left(a+b x^2\right) (b c-a d)}",1,"-(x*Sqrt[c + d*x^2])/(2*(b*c - a*d)*(a + b*x^2)) + (c*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*(b*c - a*d)^(3/2))","A",4,4,24,0.1667,1,"{471, 12, 377, 205}"
761,1,87,0,0.0678864,"\int \frac{x}{\left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[x/((a + b*x^2)^2*Sqrt[c + d*x^2]),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^2}}{2 \left(a+b x^2\right) (b c-a d)}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 \sqrt{b} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^2}}{2 \left(a+b x^2\right) (b c-a d)}",1,"-Sqrt[c + d*x^2]/(2*(b*c - a*d)*(a + b*x^2)) + (d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*Sqrt[b]*(b*c - a*d)^(3/2))","A",4,4,22,0.1818,1,"{444, 51, 63, 208}"
762,1,100,0,0.0529042,"\int \frac{1}{\left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[1/((a + b*x^2)^2*Sqrt[c + d*x^2]),x]","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} (b c-a d)^{3/2}}+\frac{b x \sqrt{c+d x^2}}{2 a \left(a+b x^2\right) (b c-a d)}","\frac{(b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} (b c-a d)^{3/2}}+\frac{b x \sqrt{c+d x^2}}{2 a \left(a+b x^2\right) (b c-a d)}",1,"(b*x*Sqrt[c + d*x^2])/(2*a*(b*c - a*d)*(a + b*x^2)) + ((b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*(b*c - a*d)^(3/2))","A",3,3,21,0.1429,1,"{382, 377, 205}"
763,1,130,0,0.1358014,"\int \frac{1}{x \left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[1/(x*(a + b*x^2)^2*Sqrt[c + d*x^2]),x]","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^2}}{2 a \left(a+b x^2\right) (b c-a d)}","\frac{\sqrt{b} (2 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 (b c-a d)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2 \sqrt{c}}+\frac{b \sqrt{c+d x^2}}{2 a \left(a+b x^2\right) (b c-a d)}",1,"(b*Sqrt[c + d*x^2])/(2*a*(b*c - a*d)*(a + b*x^2)) - ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]/(a^2*Sqrt[c]) + (Sqrt[b]*(2*b*c - 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^2*(b*c - a*d)^(3/2))","A",7,5,24,0.2083,1,"{446, 103, 156, 63, 208}"
764,1,147,0,0.1357476,"\int \frac{1}{x^2 \left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[1/(x^2*(a + b*x^2)^2*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{c+d x^2} (3 b c-2 a d)}{2 a^2 c x (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^2}}{2 a x \left(a+b x^2\right) (b c-a d)}","-\frac{\sqrt{c+d x^2} (3 b c-2 a d)}{2 a^2 c x (b c-a d)}-\frac{b (3 b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} (b c-a d)^{3/2}}+\frac{b \sqrt{c+d x^2}}{2 a x \left(a+b x^2\right) (b c-a d)}",1,"-((3*b*c - 2*a*d)*Sqrt[c + d*x^2])/(2*a^2*c*(b*c - a*d)*x) + (b*Sqrt[c + d*x^2])/(2*a*(b*c - a*d)*x*(a + b*x^2)) - (b*(3*b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(5/2)*(b*c - a*d)^(3/2))","A",5,5,24,0.2083,1,"{472, 583, 12, 377, 205}"
765,1,185,0,0.2434836,"\int \frac{1}{x^3 \left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[1/(x^3*(a + b*x^2)^2*Sqrt[c + d*x^2]),x]","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^2} (2 b c-a d)}{2 a^2 c \left(a+b x^2\right) (b c-a d)}-\frac{\sqrt{c+d x^2}}{2 a c x^2 \left(a+b x^2\right)}","-\frac{b^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 (b c-a d)^{3/2}}+\frac{(a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 c^{3/2}}-\frac{b \sqrt{c+d x^2} (2 b c-a d)}{2 a^2 c \left(a+b x^2\right) (b c-a d)}-\frac{\sqrt{c+d x^2}}{2 a c x^2 \left(a+b x^2\right)}",1,"-(b*(2*b*c - a*d)*Sqrt[c + d*x^2])/(2*a^2*c*(b*c - a*d)*(a + b*x^2)) - Sqrt[c + d*x^2]/(2*a*c*x^2*(a + b*x^2)) + ((4*b*c + a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^3*c^(3/2)) - (b^(3/2)*(4*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^3*(b*c - a*d)^(3/2))","A",8,6,24,0.2500,1,"{446, 103, 151, 156, 63, 208}"
766,1,206,0,0.2523857,"\int \frac{1}{x^4 \left(a+b x^2\right)^2 \sqrt{c+d x^2}} \, dx","Int[1/(x^4*(a + b*x^2)^2*Sqrt[c + d*x^2]),x]","\frac{\sqrt{c+d x^2} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{6 a^3 c^2 x (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^2} (5 b c-2 a d)}{6 a^2 c x^3 (b c-a d)}+\frac{b \sqrt{c+d x^2}}{2 a x^3 \left(a+b x^2\right) (b c-a d)}","\frac{\sqrt{c+d x^2} \left(-4 a^2 d^2-8 a b c d+15 b^2 c^2\right)}{6 a^3 c^2 x (b c-a d)}+\frac{b^2 (5 b c-6 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} (b c-a d)^{3/2}}-\frac{\sqrt{c+d x^2} (5 b c-2 a d)}{6 a^2 c x^3 (b c-a d)}+\frac{b \sqrt{c+d x^2}}{2 a x^3 \left(a+b x^2\right) (b c-a d)}",1,"-((5*b*c - 2*a*d)*Sqrt[c + d*x^2])/(6*a^2*c*(b*c - a*d)*x^3) + ((15*b^2*c^2 - 8*a*b*c*d - 4*a^2*d^2)*Sqrt[c + d*x^2])/(6*a^3*c^2*(b*c - a*d)*x) + (b*Sqrt[c + d*x^2])/(2*a*(b*c - a*d)*x^3*(a + b*x^2)) + (b^2*(5*b*c - 6*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(7/2)*(b*c - a*d)^(3/2))","A",6,5,24,0.2083,1,"{472, 583, 12, 377, 205}"
767,1,130,0,0.1016056,"\int \frac{x^4}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[x^4/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","\frac{x (a d+2 b c)}{2 b \sqrt{c+d x^2} (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}-\frac{3 \sqrt{a} c \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 (b c-a d)^{5/2}}","\frac{x (a d+2 b c)}{2 b \sqrt{c+d x^2} (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}-\frac{3 \sqrt{a} c \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 (b c-a d)^{5/2}}",1,"((2*b*c + a*d)*x)/(2*b*(b*c - a*d)^2*Sqrt[c + d*x^2]) + (a*x)/(2*b*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) - (3*Sqrt[a]*c*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*(b*c - a*d)^(5/2))","A",5,5,24,0.2083,1,"{470, 527, 12, 377, 205}"
768,1,134,0,0.1192744,"\int \frac{x^3}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[x^3/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","\frac{a}{2 b \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{a d+2 b c}{2 b \sqrt{c+d x^2} (b c-a d)^2}-\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 \sqrt{b} (b c-a d)^{5/2}}","\frac{a}{2 b \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{a d+2 b c}{2 b \sqrt{c+d x^2} (b c-a d)^2}-\frac{(a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 \sqrt{b} (b c-a d)^{5/2}}",1,"(2*b*c + a*d)/(2*b*(b*c - a*d)^2*Sqrt[c + d*x^2]) + a/(2*b*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) - ((2*b*c + a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*Sqrt[b]*(b*c - a*d)^(5/2))","A",5,5,24,0.2083,1,"{446, 78, 51, 63, 208}"
769,1,123,0,0.0909396,"\int \frac{x^2}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[x^2/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","-\frac{x}{2 \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}-\frac{3 d x}{2 \sqrt{c+d x^2} (b c-a d)^2}+\frac{(2 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} (b c-a d)^{5/2}}","-\frac{x}{2 \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}-\frac{3 d x}{2 \sqrt{c+d x^2} (b c-a d)^2}+\frac{(2 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} (b c-a d)^{5/2}}",1,"(-3*d*x)/(2*(b*c - a*d)^2*Sqrt[c + d*x^2]) - x/(2*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) + ((b*c + 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*(b*c - a*d)^(5/2))","A",5,5,24,0.2083,1,"{471, 527, 12, 377, 205}"
770,1,113,0,0.0852439,"\int \frac{x}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[x/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","-\frac{3 d}{2 \sqrt{c+d x^2} (b c-a d)^2}-\frac{1}{2 \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{3 \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 (b c-a d)^{5/2}}","-\frac{3 d}{2 \sqrt{c+d x^2} (b c-a d)^2}-\frac{1}{2 \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{3 \sqrt{b} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 (b c-a d)^{5/2}}",1,"(-3*d)/(2*(b*c - a*d)^2*Sqrt[c + d*x^2]) - 1/(2*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) + (3*Sqrt[b]*d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*(b*c - a*d)^(5/2))","A",5,4,22,0.1818,1,"{444, 51, 63, 208}"
771,1,142,0,0.1021816,"\int \frac{1}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[1/((a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","\frac{b (b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} (b c-a d)^{5/2}}+\frac{d x (2 a d+b c)}{2 a c \sqrt{c+d x^2} (b c-a d)^2}+\frac{b x}{2 a \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}","\frac{b (b c-4 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} (b c-a d)^{5/2}}+\frac{d x (2 a d+b c)}{2 a c \sqrt{c+d x^2} (b c-a d)^2}+\frac{b x}{2 a \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}",1,"(d*(b*c + 2*a*d)*x)/(2*a*c*(b*c - a*d)^2*Sqrt[c + d*x^2]) + (b*x)/(2*a*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) + (b*(b*c - 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*(b*c - a*d)^(5/2))","A",5,5,21,0.2381,1,"{414, 527, 12, 377, 205}"
772,1,170,0,0.2443082,"\int \frac{1}{x \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","\frac{b^{3/2} (2 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 (b c-a d)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2 c^{3/2}}+\frac{b}{2 a \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c \sqrt{c+d x^2} (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^2}}{\sqrt{b c-a d}}\right)}{2 a^2 (b c-a d)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2 c^{3/2}}+\frac{b}{2 a \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c \sqrt{c+d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d))/(2*a*c*(b*c - a*d)^2*Sqrt[c + d*x^2]) + b/(2*a*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) - ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]/(a^2*c^(3/2)) + (b^(3/2)*(2*b*c - 5*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^2*(b*c - a*d)^(5/2))","A",8,6,24,0.2500,1,"{446, 103, 152, 156, 63, 208}"
773,1,205,0,0.2683324,"\int \frac{1}{x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","-\frac{\sqrt{c+d x^2} \left(4 a^2 d^2-4 a b c d+3 b^2 c^2\right)}{2 a^2 c^2 x (b c-a d)^2}-\frac{3 b^2 (b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} (b c-a d)^{5/2}}+\frac{b}{2 a x \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c x \sqrt{c+d x^2} (b c-a d)^2}","-\frac{\sqrt{c+d x^2} \left(4 a^2 d^2-4 a b c d+3 b^2 c^2\right)}{2 a^2 c^2 x (b c-a d)^2}-\frac{3 b^2 (b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} (b c-a d)^{5/2}}+\frac{b}{2 a x \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c x \sqrt{c+d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d))/(2*a*c*(b*c - a*d)^2*x*Sqrt[c + d*x^2]) + b/(2*a*(b*c - a*d)*x*(a + b*x^2)*Sqrt[c + d*x^2]) - ((3*b^2*c^2 - 4*a*b*c*d + 4*a^2*d^2)*Sqrt[c + d*x^2])/(2*a^2*c^2*(b*c - a*d)^2*x) - (3*b^2*(b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(5/2)*(b*c - a*d)^(5/2))","A",6,6,24,0.2500,1,"{472, 579, 583, 12, 377, 205}"
774,1,241,0,0.3361231,"\int \frac{1}{x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x^3*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","-\frac{d \left(3 a^2 d^2-2 a b c d+2 b^2 c^2\right)}{2 a^2 c^2 \sqrt{c+d x^2} (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^2}}{\sqrt{b c-a d}}\right)}{2 a^3 (b c-a d)^{5/2}}+\frac{(3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 c^{5/2}}-\frac{b (2 b c-a d)}{2 a^2 c \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}-\frac{1}{2 a c x^2 \left(a+b x^2\right) \sqrt{c+d x^2}}","-\frac{d \left(3 a^2 d^2-2 a b c d+2 b^2 c^2\right)}{2 a^2 c^2 \sqrt{c+d x^2} (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^2}}{\sqrt{b c-a d}}\right)}{2 a^3 (b c-a d)^{5/2}}+\frac{(3 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 c^{5/2}}-\frac{b (2 b c-a d)}{2 a^2 c \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}-\frac{1}{2 a c x^2 \left(a+b x^2\right) \sqrt{c+d x^2}}",1,"-(d*(2*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2))/(2*a^2*c^2*(b*c - a*d)^2*Sqrt[c + d*x^2]) - (b*(2*b*c - a*d))/(2*a^2*c*(b*c - a*d)*(a + b*x^2)*Sqrt[c + d*x^2]) - 1/(2*a*c*x^2*(a + b*x^2)*Sqrt[c + d*x^2]) + ((4*b*c + 3*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^3*c^(5/2)) - (b^(5/2)*(4*b*c - 7*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^3*(b*c - a*d)^(5/2))","A",9,7,24,0.2917,1,"{446, 103, 151, 152, 156, 63, 208}"
775,1,277,0,0.3964692,"\int \frac{1}{x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}} \, dx","Int[1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(3/2)),x]","\frac{\sqrt{c+d x^2} \left(-8 a^2 b c d^2+16 a^3 d^3-14 a b^2 c^2 d+15 b^3 c^3\right)}{6 a^3 c^3 x (b c-a d)^2}-\frac{\sqrt{c+d x^2} \left(8 a^2 d^2-4 a b c d+5 b^2 c^2\right)}{6 a^2 c^2 x^3 (b c-a d)^2}+\frac{b^3 (5 b c-8 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} (b c-a d)^{5/2}}+\frac{b}{2 a x^3 \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c x^3 \sqrt{c+d x^2} (b c-a d)^2}","\frac{\sqrt{c+d x^2} \left(-8 a^2 b c d^2+16 a^3 d^3-14 a b^2 c^2 d+15 b^3 c^3\right)}{6 a^3 c^3 x (b c-a d)^2}-\frac{\sqrt{c+d x^2} \left(8 a^2 d^2-4 a b c d+5 b^2 c^2\right)}{6 a^2 c^2 x^3 (b c-a d)^2}+\frac{b^3 (5 b c-8 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} (b c-a d)^{5/2}}+\frac{b}{2 a x^3 \left(a+b x^2\right) \sqrt{c+d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c x^3 \sqrt{c+d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d))/(2*a*c*(b*c - a*d)^2*x^3*Sqrt[c + d*x^2]) + b/(2*a*(b*c - a*d)*x^3*(a + b*x^2)*Sqrt[c + d*x^2]) - ((5*b^2*c^2 - 4*a*b*c*d + 8*a^2*d^2)*Sqrt[c + d*x^2])/(6*a^2*c^2*(b*c - a*d)^2*x^3) + ((15*b^3*c^3 - 14*a*b^2*c^2*d - 8*a^2*b*c*d^2 + 16*a^3*d^3)*Sqrt[c + d*x^2])/(6*a^3*c^3*(b*c - a*d)^2*x) + (b^3*(5*b*c - 8*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(7/2)*(b*c - a*d)^(5/2))","A",7,6,24,0.2500,1,"{472, 579, 583, 12, 377, 205}"
776,1,174,0,0.2110193,"\int \frac{x^4}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[x^4/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","\frac{x (11 a d+4 b c)}{6 \sqrt{c+d x^2} (b c-a d)^3}+\frac{x (3 a d+2 b c)}{6 b \left(c+d x^2\right)^{3/2} (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{\sqrt{a} (2 a d+3 b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 (b c-a d)^{7/2}}","\frac{x (11 a d+4 b c)}{6 \sqrt{c+d x^2} (b c-a d)^3}+\frac{x (3 a d+2 b c)}{6 b \left(c+d x^2\right)^{3/2} (b c-a d)^2}+\frac{a x}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{\sqrt{a} (2 a d+3 b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 (b c-a d)^{7/2}}",1,"((2*b*c + 3*a*d)*x)/(6*b*(b*c - a*d)^2*(c + d*x^2)^(3/2)) + (a*x)/(2*b*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) + ((4*b*c + 11*a*d)*x)/(6*(b*c - a*d)^3*Sqrt[c + d*x^2]) - (Sqrt[a]*(3*b*c + 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*(b*c - a*d)^(7/2))","A",6,5,24,0.2083,1,"{470, 527, 12, 377, 205}"
777,1,170,0,0.1646256,"\int \frac{x^3}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[x^3/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","\frac{a}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{3 a d+2 b c}{2 \sqrt{c+d x^2} (b c-a d)^3}+\frac{3 a d+2 b c}{6 b \left(c+d x^2\right)^{3/2} (b c-a d)^2}-\frac{\sqrt{b} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 (b c-a d)^{7/2}}","\frac{a}{2 b \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{3 a d+2 b c}{2 \sqrt{c+d x^2} (b c-a d)^3}+\frac{3 a d+2 b c}{6 b \left(c+d x^2\right)^{3/2} (b c-a d)^2}-\frac{\sqrt{b} (3 a d+2 b c) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 (b c-a d)^{7/2}}",1,"(2*b*c + 3*a*d)/(6*b*(b*c - a*d)^2*(c + d*x^2)^(3/2)) + a/(2*b*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) + (2*b*c + 3*a*d)/(2*(b*c - a*d)^3*Sqrt[c + d*x^2]) - (Sqrt[b]*(2*b*c + 3*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*(b*c - a*d)^(7/2))","A",6,5,24,0.2083,1,"{446, 78, 51, 63, 208}"
778,1,163,0,0.1603894,"\int \frac{x^2}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[x^2/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","-\frac{d x (2 a d+13 b c)}{6 c \sqrt{c+d x^2} (b c-a d)^3}-\frac{x}{2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{5 d x}{6 \left(c+d x^2\right)^{3/2} (b c-a d)^2}+\frac{b (4 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} (b c-a d)^{7/2}}","-\frac{d x (2 a d+13 b c)}{6 c \sqrt{c+d x^2} (b c-a d)^3}-\frac{x}{2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{5 d x}{6 \left(c+d x^2\right)^{3/2} (b c-a d)^2}+\frac{b (4 a d+b c) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} (b c-a d)^{7/2}}",1,"(-5*d*x)/(6*(b*c - a*d)^2*(c + d*x^2)^(3/2)) - x/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) - (d*(13*b*c + 2*a*d)*x)/(6*c*(b*c - a*d)^3*Sqrt[c + d*x^2]) + (b*(b*c + 4*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*(b*c - a*d)^(7/2))","A",6,5,24,0.2083,1,"{471, 527, 12, 377, 205}"
779,1,140,0,0.1028211,"\int \frac{x}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[x/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","\frac{5 b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 (b c-a d)^{7/2}}-\frac{5 b d}{2 \sqrt{c+d x^2} (b c-a d)^3}-\frac{1}{2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{5 d}{6 \left(c+d x^2\right)^{3/2} (b c-a d)^2}","\frac{5 b^{3/2} d \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 (b c-a d)^{7/2}}-\frac{5 b d}{2 \sqrt{c+d x^2} (b c-a d)^3}-\frac{1}{2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{5 d}{6 \left(c+d x^2\right)^{3/2} (b c-a d)^2}",1,"(-5*d)/(6*(b*c - a*d)^2*(c + d*x^2)^(3/2)) - 1/(2*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) - (5*b*d)/(2*(b*c - a*d)^3*Sqrt[c + d*x^2]) + (5*b^(3/2)*d*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*(b*c - a*d)^(7/2))","A",6,4,22,0.1818,1,"{444, 51, 63, 208}"
780,1,201,0,0.2217516,"\int \frac{1}{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[1/((a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","\frac{d x \left(-4 a^2 d^2+16 a b c d+3 b^2 c^2\right)}{6 a c^2 \sqrt{c+d x^2} (b c-a d)^3}+\frac{b^2 (b c-6 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} (b c-a d)^{7/2}}+\frac{b x}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d x (2 a d+3 b c)}{6 a c \left(c+d x^2\right)^{3/2} (b c-a d)^2}","\frac{d x \left(-4 a^2 d^2+16 a b c d+3 b^2 c^2\right)}{6 a c^2 \sqrt{c+d x^2} (b c-a d)^3}+\frac{b^2 (b c-6 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} (b c-a d)^{7/2}}+\frac{b x}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d x (2 a d+3 b c)}{6 a c \left(c+d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d)*x)/(6*a*c*(b*c - a*d)^2*(c + d*x^2)^(3/2)) + (b*x)/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) + (d*(3*b^2*c^2 + 16*a*b*c*d - 4*a^2*d^2)*x)/(6*a*c^2*(b*c - a*d)^3*Sqrt[c + d*x^2]) + (b^2*(b*c - 6*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*(b*c - a*d)^(7/2))","A",6,5,21,0.2381,1,"{414, 527, 12, 377, 205}"
781,1,225,0,0.327889,"\int \frac{1}{x \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","\frac{d \left(-2 a^2 d^2+6 a b c d+b^2 c^2\right)}{2 a c^2 \sqrt{c+d x^2} (b c-a d)^3}+\frac{b^{5/2} (2 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 (b c-a d)^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2 c^{5/2}}+\frac{b}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c \left(c+d x^2\right)^{3/2} (b c-a d)^2}","\frac{d \left(-2 a^2 d^2+6 a b c d+b^2 c^2\right)}{2 a c^2 \sqrt{c+d x^2} (b c-a d)^3}+\frac{b^{5/2} (2 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^2 (b c-a d)^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{a^2 c^{5/2}}+\frac{b}{2 a \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c \left(c+d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d))/(6*a*c*(b*c - a*d)^2*(c + d*x^2)^(3/2)) + b/(2*a*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) + (d*(b^2*c^2 + 6*a*b*c*d - 2*a^2*d^2))/(2*a*c^2*(b*c - a*d)^3*Sqrt[c + d*x^2]) - ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]]/(a^2*c^(5/2)) + (b^(5/2)*(2*b*c - 7*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^2*(b*c - a*d)^(7/2))","A",9,6,24,0.2500,1,"{446, 103, 152, 156, 63, 208}"
782,1,279,0,0.4432018,"\int \frac{1}{x^2 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x^2*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","-\frac{\sqrt{c+d x^2} \left(40 a^2 b c d^2-16 a^3 d^3-18 a b^2 c^2 d+9 b^3 c^3\right)}{6 a^2 c^3 x (b c-a d)^3}+\frac{d \left(-8 a^2 d^2+20 a b c d+3 b^2 c^2\right)}{6 a c^2 x \sqrt{c+d x^2} (b c-a d)^3}-\frac{b^3 (3 b c-8 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} (b c-a d)^{7/2}}+\frac{b}{2 a x \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c x \left(c+d x^2\right)^{3/2} (b c-a d)^2}","-\frac{\sqrt{c+d x^2} \left(40 a^2 b c d^2-16 a^3 d^3-18 a b^2 c^2 d+9 b^3 c^3\right)}{6 a^2 c^3 x (b c-a d)^3}+\frac{d \left(-8 a^2 d^2+20 a b c d+3 b^2 c^2\right)}{6 a c^2 x \sqrt{c+d x^2} (b c-a d)^3}-\frac{b^3 (3 b c-8 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{5/2} (b c-a d)^{7/2}}+\frac{b}{2 a x \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c x \left(c+d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d))/(6*a*c*(b*c - a*d)^2*x*(c + d*x^2)^(3/2)) + b/(2*a*(b*c - a*d)*x*(a + b*x^2)*(c + d*x^2)^(3/2)) + (d*(3*b^2*c^2 + 20*a*b*c*d - 8*a^2*d^2))/(6*a*c^2*(b*c - a*d)^3*x*Sqrt[c + d*x^2]) - ((9*b^3*c^3 - 18*a*b^2*c^2*d + 40*a^2*b*c*d^2 - 16*a^3*d^3)*Sqrt[c + d*x^2])/(6*a^2*c^3*(b*c - a*d)^3*x) - (b^3*(3*b*c - 8*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(5/2)*(b*c - a*d)^(7/2))","A",7,6,24,0.2500,1,"{472, 579, 583, 12, 377, 205}"
783,1,304,0,0.4843417,"\int \frac{1}{x^3 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x^3*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","-\frac{d (2 b c-a d) \left(5 a^2 d^2-a b c d+b^2 c^2\right)}{2 a^2 c^3 \sqrt{c+d x^2} (b c-a d)^3}-\frac{d \left(5 a^2 d^2-6 a b c d+6 b^2 c^2\right)}{6 a^2 c^2 \left(c+d x^2\right)^{3/2} (b c-a d)^2}-\frac{b^{7/2} (4 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 (b c-a d)^{7/2}}+\frac{(5 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 c^{7/2}}-\frac{b (2 b c-a d)}{2 a^2 c \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{1}{2 a c x^2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}}","-\frac{d (2 b c-a d) \left(5 a^2 d^2-a b c d+b^2 c^2\right)}{2 a^2 c^3 \sqrt{c+d x^2} (b c-a d)^3}-\frac{d \left(5 a^2 d^2-6 a b c d+6 b^2 c^2\right)}{6 a^2 c^2 \left(c+d x^2\right)^{3/2} (b c-a d)^2}-\frac{b^{7/2} (4 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{c+d x^2}}{\sqrt{b c-a d}}\right)}{2 a^3 (b c-a d)^{7/2}}+\frac{(5 a d+4 b c) \tanh ^{-1}\left(\frac{\sqrt{c+d x^2}}{\sqrt{c}}\right)}{2 a^3 c^{7/2}}-\frac{b (2 b c-a d)}{2 a^2 c \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}-\frac{1}{2 a c x^2 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2}}",1,"-(d*(6*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2))/(6*a^2*c^2*(b*c - a*d)^2*(c + d*x^2)^(3/2)) - (b*(2*b*c - a*d))/(2*a^2*c*(b*c - a*d)*(a + b*x^2)*(c + d*x^2)^(3/2)) - 1/(2*a*c*x^2*(a + b*x^2)*(c + d*x^2)^(3/2)) - (d*(2*b*c - a*d)*(b^2*c^2 - a*b*c*d + 5*a^2*d^2))/(2*a^2*c^3*(b*c - a*d)^3*Sqrt[c + d*x^2]) + ((4*b*c + 5*a*d)*ArcTanh[Sqrt[c + d*x^2]/Sqrt[c]])/(2*a^3*c^(7/2)) - (b^(7/2)*(4*b*c - 9*a*d)*ArcTanh[(Sqrt[b]*Sqrt[c + d*x^2])/Sqrt[b*c - a*d]])/(2*a^3*(b*c - a*d)^(7/2))","A",10,7,24,0.2917,1,"{446, 103, 151, 152, 156, 63, 208}"
784,1,362,0,0.5960452,"\int \frac{1}{x^4 \left(a+b x^2\right)^2 \left(c+d x^2\right)^{5/2}} \, dx","Int[1/(x^4*(a + b*x^2)^2*(c + d*x^2)^(5/2)),x]","\frac{\sqrt{c+d x^2} \left(-12 a^2 b^2 c^2 d^2+64 a^3 b c d^3-32 a^4 d^4-20 a b^3 c^3 d+15 b^4 c^4\right)}{6 a^3 c^4 x (b c-a d)^3}-\frac{\sqrt{c+d x^2} \left(32 a^2 b c d^2-16 a^3 d^3-6 a b^2 c^2 d+5 b^3 c^3\right)}{6 a^2 c^3 x^3 (b c-a d)^3}+\frac{d \left(-4 a^2 d^2+8 a b c d+b^2 c^2\right)}{2 a c^2 x^3 \sqrt{c+d x^2} (b c-a d)^3}+\frac{5 b^4 (b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} (b c-a d)^{7/2}}+\frac{b}{2 a x^3 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c x^3 \left(c+d x^2\right)^{3/2} (b c-a d)^2}","\frac{\sqrt{c+d x^2} \left(-12 a^2 b^2 c^2 d^2+64 a^3 b c d^3-32 a^4 d^4-20 a b^3 c^3 d+15 b^4 c^4\right)}{6 a^3 c^4 x (b c-a d)^3}-\frac{\sqrt{c+d x^2} \left(32 a^2 b c d^2-16 a^3 d^3-6 a b^2 c^2 d+5 b^3 c^3\right)}{6 a^2 c^3 x^3 (b c-a d)^3}+\frac{d \left(-4 a^2 d^2+8 a b c d+b^2 c^2\right)}{2 a c^2 x^3 \sqrt{c+d x^2} (b c-a d)^3}+\frac{5 b^4 (b c-2 a d) \tan ^{-1}\left(\frac{x \sqrt{b c-a d}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{7/2} (b c-a d)^{7/2}}+\frac{b}{2 a x^3 \left(a+b x^2\right) \left(c+d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c x^3 \left(c+d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d))/(6*a*c*(b*c - a*d)^2*x^3*(c + d*x^2)^(3/2)) + b/(2*a*(b*c - a*d)*x^3*(a + b*x^2)*(c + d*x^2)^(3/2)) + (d*(b^2*c^2 + 8*a*b*c*d - 4*a^2*d^2))/(2*a*c^2*(b*c - a*d)^3*x^3*Sqrt[c + d*x^2]) - ((5*b^3*c^3 - 6*a*b^2*c^2*d + 32*a^2*b*c*d^2 - 16*a^3*d^3)*Sqrt[c + d*x^2])/(6*a^2*c^3*(b*c - a*d)^3*x^3) + ((15*b^4*c^4 - 20*a*b^3*c^3*d - 12*a^2*b^2*c^2*d^2 + 64*a^3*b*c*d^3 - 32*a^4*d^4)*Sqrt[c + d*x^2])/(6*a^3*c^4*(b*c - a*d)^3*x) + (5*b^4*(b*c - 2*a*d)*ArcTan[(Sqrt[b*c - a*d]*x)/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(7/2)*(b*c - a*d)^(7/2))","A",8,6,24,0.2500,1,"{472, 579, 583, 12, 377, 205}"
785,1,212,0,0.1599388,"\int (e x)^{3/2} \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[(e*x)^(3/2)*Sqrt[a + b*x^2]*(A + B*x^2),x]","-\frac{2 a^{7/4} e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (11 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{4 a e \sqrt{e x} \sqrt{a+b x^2} (11 A b-5 a B)}{231 b^2}+\frac{2 (e x)^{5/2} \sqrt{a+b x^2} (11 A b-5 a B)}{77 b e}+\frac{2 B (e x)^{5/2} \left(a+b x^2\right)^{3/2}}{11 b e}","-\frac{2 a^{7/4} e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (11 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{4 a e \sqrt{e x} \sqrt{a+b x^2} (11 A b-5 a B)}{231 b^2}+\frac{2 (e x)^{5/2} \sqrt{a+b x^2} (11 A b-5 a B)}{77 b e}+\frac{2 B (e x)^{5/2} \left(a+b x^2\right)^{3/2}}{11 b e}",1,"(4*a*(11*A*b - 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^2])/(231*b^2) + (2*(11*A*b - 5*a*B)*(e*x)^(5/2)*Sqrt[a + b*x^2])/(77*b*e) + (2*B*(e*x)^(5/2)*(a + b*x^2)^(3/2))/(11*b*e) - (2*a^(7/4)*(11*A*b - 5*a*B)*e^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(231*b^(9/4)*Sqrt[a + b*x^2])","A",5,5,26,0.1923,1,"{459, 279, 321, 329, 220}"
786,1,337,0,0.2698527,"\int \sqrt{e x} \sqrt{a+b x^2} \left(A+B x^2\right) \, dx","Int[Sqrt[e*x]*Sqrt[a + b*x^2]*(A + B*x^2),x]","\frac{2 a^{5/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}-\frac{4 a^{5/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}+\frac{4 a \sqrt{e x} \sqrt{a+b x^2} (3 A b-a B)}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 (e x)^{3/2} \sqrt{a+b x^2} (3 A b-a B)}{15 b e}+\frac{2 B (e x)^{3/2} \left(a+b x^2\right)^{3/2}}{9 b e}","\frac{2 a^{5/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}-\frac{4 a^{5/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{a+b x^2}}+\frac{4 a \sqrt{e x} \sqrt{a+b x^2} (3 A b-a B)}{15 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 (e x)^{3/2} \sqrt{a+b x^2} (3 A b-a B)}{15 b e}+\frac{2 B (e x)^{3/2} \left(a+b x^2\right)^{3/2}}{9 b e}",1,"(2*(3*A*b - a*B)*(e*x)^(3/2)*Sqrt[a + b*x^2])/(15*b*e) + (4*a*(3*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(15*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + (2*B*(e*x)^(3/2)*(a + b*x^2)^(3/2))/(9*b*e) - (4*a^(5/4)*(3*A*b - a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(15*b^(7/4)*Sqrt[a + b*x^2]) + (2*a^(5/4)*(3*A*b - a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(15*b^(7/4)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{459, 279, 329, 305, 220, 1196}"
787,1,176,0,0.1107923,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{\sqrt{e x}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/Sqrt[e*x],x]","\frac{2 a^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \sqrt{a+b x^2} (7 A b-a B)}{21 b e}+\frac{2 B \sqrt{e x} \left(a+b x^2\right)^{3/2}}{7 b e}","\frac{2 a^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \sqrt{a+b x^2} (7 A b-a B)}{21 b e}+\frac{2 B \sqrt{e x} \left(a+b x^2\right)^{3/2}}{7 b e}",1,"(2*(7*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(21*b*e) + (2*B*Sqrt[e*x]*(a + b*x^2)^(3/2))/(7*b*e) + (2*a^(3/4)*(7*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(21*b^(5/4)*Sqrt[e]*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{459, 279, 329, 220}"
788,1,333,0,0.2612731,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{(e x)^{3/2}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/(e*x)^(3/2),x]","\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+5 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{4 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+5 A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{3/4} e^{3/2} \sqrt{a+b x^2}}+\frac{2 (e x)^{3/2} \sqrt{a+b x^2} (a B+5 A b)}{5 a e^3}+\frac{4 \sqrt{e x} \sqrt{a+b x^2} (a B+5 A b)}{5 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \left(a+b x^2\right)^{3/2}}{a e \sqrt{e x}}","\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+5 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{4 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+5 A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{3/4} e^{3/2} \sqrt{a+b x^2}}+\frac{2 (e x)^{3/2} \sqrt{a+b x^2} (a B+5 A b)}{5 a e^3}+\frac{4 \sqrt{e x} \sqrt{a+b x^2} (a B+5 A b)}{5 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \left(a+b x^2\right)^{3/2}}{a e \sqrt{e x}}",1,"(2*(5*A*b + a*B)*(e*x)^(3/2)*Sqrt[a + b*x^2])/(5*a*e^3) + (4*(5*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*Sqrt[b]*e^2*(Sqrt[a] + Sqrt[b]*x)) - (2*A*(a + b*x^2)^(3/2))/(a*e*Sqrt[e*x]) - (4*a^(1/4)*(5*A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2]) + (2*a^(1/4)*(5*A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{453, 279, 329, 305, 220, 1196}"
789,1,172,0,0.1104402,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{(e x)^{5/2}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/(e*x)^(5/2),x]","\frac{2 \sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{3 a e^3}+\frac{2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{3 a e (e x)^{3/2}}","\frac{2 \sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{3 a e^3}+\frac{2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{3 a e (e x)^{3/2}}",1,"(2*(A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(3*a*e^3) - (2*A*(a + b*x^2)^(3/2))/(3*a*e*(e*x)^(3/2)) + (2*(A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(3*a^(1/4)*b^(1/4)*e^(5/2)*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{453, 279, 329, 220}"
790,1,338,0,0.2643403,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{(e x)^{7/2}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/(e*x)^(7/2),x]","\frac{2 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^{7/2} \sqrt{a+b x^2}}-\frac{4 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^{7/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2} (5 a B+A b)}{5 a e^3 \sqrt{e x}}+\frac{4 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (5 a B+A b)}{5 a e^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \left(a+b x^2\right)^{3/2}}{5 a e (e x)^{5/2}}","\frac{2 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^{7/2} \sqrt{a+b x^2}}-\frac{4 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^{7/2} \sqrt{a+b x^2}}-\frac{2 \sqrt{a+b x^2} (5 a B+A b)}{5 a e^3 \sqrt{e x}}+\frac{4 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (5 a B+A b)}{5 a e^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \left(a+b x^2\right)^{3/2}}{5 a e (e x)^{5/2}}",1,"(-2*(A*b + 5*a*B)*Sqrt[a + b*x^2])/(5*a*e^3*Sqrt[e*x]) + (4*Sqrt[b]*(A*b + 5*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*a*e^4*(Sqrt[a] + Sqrt[b]*x)) - (2*A*(a + b*x^2)^(3/2))/(5*a*e*(e*x)^(5/2)) - (4*b^(1/4)*(A*b + 5*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*a^(3/4)*e^(7/2)*Sqrt[a + b*x^2]) + (2*b^(1/4)*(A*b + 5*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*a^(3/4)*e^(7/2)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{453, 277, 329, 305, 220, 1196}"
791,1,152,0,0.0930551,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^{9/2}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^(9/2),x]","-\frac{2 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 a^{5/4} \sqrt{a+b x^2}}+\frac{2 \sqrt{a+b x^2} (A b-7 a B)}{21 a x^{3/2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{7 a x^{7/2}}","-\frac{2 b^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 a^{5/4} \sqrt{a+b x^2}}+\frac{2 \sqrt{a+b x^2} (A b-7 a B)}{21 a x^{3/2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{7 a x^{7/2}}",1,"(2*(A*b - 7*a*B)*Sqrt[a + b*x^2])/(21*a*x^(3/2)) - (2*A*(a + b*x^2)^(3/2))/(7*a*x^(7/2)) - (2*b^(3/4)*(A*b - 7*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(21*a^(5/4)*Sqrt[a + b*x^2])","A",4,4,24,0.1667,1,"{453, 277, 329, 220}"
792,1,331,0,0.2333389,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^{11/2}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^(11/2),x]","-\frac{4 b^{3/2} \sqrt{x} \sqrt{a+b x^2} (A b-3 a B)}{15 a^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} \sqrt{a+b x^2}}+\frac{4 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} \sqrt{a+b x^2}}+\frac{4 b \sqrt{a+b x^2} (A b-3 a B)}{15 a^2 \sqrt{x}}+\frac{2 \sqrt{a+b x^2} (A b-3 a B)}{15 a x^{5/2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{9 a x^{9/2}}","-\frac{4 b^{3/2} \sqrt{x} \sqrt{a+b x^2} (A b-3 a B)}{15 a^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} \sqrt{a+b x^2}}+\frac{4 b^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} \sqrt{a+b x^2}}+\frac{4 b \sqrt{a+b x^2} (A b-3 a B)}{15 a^2 \sqrt{x}}+\frac{2 \sqrt{a+b x^2} (A b-3 a B)}{15 a x^{5/2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{9 a x^{9/2}}",1,"(2*(A*b - 3*a*B)*Sqrt[a + b*x^2])/(15*a*x^(5/2)) + (4*b*(A*b - 3*a*B)*Sqrt[a + b*x^2])/(15*a^2*Sqrt[x]) - (4*b^(3/2)*(A*b - 3*a*B)*Sqrt[x]*Sqrt[a + b*x^2])/(15*a^2*(Sqrt[a] + Sqrt[b]*x)) - (2*A*(a + b*x^2)^(3/2))/(9*a*x^(9/2)) + (4*b^(5/4)*(A*b - 3*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*a^(7/4)*Sqrt[a + b*x^2]) - (2*b^(5/4)*(A*b - 3*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*a^(7/4)*Sqrt[a + b*x^2])","A",7,7,24,0.2917,1,"{453, 277, 325, 329, 305, 220, 1196}"
793,1,187,0,0.1123521,"\int \frac{\sqrt{a+b x^2} \left(A+B x^2\right)}{x^{13/2}} \, dx","Int[(Sqrt[a + b*x^2]*(A + B*x^2))/x^(13/2),x]","\frac{2 b^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-11 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 a^{9/4} \sqrt{a+b x^2}}+\frac{4 b \sqrt{a+b x^2} (5 A b-11 a B)}{231 a^2 x^{3/2}}+\frac{2 \sqrt{a+b x^2} (5 A b-11 a B)}{77 a x^{7/2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{11 a x^{11/2}}","\frac{2 b^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-11 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 a^{9/4} \sqrt{a+b x^2}}+\frac{4 b \sqrt{a+b x^2} (5 A b-11 a B)}{231 a^2 x^{3/2}}+\frac{2 \sqrt{a+b x^2} (5 A b-11 a B)}{77 a x^{7/2}}-\frac{2 A \left(a+b x^2\right)^{3/2}}{11 a x^{11/2}}",1,"(2*(5*A*b - 11*a*B)*Sqrt[a + b*x^2])/(77*a*x^(7/2)) + (4*b*(5*A*b - 11*a*B)*Sqrt[a + b*x^2])/(231*a^2*x^(3/2)) - (2*A*(a + b*x^2)^(3/2))/(11*a*x^(11/2)) + (2*b^(7/4)*(5*A*b - 11*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(231*a^(9/4)*Sqrt[a + b*x^2])","A",5,5,24,0.2083,1,"{453, 277, 325, 329, 220}"
794,1,252,0,0.1667862,"\int (e x)^{3/2} \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[(e*x)^(3/2)*(a + b*x^2)^(3/2)*(A + B*x^2),x]","-\frac{4 a^{11/4} e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{8 a^2 e \sqrt{e x} \sqrt{a+b x^2} (3 A b-a B)}{231 b^2}+\frac{4 a (e x)^{5/2} \sqrt{a+b x^2} (3 A b-a B)}{77 b e}+\frac{2 (e x)^{5/2} \left(a+b x^2\right)^{3/2} (3 A b-a B)}{33 b e}+\frac{2 B (e x)^{5/2} \left(a+b x^2\right)^{5/2}}{15 b e}","-\frac{4 a^{11/4} e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{a+b x^2}}+\frac{8 a^2 e \sqrt{e x} \sqrt{a+b x^2} (3 A b-a B)}{231 b^2}+\frac{4 a (e x)^{5/2} \sqrt{a+b x^2} (3 A b-a B)}{77 b e}+\frac{2 (e x)^{5/2} \left(a+b x^2\right)^{3/2} (3 A b-a B)}{33 b e}+\frac{2 B (e x)^{5/2} \left(a+b x^2\right)^{5/2}}{15 b e}",1,"(8*a^2*(3*A*b - a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^2])/(231*b^2) + (4*a*(3*A*b - a*B)*(e*x)^(5/2)*Sqrt[a + b*x^2])/(77*b*e) + (2*(3*A*b - a*B)*(e*x)^(5/2)*(a + b*x^2)^(3/2))/(33*b*e) + (2*B*(e*x)^(5/2)*(a + b*x^2)^(5/2))/(15*b*e) - (4*a^(11/4)*(3*A*b - a*B)*e^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(231*b^(9/4)*Sqrt[a + b*x^2])","A",6,5,26,0.1923,1,"{459, 279, 321, 329, 220}"
795,1,377,0,0.289959,"\int \sqrt{e x} \left(a+b x^2\right)^{3/2} \left(A+B x^2\right) \, dx","Int[Sqrt[e*x]*(a + b*x^2)^(3/2)*(A + B*x^2),x]","\frac{8 a^2 \sqrt{e x} \sqrt{a+b x^2} (13 A b-3 a B)}{195 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{4 a^{9/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (13 A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 b^{7/4} \sqrt{a+b x^2}}-\frac{8 a^{9/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (13 A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 b^{7/4} \sqrt{a+b x^2}}+\frac{2 (e x)^{3/2} \left(a+b x^2\right)^{3/2} (13 A b-3 a B)}{117 b e}+\frac{4 a (e x)^{3/2} \sqrt{a+b x^2} (13 A b-3 a B)}{195 b e}+\frac{2 B (e x)^{3/2} \left(a+b x^2\right)^{5/2}}{13 b e}","\frac{8 a^2 \sqrt{e x} \sqrt{a+b x^2} (13 A b-3 a B)}{195 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{4 a^{9/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (13 A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 b^{7/4} \sqrt{a+b x^2}}-\frac{8 a^{9/4} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (13 A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 b^{7/4} \sqrt{a+b x^2}}+\frac{2 (e x)^{3/2} \left(a+b x^2\right)^{3/2} (13 A b-3 a B)}{117 b e}+\frac{4 a (e x)^{3/2} \sqrt{a+b x^2} (13 A b-3 a B)}{195 b e}+\frac{2 B (e x)^{3/2} \left(a+b x^2\right)^{5/2}}{13 b e}",1,"(4*a*(13*A*b - 3*a*B)*(e*x)^(3/2)*Sqrt[a + b*x^2])/(195*b*e) + (8*a^2*(13*A*b - 3*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(195*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + (2*(13*A*b - 3*a*B)*(e*x)^(3/2)*(a + b*x^2)^(3/2))/(117*b*e) + (2*B*(e*x)^(3/2)*(a + b*x^2)^(5/2))/(13*b*e) - (8*a^(9/4)*(13*A*b - 3*a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(195*b^(7/4)*Sqrt[a + b*x^2]) + (4*a^(9/4)*(13*A*b - 3*a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(195*b^(7/4)*Sqrt[a + b*x^2])","A",7,6,26,0.2308,1,"{459, 279, 329, 305, 220, 1196}"
796,1,214,0,0.1364284,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{\sqrt{e x}} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/Sqrt[e*x],x]","\frac{4 a^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (11 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \left(a+b x^2\right)^{3/2} (11 A b-a B)}{77 b e}+\frac{4 a \sqrt{e x} \sqrt{a+b x^2} (11 A b-a B)}{77 b e}+\frac{2 B \sqrt{e x} \left(a+b x^2\right)^{5/2}}{11 b e}","\frac{4 a^{7/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (11 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{77 b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \left(a+b x^2\right)^{3/2} (11 A b-a B)}{77 b e}+\frac{4 a \sqrt{e x} \sqrt{a+b x^2} (11 A b-a B)}{77 b e}+\frac{2 B \sqrt{e x} \left(a+b x^2\right)^{5/2}}{11 b e}",1,"(4*a*(11*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(77*b*e) + (2*(11*A*b - a*B)*Sqrt[e*x]*(a + b*x^2)^(3/2))/(77*b*e) + (2*B*Sqrt[e*x]*(a + b*x^2)^(5/2))/(11*b*e) + (4*a^(7/4)*(11*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(77*b^(5/4)*Sqrt[e]*Sqrt[a + b*x^2])","A",5,4,26,0.1538,1,"{459, 279, 329, 220}"
797,1,367,0,0.2945091,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{(e x)^{3/2}} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/(e*x)^(3/2),x]","\frac{4 a^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+9 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{8 a^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+9 A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{3/4} e^{3/2} \sqrt{a+b x^2}}+\frac{2 (e x)^{3/2} \left(a+b x^2\right)^{3/2} (a B+9 A b)}{9 a e^3}+\frac{4 (e x)^{3/2} \sqrt{a+b x^2} (a B+9 A b)}{15 e^3}+\frac{8 a \sqrt{e x} \sqrt{a+b x^2} (a B+9 A b)}{15 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \left(a+b x^2\right)^{5/2}}{a e \sqrt{e x}}","\frac{4 a^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+9 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{8 a^{5/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+9 A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{3/4} e^{3/2} \sqrt{a+b x^2}}+\frac{2 (e x)^{3/2} \left(a+b x^2\right)^{3/2} (a B+9 A b)}{9 a e^3}+\frac{4 (e x)^{3/2} \sqrt{a+b x^2} (a B+9 A b)}{15 e^3}+\frac{8 a \sqrt{e x} \sqrt{a+b x^2} (a B+9 A b)}{15 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \left(a+b x^2\right)^{5/2}}{a e \sqrt{e x}}",1,"(4*(9*A*b + a*B)*(e*x)^(3/2)*Sqrt[a + b*x^2])/(15*e^3) + (8*a*(9*A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(15*Sqrt[b]*e^2*(Sqrt[a] + Sqrt[b]*x)) + (2*(9*A*b + a*B)*(e*x)^(3/2)*(a + b*x^2)^(3/2))/(9*a*e^3) - (2*A*(a + b*x^2)^(5/2))/(a*e*Sqrt[e*x]) - (8*a^(5/4)*(9*A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(15*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2]) + (4*a^(5/4)*(9*A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(15*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2])","A",7,6,26,0.2308,1,"{453, 279, 329, 305, 220, 1196}"
798,1,210,0,0.1366153,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{(e x)^{5/2}} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/(e*x)^(5/2),x]","\frac{4 a^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 a B+7 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \left(a+b x^2\right)^{3/2} (3 a B+7 A b)}{21 a e^3}+\frac{4 \sqrt{e x} \sqrt{a+b x^2} (3 a B+7 A b)}{21 e^3}-\frac{2 A \left(a+b x^2\right)^{5/2}}{3 a e (e x)^{3/2}}","\frac{4 a^{3/4} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 a B+7 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \left(a+b x^2\right)^{3/2} (3 a B+7 A b)}{21 a e^3}+\frac{4 \sqrt{e x} \sqrt{a+b x^2} (3 a B+7 A b)}{21 e^3}-\frac{2 A \left(a+b x^2\right)^{5/2}}{3 a e (e x)^{3/2}}",1,"(4*(7*A*b + 3*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(21*e^3) + (2*(7*A*b + 3*a*B)*Sqrt[e*x]*(a + b*x^2)^(3/2))/(21*a*e^3) - (2*A*(a + b*x^2)^(5/2))/(3*a*e*(e*x)^(3/2)) + (4*a^(3/4)*(7*A*b + 3*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(21*b^(1/4)*e^(5/2)*Sqrt[a + b*x^2])","A",5,4,26,0.1538,1,"{453, 279, 329, 220}"
799,1,365,0,0.2887362,"\int \frac{\left(a+b x^2\right)^{3/2} \left(A+B x^2\right)}{(e x)^{7/2}} \, dx","Int[((a + b*x^2)^(3/2)*(A + B*x^2))/(e*x)^(7/2),x]","-\frac{2 \left(a+b x^2\right)^{3/2} (a B+A b)}{a e^3 \sqrt{e x}}+\frac{12 b (e x)^{3/2} \sqrt{a+b x^2} (a B+A b)}{5 a e^5}+\frac{24 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{5 e^4 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{12 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 e^{7/2} \sqrt{a+b x^2}}-\frac{24 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 e^{7/2} \sqrt{a+b x^2}}-\frac{2 A \left(a+b x^2\right)^{5/2}}{5 a e (e x)^{5/2}}","-\frac{2 \left(a+b x^2\right)^{3/2} (a B+A b)}{a e^3 \sqrt{e x}}+\frac{12 b (e x)^{3/2} \sqrt{a+b x^2} (a B+A b)}{5 a e^5}+\frac{24 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{5 e^4 \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{12 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 e^{7/2} \sqrt{a+b x^2}}-\frac{24 \sqrt[4]{a} \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 e^{7/2} \sqrt{a+b x^2}}-\frac{2 A \left(a+b x^2\right)^{5/2}}{5 a e (e x)^{5/2}}",1,"(12*b*(A*b + a*B)*(e*x)^(3/2)*Sqrt[a + b*x^2])/(5*a*e^5) + (24*Sqrt[b]*(A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*e^4*(Sqrt[a] + Sqrt[b]*x)) - (2*(A*b + a*B)*(a + b*x^2)^(3/2))/(a*e^3*Sqrt[e*x]) - (2*A*(a + b*x^2)^(5/2))/(5*a*e*(e*x)^(5/2)) - (24*a^(1/4)*b^(1/4)*(A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*e^(7/2)*Sqrt[a + b*x^2]) + (12*a^(1/4)*b^(1/4)*(A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*e^(7/2)*Sqrt[a + b*x^2])","A",7,7,26,0.2692,1,"{453, 277, 279, 329, 305, 220, 1196}"
800,1,338,0,0.2575839,"\int \frac{(e x)^{5/2} \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[((e*x)^(5/2)*(A + B*x^2))/Sqrt[a + b*x^2],x]","-\frac{a^{5/4} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (9 A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{a+b x^2}}+\frac{2 a^{5/4} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (9 A b-7 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{a+b x^2}}-\frac{2 a e^2 \sqrt{e x} \sqrt{a+b x^2} (9 A b-7 a B)}{15 b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 e (e x)^{3/2} \sqrt{a+b x^2} (9 A b-7 a B)}{45 b^2}+\frac{2 B (e x)^{7/2} \sqrt{a+b x^2}}{9 b e}","-\frac{a^{5/4} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (9 A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{a+b x^2}}+\frac{2 a^{5/4} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (9 A b-7 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{a+b x^2}}-\frac{2 a e^2 \sqrt{e x} \sqrt{a+b x^2} (9 A b-7 a B)}{15 b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{2 e (e x)^{3/2} \sqrt{a+b x^2} (9 A b-7 a B)}{45 b^2}+\frac{2 B (e x)^{7/2} \sqrt{a+b x^2}}{9 b e}",1,"(2*(9*A*b - 7*a*B)*e*(e*x)^(3/2)*Sqrt[a + b*x^2])/(45*b^2) + (2*B*(e*x)^(7/2)*Sqrt[a + b*x^2])/(9*b*e) - (2*a*(9*A*b - 7*a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^2])/(15*b^(5/2)*(Sqrt[a] + Sqrt[b]*x)) + (2*a^(5/4)*(9*A*b - 7*a*B)*e^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(15*b^(11/4)*Sqrt[a + b*x^2]) - (a^(5/4)*(9*A*b - 7*a*B)*e^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(15*b^(11/4)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{459, 321, 329, 305, 220, 1196}"
801,1,174,0,0.1096483,"\int \frac{(e x)^{3/2} \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[((e*x)^(3/2)*(A + B*x^2))/Sqrt[a + b*x^2],x]","-\frac{a^{3/4} e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{a+b x^2}}+\frac{2 e \sqrt{e x} \sqrt{a+b x^2} (7 A b-5 a B)}{21 b^2}+\frac{2 B (e x)^{5/2} \sqrt{a+b x^2}}{7 b e}","-\frac{a^{3/4} e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{a+b x^2}}+\frac{2 e \sqrt{e x} \sqrt{a+b x^2} (7 A b-5 a B)}{21 b^2}+\frac{2 B (e x)^{5/2} \sqrt{a+b x^2}}{7 b e}",1,"(2*(7*A*b - 5*a*B)*e*Sqrt[e*x]*Sqrt[a + b*x^2])/(21*b^2) + (2*B*(e*x)^(5/2)*Sqrt[a + b*x^2])/(7*b*e) - (a^(3/4)*(7*A*b - 5*a*B)*e^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(21*b^(9/4)*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{459, 321, 329, 220}"
802,1,299,0,0.2142028,"\int \frac{\sqrt{e x} \left(A+B x^2\right)}{\sqrt{a+b x^2}} \, dx","Int[(Sqrt[e*x]*(A + B*x^2))/Sqrt[a + b*x^2],x]","\frac{2 \sqrt{e x} \sqrt{a+b x^2} (5 A b-3 a B)}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{\sqrt[4]{a} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}-\frac{2 \sqrt[4]{a} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}+\frac{2 B (e x)^{3/2} \sqrt{a+b x^2}}{5 b e}","\frac{2 \sqrt{e x} \sqrt{a+b x^2} (5 A b-3 a B)}{5 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{\sqrt[4]{a} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}-\frac{2 \sqrt[4]{a} \sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{a+b x^2}}+\frac{2 B (e x)^{3/2} \sqrt{a+b x^2}}{5 b e}",1,"(2*B*(e*x)^(3/2)*Sqrt[a + b*x^2])/(5*b*e) + (2*(5*A*b - 3*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) - (2*a^(1/4)*(5*A*b - 3*a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^2]) + (a^(1/4)*(5*A*b - 3*a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*b^(7/4)*Sqrt[a + b*x^2])","A",5,5,26,0.1923,1,"{459, 329, 305, 220, 1196}"
803,1,139,0,0.0811609,"\int \frac{A+B x^2}{\sqrt{e x} \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/(Sqrt[e*x]*Sqrt[a + b*x^2]),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{2 B \sqrt{e x} \sqrt{a+b x^2}}{3 b e}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{2 B \sqrt{e x} \sqrt{a+b x^2}}{3 b e}",1,"(2*B*Sqrt[e*x]*Sqrt[a + b*x^2])/(3*b*e) + ((3*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(3*a^(1/4)*b^(5/4)*Sqrt[e]*Sqrt[a + b*x^2])","A",3,3,26,0.1154,1,"{459, 329, 220}"
804,1,290,0,0.2227481,"\int \frac{A+B x^2}{(e x)^{3/2} \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/((e*x)^(3/2)*Sqrt[a + b*x^2]),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{a \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \sqrt{a+b x^2}}{a e \sqrt{e x}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{2 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}+\frac{2 \sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{a \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A \sqrt{a+b x^2}}{a e \sqrt{e x}}",1,"(-2*A*Sqrt[a + b*x^2])/(a*e*Sqrt[e*x]) + (2*(A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(a*Sqrt[b]*e^2*(Sqrt[a] + Sqrt[b]*x)) - (2*(A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(a^(3/4)*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2]) + ((A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(a^(3/4)*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2])","A",5,5,26,0.1923,1,"{453, 329, 305, 220, 1196}"
805,1,138,0,0.0864553,"\int \frac{A+B x^2}{(e x)^{5/2} \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/((e*x)^(5/2)*Sqrt[a + b*x^2]),x]","-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 a^{5/4} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A \sqrt{a+b x^2}}{3 a e (e x)^{3/2}}","-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 a^{5/4} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A \sqrt{a+b x^2}}{3 a e (e x)^{3/2}}",1,"(-2*A*Sqrt[a + b*x^2])/(3*a*e*(e*x)^(3/2)) - ((A*b - 3*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(3*a^(5/4)*b^(1/4)*e^(5/2)*Sqrt[a + b*x^2])","A",3,3,26,0.1154,1,"{453, 329, 220}"
806,1,342,0,0.2514161,"\int \frac{A+B x^2}{(e x)^{7/2} \sqrt{a+b x^2}} \, dx","Int[(A + B*x^2)/((e*x)^(7/2)*Sqrt[a + b*x^2]),x]","\frac{2 \sqrt{a+b x^2} (3 A b-5 a B)}{5 a^2 e^3 \sqrt{e x}}-\frac{2 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (3 A b-5 a B)}{5 a^2 e^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{7/4} e^{7/2} \sqrt{a+b x^2}}+\frac{2 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-5 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{7/4} e^{7/2} \sqrt{a+b x^2}}-\frac{2 A \sqrt{a+b x^2}}{5 a e (e x)^{5/2}}","\frac{2 \sqrt{a+b x^2} (3 A b-5 a B)}{5 a^2 e^3 \sqrt{e x}}-\frac{2 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (3 A b-5 a B)}{5 a^2 e^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{\sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{7/4} e^{7/2} \sqrt{a+b x^2}}+\frac{2 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-5 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{7/4} e^{7/2} \sqrt{a+b x^2}}-\frac{2 A \sqrt{a+b x^2}}{5 a e (e x)^{5/2}}",1,"(-2*A*Sqrt[a + b*x^2])/(5*a*e*(e*x)^(5/2)) + (2*(3*A*b - 5*a*B)*Sqrt[a + b*x^2])/(5*a^2*e^3*Sqrt[e*x]) - (2*Sqrt[b]*(3*A*b - 5*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*a^2*e^4*(Sqrt[a] + Sqrt[b]*x)) + (2*b^(1/4)*(3*A*b - 5*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*a^(7/4)*e^(7/2)*Sqrt[a + b*x^2]) - (b^(1/4)*(3*A*b - 5*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*a^(7/4)*e^(7/2)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{453, 325, 329, 305, 220, 1196}"
807,1,211,0,0.1370747,"\int \frac{(e x)^{7/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[((e*x)^(7/2)*(A + B*x^2))/(a + b*x^2)^(3/2),x]","-\frac{5 a^{3/4} e^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-9 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{42 b^{13/4} \sqrt{a+b x^2}}+\frac{5 e^3 \sqrt{e x} \sqrt{a+b x^2} (7 A b-9 a B)}{21 b^3}-\frac{e (e x)^{5/2} (7 A b-9 a B)}{7 b^2 \sqrt{a+b x^2}}+\frac{2 B (e x)^{9/2}}{7 b e \sqrt{a+b x^2}}","-\frac{5 a^{3/4} e^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-9 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{42 b^{13/4} \sqrt{a+b x^2}}+\frac{5 e^3 \sqrt{e x} \sqrt{a+b x^2} (7 A b-9 a B)}{21 b^3}-\frac{e (e x)^{5/2} (7 A b-9 a B)}{7 b^2 \sqrt{a+b x^2}}+\frac{2 B (e x)^{9/2}}{7 b e \sqrt{a+b x^2}}",1,"-((7*A*b - 9*a*B)*e*(e*x)^(5/2))/(7*b^2*Sqrt[a + b*x^2]) + (2*B*(e*x)^(9/2))/(7*b*e*Sqrt[a + b*x^2]) + (5*(7*A*b - 9*a*B)*e^3*Sqrt[e*x]*Sqrt[a + b*x^2])/(21*b^3) - (5*a^(3/4)*(7*A*b - 9*a*B)*e^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(42*b^(13/4)*Sqrt[a + b*x^2])","A",5,5,26,0.1923,1,"{459, 288, 321, 329, 220}"
808,1,337,0,0.2520368,"\int \frac{(e x)^{5/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[((e*x)^(5/2)*(A + B*x^2))/(a + b*x^2)^(3/2),x]","\frac{3 e^2 \sqrt{e x} \sqrt{a+b x^2} (5 A b-7 a B)}{5 b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{3 \sqrt[4]{a} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{a} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-7 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{a+b x^2}}-\frac{e (e x)^{3/2} (5 A b-7 a B)}{5 b^2 \sqrt{a+b x^2}}+\frac{2 B (e x)^{7/2}}{5 b e \sqrt{a+b x^2}}","\frac{3 e^2 \sqrt{e x} \sqrt{a+b x^2} (5 A b-7 a B)}{5 b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{3 \sqrt[4]{a} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{a} e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-7 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{a+b x^2}}-\frac{e (e x)^{3/2} (5 A b-7 a B)}{5 b^2 \sqrt{a+b x^2}}+\frac{2 B (e x)^{7/2}}{5 b e \sqrt{a+b x^2}}",1,"-((5*A*b - 7*a*B)*e*(e*x)^(3/2))/(5*b^2*Sqrt[a + b*x^2]) + (2*B*(e*x)^(7/2))/(5*b*e*Sqrt[a + b*x^2]) + (3*(5*A*b - 7*a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*b^(5/2)*(Sqrt[a] + Sqrt[b]*x)) - (3*a^(1/4)*(5*A*b - 7*a*B)*e^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*b^(11/4)*Sqrt[a + b*x^2]) + (3*a^(1/4)*(5*A*b - 7*a*B)*e^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(10*b^(11/4)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{459, 288, 329, 305, 220, 1196}"
809,1,174,0,0.1116409,"\int \frac{(e x)^{3/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[((e*x)^(3/2)*(A + B*x^2))/(a + b*x^2)^(3/2),x]","\frac{e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{a} b^{9/4} \sqrt{a+b x^2}}-\frac{e \sqrt{e x} (3 A b-5 a B)}{3 b^2 \sqrt{a+b x^2}}+\frac{2 B (e x)^{5/2}}{3 b e \sqrt{a+b x^2}}","\frac{e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{a} b^{9/4} \sqrt{a+b x^2}}-\frac{e \sqrt{e x} (3 A b-5 a B)}{3 b^2 \sqrt{a+b x^2}}+\frac{2 B (e x)^{5/2}}{3 b e \sqrt{a+b x^2}}",1,"-((3*A*b - 5*a*B)*e*Sqrt[e*x])/(3*b^2*Sqrt[a + b*x^2]) + (2*B*(e*x)^(5/2))/(3*b*e*Sqrt[a + b*x^2]) + ((3*A*b - 5*a*B)*e^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(6*a^(1/4)*b^(9/4)*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{459, 288, 329, 220}"
810,1,301,0,0.2248513,"\int \frac{\sqrt{e x} \left(A+B x^2\right)}{\left(a+b x^2\right)^{3/2}} \, dx","Int[(Sqrt[e*x]*(A + B*x^2))/(a + b*x^2)^(3/2),x]","-\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{7/4} \sqrt{a+b x^2}}+\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{7/4} \sqrt{a+b x^2}}-\frac{\sqrt{e x} \sqrt{a+b x^2} (A b-3 a B)}{a b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{(e x)^{3/2} (A b-a B)}{a b e \sqrt{a+b x^2}}","-\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{7/4} \sqrt{a+b x^2}}+\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{3/4} b^{7/4} \sqrt{a+b x^2}}-\frac{\sqrt{e x} \sqrt{a+b x^2} (A b-3 a B)}{a b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{(e x)^{3/2} (A b-a B)}{a b e \sqrt{a+b x^2}}",1,"((A*b - a*B)*(e*x)^(3/2))/(a*b*e*Sqrt[a + b*x^2]) - ((A*b - 3*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(a*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + ((A*b - 3*a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(a^(3/4)*b^(7/4)*Sqrt[a + b*x^2]) - ((A*b - 3*a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(2*a^(3/4)*b^(7/4)*Sqrt[a + b*x^2])","A",5,5,26,0.1923,1,"{457, 329, 305, 220, 1196}"
811,1,144,0,0.0899193,"\int \frac{A+B x^2}{\sqrt{e x} \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/(Sqrt[e*x]*(a + b*x^2)^(3/2)),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{5/4} b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{\sqrt{e x} (A b-a B)}{a b e \sqrt{a+b x^2}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{5/4} b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{\sqrt{e x} (A b-a B)}{a b e \sqrt{a+b x^2}}",1,"((A*b - a*B)*Sqrt[e*x])/(a*b*e*Sqrt[a + b*x^2]) + ((A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(2*a^(5/4)*b^(5/4)*Sqrt[e]*Sqrt[a + b*x^2])","A",3,3,26,0.1154,1,"{457, 329, 220}"
812,1,333,0,0.2570153,"\int \frac{A+B x^2}{(e x)^{3/2} \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(3/2)),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{7/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{7/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{(e x)^{3/2} (3 A b-a B)}{a^2 e^3 \sqrt{a+b x^2}}+\frac{\sqrt{e x} \sqrt{a+b x^2} (3 A b-a B)}{a^2 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A}{a e \sqrt{e x} \sqrt{a+b x^2}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{7/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{a^{7/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{(e x)^{3/2} (3 A b-a B)}{a^2 e^3 \sqrt{a+b x^2}}+\frac{\sqrt{e x} \sqrt{a+b x^2} (3 A b-a B)}{a^2 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A}{a e \sqrt{e x} \sqrt{a+b x^2}}",1,"(-2*A)/(a*e*Sqrt[e*x]*Sqrt[a + b*x^2]) - ((3*A*b - a*B)*(e*x)^(3/2))/(a^2*e^3*Sqrt[a + b*x^2]) + ((3*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(a^2*Sqrt[b]*e^2*(Sqrt[a] + Sqrt[b]*x)) - ((3*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(a^(7/4)*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2]) + ((3*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(2*a^(7/4)*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{453, 290, 329, 305, 220, 1196}"
813,1,176,0,0.1133329,"\int \frac{A+B x^2}{(e x)^{5/2} \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(3/2)),x]","-\frac{\sqrt{e x} (5 A b-3 a B)}{3 a^2 e^3 \sqrt{a+b x^2}}-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 a^{9/4} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A}{3 a e (e x)^{3/2} \sqrt{a+b x^2}}","-\frac{\sqrt{e x} (5 A b-3 a B)}{3 a^2 e^3 \sqrt{a+b x^2}}-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 a^{9/4} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A}{3 a e (e x)^{3/2} \sqrt{a+b x^2}}",1,"(-2*A)/(3*a*e*(e*x)^(3/2)*Sqrt[a + b*x^2]) - ((5*A*b - 3*a*B)*Sqrt[e*x])/(3*a^2*e^3*Sqrt[a + b*x^2]) - ((5*A*b - 3*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(6*a^(9/4)*b^(1/4)*e^(5/2)*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{453, 290, 329, 220}"
814,1,379,0,0.298067,"\int \frac{A+B x^2}{(e x)^{7/2} \left(a+b x^2\right)^{3/2}} \, dx","Int[(A + B*x^2)/((e*x)^(7/2)*(a + b*x^2)^(3/2)),x]","\frac{3 \sqrt{a+b x^2} (7 A b-5 a B)}{5 a^3 e^3 \sqrt{e x}}-\frac{3 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (7 A b-5 a B)}{5 a^3 e^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{7 A b-5 a B}{5 a^2 e^3 \sqrt{e x} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 a^{11/4} e^{7/2} \sqrt{a+b x^2}}+\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-5 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{11/4} e^{7/2} \sqrt{a+b x^2}}-\frac{2 A}{5 a e (e x)^{5/2} \sqrt{a+b x^2}}","\frac{3 \sqrt{a+b x^2} (7 A b-5 a B)}{5 a^3 e^3 \sqrt{e x}}-\frac{3 \sqrt{b} \sqrt{e x} \sqrt{a+b x^2} (7 A b-5 a B)}{5 a^3 e^4 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{7 A b-5 a B}{5 a^2 e^3 \sqrt{e x} \sqrt{a+b x^2}}-\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-5 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 a^{11/4} e^{7/2} \sqrt{a+b x^2}}+\frac{3 \sqrt[4]{b} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-5 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 a^{11/4} e^{7/2} \sqrt{a+b x^2}}-\frac{2 A}{5 a e (e x)^{5/2} \sqrt{a+b x^2}}",1,"(-2*A)/(5*a*e*(e*x)^(5/2)*Sqrt[a + b*x^2]) - (7*A*b - 5*a*B)/(5*a^2*e^3*Sqrt[e*x]*Sqrt[a + b*x^2]) + (3*(7*A*b - 5*a*B)*Sqrt[a + b*x^2])/(5*a^3*e^3*Sqrt[e*x]) - (3*Sqrt[b]*(7*A*b - 5*a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(5*a^3*e^4*(Sqrt[a] + Sqrt[b]*x)) + (3*b^(1/4)*(7*A*b - 5*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(5*a^(11/4)*e^(7/2)*Sqrt[a + b*x^2]) - (3*b^(1/4)*(7*A*b - 5*a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(10*a^(11/4)*e^(7/2)*Sqrt[a + b*x^2])","A",7,7,26,0.2692,1,"{453, 290, 325, 329, 305, 220, 1196}"
815,1,208,0,0.1328415,"\int \frac{(e x)^{7/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[((e*x)^(7/2)*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{5 e^3 \sqrt{e x} (A b-3 a B)}{6 b^3 \sqrt{a+b x^2}}+\frac{5 e^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 \sqrt[4]{a} b^{13/4} \sqrt{a+b x^2}}-\frac{e (e x)^{5/2} (A b-3 a B)}{3 b^2 \left(a+b x^2\right)^{3/2}}+\frac{2 B (e x)^{9/2}}{3 b e \left(a+b x^2\right)^{3/2}}","-\frac{5 e^3 \sqrt{e x} (A b-3 a B)}{6 b^3 \sqrt{a+b x^2}}+\frac{5 e^{7/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-3 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 \sqrt[4]{a} b^{13/4} \sqrt{a+b x^2}}-\frac{e (e x)^{5/2} (A b-3 a B)}{3 b^2 \left(a+b x^2\right)^{3/2}}+\frac{2 B (e x)^{9/2}}{3 b e \left(a+b x^2\right)^{3/2}}",1,"-((A*b - 3*a*B)*e*(e*x)^(5/2))/(3*b^2*(a + b*x^2)^(3/2)) + (2*B*(e*x)^(9/2))/(3*b*e*(a + b*x^2)^(3/2)) - (5*(A*b - 3*a*B)*e^3*Sqrt[e*x])/(6*b^3*Sqrt[a + b*x^2]) + (5*(A*b - 3*a*B)*e^(7/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(12*a^(1/4)*b^(13/4)*Sqrt[a + b*x^2])","A",5,4,26,0.1538,1,"{459, 288, 329, 220}"
816,1,349,0,0.2601689,"\int \frac{(e x)^{5/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[((e*x)^(5/2)*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{11/4} \sqrt{a+b x^2}}+\frac{e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-7 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{11/4} \sqrt{a+b x^2}}-\frac{e^2 \sqrt{e x} \sqrt{a+b x^2} (A b-7 a B)}{2 a b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{e (e x)^{3/2} (A b-7 a B)}{6 a b^2 \sqrt{a+b x^2}}+\frac{(e x)^{7/2} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}","-\frac{e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-7 a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 a^{3/4} b^{11/4} \sqrt{a+b x^2}}+\frac{e^{5/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (A b-7 a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{3/4} b^{11/4} \sqrt{a+b x^2}}-\frac{e^2 \sqrt{e x} \sqrt{a+b x^2} (A b-7 a B)}{2 a b^{5/2} \left(\sqrt{a}+\sqrt{b} x\right)}+\frac{e (e x)^{3/2} (A b-7 a B)}{6 a b^2 \sqrt{a+b x^2}}+\frac{(e x)^{7/2} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}",1,"((A*b - a*B)*(e*x)^(7/2))/(3*a*b*e*(a + b*x^2)^(3/2)) + ((A*b - 7*a*B)*e*(e*x)^(3/2))/(6*a*b^2*Sqrt[a + b*x^2]) - ((A*b - 7*a*B)*e^2*Sqrt[e*x]*Sqrt[a + b*x^2])/(2*a*b^(5/2)*(Sqrt[a] + Sqrt[b]*x)) + ((A*b - 7*a*B)*e^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(2*a^(3/4)*b^(11/4)*Sqrt[a + b*x^2]) - ((A*b - 7*a*B)*e^(5/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(4*a^(3/4)*b^(11/4)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{457, 288, 329, 305, 220, 1196}"
817,1,185,0,0.1142548,"\int \frac{(e x)^{3/2} \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[((e*x)^(3/2)*(A + B*x^2))/(a + b*x^2)^(5/2),x]","\frac{e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 a^{5/4} b^{9/4} \sqrt{a+b x^2}}-\frac{e \sqrt{e x} (5 a B+A b)}{6 a b^2 \sqrt{a+b x^2}}+\frac{(e x)^{5/2} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}","\frac{e^{3/2} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (5 a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 a^{5/4} b^{9/4} \sqrt{a+b x^2}}-\frac{e \sqrt{e x} (5 a B+A b)}{6 a b^2 \sqrt{a+b x^2}}+\frac{(e x)^{5/2} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}",1,"((A*b - a*B)*(e*x)^(5/2))/(3*a*b*e*(a + b*x^2)^(3/2)) - ((A*b + 5*a*B)*e*Sqrt[e*x])/(6*a*b^2*Sqrt[a + b*x^2]) + ((A*b + 5*a*B)*e^(3/2)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(12*a^(5/4)*b^(9/4)*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{457, 288, 329, 220}"
818,1,344,0,0.2587905,"\int \frac{\sqrt{e x} \left(A+B x^2\right)}{\left(a+b x^2\right)^{5/2}} \, dx","Int[(Sqrt[e*x]*(A + B*x^2))/(a + b*x^2)^(5/2),x]","-\frac{\sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{2 a^2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 a^{7/4} b^{7/4} \sqrt{a+b x^2}}+\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{7/4} b^{7/4} \sqrt{a+b x^2}}+\frac{(e x)^{3/2} (a B+A b)}{2 a^2 b e \sqrt{a+b x^2}}+\frac{(e x)^{3/2} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}","-\frac{\sqrt{e x} \sqrt{a+b x^2} (a B+A b)}{2 a^2 b^{3/2} \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 a^{7/4} b^{7/4} \sqrt{a+b x^2}}+\frac{\sqrt{e} \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+A b) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{7/4} b^{7/4} \sqrt{a+b x^2}}+\frac{(e x)^{3/2} (a B+A b)}{2 a^2 b e \sqrt{a+b x^2}}+\frac{(e x)^{3/2} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}",1,"((A*b - a*B)*(e*x)^(3/2))/(3*a*b*e*(a + b*x^2)^(3/2)) + ((A*b + a*B)*(e*x)^(3/2))/(2*a^2*b*e*Sqrt[a + b*x^2]) - ((A*b + a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(2*a^2*b^(3/2)*(Sqrt[a] + Sqrt[b]*x)) + ((A*b + a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(2*a^(7/4)*b^(7/4)*Sqrt[a + b*x^2]) - ((A*b + a*B)*Sqrt[e]*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(4*a^(7/4)*b^(7/4)*Sqrt[a + b*x^2])","A",6,6,26,0.2308,1,"{457, 290, 329, 305, 220, 1196}"
819,1,187,0,0.1117936,"\int \frac{A+B x^2}{\sqrt{e x} \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/(Sqrt[e*x]*(a + b*x^2)^(5/2)),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+5 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 a^{9/4} b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{\sqrt{e x} (a B+5 A b)}{6 a^2 b e \sqrt{a+b x^2}}+\frac{\sqrt{e x} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (a B+5 A b) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 a^{9/4} b^{5/4} \sqrt{e} \sqrt{a+b x^2}}+\frac{\sqrt{e x} (a B+5 A b)}{6 a^2 b e \sqrt{a+b x^2}}+\frac{\sqrt{e x} (A b-a B)}{3 a b e \left(a+b x^2\right)^{3/2}}",1,"((A*b - a*B)*Sqrt[e*x])/(3*a*b*e*(a + b*x^2)^(3/2)) + ((5*A*b + a*B)*Sqrt[e*x])/(6*a^2*b*e*Sqrt[a + b*x^2]) + ((5*A*b + a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(12*a^(9/4)*b^(5/4)*Sqrt[e]*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{457, 290, 329, 220}"
820,1,377,0,0.2924283,"\int \frac{A+B x^2}{(e x)^{3/2} \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/((e*x)^(3/2)*(a + b*x^2)^(5/2)),x]","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 a^{11/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{11/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{(e x)^{3/2} (7 A b-a B)}{2 a^3 e^3 \sqrt{a+b x^2}}-\frac{(e x)^{3/2} (7 A b-a B)}{3 a^2 e^3 \left(a+b x^2\right)^{3/2}}+\frac{\sqrt{e x} \sqrt{a+b x^2} (7 A b-a B)}{2 a^3 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A}{a e \sqrt{e x} \left(a+b x^2\right)^{3/2}}","\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 a^{11/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{\left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (7 A b-a B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 a^{11/4} b^{3/4} e^{3/2} \sqrt{a+b x^2}}-\frac{(e x)^{3/2} (7 A b-a B)}{2 a^3 e^3 \sqrt{a+b x^2}}-\frac{(e x)^{3/2} (7 A b-a B)}{3 a^2 e^3 \left(a+b x^2\right)^{3/2}}+\frac{\sqrt{e x} \sqrt{a+b x^2} (7 A b-a B)}{2 a^3 \sqrt{b} e^2 \left(\sqrt{a}+\sqrt{b} x\right)}-\frac{2 A}{a e \sqrt{e x} \left(a+b x^2\right)^{3/2}}",1,"(-2*A)/(a*e*Sqrt[e*x]*(a + b*x^2)^(3/2)) - ((7*A*b - a*B)*(e*x)^(3/2))/(3*a^2*e^3*(a + b*x^2)^(3/2)) - ((7*A*b - a*B)*(e*x)^(3/2))/(2*a^3*e^3*Sqrt[a + b*x^2]) + ((7*A*b - a*B)*Sqrt[e*x]*Sqrt[a + b*x^2])/(2*a^3*Sqrt[b]*e^2*(Sqrt[a] + Sqrt[b]*x)) - ((7*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticE[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(2*a^(11/4)*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2]) + ((7*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(4*a^(11/4)*b^(3/4)*e^(3/2)*Sqrt[a + b*x^2])","A",7,6,26,0.2308,1,"{453, 290, 329, 305, 220, 1196}"
821,1,213,0,0.141613,"\int \frac{A+B x^2}{(e x)^{5/2} \left(a+b x^2\right)^{5/2}} \, dx","Int[(A + B*x^2)/((e*x)^(5/2)*(a + b*x^2)^(5/2)),x]","-\frac{5 \sqrt{e x} (3 A b-a B)}{6 a^3 e^3 \sqrt{a+b x^2}}-\frac{\sqrt{e x} (3 A b-a B)}{3 a^2 e^3 \left(a+b x^2\right)^{3/2}}-\frac{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 a^{13/4} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A}{3 a e (e x)^{3/2} \left(a+b x^2\right)^{3/2}}","-\frac{5 \sqrt{e x} (3 A b-a B)}{6 a^3 e^3 \sqrt{a+b x^2}}-\frac{\sqrt{e x} (3 A b-a B)}{3 a^2 e^3 \left(a+b x^2\right)^{3/2}}-\frac{5 \left(\sqrt{a}+\sqrt{b} x\right) \sqrt{\frac{a+b x^2}{\left(\sqrt{a}+\sqrt{b} x\right)^2}} (3 A b-a B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt[4]{a} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 a^{13/4} \sqrt[4]{b} e^{5/2} \sqrt{a+b x^2}}-\frac{2 A}{3 a e (e x)^{3/2} \left(a+b x^2\right)^{3/2}}",1,"(-2*A)/(3*a*e*(e*x)^(3/2)*(a + b*x^2)^(3/2)) - ((3*A*b - a*B)*Sqrt[e*x])/(3*a^2*e^3*(a + b*x^2)^(3/2)) - (5*(3*A*b - a*B)*Sqrt[e*x])/(6*a^3*e^3*Sqrt[a + b*x^2]) - (5*(3*A*b - a*B)*(Sqrt[a] + Sqrt[b]*x)*Sqrt[(a + b*x^2)/(Sqrt[a] + Sqrt[b]*x)^2]*EllipticF[2*ArcTan[(b^(1/4)*Sqrt[e*x])/(a^(1/4)*Sqrt[e])], 1/2])/(12*a^(13/4)*b^(1/4)*e^(5/2)*Sqrt[a + b*x^2])","A",5,4,26,0.1538,1,"{453, 290, 329, 220}"
822,1,288,0,0.2912955,"\int (e x)^{3/2} \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[(e*x)^(3/2)*(a + b*x^2)^2*Sqrt[c + d*x^2],x]","-\frac{2 c^{7/4} e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(11 a^2 d^2+b c (3 b c-10 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{13/4} \sqrt{c+d x^2}}+\frac{2 (e x)^{5/2} \sqrt{c+d x^2} \left(11 a^2 d^2+b c (3 b c-10 a d)\right)}{77 d^2 e}+\frac{4 c e \sqrt{e x} \sqrt{c+d x^2} \left(11 a^2 d^2+b c (3 b c-10 a d)\right)}{231 d^3}-\frac{2 b (e x)^{5/2} \left(c+d x^2\right)^{3/2} (3 b c-10 a d)}{55 d^2 e}+\frac{2 b^2 (e x)^{9/2} \left(c+d x^2\right)^{3/2}}{15 d e^3}","-\frac{2 c^{7/4} e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(11 a^2 d^2+b c (3 b c-10 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{13/4} \sqrt{c+d x^2}}+\frac{2 (e x)^{5/2} \sqrt{c+d x^2} \left(11 a^2 d^2+b c (3 b c-10 a d)\right)}{77 d^2 e}+\frac{4 c e \sqrt{e x} \sqrt{c+d x^2} \left(11 a^2 d^2+b c (3 b c-10 a d)\right)}{231 d^3}-\frac{2 b (e x)^{5/2} \left(c+d x^2\right)^{3/2} (3 b c-10 a d)}{55 d^2 e}+\frac{2 b^2 (e x)^{9/2} \left(c+d x^2\right)^{3/2}}{15 d e^3}",1,"(4*c*(11*a^2*d^2 + b*c*(3*b*c - 10*a*d))*e*Sqrt[e*x]*Sqrt[c + d*x^2])/(231*d^3) + (2*(11*a^2*d^2 + b*c*(3*b*c - 10*a*d))*(e*x)^(5/2)*Sqrt[c + d*x^2])/(77*d^2*e) - (2*b*(3*b*c - 10*a*d)*(e*x)^(5/2)*(c + d*x^2)^(3/2))/(55*d^2*e) + (2*b^2*(e*x)^(9/2)*(c + d*x^2)^(3/2))/(15*d*e^3) - (2*c^(7/4)*(11*a^2*d^2 + b*c*(3*b*c - 10*a*d))*e^(3/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(231*d^(13/4)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{464, 459, 279, 321, 329, 220}"
823,1,425,0,0.4148614,"\int \sqrt{e x} \left(a+b x^2\right)^2 \sqrt{c+d x^2} \, dx","Int[Sqrt[e*x]*(a + b*x^2)^2*Sqrt[c + d*x^2],x]","\frac{2 c^{5/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(39 a^2 d^2+b c (7 b c-26 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{11/4} \sqrt{c+d x^2}}-\frac{4 c^{5/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(39 a^2 d^2+b c (7 b c-26 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{11/4} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \sqrt{c+d x^2} \left(39 a^2 d^2+b c (7 b c-26 a d)\right)}{195 d^2 e}+\frac{4 c \sqrt{e x} \sqrt{c+d x^2} \left(39 a^2 d^2+b c (7 b c-26 a d)\right)}{195 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 b (e x)^{3/2} \left(c+d x^2\right)^{3/2} (7 b c-26 a d)}{117 d^2 e}+\frac{2 b^2 (e x)^{7/2} \left(c+d x^2\right)^{3/2}}{13 d e^3}","\frac{2 c^{5/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(39 a^2 d^2+b c (7 b c-26 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{11/4} \sqrt{c+d x^2}}-\frac{4 c^{5/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(39 a^2 d^2+b c (7 b c-26 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{11/4} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \sqrt{c+d x^2} \left(39 a^2 d^2+b c (7 b c-26 a d)\right)}{195 d^2 e}+\frac{4 c \sqrt{e x} \sqrt{c+d x^2} \left(39 a^2 d^2+b c (7 b c-26 a d)\right)}{195 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 b (e x)^{3/2} \left(c+d x^2\right)^{3/2} (7 b c-26 a d)}{117 d^2 e}+\frac{2 b^2 (e x)^{7/2} \left(c+d x^2\right)^{3/2}}{13 d e^3}",1,"(2*(39*a^2*d^2 + b*c*(7*b*c - 26*a*d))*(e*x)^(3/2)*Sqrt[c + d*x^2])/(195*d^2*e) + (4*c*(39*a^2*d^2 + b*c*(7*b*c - 26*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(195*d^(5/2)*(Sqrt[c] + Sqrt[d]*x)) - (2*b*(7*b*c - 26*a*d)*(e*x)^(3/2)*(c + d*x^2)^(3/2))/(117*d^2*e) + (2*b^2*(e*x)^(7/2)*(c + d*x^2)^(3/2))/(13*d*e^3) - (4*c^(5/4)*(39*a^2*d^2 + b*c*(7*b*c - 26*a*d))*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(195*d^(11/4)*Sqrt[c + d*x^2]) + (2*c^(5/4)*(39*a^2*d^2 + b*c*(7*b*c - 26*a*d))*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(195*d^(11/4)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{464, 459, 279, 329, 305, 220, 1196}"
824,1,244,0,0.203183,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{\sqrt{e x}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/Sqrt[e*x],x]","\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2-22 a b c d+5 b^2 c^2\right)}{231 d^2 e}+\frac{2 c^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-22 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{9/4} \sqrt{e} \sqrt{c+d x^2}}-\frac{2 b \sqrt{e x} \left(c+d x^2\right)^{3/2} (5 b c-22 a d)}{77 d^2 e}+\frac{2 b^2 (e x)^{5/2} \left(c+d x^2\right)^{3/2}}{11 d e^3}","\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2-22 a b c d+5 b^2 c^2\right)}{231 d^2 e}+\frac{2 c^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-22 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{9/4} \sqrt{e} \sqrt{c+d x^2}}-\frac{2 b \sqrt{e x} \left(c+d x^2\right)^{3/2} (5 b c-22 a d)}{77 d^2 e}+\frac{2 b^2 (e x)^{5/2} \left(c+d x^2\right)^{3/2}}{11 d e^3}",1,"(2*(5*b^2*c^2 - 22*a*b*c*d + 77*a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(231*d^2*e) - (2*b*(5*b*c - 22*a*d)*Sqrt[e*x]*(c + d*x^2)^(3/2))/(77*d^2*e) + (2*b^2*(e*x)^(5/2)*(c + d*x^2)^(3/2))/(11*d*e^3) + (2*c^(3/4)*(5*b^2*c^2 - 22*a*b*c*d + 77*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(231*d^(9/4)*Sqrt[e]*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{464, 459, 279, 329, 220}"
825,1,421,0,0.3957734,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{(e x)^{3/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/(e*x)^(3/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{c e \sqrt{e x}}-\frac{4 \sqrt{e x} \sqrt{c+d x^2} \left(b^2 c^2-3 a d (5 a d+2 b c)\right)}{15 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(b^2 c^2-3 a d (5 a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{4 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(b^2 c^2-3 a d (5 a d+2 b c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{2 (e x)^{3/2} \sqrt{c+d x^2} \left(b^2 c^2-3 a d (5 a d+2 b c)\right)}{15 c d e^3}+\frac{2 b^2 (e x)^{3/2} \left(c+d x^2\right)^{3/2}}{9 d e^3}","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{c e \sqrt{e x}}-\frac{4 \sqrt{e x} \sqrt{c+d x^2} \left(b^2 c^2-3 a d (5 a d+2 b c)\right)}{15 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(b^2 c^2-3 a d (5 a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{4 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(b^2 c^2-3 a d (5 a d+2 b c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{2 (e x)^{3/2} \sqrt{c+d x^2} \left(b^2 c^2-3 a d (5 a d+2 b c)\right)}{15 c d e^3}+\frac{2 b^2 (e x)^{3/2} \left(c+d x^2\right)^{3/2}}{9 d e^3}",1,"(-2*(b^2*c^2 - 3*a*d*(2*b*c + 5*a*d))*(e*x)^(3/2)*Sqrt[c + d*x^2])/(15*c*d*e^3) - (4*(b^2*c^2 - 3*a*d*(2*b*c + 5*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(15*d^(3/2)*e^2*(Sqrt[c] + Sqrt[d]*x)) - (2*a^2*(c + d*x^2)^(3/2))/(c*e*Sqrt[e*x]) + (2*b^2*(e*x)^(3/2)*(c + d*x^2)^(3/2))/(9*d*e^3) + (4*c^(1/4)*(b^2*c^2 - 3*a*d*(2*b*c + 5*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2]) - (2*c^(1/4)*(b^2*c^2 - 3*a*d*(2*b*c + 5*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{462, 459, 279, 329, 305, 220, 1196}"
826,1,234,0,0.1905623,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{(e x)^{5/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/(e*x)^(5/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{3 c e (e x)^{3/2}}-\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(b^2 c^2-7 a d (a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{c} d^{5/4} e^{5/2} \sqrt{c+d x^2}}-\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(b^2 c^2-7 a d (a d+2 b c)\right)}{21 c d e^3}+\frac{2 b^2 \sqrt{e x} \left(c+d x^2\right)^{3/2}}{7 d e^3}","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{3 c e (e x)^{3/2}}-\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(b^2 c^2-7 a d (a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{c} d^{5/4} e^{5/2} \sqrt{c+d x^2}}-\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(b^2 c^2-7 a d (a d+2 b c)\right)}{21 c d e^3}+\frac{2 b^2 \sqrt{e x} \left(c+d x^2\right)^{3/2}}{7 d e^3}",1,"(-2*(b^2*c^2 - 7*a*d*(2*b*c + a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(21*c*d*e^3) - (2*a^2*(c + d*x^2)^(3/2))/(3*c*e*(e*x)^(3/2)) + (2*b^2*Sqrt[e*x]*(c + d*x^2)^(3/2))/(7*d*e^3) - (2*(b^2*c^2 - 7*a*d*(2*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(21*c^(1/4)*d^(5/4)*e^(5/2)*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{462, 459, 279, 329, 220}"
827,1,421,0,0.3955674,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{(e x)^{7/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/(e*x)^(7/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{5 c e (e x)^{5/2}}+\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (a d+10 b c)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{4 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (a d+10 b c)+b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \sqrt{c+d x^2} \left(a d (a d+10 b c)+b^2 c^2\right)}{5 c^2 e^5}+\frac{4 \sqrt{e x} \sqrt{c+d x^2} \left(a d (a d+10 b c)+b^2 c^2\right)}{5 c \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 a \left(c+d x^2\right)^{3/2} (a d+10 b c)}{5 c^2 e^3 \sqrt{e x}}","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{5 c e (e x)^{5/2}}+\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (a d+10 b c)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{4 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (a d+10 b c)+b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \sqrt{c+d x^2} \left(a d (a d+10 b c)+b^2 c^2\right)}{5 c^2 e^5}+\frac{4 \sqrt{e x} \sqrt{c+d x^2} \left(a d (a d+10 b c)+b^2 c^2\right)}{5 c \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 a \left(c+d x^2\right)^{3/2} (a d+10 b c)}{5 c^2 e^3 \sqrt{e x}}",1,"(2*(b^2*c^2 + a*d*(10*b*c + a*d))*(e*x)^(3/2)*Sqrt[c + d*x^2])/(5*c^2*e^5) + (4*(b^2*c^2 + a*d*(10*b*c + a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(5*c*Sqrt[d]*e^4*(Sqrt[c] + Sqrt[d]*x)) - (2*a^2*(c + d*x^2)^(3/2))/(5*c*e*(e*x)^(5/2)) - (2*a*(10*b*c + a*d)*(c + d*x^2)^(3/2))/(5*c^2*e^3*Sqrt[e*x]) - (4*(b^2*c^2 + a*d*(10*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(3/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2]) + (2*(b^2*c^2 + a*d*(10*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(3/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{462, 453, 279, 329, 305, 220, 1196}"
828,1,210,0,0.1707689,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^{9/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^(9/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{7 c x^{7/2}}+\frac{2}{21} \sqrt{x} \sqrt{c+d x^2} \left(\frac{a d (14 b c-a d)}{c^2}+7 b^2\right)+\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (14 b c-a d)+7 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt[4]{d} \sqrt{c+d x^2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (14 b c-a d)}{21 c^2 x^{3/2}}","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{7 c x^{7/2}}+\frac{2 \sqrt{x} \sqrt{c+d x^2} \left(a d (14 b c-a d)+7 b^2 c^2\right)}{21 c^2}+\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (14 b c-a d)+7 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt[4]{d} \sqrt{c+d x^2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (14 b c-a d)}{21 c^2 x^{3/2}}",1,"(2*(7*b^2 + (a*d*(14*b*c - a*d))/c^2)*Sqrt[x]*Sqrt[c + d*x^2])/21 - (2*a^2*(c + d*x^2)^(3/2))/(7*c*x^(7/2)) - (2*a*(14*b*c - a*d)*(c + d*x^2)^(3/2))/(21*c^2*x^(3/2)) + (2*(7*b^2*c^2 + a*d*(14*b*c - a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[x])/c^(1/4)], 1/2])/(21*c^(5/4)*d^(1/4)*Sqrt[c + d*x^2])","A",5,5,26,0.1923,1,"{462, 453, 279, 329, 220}"
829,1,383,0,0.323593,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^{11/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^(11/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{9 c x^{9/2}}-\frac{2 \sqrt{c+d x^2} \left(\frac{a d (6 b c-a d)}{c^2}+15 b^2\right)}{15 \sqrt{x}}+\frac{4 \sqrt{d} \sqrt{x} \sqrt{c+d x^2} \left(a d (6 b c-a d)+15 b^2 c^2\right)}{15 c^2 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{2 \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (6 b c-a d)+15 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{c+d x^2}}-\frac{4 \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (6 b c-a d)+15 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{c+d x^2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (6 b c-a d)}{15 c^2 x^{5/2}}","-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{9 c x^{9/2}}-\frac{2 \sqrt{c+d x^2} \left(a d (6 b c-a d)+15 b^2 c^2\right)}{15 c^2 \sqrt{x}}+\frac{4 \sqrt{d} \sqrt{x} \sqrt{c+d x^2} \left(a d (6 b c-a d)+15 b^2 c^2\right)}{15 c^2 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{2 \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (6 b c-a d)+15 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{c+d x^2}}-\frac{4 \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (6 b c-a d)+15 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{c+d x^2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (6 b c-a d)}{15 c^2 x^{5/2}}",1,"(-2*(15*b^2 + (a*d*(6*b*c - a*d))/c^2)*Sqrt[c + d*x^2])/(15*Sqrt[x]) + (4*Sqrt[d]*(15*b^2*c^2 + a*d*(6*b*c - a*d))*Sqrt[x]*Sqrt[c + d*x^2])/(15*c^2*(Sqrt[c] + Sqrt[d]*x)) - (2*a^2*(c + d*x^2)^(3/2))/(9*c*x^(9/2)) - (2*a*(6*b*c - a*d)*(c + d*x^2)^(3/2))/(15*c^2*x^(5/2)) - (4*d^(1/4)*(15*b^2*c^2 + a*d*(6*b*c - a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[x])/c^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[c + d*x^2]) + (2*d^(1/4)*(15*b^2*c^2 + a*d*(6*b*c - a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[x])/c^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[c + d*x^2])","A",7,7,26,0.2692,1,"{462, 453, 277, 329, 305, 220, 1196}"
830,1,213,0,0.1895664,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^{13/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^(13/2),x]","\frac{2 d^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-22 a b c d+77 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{c+d x^2}}-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{11 c x^{11/2}}-\frac{2 \sqrt{c+d x^2} \left(77 b^2-\frac{a d (22 b c-5 a d)}{c^2}\right)}{231 x^{3/2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (22 b c-5 a d)}{77 c^2 x^{7/2}}","-\frac{2 \sqrt{c+d x^2} \left(5 a^2 d^2-22 a b c d+77 b^2 c^2\right)}{231 c^2 x^{3/2}}+\frac{2 d^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-22 a b c d+77 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{c+d x^2}}-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{11 c x^{11/2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (22 b c-5 a d)}{77 c^2 x^{7/2}}",1,"(-2*(77*b^2 - (a*d*(22*b*c - 5*a*d))/c^2)*Sqrt[c + d*x^2])/(231*x^(3/2)) - (2*a^2*(c + d*x^2)^(3/2))/(11*c*x^(11/2)) - (2*a*(22*b*c - 5*a*d)*(c + d*x^2)^(3/2))/(77*c^2*x^(7/2)) + (2*d^(3/4)*(77*b^2*c^2 - 22*a*b*c*d + 5*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[x])/c^(1/4)], 1/2])/(231*c^(9/4)*Sqrt[c + d*x^2])","A",5,5,26,0.1923,1,"{462, 453, 277, 329, 220}"
831,1,437,0,0.3929789,"\int \frac{\left(a+b x^2\right)^2 \sqrt{c+d x^2}}{x^{15/2}} \, dx","Int[((a + b*x^2)^2*Sqrt[c + d*x^2])/x^(15/2),x]","-\frac{4 d \sqrt{c+d x^2} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right)}{195 c^3 \sqrt{x}}+\frac{4 d^{3/2} \sqrt{x} \sqrt{c+d x^2} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right)}{195 c^3 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{2 d^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{c+d x^2}}-\frac{4 d^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{c+d x^2}}-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{13 c x^{13/2}}-\frac{2 \sqrt{c+d x^2} \left(39 b^2-\frac{a d (26 b c-7 a d)}{c^2}\right)}{195 x^{5/2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (26 b c-7 a d)}{117 c^2 x^{9/2}}","-\frac{4 d \sqrt{c+d x^2} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right)}{195 c^3 \sqrt{x}}+\frac{4 d^{3/2} \sqrt{x} \sqrt{c+d x^2} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right)}{195 c^3 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 \sqrt{c+d x^2} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right)}{195 c^2 x^{5/2}}+\frac{2 d^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{c+d x^2}}-\frac{4 d^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-26 a b c d+39 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{x}}{\sqrt[4]{c}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{c+d x^2}}-\frac{2 a^2 \left(c+d x^2\right)^{3/2}}{13 c x^{13/2}}-\frac{2 a \left(c+d x^2\right)^{3/2} (26 b c-7 a d)}{117 c^2 x^{9/2}}",1,"(-2*(39*b^2 - (a*d*(26*b*c - 7*a*d))/c^2)*Sqrt[c + d*x^2])/(195*x^(5/2)) - (4*d*(39*b^2*c^2 - 26*a*b*c*d + 7*a^2*d^2)*Sqrt[c + d*x^2])/(195*c^3*Sqrt[x]) + (4*d^(3/2)*(39*b^2*c^2 - 26*a*b*c*d + 7*a^2*d^2)*Sqrt[x]*Sqrt[c + d*x^2])/(195*c^3*(Sqrt[c] + Sqrt[d]*x)) - (2*a^2*(c + d*x^2)^(3/2))/(13*c*x^(13/2)) - (2*a*(26*b*c - 7*a*d)*(c + d*x^2)^(3/2))/(117*c^2*x^(9/2)) - (4*d^(5/4)*(39*b^2*c^2 - 26*a*b*c*d + 7*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[x])/c^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[c + d*x^2]) + (2*d^(5/4)*(39*b^2*c^2 - 26*a*b*c*d + 7*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[x])/c^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[c + d*x^2])","A",8,8,26,0.3077,1,"{462, 453, 277, 325, 329, 305, 220, 1196}"
832,1,530,0,0.5623246,"\int (e x)^{5/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[(e*x)^(5/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","-\frac{8 c^3 e^2 \sqrt{e x} \sqrt{c+d x^2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{3315 d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{4 c^{13/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(51 a^2 d^2+b c (11 b c-42 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{15/4} \sqrt{c+d x^2}}+\frac{8 c^{13/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(51 a^2 d^2+b c (11 b c-42 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{15/4} \sqrt{c+d x^2}}+\frac{8 c^2 e (e x)^{3/2} \sqrt{c+d x^2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{9945 d^3}+\frac{2 (e x)^{7/2} \left(c+d x^2\right)^{3/2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{663 d^2 e}+\frac{4 c (e x)^{7/2} \sqrt{c+d x^2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{1989 d^2 e}-\frac{2 b (e x)^{7/2} \left(c+d x^2\right)^{5/2} (11 b c-42 a d)}{357 d^2 e}+\frac{2 b^2 (e x)^{11/2} \left(c+d x^2\right)^{5/2}}{21 d e^3}","-\frac{8 c^3 e^2 \sqrt{e x} \sqrt{c+d x^2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{3315 d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{4 c^{13/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(51 a^2 d^2+b c (11 b c-42 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{15/4} \sqrt{c+d x^2}}+\frac{8 c^{13/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(51 a^2 d^2+b c (11 b c-42 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{15/4} \sqrt{c+d x^2}}+\frac{8 c^2 e (e x)^{3/2} \sqrt{c+d x^2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{9945 d^3}+\frac{2 (e x)^{7/2} \left(c+d x^2\right)^{3/2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{663 d^2 e}+\frac{4 c (e x)^{7/2} \sqrt{c+d x^2} \left(51 a^2 d^2+b c (11 b c-42 a d)\right)}{1989 d^2 e}-\frac{2 b (e x)^{7/2} \left(c+d x^2\right)^{5/2} (11 b c-42 a d)}{357 d^2 e}+\frac{2 b^2 (e x)^{11/2} \left(c+d x^2\right)^{5/2}}{21 d e^3}",1,"(8*c^2*(51*a^2*d^2 + b*c*(11*b*c - 42*a*d))*e*(e*x)^(3/2)*Sqrt[c + d*x^2])/(9945*d^3) + (4*c*(51*a^2*d^2 + b*c*(11*b*c - 42*a*d))*(e*x)^(7/2)*Sqrt[c + d*x^2])/(1989*d^2*e) - (8*c^3*(51*a^2*d^2 + b*c*(11*b*c - 42*a*d))*e^2*Sqrt[e*x]*Sqrt[c + d*x^2])/(3315*d^(7/2)*(Sqrt[c] + Sqrt[d]*x)) + (2*(51*a^2*d^2 + b*c*(11*b*c - 42*a*d))*(e*x)^(7/2)*(c + d*x^2)^(3/2))/(663*d^2*e) - (2*b*(11*b*c - 42*a*d)*(e*x)^(7/2)*(c + d*x^2)^(5/2))/(357*d^2*e) + (2*b^2*(e*x)^(11/2)*(c + d*x^2)^(5/2))/(21*d*e^3) + (8*c^(13/4)*(51*a^2*d^2 + b*c*(11*b*c - 42*a*d))*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(3315*d^(15/4)*Sqrt[c + d*x^2]) - (4*c^(13/4)*(51*a^2*d^2 + b*c*(11*b*c - 42*a*d))*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(3315*d^(15/4)*Sqrt[c + d*x^2])","A",9,8,28,0.2857,1,"{464, 459, 279, 321, 329, 305, 220, 1196}"
833,1,340,0,0.3232889,"\int (e x)^{3/2} \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[(e*x)^(3/2)*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","-\frac{4 c^{11/4} e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(57 a^2 d^2+b c (9 b c-38 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{4389 d^{13/4} \sqrt{c+d x^2}}+\frac{8 c^2 e \sqrt{e x} \sqrt{c+d x^2} \left(57 a^2 d^2+b c (9 b c-38 a d)\right)}{4389 d^3}+\frac{2 (e x)^{5/2} \left(c+d x^2\right)^{3/2} \left(57 a^2 d^2+b c (9 b c-38 a d)\right)}{627 d^2 e}+\frac{4 c (e x)^{5/2} \sqrt{c+d x^2} \left(57 a^2 d^2+b c (9 b c-38 a d)\right)}{1463 d^2 e}-\frac{2 b (e x)^{5/2} \left(c+d x^2\right)^{5/2} (9 b c-38 a d)}{285 d^2 e}+\frac{2 b^2 (e x)^{9/2} \left(c+d x^2\right)^{5/2}}{19 d e^3}","-\frac{4 c^{11/4} e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(57 a^2 d^2+b c (9 b c-38 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{4389 d^{13/4} \sqrt{c+d x^2}}+\frac{8 c^2 e \sqrt{e x} \sqrt{c+d x^2} \left(57 a^2 d^2+b c (9 b c-38 a d)\right)}{4389 d^3}+\frac{2 (e x)^{5/2} \left(c+d x^2\right)^{3/2} \left(57 a^2 d^2+b c (9 b c-38 a d)\right)}{627 d^2 e}+\frac{4 c (e x)^{5/2} \sqrt{c+d x^2} \left(57 a^2 d^2+b c (9 b c-38 a d)\right)}{1463 d^2 e}-\frac{2 b (e x)^{5/2} \left(c+d x^2\right)^{5/2} (9 b c-38 a d)}{285 d^2 e}+\frac{2 b^2 (e x)^{9/2} \left(c+d x^2\right)^{5/2}}{19 d e^3}",1,"(8*c^2*(57*a^2*d^2 + b*c*(9*b*c - 38*a*d))*e*Sqrt[e*x]*Sqrt[c + d*x^2])/(4389*d^3) + (4*c*(57*a^2*d^2 + b*c*(9*b*c - 38*a*d))*(e*x)^(5/2)*Sqrt[c + d*x^2])/(1463*d^2*e) + (2*(57*a^2*d^2 + b*c*(9*b*c - 38*a*d))*(e*x)^(5/2)*(c + d*x^2)^(3/2))/(627*d^2*e) - (2*b*(9*b*c - 38*a*d)*(e*x)^(5/2)*(c + d*x^2)^(5/2))/(285*d^2*e) + (2*b^2*(e*x)^(9/2)*(c + d*x^2)^(5/2))/(19*d*e^3) - (4*c^(11/4)*(57*a^2*d^2 + b*c*(9*b*c - 38*a*d))*e^(3/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(4389*d^(13/4)*Sqrt[c + d*x^2])","A",7,6,28,0.2143,1,"{464, 459, 279, 321, 329, 220}"
834,1,482,0,0.4686456,"\int \sqrt{e x} \left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2} \, dx","Int[Sqrt[e*x]*(a + b*x^2)^2*(c + d*x^2)^(3/2),x]","\frac{8 c^2 \sqrt{e x} \sqrt{c+d x^2} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right)}{3315 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{4 c^{9/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{11/4} \sqrt{c+d x^2}}-\frac{8 c^{9/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{11/4} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \left(c+d x^2\right)^{3/2} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right)}{1989 d^2 e}+\frac{4 c (e x)^{3/2} \sqrt{c+d x^2} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right)}{3315 d^2 e}-\frac{2 b (e x)^{3/2} \left(c+d x^2\right)^{5/2} (7 b c-34 a d)}{221 d^2 e}+\frac{2 b^2 (e x)^{7/2} \left(c+d x^2\right)^{5/2}}{17 d e^3}","\frac{8 c^2 \sqrt{e x} \sqrt{c+d x^2} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right)}{3315 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{4 c^{9/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{11/4} \sqrt{c+d x^2}}-\frac{8 c^{9/4} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3315 d^{11/4} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \left(c+d x^2\right)^{3/2} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right)}{1989 d^2 e}+\frac{4 c (e x)^{3/2} \sqrt{c+d x^2} \left(221 a^2 d^2+3 b c (7 b c-34 a d)\right)}{3315 d^2 e}-\frac{2 b (e x)^{3/2} \left(c+d x^2\right)^{5/2} (7 b c-34 a d)}{221 d^2 e}+\frac{2 b^2 (e x)^{7/2} \left(c+d x^2\right)^{5/2}}{17 d e^3}",1,"(4*c*(221*a^2*d^2 + 3*b*c*(7*b*c - 34*a*d))*(e*x)^(3/2)*Sqrt[c + d*x^2])/(3315*d^2*e) + (8*c^2*(221*a^2*d^2 + 3*b*c*(7*b*c - 34*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(3315*d^(5/2)*(Sqrt[c] + Sqrt[d]*x)) + (2*(221*a^2*d^2 + 3*b*c*(7*b*c - 34*a*d))*(e*x)^(3/2)*(c + d*x^2)^(3/2))/(1989*d^2*e) - (2*b*(7*b*c - 34*a*d)*(e*x)^(3/2)*(c + d*x^2)^(5/2))/(221*d^2*e) + (2*b^2*(e*x)^(7/2)*(c + d*x^2)^(5/2))/(17*d*e^3) - (8*c^(9/4)*(221*a^2*d^2 + 3*b*c*(7*b*c - 34*a*d))*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(3315*d^(11/4)*Sqrt[c + d*x^2]) + (4*c^(9/4)*(221*a^2*d^2 + 3*b*c*(7*b*c - 34*a*d))*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(3315*d^(11/4)*Sqrt[c + d*x^2])","A",8,7,28,0.2500,1,"{464, 459, 279, 329, 305, 220, 1196}"
835,1,286,0,0.2668176,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{\sqrt{e x}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/Sqrt[e*x],x]","\frac{4 c^{7/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(33 a^2 d^2+b c (b c-6 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{9/4} \sqrt{e} \sqrt{c+d x^2}}+\frac{2 \sqrt{e x} \left(c+d x^2\right)^{3/2} \left(33 a^2 d^2+b c (b c-6 a d)\right)}{231 d^2 e}+\frac{4 c \sqrt{e x} \sqrt{c+d x^2} \left(33 a^2 d^2+b c (b c-6 a d)\right)}{231 d^2 e}-\frac{2 b \sqrt{e x} \left(c+d x^2\right)^{5/2} (b c-6 a d)}{33 d^2 e}+\frac{2 b^2 (e x)^{5/2} \left(c+d x^2\right)^{5/2}}{15 d e^3}","\frac{4 c^{7/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(33 a^2 d^2+b c (b c-6 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{9/4} \sqrt{e} \sqrt{c+d x^2}}+\frac{2 \sqrt{e x} \left(c+d x^2\right)^{3/2} \left(33 a^2 d^2+b c (b c-6 a d)\right)}{231 d^2 e}+\frac{4 c \sqrt{e x} \sqrt{c+d x^2} \left(33 a^2 d^2+b c (b c-6 a d)\right)}{231 d^2 e}-\frac{2 b \sqrt{e x} \left(c+d x^2\right)^{5/2} (b c-6 a d)}{33 d^2 e}+\frac{2 b^2 (e x)^{5/2} \left(c+d x^2\right)^{5/2}}{15 d e^3}",1,"(4*c*(33*a^2*d^2 + b*c*(b*c - 6*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(231*d^2*e) + (2*(33*a^2*d^2 + b*c*(b*c - 6*a*d))*Sqrt[e*x]*(c + d*x^2)^(3/2))/(231*d^2*e) - (2*b*(b*c - 6*a*d)*Sqrt[e*x]*(c + d*x^2)^(5/2))/(33*d^2*e) + (2*b^2*(e*x)^(5/2)*(c + d*x^2)^(5/2))/(15*d*e^3) + (4*c^(7/4)*(33*a^2*d^2 + b*c*(b*c - 6*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(231*d^(9/4)*Sqrt[e]*Sqrt[c + d*x^2])","A",6,5,28,0.1786,1,"{464, 459, 279, 329, 220}"
836,1,476,0,0.4537055,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{(e x)^{3/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(3/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{5/2}}{c e \sqrt{e x}}-\frac{8 c \sqrt{e x} \sqrt{c+d x^2} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right)}{195 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{4 c^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{8 c^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{2 (e x)^{3/2} \left(c+d x^2\right)^{3/2} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right)}{117 c d e^3}-\frac{4 (e x)^{3/2} \sqrt{c+d x^2} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right)}{195 d e^3}+\frac{2 b^2 (e x)^{3/2} \left(c+d x^2\right)^{5/2}}{13 d e^3}","-\frac{2 a^2 \left(c+d x^2\right)^{5/2}}{c e \sqrt{e x}}-\frac{8 c \sqrt{e x} \sqrt{c+d x^2} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right)}{195 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{4 c^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{8 c^{5/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{2 (e x)^{3/2} \left(c+d x^2\right)^{3/2} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right)}{117 c d e^3}-\frac{4 (e x)^{3/2} \sqrt{c+d x^2} \left(3 b^2 c^2-13 a d (9 a d+2 b c)\right)}{195 d e^3}+\frac{2 b^2 (e x)^{3/2} \left(c+d x^2\right)^{5/2}}{13 d e^3}",1,"(-4*(3*b^2*c^2 - 13*a*d*(2*b*c + 9*a*d))*(e*x)^(3/2)*Sqrt[c + d*x^2])/(195*d*e^3) - (8*c*(3*b^2*c^2 - 13*a*d*(2*b*c + 9*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(195*d^(3/2)*e^2*(Sqrt[c] + Sqrt[d]*x)) - (2*(3*b^2*c^2 - 13*a*d*(2*b*c + 9*a*d))*(e*x)^(3/2)*(c + d*x^2)^(3/2))/(117*c*d*e^3) - (2*a^2*(c + d*x^2)^(5/2))/(c*e*Sqrt[e*x]) + (2*b^2*(e*x)^(3/2)*(c + d*x^2)^(5/2))/(13*d*e^3) + (8*c^(5/4)*(3*b^2*c^2 - 13*a*d*(2*b*c + 9*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(195*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2]) - (4*c^(5/4)*(3*b^2*c^2 - 13*a*d*(2*b*c + 9*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(195*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2])","A",8,7,28,0.2500,1,"{462, 459, 279, 329, 305, 220, 1196}"
837,1,288,0,0.2416528,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{(e x)^{5/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(5/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{5/2}}{3 c e (e x)^{3/2}}-\frac{4 c^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-11 a d (7 a d+6 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{5/4} e^{5/2} \sqrt{c+d x^2}}-\frac{2 \sqrt{e x} \left(c+d x^2\right)^{3/2} \left(3 b^2 c^2-11 a d (7 a d+6 b c)\right)}{231 c d e^3}-\frac{4 \sqrt{e x} \sqrt{c+d x^2} \left(3 b^2 c^2-11 a d (7 a d+6 b c)\right)}{231 d e^3}+\frac{2 b^2 \sqrt{e x} \left(c+d x^2\right)^{5/2}}{11 d e^3}","-\frac{2 a^2 \left(c+d x^2\right)^{5/2}}{3 c e (e x)^{3/2}}-\frac{4 c^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-11 a d (7 a d+6 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{5/4} e^{5/2} \sqrt{c+d x^2}}-\frac{2 \sqrt{e x} \left(c+d x^2\right)^{3/2} \left(3 b^2 c^2-11 a d (7 a d+6 b c)\right)}{231 c d e^3}-\frac{4 \sqrt{e x} \sqrt{c+d x^2} \left(3 b^2 c^2-11 a d (7 a d+6 b c)\right)}{231 d e^3}+\frac{2 b^2 \sqrt{e x} \left(c+d x^2\right)^{5/2}}{11 d e^3}",1,"(-4*(3*b^2*c^2 - 11*a*d*(6*b*c + 7*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(231*d*e^3) - (2*(3*b^2*c^2 - 11*a*d*(6*b*c + 7*a*d))*Sqrt[e*x]*(c + d*x^2)^(3/2))/(231*c*d*e^3) - (2*a^2*(c + d*x^2)^(5/2))/(3*c*e*(e*x)^(3/2)) + (2*b^2*Sqrt[e*x]*(c + d*x^2)^(5/2))/(11*d*e^3) - (4*c^(3/4)*(3*b^2*c^2 - 11*a*d*(6*b*c + 7*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(231*d^(5/4)*e^(5/2)*Sqrt[c + d*x^2])","A",6,5,28,0.1786,1,"{462, 459, 279, 329, 220}"
838,1,468,0,0.4446679,"\int \frac{\left(a+b x^2\right)^2 \left(c+d x^2\right)^{3/2}}{(e x)^{7/2}} \, dx","Int[((a + b*x^2)^2*(c + d*x^2)^(3/2))/(e*x)^(7/2),x]","-\frac{2 a^2 \left(c+d x^2\right)^{5/2}}{5 c e (e x)^{5/2}}+\frac{4 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(9 a d (a d+2 b c)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{8 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(9 a d (a d+2 b c)+b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \left(c+d x^2\right)^{3/2} \left(9 a d (a d+2 b c)+b^2 c^2\right)}{9 c^2 e^5}+\frac{4 (e x)^{3/2} \sqrt{c+d x^2} \left(9 a d (a d+2 b c)+b^2 c^2\right)}{15 c e^5}+\frac{8 \sqrt{e x} \sqrt{c+d x^2} \left(9 a d (a d+2 b c)+b^2 c^2\right)}{15 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 a \left(c+d x^2\right)^{5/2} (a d+2 b c)}{c^2 e^3 \sqrt{e x}}","-\frac{2 a^2 \left(c+d x^2\right)^{5/2}}{5 c e (e x)^{5/2}}+\frac{4 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(9 a d (a d+2 b c)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{8 \sqrt[4]{c} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(9 a d (a d+2 b c)+b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{2 (e x)^{3/2} \left(c+d x^2\right)^{3/2} \left(9 a d (a d+2 b c)+b^2 c^2\right)}{9 c^2 e^5}+\frac{4 (e x)^{3/2} \sqrt{c+d x^2} \left(9 a d (a d+2 b c)+b^2 c^2\right)}{15 c e^5}+\frac{8 \sqrt{e x} \sqrt{c+d x^2} \left(9 a d (a d+2 b c)+b^2 c^2\right)}{15 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{2 a \left(c+d x^2\right)^{5/2} (a d+2 b c)}{c^2 e^3 \sqrt{e x}}",1,"(4*(b^2*c^2 + 9*a*d*(2*b*c + a*d))*(e*x)^(3/2)*Sqrt[c + d*x^2])/(15*c*e^5) + (8*(b^2*c^2 + 9*a*d*(2*b*c + a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(15*Sqrt[d]*e^4*(Sqrt[c] + Sqrt[d]*x)) + (2*(b^2*c^2 + 9*a*d*(2*b*c + a*d))*(e*x)^(3/2)*(c + d*x^2)^(3/2))/(9*c^2*e^5) - (2*a^2*(c + d*x^2)^(5/2))/(5*c*e*(e*x)^(5/2)) - (2*a*(2*b*c + a*d)*(c + d*x^2)^(5/2))/(c^2*e^3*Sqrt[e*x]) - (8*c^(1/4)*(b^2*c^2 + 9*a*d*(2*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2]) + (4*c^(1/4)*(b^2*c^2 + 9*a*d*(2*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2])","A",8,7,28,0.2500,1,"{462, 453, 279, 329, 305, 220, 1196}"
839,1,430,0,0.4055693,"\int \frac{(e x)^{5/2} \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[((e*x)^(5/2)*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","-\frac{c^{5/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{15/4} \sqrt{c+d x^2}}+\frac{2 c^{5/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{15/4} \sqrt{c+d x^2}}-\frac{2 c e^2 \sqrt{e x} \sqrt{c+d x^2} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right)}{195 d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{2 e (e x)^{3/2} \sqrt{c+d x^2} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right)}{585 d^3}-\frac{2 b (e x)^{7/2} \sqrt{c+d x^2} (11 b c-26 a d)}{117 d^2 e}+\frac{2 b^2 (e x)^{11/2} \sqrt{c+d x^2}}{13 d e^3}","-\frac{c^{5/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{15/4} \sqrt{c+d x^2}}+\frac{2 c^{5/4} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{195 d^{15/4} \sqrt{c+d x^2}}-\frac{2 c e^2 \sqrt{e x} \sqrt{c+d x^2} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right)}{195 d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{2 e (e x)^{3/2} \sqrt{c+d x^2} \left(117 a^2 d^2+7 b c (11 b c-26 a d)\right)}{585 d^3}-\frac{2 b (e x)^{7/2} \sqrt{c+d x^2} (11 b c-26 a d)}{117 d^2 e}+\frac{2 b^2 (e x)^{11/2} \sqrt{c+d x^2}}{13 d e^3}",1,"(2*(117*a^2*d^2 + 7*b*c*(11*b*c - 26*a*d))*e*(e*x)^(3/2)*Sqrt[c + d*x^2])/(585*d^3) - (2*b*(11*b*c - 26*a*d)*(e*x)^(7/2)*Sqrt[c + d*x^2])/(117*d^2*e) + (2*b^2*(e*x)^(11/2)*Sqrt[c + d*x^2])/(13*d*e^3) - (2*c*(117*a^2*d^2 + 7*b*c*(11*b*c - 26*a*d))*e^2*Sqrt[e*x]*Sqrt[c + d*x^2])/(195*d^(7/2)*(Sqrt[c] + Sqrt[d]*x)) + (2*c^(5/4)*(117*a^2*d^2 + 7*b*c*(11*b*c - 26*a*d))*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(195*d^(15/4)*Sqrt[c + d*x^2]) - (c^(5/4)*(117*a^2*d^2 + 7*b*c*(11*b*c - 26*a*d))*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(195*d^(15/4)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{464, 459, 321, 329, 305, 220, 1196}"
840,1,240,0,0.2191032,"\int \frac{(e x)^{3/2} \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[((e*x)^(3/2)*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","-\frac{c^{3/4} e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2+5 b c (9 b c-22 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{13/4} \sqrt{c+d x^2}}+\frac{2 e \sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2+5 b c (9 b c-22 a d)\right)}{231 d^3}-\frac{2 b (e x)^{5/2} \sqrt{c+d x^2} (9 b c-22 a d)}{77 d^2 e}+\frac{2 b^2 (e x)^{9/2} \sqrt{c+d x^2}}{11 d e^3}","-\frac{c^{3/4} e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2+5 b c (9 b c-22 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 d^{13/4} \sqrt{c+d x^2}}+\frac{2 e \sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2+5 b c (9 b c-22 a d)\right)}{231 d^3}-\frac{2 b (e x)^{5/2} \sqrt{c+d x^2} (9 b c-22 a d)}{77 d^2 e}+\frac{2 b^2 (e x)^{9/2} \sqrt{c+d x^2}}{11 d e^3}",1,"(2*(77*a^2*d^2 + 5*b*c*(9*b*c - 22*a*d))*e*Sqrt[e*x]*Sqrt[c + d*x^2])/(231*d^3) - (2*b*(9*b*c - 22*a*d)*(e*x)^(5/2)*Sqrt[c + d*x^2])/(77*d^2*e) + (2*b^2*(e*x)^(9/2)*Sqrt[c + d*x^2])/(11*d*e^3) - (c^(3/4)*(77*a^2*d^2 + 5*b*c*(9*b*c - 22*a*d))*e^(3/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(231*d^(13/4)*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{464, 459, 321, 329, 220}"
841,1,375,0,0.3556253,"\int \frac{\sqrt{e x} \left(a+b x^2\right)^2}{\sqrt{c+d x^2}} \, dx","Int[(Sqrt[e*x]*(a + b*x^2)^2)/Sqrt[c + d*x^2],x]","\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(15 a^2 d^2+b c (7 b c-18 a d)\right)}{15 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt[4]{c} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(15 a^2 d^2+b c (7 b c-18 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{11/4} \sqrt{c+d x^2}}-\frac{2 \sqrt[4]{c} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(15 a^2 d^2+b c (7 b c-18 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{11/4} \sqrt{c+d x^2}}-\frac{2 b (e x)^{3/2} \sqrt{c+d x^2} (7 b c-18 a d)}{45 d^2 e}+\frac{2 b^2 (e x)^{7/2} \sqrt{c+d x^2}}{9 d e^3}","\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(15 a^2 d^2+b c (7 b c-18 a d)\right)}{15 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt[4]{c} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(15 a^2 d^2+b c (7 b c-18 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{11/4} \sqrt{c+d x^2}}-\frac{2 \sqrt[4]{c} \sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(15 a^2 d^2+b c (7 b c-18 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{11/4} \sqrt{c+d x^2}}-\frac{2 b (e x)^{3/2} \sqrt{c+d x^2} (7 b c-18 a d)}{45 d^2 e}+\frac{2 b^2 (e x)^{7/2} \sqrt{c+d x^2}}{9 d e^3}",1,"(-2*b*(7*b*c - 18*a*d)*(e*x)^(3/2)*Sqrt[c + d*x^2])/(45*d^2*e) + (2*b^2*(e*x)^(7/2)*Sqrt[c + d*x^2])/(9*d*e^3) + (2*(15*a^2*d^2 + b*c*(7*b*c - 18*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(15*d^(5/2)*(Sqrt[c] + Sqrt[d]*x)) - (2*c^(1/4)*(15*a^2*d^2 + b*c*(7*b*c - 18*a*d))*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(11/4)*Sqrt[c + d*x^2]) + (c^(1/4)*(15*a^2*d^2 + b*c*(7*b*c - 18*a*d))*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(11/4)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{464, 459, 329, 305, 220, 1196}"
842,1,193,0,0.1561236,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{e x} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/(Sqrt[e*x]*Sqrt[c + d*x^2]),x]","\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(21 a^2 d^2-14 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{c} d^{9/4} \sqrt{e} \sqrt{c+d x^2}}-\frac{2 b \sqrt{e x} \sqrt{c+d x^2} (5 b c-14 a d)}{21 d^2 e}+\frac{2 b^2 (e x)^{5/2} \sqrt{c+d x^2}}{7 d e^3}","\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(21 a^2 d^2-14 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{c} d^{9/4} \sqrt{e} \sqrt{c+d x^2}}-\frac{2 b \sqrt{e x} \sqrt{c+d x^2} (5 b c-14 a d)}{21 d^2 e}+\frac{2 b^2 (e x)^{5/2} \sqrt{c+d x^2}}{7 d e^3}",1,"(-2*b*(5*b*c - 14*a*d)*Sqrt[e*x]*Sqrt[c + d*x^2])/(21*d^2*e) + (2*b^2*(e*x)^(5/2)*Sqrt[c + d*x^2])/(7*d*e^3) + ((5*b^2*c^2 - 14*a*b*c*d + 21*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(21*c^(1/4)*d^(9/4)*Sqrt[e]*Sqrt[c + d*x^2])","A",4,4,28,0.1429,1,"{464, 459, 329, 220}"
843,1,372,0,0.3402673,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{3/2} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(3/2)*Sqrt[c + d*x^2]),x]","-\frac{2 a^2 \sqrt{c+d x^2}}{c e \sqrt{e x}}-\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(3 b^2 c^2-5 a d (a d+2 b c)\right)}{5 c d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-5 a d (a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-5 a d (a d+2 b c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{3/2} \sqrt{c+d x^2}}{5 d e^3}","-\frac{2 a^2 \sqrt{c+d x^2}}{c e \sqrt{e x}}-\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(3 b^2 c^2-5 a d (a d+2 b c)\right)}{5 c d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-5 a d (a d+2 b c)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 b^2 c^2-5 a d (a d+2 b c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{3/2} \sqrt{c+d x^2}}{5 d e^3}",1,"(-2*a^2*Sqrt[c + d*x^2])/(c*e*Sqrt[e*x]) + (2*b^2*(e*x)^(3/2)*Sqrt[c + d*x^2])/(5*d*e^3) - (2*(3*b^2*c^2 - 5*a*d*(2*b*c + a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(5*c*d^(3/2)*e^2*(Sqrt[c] + Sqrt[d]*x)) + (2*(3*b^2*c^2 - 5*a*d*(2*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(3/4)*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2]) - ((3*b^2*c^2 - 5*a*d*(2*b*c + a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(3/4)*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{462, 459, 329, 305, 220, 1196}"
844,1,184,0,0.1389262,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{5/2} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(5/2)*Sqrt[c + d*x^2]),x]","-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a^2 d^2-6 a b c d+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 c^{5/4} d^{5/4} e^{5/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{3 c e (e x)^{3/2}}+\frac{2 b^2 \sqrt{e x} \sqrt{c+d x^2}}{3 d e^3}","-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a^2 d^2-6 a b c d+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{3 c^{5/4} d^{5/4} e^{5/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{3 c e (e x)^{3/2}}+\frac{2 b^2 \sqrt{e x} \sqrt{c+d x^2}}{3 d e^3}",1,"(-2*a^2*Sqrt[c + d*x^2])/(3*c*e*(e*x)^(3/2)) + (2*b^2*Sqrt[e*x]*Sqrt[c + d*x^2])/(3*d*e^3) - ((b^2*c^2 - 6*a*b*c*d + a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(3*c^(5/4)*d^(5/4)*e^(5/2)*Sqrt[c + d*x^2])","A",4,4,28,0.1429,1,"{462, 459, 329, 220}"
845,1,387,0,0.3458411,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{7/2} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(7/2)*Sqrt[c + d*x^2]),x]","\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(-3 a^2 d^2+10 a b c d+5 b^2 c^2\right)}{5 c^2 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-3 a^2 d^2+10 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{7/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-3 a^2 d^2+10 a b c d+5 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{7/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{5 c e (e x)^{5/2}}-\frac{2 a \sqrt{c+d x^2} (10 b c-3 a d)}{5 c^2 e^3 \sqrt{e x}}","\frac{2 \sqrt{e x} \sqrt{c+d x^2} \left(-3 a^2 d^2+10 a b c d+5 b^2 c^2\right)}{5 c^2 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-3 a^2 d^2+10 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{7/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{2 \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-3 a^2 d^2+10 a b c d+5 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{7/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{5 c e (e x)^{5/2}}-\frac{2 a \sqrt{c+d x^2} (10 b c-3 a d)}{5 c^2 e^3 \sqrt{e x}}",1,"(-2*a^2*Sqrt[c + d*x^2])/(5*c*e*(e*x)^(5/2)) - (2*a*(10*b*c - 3*a*d)*Sqrt[c + d*x^2])/(5*c^2*e^3*Sqrt[e*x]) + (2*(5*b^2*c^2 + 10*a*b*c*d - 3*a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(5*c^2*Sqrt[d]*e^4*(Sqrt[c] + Sqrt[d]*x)) - (2*(5*b^2*c^2 + 10*a*b*c*d - 3*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(7/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2]) + ((5*b^2*c^2 + 10*a*b*c*d - 3*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(7/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{462, 453, 329, 305, 220, 1196}"
846,1,193,0,0.1683044,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{9/2} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(9/2)*Sqrt[c + d*x^2]),x]","\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-14 a b c d+21 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 c^{9/4} \sqrt[4]{d} e^{9/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{7 c e (e x)^{7/2}}-\frac{2 a \sqrt{c+d x^2} (14 b c-5 a d)}{21 c^2 e^3 (e x)^{3/2}}","\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-14 a b c d+21 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{21 c^{9/4} \sqrt[4]{d} e^{9/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{7 c e (e x)^{7/2}}-\frac{2 a \sqrt{c+d x^2} (14 b c-5 a d)}{21 c^2 e^3 (e x)^{3/2}}",1,"(-2*a^2*Sqrt[c + d*x^2])/(7*c*e*(e*x)^(7/2)) - (2*a*(14*b*c - 5*a*d)*Sqrt[c + d*x^2])/(21*c^2*e^3*(e*x)^(3/2)) + ((21*b^2*c^2 - 14*a*b*c*d + 5*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(21*c^(9/4)*d^(1/4)*e^(9/2)*Sqrt[c + d*x^2])","A",4,4,28,0.1429,1,"{462, 453, 329, 220}"
847,1,438,0,0.4233632,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{11/2} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(11/2)*Sqrt[c + d*x^2]),x]","-\frac{2 \sqrt{c+d x^2} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right)}{15 c^3 e^5 \sqrt{e x}}+\frac{2 \sqrt{d} \sqrt{e x} \sqrt{c+d x^2} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right)}{15 c^3 e^6 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 c^{11/4} e^{11/2} \sqrt{c+d x^2}}-\frac{2 \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 c^{11/4} e^{11/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{9 c e (e x)^{9/2}}-\frac{2 a \sqrt{c+d x^2} (18 b c-7 a d)}{45 c^2 e^3 (e x)^{5/2}}","-\frac{2 \sqrt{c+d x^2} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right)}{15 c^3 e^5 \sqrt{e x}}+\frac{2 \sqrt{d} \sqrt{e x} \sqrt{c+d x^2} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right)}{15 c^3 e^6 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 c^{11/4} e^{11/2} \sqrt{c+d x^2}}-\frac{2 \sqrt[4]{d} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-18 a b c d+15 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 c^{11/4} e^{11/2} \sqrt{c+d x^2}}-\frac{2 a^2 \sqrt{c+d x^2}}{9 c e (e x)^{9/2}}-\frac{2 a \sqrt{c+d x^2} (18 b c-7 a d)}{45 c^2 e^3 (e x)^{5/2}}",1,"(-2*a^2*Sqrt[c + d*x^2])/(9*c*e*(e*x)^(9/2)) - (2*a*(18*b*c - 7*a*d)*Sqrt[c + d*x^2])/(45*c^2*e^3*(e*x)^(5/2)) - (2*(15*b^2*c^2 - 18*a*b*c*d + 7*a^2*d^2)*Sqrt[c + d*x^2])/(15*c^3*e^5*Sqrt[e*x]) + (2*Sqrt[d]*(15*b^2*c^2 - 18*a*b*c*d + 7*a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(15*c^3*e^6*(Sqrt[c] + Sqrt[d]*x)) - (2*d^(1/4)*(15*b^2*c^2 - 18*a*b*c*d + 7*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*c^(11/4)*e^(11/2)*Sqrt[c + d*x^2]) + (d^(1/4)*(15*b^2*c^2 - 18*a*b*c*d + 7*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*c^(11/4)*e^(11/2)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{462, 453, 325, 329, 305, 220, 1196}"
848,1,242,0,0.2216003,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{13/2} \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(13/2)*Sqrt[c + d*x^2]),x]","-\frac{2 a^2 \sqrt{c+d x^2}}{11 c e (e x)^{11/2}}-\frac{d^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 b^2 c^2-5 a d (22 b c-9 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 c^{13/4} e^{13/2} \sqrt{c+d x^2}}-\frac{2 \sqrt{c+d x^2} \left(77 b^2 c^2-5 a d (22 b c-9 a d)\right)}{231 c^3 e^5 (e x)^{3/2}}-\frac{2 a \sqrt{c+d x^2} (22 b c-9 a d)}{77 c^2 e^3 (e x)^{7/2}}","-\frac{2 a^2 \sqrt{c+d x^2}}{11 c e (e x)^{11/2}}-\frac{d^{3/4} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 b^2 c^2-5 a d (22 b c-9 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{231 c^{13/4} e^{13/2} \sqrt{c+d x^2}}-\frac{2 \sqrt{c+d x^2} \left(77 b^2 c^2-5 a d (22 b c-9 a d)\right)}{231 c^3 e^5 (e x)^{3/2}}-\frac{2 a \sqrt{c+d x^2} (22 b c-9 a d)}{77 c^2 e^3 (e x)^{7/2}}",1,"(-2*a^2*Sqrt[c + d*x^2])/(11*c*e*(e*x)^(11/2)) - (2*a*(22*b*c - 9*a*d)*Sqrt[c + d*x^2])/(77*c^2*e^3*(e*x)^(7/2)) - (2*(77*b^2*c^2 - 5*a*d*(22*b*c - 9*a*d))*Sqrt[c + d*x^2])/(231*c^3*e^5*(e*x)^(3/2)) - (d^(3/4)*(77*b^2*c^2 - 5*a*d*(22*b*c - 9*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(231*c^(13/4)*e^(13/2)*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{462, 453, 325, 329, 220}"
849,1,296,0,0.248713,"\int \frac{(e x)^{7/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[((e*x)^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","\frac{5 e^3 \sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2-198 a b c d+117 b^2 c^2\right)}{231 d^4}-\frac{5 c^{3/4} e^{7/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-198 a b c d+117 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{462 d^{17/4} \sqrt{c+d x^2}}-\frac{e (e x)^{5/2} \sqrt{c+d x^2} \left(77 a^2 d^2-198 a b c d+117 b^2 c^2\right)}{77 c d^3}+\frac{(e x)^{9/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{9/2} \sqrt{c+d x^2}}{11 d^2 e}","\frac{5 e^3 \sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2-198 a b c d+117 b^2 c^2\right)}{231 d^4}-\frac{5 c^{3/4} e^{7/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-198 a b c d+117 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{462 d^{17/4} \sqrt{c+d x^2}}-\frac{e (e x)^{5/2} \sqrt{c+d x^2} \left(77 a^2 d^2-198 a b c d+117 b^2 c^2\right)}{77 c d^3}+\frac{(e x)^{9/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{9/2} \sqrt{c+d x^2}}{11 d^2 e}",1,"((b*c - a*d)^2*(e*x)^(9/2))/(c*d^2*e*Sqrt[c + d*x^2]) + (5*(117*b^2*c^2 - 198*a*b*c*d + 77*a^2*d^2)*e^3*Sqrt[e*x]*Sqrt[c + d*x^2])/(231*d^4) - ((117*b^2*c^2 - 198*a*b*c*d + 77*a^2*d^2)*e*(e*x)^(5/2)*Sqrt[c + d*x^2])/(77*c*d^3) + (2*b^2*(e*x)^(9/2)*Sqrt[c + d*x^2])/(11*d^2*e) - (5*c^(3/4)*(117*b^2*c^2 - 198*a*b*c*d + 77*a^2*d^2)*e^(7/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(462*d^(17/4)*Sqrt[c + d*x^2])","A",6,5,28,0.1786,1,"{463, 459, 321, 329, 220}"
850,1,436,0,0.3780286,"\int \frac{(e x)^{5/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","\frac{e^2 \sqrt{e x} \sqrt{c+d x^2} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right)}{15 d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt[4]{c} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{30 d^{15/4} \sqrt{c+d x^2}}-\frac{\sqrt[4]{c} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{15/4} \sqrt{c+d x^2}}-\frac{e (e x)^{3/2} \sqrt{c+d x^2} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right)}{45 c d^3}+\frac{(e x)^{7/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{7/2} \sqrt{c+d x^2}}{9 d^2 e}","\frac{e^2 \sqrt{e x} \sqrt{c+d x^2} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right)}{15 d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt[4]{c} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{30 d^{15/4} \sqrt{c+d x^2}}-\frac{\sqrt[4]{c} e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{15 d^{15/4} \sqrt{c+d x^2}}-\frac{e (e x)^{3/2} \sqrt{c+d x^2} \left(45 a^2 d^2-126 a b c d+77 b^2 c^2\right)}{45 c d^3}+\frac{(e x)^{7/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{7/2} \sqrt{c+d x^2}}{9 d^2 e}",1,"((b*c - a*d)^2*(e*x)^(7/2))/(c*d^2*e*Sqrt[c + d*x^2]) - ((77*b^2*c^2 - 126*a*b*c*d + 45*a^2*d^2)*e*(e*x)^(3/2)*Sqrt[c + d*x^2])/(45*c*d^3) + (2*b^2*(e*x)^(7/2)*Sqrt[c + d*x^2])/(9*d^2*e) + ((77*b^2*c^2 - 126*a*b*c*d + 45*a^2*d^2)*e^2*Sqrt[e*x]*Sqrt[c + d*x^2])/(15*d^(7/2)*(Sqrt[c] + Sqrt[d]*x)) - (c^(1/4)*(77*b^2*c^2 - 126*a*b*c*d + 45*a^2*d^2)*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(15*d^(15/4)*Sqrt[c + d*x^2]) + (c^(1/4)*(77*b^2*c^2 - 126*a*b*c*d + 45*a^2*d^2)*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(30*d^(15/4)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{463, 459, 321, 329, 305, 220, 1196}"
851,1,245,0,0.1977841,"\int \frac{(e x)^{3/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","\frac{e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(21 a^2 d^2-70 a b c d+45 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{42 \sqrt[4]{c} d^{13/4} \sqrt{c+d x^2}}-\frac{e \sqrt{e x} \sqrt{c+d x^2} \left(21 a^2 d^2-70 a b c d+45 b^2 c^2\right)}{21 c d^3}+\frac{(e x)^{5/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{5/2} \sqrt{c+d x^2}}{7 d^2 e}","\frac{e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(21 a^2 d^2-70 a b c d+45 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{42 \sqrt[4]{c} d^{13/4} \sqrt{c+d x^2}}-\frac{e \sqrt{e x} \sqrt{c+d x^2} \left(21 a^2 d^2-70 a b c d+45 b^2 c^2\right)}{21 c d^3}+\frac{(e x)^{5/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{5/2} \sqrt{c+d x^2}}{7 d^2 e}",1,"((b*c - a*d)^2*(e*x)^(5/2))/(c*d^2*e*Sqrt[c + d*x^2]) - ((45*b^2*c^2 - 70*a*b*c*d + 21*a^2*d^2)*e*Sqrt[e*x]*Sqrt[c + d*x^2])/(21*c*d^3) + (2*b^2*(e*x)^(5/2)*Sqrt[c + d*x^2])/(7*d^2*e) + ((45*b^2*c^2 - 70*a*b*c*d + 21*a^2*d^2)*e^(3/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(42*c^(1/4)*d^(13/4)*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{463, 459, 321, 329, 220}"
852,1,384,0,0.3265079,"\int \frac{\sqrt{e x} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{3/2}} \, dx","Int[(Sqrt[e*x]*(a + b*x^2)^2)/(c + d*x^2)^(3/2),x]","-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(5 a^2 d^2-30 a b c d+21 b^2 c^2\right)}{5 c d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-30 a b c d+21 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{3/4} d^{11/4} \sqrt{c+d x^2}}+\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-30 a b c d+21 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{11/4} \sqrt{c+d x^2}}+\frac{(e x)^{3/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{3/2} \sqrt{c+d x^2}}{5 d^2 e}","-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(5 a^2 d^2-30 a b c d+21 b^2 c^2\right)}{5 c d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-30 a b c d+21 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{3/4} d^{11/4} \sqrt{c+d x^2}}+\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-30 a b c d+21 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{3/4} d^{11/4} \sqrt{c+d x^2}}+\frac{(e x)^{3/2} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 (e x)^{3/2} \sqrt{c+d x^2}}{5 d^2 e}",1,"((b*c - a*d)^2*(e*x)^(3/2))/(c*d^2*e*Sqrt[c + d*x^2]) + (2*b^2*(e*x)^(3/2)*Sqrt[c + d*x^2])/(5*d^2*e) - ((21*b^2*c^2 - 30*a*b*c*d + 5*a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(5*c*d^(5/2)*(Sqrt[c] + Sqrt[d]*x)) + ((21*b^2*c^2 - 30*a*b*c*d + 5*a^2*d^2)*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(3/4)*d^(11/4)*Sqrt[c + d*x^2]) - ((21*b^2*c^2 - 30*a*b*c*d + 5*a^2*d^2)*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(10*c^(3/4)*d^(11/4)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{463, 459, 329, 305, 220, 1196}"
853,1,193,0,0.1556657,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{e x} \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/(Sqrt[e*x]*(c + d*x^2)^(3/2)),x]","-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-3 a^2 d^2-6 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 c^{5/4} d^{9/4} \sqrt{e} \sqrt{c+d x^2}}+\frac{\sqrt{e x} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 \sqrt{e x} \sqrt{c+d x^2}}{3 d^2 e}","-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-3 a^2 d^2-6 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 c^{5/4} d^{9/4} \sqrt{e} \sqrt{c+d x^2}}+\frac{\sqrt{e x} (b c-a d)^2}{c d^2 e \sqrt{c+d x^2}}+\frac{2 b^2 \sqrt{e x} \sqrt{c+d x^2}}{3 d^2 e}",1,"((b*c - a*d)^2*Sqrt[e*x])/(c*d^2*e*Sqrt[c + d*x^2]) + (2*b^2*Sqrt[e*x]*Sqrt[c + d*x^2])/(3*d^2*e) - ((5*b^2*c^2 - 6*a*b*c*d - 3*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(6*c^(5/4)*d^(9/4)*Sqrt[e]*Sqrt[c + d*x^2])","A",4,4,28,0.1429,1,"{463, 459, 329, 220}"
854,1,393,0,0.3611887,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{3/2} \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(3/2)),x]","\frac{\sqrt{e x} \sqrt{c+d x^2} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right)}{c^2 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{(e x)^{3/2} \left(3 a^2 d^2-2 a b c d+b^2 c^2\right)}{c^2 d e^3 \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 c^{7/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{c^{7/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{2 a^2}{c e \sqrt{e x} \sqrt{c+d x^2}}","\frac{\sqrt{e x} \sqrt{c+d x^2} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right)}{c^2 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{(e x)^{3/2} \left(3 a^2 d^2-2 a b c d+b^2 c^2\right)}{c^2 d e^3 \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 c^{7/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(3 a^2 d^2-2 a b c d+3 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{c^{7/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}-\frac{2 a^2}{c e \sqrt{e x} \sqrt{c+d x^2}}",1,"(-2*a^2)/(c*e*Sqrt[e*x]*Sqrt[c + d*x^2]) - ((b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*(e*x)^(3/2))/(c^2*d*e^3*Sqrt[c + d*x^2]) + ((3*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(c^2*d^(3/2)*e^2*(Sqrt[c] + Sqrt[d]*x)) - ((3*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(c^(7/4)*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2]) + ((3*b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(2*c^(7/4)*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{462, 457, 329, 305, 220, 1196}"
855,1,207,0,0.1812233,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{5/2} \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(3/2)),x]","-\frac{\sqrt{e x} \left(5 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{3 c^2 d e^3 \sqrt{c+d x^2}}-\frac{2 a^2}{3 c e (e x)^{3/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (6 b c-5 a d)+3 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 c^{9/4} d^{5/4} e^{5/2} \sqrt{c+d x^2}}","-\frac{\sqrt{e x} \left(5 a^2 d^2-6 a b c d+3 b^2 c^2\right)}{3 c^2 d e^3 \sqrt{c+d x^2}}-\frac{2 a^2}{3 c e (e x)^{3/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (6 b c-5 a d)+3 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{6 c^{9/4} d^{5/4} e^{5/2} \sqrt{c+d x^2}}",1,"(-2*a^2)/(3*c*e*(e*x)^(3/2)*Sqrt[c + d*x^2]) - ((3*b^2*c^2 - 6*a*b*c*d + 5*a^2*d^2)*Sqrt[e*x])/(3*c^2*d*e^3*Sqrt[c + d*x^2]) + ((3*b^2*c^2 + a*d*(6*b*c - 5*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(6*c^(9/4)*d^(5/4)*e^(5/2)*Sqrt[c + d*x^2])","A",4,4,28,0.1429,1,"{462, 457, 329, 220}"
856,1,434,0,0.4224968,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{7/2} \left(c+d x^2\right)^{3/2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(3/2)),x]","-\frac{2 a^2}{5 c e (e x)^{5/2} \sqrt{c+d x^2}}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{11/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{11/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right)}{5 c^3 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{(e x)^{3/2} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right)}{5 c^3 e^5 \sqrt{c+d x^2}}-\frac{2 a (10 b c-7 a d)}{5 c^2 e^3 \sqrt{e x} \sqrt{c+d x^2}}","-\frac{2 a^2}{5 c e (e x)^{5/2} \sqrt{c+d x^2}}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{11/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{5 c^{11/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right)}{5 c^3 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{(e x)^{3/2} \left(5 b^2 c^2-3 a d (10 b c-7 a d)\right)}{5 c^3 e^5 \sqrt{c+d x^2}}-\frac{2 a (10 b c-7 a d)}{5 c^2 e^3 \sqrt{e x} \sqrt{c+d x^2}}",1,"(-2*a^2)/(5*c*e*(e*x)^(5/2)*Sqrt[c + d*x^2]) - (2*a*(10*b*c - 7*a*d))/(5*c^2*e^3*Sqrt[e*x]*Sqrt[c + d*x^2]) + ((5*b^2*c^2 - 3*a*d*(10*b*c - 7*a*d))*(e*x)^(3/2))/(5*c^3*e^5*Sqrt[c + d*x^2]) - ((5*b^2*c^2 - 3*a*d*(10*b*c - 7*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(5*c^3*Sqrt[d]*e^4*(Sqrt[c] + Sqrt[d]*x)) + ((5*b^2*c^2 - 3*a*d*(10*b*c - 7*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(5*c^(11/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2]) - ((5*b^2*c^2 - 3*a*d*(10*b*c - 7*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(10*c^(11/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{462, 453, 290, 329, 305, 220, 1196}"
857,1,302,0,0.2337107,"\int \frac{(e x)^{7/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[((e*x)^(7/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","-\frac{5 e^3 \sqrt{e x} \sqrt{c+d x^2} \left(7 a^2 d^2-42 a b c d+39 b^2 c^2\right)}{42 c d^4}+\frac{5 e^{7/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-42 a b c d+39 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{84 \sqrt[4]{c} d^{17/4} \sqrt{c+d x^2}}+\frac{e (e x)^{5/2} \left(7 a^2 d^2-42 a b c d+39 b^2 c^2\right)}{14 c d^3 \sqrt{c+d x^2}}+\frac{(e x)^{9/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}+\frac{2 b^2 (e x)^{9/2}}{7 d^2 e \sqrt{c+d x^2}}","-\frac{5 e^3 \sqrt{e x} \sqrt{c+d x^2} \left(7 a^2 d^2-42 a b c d+39 b^2 c^2\right)}{42 c d^4}+\frac{5 e^{7/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(7 a^2 d^2-42 a b c d+39 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{84 \sqrt[4]{c} d^{17/4} \sqrt{c+d x^2}}+\frac{e (e x)^{5/2} \left(7 a^2 d^2-42 a b c d+39 b^2 c^2\right)}{14 c d^3 \sqrt{c+d x^2}}+\frac{(e x)^{9/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}+\frac{2 b^2 (e x)^{9/2}}{7 d^2 e \sqrt{c+d x^2}}",1,"((b*c - a*d)^2*(e*x)^(9/2))/(3*c*d^2*e*(c + d*x^2)^(3/2)) + ((39*b^2*c^2 - 42*a*b*c*d + 7*a^2*d^2)*e*(e*x)^(5/2))/(14*c*d^3*Sqrt[c + d*x^2]) + (2*b^2*(e*x)^(9/2))/(7*d^2*e*Sqrt[c + d*x^2]) - (5*(39*b^2*c^2 - 42*a*b*c*d + 7*a^2*d^2)*e^3*Sqrt[e*x]*Sqrt[c + d*x^2])/(42*c*d^4) + (5*(39*b^2*c^2 - 42*a*b*c*d + 7*a^2*d^2)*e^(7/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(84*c^(1/4)*d^(17/4)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{463, 459, 288, 321, 329, 220}"
858,1,442,0,0.3837118,"\int \frac{(e x)^{5/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[((e*x)^(5/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","-\frac{e^2 \sqrt{e x} \sqrt{c+d x^2} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right)}{10 c d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{20 c^{3/4} d^{15/4} \sqrt{c+d x^2}}+\frac{e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{3/4} d^{15/4} \sqrt{c+d x^2}}+\frac{e (e x)^{3/2} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right)}{30 c d^3 \sqrt{c+d x^2}}+\frac{(e x)^{7/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}+\frac{2 b^2 (e x)^{7/2}}{5 d^2 e \sqrt{c+d x^2}}","-\frac{e^2 \sqrt{e x} \sqrt{c+d x^2} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right)}{10 c d^{7/2} \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{20 c^{3/4} d^{15/4} \sqrt{c+d x^2}}+\frac{e^{5/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{3/4} d^{15/4} \sqrt{c+d x^2}}+\frac{e (e x)^{3/2} \left(5 a^2 d^2-70 a b c d+77 b^2 c^2\right)}{30 c d^3 \sqrt{c+d x^2}}+\frac{(e x)^{7/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}+\frac{2 b^2 (e x)^{7/2}}{5 d^2 e \sqrt{c+d x^2}}",1,"((b*c - a*d)^2*(e*x)^(7/2))/(3*c*d^2*e*(c + d*x^2)^(3/2)) + ((77*b^2*c^2 - 70*a*b*c*d + 5*a^2*d^2)*e*(e*x)^(3/2))/(30*c*d^3*Sqrt[c + d*x^2]) + (2*b^2*(e*x)^(7/2))/(5*d^2*e*Sqrt[c + d*x^2]) - ((77*b^2*c^2 - 70*a*b*c*d + 5*a^2*d^2)*e^2*Sqrt[e*x]*Sqrt[c + d*x^2])/(10*c*d^(7/2)*(Sqrt[c] + Sqrt[d]*x)) + ((77*b^2*c^2 - 70*a*b*c*d + 5*a^2*d^2)*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(10*c^(3/4)*d^(15/4)*Sqrt[c + d*x^2]) - ((77*b^2*c^2 - 70*a*b*c*d + 5*a^2*d^2)*e^(5/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(20*c^(3/4)*d^(15/4)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{463, 459, 288, 329, 305, 220, 1196}"
859,1,248,0,0.1942386,"\int \frac{(e x)^{3/2} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[((e*x)^(3/2)*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","-\frac{e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-a^2 d^2-10 a b c d+15 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 c^{5/4} d^{13/4} \sqrt{c+d x^2}}+\frac{e \sqrt{e x} \left(-a^2 d^2-10 a b c d+15 b^2 c^2\right)}{6 c d^3 \sqrt{c+d x^2}}+\frac{(e x)^{5/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}+\frac{2 b^2 (e x)^{5/2}}{3 d^2 e \sqrt{c+d x^2}}","-\frac{e^{3/2} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-a^2 d^2-10 a b c d+15 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 c^{5/4} d^{13/4} \sqrt{c+d x^2}}+\frac{e \sqrt{e x} \left(-a^2 d^2-10 a b c d+15 b^2 c^2\right)}{6 c d^3 \sqrt{c+d x^2}}+\frac{(e x)^{5/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}+\frac{2 b^2 (e x)^{5/2}}{3 d^2 e \sqrt{c+d x^2}}",1,"((b*c - a*d)^2*(e*x)^(5/2))/(3*c*d^2*e*(c + d*x^2)^(3/2)) + ((15*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*e*Sqrt[e*x])/(6*c*d^3*Sqrt[c + d*x^2]) + (2*b^2*(e*x)^(5/2))/(3*d^2*e*Sqrt[c + d*x^2]) - ((15*b^2*c^2 - 10*a*b*c*d - a^2*d^2)*e^(3/2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(12*c^(5/4)*d^(13/4)*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{463, 459, 288, 329, 220}"
860,1,403,0,0.3419721,"\int \frac{\sqrt{e x} \left(a+b x^2\right)^2}{\left(c+d x^2\right)^{5/2}} \, dx","Int[(Sqrt[e*x]*(a + b*x^2)^2)/(c + d*x^2)^(5/2),x]","\frac{\sqrt{e x} \sqrt{c+d x^2} \left(-a^2 d^2-2 a b c d+7 b^2 c^2\right)}{2 c^2 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-a^2 d^2-2 a b c d+7 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 c^{7/4} d^{11/4} \sqrt{c+d x^2}}-\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-a^2 d^2-2 a b c d+7 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 c^{7/4} d^{11/4} \sqrt{c+d x^2}}-\frac{(e x)^{3/2} (a d+3 b c) (b c-a d)}{2 c^2 d^2 e \sqrt{c+d x^2}}+\frac{(e x)^{3/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}","\frac{\sqrt{e x} \sqrt{c+d x^2} \left(-a^2 d^2-2 a b c d+7 b^2 c^2\right)}{2 c^2 d^{5/2} \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-a^2 d^2-2 a b c d+7 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 c^{7/4} d^{11/4} \sqrt{c+d x^2}}-\frac{\sqrt{e} \left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(-a^2 d^2-2 a b c d+7 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 c^{7/4} d^{11/4} \sqrt{c+d x^2}}-\frac{(e x)^{3/2} (a d+3 b c) (b c-a d)}{2 c^2 d^2 e \sqrt{c+d x^2}}+\frac{(e x)^{3/2} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}",1,"((b*c - a*d)^2*(e*x)^(3/2))/(3*c*d^2*e*(c + d*x^2)^(3/2)) - ((b*c - a*d)*(3*b*c + a*d)*(e*x)^(3/2))/(2*c^2*d^2*e*Sqrt[c + d*x^2]) + ((7*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(2*c^2*d^(5/2)*(Sqrt[c] + Sqrt[d]*x)) - ((7*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(2*c^(7/4)*d^(11/4)*Sqrt[c + d*x^2]) + ((7*b^2*c^2 - 2*a*b*c*d - a^2*d^2)*Sqrt[e]*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(4*c^(7/4)*d^(11/4)*Sqrt[c + d*x^2])","A",6,6,28,0.2143,1,"{463, 457, 329, 305, 220, 1196}"
861,1,213,0,0.1623654,"\int \frac{\left(a+b x^2\right)^2}{\sqrt{e x} \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/(Sqrt[e*x]*(c + d*x^2)^(5/2)),x]","\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2+2 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 c^{9/4} d^{9/4} \sqrt{e} \sqrt{c+d x^2}}-\frac{\sqrt{e x} (5 a d+7 b c) (b c-a d)}{6 c^2 d^2 e \sqrt{c+d x^2}}+\frac{\sqrt{e x} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}","\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a^2 d^2+2 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 c^{9/4} d^{9/4} \sqrt{e} \sqrt{c+d x^2}}-\frac{\sqrt{e x} (5 a d+7 b c) (b c-a d)}{6 c^2 d^2 e \sqrt{c+d x^2}}+\frac{\sqrt{e x} (b c-a d)^2}{3 c d^2 e \left(c+d x^2\right)^{3/2}}",1,"((b*c - a*d)^2*Sqrt[e*x])/(3*c*d^2*e*(c + d*x^2)^(3/2)) - ((b*c - a*d)*(7*b*c + 5*a*d)*Sqrt[e*x])/(6*c^2*d^2*e*Sqrt[c + d*x^2]) + ((5*b^2*c^2 + 2*a*b*c*d + 5*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(12*c^(9/4)*d^(9/4)*Sqrt[e]*Sqrt[c + d*x^2])","A",4,4,28,0.1429,1,"{463, 457, 329, 220}"
862,1,442,0,0.4208588,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{3/2} \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(3/2)*(c + d*x^2)^(5/2)),x]","-\frac{(e x)^{3/2} \left(7 a^2 d^2-2 a b c d+b^2 c^2\right)}{3 c^2 d e^3 \left(c+d x^2\right)^{3/2}}-\frac{2 a^2}{c e \sqrt{e x} \left(c+d x^2\right)^{3/2}}-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(a d (2 b c-7 a d)+b^2 c^2\right)}{2 c^3 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (2 b c-7 a d)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 c^{11/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (2 b c-7 a d)+b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 c^{11/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{(e x)^{3/2} \left(a d (2 b c-7 a d)+b^2 c^2\right)}{2 c^3 d e^3 \sqrt{c+d x^2}}","-\frac{(e x)^{3/2} \left(7 a^2 d^2-2 a b c d+b^2 c^2\right)}{3 c^2 d e^3 \left(c+d x^2\right)^{3/2}}-\frac{2 a^2}{c e \sqrt{e x} \left(c+d x^2\right)^{3/2}}-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(a d (2 b c-7 a d)+b^2 c^2\right)}{2 c^3 d^{3/2} e^2 \left(\sqrt{c}+\sqrt{d} x\right)}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (2 b c-7 a d)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{4 c^{11/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(a d (2 b c-7 a d)+b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{2 c^{11/4} d^{7/4} e^{3/2} \sqrt{c+d x^2}}+\frac{(e x)^{3/2} \left(a d (2 b c-7 a d)+b^2 c^2\right)}{2 c^3 d e^3 \sqrt{c+d x^2}}",1,"(-2*a^2)/(c*e*Sqrt[e*x]*(c + d*x^2)^(3/2)) - ((b^2*c^2 - 2*a*b*c*d + 7*a^2*d^2)*(e*x)^(3/2))/(3*c^2*d*e^3*(c + d*x^2)^(3/2)) + ((b^2*c^2 + a*d*(2*b*c - 7*a*d))*(e*x)^(3/2))/(2*c^3*d*e^3*Sqrt[c + d*x^2]) - ((b^2*c^2 + a*d*(2*b*c - 7*a*d))*Sqrt[e*x]*Sqrt[c + d*x^2])/(2*c^3*d^(3/2)*e^2*(Sqrt[c] + Sqrt[d]*x)) + ((b^2*c^2 + a*d*(2*b*c - 7*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(2*c^(11/4)*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2]) - ((b^2*c^2 + a*d*(2*b*c - 7*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(4*c^(11/4)*d^(7/4)*e^(3/2)*Sqrt[c + d*x^2])","A",7,7,28,0.2500,1,"{462, 457, 290, 329, 305, 220, 1196}"
863,1,258,0,0.2344093,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{5/2} \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(5/2)*(c + d*x^2)^(5/2)),x]","-\frac{\sqrt{e x} \left(3 a^2 d^2-2 a b c d+b^2 c^2\right)}{3 c^2 d e^3 \left(c+d x^2\right)^{3/2}}-\frac{2 a^2}{3 c e (e x)^{3/2} \left(c+d x^2\right)^{3/2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a d (2 b c-3 a d)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 c^{13/4} d^{5/4} e^{5/2} \sqrt{c+d x^2}}+\frac{\sqrt{e x} \left(5 a d (2 b c-3 a d)+b^2 c^2\right)}{6 c^3 d e^3 \sqrt{c+d x^2}}","-\frac{\sqrt{e x} \left(3 a^2 d^2-2 a b c d+b^2 c^2\right)}{3 c^2 d e^3 \left(c+d x^2\right)^{3/2}}-\frac{2 a^2}{3 c e (e x)^{3/2} \left(c+d x^2\right)^{3/2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(5 a d (2 b c-3 a d)+b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{12 c^{13/4} d^{5/4} e^{5/2} \sqrt{c+d x^2}}+\frac{\sqrt{e x} \left(5 a d (2 b c-3 a d)+b^2 c^2\right)}{6 c^3 d e^3 \sqrt{c+d x^2}}",1,"(-2*a^2)/(3*c*e*(e*x)^(3/2)*(c + d*x^2)^(3/2)) - ((b^2*c^2 - 2*a*b*c*d + 3*a^2*d^2)*Sqrt[e*x])/(3*c^2*d*e^3*(c + d*x^2)^(3/2)) + ((b^2*c^2 + 5*a*d*(2*b*c - 3*a*d))*Sqrt[e*x])/(6*c^3*d*e^3*Sqrt[c + d*x^2]) + ((b^2*c^2 + 5*a*d*(2*b*c - 3*a*d))*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(12*c^(13/4)*d^(5/4)*e^(5/2)*Sqrt[c + d*x^2])","A",5,5,28,0.1786,1,"{462, 457, 290, 329, 220}"
864,1,489,0,0.4695825,"\int \frac{\left(a+b x^2\right)^2}{(e x)^{7/2} \left(c+d x^2\right)^{5/2}} \, dx","Int[(a + b*x^2)^2/((e*x)^(7/2)*(c + d*x^2)^(5/2)),x]","-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right)}{10 c^4 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{(e x)^{3/2} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right)}{10 c^4 e^5 \sqrt{c+d x^2}}+\frac{(e x)^{3/2} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right)}{15 c^3 e^5 \left(c+d x^2\right)^{3/2}}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{20 c^{15/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{15/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{2 a^2}{5 c e (e x)^{5/2} \left(c+d x^2\right)^{3/2}}-\frac{2 a (10 b c-11 a d)}{5 c^2 e^3 \sqrt{e x} \left(c+d x^2\right)^{3/2}}","-\frac{\sqrt{e x} \sqrt{c+d x^2} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right)}{10 c^4 \sqrt{d} e^4 \left(\sqrt{c}+\sqrt{d} x\right)}+\frac{(e x)^{3/2} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right)}{10 c^4 e^5 \sqrt{c+d x^2}}+\frac{(e x)^{3/2} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right)}{15 c^3 e^5 \left(c+d x^2\right)^{3/2}}-\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{20 c^{15/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}+\frac{\left(\sqrt{c}+\sqrt{d} x\right) \sqrt{\frac{c+d x^2}{\left(\sqrt{c}+\sqrt{d} x\right)^2}} \left(77 a^2 d^2-70 a b c d+5 b^2 c^2\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)|\frac{1}{2}\right)}{10 c^{15/4} d^{3/4} e^{7/2} \sqrt{c+d x^2}}-\frac{2 a^2}{5 c e (e x)^{5/2} \left(c+d x^2\right)^{3/2}}-\frac{2 a (10 b c-11 a d)}{5 c^2 e^3 \sqrt{e x} \left(c+d x^2\right)^{3/2}}",1,"(-2*a^2)/(5*c*e*(e*x)^(5/2)*(c + d*x^2)^(3/2)) - (2*a*(10*b*c - 11*a*d))/(5*c^2*e^3*Sqrt[e*x]*(c + d*x^2)^(3/2)) + ((5*b^2*c^2 - 70*a*b*c*d + 77*a^2*d^2)*(e*x)^(3/2))/(15*c^3*e^5*(c + d*x^2)^(3/2)) + ((5*b^2*c^2 - 70*a*b*c*d + 77*a^2*d^2)*(e*x)^(3/2))/(10*c^4*e^5*Sqrt[c + d*x^2]) - ((5*b^2*c^2 - 70*a*b*c*d + 77*a^2*d^2)*Sqrt[e*x]*Sqrt[c + d*x^2])/(10*c^4*Sqrt[d]*e^4*(Sqrt[c] + Sqrt[d]*x)) + ((5*b^2*c^2 - 70*a*b*c*d + 77*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticE[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(10*c^(15/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2]) - ((5*b^2*c^2 - 70*a*b*c*d + 77*a^2*d^2)*(Sqrt[c] + Sqrt[d]*x)*Sqrt[(c + d*x^2)/(Sqrt[c] + Sqrt[d]*x)^2]*EllipticF[2*ArcTan[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], 1/2])/(20*c^(15/4)*d^(3/4)*e^(7/2)*Sqrt[c + d*x^2])","A",8,7,28,0.2500,1,"{462, 453, 290, 329, 305, 220, 1196}"
865,1,372,0,0.80242,"\int \frac{(e x)^{7/2} \sqrt{c-d x^2}}{a-b x^2} \, dx","Int[((e*x)^(7/2)*Sqrt[c - d*x^2])/(a - b*x^2),x]","-\frac{2 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \left(-21 a^2 d^2+14 a b c d+2 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{21 b^3 d^{5/4} \sqrt{c-d x^2}}+\frac{2 e^3 \sqrt{e x} \sqrt{c-d x^2} (2 b c-7 a d)}{21 b^2 d}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e (e x)^{5/2} \sqrt{c-d x^2}}{7 b}","-\frac{2 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \left(-21 a^2 d^2+14 a b c d+2 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{21 b^3 d^{5/4} \sqrt{c-d x^2}}+\frac{2 e^3 \sqrt{e x} \sqrt{c-d x^2} (2 b c-7 a d)}{21 b^2 d}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e (e x)^{5/2} \sqrt{c-d x^2}}{7 b}",1,"(2*(2*b*c - 7*a*d)*e^3*Sqrt[e*x]*Sqrt[c - d*x^2])/(21*b^2*d) - (2*e*(e*x)^(5/2)*Sqrt[c - d*x^2])/(7*b) - (2*c^(1/4)*(2*b^2*c^2 + 14*a*b*c*d - 21*a^2*d^2)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(21*b^3*d^(5/4)*Sqrt[c - d*x^2]) + (a*c^(1/4)*(b*c - a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^3*d^(1/4)*Sqrt[c - d*x^2]) + (a*c^(1/4)*(b*c - a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^3*d^(1/4)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 478, 582, 523, 224, 221, 409, 1219, 1218}"
866,1,414,0,0.8173715,"\int \frac{(e x)^{5/2} \sqrt{c-d x^2}}{a-b x^2} \, dx","Int[((e*x)^(5/2)*Sqrt[c - d*x^2])/(a - b*x^2),x]","\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (2 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 d^{3/4} \sqrt{c-d x^2}}-\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (2 b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 d^{3/4} \sqrt{c-d x^2}}-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e (e x)^{3/2} \sqrt{c-d x^2}}{5 b}","\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (2 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 d^{3/4} \sqrt{c-d x^2}}-\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (2 b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 d^{3/4} \sqrt{c-d x^2}}-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e (e x)^{3/2} \sqrt{c-d x^2}}{5 b}",1,"(-2*e*(e*x)^(3/2)*Sqrt[c - d*x^2])/(5*b) - (2*c^(3/4)*(2*b*c - 5*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*b^2*d^(3/4)*Sqrt[c - d*x^2]) + (2*c^(3/4)*(2*b*c - 5*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*b^2*d^(3/4)*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*(b*c - a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(5/2)*d^(1/4)*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*(b*c - a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(5/2)*d^(1/4)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 478, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
867,1,315,0,0.5089943,"\int \frac{(e x)^{3/2} \sqrt{c-d x^2}}{a-b x^2} \, dx","Int[((e*x)^(3/2)*Sqrt[c - d*x^2])/(a - b*x^2),x]","-\frac{2 \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (2 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e \sqrt{e x} \sqrt{c-d x^2}}{3 b}","-\frac{2 \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (2 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e \sqrt{e x} \sqrt{c-d x^2}}{3 b}",1,"(-2*e*Sqrt[e*x]*Sqrt[c - d*x^2])/(3*b) - (2*c^(1/4)*(2*b*c - 3*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*b^2*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^2*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^2*d^(1/4)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 478, 523, 224, 221, 409, 1219, 1218}"
868,1,365,0,0.5353325,"\int \frac{\sqrt{e x} \sqrt{c-d x^2}}{a-b x^2} \, dx","Int[(Sqrt[e*x]*Sqrt[c - d*x^2])/(a - b*x^2),x]","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt{c-d x^2}}","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt{c-d x^2}}",1,"(2*c^(3/4)*d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*Sqrt[c - d*x^2]) - (2*c^(3/4)*d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*b^(3/2)*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*b^(3/2)*d^(1/4)*Sqrt[c - d*x^2])","A",13,11,30,0.3667,1,"{466, 491, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
869,1,283,0,0.3705847,"\int \frac{\sqrt{c-d x^2}}{\sqrt{e x} \left(a-b x^2\right)} \, dx","Int[Sqrt[c - d*x^2]/(Sqrt[e*x]*(a - b*x^2)),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt{e} \sqrt{c-d x^2}}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt{e} \sqrt{c-d x^2}}",1,"(2*c^(1/4)*d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*b*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*b*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2])","A",9,7,30,0.2333,1,"{466, 406, 224, 221, 409, 1219, 1218}"
870,1,392,0,0.7179338,"\int \frac{\sqrt{c-d x^2}}{(e x)^{3/2} \left(a-b x^2\right)} \, dx","Int[Sqrt[c - d*x^2]/((e*x)^(3/2)*(a - b*x^2)),x]","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a e^{3/2} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a e^{3/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{a e \sqrt{e x}}","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a e^{3/2} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a e^{3/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{a e \sqrt{e x}}",1,"(-2*Sqrt[c - d*x^2])/(a*e*Sqrt[e*x]) - (2*c^(3/4)*d^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*e^(3/2)*Sqrt[c - d*x^2]) + (2*c^(3/4)*d^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*e^(3/2)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*Sqrt[b]*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*Sqrt[b]*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 475, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
871,1,308,0,0.4950977,"\int \frac{\sqrt{c-d x^2}}{(e x)^{5/2} \left(a-b x^2\right)} \, dx","Int[Sqrt[c - d*x^2]/((e*x)^(5/2)*(a - b*x^2)),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a e^{5/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{3 a e (e x)^{3/2}}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a e^{5/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{3 a e (e x)^{3/2}}",1,"(-2*Sqrt[c - d*x^2])/(3*a*e*(e*x)^(3/2)) + (2*c^(1/4)*d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*a*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 475, 523, 224, 221, 409, 1219, 1218}"
872,1,457,0,0.9839837,"\int \frac{\sqrt{c-d x^2}}{(e x)^{7/2} \left(a-b x^2\right)} \, dx","Int[Sqrt[c - d*x^2]/((e*x)^(7/2)*(a - b*x^2)),x]","-\frac{2 \sqrt{c-d x^2} (5 b c-2 a d)}{5 a^2 c e^3 \sqrt{e x}}+\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-2 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 \sqrt[4]{c} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-2 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 \sqrt[4]{c} e^{7/2} \sqrt{c-d x^2}}-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{5 a e (e x)^{5/2}}","-\frac{2 \sqrt{c-d x^2} (5 b c-2 a d)}{5 a^2 c e^3 \sqrt{e x}}+\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-2 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 \sqrt[4]{c} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-2 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 \sqrt[4]{c} e^{7/2} \sqrt{c-d x^2}}-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{5 a e (e x)^{5/2}}",1,"(-2*Sqrt[c - d*x^2])/(5*a*e*(e*x)^(5/2)) - (2*(5*b*c - 2*a*d)*Sqrt[c - d*x^2])/(5*a^2*c*e^3*Sqrt[e*x]) - (2*d^(1/4)*(5*b*c - 2*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*a^2*c^(1/4)*e^(7/2)*Sqrt[c - d*x^2]) + (2*d^(1/4)*(5*b*c - 2*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*a^2*c^(1/4)*e^(7/2)*Sqrt[c - d*x^2]) - (Sqrt[b]*c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(5/2)*d^(1/4)*e^(7/2)*Sqrt[c - d*x^2]) + (Sqrt[b]*c^(1/4)*(b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(5/2)*d^(1/4)*e^(7/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 475, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
873,1,485,0,1.1064464,"\int \frac{(e x)^{5/2} \left(c-d x^2\right)^{3/2}}{a-b x^2} \, dx","Int[((e*x)^(5/2)*(c - d*x^2)^(3/2))/(a - b*x^2),x]","\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(15 a^2 d^2-21 a b c d+4 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{15 b^3 d^{3/4} \sqrt{c-d x^2}}-\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(15 a^2 d^2-21 a b c d+4 b^2 c^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{15 b^3 d^{3/4} \sqrt{c-d x^2}}-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e (e x)^{3/2} \sqrt{c-d x^2} (11 b c-9 a d)}{45 b^2}+\frac{2 d (e x)^{7/2} \sqrt{c-d x^2}}{9 b e}","\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(15 a^2 d^2-21 a b c d+4 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{15 b^3 d^{3/4} \sqrt{c-d x^2}}-\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(15 a^2 d^2-21 a b c d+4 b^2 c^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{15 b^3 d^{3/4} \sqrt{c-d x^2}}-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e (e x)^{3/2} \sqrt{c-d x^2} (11 b c-9 a d)}{45 b^2}+\frac{2 d (e x)^{7/2} \sqrt{c-d x^2}}{9 b e}",1,"(-2*(11*b*c - 9*a*d)*e*(e*x)^(3/2)*Sqrt[c - d*x^2])/(45*b^2) + (2*d*(e*x)^(7/2)*Sqrt[c - d*x^2])/(9*b*e) - (2*c^(3/4)*(4*b^2*c^2 - 21*a*b*c*d + 15*a^2*d^2)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(15*b^3*d^(3/4)*Sqrt[c - d*x^2]) + (2*c^(3/4)*(4*b^2*c^2 - 21*a*b*c*d + 15*a^2*d^2)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(15*b^3*d^(3/4)*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*(b*c - a*d)^2*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(7/2)*d^(1/4)*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*(b*c - a*d)^2*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(7/2)*d^(1/4)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 477, 582, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
874,1,372,0,0.7783666,"\int \frac{(e x)^{3/2} \left(c-d x^2\right)^{3/2}}{a-b x^2} \, dx","Int[((e*x)^(3/2)*(c - d*x^2)^(3/2))/(a - b*x^2),x]","-\frac{2 \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \left(21 a^2 d^2-35 a b c d+12 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{21 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e \sqrt{e x} \sqrt{c-d x^2} (9 b c-7 a d)}{21 b^2}+\frac{2 d (e x)^{5/2} \sqrt{c-d x^2}}{7 b e}","-\frac{2 \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \left(21 a^2 d^2-35 a b c d+12 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{21 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 e \sqrt{e x} \sqrt{c-d x^2} (9 b c-7 a d)}{21 b^2}+\frac{2 d (e x)^{5/2} \sqrt{c-d x^2}}{7 b e}",1,"(-2*(9*b*c - 7*a*d)*e*Sqrt[e*x]*Sqrt[c - d*x^2])/(21*b^2) + (2*d*(e*x)^(5/2)*Sqrt[c - d*x^2])/(7*b*e) - (2*c^(1/4)*(12*b^2*c^2 - 35*a*b*c*d + 21*a^2*d^2)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(21*b^3*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^3*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^3*d^(1/4)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 477, 582, 523, 224, 221, 409, 1219, 1218}"
875,1,421,0,0.8234607,"\int \frac{\sqrt{e x} \left(c-d x^2\right)^{3/2}}{a-b x^2} \, dx","Int[(Sqrt[e*x]*(c - d*x^2)^(3/2))/(a - b*x^2),x]","-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{2 d (e x)^{3/2} \sqrt{c-d x^2}}{5 b e}","-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 b^2 \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{2 d (e x)^{3/2} \sqrt{c-d x^2}}{5 b e}",1,"(2*d*(e*x)^(3/2)*Sqrt[c - d*x^2])/(5*b*e) + (2*c^(3/4)*d^(1/4)*(7*b*c - 5*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*b^2*Sqrt[c - d*x^2]) - (2*c^(3/4)*d^(1/4)*(7*b*c - 5*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*b^2*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - a*d)^2*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*b^(5/2)*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*b^(5/2)*d^(1/4)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 477, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
876,1,328,0,0.5620448,"\int \frac{\left(c-d x^2\right)^{3/2}}{\sqrt{e x} \left(a-b x^2\right)} \, dx","Int[(c - d*x^2)^(3/2)/(Sqrt[e*x]*(a - b*x^2)),x]","\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 b^2 \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{2 d \sqrt{e x} \sqrt{c-d x^2}}{3 b e}","\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 b^2 \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{2 d \sqrt{e x} \sqrt{c-d x^2}}{3 b e}",1,"(2*d*Sqrt[e*x]*Sqrt[c - d*x^2])/(3*b*e) + (2*c^(1/4)*d^(3/4)*(5*b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*b^2*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*b^2*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*b^2*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 416, 523, 224, 221, 409, 1219, 1218}"
877,1,417,0,0.7886956,"\int \frac{\left(c-d x^2\right)^{3/2}}{(e x)^{3/2} \left(a-b x^2\right)} \, dx","Int[(c - d*x^2)^(3/2)/((e*x)^(3/2)*(a - b*x^2)),x]","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b e^{3/2} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (a d+b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b e^{3/2} \sqrt{c-d x^2}}-\frac{2 c \sqrt{c-d x^2}}{a e \sqrt{e x}}","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b e^{3/2} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (a d+b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a b e^{3/2} \sqrt{c-d x^2}}-\frac{2 c \sqrt{c-d x^2}}{a e \sqrt{e x}}",1,"(-2*c*Sqrt[c - d*x^2])/(a*e*Sqrt[e*x]) - (2*c^(3/4)*d^(1/4)*(b*c + a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*b*e^(3/2)*Sqrt[c - d*x^2]) + (2*c^(3/4)*d^(1/4)*(b*c + a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*b*e^(3/2)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*b^(3/2)*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*b^(3/2)*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 474, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
878,1,330,0,0.591964,"\int \frac{\left(c-d x^2\right)^{3/2}}{(e x)^{5/2} \left(a-b x^2\right)} \, dx","Int[(c - d*x^2)^(3/2)/((e*x)^(5/2)*(a - b*x^2)),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a b e^{5/2} \sqrt{c-d x^2}}-\frac{2 c \sqrt{c-d x^2}}{3 a e (e x)^{3/2}}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a b e^{5/2} \sqrt{c-d x^2}}-\frac{2 c \sqrt{c-d x^2}}{3 a e (e x)^{3/2}}",1,"(-2*c*Sqrt[c - d*x^2])/(3*a*e*(e*x)^(3/2)) + (2*c^(1/4)*d^(3/4)*(b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*a*b*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*b*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*b*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 474, 523, 224, 221, 409, 1219, 1218}"
879,1,459,0,1.059309,"\int \frac{\left(c-d x^2\right)^{3/2}}{(e x)^{7/2} \left(a-b x^2\right)} \, dx","Int[(c - d*x^2)^(3/2)/((e*x)^(7/2)*(a - b*x^2)),x]","\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 e^{7/2} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2} (5 b c-7 a d)}{5 a^2 e^3 \sqrt{e x}}-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt{b} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt{b} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}-\frac{2 c \sqrt{c-d x^2}}{5 a e (e x)^{5/2}}","\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 e^{7/2} \sqrt{c-d x^2}}-\frac{2 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2} (5 b c-7 a d)}{5 a^2 e^3 \sqrt{e x}}-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt{b} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d)^2 \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt{b} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}-\frac{2 c \sqrt{c-d x^2}}{5 a e (e x)^{5/2}}",1,"(-2*c*Sqrt[c - d*x^2])/(5*a*e*(e*x)^(5/2)) - (2*(5*b*c - 7*a*d)*Sqrt[c - d*x^2])/(5*a^2*e^3*Sqrt[e*x]) - (2*c^(3/4)*d^(1/4)*(5*b*c - 7*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*a^2*e^(7/2)*Sqrt[c - d*x^2]) + (2*c^(3/4)*d^(1/4)*(5*b*c - 7*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*a^2*e^(7/2)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(5/2)*Sqrt[b]*d^(1/4)*e^(7/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)^2*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(5/2)*Sqrt[b]*d^(1/4)*e^(7/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 474, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
880,1,305,0,0.4895007,"\int \frac{(e x)^{7/2}}{\left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[(e*x)^(7/2)/((a - b*x^2)*Sqrt[c - d*x^2]),x]","-\frac{2 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (3 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 b^2 d^{5/4} \sqrt{c-d x^2}}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{2 e^3 \sqrt{e x} \sqrt{c-d x^2}}{3 b d}","-\frac{2 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (3 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 b^2 d^{5/4} \sqrt{c-d x^2}}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{2 e^3 \sqrt{e x} \sqrt{c-d x^2}}{3 b d}",1,"(2*e^3*Sqrt[e*x]*Sqrt[c - d*x^2])/(3*b*d) - (2*c^(1/4)*(b*c + 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*b^2*d^(5/4)*Sqrt[c - d*x^2]) + (a*c^(1/4)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^2*d^(1/4)*Sqrt[c - d*x^2]) + (a*c^(1/4)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^2*d^(1/4)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 479, 523, 224, 221, 409, 1219, 1218}"
881,1,349,0,0.4918569,"\int \frac{(e x)^{5/2}}{\left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[(e*x)^(5/2)/((a - b*x^2)*Sqrt[c - d*x^2]),x]","-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{3/4} \sqrt{c-d x^2}}-\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{3/4} \sqrt{c-d x^2}}","-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{3/4} \sqrt{c-d x^2}}-\frac{2 c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{3/4} \sqrt{c-d x^2}}",1,"(-2*c^(3/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(3/4)*Sqrt[c - d*x^2]) + (2*c^(3/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(3/4)*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(3/2)*d^(1/4)*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(3/2)*d^(1/4)*Sqrt[c - d*x^2])","A",13,11,30,0.3667,1,"{466, 483, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
882,1,261,0,0.3563943,"\int \frac{(e x)^{3/2}}{\left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[(e*x)^(3/2)/((a - b*x^2)*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2}}","\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2}}",1,"(-2*c^(1/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(1/4)*Sqrt[c - d*x^2])","A",9,7,30,0.2333,1,"{466, 483, 224, 221, 409, 1219, 1218}"
883,1,203,0,0.2602191,"\int \frac{\sqrt{e x}}{\left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[Sqrt[e*x]/((a - b*x^2)*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2}}","\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2}}",1,"-((c^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*Sqrt[b]*d^(1/4)*Sqrt[c - d*x^2])) + (c^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*Sqrt[b]*d^(1/4)*Sqrt[c - d*x^2])","A",6,4,30,0.1333,1,"{466, 490, 1219, 1218}"
884,1,188,0,0.2515746,"\int \frac{1}{\sqrt{e x} \left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[1/(Sqrt[e*x]*(a - b*x^2)*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}",1,"(c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2])","A",6,4,30,0.1333,1,"{466, 409, 1219, 1218}"
885,1,379,0,0.6830641,"\int \frac{1}{(e x)^{3/2} \left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[1/((e*x)^(3/2)*(a - b*x^2)*Sqrt[c - d*x^2]),x]","-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{a c e \sqrt{e x}}","-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{a c e \sqrt{e x}}",1,"(-2*Sqrt[c - d*x^2])/(a*c*e*Sqrt[e*x]) - (2*d^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*c^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) + (2*d^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*c^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) - (Sqrt[b]*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) + (Sqrt[b]*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 480, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
886,1,297,0,0.4648903,"\int \frac{1}{(e x)^{5/2} \left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[1/((e*x)^(5/2)*(a - b*x^2)*Sqrt[c - d*x^2]),x]","\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{2 d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a c^{3/4} e^{5/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{3 a c e (e x)^{3/2}}","\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{2 d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a c^{3/4} e^{5/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{3 a c e (e x)^{3/2}}",1,"(-2*Sqrt[c - d*x^2])/(3*a*c*e*(e*x)^(3/2)) + (2*d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*a*c^(3/4)*e^(5/2)*Sqrt[c - d*x^2]) + (b*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2]) + (b*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 480, 523, 224, 221, 409, 1219, 1218}"
887,1,444,0,0.9205946,"\int \frac{1}{(e x)^{7/2} \left(a-b x^2\right) \sqrt{c-d x^2}} \, dx","Int[1/((e*x)^(7/2)*(a - b*x^2)*Sqrt[c - d*x^2]),x]","-\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2} (3 a d+5 b c)}{5 a^2 c^2 e^3 \sqrt{e x}}+\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (3 a d+5 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 c^{5/4} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (3 a d+5 b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 c^{5/4} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{5 a c e (e x)^{5/2}}","-\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{5/2} \sqrt[4]{d} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2} (3 a d+5 b c)}{5 a^2 c^2 e^3 \sqrt{e x}}+\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (3 a d+5 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 c^{5/4} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (3 a d+5 b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{5 a^2 c^{5/4} e^{7/2} \sqrt{c-d x^2}}-\frac{2 \sqrt{c-d x^2}}{5 a c e (e x)^{5/2}}",1,"(-2*Sqrt[c - d*x^2])/(5*a*c*e*(e*x)^(5/2)) - (2*(5*b*c + 3*a*d)*Sqrt[c - d*x^2])/(5*a^2*c^2*e^3*Sqrt[e*x]) - (2*d^(1/4)*(5*b*c + 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*a^2*c^(5/4)*e^(7/2)*Sqrt[c - d*x^2]) + (2*d^(1/4)*(5*b*c + 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(5*a^2*c^(5/4)*e^(7/2)*Sqrt[c - d*x^2]) - (b^(3/2)*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(5/2)*d^(1/4)*e^(7/2)*Sqrt[c - d*x^2]) + (b^(3/2)*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(5/2)*d^(1/4)*e^(7/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 480, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
888,1,444,0,0.7906806,"\int \frac{(e x)^{9/2}}{\left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(9/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x]","-\frac{a^{3/2} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a^{3/2} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-2 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{7/4} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-2 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{7/4} \sqrt{c-d x^2} (b c-a d)}-\frac{c e^3 (e x)^{3/2}}{d \sqrt{c-d x^2} (b c-a d)}","-\frac{a^{3/2} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a^{3/2} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-2 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{7/4} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-2 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{7/4} \sqrt{c-d x^2} (b c-a d)}-\frac{c e^3 (e x)^{3/2}}{d \sqrt{c-d x^2} (b c-a d)}",1,"-((c*e^3*(e*x)^(3/2))/(d*(b*c - a*d)*Sqrt[c - d*x^2])) + (c^(3/4)*(3*b*c - 2*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(7/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(3/4)*(3*b*c - 2*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(7/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (a^(3/2)*c^(1/4)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(3/2)*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (a^(3/2)*c^(1/4)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b^(3/2)*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 470, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
889,1,338,0,0.5204738,"\int \frac{(e x)^{7/2}}{\left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(7/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x]","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (b c-2 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{5/4} \sqrt{c-d x^2} (b c-a d)}-\frac{c e^3 \sqrt{e x}}{d \sqrt{c-d x^2} (b c-a d)}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (b c-2 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b d^{5/4} \sqrt{c-d x^2} (b c-a d)}-\frac{c e^3 \sqrt{e x}}{d \sqrt{c-d x^2} (b c-a d)}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}",1,"-((c*e^3*Sqrt[e*x])/(d*(b*c - a*d)*Sqrt[c - d*x^2])) + (c^(1/4)*(b*c - 2*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(5/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (a*c^(1/4)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (a*c^(1/4)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(b*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 470, 523, 224, 221, 409, 1219, 1218}"
890,1,414,0,0.6910379,"\int \frac{(e x)^{5/2}}{\left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(5/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x]","-\frac{c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{d^{3/4} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{d^{3/4} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{e (e x)^{3/2}}{\sqrt{c-d x^2} (b c-a d)}","-\frac{c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{d^{3/4} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{d^{3/4} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{a} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{e (e x)^{3/2}}{\sqrt{c-d x^2} (b c-a d)}",1,"-((e*(e*x)^(3/2))/((b*c - a*d)*Sqrt[c - d*x^2])) + (c^(3/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(d^(3/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(3/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(d^(3/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[b]*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[b]*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 471, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
891,1,314,0,0.426559,"\int \frac{(e x)^{3/2}}{\left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(3/2)/((a - b*x^2)*(c - d*x^2)^(3/2)),x]","-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{e \sqrt{e x}}{\sqrt{c-d x^2} (b c-a d)}","-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{e \sqrt{e x}}{\sqrt{c-d x^2} (b c-a d)}",1,"-((e*Sqrt[e*x])/((b*c - a*d)*Sqrt[c - d*x^2])) - (c^(1/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (c^(1/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (c^(1/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 471, 523, 224, 221, 409, 1219, 1218}"
892,1,420,0,0.7166676,"\int \frac{\sqrt{e x}}{\left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[Sqrt[e*x]/((a - b*x^2)*(c - d*x^2)^(3/2)),x]","-\frac{d (e x)^{3/2}}{c e \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}","-\frac{d (e x)^{3/2}}{c e \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{\sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}",1,"-((d*(e*x)^(3/2))/(c*(b*c - a*d)*e*Sqrt[c - d*x^2])) + (d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(c^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(c^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (Sqrt[b]*c^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (Sqrt[b]*c^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(Sqrt[a]*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 472, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
893,1,328,0,0.4878195,"\int \frac{1}{\sqrt{e x} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[e*x]*(a - b*x^2)*(c - d*x^2)^(3/2)),x]","-\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{c^{3/4} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}-\frac{d \sqrt{e x}}{c e \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}","-\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{c^{3/4} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}-\frac{d \sqrt{e x}}{c e \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}",1,"-((d*Sqrt[e*x])/(c*(b*c - a*d)*e*Sqrt[c - d*x^2])) - (d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(c^(3/4)*(b*c - a*d)*Sqrt[e]*Sqrt[c - d*x^2]) + (b*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*d^(1/4)*(b*c - a*d)*Sqrt[e]*Sqrt[c - d*x^2]) + (b*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*d^(1/4)*(b*c - a*d)*Sqrt[e]*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 414, 523, 224, 221, 409, 1219, 1218}"
894,1,493,0,0.984656,"\int \frac{1}{(e x)^{3/2} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[1/((e*x)^(3/2)*(a - b*x^2)*(c - d*x^2)^(3/2)),x]","-\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (2 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (2 b c-3 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (2 b c-3 a d)}{a c^2 e \sqrt{e x} (b c-a d)}-\frac{d}{c e \sqrt{e x} \sqrt{c-d x^2} (b c-a d)}","-\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (2 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (2 b c-3 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (2 b c-3 a d)}{a c^2 e \sqrt{e x} (b c-a d)}-\frac{d}{c e \sqrt{e x} \sqrt{c-d x^2} (b c-a d)}",1,"-(d/(c*(b*c - a*d)*e*Sqrt[e*x]*Sqrt[c - d*x^2])) - ((2*b*c - 3*a*d)*Sqrt[c - d*x^2])/(a*c^2*(b*c - a*d)*e*Sqrt[e*x]) - (d^(1/4)*(2*b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*c^(5/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2]) + (d^(1/4)*(2*b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a*c^(5/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2]) - (b^(3/2)*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*d^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2]) + (b^(3/2)*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^(3/2)*d^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 472, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
895,1,397,0,0.7892514,"\int \frac{1}{(e x)^{5/2} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2}} \, dx","Int[1/((e*x)^(5/2)*(a - b*x^2)*(c - d*x^2)^(3/2)),x]","\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} (2 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a c^{7/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (2 b c-5 a d)}{3 a c^2 e (e x)^{3/2} (b c-a d)}-\frac{d}{c e (e x)^{3/2} \sqrt{c-d x^2} (b c-a d)}","\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{a^2 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} (2 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{3 a c^{7/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (2 b c-5 a d)}{3 a c^2 e (e x)^{3/2} (b c-a d)}-\frac{d}{c e (e x)^{3/2} \sqrt{c-d x^2} (b c-a d)}",1,"-(d/(c*(b*c - a*d)*e*(e*x)^(3/2)*Sqrt[c - d*x^2])) - ((2*b*c - 5*a*d)*Sqrt[c - d*x^2])/(3*a*c^2*(b*c - a*d)*e*(e*x)^(3/2)) + (d^(3/4)*(2*b*c - 5*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(3*a*c^(7/4)*(b*c - a*d)*e^(5/2)*Sqrt[c - d*x^2]) + (b^2*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*d^(1/4)*(b*c - a*d)*e^(5/2)*Sqrt[c - d*x^2]) + (b^2*c^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(a^2*d^(1/4)*(b*c - a*d)*e^(5/2)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 472, 583, 523, 224, 221, 409, 1219, 1218}"
896,1,362,0,0.6974411,"\int \frac{(e x)^{7/2} \sqrt{c-d x^2}}{\left(a-b x^2\right)^2} \, dx","Int[((e*x)^(7/2)*Sqrt[c - d*x^2])/(a - b*x^2)^2,x]","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (8 b c-21 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e (e x)^{5/2} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right)}+\frac{7 e^3 \sqrt{e x} \sqrt{c-d x^2}}{6 b^2}","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (8 b c-21 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e (e x)^{5/2} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right)}+\frac{7 e^3 \sqrt{e x} \sqrt{c-d x^2}}{6 b^2}",1,"(7*e^3*Sqrt[e*x]*Sqrt[c - d*x^2])/(6*b^2) + (e*(e*x)^(5/2)*Sqrt[c - d*x^2])/(2*b*(a - b*x^2)) + (c^(1/4)*(8*b*c - 21*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*b^3*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 7*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^3*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 7*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^3*d^(1/4)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 467, 582, 523, 224, 221, 409, 1219, 1218}"
897,1,413,0,0.7596537,"\int \frac{(e x)^{5/2} \sqrt{c-d x^2}}{\left(a-b x^2\right)^2} \, dx","Int[((e*x)^(5/2)*Sqrt[c - d*x^2])/(a - b*x^2)^2,x]","\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e (e x)^{3/2} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right)}+\frac{5 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt{c-d x^2}}-\frac{5 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt{c-d x^2}}","\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e (e x)^{3/2} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right)}+\frac{5 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt{c-d x^2}}-\frac{5 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt{c-d x^2}}",1,"(e*(e*x)^(3/2)*Sqrt[c - d*x^2])/(2*b*(a - b*x^2)) - (5*c^(3/4)*d^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b^2*Sqrt[c - d*x^2]) + (5*c^(3/4)*d^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b^2*Sqrt[c - d*x^2]) + (c^(1/4)*(3*b*c - 5*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*b^(5/2)*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(3*b*c - 5*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*b^(5/2)*d^(1/4)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 467, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
898,1,328,0,0.4852839,"\int \frac{(e x)^{3/2} \sqrt{c-d x^2}}{\left(a-b x^2\right)^2} \, dx","Int[((e*x)^(3/2)*Sqrt[c - d*x^2])/(a - b*x^2)^2,x]","-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^2 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e \sqrt{e x} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right)}-\frac{3 \sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt{c-d x^2}}","-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^2 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^2 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e \sqrt{e x} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right)}-\frac{3 \sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt{c-d x^2}}",1,"(e*Sqrt[e*x]*Sqrt[c - d*x^2])/(2*b*(a - b*x^2)) - (3*c^(1/4)*d^(3/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b^2*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - 3*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*b^2*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - 3*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*b^2*d^(1/4)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 467, 523, 224, 221, 409, 1219, 1218}"
899,1,417,0,0.72038,"\int \frac{\sqrt{e x} \sqrt{c-d x^2}}{\left(a-b x^2\right)^2} \, dx","Int[(Sqrt[e*x]*Sqrt[c - d*x^2])/(a - b*x^2)^2,x]","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b \sqrt{c-d x^2}}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b \sqrt{c-d x^2}}+\frac{(e x)^{3/2} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right)}","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b \sqrt{c-d x^2}}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b \sqrt{c-d x^2}}+\frac{(e x)^{3/2} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right)}",1,"((e*x)^(3/2)*Sqrt[c - d*x^2])/(2*a*e*(a - b*x^2)) - (c^(3/4)*d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*b*Sqrt[c - d*x^2]) + (c^(3/4)*d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*b*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c + a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*b^(3/2)*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c + a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*b^(3/2)*d^(1/4)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 469, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
900,1,335,0,0.4512967,"\int \frac{\sqrt{c-d x^2}}{\sqrt{e x} \left(a-b x^2\right)^2} \, dx","Int[Sqrt[c - d*x^2]/(Sqrt[e*x]*(a - b*x^2)^2),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt{e x} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right)}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt{e x} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right)}",1,"(Sqrt[e*x]*Sqrt[c - d*x^2])/(2*a*e*(a - b*x^2)) + (c^(1/4)*d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*b*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(3*b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*b*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(3*b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*b*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 412, 523, 224, 221, 409, 1219, 1218}"
901,1,444,0,0.9115189,"\int \frac{\sqrt{c-d x^2}}{(e x)^{3/2} \left(a-b x^2\right)^2} \, dx","Int[Sqrt[c - d*x^2]/((e*x)^(3/2)*(a - b*x^2)^2),x]","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{5 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 e^{3/2} \sqrt{c-d x^2}}-\frac{5 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 e^{3/2} \sqrt{c-d x^2}}-\frac{5 \sqrt{c-d x^2}}{2 a^2 e \sqrt{e x}}+\frac{\sqrt{c-d x^2}}{2 a e \sqrt{e x} \left(a-b x^2\right)}","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt{b} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{5 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 e^{3/2} \sqrt{c-d x^2}}-\frac{5 c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 e^{3/2} \sqrt{c-d x^2}}-\frac{5 \sqrt{c-d x^2}}{2 a^2 e \sqrt{e x}}+\frac{\sqrt{c-d x^2}}{2 a e \sqrt{e x} \left(a-b x^2\right)}",1,"(-5*Sqrt[c - d*x^2])/(2*a^2*e*Sqrt[e*x]) + Sqrt[c - d*x^2]/(2*a*e*Sqrt[e*x]*(a - b*x^2)) - (5*c^(3/4)*d^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*e^(3/2)*Sqrt[c - d*x^2]) + (5*c^(3/4)*d^(1/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*e^(3/2)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*Sqrt[b]*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(5*b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*Sqrt[b]*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 469, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
902,1,355,0,0.6519048,"\int \frac{\sqrt{c-d x^2}}{(e x)^{5/2} \left(a-b x^2\right)^2} \, dx","Int[Sqrt[c - d*x^2]/((e*x)^(5/2)*(a - b*x^2)^2),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{7 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 e^{5/2} \sqrt{c-d x^2}}-\frac{7 \sqrt{c-d x^2}}{6 a^2 e (e x)^{3/2}}+\frac{\sqrt{c-d x^2}}{2 a e (e x)^{3/2} \left(a-b x^2\right)}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{7 \sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 e^{5/2} \sqrt{c-d x^2}}-\frac{7 \sqrt{c-d x^2}}{6 a^2 e (e x)^{3/2}}+\frac{\sqrt{c-d x^2}}{2 a e (e x)^{3/2} \left(a-b x^2\right)}",1,"(-7*Sqrt[c - d*x^2])/(6*a^2*e*(e*x)^(3/2)) + Sqrt[c - d*x^2]/(2*a*e*(e*x)^(3/2)*(a - b*x^2)) + (7*c^(1/4)*d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*a^2*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(7*b*c - 5*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(7*b*c - 5*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 469, 583, 523, 224, 221, 409, 1219, 1218}"
903,1,429,0,0.9748498,"\int \frac{(e x)^{7/2} \left(c-d x^2\right)^{3/2}}{\left(a-b x^2\right)^2} \, dx","Int[((e*x)^(7/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x]","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \left(231 a^2 d^2-259 a b c d+48 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{42 b^4 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e^3 \sqrt{e x} \sqrt{c-d x^2} (57 b c-77 a d)}{42 b^3}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^4 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^4 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e (e x)^{5/2} \left(c-d x^2\right)^{3/2}}{2 b \left(a-b x^2\right)}-\frac{11 d e (e x)^{5/2} \sqrt{c-d x^2}}{14 b^2}","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} \left(231 a^2 d^2-259 a b c d+48 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{42 b^4 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e^3 \sqrt{e x} \sqrt{c-d x^2} (57 b c-77 a d)}{42 b^3}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^4 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^4 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e (e x)^{5/2} \left(c-d x^2\right)^{3/2}}{2 b \left(a-b x^2\right)}-\frac{11 d e (e x)^{5/2} \sqrt{c-d x^2}}{14 b^2}",1,"((57*b*c - 77*a*d)*e^3*Sqrt[e*x]*Sqrt[c - d*x^2])/(42*b^3) - (11*d*e*(e*x)^(5/2)*Sqrt[c - d*x^2])/(14*b^2) + (e*(e*x)^(5/2)*(c - d*x^2)^(3/2))/(2*b*(a - b*x^2)) + (c^(1/4)*(48*b^2*c^2 - 259*a*b*c*d + 231*a^2*d^2)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(42*b^4*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 11*a*d)*(b*c - a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^4*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 11*a*d)*(b*c - a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^4*d^(1/4)*Sqrt[c - d*x^2])","A",12,10,30,0.3333,1,"{466, 467, 581, 582, 523, 224, 221, 409, 1219, 1218}"
904,1,485,0,1.0120543,"\int \frac{(e x)^{5/2} \left(c-d x^2\right)^{3/2}}{\left(a-b x^2\right)^2} \, dx","Int[((e*x)^(5/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x]","\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (11 b c-15 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{10 b^3 \sqrt{c-d x^2}}-\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (11 b c-15 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{10 b^3 \sqrt{c-d x^2}}+\frac{e (e x)^{3/2} \left(c-d x^2\right)^{3/2}}{2 b \left(a-b x^2\right)}-\frac{9 d e (e x)^{3/2} \sqrt{c-d x^2}}{10 b^2}","\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} \left(3 a^2 d^2-4 a b c d+b^2 c^2\right) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{7/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (11 b c-15 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{10 b^3 \sqrt{c-d x^2}}-\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (11 b c-15 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{10 b^3 \sqrt{c-d x^2}}+\frac{e (e x)^{3/2} \left(c-d x^2\right)^{3/2}}{2 b \left(a-b x^2\right)}-\frac{9 d e (e x)^{3/2} \sqrt{c-d x^2}}{10 b^2}",1,"(-9*d*e*(e*x)^(3/2)*Sqrt[c - d*x^2])/(10*b^2) + (e*(e*x)^(3/2)*(c - d*x^2)^(3/2))/(2*b*(a - b*x^2)) - (3*c^(3/4)*d^(1/4)*(11*b*c - 15*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(10*b^3*Sqrt[c - d*x^2]) + (3*c^(3/4)*d^(1/4)*(11*b*c - 15*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(10*b^3*Sqrt[c - d*x^2]) + (3*c^(1/4)*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*b^(7/2)*d^(1/4)*Sqrt[c - d*x^2]) - (3*c^(1/4)*(b^2*c^2 - 4*a*b*c*d + 3*a^2*d^2)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*b^(7/2)*d^(1/4)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 467, 581, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
905,1,381,0,0.7289813,"\int \frac{(e x)^{3/2} \left(c-d x^2\right)^{3/2}}{\left(a-b x^2\right)^2} \, dx","Int[((e*x)^(3/2)*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x]","-\frac{\sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (17 b c-21 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 b^3 \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e \sqrt{e x} \left(c-d x^2\right)^{3/2}}{2 b \left(a-b x^2\right)}-\frac{7 d e \sqrt{e x} \sqrt{c-d x^2}}{6 b^2}","-\frac{\sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (17 b c-21 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 b^3 \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^3 \sqrt[4]{d} \sqrt{c-d x^2}}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b^3 \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{e \sqrt{e x} \left(c-d x^2\right)^{3/2}}{2 b \left(a-b x^2\right)}-\frac{7 d e \sqrt{e x} \sqrt{c-d x^2}}{6 b^2}",1,"(-7*d*e*Sqrt[e*x]*Sqrt[c - d*x^2])/(6*b^2) + (e*Sqrt[e*x]*(c - d*x^2)^(3/2))/(2*b*(a - b*x^2)) - (c^(1/4)*d^(3/4)*(17*b*c - 21*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*b^3*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - 7*a*d)*(b*c - a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*b^3*d^(1/4)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - 7*a*d)*(b*c - a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*b^3*d^(1/4)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 467, 528, 523, 224, 221, 409, 1219, 1218}"
906,1,474,0,0.8395434,"\int \frac{\sqrt{e x} \left(c-d x^2\right)^{3/2}}{\left(a-b x^2\right)^2} \, dx","Int[(Sqrt[e*x]*(c - d*x^2)^(3/2))/(a - b*x^2)^2,x]","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-5 a^2 d^2+4 a b c d+b^2 c^2\right) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-5 a^2 d^2+4 a b c d+b^2 c^2\right) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b^2 \sqrt{c-d x^2}}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b^2 \sqrt{c-d x^2}}+\frac{(e x)^{3/2} \sqrt{c-d x^2} (b c-a d)}{2 a b e \left(a-b x^2\right)}","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-5 a^2 d^2+4 a b c d+b^2 c^2\right) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-5 a^2 d^2+4 a b c d+b^2 c^2\right) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2}}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b^2 \sqrt{c-d x^2}}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b^2 \sqrt{c-d x^2}}+\frac{(e x)^{3/2} \sqrt{c-d x^2} (b c-a d)}{2 a b e \left(a-b x^2\right)}",1,"((b*c - a*d)*(e*x)^(3/2)*Sqrt[c - d*x^2])/(2*a*b*e*(a - b*x^2)) - (c^(3/4)*d^(1/4)*(b*c - 5*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*b^2*Sqrt[c - d*x^2]) + (c^(3/4)*d^(1/4)*(b*c - 5*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*b^2*Sqrt[c - d*x^2]) - (c^(1/4)*(b^2*c^2 + 4*a*b*c*d - 5*a^2*d^2)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*b^(5/2)*d^(1/4)*Sqrt[c - d*x^2]) + (c^(1/4)*(b^2*c^2 + 4*a*b*c*d - 5*a^2*d^2)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*b^(5/2)*d^(1/4)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 468, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
907,1,366,0,0.5971674,"\int \frac{\left(c-d x^2\right)^{3/2}}{\sqrt{e x} \left(a-b x^2\right)^2} \, dx","Int[(c - d*x^2)^(3/2)/(Sqrt[e*x]*(a - b*x^2)^2),x]","\frac{3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (a d+b c) (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (a d+b c) (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (3 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b^2 \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt{e x} \sqrt{c-d x^2} (b c-a d)}{2 a b e \left(a-b x^2\right)}","\frac{3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (a d+b c) (b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (a d+b c) (b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 b^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (3 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a b^2 \sqrt{e} \sqrt{c-d x^2}}+\frac{\sqrt{e x} \sqrt{c-d x^2} (b c-a d)}{2 a b e \left(a-b x^2\right)}",1,"((b*c - a*d)*Sqrt[e*x]*Sqrt[c - d*x^2])/(2*a*b*e*(a - b*x^2)) + (c^(1/4)*d^(3/4)*(b*c + 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*b^2*Sqrt[e]*Sqrt[c - d*x^2]) + (3*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*b^2*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2]) + (3*c^(1/4)*(b*c - a*d)*(b*c + a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*b^2*d^(1/4)*Sqrt[e]*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 413, 523, 224, 221, 409, 1219, 1218}"
908,1,519,0,1.1201962,"\int \frac{\left(c-d x^2\right)^{3/2}}{(e x)^{3/2} \left(a-b x^2\right)^2} \, dx","Int[(c - d*x^2)^(3/2)/((e*x)^(3/2)*(a - b*x^2)^2),x]","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2-4 a b c d+5 b^2 c^2\right) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2-4 a b c d+5 b^2 c^2\right) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 b e^{3/2} \sqrt{c-d x^2}}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 b e^{3/2} \sqrt{c-d x^2}}-\frac{\sqrt{c-d x^2} (5 b c-a d)}{2 a^2 b e \sqrt{e x}}+\frac{\sqrt{c-d x^2} (b c-a d)}{2 a b e \sqrt{e x} \left(a-b x^2\right)}","-\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2-4 a b c d+5 b^2 c^2\right) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2-4 a b c d+5 b^2 c^2\right) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} b^{3/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2}}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 b e^{3/2} \sqrt{c-d x^2}}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 b e^{3/2} \sqrt{c-d x^2}}-\frac{\sqrt{c-d x^2} (5 b c-a d)}{2 a^2 b e \sqrt{e x}}+\frac{\sqrt{c-d x^2} (b c-a d)}{2 a b e \sqrt{e x} \left(a-b x^2\right)}",1,"-((5*b*c - a*d)*Sqrt[c - d*x^2])/(2*a^2*b*e*Sqrt[e*x]) + ((b*c - a*d)*Sqrt[c - d*x^2])/(2*a*b*e*Sqrt[e*x]*(a - b*x^2)) - (c^(3/4)*d^(1/4)*(5*b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*b*e^(3/2)*Sqrt[c - d*x^2]) + (c^(3/4)*d^(1/4)*(5*b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*b*e^(3/2)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b^2*c^2 - 4*a*b*c*d - a^2*d^2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*b^(3/2)*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(5*b^2*c^2 - 4*a*b*c*d - a^2*d^2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*b^(3/2)*d^(1/4)*e^(3/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 468, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
909,1,412,0,0.8513499,"\int \frac{\left(c-d x^2\right)^{3/2}}{(e x)^{5/2} \left(a-b x^2\right)^2} \, dx","Int[(c - d*x^2)^(3/2)/((e*x)^(5/2)*(a - b*x^2)^2),x]","\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (7 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 b e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) (7 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) (7 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}-\frac{\sqrt{c-d x^2} (7 b c-3 a d)}{6 a^2 b e (e x)^{3/2}}+\frac{\sqrt{c-d x^2} (b c-a d)}{2 a b e (e x)^{3/2} \left(a-b x^2\right)}","\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} (7 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 b e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) (7 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-a d) (7 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 b \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2}}-\frac{\sqrt{c-d x^2} (7 b c-3 a d)}{6 a^2 b e (e x)^{3/2}}+\frac{\sqrt{c-d x^2} (b c-a d)}{2 a b e (e x)^{3/2} \left(a-b x^2\right)}",1,"-((7*b*c - 3*a*d)*Sqrt[c - d*x^2])/(6*a^2*b*e*(e*x)^(3/2)) + ((b*c - a*d)*Sqrt[c - d*x^2])/(2*a*b*e*(e*x)^(3/2)*(a - b*x^2)) + (c^(1/4)*d^(3/4)*(7*b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*a^2*b*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*(7*b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*b*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - a*d)*(7*b*c - a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*b*d^(1/4)*e^(5/2)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 468, 583, 523, 224, 221, 409, 1219, 1218}"
910,1,484,0,0.8739916,"\int \frac{(e x)^{9/2}}{\left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[(e*x)^(9/2)/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]","-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 d^{3/4} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 d^{3/4} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a e^3 (e x)^{3/2} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right) (b c-a d)}","-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-5 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 d^{3/4} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-5 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 d^{3/4} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{5/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a e^3 (e x)^{3/2} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right) (b c-a d)}",1,"(a*e^3*(e*x)^(3/2)*Sqrt[c - d*x^2])/(2*b*(b*c - a*d)*(a - b*x^2)) + (c^(3/4)*(4*b*c - 5*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b^2*d^(3/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(3/4)*(4*b*c - 5*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b^2*d^(3/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*(7*b*c - 5*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^(5/2)*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*(7*b*c - 5*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^(5/2)*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 470, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
911,1,376,0,0.5454674,"\int \frac{(e x)^{7/2}}{\left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[(e*x)^(7/2)/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^2 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^2 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a e^3 \sqrt{e x} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right) (b c-a d)}","\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (4 b c-3 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b^2 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^2 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (5 b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^2 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{a e^3 \sqrt{e x} \sqrt{c-d x^2}}{2 b \left(a-b x^2\right) (b c-a d)}",1,"(a*e^3*Sqrt[e*x]*Sqrt[c - d*x^2])/(2*b*(b*c - a*d)*(a - b*x^2)) + (c^(1/4)*(4*b*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c - 3*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^2*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 470, 523, 224, 221, 409, 1219, 1218}"
912,1,460,0,0.7796074,"\int \frac{(e x)^{5/2}}{\left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[(e*x)^(5/2)/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt{c-d x^2} (b c-a d)}-\frac{c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt{c-d x^2} (b c-a d)}+\frac{e (e x)^{3/2} \sqrt{c-d x^2}}{2 \left(a-b x^2\right) (b c-a d)}","\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (3 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt{c-d x^2} (b c-a d)}-\frac{c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt{c-d x^2} (b c-a d)}+\frac{e (e x)^{3/2} \sqrt{c-d x^2}}{2 \left(a-b x^2\right) (b c-a d)}",1,"(e*(e*x)^(3/2)*Sqrt[c - d*x^2])/(2*(b*c - a*d)*(a - b*x^2)) - (c^(3/4)*d^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b*(b*c - a*d)*Sqrt[c - d*x^2]) + (c^(3/4)*d^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b*(b*c - a*d)*Sqrt[c - d*x^2]) + (c^(1/4)*(3*b*c - a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*b^(3/2)*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(3*b*c - a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*b^(3/2)*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 471, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
913,1,363,0,0.511338,"\int \frac{(e x)^{3/2}}{\left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[(e*x)^(3/2)/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{e \sqrt{e x} \sqrt{c-d x^2}}{2 \left(a-b x^2\right) (b c-a d)}","\frac{\sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{e \sqrt{e x} \sqrt{c-d x^2}}{2 \left(a-b x^2\right) (b c-a d)}",1,"(e*Sqrt[e*x]*Sqrt[c - d*x^2])/(2*(b*c - a*d)*(a - b*x^2)) + (c^(1/4)*d^(3/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c + a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*b*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c + a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*b*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 471, 523, 224, 221, 409, 1219, 1218}"
914,1,464,0,0.7865532,"\int \frac{\sqrt{e x}}{\left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[Sqrt[e*x]/((a - b*x^2)^2*Sqrt[c - d*x^2]),x]","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt{c-d x^2} (b c-a d)}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt{c-d x^2} (b c-a d)}+\frac{b (e x)^{3/2} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right) (b c-a d)}","-\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)}+\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt{c-d x^2} (b c-a d)}-\frac{c^{3/4} \sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt{c-d x^2} (b c-a d)}+\frac{b (e x)^{3/2} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right) (b c-a d)}",1,"(b*(e*x)^(3/2)*Sqrt[c - d*x^2])/(2*a*(b*c - a*d)*e*(a - b*x^2)) - (c^(3/4)*d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*(b*c - a*d)*Sqrt[c - d*x^2]) + (c^(3/4)*d^(1/4)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*(b*c - a*d)*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c - 3*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*Sqrt[b]*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2]) + (c^(1/4)*(b*c - 3*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*Sqrt[b]*d^(1/4)*(b*c - a*d)*Sqrt[c - d*x^2])","A",15,12,30,0.4000,1,"{466, 472, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
915,1,367,0,0.518724,"\int \frac{1}{\sqrt{e x} \left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[1/(Sqrt[e*x]*(a - b*x^2)^2*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt{e x} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right) (b c-a d)}","\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-5 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} d^{3/4} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt{e} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt{e x} \sqrt{c-d x^2}}{2 a e \left(a-b x^2\right) (b c-a d)}",1,"(b*Sqrt[e*x]*Sqrt[c - d*x^2])/(2*a*(b*c - a*d)*e*(a - b*x^2)) + (c^(1/4)*d^(3/4)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*(b*c - a*d)*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(3*b*c - 5*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*d^(1/4)*(b*c - a*d)*Sqrt[e]*Sqrt[c - d*x^2]) + (c^(1/4)*(3*b*c - 5*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*d^(1/4)*(b*c - a*d)*Sqrt[e]*Sqrt[c - d*x^2])","A",10,8,30,0.2667,1,"{466, 414, 523, 224, 221, 409, 1219, 1218}"
916,1,535,0,1.0772543,"\int \frac{1}{(e x)^{3/2} \left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[1/((e*x)^(3/2)*(a - b*x^2)^2*Sqrt[c - d*x^2]),x]","\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-4 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-4 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (5 b c-4 a d)}{2 a^2 c e \sqrt{e x} (b c-a d)}+\frac{b \sqrt{c-d x^2}}{2 a e \sqrt{e x} \left(a-b x^2\right) (b c-a d)}","\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-4 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} (5 b c-4 a d) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 \sqrt[4]{c} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-7 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (5 b c-4 a d)}{2 a^2 c e \sqrt{e x} (b c-a d)}+\frac{b \sqrt{c-d x^2}}{2 a e \sqrt{e x} \left(a-b x^2\right) (b c-a d)}",1,"-((5*b*c - 4*a*d)*Sqrt[c - d*x^2])/(2*a^2*c*(b*c - a*d)*e*Sqrt[e*x]) + (b*Sqrt[c - d*x^2])/(2*a*(b*c - a*d)*e*Sqrt[e*x]*(a - b*x^2)) - (d^(1/4)*(5*b*c - 4*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*c^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2]) + (d^(1/4)*(5*b*c - 4*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*c^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2]) - (Sqrt[b]*c^(1/4)*(5*b*c - 7*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*d^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2]) + (Sqrt[b]*c^(1/4)*(5*b*c - 7*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*d^(1/4)*(b*c - a*d)*e^(3/2)*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 472, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
917,1,429,0,0.8142805,"\int \frac{1}{(e x)^{5/2} \left(a-b x^2\right)^2 \sqrt{c-d x^2}} \, dx","Int[1/((e*x)^(5/2)*(a - b*x^2)^2*Sqrt[c - d*x^2]),x]","\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} (7 b c-4 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 c^{3/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-9 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-9 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (7 b c-4 a d)}{6 a^2 c e (e x)^{3/2} (b c-a d)}+\frac{b \sqrt{c-d x^2}}{2 a e (e x)^{3/2} \left(a-b x^2\right) (b c-a d)}","\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} (7 b c-4 a d) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 c^{3/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-9 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}+\frac{b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-9 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)}-\frac{\sqrt{c-d x^2} (7 b c-4 a d)}{6 a^2 c e (e x)^{3/2} (b c-a d)}+\frac{b \sqrt{c-d x^2}}{2 a e (e x)^{3/2} \left(a-b x^2\right) (b c-a d)}",1,"-((7*b*c - 4*a*d)*Sqrt[c - d*x^2])/(6*a^2*c*(b*c - a*d)*e*(e*x)^(3/2)) + (b*Sqrt[c - d*x^2])/(2*a*(b*c - a*d)*e*(e*x)^(3/2)*(a - b*x^2)) + (d^(3/4)*(7*b*c - 4*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*a^2*c^(3/4)*(b*c - a*d)*e^(5/2)*Sqrt[c - d*x^2]) + (b*c^(1/4)*(7*b*c - 9*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*(b*c - a*d)*e^(5/2)*Sqrt[c - d*x^2]) + (b*c^(1/4)*(7*b*c - 9*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*(b*c - a*d)*e^(5/2)*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 472, 583, 523, 224, 221, 409, 1219, 1218}"
918,1,529,0,1.0799353,"\int \frac{(e x)^{9/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (a d+2 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b d^{3/4} \sqrt{c-d x^2} (b c-a d)^2}-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (a d+2 b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b d^{3/4} \sqrt{c-d x^2} (b c-a d)^2}+\frac{e^3 (e x)^{3/2} (a d+2 b c)}{2 b \sqrt{c-d x^2} (b c-a d)^2}+\frac{a e^3 (e x)^{3/2}}{2 b \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}","\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (7 b c-a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (a d+2 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b d^{3/4} \sqrt{c-d x^2} (b c-a d)^2}-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (a d+2 b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b d^{3/4} \sqrt{c-d x^2} (b c-a d)^2}+\frac{e^3 (e x)^{3/2} (a d+2 b c)}{2 b \sqrt{c-d x^2} (b c-a d)^2}+\frac{a e^3 (e x)^{3/2}}{2 b \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}",1,"((2*b*c + a*d)*e^3*(e*x)^(3/2))/(2*b*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (a*e^3*(e*x)^(3/2))/(2*b*(b*c - a*d)*(a - b*x^2)*Sqrt[c - d*x^2]) - (c^(3/4)*(2*b*c + a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b*d^(3/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (c^(3/4)*(2*b*c + a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b*d^(3/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*(7*b*c - a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^(3/2)*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*(7*b*c - a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b^(3/2)*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 470, 579, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
919,1,420,0,0.6922436,"\int \frac{(e x)^{7/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{e^3 \sqrt{e x} (a d+2 b c)}{2 b \sqrt{c-d x^2} (b c-a d)^2}+\frac{a e^3 \sqrt{e x}}{2 b \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+2 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+5 b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+5 b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}","\frac{e^3 \sqrt{e x} (a d+2 b c)}{2 b \sqrt{c-d x^2} (b c-a d)^2}+\frac{a e^3 \sqrt{e x}}{2 b \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+2 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+5 b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+5 b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 b \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}",1,"((2*b*c + a*d)*e^3*Sqrt[e*x])/(2*b*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (a*e^3*Sqrt[e*x])/(2*b*(b*c - a*d)*(a - b*x^2)*Sqrt[c - d*x^2]) + (c^(1/4)*(2*b*c + a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*b*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c + a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (c^(1/4)*(5*b*c + a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*b*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 470, 527, 523, 224, 221, 409, 1219, 1218}"
920,1,485,0,0.957945,"\int \frac{(e x)^{5/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt{c-d x^2} (b c-a d)^2}-\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 d e (e x)^{3/2}}{2 \sqrt{c-d x^2} (b c-a d)^2}+\frac{e (e x)^{3/2}}{2 \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}","\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt{c-d x^2} (b c-a d)^2}-\frac{3 c^{3/4} \sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{3 \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 d e (e x)^{3/2}}{2 \sqrt{c-d x^2} (b c-a d)^2}+\frac{e (e x)^{3/2}}{2 \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}",1,"(3*d*e*(e*x)^(3/2))/(2*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (e*(e*x)^(3/2))/(2*(b*c - a*d)*(a - b*x^2)*Sqrt[c - d*x^2]) - (3*c^(3/4)*d^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (3*c^(3/4)*d^(1/4)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (3*c^(1/4)*(b*c + a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*Sqrt[b]*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (3*c^(1/4)*(b*c + a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*Sqrt[b]*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 471, 579, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
921,1,391,0,0.6454622,"\int \frac{(e x)^{3/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[(e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{3 \sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (5 a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (5 a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 d e \sqrt{e x}}{2 \sqrt{c-d x^2} (b c-a d)^2}+\frac{e \sqrt{e x}}{2 \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}","\frac{3 \sqrt[4]{c} d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (5 a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (5 a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 d e \sqrt{e x}}{2 \sqrt{c-d x^2} (b c-a d)^2}+\frac{e \sqrt{e x}}{2 \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}",1,"(3*d*e*Sqrt[e*x])/(2*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (e*Sqrt[e*x])/(2*(b*c - a*d)*(a - b*x^2)*Sqrt[c - d*x^2]) + (3*c^(1/4)*d^(3/4)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c + 5*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (c^(1/4)*(b*c + 5*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 471, 527, 523, 224, 221, 409, 1219, 1218}"
922,1,531,0,1.0903046,"\int \frac{\sqrt{e x}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[Sqrt[e*x]/((a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{d (e x)^{3/2} (2 a d+b c)}{2 a c e \sqrt{c-d x^2} (b c-a d)^2}+\frac{b (e x)^{3/2}}{2 a e \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^2}","-\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{\sqrt{b} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-7 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^2}+\frac{d (e x)^{3/2} (2 a d+b c)}{2 a c e \sqrt{c-d x^2} (b c-a d)^2}+\frac{b (e x)^{3/2}}{2 a e \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d)*(e*x)^(3/2))/(2*a*c*(b*c - a*d)^2*e*Sqrt[c - d*x^2]) + (b*(e*x)^(3/2))/(2*a*(b*c - a*d)*e*(a - b*x^2)*Sqrt[c - d*x^2]) - (d^(1/4)*(b*c + 2*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*c^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (d^(1/4)*(b*c + 2*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*c^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) - (Sqrt[b]*c^(1/4)*(b*c - 7*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2]) + (Sqrt[b]*c^(1/4)*(b*c - 7*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*d^(1/4)*(b*c - a*d)^2*Sqrt[c - d*x^2])","A",16,13,30,0.4333,1,"{466, 472, 579, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
923,1,426,0,0.7745807,"\int \frac{1}{\sqrt{e x} \left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[1/(Sqrt[e*x]*(a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{3 b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^2}+\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a c^{3/4} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b \sqrt{e x}}{2 a e \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{d \sqrt{e x} (2 a d+b c)}{2 a c e \sqrt{c-d x^2} (b c-a d)^2}","\frac{3 b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^2}+\frac{3 b \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^2}+\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a c^{3/4} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b \sqrt{e x}}{2 a e \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{d \sqrt{e x} (2 a d+b c)}{2 a c e \sqrt{c-d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d)*Sqrt[e*x])/(2*a*c*(b*c - a*d)^2*e*Sqrt[c - d*x^2]) + (b*Sqrt[e*x])/(2*a*(b*c - a*d)*e*(a - b*x^2)*Sqrt[c - d*x^2]) + (d^(3/4)*(b*c + 2*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*c^(3/4)*(b*c - a*d)^2*Sqrt[e]*Sqrt[c - d*x^2]) + (3*b*c^(1/4)*(b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*d^(1/4)*(b*c - a*d)^2*Sqrt[e]*Sqrt[c - d*x^2]) + (3*b*c^(1/4)*(b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*d^(1/4)*(b*c - a*d)^2*Sqrt[e]*Sqrt[c - d*x^2])","A",11,9,30,0.3000,1,"{466, 414, 527, 523, 224, 221, 409, 1219, 1218}"
924,1,628,0,1.403393,"\int \frac{1}{(e x)^{3/2} \left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(6 a^2 d^2-8 a b c d+5 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(6 a^2 d^2-8 a b c d+5 b^2 c^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt{c-d x^2} \left(6 a^2 d^2-8 a b c d+5 b^2 c^2\right)}{2 a^2 c^2 e \sqrt{e x} (b c-a d)^2}-\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b}{2 a e \sqrt{e x} \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c e \sqrt{e x} \sqrt{c-d x^2} (b c-a d)^2}","\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(6 a^2 d^2-8 a b c d+5 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(6 a^2 d^2-8 a b c d+5 b^2 c^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{5/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt{c-d x^2} \left(6 a^2 d^2-8 a b c d+5 b^2 c^2\right)}{2 a^2 c^2 e \sqrt{e x} (b c-a d)^2}-\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (5 b c-11 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b}{2 a e \sqrt{e x} \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c e \sqrt{e x} \sqrt{c-d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d))/(2*a*c*(b*c - a*d)^2*e*Sqrt[e*x]*Sqrt[c - d*x^2]) + b/(2*a*(b*c - a*d)*e*Sqrt[e*x]*(a - b*x^2)*Sqrt[c - d*x^2]) - ((5*b^2*c^2 - 8*a*b*c*d + 6*a^2*d^2)*Sqrt[c - d*x^2])/(2*a^2*c^2*(b*c - a*d)^2*e*Sqrt[e*x]) - (d^(1/4)*(5*b^2*c^2 - 8*a*b*c*d + 6*a^2*d^2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*c^(5/4)*(b*c - a*d)^2*e^(3/2)*Sqrt[c - d*x^2]) + (d^(1/4)*(5*b^2*c^2 - 8*a*b*c*d + 6*a^2*d^2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*c^(5/4)*(b*c - a*d)^2*e^(3/2)*Sqrt[c - d*x^2]) - (b^(3/2)*c^(1/4)*(5*b*c - 11*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*d^(1/4)*(b*c - a*d)^2*e^(3/2)*Sqrt[c - d*x^2]) + (b^(3/2)*c^(1/4)*(5*b*c - 11*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*d^(1/4)*(b*c - a*d)^2*e^(3/2)*Sqrt[c - d*x^2])","A",17,14,30,0.4667,1,"{466, 472, 579, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
925,1,512,0,1.0783948,"\int \frac{1}{(e x)^{5/2} \left(a-b x^2\right)^2 \left(c-d x^2\right)^{3/2}} \, dx","Int[1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(3/2)),x]","\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} \left(10 a^2 d^2-8 a b c d+7 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 c^{7/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt{c-d x^2} \left(10 a^2 d^2-8 a b c d+7 b^2 c^2\right)}{6 a^2 c^2 e (e x)^{3/2} (b c-a d)^2}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-13 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-13 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b}{2 a e (e x)^{3/2} \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c e (e x)^{3/2} \sqrt{c-d x^2} (b c-a d)^2}","\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} \left(10 a^2 d^2-8 a b c d+7 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 c^{7/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)^2}-\frac{\sqrt{c-d x^2} \left(10 a^2 d^2-8 a b c d+7 b^2 c^2\right)}{6 a^2 c^2 e (e x)^{3/2} (b c-a d)^2}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-13 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-13 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^2}+\frac{b}{2 a e (e x)^{3/2} \left(a-b x^2\right) \sqrt{c-d x^2} (b c-a d)}+\frac{d (2 a d+b c)}{2 a c e (e x)^{3/2} \sqrt{c-d x^2} (b c-a d)^2}",1,"(d*(b*c + 2*a*d))/(2*a*c*(b*c - a*d)^2*e*(e*x)^(3/2)*Sqrt[c - d*x^2]) + b/(2*a*(b*c - a*d)*e*(e*x)^(3/2)*(a - b*x^2)*Sqrt[c - d*x^2]) - ((7*b^2*c^2 - 8*a*b*c*d + 10*a^2*d^2)*Sqrt[c - d*x^2])/(6*a^2*c^2*(b*c - a*d)^2*e*(e*x)^(3/2)) + (d^(3/4)*(7*b^2*c^2 - 8*a*b*c*d + 10*a^2*d^2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*a^2*c^(7/4)*(b*c - a*d)^2*e^(5/2)*Sqrt[c - d*x^2]) + (b^2*c^(1/4)*(7*b*c - 13*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*(b*c - a*d)^2*e^(5/2)*Sqrt[c - d*x^2]) + (b^2*c^(1/4)*(7*b*c - 13*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*(b*c - a*d)^2*e^(5/2)*Sqrt[c - d*x^2])","A",12,10,30,0.3333,1,"{466, 472, 579, 583, 523, 224, 221, 409, 1219, 1218}"
926,1,568,0,1.3622899,"\int \frac{(e x)^{9/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[(e*x)^(9/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 d^{3/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 a d+b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 d^{3/4} \sqrt{c-d x^2} (b c-a d)^3}+\frac{e^3 (e x)^{3/2} (4 a d+b c)}{2 \sqrt{c-d x^2} (b c-a d)^3}+\frac{e^3 (e x)^{3/2} (3 a d+2 b c)}{6 b \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{a e^3 (e x)^{3/2}}{2 b \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 a d+7 b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 a d+7 b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}","\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 d^{3/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{c^{3/4} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (4 a d+b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 d^{3/4} \sqrt{c-d x^2} (b c-a d)^3}+\frac{e^3 (e x)^{3/2} (4 a d+b c)}{2 \sqrt{c-d x^2} (b c-a d)^3}+\frac{e^3 (e x)^{3/2} (3 a d+2 b c)}{6 b \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{a e^3 (e x)^{3/2}}{2 b \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 a d+7 b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{a} \sqrt[4]{c} e^{9/2} \sqrt{1-\frac{d x^2}{c}} (3 a d+7 b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{b} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}",1,"((2*b*c + 3*a*d)*e^3*(e*x)^(3/2))/(6*b*(b*c - a*d)^2*(c - d*x^2)^(3/2)) + (a*e^3*(e*x)^(3/2))/(2*b*(b*c - a*d)*(a - b*x^2)*(c - d*x^2)^(3/2)) + ((b*c + 4*a*d)*e^3*(e*x)^(3/2))/(2*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (c^(3/4)*(b*c + 4*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*d^(3/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (c^(3/4)*(b*c + 4*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*d^(3/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (Sqrt[a]*c^(1/4)*(7*b*c + 3*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[b]*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (Sqrt[a]*c^(1/4)*(7*b*c + 3*a*d)*e^(9/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[b]*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2])","A",17,13,30,0.4333,1,"{466, 470, 579, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
927,1,454,0,0.8672196,"\int \frac{(e x)^{7/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[(e*x)^(7/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{5 e^3 \sqrt{e x} (2 a d+b c)}{6 \sqrt{c-d x^2} (b c-a d)^3}+\frac{e^3 \sqrt{e x} (3 a d+2 b c)}{6 b \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{a e^3 \sqrt{e x}}{2 b \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{5 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{5 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{5 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}","\frac{5 e^3 \sqrt{e x} (2 a d+b c)}{6 \sqrt{c-d x^2} (b c-a d)^3}+\frac{e^3 \sqrt{e x} (3 a d+2 b c)}{6 b \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{a e^3 \sqrt{e x}}{2 b \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{5 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (2 a d+b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{5 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{5 \sqrt[4]{c} e^{7/2} \sqrt{1-\frac{d x^2}{c}} (a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}",1,"((2*b*c + 3*a*d)*e^3*Sqrt[e*x])/(6*b*(b*c - a*d)^2*(c - d*x^2)^(3/2)) + (a*e^3*Sqrt[e*x])/(2*b*(b*c - a*d)*(a - b*x^2)*(c - d*x^2)^(3/2)) + (5*(b*c + 2*a*d)*e^3*Sqrt[e*x])/(6*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (5*c^(1/4)*(b*c + 2*a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (5*c^(1/4)*(b*c + a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (5*c^(1/4)*(b*c + a*d)*e^(7/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2])","A",12,9,30,0.3000,1,"{466, 470, 527, 523, 224, 221, 409, 1219, 1218}"
928,1,551,0,1.2964158,"\int \frac{(e x)^{5/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[(e*x)^(5/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{\sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+4 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+4 b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^3}+\frac{\sqrt{b} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (7 a d+3 b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{b} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (7 a d+3 b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{d e (e x)^{3/2} (a d+4 b c)}{2 c \sqrt{c-d x^2} (b c-a d)^3}+\frac{5 d e (e x)^{3/2}}{6 \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{e (e x)^{3/2}}{2 \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}","\frac{\sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+4 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt[4]{d} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (a d+4 b c) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 \sqrt[4]{c} \sqrt{c-d x^2} (b c-a d)^3}+\frac{\sqrt{b} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (7 a d+3 b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{b} \sqrt[4]{c} e^{5/2} \sqrt{1-\frac{d x^2}{c}} (7 a d+3 b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 \sqrt{a} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{d e (e x)^{3/2} (a d+4 b c)}{2 c \sqrt{c-d x^2} (b c-a d)^3}+\frac{5 d e (e x)^{3/2}}{6 \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{e (e x)^{3/2}}{2 \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}",1,"(5*d*e*(e*x)^(3/2))/(6*(b*c - a*d)^2*(c - d*x^2)^(3/2)) + (e*(e*x)^(3/2))/(2*(b*c - a*d)*(a - b*x^2)*(c - d*x^2)^(3/2)) + (d*(4*b*c + a*d)*e*(e*x)^(3/2))/(2*c*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (d^(1/4)*(4*b*c + a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*c^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (d^(1/4)*(4*b*c + a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*c^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (Sqrt[b]*c^(1/4)*(3*b*c + 7*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (Sqrt[b]*c^(1/4)*(3*b*c + 7*a*d)*e^(5/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*Sqrt[a]*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2])","A",17,13,30,0.4333,1,"{466, 471, 579, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
929,1,447,0,0.9167646,"\int \frac{(e x)^{3/2}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[(e*x)^(3/2)/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (a d+14 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 c^{3/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{b \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (9 a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{b \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (9 a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{d e \sqrt{e x} (a d+14 b c)}{6 c \sqrt{c-d x^2} (b c-a d)^3}+\frac{5 d e \sqrt{e x}}{6 \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{e \sqrt{e x}}{2 \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}","\frac{d^{3/4} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (a d+14 b c) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 c^{3/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{b \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (9 a d+b c) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}-\frac{b \sqrt[4]{c} e^{3/2} \sqrt{1-\frac{d x^2}{c}} (9 a d+b c) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{d e \sqrt{e x} (a d+14 b c)}{6 c \sqrt{c-d x^2} (b c-a d)^3}+\frac{5 d e \sqrt{e x}}{6 \left(c-d x^2\right)^{3/2} (b c-a d)^2}+\frac{e \sqrt{e x}}{2 \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}",1,"(5*d*e*Sqrt[e*x])/(6*(b*c - a*d)^2*(c - d*x^2)^(3/2)) + (e*Sqrt[e*x])/(2*(b*c - a*d)*(a - b*x^2)*(c - d*x^2)^(3/2)) + (d*(14*b*c + a*d)*e*Sqrt[e*x])/(6*c*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (d^(3/4)*(14*b*c + a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*c^(3/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (b*c^(1/4)*(b*c + 9*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (b*c^(1/4)*(b*c + 9*a*d)*e^(3/2)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2])","A",12,9,30,0.3000,1,"{466, 471, 527, 523, 224, 221, 409, 1219, 1218}"
930,1,625,0,1.4308717,"\int \frac{\sqrt{e x}}{\left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[Sqrt[e*x]/((a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{d (e x)^{3/2} \left(-a^2 d^2+5 a b c d+b^2 c^2\right)}{2 a c^2 e \sqrt{c-d x^2} (b c-a d)^3}+\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2+5 a b c d+b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a c^{5/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2+5 a b c d+b^2 c^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a c^{5/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{b^{3/2} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-11 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-11 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b (e x)^{3/2}}{2 a e \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d (e x)^{3/2} (2 a d+3 b c)}{6 a c e \left(c-d x^2\right)^{3/2} (b c-a d)^2}","\frac{d (e x)^{3/2} \left(-a^2 d^2+5 a b c d+b^2 c^2\right)}{2 a c^2 e \sqrt{c-d x^2} (b c-a d)^3}+\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2+5 a b c d+b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a c^{5/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt[4]{d} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} \left(-a^2 d^2+5 a b c d+b^2 c^2\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a c^{5/4} \sqrt{c-d x^2} (b c-a d)^3}-\frac{b^{3/2} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-11 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^{3/2} \sqrt[4]{c} \sqrt{e} \sqrt{1-\frac{d x^2}{c}} (b c-11 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{3/2} \sqrt[4]{d} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b (e x)^{3/2}}{2 a e \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d (e x)^{3/2} (2 a d+3 b c)}{6 a c e \left(c-d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d)*(e*x)^(3/2))/(6*a*c*(b*c - a*d)^2*e*(c - d*x^2)^(3/2)) + (b*(e*x)^(3/2))/(2*a*(b*c - a*d)*e*(a - b*x^2)*(c - d*x^2)^(3/2)) + (d*(b^2*c^2 + 5*a*b*c*d - a^2*d^2)*(e*x)^(3/2))/(2*a*c^2*(b*c - a*d)^3*e*Sqrt[c - d*x^2]) - (d^(1/4)*(b^2*c^2 + 5*a*b*c*d - a^2*d^2)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*c^(5/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (d^(1/4)*(b^2*c^2 + 5*a*b*c*d - a^2*d^2)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a*c^(5/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) - (b^(3/2)*c^(1/4)*(b*c - 11*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2]) + (b^(3/2)*c^(1/4)*(b*c - 11*a*d)*Sqrt[e]*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(3/2)*d^(1/4)*(b*c - a*d)^3*Sqrt[c - d*x^2])","A",17,13,30,0.4333,1,"{466, 472, 579, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
931,1,514,0,0.9753882,"\int \frac{1}{\sqrt{e x} \left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[1/(Sqrt[e*x]*(a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{d \sqrt{e x} \left(-5 a^2 d^2+17 a b c d+3 b^2 c^2\right)}{6 a c^2 e \sqrt{c-d x^2} (b c-a d)^3}+\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} \left(-5 a^2 d^2+17 a b c d+3 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a c^{7/4} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-13 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-13 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b \sqrt{e x}}{2 a e \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d \sqrt{e x} (2 a d+3 b c)}{6 a c e \left(c-d x^2\right)^{3/2} (b c-a d)^2}","\frac{d \sqrt{e x} \left(-5 a^2 d^2+17 a b c d+3 b^2 c^2\right)}{6 a c^2 e \sqrt{c-d x^2} (b c-a d)^3}+\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} \left(-5 a^2 d^2+17 a b c d+3 b^2 c^2\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a c^{7/4} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-13 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^2 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (3 b c-13 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^2 \sqrt[4]{d} \sqrt{e} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b \sqrt{e x}}{2 a e \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d \sqrt{e x} (2 a d+3 b c)}{6 a c e \left(c-d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d)*Sqrt[e*x])/(6*a*c*(b*c - a*d)^2*e*(c - d*x^2)^(3/2)) + (b*Sqrt[e*x])/(2*a*(b*c - a*d)*e*(a - b*x^2)*(c - d*x^2)^(3/2)) + (d*(3*b^2*c^2 + 17*a*b*c*d - 5*a^2*d^2)*Sqrt[e*x])/(6*a*c^2*(b*c - a*d)^3*e*Sqrt[c - d*x^2]) + (d^(3/4)*(3*b^2*c^2 + 17*a*b*c*d - 5*a^2*d^2)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*a*c^(7/4)*(b*c - a*d)^3*Sqrt[e]*Sqrt[c - d*x^2]) + (b^2*c^(1/4)*(3*b*c - 13*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*d^(1/4)*(b*c - a*d)^3*Sqrt[e]*Sqrt[c - d*x^2]) + (b^2*c^(1/4)*(3*b*c - 13*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^2*d^(1/4)*(b*c - a*d)^3*Sqrt[e]*Sqrt[c - d*x^2])","A",12,9,30,0.3000,1,"{466, 414, 527, 523, 224, 221, 409, 1219, 1218}"
932,1,735,0,1.8429306,"\int \frac{1}{(e x)^{3/2} \left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[1/((e*x)^(3/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(19 a^2 b c d^2-7 a^3 d^3-12 a b^2 c^2 d+5 b^3 c^3\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{9/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(19 a^2 b c d^2-7 a^3 d^3-12 a b^2 c^2 d+5 b^3 c^3\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{9/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{c-d x^2} \left(19 a^2 b c d^2-7 a^3 d^3-12 a b^2 c^2 d+5 b^3 c^3\right)}{2 a^2 c^3 e \sqrt{e x} (b c-a d)^3}+\frac{d \left(-7 a^2 d^2+19 a b c d+3 b^2 c^2\right)}{6 a c^2 e \sqrt{e x} \sqrt{c-d x^2} (b c-a d)^3}-\frac{5 b^{5/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{5 b^{5/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b}{2 a e \sqrt{e x} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c e \sqrt{e x} \left(c-d x^2\right)^{3/2} (b c-a d)^2}","\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(19 a^2 b c d^2-7 a^3 d^3-12 a b^2 c^2 d+5 b^3 c^3\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{9/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt[4]{d} \sqrt{1-\frac{d x^2}{c}} \left(19 a^2 b c d^2-7 a^3 d^3-12 a b^2 c^2 d+5 b^3 c^3\right) E\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{2 a^2 c^{9/4} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{c-d x^2} \left(19 a^2 b c d^2-7 a^3 d^3-12 a b^2 c^2 d+5 b^3 c^3\right)}{2 a^2 c^3 e \sqrt{e x} (b c-a d)^3}+\frac{d \left(-7 a^2 d^2+19 a b c d+3 b^2 c^2\right)}{6 a c^2 e \sqrt{e x} \sqrt{c-d x^2} (b c-a d)^3}-\frac{5 b^{5/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{5 b^{5/2} \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (b c-3 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^{5/2} \sqrt[4]{d} e^{3/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b}{2 a e \sqrt{e x} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c e \sqrt{e x} \left(c-d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d))/(6*a*c*(b*c - a*d)^2*e*Sqrt[e*x]*(c - d*x^2)^(3/2)) + b/(2*a*(b*c - a*d)*e*Sqrt[e*x]*(a - b*x^2)*(c - d*x^2)^(3/2)) + (d*(3*b^2*c^2 + 19*a*b*c*d - 7*a^2*d^2))/(6*a*c^2*(b*c - a*d)^3*e*Sqrt[e*x]*Sqrt[c - d*x^2]) - ((5*b^3*c^3 - 12*a*b^2*c^2*d + 19*a^2*b*c*d^2 - 7*a^3*d^3)*Sqrt[c - d*x^2])/(2*a^2*c^3*(b*c - a*d)^3*e*Sqrt[e*x]) - (d^(1/4)*(5*b^3*c^3 - 12*a*b^2*c^2*d + 19*a^2*b*c*d^2 - 7*a^3*d^3)*Sqrt[1 - (d*x^2)/c]*EllipticE[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*c^(9/4)*(b*c - a*d)^3*e^(3/2)*Sqrt[c - d*x^2]) + (d^(1/4)*(5*b^3*c^3 - 12*a*b^2*c^2*d + 19*a^2*b*c*d^2 - 7*a^3*d^3)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(2*a^2*c^(9/4)*(b*c - a*d)^3*e^(3/2)*Sqrt[c - d*x^2]) - (5*b^(5/2)*c^(1/4)*(b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*d^(1/4)*(b*c - a*d)^3*e^(3/2)*Sqrt[c - d*x^2]) + (5*b^(5/2)*c^(1/4)*(b*c - 3*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^(5/2)*d^(1/4)*(b*c - a*d)^3*e^(3/2)*Sqrt[c - d*x^2])","A",18,14,30,0.4667,1,"{466, 472, 579, 583, 584, 307, 224, 221, 1200, 1199, 424, 490, 1219, 1218}"
933,1,606,0,1.4611904,"\int \frac{1}{(e x)^{5/2} \left(a-b x^2\right)^2 \left(c-d x^2\right)^{5/2}} \, dx","Int[1/((e*x)^(5/2)*(a - b*x^2)^2*(c - d*x^2)^(5/2)),x]","\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} \left(35 a^2 b c d^2-15 a^3 d^3-12 a b^2 c^2 d+7 b^3 c^3\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 c^{11/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{c-d x^2} \left(35 a^2 b c d^2-15 a^3 d^3-12 a b^2 c^2 d+7 b^3 c^3\right)}{6 a^2 c^3 e (e x)^{3/2} (b c-a d)^3}+\frac{d \left(-3 a^2 d^2+7 a b c d+b^2 c^2\right)}{2 a c^2 e (e x)^{3/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-17 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-17 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b}{2 a e (e x)^{3/2} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c e (e x)^{3/2} \left(c-d x^2\right)^{3/2} (b c-a d)^2}","\frac{d^{3/4} \sqrt{1-\frac{d x^2}{c}} \left(35 a^2 b c d^2-15 a^3 d^3-12 a b^2 c^2 d+7 b^3 c^3\right) F\left(\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{6 a^2 c^{11/4} e^{5/2} \sqrt{c-d x^2} (b c-a d)^3}-\frac{\sqrt{c-d x^2} \left(35 a^2 b c d^2-15 a^3 d^3-12 a b^2 c^2 d+7 b^3 c^3\right)}{6 a^2 c^3 e (e x)^{3/2} (b c-a d)^3}+\frac{d \left(-3 a^2 d^2+7 a b c d+b^2 c^2\right)}{2 a c^2 e (e x)^{3/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-17 a d) \Pi \left(-\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b^3 \sqrt[4]{c} \sqrt{1-\frac{d x^2}{c}} (7 b c-17 a d) \Pi \left(\frac{\sqrt{b} \sqrt{c}}{\sqrt{a} \sqrt{d}};\left.\sin ^{-1}\left(\frac{\sqrt[4]{d} \sqrt{e x}}{\sqrt[4]{c} \sqrt{e}}\right)\right|-1\right)}{4 a^3 \sqrt[4]{d} e^{5/2} \sqrt{c-d x^2} (b c-a d)^3}+\frac{b}{2 a e (e x)^{3/2} \left(a-b x^2\right) \left(c-d x^2\right)^{3/2} (b c-a d)}+\frac{d (2 a d+3 b c)}{6 a c e (e x)^{3/2} \left(c-d x^2\right)^{3/2} (b c-a d)^2}",1,"(d*(3*b*c + 2*a*d))/(6*a*c*(b*c - a*d)^2*e*(e*x)^(3/2)*(c - d*x^2)^(3/2)) + b/(2*a*(b*c - a*d)*e*(e*x)^(3/2)*(a - b*x^2)*(c - d*x^2)^(3/2)) + (d*(b^2*c^2 + 7*a*b*c*d - 3*a^2*d^2))/(2*a*c^2*(b*c - a*d)^3*e*(e*x)^(3/2)*Sqrt[c - d*x^2]) - ((7*b^3*c^3 - 12*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 15*a^3*d^3)*Sqrt[c - d*x^2])/(6*a^2*c^3*(b*c - a*d)^3*e*(e*x)^(3/2)) + (d^(3/4)*(7*b^3*c^3 - 12*a*b^2*c^2*d + 35*a^2*b*c*d^2 - 15*a^3*d^3)*Sqrt[1 - (d*x^2)/c]*EllipticF[ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(6*a^2*c^(11/4)*(b*c - a*d)^3*e^(5/2)*Sqrt[c - d*x^2]) + (b^3*c^(1/4)*(7*b*c - 17*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[-((Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d])), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*(b*c - a*d)^3*e^(5/2)*Sqrt[c - d*x^2]) + (b^3*c^(1/4)*(7*b*c - 17*a*d)*Sqrt[1 - (d*x^2)/c]*EllipticPi[(Sqrt[b]*Sqrt[c])/(Sqrt[a]*Sqrt[d]), ArcSin[(d^(1/4)*Sqrt[e*x])/(c^(1/4)*Sqrt[e])], -1])/(4*a^3*d^(1/4)*(b*c - a*d)^3*e^(5/2)*Sqrt[c - d*x^2])","A",13,10,30,0.3333,1,"{466, 472, 579, 583, 523, 224, 221, 409, 1219, 1218}"
934,1,209,0,0.2487243,"\int \frac{x^5 \sqrt{a+b x^2}}{\sqrt{c+d x^2}} \, dx","Int[(x^5*Sqrt[a + b*x^2])/Sqrt[c + d*x^2],x]","\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} \left(a^2 d^2+2 a b c d+5 b^2 c^2\right)}{16 b^2 d^3}-\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^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{16 b^{5/2} d^{7/2}}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (3 a d+5 b c)}{24 b^2 d^2}+\frac{x^2 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{6 b d}","\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} \left(a^2 d^2+2 a b c d+5 b^2 c^2\right)}{16 b^2 d^3}-\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^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{16 b^{5/2} d^{7/2}}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (3 a d+5 b c)}{24 b^2 d^2}+\frac{x^2 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{6 b d}",1,"((5*b^2*c^2 + 2*a*b*c*d + a^2*d^2)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(16*b^2*d^3) - ((5*b*c + 3*a*d)*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(24*b^2*d^2) + (x^2*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(6*b*d) - ((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^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(16*b^(5/2)*d^(7/2))","A",7,7,26,0.2692,1,"{446, 90, 80, 50, 63, 217, 206}"
935,1,137,0,0.1272004,"\int \frac{x^3 \sqrt{a+b x^2}}{\sqrt{c+d x^2}} \, dx","Int[(x^3*Sqrt[a + b*x^2])/Sqrt[c + d*x^2],x]","\frac{(b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (a d+3 b c)}{8 b d^2}+\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 b d}","\frac{(b c-a d) (a d+3 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 b^{3/2} d^{5/2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (a d+3 b c)}{8 b d^2}+\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 b d}",1,"-((3*b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*b*d^2) + ((a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(4*b*d) + ((b*c - a*d)*(3*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(8*b^(3/2)*d^(5/2))","A",6,6,26,0.2308,1,"{446, 80, 50, 63, 217, 206}"
936,1,86,0,0.0745375,"\int \frac{x \sqrt{a+b x^2}}{\sqrt{c+d x^2}} \, dx","Int[(x*Sqrt[a + b*x^2])/Sqrt[c + d*x^2],x]","\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 \sqrt{b} d^{3/2}}","\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 d}-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 \sqrt{b} d^{3/2}}",1,"(Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*d) - ((b*c - a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(2*Sqrt[b]*d^(3/2))","A",5,5,24,0.2083,1,"{444, 50, 63, 217, 206}"
937,1,92,0,0.0953195,"\int \frac{\sqrt{a+b x^2}}{x \sqrt{c+d x^2}} \, dx","Int[Sqrt[a + b*x^2]/(x*Sqrt[c + d*x^2]),x]","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{d}}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{c}}","\frac{\sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{d}}-\frac{\sqrt{a} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{c}}",1,"-((Sqrt[a]*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/Sqrt[c]) + (Sqrt[b]*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/Sqrt[d]","A",7,7,26,0.2692,1,"{446, 105, 63, 217, 206, 93, 208}"
938,1,89,0,0.0719323,"\int \frac{\sqrt{a+b x^2}}{x^3 \sqrt{c+d x^2}} \, dx","Int[Sqrt[a + b*x^2]/(x^3*Sqrt[c + d*x^2]),x]","-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} c^{3/2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 c x^2}","-\frac{(b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 \sqrt{a} c^{3/2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 c x^2}",1,"-(Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*c*x^2) - ((b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*Sqrt[a]*c^(3/2))","A",4,4,26,0.1538,1,"{446, 94, 93, 208}"
939,1,143,0,0.1160612,"\int \frac{\sqrt{a+b x^2}}{x^5 \sqrt{c+d x^2}} \, dx","Int[Sqrt[a + b*x^2]/(x^5*Sqrt[c + d*x^2]),x]","\frac{(b c-a d) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 a^{3/2} c^{5/2}}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (3 a d+b c)}{8 a c^2 x^2}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 a c x^4}","\frac{(b c-a d) (3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 a^{3/2} c^{5/2}}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (3 a d+b c)}{8 a c^2 x^2}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 a c x^4}",1,"((b*c + 3*a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*a*c^2*x^2) - ((a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(4*a*c*x^4) + ((b*c - a*d)*(b*c + 3*a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(8*a^(3/2)*c^(5/2))","A",5,5,26,0.1923,1,"{446, 96, 94, 93, 208}"
940,1,343,0,0.3059716,"\int \frac{x^4 \sqrt{a+b x^2}}{\sqrt{c+d x^2}} \, dx","Int[(x^4*Sqrt[a + b*x^2])/Sqrt[c + d*x^2],x]","\frac{x \sqrt{a+b x^2} \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right)}{15 b^2 d^2 \sqrt{c+d x^2}}-\frac{\sqrt{c} \sqrt{a+b x^2} \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{c^{3/2} \sqrt{a+b x^2} (4 b c-a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} (4 b c-a d)}{15 b d^2}+\frac{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}}{5 d}","\frac{x \sqrt{a+b x^2} \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right)}{15 b^2 d^2 \sqrt{c+d x^2}}-\frac{\sqrt{c} \sqrt{a+b x^2} \left(-2 a^2 d^2-3 a b c d+8 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{c^{3/2} \sqrt{a+b x^2} (4 b c-a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} (4 b c-a d)}{15 b d^2}+\frac{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}}{5 d}",1,"((8*b^2*c^2 - 3*a*b*c*d - 2*a^2*d^2)*x*Sqrt[a + b*x^2])/(15*b^2*d^2*Sqrt[c + d*x^2]) - ((4*b*c - a*d)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(15*b*d^2) + (x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(5*d) - (Sqrt[c]*(8*b^2*c^2 - 3*a*b*c*d - 2*a^2*d^2)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b^2*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (c^(3/2)*(4*b*c - a*d)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{478, 582, 531, 418, 492, 411}"
941,1,259,0,0.1635466,"\int \frac{x^2 \sqrt{a+b x^2}}{\sqrt{c+d x^2}} \, dx","Int[(x^2*Sqrt[a + b*x^2])/Sqrt[c + d*x^2],x]","-\frac{c^{3/2} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} \sqrt{a+b x^2} (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2}}{3 d}-\frac{x \sqrt{a+b x^2} (2 b c-a d)}{3 b d \sqrt{c+d x^2}}","-\frac{c^{3/2} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} \sqrt{a+b x^2} (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2}}{3 d}-\frac{x \sqrt{a+b x^2} (2 b c-a d)}{3 b d \sqrt{c+d x^2}}",1,"-((2*b*c - a*d)*x*Sqrt[a + b*x^2])/(3*b*d*Sqrt[c + d*x^2]) + (x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*d) + (Sqrt[c]*(2*b*c - a*d)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (c^(3/2)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",5,5,26,0.1923,1,"{478, 531, 418, 492, 411}"
942,1,232,0,0.148864,"\int \frac{\sqrt{a+b x^2}}{x^2 \sqrt{c+d x^2}} \, dx","Int[Sqrt[a + b*x^2]/(x^2*Sqrt[c + d*x^2]),x]","\frac{d x \sqrt{a+b x^2}}{c \sqrt{c+d x^2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{c x}+\frac{b \sqrt{c} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{d} \sqrt{a+b x^2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{d x \sqrt{a+b x^2}}{c \sqrt{c+d x^2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{c x}+\frac{b \sqrt{c} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{d} \sqrt{a+b x^2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(d*x*Sqrt[a + b*x^2])/(c*Sqrt[c + d*x^2]) - (Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(c*x) - (Sqrt[d]*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (b*Sqrt[c]*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{475, 21, 422, 418, 492, 411}"
943,1,307,0,0.262819,"\int \frac{\sqrt{a+b x^2}}{x^4 \sqrt{c+d x^2}} \, dx","Int[Sqrt[a + b*x^2]/(x^4*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-2 a d)}{3 a c^2 x}+\frac{d x \sqrt{a+b x^2} (b c-2 a d)}{3 a c^2 \sqrt{c+d x^2}}-\frac{\sqrt{d} \sqrt{a+b x^2} (b c-2 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a c^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{3 c x^3}-\frac{b \sqrt{d} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a \sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-2 a d)}{3 a c^2 x}+\frac{d x \sqrt{a+b x^2} (b c-2 a d)}{3 a c^2 \sqrt{c+d x^2}}-\frac{\sqrt{d} \sqrt{a+b x^2} (b c-2 a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a c^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{3 c x^3}-\frac{b \sqrt{d} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a \sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(d*(b*c - 2*a*d)*x*Sqrt[a + b*x^2])/(3*a*c^2*Sqrt[c + d*x^2]) - (Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*c*x^3) - ((b*c - 2*a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*a*c^2*x) - (Sqrt[d]*(b*c - 2*a*d)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*c^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (b*Sqrt[d]*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{475, 583, 531, 418, 492, 411}"
944,1,276,0,0.3254396,"\int \frac{x^5 \left(a+b x^2\right)^{3/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^5*(a + b*x^2)^(3/2))/Sqrt[c + d*x^2],x]","\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right)}{192 b^2 d^3}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d) \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right)}{128 b^2 d^4}+\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^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{128 b^{5/2} d^{9/2}}-\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2} (3 a d+7 b c)}{48 b^2 d^2}+\frac{x^2 \left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}}{8 b d}","\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right)}{192 b^2 d^3}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d) \left(3 a^2 d^2+10 a b c d+35 b^2 c^2\right)}{128 b^2 d^4}+\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^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{128 b^{5/2} d^{9/2}}-\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2} (3 a d+7 b c)}{48 b^2 d^2}+\frac{x^2 \left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}}{8 b d}",1,"-((b*c - a*d)*(35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(128*b^2*d^4) + ((35*b^2*c^2 + 10*a*b*c*d + 3*a^2*d^2)*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(192*b^2*d^3) - ((7*b*c + 3*a*d)*(a + b*x^2)^(5/2)*Sqrt[c + d*x^2])/(48*b^2*d^2) + (x^2*(a + b*x^2)^(5/2)*Sqrt[c + d*x^2])/(8*b*d) + ((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^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(128*b^(5/2)*d^(9/2))","A",8,7,26,0.2692,1,"{446, 90, 80, 50, 63, 217, 206}"
945,1,187,0,0.1717485,"\int \frac{x^3 \left(a+b x^2\right)^{3/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^3*(a + b*x^2)^(3/2))/Sqrt[c + d*x^2],x]","-\frac{(b c-a d)^2 (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{16 b^{3/2} d^{7/2}}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (a d+5 b c)}{24 b d^2}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d) (a d+5 b c)}{16 b d^3}+\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}}{6 b d}","-\frac{(b c-a d)^2 (a d+5 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{16 b^{3/2} d^{7/2}}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (a d+5 b c)}{24 b d^2}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d) (a d+5 b c)}{16 b d^3}+\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}}{6 b d}",1,"((b*c - a*d)*(5*b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(16*b*d^3) - ((5*b*c + a*d)*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(24*b*d^2) + ((a + b*x^2)^(5/2)*Sqrt[c + d*x^2])/(6*b*d) - ((b*c - a*d)^2*(5*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(16*b^(3/2)*d^(7/2))","A",7,6,26,0.2308,1,"{446, 80, 50, 63, 217, 206}"
946,1,125,0,0.1040953,"\int \frac{x \left(a+b x^2\right)^{3/2}}{\sqrt{c+d x^2}} \, dx","Int[(x*(a + b*x^2)^(3/2))/Sqrt[c + d*x^2],x]","-\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)}{8 d^2}+\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 \sqrt{b} d^{5/2}}+\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 d}","-\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)}{8 d^2}+\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 \sqrt{b} d^{5/2}}+\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 d}",1,"(-3*(b*c - a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*d^2) + ((a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(4*d) + (3*(b*c - a*d)^2*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(8*Sqrt[b]*d^(5/2))","A",6,5,24,0.2083,1,"{444, 50, 63, 217, 206}"
947,1,133,0,0.1397942,"\int \frac{\left(a+b x^2\right)^{3/2}}{x \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(3/2)/(x*Sqrt[c + d*x^2]),x]","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{c}}-\frac{\sqrt{b} (b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 d^{3/2}}+\frac{b \sqrt{a+b x^2} \sqrt{c+d x^2}}{2 d}","-\frac{a^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{c}}-\frac{\sqrt{b} (b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 d^{3/2}}+\frac{b \sqrt{a+b x^2} \sqrt{c+d x^2}}{2 d}",1,"(b*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*d) - (a^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/Sqrt[c] - (Sqrt[b]*(b*c - 3*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(2*d^(3/2))","A",8,8,26,0.3077,1,"{446, 102, 157, 63, 217, 206, 93, 208}"
948,1,136,0,0.1402478,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^3 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(3/2)/(x^3*Sqrt[c + d*x^2]),x]","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{d}}-\frac{\sqrt{a} (3 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 c^{3/2}}-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2}}{2 c x^2}","\frac{b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{d}}-\frac{\sqrt{a} (3 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 c^{3/2}}-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2}}{2 c x^2}",1,"-(a*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*c*x^2) - (Sqrt[a]*(3*b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*c^(3/2)) + (b^(3/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/Sqrt[d]","A",8,8,26,0.3077,1,"{446, 98, 157, 63, 217, 206, 93, 208}"
949,1,131,0,0.1060268,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^5 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(3/2)/(x^5*Sqrt[c + d*x^2]),x]","-\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)}{8 c^2 x^2}-\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 \sqrt{a} c^{5/2}}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 c x^4}","-\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)}{8 c^2 x^2}-\frac{3 (b c-a d)^2 \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 \sqrt{a} c^{5/2}}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 c x^4}",1,"(-3*(b*c - a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*c^2*x^2) - ((a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(4*c*x^4) - (3*(b*c - a*d)^2*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(8*Sqrt[a]*c^(5/2))","A",5,4,26,0.1538,1,"{446, 94, 93, 208}"
950,1,429,0,0.5182542,"\int \frac{x^4 \left(a+b x^2\right)^{3/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^4*(a + b*x^2)^(3/2))/Sqrt[c + d*x^2],x]","\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} \left(a^2 d^2-11 a b c d+8 b^2 c^2\right)}{35 b d^3}-\frac{2 x \sqrt{a+b x^2} (2 b c-a d) \left(-a^2 d^2-4 a b c d+4 b^2 c^2\right)}{35 b^2 d^3 \sqrt{c+d x^2}}-\frac{c^{3/2} \sqrt{a+b x^2} \left(a^2 d^2-11 a b c d+8 b^2 c^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{35 b d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{2 \sqrt{c} \sqrt{a+b x^2} (2 b c-a d) \left(-a^2 d^2-4 a b c d+4 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{35 b^2 d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 x^3 \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-4 a d)}{35 d^2}+\frac{b x^5 \sqrt{a+b x^2} \sqrt{c+d x^2}}{7 d}","\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} \left(a^2 d^2-11 a b c d+8 b^2 c^2\right)}{35 b d^3}-\frac{2 x \sqrt{a+b x^2} (2 b c-a d) \left(-a^2 d^2-4 a b c d+4 b^2 c^2\right)}{35 b^2 d^3 \sqrt{c+d x^2}}-\frac{c^{3/2} \sqrt{a+b x^2} \left(a^2 d^2-11 a b c d+8 b^2 c^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{35 b d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{2 \sqrt{c} \sqrt{a+b x^2} (2 b c-a d) \left(-a^2 d^2-4 a b c d+4 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{35 b^2 d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 x^3 \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-4 a d)}{35 d^2}+\frac{b x^5 \sqrt{a+b x^2} \sqrt{c+d x^2}}{7 d}",1,"(-2*(2*b*c - a*d)*(4*b^2*c^2 - 4*a*b*c*d - a^2*d^2)*x*Sqrt[a + b*x^2])/(35*b^2*d^3*Sqrt[c + d*x^2]) + ((8*b^2*c^2 - 11*a*b*c*d + a^2*d^2)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(35*b*d^3) - (2*(3*b*c - 4*a*d)*x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(35*d^2) + (b*x^5*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(7*d) + (2*Sqrt[c]*(2*b*c - a*d)*(4*b^2*c^2 - 4*a*b*c*d - a^2*d^2)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(35*b^2*d^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (c^(3/2)*(8*b^2*c^2 - 11*a*b*c*d + a^2*d^2)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(35*b*d^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",7,6,26,0.2308,1,"{477, 582, 531, 418, 492, 411}"
951,1,335,0,0.3402885,"\int \frac{x^2 \left(a+b x^2\right)^{3/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^2*(a + b*x^2)^(3/2))/Sqrt[c + d*x^2],x]","-\frac{\sqrt{c} \sqrt{a+b x^2} \left(3 a^2 d^2-13 a b c d+8 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{x \sqrt{a+b x^2} \left(-\frac{3 a^2 d}{b}+13 a c-\frac{8 b c^2}{d}\right)}{15 d \sqrt{c+d x^2}}+\frac{2 c^{3/2} \sqrt{a+b x^2} (2 b c-3 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 x \sqrt{a+b x^2} \sqrt{c+d x^2} (2 b c-3 a d)}{15 d^2}+\frac{b x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}}{5 d}","-\frac{\sqrt{c} \sqrt{a+b x^2} \left(3 a^2 d^2-13 a b c d+8 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{x \sqrt{a+b x^2} \left(-\frac{3 a^2 d}{b}+13 a c-\frac{8 b c^2}{d}\right)}{15 d \sqrt{c+d x^2}}+\frac{2 c^{3/2} \sqrt{a+b x^2} (2 b c-3 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 x \sqrt{a+b x^2} \sqrt{c+d x^2} (2 b c-3 a d)}{15 d^2}+\frac{b x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}}{5 d}",1,"-((13*a*c - (8*b*c^2)/d - (3*a^2*d)/b)*x*Sqrt[a + b*x^2])/(15*d*Sqrt[c + d*x^2]) - (2*(2*b*c - 3*a*d)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(15*d^2) + (b*x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(5*d) - (Sqrt[c]*(8*b^2*c^2 - 13*a*b*c*d + 3*a^2*d^2)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (2*c^(3/2)*(2*b*c - 3*a*d)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{477, 582, 531, 418, 492, 411}"
952,1,244,0,0.1604781,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^2 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(3/2)/(x^2*Sqrt[c + d*x^2]),x]","-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2}}{c x}+\frac{x \sqrt{a+b x^2} (a d+b c)}{c \sqrt{c+d x^2}}+\frac{2 b \sqrt{c} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{a+b x^2} (a d+b c) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2}}{c x}+\frac{x \sqrt{a+b x^2} (a d+b c)}{c \sqrt{c+d x^2}}+\frac{2 b \sqrt{c} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{a+b x^2} (a d+b c) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{\sqrt{c} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"((b*c + a*d)*x*Sqrt[a + b*x^2])/(c*Sqrt[c + d*x^2]) - (a*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(c*x) - ((b*c + a*d)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[c]*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (2*b*Sqrt[c]*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",5,5,26,0.1923,1,"{474, 531, 418, 492, 411}"
953,1,311,0,0.2921506,"\int \frac{\left(a+b x^2\right)^{3/2}}{x^4 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(3/2)/(x^4*Sqrt[c + d*x^2]),x]","-\frac{2 \sqrt{a+b x^2} \sqrt{c+d x^2} (2 b c-a d)}{3 c^2 x}+\frac{2 d x \sqrt{a+b x^2} (2 b c-a d)}{3 c^2 \sqrt{c+d x^2}}-\frac{2 \sqrt{d} \sqrt{a+b x^2} (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 c^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2}}{3 c x^3}+\frac{b \sqrt{a+b x^2} (3 b c-a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a \sqrt{c} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","-\frac{2 \sqrt{a+b x^2} \sqrt{c+d x^2} (2 b c-a d)}{3 c^2 x}+\frac{2 d x \sqrt{a+b x^2} (2 b c-a d)}{3 c^2 \sqrt{c+d x^2}}-\frac{2 \sqrt{d} \sqrt{a+b x^2} (2 b c-a d) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 c^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2}}{3 c x^3}+\frac{b \sqrt{a+b x^2} (3 b c-a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a \sqrt{c} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(2*d*(2*b*c - a*d)*x*Sqrt[a + b*x^2])/(3*c^2*Sqrt[c + d*x^2]) - (a*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*c*x^3) - (2*(2*b*c - a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*c^2*x) - (2*Sqrt[d]*(2*b*c - a*d)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*c^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (b*(3*b*c - a*d)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a*Sqrt[c]*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{474, 583, 531, 418, 492, 411}"
954,1,340,0,0.4175316,"\int \frac{x^5 \left(a+b x^2\right)^{5/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^5*(a + b*x^2)^(5/2))/Sqrt[c + d*x^2],x]","\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2} \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{480 b^2 d^3}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (b c-a d) \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{384 b^2 d^4}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)^2 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{256 b^2 d^5}-\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^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{256 b^{5/2} d^{11/2}}-\frac{3 \left(a+b x^2\right)^{7/2} \sqrt{c+d x^2} (a d+3 b c)}{80 b^2 d^2}+\frac{x^2 \left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}}{10 b d}","\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2} \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{480 b^2 d^3}-\frac{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (b c-a d) \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{384 b^2 d^4}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)^2 \left(3 a^2 d^2+14 a b c d+63 b^2 c^2\right)}{256 b^2 d^5}-\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^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{256 b^{5/2} d^{11/2}}-\frac{3 \left(a+b x^2\right)^{7/2} \sqrt{c+d x^2} (a d+3 b c)}{80 b^2 d^2}+\frac{x^2 \left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}}{10 b d}",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^2]*Sqrt[c + d*x^2])/(256*b^2*d^5) - ((b*c - a*d)*(63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(384*b^2*d^4) + ((63*b^2*c^2 + 14*a*b*c*d + 3*a^2*d^2)*(a + b*x^2)^(5/2)*Sqrt[c + d*x^2])/(480*b^2*d^3) - (3*(3*b*c + a*d)*(a + b*x^2)^(7/2)*Sqrt[c + d*x^2])/(80*b^2*d^2) + (x^2*(a + b*x^2)^(7/2)*Sqrt[c + d*x^2])/(10*b*d) - ((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^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(256*b^(5/2)*d^(11/2))","A",9,7,26,0.2692,1,"{446, 90, 80, 50, 63, 217, 206}"
955,1,237,0,0.2296256,"\int \frac{x^3 \left(a+b x^2\right)^{5/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^3*(a + b*x^2)^(5/2))/Sqrt[c + d*x^2],x]","\frac{5 (b c-a d)^3 (a d+7 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{128 b^{3/2} d^{9/2}}-\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2} (a d+7 b c)}{48 b d^2}+\frac{5 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (b c-a d) (a d+7 b c)}{192 b d^3}-\frac{5 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)^2 (a d+7 b c)}{128 b d^4}+\frac{\left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}}{8 b d}","\frac{5 (b c-a d)^3 (a d+7 b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{128 b^{3/2} d^{9/2}}-\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2} (a d+7 b c)}{48 b d^2}+\frac{5 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (b c-a d) (a d+7 b c)}{192 b d^3}-\frac{5 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)^2 (a d+7 b c)}{128 b d^4}+\frac{\left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}}{8 b d}",1,"(-5*(b*c - a*d)^2*(7*b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(128*b*d^4) + (5*(b*c - a*d)*(7*b*c + a*d)*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(192*b*d^3) - ((7*b*c + a*d)*(a + b*x^2)^(5/2)*Sqrt[c + d*x^2])/(48*b*d^2) + ((a + b*x^2)^(7/2)*Sqrt[c + d*x^2])/(8*b*d) + (5*(b*c - a*d)^3*(7*b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(128*b^(3/2)*d^(9/2))","A",8,6,26,0.2308,1,"{446, 80, 50, 63, 217, 206}"
956,1,164,0,0.1409622,"\int \frac{x \left(a+b x^2\right)^{5/2}}{\sqrt{c+d x^2}} \, dx","Int[(x*(a + b*x^2)^(5/2))/Sqrt[c + d*x^2],x]","\frac{5 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)^2}{16 d^3}-\frac{5 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (b c-a d)}{24 d^2}-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{16 \sqrt{b} d^{7/2}}+\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}}{6 d}","\frac{5 \sqrt{a+b x^2} \sqrt{c+d x^2} (b c-a d)^2}{16 d^3}-\frac{5 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2} (b c-a d)}{24 d^2}-\frac{5 (b c-a d)^3 \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{16 \sqrt{b} d^{7/2}}+\frac{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}}{6 d}",1,"(5*(b*c - a*d)^2*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(16*d^3) - (5*(b*c - a*d)*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(24*d^2) + ((a + b*x^2)^(5/2)*Sqrt[c + d*x^2])/(6*d) - (5*(b*c - a*d)^3*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(16*Sqrt[b]*d^(7/2))","A",7,5,24,0.2083,1,"{444, 50, 63, 217, 206}"
957,1,187,0,0.2259275,"\int \frac{\left(a+b x^2\right)^{5/2}}{x \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(5/2)/(x*Sqrt[c + d*x^2]),x]","\frac{\sqrt{b} \left(15 a^2 d^2-10 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 d^{5/2}}-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{c}}-\frac{b \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-7 a d)}{8 d^2}+\frac{b \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 d}","\frac{\sqrt{b} \left(15 a^2 d^2-10 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 d^{5/2}}-\frac{a^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{c}}-\frac{b \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-7 a d)}{8 d^2}+\frac{b \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 d}",1,"-(b*(3*b*c - 7*a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*d^2) + (b*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(4*d) - (a^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/Sqrt[c] + (Sqrt[b]*(3*b^2*c^2 - 10*a*b*c*d + 15*a^2*d^2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(8*d^(5/2))","A",9,9,26,0.3462,1,"{446, 102, 154, 157, 63, 217, 206, 93, 208}"
958,1,187,0,0.2295051,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^3 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(5/2)/(x^3*Sqrt[c + d*x^2]),x]","-\frac{a^{3/2} (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 c^{3/2}}-\frac{b^{3/2} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 d^{3/2}}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{2 c x^2}+\frac{b \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{2 c d}","-\frac{a^{3/2} (5 b c-a d) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 c^{3/2}}-\frac{b^{3/2} (b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 d^{3/2}}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{2 c x^2}+\frac{b \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{2 c d}",1,"(b*(b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*c*d) - (a*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(2*c*x^2) - (a^(3/2)*(5*b*c - a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*c^(3/2)) - (b^(3/2)*(b*c - 5*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(2*d^(3/2))","A",9,9,26,0.3462,1,"{446, 98, 154, 157, 63, 217, 206, 93, 208}"
959,1,192,0,0.2007997,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^5 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(5/2)/(x^5*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{a} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 c^{5/2}}+\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{d}}-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2} (7 b c-3 a d)}{8 c^2 x^2}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 c x^4}","-\frac{\sqrt{a} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 c^{5/2}}+\frac{b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{d}}-\frac{a \sqrt{a+b x^2} \sqrt{c+d x^2} (7 b c-3 a d)}{8 c^2 x^2}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{4 c x^4}",1,"-(a*(7*b*c - 3*a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*c^2*x^2) - (a*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(4*c*x^4) - (Sqrt[a]*(15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(8*c^(5/2)) + (b^(5/2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/Sqrt[d]","A",9,9,26,0.3462,1,"{446, 98, 149, 157, 63, 217, 206, 93, 208}"
960,1,553,0,0.7180354,"\int \frac{x^4 \left(a+b x^2\right)^{5/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^4*(a + b*x^2)^(5/2))/Sqrt[c + d*x^2],x]","\frac{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2} \left(75 a^2 d^2-115 a b c d+48 b^2 c^2\right)}{315 d^3}-\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} \left(105 a^2 b c d^2-5 a^3 d^3-156 a b^2 c^2 d+64 b^3 c^3\right)}{315 b d^4}+\frac{x \sqrt{a+b x^2} \left(243 a^2 b^2 c^2 d^2-25 a^3 b c d^3-10 a^4 d^4-328 a b^3 c^3 d+128 b^4 c^4\right)}{315 b^2 d^4 \sqrt{c+d x^2}}+\frac{c^{3/2} \sqrt{a+b x^2} \left(105 a^2 b c d^2-5 a^3 d^3-156 a b^2 c^2 d+64 b^3 c^3\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{315 b d^{9/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{c} \sqrt{a+b x^2} \left(243 a^2 b^2 c^2 d^2-25 a^3 b c d^3-10 a^4 d^4-328 a b^3 c^3 d+128 b^4 c^4\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{315 b^2 d^{9/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{4 b x^5 \sqrt{a+b x^2} \sqrt{c+d x^2} (2 b c-3 a d)}{63 d^2}+\frac{b x^5 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{9 d}","\frac{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2} \left(75 a^2 d^2-115 a b c d+48 b^2 c^2\right)}{315 d^3}-\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} \left(105 a^2 b c d^2-5 a^3 d^3-156 a b^2 c^2 d+64 b^3 c^3\right)}{315 b d^4}+\frac{x \sqrt{a+b x^2} \left(243 a^2 b^2 c^2 d^2-25 a^3 b c d^3-10 a^4 d^4-328 a b^3 c^3 d+128 b^4 c^4\right)}{315 b^2 d^4 \sqrt{c+d x^2}}+\frac{c^{3/2} \sqrt{a+b x^2} \left(105 a^2 b c d^2-5 a^3 d^3-156 a b^2 c^2 d+64 b^3 c^3\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{315 b d^{9/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{c} \sqrt{a+b x^2} \left(243 a^2 b^2 c^2 d^2-25 a^3 b c d^3-10 a^4 d^4-328 a b^3 c^3 d+128 b^4 c^4\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{315 b^2 d^{9/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{4 b x^5 \sqrt{a+b x^2} \sqrt{c+d x^2} (2 b c-3 a d)}{63 d^2}+\frac{b x^5 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{9 d}",1,"((128*b^4*c^4 - 328*a*b^3*c^3*d + 243*a^2*b^2*c^2*d^2 - 25*a^3*b*c*d^3 - 10*a^4*d^4)*x*Sqrt[a + b*x^2])/(315*b^2*d^4*Sqrt[c + d*x^2]) - ((64*b^3*c^3 - 156*a*b^2*c^2*d + 105*a^2*b*c*d^2 - 5*a^3*d^3)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(315*b*d^4) + ((48*b^2*c^2 - 115*a*b*c*d + 75*a^2*d^2)*x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(315*d^3) - (4*b*(2*b*c - 3*a*d)*x^5*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(63*d^2) + (b*x^5*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(9*d) - (Sqrt[c]*(128*b^4*c^4 - 328*a*b^3*c^3*d + 243*a^2*b^2*c^2*d^2 - 25*a^3*b*c*d^3 - 10*a^4*d^4)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(315*b^2*d^(9/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (c^(3/2)*(64*b^3*c^3 - 156*a*b^2*c^2*d + 105*a^2*b*c*d^2 - 5*a^3*d^3)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(315*b*d^(9/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",8,7,26,0.2692,1,"{477, 581, 582, 531, 418, 492, 411}"
961,1,436,0,0.4892405,"\int \frac{x^2 \left(a+b x^2\right)^{5/2}}{\sqrt{c+d x^2}} \, dx","Int[(x^2*(a + b*x^2)^(5/2))/Sqrt[c + d*x^2],x]","\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} \left(45 a^2 d^2-61 a b c d+24 b^2 c^2\right)}{105 d^3}-\frac{x \sqrt{a+b x^2} \left(103 a^2 b c d^2-15 a^3 d^3-128 a b^2 c^2 d+48 b^3 c^3\right)}{105 b d^3 \sqrt{c+d x^2}}-\frac{c^{3/2} \sqrt{a+b x^2} \left(45 a^2 d^2-61 a b c d+24 b^2 c^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{105 d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} \sqrt{a+b x^2} \left(103 a^2 b c d^2-15 a^3 d^3-128 a b^2 c^2 d+48 b^3 c^3\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{105 b d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 b x^3 \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-5 a d)}{35 d^2}+\frac{b x^3 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{7 d}","\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2} \left(45 a^2 d^2-61 a b c d+24 b^2 c^2\right)}{105 d^3}-\frac{x \sqrt{a+b x^2} \left(103 a^2 b c d^2-15 a^3 d^3-128 a b^2 c^2 d+48 b^3 c^3\right)}{105 b d^3 \sqrt{c+d x^2}}-\frac{c^{3/2} \sqrt{a+b x^2} \left(45 a^2 d^2-61 a b c d+24 b^2 c^2\right) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{105 d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{\sqrt{c} \sqrt{a+b x^2} \left(103 a^2 b c d^2-15 a^3 d^3-128 a b^2 c^2 d+48 b^3 c^3\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{105 b d^{7/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 b x^3 \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-5 a d)}{35 d^2}+\frac{b x^3 \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{7 d}",1,"-((48*b^3*c^3 - 128*a*b^2*c^2*d + 103*a^2*b*c*d^2 - 15*a^3*d^3)*x*Sqrt[a + b*x^2])/(105*b*d^3*Sqrt[c + d*x^2]) + ((24*b^2*c^2 - 61*a*b*c*d + 45*a^2*d^2)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(105*d^3) - (2*b*(3*b*c - 5*a*d)*x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(35*d^2) + (b*x^3*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(7*d) + (Sqrt[c]*(48*b^3*c^3 - 128*a*b^2*c^2*d + 103*a^2*b*c*d^2 - 15*a^3*d^3)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(105*b*d^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (c^(3/2)*(24*b^2*c^2 - 61*a*b*c*d + 45*a^2*d^2)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(105*d^(7/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",7,7,26,0.2692,1,"{477, 581, 582, 531, 418, 492, 411}"
962,1,330,0,0.2909337,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^2 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(5/2)/(x^2*Sqrt[c + d*x^2]),x]","\frac{\sqrt{a+b x^2} \left(-3 a^2 d^2-7 a b c d+2 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 \sqrt{c} d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \sqrt{a+b x^2} \left(\frac{3 a^2 d}{c}+7 a b-\frac{2 b^2 c}{d}\right)}{3 \sqrt{c+d x^2}}-\frac{b \sqrt{c} \sqrt{a+b x^2} (b c-9 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{c x}+\frac{b x \sqrt{a+b x^2} \sqrt{c+d x^2} (3 a d+b c)}{3 c d}","\frac{\sqrt{a+b x^2} \left(-3 a^2 d^2-7 a b c d+2 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 \sqrt{c} d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \sqrt{a+b x^2} \left(\frac{3 a^2 d}{c}+7 a b-\frac{2 b^2 c}{d}\right)}{3 \sqrt{c+d x^2}}-\frac{b \sqrt{c} \sqrt{a+b x^2} (b c-9 a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{c x}+\frac{b x \sqrt{a+b x^2} \sqrt{c+d x^2} (3 a d+b c)}{3 c d}",1,"((7*a*b - (2*b^2*c)/d + (3*a^2*d)/c)*x*Sqrt[a + b*x^2])/(3*Sqrt[c + d*x^2]) + (b*(b*c + 3*a*d)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*c*d) - (a*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(c*x) + ((2*b^2*c^2 - 7*a*b*c*d - 3*a^2*d^2)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*Sqrt[c]*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (b*Sqrt[c]*(b*c - 9*a*d)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{474, 528, 531, 418, 492, 411}"
963,1,336,0,0.2911609,"\int \frac{\left(a+b x^2\right)^{5/2}}{x^4 \sqrt{c+d x^2}} \, dx","Int[(a + b*x^2)^(5/2)/(x^4*Sqrt[c + d*x^2]),x]","\frac{x \sqrt{a+b x^2} \left(-2 a^2 d^2+7 a b c d+3 b^2 c^2\right)}{3 c^2 \sqrt{c+d x^2}}-\frac{\sqrt{a+b x^2} \left(-2 a^2 d^2+7 a b c d+3 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 c^{3/2} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 a \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-a d)}{3 c^2 x}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{3 c x^3}+\frac{b \sqrt{a+b x^2} (9 b c-a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 \sqrt{c} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{x \sqrt{a+b x^2} \left(-2 a^2 d^2+7 a b c d+3 b^2 c^2\right)}{3 c^2 \sqrt{c+d x^2}}-\frac{\sqrt{a+b x^2} \left(-2 a^2 d^2+7 a b c d+3 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 c^{3/2} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 a \sqrt{a+b x^2} \sqrt{c+d x^2} (3 b c-a d)}{3 c^2 x}-\frac{a \left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}}{3 c x^3}+\frac{b \sqrt{a+b x^2} (9 b c-a d) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 \sqrt{c} \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"((3*b^2*c^2 + 7*a*b*c*d - 2*a^2*d^2)*x*Sqrt[a + b*x^2])/(3*c^2*Sqrt[c + d*x^2]) - (2*a*(3*b*c - a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*c^2*x) - (a*(a + b*x^2)^(3/2)*Sqrt[c + d*x^2])/(3*c*x^3) - ((3*b^2*c^2 + 7*a*b*c*d - 2*a^2*d^2)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*c^(3/2)*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (b*(9*b*c - a*d)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*Sqrt[c]*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{474, 580, 531, 418, 492, 411}"
964,1,99,0,0.0934089,"\int \frac{x^4 \sqrt{-1+3 x^2}}{\sqrt{2-3 x^2}} \, dx","Int[(x^4*Sqrt[-1 + 3*x^2])/Sqrt[2 - 3*x^2],x]","-\frac{1}{15} \sqrt{2-3 x^2} \sqrt{3 x^2-1} x^3-\frac{7}{135} \sqrt{2-3 x^2} \sqrt{3 x^2-1} x-\frac{2 F\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{27 \sqrt{3}}-\frac{8 E\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{45 \sqrt{3}}","-\frac{1}{15} \sqrt{2-3 x^2} \sqrt{3 x^2-1} x^3-\frac{7}{135} \sqrt{2-3 x^2} \sqrt{3 x^2-1} x-\frac{2 F\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{27 \sqrt{3}}-\frac{8 E\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{45 \sqrt{3}}",1,"(-7*x*Sqrt[2 - 3*x^2]*Sqrt[-1 + 3*x^2])/135 - (x^3*Sqrt[2 - 3*x^2]*Sqrt[-1 + 3*x^2])/15 - (8*EllipticE[ArcCos[Sqrt[3/2]*x], 2])/(45*Sqrt[3]) - (2*EllipticF[ArcCos[Sqrt[3/2]*x], 2])/(27*Sqrt[3])","A",5,5,26,0.1923,1,"{478, 582, 524, 425, 420}"
965,1,65,0,0.0492191,"\int \frac{x^3 \sqrt{-1+3 x^2}}{\sqrt{2-3 x^2}} \, dx","Int[(x^3*Sqrt[-1 + 3*x^2])/Sqrt[2 - 3*x^2],x]","-\frac{1}{36} \sqrt{2-3 x^2} \left(3 x^2-1\right)^{3/2}-\frac{7}{72} \sqrt{2-3 x^2} \sqrt{3 x^2-1}-\frac{7}{144} \sin ^{-1}\left(3-6 x^2\right)","-\frac{1}{36} \sqrt{2-3 x^2} \left(3 x^2-1\right)^{3/2}-\frac{7}{72} \sqrt{2-3 x^2} \sqrt{3 x^2-1}-\frac{7}{144} \sin ^{-1}\left(3-6 x^2\right)",1,"(-7*Sqrt[2 - 3*x^2]*Sqrt[-1 + 3*x^2])/72 - (Sqrt[2 - 3*x^2]*(-1 + 3*x^2)^(3/2))/36 - (7*ArcSin[3 - 6*x^2])/144","A",6,6,26,0.2308,1,"{446, 80, 50, 53, 619, 216}"
966,1,70,0,0.0455551,"\int \frac{x^2 \sqrt{-1+3 x^2}}{\sqrt{2-3 x^2}} \, dx","Int[(x^2*Sqrt[-1 + 3*x^2])/Sqrt[2 - 3*x^2],x]","-\frac{1}{9} \sqrt{2-3 x^2} \sqrt{3 x^2-1} x-\frac{F\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{9 \sqrt{3}}-\frac{E\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{3 \sqrt{3}}","-\frac{1}{9} \sqrt{2-3 x^2} \sqrt{3 x^2-1} x-\frac{F\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{9 \sqrt{3}}-\frac{E\left(\left.\cos ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{3 \sqrt{3}}",1,"-(x*Sqrt[2 - 3*x^2]*Sqrt[-1 + 3*x^2])/9 - EllipticE[ArcCos[Sqrt[3/2]*x], 2]/(3*Sqrt[3]) - EllipticF[ArcCos[Sqrt[3/2]*x], 2]/(9*Sqrt[3])","A",4,4,26,0.1538,1,"{478, 524, 425, 420}"
967,1,39,0,0.0310672,"\int \frac{x \sqrt{-1+3 x^2}}{\sqrt{2-3 x^2}} \, dx","Int[(x*Sqrt[-1 + 3*x^2])/Sqrt[2 - 3*x^2],x]","-\frac{1}{6} \sqrt{2-3 x^2} \sqrt{3 x^2-1}-\frac{1}{12} \sin ^{-1}\left(3-6 x^2\right)","-\frac{1}{6} \sqrt{2-3 x^2} \sqrt{3 x^2-1}-\frac{1}{12} \sin ^{-1}\left(3-6 x^2\right)",1,"-(Sqrt[2 - 3*x^2]*Sqrt[-1 + 3*x^2])/6 - ArcSin[3 - 6*x^2]/12","A",5,5,24,0.2083,1,"{444, 50, 53, 619, 216}"
968,1,241,0,0.149874,"\int \frac{x^2 \sqrt{2+b x^2}}{\sqrt{3+d x^2}} \, dx","Int[(x^2*Sqrt[2 + b*x^2])/Sqrt[3 + d*x^2],x]","-\frac{\sqrt{2} \sqrt{b x^2+2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{3}}\right)|1-\frac{3 b}{2 d}\right)}{d^{3/2} \sqrt{d x^2+3} \sqrt{\frac{b x^2+2}{d x^2+3}}}+\frac{2 \sqrt{2} (3 b-d) \sqrt{b x^2+2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{3}}\right)|1-\frac{3 b}{2 d}\right)}{3 b d^{3/2} \sqrt{d x^2+3} \sqrt{\frac{b x^2+2}{d x^2+3}}}+\frac{x \sqrt{b x^2+2} \sqrt{d x^2+3}}{3 d}-\frac{2 x (3 b-d) \sqrt{b x^2+2}}{3 b d \sqrt{d x^2+3}}","-\frac{\sqrt{2} \sqrt{b x^2+2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{3}}\right)|1-\frac{3 b}{2 d}\right)}{d^{3/2} \sqrt{d x^2+3} \sqrt{\frac{b x^2+2}{d x^2+3}}}+\frac{2 \sqrt{2} (3 b-d) \sqrt{b x^2+2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{3}}\right)|1-\frac{3 b}{2 d}\right)}{3 b d^{3/2} \sqrt{d x^2+3} \sqrt{\frac{b x^2+2}{d x^2+3}}}+\frac{x \sqrt{b x^2+2} \sqrt{d x^2+3}}{3 d}-\frac{2 x (3 b-d) \sqrt{b x^2+2}}{3 b d \sqrt{d x^2+3}}",1,"(-2*(3*b - d)*x*Sqrt[2 + b*x^2])/(3*b*d*Sqrt[3 + d*x^2]) + (x*Sqrt[2 + b*x^2]*Sqrt[3 + d*x^2])/(3*d) + (2*Sqrt[2]*(3*b - d)*Sqrt[2 + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[3]], 1 - (3*b)/(2*d)])/(3*b*d^(3/2)*Sqrt[(2 + b*x^2)/(3 + d*x^2)]*Sqrt[3 + d*x^2]) - (Sqrt[2]*Sqrt[2 + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[3]], 1 - (3*b)/(2*d)])/(d^(3/2)*Sqrt[(2 + b*x^2)/(3 + d*x^2)]*Sqrt[3 + d*x^2])","A",5,5,26,0.1923,1,"{478, 531, 418, 492, 411}"
969,1,141,0,0.1586308,"\int \frac{x^5}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[x^5/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","-\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{8 b^2 d^2}-\frac{\left(4 a b c d-3 (a d+b c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 b^{5/2} d^{5/2}}+\frac{x^2 \sqrt{a+b x^2} \sqrt{c+d x^2}}{4 b d}","-\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{8 b^2 d^2}-\frac{\left(4 a b c d-3 (a d+b c)^2\right) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{8 b^{5/2} d^{5/2}}+\frac{x^2 \sqrt{a+b x^2} \sqrt{c+d x^2}}{4 b d}",1,"(-3*(b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*b^2*d^2) + (x^2*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(4*b*d) - ((4*a*b*c*d - 3*(b*c + a*d)^2)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(8*b^(5/2)*d^(5/2))","A",6,6,26,0.2308,1,"{446, 90, 80, 63, 217, 206}"
970,1,88,0,0.0934393,"\int \frac{x^3}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[x^3/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 b d}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 b^{3/2} d^{3/2}}","\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 b d}-\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 b^{3/2} d^{3/2}}",1,"(Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*b*d) - ((b*c + a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(2*b^(3/2)*d^(3/2))","A",5,5,26,0.1923,1,"{446, 80, 63, 217, 206}"
971,1,45,0,0.0545664,"\int \frac{x}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[x/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{b} \sqrt{d}}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{b} \sqrt{d}}",1,"ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])]/(Sqrt[b]*Sqrt[d])","A",4,4,24,0.1667,1,"{444, 63, 217, 206}"
972,1,46,0,0.0468969,"\int \frac{1}{x \sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[1/(x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} \sqrt{c}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{\sqrt{a} \sqrt{c}}",1,"-(ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])]/(Sqrt[a]*Sqrt[c]))","A",3,3,26,0.1154,1,"{446, 93, 208}"
973,1,91,0,0.0785099,"\int \frac{1}{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[1/(x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 a c x^2}","\frac{(a d+b c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{2 a^{3/2} c^{3/2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 a c x^2}",1,"-(Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*a*c*x^2) + ((b*c + a*d)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(2*a^(3/2)*c^(3/2))","A",4,4,26,0.1538,1,"{446, 96, 93, 208}"
974,1,149,0,0.1368098,"\int \frac{1}{x^5 \sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[1/(x^5*Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","-\frac{\left(3 a^2 d^2+2 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 a^{5/2} c^{5/2}}+\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{8 a^2 c^2 x^2}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{4 a c x^4}","-\frac{\left(3 a^2 d^2+2 a b c d+3 b^2 c^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{a+b x^2}}{\sqrt{a} \sqrt{c+d x^2}}\right)}{8 a^{5/2} c^{5/2}}+\frac{3 \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{8 a^2 c^2 x^2}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{4 a c x^4}",1,"-(Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(4*a*c*x^4) + (3*(b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(8*a^2*c^2*x^2) - ((3*b^2*c^2 + 2*a*b*c*d + 3*a^2*d^2)*ArcTanh[(Sqrt[c]*Sqrt[a + b*x^2])/(Sqrt[a]*Sqrt[c + d*x^2])])/(8*a^(5/2)*c^(5/2))","A",6,6,26,0.2308,1,"{446, 103, 151, 12, 93, 208}"
975,1,342,0,0.3108496,"\int \frac{x^6}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[x^6/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{x \sqrt{a+b x^2} \left(8 a^2 d^2+7 a b c d+8 b^2 c^2\right)}{15 b^3 d^2 \sqrt{c+d x^2}}-\frac{\sqrt{c} \sqrt{a+b x^2} \left(8 a^2 d^2+7 a b c d+8 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^3 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{4 c^{3/2} \sqrt{a+b x^2} (a d+b c) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{4 x \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{15 b^2 d^2}+\frac{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}}{5 b d}","\frac{x \sqrt{a+b x^2} \left(8 a^2 d^2+7 a b c d+8 b^2 c^2\right)}{15 b^3 d^2 \sqrt{c+d x^2}}-\frac{\sqrt{c} \sqrt{a+b x^2} \left(8 a^2 d^2+7 a b c d+8 b^2 c^2\right) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^3 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{4 c^{3/2} \sqrt{a+b x^2} (a d+b c) F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{15 b^2 d^{5/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{4 x \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{15 b^2 d^2}+\frac{x^3 \sqrt{a+b x^2} \sqrt{c+d x^2}}{5 b d}",1,"((8*b^2*c^2 + 7*a*b*c*d + 8*a^2*d^2)*x*Sqrt[a + b*x^2])/(15*b^3*d^2*Sqrt[c + d*x^2]) - (4*(b*c + a*d)*x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(15*b^2*d^2) + (x^3*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(5*b*d) - (Sqrt[c]*(8*b^2*c^2 + 7*a*b*c*d + 8*a^2*d^2)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b^3*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) + (4*c^(3/2)*(b*c + a*d)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(15*b^2*d^(5/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{479, 582, 531, 418, 492, 411}"
976,1,261,0,0.1622984,"\int \frac{x^4}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[x^4/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{2 \sqrt{c} \sqrt{a+b x^2} (a d+b c) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b^2 d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 x \sqrt{a+b x^2} (a d+b c)}{3 b^2 d \sqrt{c+d x^2}}-\frac{c^{3/2} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2}}{3 b d}","\frac{2 \sqrt{c} \sqrt{a+b x^2} (a d+b c) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b^2 d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{2 x \sqrt{a+b x^2} (a d+b c)}{3 b^2 d \sqrt{c+d x^2}}-\frac{c^{3/2} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 b d^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}+\frac{x \sqrt{a+b x^2} \sqrt{c+d x^2}}{3 b d}",1,"(-2*(b*c + a*d)*x*Sqrt[a + b*x^2])/(3*b^2*d*Sqrt[c + d*x^2]) + (x*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*b*d) + (2*Sqrt[c]*(b*c + a*d)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b^2*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (c^(3/2)*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*b*d^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",5,5,26,0.1923,1,"{479, 531, 418, 492, 411}"
977,1,116,0,0.0492409,"\int \frac{x^2}{\sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[x^2/(Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{x \sqrt{a+b x^2}}{b \sqrt{c+d x^2}}-\frac{\sqrt{c} \sqrt{a+b x^2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{b \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{x \sqrt{a+b x^2}}{b \sqrt{c+d x^2}}-\frac{\sqrt{c} \sqrt{a+b x^2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{b \sqrt{d} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(x*Sqrt[a + b*x^2])/(b*Sqrt[c + d*x^2]) - (Sqrt[c]*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(b*Sqrt[d]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",2,2,26,0.07692,1,"{492, 411}"
978,1,153,0,0.0948289,"\int \frac{1}{x^2 \sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[1/(x^2*Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{d x \sqrt{a+b x^2}}{a c \sqrt{c+d x^2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{a c x}-\frac{\sqrt{d} \sqrt{a+b x^2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}","\frac{d x \sqrt{a+b x^2}}{a c \sqrt{c+d x^2}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{a c x}-\frac{\sqrt{d} \sqrt{a+b x^2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{a \sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}",1,"(d*x*Sqrt[a + b*x^2])/(a*c*Sqrt[c + d*x^2]) - (Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(a*c*x) - (Sqrt[d]*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(a*Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",4,4,26,0.1538,1,"{480, 12, 492, 411}"
979,1,307,0,0.2504997,"\int \frac{1}{x^4 \sqrt{a+b x^2} \sqrt{c+d x^2}} \, dx","Int[1/(x^4*Sqrt[a + b*x^2]*Sqrt[c + d*x^2]),x]","\frac{2 \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{3 a^2 c^2 x}-\frac{2 d x \sqrt{a+b x^2} (a d+b c)}{3 a^2 c^2 \sqrt{c+d x^2}}+\frac{2 \sqrt{d} \sqrt{a+b x^2} (a d+b c) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 c^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{b \sqrt{d} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 \sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{3 a c x^3}","\frac{2 \sqrt{a+b x^2} \sqrt{c+d x^2} (a d+b c)}{3 a^2 c^2 x}-\frac{2 d x \sqrt{a+b x^2} (a d+b c)}{3 a^2 c^2 \sqrt{c+d x^2}}+\frac{2 \sqrt{d} \sqrt{a+b x^2} (a d+b c) E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 c^{3/2} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{b \sqrt{d} \sqrt{a+b x^2} F\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{c}}\right)|1-\frac{b c}{a d}\right)}{3 a^2 \sqrt{c} \sqrt{c+d x^2} \sqrt{\frac{c \left(a+b x^2\right)}{a \left(c+d x^2\right)}}}-\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{3 a c x^3}",1,"(-2*d*(b*c + a*d)*x*Sqrt[a + b*x^2])/(3*a^2*c^2*Sqrt[c + d*x^2]) - (Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*a*c*x^3) + (2*(b*c + a*d)*Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(3*a^2*c^2*x) + (2*Sqrt[d]*(b*c + a*d)*Sqrt[a + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a^2*c^(3/2)*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2]) - (b*Sqrt[d]*Sqrt[a + b*x^2]*EllipticF[ArcTan[(Sqrt[d]*x)/Sqrt[c]], 1 - (b*c)/(a*d)])/(3*a^2*Sqrt[c]*Sqrt[(c*(a + b*x^2))/(a*(c + d*x^2))]*Sqrt[c + d*x^2])","A",6,6,26,0.2308,1,"{480, 583, 531, 418, 492, 411}"
980,1,129,0,0.1644619,"\int \frac{x^5}{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}} \, dx","Int[x^5/((a + b*x^2)^(3/2)*Sqrt[c + d*x^2]),x]","-\frac{a^2 \sqrt{c+d x^2}}{b^2 \sqrt{a+b x^2} (b c-a d)}-\frac{(3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 b^{5/2} d^{3/2}}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 b^2 d}","-\frac{a^2 \sqrt{c+d x^2}}{b^2 \sqrt{a+b x^2} (b c-a d)}-\frac{(3 a d+b c) \tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{2 b^{5/2} d^{3/2}}+\frac{\sqrt{a+b x^2} \sqrt{c+d x^2}}{2 b^2 d}",1,"-((a^2*Sqrt[c + d*x^2])/(b^2*(b*c - a*d)*Sqrt[a + b*x^2])) + (Sqrt[a + b*x^2]*Sqrt[c + d*x^2])/(2*b^2*d) - ((b*c + 3*a*d)*ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])])/(2*b^(5/2)*d^(3/2))","A",6,6,26,0.2308,1,"{446, 89, 80, 63, 217, 206}"
981,1,83,0,0.0885643,"\int \frac{x^3}{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}} \, dx","Int[x^3/((a + b*x^2)^(3/2)*Sqrt[c + d*x^2]),x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{b^{3/2} \sqrt{d}}+\frac{a \sqrt{c+d x^2}}{b \sqrt{a+b x^2} (b c-a d)}","\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{b^{3/2} \sqrt{d}}+\frac{a \sqrt{c+d x^2}}{b \sqrt{a+b x^2} (b c-a d)}",1,"(a*Sqrt[c + d*x^2])/(b*(b*c - a*d)*Sqrt[a + b*x^2]) + ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])]/(b^(3/2)*Sqrt[d])","A",5,5,26,0.1923,1,"{446, 78, 63, 217, 206}"
982,1,34,0,0.0268717,"\int \frac{x}{\left(a+b x^2\right)^{3/2} \sqrt{c+d x^2}} \, dx","Int[x/((a + b*x^2)^(3/2)*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{c+d x^2}}{\sqrt{a+b x^2} (b c-a d)}","-\frac{\sqrt{c+d x^2}}{\sqrt{a+b x^2} (b c-a d)}",1,"-(Sqrt[c + d*x^2]/((b*c - a*d)*Sqrt[a + b*x^2]))","A",2,2,24,0.08333,1,"{444, 37}"
983,1,137,0,0.1414491,"\int \frac{x^5}{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}} \, dx","Int[x^5/((a + b*x^2)^(5/2)*Sqrt[c + d*x^2]),x]","-\frac{a^2 \sqrt{c+d x^2}}{3 b^2 \left(a+b x^2\right)^{3/2} (b c-a d)}+\frac{2 a \sqrt{c+d x^2} (3 b c-2 a d)}{3 b^2 \sqrt{a+b x^2} (b c-a d)^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{b^{5/2} \sqrt{d}}","-\frac{a^2 \sqrt{c+d x^2}}{3 b^2 \left(a+b x^2\right)^{3/2} (b c-a d)}+\frac{2 a \sqrt{c+d x^2} (3 b c-2 a d)}{3 b^2 \sqrt{a+b x^2} (b c-a d)^2}+\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a+b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{b^{5/2} \sqrt{d}}",1,"-(a^2*Sqrt[c + d*x^2])/(3*b^2*(b*c - a*d)*(a + b*x^2)^(3/2)) + (2*a*(3*b*c - 2*a*d)*Sqrt[c + d*x^2])/(3*b^2*(b*c - a*d)^2*Sqrt[a + b*x^2]) + ArcTanh[(Sqrt[d]*Sqrt[a + b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])]/(b^(5/2)*Sqrt[d])","A",6,6,26,0.2308,1,"{446, 89, 78, 63, 217, 206}"
984,1,89,0,0.0664083,"\int \frac{x^3}{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}} \, dx","Int[x^3/((a + b*x^2)^(5/2)*Sqrt[c + d*x^2]),x]","\frac{a \sqrt{c+d x^2}}{3 b \left(a+b x^2\right)^{3/2} (b c-a d)}-\frac{\sqrt{c+d x^2} (3 b c-a d)}{3 b \sqrt{a+b x^2} (b c-a d)^2}","\frac{a \sqrt{c+d x^2}}{3 b \left(a+b x^2\right)^{3/2} (b c-a d)}-\frac{\sqrt{c+d x^2} (3 b c-a d)}{3 b \sqrt{a+b x^2} (b c-a d)^2}",1,"(a*Sqrt[c + d*x^2])/(3*b*(b*c - a*d)*(a + b*x^2)^(3/2)) - ((3*b*c - a*d)*Sqrt[c + d*x^2])/(3*b*(b*c - a*d)^2*Sqrt[a + b*x^2])","A",3,3,26,0.1154,1,"{446, 78, 37}"
985,1,74,0,0.0438094,"\int \frac{x}{\left(a+b x^2\right)^{5/2} \sqrt{c+d x^2}} \, dx","Int[x/((a + b*x^2)^(5/2)*Sqrt[c + d*x^2]),x]","\frac{2 d \sqrt{c+d x^2}}{3 \sqrt{a+b x^2} (b c-a d)^2}-\frac{\sqrt{c+d x^2}}{3 \left(a+b x^2\right)^{3/2} (b c-a d)}","\frac{2 d \sqrt{c+d x^2}}{3 \sqrt{a+b x^2} (b c-a d)^2}-\frac{\sqrt{c+d x^2}}{3 \left(a+b x^2\right)^{3/2} (b c-a d)}",1,"-Sqrt[c + d*x^2]/(3*(b*c - a*d)*(a + b*x^2)^(3/2)) + (2*d*Sqrt[c + d*x^2])/(3*(b*c - a*d)^2*Sqrt[a + b*x^2])","A",3,3,24,0.1250,1,"{444, 45, 37}"
986,1,154,0,0.1802428,"\int \frac{x^5}{\left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}} \, dx","Int[x^5/((a + b*x^2)^(7/2)*Sqrt[c + d*x^2]),x]","-\frac{\sqrt{c+d x^2} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right)}{15 b^2 \sqrt{a+b x^2} (b c-a d)^3}-\frac{a^2 \sqrt{c+d x^2}}{5 b^2 \left(a+b x^2\right)^{5/2} (b c-a d)}+\frac{2 a \sqrt{c+d x^2} (5 b c-3 a d)}{15 b^2 \left(a+b x^2\right)^{3/2} (b c-a d)^2}","-\frac{\sqrt{c+d x^2} \left(3 a^2 d^2-10 a b c d+15 b^2 c^2\right)}{15 b^2 \sqrt{a+b x^2} (b c-a d)^3}-\frac{a^2 \sqrt{c+d x^2}}{5 b^2 \left(a+b x^2\right)^{5/2} (b c-a d)}+\frac{2 a \sqrt{c+d x^2} (5 b c-3 a d)}{15 b^2 \left(a+b x^2\right)^{3/2} (b c-a d)^2}",1,"-(a^2*Sqrt[c + d*x^2])/(5*b^2*(b*c - a*d)*(a + b*x^2)^(5/2)) + (2*a*(5*b*c - 3*a*d)*Sqrt[c + d*x^2])/(15*b^2*(b*c - a*d)^2*(a + b*x^2)^(3/2)) - ((15*b^2*c^2 - 10*a*b*c*d + 3*a^2*d^2)*Sqrt[c + d*x^2])/(15*b^2*(b*c - a*d)^3*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{446, 89, 78, 37}"
987,1,138,0,0.100783,"\int \frac{x^3}{\left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}} \, dx","Int[x^3/((a + b*x^2)^(7/2)*Sqrt[c + d*x^2]),x]","\frac{a \sqrt{c+d x^2}}{5 b \left(a+b x^2\right)^{5/2} (b c-a d)}+\frac{2 d \sqrt{c+d x^2} (5 b c-a d)}{15 b \sqrt{a+b x^2} (b c-a d)^3}-\frac{\sqrt{c+d x^2} (5 b c-a d)}{15 b \left(a+b x^2\right)^{3/2} (b c-a d)^2}","\frac{a \sqrt{c+d x^2}}{5 b \left(a+b x^2\right)^{5/2} (b c-a d)}+\frac{2 d \sqrt{c+d x^2} (5 b c-a d)}{15 b \sqrt{a+b x^2} (b c-a d)^3}-\frac{\sqrt{c+d x^2} (5 b c-a d)}{15 b \left(a+b x^2\right)^{3/2} (b c-a d)^2}",1,"(a*Sqrt[c + d*x^2])/(5*b*(b*c - a*d)*(a + b*x^2)^(5/2)) - ((5*b*c - a*d)*Sqrt[c + d*x^2])/(15*b*(b*c - a*d)^2*(a + b*x^2)^(3/2)) + (2*d*(5*b*c - a*d)*Sqrt[c + d*x^2])/(15*b*(b*c - a*d)^3*Sqrt[a + b*x^2])","A",4,4,26,0.1538,1,"{446, 78, 45, 37}"
988,1,113,0,0.0636799,"\int \frac{x}{\left(a+b x^2\right)^{7/2} \sqrt{c+d x^2}} \, dx","Int[x/((a + b*x^2)^(7/2)*Sqrt[c + d*x^2]),x]","-\frac{8 d^2 \sqrt{c+d x^2}}{15 \sqrt{a+b x^2} (b c-a d)^3}+\frac{4 d \sqrt{c+d x^2}}{15 \left(a+b x^2\right)^{3/2} (b c-a d)^2}-\frac{\sqrt{c+d x^2}}{5 \left(a+b x^2\right)^{5/2} (b c-a d)}","-\frac{8 d^2 \sqrt{c+d x^2}}{15 \sqrt{a+b x^2} (b c-a d)^3}+\frac{4 d \sqrt{c+d x^2}}{15 \left(a+b x^2\right)^{3/2} (b c-a d)^2}-\frac{\sqrt{c+d x^2}}{5 \left(a+b x^2\right)^{5/2} (b c-a d)}",1,"-Sqrt[c + d*x^2]/(5*(b*c - a*d)*(a + b*x^2)^(5/2)) + (4*d*Sqrt[c + d*x^2])/(15*(b*c - a*d)^2*(a + b*x^2)^(3/2)) - (8*d^2*Sqrt[c + d*x^2])/(15*(b*c - a*d)^3*Sqrt[a + b*x^2])","A",4,3,24,0.1250,1,"{444, 45, 37}"
989,1,217,0,0.2686551,"\int \frac{x^5}{\left(a+b x^2\right)^{9/2} \sqrt{c+d x^2}} \, dx","Int[x^5/((a + b*x^2)^(9/2)*Sqrt[c + d*x^2]),x]","\frac{2 d \sqrt{c+d x^2} \left(3 a^2 d^2-14 a b c d+35 b^2 c^2\right)}{105 b^2 \sqrt{a+b x^2} (b c-a d)^4}-\frac{\sqrt{c+d x^2} \left(3 a^2 d^2-14 a b c d+35 b^2 c^2\right)}{105 b^2 \left(a+b x^2\right)^{3/2} (b c-a d)^3}-\frac{a^2 \sqrt{c+d x^2}}{7 b^2 \left(a+b x^2\right)^{7/2} (b c-a d)}+\frac{2 a \sqrt{c+d x^2} (7 b c-4 a d)}{35 b^2 \left(a+b x^2\right)^{5/2} (b c-a d)^2}","\frac{2 d \sqrt{c+d x^2} \left(3 a^2 d^2-14 a b c d+35 b^2 c^2\right)}{105 b^2 \sqrt{a+b x^2} (b c-a d)^4}-\frac{\sqrt{c+d x^2} \left(3 a^2 d^2-14 a b c d+35 b^2 c^2\right)}{105 b^2 \left(a+b x^2\right)^{3/2} (b c-a d)^3}-\frac{a^2 \sqrt{c+d x^2}}{7 b^2 \left(a+b x^2\right)^{7/2} (b c-a d)}+\frac{2 a \sqrt{c+d x^2} (7 b c-4 a d)}{35 b^2 \left(a+b x^2\right)^{5/2} (b c-a d)^2}",1,"-(a^2*Sqrt[c + d*x^2])/(7*b^2*(b*c - a*d)*(a + b*x^2)^(7/2)) + (2*a*(7*b*c - 4*a*d)*Sqrt[c + d*x^2])/(35*b^2*(b*c - a*d)^2*(a + b*x^2)^(5/2)) - ((35*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2)*Sqrt[c + d*x^2])/(105*b^2*(b*c - a*d)^3*(a + b*x^2)^(3/2)) + (2*d*(35*b^2*c^2 - 14*a*b*c*d + 3*a^2*d^2)*Sqrt[c + d*x^2])/(105*b^2*(b*c - a*d)^4*Sqrt[a + b*x^2])","A",5,5,26,0.1923,1,"{446, 89, 78, 45, 37}"
990,1,47,0,0.0570364,"\int \frac{x}{\sqrt{a-b x^2} \sqrt{c+d x^2}} \, dx","Int[x/(Sqrt[a - b*x^2]*Sqrt[c + d*x^2]),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{b} \sqrt{d}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x^2}}{\sqrt{b} \sqrt{c+d x^2}}\right)}{\sqrt{b} \sqrt{d}}",1,"-(ArcTan[(Sqrt[d]*Sqrt[a - b*x^2])/(Sqrt[b]*Sqrt[c + d*x^2])]/(Sqrt[b]*Sqrt[d]))","A",4,4,25,0.1600,1,"{444, 63, 217, 203}"
991,1,48,0,0.0580089,"\int \frac{x}{\sqrt{a-b x^2} \sqrt{c-d x^2}} \, dx","Int[x/(Sqrt[a - b*x^2]*Sqrt[c - d*x^2]),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x^2}}{\sqrt{b} \sqrt{c-d x^2}}\right)}{\sqrt{b} \sqrt{d}}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{d} \sqrt{a-b x^2}}{\sqrt{b} \sqrt{c-d x^2}}\right)}{\sqrt{b} \sqrt{d}}",1,"-(ArcTanh[(Sqrt[d]*Sqrt[a - b*x^2])/(Sqrt[b]*Sqrt[c - d*x^2])]/(Sqrt[b]*Sqrt[d]))","A",4,4,26,0.1538,1,"{444, 63, 217, 206}"
992,1,110,0,0.0451851,"\int \frac{x^2}{\sqrt{2+b x^2} \sqrt{3+d x^2}} \, dx","Int[x^2/(Sqrt[2 + b*x^2]*Sqrt[3 + d*x^2]),x]","\frac{x \sqrt{b x^2+2}}{b \sqrt{d x^2+3}}-\frac{\sqrt{2} \sqrt{b x^2+2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{3}}\right)|1-\frac{3 b}{2 d}\right)}{b \sqrt{d} \sqrt{d x^2+3} \sqrt{\frac{b x^2+2}{d x^2+3}}}","\frac{x \sqrt{b x^2+2}}{b \sqrt{d x^2+3}}-\frac{\sqrt{2} \sqrt{b x^2+2} E\left(\tan ^{-1}\left(\frac{\sqrt{d} x}{\sqrt{3}}\right)|1-\frac{3 b}{2 d}\right)}{b \sqrt{d} \sqrt{d x^2+3} \sqrt{\frac{b x^2+2}{d x^2+3}}}",1,"(x*Sqrt[2 + b*x^2])/(b*Sqrt[3 + d*x^2]) - (Sqrt[2]*Sqrt[2 + b*x^2]*EllipticE[ArcTan[(Sqrt[d]*x)/Sqrt[3]], 1 - (3*b)/(2*d)])/(b*Sqrt[d]*Sqrt[(2 + b*x^2)/(3 + d*x^2)]*Sqrt[3 + d*x^2])","A",2,2,26,0.07692,1,"{492, 411}"
993,1,87,0,0.0697967,"\int \frac{x^2}{\sqrt{4-x^2} \sqrt{c+d x^2}} \, dx","Int[x^2/(Sqrt[4 - x^2]*Sqrt[c + d*x^2]),x]","\frac{\sqrt{c+d x^2} E\left(\sin ^{-1}\left(\frac{x}{2}\right)|-\frac{4 d}{c}\right)}{d \sqrt{\frac{d x^2}{c}+1}}-\frac{c \sqrt{\frac{d x^2}{c}+1} F\left(\sin ^{-1}\left(\frac{x}{2}\right)|-\frac{4 d}{c}\right)}{d \sqrt{c+d x^2}}","\frac{\sqrt{c+d x^2} E\left(\sin ^{-1}\left(\frac{x}{2}\right)|-\frac{4 d}{c}\right)}{d \sqrt{\frac{d x^2}{c}+1}}-\frac{c \sqrt{\frac{d x^2}{c}+1} F\left(\sin ^{-1}\left(\frac{x}{2}\right)|-\frac{4 d}{c}\right)}{d \sqrt{c+d x^2}}",1,"(Sqrt[c + d*x^2]*EllipticE[ArcSin[x/2], (-4*d)/c])/(d*Sqrt[1 + (d*x^2)/c]) - (c*Sqrt[1 + (d*x^2)/c]*EllipticF[ArcSin[x/2], (-4*d)/c])/(d*Sqrt[c + d*x^2])","A",5,5,26,0.1923,1,"{493, 426, 424, 421, 419}"
994,1,88,0,0.0361522,"\int \frac{x^2}{\sqrt{4+x^2} \sqrt{c+d x^2}} \, dx","Int[x^2/(Sqrt[4 + x^2]*Sqrt[c + d*x^2]),x]","\frac{x \sqrt{c+d x^2}}{d \sqrt{x^2+4}}-\frac{\sqrt{c+d x^2} E\left(\tan ^{-1}\left(\frac{x}{2}\right)|1-\frac{4 d}{c}\right)}{d \sqrt{x^2+4} \sqrt{\frac{c+d x^2}{c \left(x^2+4\right)}}}","\frac{x \sqrt{c+d x^2}}{d \sqrt{x^2+4}}-\frac{\sqrt{c+d x^2} E\left(\tan ^{-1}\left(\frac{x}{2}\right)|1-\frac{4 d}{c}\right)}{d \sqrt{x^2+4} \sqrt{\frac{c+d x^2}{c \left(x^2+4\right)}}}",1,"(x*Sqrt[c + d*x^2])/(d*Sqrt[4 + x^2]) - (Sqrt[c + d*x^2]*EllipticE[ArcTan[x/2], 1 - (4*d)/c])/(d*Sqrt[4 + x^2]*Sqrt[(c + d*x^2)/(c*(4 + x^2))])","A",2,2,24,0.08333,1,"{492, 411}"
995,1,31,0,0.0296919,"\int \frac{x^2}{\sqrt{1-x^2} \sqrt{2+3 x^2}} \, dx","Int[x^2/(Sqrt[1 - x^2]*Sqrt[2 + 3*x^2]),x]","\frac{1}{3} \sqrt{2} E\left(\sin ^{-1}(x)|-\frac{3}{2}\right)-\frac{1}{3} \sqrt{2} F\left(\sin ^{-1}(x)|-\frac{3}{2}\right)","\frac{1}{3} \sqrt{2} E\left(\sin ^{-1}(x)|-\frac{3}{2}\right)-\frac{1}{3} \sqrt{2} F\left(\sin ^{-1}(x)|-\frac{3}{2}\right)",1,"(Sqrt[2]*EllipticE[ArcSin[x], -3/2])/3 - (Sqrt[2]*EllipticF[ArcSin[x], -3/2])/3","A",3,3,26,0.1154,1,"{493, 424, 419}"
996,1,31,0,0.0297203,"\int \frac{x^2}{\sqrt{2-3 x^2} \sqrt{1-x^2}} \, dx","Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[1 - x^2]),x]","\frac{1}{3} \sqrt{2} F\left(\sin ^{-1}(x)|\frac{3}{2}\right)-\frac{1}{3} \sqrt{2} E\left(\sin ^{-1}(x)|\frac{3}{2}\right)","\frac{1}{3} \sqrt{2} F\left(\sin ^{-1}(x)|\frac{3}{2}\right)-\frac{1}{3} \sqrt{2} E\left(\sin ^{-1}(x)|\frac{3}{2}\right)",1,"-(Sqrt[2]*EllipticE[ArcSin[x], 3/2])/3 + (Sqrt[2]*EllipticF[ArcSin[x], 3/2])/3","A",3,3,26,0.1154,1,"{493, 424, 419}"
997,1,35,0,0.0314943,"\int \frac{x^2}{\sqrt{4-x^2} \sqrt{2+3 x^2}} \, dx","Int[x^2/(Sqrt[4 - x^2]*Sqrt[2 + 3*x^2]),x]","\frac{1}{3} \sqrt{2} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-6\right)-\frac{1}{3} \sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-6\right)","\frac{1}{3} \sqrt{2} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-6\right)-\frac{1}{3} \sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|-6\right)",1,"(Sqrt[2]*EllipticE[ArcSin[x/2], -6])/3 - (Sqrt[2]*EllipticF[ArcSin[x/2], -6])/3","A",3,3,26,0.1154,1,"{493, 424, 419}"
998,1,35,0,0.0316317,"\int \frac{x^2}{\sqrt{2-3 x^2} \sqrt{4-x^2}} \, dx","Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[4 - x^2]),x]","\frac{1}{3} \sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|6\right)-\frac{1}{3} \sqrt{2} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|6\right)","\frac{1}{3} \sqrt{2} F\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|6\right)-\frac{1}{3} \sqrt{2} E\left(\left.\sin ^{-1}\left(\frac{x}{2}\right)\right|6\right)",1,"-(Sqrt[2]*EllipticE[ArcSin[x/2], 6])/3 + (Sqrt[2]*EllipticF[ArcSin[x/2], 6])/3","A",3,3,26,0.1154,1,"{493, 424, 419}"
999,1,35,0,0.0301921,"\int \frac{x^2}{\sqrt{1-4 x^2} \sqrt{2+3 x^2}} \, dx","Int[x^2/(Sqrt[1 - 4*x^2]*Sqrt[2 + 3*x^2]),x]","\frac{E\left(\sin ^{-1}(2 x)|-\frac{3}{8}\right)}{3 \sqrt{2}}-\frac{F\left(\sin ^{-1}(2 x)|-\frac{3}{8}\right)}{3 \sqrt{2}}","\frac{E\left(\sin ^{-1}(2 x)|-\frac{3}{8}\right)}{3 \sqrt{2}}-\frac{F\left(\sin ^{-1}(2 x)|-\frac{3}{8}\right)}{3 \sqrt{2}}",1,"EllipticE[ArcSin[2*x], -3/8]/(3*Sqrt[2]) - EllipticF[ArcSin[2*x], -3/8]/(3*Sqrt[2])","A",3,3,26,0.1154,1,"{493, 424, 419}"
1000,1,35,0,0.0319154,"\int \frac{x^2}{\sqrt{1-4 x^2} \sqrt{2-3 x^2}} \, dx","Int[x^2/(Sqrt[1 - 4*x^2]*Sqrt[2 - 3*x^2]),x]","\frac{F\left(\sin ^{-1}(2 x)|\frac{3}{8}\right)}{3 \sqrt{2}}-\frac{E\left(\sin ^{-1}(2 x)|\frac{3}{8}\right)}{3 \sqrt{2}}","\frac{F\left(\sin ^{-1}(2 x)|\frac{3}{8}\right)}{3 \sqrt{2}}-\frac{E\left(\sin ^{-1}(2 x)|\frac{3}{8}\right)}{3 \sqrt{2}}",1,"-EllipticE[ArcSin[2*x], 3/8]/(3*Sqrt[2]) + EllipticF[ArcSin[2*x], 3/8]/(3*Sqrt[2])","A",3,3,26,0.1154,1,"{493, 424, 419}"
1001,1,42,0,0.0282783,"\int \frac{x^2}{\sqrt{2-3 x^2} \sqrt{1+x^2}} \, dx","Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[1 + x^2]),x]","\frac{E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{2}{3}\right)}{\sqrt{3}}-\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{2}{3}\right)}{\sqrt{3}}","\frac{E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{2}{3}\right)}{\sqrt{3}}-\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{2}{3}\right)}{\sqrt{3}}",1,"EllipticE[ArcSin[Sqrt[3/2]*x], -2/3]/Sqrt[3] - EllipticF[ArcSin[Sqrt[3/2]*x], -2/3]/Sqrt[3]","A",3,3,24,0.1250,1,"{493, 424, 419}"
1002,1,43,0,0.0289706,"\int \frac{x^2}{\sqrt{2-3 x^2} \sqrt{4+x^2}} \, dx","Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[4 + x^2]),x]","\frac{2 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{1}{6}\right)}{\sqrt{3}}-\frac{2 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{1}{6}\right)}{\sqrt{3}}","\frac{2 E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{1}{6}\right)}{\sqrt{3}}-\frac{2 F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{1}{6}\right)}{\sqrt{3}}",1,"(2*EllipticE[ArcSin[Sqrt[3/2]*x], -1/6])/Sqrt[3] - (2*EllipticF[ArcSin[Sqrt[3/2]*x], -1/6])/Sqrt[3]","A",3,3,24,0.1250,1,"{493, 424, 419}"
1003,1,47,0,0.0312434,"\int \frac{x^2}{\sqrt{2-3 x^2} \sqrt{1+4 x^2}} \, dx","Int[x^2/(Sqrt[2 - 3*x^2]*Sqrt[1 + 4*x^2]),x]","\frac{E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{8}{3}\right)}{4 \sqrt{3}}-\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{8}{3}\right)}{4 \sqrt{3}}","\frac{E\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{8}{3}\right)}{4 \sqrt{3}}-\frac{F\left(\sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)|-\frac{8}{3}\right)}{4 \sqrt{3}}",1,"EllipticE[ArcSin[Sqrt[3/2]*x], -8/3]/(4*Sqrt[3]) - EllipticF[ArcSin[Sqrt[3/2]*x], -8/3]/(4*Sqrt[3])","A",3,3,26,0.1154,1,"{493, 424, 419}"
1004,1,80,0,0.0275457,"\int \frac{x^2}{\sqrt{1+x^2} \sqrt{2+3 x^2}} \, dx","Int[x^2/(Sqrt[1 + x^2]*Sqrt[2 + 3*x^2]),x]","\frac{x \sqrt{3 x^2+2}}{3 \sqrt{x^2+1}}-\frac{\sqrt{2} \sqrt{3 x^2+2} E\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{3 \sqrt{x^2+1} \sqrt{\frac{3 x^2+2}{x^2+1}}}","\frac{x \sqrt{3 x^2+2}}{3 \sqrt{x^2+1}}-\frac{\sqrt{2} \sqrt{3 x^2+2} E\left(\tan ^{-1}(x)|-\frac{1}{2}\right)}{3 \sqrt{x^2+1} \sqrt{\frac{3 x^2+2}{x^2+1}}}",1,"(x*Sqrt[2 + 3*x^2])/(3*Sqrt[1 + x^2]) - (Sqrt[2]*Sqrt[2 + 3*x^2]*EllipticE[ArcTan[x], -1/2])/(3*Sqrt[1 + x^2]*Sqrt[(2 + 3*x^2)/(1 + x^2)])","A",2,2,24,0.08333,1,"{492, 411}"
1005,1,82,0,0.0291869,"\int \frac{x^2}{\sqrt{4+x^2} \sqrt{2+3 x^2}} \, dx","Int[x^2/(Sqrt[4 + x^2]*Sqrt[2 + 3*x^2]),x]","\frac{x \sqrt{3 x^2+2}}{3 \sqrt{x^2+4}}-\frac{\sqrt{2} \sqrt{3 x^2+2} E\left(\left.\tan ^{-1}\left(\frac{x}{2}\right)\right|-5\right)}{3 \sqrt{x^2+4} \sqrt{\frac{3 x^2+2}{x^2+4}}}","\frac{x \sqrt{3 x^2+2}}{3 \sqrt{x^2+4}}-\frac{\sqrt{2} \sqrt{3 x^2+2} E\left(\left.\tan ^{-1}\left(\frac{x}{2}\right)\right|-5\right)}{3 \sqrt{x^2+4} \sqrt{\frac{3 x^2+2}{x^2+4}}}",1,"(x*Sqrt[2 + 3*x^2])/(3*Sqrt[4 + x^2]) - (Sqrt[2]*Sqrt[2 + 3*x^2]*EllipticE[ArcTan[x/2], -5])/(3*Sqrt[4 + x^2]*Sqrt[(2 + 3*x^2)/(4 + x^2)])","A",2,2,24,0.08333,1,"{492, 411}"
1006,1,88,0,0.0307442,"\int \frac{x^2}{\sqrt{2+3 x^2} \sqrt{1+4 x^2}} \, dx","Int[x^2/(Sqrt[2 + 3*x^2]*Sqrt[1 + 4*x^2]),x]","\frac{x \sqrt{3 x^2+2}}{3 \sqrt{4 x^2+1}}-\frac{\sqrt{3 x^2+2} E\left(\tan ^{-1}(2 x)|\frac{5}{8}\right)}{3 \sqrt{2} \sqrt{\frac{3 x^2+2}{4 x^2+1}} \sqrt{4 x^2+1}}","\frac{x \sqrt{3 x^2+2}}{3 \sqrt{4 x^2+1}}-\frac{\sqrt{3 x^2+2} E\left(\tan ^{-1}(2 x)|\frac{5}{8}\right)}{3 \sqrt{2} \sqrt{\frac{3 x^2+2}{4 x^2+1}} \sqrt{4 x^2+1}}",1,"(x*Sqrt[2 + 3*x^2])/(3*Sqrt[1 + 4*x^2]) - (Sqrt[2 + 3*x^2]*EllipticE[ArcTan[2*x], 5/8])/(3*Sqrt[2]*Sqrt[(2 + 3*x^2)/(1 + 4*x^2)]*Sqrt[1 + 4*x^2])","A",2,2,26,0.07692,1,"{492, 411}"
1007,1,17,0,0.0278453,"\int \frac{x^2}{\sqrt{1-x^2} \sqrt{-1+2 x^2}} \, dx","Int[x^2/(Sqrt[1 - x^2]*Sqrt[-1 + 2*x^2]),x]","-\frac{1}{2} F\left(\left.\cos ^{-1}(x)\right|2\right)-\frac{1}{2} E\left(\left.\cos ^{-1}(x)\right|2\right)","-\frac{1}{2} F\left(\left.\cos ^{-1}(x)\right|2\right)-\frac{1}{2} E\left(\left.\cos ^{-1}(x)\right|2\right)",1,"-EllipticE[ArcCos[x], 2]/2 - EllipticF[ArcCos[x], 2]/2","A",3,3,26,0.1154,1,"{493, 425, 420}"
1008,1,109,0,0.0877867,"\int \frac{x^5}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[x^5/((1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{3}{10} \left(1-x^2\right)^{5/3}+\frac{3}{2} \left(1-x^2\right)^{2/3}-\frac{9 \log \left(x^2+3\right)}{4\ 2^{2/3}}+\frac{27 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}+\frac{9 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}","\frac{3}{10} \left(1-x^2\right)^{5/3}+\frac{3}{2} \left(1-x^2\right)^{2/3}-\frac{9 \log \left(x^2+3\right)}{4\ 2^{2/3}}+\frac{27 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}+\frac{9 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}",1,"(3*(1 - x^2)^(2/3))/2 + (3*(1 - x^2)^(5/3))/10 + (9*Sqrt[3]*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)) - (9*Log[3 + x^2])/(4*2^(2/3)) + (27*Log[2^(2/3) - (1 - x^2)^(1/3)])/(4*2^(2/3))","A",7,6,22,0.2727,1,"{446, 88, 55, 617, 204, 31}"
1009,1,94,0,0.0653427,"\int \frac{x^3}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[x^3/((1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{3}{4} \left(1-x^2\right)^{2/3}+\frac{3 \log \left(x^2+3\right)}{4\ 2^{2/3}}-\frac{9 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}-\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}","-\frac{3}{4} \left(1-x^2\right)^{2/3}+\frac{3 \log \left(x^2+3\right)}{4\ 2^{2/3}}-\frac{9 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}-\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}",1,"(-3*(1 - x^2)^(2/3))/4 - (3*Sqrt[3]*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)) + (3*Log[3 + x^2])/(4*2^(2/3)) - (9*Log[2^(2/3) - (1 - x^2)^(1/3)])/(4*2^(2/3))","A",6,6,22,0.2727,1,"{446, 80, 55, 617, 204, 31}"
1010,1,79,0,0.052399,"\int \frac{x}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[x/((1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{\log \left(x^2+3\right)}{4\ 2^{2/3}}+\frac{3 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}","-\frac{\log \left(x^2+3\right)}{4\ 2^{2/3}}+\frac{3 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3}}",1,"(Sqrt[3]*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(2*2^(2/3)) - Log[3 + x^2]/(4*2^(2/3)) + (3*Log[2^(2/3) - (1 - x^2)^(1/3)])/(4*2^(2/3))","A",5,5,20,0.2500,1,"{444, 55, 617, 204, 31}"
1011,1,136,0,0.0990665,"\int \frac{1}{x \sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/(x*(1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{\log \left(x^2+3\right)}{12\ 2^{2/3}}+\frac{1}{4} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\log (x)}{6}","\frac{\log \left(x^2+3\right)}{12\ 2^{2/3}}+\frac{1}{4} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{4\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{2 \sqrt{3}}-\frac{\log (x)}{6}",1,"-ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]]/(2*2^(2/3)*Sqrt[3]) + ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]]/(2*Sqrt[3]) - Log[x]/6 + Log[3 + x^2]/(12*2^(2/3)) + Log[1 - (1 - x^2)^(1/3)]/4 - Log[2^(2/3) - (1 - x^2)^(1/3)]/(4*2^(2/3))","A",10,7,22,0.3182,1,"{446, 86, 55, 618, 204, 31, 617}"
1012,1,97,0,0.0744409,"\int \frac{1}{x^3 \sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/(x^3*(1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{\left(1-x^2\right)^{2/3}}{6 x^2}-\frac{\log \left(x^2+3\right)}{36\ 2^{2/3}}+\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{12\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt{3}}","-\frac{\left(1-x^2\right)^{2/3}}{6 x^2}-\frac{\log \left(x^2+3\right)}{36\ 2^{2/3}}+\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{12\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{6\ 2^{2/3} \sqrt{3}}",1,"-(1 - x^2)^(2/3)/(6*x^2) + ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]]/(6*2^(2/3)*Sqrt[3]) - Log[3 + x^2]/(36*2^(2/3)) + Log[2^(2/3) - (1 - x^2)^(1/3)]/(12*2^(2/3))","A",7,7,22,0.3182,1,"{446, 103, 12, 55, 617, 204, 31}"
1013,1,172,0,0.1298593,"\int \frac{1}{x^5 \sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/(x^5*(1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{\left(1-x^2\right)^{2/3}}{18 x^2}-\frac{\left(1-x^2\right)^{2/3}}{12 x^4}+\frac{\log \left(x^2+3\right)}{108\ 2^{2/3}}+\frac{1}{18} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{36\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{18\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}-\frac{\log (x)}{27}","-\frac{\left(1-x^2\right)^{2/3}}{18 x^2}-\frac{\left(1-x^2\right)^{2/3}}{12 x^4}+\frac{\log \left(x^2+3\right)}{108\ 2^{2/3}}+\frac{1}{18} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{36\ 2^{2/3}}-\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{18\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{9 \sqrt{3}}-\frac{\log (x)}{27}",1,"-(1 - x^2)^(2/3)/(12*x^4) - (1 - x^2)^(2/3)/(18*x^2) - ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]]/(18*2^(2/3)*Sqrt[3]) + ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]]/(9*Sqrt[3]) - Log[x]/27 + Log[3 + x^2]/(108*2^(2/3)) + Log[1 - (1 - x^2)^(1/3)]/18 - Log[2^(2/3) - (1 - x^2)^(1/3)]/(36*2^(2/3))","A",12,9,22,0.4091,1,"{446, 103, 151, 156, 55, 618, 204, 31, 617}"
1014,1,536,0,0.2783917,"\int \frac{x^4}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[x^4/((1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{3}{7} \left(1-x^2\right)^{2/3} x+\frac{54 x}{7 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3}}+\frac{9 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}-\frac{18 \sqrt{2} 3^{3/4} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{27 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3}}-\frac{3 \tanh ^{-1}(x)}{2\ 2^{2/3}}","-\frac{3}{7} \left(1-x^2\right)^{2/3} x+\frac{54 x}{7 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3}}+\frac{9 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}-\frac{18 \sqrt{2} 3^{3/4} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{27 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{7 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3}}-\frac{3 \tanh ^{-1}(x)}{2\ 2^{2/3}}",1,"(-3*x*(1 - x^2)^(2/3))/7 + (54*x)/(7*(1 - Sqrt[3] - (1 - x^2)^(1/3))) + (3*Sqrt[3]*ArcTan[Sqrt[3]/x])/(2*2^(2/3)) + (3*Sqrt[3]*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x])/(2*2^(2/3)) - (3*ArcTanh[x])/(2*2^(2/3)) + (9*ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))])/(2*2^(2/3)) + (27*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) - (18*Sqrt[2]*3^(3/4)*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(7*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{479, 530, 235, 304, 219, 1879, 393}"
1015,1,515,0,0.1674022,"\int \frac{x^2}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[x^2/((1 - x^2)^(1/3)*(3 + x^2)),x]","-\frac{3 x}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3}}-\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}+\frac{\sqrt{2} 3^{3/4} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3}}+\frac{\tanh ^{-1}(x)}{2\ 2^{2/3}}","-\frac{3 x}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3}}-\frac{3 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}+\frac{\sqrt{2} 3^{3/4} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{\sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{3 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{\sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3}}+\frac{\tanh ^{-1}(x)}{2\ 2^{2/3}}",1,"(-3*x)/(1 - Sqrt[3] - (1 - x^2)^(1/3)) - (Sqrt[3]*ArcTan[Sqrt[3]/x])/(2*2^(2/3)) - (Sqrt[3]*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x])/(2*2^(2/3)) + ArcTanh[x]/(2*2^(2/3)) - (3*ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))])/(2*2^(2/3)) - (3*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(2*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) + (Sqrt[2]*3^(3/4)*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",6,6,22,0.2727,1,"{483, 235, 304, 219, 1879, 393}"
1016,1,113,0,0.0130406,"\int \frac{1}{\sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/((1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{6\ 2^{2/3}}","\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{2\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{2\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{2\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{6\ 2^{2/3}}",1,"ArcTan[Sqrt[3]/x]/(2*2^(2/3)*Sqrt[3]) + ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x]/(2*2^(2/3)*Sqrt[3]) - ArcTanh[x]/(6*2^(2/3)) + ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))]/(2*2^(2/3))","A",1,1,19,0.05263,1,"{393}"
1017,1,538,0,0.2359803,"\int \frac{1}{x^2 \sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/(x^2*(1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{x}{3 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{\left(1-x^2\right)^{2/3}}{3 x}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{6\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{6\ 2^{2/3}}-\frac{\sqrt{2} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{6\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}(x)}{18\ 2^{2/3}}","\frac{x}{3 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{\left(1-x^2\right)^{2/3}}{3 x}-\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{6\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{6\ 2^{2/3}}-\frac{\sqrt{2} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{2\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{6\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}(x)}{18\ 2^{2/3}}",1,"-(1 - x^2)^(2/3)/(3*x) + x/(3*(1 - Sqrt[3] - (1 - x^2)^(1/3))) - ArcTan[Sqrt[3]/x]/(6*2^(2/3)*Sqrt[3]) - ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x]/(6*2^(2/3)*Sqrt[3]) + ArcTanh[x]/(18*2^(2/3)) - ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))]/(6*2^(2/3)) + (Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(2*3^(3/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) - (Sqrt[2]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(3*3^(1/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{480, 530, 235, 304, 219, 1879, 393}"
1018,1,556,0,0.3099753,"\int \frac{1}{x^4 \sqrt[3]{1-x^2} \left(3+x^2\right)} \, dx","Int[1/(x^4*(1 - x^2)^(1/3)*(3 + x^2)),x]","\frac{2 x}{27 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{2 \left(1-x^2\right)^{2/3}}{27 x}-\frac{\left(1-x^2\right)^{2/3}}{9 x^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{18\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{18\ 2^{2/3}}-\frac{2 \sqrt{2} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{18\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{54\ 2^{2/3}}","\frac{2 x}{27 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{2 \left(1-x^2\right)^{2/3}}{27 x}-\frac{\left(1-x^2\right)^{2/3}}{9 x^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{18\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{18\ 2^{2/3}}-\frac{2 \sqrt{2} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{18\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{54\ 2^{2/3}}",1,"-(1 - x^2)^(2/3)/(9*x^3) - (2*(1 - x^2)^(2/3))/(27*x) + (2*x)/(27*(1 - Sqrt[3] - (1 - x^2)^(1/3))) + ArcTan[Sqrt[3]/x]/(18*2^(2/3)*Sqrt[3]) + ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x]/(18*2^(2/3)*Sqrt[3]) - ArcTanh[x]/(54*2^(2/3)) + ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))]/(18*2^(2/3)) + (Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(9*3^(3/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) - (2*Sqrt[2]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(27*3^(1/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",8,8,22,0.3636,1,"{480, 583, 530, 235, 304, 219, 1879, 393}"
1019,1,133,0,0.0857265,"\int \frac{x^7}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[x^7/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{3 \left(1-x^2\right)^{2/3} x^4}{10 \left(x^2+3\right)}+\frac{9 \left(1-x^2\right)^{2/3} \left(14 x^2+69\right)}{40 \left(x^2+3\right)}-\frac{99 \log \left(x^2+3\right)}{16\ 2^{2/3}}+\frac{297 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{99 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3}}","-\frac{3 \left(1-x^2\right)^{2/3} x^4}{10 \left(x^2+3\right)}+\frac{9 \left(1-x^2\right)^{2/3} \left(14 x^2+69\right)}{40 \left(x^2+3\right)}-\frac{99 \log \left(x^2+3\right)}{16\ 2^{2/3}}+\frac{297 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{99 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3}}",1,"(-3*x^4*(1 - x^2)^(2/3))/(10*(3 + x^2)) + (9*(1 - x^2)^(2/3)*(69 + 14*x^2))/(40*(3 + x^2)) + (99*Sqrt[3]*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(8*2^(2/3)) - (99*Log[3 + x^2])/(16*2^(2/3)) + (297*Log[2^(2/3) - (1 - x^2)^(1/3)])/(16*2^(2/3))","A",7,7,22,0.3182,1,"{446, 100, 146, 55, 617, 204, 31}"
1020,1,116,0,0.0774002,"\int \frac{x^5}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[x^5/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{3}{4} \left(1-x^2\right)^{2/3}-\frac{9 \left(1-x^2\right)^{2/3}}{8 \left(x^2+3\right)}+\frac{21 \log \left(x^2+3\right)}{16\ 2^{2/3}}-\frac{63 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}-\frac{21 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3}}","-\frac{3}{4} \left(1-x^2\right)^{2/3}-\frac{9 \left(1-x^2\right)^{2/3}}{8 \left(x^2+3\right)}+\frac{21 \log \left(x^2+3\right)}{16\ 2^{2/3}}-\frac{63 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}-\frac{21 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3}}",1,"(-3*(1 - x^2)^(2/3))/4 - (9*(1 - x^2)^(2/3))/(8*(3 + x^2)) - (21*Sqrt[3]*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(8*2^(2/3)) + (21*Log[3 + x^2])/(16*2^(2/3)) - (63*Log[2^(2/3) - (1 - x^2)^(1/3)])/(16*2^(2/3))","A",7,7,22,0.3182,1,"{446, 89, 80, 55, 617, 204, 31}"
1021,1,101,0,0.0659721,"\int \frac{x^3}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[x^3/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","\frac{3 \left(1-x^2\right)^{2/3}}{8 \left(x^2+3\right)}-\frac{3 \log \left(x^2+3\right)}{16\ 2^{2/3}}+\frac{9 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3}}","\frac{3 \left(1-x^2\right)^{2/3}}{8 \left(x^2+3\right)}-\frac{3 \log \left(x^2+3\right)}{16\ 2^{2/3}}+\frac{9 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3}}",1,"(3*(1 - x^2)^(2/3))/(8*(3 + x^2)) + (3*Sqrt[3]*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(8*2^(2/3)) - (3*Log[3 + x^2])/(16*2^(2/3)) + (9*Log[2^(2/3) - (1 - x^2)^(1/3)])/(16*2^(2/3))","A",6,6,22,0.2727,1,"{446, 78, 55, 617, 204, 31}"
1022,1,101,0,0.0630688,"\int \frac{x}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[x/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{\left(1-x^2\right)^{2/3}}{8 \left(x^2+3\right)}-\frac{\log \left(x^2+3\right)}{48\ 2^{2/3}}+\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3} \sqrt{3}}","-\frac{\left(1-x^2\right)^{2/3}}{8 \left(x^2+3\right)}-\frac{\log \left(x^2+3\right)}{48\ 2^{2/3}}+\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3} \sqrt{3}}",1,"-(1 - x^2)^(2/3)/(8*(3 + x^2)) + ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]]/(8*2^(2/3)*Sqrt[3]) - Log[3 + x^2]/(48*2^(2/3)) + Log[2^(2/3) - (1 - x^2)^(1/3)]/(16*2^(2/3))","A",6,6,20,0.3000,1,"{444, 51, 55, 617, 204, 31}"
1023,1,158,0,0.1107377,"\int \frac{1}{x \sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[1/(x*(1 - x^2)^(1/3)*(3 + x^2)^2),x]","\frac{\left(1-x^2\right)^{2/3}}{24 \left(x^2+3\right)}+\frac{5 \log \left(x^2+3\right)}{144\ 2^{2/3}}+\frac{1}{12} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{5 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{48\ 2^{2/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{24\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{\log (x)}{18}","\frac{\left(1-x^2\right)^{2/3}}{24 \left(x^2+3\right)}+\frac{5 \log \left(x^2+3\right)}{144\ 2^{2/3}}+\frac{1}{12} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{5 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{48\ 2^{2/3}}-\frac{5 \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{24\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{6 \sqrt{3}}-\frac{\log (x)}{18}",1,"(1 - x^2)^(2/3)/(24*(3 + x^2)) - (5*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(24*2^(2/3)*Sqrt[3]) + ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]]/(6*Sqrt[3]) - Log[x]/18 + (5*Log[3 + x^2])/(144*2^(2/3)) + Log[1 - (1 - x^2)^(1/3)]/12 - (5*Log[2^(2/3) - (1 - x^2)^(1/3)])/(48*2^(2/3))","A",11,8,22,0.3636,1,"{446, 103, 156, 55, 618, 204, 31, 617}"
1024,1,183,0,0.1300415,"\int \frac{1}{x^3 \sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[1/(x^3*(1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{\left(1-x^2\right)^{2/3}}{6 x^2 \left(x^2+3\right)}-\frac{5 \left(1-x^2\right)^{2/3}}{72 \left(x^2+3\right)}-\frac{\log \left(x^2+3\right)}{48\ 2^{2/3}}-\frac{1}{36} \log \left(1-\sqrt[3]{1-x^2}\right)+\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}+\frac{\log (x)}{54}","-\frac{\left(1-x^2\right)^{2/3}}{6 x^2 \left(x^2+3\right)}-\frac{5 \left(1-x^2\right)^{2/3}}{72 \left(x^2+3\right)}-\frac{\log \left(x^2+3\right)}{48\ 2^{2/3}}-\frac{1}{36} \log \left(1-\sqrt[3]{1-x^2}\right)+\frac{\log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{16\ 2^{2/3}}+\frac{\tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{8\ 2^{2/3} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}+\frac{\log (x)}{54}",1,"(-5*(1 - x^2)^(2/3))/(72*(3 + x^2)) - (1 - x^2)^(2/3)/(6*x^2*(3 + x^2)) + ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]]/(8*2^(2/3)*Sqrt[3]) - ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) + Log[x]/54 - Log[3 + x^2]/(48*2^(2/3)) - Log[1 - (1 - x^2)^(1/3)]/36 + Log[2^(2/3) - (1 - x^2)^(1/3)]/(16*2^(2/3))","A",12,9,22,0.4091,1,"{446, 103, 151, 156, 55, 618, 204, 31, 617}"
1025,1,208,0,0.1467184,"\int \frac{1}{x^5 \sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[1/(x^5*(1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{\left(1-x^2\right)^{2/3}}{36 x^2 \left(x^2+3\right)}-\frac{\left(1-x^2\right)^{2/3}}{12 x^4 \left(x^2+3\right)}+\frac{\left(1-x^2\right)^{2/3}}{216 \left(x^2+3\right)}+\frac{13 \log \left(x^2+3\right)}{1296\ 2^{2/3}}+\frac{1}{36} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{13 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{432\ 2^{2/3}}-\frac{13 \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{216\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}-\frac{\log (x)}{54}","-\frac{\left(1-x^2\right)^{2/3}}{36 x^2 \left(x^2+3\right)}-\frac{\left(1-x^2\right)^{2/3}}{12 x^4 \left(x^2+3\right)}+\frac{\left(1-x^2\right)^{2/3}}{216 \left(x^2+3\right)}+\frac{13 \log \left(x^2+3\right)}{1296\ 2^{2/3}}+\frac{1}{36} \log \left(1-\sqrt[3]{1-x^2}\right)-\frac{13 \log \left(2^{2/3}-\sqrt[3]{1-x^2}\right)}{432\ 2^{2/3}}-\frac{13 \tan ^{-1}\left(\frac{\sqrt[3]{2-2 x^2}+1}{\sqrt{3}}\right)}{216\ 2^{2/3} \sqrt{3}}+\frac{\tan ^{-1}\left(\frac{2 \sqrt[3]{1-x^2}+1}{\sqrt{3}}\right)}{18 \sqrt{3}}-\frac{\log (x)}{54}",1,"(1 - x^2)^(2/3)/(216*(3 + x^2)) - (1 - x^2)^(2/3)/(12*x^4*(3 + x^2)) - (1 - x^2)^(2/3)/(36*x^2*(3 + x^2)) - (13*ArcTan[(1 + (2 - 2*x^2)^(1/3))/Sqrt[3]])/(216*2^(2/3)*Sqrt[3]) + ArcTan[(1 + 2*(1 - x^2)^(1/3))/Sqrt[3]]/(18*Sqrt[3]) - Log[x]/54 + (13*Log[3 + x^2])/(1296*2^(2/3)) + Log[1 - (1 - x^2)^(1/3)]/36 - (13*Log[2^(2/3) - (1 - x^2)^(1/3)])/(432*2^(2/3))","A",13,9,22,0.4091,1,"{446, 103, 151, 156, 55, 618, 204, 31, 617}"
1026,1,543,0,0.2381368,"\int \frac{x^4}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[x^4/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","\frac{3 \left(1-x^2\right)^{2/3} x}{8 \left(x^2+3\right)}-\frac{27 x}{8 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{5 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{8\ 2^{2/3}}-\frac{15 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{8\ 2^{2/3}}+\frac{9\ 3^{3/4} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{27 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{5 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{8\ 2^{2/3}}+\frac{5 \tanh ^{-1}(x)}{8\ 2^{2/3}}","\frac{3 \left(1-x^2\right)^{2/3} x}{8 \left(x^2+3\right)}-\frac{27 x}{8 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{5 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{8\ 2^{2/3}}-\frac{15 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{8\ 2^{2/3}}+\frac{9\ 3^{3/4} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{27 \sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{5 \sqrt{3} \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{8\ 2^{2/3}}+\frac{5 \tanh ^{-1}(x)}{8\ 2^{2/3}}",1,"(3*x*(1 - x^2)^(2/3))/(8*(3 + x^2)) - (27*x)/(8*(1 - Sqrt[3] - (1 - x^2)^(1/3))) - (5*Sqrt[3]*ArcTan[Sqrt[3]/x])/(8*2^(2/3)) - (5*Sqrt[3]*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x])/(8*2^(2/3)) + (5*ArcTanh[x])/(8*2^(2/3)) - (15*ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))])/(8*2^(2/3)) - (27*3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(16*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) + (9*3^(3/4)*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(4*Sqrt[2]*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{470, 530, 235, 304, 219, 1879, 393}"
1027,1,543,0,0.2367462,"\int \frac{x^2}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[x^2/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{\left(1-x^2\right)^{2/3} x}{8 \left(x^2+3\right)}+\frac{x}{8 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{8\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{8\ 2^{2/3}}-\frac{\left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{8\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{24\ 2^{2/3}}","-\frac{\left(1-x^2\right)^{2/3} x}{8 \left(x^2+3\right)}+\frac{x}{8 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{8\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{8\ 2^{2/3}}-\frac{\left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{8\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{24\ 2^{2/3}}",1,"-(x*(1 - x^2)^(2/3))/(8*(3 + x^2)) + x/(8*(1 - Sqrt[3] - (1 - x^2)^(1/3))) + ArcTan[Sqrt[3]/x]/(8*2^(2/3)*Sqrt[3]) + ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x]/(8*2^(2/3)*Sqrt[3]) - ArcTanh[x]/(24*2^(2/3)) + ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))]/(8*2^(2/3)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(16*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) - ((1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",7,7,22,0.3182,1,"{471, 530, 235, 304, 219, 1879, 393}"
1028,1,543,0,0.2294808,"\int \frac{1}{\sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[1/((1 - x^2)^(1/3)*(3 + x^2)^2),x]","\frac{\left(1-x^2\right)^{2/3} x}{24 \left(x^2+3\right)}-\frac{x}{24 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{8\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{8\ 2^{2/3}}+\frac{\left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{\sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{8\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{24\ 2^{2/3}}","\frac{\left(1-x^2\right)^{2/3} x}{24 \left(x^2+3\right)}-\frac{x}{24 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{8\ 2^{2/3} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{8\ 2^{2/3}}+\frac{\left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{12 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{\sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{8\ 2^{2/3} \sqrt{3}}-\frac{\tanh ^{-1}(x)}{24\ 2^{2/3}}",1,"(x*(1 - x^2)^(2/3))/(24*(3 + x^2)) - x/(24*(1 - Sqrt[3] - (1 - x^2)^(1/3))) + ArcTan[Sqrt[3]/x]/(8*2^(2/3)*Sqrt[3]) + ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x]/(8*2^(2/3)*Sqrt[3]) - ArcTanh[x]/(24*2^(2/3)) + ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))]/(8*2^(2/3)) - (Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(16*3^(3/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) + ((1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(12*Sqrt[2]*3^(1/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",7,7,19,0.3684,1,"{414, 530, 235, 304, 219, 1879, 393}"
1029,1,563,0,0.3090291,"\int \frac{1}{x^2 \sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[1/(x^2*(1 - x^2)^(1/3)*(3 + x^2)^2),x]","\frac{x}{8 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{\left(1-x^2\right)^{2/3}}{8 x}+\frac{\left(1-x^2\right)^{2/3}}{24 \left(x^2+3\right) x}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{72\ 2^{2/3} \sqrt{3}}-\frac{7 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{72\ 2^{2/3}}-\frac{\left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{72\ 2^{2/3} \sqrt{3}}+\frac{7 \tanh ^{-1}(x)}{216\ 2^{2/3}}","\frac{x}{8 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}-\frac{\left(1-x^2\right)^{2/3}}{8 x}+\frac{\left(1-x^2\right)^{2/3}}{24 \left(x^2+3\right) x}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{72\ 2^{2/3} \sqrt{3}}-\frac{7 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{72\ 2^{2/3}}-\frac{\left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{4 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{\sqrt[4]{3} \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{16 \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{7 \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{72\ 2^{2/3} \sqrt{3}}+\frac{7 \tanh ^{-1}(x)}{216\ 2^{2/3}}",1,"-(1 - x^2)^(2/3)/(8*x) + (1 - x^2)^(2/3)/(24*x*(3 + x^2)) + x/(8*(1 - Sqrt[3] - (1 - x^2)^(1/3))) - (7*ArcTan[Sqrt[3]/x])/(72*2^(2/3)*Sqrt[3]) - (7*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x])/(72*2^(2/3)*Sqrt[3]) + (7*ArcTanh[x])/(216*2^(2/3)) - (7*ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))])/(72*2^(2/3)) + (3^(1/4)*Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(16*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) - ((1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(4*Sqrt[2]*3^(1/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",8,8,22,0.3636,1,"{472, 583, 530, 235, 304, 219, 1879, 393}"
1030,1,581,0,0.3695096,"\int \frac{1}{x^4 \sqrt[3]{1-x^2} \left(3+x^2\right)^2} \, dx","Int[1/(x^4*(1 - x^2)^(1/3)*(3 + x^2)^2),x]","-\frac{11 x}{648 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{11 \left(1-x^2\right)^{2/3}}{648 x}-\frac{11 \left(1-x^2\right)^{2/3}}{216 x^3}+\frac{\left(1-x^2\right)^{2/3}}{24 \left(x^2+3\right) x^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{216\ 2^{2/3} \sqrt{3}}+\frac{11 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{216\ 2^{2/3}}+\frac{11 \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{324 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{11 \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{432\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{216\ 2^{2/3} \sqrt{3}}-\frac{11 \tanh ^{-1}(x)}{648\ 2^{2/3}}","-\frac{11 x}{648 \left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)}+\frac{11 \left(1-x^2\right)^{2/3}}{648 x}-\frac{11 \left(1-x^2\right)^{2/3}}{216 x^3}+\frac{\left(1-x^2\right)^{2/3}}{24 \left(x^2+3\right) x^3}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{3} \left(1-\sqrt[3]{2} \sqrt[3]{1-x^2}\right)}{x}\right)}{216\ 2^{2/3} \sqrt{3}}+\frac{11 \tanh ^{-1}\left(\frac{x}{\sqrt[3]{2} \sqrt[3]{1-x^2}+1}\right)}{216\ 2^{2/3}}+\frac{11 \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} F\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{324 \sqrt{2} \sqrt[4]{3} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}-\frac{11 \sqrt{2+\sqrt{3}} \left(1-\sqrt[3]{1-x^2}\right) \sqrt{\frac{\left(1-x^2\right)^{2/3}+\sqrt[3]{1-x^2}+1}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{-\sqrt[3]{1-x^2}+\sqrt{3}+1}{-\sqrt[3]{1-x^2}-\sqrt{3}+1}\right)|-7+4 \sqrt{3}\right)}{432\ 3^{3/4} \sqrt{-\frac{1-\sqrt[3]{1-x^2}}{\left(-\sqrt[3]{1-x^2}-\sqrt{3}+1\right)^2}} x}+\frac{11 \tan ^{-1}\left(\frac{\sqrt{3}}{x}\right)}{216\ 2^{2/3} \sqrt{3}}-\frac{11 \tanh ^{-1}(x)}{648\ 2^{2/3}}",1,"(-11*(1 - x^2)^(2/3))/(216*x^3) + (11*(1 - x^2)^(2/3))/(648*x) + (1 - x^2)^(2/3)/(24*x^3*(3 + x^2)) - (11*x)/(648*(1 - Sqrt[3] - (1 - x^2)^(1/3))) + (11*ArcTan[Sqrt[3]/x])/(216*2^(2/3)*Sqrt[3]) + (11*ArcTan[(Sqrt[3]*(1 - 2^(1/3)*(1 - x^2)^(1/3)))/x])/(216*2^(2/3)*Sqrt[3]) - (11*ArcTanh[x])/(648*2^(2/3)) + (11*ArcTanh[x/(1 + 2^(1/3)*(1 - x^2)^(1/3))])/(216*2^(2/3)) - (11*Sqrt[2 + Sqrt[3]]*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticE[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(432*3^(3/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)]) + (11*(1 - (1 - x^2)^(1/3))*Sqrt[(1 + (1 - x^2)^(1/3) + (1 - x^2)^(2/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2]*EllipticF[ArcSin[(1 + Sqrt[3] - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))], -7 + 4*Sqrt[3]])/(324*Sqrt[2]*3^(1/4)*x*Sqrt[-((1 - (1 - x^2)^(1/3))/(1 - Sqrt[3] - (1 - x^2)^(1/3))^2)])","A",9,8,22,0.3636,1,"{472, 583, 530, 235, 304, 219, 1879, 393}"
1031,1,136,0,0.0878525,"\int \frac{x^7}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[x^7/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{2}{891} \left(2-3 x^2\right)^{11/4}-\frac{16}{567} \left(2-3 x^2\right)^{7/4}+\frac{56}{243} \left(2-3 x^2\right)^{3/4}+\frac{32}{81} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)+\frac{32}{81} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)","\frac{2}{891} \left(2-3 x^2\right)^{11/4}-\frac{16}{567} \left(2-3 x^2\right)^{7/4}+\frac{56}{243} \left(2-3 x^2\right)^{3/4}+\frac{32}{81} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)+\frac{32}{81} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)",1,"(56*(2 - 3*x^2)^(3/4))/243 - (16*(2 - 3*x^2)^(7/4))/567 + (2*(2 - 3*x^2)^(11/4))/891 + (32*2^(1/4)*ArcTan[(Sqrt[2] - Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/81 + (32*2^(1/4)*ArcTanh[(Sqrt[2] + Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/81","A",10,5,24,0.2083,1,"{440, 261, 266, 43, 439}"
1032,1,121,0,0.0645026,"\int \frac{x^5}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[x^5/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","-\frac{2}{189} \left(2-3 x^2\right)^{7/4}+\frac{4}{27} \left(2-3 x^2\right)^{3/4}+\frac{8}{27} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)+\frac{8}{27} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)","-\frac{2}{189} \left(2-3 x^2\right)^{7/4}+\frac{4}{27} \left(2-3 x^2\right)^{3/4}+\frac{8}{27} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)+\frac{8}{27} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)",1,"(4*(2 - 3*x^2)^(3/4))/27 - (2*(2 - 3*x^2)^(7/4))/189 + (8*2^(1/4)*ArcTan[(Sqrt[2] - Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/27 + (8*2^(1/4)*ArcTanh[(Sqrt[2] + Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/27","A",7,5,24,0.2083,1,"{440, 261, 266, 43, 439}"
1033,1,106,0,0.0461909,"\int \frac{x^3}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[x^3/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{2}{27} \left(2-3 x^2\right)^{3/4}+\frac{2}{9} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)+\frac{2}{9} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)","\frac{2}{27} \left(2-3 x^2\right)^{3/4}+\frac{2}{9} \sqrt[4]{2} \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)+\frac{2}{9} \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)",1,"(2*(2 - 3*x^2)^(3/4))/27 + (2*2^(1/4)*ArcTan[(Sqrt[2] - Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/9 + (2*2^(1/4)*ArcTanh[(Sqrt[2] + Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/9","A",4,3,24,0.1250,1,"{440, 261, 439}"
1034,1,91,0,0.0134464,"\int \frac{x}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[x/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{3\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{3\ 2^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{3\ 2^{3/4}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{3\ 2^{3/4}}",1,"ArcTan[(Sqrt[2] - Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))]/(3*2^(3/4)) + ArcTanh[(Sqrt[2] + Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))]/(3*2^(3/4))","A",1,1,22,0.04545,1,"{439}"
1035,1,145,0,0.0833905,"\int \frac{1}{x \sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[1/(x*(2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{4\ 2^{3/4}}","\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{4\ 2^{3/4}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4 \sqrt[4]{2}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{4\ 2^{3/4}}",1,"ArcTan[(2 - 3*x^2)^(1/4)/2^(1/4)]/(4*2^(1/4)) + ArcTan[(Sqrt[2] - Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))]/(4*2^(3/4)) - ArcTanh[(2 - 3*x^2)^(1/4)/2^(1/4)]/(4*2^(1/4)) + ArcTanh[(Sqrt[2] + Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))]/(4*2^(3/4))","A",8,7,24,0.2917,1,"{440, 266, 63, 298, 203, 206, 439}"
1036,1,163,0,0.1327885,"\int \frac{1}{x^3 \sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[1/(x^3*(2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","-\frac{\left(2-3 x^2\right)^{3/4}}{16 x^2}+\frac{9 \tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32 \sqrt[4]{2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{16\ 2^{3/4}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32 \sqrt[4]{2}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{16\ 2^{3/4}}","-\frac{\left(2-3 x^2\right)^{3/4}}{16 x^2}+\frac{9 \tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32 \sqrt[4]{2}}+\frac{3 \tan ^{-1}\left(\frac{\sqrt{2}-\sqrt{2-3 x^2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{16\ 2^{3/4}}-\frac{9 \tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32 \sqrt[4]{2}}+\frac{3 \tanh ^{-1}\left(\frac{\sqrt{2-3 x^2}+\sqrt{2}}{2^{3/4} \sqrt[4]{2-3 x^2}}\right)}{16\ 2^{3/4}}",1,"-(2 - 3*x^2)^(3/4)/(16*x^2) + (9*ArcTan[(2 - 3*x^2)^(1/4)/2^(1/4)])/(32*2^(1/4)) + (3*ArcTan[(Sqrt[2] - Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/(16*2^(3/4)) - (9*ArcTanh[(2 - 3*x^2)^(1/4)/2^(1/4)])/(32*2^(1/4)) + (3*ArcTanh[(Sqrt[2] + Sqrt[2 - 3*x^2])/(2^(3/4)*(2 - 3*x^2)^(1/4))])/(16*2^(3/4))","A",14,8,24,0.3333,1,"{440, 266, 51, 63, 298, 203, 206, 439}"
1037,1,164,0,0.072696,"\int \frac{x^4}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[x^4/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{2}{45} \left(2-3 x^2\right)^{3/4} x+\frac{4 \sqrt[4]{2} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}+\frac{4 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}-\frac{16 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{15 \sqrt{3}}","\frac{2}{45} \left(2-3 x^2\right)^{3/4} x+\frac{4 \sqrt[4]{2} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}+\frac{4 \sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}-\frac{16 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{15 \sqrt{3}}",1,"(2*x*(2 - 3*x^2)^(3/4))/45 + (4*2^(1/4)*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(9*Sqrt[3]) + (4*2^(1/4)*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(9*Sqrt[3]) - (16*2^(1/4)*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(15*Sqrt[3])","A",6,4,24,0.1667,1,"{440, 228, 321, 397}"
1038,1,148,0,0.0555915,"\int \frac{x^2}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[x^2/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{\sqrt[4]{2} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt{3}}+\frac{\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt{3}}-\frac{2 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{3 \sqrt{3}}","\frac{\sqrt[4]{2} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt{3}}+\frac{\sqrt[4]{2} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt{3}}-\frac{2 \sqrt[4]{2} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{3 \sqrt{3}}",1,"(2^(1/4)*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(3*Sqrt[3]) + (2^(1/4)*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(3*Sqrt[3]) - (2*2^(1/4)*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(3*Sqrt[3])","A",4,3,24,0.1250,1,"{440, 228, 397}"
1039,1,120,0,0.0153221,"\int \frac{1}{\sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[1/((2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-3 x^2}}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{2\ 2^{3/4} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-3 x^2}+2}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{2\ 2^{3/4} \sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-3 x^2}}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{2\ 2^{3/4} \sqrt{3}}+\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-3 x^2}+2}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{2\ 2^{3/4} \sqrt{3}}",1,"ArcTan[(2 - Sqrt[2]*Sqrt[2 - 3*x^2])/(2^(1/4)*Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(2*2^(3/4)*Sqrt[3]) + ArcTanh[(2 + Sqrt[2]*Sqrt[2 - 3*x^2])/(2^(1/4)*Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(2*2^(3/4)*Sqrt[3])","A",1,1,21,0.04762,1,"{397}"
1040,1,166,0,0.0640898,"\int \frac{1}{x^2 \sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[1/(x^2*(2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","-\frac{\left(2-3 x^2\right)^{3/4}}{8 x}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{8\ 2^{3/4}}+\frac{\sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{8\ 2^{3/4}}-\frac{\sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4\ 2^{3/4}}","-\frac{\left(2-3 x^2\right)^{3/4}}{8 x}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{8\ 2^{3/4}}+\frac{\sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{8\ 2^{3/4}}-\frac{\sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4\ 2^{3/4}}",1,"-(2 - 3*x^2)^(3/4)/(8*x) + (Sqrt[3]*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(8*2^(3/4)) + (Sqrt[3]*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(8*2^(3/4)) - (Sqrt[3]*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(4*2^(3/4))","A",5,4,24,0.1667,1,"{440, 325, 228, 397}"
1041,1,184,0,0.0870461,"\int \frac{1}{x^4 \sqrt[4]{2-3 x^2} \left(4-3 x^2\right)} \, dx","Int[1/(x^4*(2 - 3*x^2)^(1/4)*(4 - 3*x^2)),x]","-\frac{3 \left(2-3 x^2\right)^{3/4}}{16 x}-\frac{\left(2-3 x^2\right)^{3/4}}{24 x^3}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{32\ 2^{3/4}}+\frac{3 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{32\ 2^{3/4}}-\frac{3 \sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{8\ 2^{3/4}}","-\frac{3 \left(2-3 x^2\right)^{3/4}}{16 x}-\frac{\left(2-3 x^2\right)^{3/4}}{24 x^3}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{32\ 2^{3/4}}+\frac{3 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{32\ 2^{3/4}}-\frac{3 \sqrt{3} E\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{8\ 2^{3/4}}",1,"-(2 - 3*x^2)^(3/4)/(24*x^3) - (3*(2 - 3*x^2)^(3/4))/(16*x) + (3*Sqrt[3]*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(32*2^(3/4)) + (3*Sqrt[3]*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(32*2^(3/4)) - (3*Sqrt[3]*EllipticE[ArcSin[Sqrt[3/2]*x]/2, 2])/(8*2^(3/4))","A",8,4,24,0.1667,1,"{440, 325, 228, 397}"
1042,1,78,0,0.0532299,"\int \frac{x^7}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[x^7/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{2}{891} \left(3 x^2-1\right)^{11/4}+\frac{8}{567} \left(3 x^2-1\right)^{7/4}+\frac{14}{243} \left(3 x^2-1\right)^{3/4}+\frac{8}{81} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{8}{81} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{2}{891} \left(3 x^2-1\right)^{11/4}+\frac{8}{567} \left(3 x^2-1\right)^{7/4}+\frac{14}{243} \left(3 x^2-1\right)^{3/4}+\frac{8}{81} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{8}{81} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"(14*(-1 + 3*x^2)^(3/4))/243 + (8*(-1 + 3*x^2)^(7/4))/567 + (2*(-1 + 3*x^2)^(11/4))/891 + (8*ArcTan[(-1 + 3*x^2)^(1/4)])/81 - (8*ArcTanh[(-1 + 3*x^2)^(1/4)])/81","A",7,6,24,0.2500,1,"{446, 88, 63, 298, 203, 206}"
1043,1,63,0,0.0480356,"\int \frac{x^5}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[x^5/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{2}{189} \left(3 x^2-1\right)^{7/4}+\frac{2}{27} \left(3 x^2-1\right)^{3/4}+\frac{4}{27} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{4}{27} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{2}{189} \left(3 x^2-1\right)^{7/4}+\frac{2}{27} \left(3 x^2-1\right)^{3/4}+\frac{4}{27} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{4}{27} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"(2*(-1 + 3*x^2)^(3/4))/27 + (2*(-1 + 3*x^2)^(7/4))/189 + (4*ArcTan[(-1 + 3*x^2)^(1/4)])/27 - (4*ArcTanh[(-1 + 3*x^2)^(1/4)])/27","A",7,6,24,0.2500,1,"{446, 88, 63, 298, 203, 206}"
1044,1,48,0,0.032934,"\int \frac{x^3}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[x^3/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{2}{27} \left(3 x^2-1\right)^{3/4}+\frac{2}{9} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{2}{9} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{2}{27} \left(3 x^2-1\right)^{3/4}+\frac{2}{9} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{2}{9} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"(2*(-1 + 3*x^2)^(3/4))/27 + (2*ArcTan[(-1 + 3*x^2)^(1/4)])/9 - (2*ArcTanh[(-1 + 3*x^2)^(1/4)])/9","A",6,6,24,0.2500,1,"{446, 80, 63, 298, 203, 206}"
1045,1,33,0,0.0224928,"\int \frac{x}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[x/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{1}{3} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{1}{3} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{1}{3} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{1}{3} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"ArcTan[(-1 + 3*x^2)^(1/4)]/3 - ArcTanh[(-1 + 3*x^2)^(1/4)]/3","A",5,5,22,0.2273,1,"{444, 63, 298, 203, 206}"
1046,1,173,0,0.1319845,"\int \frac{1}{x \left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[1/(x*(-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","-\frac{\log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}+\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","-\frac{\log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}+\frac{\log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}+\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"ArcTan[(-1 + 3*x^2)^(1/4)]/2 + ArcTan[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4)]/(2*Sqrt[2]) - ArcTan[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4)]/(2*Sqrt[2]) - ArcTanh[(-1 + 3*x^2)^(1/4)]/2 - Log[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]]/(4*Sqrt[2]) + Log[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]]/(4*Sqrt[2])","A",16,12,24,0.5000,1,"{446, 86, 63, 297, 1162, 617, 204, 1165, 628, 298, 203, 206}"
1047,1,191,0,0.1473344,"\int \frac{1}{x^3 \left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[1/(x^3*(-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","-\frac{\left(3 x^2-1\right)^{3/4}}{4 x^2}-\frac{9 \log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}+\frac{9 \log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}+\frac{3}{4} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{9 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{8 \sqrt{2}}-\frac{9 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{8 \sqrt{2}}-\frac{3}{4} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","-\frac{\left(3 x^2-1\right)^{3/4}}{4 x^2}-\frac{9 \log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}+\frac{9 \log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}+\frac{3}{4} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{9 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{8 \sqrt{2}}-\frac{9 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{8 \sqrt{2}}-\frac{3}{4} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"-(-1 + 3*x^2)^(3/4)/(4*x^2) + (3*ArcTan[(-1 + 3*x^2)^(1/4)])/4 + (9*ArcTan[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4)])/(8*Sqrt[2]) - (9*ArcTan[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4)])/(8*Sqrt[2]) - (3*ArcTanh[(-1 + 3*x^2)^(1/4)])/4 - (9*Log[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]])/(16*Sqrt[2]) + (9*Log[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]])/(16*Sqrt[2])","A",17,13,24,0.5417,1,"{446, 103, 156, 63, 297, 1162, 617, 204, 1165, 628, 298, 203, 206}"
1048,1,244,0,0.1858308,"\int \frac{x^4}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[x^4/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{2}{45} \left(3 x^2-1\right)^{3/4} x+\frac{8 \sqrt[4]{3 x^2-1} x}{15 \left(\sqrt{3 x^2-1}+1\right)}-\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{9} \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{4 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}-\frac{8 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}","\frac{2}{45} \left(3 x^2-1\right)^{3/4} x+\frac{8 \sqrt[4]{3 x^2-1} x}{15 \left(\sqrt{3 x^2-1}+1\right)}-\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{9} \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{4 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}-\frac{8 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{15 \sqrt{3} x}",1,"(2*x*(-1 + 3*x^2)^(3/4))/45 + (8*x*(-1 + 3*x^2)^(1/4))/(15*(1 + Sqrt[-1 + 3*x^2])) - (Sqrt[2/3]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/9 - (Sqrt[2/3]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/9 - (8*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticE[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(15*Sqrt[3]*x) + (4*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(15*Sqrt[3]*x)","A",12,7,24,0.2917,1,"{440, 230, 305, 220, 1196, 321, 398}"
1049,1,224,0,0.1048385,"\int \frac{x^2}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[x^2/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{2 \sqrt[4]{3 x^2-1} x}{3 \left(\sqrt{3 x^2-1}+1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}+\frac{\sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{3 \sqrt{3} x}-\frac{2 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{3 \sqrt{3} x}","\frac{2 \sqrt[4]{3 x^2-1} x}{3 \left(\sqrt{3 x^2-1}+1\right)}-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}+\frac{\sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{3 \sqrt{3} x}-\frac{2 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{3 \sqrt{3} x}",1,"(2*x*(-1 + 3*x^2)^(1/4))/(3*(1 + Sqrt[-1 + 3*x^2])) - ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(3*Sqrt[6]) - ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(3*Sqrt[6]) - (2*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticE[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(3*Sqrt[3]*x) + (Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(3*Sqrt[3]*x)","A",7,6,24,0.2500,1,"{440, 230, 305, 220, 1196, 398}"
1050,1,61,0,0.0089125,"\int \frac{1}{\left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[1/((-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}","-\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}",1,"-ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(2*Sqrt[6]) - ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(2*Sqrt[6])","A",1,1,21,0.04762,1,"{398}"
1051,1,246,0,0.1222606,"\int \frac{1}{x^2 \left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[1/(x^2*(-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{3 \sqrt[4]{3 x^2-1} x}{2 \left(\sqrt{3 x^2-1}+1\right)}-\frac{\left(3 x^2-1\right)^{3/4}}{2 x}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{4} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{4 x}-\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 x}","\frac{3 \sqrt[4]{3 x^2-1} x}{2 \left(\sqrt{3 x^2-1}+1\right)}-\frac{\left(3 x^2-1\right)^{3/4}}{2 x}-\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{4} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{4 x}-\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 x}",1,"-(-1 + 3*x^2)^(3/4)/(2*x) + (3*x*(-1 + 3*x^2)^(1/4))/(2*(1 + Sqrt[-1 + 3*x^2])) - (Sqrt[3/2]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/4 - (Sqrt[3/2]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/4 - (Sqrt[3]*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticE[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(2*x) + (Sqrt[3]*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(4*x)","A",8,7,24,0.2917,1,"{440, 325, 230, 305, 220, 1196, 398}"
1052,1,264,0,0.2149059,"\int \frac{1}{x^4 \left(-2+3 x^2\right) \sqrt[4]{-1+3 x^2}} \, dx","Int[1/(x^4*(-2 + 3*x^2)*(-1 + 3*x^2)^(1/4)),x]","\frac{9 \sqrt[4]{3 x^2-1} x}{2 \left(\sqrt{3 x^2-1}+1\right)}-\frac{3 \left(3 x^2-1\right)^{3/4}}{2 x}-\frac{\left(3 x^2-1\right)^{3/4}}{6 x^3}-\frac{3}{8} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{3}{8} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{4 x}-\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 x}","\frac{9 \sqrt[4]{3 x^2-1} x}{2 \left(\sqrt{3 x^2-1}+1\right)}-\frac{3 \left(3 x^2-1\right)^{3/4}}{2 x}-\frac{\left(3 x^2-1\right)^{3/4}}{6 x^3}-\frac{3}{8} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{3}{8} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{4 x}-\frac{3 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) E\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 x}",1,"-(-1 + 3*x^2)^(3/4)/(6*x^3) - (3*(-1 + 3*x^2)^(3/4))/(2*x) + (9*x*(-1 + 3*x^2)^(1/4))/(2*(1 + Sqrt[-1 + 3*x^2])) - (3*Sqrt[3/2]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/8 - (3*Sqrt[3/2]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/8 - (3*Sqrt[3]*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticE[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(2*x) + (3*Sqrt[3]*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(4*x)","A",14,7,24,0.2917,1,"{440, 325, 230, 305, 220, 1196, 398}"
1053,1,129,0,0.0226888,"\int \frac{x^2}{\left(2+3 x^2\right)^{3/4} \left(4+3 x^2\right)} \, dx","Int[x^2/((2 + 3*x^2)^(3/4)*(4 + 3*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{2\ 2^{3/4}-2 \sqrt[4]{2} \sqrt{3 x^2+2}}{2 \sqrt{3} x \sqrt[4]{3 x^2+2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{2} \sqrt{3 x^2+2}+2\ 2^{3/4}}{2 \sqrt{3} x \sqrt[4]{3 x^2+2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}","\frac{\tanh ^{-1}\left(\frac{2\ 2^{3/4}-2 \sqrt[4]{2} \sqrt{3 x^2+2}}{2 \sqrt{3} x \sqrt[4]{3 x^2+2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{2} \sqrt{3 x^2+2}+2\ 2^{3/4}}{2 \sqrt{3} x \sqrt[4]{3 x^2+2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}",1,"-ArcTan[(2*2^(3/4) + 2*2^(1/4)*Sqrt[2 + 3*x^2])/(2*Sqrt[3]*x*(2 + 3*x^2)^(1/4))]/(3*2^(1/4)*Sqrt[3]) + ArcTanh[(2*2^(3/4) - 2*2^(1/4)*Sqrt[2 + 3*x^2])/(2*Sqrt[3]*x*(2 + 3*x^2)^(1/4))]/(3*2^(1/4)*Sqrt[3])","A",1,1,24,0.04167,1,"{441}"
1054,1,120,0,0.0226413,"\int \frac{x^2}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^2/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-3 x^2}}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-3 x^2}+2}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-3 x^2}}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-3 x^2}+2}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}",1,"ArcTan[(2 - Sqrt[2]*Sqrt[2 - 3*x^2])/(2^(1/4)*Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(3*2^(1/4)*Sqrt[3]) - ArcTanh[(2 + Sqrt[2]*Sqrt[2 - 3*x^2])/(2^(1/4)*Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(3*2^(1/4)*Sqrt[3])","A",1,1,24,0.04167,1,"{441}"
1055,1,124,0,0.030975,"\int \frac{x^2}{\left(2+b x^2\right)^{3/4} \left(4+b x^2\right)} \, dx","Int[x^2/((2 + b*x^2)^(3/4)*(4 + b*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{2\ 2^{3/4}-2 \sqrt[4]{2} \sqrt{b x^2+2}}{2 \sqrt{b} x \sqrt[4]{b x^2+2}}\right)}{\sqrt[4]{2} b^{3/2}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{2} \sqrt{b x^2+2}+2\ 2^{3/4}}{2 \sqrt{b} x \sqrt[4]{b x^2+2}}\right)}{\sqrt[4]{2} b^{3/2}}","\frac{\tanh ^{-1}\left(\frac{2\ 2^{3/4}-2 \sqrt[4]{2} \sqrt{b x^2+2}}{2 \sqrt{b} x \sqrt[4]{b x^2+2}}\right)}{\sqrt[4]{2} b^{3/2}}-\frac{\tan ^{-1}\left(\frac{2 \sqrt[4]{2} \sqrt{b x^2+2}+2\ 2^{3/4}}{2 \sqrt{b} x \sqrt[4]{b x^2+2}}\right)}{\sqrt[4]{2} b^{3/2}}",1,"-(ArcTan[(2*2^(3/4) + 2*2^(1/4)*Sqrt[2 + b*x^2])/(2*Sqrt[b]*x*(2 + b*x^2)^(1/4))]/(2^(1/4)*b^(3/2))) + ArcTanh[(2*2^(3/4) - 2*2^(1/4)*Sqrt[2 + b*x^2])/(2*Sqrt[b]*x*(2 + b*x^2)^(1/4))]/(2^(1/4)*b^(3/2))","A",1,1,24,0.04167,1,"{441}"
1056,1,119,0,0.0317682,"\int \frac{x^2}{\left(2-b x^2\right)^{3/4} \left(4-b x^2\right)} \, dx","Int[x^2/((2 - b*x^2)^(3/4)*(4 - b*x^2)),x]","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-b x^2}}{\sqrt[4]{2} \sqrt{b} x \sqrt[4]{2-b x^2}}\right)}{\sqrt[4]{2} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-b x^2}+2}{\sqrt[4]{2} \sqrt{b} x \sqrt[4]{2-b x^2}}\right)}{\sqrt[4]{2} b^{3/2}}","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-b x^2}}{\sqrt[4]{2} \sqrt{b} x \sqrt[4]{2-b x^2}}\right)}{\sqrt[4]{2} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-b x^2}+2}{\sqrt[4]{2} \sqrt{b} x \sqrt[4]{2-b x^2}}\right)}{\sqrt[4]{2} b^{3/2}}",1,"ArcTan[(2 - Sqrt[2]*Sqrt[2 - b*x^2])/(2^(1/4)*Sqrt[b]*x*(2 - b*x^2)^(1/4))]/(2^(1/4)*b^(3/2)) - ArcTanh[(2 + Sqrt[2]*Sqrt[2 - b*x^2])/(2^(1/4)*Sqrt[b]*x*(2 - b*x^2)^(1/4))]/(2^(1/4)*b^(3/2))","A",1,1,26,0.03846,1,"{441}"
1057,1,120,0,0.0282203,"\int \frac{x^2}{\left(a+3 x^2\right)^{3/4} \left(2 a+3 x^2\right)} \, dx","Int[x^2/((a + 3*x^2)^(3/4)*(2*a + 3*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a+3 x^2}}{\sqrt{a}}\right)}{\sqrt{3} x \sqrt[4]{a+3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}-\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a+3 x^2}}{\sqrt{a}}+1\right)}{\sqrt{3} x \sqrt[4]{a+3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}","\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a+3 x^2}}{\sqrt{a}}\right)}{\sqrt{3} x \sqrt[4]{a+3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}-\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a+3 x^2}}{\sqrt{a}}+1\right)}{\sqrt{3} x \sqrt[4]{a+3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}",1,"-ArcTan[(a^(3/4)*(1 + Sqrt[a + 3*x^2]/Sqrt[a]))/(Sqrt[3]*x*(a + 3*x^2)^(1/4))]/(3*Sqrt[3]*a^(1/4)) + ArcTanh[(a^(3/4)*(1 - Sqrt[a + 3*x^2]/Sqrt[a]))/(Sqrt[3]*x*(a + 3*x^2)^(1/4))]/(3*Sqrt[3]*a^(1/4))","A",1,1,26,0.03846,1,"{441}"
1058,1,120,0,0.026276,"\int \frac{x^2}{\left(a-3 x^2\right)^{3/4} \left(2 a-3 x^2\right)} \, dx","Int[x^2/((a - 3*x^2)^(3/4)*(2*a - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a-3 x^2}}{\sqrt{a}}\right)}{\sqrt{3} x \sqrt[4]{a-3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a-3 x^2}}{\sqrt{a}}+1\right)}{\sqrt{3} x \sqrt[4]{a-3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a-3 x^2}}{\sqrt{a}}\right)}{\sqrt{3} x \sqrt[4]{a-3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a-3 x^2}}{\sqrt{a}}+1\right)}{\sqrt{3} x \sqrt[4]{a-3 x^2}}\right)}{3 \sqrt{3} \sqrt[4]{a}}",1,"ArcTan[(a^(3/4)*(1 - Sqrt[a - 3*x^2]/Sqrt[a]))/(Sqrt[3]*x*(a - 3*x^2)^(1/4))]/(3*Sqrt[3]*a^(1/4)) - ArcTanh[(a^(3/4)*(1 + Sqrt[a - 3*x^2]/Sqrt[a]))/(Sqrt[3]*x*(a - 3*x^2)^(1/4))]/(3*Sqrt[3]*a^(1/4))","A",1,1,26,0.03846,1,"{441}"
1059,1,115,0,0.0346536,"\int \frac{x^2}{\left(a+b x^2\right)^{3/4} \left(2 a+b x^2\right)} \, dx","Int[x^2/((a + b*x^2)^(3/4)*(2*a + b*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{b} x \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}-\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}+1\right)}{\sqrt{b} x \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}","\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a+b x^2}}{\sqrt{a}}\right)}{\sqrt{b} x \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}-\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a+b x^2}}{\sqrt{a}}+1\right)}{\sqrt{b} x \sqrt[4]{a+b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}",1,"-(ArcTan[(a^(3/4)*(1 + Sqrt[a + b*x^2]/Sqrt[a]))/(Sqrt[b]*x*(a + b*x^2)^(1/4))]/(a^(1/4)*b^(3/2))) + ArcTanh[(a^(3/4)*(1 - Sqrt[a + b*x^2]/Sqrt[a]))/(Sqrt[b]*x*(a + b*x^2)^(1/4))]/(a^(1/4)*b^(3/2))","A",1,1,26,0.03846,1,"{441}"
1060,1,119,0,0.0371274,"\int \frac{x^2}{\left(a-b x^2\right)^{3/4} \left(2 a-b x^2\right)} \, dx","Int[x^2/((a - b*x^2)^(3/4)*(2*a - b*x^2)),x]","\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a-b x^2}}{\sqrt{a}}\right)}{\sqrt{b} x \sqrt[4]{a-b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a-b x^2}}{\sqrt{a}}+1\right)}{\sqrt{b} x \sqrt[4]{a-b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}","\frac{\tan ^{-1}\left(\frac{a^{3/4} \left(1-\frac{\sqrt{a-b x^2}}{\sqrt{a}}\right)}{\sqrt{b} x \sqrt[4]{a-b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{a^{3/4} \left(\frac{\sqrt{a-b x^2}}{\sqrt{a}}+1\right)}{\sqrt{b} x \sqrt[4]{a-b x^2}}\right)}{\sqrt[4]{a} b^{3/2}}",1,"ArcTan[(a^(3/4)*(1 - Sqrt[a - b*x^2]/Sqrt[a]))/(Sqrt[b]*x*(a - b*x^2)^(1/4))]/(a^(1/4)*b^(3/2)) - ArcTanh[(a^(3/4)*(1 + Sqrt[a - b*x^2]/Sqrt[a]))/(Sqrt[b]*x*(a - b*x^2)^(1/4))]/(a^(1/4)*b^(3/2))","A",1,1,28,0.03571,1,"{441}"
1061,1,188,0,0.2114573,"\int \frac{x^7}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^7/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{2}{729} \left(2-3 x^2\right)^{9/4}-\frac{16}{405} \left(2-3 x^2\right)^{5/4}+\frac{56}{81} \sqrt[4]{2-3 x^2}+\frac{8}{81} 2^{3/4} \log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{8}{81} 2^{3/4} \log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{16}{81} 2^{3/4} \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)+\frac{16}{81} 2^{3/4} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)","\frac{2}{729} \left(2-3 x^2\right)^{9/4}-\frac{16}{405} \left(2-3 x^2\right)^{5/4}+\frac{56}{81} \sqrt[4]{2-3 x^2}+\frac{8}{81} 2^{3/4} \log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{8}{81} 2^{3/4} \log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{16}{81} 2^{3/4} \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)+\frac{16}{81} 2^{3/4} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)",1,"(56*(2 - 3*x^2)^(1/4))/81 - (16*(2 - 3*x^2)^(5/4))/405 + (2*(2 - 3*x^2)^(9/4))/729 - (16*2^(3/4)*ArcTan[1 + (4 - 6*x^2)^(1/4)])/81 + (16*2^(3/4)*ArcTan[1 - 2^(1/4)*(2 - 3*x^2)^(1/4)])/81 + (8*2^(3/4)*Log[Sqrt[2] - 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]])/81 - (8*2^(3/4)*Log[Sqrt[2] + 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]])/81","A",20,12,24,0.5000,1,"{443, 261, 266, 43, 444, 63, 211, 1165, 628, 1162, 617, 204}"
1062,1,173,0,0.1802852,"\int \frac{x^5}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^5/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","-\frac{2}{135} \left(2-3 x^2\right)^{5/4}+\frac{4}{9} \sqrt[4]{2-3 x^2}+\frac{2}{27} 2^{3/4} \log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{2}{27} 2^{3/4} \log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{4}{27} 2^{3/4} \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)+\frac{4}{27} 2^{3/4} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)","-\frac{2}{135} \left(2-3 x^2\right)^{5/4}+\frac{4}{9} \sqrt[4]{2-3 x^2}+\frac{2}{27} 2^{3/4} \log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{2}{27} 2^{3/4} \log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)-\frac{4}{27} 2^{3/4} \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)+\frac{4}{27} 2^{3/4} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)",1,"(4*(2 - 3*x^2)^(1/4))/9 - (2*(2 - 3*x^2)^(5/4))/135 - (4*2^(3/4)*ArcTan[1 + (4 - 6*x^2)^(1/4)])/27 + (4*2^(3/4)*ArcTan[1 - 2^(1/4)*(2 - 3*x^2)^(1/4)])/27 + (2*2^(3/4)*Log[Sqrt[2] - 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]])/27 - (2*2^(3/4)*Log[Sqrt[2] + 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]])/27","A",17,12,24,0.5000,1,"{443, 261, 266, 43, 444, 63, 211, 1165, 628, 1162, 617, 204}"
1063,1,158,0,0.1524805,"\int \frac{x^3}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^3/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{2}{9} \sqrt[4]{2-3 x^2}+\frac{\log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{9 \sqrt[4]{2}}-\frac{\log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{9 \sqrt[4]{2}}-\frac{1}{9} 2^{3/4} \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)+\frac{1}{9} 2^{3/4} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)","\frac{2}{9} \sqrt[4]{2-3 x^2}+\frac{\log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{9 \sqrt[4]{2}}-\frac{\log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{9 \sqrt[4]{2}}-\frac{1}{9} 2^{3/4} \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)+\frac{1}{9} 2^{3/4} \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)",1,"(2*(2 - 3*x^2)^(1/4))/9 - (2^(3/4)*ArcTan[1 + (4 - 6*x^2)^(1/4)])/9 + (2^(3/4)*ArcTan[1 - 2^(1/4)*(2 - 3*x^2)^(1/4)])/9 + Log[Sqrt[2] - 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]]/(9*2^(1/4)) - Log[Sqrt[2] + 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]]/(9*2^(1/4))","A",14,10,24,0.4167,1,"{443, 261, 444, 63, 211, 1165, 628, 1162, 617, 204}"
1064,1,143,0,0.1176275,"\int \frac{x}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{\log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{12 \sqrt[4]{2}}-\frac{\log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{12 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)}{6 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)}{6 \sqrt[4]{2}}","\frac{\log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{12 \sqrt[4]{2}}-\frac{\log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{12 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)}{6 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)}{6 \sqrt[4]{2}}",1,"-ArcTan[1 + (4 - 6*x^2)^(1/4)]/(6*2^(1/4)) + ArcTan[1 - 2^(1/4)*(2 - 3*x^2)^(1/4)]/(6*2^(1/4)) + Log[Sqrt[2] - 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]]/(12*2^(1/4)) - Log[Sqrt[2] + 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]]/(12*2^(1/4))","A",11,8,22,0.3636,1,"{444, 63, 211, 1165, 628, 1162, 617, 204}"
1065,1,197,0,0.1893945,"\int \frac{1}{x \left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[1/(x*(2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{\log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{16 \sqrt[4]{2}}-\frac{\log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{16 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4\ 2^{3/4}}-\frac{\tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)}{8 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)}{8 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4\ 2^{3/4}}","\frac{\log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{16 \sqrt[4]{2}}-\frac{\log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{16 \sqrt[4]{2}}-\frac{\tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4\ 2^{3/4}}-\frac{\tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)}{8 \sqrt[4]{2}}+\frac{\tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)}{8 \sqrt[4]{2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{4\ 2^{3/4}}",1,"-ArcTan[(2 - 3*x^2)^(1/4)/2^(1/4)]/(4*2^(3/4)) - ArcTan[1 + (4 - 6*x^2)^(1/4)]/(8*2^(1/4)) + ArcTan[1 - 2^(1/4)*(2 - 3*x^2)^(1/4)]/(8*2^(1/4)) - ArcTanh[(2 - 3*x^2)^(1/4)/2^(1/4)]/(4*2^(3/4)) + Log[Sqrt[2] - 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]]/(16*2^(1/4)) - Log[Sqrt[2] + 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]]/(16*2^(1/4))","A",18,13,24,0.5417,1,"{443, 266, 63, 212, 206, 203, 444, 211, 1165, 628, 1162, 617, 204}"
1066,1,215,0,0.2408965,"\int \frac{1}{x^3 \left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[1/(x^3*(2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","-\frac{\sqrt[4]{2-3 x^2}}{16 x^2}+\frac{3 \log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{64 \sqrt[4]{2}}-\frac{3 \log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{64 \sqrt[4]{2}}-\frac{15 \tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32\ 2^{3/4}}-\frac{3 \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)}{32 \sqrt[4]{2}}+\frac{3 \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)}{32 \sqrt[4]{2}}-\frac{15 \tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32\ 2^{3/4}}","-\frac{\sqrt[4]{2-3 x^2}}{16 x^2}+\frac{3 \log \left(\sqrt{2-3 x^2}-2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{64 \sqrt[4]{2}}-\frac{3 \log \left(\sqrt{2-3 x^2}+2^{3/4} \sqrt[4]{2-3 x^2}+\sqrt{2}\right)}{64 \sqrt[4]{2}}-\frac{15 \tan ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32\ 2^{3/4}}-\frac{3 \tan ^{-1}\left(\sqrt[4]{4-6 x^2}+1\right)}{32 \sqrt[4]{2}}+\frac{3 \tan ^{-1}\left(1-\sqrt[4]{2} \sqrt[4]{2-3 x^2}\right)}{32 \sqrt[4]{2}}-\frac{15 \tanh ^{-1}\left(\frac{\sqrt[4]{2-3 x^2}}{\sqrt[4]{2}}\right)}{32\ 2^{3/4}}",1,"-(2 - 3*x^2)^(1/4)/(16*x^2) - (15*ArcTan[(2 - 3*x^2)^(1/4)/2^(1/4)])/(32*2^(3/4)) - (3*ArcTan[1 + (4 - 6*x^2)^(1/4)])/(32*2^(1/4)) + (3*ArcTan[1 - 2^(1/4)*(2 - 3*x^2)^(1/4)])/(32*2^(1/4)) - (15*ArcTanh[(2 - 3*x^2)^(1/4)/2^(1/4)])/(32*2^(3/4)) + (3*Log[Sqrt[2] - 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]])/(64*2^(1/4)) - (3*Log[Sqrt[2] + 2^(3/4)*(2 - 3*x^2)^(1/4) + Sqrt[2 - 3*x^2]])/(64*2^(1/4))","A",24,14,24,0.5833,1,"{443, 266, 51, 63, 212, 206, 203, 444, 211, 1165, 628, 1162, 617, 204}"
1067,1,182,0,0.1181292,"\int \frac{x^6}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^6/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{2}{63} \sqrt[4]{2-3 x^2} x^3+\frac{80}{567} \sqrt[4]{2-3 x^2} x+\frac{8\ 2^{3/4} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{27 \sqrt{3}}-\frac{8\ 2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{27 \sqrt{3}}-\frac{160\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{567 \sqrt{3}}","\frac{2}{63} \sqrt[4]{2-3 x^2} x^3+\frac{80}{567} \sqrt[4]{2-3 x^2} x+\frac{8\ 2^{3/4} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{27 \sqrt{3}}-\frac{8\ 2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{27 \sqrt{3}}-\frac{160\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{567 \sqrt{3}}",1,"(80*x*(2 - 3*x^2)^(1/4))/567 + (2*x^3*(2 - 3*x^2)^(1/4))/63 + (8*2^(3/4)*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(27*Sqrt[3]) - (8*2^(3/4)*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(27*Sqrt[3]) - (160*2^(3/4)*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(567*Sqrt[3])","A",11,5,24,0.2083,1,"{443, 232, 321, 400, 441}"
1068,1,164,0,0.0984093,"\int \frac{x^4}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^4/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{2}{27} \sqrt[4]{2-3 x^2} x+\frac{2\ 2^{3/4} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}-\frac{2\ 2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}-\frac{4\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{27 \sqrt{3}}","\frac{2}{27} \sqrt[4]{2-3 x^2} x+\frac{2\ 2^{3/4} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}-\frac{2\ 2^{3/4} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{9 \sqrt{3}}-\frac{4\ 2^{3/4} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{27 \sqrt{3}}",1,"(2*x*(2 - 3*x^2)^(1/4))/27 + (2*2^(3/4)*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(9*Sqrt[3]) - (2*2^(3/4)*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(9*Sqrt[3]) - (4*2^(3/4)*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(27*Sqrt[3])","A",8,5,24,0.2083,1,"{443, 232, 321, 400, 441}"
1069,1,120,0,0.0225193,"\int \frac{x^2}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[x^2/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-3 x^2}}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-3 x^2}+2}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2-\sqrt{2} \sqrt{2-3 x^2}}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{2-3 x^2}+2}{\sqrt[4]{2} \sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{3 \sqrt[4]{2} \sqrt{3}}",1,"ArcTan[(2 - Sqrt[2]*Sqrt[2 - 3*x^2])/(2^(1/4)*Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(3*2^(1/4)*Sqrt[3]) - ArcTanh[(2 + Sqrt[2]*Sqrt[2 - 3*x^2])/(2^(1/4)*Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(3*2^(1/4)*Sqrt[3])","A",1,1,24,0.04167,1,"{441}"
1070,1,148,0,0.0419964,"\int \frac{1}{\left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[1/((2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","\frac{\tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{4 \sqrt[4]{2} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{4 \sqrt[4]{2} \sqrt{3}}+\frac{F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2 \sqrt[4]{2} \sqrt{3}}","\frac{\tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{4 \sqrt[4]{2} \sqrt{3}}-\frac{\tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{4 \sqrt[4]{2} \sqrt{3}}+\frac{F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{2 \sqrt[4]{2} \sqrt{3}}",1,"ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(4*2^(1/4)*Sqrt[3]) - ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))]/(4*2^(1/4)*Sqrt[3]) + EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2]/(2*2^(1/4)*Sqrt[3])","A",3,3,21,0.1429,1,"{400, 232, 441}"
1071,1,166,0,0.090179,"\int \frac{1}{x^2 \left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[1/(x^2*(2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","-\frac{\sqrt[4]{2-3 x^2}}{8 x}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{16 \sqrt[4]{2}}-\frac{\sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{16 \sqrt[4]{2}}+\frac{\sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4 \sqrt[4]{2}}","-\frac{\sqrt[4]{2-3 x^2}}{8 x}+\frac{\sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{16 \sqrt[4]{2}}-\frac{\sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{16 \sqrt[4]{2}}+\frac{\sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{4 \sqrt[4]{2}}",1,"-(2 - 3*x^2)^(1/4)/(8*x) + (Sqrt[3]*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(16*2^(1/4)) - (Sqrt[3]*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(16*2^(1/4)) + (Sqrt[3]*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(4*2^(1/4))","A",7,5,24,0.2083,1,"{443, 325, 232, 400, 441}"
1072,1,184,0,0.1160899,"\int \frac{1}{x^4 \left(2-3 x^2\right)^{3/4} \left(4-3 x^2\right)} \, dx","Int[1/(x^4*(2 - 3*x^2)^(3/4)*(4 - 3*x^2)),x]","-\frac{\sqrt[4]{2-3 x^2}}{4 x}-\frac{\sqrt[4]{2-3 x^2}}{24 x^3}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{64 \sqrt[4]{2}}-\frac{3 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{64 \sqrt[4]{2}}+\frac{11 \sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{32 \sqrt[4]{2}}","-\frac{\sqrt[4]{2-3 x^2}}{4 x}-\frac{\sqrt[4]{2-3 x^2}}{24 x^3}+\frac{3 \sqrt{3} \tan ^{-1}\left(\frac{2^{3/4}-\sqrt[4]{2} \sqrt{2-3 x^2}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{64 \sqrt[4]{2}}-\frac{3 \sqrt{3} \tanh ^{-1}\left(\frac{\sqrt[4]{2} \sqrt{2-3 x^2}+2^{3/4}}{\sqrt{3} x \sqrt[4]{2-3 x^2}}\right)}{64 \sqrt[4]{2}}+\frac{11 \sqrt{3} F\left(\left.\frac{1}{2} \sin ^{-1}\left(\sqrt{\frac{3}{2}} x\right)\right|2\right)}{32 \sqrt[4]{2}}",1,"-(2 - 3*x^2)^(1/4)/(24*x^3) - (2 - 3*x^2)^(1/4)/(4*x) + (3*Sqrt[3]*ArcTan[(2^(3/4) - 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(64*2^(1/4)) - (3*Sqrt[3]*ArcTanh[(2^(3/4) + 2^(1/4)*Sqrt[2 - 3*x^2])/(Sqrt[3]*x*(2 - 3*x^2)^(1/4))])/(64*2^(1/4)) + (11*Sqrt[3]*EllipticF[ArcSin[Sqrt[3/2]*x]/2, 2])/(32*2^(1/4))","A",10,5,24,0.2083,1,"{443, 325, 232, 400, 441}"
1073,1,61,0,0.0163922,"\int \frac{x^2}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^2/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}",1,"ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(3*Sqrt[6]) - ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(3*Sqrt[6])","A",1,1,24,0.04167,1,"{442}"
1074,1,61,0,0.016959,"\int \frac{x^2}{\left(-2-3 x^2\right) \left(-1-3 x^2\right)^{3/4}} \, dx","Int[x^2/((-2 - 3*x^2)*(-1 - 3*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{-3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{-3 x^2-1}}\right)}{3 \sqrt{6}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{-3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{-3 x^2-1}}\right)}{3 \sqrt{6}}",1,"ArcTan[(Sqrt[3/2]*x)/(-1 - 3*x^2)^(1/4)]/(3*Sqrt[6]) - ArcTanh[(Sqrt[3/2]*x)/(-1 - 3*x^2)^(1/4)]/(3*Sqrt[6])","A",1,1,24,0.04167,1,"{442}"
1075,1,72,0,0.0242826,"\int \frac{x^2}{\left(-2+b x^2\right) \left(-1+b x^2\right)^{3/4}} \, dx","Int[x^2/((-2 + b*x^2)*(-1 + b*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{b x^2-1}}\right)}{\sqrt{2} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{b x^2-1}}\right)}{\sqrt{2} b^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{b x^2-1}}\right)}{\sqrt{2} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{b x^2-1}}\right)}{\sqrt{2} b^{3/2}}",1,"ArcTan[(Sqrt[b]*x)/(Sqrt[2]*(-1 + b*x^2)^(1/4))]/(Sqrt[2]*b^(3/2)) - ArcTanh[(Sqrt[b]*x)/(Sqrt[2]*(-1 + b*x^2)^(1/4))]/(Sqrt[2]*b^(3/2))","A",1,1,24,0.04167,1,"{442}"
1076,1,74,0,0.025874,"\int \frac{x^2}{\left(-2-b x^2\right) \left(-1-b x^2\right)^{3/4}} \, dx","Int[x^2/((-2 - b*x^2)*(-1 - b*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{-b x^2-1}}\right)}{\sqrt{2} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{-b x^2-1}}\right)}{\sqrt{2} b^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{-b x^2-1}}\right)}{\sqrt{2} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{-b x^2-1}}\right)}{\sqrt{2} b^{3/2}}",1,"ArcTan[(Sqrt[b]*x)/(Sqrt[2]*(-1 - b*x^2)^(1/4))]/(Sqrt[2]*b^(3/2)) - ArcTanh[(Sqrt[b]*x)/(Sqrt[2]*(-1 - b*x^2)^(1/4))]/(Sqrt[2]*b^(3/2))","A",1,1,26,0.03846,1,"{442}"
1077,1,85,0,0.026389,"\int \frac{x^2}{\left(-2 a+3 x^2\right) \left(-a+3 x^2\right)^{3/4}} \, dx","Int[x^2/((-2*a + 3*x^2)*(-a + 3*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{3 x^2-a}}\right)}{3 \sqrt{6} \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{3 x^2-a}}\right)}{3 \sqrt{6} \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{3 x^2-a}}\right)}{3 \sqrt{6} \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{3 x^2-a}}\right)}{3 \sqrt{6} \sqrt[4]{a}}",1,"ArcTan[(Sqrt[3/2]*x)/(a^(1/4)*(-a + 3*x^2)^(1/4))]/(3*Sqrt[6]*a^(1/4)) - ArcTanh[(Sqrt[3/2]*x)/(a^(1/4)*(-a + 3*x^2)^(1/4))]/(3*Sqrt[6]*a^(1/4))","A",1,1,28,0.03571,1,"{442}"
1078,1,85,0,0.0235324,"\int \frac{x^2}{\left(-2 a-3 x^2\right) \left(-a-3 x^2\right)^{3/4}} \, dx","Int[x^2/((-2*a - 3*x^2)*(-a - 3*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{-a-3 x^2}}\right)}{3 \sqrt{6} \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{-a-3 x^2}}\right)}{3 \sqrt{6} \sqrt[4]{a}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{-a-3 x^2}}\right)}{3 \sqrt{6} \sqrt[4]{a}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{a} \sqrt[4]{-a-3 x^2}}\right)}{3 \sqrt{6} \sqrt[4]{a}}",1,"ArcTan[(Sqrt[3/2]*x)/(a^(1/4)*(-a - 3*x^2)^(1/4))]/(3*Sqrt[6]*a^(1/4)) - ArcTanh[(Sqrt[3/2]*x)/(a^(1/4)*(-a - 3*x^2)^(1/4))]/(3*Sqrt[6]*a^(1/4))","A",1,1,28,0.03571,1,"{442}"
1079,1,96,0,0.0330777,"\int \frac{x^2}{\left(-2 a+b x^2\right) \left(-a+b x^2\right)^{3/4}} \, dx","Int[x^2/((-2*a + b*x^2)*(-a + b*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b x^2-a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b x^2-a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b x^2-a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{b x^2-a}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}",1,"ArcTan[(Sqrt[b]*x)/(Sqrt[2]*a^(1/4)*(-a + b*x^2)^(1/4))]/(Sqrt[2]*a^(1/4)*b^(3/2)) - ArcTanh[(Sqrt[b]*x)/(Sqrt[2]*a^(1/4)*(-a + b*x^2)^(1/4))]/(Sqrt[2]*a^(1/4)*b^(3/2))","A",1,1,28,0.03571,1,"{442}"
1080,1,98,0,0.0332707,"\int \frac{x^2}{\left(-2 a-b x^2\right) \left(-a-b x^2\right)^{3/4}} \, dx","Int[x^2/((-2*a - b*x^2)*(-a - b*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{-a-b x^2}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{-a-b x^2}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}","\frac{\tan ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{-a-b x^2}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{2} \sqrt[4]{a} \sqrt[4]{-a-b x^2}}\right)}{\sqrt{2} \sqrt[4]{a} b^{3/2}}",1,"ArcTan[(Sqrt[b]*x)/(Sqrt[2]*a^(1/4)*(-a - b*x^2)^(1/4))]/(Sqrt[2]*a^(1/4)*b^(3/2)) - ArcTanh[(Sqrt[b]*x)/(Sqrt[2]*a^(1/4)*(-a - b*x^2)^(1/4))]/(Sqrt[2]*a^(1/4)*b^(3/2))","A",1,1,30,0.03333,1,"{442}"
1081,1,78,0,0.0509349,"\int \frac{x^7}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^7/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{2}{729} \left(3 x^2-1\right)^{9/4}+\frac{8}{405} \left(3 x^2-1\right)^{5/4}+\frac{14}{81} \sqrt[4]{3 x^2-1}-\frac{8}{81} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{8}{81} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{2}{729} \left(3 x^2-1\right)^{9/4}+\frac{8}{405} \left(3 x^2-1\right)^{5/4}+\frac{14}{81} \sqrt[4]{3 x^2-1}-\frac{8}{81} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{8}{81} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"(14*(-1 + 3*x^2)^(1/4))/81 + (8*(-1 + 3*x^2)^(5/4))/405 + (2*(-1 + 3*x^2)^(9/4))/729 - (8*ArcTan[(-1 + 3*x^2)^(1/4)])/81 - (8*ArcTanh[(-1 + 3*x^2)^(1/4)])/81","A",7,6,24,0.2500,1,"{446, 88, 63, 212, 206, 203}"
1082,1,63,0,0.0460011,"\int \frac{x^5}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^5/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{2}{135} \left(3 x^2-1\right)^{5/4}+\frac{2}{9} \sqrt[4]{3 x^2-1}-\frac{4}{27} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{4}{27} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{2}{135} \left(3 x^2-1\right)^{5/4}+\frac{2}{9} \sqrt[4]{3 x^2-1}-\frac{4}{27} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{4}{27} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"(2*(-1 + 3*x^2)^(1/4))/9 + (2*(-1 + 3*x^2)^(5/4))/135 - (4*ArcTan[(-1 + 3*x^2)^(1/4)])/27 - (4*ArcTanh[(-1 + 3*x^2)^(1/4)])/27","A",7,6,24,0.2500,1,"{446, 88, 63, 212, 206, 203}"
1083,1,48,0,0.0323884,"\int \frac{x^3}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^3/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{2}{9} \sqrt[4]{3 x^2-1}-\frac{2}{9} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{2}{9} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{2}{9} \sqrt[4]{3 x^2-1}-\frac{2}{9} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{2}{9} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"(2*(-1 + 3*x^2)^(1/4))/9 - (2*ArcTan[(-1 + 3*x^2)^(1/4)])/9 - (2*ArcTanh[(-1 + 3*x^2)^(1/4)])/9","A",6,6,24,0.2500,1,"{446, 80, 63, 212, 206, 203}"
1084,1,33,0,0.0212163,"\int \frac{x}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","-\frac{1}{3} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{1}{3} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","-\frac{1}{3} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)-\frac{1}{3} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"-ArcTan[(-1 + 3*x^2)^(1/4)]/3 - ArcTanh[(-1 + 3*x^2)^(1/4)]/3","A",5,5,22,0.2273,1,"{444, 63, 212, 206, 203}"
1085,1,173,0,0.1257183,"\int \frac{1}{x \left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[1/(x*(-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{\log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}-\frac{\log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}-\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","\frac{\log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}-\frac{\log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{4 \sqrt{2}}-\frac{1}{2} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{\tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{2 \sqrt{2}}-\frac{\tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{2 \sqrt{2}}-\frac{1}{2} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"-ArcTan[(-1 + 3*x^2)^(1/4)]/2 + ArcTan[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4)]/(2*Sqrt[2]) - ArcTan[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4)]/(2*Sqrt[2]) - ArcTanh[(-1 + 3*x^2)^(1/4)]/2 + Log[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]]/(4*Sqrt[2]) - Log[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]]/(4*Sqrt[2])","A",16,12,24,0.5000,1,"{446, 86, 63, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
1086,1,191,0,0.1462509,"\int \frac{1}{x^3 \left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[1/(x^3*(-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","-\frac{\sqrt[4]{3 x^2-1}}{4 x^2}+\frac{15 \log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}-\frac{15 \log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}-\frac{3}{4} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{15 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{8 \sqrt{2}}-\frac{15 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{8 \sqrt{2}}-\frac{3}{4} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)","-\frac{\sqrt[4]{3 x^2-1}}{4 x^2}+\frac{15 \log \left(\sqrt{3 x^2-1}-\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}-\frac{15 \log \left(\sqrt{3 x^2-1}+\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{16 \sqrt{2}}-\frac{3}{4} \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)+\frac{15 \tan ^{-1}\left(1-\sqrt{2} \sqrt[4]{3 x^2-1}\right)}{8 \sqrt{2}}-\frac{15 \tan ^{-1}\left(\sqrt{2} \sqrt[4]{3 x^2-1}+1\right)}{8 \sqrt{2}}-\frac{3}{4} \tanh ^{-1}\left(\sqrt[4]{3 x^2-1}\right)",1,"-(-1 + 3*x^2)^(1/4)/(4*x^2) - (3*ArcTan[(-1 + 3*x^2)^(1/4)])/4 + (15*ArcTan[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4)])/(8*Sqrt[2]) - (15*ArcTan[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4)])/(8*Sqrt[2]) - (3*ArcTanh[(-1 + 3*x^2)^(1/4)])/4 + (15*Log[1 - Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]])/(16*Sqrt[2]) - (15*Log[1 + Sqrt[2]*(-1 + 3*x^2)^(1/4) + Sqrt[-1 + 3*x^2]])/(16*Sqrt[2])","A",17,13,24,0.5417,1,"{446, 103, 156, 63, 211, 1165, 628, 1162, 617, 204, 212, 206, 203}"
1087,1,165,0,0.181692,"\int \frac{x^6}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^6/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{2}{63} \sqrt[4]{3 x^2-1} x^3+\frac{40}{567} \sqrt[4]{3 x^2-1} x+\frac{2}{27} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{2}{27} \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{40 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{567 \sqrt{3} x}","\frac{2}{63} \sqrt[4]{3 x^2-1} x^3+\frac{40}{567} \sqrt[4]{3 x^2-1} x+\frac{2}{27} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{2}{27} \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{40 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{567 \sqrt{3} x}",1,"(40*x*(-1 + 3*x^2)^(1/4))/567 + (2*x^3*(-1 + 3*x^2)^(1/4))/63 + (2*Sqrt[2/3]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/27 - (2*Sqrt[2/3]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/27 + (40*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(567*Sqrt[3]*x)","A",15,6,24,0.2500,1,"{443, 234, 220, 321, 400, 442}"
1088,1,147,0,0.1370395,"\int \frac{x^4}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^4/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{2}{27} \sqrt[4]{3 x^2-1} x+\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{9} \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{2 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{27 \sqrt{3} x}","\frac{2}{27} \sqrt[4]{3 x^2-1} x+\frac{1}{9} \sqrt{\frac{2}{3}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{9} \sqrt{\frac{2}{3}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)+\frac{2 \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{27 \sqrt{3} x}",1,"(2*x*(-1 + 3*x^2)^(1/4))/27 + (Sqrt[2/3]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/9 - (Sqrt[2/3]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/9 + (2*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(27*Sqrt[3]*x)","A",11,6,24,0.2500,1,"{443, 234, 220, 321, 400, 442}"
1089,1,61,0,0.0164688,"\int \frac{x^2}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[x^2/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{3 \sqrt{6}}",1,"ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(3*Sqrt[6]) - ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(3*Sqrt[6])","A",1,1,24,0.04167,1,"{442}"
1090,1,127,0,0.0481679,"\int \frac{1}{\left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[1/((-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}-\frac{\sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 \sqrt{3} x}","\frac{\tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)}{2 \sqrt{6}}-\frac{\sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 \sqrt{3} x}",1,"ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(2*Sqrt[6]) - ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)]/(2*Sqrt[6]) - (Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(2*Sqrt[3]*x)","A",4,4,21,0.1905,1,"{400, 234, 220, 442}"
1091,1,149,0,0.1292884,"\int \frac{1}{x^2 \left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[1/(x^2*(-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","-\frac{\sqrt[4]{3 x^2-1}}{2 x}+\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{4} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 x}","-\frac{\sqrt[4]{3 x^2-1}}{2 x}+\frac{1}{4} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{1}{4} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{\sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{2 x}",1,"-(-1 + 3*x^2)^(1/4)/(2*x) + (Sqrt[3/2]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/4 - (Sqrt[3/2]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/4 - (Sqrt[3]*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(2*x)","A",9,6,24,0.2500,1,"{443, 325, 234, 220, 400, 442}"
1092,1,165,0,0.1669663,"\int \frac{1}{x^4 \left(-2+3 x^2\right) \left(-1+3 x^2\right)^{3/4}} \, dx","Int[1/(x^4*(-2 + 3*x^2)*(-1 + 3*x^2)^(3/4)),x]","-\frac{2 \sqrt[4]{3 x^2-1}}{x}-\frac{\sqrt[4]{3 x^2-1}}{6 x^3}+\frac{3}{8} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{3}{8} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{11 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{8 x}","-\frac{2 \sqrt[4]{3 x^2-1}}{x}-\frac{\sqrt[4]{3 x^2-1}}{6 x^3}+\frac{3}{8} \sqrt{\frac{3}{2}} \tan ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{3}{8} \sqrt{\frac{3}{2}} \tanh ^{-1}\left(\frac{\sqrt{\frac{3}{2}} x}{\sqrt[4]{3 x^2-1}}\right)-\frac{11 \sqrt{3} \sqrt{\frac{x^2}{\left(\sqrt{3 x^2-1}+1\right)^2}} \left(\sqrt{3 x^2-1}+1\right) F\left(2 \tan ^{-1}\left(\sqrt[4]{3 x^2-1}\right)|\frac{1}{2}\right)}{8 x}",1,"-(-1 + 3*x^2)^(1/4)/(6*x^3) - (2*(-1 + 3*x^2)^(1/4))/x + (3*Sqrt[3/2]*ArcTan[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/8 - (3*Sqrt[3/2]*ArcTanh[(Sqrt[3/2]*x)/(-1 + 3*x^2)^(1/4)])/8 - (11*Sqrt[3]*Sqrt[x^2/(1 + Sqrt[-1 + 3*x^2])^2]*(1 + Sqrt[-1 + 3*x^2])*EllipticF[2*ArcTan[(-1 + 3*x^2)^(1/4)], 1/2])/(8*x)","A",13,6,24,0.2500,1,"{443, 325, 234, 220, 400, 442}"
1093,1,173,0,0.1262318,"\int \frac{(e x)^{5/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{3/4}} \, dx","Int[((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x]","\frac{3 a e^{5/2} (8 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{32 b^{11/4}}-\frac{3 a e^{5/2} (8 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{32 b^{11/4}}+\frac{e (e x)^{3/2} \sqrt[4]{a+b x^2} (8 b c-7 a d)}{16 b^2}+\frac{d (e x)^{7/2} \sqrt[4]{a+b x^2}}{4 b e}","\frac{3 a e^{5/2} (8 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{32 b^{11/4}}-\frac{3 a e^{5/2} (8 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{32 b^{11/4}}+\frac{e (e x)^{3/2} \sqrt[4]{a+b x^2} (8 b c-7 a d)}{16 b^2}+\frac{d (e x)^{7/2} \sqrt[4]{a+b x^2}}{4 b e}",1,"((8*b*c - 7*a*d)*e*(e*x)^(3/2)*(a + b*x^2)^(1/4))/(16*b^2) + (d*(e*x)^(7/2)*(a + b*x^2)^(1/4))/(4*b*e) + (3*a*(8*b*c - 7*a*d)*e^(5/2)*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(32*b^(11/4)) - (3*a*(8*b*c - 7*a*d)*e^(5/2)*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(32*b^(11/4))","A",7,7,26,0.2692,1,"{459, 321, 329, 331, 298, 205, 208}"
1094,1,136,0,0.0939556,"\int \frac{\sqrt{e x} \left(c+d x^2\right)}{\left(a+b x^2\right)^{3/4}} \, dx","Int[(Sqrt[e*x]*(c + d*x^2))/(a + b*x^2)^(3/4),x]","-\frac{\sqrt{e} (4 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}+\frac{\sqrt{e} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}+\frac{d (e x)^{3/2} \sqrt[4]{a+b x^2}}{2 b e}","-\frac{\sqrt{e} (4 b c-3 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}+\frac{\sqrt{e} (4 b c-3 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{7/4}}+\frac{d (e x)^{3/2} \sqrt[4]{a+b x^2}}{2 b e}",1,"(d*(e*x)^(3/2)*(a + b*x^2)^(1/4))/(2*b*e) - ((4*b*c - 3*a*d)*Sqrt[e]*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(7/4)) + ((4*b*c - 3*a*d)*Sqrt[e]*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(7/4))","A",6,6,26,0.2308,1,"{459, 329, 331, 298, 205, 208}"
1095,1,113,0,0.0800657,"\int \frac{c+d x^2}{(e x)^{3/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(3/4)),x]","-\frac{d \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{3/4} e^{3/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{3/4} e^{3/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{a e \sqrt{e x}}","-\frac{d \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{3/4} e^{3/2}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{3/4} e^{3/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{a e \sqrt{e x}}",1,"(-2*c*(a + b*x^2)^(1/4))/(a*e*Sqrt[e*x]) - (d*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(b^(3/4)*e^(3/2)) + (d*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(b^(3/4)*e^(3/2))","A",6,6,26,0.2308,1,"{451, 329, 331, 298, 205, 208}"
1096,1,67,0,0.0371541,"\int \frac{c+d x^2}{(e x)^{7/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(3/4)),x]","\frac{2 \sqrt[4]{a+b x^2} (4 b c-5 a d)}{5 a^2 e^3 \sqrt{e x}}-\frac{2 c \sqrt[4]{a+b x^2}}{5 a e (e x)^{5/2}}","\frac{2 \sqrt[4]{a+b x^2} (4 b c-5 a d)}{5 a^2 e^3 \sqrt{e x}}-\frac{2 c \sqrt[4]{a+b x^2}}{5 a e (e x)^{5/2}}",1,"(-2*c*(a + b*x^2)^(1/4))/(5*a*e*(e*x)^(5/2)) + (2*(4*b*c - 5*a*d)*(a + b*x^2)^(1/4))/(5*a^2*e^3*Sqrt[e*x])","A",2,2,26,0.07692,1,"{453, 264}"
1097,1,104,0,0.0508128,"\int \frac{c+d x^2}{(e x)^{11/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(3/4)),x]","-\frac{8 \left(a+b x^2\right)^{5/4} (8 b c-9 a d)}{45 a^3 e^3 (e x)^{5/2}}+\frac{2 \sqrt[4]{a+b x^2} (8 b c-9 a d)}{9 a^2 e^3 (e x)^{5/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{9 a e (e x)^{9/2}}","-\frac{8 \left(a+b x^2\right)^{5/4} (8 b c-9 a d)}{45 a^3 e^3 (e x)^{5/2}}+\frac{2 \sqrt[4]{a+b x^2} (8 b c-9 a d)}{9 a^2 e^3 (e x)^{5/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{9 a e (e x)^{9/2}}",1,"(-2*c*(a + b*x^2)^(1/4))/(9*a*e*(e*x)^(9/2)) + (2*(8*b*c - 9*a*d)*(a + b*x^2)^(1/4))/(9*a^2*e^3*(e*x)^(5/2)) - (8*(8*b*c - 9*a*d)*(a + b*x^2)^(5/4))/(45*a^3*e^3*(e*x)^(5/2))","A",3,3,26,0.1154,1,"{453, 273, 264}"
1098,1,141,0,0.0696162,"\int \frac{c+d x^2}{(e x)^{15/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(15/2)*(a + b*x^2)^(3/4)),x]","\frac{64 \left(a+b x^2\right)^{9/4} (12 b c-13 a d)}{585 a^4 e^3 (e x)^{9/2}}-\frac{16 \left(a+b x^2\right)^{5/4} (12 b c-13 a d)}{65 a^3 e^3 (e x)^{9/2}}+\frac{2 \sqrt[4]{a+b x^2} (12 b c-13 a d)}{13 a^2 e^3 (e x)^{9/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{13 a e (e x)^{13/2}}","\frac{64 \left(a+b x^2\right)^{9/4} (12 b c-13 a d)}{585 a^4 e^3 (e x)^{9/2}}-\frac{16 \left(a+b x^2\right)^{5/4} (12 b c-13 a d)}{65 a^3 e^3 (e x)^{9/2}}+\frac{2 \sqrt[4]{a+b x^2} (12 b c-13 a d)}{13 a^2 e^3 (e x)^{9/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{13 a e (e x)^{13/2}}",1,"(-2*c*(a + b*x^2)^(1/4))/(13*a*e*(e*x)^(13/2)) + (2*(12*b*c - 13*a*d)*(a + b*x^2)^(1/4))/(13*a^2*e^3*(e*x)^(9/2)) - (16*(12*b*c - 13*a*d)*(a + b*x^2)^(5/4))/(65*a^3*e^3*(e*x)^(9/2)) + (64*(12*b*c - 13*a*d)*(a + b*x^2)^(9/4))/(585*a^4*e^3*(e*x)^(9/2))","A",4,3,26,0.1154,1,"{453, 273, 264}"
1099,1,180,0,0.1459377,"\int \frac{(e x)^{7/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{3/4}} \, dx","Int[((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x]","-\frac{a^{3/2} e^2 (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (10 b c-9 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 b^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{a e^3 \sqrt{e x} \sqrt[4]{a+b x^2} (10 b c-9 a d)}{12 b^3}+\frac{e (e x)^{5/2} \sqrt[4]{a+b x^2} (10 b c-9 a d)}{30 b^2}+\frac{d (e x)^{9/2} \sqrt[4]{a+b x^2}}{5 b e}","-\frac{a^{3/2} e^2 (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (10 b c-9 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{12 b^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{a e^3 \sqrt{e x} \sqrt[4]{a+b x^2} (10 b c-9 a d)}{12 b^3}+\frac{e (e x)^{5/2} \sqrt[4]{a+b x^2} (10 b c-9 a d)}{30 b^2}+\frac{d (e x)^{9/2} \sqrt[4]{a+b x^2}}{5 b e}",1,"-(a*(10*b*c - 9*a*d)*e^3*Sqrt[e*x]*(a + b*x^2)^(1/4))/(12*b^3) + ((10*b*c - 9*a*d)*e*(e*x)^(5/2)*(a + b*x^2)^(1/4))/(30*b^2) + (d*(e*x)^(9/2)*(a + b*x^2)^(1/4))/(5*b*e) - (a^(3/2)*(10*b*c - 9*a*d)*e^2*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(12*b^(5/2)*(a + b*x^2)^(3/4))","A",8,7,26,0.2692,1,"{459, 321, 329, 237, 335, 275, 231}"
1100,1,139,0,0.1086027,"\int \frac{(e x)^{3/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{3/4}} \, dx","Int[((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(3/4),x]","\frac{e \sqrt{e x} \sqrt[4]{a+b x^2} (6 b c-5 a d)}{6 b^2}+\frac{\sqrt{a} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (6 b c-5 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{d (e x)^{5/2} \sqrt[4]{a+b x^2}}{3 b e}","\frac{e \sqrt{e x} \sqrt[4]{a+b x^2} (6 b c-5 a d)}{6 b^2}+\frac{\sqrt{a} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (6 b c-5 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{d (e x)^{5/2} \sqrt[4]{a+b x^2}}{3 b e}",1,"((6*b*c - 5*a*d)*e*Sqrt[e*x]*(a + b*x^2)^(1/4))/(6*b^2) + (d*(e*x)^(5/2)*(a + b*x^2)^(1/4))/(3*b*e) + (Sqrt[a]*(6*b*c - 5*a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*b^(3/2)*(a + b*x^2)^(3/4))","A",7,7,26,0.2692,1,"{459, 321, 329, 237, 335, 275, 231}"
1101,1,102,0,0.0879124,"\int \frac{c+d x^2}{\sqrt{e x} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/(Sqrt[e*x]*(a + b*x^2)^(3/4)),x]","\frac{d \sqrt{e x} \sqrt[4]{a+b x^2}}{b e}-\frac{(e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} e^2 \left(a+b x^2\right)^{3/4}}","\frac{d \sqrt{e x} \sqrt[4]{a+b x^2}}{b e}-\frac{(e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} \sqrt{b} e^2 \left(a+b x^2\right)^{3/4}}",1,"(d*Sqrt[e*x]*(a + b*x^2)^(1/4))/(b*e) - ((2*b*c - a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*Sqrt[b]*e^2*(a + b*x^2)^(3/4))","A",6,6,26,0.2308,1,"{459, 329, 237, 335, 275, 231}"
1102,1,107,0,0.0972325,"\int \frac{c+d x^2}{(e x)^{5/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(3/4)),x]","\frac{2 \sqrt{b} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-3 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} e^4 \left(a+b x^2\right)^{3/4}}-\frac{2 c \sqrt[4]{a+b x^2}}{3 a e (e x)^{3/2}}","\frac{2 \sqrt{b} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-3 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} e^4 \left(a+b x^2\right)^{3/4}}-\frac{2 c \sqrt[4]{a+b x^2}}{3 a e (e x)^{3/2}}",1,"(-2*c*(a + b*x^2)^(1/4))/(3*a*e*(e*x)^(3/2)) + (2*Sqrt[b]*(2*b*c - 3*a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*a^(3/2)*e^4*(a + b*x^2)^(3/4))","A",6,6,26,0.2308,1,"{453, 329, 237, 335, 275, 231}"
1103,1,144,0,0.1170435,"\int \frac{c+d x^2}{(e x)^{9/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(3/4)),x]","-\frac{4 b^{3/2} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (6 b c-7 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{5/2} e^6 \left(a+b x^2\right)^{3/4}}+\frac{2 \sqrt[4]{a+b x^2} (6 b c-7 a d)}{21 a^2 e^3 (e x)^{3/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{7 a e (e x)^{7/2}}","-\frac{4 b^{3/2} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (6 b c-7 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{5/2} e^6 \left(a+b x^2\right)^{3/4}}+\frac{2 \sqrt[4]{a+b x^2} (6 b c-7 a d)}{21 a^2 e^3 (e x)^{3/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{7 a e (e x)^{7/2}}",1,"(-2*c*(a + b*x^2)^(1/4))/(7*a*e*(e*x)^(7/2)) + (2*(6*b*c - 7*a*d)*(a + b*x^2)^(1/4))/(21*a^2*e^3*(e*x)^(3/2)) - (4*b^(3/2)*(6*b*c - 7*a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*a^(5/2)*e^6*(a + b*x^2)^(3/4))","A",7,7,26,0.2692,1,"{453, 325, 329, 237, 335, 275, 231}"
1104,1,182,0,0.1405978,"\int \frac{c+d x^2}{(e x)^{13/2} \left(a+b x^2\right)^{3/4}} \, dx","Int[(c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(3/4)),x]","\frac{8 b^{5/2} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (10 b c-11 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} e^8 \left(a+b x^2\right)^{3/4}}-\frac{4 b \sqrt[4]{a+b x^2} (10 b c-11 a d)}{77 a^3 e^5 (e x)^{3/2}}+\frac{2 \sqrt[4]{a+b x^2} (10 b c-11 a d)}{77 a^2 e^3 (e x)^{7/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{11 a e (e x)^{11/2}}","\frac{8 b^{5/2} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (10 b c-11 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{77 a^{7/2} e^8 \left(a+b x^2\right)^{3/4}}-\frac{4 b \sqrt[4]{a+b x^2} (10 b c-11 a d)}{77 a^3 e^5 (e x)^{3/2}}+\frac{2 \sqrt[4]{a+b x^2} (10 b c-11 a d)}{77 a^2 e^3 (e x)^{7/2}}-\frac{2 c \sqrt[4]{a+b x^2}}{11 a e (e x)^{11/2}}",1,"(-2*c*(a + b*x^2)^(1/4))/(11*a*e*(e*x)^(11/2)) + (2*(10*b*c - 11*a*d)*(a + b*x^2)^(1/4))/(77*a^2*e^3*(e*x)^(7/2)) - (4*b*(10*b*c - 11*a*d)*(a + b*x^2)^(1/4))/(77*a^3*e^5*(e*x)^(3/2)) + (8*b^(5/2)*(10*b*c - 11*a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(77*a^(7/2)*e^8*(a + b*x^2)^(3/4))","A",8,7,26,0.2692,1,"{453, 325, 329, 237, 335, 275, 231}"
1105,1,171,0,0.107683,"\int \frac{(e x)^{3/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{5/4}} \, dx","Int[((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x]","\frac{e^{3/2} (4 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}+\frac{e^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}-\frac{e \sqrt{e x} (4 b c-5 a d)}{2 b^2 \sqrt[4]{a+b x^2}}+\frac{d (e x)^{5/2}}{2 b e \sqrt[4]{a+b x^2}}","\frac{e^{3/2} (4 b c-5 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}+\frac{e^{3/2} (4 b c-5 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{9/4}}-\frac{e \sqrt{e x} (4 b c-5 a d)}{2 b^2 \sqrt[4]{a+b x^2}}+\frac{d (e x)^{5/2}}{2 b e \sqrt[4]{a+b x^2}}",1,"-((4*b*c - 5*a*d)*e*Sqrt[e*x])/(2*b^2*(a + b*x^2)^(1/4)) + (d*(e*x)^(5/2))/(2*b*e*(a + b*x^2)^(1/4)) + ((4*b*c - 5*a*d)*e^(3/2)*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(9/4)) + ((4*b*c - 5*a*d)*e^(3/2)*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(9/4))","A",7,7,26,0.2692,1,"{459, 288, 329, 240, 212, 208, 205}"
1106,1,122,0,0.0717827,"\int \frac{c+d x^2}{\sqrt{e x} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/(Sqrt[e*x]*(a + b*x^2)^(5/4)),x]","\frac{d \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{5/4} \sqrt{e}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{5/4} \sqrt{e}}+\frac{2 \sqrt{e x} (b c-a d)}{a b e \sqrt[4]{a+b x^2}}","\frac{d \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{5/4} \sqrt{e}}+\frac{d \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{5/4} \sqrt{e}}+\frac{2 \sqrt{e x} (b c-a d)}{a b e \sqrt[4]{a+b x^2}}",1,"(2*(b*c - a*d)*Sqrt[e*x])/(a*b*e*(a + b*x^2)^(1/4)) + (d*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(b^(5/4)*Sqrt[e]) + (d*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(b^(5/4)*Sqrt[e])","A",6,6,26,0.2308,1,"{452, 329, 240, 212, 208, 205}"
1107,1,67,0,0.0305918,"\int \frac{c+d x^2}{(e x)^{5/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(5/4)),x]","-\frac{2 \sqrt{e x} (4 b c-3 a d)}{3 a^2 e^3 \sqrt[4]{a+b x^2}}-\frac{2 c}{3 a e (e x)^{3/2} \sqrt[4]{a+b x^2}}","-\frac{2 \sqrt{e x} (4 b c-3 a d)}{3 a^2 e^3 \sqrt[4]{a+b x^2}}-\frac{2 c}{3 a e (e x)^{3/2} \sqrt[4]{a+b x^2}}",1,"(-2*c)/(3*a*e*(e*x)^(3/2)*(a + b*x^2)^(1/4)) - (2*(4*b*c - 3*a*d)*Sqrt[e*x])/(3*a^2*e^3*(a + b*x^2)^(1/4))","A",2,2,26,0.07692,1,"{453, 264}"
1108,1,104,0,0.047096,"\int \frac{c+d x^2}{(e x)^{9/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(5/4)),x]","\frac{8 \left(a+b x^2\right)^{3/4} (8 b c-7 a d)}{21 a^3 e^3 (e x)^{3/2}}-\frac{2 (8 b c-7 a d)}{7 a^2 e^3 (e x)^{3/2} \sqrt[4]{a+b x^2}}-\frac{2 c}{7 a e (e x)^{7/2} \sqrt[4]{a+b x^2}}","\frac{8 \left(a+b x^2\right)^{3/4} (8 b c-7 a d)}{21 a^3 e^3 (e x)^{3/2}}-\frac{2 (8 b c-7 a d)}{7 a^2 e^3 (e x)^{3/2} \sqrt[4]{a+b x^2}}-\frac{2 c}{7 a e (e x)^{7/2} \sqrt[4]{a+b x^2}}",1,"(-2*c)/(7*a*e*(e*x)^(7/2)*(a + b*x^2)^(1/4)) - (2*(8*b*c - 7*a*d))/(7*a^2*e^3*(e*x)^(3/2)*(a + b*x^2)^(1/4)) + (8*(8*b*c - 7*a*d)*(a + b*x^2)^(3/4))/(21*a^3*e^3*(e*x)^(3/2))","A",3,3,26,0.1154,1,"{453, 273, 264}"
1109,1,141,0,0.0645813,"\int \frac{c+d x^2}{(e x)^{13/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(5/4)),x]","-\frac{64 \left(a+b x^2\right)^{7/4} (12 b c-11 a d)}{231 a^4 e^3 (e x)^{7/2}}+\frac{16 \left(a+b x^2\right)^{3/4} (12 b c-11 a d)}{33 a^3 e^3 (e x)^{7/2}}-\frac{2 (12 b c-11 a d)}{11 a^2 e^3 (e x)^{7/2} \sqrt[4]{a+b x^2}}-\frac{2 c}{11 a e (e x)^{11/2} \sqrt[4]{a+b x^2}}","-\frac{64 \left(a+b x^2\right)^{7/4} (12 b c-11 a d)}{231 a^4 e^3 (e x)^{7/2}}+\frac{16 \left(a+b x^2\right)^{3/4} (12 b c-11 a d)}{33 a^3 e^3 (e x)^{7/2}}-\frac{2 (12 b c-11 a d)}{11 a^2 e^3 (e x)^{7/2} \sqrt[4]{a+b x^2}}-\frac{2 c}{11 a e (e x)^{11/2} \sqrt[4]{a+b x^2}}",1,"(-2*c)/(11*a*e*(e*x)^(11/2)*(a + b*x^2)^(1/4)) - (2*(12*b*c - 11*a*d))/(11*a^2*e^3*(e*x)^(7/2)*(a + b*x^2)^(1/4)) + (16*(12*b*c - 11*a*d)*(a + b*x^2)^(3/4))/(33*a^3*e^3*(e*x)^(7/2)) - (64*(12*b*c - 11*a*d)*(a + b*x^2)^(7/4))/(231*a^4*e^3*(e*x)^(7/2))","A",4,3,26,0.1154,1,"{453, 273, 264}"
1110,1,180,0,0.0984225,"\int \frac{(e x)^{9/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{5/4}} \, dx","Int[((e*x)^(9/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x]","-\frac{7 a^{3/2} e^4 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (10 b c-11 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{7 a e^3 (e x)^{3/2} (10 b c-11 a d)}{60 b^3 \sqrt[4]{a+b x^2}}+\frac{e (e x)^{7/2} (10 b c-11 a d)}{30 b^2 \sqrt[4]{a+b x^2}}+\frac{d (e x)^{11/2}}{5 b e \sqrt[4]{a+b x^2}}","-\frac{7 a^{3/2} e^4 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (10 b c-11 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{7 a e^3 (e x)^{3/2} (10 b c-11 a d)}{60 b^3 \sqrt[4]{a+b x^2}}+\frac{e (e x)^{7/2} (10 b c-11 a d)}{30 b^2 \sqrt[4]{a+b x^2}}+\frac{d (e x)^{11/2}}{5 b e \sqrt[4]{a+b x^2}}",1,"(-7*a*(10*b*c - 11*a*d)*e^3*(e*x)^(3/2))/(60*b^3*(a + b*x^2)^(1/4)) + ((10*b*c - 11*a*d)*e*(e*x)^(7/2))/(30*b^2*(a + b*x^2)^(1/4)) + (d*(e*x)^(11/2))/(5*b*e*(a + b*x^2)^(1/4)) - (7*a^(3/2)*(10*b*c - 11*a*d)*e^4*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*b^(7/2)*(a + b*x^2)^(1/4))","A",6,5,26,0.1923,1,"{459, 285, 284, 335, 196}"
1111,1,142,0,0.0697724,"\int \frac{(e x)^{5/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{5/4}} \, dx","Int[((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(5/4),x]","\frac{\sqrt{a} e^2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-7 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{5/2} \sqrt[4]{a+b x^2}}+\frac{e (e x)^{3/2} (6 b c-7 a d)}{6 b^2 \sqrt[4]{a+b x^2}}+\frac{d (e x)^{7/2}}{3 b e \sqrt[4]{a+b x^2}}","\frac{\sqrt{a} e^2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-7 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{2 b^{5/2} \sqrt[4]{a+b x^2}}+\frac{e (e x)^{3/2} (6 b c-7 a d)}{6 b^2 \sqrt[4]{a+b x^2}}+\frac{d (e x)^{7/2}}{3 b e \sqrt[4]{a+b x^2}}",1,"((6*b*c - 7*a*d)*e*(e*x)^(3/2))/(6*b^2*(a + b*x^2)^(1/4)) + (d*(e*x)^(7/2))/(3*b*e*(a + b*x^2)^(1/4)) + (Sqrt[a]*(6*b*c - 7*a*d)*e^2*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(2*b^(5/2)*(a + b*x^2)^(1/4))","A",5,5,26,0.1923,1,"{459, 285, 284, 335, 196}"
1112,1,99,0,0.0482421,"\int \frac{\sqrt{e x} \left(c+d x^2\right)}{\left(a+b x^2\right)^{5/4}} \, dx","Int[(Sqrt[e*x]*(c + d*x^2))/(a + b*x^2)^(5/4),x]","\frac{d (e x)^{3/2}}{b e \sqrt[4]{a+b x^2}}-\frac{\sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-3 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} b^{3/2} \sqrt[4]{a+b x^2}}","\frac{d (e x)^{3/2}}{b e \sqrt[4]{a+b x^2}}-\frac{\sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-3 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{\sqrt{a} b^{3/2} \sqrt[4]{a+b x^2}}",1,"(d*(e*x)^(3/2))/(b*e*(a + b*x^2)^(1/4)) - ((2*b*c - 3*a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(Sqrt[a]*b^(3/2)*(a + b*x^2)^(1/4))","A",4,4,26,0.1538,1,"{459, 284, 335, 196}"
1113,1,103,0,0.0592124,"\int \frac{c+d x^2}{(e x)^{3/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(5/4)),x]","\frac{2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt{b} e^2 \sqrt[4]{a+b x^2}}-\frac{2 c}{a e \sqrt{e x} \sqrt[4]{a+b x^2}}","\frac{2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{a^{3/2} \sqrt{b} e^2 \sqrt[4]{a+b x^2}}-\frac{2 c}{a e \sqrt{e x} \sqrt[4]{a+b x^2}}",1,"(-2*c)/(a*e*Sqrt[e*x]*(a + b*x^2)^(1/4)) + (2*(2*b*c - a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(a^(3/2)*Sqrt[b]*e^2*(a + b*x^2)^(1/4))","A",4,4,26,0.1538,1,"{453, 284, 335, 196}"
1114,1,144,0,0.0748738,"\int \frac{c+d x^2}{(e x)^{7/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(5/4)),x]","\frac{2 (6 b c-5 a d)}{5 a^2 e^3 \sqrt{e x} \sqrt[4]{a+b x^2}}-\frac{4 \sqrt{b} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-5 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} e^4 \sqrt[4]{a+b x^2}}-\frac{2 c}{5 a e (e x)^{5/2} \sqrt[4]{a+b x^2}}","\frac{2 (6 b c-5 a d)}{5 a^2 e^3 \sqrt{e x} \sqrt[4]{a+b x^2}}-\frac{4 \sqrt{b} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-5 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} e^4 \sqrt[4]{a+b x^2}}-\frac{2 c}{5 a e (e x)^{5/2} \sqrt[4]{a+b x^2}}",1,"(-2*c)/(5*a*e*(e*x)^(5/2)*(a + b*x^2)^(1/4)) + (2*(6*b*c - 5*a*d))/(5*a^2*e^3*Sqrt[e*x]*(a + b*x^2)^(1/4)) - (4*Sqrt[b]*(6*b*c - 5*a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(5/2)*e^4*(a + b*x^2)^(1/4))","A",5,5,26,0.1923,1,"{453, 286, 284, 335, 196}"
1115,1,182,0,0.0996455,"\int \frac{c+d x^2}{(e x)^{11/2} \left(a+b x^2\right)^{5/4}} \, dx","Int[(c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(5/4)),x]","\frac{8 b^{3/2} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (10 b c-9 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{7/2} e^6 \sqrt[4]{a+b x^2}}-\frac{4 b (10 b c-9 a d)}{15 a^3 e^5 \sqrt{e x} \sqrt[4]{a+b x^2}}+\frac{2 (10 b c-9 a d)}{45 a^2 e^3 (e x)^{5/2} \sqrt[4]{a+b x^2}}-\frac{2 c}{9 a e (e x)^{9/2} \sqrt[4]{a+b x^2}}","\frac{8 b^{3/2} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (10 b c-9 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{7/2} e^6 \sqrt[4]{a+b x^2}}-\frac{4 b (10 b c-9 a d)}{15 a^3 e^5 \sqrt{e x} \sqrt[4]{a+b x^2}}+\frac{2 (10 b c-9 a d)}{45 a^2 e^3 (e x)^{5/2} \sqrt[4]{a+b x^2}}-\frac{2 c}{9 a e (e x)^{9/2} \sqrt[4]{a+b x^2}}",1,"(-2*c)/(9*a*e*(e*x)^(9/2)*(a + b*x^2)^(1/4)) + (2*(10*b*c - 9*a*d))/(45*a^2*e^3*(e*x)^(5/2)*(a + b*x^2)^(1/4)) - (4*b*(10*b*c - 9*a*d))/(15*a^3*e^5*Sqrt[e*x]*(a + b*x^2)^(1/4)) + (8*b^(3/2)*(10*b*c - 9*a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*a^(7/2)*e^6*(a + b*x^2)^(1/4))","A",6,5,26,0.1923,1,"{453, 286, 284, 335, 196}"
1116,1,184,0,0.119237,"\int \frac{(e x)^{5/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{7/4}} \, dx","Int[((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x]","-\frac{e^{5/2} (4 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{11/4}}+\frac{e^{5/2} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{11/4}}-\frac{e (e x)^{3/2} \sqrt[4]{a+b x^2} (4 b c-7 a d)}{6 a b^2}+\frac{2 (e x)^{7/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}","-\frac{e^{5/2} (4 b c-7 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{11/4}}+\frac{e^{5/2} (4 b c-7 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{11/4}}-\frac{e (e x)^{3/2} \sqrt[4]{a+b x^2} (4 b c-7 a d)}{6 a b^2}+\frac{2 (e x)^{7/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}",1,"(2*(b*c - a*d)*(e*x)^(7/2))/(3*a*b*e*(a + b*x^2)^(3/4)) - ((4*b*c - 7*a*d)*e*(e*x)^(3/2)*(a + b*x^2)^(1/4))/(6*a*b^2) - ((4*b*c - 7*a*d)*e^(5/2)*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(11/4)) + ((4*b*c - 7*a*d)*e^(5/2)*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(11/4))","A",7,7,26,0.2692,1,"{457, 321, 329, 331, 298, 205, 208}"
1117,1,125,0,0.0764689,"\int \frac{\sqrt{e x} \left(c+d x^2\right)}{\left(a+b x^2\right)^{7/4}} \, dx","Int[(Sqrt[e*x]*(c + d*x^2))/(a + b*x^2)^(7/4),x]","-\frac{d \sqrt{e} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{7/4}}+\frac{d \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{7/4}}+\frac{2 (e x)^{3/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}","-\frac{d \sqrt{e} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{7/4}}+\frac{d \sqrt{e} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{7/4}}+\frac{2 (e x)^{3/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}",1,"(2*(b*c - a*d)*(e*x)^(3/2))/(3*a*b*e*(a + b*x^2)^(3/4)) - (d*Sqrt[e]*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/b^(7/4) + (d*Sqrt[e]*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/b^(7/4)","A",6,6,26,0.2308,1,"{452, 329, 331, 298, 205, 208}"
1118,1,65,0,0.0311342,"\int \frac{c+d x^2}{(e x)^{3/2} \left(a+b x^2\right)^{7/4}} \, dx","Int[(c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(7/4)),x]","-\frac{2 (e x)^{3/2} (4 b c-a d)}{3 a^2 e^3 \left(a+b x^2\right)^{3/4}}-\frac{2 c}{a e \sqrt{e x} \left(a+b x^2\right)^{3/4}}","-\frac{2 (e x)^{3/2} (4 b c-a d)}{3 a^2 e^3 \left(a+b x^2\right)^{3/4}}-\frac{2 c}{a e \sqrt{e x} \left(a+b x^2\right)^{3/4}}",1,"(-2*c)/(a*e*Sqrt[e*x]*(a + b*x^2)^(3/4)) - (2*(4*b*c - a*d)*(e*x)^(3/2))/(3*a^2*e^3*(a + b*x^2)^(3/4))","A",2,2,26,0.07692,1,"{453, 264}"
1119,1,104,0,0.0518137,"\int \frac{c+d x^2}{(e x)^{7/2} \left(a+b x^2\right)^{7/4}} \, dx","Int[(c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(7/4)),x]","\frac{8 \sqrt[4]{a+b x^2} (8 b c-5 a d)}{15 a^3 e^3 \sqrt{e x}}-\frac{2 (8 b c-5 a d)}{15 a^2 e^3 \sqrt{e x} \left(a+b x^2\right)^{3/4}}-\frac{2 c}{5 a e (e x)^{5/2} \left(a+b x^2\right)^{3/4}}","\frac{8 \sqrt[4]{a+b x^2} (8 b c-5 a d)}{15 a^3 e^3 \sqrt{e x}}-\frac{2 (8 b c-5 a d)}{15 a^2 e^3 \sqrt{e x} \left(a+b x^2\right)^{3/4}}-\frac{2 c}{5 a e (e x)^{5/2} \left(a+b x^2\right)^{3/4}}",1,"(-2*c)/(5*a*e*(e*x)^(5/2)*(a + b*x^2)^(3/4)) - (2*(8*b*c - 5*a*d))/(15*a^2*e^3*Sqrt[e*x]*(a + b*x^2)^(3/4)) + (8*(8*b*c - 5*a*d)*(a + b*x^2)^(1/4))/(15*a^3*e^3*Sqrt[e*x])","A",3,3,26,0.1154,1,"{453, 273, 264}"
1120,1,141,0,0.0656395,"\int \frac{c+d x^2}{(e x)^{11/2} \left(a+b x^2\right)^{7/4}} \, dx","Int[(c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(7/4)),x]","-\frac{64 \left(a+b x^2\right)^{5/4} (4 b c-3 a d)}{45 a^4 e^3 (e x)^{5/2}}+\frac{16 \sqrt[4]{a+b x^2} (4 b c-3 a d)}{9 a^3 e^3 (e x)^{5/2}}-\frac{2 (4 b c-3 a d)}{9 a^2 e^3 (e x)^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{2 c}{9 a e (e x)^{9/2} \left(a+b x^2\right)^{3/4}}","-\frac{64 \left(a+b x^2\right)^{5/4} (4 b c-3 a d)}{45 a^4 e^3 (e x)^{5/2}}+\frac{16 \sqrt[4]{a+b x^2} (4 b c-3 a d)}{9 a^3 e^3 (e x)^{5/2}}-\frac{2 (4 b c-3 a d)}{9 a^2 e^3 (e x)^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{2 c}{9 a e (e x)^{9/2} \left(a+b x^2\right)^{3/4}}",1,"(-2*c)/(9*a*e*(e*x)^(9/2)*(a + b*x^2)^(3/4)) - (2*(4*b*c - 3*a*d))/(9*a^2*e^3*(e*x)^(5/2)*(a + b*x^2)^(3/4)) + (16*(4*b*c - 3*a*d)*(a + b*x^2)^(1/4))/(9*a^3*e^3*(e*x)^(5/2)) - (64*(4*b*c - 3*a*d)*(a + b*x^2)^(5/4))/(45*a^4*e^3*(e*x)^(5/2))","A",4,3,26,0.1154,1,"{453, 273, 264}"
1121,1,192,0,0.1348268,"\int \frac{(e x)^{7/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{7/4}} \, dx","Int[((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x]","\frac{5 e^3 \sqrt{e x} \sqrt[4]{a+b x^2} (2 b c-3 a d)}{6 b^3}+\frac{5 \sqrt{a} e^2 (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-3 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 b^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{e (e x)^{5/2} \sqrt[4]{a+b x^2} (2 b c-3 a d)}{3 a b^2}+\frac{2 (e x)^{9/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}","\frac{5 e^3 \sqrt{e x} \sqrt[4]{a+b x^2} (2 b c-3 a d)}{6 b^3}+\frac{5 \sqrt{a} e^2 (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-3 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{6 b^{5/2} \left(a+b x^2\right)^{3/4}}-\frac{e (e x)^{5/2} \sqrt[4]{a+b x^2} (2 b c-3 a d)}{3 a b^2}+\frac{2 (e x)^{9/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}",1,"(2*(b*c - a*d)*(e*x)^(9/2))/(3*a*b*e*(a + b*x^2)^(3/4)) + (5*(2*b*c - 3*a*d)*e^3*Sqrt[e*x]*(a + b*x^2)^(1/4))/(6*b^3) - ((2*b*c - 3*a*d)*e*(e*x)^(5/2)*(a + b*x^2)^(1/4))/(3*a*b^2) + (5*Sqrt[a]*(2*b*c - 3*a*d)*e^2*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(6*b^(5/2)*(a + b*x^2)^(3/4))","A",8,7,26,0.2692,1,"{457, 321, 329, 237, 335, 275, 231}"
1122,1,152,0,0.1115194,"\int \frac{(e x)^{3/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{7/4}} \, dx","Int[((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(7/4),x]","-\frac{e \sqrt{e x} \sqrt[4]{a+b x^2} (2 b c-5 a d)}{3 a b^2}-\frac{(e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-5 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{2 (e x)^{5/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}","-\frac{e \sqrt{e x} \sqrt[4]{a+b x^2} (2 b c-5 a d)}{3 a b^2}-\frac{(e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-5 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 \sqrt{a} b^{3/2} \left(a+b x^2\right)^{3/4}}+\frac{2 (e x)^{5/2} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}",1,"(2*(b*c - a*d)*(e*x)^(5/2))/(3*a*b*e*(a + b*x^2)^(3/4)) - ((2*b*c - 5*a*d)*e*Sqrt[e*x]*(a + b*x^2)^(1/4))/(3*a*b^2) - ((2*b*c - 5*a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*Sqrt[a]*b^(3/2)*(a + b*x^2)^(3/4))","A",7,7,26,0.2692,1,"{457, 321, 329, 237, 335, 275, 231}"
1123,1,116,0,0.0934183,"\int \frac{c+d x^2}{\sqrt{e x} \left(a+b x^2\right)^{7/4}} \, dx","Int[(c + d*x^2)/(Sqrt[e*x]*(a + b*x^2)^(7/4)),x]","\frac{2 \sqrt{e x} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}-\frac{2 (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (a d+2 b c) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \sqrt{b} e^2 \left(a+b x^2\right)^{3/4}}","\frac{2 \sqrt{e x} (b c-a d)}{3 a b e \left(a+b x^2\right)^{3/4}}-\frac{2 (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (a d+2 b c) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{3/2} \sqrt{b} e^2 \left(a+b x^2\right)^{3/4}}",1,"(2*(b*c - a*d)*Sqrt[e*x])/(3*a*b*e*(a + b*x^2)^(3/4)) - (2*(2*b*c + a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*a^(3/2)*Sqrt[b]*e^2*(a + b*x^2)^(3/4))","A",6,6,26,0.2308,1,"{457, 329, 237, 335, 275, 231}"
1124,1,144,0,0.1123123,"\int \frac{c+d x^2}{(e x)^{5/2} \left(a+b x^2\right)^{7/4}} \, dx","Int[(c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(7/4)),x]","-\frac{2 \sqrt{e x} (2 b c-a d)}{3 a^2 e^3 \left(a+b x^2\right)^{3/4}}+\frac{4 \sqrt{b} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{5/2} e^4 \left(a+b x^2\right)^{3/4}}-\frac{2 c}{3 a e (e x)^{3/2} \left(a+b x^2\right)^{3/4}}","-\frac{2 \sqrt{e x} (2 b c-a d)}{3 a^2 e^3 \left(a+b x^2\right)^{3/4}}+\frac{4 \sqrt{b} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (2 b c-a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{3 a^{5/2} e^4 \left(a+b x^2\right)^{3/4}}-\frac{2 c}{3 a e (e x)^{3/2} \left(a+b x^2\right)^{3/4}}",1,"(-2*c)/(3*a*e*(e*x)^(3/2)*(a + b*x^2)^(3/4)) - (2*(2*b*c - a*d)*Sqrt[e*x])/(3*a^2*e^3*(a + b*x^2)^(3/4)) + (4*Sqrt[b]*(2*b*c - a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(3*a^(5/2)*e^4*(a + b*x^2)^(3/4))","A",7,7,26,0.2692,1,"{453, 290, 329, 237, 335, 275, 231}"
1125,1,181,0,0.1365642,"\int \frac{c+d x^2}{(e x)^{9/2} \left(a+b x^2\right)^{7/4}} \, dx","Int[(c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(7/4)),x]","-\frac{8 b^{3/2} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (10 b c-7 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{7/2} e^6 \left(a+b x^2\right)^{3/4}}+\frac{4 \sqrt[4]{a+b x^2} (10 b c-7 a d)}{21 a^3 e^3 (e x)^{3/2}}-\frac{2 (10 b c-7 a d)}{21 a^2 e^3 (e x)^{3/2} \left(a+b x^2\right)^{3/4}}-\frac{2 c}{7 a e (e x)^{7/2} \left(a+b x^2\right)^{3/4}}","-\frac{8 b^{3/2} (e x)^{3/2} \left(\frac{a}{b x^2}+1\right)^{3/4} (10 b c-7 a d) F\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{21 a^{7/2} e^6 \left(a+b x^2\right)^{3/4}}+\frac{4 \sqrt[4]{a+b x^2} (10 b c-7 a d)}{21 a^3 e^3 (e x)^{3/2}}-\frac{2 (10 b c-7 a d)}{21 a^2 e^3 (e x)^{3/2} \left(a+b x^2\right)^{3/4}}-\frac{2 c}{7 a e (e x)^{7/2} \left(a+b x^2\right)^{3/4}}",1,"(-2*c)/(7*a*e*(e*x)^(7/2)*(a + b*x^2)^(3/4)) - (2*(10*b*c - 7*a*d))/(21*a^2*e^3*(e*x)^(3/2)*(a + b*x^2)^(3/4)) + (4*(10*b*c - 7*a*d)*(a + b*x^2)^(1/4))/(21*a^3*e^3*(e*x)^(3/2)) - (8*b^(3/2)*(10*b*c - 7*a*d)*(1 + a/(b*x^2))^(3/4)*(e*x)^(3/2)*EllipticF[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(21*a^(7/2)*e^6*(a + b*x^2)^(3/4))","A",8,8,26,0.3077,1,"{453, 290, 325, 329, 237, 335, 275, 231}"
1126,1,221,0,0.1347504,"\int \frac{(e x)^{7/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{9/4}} \, dx","Int[((e*x)^(7/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x]","-\frac{e^3 \sqrt{e x} (4 b c-9 a d)}{2 b^3 \sqrt[4]{a+b x^2}}+\frac{e^{7/2} (4 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{13/4}}+\frac{e^{7/2} (4 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{13/4}}-\frac{e (e x)^{5/2} (4 b c-9 a d)}{10 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{9/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}","-\frac{e^3 \sqrt{e x} (4 b c-9 a d)}{2 b^3 \sqrt[4]{a+b x^2}}+\frac{e^{7/2} (4 b c-9 a d) \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{13/4}}+\frac{e^{7/2} (4 b c-9 a d) \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{4 b^{13/4}}-\frac{e (e x)^{5/2} (4 b c-9 a d)}{10 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{9/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}",1,"(2*(b*c - a*d)*(e*x)^(9/2))/(5*a*b*e*(a + b*x^2)^(5/4)) - ((4*b*c - 9*a*d)*e^3*Sqrt[e*x])/(2*b^3*(a + b*x^2)^(1/4)) - ((4*b*c - 9*a*d)*e*(e*x)^(5/2))/(10*a*b^2*(a + b*x^2)^(1/4)) + ((4*b*c - 9*a*d)*e^(7/2)*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(13/4)) + ((4*b*c - 9*a*d)*e^(7/2)*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/(4*b^(13/4))","A",8,8,26,0.3077,1,"{457, 285, 288, 329, 240, 212, 208, 205}"
1127,1,149,0,0.0872398,"\int \frac{(e x)^{3/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{9/4}} \, dx","Int[((e*x)^(3/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x]","\frac{d e^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{9/4}}+\frac{d e^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{9/4}}-\frac{2 d e \sqrt{e x}}{b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{5/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}","\frac{d e^{3/2} \tan ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{9/4}}+\frac{d e^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{b} \sqrt{e x}}{\sqrt{e} \sqrt[4]{a+b x^2}}\right)}{b^{9/4}}-\frac{2 d e \sqrt{e x}}{b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{5/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}",1,"(2*(b*c - a*d)*(e*x)^(5/2))/(5*a*b*e*(a + b*x^2)^(5/4)) - (2*d*e*Sqrt[e*x])/(b^2*(a + b*x^2)^(1/4)) + (d*e^(3/2)*ArcTan[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/b^(9/4) + (d*e^(3/2)*ArcTanh[(b^(1/4)*Sqrt[e*x])/(Sqrt[e]*(a + b*x^2)^(1/4))])/b^(9/4)","A",7,7,26,0.2692,1,"{452, 288, 329, 240, 212, 208, 205}"
1128,1,79,0,0.0328255,"\int \frac{c+d x^2}{\sqrt{e x} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/(Sqrt[e*x]*(a + b*x^2)^(9/4)),x]","\frac{2 \sqrt{e x} (a d+4 b c)}{5 a^2 b e \sqrt[4]{a+b x^2}}+\frac{2 \sqrt{e x} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}","\frac{2 \sqrt{e x} (a d+4 b c)}{5 a^2 b e \sqrt[4]{a+b x^2}}+\frac{2 \sqrt{e x} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}",1,"(2*(b*c - a*d)*Sqrt[e*x])/(5*a*b*e*(a + b*x^2)^(5/4)) + (2*(4*b*c + a*d)*Sqrt[e*x])/(5*a^2*b*e*(a + b*x^2)^(1/4))","A",2,2,26,0.07692,1,"{457, 264}"
1129,1,104,0,0.0481076,"\int \frac{c+d x^2}{(e x)^{5/2} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/((e*x)^(5/2)*(a + b*x^2)^(9/4)),x]","-\frac{8 \sqrt{e x} (8 b c-3 a d)}{15 a^3 e^3 \sqrt[4]{a+b x^2}}-\frac{2 \sqrt{e x} (8 b c-3 a d)}{15 a^2 e^3 \left(a+b x^2\right)^{5/4}}-\frac{2 c}{3 a e (e x)^{3/2} \left(a+b x^2\right)^{5/4}}","-\frac{8 \sqrt{e x} (8 b c-3 a d)}{15 a^3 e^3 \sqrt[4]{a+b x^2}}-\frac{2 \sqrt{e x} (8 b c-3 a d)}{15 a^2 e^3 \left(a+b x^2\right)^{5/4}}-\frac{2 c}{3 a e (e x)^{3/2} \left(a+b x^2\right)^{5/4}}",1,"(-2*c)/(3*a*e*(e*x)^(3/2)*(a + b*x^2)^(5/4)) - (2*(8*b*c - 3*a*d)*Sqrt[e*x])/(15*a^2*e^3*(a + b*x^2)^(5/4)) - (8*(8*b*c - 3*a*d)*Sqrt[e*x])/(15*a^3*e^3*(a + b*x^2)^(1/4))","A",3,3,26,0.1154,1,"{453, 273, 264}"
1130,1,141,0,0.06919,"\int \frac{c+d x^2}{(e x)^{9/2} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/((e*x)^(9/2)*(a + b*x^2)^(9/4)),x]","\frac{64 \left(a+b x^2\right)^{3/4} (12 b c-7 a d)}{105 a^4 e^3 (e x)^{3/2}}-\frac{16 (12 b c-7 a d)}{35 a^3 e^3 (e x)^{3/2} \sqrt[4]{a+b x^2}}-\frac{2 (12 b c-7 a d)}{35 a^2 e^3 (e x)^{3/2} \left(a+b x^2\right)^{5/4}}-\frac{2 c}{7 a e (e x)^{7/2} \left(a+b x^2\right)^{5/4}}","\frac{64 \left(a+b x^2\right)^{3/4} (12 b c-7 a d)}{105 a^4 e^3 (e x)^{3/2}}-\frac{16 (12 b c-7 a d)}{35 a^3 e^3 (e x)^{3/2} \sqrt[4]{a+b x^2}}-\frac{2 (12 b c-7 a d)}{35 a^2 e^3 (e x)^{3/2} \left(a+b x^2\right)^{5/4}}-\frac{2 c}{7 a e (e x)^{7/2} \left(a+b x^2\right)^{5/4}}",1,"(-2*c)/(7*a*e*(e*x)^(7/2)*(a + b*x^2)^(5/4)) - (2*(12*b*c - 7*a*d))/(35*a^2*e^3*(e*x)^(3/2)*(a + b*x^2)^(5/4)) - (16*(12*b*c - 7*a*d))/(35*a^3*e^3*(e*x)^(3/2)*(a + b*x^2)^(1/4)) + (64*(12*b*c - 7*a*d)*(a + b*x^2)^(3/4))/(105*a^4*e^3*(e*x)^(3/2))","A",4,3,26,0.1154,1,"{453, 273, 264}"
1131,1,178,0,0.0903243,"\int \frac{c+d x^2}{(e x)^{13/2} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/((e*x)^(13/2)*(a + b*x^2)^(9/4)),x]","-\frac{256 \left(a+b x^2\right)^{7/4} (16 b c-11 a d)}{385 a^5 e^3 (e x)^{7/2}}+\frac{64 \left(a+b x^2\right)^{3/4} (16 b c-11 a d)}{55 a^4 e^3 (e x)^{7/2}}-\frac{24 (16 b c-11 a d)}{55 a^3 e^3 (e x)^{7/2} \sqrt[4]{a+b x^2}}-\frac{2 (16 b c-11 a d)}{55 a^2 e^3 (e x)^{7/2} \left(a+b x^2\right)^{5/4}}-\frac{2 c}{11 a e (e x)^{11/2} \left(a+b x^2\right)^{5/4}}","-\frac{256 \left(a+b x^2\right)^{7/4} (16 b c-11 a d)}{385 a^5 e^3 (e x)^{7/2}}+\frac{64 \left(a+b x^2\right)^{3/4} (16 b c-11 a d)}{55 a^4 e^3 (e x)^{7/2}}-\frac{24 (16 b c-11 a d)}{55 a^3 e^3 (e x)^{7/2} \sqrt[4]{a+b x^2}}-\frac{2 (16 b c-11 a d)}{55 a^2 e^3 (e x)^{7/2} \left(a+b x^2\right)^{5/4}}-\frac{2 c}{11 a e (e x)^{11/2} \left(a+b x^2\right)^{5/4}}",1,"(-2*c)/(11*a*e*(e*x)^(11/2)*(a + b*x^2)^(5/4)) - (2*(16*b*c - 11*a*d))/(55*a^2*e^3*(e*x)^(7/2)*(a + b*x^2)^(5/4)) - (24*(16*b*c - 11*a*d))/(55*a^3*e^3*(e*x)^(7/2)*(a + b*x^2)^(1/4)) + (64*(16*b*c - 11*a*d)*(a + b*x^2)^(3/4))/(55*a^4*e^3*(e*x)^(7/2)) - (256*(16*b*c - 11*a*d)*(a + b*x^2)^(7/4))/(385*a^5*e^3*(e*x)^(7/2))","A",5,3,26,0.1154,1,"{453, 273, 264}"
1132,1,230,0,0.127523,"\int \frac{(e x)^{13/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{9/4}} \, dx","Int[((e*x)^(13/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x]","-\frac{77 a^{3/2} e^6 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-3 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{9/2} \sqrt[4]{a+b x^2}}+\frac{11 e^3 (e x)^{7/2} (2 b c-3 a d)}{30 b^3 \sqrt[4]{a+b x^2}}-\frac{77 a e^5 (e x)^{3/2} (2 b c-3 a d)}{60 b^4 \sqrt[4]{a+b x^2}}-\frac{e (e x)^{11/2} (2 b c-3 a d)}{5 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{15/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}","-\frac{77 a^{3/2} e^6 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-3 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{20 b^{9/2} \sqrt[4]{a+b x^2}}+\frac{11 e^3 (e x)^{7/2} (2 b c-3 a d)}{30 b^3 \sqrt[4]{a+b x^2}}-\frac{77 a e^5 (e x)^{3/2} (2 b c-3 a d)}{60 b^4 \sqrt[4]{a+b x^2}}-\frac{e (e x)^{11/2} (2 b c-3 a d)}{5 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{15/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}",1,"(2*(b*c - a*d)*(e*x)^(15/2))/(5*a*b*e*(a + b*x^2)^(5/4)) - (77*a*(2*b*c - 3*a*d)*e^5*(e*x)^(3/2))/(60*b^4*(a + b*x^2)^(1/4)) + (11*(2*b*c - 3*a*d)*e^3*(e*x)^(7/2))/(30*b^3*(a + b*x^2)^(1/4)) - ((2*b*c - 3*a*d)*e*(e*x)^(11/2))/(5*a*b^2*(a + b*x^2)^(1/4)) - (77*a^(3/2)*(2*b*c - 3*a*d)*e^6*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(20*b^(9/2)*(a + b*x^2)^(1/4))","A",7,5,26,0.1923,1,"{457, 285, 284, 335, 196}"
1133,1,192,0,0.1062907,"\int \frac{(e x)^{9/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{9/4}} \, dx","Int[((e*x)^(9/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x]","\frac{7 e^3 (e x)^{3/2} (6 b c-11 a d)}{30 b^3 \sqrt[4]{a+b x^2}}+\frac{7 \sqrt{a} e^4 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-11 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{10 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{e (e x)^{7/2} (6 b c-11 a d)}{15 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{11/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}","\frac{7 e^3 (e x)^{3/2} (6 b c-11 a d)}{30 b^3 \sqrt[4]{a+b x^2}}+\frac{7 \sqrt{a} e^4 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-11 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{10 b^{7/2} \sqrt[4]{a+b x^2}}-\frac{e (e x)^{7/2} (6 b c-11 a d)}{15 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{11/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}",1,"(2*(b*c - a*d)*(e*x)^(11/2))/(5*a*b*e*(a + b*x^2)^(5/4)) + (7*(6*b*c - 11*a*d)*e^3*(e*x)^(3/2))/(30*b^3*(a + b*x^2)^(1/4)) - ((6*b*c - 11*a*d)*e*(e*x)^(7/2))/(15*a*b^2*(a + b*x^2)^(1/4)) + (7*Sqrt[a]*(6*b*c - 11*a*d)*e^4*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(10*b^(7/2)*(a + b*x^2)^(1/4))","A",6,5,26,0.1923,1,"{457, 285, 284, 335, 196}"
1134,1,155,0,0.0765485,"\int \frac{(e x)^{5/2} \left(c+d x^2\right)}{\left(a+b x^2\right)^{9/4}} \, dx","Int[((e*x)^(5/2)*(c + d*x^2))/(a + b*x^2)^(9/4),x]","-\frac{3 e^2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-7 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{a} b^{5/2} \sqrt[4]{a+b x^2}}-\frac{e (e x)^{3/2} (2 b c-7 a d)}{5 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{7/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}","-\frac{3 e^2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-7 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 \sqrt{a} b^{5/2} \sqrt[4]{a+b x^2}}-\frac{e (e x)^{3/2} (2 b c-7 a d)}{5 a b^2 \sqrt[4]{a+b x^2}}+\frac{2 (e x)^{7/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}",1,"(2*(b*c - a*d)*(e*x)^(7/2))/(5*a*b*e*(a + b*x^2)^(5/4)) - ((2*b*c - 7*a*d)*e*(e*x)^(3/2))/(5*a*b^2*(a + b*x^2)^(1/4)) - (3*(2*b*c - 7*a*d)*e^2*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*Sqrt[a]*b^(5/2)*(a + b*x^2)^(1/4))","A",5,5,26,0.1923,1,"{457, 285, 284, 335, 196}"
1135,1,114,0,0.0515974,"\int \frac{\sqrt{e x} \left(c+d x^2\right)}{\left(a+b x^2\right)^{9/4}} \, dx","Int[(Sqrt[e*x]*(c + d*x^2))/(a + b*x^2)^(9/4),x]","\frac{2 (e x)^{3/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}-\frac{2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (3 a d+2 b c) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} b^{3/2} \sqrt[4]{a+b x^2}}","\frac{2 (e x)^{3/2} (b c-a d)}{5 a b e \left(a+b x^2\right)^{5/4}}-\frac{2 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (3 a d+2 b c) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{3/2} b^{3/2} \sqrt[4]{a+b x^2}}",1,"(2*(b*c - a*d)*(e*x)^(3/2))/(5*a*b*e*(a + b*x^2)^(5/4)) - (2*(2*b*c + 3*a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(3/2)*b^(3/2)*(a + b*x^2)^(1/4))","A",4,4,26,0.1538,1,"{457, 284, 335, 196}"
1136,1,142,0,0.0730283,"\int \frac{c+d x^2}{(e x)^{3/2} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/((e*x)^(3/2)*(a + b*x^2)^(9/4)),x]","-\frac{2 (e x)^{3/2} (6 b c-a d)}{5 a^2 e^3 \left(a+b x^2\right)^{5/4}}+\frac{4 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} \sqrt{b} e^2 \sqrt[4]{a+b x^2}}-\frac{2 c}{a e \sqrt{e x} \left(a+b x^2\right)^{5/4}}","-\frac{2 (e x)^{3/2} (6 b c-a d)}{5 a^2 e^3 \left(a+b x^2\right)^{5/4}}+\frac{4 \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (6 b c-a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{5/2} \sqrt{b} e^2 \sqrt[4]{a+b x^2}}-\frac{2 c}{a e \sqrt{e x} \left(a+b x^2\right)^{5/4}}",1,"(-2*c)/(a*e*Sqrt[e*x]*(a + b*x^2)^(5/4)) - (2*(6*b*c - a*d)*(e*x)^(3/2))/(5*a^2*e^3*(a + b*x^2)^(5/4)) + (4*(6*b*c - a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(5/2)*Sqrt[b]*e^2*(a + b*x^2)^(1/4))","A",5,5,26,0.1923,1,"{453, 290, 284, 335, 196}"
1137,1,181,0,0.0949316,"\int \frac{c+d x^2}{(e x)^{7/2} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/((e*x)^(7/2)*(a + b*x^2)^(9/4)),x]","\frac{12 (2 b c-a d)}{5 a^3 e^3 \sqrt{e x} \sqrt[4]{a+b x^2}}-\frac{2 (2 b c-a d)}{5 a^2 e^3 \sqrt{e x} \left(a+b x^2\right)^{5/4}}-\frac{24 \sqrt{b} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{7/2} e^4 \sqrt[4]{a+b x^2}}-\frac{2 c}{5 a e (e x)^{5/2} \left(a+b x^2\right)^{5/4}}","\frac{12 (2 b c-a d)}{5 a^3 e^3 \sqrt{e x} \sqrt[4]{a+b x^2}}-\frac{2 (2 b c-a d)}{5 a^2 e^3 \sqrt{e x} \left(a+b x^2\right)^{5/4}}-\frac{24 \sqrt{b} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (2 b c-a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{5 a^{7/2} e^4 \sqrt[4]{a+b x^2}}-\frac{2 c}{5 a e (e x)^{5/2} \left(a+b x^2\right)^{5/4}}",1,"(-2*c)/(5*a*e*(e*x)^(5/2)*(a + b*x^2)^(5/4)) - (2*(2*b*c - a*d))/(5*a^2*e^3*Sqrt[e*x]*(a + b*x^2)^(5/4)) + (12*(2*b*c - a*d))/(5*a^3*e^3*Sqrt[e*x]*(a + b*x^2)^(1/4)) - (24*Sqrt[b]*(2*b*c - a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(5*a^(7/2)*e^4*(a + b*x^2)^(1/4))","A",6,6,26,0.2308,1,"{453, 290, 286, 284, 335, 196}"
1138,1,219,0,0.1233401,"\int \frac{c+d x^2}{(e x)^{11/2} \left(a+b x^2\right)^{9/4}} \, dx","Int[(c + d*x^2)/((e*x)^(11/2)*(a + b*x^2)^(9/4)),x]","\frac{16 b^{3/2} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (14 b c-9 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{9/2} e^6 \sqrt[4]{a+b x^2}}-\frac{8 b (14 b c-9 a d)}{15 a^4 e^5 \sqrt{e x} \sqrt[4]{a+b x^2}}+\frac{4 (14 b c-9 a d)}{45 a^3 e^3 (e x)^{5/2} \sqrt[4]{a+b x^2}}-\frac{2 (14 b c-9 a d)}{45 a^2 e^3 (e x)^{5/2} \left(a+b x^2\right)^{5/4}}-\frac{2 c}{9 a e (e x)^{9/2} \left(a+b x^2\right)^{5/4}}","\frac{16 b^{3/2} \sqrt{e x} \sqrt[4]{\frac{a}{b x^2}+1} (14 b c-9 a d) E\left(\left.\frac{1}{2} \cot ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{a}}\right)\right|2\right)}{15 a^{9/2} e^6 \sqrt[4]{a+b x^2}}-\frac{8 b (14 b c-9 a d)}{15 a^4 e^5 \sqrt{e x} \sqrt[4]{a+b x^2}}+\frac{4 (14 b c-9 a d)}{45 a^3 e^3 (e x)^{5/2} \sqrt[4]{a+b x^2}}-\frac{2 (14 b c-9 a d)}{45 a^2 e^3 (e x)^{5/2} \left(a+b x^2\right)^{5/4}}-\frac{2 c}{9 a e (e x)^{9/2} \left(a+b x^2\right)^{5/4}}",1,"(-2*c)/(9*a*e*(e*x)^(9/2)*(a + b*x^2)^(5/4)) - (2*(14*b*c - 9*a*d))/(45*a^2*e^3*(e*x)^(5/2)*(a + b*x^2)^(5/4)) + (4*(14*b*c - 9*a*d))/(45*a^3*e^3*(e*x)^(5/2)*(a + b*x^2)^(1/4)) - (8*b*(14*b*c - 9*a*d))/(15*a^4*e^5*Sqrt[e*x]*(a + b*x^2)^(1/4)) + (16*b^(3/2)*(14*b*c - 9*a*d)*(1 + a/(b*x^2))^(1/4)*Sqrt[e*x]*EllipticE[ArcCot[(Sqrt[b]*x)/Sqrt[a]]/2, 2])/(15*a^(9/2)*e^6*(a + b*x^2)^(1/4))","A",7,6,26,0.2308,1,"{453, 290, 286, 284, 335, 196}"
1139,1,101,0,0.0790094,"\int (e x)^m \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[(e*x)^m*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{m+1}{2};-p,-q;\frac{m+3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{e (m+1)}","\frac{(e x)^{m+1} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{m+1}{2};-p,-q;\frac{m+3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{e (m+1)}",1,"((e*x)^(1 + m)*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[(1 + m)/2, -p, -q, (3 + m)/2, -((b*x^2)/a), -((d*x^2)/c)])/(e*(1 + m)*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,24,0.08333,1,"{511, 510}"
1140,1,84,0,0.0693624,"\int x^4 \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[x^4*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{1}{5} x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{5}{2};-p,-q;\frac{7}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)","\frac{1}{5} x^5 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{5}{2};-p,-q;\frac{7}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)",1,"(x^5*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[5/2, -p, -q, 7/2, -((b*x^2)/a), -((d*x^2)/c)])/(5*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,22,0.09091,1,"{511, 510}"
1141,1,84,0,0.0700929,"\int x^2 \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[x^2*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{1}{3} x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)","\frac{1}{3} x^3 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{3}{2};-p,-q;\frac{5}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)",1,"(x^3*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[3/2, -p, -q, 5/2, -((b*x^2)/a), -((d*x^2)/c)])/(3*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,22,0.09091,1,"{511, 510}"
1142,1,79,0,0.0421726,"\int \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[(a + b*x^2)^p*(c + d*x^2)^q,x]","x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)","x \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{1}{2};-p,-q;\frac{3}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)",1,"(x*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[1/2, -p, -q, 3/2, -((b*x^2)/a), -((d*x^2)/c)])/((1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,19,0.1053,1,"{430, 429}"
1143,1,82,0,0.0686437,"\int \frac{\left(a+b x^2\right)^p \left(c+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+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{1}{2};-p,-q;\frac{1}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{x}","-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{1}{2};-p,-q;\frac{1}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{x}",1,"-(((a + b*x^2)^p*(c + d*x^2)^q*AppellF1[-1/2, -p, -q, 1/2, -((b*x^2)/a), -((d*x^2)/c)])/(x*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q))","A",3,2,22,0.09091,1,"{511, 510}"
1144,1,84,0,0.0696001,"\int \frac{\left(a+b x^2\right)^p \left(c+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+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{3}{2};-p,-q;-\frac{1}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{3 x^3}","-\frac{\left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{3}{2};-p,-q;-\frac{1}{2};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{3 x^3}",1,"-((a + b*x^2)^p*(c + d*x^2)^q*AppellF1[-3/2, -p, -q, -1/2, -((b*x^2)/a), -((d*x^2)/c)])/(3*x^3*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,22,0.09091,1,"{511, 510}"
1145,1,242,0,0.3102256,"\int x^5 \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[x^5*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(a^2 d^2 \left(q^2+3 q+2\right)+2 a b c d (p+1) (q+1)+b^2 c^2 \left(p^2+3 p+2\right)\right) \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d}\right)}{2 b^3 d^2 (p+1) (p+q+2) (p+q+3)}-\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^{q+1} (a d (q+2)+b c (p+2))}{2 b^2 d^2 (p+q+2) (p+q+3)}+\frac{x^2 \left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^{q+1}}{2 b d (p+q+3)}","\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(a^2 d^2 \left(q^2+3 q+2\right)+2 a b c d (p+1) (q+1)+b^2 c^2 \left(p^2+3 p+2\right)\right) \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d}\right)}{2 b^3 d^2 (p+1) (p+q+2) (p+q+3)}-\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^{q+1} (a d (q+2)+b c (p+2))}{2 b^2 d^2 (p+q+2) (p+q+3)}+\frac{x^2 \left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^{q+1}}{2 b d (p+q+3)}",1,"-((b*c*(2 + p) + a*d*(2 + q))*(a + b*x^2)^(1 + p)*(c + d*x^2)^(1 + q))/(2*b^2*d^2*(2 + p + q)*(3 + p + q)) + (x^2*(a + b*x^2)^(1 + p)*(c + d*x^2)^(1 + q))/(2*b*d*(3 + p + q)) + ((b^2*c^2*(2 + 3*p + p^2) + 2*a*b*c*d*(1 + p)*(1 + q) + a^2*d^2*(2 + 3*q + q^2))*(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^3*d^2*(1 + p)*(2 + p + q)*(3 + p + q)*((b*(c + d*x^2))/(b*c - a*d))^q)","A",5,5,22,0.2273,1,"{446, 90, 80, 70, 69}"
1146,1,146,0,0.1231539,"\int x^3 \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[x^3*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^{q+1}}{2 b d (p+q+2)}-\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q (a d (q+1)+b c (p+1)) \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d}\right)}{2 b^2 d (p+1) (p+q+2)}","\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^{q+1}}{2 b d (p+q+2)}-\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q (a d (q+1)+b c (p+1)) \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d}\right)}{2 b^2 d (p+1) (p+q+2)}",1,"((a + b*x^2)^(1 + p)*(c + d*x^2)^(1 + q))/(2*b*d*(2 + p + q)) - ((b*c*(1 + p) + a*d*(1 + q))*(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^2*d*(1 + p)*(2 + p + q)*((b*(c + d*x^2))/(b*c - a*d))^q)","A",4,4,22,0.1818,1,"{446, 80, 70, 69}"
1147,1,85,0,0.062654,"\int x \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[x*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d}\right)}{2 b (p+1)}","\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} \, _2F_1\left(p+1,-q;p+2;-\frac{d \left(b x^2+a\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",3,3,20,0.1500,1,"{444, 70, 69}"
1148,1,97,0,0.0934395,"\int \frac{\left(a+b x^2\right)^p \left(c+d x^2\right)^q}{x} \, dx","Int[((a + b*x^2)^p*(c + d*x^2)^q)/x,x]","-\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,1;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d},\frac{b x^2+a}{a}\right)}{2 a (p+1)}","-\frac{\left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,1;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d},\frac{b x^2+a}{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}"
1149,1,98,0,0.0884946,"\int \frac{\left(a+b x^2\right)^p \left(c+d x^2\right)^q}{x^3} \, dx","Int[((a + b*x^2)^p*(c + d*x^2)^q)/x^3,x]","\frac{b \left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,2;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d},\frac{b x^2+a}{a}\right)}{2 a^2 (p+1)}","\frac{b \left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,2;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d},\frac{b x^2+a}{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",3,3,22,0.1364,1,"{446, 137, 136}"
1150,1,100,0,0.0891192,"\int \frac{\left(a+b x^2\right)^p \left(c+d x^2\right)^q}{x^5} \, dx","Int[((a + b*x^2)^p*(c + d*x^2)^q)/x^5,x]","-\frac{b^2 \left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,3;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d},\frac{b x^2+a}{a}\right)}{2 a^3 (p+1)}","-\frac{b^2 \left(a+b x^2\right)^{p+1} \left(c+d x^2\right)^q \left(\frac{b \left(c+d x^2\right)}{b c-a d}\right)^{-q} F_1\left(p+1;-q,3;p+2;-\frac{d \left(b x^2+a\right)}{b c-a d},\frac{b x^2+a}{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}"
1151,1,91,0,0.0781048,"\int (e x)^{5/2} \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[(e*x)^(5/2)*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{2 (e x)^{7/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{7}{4};-p,-q;\frac{11}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{7 e}","\frac{2 (e x)^{7/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{7}{4};-p,-q;\frac{11}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{7 e}",1,"(2*(e*x)^(7/2)*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[7/4, -p, -q, 11/4, -((b*x^2)/a), -((d*x^2)/c)])/(7*e*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,26,0.07692,1,"{511, 510}"
1152,1,91,0,0.0747216,"\int (e x)^{3/2} \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[(e*x)^(3/2)*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{2 (e x)^{5/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{5}{4};-p,-q;\frac{9}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{5 e}","\frac{2 (e x)^{5/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{5}{4};-p,-q;\frac{9}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{5 e}",1,"(2*(e*x)^(5/2)*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[5/4, -p, -q, 9/4, -((b*x^2)/a), -((d*x^2)/c)])/(5*e*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,26,0.07692,1,"{511, 510}"
1153,1,91,0,0.0716873,"\int \sqrt{e x} \left(a+b x^2\right)^p \left(c+d x^2\right)^q \, dx","Int[Sqrt[e*x]*(a + b*x^2)^p*(c + d*x^2)^q,x]","\frac{2 (e x)^{3/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{3}{4};-p,-q;\frac{7}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{3 e}","\frac{2 (e x)^{3/2} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{3}{4};-p,-q;\frac{7}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{3 e}",1,"(2*(e*x)^(3/2)*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[3/4, -p, -q, 7/4, -((b*x^2)/a), -((d*x^2)/c)])/(3*e*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,26,0.07692,1,"{511, 510}"
1154,1,89,0,0.0720401,"\int \frac{\left(a+b x^2\right)^p \left(c+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+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{1}{4};-p,-q;\frac{5}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{e}","\frac{2 \sqrt{e x} \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(\frac{1}{4};-p,-q;\frac{5}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{e}",1,"(2*Sqrt[e*x]*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[1/4, -p, -q, 5/4, -((b*x^2)/a), -((d*x^2)/c)])/(e*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,26,0.07692,1,"{511, 510}"
1155,1,89,0,0.0762054,"\int \frac{\left(a+b x^2\right)^p \left(c+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+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{1}{4};-p,-q;\frac{3}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{e \sqrt{e x}}","-\frac{2 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{1}{4};-p,-q;\frac{3}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{e \sqrt{e x}}",1,"(-2*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[-1/4, -p, -q, 3/4, -((b*x^2)/a), -((d*x^2)/c)])/(e*Sqrt[e*x]*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,26,0.07692,1,"{511, 510}"
1156,1,91,0,0.076363,"\int \frac{\left(a+b x^2\right)^p \left(c+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+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{3}{4};-p,-q;\frac{1}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{3 e (e x)^{3/2}}","-\frac{2 \left(a+b x^2\right)^p \left(\frac{b x^2}{a}+1\right)^{-p} \left(c+d x^2\right)^q \left(\frac{d x^2}{c}+1\right)^{-q} F_1\left(-\frac{3}{4};-p,-q;\frac{1}{4};-\frac{b x^2}{a},-\frac{d x^2}{c}\right)}{3 e (e x)^{3/2}}",1,"(-2*(a + b*x^2)^p*(c + d*x^2)^q*AppellF1[-3/4, -p, -q, 1/4, -((b*x^2)/a), -((d*x^2)/c)])/(3*e*(e*x)^(3/2)*(1 + (b*x^2)/a)^p*(1 + (d*x^2)/c)^q)","A",3,2,26,0.07692,1,"{511, 510}"