1,1,33,0,0.027026,"\int x^2 \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[x^2*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{1}{7} x^7 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{9} B c x^9","\frac{1}{7} x^7 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{9} B c x^9",1,"(A*b*x^5)/5 + ((b*B + A*c)*x^7)/7 + (B*c*x^9)/9","A",3,2,22,0.09091,1,"{1584, 448}"
2,1,33,0,0.0405135,"\int x \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[x*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{1}{6} x^6 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{8} B c x^8","\frac{1}{6} x^6 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{8} B c x^8",1,"(A*b*x^4)/4 + ((b*B + A*c)*x^6)/6 + (B*c*x^8)/8","A",4,3,20,0.1500,1,"{1584, 446, 76}"
3,1,33,0,0.0242327,"\int \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{1}{5} x^5 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{7} B c x^7","\frac{1}{5} x^5 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{7} B c x^7",1,"(A*b*x^3)/3 + ((b*B + A*c)*x^5)/5 + (B*c*x^7)/7","A",3,2,19,0.1053,1,"{1593, 448}"
4,1,33,0,0.0375626,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x,x]","\frac{1}{4} x^4 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{6} B c x^6","\frac{1}{4} x^4 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{6} B c x^6",1,"(A*b*x^2)/2 + ((b*B + A*c)*x^4)/4 + (B*c*x^6)/6","A",4,3,22,0.1364,1,"{1584, 444, 43}"
5,1,28,0,0.018882,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^2} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^2,x]","\frac{1}{3} x^3 (A c+b B)+A b x+\frac{1}{5} B c x^5","\frac{1}{3} x^3 (A c+b B)+A b x+\frac{1}{5} B c x^5",1,"A*b*x + ((b*B + A*c)*x^3)/3 + (B*c*x^5)/5","A",3,2,22,0.09091,1,"{1584, 373}"
6,1,29,0,0.027211,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^3} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^3,x]","\frac{1}{2} x^2 (A c+b B)+A b \log (x)+\frac{1}{4} B c x^4","\frac{1}{2} x^2 (A c+b B)+A b \log (x)+\frac{1}{4} B c x^4",1,"((b*B + A*c)*x^2)/2 + (B*c*x^4)/4 + A*b*Log[x]","A",4,3,22,0.1364,1,"{1584, 446, 76}"
7,1,26,0,0.0234336,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^4} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^4,x]","x (A c+b B)-\frac{A b}{x}+\frac{1}{3} B c x^3","x (A c+b B)-\frac{A b}{x}+\frac{1}{3} B c x^3",1,"-((A*b)/x) + (b*B + A*c)*x + (B*c*x^3)/3","A",3,2,22,0.09091,1,"{1584, 448}"
8,1,29,0,0.0275993,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^5} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^5,x]","\log (x) (A c+b B)-\frac{A b}{2 x^2}+\frac{1}{2} B c x^2","\log (x) (A c+b B)-\frac{A b}{2 x^2}+\frac{1}{2} B c x^2",1,"-(A*b)/(2*x^2) + (B*c*x^2)/2 + (b*B + A*c)*Log[x]","A",4,3,22,0.1364,1,"{1584, 446, 76}"
9,1,26,0,0.0220519,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^6} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^6,x]","-\frac{A c+b B}{x}-\frac{A b}{3 x^3}+B c x","-\frac{A c+b B}{x}-\frac{A b}{3 x^3}+B c x",1,"-(A*b)/(3*x^3) - (b*B + A*c)/x + B*c*x","A",3,2,22,0.09091,1,"{1584, 448}"
10,1,29,0,0.0269632,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^7} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^7,x]","-\frac{A c+b B}{2 x^2}-\frac{A b}{4 x^4}+B c \log (x)","-\frac{A c+b B}{2 x^2}-\frac{A b}{4 x^4}+B c \log (x)",1,"-(A*b)/(4*x^4) - (b*B + A*c)/(2*x^2) + B*c*Log[x]","A",4,3,22,0.1364,1,"{1584, 446, 76}"
11,1,31,0,0.0218235,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^8} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^8,x]","-\frac{A c+b B}{3 x^3}-\frac{A b}{5 x^5}-\frac{B c}{x}","-\frac{A c+b B}{3 x^3}-\frac{A b}{5 x^5}-\frac{B c}{x}",1,"-(A*b)/(5*x^5) - (b*B + A*c)/(3*x^3) - (B*c)/x","A",3,2,22,0.09091,1,"{1584, 448}"
12,1,55,0,0.0475207,"\int \left(A+B x^2\right) \left(b x^2+c x^4\right)^2 \, dx","Int[(A + B*x^2)*(b*x^2 + c*x^4)^2,x]","\frac{1}{5} A b^2 x^5+\frac{1}{9} c x^9 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{11} B c^2 x^{11}","\frac{1}{5} A b^2 x^5+\frac{1}{9} c x^9 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{11} B c^2 x^{11}",1,"(A*b^2*x^5)/5 + (b*(b*B + 2*A*c)*x^7)/7 + (c*(2*b*B + A*c)*x^9)/9 + (B*c^2*x^11)/11","A",3,2,21,0.09524,1,"{1593, 448}"
13,1,55,0,0.0676805,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x,x]","\frac{1}{4} A b^2 x^4+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{10} B c^2 x^{10}","\frac{1}{4} A b^2 x^4+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{10} B c^2 x^{10}",1,"(A*b^2*x^4)/4 + (b*(b*B + 2*A*c)*x^6)/6 + (c*(2*b*B + A*c)*x^8)/8 + (B*c^2*x^10)/10","A",4,3,24,0.1250,1,"{1584, 446, 76}"
14,1,55,0,0.038727,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^2} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^2,x]","\frac{1}{3} A b^2 x^3+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{9} B c^2 x^9","\frac{1}{3} A b^2 x^3+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{9} B c^2 x^9",1,"(A*b^2*x^3)/3 + (b*(b*B + 2*A*c)*x^5)/5 + (c*(2*b*B + A*c)*x^7)/7 + (B*c^2*x^9)/9","A",3,2,24,0.08333,1,"{1584, 448}"
15,1,42,0,0.0696529,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^3} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^3,x]","\frac{B \left(b+c x^2\right)^4}{8 c^2}-\frac{\left(b+c x^2\right)^3 (b B-A c)}{6 c^2}","\frac{B \left(b+c x^2\right)^4}{8 c^2}-\frac{\left(b+c x^2\right)^3 (b B-A c)}{6 c^2}",1,"-((b*B - A*c)*(b + c*x^2)^3)/(6*c^2) + (B*(b + c*x^2)^4)/(8*c^2)","A",4,3,24,0.1250,1,"{1584, 444, 43}"
16,1,50,0,0.0322901,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^4} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^4,x]","A b^2 x+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{7} B c^2 x^7","A b^2 x+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{7} B c^2 x^7",1,"A*b^2*x + (b*(b*B + 2*A*c)*x^3)/3 + (c*(2*b*B + A*c)*x^5)/5 + (B*c^2*x^7)/7","A",3,2,24,0.08333,1,"{1584, 373}"
17,1,43,0,0.0402506,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^5} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^5,x]","A b^2 \log (x)+A b c x^2+\frac{1}{4} A c^2 x^4+\frac{B \left(b+c x^2\right)^3}{6 c}","A b^2 \log (x)+A b c x^2+\frac{1}{4} A c^2 x^4+\frac{B \left(b+c x^2\right)^3}{6 c}",1,"A*b*c*x^2 + (A*c^2*x^4)/4 + (B*(b + c*x^2)^3)/(6*c) + A*b^2*Log[x]","A",5,4,24,0.1667,1,"{1584, 446, 80, 43}"
18,1,48,0,0.037229,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^6} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^6,x]","-\frac{A b^2}{x}+\frac{1}{3} c x^3 (A c+2 b B)+b x (2 A c+b B)+\frac{1}{5} B c^2 x^5","-\frac{A b^2}{x}+\frac{1}{3} c x^3 (A c+2 b B)+b x (2 A c+b B)+\frac{1}{5} B c^2 x^5",1,"-((A*b^2)/x) + b*(b*B + 2*A*c)*x + (c*(2*b*B + A*c)*x^3)/3 + (B*c^2*x^5)/5","A",3,2,24,0.08333,1,"{1584, 448}"
19,1,51,0,0.053257,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^7} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^7,x]","-\frac{A b^2}{2 x^2}+\frac{1}{2} c x^2 (A c+2 b B)+b \log (x) (2 A c+b B)+\frac{1}{4} B c^2 x^4","-\frac{A b^2}{2 x^2}+\frac{1}{2} c x^2 (A c+2 b B)+b \log (x) (2 A c+b B)+\frac{1}{4} B c^2 x^4",1,"-(A*b^2)/(2*x^2) + (c*(2*b*B + A*c)*x^2)/2 + (B*c^2*x^4)/4 + b*(b*B + 2*A*c)*Log[x]","A",4,3,24,0.1250,1,"{1584, 446, 76}"
20,1,48,0,0.0368726,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^8} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^8,x]","-\frac{A b^2}{3 x^3}+c x (A c+2 b B)-\frac{b (2 A c+b B)}{x}+\frac{1}{3} B c^2 x^3","-\frac{A b^2}{3 x^3}+c x (A c+2 b B)-\frac{b (2 A c+b B)}{x}+\frac{1}{3} B c^2 x^3",1,"-(A*b^2)/(3*x^3) - (b*(b*B + 2*A*c))/x + c*(2*b*B + A*c)*x + (B*c^2*x^3)/3","A",3,2,24,0.08333,1,"{1584, 448}"
21,1,51,0,0.0473707,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^9} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^9,x]","-\frac{A b^2}{4 x^4}-\frac{b (2 A c+b B)}{2 x^2}+c \log (x) (A c+2 b B)+\frac{1}{2} B c^2 x^2","-\frac{A b^2}{4 x^4}-\frac{b (2 A c+b B)}{2 x^2}+c \log (x) (A c+2 b B)+\frac{1}{2} B c^2 x^2",1,"-(A*b^2)/(4*x^4) - (b*(b*B + 2*A*c))/(2*x^2) + (B*c^2*x^2)/2 + c*(2*b*B + A*c)*Log[x]","A",4,3,24,0.1250,1,"{1584, 446, 76}"
22,1,48,0,0.036689,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^{10}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^10,x]","-\frac{A b^2}{5 x^5}-\frac{b (2 A c+b B)}{3 x^3}-\frac{c (A c+2 b B)}{x}+B c^2 x","-\frac{A b^2}{5 x^5}-\frac{b (2 A c+b B)}{3 x^3}-\frac{c (A c+2 b B)}{x}+B c^2 x",1,"-(A*b^2)/(5*x^5) - (b*(b*B + 2*A*c))/(3*x^3) - (c*(2*b*B + A*c))/x + B*c^2*x","A",3,2,24,0.08333,1,"{1584, 448}"
23,1,51,0,0.044925,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^{11}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^11,x]","-\frac{A b^2}{6 x^6}-\frac{b (2 A c+b B)}{4 x^4}-\frac{c (A c+2 b B)}{2 x^2}+B c^2 \log (x)","-\frac{A b^2}{6 x^6}-\frac{b (2 A c+b B)}{4 x^4}-\frac{c (A c+2 b B)}{2 x^2}+B c^2 \log (x)",1,"-(A*b^2)/(6*x^6) - (b*(b*B + 2*A*c))/(4*x^4) - (c*(2*b*B + A*c))/(2*x^2) + B*c^2*Log[x]","A",4,3,24,0.1250,1,"{1584, 446, 76}"
24,1,53,0,0.0358008,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^{12}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^12,x]","-\frac{A b^2}{7 x^7}-\frac{b (2 A c+b B)}{5 x^5}-\frac{c (A c+2 b B)}{3 x^3}-\frac{B c^2}{x}","-\frac{A b^2}{7 x^7}-\frac{b (2 A c+b B)}{5 x^5}-\frac{c (A c+2 b B)}{3 x^3}-\frac{B c^2}{x}",1,"-(A*b^2)/(7*x^7) - (b*(b*B + 2*A*c))/(5*x^5) - (c*(2*b*B + A*c))/(3*x^3) - (B*c^2)/x","A",3,2,24,0.08333,1,"{1584, 448}"
25,1,75,0,0.0643977,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^2} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^2,x]","\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{13} B c^3 x^{13}","\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{11} c^2 x^{11} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{13} B c^3 x^{13}",1,"(A*b^3*x^5)/5 + (b^2*(b*B + 3*A*c)*x^7)/7 + (b*c*(b*B + A*c)*x^9)/3 + (c^2*(3*b*B + A*c)*x^11)/11 + (B*c^3*x^13)/13","A",3,2,24,0.08333,1,"{1584, 448}"
26,1,68,0,0.1343469,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^3} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^3,x]","-\frac{\left(b+c x^2\right)^5 (2 b B-A c)}{10 c^3}+\frac{b \left(b+c x^2\right)^4 (b B-A c)}{8 c^3}+\frac{B \left(b+c x^2\right)^6}{12 c^3}","-\frac{\left(b+c x^2\right)^5 (2 b B-A c)}{10 c^3}+\frac{b \left(b+c x^2\right)^4 (b B-A c)}{8 c^3}+\frac{B \left(b+c x^2\right)^6}{12 c^3}",1,"(b*(b*B - A*c)*(b + c*x^2)^4)/(8*c^3) - ((2*b*B - A*c)*(b + c*x^2)^5)/(10*c^3) + (B*(b + c*x^2)^6)/(12*c^3)","A",4,3,24,0.1250,1,"{1584, 446, 76}"
27,1,75,0,0.0552321,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^4} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^4,x]","\frac{1}{5} b^2 x^5 (3 A c+b B)+\frac{1}{3} A b^3 x^3+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{11} B c^3 x^{11}","\frac{1}{5} b^2 x^5 (3 A c+b B)+\frac{1}{3} A b^3 x^3+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{11} B c^3 x^{11}",1,"(A*b^3*x^3)/3 + (b^2*(b*B + 3*A*c)*x^5)/5 + (3*b*c*(b*B + A*c)*x^7)/7 + (c^2*(3*b*B + A*c)*x^9)/9 + (B*c^3*x^11)/11","A",3,2,24,0.08333,1,"{1584, 448}"
28,1,42,0,0.0706387,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^5} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^5,x]","\frac{B \left(b+c x^2\right)^5}{10 c^2}-\frac{\left(b+c x^2\right)^4 (b B-A c)}{8 c^2}","\frac{B \left(b+c x^2\right)^5}{10 c^2}-\frac{\left(b+c x^2\right)^4 (b B-A c)}{8 c^2}",1,"-((b*B - A*c)*(b + c*x^2)^4)/(8*c^2) + (B*(b + c*x^2)^5)/(10*c^2)","A",4,3,24,0.1250,1,"{1584, 444, 43}"
29,1,70,0,0.0416425,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^6} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^6,x]","\frac{1}{3} b^2 x^3 (3 A c+b B)+A b^3 x+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{9} B c^3 x^9","\frac{1}{3} b^2 x^3 (3 A c+b B)+A b^3 x+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{9} B c^3 x^9",1,"A*b^3*x + (b^2*(b*B + 3*A*c)*x^3)/3 + (3*b*c*(b*B + A*c)*x^5)/5 + (c^2*(3*b*B + A*c)*x^7)/7 + (B*c^3*x^9)/9","A",3,2,24,0.08333,1,"{1584, 373}"
30,1,60,0,0.0528008,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^7} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^7,x]","\frac{3}{2} A b^2 c x^2+A b^3 \log (x)+\frac{3}{4} A b c^2 x^4+\frac{1}{6} A c^3 x^6+\frac{B \left(b+c x^2\right)^4}{8 c}","\frac{3}{2} A b^2 c x^2+A b^3 \log (x)+\frac{3}{4} A b c^2 x^4+\frac{1}{6} A c^3 x^6+\frac{B \left(b+c x^2\right)^4}{8 c}",1,"(3*A*b^2*c*x^2)/2 + (3*A*b*c^2*x^4)/4 + (A*c^3*x^6)/6 + (B*(b + c*x^2)^4)/(8*c) + A*b^3*Log[x]","A",5,4,24,0.1667,1,"{1584, 446, 80, 43}"
31,1,65,0,0.0454822,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^8} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^8,x]","b^2 x (3 A c+b B)-\frac{A b^3}{x}+\frac{1}{5} c^2 x^5 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{7} B c^3 x^7","b^2 x (3 A c+b B)-\frac{A b^3}{x}+\frac{1}{5} c^2 x^5 (A c+3 b B)+b c x^3 (A c+b B)+\frac{1}{7} B c^3 x^7",1,"-((A*b^3)/x) + b^2*(b*B + 3*A*c)*x + b*c*(b*B + A*c)*x^3 + (c^2*(3*b*B + A*c)*x^5)/5 + (B*c^3*x^7)/7","A",3,2,24,0.08333,1,"{1584, 448}"
32,1,71,0,0.0789122,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^9} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^9,x]","b^2 \log (x) (3 A c+b B)-\frac{A b^3}{2 x^2}+\frac{1}{4} c^2 x^4 (A c+3 b B)+\frac{3}{2} b c x^2 (A c+b B)+\frac{1}{6} B c^3 x^6","b^2 \log (x) (3 A c+b B)-\frac{A b^3}{2 x^2}+\frac{1}{4} c^2 x^4 (A c+3 b B)+\frac{3}{2} b c x^2 (A c+b B)+\frac{1}{6} B c^3 x^6",1,"-(A*b^3)/(2*x^2) + (3*b*c*(b*B + A*c)*x^2)/2 + (c^2*(3*b*B + A*c)*x^4)/4 + (B*c^3*x^6)/6 + b^2*(b*B + 3*A*c)*Log[x]","A",4,3,24,0.1250,1,"{1584, 446, 76}"
33,1,69,0,0.0495511,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{10}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^10,x]","-\frac{b^2 (3 A c+b B)}{x}-\frac{A b^3}{3 x^3}+\frac{1}{3} c^2 x^3 (A c+3 b B)+3 b c x (A c+b B)+\frac{1}{5} B c^3 x^5","-\frac{b^2 (3 A c+b B)}{x}-\frac{A b^3}{3 x^3}+\frac{1}{3} c^2 x^3 (A c+3 b B)+3 b c x (A c+b B)+\frac{1}{5} B c^3 x^5",1,"-(A*b^3)/(3*x^3) - (b^2*(b*B + 3*A*c))/x + 3*b*c*(b*B + A*c)*x + (c^2*(3*b*B + A*c)*x^3)/3 + (B*c^3*x^5)/5","A",3,2,24,0.08333,1,"{1584, 448}"
34,1,72,0,0.0719043,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{11}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^11,x]","-\frac{b^2 (3 A c+b B)}{2 x^2}-\frac{A b^3}{4 x^4}+\frac{1}{2} c^2 x^2 (A c+3 b B)+3 b c \log (x) (A c+b B)+\frac{1}{4} B c^3 x^4","-\frac{b^2 (3 A c+b B)}{2 x^2}-\frac{A b^3}{4 x^4}+\frac{1}{2} c^2 x^2 (A c+3 b B)+3 b c \log (x) (A c+b B)+\frac{1}{4} B c^3 x^4",1,"-(A*b^3)/(4*x^4) - (b^2*(b*B + 3*A*c))/(2*x^2) + (c^2*(3*b*B + A*c)*x^2)/2 + (B*c^3*x^4)/4 + 3*b*c*(b*B + A*c)*Log[x]","A",4,3,24,0.1250,1,"{1584, 446, 76}"
35,1,68,0,0.0495744,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{12}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^12,x]","-\frac{b^2 (3 A c+b B)}{3 x^3}-\frac{A b^3}{5 x^5}+c^2 x (A c+3 b B)-\frac{3 b c (A c+b B)}{x}+\frac{1}{3} B c^3 x^3","-\frac{b^2 (3 A c+b B)}{3 x^3}-\frac{A b^3}{5 x^5}+c^2 x (A c+3 b B)-\frac{3 b c (A c+b B)}{x}+\frac{1}{3} B c^3 x^3",1,"-(A*b^3)/(5*x^5) - (b^2*(b*B + 3*A*c))/(3*x^3) - (3*b*c*(b*B + A*c))/x + c^2*(3*b*B + A*c)*x + (B*c^3*x^3)/3","A",3,2,24,0.08333,1,"{1584, 448}"
36,1,71,0,0.0640838,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{13}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^13,x]","-\frac{b^2 (3 A c+b B)}{4 x^4}-\frac{A b^3}{6 x^6}+c^2 \log (x) (A c+3 b B)-\frac{3 b c (A c+b B)}{2 x^2}+\frac{1}{2} B c^3 x^2","-\frac{b^2 (3 A c+b B)}{4 x^4}-\frac{A b^3}{6 x^6}+c^2 \log (x) (A c+3 b B)-\frac{3 b c (A c+b B)}{2 x^2}+\frac{1}{2} B c^3 x^2",1,"-(A*b^3)/(6*x^6) - (b^2*(b*B + 3*A*c))/(4*x^4) - (3*b*c*(b*B + A*c))/(2*x^2) + (B*c^3*x^2)/2 + c^2*(3*b*B + A*c)*Log[x]","A",4,3,24,0.1250,1,"{1584, 446, 76}"
37,1,66,0,0.0495761,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{14}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^14,x]","-\frac{b^2 (3 A c+b B)}{5 x^5}-\frac{A b^3}{7 x^7}-\frac{c^2 (A c+3 b B)}{x}-\frac{b c (A c+b B)}{x^3}+B c^3 x","-\frac{b^2 (3 A c+b B)}{5 x^5}-\frac{A b^3}{7 x^7}-\frac{c^2 (A c+3 b B)}{x}-\frac{b c (A c+b B)}{x^3}+B c^3 x",1,"-(A*b^3)/(7*x^7) - (b^2*(b*B + 3*A*c))/(5*x^5) - (b*c*(b*B + A*c))/x^3 - (c^2*(3*b*B + A*c))/x + B*c^3*x","A",3,2,24,0.08333,1,"{1584, 448}"
38,1,63,0,0.0467981,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{15}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^15,x]","-\frac{A \left(b+c x^2\right)^4}{8 b x^8}-\frac{3 b^2 B c}{4 x^4}-\frac{b^3 B}{6 x^6}-\frac{3 b B c^2}{2 x^2}+B c^3 \log (x)","-\frac{A \left(b+c x^2\right)^4}{8 b x^8}-\frac{3 b^2 B c}{4 x^4}-\frac{b^3 B}{6 x^6}-\frac{3 b B c^2}{2 x^2}+B c^3 \log (x)",1,"-(b^3*B)/(6*x^6) - (3*b^2*B*c)/(4*x^4) - (3*b*B*c^2)/(2*x^2) - (A*(b + c*x^2)^4)/(8*b*x^8) + B*c^3*Log[x]","A",5,4,24,0.1667,1,"{1584, 446, 78, 43}"
39,1,73,0,0.0490503,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{16}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^16,x]","-\frac{b^2 (3 A c+b B)}{7 x^7}-\frac{A b^3}{9 x^9}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{x}","-\frac{b^2 (3 A c+b B)}{7 x^7}-\frac{A b^3}{9 x^9}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{x}",1,"-(A*b^3)/(9*x^9) - (b^2*(b*B + 3*A*c))/(7*x^7) - (3*b*c*(b*B + A*c))/(5*x^5) - (c^2*(3*b*B + A*c))/(3*x^3) - (B*c^3)/x","A",3,2,24,0.08333,1,"{1584, 448}"
40,1,49,0,0.0397545,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{17}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^17,x]","-\frac{\left(b+c x^2\right)^4 (5 b B-A c)}{40 b^2 x^8}-\frac{A \left(b+c x^2\right)^4}{10 b x^{10}}","-\frac{\left(b+c x^2\right)^4 (5 b B-A c)}{40 b^2 x^8}-\frac{A \left(b+c x^2\right)^4}{10 b x^{10}}",1,"-(A*(b + c*x^2)^4)/(10*b*x^10) - ((5*b*B - A*c)*(b + c*x^2)^4)/(40*b^2*x^8)","A",4,4,24,0.1667,1,"{1584, 446, 78, 37}"
41,1,119,0,0.0874827,"\int \frac{x^{10} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^10*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{b^2 x^3 (b B-A c)}{3 c^4}+\frac{b^3 x (b B-A c)}{c^5}-\frac{b^{7/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{11/2}}-\frac{x^7 (b B-A c)}{7 c^2}+\frac{b x^5 (b B-A c)}{5 c^3}+\frac{B x^9}{9 c}","-\frac{b^2 x^3 (b B-A c)}{3 c^4}+\frac{b^3 x (b B-A c)}{c^5}-\frac{b^{7/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{11/2}}-\frac{x^7 (b B-A c)}{7 c^2}+\frac{b x^5 (b B-A c)}{5 c^3}+\frac{B x^9}{9 c}",1,"(b^3*(b*B - A*c)*x)/c^5 - (b^2*(b*B - A*c)*x^3)/(3*c^4) + (b*(b*B - A*c)*x^5)/(5*c^3) - ((b*B - A*c)*x^7)/(7*c^2) + (B*x^9)/(9*c) - (b^(7/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(11/2)","A",5,4,24,0.1667,1,"{1584, 459, 302, 205}"
42,1,96,0,0.1264031,"\int \frac{x^9 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^9*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{b^2 x^2 (b B-A c)}{2 c^4}+\frac{b^3 (b B-A c) \log \left(b+c x^2\right)}{2 c^5}-\frac{x^6 (b B-A c)}{6 c^2}+\frac{b x^4 (b B-A c)}{4 c^3}+\frac{B x^8}{8 c}","-\frac{b^2 x^2 (b B-A c)}{2 c^4}+\frac{b^3 (b B-A c) \log \left(b+c x^2\right)}{2 c^5}-\frac{x^6 (b B-A c)}{6 c^2}+\frac{b x^4 (b B-A c)}{4 c^3}+\frac{B x^8}{8 c}",1,"-(b^2*(b*B - A*c)*x^2)/(2*c^4) + (b*(b*B - A*c)*x^4)/(4*c^3) - ((b*B - A*c)*x^6)/(6*c^2) + (B*x^8)/(8*c) + (b^3*(b*B - A*c)*Log[b + c*x^2])/(2*c^5)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
43,1,98,0,0.0762564,"\int \frac{x^8 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^8*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{b^2 x (b B-A c)}{c^4}+\frac{b^{5/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{9/2}}-\frac{x^5 (b B-A c)}{5 c^2}+\frac{b x^3 (b B-A c)}{3 c^3}+\frac{B x^7}{7 c}","-\frac{b^2 x (b B-A c)}{c^4}+\frac{b^{5/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{9/2}}-\frac{x^5 (b B-A c)}{5 c^2}+\frac{b x^3 (b B-A c)}{3 c^3}+\frac{B x^7}{7 c}",1,"-((b^2*(b*B - A*c)*x)/c^4) + (b*(b*B - A*c)*x^3)/(3*c^3) - ((b*B - A*c)*x^5)/(5*c^2) + (B*x^7)/(7*c) + (b^(5/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(9/2)","A",5,4,24,0.1667,1,"{1584, 459, 302, 205}"
44,1,75,0,0.0938306,"\int \frac{x^7 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^7*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{b^2 (b B-A c) \log \left(b+c x^2\right)}{2 c^4}-\frac{x^4 (b B-A c)}{4 c^2}+\frac{b x^2 (b B-A c)}{2 c^3}+\frac{B x^6}{6 c}","-\frac{b^2 (b B-A c) \log \left(b+c x^2\right)}{2 c^4}-\frac{x^4 (b B-A c)}{4 c^2}+\frac{b x^2 (b B-A c)}{2 c^3}+\frac{B x^6}{6 c}",1,"(b*(b*B - A*c)*x^2)/(2*c^3) - ((b*B - A*c)*x^4)/(4*c^2) + (B*x^6)/(6*c) - (b^2*(b*B - A*c)*Log[b + c*x^2])/(2*c^4)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
45,1,77,0,0.0657095,"\int \frac{x^6 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^6*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{b^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{7/2}}-\frac{x^3 (b B-A c)}{3 c^2}+\frac{b x (b B-A c)}{c^3}+\frac{B x^5}{5 c}","-\frac{b^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{7/2}}-\frac{x^3 (b B-A c)}{3 c^2}+\frac{b x (b B-A c)}{c^3}+\frac{B x^5}{5 c}",1,"(b*(b*B - A*c)*x)/c^3 - ((b*B - A*c)*x^3)/(3*c^2) + (B*x^5)/(5*c) - (b^(3/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(7/2)","A",5,4,24,0.1667,1,"{1584, 459, 302, 205}"
46,1,54,0,0.0687733,"\int \frac{x^5 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^5*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{x^2 (b B-A c)}{2 c^2}+\frac{b (b B-A c) \log \left(b+c x^2\right)}{2 c^3}+\frac{B x^4}{4 c}","-\frac{x^2 (b B-A c)}{2 c^2}+\frac{b (b B-A c) \log \left(b+c x^2\right)}{2 c^3}+\frac{B x^4}{4 c}",1,"-((b*B - A*c)*x^2)/(2*c^2) + (B*x^4)/(4*c) + (b*(b*B - A*c)*Log[b + c*x^2])/(2*c^3)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
47,1,58,0,0.0498338,"\int \frac{x^4 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^4*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{x (b B-A c)}{c^2}+\frac{\sqrt{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{5/2}}+\frac{B x^3}{3 c}","-\frac{x (b B-A c)}{c^2}+\frac{\sqrt{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{c^{5/2}}+\frac{B x^3}{3 c}",1,"-(((b*B - A*c)*x)/c^2) + (B*x^3)/(3*c) + (Sqrt[b]*(b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/c^(5/2)","A",4,4,24,0.1667,1,"{1584, 459, 321, 205}"
48,1,35,0,0.0431874,"\int \frac{x^3 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^3*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{B x^2}{2 c}-\frac{(b B-A c) \log \left(b+c x^2\right)}{2 c^2}","\frac{B x^2}{2 c}-\frac{(b B-A c) \log \left(b+c x^2\right)}{2 c^2}",1,"(B*x^2)/(2*c) - ((b*B - A*c)*Log[b + c*x^2])/(2*c^2)","A",4,3,24,0.1250,1,"{1584, 444, 43}"
49,1,40,0,0.0280687,"\int \frac{x^2 \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^2*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{B x}{c}-\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{\sqrt{b} c^{3/2}}","\frac{B x}{c}-\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{\sqrt{b} c^{3/2}}",1,"(B*x)/c - ((b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(Sqrt[b]*c^(3/2))","A",3,3,24,0.1250,1,"{1584, 388, 205}"
50,1,34,0,0.0407605,"\int \frac{x \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{(b B-A c) \log \left(b+c x^2\right)}{2 b c}+\frac{A \log (x)}{b}","\frac{(b B-A c) \log \left(b+c x^2\right)}{2 b c}+\frac{A \log (x)}{b}",1,"(A*Log[x])/b + ((b*B - A*c)*Log[b + c*x^2])/(2*b*c)","A",4,3,22,0.1364,1,"{1584, 446, 72}"
51,1,42,0,0.0318716,"\int \frac{A+B x^2}{b x^2+c x^4} \, dx","Int[(A + B*x^2)/(b*x^2 + c*x^4),x]","\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{3/2} \sqrt{c}}-\frac{A}{b x}","\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{3/2} \sqrt{c}}-\frac{A}{b x}",1,"-(A/(b*x)) + ((b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(b^(3/2)*Sqrt[c])","A",3,3,21,0.1429,1,"{1593, 453, 205}"
52,1,41,0,0.0344379,"\int \frac{A+B x^2}{b x^2-c x^4} \, dx","Int[(A + B*x^2)/(b*x^2 - c*x^4),x]","\frac{(A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{3/2} \sqrt{c}}-\frac{A}{b x}","\frac{(A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{3/2} \sqrt{c}}-\frac{A}{b x}",1,"-(A/(b*x)) + ((b*B + A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b]])/(b^(3/2)*Sqrt[c])","A",3,3,22,0.1364,1,"{1593, 453, 208}"
53,1,49,0,0.0557434,"\int \frac{A+B x^2}{x \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x*(b*x^2 + c*x^4)),x]","-\frac{(b B-A c) \log \left(b+c x^2\right)}{2 b^2}+\frac{\log (x) (b B-A c)}{b^2}-\frac{A}{2 b x^2}","-\frac{(b B-A c) \log \left(b+c x^2\right)}{2 b^2}+\frac{\log (x) (b B-A c)}{b^2}-\frac{A}{2 b x^2}",1,"-A/(2*b*x^2) + ((b*B - A*c)*Log[x])/b^2 - ((b*B - A*c)*Log[b + c*x^2])/(2*b^2)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
54,1,61,0,0.0558791,"\int \frac{A+B x^2}{x^2 \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^2*(b*x^2 + c*x^4)),x]","-\frac{b B-A c}{b^2 x}-\frac{\sqrt{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{5/2}}-\frac{A}{3 b x^3}","-\frac{b B-A c}{b^2 x}-\frac{\sqrt{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{5/2}}-\frac{A}{3 b x^3}",1,"-A/(3*b*x^3) - (b*B - A*c)/(b^2*x) - (Sqrt[c]*(b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/b^(5/2)","A",4,4,24,0.1667,1,"{1584, 453, 325, 205}"
55,1,70,0,0.0722856,"\int \frac{A+B x^2}{x^3 \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^3*(b*x^2 + c*x^4)),x]","-\frac{b B-A c}{2 b^2 x^2}+\frac{c (b B-A c) \log \left(b+c x^2\right)}{2 b^3}-\frac{c \log (x) (b B-A c)}{b^3}-\frac{A}{4 b x^4}","-\frac{b B-A c}{2 b^2 x^2}+\frac{c (b B-A c) \log \left(b+c x^2\right)}{2 b^3}-\frac{c \log (x) (b B-A c)}{b^3}-\frac{A}{4 b x^4}",1,"-A/(4*b*x^4) - (b*B - A*c)/(2*b^2*x^2) - (c*(b*B - A*c)*Log[x])/b^3 + (c*(b*B - A*c)*Log[b + c*x^2])/(2*b^3)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
56,1,78,0,0.0681362,"\int \frac{A+B x^2}{x^4 \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^4*(b*x^2 + c*x^4)),x]","\frac{c^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{7/2}}-\frac{b B-A c}{3 b^2 x^3}+\frac{c (b B-A c)}{b^3 x}-\frac{A}{5 b x^5}","\frac{c^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{b^{7/2}}-\frac{b B-A c}{3 b^2 x^3}+\frac{c (b B-A c)}{b^3 x}-\frac{A}{5 b x^5}",1,"-A/(5*b*x^5) - (b*B - A*c)/(3*b^2*x^3) + (c*(b*B - A*c))/(b^3*x) + (c^(3/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/b^(7/2)","A",5,4,24,0.1667,1,"{1584, 453, 325, 205}"
57,1,92,0,0.0897576,"\int \frac{A+B x^2}{x^5 \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^5*(b*x^2 + c*x^4)),x]","-\frac{c^2 (b B-A c) \log \left(b+c x^2\right)}{2 b^4}+\frac{c^2 \log (x) (b B-A c)}{b^4}+\frac{c (b B-A c)}{2 b^3 x^2}-\frac{b B-A c}{4 b^2 x^4}-\frac{A}{6 b x^6}","-\frac{c^2 (b B-A c) \log \left(b+c x^2\right)}{2 b^4}+\frac{c^2 \log (x) (b B-A c)}{b^4}+\frac{c (b B-A c)}{2 b^3 x^2}-\frac{b B-A c}{4 b^2 x^4}-\frac{A}{6 b x^6}",1,"-A/(6*b*x^6) - (b*B - A*c)/(4*b^2*x^4) + (c*(b*B - A*c))/(2*b^3*x^2) + (c^2*(b*B - A*c)*Log[x])/b^4 - (c^2*(b*B - A*c)*Log[b + c*x^2])/(2*b^4)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
58,1,133,0,0.1662862,"\int \frac{x^{12} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^12*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","-\frac{b^3 x (b B-A c)}{2 c^5 \left(b+c x^2\right)}-\frac{b^2 x (4 b B-3 A c)}{c^5}+\frac{b^{5/2} (9 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{11/2}}-\frac{x^5 (2 b B-A c)}{5 c^3}+\frac{b x^3 (3 b B-2 A c)}{3 c^4}+\frac{B x^7}{7 c^2}","-\frac{b^3 x (b B-A c)}{2 c^5 \left(b+c x^2\right)}-\frac{b^2 x (4 b B-3 A c)}{c^5}+\frac{b^{5/2} (9 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{11/2}}-\frac{x^5 (2 b B-A c)}{5 c^3}+\frac{b x^3 (3 b B-2 A c)}{3 c^4}+\frac{B x^7}{7 c^2}",1,"-((b^2*(4*b*B - 3*A*c)*x)/c^5) + (b*(3*b*B - 2*A*c)*x^3)/(3*c^4) - ((2*b*B - A*c)*x^5)/(5*c^3) + (B*x^7)/(7*c^2) - (b^3*(b*B - A*c)*x)/(2*c^5*(b + c*x^2)) + (b^(5/2)*(9*b*B - 7*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*c^(11/2))","A",5,4,24,0.1667,1,"{1584, 455, 1810, 205}"
59,1,105,0,0.1350177,"\int \frac{x^{11} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^11*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","-\frac{b^3 (b B-A c)}{2 c^5 \left(b+c x^2\right)}-\frac{b^2 (4 b B-3 A c) \log \left(b+c x^2\right)}{2 c^5}-\frac{x^4 (2 b B-A c)}{4 c^3}+\frac{b x^2 (3 b B-2 A c)}{2 c^4}+\frac{B x^6}{6 c^2}","-\frac{b^3 (b B-A c)}{2 c^5 \left(b+c x^2\right)}-\frac{b^2 (4 b B-3 A c) \log \left(b+c x^2\right)}{2 c^5}-\frac{x^4 (2 b B-A c)}{4 c^3}+\frac{b x^2 (3 b B-2 A c)}{2 c^4}+\frac{B x^6}{6 c^2}",1,"(b*(3*b*B - 2*A*c)*x^2)/(2*c^4) - ((2*b*B - A*c)*x^4)/(4*c^3) + (B*x^6)/(6*c^2) - (b^3*(b*B - A*c))/(2*c^5*(b + c*x^2)) - (b^2*(4*b*B - 3*A*c)*Log[b + c*x^2])/(2*c^5)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
60,1,110,0,0.1184712,"\int \frac{x^{10} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^10*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{b^2 x (b B-A c)}{2 c^4 \left(b+c x^2\right)}-\frac{b^{3/2} (7 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{9/2}}-\frac{x^3 (2 b B-A c)}{3 c^3}+\frac{b x (3 b B-2 A c)}{c^4}+\frac{B x^5}{5 c^2}","\frac{b^2 x (b B-A c)}{2 c^4 \left(b+c x^2\right)}-\frac{b^{3/2} (7 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{9/2}}-\frac{x^3 (2 b B-A c)}{3 c^3}+\frac{b x (3 b B-2 A c)}{c^4}+\frac{B x^5}{5 c^2}",1,"(b*(3*b*B - 2*A*c)*x)/c^4 - ((2*b*B - A*c)*x^3)/(3*c^3) + (B*x^5)/(5*c^2) + (b^2*(b*B - A*c)*x)/(2*c^4*(b + c*x^2)) - (b^(3/2)*(7*b*B - 5*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*c^(9/2))","A",5,4,24,0.1667,1,"{1584, 455, 1810, 205}"
61,1,83,0,0.0984574,"\int \frac{x^9 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^9*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{b^2 (b B-A c)}{2 c^4 \left(b+c x^2\right)}-\frac{x^2 (2 b B-A c)}{2 c^3}+\frac{b (3 b B-2 A c) \log \left(b+c x^2\right)}{2 c^4}+\frac{B x^4}{4 c^2}","\frac{b^2 (b B-A c)}{2 c^4 \left(b+c x^2\right)}-\frac{x^2 (2 b B-A c)}{2 c^3}+\frac{b (3 b B-2 A c) \log \left(b+c x^2\right)}{2 c^4}+\frac{B x^4}{4 c^2}",1,"-((2*b*B - A*c)*x^2)/(2*c^3) + (B*x^4)/(4*c^2) + (b^2*(b*B - A*c))/(2*c^4*(b + c*x^2)) + (b*(3*b*B - 2*A*c)*Log[b + c*x^2])/(2*c^4)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
62,1,89,0,0.0885159,"\int \frac{x^8 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^8*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","-\frac{b x (b B-A c)}{2 c^3 \left(b+c x^2\right)}-\frac{x (2 b B-A c)}{c^3}+\frac{\sqrt{b} (5 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{7/2}}+\frac{B x^3}{3 c^2}","-\frac{b x (b B-A c)}{2 c^3 \left(b+c x^2\right)}-\frac{x (2 b B-A c)}{c^3}+\frac{\sqrt{b} (5 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 c^{7/2}}+\frac{B x^3}{3 c^2}",1,"-(((2*b*B - A*c)*x)/c^3) + (B*x^3)/(3*c^2) - (b*(b*B - A*c)*x)/(2*c^3*(b + c*x^2)) + (Sqrt[b]*(5*b*B - 3*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*c^(7/2))","A",5,4,24,0.1667,1,"{1584, 455, 1153, 205}"
63,1,61,0,0.0697961,"\int \frac{x^7 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^7*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","-\frac{b (b B-A c)}{2 c^3 \left(b+c x^2\right)}-\frac{(2 b B-A c) \log \left(b+c x^2\right)}{2 c^3}+\frac{B x^2}{2 c^2}","-\frac{b (b B-A c)}{2 c^3 \left(b+c x^2\right)}-\frac{(2 b B-A c) \log \left(b+c x^2\right)}{2 c^3}+\frac{B x^2}{2 c^2}",1,"(B*x^2)/(2*c^2) - (b*(b*B - A*c))/(2*c^3*(b + c*x^2)) - ((2*b*B - A*c)*Log[b + c*x^2])/(2*c^3)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
64,1,68,0,0.0610082,"\int \frac{x^6 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^6*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{x (b B-A c)}{2 c^2 \left(b+c x^2\right)}-\frac{(3 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 \sqrt{b} c^{5/2}}+\frac{B x}{c^2}","\frac{x (b B-A c)}{2 c^2 \left(b+c x^2\right)}-\frac{(3 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 \sqrt{b} c^{5/2}}+\frac{B x}{c^2}",1,"(B*x)/c^2 + ((b*B - A*c)*x)/(2*c^2*(b + c*x^2)) - ((3*b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*Sqrt[b]*c^(5/2))","A",4,4,24,0.1667,1,"{1584, 455, 388, 205}"
65,1,41,0,0.0467391,"\int \frac{x^5 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^5*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{b B-A c}{2 c^2 \left(b+c x^2\right)}+\frac{B \log \left(b+c x^2\right)}{2 c^2}","\frac{b B-A c}{2 c^2 \left(b+c x^2\right)}+\frac{B \log \left(b+c x^2\right)}{2 c^2}",1,"(b*B - A*c)/(2*c^2*(b + c*x^2)) + (B*Log[b + c*x^2])/(2*c^2)","A",4,3,24,0.1250,1,"{1584, 444, 43}"
66,1,63,0,0.0327217,"\int \frac{x^4 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^4*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{(A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{3/2} c^{3/2}}-\frac{x (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{(A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{3/2} c^{3/2}}-\frac{x (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"-((b*B - A*c)*x)/(2*b*c*(b + c*x^2)) + ((b*B + A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(3/2)*c^(3/2))","A",3,3,24,0.1250,1,"{1584, 385, 205}"
67,1,51,0,0.0547747,"\int \frac{x^3 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^3*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","-\frac{A \log \left(b+c x^2\right)}{2 b^2}+\frac{A \log (x)}{b^2}-\frac{b B-A c}{2 b c \left(b+c x^2\right)}","-\frac{A \log \left(b+c x^2\right)}{2 b^2}+\frac{A \log (x)}{b^2}-\frac{b B-A c}{2 b c \left(b+c x^2\right)}",1,"-(b*B - A*c)/(2*b*c*(b + c*x^2)) + (A*Log[x])/b^2 - (A*Log[b + c*x^2])/(2*b^2)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
68,1,70,0,0.0743364,"\int \frac{x^2 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^2*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{x (b B-A c)}{2 b^2 \left(b+c x^2\right)}+\frac{(b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{5/2} \sqrt{c}}-\frac{A}{b^2 x}","\frac{x (b B-A c)}{2 b^2 \left(b+c x^2\right)}+\frac{(b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{5/2} \sqrt{c}}-\frac{A}{b^2 x}",1,"-(A/(b^2*x)) + ((b*B - A*c)*x)/(2*b^2*(b + c*x^2)) + ((b*B - 3*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(5/2)*Sqrt[c])","A",4,4,24,0.1667,1,"{1584, 456, 453, 205}"
69,1,73,0,0.0796694,"\int \frac{x \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{b B-A c}{2 b^2 \left(b+c x^2\right)}-\frac{(b B-2 A c) \log \left(b+c x^2\right)}{2 b^3}+\frac{\log (x) (b B-2 A c)}{b^3}-\frac{A}{2 b^2 x^2}","\frac{b B-A c}{2 b^2 \left(b+c x^2\right)}-\frac{(b B-2 A c) \log \left(b+c x^2\right)}{2 b^3}+\frac{\log (x) (b B-2 A c)}{b^3}-\frac{A}{2 b^2 x^2}",1,"-A/(2*b^2*x^2) + (b*B - A*c)/(2*b^2*(b + c*x^2)) + ((b*B - 2*A*c)*Log[x])/b^3 - ((b*B - 2*A*c)*Log[b + c*x^2])/(2*b^3)","A",4,3,22,0.1364,1,"{1584, 446, 77}"
70,1,90,0,0.1174386,"\int \frac{A+B x^2}{\left(b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(b*x^2 + c*x^4)^2,x]","-\frac{c x (b B-A c)}{2 b^3 \left(b+c x^2\right)}-\frac{b B-2 A c}{b^3 x}-\frac{\sqrt{c} (3 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{7/2}}-\frac{A}{3 b^2 x^3}","-\frac{c x (b B-A c)}{2 b^3 \left(b+c x^2\right)}-\frac{b B-2 A c}{b^3 x}-\frac{\sqrt{c} (3 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{7/2}}-\frac{A}{3 b^2 x^3}",1,"-A/(3*b^2*x^3) - (b*B - 2*A*c)/(b^3*x) - (c*(b*B - A*c)*x)/(2*b^3*(b + c*x^2)) - (Sqrt[c]*(3*b*B - 5*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(7/2))","A",5,4,21,0.1905,1,"{1593, 456, 1261, 205}"
71,1,97,0,0.1084162,"\int \frac{A+B x^2}{x \left(b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x*(b*x^2 + c*x^4)^2),x]","-\frac{c (b B-A c)}{2 b^3 \left(b+c x^2\right)}-\frac{b B-2 A c}{2 b^3 x^2}+\frac{c (2 b B-3 A c) \log \left(b+c x^2\right)}{2 b^4}-\frac{c \log (x) (2 b B-3 A c)}{b^4}-\frac{A}{4 b^2 x^4}","-\frac{c (b B-A c)}{2 b^3 \left(b+c x^2\right)}-\frac{b B-2 A c}{2 b^3 x^2}+\frac{c (2 b B-3 A c) \log \left(b+c x^2\right)}{2 b^4}-\frac{c \log (x) (2 b B-3 A c)}{b^4}-\frac{A}{4 b^2 x^4}",1,"-A/(4*b^2*x^4) - (b*B - 2*A*c)/(2*b^3*x^2) - (c*(b*B - A*c))/(2*b^3*(b + c*x^2)) - (c*(2*b*B - 3*A*c)*Log[x])/b^4 + (c*(2*b*B - 3*A*c)*Log[b + c*x^2])/(2*b^4)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
72,1,111,0,0.1981591,"\int \frac{A+B x^2}{x^2 \left(b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x^2*(b*x^2 + c*x^4)^2),x]","\frac{c^2 x (b B-A c)}{2 b^4 \left(b+c x^2\right)}+\frac{c^{3/2} (5 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{9/2}}-\frac{b B-2 A c}{3 b^3 x^3}+\frac{c (2 b B-3 A c)}{b^4 x}-\frac{A}{5 b^2 x^5}","\frac{c^2 x (b B-A c)}{2 b^4 \left(b+c x^2\right)}+\frac{c^{3/2} (5 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{2 b^{9/2}}-\frac{b B-2 A c}{3 b^3 x^3}+\frac{c (2 b B-3 A c)}{b^4 x}-\frac{A}{5 b^2 x^5}",1,"-A/(5*b^2*x^5) - (b*B - 2*A*c)/(3*b^3*x^3) + (c*(2*b*B - 3*A*c))/(b^4*x) + (c^2*(b*B - A*c)*x)/(2*b^4*(b + c*x^2)) + (c^(3/2)*(5*b*B - 7*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(2*b^(9/2))","A",5,4,24,0.1667,1,"{1584, 456, 1802, 205}"
73,1,140,0,0.2346234,"\int \frac{x^{14} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^14*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{b^2 x (17 b B-13 A c)}{8 c^5 \left(b+c x^2\right)}-\frac{b^3 x (b B-A c)}{4 c^5 \left(b+c x^2\right)^2}-\frac{7 b^{3/2} (9 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{11/2}}-\frac{x^3 (3 b B-A c)}{3 c^4}+\frac{3 b x (2 b B-A c)}{c^5}+\frac{B x^5}{5 c^3}","\frac{b^2 x (17 b B-13 A c)}{8 c^5 \left(b+c x^2\right)}-\frac{b^3 x (b B-A c)}{4 c^5 \left(b+c x^2\right)^2}-\frac{7 b^{3/2} (9 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{11/2}}-\frac{x^3 (3 b B-A c)}{3 c^4}+\frac{3 b x (2 b B-A c)}{c^5}+\frac{B x^5}{5 c^3}",1,"(3*b*(2*b*B - A*c)*x)/c^5 - ((3*b*B - A*c)*x^3)/(3*c^4) + (B*x^5)/(5*c^3) - (b^3*(b*B - A*c)*x)/(4*c^5*(b + c*x^2)^2) + (b^2*(17*b*B - 13*A*c)*x)/(8*c^5*(b + c*x^2)) - (7*b^(3/2)*(9*b*B - 5*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*c^(11/2))","A",6,5,24,0.2083,1,"{1584, 455, 1814, 1810, 205}"
74,1,111,0,0.1360475,"\int \frac{x^{13} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^13*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{b^2 (4 b B-3 A c)}{2 c^5 \left(b+c x^2\right)}-\frac{b^3 (b B-A c)}{4 c^5 \left(b+c x^2\right)^2}-\frac{x^2 (3 b B-A c)}{2 c^4}+\frac{3 b (2 b B-A c) \log \left(b+c x^2\right)}{2 c^5}+\frac{B x^4}{4 c^3}","\frac{b^2 (4 b B-3 A c)}{2 c^5 \left(b+c x^2\right)}-\frac{b^3 (b B-A c)}{4 c^5 \left(b+c x^2\right)^2}-\frac{x^2 (3 b B-A c)}{2 c^4}+\frac{3 b (2 b B-A c) \log \left(b+c x^2\right)}{2 c^5}+\frac{B x^4}{4 c^3}",1,"-((3*b*B - A*c)*x^2)/(2*c^4) + (B*x^4)/(4*c^3) - (b^3*(b*B - A*c))/(4*c^5*(b + c*x^2)^2) + (b^2*(4*b*B - 3*A*c))/(2*c^5*(b + c*x^2)) + (3*b*(2*b*B - A*c)*Log[b + c*x^2])/(2*c^5)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
75,1,118,0,0.1620003,"\int \frac{x^{12} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^12*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{b^2 x (b B-A c)}{4 c^4 \left(b+c x^2\right)^2}-\frac{b x (13 b B-9 A c)}{8 c^4 \left(b+c x^2\right)}-\frac{x (3 b B-A c)}{c^4}+\frac{5 \sqrt{b} (7 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{9/2}}+\frac{B x^3}{3 c^3}","\frac{b^2 x (b B-A c)}{4 c^4 \left(b+c x^2\right)^2}-\frac{b x (13 b B-9 A c)}{8 c^4 \left(b+c x^2\right)}-\frac{x (3 b B-A c)}{c^4}+\frac{5 \sqrt{b} (7 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 c^{9/2}}+\frac{B x^3}{3 c^3}",1,"-(((3*b*B - A*c)*x)/c^4) + (B*x^3)/(3*c^3) + (b^2*(b*B - A*c)*x)/(4*c^4*(b + c*x^2)^2) - (b*(13*b*B - 9*A*c)*x)/(8*c^4*(b + c*x^2)) + (5*Sqrt[b]*(7*b*B - 3*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*c^(9/2))","A",6,5,24,0.2083,1,"{1584, 455, 1814, 1153, 205}"
76,1,89,0,0.1017306,"\int \frac{x^{11} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^11*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{b^2 (b B-A c)}{4 c^4 \left(b+c x^2\right)^2}-\frac{b (3 b B-2 A c)}{2 c^4 \left(b+c x^2\right)}-\frac{(3 b B-A c) \log \left(b+c x^2\right)}{2 c^4}+\frac{B x^2}{2 c^3}","\frac{b^2 (b B-A c)}{4 c^4 \left(b+c x^2\right)^2}-\frac{b (3 b B-2 A c)}{2 c^4 \left(b+c x^2\right)}-\frac{(3 b B-A c) \log \left(b+c x^2\right)}{2 c^4}+\frac{B x^2}{2 c^3}",1,"(B*x^2)/(2*c^3) + (b^2*(b*B - A*c))/(4*c^4*(b + c*x^2)^2) - (b*(3*b*B - 2*A*c))/(2*c^4*(b + c*x^2)) - ((3*b*B - A*c)*Log[b + c*x^2])/(2*c^4)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
77,1,95,0,0.0991359,"\int \frac{x^{10} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^10*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{x (9 b B-5 A c)}{8 c^3 \left(b+c x^2\right)}-\frac{b x (b B-A c)}{4 c^3 \left(b+c x^2\right)^2}-\frac{3 (5 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 \sqrt{b} c^{7/2}}+\frac{B x}{c^3}","\frac{x (9 b B-5 A c)}{8 c^3 \left(b+c x^2\right)}-\frac{b x (b B-A c)}{4 c^3 \left(b+c x^2\right)^2}-\frac{3 (5 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 \sqrt{b} c^{7/2}}+\frac{B x}{c^3}",1,"(B*x)/c^3 - (b*(b*B - A*c)*x)/(4*c^3*(b + c*x^2)^2) + ((9*b*B - 5*A*c)*x)/(8*c^3*(b + c*x^2)) - (3*(5*b*B - A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*Sqrt[b]*c^(7/2))","A",5,5,24,0.2083,1,"{1584, 455, 1157, 388, 205}"
78,1,67,0,0.0758642,"\int \frac{x^9 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^9*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{b (b B-A c)}{4 c^3 \left(b+c x^2\right)^2}+\frac{2 b B-A c}{2 c^3 \left(b+c x^2\right)}+\frac{B \log \left(b+c x^2\right)}{2 c^3}","-\frac{b (b B-A c)}{4 c^3 \left(b+c x^2\right)^2}+\frac{2 b B-A c}{2 c^3 \left(b+c x^2\right)}+\frac{B \log \left(b+c x^2\right)}{2 c^3}",1,"-(b*(b*B - A*c))/(4*c^3*(b + c*x^2)^2) + (2*b*B - A*c)/(2*c^3*(b + c*x^2)) + (B*Log[b + c*x^2])/(2*c^3)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
79,1,90,0,0.0757985,"\int \frac{x^8 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^8*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{(A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{3/2} c^{5/2}}-\frac{x (5 b B-A c)}{8 b c^2 \left(b+c x^2\right)}+\frac{x (b B-A c)}{4 c^2 \left(b+c x^2\right)^2}","\frac{(A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{3/2} c^{5/2}}-\frac{x (5 b B-A c)}{8 b c^2 \left(b+c x^2\right)}+\frac{x (b B-A c)}{4 c^2 \left(b+c x^2\right)^2}",1,"((b*B - A*c)*x)/(4*c^2*(b + c*x^2)^2) - ((5*b*B - A*c)*x)/(8*b*c^2*(b + c*x^2)) + ((3*b*B + A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(3/2)*c^(5/2))","A",4,4,24,0.1667,1,"{1584, 455, 385, 205}"
80,1,32,0,0.0307202,"\int \frac{x^7 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^7*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{\left(A+B x^2\right)^2}{4 \left(b+c x^2\right)^2 (b B-A c)}","\frac{\left(A+B x^2\right)^2}{4 \left(b+c x^2\right)^2 (b B-A c)}",1,"(A + B*x^2)^2/(4*(b*B - A*c)*(b + c*x^2)^2)","A",3,3,24,0.1250,1,"{1584, 444, 37}"
81,1,92,0,0.0452505,"\int \frac{x^6 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^6*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{(3 A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{5/2} c^{3/2}}+\frac{x (3 A c+b B)}{8 b^2 c \left(b+c x^2\right)}-\frac{x (b B-A c)}{4 b c \left(b+c x^2\right)^2}","\frac{(3 A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{5/2} c^{3/2}}+\frac{x (3 A c+b B)}{8 b^2 c \left(b+c x^2\right)}-\frac{x (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"-((b*B - A*c)*x)/(4*b*c*(b + c*x^2)^2) + ((b*B + 3*A*c)*x)/(8*b^2*c*(b + c*x^2)) + ((b*B + 3*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(5/2)*c^(3/2))","A",4,4,24,0.1667,1,"{1584, 385, 199, 205}"
82,1,68,0,0.0728484,"\int \frac{x^5 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^5*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{A}{2 b^2 \left(b+c x^2\right)}-\frac{A \log \left(b+c x^2\right)}{2 b^3}+\frac{A \log (x)}{b^3}-\frac{b B-A c}{4 b c \left(b+c x^2\right)^2}","\frac{A}{2 b^2 \left(b+c x^2\right)}-\frac{A \log \left(b+c x^2\right)}{2 b^3}+\frac{A \log (x)}{b^3}-\frac{b B-A c}{4 b c \left(b+c x^2\right)^2}",1,"-(b*B - A*c)/(4*b*c*(b + c*x^2)^2) + A/(2*b^2*(b + c*x^2)) + (A*Log[x])/b^3 - (A*Log[b + c*x^2])/(2*b^3)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
83,1,96,0,0.1182092,"\int \frac{x^4 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^4*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{x (3 b B-7 A c)}{8 b^3 \left(b+c x^2\right)}+\frac{x (b B-A c)}{4 b^2 \left(b+c x^2\right)^2}+\frac{3 (b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{7/2} \sqrt{c}}-\frac{A}{b^3 x}","\frac{x (3 b B-7 A c)}{8 b^3 \left(b+c x^2\right)}+\frac{x (b B-A c)}{4 b^2 \left(b+c x^2\right)^2}+\frac{3 (b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{7/2} \sqrt{c}}-\frac{A}{b^3 x}",1,"-(A/(b^3*x)) + ((b*B - A*c)*x)/(4*b^2*(b + c*x^2)^2) + ((3*b*B - 7*A*c)*x)/(8*b^3*(b + c*x^2)) + (3*(b*B - 5*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(7/2)*Sqrt[c])","A",5,4,24,0.1667,1,"{1584, 456, 453, 205}"
84,1,97,0,0.1173114,"\int \frac{x^3 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^3*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{b B-2 A c}{2 b^3 \left(b+c x^2\right)}+\frac{b B-A c}{4 b^2 \left(b+c x^2\right)^2}-\frac{(b B-3 A c) \log \left(b+c x^2\right)}{2 b^4}+\frac{\log (x) (b B-3 A c)}{b^4}-\frac{A}{2 b^3 x^2}","\frac{b B-2 A c}{2 b^3 \left(b+c x^2\right)}+\frac{b B-A c}{4 b^2 \left(b+c x^2\right)^2}-\frac{(b B-3 A c) \log \left(b+c x^2\right)}{2 b^4}+\frac{\log (x) (b B-3 A c)}{b^4}-\frac{A}{2 b^3 x^2}",1,"-A/(2*b^3*x^2) + (b*B - A*c)/(4*b^2*(b + c*x^2)^2) + (b*B - 2*A*c)/(2*b^3*(b + c*x^2)) + ((b*B - 3*A*c)*Log[x])/b^4 - ((b*B - 3*A*c)*Log[b + c*x^2])/(2*b^4)","A",4,3,24,0.1250,1,"{1584, 446, 77}"
85,1,117,0,0.176717,"\int \frac{x^2 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^2*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{c x (7 b B-11 A c)}{8 b^4 \left(b+c x^2\right)}-\frac{c x (b B-A c)}{4 b^3 \left(b+c x^2\right)^2}-\frac{b B-3 A c}{b^4 x}-\frac{5 \sqrt{c} (3 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{9/2}}-\frac{A}{3 b^3 x^3}","-\frac{c x (7 b B-11 A c)}{8 b^4 \left(b+c x^2\right)}-\frac{c x (b B-A c)}{4 b^3 \left(b+c x^2\right)^2}-\frac{b B-3 A c}{b^4 x}-\frac{5 \sqrt{c} (3 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{9/2}}-\frac{A}{3 b^3 x^3}",1,"-A/(3*b^3*x^3) - (b*B - 3*A*c)/(b^4*x) - (c*(b*B - A*c)*x)/(4*b^3*(b + c*x^2)^2) - (c*(7*b*B - 11*A*c)*x)/(8*b^4*(b + c*x^2)) - (5*Sqrt[c]*(3*b*B - 7*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(9/2))","A",6,5,24,0.2083,1,"{1584, 456, 1259, 1261, 205}"
86,1,121,0,0.1309004,"\int \frac{x \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{c (2 b B-3 A c)}{2 b^4 \left(b+c x^2\right)}-\frac{b B-3 A c}{2 b^4 x^2}-\frac{c (b B-A c)}{4 b^3 \left(b+c x^2\right)^2}+\frac{3 c (b B-2 A c) \log \left(b+c x^2\right)}{2 b^5}-\frac{3 c \log (x) (b B-2 A c)}{b^5}-\frac{A}{4 b^3 x^4}","-\frac{c (2 b B-3 A c)}{2 b^4 \left(b+c x^2\right)}-\frac{b B-3 A c}{2 b^4 x^2}-\frac{c (b B-A c)}{4 b^3 \left(b+c x^2\right)^2}+\frac{3 c (b B-2 A c) \log \left(b+c x^2\right)}{2 b^5}-\frac{3 c \log (x) (b B-2 A c)}{b^5}-\frac{A}{4 b^3 x^4}",1,"-A/(4*b^3*x^4) - (b*B - 3*A*c)/(2*b^4*x^2) - (c*(b*B - A*c))/(4*b^3*(b + c*x^2)^2) - (c*(2*b*B - 3*A*c))/(2*b^4*(b + c*x^2)) - (3*c*(b*B - 2*A*c)*Log[x])/b^5 + (3*c*(b*B - 2*A*c)*Log[b + c*x^2])/(2*b^5)","A",4,3,22,0.1364,1,"{1584, 446, 77}"
87,1,140,0,0.3319621,"\int \frac{A+B x^2}{\left(b x^2+c x^4\right)^3} \, dx","Int[(A + B*x^2)/(b*x^2 + c*x^4)^3,x]","\frac{c^2 x (11 b B-15 A c)}{8 b^5 \left(b+c x^2\right)}+\frac{c^2 x (b B-A c)}{4 b^4 \left(b+c x^2\right)^2}+\frac{7 c^{3/2} (5 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{11/2}}-\frac{b B-3 A c}{3 b^4 x^3}+\frac{3 c (b B-2 A c)}{b^5 x}-\frac{A}{5 b^3 x^5}","\frac{c^2 x (11 b B-15 A c)}{8 b^5 \left(b+c x^2\right)}+\frac{c^2 x (b B-A c)}{4 b^4 \left(b+c x^2\right)^2}+\frac{7 c^{3/2} (5 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b}}\right)}{8 b^{11/2}}-\frac{b B-3 A c}{3 b^4 x^3}+\frac{3 c (b B-2 A c)}{b^5 x}-\frac{A}{5 b^3 x^5}",1,"-A/(5*b^3*x^5) - (b*B - 3*A*c)/(3*b^4*x^3) + (3*c*(b*B - 2*A*c))/(b^5*x) + (c^2*(b*B - A*c)*x)/(4*b^4*(b + c*x^2)^2) + (c^2*(11*b*B - 15*A*c)*x)/(8*b^5*(b + c*x^2)) + (7*c^(3/2)*(5*b*B - 9*A*c)*ArcTan[(Sqrt[c]*x)/Sqrt[b]])/(8*b^(11/2))","A",6,5,21,0.2381,1,"{1593, 456, 1805, 1802, 205}"
88,1,148,0,0.1726817,"\int \frac{A+B x^2}{x \left(b x^2+c x^4\right)^3} \, dx","Int[(A + B*x^2)/(x*(b*x^2 + c*x^4)^3),x]","\frac{c^2 (3 b B-4 A c)}{2 b^5 \left(b+c x^2\right)}+\frac{c^2 (b B-A c)}{4 b^4 \left(b+c x^2\right)^2}-\frac{c^2 (3 b B-5 A c) \log \left(b+c x^2\right)}{b^6}+\frac{2 c^2 \log (x) (3 b B-5 A c)}{b^6}+\frac{3 c (b B-2 A c)}{2 b^5 x^2}-\frac{b B-3 A c}{4 b^4 x^4}-\frac{A}{6 b^3 x^6}","\frac{c^2 (3 b B-4 A c)}{2 b^5 \left(b+c x^2\right)}+\frac{c^2 (b B-A c)}{4 b^4 \left(b+c x^2\right)^2}-\frac{c^2 (3 b B-5 A c) \log \left(b+c x^2\right)}{b^6}+\frac{2 c^2 \log (x) (3 b B-5 A c)}{b^6}+\frac{3 c (b B-2 A c)}{2 b^5 x^2}-\frac{b B-3 A c}{4 b^4 x^4}-\frac{A}{6 b^3 x^6}",1,"-A/(6*b^3*x^6) - (b*B - 3*A*c)/(4*b^4*x^4) + (3*c*(b*B - 2*A*c))/(2*b^5*x^2) + (c^2*(b*B - A*c))/(4*b^4*(b + c*x^2)^2) + (c^2*(3*b*B - 4*A*c))/(2*b^5*(b + c*x^2)) + (2*c^2*(3*b*B - 5*A*c)*Log[x])/b^6 - (c^2*(3*b*B - 5*A*c)*Log[b + c*x^2])/b^6","A",4,3,24,0.1250,1,"{1584, 446, 77}"
89,1,218,0,0.3810842,"\int x^7 \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^7*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{7 b^2 \left(b x^2+c x^4\right)^{3/2} (3 b B-4 A c)}{384 c^4}+\frac{7 b^3 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (3 b B-4 A c)}{1024 c^5}-\frac{7 b^5 (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{1024 c^{11/2}}-\frac{x^4 \left(b x^2+c x^4\right)^{3/2} (3 b B-4 A c)}{40 c^2}+\frac{7 b x^2 \left(b x^2+c x^4\right)^{3/2} (3 b B-4 A c)}{320 c^3}+\frac{B x^6 \left(b x^2+c x^4\right)^{3/2}}{12 c}","-\frac{7 b^2 \left(b x^2+c x^4\right)^{3/2} (3 b B-4 A c)}{384 c^4}+\frac{7 b^3 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (3 b B-4 A c)}{1024 c^5}-\frac{7 b^5 (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{1024 c^{11/2}}-\frac{x^4 \left(b x^2+c x^4\right)^{3/2} (3 b B-4 A c)}{40 c^2}+\frac{7 b x^2 \left(b x^2+c x^4\right)^{3/2} (3 b B-4 A c)}{320 c^3}+\frac{B x^6 \left(b x^2+c x^4\right)^{3/2}}{12 c}",1,"(7*b^3*(3*b*B - 4*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(1024*c^5) - (7*b^2*(3*b*B - 4*A*c)*(b*x^2 + c*x^4)^(3/2))/(384*c^4) + (7*b*(3*b*B - 4*A*c)*x^2*(b*x^2 + c*x^4)^(3/2))/(320*c^3) - ((3*b*B - 4*A*c)*x^4*(b*x^2 + c*x^4)^(3/2))/(40*c^2) + (B*x^6*(b*x^2 + c*x^4)^(3/2))/(12*c) - (7*b^5*(3*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(1024*c^(11/2))","A",8,7,26,0.2692,1,"{2034, 794, 670, 640, 612, 620, 206}"
90,1,181,0,0.3343549,"\int x^5 \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^5*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (7 b B-10 A c)}{256 c^4}+\frac{b^4 (7 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{256 c^{9/2}}+\frac{b \left(b x^2+c x^4\right)^{3/2} (7 b B-10 A c)}{96 c^3}-\frac{x^2 \left(b x^2+c x^4\right)^{3/2} (7 b B-10 A c)}{80 c^2}+\frac{B x^4 \left(b x^2+c x^4\right)^{3/2}}{10 c}","-\frac{b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (7 b B-10 A c)}{256 c^4}+\frac{b^4 (7 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{256 c^{9/2}}+\frac{b \left(b x^2+c x^4\right)^{3/2} (7 b B-10 A c)}{96 c^3}-\frac{x^2 \left(b x^2+c x^4\right)^{3/2} (7 b B-10 A c)}{80 c^2}+\frac{B x^4 \left(b x^2+c x^4\right)^{3/2}}{10 c}",1,"-(b^2*(7*b*B - 10*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(256*c^4) + (b*(7*b*B - 10*A*c)*(b*x^2 + c*x^4)^(3/2))/(96*c^3) - ((7*b*B - 10*A*c)*x^2*(b*x^2 + c*x^4)^(3/2))/(80*c^2) + (B*x^4*(b*x^2 + c*x^4)^(3/2))/(10*c) + (b^4*(7*b*B - 10*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(256*c^(9/2))","A",7,7,26,0.2692,1,"{2034, 794, 670, 640, 612, 620, 206}"
91,1,125,0,0.1988953,"\int x^3 \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^3*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{b^3 (5 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{7/2}}+\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (5 b B-8 A c)}{128 c^3}-\frac{\left(b x^2+c x^4\right)^{3/2} \left(-8 A c+5 b B-6 B c x^2\right)}{48 c^2}","-\frac{b^3 (5 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{7/2}}+\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (5 b B-8 A c)}{128 c^3}-\frac{\left(b x^2+c x^4\right)^{3/2} \left(-8 A c+5 b B-6 B c x^2\right)}{48 c^2}",1,"(b*(5*b*B - 8*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(128*c^3) - ((5*b*B - 8*A*c - 6*B*c*x^2)*(b*x^2 + c*x^4)^(3/2))/(48*c^2) - (b^3*(5*b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(128*c^(7/2))","A",5,5,26,0.1923,1,"{2034, 779, 612, 620, 206}"
92,1,107,0,0.1538591,"\int x \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","\frac{b^2 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{\left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (b B-2 A c)}{16 c^2}+\frac{B \left(b x^2+c x^4\right)^{3/2}}{6 c}","\frac{b^2 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{5/2}}-\frac{\left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (b B-2 A c)}{16 c^2}+\frac{B \left(b x^2+c x^4\right)^{3/2}}{6 c}",1,"-((b*B - 2*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(16*c^2) + (B*(b*x^2 + c*x^4)^(3/2))/(6*c) + (b^2*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(5/2))","A",5,5,24,0.2083,1,"{2034, 640, 612, 620, 206}"
93,1,100,0,0.1970199,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x,x]","-\frac{b (b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{3/2}}-\frac{\sqrt{b x^2+c x^4} (b B-4 A c)}{8 c}+\frac{B \left(b x^2+c x^4\right)^{3/2}}{4 c x^2}","-\frac{b (b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{3/2}}-\frac{\sqrt{b x^2+c x^4} (b B-4 A c)}{8 c}+\frac{B \left(b x^2+c x^4\right)^{3/2}}{4 c x^2}",1,"-((b*B - 4*A*c)*Sqrt[b*x^2 + c*x^4])/(8*c) + (B*(b*x^2 + c*x^4)^(3/2))/(4*c*x^2) - (b*(b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*c^(3/2))","A",5,5,26,0.1923,1,"{2034, 794, 664, 620, 206}"
94,1,97,0,0.2133953,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^3} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^3,x]","\frac{\sqrt{b x^2+c x^4} (2 A c+b B)}{2 b}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{c}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{b x^4}","\frac{\sqrt{b x^2+c x^4} (2 A c+b B)}{2 b}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{c}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{b x^4}",1,"((b*B + 2*A*c)*Sqrt[b*x^2 + c*x^4])/(2*b) - (A*(b*x^2 + c*x^4)^(3/2))/(b*x^4) + ((b*B + 2*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*Sqrt[c])","A",5,5,26,0.1923,1,"{2034, 792, 664, 620, 206}"
95,1,80,0,0.1956147,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^5} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^5,x]","-\frac{A \left(b x^2+c x^4\right)^{3/2}}{3 b x^6}-\frac{B \sqrt{b x^2+c x^4}}{x^2}+B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)","-\frac{A \left(b x^2+c x^4\right)^{3/2}}{3 b x^6}-\frac{B \sqrt{b x^2+c x^4}}{x^2}+B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)",1,"-((B*Sqrt[b*x^2 + c*x^4])/x^2) - (A*(b*x^2 + c*x^4)^(3/2))/(3*b*x^6) + B*Sqrt[c]*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]","A",5,5,26,0.1923,1,"{2034, 792, 662, 620, 206}"
96,1,61,0,0.1618129,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^7} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^7,x]","-\frac{\left(b x^2+c x^4\right)^{3/2} (5 b B-2 A c)}{15 b^2 x^6}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{5 b x^8}","-\frac{\left(b x^2+c x^4\right)^{3/2} (5 b B-2 A c)}{15 b^2 x^6}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{5 b x^8}",1,"-(A*(b*x^2 + c*x^4)^(3/2))/(5*b*x^8) - ((5*b*B - 2*A*c)*(b*x^2 + c*x^4)^(3/2))/(15*b^2*x^6)","A",3,3,26,0.1154,1,"{2034, 792, 650}"
97,1,96,0,0.2108899,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^9} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^9,x]","\frac{2 c \left(b x^2+c x^4\right)^{3/2} (7 b B-4 A c)}{105 b^3 x^6}-\frac{\left(b x^2+c x^4\right)^{3/2} (7 b B-4 A c)}{35 b^2 x^8}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{7 b x^{10}}","\frac{2 c \left(b x^2+c x^4\right)^{3/2} (7 b B-4 A c)}{105 b^3 x^6}-\frac{\left(b x^2+c x^4\right)^{3/2} (7 b B-4 A c)}{35 b^2 x^8}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{7 b x^{10}}",1,"-(A*(b*x^2 + c*x^4)^(3/2))/(7*b*x^10) - ((7*b*B - 4*A*c)*(b*x^2 + c*x^4)^(3/2))/(35*b^2*x^8) + (2*c*(7*b*B - 4*A*c)*(b*x^2 + c*x^4)^(3/2))/(105*b^3*x^6)","A",4,4,26,0.1538,1,"{2034, 792, 658, 650}"
98,1,133,0,0.2449986,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{11}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^11,x]","-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2} (3 b B-2 A c)}{315 b^4 x^6}+\frac{4 c \left(b x^2+c x^4\right)^{3/2} (3 b B-2 A c)}{105 b^3 x^8}-\frac{\left(b x^2+c x^4\right)^{3/2} (3 b B-2 A c)}{21 b^2 x^{10}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{9 b x^{12}}","-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2} (3 b B-2 A c)}{315 b^4 x^6}+\frac{4 c \left(b x^2+c x^4\right)^{3/2} (3 b B-2 A c)}{105 b^3 x^8}-\frac{\left(b x^2+c x^4\right)^{3/2} (3 b B-2 A c)}{21 b^2 x^{10}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{9 b x^{12}}",1,"-(A*(b*x^2 + c*x^4)^(3/2))/(9*b*x^12) - ((3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(3/2))/(21*b^2*x^10) + (4*c*(3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(3/2))/(105*b^3*x^8) - (8*c^2*(3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(3/2))/(315*b^4*x^6)","A",5,4,26,0.1538,1,"{2034, 792, 658, 650}"
99,1,170,0,0.3001118,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{13}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^13,x]","\frac{16 c^3 \left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{3465 b^5 x^6}-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{1155 b^4 x^8}+\frac{2 c \left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{231 b^3 x^{10}}-\frac{\left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{99 b^2 x^{12}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{11 b x^{14}}","\frac{16 c^3 \left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{3465 b^5 x^6}-\frac{8 c^2 \left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{1155 b^4 x^8}+\frac{2 c \left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{231 b^3 x^{10}}-\frac{\left(b x^2+c x^4\right)^{3/2} (11 b B-8 A c)}{99 b^2 x^{12}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{11 b x^{14}}",1,"-(A*(b*x^2 + c*x^4)^(3/2))/(11*b*x^14) - ((11*b*B - 8*A*c)*(b*x^2 + c*x^4)^(3/2))/(99*b^2*x^12) + (2*c*(11*b*B - 8*A*c)*(b*x^2 + c*x^4)^(3/2))/(231*b^3*x^10) - (8*c^2*(11*b*B - 8*A*c)*(b*x^2 + c*x^4)^(3/2))/(1155*b^4*x^8) + (16*c^3*(11*b*B - 8*A*c)*(b*x^2 + c*x^4)^(3/2))/(3465*b^5*x^6)","A",6,4,26,0.1538,1,"{2034, 792, 658, 650}"
100,1,131,0,0.2198356,"\int x^4 \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^4*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{8 b^2 \left(b x^2+c x^4\right)^{3/2} (2 b B-3 A c)}{315 c^4 x^3}-\frac{x \left(b x^2+c x^4\right)^{3/2} (2 b B-3 A c)}{21 c^2}+\frac{4 b \left(b x^2+c x^4\right)^{3/2} (2 b B-3 A c)}{105 c^3 x}+\frac{B x^3 \left(b x^2+c x^4\right)^{3/2}}{9 c}","-\frac{8 b^2 \left(b x^2+c x^4\right)^{3/2} (2 b B-3 A c)}{315 c^4 x^3}-\frac{x \left(b x^2+c x^4\right)^{3/2} (2 b B-3 A c)}{21 c^2}+\frac{4 b \left(b x^2+c x^4\right)^{3/2} (2 b B-3 A c)}{105 c^3 x}+\frac{B x^3 \left(b x^2+c x^4\right)^{3/2}}{9 c}",1,"(-8*b^2*(2*b*B - 3*A*c)*(b*x^2 + c*x^4)^(3/2))/(315*c^4*x^3) + (4*b*(2*b*B - 3*A*c)*(b*x^2 + c*x^4)^(3/2))/(105*c^3*x) - ((2*b*B - 3*A*c)*x*(b*x^2 + c*x^4)^(3/2))/(21*c^2) + (B*x^3*(b*x^2 + c*x^4)^(3/2))/(9*c)","A",4,3,26,0.1154,1,"{2039, 2016, 2000}"
101,1,94,0,0.1658061,"\int x^2 \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^2*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","-\frac{\left(b x^2+c x^4\right)^{3/2} (4 b B-7 A c)}{35 c^2 x}+\frac{2 b \left(b x^2+c x^4\right)^{3/2} (4 b B-7 A c)}{105 c^3 x^3}+\frac{B x \left(b x^2+c x^4\right)^{3/2}}{7 c}","-\frac{\left(b x^2+c x^4\right)^{3/2} (4 b B-7 A c)}{35 c^2 x}+\frac{2 b \left(b x^2+c x^4\right)^{3/2} (4 b B-7 A c)}{105 c^3 x^3}+\frac{B x \left(b x^2+c x^4\right)^{3/2}}{7 c}",1,"(2*b*(4*b*B - 7*A*c)*(b*x^2 + c*x^4)^(3/2))/(105*c^3*x^3) - ((4*b*B - 7*A*c)*(b*x^2 + c*x^4)^(3/2))/(35*c^2*x) + (B*x*(b*x^2 + c*x^4)^(3/2))/(7*c)","A",3,3,26,0.1154,1,"{2039, 2016, 2000}"
102,1,61,0,0.018547,"\int \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","\frac{B \left(b x^2+c x^4\right)^{3/2}}{5 c x}-\frac{\left(b x^2+c x^4\right)^{3/2} (2 b B-5 A c)}{15 c^2 x^3}","\frac{B \left(b x^2+c x^4\right)^{3/2}}{5 c x}-\frac{\left(b x^2+c x^4\right)^{3/2} (2 b B-5 A c)}{15 c^2 x^3}",1,"-((2*b*B - 5*A*c)*(b*x^2 + c*x^4)^(3/2))/(15*c^2*x^3) + (B*(b*x^2 + c*x^4)^(3/2))/(5*c*x)","A",2,2,23,0.08696,1,"{1145, 2000}"
103,1,78,0,0.1459522,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^2} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^2,x]","\frac{A \sqrt{b x^2+c x^4}}{x}-A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)+\frac{B \left(b x^2+c x^4\right)^{3/2}}{3 c x^3}","\frac{A \sqrt{b x^2+c x^4}}{x}-A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)+\frac{B \left(b x^2+c x^4\right)^{3/2}}{3 c x^3}",1,"(A*Sqrt[b*x^2 + c*x^4])/x + (B*(b*x^2 + c*x^4)^(3/2))/(3*c*x^3) - A*Sqrt[b]*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]","A",4,4,26,0.1538,1,"{2039, 2021, 2008, 206}"
104,1,100,0,0.1608599,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^4} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^4,x]","\frac{\sqrt{b x^2+c x^4} (A c+2 b B)}{2 b x}-\frac{(A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{b}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{2 b x^5}","\frac{\sqrt{b x^2+c x^4} (A c+2 b B)}{2 b x}-\frac{(A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 \sqrt{b}}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{2 b x^5}",1,"((2*b*B + A*c)*Sqrt[b*x^2 + c*x^4])/(2*b*x) - (A*(b*x^2 + c*x^4)^(3/2))/(2*b*x^5) - ((2*b*B + A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*Sqrt[b])","A",4,4,26,0.1538,1,"{2038, 2021, 2008, 206}"
105,1,103,0,0.1576213,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^6} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^6,x]","-\frac{c (4 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{3/2}}-\frac{\sqrt{b x^2+c x^4} (4 b B-A c)}{8 b x^3}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{4 b x^7}","-\frac{c (4 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{3/2}}-\frac{\sqrt{b x^2+c x^4} (4 b B-A c)}{8 b x^3}-\frac{A \left(b x^2+c x^4\right)^{3/2}}{4 b x^7}",1,"-((4*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(8*b*x^3) - (A*(b*x^2 + c*x^4)^(3/2))/(4*b*x^7) - (c*(4*b*B - A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(3/2))","A",4,4,26,0.1538,1,"{2038, 2020, 2008, 206}"
106,1,223,0,0.4036461,"\int x^5 \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^5*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","\frac{b^4 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (9 b B-14 A c)}{2048 c^5}-\frac{b^2 \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2} (9 b B-14 A c)}{768 c^4}-\frac{b^6 (9 b B-14 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2048 c^{11/2}}+\frac{b \left(b x^2+c x^4\right)^{5/2} (9 b B-14 A c)}{240 c^3}-\frac{x^2 \left(b x^2+c x^4\right)^{5/2} (9 b B-14 A c)}{168 c^2}+\frac{B x^4 \left(b x^2+c x^4\right)^{5/2}}{14 c}","\frac{b^4 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (9 b B-14 A c)}{2048 c^5}-\frac{b^2 \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2} (9 b B-14 A c)}{768 c^4}-\frac{b^6 (9 b B-14 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2048 c^{11/2}}+\frac{b \left(b x^2+c x^4\right)^{5/2} (9 b B-14 A c)}{240 c^3}-\frac{x^2 \left(b x^2+c x^4\right)^{5/2} (9 b B-14 A c)}{168 c^2}+\frac{B x^4 \left(b x^2+c x^4\right)^{5/2}}{14 c}",1,"(b^4*(9*b*B - 14*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(2048*c^5) - (b^2*(9*b*B - 14*A*c)*(b + 2*c*x^2)*(b*x^2 + c*x^4)^(3/2))/(768*c^4) + (b*(9*b*B - 14*A*c)*(b*x^2 + c*x^4)^(5/2))/(240*c^3) - ((9*b*B - 14*A*c)*x^2*(b*x^2 + c*x^4)^(5/2))/(168*c^2) + (B*x^4*(b*x^2 + c*x^4)^(5/2))/(14*c) - (b^6*(9*b*B - 14*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2048*c^(11/2))","A",8,7,26,0.2692,1,"{2034, 794, 670, 640, 612, 620, 206}"
107,1,167,0,0.2478517,"\int x^3 \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^3*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","-\frac{b^3 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (7 b B-12 A c)}{1024 c^4}+\frac{b^5 (7 b B-12 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{1024 c^{9/2}}+\frac{b \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2} (7 b B-12 A c)}{384 c^3}-\frac{\left(b x^2+c x^4\right)^{5/2} \left(-12 A c+7 b B-10 B c x^2\right)}{120 c^2}","-\frac{b^3 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (7 b B-12 A c)}{1024 c^4}+\frac{b^5 (7 b B-12 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{1024 c^{9/2}}+\frac{b \left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2} (7 b B-12 A c)}{384 c^3}-\frac{\left(b x^2+c x^4\right)^{5/2} \left(-12 A c+7 b B-10 B c x^2\right)}{120 c^2}",1,"-(b^3*(7*b*B - 12*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(1024*c^4) + (b*(7*b*B - 12*A*c)*(b + 2*c*x^2)*(b*x^2 + c*x^4)^(3/2))/(384*c^3) - ((7*b*B - 12*A*c - 10*B*c*x^2)*(b*x^2 + c*x^4)^(5/2))/(120*c^2) + (b^5*(7*b*B - 12*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(1024*c^(9/2))","A",6,5,26,0.1923,1,"{2034, 779, 612, 620, 206}"
108,1,148,0,0.1914461,"\int x \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","\frac{3 b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (b B-2 A c)}{256 c^3}-\frac{3 b^4 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{256 c^{7/2}}-\frac{\left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2} (b B-2 A c)}{32 c^2}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{10 c}","\frac{3 b^2 \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (b B-2 A c)}{256 c^3}-\frac{3 b^4 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{256 c^{7/2}}-\frac{\left(b+2 c x^2\right) \left(b x^2+c x^4\right)^{3/2} (b B-2 A c)}{32 c^2}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{10 c}",1,"(3*b^2*(b*B - 2*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(256*c^3) - ((b*B - 2*A*c)*(b + 2*c*x^2)*(b*x^2 + c*x^4)^(3/2))/(32*c^2) + (B*(b*x^2 + c*x^4)^(5/2))/(10*c) - (3*b^4*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(256*c^(7/2))","A",6,5,24,0.2083,1,"{2034, 640, 612, 620, 206}"
109,1,144,0,0.2657804,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x,x]","\frac{b^3 (3 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{5/2}}-\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (3 b B-8 A c)}{128 c^2}-\frac{\left(b x^2+c x^4\right)^{3/2} (3 b B-8 A c)}{48 c}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{8 c x^2}","\frac{b^3 (3 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{5/2}}-\frac{b \left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (3 b B-8 A c)}{128 c^2}-\frac{\left(b x^2+c x^4\right)^{3/2} (3 b B-8 A c)}{48 c}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{8 c x^2}",1,"-(b*(3*b*B - 8*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(128*c^2) - ((3*b*B - 8*A*c)*(b*x^2 + c*x^4)^(3/2))/(48*c) + (B*(b*x^2 + c*x^4)^(5/2))/(8*c*x^2) + (b^3*(3*b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(128*c^(5/2))","A",6,6,26,0.2308,1,"{2034, 794, 664, 612, 620, 206}"
110,1,137,0,0.2959046,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^3} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^3,x]","-\frac{b^2 (b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{3/2}}+\frac{\left(b x^2+c x^4\right)^{3/2} (b B-6 A c)}{6 b}+\frac{\left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (b B-6 A c)}{16 c}+\frac{A \left(b x^2+c x^4\right)^{5/2}}{b x^4}","-\frac{b^2 (b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{3/2}}+\frac{\left(b x^2+c x^4\right)^{3/2} (b B-6 A c)}{6 b}+\frac{\left(b+2 c x^2\right) \sqrt{b x^2+c x^4} (b B-6 A c)}{16 c}+\frac{A \left(b x^2+c x^4\right)^{5/2}}{b x^4}",1,"((b*B - 6*A*c)*(b + 2*c*x^2)*Sqrt[b*x^2 + c*x^4])/(16*c) + ((b*B - 6*A*c)*(b*x^2 + c*x^4)^(3/2))/(6*b) + (A*(b*x^2 + c*x^4)^(5/2))/(b*x^4) - (b^2*(b*B - 6*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(3/2))","A",6,6,26,0.2308,1,"{2034, 792, 664, 612, 620, 206}"
111,1,128,0,0.2773218,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^5} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^5,x]","\frac{\left(b x^2+c x^4\right)^{3/2} (4 A c+b B)}{4 b x^2}+\frac{3}{8} \sqrt{b x^2+c x^4} (4 A c+b B)+\frac{3 b (4 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{c}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{b x^6}","\frac{\left(b x^2+c x^4\right)^{3/2} (4 A c+b B)}{4 b x^2}+\frac{3}{8} \sqrt{b x^2+c x^4} (4 A c+b B)+\frac{3 b (4 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{c}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{b x^6}",1,"(3*(b*B + 4*A*c)*Sqrt[b*x^2 + c*x^4])/8 + ((b*B + 4*A*c)*(b*x^2 + c*x^4)^(3/2))/(4*b*x^2) - (A*(b*x^2 + c*x^4)^(5/2))/(b*x^6) + (3*b*(b*B + 4*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*Sqrt[c])","A",6,5,26,0.1923,1,"{2034, 792, 664, 620, 206}"
112,1,136,0,0.2735276,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^7} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^7,x]","-\frac{\left(b x^2+c x^4\right)^{3/2} (2 A c+3 b B)}{3 b x^4}+\frac{c \sqrt{b x^2+c x^4} (2 A c+3 b B)}{2 b}+\frac{1}{2} \sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{A \left(b x^2+c x^4\right)^{5/2}}{3 b x^8}","-\frac{\left(b x^2+c x^4\right)^{3/2} (2 A c+3 b B)}{3 b x^4}+\frac{c \sqrt{b x^2+c x^4} (2 A c+3 b B)}{2 b}+\frac{1}{2} \sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{A \left(b x^2+c x^4\right)^{5/2}}{3 b x^8}",1,"(c*(3*b*B + 2*A*c)*Sqrt[b*x^2 + c*x^4])/(2*b) - ((3*b*B + 2*A*c)*(b*x^2 + c*x^4)^(3/2))/(3*b*x^4) - (A*(b*x^2 + c*x^4)^(5/2))/(3*b*x^8) + (Sqrt[c]*(3*b*B + 2*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/2","A",6,6,26,0.2308,1,"{2034, 792, 662, 664, 620, 206}"
113,1,104,0,0.2513625,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^9} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^9,x]","-\frac{A \left(b x^2+c x^4\right)^{5/2}}{5 b x^{10}}+B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{B \left(b x^2+c x^4\right)^{3/2}}{3 x^6}-\frac{B c \sqrt{b x^2+c x^4}}{x^2}","-\frac{A \left(b x^2+c x^4\right)^{5/2}}{5 b x^{10}}+B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)-\frac{B \left(b x^2+c x^4\right)^{3/2}}{3 x^6}-\frac{B c \sqrt{b x^2+c x^4}}{x^2}",1,"-((B*c*Sqrt[b*x^2 + c*x^4])/x^2) - (B*(b*x^2 + c*x^4)^(3/2))/(3*x^6) - (A*(b*x^2 + c*x^4)^(5/2))/(5*b*x^10) + B*c^(3/2)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]]","A",6,5,26,0.1923,1,"{2034, 792, 662, 620, 206}"
114,1,61,0,0.1730043,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{11}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^11,x]","-\frac{\left(b x^2+c x^4\right)^{5/2} (7 b B-2 A c)}{35 b^2 x^{10}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{7 b x^{12}}","-\frac{\left(b x^2+c x^4\right)^{5/2} (7 b B-2 A c)}{35 b^2 x^{10}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{7 b x^{12}}",1,"-(A*(b*x^2 + c*x^4)^(5/2))/(7*b*x^12) - ((7*b*B - 2*A*c)*(b*x^2 + c*x^4)^(5/2))/(35*b^2*x^10)","A",3,3,26,0.1154,1,"{2034, 792, 650}"
115,1,96,0,0.2334313,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{13}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^13,x]","\frac{2 c \left(b x^2+c x^4\right)^{5/2} (9 b B-4 A c)}{315 b^3 x^{10}}-\frac{\left(b x^2+c x^4\right)^{5/2} (9 b B-4 A c)}{63 b^2 x^{12}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{9 b x^{14}}","\frac{2 c \left(b x^2+c x^4\right)^{5/2} (9 b B-4 A c)}{315 b^3 x^{10}}-\frac{\left(b x^2+c x^4\right)^{5/2} (9 b B-4 A c)}{63 b^2 x^{12}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{9 b x^{14}}",1,"-(A*(b*x^2 + c*x^4)^(5/2))/(9*b*x^14) - ((9*b*B - 4*A*c)*(b*x^2 + c*x^4)^(5/2))/(63*b^2*x^12) + (2*c*(9*b*B - 4*A*c)*(b*x^2 + c*x^4)^(5/2))/(315*b^3*x^10)","A",4,4,26,0.1538,1,"{2034, 792, 658, 650}"
116,1,133,0,0.2788388,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{15}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^15,x]","-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2} (11 b B-6 A c)}{3465 b^4 x^{10}}+\frac{4 c \left(b x^2+c x^4\right)^{5/2} (11 b B-6 A c)}{693 b^3 x^{12}}-\frac{\left(b x^2+c x^4\right)^{5/2} (11 b B-6 A c)}{99 b^2 x^{14}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{11 b x^{16}}","-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2} (11 b B-6 A c)}{3465 b^4 x^{10}}+\frac{4 c \left(b x^2+c x^4\right)^{5/2} (11 b B-6 A c)}{693 b^3 x^{12}}-\frac{\left(b x^2+c x^4\right)^{5/2} (11 b B-6 A c)}{99 b^2 x^{14}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{11 b x^{16}}",1,"-(A*(b*x^2 + c*x^4)^(5/2))/(11*b*x^16) - ((11*b*B - 6*A*c)*(b*x^2 + c*x^4)^(5/2))/(99*b^2*x^14) + (4*c*(11*b*B - 6*A*c)*(b*x^2 + c*x^4)^(5/2))/(693*b^3*x^12) - (8*c^2*(11*b*B - 6*A*c)*(b*x^2 + c*x^4)^(5/2))/(3465*b^4*x^10)","A",5,4,26,0.1538,1,"{2034, 792, 658, 650}"
117,1,170,0,0.3213323,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{17}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^17,x]","\frac{16 c^3 \left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{15015 b^5 x^{10}}-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{3003 b^4 x^{12}}+\frac{2 c \left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{429 b^3 x^{14}}-\frac{\left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{143 b^2 x^{16}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{13 b x^{18}}","\frac{16 c^3 \left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{15015 b^5 x^{10}}-\frac{8 c^2 \left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{3003 b^4 x^{12}}+\frac{2 c \left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{429 b^3 x^{14}}-\frac{\left(b x^2+c x^4\right)^{5/2} (13 b B-8 A c)}{143 b^2 x^{16}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{13 b x^{18}}",1,"-(A*(b*x^2 + c*x^4)^(5/2))/(13*b*x^18) - ((13*b*B - 8*A*c)*(b*x^2 + c*x^4)^(5/2))/(143*b^2*x^16) + (2*c*(13*b*B - 8*A*c)*(b*x^2 + c*x^4)^(5/2))/(429*b^3*x^14) - (8*c^2*(13*b*B - 8*A*c)*(b*x^2 + c*x^4)^(5/2))/(3003*b^4*x^12) + (16*c^3*(13*b*B - 8*A*c)*(b*x^2 + c*x^4)^(5/2))/(15015*b^5*x^10)","A",6,4,26,0.1538,1,"{2034, 792, 658, 650}"
118,1,207,0,0.3516769,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{19}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^19,x]","-\frac{128 c^4 \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{45045 b^6 x^{10}}+\frac{64 c^3 \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{9009 b^5 x^{12}}-\frac{16 c^2 \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{1287 b^4 x^{14}}+\frac{8 c \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{429 b^3 x^{16}}-\frac{\left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{39 b^2 x^{18}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{15 b x^{20}}","-\frac{128 c^4 \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{45045 b^6 x^{10}}+\frac{64 c^3 \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{9009 b^5 x^{12}}-\frac{16 c^2 \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{1287 b^4 x^{14}}+\frac{8 c \left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{429 b^3 x^{16}}-\frac{\left(b x^2+c x^4\right)^{5/2} (3 b B-2 A c)}{39 b^2 x^{18}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{15 b x^{20}}",1,"-(A*(b*x^2 + c*x^4)^(5/2))/(15*b*x^20) - ((3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(5/2))/(39*b^2*x^18) + (8*c*(3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(5/2))/(429*b^3*x^16) - (16*c^2*(3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(5/2))/(1287*b^4*x^14) + (64*c^3*(3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(5/2))/(9009*b^5*x^12) - (128*c^4*(3*b*B - 2*A*c)*(b*x^2 + c*x^4)^(5/2))/(45045*b^6*x^10)","A",7,4,26,0.1538,1,"{2034, 792, 658, 650}"
119,1,168,0,0.2971789,"\int x^4 \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^4*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","\frac{16 b^3 \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{15015 c^5 x^5}-\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{3003 c^4 x^3}+\frac{2 b \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{429 c^3 x}-\frac{x \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{143 c^2}+\frac{B x^3 \left(b x^2+c x^4\right)^{5/2}}{13 c}","\frac{16 b^3 \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{15015 c^5 x^5}-\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{3003 c^4 x^3}+\frac{2 b \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{429 c^3 x}-\frac{x \left(b x^2+c x^4\right)^{5/2} (8 b B-13 A c)}{143 c^2}+\frac{B x^3 \left(b x^2+c x^4\right)^{5/2}}{13 c}",1,"(16*b^3*(8*b*B - 13*A*c)*(b*x^2 + c*x^4)^(5/2))/(15015*c^5*x^5) - (8*b^2*(8*b*B - 13*A*c)*(b*x^2 + c*x^4)^(5/2))/(3003*c^4*x^3) + (2*b*(8*b*B - 13*A*c)*(b*x^2 + c*x^4)^(5/2))/(429*c^3*x) - ((8*b*B - 13*A*c)*x*(b*x^2 + c*x^4)^(5/2))/(143*c^2) + (B*x^3*(b*x^2 + c*x^4)^(5/2))/(13*c)","A",5,4,26,0.1538,1,"{2039, 2016, 2002, 2014}"
120,1,131,0,0.2413936,"\int x^2 \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^2*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","-\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2} (6 b B-11 A c)}{3465 c^4 x^5}-\frac{\left(b x^2+c x^4\right)^{5/2} (6 b B-11 A c)}{99 c^2 x}+\frac{4 b \left(b x^2+c x^4\right)^{5/2} (6 b B-11 A c)}{693 c^3 x^3}+\frac{B x \left(b x^2+c x^4\right)^{5/2}}{11 c}","-\frac{8 b^2 \left(b x^2+c x^4\right)^{5/2} (6 b B-11 A c)}{3465 c^4 x^5}-\frac{\left(b x^2+c x^4\right)^{5/2} (6 b B-11 A c)}{99 c^2 x}+\frac{4 b \left(b x^2+c x^4\right)^{5/2} (6 b B-11 A c)}{693 c^3 x^3}+\frac{B x \left(b x^2+c x^4\right)^{5/2}}{11 c}",1,"(-8*b^2*(6*b*B - 11*A*c)*(b*x^2 + c*x^4)^(5/2))/(3465*c^4*x^5) + (4*b*(6*b*B - 11*A*c)*(b*x^2 + c*x^4)^(5/2))/(693*c^3*x^3) - ((6*b*B - 11*A*c)*(b*x^2 + c*x^4)^(5/2))/(99*c^2*x) + (B*x*(b*x^2 + c*x^4)^(5/2))/(11*c)","A",4,4,26,0.1538,1,"{2039, 2016, 2002, 2014}"
121,1,96,0,0.069621,"\int \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","-\frac{\left(b x^2+c x^4\right)^{5/2} (4 b B-9 A c)}{63 c^2 x^3}+\frac{2 b \left(b x^2+c x^4\right)^{5/2} (4 b B-9 A c)}{315 c^3 x^5}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{9 c x}","-\frac{\left(b x^2+c x^4\right)^{5/2} (4 b B-9 A c)}{63 c^2 x^3}+\frac{2 b \left(b x^2+c x^4\right)^{5/2} (4 b B-9 A c)}{315 c^3 x^5}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{9 c x}",1,"(2*b*(4*b*B - 9*A*c)*(b*x^2 + c*x^4)^(5/2))/(315*c^3*x^5) - ((4*b*B - 9*A*c)*(b*x^2 + c*x^4)^(5/2))/(63*c^2*x^3) + (B*(b*x^2 + c*x^4)^(5/2))/(9*c*x)","A",3,3,23,0.1304,1,"{1145, 2002, 2014}"
122,1,61,0,0.159236,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^2} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^2,x]","\frac{B \left(b x^2+c x^4\right)^{5/2}}{7 c x^3}-\frac{\left(b x^2+c x^4\right)^{5/2} (2 b B-7 A c)}{35 c^2 x^5}","\frac{B \left(b x^2+c x^4\right)^{5/2}}{7 c x^3}-\frac{\left(b x^2+c x^4\right)^{5/2} (2 b B-7 A c)}{35 c^2 x^5}",1,"-((2*b*B - 7*A*c)*(b*x^2 + c*x^4)^(5/2))/(35*c^2*x^5) + (B*(b*x^2 + c*x^4)^(5/2))/(7*c*x^3)","A",2,2,26,0.07692,1,"{2039, 2014}"
123,1,102,0,0.2054079,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^4} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^4,x]","-A b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)+\frac{A \left(b x^2+c x^4\right)^{3/2}}{3 x^3}+\frac{A b \sqrt{b x^2+c x^4}}{x}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{5 c x^5}","-A b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)+\frac{A \left(b x^2+c x^4\right)^{3/2}}{3 x^3}+\frac{A b \sqrt{b x^2+c x^4}}{x}+\frac{B \left(b x^2+c x^4\right)^{5/2}}{5 c x^5}",1,"(A*b*Sqrt[b*x^2 + c*x^4])/x + (A*(b*x^2 + c*x^4)^(3/2))/(3*x^3) + (B*(b*x^2 + c*x^4)^(5/2))/(5*c*x^5) - A*b^(3/2)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]]","A",5,4,26,0.1538,1,"{2039, 2021, 2008, 206}"
124,1,133,0,0.2196479,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^6} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^6,x]","\frac{\left(b x^2+c x^4\right)^{3/2} (3 A c+2 b B)}{6 b x^3}+\frac{\sqrt{b x^2+c x^4} (3 A c+2 b B)}{2 x}-\frac{1}{2} \sqrt{b} (3 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)-\frac{A \left(b x^2+c x^4\right)^{5/2}}{2 b x^7}","\frac{\left(b x^2+c x^4\right)^{3/2} (3 A c+2 b B)}{6 b x^3}+\frac{\sqrt{b x^2+c x^4} (3 A c+2 b B)}{2 x}-\frac{1}{2} \sqrt{b} (3 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)-\frac{A \left(b x^2+c x^4\right)^{5/2}}{2 b x^7}",1,"((2*b*B + 3*A*c)*Sqrt[b*x^2 + c*x^4])/(2*x) + ((2*b*B + 3*A*c)*(b*x^2 + c*x^4)^(3/2))/(6*b*x^3) - (A*(b*x^2 + c*x^4)^(5/2))/(2*b*x^7) - (Sqrt[b]*(2*b*B + 3*A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/2","A",5,4,26,0.1538,1,"{2038, 2021, 2008, 206}"
125,1,135,0,0.2161104,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^8} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^8,x]","-\frac{\left(b x^2+c x^4\right)^{3/2} (A c+4 b B)}{8 b x^5}+\frac{3 c \sqrt{b x^2+c x^4} (A c+4 b B)}{8 b x}-\frac{3 c (A c+4 b B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{b}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{4 b x^9}","-\frac{\left(b x^2+c x^4\right)^{3/2} (A c+4 b B)}{8 b x^5}+\frac{3 c \sqrt{b x^2+c x^4} (A c+4 b B)}{8 b x}-\frac{3 c (A c+4 b B) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 \sqrt{b}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{4 b x^9}",1,"(3*c*(4*b*B + A*c)*Sqrt[b*x^2 + c*x^4])/(8*b*x) - ((4*b*B + A*c)*(b*x^2 + c*x^4)^(3/2))/(8*b*x^5) - (A*(b*x^2 + c*x^4)^(5/2))/(4*b*x^9) - (3*c*(4*b*B + A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*Sqrt[b])","A",5,5,26,0.1923,1,"{2038, 2020, 2021, 2008, 206}"
126,1,140,0,0.2233416,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{10}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^10,x]","-\frac{c^2 (6 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{16 b^{3/2}}-\frac{\left(b x^2+c x^4\right)^{3/2} (6 b B-A c)}{24 b x^7}-\frac{c \sqrt{b x^2+c x^4} (6 b B-A c)}{16 b x^3}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{6 b x^{11}}","-\frac{c^2 (6 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{16 b^{3/2}}-\frac{\left(b x^2+c x^4\right)^{3/2} (6 b B-A c)}{24 b x^7}-\frac{c \sqrt{b x^2+c x^4} (6 b B-A c)}{16 b x^3}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{6 b x^{11}}",1,"-(c*(6*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(16*b*x^3) - ((6*b*B - A*c)*(b*x^2 + c*x^4)^(3/2))/(24*b*x^7) - (A*(b*x^2 + c*x^4)^(5/2))/(6*b*x^11) - (c^2*(6*b*B - A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(16*b^(3/2))","A",5,4,26,0.1538,1,"{2038, 2020, 2008, 206}"
127,1,177,0,0.281209,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{12}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^12,x]","-\frac{c^2 \sqrt{b x^2+c x^4} (8 b B-3 A c)}{128 b^2 x^3}+\frac{c^3 (8 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{128 b^{5/2}}-\frac{c \sqrt{b x^2+c x^4} (8 b B-3 A c)}{64 b x^5}-\frac{\left(b x^2+c x^4\right)^{3/2} (8 b B-3 A c)}{48 b x^9}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{8 b x^{13}}","-\frac{c^2 \sqrt{b x^2+c x^4} (8 b B-3 A c)}{128 b^2 x^3}+\frac{c^3 (8 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{128 b^{5/2}}-\frac{c \sqrt{b x^2+c x^4} (8 b B-3 A c)}{64 b x^5}-\frac{\left(b x^2+c x^4\right)^{3/2} (8 b B-3 A c)}{48 b x^9}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{8 b x^{13}}",1,"-(c*(8*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(64*b*x^5) - (c^2*(8*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(128*b^2*x^3) - ((8*b*B - 3*A*c)*(b*x^2 + c*x^4)^(3/2))/(48*b*x^9) - (A*(b*x^2 + c*x^4)^(5/2))/(8*b*x^13) + (c^3*(8*b*B - 3*A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(128*b^(5/2))","A",6,5,26,0.1923,1,"{2038, 2020, 2025, 2008, 206}"
128,1,214,0,0.3394158,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{14}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^14,x]","\frac{3 c^3 \sqrt{b x^2+c x^4} (2 b B-A c)}{256 b^3 x^3}-\frac{c^2 \sqrt{b x^2+c x^4} (2 b B-A c)}{128 b^2 x^5}-\frac{3 c^4 (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{256 b^{7/2}}-\frac{c \sqrt{b x^2+c x^4} (2 b B-A c)}{32 b x^7}-\frac{\left(b x^2+c x^4\right)^{3/2} (2 b B-A c)}{16 b x^{11}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{10 b x^{15}}","\frac{3 c^3 \sqrt{b x^2+c x^4} (2 b B-A c)}{256 b^3 x^3}-\frac{c^2 \sqrt{b x^2+c x^4} (2 b B-A c)}{128 b^2 x^5}-\frac{3 c^4 (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{256 b^{7/2}}-\frac{c \sqrt{b x^2+c x^4} (2 b B-A c)}{32 b x^7}-\frac{\left(b x^2+c x^4\right)^{3/2} (2 b B-A c)}{16 b x^{11}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{10 b x^{15}}",1,"-(c*(2*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(32*b*x^7) - (c^2*(2*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(128*b^2*x^5) + (3*c^3*(2*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(256*b^3*x^3) - ((2*b*B - A*c)*(b*x^2 + c*x^4)^(3/2))/(16*b*x^11) - (A*(b*x^2 + c*x^4)^(5/2))/(10*b*x^15) - (3*c^4*(2*b*B - A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(256*b^(7/2))","A",7,5,26,0.1923,1,"{2038, 2020, 2025, 2008, 206}"
129,1,251,0,0.3897822,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{16}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^16,x]","-\frac{c^4 \sqrt{b x^2+c x^4} (12 b B-7 A c)}{1024 b^4 x^3}+\frac{c^3 \sqrt{b x^2+c x^4} (12 b B-7 A c)}{1536 b^3 x^5}-\frac{c^2 \sqrt{b x^2+c x^4} (12 b B-7 A c)}{1920 b^2 x^7}+\frac{c^5 (12 b B-7 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{1024 b^{9/2}}-\frac{c \sqrt{b x^2+c x^4} (12 b B-7 A c)}{320 b x^9}-\frac{\left(b x^2+c x^4\right)^{3/2} (12 b B-7 A c)}{120 b x^{13}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{12 b x^{17}}","-\frac{c^4 \sqrt{b x^2+c x^4} (12 b B-7 A c)}{1024 b^4 x^3}+\frac{c^3 \sqrt{b x^2+c x^4} (12 b B-7 A c)}{1536 b^3 x^5}-\frac{c^2 \sqrt{b x^2+c x^4} (12 b B-7 A c)}{1920 b^2 x^7}+\frac{c^5 (12 b B-7 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{1024 b^{9/2}}-\frac{c \sqrt{b x^2+c x^4} (12 b B-7 A c)}{320 b x^9}-\frac{\left(b x^2+c x^4\right)^{3/2} (12 b B-7 A c)}{120 b x^{13}}-\frac{A \left(b x^2+c x^4\right)^{5/2}}{12 b x^{17}}",1,"-(c*(12*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(320*b*x^9) - (c^2*(12*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(1920*b^2*x^7) + (c^3*(12*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(1536*b^3*x^5) - (c^4*(12*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(1024*b^4*x^3) - ((12*b*B - 7*A*c)*(b*x^2 + c*x^4)^(3/2))/(120*b*x^13) - (A*(b*x^2 + c*x^4)^(5/2))/(12*b*x^17) + (c^5*(12*b*B - 7*A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(1024*b^(9/2))","A",8,5,26,0.1923,1,"{2038, 2020, 2025, 2008, 206}"
130,1,176,0,0.3284477,"\int \frac{x^7 \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^7*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{5 b^2 \sqrt{b x^2+c x^4} (7 b B-8 A c)}{128 c^4}+\frac{5 b^3 (7 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{9/2}}-\frac{x^4 \sqrt{b x^2+c x^4} (7 b B-8 A c)}{48 c^2}+\frac{5 b x^2 \sqrt{b x^2+c x^4} (7 b B-8 A c)}{192 c^3}+\frac{B x^6 \sqrt{b x^2+c x^4}}{8 c}","-\frac{5 b^2 \sqrt{b x^2+c x^4} (7 b B-8 A c)}{128 c^4}+\frac{5 b^3 (7 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{128 c^{9/2}}-\frac{x^4 \sqrt{b x^2+c x^4} (7 b B-8 A c)}{48 c^2}+\frac{5 b x^2 \sqrt{b x^2+c x^4} (7 b B-8 A c)}{192 c^3}+\frac{B x^6 \sqrt{b x^2+c x^4}}{8 c}",1,"(-5*b^2*(7*b*B - 8*A*c)*Sqrt[b*x^2 + c*x^4])/(128*c^4) + (5*b*(7*b*B - 8*A*c)*x^2*Sqrt[b*x^2 + c*x^4])/(192*c^3) - ((7*b*B - 8*A*c)*x^4*Sqrt[b*x^2 + c*x^4])/(48*c^2) + (B*x^6*Sqrt[b*x^2 + c*x^4])/(8*c) + (5*b^3*(7*b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(128*c^(9/2))","A",7,6,26,0.2308,1,"{2034, 794, 670, 640, 620, 206}"
131,1,139,0,0.2749164,"\int \frac{x^5 \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^5*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{b^2 (5 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{7/2}}-\frac{x^2 \sqrt{b x^2+c x^4} (5 b B-6 A c)}{24 c^2}+\frac{b \sqrt{b x^2+c x^4} (5 b B-6 A c)}{16 c^3}+\frac{B x^4 \sqrt{b x^2+c x^4}}{6 c}","-\frac{b^2 (5 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{7/2}}-\frac{x^2 \sqrt{b x^2+c x^4} (5 b B-6 A c)}{24 c^2}+\frac{b \sqrt{b x^2+c x^4} (5 b B-6 A c)}{16 c^3}+\frac{B x^4 \sqrt{b x^2+c x^4}}{6 c}",1,"(b*(5*b*B - 6*A*c)*Sqrt[b*x^2 + c*x^4])/(16*c^3) - ((5*b*B - 6*A*c)*x^2*Sqrt[b*x^2 + c*x^4])/(24*c^2) + (B*x^4*Sqrt[b*x^2 + c*x^4])/(6*c) - (b^2*(5*b*B - 6*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(7/2))","A",6,6,26,0.2308,1,"{2034, 794, 670, 640, 620, 206}"
132,1,83,0,0.1712455,"\int \frac{x^3 \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^3*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","\frac{b (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{5/2}}-\frac{\sqrt{b x^2+c x^4} \left(-4 A c+3 b B-2 B c x^2\right)}{8 c^2}","\frac{b (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{5/2}}-\frac{\sqrt{b x^2+c x^4} \left(-4 A c+3 b B-2 B c x^2\right)}{8 c^2}",1,"-((3*b*B - 4*A*c - 2*B*c*x^2)*Sqrt[b*x^2 + c*x^4])/(8*c^2) + (b*(3*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*c^(5/2))","A",4,4,26,0.1538,1,"{2034, 779, 620, 206}"
133,1,66,0,0.1231517,"\int \frac{x \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","\frac{B \sqrt{b x^2+c x^4}}{2 c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{3/2}}","\frac{B \sqrt{b x^2+c x^4}}{2 c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{3/2}}",1,"(B*Sqrt[b*x^2 + c*x^4])/(2*c) - ((b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*c^(3/2))","A",4,4,24,0.1667,1,"{2034, 640, 620, 206}"
134,1,57,0,0.1508431,"\int \frac{A+B x^2}{x \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x*Sqrt[b*x^2 + c*x^4]),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{c}}-\frac{A \sqrt{b x^2+c x^4}}{b x^2}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{c}}-\frac{A \sqrt{b x^2+c x^4}}{b x^2}",1,"-((A*Sqrt[b*x^2 + c*x^4])/(b*x^2)) + (B*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/Sqrt[c]","A",4,4,26,0.1538,1,"{2034, 792, 620, 206}"
135,1,61,0,0.1684002,"\int \frac{A+B x^2}{x^3 \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^3*Sqrt[b*x^2 + c*x^4]),x]","-\frac{\sqrt{b x^2+c x^4} (3 b B-2 A c)}{3 b^2 x^2}-\frac{A \sqrt{b x^2+c x^4}}{3 b x^4}","-\frac{\sqrt{b x^2+c x^4} (3 b B-2 A c)}{3 b^2 x^2}-\frac{A \sqrt{b x^2+c x^4}}{3 b x^4}",1,"-(A*Sqrt[b*x^2 + c*x^4])/(3*b*x^4) - ((3*b*B - 2*A*c)*Sqrt[b*x^2 + c*x^4])/(3*b^2*x^2)","A",3,3,26,0.1154,1,"{2034, 792, 650}"
136,1,96,0,0.2092513,"\int \frac{A+B x^2}{x^5 \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^5*Sqrt[b*x^2 + c*x^4]),x]","\frac{2 c \sqrt{b x^2+c x^4} (5 b B-4 A c)}{15 b^3 x^2}-\frac{\sqrt{b x^2+c x^4} (5 b B-4 A c)}{15 b^2 x^4}-\frac{A \sqrt{b x^2+c x^4}}{5 b x^6}","\frac{2 c \sqrt{b x^2+c x^4} (5 b B-4 A c)}{15 b^3 x^2}-\frac{\sqrt{b x^2+c x^4} (5 b B-4 A c)}{15 b^2 x^4}-\frac{A \sqrt{b x^2+c x^4}}{5 b x^6}",1,"-(A*Sqrt[b*x^2 + c*x^4])/(5*b*x^6) - ((5*b*B - 4*A*c)*Sqrt[b*x^2 + c*x^4])/(15*b^2*x^4) + (2*c*(5*b*B - 4*A*c)*Sqrt[b*x^2 + c*x^4])/(15*b^3*x^2)","A",4,4,26,0.1538,1,"{2034, 792, 658, 650}"
137,1,133,0,0.2534813,"\int \frac{A+B x^2}{x^7 \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^7*Sqrt[b*x^2 + c*x^4]),x]","-\frac{8 c^2 \sqrt{b x^2+c x^4} (7 b B-6 A c)}{105 b^4 x^2}+\frac{4 c \sqrt{b x^2+c x^4} (7 b B-6 A c)}{105 b^3 x^4}-\frac{\sqrt{b x^2+c x^4} (7 b B-6 A c)}{35 b^2 x^6}-\frac{A \sqrt{b x^2+c x^4}}{7 b x^8}","-\frac{8 c^2 \sqrt{b x^2+c x^4} (7 b B-6 A c)}{105 b^4 x^2}+\frac{4 c \sqrt{b x^2+c x^4} (7 b B-6 A c)}{105 b^3 x^4}-\frac{\sqrt{b x^2+c x^4} (7 b B-6 A c)}{35 b^2 x^6}-\frac{A \sqrt{b x^2+c x^4}}{7 b x^8}",1,"-(A*Sqrt[b*x^2 + c*x^4])/(7*b*x^8) - ((7*b*B - 6*A*c)*Sqrt[b*x^2 + c*x^4])/(35*b^2*x^6) + (4*c*(7*b*B - 6*A*c)*Sqrt[b*x^2 + c*x^4])/(105*b^3*x^4) - (8*c^2*(7*b*B - 6*A*c)*Sqrt[b*x^2 + c*x^4])/(105*b^4*x^2)","A",5,4,26,0.1538,1,"{2034, 792, 658, 650}"
138,1,170,0,0.3026595,"\int \frac{A+B x^2}{x^9 \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^9*Sqrt[b*x^2 + c*x^4]),x]","\frac{16 c^3 \sqrt{b x^2+c x^4} (9 b B-8 A c)}{315 b^5 x^2}-\frac{8 c^2 \sqrt{b x^2+c x^4} (9 b B-8 A c)}{315 b^4 x^4}+\frac{2 c \sqrt{b x^2+c x^4} (9 b B-8 A c)}{105 b^3 x^6}-\frac{\sqrt{b x^2+c x^4} (9 b B-8 A c)}{63 b^2 x^8}-\frac{A \sqrt{b x^2+c x^4}}{9 b x^{10}}","\frac{16 c^3 \sqrt{b x^2+c x^4} (9 b B-8 A c)}{315 b^5 x^2}-\frac{8 c^2 \sqrt{b x^2+c x^4} (9 b B-8 A c)}{315 b^4 x^4}+\frac{2 c \sqrt{b x^2+c x^4} (9 b B-8 A c)}{105 b^3 x^6}-\frac{\sqrt{b x^2+c x^4} (9 b B-8 A c)}{63 b^2 x^8}-\frac{A \sqrt{b x^2+c x^4}}{9 b x^{10}}",1,"-(A*Sqrt[b*x^2 + c*x^4])/(9*b*x^10) - ((9*b*B - 8*A*c)*Sqrt[b*x^2 + c*x^4])/(63*b^2*x^8) + (2*c*(9*b*B - 8*A*c)*Sqrt[b*x^2 + c*x^4])/(105*b^3*x^6) - (8*c^2*(9*b*B - 8*A*c)*Sqrt[b*x^2 + c*x^4])/(315*b^4*x^4) + (16*c^3*(9*b*B - 8*A*c)*Sqrt[b*x^2 + c*x^4])/(315*b^5*x^2)","A",6,4,26,0.1538,1,"{2034, 792, 658, 650}"
139,1,131,0,0.2398658,"\int \frac{x^6 \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^6*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{8 b^2 \sqrt{b x^2+c x^4} (6 b B-7 A c)}{105 c^4 x}-\frac{x^3 \sqrt{b x^2+c x^4} (6 b B-7 A c)}{35 c^2}+\frac{4 b x \sqrt{b x^2+c x^4} (6 b B-7 A c)}{105 c^3}+\frac{B x^5 \sqrt{b x^2+c x^4}}{7 c}","-\frac{8 b^2 \sqrt{b x^2+c x^4} (6 b B-7 A c)}{105 c^4 x}-\frac{x^3 \sqrt{b x^2+c x^4} (6 b B-7 A c)}{35 c^2}+\frac{4 b x \sqrt{b x^2+c x^4} (6 b B-7 A c)}{105 c^3}+\frac{B x^5 \sqrt{b x^2+c x^4}}{7 c}",1,"(-8*b^2*(6*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(105*c^4*x) + (4*b*(6*b*B - 7*A*c)*x*Sqrt[b*x^2 + c*x^4])/(105*c^3) - ((6*b*B - 7*A*c)*x^3*Sqrt[b*x^2 + c*x^4])/(35*c^2) + (B*x^5*Sqrt[b*x^2 + c*x^4])/(7*c)","A",4,3,26,0.1154,1,"{2039, 2016, 1588}"
140,1,94,0,0.1933941,"\int \frac{x^4 \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^4*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{x \sqrt{b x^2+c x^4} (4 b B-5 A c)}{15 c^2}+\frac{2 b \sqrt{b x^2+c x^4} (4 b B-5 A c)}{15 c^3 x}+\frac{B x^3 \sqrt{b x^2+c x^4}}{5 c}","-\frac{x \sqrt{b x^2+c x^4} (4 b B-5 A c)}{15 c^2}+\frac{2 b \sqrt{b x^2+c x^4} (4 b B-5 A c)}{15 c^3 x}+\frac{B x^3 \sqrt{b x^2+c x^4}}{5 c}",1,"(2*b*(4*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(15*c^3*x) - ((4*b*B - 5*A*c)*x*Sqrt[b*x^2 + c*x^4])/(15*c^2) + (B*x^3*Sqrt[b*x^2 + c*x^4])/(5*c)","A",3,3,26,0.1154,1,"{2039, 2016, 1588}"
141,1,59,0,0.1351745,"\int \frac{x^2 \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^2*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","\frac{B x \sqrt{b x^2+c x^4}}{3 c}-\frac{\sqrt{b x^2+c x^4} (2 b B-3 A c)}{3 c^2 x}","\frac{B x \sqrt{b x^2+c x^4}}{3 c}-\frac{\sqrt{b x^2+c x^4} (2 b B-3 A c)}{3 c^2 x}",1,"-((2*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(3*c^2*x) + (B*x*Sqrt[b*x^2 + c*x^4])/(3*c)","A",2,2,26,0.07692,1,"{2039, 1588}"
142,1,55,0,0.0197414,"\int \frac{A+B x^2}{\sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/Sqrt[b*x^2 + c*x^4],x]","\frac{B \sqrt{b x^2+c x^4}}{c x}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{b}}","\frac{B \sqrt{b x^2+c x^4}}{c x}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{\sqrt{b}}",1,"(B*Sqrt[b*x^2 + c*x^4])/(c*x) - (A*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/Sqrt[b]","A",3,3,23,0.1304,1,"{1145, 2008, 206}"
143,1,68,0,0.1172781,"\int \frac{A+B x^2}{x^2 \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^2*Sqrt[b*x^2 + c*x^4]),x]","-\frac{(2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{3/2}}-\frac{A \sqrt{b x^2+c x^4}}{2 b x^3}","-\frac{(2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{3/2}}-\frac{A \sqrt{b x^2+c x^4}}{2 b x^3}",1,"-(A*Sqrt[b*x^2 + c*x^4])/(2*b*x^3) - ((2*b*B - A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*b^(3/2))","A",3,3,26,0.1154,1,"{2038, 2008, 206}"
144,1,103,0,0.1654021,"\int \frac{A+B x^2}{x^4 \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^4*Sqrt[b*x^2 + c*x^4]),x]","-\frac{\sqrt{b x^2+c x^4} (4 b B-3 A c)}{8 b^2 x^3}+\frac{c (4 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{5/2}}-\frac{A \sqrt{b x^2+c x^4}}{4 b x^5}","-\frac{\sqrt{b x^2+c x^4} (4 b B-3 A c)}{8 b^2 x^3}+\frac{c (4 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{5/2}}-\frac{A \sqrt{b x^2+c x^4}}{4 b x^5}",1,"-(A*Sqrt[b*x^2 + c*x^4])/(4*b*x^5) - ((4*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(8*b^2*x^3) + (c*(4*b*B - 3*A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(5/2))","A",4,4,26,0.1538,1,"{2038, 2025, 2008, 206}"
145,1,184,0,0.3332796,"\int \frac{x^9 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^9*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","-\frac{5 b^2 (7 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{9/2}}+\frac{x^4 \sqrt{b x^2+c x^4} (7 b B-6 A c)}{6 b c^2}-\frac{5 x^2 \sqrt{b x^2+c x^4} (7 b B-6 A c)}{24 c^3}+\frac{5 b \sqrt{b x^2+c x^4} (7 b B-6 A c)}{16 c^4}-\frac{x^8 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","-\frac{5 b^2 (7 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{16 c^{9/2}}+\frac{x^4 \sqrt{b x^2+c x^4} (7 b B-6 A c)}{6 b c^2}-\frac{5 x^2 \sqrt{b x^2+c x^4} (7 b B-6 A c)}{24 c^3}+\frac{5 b \sqrt{b x^2+c x^4} (7 b B-6 A c)}{16 c^4}-\frac{x^8 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^8)/(b*c*Sqrt[b*x^2 + c*x^4])) + (5*b*(7*b*B - 6*A*c)*Sqrt[b*x^2 + c*x^4])/(16*c^4) - (5*(7*b*B - 6*A*c)*x^2*Sqrt[b*x^2 + c*x^4])/(24*c^3) + ((7*b*B - 6*A*c)*x^4*Sqrt[b*x^2 + c*x^4])/(6*b*c^2) - (5*b^2*(7*b*B - 6*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(16*c^(9/2))","A",7,6,26,0.2308,1,"{2034, 788, 670, 640, 620, 206}"
146,1,147,0,0.2804511,"\int \frac{x^7 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^7*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{x^2 \sqrt{b x^2+c x^4} (5 b B-4 A c)}{4 b c^2}-\frac{3 \sqrt{b x^2+c x^4} (5 b B-4 A c)}{8 c^3}+\frac{3 b (5 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{7/2}}-\frac{x^6 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{x^2 \sqrt{b x^2+c x^4} (5 b B-4 A c)}{4 b c^2}-\frac{3 \sqrt{b x^2+c x^4} (5 b B-4 A c)}{8 c^3}+\frac{3 b (5 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{8 c^{7/2}}-\frac{x^6 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^6)/(b*c*Sqrt[b*x^2 + c*x^4])) - (3*(5*b*B - 4*A*c)*Sqrt[b*x^2 + c*x^4])/(8*c^3) + ((5*b*B - 4*A*c)*x^2*Sqrt[b*x^2 + c*x^4])/(4*b*c^2) + (3*b*(5*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(8*c^(7/2))","A",6,6,26,0.2308,1,"{2034, 788, 670, 640, 620, 206}"
147,1,112,0,0.2416767,"\int \frac{x^5 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^5*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{\sqrt{b x^2+c x^4} (3 b B-2 A c)}{2 b c^2}-\frac{(3 b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{5/2}}-\frac{x^4 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{\sqrt{b x^2+c x^4} (3 b B-2 A c)}{2 b c^2}-\frac{(3 b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{2 c^{5/2}}-\frac{x^4 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^4)/(b*c*Sqrt[b*x^2 + c*x^4])) + ((3*b*B - 2*A*c)*Sqrt[b*x^2 + c*x^4])/(2*b*c^2) - ((3*b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/(2*c^(5/2))","A",5,5,26,0.1923,1,"{2034, 788, 640, 620, 206}"
148,1,67,0,0.1767541,"\int \frac{x^3 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^3*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{c^{3/2}}-\frac{x^2 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x^2}{\sqrt{b x^2+c x^4}}\right)}{c^{3/2}}-\frac{x^2 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^2)/(b*c*Sqrt[b*x^2 + c*x^4])) + (B*ArcTanh[(Sqrt[c]*x^2)/Sqrt[b*x^2 + c*x^4]])/c^(3/2)","A",4,4,26,0.1538,1,"{2034, 777, 620, 206}"
149,1,37,0,0.1212959,"\int \frac{x \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","-\frac{A b-x^2 (b B-2 A c)}{b^2 \sqrt{b x^2+c x^4}}","-\frac{A b-x^2 (b B-2 A c)}{b^2 \sqrt{b x^2+c x^4}}",1,"-((A*b - (b*B - 2*A*c)*x^2)/(b^2*Sqrt[b*x^2 + c*x^4]))","A",2,2,24,0.08333,1,"{2034, 636}"
150,1,66,0,0.1636367,"\int \frac{A+B x^2}{x \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{\left(b+2 c x^2\right) (3 b B-4 A c)}{3 b^3 \sqrt{b x^2+c x^4}}-\frac{A}{3 b x^2 \sqrt{b x^2+c x^4}}","-\frac{\left(b+2 c x^2\right) (3 b B-4 A c)}{3 b^3 \sqrt{b x^2+c x^4}}-\frac{A}{3 b x^2 \sqrt{b x^2+c x^4}}",1,"-A/(3*b*x^2*Sqrt[b*x^2 + c*x^4]) - ((3*b*B - 4*A*c)*(b + 2*c*x^2))/(3*b^3*Sqrt[b*x^2 + c*x^4])","A",3,3,26,0.1154,1,"{2034, 792, 613}"
151,1,101,0,0.2202005,"\int \frac{A+B x^2}{x^3 \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^3*(b*x^2 + c*x^4)^(3/2)),x]","\frac{4 c \left(b+2 c x^2\right) (5 b B-6 A c)}{15 b^4 \sqrt{b x^2+c x^4}}-\frac{5 b B-6 A c}{15 b^2 x^2 \sqrt{b x^2+c x^4}}-\frac{A}{5 b x^4 \sqrt{b x^2+c x^4}}","\frac{4 c \left(b+2 c x^2\right) (5 b B-6 A c)}{15 b^4 \sqrt{b x^2+c x^4}}-\frac{5 b B-6 A c}{15 b^2 x^2 \sqrt{b x^2+c x^4}}-\frac{A}{5 b x^4 \sqrt{b x^2+c x^4}}",1,"-A/(5*b*x^4*Sqrt[b*x^2 + c*x^4]) - (5*b*B - 6*A*c)/(15*b^2*x^2*Sqrt[b*x^2 + c*x^4]) + (4*c*(5*b*B - 6*A*c)*(b + 2*c*x^2))/(15*b^4*Sqrt[b*x^2 + c*x^4])","A",4,4,26,0.1538,1,"{2034, 792, 658, 613}"
152,1,138,0,0.2668606,"\int \frac{A+B x^2}{x^5 \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^5*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{8 c^2 \left(b+2 c x^2\right) (7 b B-8 A c)}{35 b^5 \sqrt{b x^2+c x^4}}+\frac{2 c (7 b B-8 A c)}{35 b^3 x^2 \sqrt{b x^2+c x^4}}-\frac{7 b B-8 A c}{35 b^2 x^4 \sqrt{b x^2+c x^4}}-\frac{A}{7 b x^6 \sqrt{b x^2+c x^4}}","-\frac{8 c^2 \left(b+2 c x^2\right) (7 b B-8 A c)}{35 b^5 \sqrt{b x^2+c x^4}}+\frac{2 c (7 b B-8 A c)}{35 b^3 x^2 \sqrt{b x^2+c x^4}}-\frac{7 b B-8 A c}{35 b^2 x^4 \sqrt{b x^2+c x^4}}-\frac{A}{7 b x^6 \sqrt{b x^2+c x^4}}",1,"-A/(7*b*x^6*Sqrt[b*x^2 + c*x^4]) - (7*b*B - 8*A*c)/(35*b^2*x^4*Sqrt[b*x^2 + c*x^4]) + (2*c*(7*b*B - 8*A*c))/(35*b^3*x^2*Sqrt[b*x^2 + c*x^4]) - (8*c^2*(7*b*B - 8*A*c)*(b + 2*c*x^2))/(35*b^5*Sqrt[b*x^2 + c*x^4])","A",5,4,26,0.1538,1,"{2034, 792, 658, 613}"
153,1,139,0,0.2482382,"\int \frac{x^8 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^8*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{x^3 \sqrt{b x^2+c x^4} (6 b B-5 A c)}{5 b c^2}-\frac{4 x \sqrt{b x^2+c x^4} (6 b B-5 A c)}{15 c^3}+\frac{8 b \sqrt{b x^2+c x^4} (6 b B-5 A c)}{15 c^4 x}-\frac{x^7 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{x^3 \sqrt{b x^2+c x^4} (6 b B-5 A c)}{5 b c^2}-\frac{4 x \sqrt{b x^2+c x^4} (6 b B-5 A c)}{15 c^3}+\frac{8 b \sqrt{b x^2+c x^4} (6 b B-5 A c)}{15 c^4 x}-\frac{x^7 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^7)/(b*c*Sqrt[b*x^2 + c*x^4])) + (8*b*(6*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(15*c^4*x) - (4*(6*b*B - 5*A*c)*x*Sqrt[b*x^2 + c*x^4])/(15*c^3) + ((6*b*B - 5*A*c)*x^3*Sqrt[b*x^2 + c*x^4])/(5*b*c^2)","A",4,3,26,0.1154,1,"{2037, 2016, 1588}"
154,1,104,0,0.1998741,"\int \frac{x^6 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^6*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{x \sqrt{b x^2+c x^4} (4 b B-3 A c)}{3 b c^2}-\frac{2 \sqrt{b x^2+c x^4} (4 b B-3 A c)}{3 c^3 x}-\frac{x^5 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{x \sqrt{b x^2+c x^4} (4 b B-3 A c)}{3 b c^2}-\frac{2 \sqrt{b x^2+c x^4} (4 b B-3 A c)}{3 c^3 x}-\frac{x^5 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^5)/(b*c*Sqrt[b*x^2 + c*x^4])) - (2*(4*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(3*c^3*x) + ((4*b*B - 3*A*c)*x*Sqrt[b*x^2 + c*x^4])/(3*b*c^2)","A",3,3,26,0.1154,1,"{2037, 2016, 1588}"
155,1,69,0,0.1497965,"\int \frac{x^4 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^4*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{\sqrt{b x^2+c x^4} (2 b B-A c)}{b c^2 x}-\frac{x^3 (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{\sqrt{b x^2+c x^4} (2 b B-A c)}{b c^2 x}-\frac{x^3 (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^3)/(b*c*Sqrt[b*x^2 + c*x^4])) + ((2*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(b*c^2*x)","A",2,2,26,0.07692,1,"{2037, 1588}"
156,1,64,0,0.138556,"\int \frac{x^2 \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^2*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","-\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{b^{3/2}}-\frac{x (b B-A c)}{b c \sqrt{b x^2+c x^4}}","-\frac{A \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{b^{3/2}}-\frac{x (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x)/(b*c*Sqrt[b*x^2 + c*x^4])) - (A*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/b^(3/2)","A",3,3,26,0.1154,1,"{2037, 2008, 206}"
157,1,142,0,0.0887823,"\int \frac{A+B x^2}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(b*x^2 + c*x^4)^(3/2),x]","\frac{\sqrt{b x^2+c x^4} (2 b B-3 A c)}{2 b^2 c x^3}-\frac{(2 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{5/2}}-\frac{2 b B-3 A c}{3 b c x \sqrt{b x^2+c x^4}}-\frac{B}{3 c x \sqrt{b x^2+c x^4}}","\frac{\sqrt{b x^2+c x^4} (2 b B-3 A c)}{2 b^2 c x^3}-\frac{(2 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{2 b^{5/2}}-\frac{2 b B-3 A c}{3 b c x \sqrt{b x^2+c x^4}}-\frac{B}{3 c x \sqrt{b x^2+c x^4}}",1,"-B/(3*c*x*Sqrt[b*x^2 + c*x^4]) - (2*b*B - 3*A*c)/(3*b*c*x*Sqrt[b*x^2 + c*x^4]) + ((2*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(2*b^2*c*x^3) - ((2*b*B - 3*A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(2*b^(5/2))","A",5,5,23,0.2174,1,"{1145, 2006, 2025, 2008, 206}"
158,1,137,0,0.1919074,"\int \frac{A+B x^2}{x^2 \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^2*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{3 \sqrt{b x^2+c x^4} (4 b B-5 A c)}{8 b^3 x^3}+\frac{4 b B-5 A c}{4 b^2 x \sqrt{b x^2+c x^4}}+\frac{3 c (4 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{7/2}}-\frac{A}{4 b x^3 \sqrt{b x^2+c x^4}}","-\frac{3 \sqrt{b x^2+c x^4} (4 b B-5 A c)}{8 b^3 x^3}+\frac{4 b B-5 A c}{4 b^2 x \sqrt{b x^2+c x^4}}+\frac{3 c (4 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b} x}{\sqrt{b x^2+c x^4}}\right)}{8 b^{7/2}}-\frac{A}{4 b x^3 \sqrt{b x^2+c x^4}}",1,"-A/(4*b*x^3*Sqrt[b*x^2 + c*x^4]) + (4*b*B - 5*A*c)/(4*b^2*x*Sqrt[b*x^2 + c*x^4]) - (3*(4*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(8*b^3*x^3) + (3*c*(4*b*B - 5*A*c)*ArcTanh[(Sqrt[b]*x)/Sqrt[b*x^2 + c*x^4]])/(8*b^(7/2))","A",5,5,26,0.1923,1,"{2038, 2006, 2025, 2008, 206}"
159,1,39,0,0.0226728,"\int x^{7/2} \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[x^(7/2)*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{2}{17} x^{17/2} (A c+b B)+\frac{2}{13} A b x^{13/2}+\frac{2}{21} B c x^{21/2}","\frac{2}{17} x^{17/2} (A c+b B)+\frac{2}{13} A b x^{13/2}+\frac{2}{21} B c x^{21/2}",1,"(2*A*b*x^(13/2))/13 + (2*(b*B + A*c)*x^(17/2))/17 + (2*B*c*x^(21/2))/21","A",3,2,24,0.08333,1,"{1584, 448}"
160,1,39,0,0.0225822,"\int x^{5/2} \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[x^(5/2)*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{2}{15} x^{15/2} (A c+b B)+\frac{2}{11} A b x^{11/2}+\frac{2}{19} B c x^{19/2}","\frac{2}{15} x^{15/2} (A c+b B)+\frac{2}{11} A b x^{11/2}+\frac{2}{19} B c x^{19/2}",1,"(2*A*b*x^(11/2))/11 + (2*(b*B + A*c)*x^(15/2))/15 + (2*B*c*x^(19/2))/19","A",3,2,24,0.08333,1,"{1584, 448}"
161,1,39,0,0.0229939,"\int x^{3/2} \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[x^(3/2)*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{9} A b x^{9/2}+\frac{2}{17} B c x^{17/2}","\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{9} A b x^{9/2}+\frac{2}{17} B c x^{17/2}",1,"(2*A*b*x^(9/2))/9 + (2*(b*B + A*c)*x^(13/2))/13 + (2*B*c*x^(17/2))/17","A",3,2,24,0.08333,1,"{1584, 448}"
162,1,39,0,0.0213687,"\int \sqrt{x} \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[Sqrt[x]*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{2}{11} x^{11/2} (A c+b B)+\frac{2}{7} A b x^{7/2}+\frac{2}{15} B c x^{15/2}","\frac{2}{11} x^{11/2} (A c+b B)+\frac{2}{7} A b x^{7/2}+\frac{2}{15} B c x^{15/2}",1,"(2*A*b*x^(7/2))/7 + (2*(b*B + A*c)*x^(11/2))/11 + (2*B*c*x^(15/2))/15","A",3,2,24,0.08333,1,"{1584, 448}"
163,1,39,0,0.0210477,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{\sqrt{x}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/Sqrt[x],x]","\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{5} A b x^{5/2}+\frac{2}{13} B c x^{13/2}","\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{5} A b x^{5/2}+\frac{2}{13} B c x^{13/2}",1,"(2*A*b*x^(5/2))/5 + (2*(b*B + A*c)*x^(9/2))/9 + (2*B*c*x^(13/2))/13","A",3,2,24,0.08333,1,"{1584, 448}"
164,1,39,0,0.0212394,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^{3/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^(3/2),x]","\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{3} A b x^{3/2}+\frac{2}{11} B c x^{11/2}","\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{3} A b x^{3/2}+\frac{2}{11} B c x^{11/2}",1,"(2*A*b*x^(3/2))/3 + (2*(b*B + A*c)*x^(7/2))/7 + (2*B*c*x^(11/2))/11","A",3,2,24,0.08333,1,"{1584, 448}"
165,1,37,0,0.0212557,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^{5/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^(5/2),x]","\frac{2}{5} x^{5/2} (A c+b B)+2 A b \sqrt{x}+\frac{2}{9} B c x^{9/2}","\frac{2}{5} x^{5/2} (A c+b B)+2 A b \sqrt{x}+\frac{2}{9} B c x^{9/2}",1,"2*A*b*Sqrt[x] + (2*(b*B + A*c)*x^(5/2))/5 + (2*B*c*x^(9/2))/9","A",3,2,24,0.08333,1,"{1584, 448}"
166,1,37,0,0.0205999,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)}{x^{7/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4))/x^(7/2),x]","\frac{2}{3} x^{3/2} (A c+b B)-\frac{2 A b}{\sqrt{x}}+\frac{2}{7} B c x^{7/2}","\frac{2}{3} x^{3/2} (A c+b B)-\frac{2 A b}{\sqrt{x}}+\frac{2}{7} B c x^{7/2}",1,"(-2*A*b)/Sqrt[x] + (2*(b*B + A*c)*x^(3/2))/3 + (2*B*c*x^(7/2))/7","A",3,2,24,0.08333,1,"{1584, 448}"
167,1,63,0,0.0412536,"\int x^{7/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^2 \, dx","Int[x^(7/2)*(A + B*x^2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{17} A b^2 x^{17/2}+\frac{2}{25} c x^{25/2} (A c+2 b B)+\frac{2}{21} b x^{21/2} (2 A c+b B)+\frac{2}{29} B c^2 x^{29/2}","\frac{2}{17} A b^2 x^{17/2}+\frac{2}{25} c x^{25/2} (A c+2 b B)+\frac{2}{21} b x^{21/2} (2 A c+b B)+\frac{2}{29} B c^2 x^{29/2}",1,"(2*A*b^2*x^(17/2))/17 + (2*b*(b*B + 2*A*c)*x^(21/2))/21 + (2*c*(2*b*B + A*c)*x^(25/2))/25 + (2*B*c^2*x^(29/2))/29","A",3,2,26,0.07692,1,"{1584, 448}"
168,1,63,0,0.0388137,"\int x^{5/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^2 \, dx","Int[x^(5/2)*(A + B*x^2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{15} A b^2 x^{15/2}+\frac{2}{23} c x^{23/2} (A c+2 b B)+\frac{2}{19} b x^{19/2} (2 A c+b B)+\frac{2}{27} B c^2 x^{27/2}","\frac{2}{15} A b^2 x^{15/2}+\frac{2}{23} c x^{23/2} (A c+2 b B)+\frac{2}{19} b x^{19/2} (2 A c+b B)+\frac{2}{27} B c^2 x^{27/2}",1,"(2*A*b^2*x^(15/2))/15 + (2*b*(b*B + 2*A*c)*x^(19/2))/19 + (2*c*(2*b*B + A*c)*x^(23/2))/23 + (2*B*c^2*x^(27/2))/27","A",3,2,26,0.07692,1,"{1584, 448}"
169,1,63,0,0.0380087,"\int x^{3/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^2 \, dx","Int[x^(3/2)*(A + B*x^2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{13} A b^2 x^{13/2}+\frac{2}{21} c x^{21/2} (A c+2 b B)+\frac{2}{17} b x^{17/2} (2 A c+b B)+\frac{2}{25} B c^2 x^{25/2}","\frac{2}{13} A b^2 x^{13/2}+\frac{2}{21} c x^{21/2} (A c+2 b B)+\frac{2}{17} b x^{17/2} (2 A c+b B)+\frac{2}{25} B c^2 x^{25/2}",1,"(2*A*b^2*x^(13/2))/13 + (2*b*(b*B + 2*A*c)*x^(17/2))/17 + (2*c*(2*b*B + A*c)*x^(21/2))/21 + (2*B*c^2*x^(25/2))/25","A",3,2,26,0.07692,1,"{1584, 448}"
170,1,63,0,0.0381059,"\int \sqrt{x} \left(A+B x^2\right) \left(b x^2+c x^4\right)^2 \, dx","Int[Sqrt[x]*(A + B*x^2)*(b*x^2 + c*x^4)^2,x]","\frac{2}{11} A b^2 x^{11/2}+\frac{2}{19} c x^{19/2} (A c+2 b B)+\frac{2}{15} b x^{15/2} (2 A c+b B)+\frac{2}{23} B c^2 x^{23/2}","\frac{2}{11} A b^2 x^{11/2}+\frac{2}{19} c x^{19/2} (A c+2 b B)+\frac{2}{15} b x^{15/2} (2 A c+b B)+\frac{2}{23} B c^2 x^{23/2}",1,"(2*A*b^2*x^(11/2))/11 + (2*b*(b*B + 2*A*c)*x^(15/2))/15 + (2*c*(2*b*B + A*c)*x^(19/2))/19 + (2*B*c^2*x^(23/2))/23","A",3,2,26,0.07692,1,"{1584, 448}"
171,1,63,0,0.0392227,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{\sqrt{x}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/Sqrt[x],x]","\frac{2}{9} A b^2 x^{9/2}+\frac{2}{17} c x^{17/2} (A c+2 b B)+\frac{2}{13} b x^{13/2} (2 A c+b B)+\frac{2}{21} B c^2 x^{21/2}","\frac{2}{9} A b^2 x^{9/2}+\frac{2}{17} c x^{17/2} (A c+2 b B)+\frac{2}{13} b x^{13/2} (2 A c+b B)+\frac{2}{21} B c^2 x^{21/2}",1,"(2*A*b^2*x^(9/2))/9 + (2*b*(b*B + 2*A*c)*x^(13/2))/13 + (2*c*(2*b*B + A*c)*x^(17/2))/17 + (2*B*c^2*x^(21/2))/21","A",3,2,26,0.07692,1,"{1584, 448}"
172,1,63,0,0.0393163,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^{3/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^(3/2),x]","\frac{2}{7} A b^2 x^{7/2}+\frac{2}{15} c x^{15/2} (A c+2 b B)+\frac{2}{11} b x^{11/2} (2 A c+b B)+\frac{2}{19} B c^2 x^{19/2}","\frac{2}{7} A b^2 x^{7/2}+\frac{2}{15} c x^{15/2} (A c+2 b B)+\frac{2}{11} b x^{11/2} (2 A c+b B)+\frac{2}{19} B c^2 x^{19/2}",1,"(2*A*b^2*x^(7/2))/7 + (2*b*(b*B + 2*A*c)*x^(11/2))/11 + (2*c*(2*b*B + A*c)*x^(15/2))/15 + (2*B*c^2*x^(19/2))/19","A",3,2,26,0.07692,1,"{1584, 448}"
173,1,63,0,0.038272,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^{5/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^(5/2),x]","\frac{2}{5} A b^2 x^{5/2}+\frac{2}{13} c x^{13/2} (A c+2 b B)+\frac{2}{9} b x^{9/2} (2 A c+b B)+\frac{2}{17} B c^2 x^{17/2}","\frac{2}{5} A b^2 x^{5/2}+\frac{2}{13} c x^{13/2} (A c+2 b B)+\frac{2}{9} b x^{9/2} (2 A c+b B)+\frac{2}{17} B c^2 x^{17/2}",1,"(2*A*b^2*x^(5/2))/5 + (2*b*(b*B + 2*A*c)*x^(9/2))/9 + (2*c*(2*b*B + A*c)*x^(13/2))/13 + (2*B*c^2*x^(17/2))/17","A",3,2,26,0.07692,1,"{1584, 448}"
174,1,63,0,0.0379469,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^2}{x^{7/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^2)/x^(7/2),x]","\frac{2}{3} A b^2 x^{3/2}+\frac{2}{11} c x^{11/2} (A c+2 b B)+\frac{2}{7} b x^{7/2} (2 A c+b B)+\frac{2}{15} B c^2 x^{15/2}","\frac{2}{3} A b^2 x^{3/2}+\frac{2}{11} c x^{11/2} (A c+2 b B)+\frac{2}{7} b x^{7/2} (2 A c+b B)+\frac{2}{15} B c^2 x^{15/2}",1,"(2*A*b^2*x^(3/2))/3 + (2*b*(b*B + 2*A*c)*x^(7/2))/7 + (2*c*(2*b*B + A*c)*x^(11/2))/11 + (2*B*c^2*x^(15/2))/15","A",3,2,26,0.07692,1,"{1584, 448}"
175,1,85,0,0.0523875,"\int x^{7/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^3 \, dx","Int[x^(7/2)*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]","\frac{2}{25} b^2 x^{25/2} (3 A c+b B)+\frac{2}{21} A b^3 x^{21/2}+\frac{2}{33} c^2 x^{33/2} (A c+3 b B)+\frac{6}{29} b c x^{29/2} (A c+b B)+\frac{2}{37} B c^3 x^{37/2}","\frac{2}{25} b^2 x^{25/2} (3 A c+b B)+\frac{2}{21} A b^3 x^{21/2}+\frac{2}{33} c^2 x^{33/2} (A c+3 b B)+\frac{6}{29} b c x^{29/2} (A c+b B)+\frac{2}{37} B c^3 x^{37/2}",1,"(2*A*b^3*x^(21/2))/21 + (2*b^2*(b*B + 3*A*c)*x^(25/2))/25 + (6*b*c*(b*B + A*c)*x^(29/2))/29 + (2*c^2*(3*b*B + A*c)*x^(33/2))/33 + (2*B*c^3*x^(37/2))/37","A",3,2,26,0.07692,1,"{1584, 448}"
176,1,85,0,0.0497119,"\int x^{5/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^3 \, dx","Int[x^(5/2)*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]","\frac{2}{23} b^2 x^{23/2} (3 A c+b B)+\frac{2}{19} A b^3 x^{19/2}+\frac{2}{31} c^2 x^{31/2} (A c+3 b B)+\frac{2}{9} b c x^{27/2} (A c+b B)+\frac{2}{35} B c^3 x^{35/2}","\frac{2}{23} b^2 x^{23/2} (3 A c+b B)+\frac{2}{19} A b^3 x^{19/2}+\frac{2}{31} c^2 x^{31/2} (A c+3 b B)+\frac{2}{9} b c x^{27/2} (A c+b B)+\frac{2}{35} B c^3 x^{35/2}",1,"(2*A*b^3*x^(19/2))/19 + (2*b^2*(b*B + 3*A*c)*x^(23/2))/23 + (2*b*c*(b*B + A*c)*x^(27/2))/9 + (2*c^2*(3*b*B + A*c)*x^(31/2))/31 + (2*B*c^3*x^(35/2))/35","A",3,2,26,0.07692,1,"{1584, 448}"
177,1,85,0,0.0501958,"\int x^{3/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^3 \, dx","Int[x^(3/2)*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]","\frac{2}{21} b^2 x^{21/2} (3 A c+b B)+\frac{2}{17} A b^3 x^{17/2}+\frac{2}{29} c^2 x^{29/2} (A c+3 b B)+\frac{6}{25} b c x^{25/2} (A c+b B)+\frac{2}{33} B c^3 x^{33/2}","\frac{2}{21} b^2 x^{21/2} (3 A c+b B)+\frac{2}{17} A b^3 x^{17/2}+\frac{2}{29} c^2 x^{29/2} (A c+3 b B)+\frac{6}{25} b c x^{25/2} (A c+b B)+\frac{2}{33} B c^3 x^{33/2}",1,"(2*A*b^3*x^(17/2))/17 + (2*b^2*(b*B + 3*A*c)*x^(21/2))/21 + (6*b*c*(b*B + A*c)*x^(25/2))/25 + (2*c^2*(3*b*B + A*c)*x^(29/2))/29 + (2*B*c^3*x^(33/2))/33","A",3,2,26,0.07692,1,"{1584, 448}"
178,1,85,0,0.0498296,"\int \sqrt{x} \left(A+B x^2\right) \left(b x^2+c x^4\right)^3 \, dx","Int[Sqrt[x]*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]","\frac{2}{19} b^2 x^{19/2} (3 A c+b B)+\frac{2}{15} A b^3 x^{15/2}+\frac{2}{27} c^2 x^{27/2} (A c+3 b B)+\frac{6}{23} b c x^{23/2} (A c+b B)+\frac{2}{31} B c^3 x^{31/2}","\frac{2}{19} b^2 x^{19/2} (3 A c+b B)+\frac{2}{15} A b^3 x^{15/2}+\frac{2}{27} c^2 x^{27/2} (A c+3 b B)+\frac{6}{23} b c x^{23/2} (A c+b B)+\frac{2}{31} B c^3 x^{31/2}",1,"(2*A*b^3*x^(15/2))/15 + (2*b^2*(b*B + 3*A*c)*x^(19/2))/19 + (6*b*c*(b*B + A*c)*x^(23/2))/23 + (2*c^2*(3*b*B + A*c)*x^(27/2))/27 + (2*B*c^3*x^(31/2))/31","A",3,2,26,0.07692,1,"{1584, 448}"
179,1,85,0,0.0515566,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{\sqrt{x}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/Sqrt[x],x]","\frac{2}{17} b^2 x^{17/2} (3 A c+b B)+\frac{2}{13} A b^3 x^{13/2}+\frac{2}{25} c^2 x^{25/2} (A c+3 b B)+\frac{2}{7} b c x^{21/2} (A c+b B)+\frac{2}{29} B c^3 x^{29/2}","\frac{2}{17} b^2 x^{17/2} (3 A c+b B)+\frac{2}{13} A b^3 x^{13/2}+\frac{2}{25} c^2 x^{25/2} (A c+3 b B)+\frac{2}{7} b c x^{21/2} (A c+b B)+\frac{2}{29} B c^3 x^{29/2}",1,"(2*A*b^3*x^(13/2))/13 + (2*b^2*(b*B + 3*A*c)*x^(17/2))/17 + (2*b*c*(b*B + A*c)*x^(21/2))/7 + (2*c^2*(3*b*B + A*c)*x^(25/2))/25 + (2*B*c^3*x^(29/2))/29","A",3,2,26,0.07692,1,"{1584, 448}"
180,1,85,0,0.0496143,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{3/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^(3/2),x]","\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{11} A b^3 x^{11/2}+\frac{2}{23} c^2 x^{23/2} (A c+3 b B)+\frac{6}{19} b c x^{19/2} (A c+b B)+\frac{2}{27} B c^3 x^{27/2}","\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{11} A b^3 x^{11/2}+\frac{2}{23} c^2 x^{23/2} (A c+3 b B)+\frac{6}{19} b c x^{19/2} (A c+b B)+\frac{2}{27} B c^3 x^{27/2}",1,"(2*A*b^3*x^(11/2))/11 + (2*b^2*(b*B + 3*A*c)*x^(15/2))/15 + (6*b*c*(b*B + A*c)*x^(19/2))/19 + (2*c^2*(3*b*B + A*c)*x^(23/2))/23 + (2*B*c^3*x^(27/2))/27","A",3,2,26,0.07692,1,"{1584, 448}"
181,1,85,0,0.0517297,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{5/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^(5/2),x]","\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{9} A b^3 x^{9/2}+\frac{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{25} B c^3 x^{25/2}","\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{9} A b^3 x^{9/2}+\frac{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{25} B c^3 x^{25/2}",1,"(2*A*b^3*x^(9/2))/9 + (2*b^2*(b*B + 3*A*c)*x^(13/2))/13 + (6*b*c*(b*B + A*c)*x^(17/2))/17 + (2*c^2*(3*b*B + A*c)*x^(21/2))/21 + (2*B*c^3*x^(25/2))/25","A",3,2,26,0.07692,1,"{1584, 448}"
182,1,85,0,0.0511572,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^3}{x^{7/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^3)/x^(7/2),x]","\frac{2}{11} b^2 x^{11/2} (3 A c+b B)+\frac{2}{7} A b^3 x^{7/2}+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{23} B c^3 x^{23/2}","\frac{2}{11} b^2 x^{11/2} (3 A c+b B)+\frac{2}{7} A b^3 x^{7/2}+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{23} B c^3 x^{23/2}",1,"(2*A*b^3*x^(7/2))/7 + (2*b^2*(b*B + 3*A*c)*x^(11/2))/11 + (2*b*c*(b*B + A*c)*x^(15/2))/5 + (2*c^2*(3*b*B + A*c)*x^(19/2))/19 + (2*B*c^3*x^(23/2))/23","A",3,2,26,0.07692,1,"{1584, 448}"
183,1,278,0,0.2740328,"\int \frac{x^{13/2} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^(13/2)*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{b^{7/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{15/4}}+\frac{b^{7/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{15/4}}+\frac{b^{7/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{15/4}}-\frac{b^{7/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{15/4}}-\frac{2 x^{7/2} (b B-A c)}{7 c^2}+\frac{2 b x^{3/2} (b B-A c)}{3 c^3}+\frac{2 B x^{11/2}}{11 c}","-\frac{b^{7/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{15/4}}+\frac{b^{7/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{15/4}}+\frac{b^{7/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{15/4}}-\frac{b^{7/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{15/4}}-\frac{2 x^{7/2} (b B-A c)}{7 c^2}+\frac{2 b x^{3/2} (b B-A c)}{3 c^3}+\frac{2 B x^{11/2}}{11 c}",1,"(2*b*(b*B - A*c)*x^(3/2))/(3*c^3) - (2*(b*B - A*c)*x^(7/2))/(7*c^2) + (2*B*x^(11/2))/(11*c) + (b^(7/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(15/4)) - (b^(7/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(15/4)) - (b^(7/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(15/4)) + (b^(7/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(15/4))","A",14,10,26,0.3846,1,"{1584, 459, 321, 329, 297, 1162, 617, 204, 1165, 628}"
184,1,276,0,0.2473732,"\int \frac{x^{11/2} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^(11/2)*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{b^{5/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{13/4}}-\frac{b^{5/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{13/4}}+\frac{b^{5/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{13/4}}-\frac{b^{5/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{13/4}}-\frac{2 x^{5/2} (b B-A c)}{5 c^2}+\frac{2 b \sqrt{x} (b B-A c)}{c^3}+\frac{2 B x^{9/2}}{9 c}","\frac{b^{5/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{13/4}}-\frac{b^{5/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{13/4}}+\frac{b^{5/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{13/4}}-\frac{b^{5/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{13/4}}-\frac{2 x^{5/2} (b B-A c)}{5 c^2}+\frac{2 b \sqrt{x} (b B-A c)}{c^3}+\frac{2 B x^{9/2}}{9 c}",1,"(2*b*(b*B - A*c)*Sqrt[x])/c^3 - (2*(b*B - A*c)*x^(5/2))/(5*c^2) + (2*B*x^(9/2))/(9*c) + (b^(5/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(13/4)) - (b^(5/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(13/4)) + (b^(5/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(13/4)) - (b^(5/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(13/4))","A",14,10,26,0.3846,1,"{1584, 459, 321, 329, 211, 1165, 628, 1162, 617, 204}"
185,1,257,0,0.2176375,"\int \frac{x^{9/2} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^(9/2)*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{b^{3/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{3/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{3/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{11/4}}+\frac{b^{3/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{11/4}}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 B x^{7/2}}{7 c}","\frac{b^{3/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{3/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{11/4}}-\frac{b^{3/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{11/4}}+\frac{b^{3/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{11/4}}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 B x^{7/2}}{7 c}",1,"(-2*(b*B - A*c)*x^(3/2))/(3*c^2) + (2*B*x^(7/2))/(7*c) - (b^(3/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(11/4)) + (b^(3/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(11/4)) + (b^(3/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(11/4)) - (b^(3/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(11/4))","A",13,10,26,0.3846,1,"{1584, 459, 321, 329, 297, 1162, 617, 204, 1165, 628}"
186,1,255,0,0.2092642,"\int \frac{x^{7/2} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^(7/2)*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{2 \sqrt{x} (b B-A c)}{c^2}-\frac{\sqrt[4]{b} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}+\frac{\sqrt[4]{b} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}-\frac{\sqrt[4]{b} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{9/4}}+\frac{\sqrt[4]{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{9/4}}+\frac{2 B x^{5/2}}{5 c}","-\frac{2 \sqrt{x} (b B-A c)}{c^2}-\frac{\sqrt[4]{b} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}+\frac{\sqrt[4]{b} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}-\frac{\sqrt[4]{b} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} c^{9/4}}+\frac{\sqrt[4]{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} c^{9/4}}+\frac{2 B x^{5/2}}{5 c}",1,"(-2*(b*B - A*c)*Sqrt[x])/c^2 + (2*B*x^(5/2))/(5*c) - (b^(1/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(9/4)) + (b^(1/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*c^(9/4)) - (b^(1/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(9/4)) + (b^(1/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(9/4))","A",13,10,26,0.3846,1,"{1584, 459, 321, 329, 211, 1165, 628, 1162, 617, 204}"
187,1,237,0,0.188252,"\int \frac{x^{5/2} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^(5/2)*(A + B*x^2))/(b*x^2 + c*x^4),x]","-\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{2 B x^{3/2}}{3 c}","-\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} \sqrt[4]{b} c^{7/4}}-\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} \sqrt[4]{b} c^{7/4}}+\frac{2 B x^{3/2}}{3 c}",1,"(2*B*x^(3/2))/(3*c) + ((b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(1/4)*c^(7/4)) - ((b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(1/4)*c^(7/4)) - ((b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(1/4)*c^(7/4)) + ((b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(1/4)*c^(7/4))","A",12,9,26,0.3462,1,"{1584, 459, 329, 297, 1162, 617, 204, 1165, 628}"
188,1,235,0,0.1836324,"\int \frac{x^{3/2} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^(3/2)*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} c^{5/4}}-\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} c^{5/4}}+\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{3/4} c^{5/4}}-\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{3/4} c^{5/4}}+\frac{2 B \sqrt{x}}{c}","\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} c^{5/4}}-\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{3/4} c^{5/4}}+\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{3/4} c^{5/4}}-\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{3/4} c^{5/4}}+\frac{2 B \sqrt{x}}{c}",1,"(2*B*Sqrt[x])/c + ((b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(3/4)*c^(5/4)) - ((b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(3/4)*c^(5/4)) + ((b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(3/4)*c^(5/4)) - ((b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(3/4)*c^(5/4))","A",12,9,26,0.3462,1,"{1584, 459, 329, 211, 1165, 628, 1162, 617, 204}"
189,1,235,0,0.1893784,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4} c^{3/4}}-\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4} c^{3/4}}-\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{5/4} c^{3/4}}+\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{5/4} c^{3/4}}-\frac{2 A}{b \sqrt{x}}","\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4} c^{3/4}}-\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{5/4} c^{3/4}}-\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{5/4} c^{3/4}}+\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{5/4} c^{3/4}}-\frac{2 A}{b \sqrt{x}}",1,"(-2*A)/(b*Sqrt[x]) - ((b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(5/4)*c^(3/4)) + ((b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(5/4)*c^(3/4)) + ((b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(5/4)*c^(3/4)) - ((b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(5/4)*c^(3/4))","A",12,9,26,0.3462,1,"{1584, 453, 329, 297, 1162, 617, 204, 1165, 628}"
190,1,237,0,0.1883928,"\int \frac{A+B x^2}{\sqrt{x} \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(b*x^2 + c*x^4)),x]","-\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4} \sqrt[4]{c}}-\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{7/4} \sqrt[4]{c}}-\frac{2 A}{3 b x^{3/2}}","-\frac{(b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{(b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{7/4} \sqrt[4]{c}}-\frac{(b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{7/4} \sqrt[4]{c}}+\frac{(b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{7/4} \sqrt[4]{c}}-\frac{2 A}{3 b x^{3/2}}",1,"(-2*A)/(3*b*x^(3/2)) - ((b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(7/4)*c^(1/4)) + ((b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(7/4)*c^(1/4)) - ((b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(7/4)*c^(1/4)) + ((b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(7/4)*c^(1/4))","A",12,9,26,0.3462,1,"{1584, 453, 329, 211, 1165, 628, 1162, 617, 204}"
191,1,255,0,0.2145832,"\int \frac{A+B x^2}{x^{3/2} \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^(3/2)*(b*x^2 + c*x^4)),x]","-\frac{2 (b B-A c)}{b^2 \sqrt{x}}-\frac{\sqrt[4]{c} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{\sqrt[4]{c} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{\sqrt[4]{c} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{9/4}}-\frac{\sqrt[4]{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{9/4}}-\frac{2 A}{5 b x^{5/2}}","-\frac{2 (b B-A c)}{b^2 \sqrt{x}}-\frac{\sqrt[4]{c} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{\sqrt[4]{c} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{9/4}}+\frac{\sqrt[4]{c} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{9/4}}-\frac{\sqrt[4]{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{9/4}}-\frac{2 A}{5 b x^{5/2}}",1,"(-2*A)/(5*b*x^(5/2)) - (2*(b*B - A*c))/(b^2*Sqrt[x]) + (c^(1/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(9/4)) - (c^(1/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(9/4)) - (c^(1/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(9/4)) + (c^(1/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(9/4))","A",13,10,26,0.3846,1,"{1584, 453, 325, 329, 297, 1162, 617, 204, 1165, 628}"
192,1,257,0,0.2137955,"\int \frac{A+B x^2}{x^{5/2} \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^(5/2)*(b*x^2 + c*x^4)),x]","\frac{c^{3/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}-\frac{c^{3/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{c^{3/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{11/4}}-\frac{c^{3/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{11/4}}-\frac{2 (b B-A c)}{3 b^2 x^{3/2}}-\frac{2 A}{7 b x^{7/2}}","\frac{c^{3/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}-\frac{c^{3/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{11/4}}+\frac{c^{3/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{11/4}}-\frac{c^{3/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{11/4}}-\frac{2 (b B-A c)}{3 b^2 x^{3/2}}-\frac{2 A}{7 b x^{7/2}}",1,"(-2*A)/(7*b*x^(7/2)) - (2*(b*B - A*c))/(3*b^2*x^(3/2)) + (c^(3/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(11/4)) - (c^(3/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(11/4)) + (c^(3/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(11/4)) - (c^(3/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(11/4))","A",13,10,26,0.3846,1,"{1584, 453, 325, 329, 211, 1165, 628, 1162, 617, 204}"
193,1,276,0,0.2446577,"\int \frac{A+B x^2}{x^{7/2} \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^(7/2)*(b*x^2 + c*x^4)),x]","\frac{c^{5/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}-\frac{c^{5/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}-\frac{c^{5/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{13/4}}+\frac{c^{5/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{13/4}}-\frac{2 (b B-A c)}{5 b^2 x^{5/2}}+\frac{2 c (b B-A c)}{b^3 \sqrt{x}}-\frac{2 A}{9 b x^{9/2}}","\frac{c^{5/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}-\frac{c^{5/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{13/4}}-\frac{c^{5/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{13/4}}+\frac{c^{5/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{13/4}}-\frac{2 (b B-A c)}{5 b^2 x^{5/2}}+\frac{2 c (b B-A c)}{b^3 \sqrt{x}}-\frac{2 A}{9 b x^{9/2}}",1,"(-2*A)/(9*b*x^(9/2)) - (2*(b*B - A*c))/(5*b^2*x^(5/2)) + (2*c*(b*B - A*c))/(b^3*Sqrt[x]) - (c^(5/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(13/4)) + (c^(5/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(13/4)) + (c^(5/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(13/4)) - (c^(5/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(13/4))","A",14,10,26,0.3846,1,"{1584, 453, 325, 329, 297, 1162, 617, 204, 1165, 628}"
194,1,278,0,0.2413905,"\int \frac{A+B x^2}{x^{9/2} \left(b x^2+c x^4\right)} \, dx","Int[(A + B*x^2)/(x^(9/2)*(b*x^2 + c*x^4)),x]","-\frac{c^{7/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{15/4}}+\frac{c^{7/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{15/4}}-\frac{c^{7/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{15/4}}+\frac{c^{7/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{15/4}}+\frac{2 c (b B-A c)}{3 b^3 x^{3/2}}-\frac{2 (b B-A c)}{7 b^2 x^{7/2}}-\frac{2 A}{11 b x^{11/2}}","-\frac{c^{7/4} (b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{15/4}}+\frac{c^{7/4} (b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{2 \sqrt{2} b^{15/4}}-\frac{c^{7/4} (b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{\sqrt{2} b^{15/4}}+\frac{c^{7/4} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{\sqrt{2} b^{15/4}}+\frac{2 c (b B-A c)}{3 b^3 x^{3/2}}-\frac{2 (b B-A c)}{7 b^2 x^{7/2}}-\frac{2 A}{11 b x^{11/2}}",1,"(-2*A)/(11*b*x^(11/2)) - (2*(b*B - A*c))/(7*b^2*x^(7/2)) + (2*c*(b*B - A*c))/(3*b^3*x^(3/2)) - (c^(7/4)*(b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(15/4)) + (c^(7/4)*(b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(Sqrt[2]*b^(15/4)) - (c^(7/4)*(b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(15/4)) + (c^(7/4)*(b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*b^(15/4))","A",14,10,26,0.3846,1,"{1584, 453, 325, 329, 211, 1165, 628, 1162, 617, 204}"
195,1,332,0,0.2771509,"\int \frac{x^{19/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(19/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{b^{5/4} (13 b B-9 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{17/4}}-\frac{b^{5/4} (13 b B-9 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{17/4}}+\frac{b^{5/4} (13 b B-9 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{17/4}}-\frac{b^{5/4} (13 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{17/4}}+\frac{x^{9/2} (13 b B-9 A c)}{18 b c^2}-\frac{x^{5/2} (13 b B-9 A c)}{10 c^3}+\frac{b \sqrt{x} (13 b B-9 A c)}{2 c^4}-\frac{x^{13/2} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{b^{5/4} (13 b B-9 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{17/4}}-\frac{b^{5/4} (13 b B-9 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{17/4}}+\frac{b^{5/4} (13 b B-9 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{17/4}}-\frac{b^{5/4} (13 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{17/4}}+\frac{x^{9/2} (13 b B-9 A c)}{18 b c^2}-\frac{x^{5/2} (13 b B-9 A c)}{10 c^3}+\frac{b \sqrt{x} (13 b B-9 A c)}{2 c^4}-\frac{x^{13/2} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"(b*(13*b*B - 9*A*c)*Sqrt[x])/(2*c^4) - ((13*b*B - 9*A*c)*x^(5/2))/(10*c^3) + ((13*b*B - 9*A*c)*x^(9/2))/(18*b*c^2) - ((b*B - A*c)*x^(13/2))/(2*b*c*(b + c*x^2)) + (b^(5/4)*(13*b*B - 9*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(17/4)) - (b^(5/4)*(13*b*B - 9*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(17/4)) + (b^(5/4)*(13*b*B - 9*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(17/4)) - (b^(5/4)*(13*b*B - 9*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(17/4))","A",15,10,26,0.3846,1,"{1584, 457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
196,1,310,0,0.2446692,"\int \frac{x^{17/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(17/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{b^{3/4} (11 b B-7 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{15/4}}-\frac{b^{3/4} (11 b B-7 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{15/4}}-\frac{b^{3/4} (11 b B-7 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{15/4}}+\frac{b^{3/4} (11 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{15/4}}+\frac{x^{7/2} (11 b B-7 A c)}{14 b c^2}-\frac{x^{3/2} (11 b B-7 A c)}{6 c^3}-\frac{x^{11/2} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{b^{3/4} (11 b B-7 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{15/4}}-\frac{b^{3/4} (11 b B-7 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{15/4}}-\frac{b^{3/4} (11 b B-7 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{15/4}}+\frac{b^{3/4} (11 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{15/4}}+\frac{x^{7/2} (11 b B-7 A c)}{14 b c^2}-\frac{x^{3/2} (11 b B-7 A c)}{6 c^3}-\frac{x^{11/2} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"-((11*b*B - 7*A*c)*x^(3/2))/(6*c^3) + ((11*b*B - 7*A*c)*x^(7/2))/(14*b*c^2) - ((b*B - A*c)*x^(11/2))/(2*b*c*(b + c*x^2)) - (b^(3/4)*(11*b*B - 7*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(15/4)) + (b^(3/4)*(11*b*B - 7*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(15/4)) + (b^(3/4)*(11*b*B - 7*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(15/4)) - (b^(3/4)*(11*b*B - 7*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(15/4))","A",14,10,26,0.3846,1,"{1584, 457, 321, 329, 297, 1162, 617, 204, 1165, 628}"
197,1,310,0,0.2533656,"\int \frac{x^{15/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(15/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{x^{5/2} (9 b B-5 A c)}{10 b c^2}-\frac{\sqrt{x} (9 b B-5 A c)}{2 c^3}-\frac{\sqrt[4]{b} (9 b B-5 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}+\frac{\sqrt[4]{b} (9 b B-5 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}-\frac{\sqrt[4]{b} (9 b B-5 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{13/4}}+\frac{\sqrt[4]{b} (9 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{13/4}}-\frac{x^{9/2} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{x^{5/2} (9 b B-5 A c)}{10 b c^2}-\frac{\sqrt{x} (9 b B-5 A c)}{2 c^3}-\frac{\sqrt[4]{b} (9 b B-5 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}+\frac{\sqrt[4]{b} (9 b B-5 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} c^{13/4}}-\frac{\sqrt[4]{b} (9 b B-5 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} c^{13/4}}+\frac{\sqrt[4]{b} (9 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} c^{13/4}}-\frac{x^{9/2} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"-((9*b*B - 5*A*c)*Sqrt[x])/(2*c^3) + ((9*b*B - 5*A*c)*x^(5/2))/(10*b*c^2) - ((b*B - A*c)*x^(9/2))/(2*b*c*(b + c*x^2)) - (b^(1/4)*(9*b*B - 5*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(13/4)) + (b^(1/4)*(9*b*B - 5*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*c^(13/4)) - (b^(1/4)*(9*b*B - 5*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(13/4)) + (b^(1/4)*(9*b*B - 5*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*c^(13/4))","A",14,10,26,0.3846,1,"{1584, 457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
198,1,289,0,0.2292413,"\int \frac{x^{13/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(13/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{x^{3/2} (7 b B-3 A c)}{6 b c^2}-\frac{(7 b B-3 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{11/4}}+\frac{(7 b B-3 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{11/4}}+\frac{(7 b B-3 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{(7 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{x^{7/2} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{x^{3/2} (7 b B-3 A c)}{6 b c^2}-\frac{(7 b B-3 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{11/4}}+\frac{(7 b B-3 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{b} c^{11/4}}+\frac{(7 b B-3 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{(7 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} \sqrt[4]{b} c^{11/4}}-\frac{x^{7/2} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"((7*b*B - 3*A*c)*x^(3/2))/(6*b*c^2) - ((b*B - A*c)*x^(7/2))/(2*b*c*(b + c*x^2)) + ((7*b*B - 3*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(1/4)*c^(11/4)) - ((7*b*B - 3*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(1/4)*c^(11/4)) - ((7*b*B - 3*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(1/4)*c^(11/4)) + ((7*b*B - 3*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(1/4)*c^(11/4))","A",13,10,26,0.3846,1,"{1584, 457, 321, 329, 297, 1162, 617, 204, 1165, 628}"
199,1,289,0,0.2337465,"\int \frac{x^{11/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(11/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{(5 b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{9/4}}-\frac{(5 b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{9/4}}+\frac{(5 b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{3/4} c^{9/4}}-\frac{(5 b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{3/4} c^{9/4}}+\frac{\sqrt{x} (5 b B-A c)}{2 b c^2}-\frac{x^{5/2} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{(5 b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{9/4}}-\frac{(5 b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{3/4} c^{9/4}}+\frac{(5 b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{3/4} c^{9/4}}-\frac{(5 b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{3/4} c^{9/4}}+\frac{\sqrt{x} (5 b B-A c)}{2 b c^2}-\frac{x^{5/2} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"((5*b*B - A*c)*Sqrt[x])/(2*b*c^2) - ((b*B - A*c)*x^(5/2))/(2*b*c*(b + c*x^2)) + ((5*b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(3/4)*c^(9/4)) - ((5*b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(3/4)*c^(9/4)) + ((5*b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(3/4)*c^(9/4)) - ((5*b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(3/4)*c^(9/4))","A",13,10,26,0.3846,1,"{1584, 457, 321, 329, 211, 1165, 628, 1162, 617, 204}"
200,1,261,0,0.1999603,"\int \frac{x^{9/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(9/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{(A c+3 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{7/4}}-\frac{(A c+3 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{7/4}}-\frac{(A c+3 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{5/4} c^{7/4}}+\frac{(A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{5/4} c^{7/4}}-\frac{x^{3/2} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{(A c+3 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{7/4}}-\frac{(A c+3 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{5/4} c^{7/4}}-\frac{(A c+3 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{5/4} c^{7/4}}+\frac{(A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{5/4} c^{7/4}}-\frac{x^{3/2} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"-((b*B - A*c)*x^(3/2))/(2*b*c*(b + c*x^2)) - ((3*b*B + A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(5/4)*c^(7/4)) + ((3*b*B + A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(5/4)*c^(7/4)) + ((3*b*B + A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(5/4)*c^(7/4)) - ((3*b*B + A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(5/4)*c^(7/4))","A",12,9,26,0.3462,1,"{1584, 457, 329, 297, 1162, 617, 204, 1165, 628}"
201,1,261,0,0.2001005,"\int \frac{x^{7/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(7/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","-\frac{(3 A c+b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} c^{5/4}}+\frac{(3 A c+b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} c^{5/4}}-\frac{(3 A c+b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{7/4} c^{5/4}}+\frac{(3 A c+b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{7/4} c^{5/4}}-\frac{\sqrt{x} (b B-A c)}{2 b c \left(b+c x^2\right)}","-\frac{(3 A c+b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} c^{5/4}}+\frac{(3 A c+b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{7/4} c^{5/4}}-\frac{(3 A c+b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{7/4} c^{5/4}}+\frac{(3 A c+b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{7/4} c^{5/4}}-\frac{\sqrt{x} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"-((b*B - A*c)*Sqrt[x])/(2*b*c*(b + c*x^2)) - ((b*B + 3*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(7/4)*c^(5/4)) + ((b*B + 3*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(7/4)*c^(5/4)) - ((b*B + 3*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(7/4)*c^(5/4)) + ((b*B + 3*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(7/4)*c^(5/4))","A",12,9,26,0.3462,1,"{1584, 457, 329, 211, 1165, 628, 1162, 617, 204}"
202,1,284,0,0.2301918,"\int \frac{x^{5/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(5/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{(b B-5 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4} c^{3/4}}-\frac{(b B-5 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4} c^{3/4}}-\frac{(b B-5 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{9/4} c^{3/4}}+\frac{(b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{9/4} c^{3/4}}+\frac{b B-5 A c}{2 b^2 c \sqrt{x}}-\frac{b B-A c}{2 b c \sqrt{x} \left(b+c x^2\right)}","\frac{(b B-5 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4} c^{3/4}}-\frac{(b B-5 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{9/4} c^{3/4}}-\frac{(b B-5 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{9/4} c^{3/4}}+\frac{(b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{9/4} c^{3/4}}+\frac{b B-5 A c}{2 b^2 c \sqrt{x}}-\frac{b B-A c}{2 b c \sqrt{x} \left(b+c x^2\right)}",1,"(b*B - 5*A*c)/(2*b^2*c*Sqrt[x]) - (b*B - A*c)/(2*b*c*Sqrt[x]*(b + c*x^2)) - ((b*B - 5*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(9/4)*c^(3/4)) + ((b*B - 5*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(9/4)*c^(3/4)) + ((b*B - 5*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(9/4)*c^(3/4)) - ((b*B - 5*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(9/4)*c^(3/4))","A",13,10,26,0.3846,1,"{1584, 457, 325, 329, 297, 1162, 617, 204, 1165, 628}"
203,1,289,0,0.2251644,"\int \frac{x^{3/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^(3/2)*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{3 b B-7 A c}{6 b^2 c x^{3/2}}-\frac{(3 b B-7 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{(3 b B-7 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4} \sqrt[4]{c}}-\frac{(3 b B-7 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{(3 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{11/4} \sqrt[4]{c}}-\frac{b B-A c}{2 b c x^{3/2} \left(b+c x^2\right)}","\frac{3 b B-7 A c}{6 b^2 c x^{3/2}}-\frac{(3 b B-7 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{(3 b B-7 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{11/4} \sqrt[4]{c}}-\frac{(3 b B-7 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{11/4} \sqrt[4]{c}}+\frac{(3 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{11/4} \sqrt[4]{c}}-\frac{b B-A c}{2 b c x^{3/2} \left(b+c x^2\right)}",1,"(3*b*B - 7*A*c)/(6*b^2*c*x^(3/2)) - (b*B - A*c)/(2*b*c*x^(3/2)*(b + c*x^2)) - ((3*b*B - 7*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(11/4)*c^(1/4)) + ((3*b*B - 7*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(11/4)*c^(1/4)) - ((3*b*B - 7*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(11/4)*c^(1/4)) + ((3*b*B - 7*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(11/4)*c^(1/4))","A",13,10,26,0.3846,1,"{1584, 457, 325, 329, 211, 1165, 628, 1162, 617, 204}"
204,1,310,0,0.2714735,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{5 b B-9 A c}{10 b^2 c x^{5/2}}-\frac{5 b B-9 A c}{2 b^3 \sqrt{x}}-\frac{\sqrt[4]{c} (5 b B-9 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{\sqrt[4]{c} (5 b B-9 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{\sqrt[4]{c} (5 b B-9 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{13/4}}-\frac{\sqrt[4]{c} (5 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{13/4}}-\frac{b B-A c}{2 b c x^{5/2} \left(b+c x^2\right)}","\frac{5 b B-9 A c}{10 b^2 c x^{5/2}}-\frac{5 b B-9 A c}{2 b^3 \sqrt{x}}-\frac{\sqrt[4]{c} (5 b B-9 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{\sqrt[4]{c} (5 b B-9 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{13/4}}+\frac{\sqrt[4]{c} (5 b B-9 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{13/4}}-\frac{\sqrt[4]{c} (5 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{13/4}}-\frac{b B-A c}{2 b c x^{5/2} \left(b+c x^2\right)}",1,"(5*b*B - 9*A*c)/(10*b^2*c*x^(5/2)) - (5*b*B - 9*A*c)/(2*b^3*Sqrt[x]) - (b*B - A*c)/(2*b*c*x^(5/2)*(b + c*x^2)) + (c^(1/4)*(5*b*B - 9*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(13/4)) - (c^(1/4)*(5*b*B - 9*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(13/4)) - (c^(1/4)*(5*b*B - 9*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(13/4)) + (c^(1/4)*(5*b*B - 9*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(13/4))","A",14,10,26,0.3846,1,"{1584, 457, 325, 329, 297, 1162, 617, 204, 1165, 628}"
205,1,310,0,0.2550634,"\int \frac{A+B x^2}{\sqrt{x} \left(b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(b*x^2 + c*x^4)^2),x]","\frac{c^{3/4} (7 b B-11 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}-\frac{c^{3/4} (7 b B-11 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}+\frac{c^{3/4} (7 b B-11 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{15/4}}-\frac{c^{3/4} (7 b B-11 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{15/4}}-\frac{7 b B-11 A c}{6 b^3 x^{3/2}}+\frac{7 b B-11 A c}{14 b^2 c x^{7/2}}-\frac{b B-A c}{2 b c x^{7/2} \left(b+c x^2\right)}","\frac{c^{3/4} (7 b B-11 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}-\frac{c^{3/4} (7 b B-11 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{15/4}}+\frac{c^{3/4} (7 b B-11 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{15/4}}-\frac{c^{3/4} (7 b B-11 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{15/4}}-\frac{7 b B-11 A c}{6 b^3 x^{3/2}}+\frac{7 b B-11 A c}{14 b^2 c x^{7/2}}-\frac{b B-A c}{2 b c x^{7/2} \left(b+c x^2\right)}",1,"(7*b*B - 11*A*c)/(14*b^2*c*x^(7/2)) - (7*b*B - 11*A*c)/(6*b^3*x^(3/2)) - (b*B - A*c)/(2*b*c*x^(7/2)*(b + c*x^2)) + (c^(3/4)*(7*b*B - 11*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(15/4)) - (c^(3/4)*(7*b*B - 11*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(15/4)) + (c^(3/4)*(7*b*B - 11*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(15/4)) - (c^(3/4)*(7*b*B - 11*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(15/4))","A",14,10,26,0.3846,1,"{1584, 457, 325, 329, 211, 1165, 628, 1162, 617, 204}"
206,1,332,0,0.2856604,"\int \frac{A+B x^2}{x^{3/2} \left(b x^2+c x^4\right)^2} \, dx","Int[(A + B*x^2)/(x^(3/2)*(b*x^2 + c*x^4)^2),x]","\frac{c^{5/4} (9 b B-13 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}-\frac{c^{5/4} (9 b B-13 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}-\frac{c^{5/4} (9 b B-13 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{17/4}}+\frac{c^{5/4} (9 b B-13 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{17/4}}-\frac{9 b B-13 A c}{10 b^3 x^{5/2}}+\frac{9 b B-13 A c}{18 b^2 c x^{9/2}}+\frac{c (9 b B-13 A c)}{2 b^4 \sqrt{x}}-\frac{b B-A c}{2 b c x^{9/2} \left(b+c x^2\right)}","\frac{c^{5/4} (9 b B-13 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}-\frac{c^{5/4} (9 b B-13 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{8 \sqrt{2} b^{17/4}}-\frac{c^{5/4} (9 b B-13 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{4 \sqrt{2} b^{17/4}}+\frac{c^{5/4} (9 b B-13 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{4 \sqrt{2} b^{17/4}}-\frac{9 b B-13 A c}{10 b^3 x^{5/2}}+\frac{9 b B-13 A c}{18 b^2 c x^{9/2}}+\frac{c (9 b B-13 A c)}{2 b^4 \sqrt{x}}-\frac{b B-A c}{2 b c x^{9/2} \left(b+c x^2\right)}",1,"(9*b*B - 13*A*c)/(18*b^2*c*x^(9/2)) - (9*b*B - 13*A*c)/(10*b^3*x^(5/2)) + (c*(9*b*B - 13*A*c))/(2*b^4*Sqrt[x]) - (b*B - A*c)/(2*b*c*x^(9/2)*(b + c*x^2)) - (c^(5/4)*(9*b*B - 13*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(17/4)) + (c^(5/4)*(9*b*B - 13*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(4*Sqrt[2]*b^(17/4)) + (c^(5/4)*(9*b*B - 13*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(17/4)) - (c^(5/4)*(9*b*B - 13*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*b^(17/4))","A",15,10,26,0.3846,1,"{1584, 457, 325, 329, 297, 1162, 617, 204, 1165, 628}"
207,1,343,0,0.2784373,"\int \frac{x^{23/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(23/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{x^{9/2} (13 b B-5 A c)}{16 b c^2 \left(b+c x^2\right)}+\frac{9 x^{5/2} (13 b B-5 A c)}{80 b c^3}-\frac{9 \sqrt{x} (13 b B-5 A c)}{16 c^4}-\frac{9 \sqrt[4]{b} (13 b B-5 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{17/4}}+\frac{9 \sqrt[4]{b} (13 b B-5 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{17/4}}-\frac{9 \sqrt[4]{b} (13 b B-5 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} c^{17/4}}+\frac{9 \sqrt[4]{b} (13 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} c^{17/4}}-\frac{x^{13/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","-\frac{x^{9/2} (13 b B-5 A c)}{16 b c^2 \left(b+c x^2\right)}+\frac{9 x^{5/2} (13 b B-5 A c)}{80 b c^3}-\frac{9 \sqrt{x} (13 b B-5 A c)}{16 c^4}-\frac{9 \sqrt[4]{b} (13 b B-5 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{17/4}}+\frac{9 \sqrt[4]{b} (13 b B-5 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} c^{17/4}}-\frac{9 \sqrt[4]{b} (13 b B-5 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} c^{17/4}}+\frac{9 \sqrt[4]{b} (13 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} c^{17/4}}-\frac{x^{13/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"(-9*(13*b*B - 5*A*c)*Sqrt[x])/(16*c^4) + (9*(13*b*B - 5*A*c)*x^(5/2))/(80*b*c^3) - ((b*B - A*c)*x^(13/2))/(4*b*c*(b + c*x^2)^2) - ((13*b*B - 5*A*c)*x^(9/2))/(16*b*c^2*(b + c*x^2)) - (9*b^(1/4)*(13*b*B - 5*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*c^(17/4)) + (9*b^(1/4)*(13*b*B - 5*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*c^(17/4)) - (9*b^(1/4)*(13*b*B - 5*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*c^(17/4)) + (9*b^(1/4)*(13*b*B - 5*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*c^(17/4))","A",15,11,26,0.4231,1,"{1584, 457, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
208,1,322,0,0.2466619,"\int \frac{x^{21/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(21/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{x^{7/2} (11 b B-3 A c)}{16 b c^2 \left(b+c x^2\right)}+\frac{7 x^{3/2} (11 b B-3 A c)}{48 b c^3}-\frac{7 (11 b B-3 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{15/4}}+\frac{7 (11 b B-3 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{15/4}}+\frac{7 (11 b B-3 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} \sqrt[4]{b} c^{15/4}}-\frac{7 (11 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} \sqrt[4]{b} c^{15/4}}-\frac{x^{11/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","-\frac{x^{7/2} (11 b B-3 A c)}{16 b c^2 \left(b+c x^2\right)}+\frac{7 x^{3/2} (11 b B-3 A c)}{48 b c^3}-\frac{7 (11 b B-3 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{15/4}}+\frac{7 (11 b B-3 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} \sqrt[4]{b} c^{15/4}}+\frac{7 (11 b B-3 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} \sqrt[4]{b} c^{15/4}}-\frac{7 (11 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} \sqrt[4]{b} c^{15/4}}-\frac{x^{11/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"(7*(11*b*B - 3*A*c)*x^(3/2))/(48*b*c^3) - ((b*B - A*c)*x^(11/2))/(4*b*c*(b + c*x^2)^2) - ((11*b*B - 3*A*c)*x^(7/2))/(16*b*c^2*(b + c*x^2)) + (7*(11*b*B - 3*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(1/4)*c^(15/4)) - (7*(11*b*B - 3*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(1/4)*c^(15/4)) - (7*(11*b*B - 3*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(1/4)*c^(15/4)) + (7*(11*b*B - 3*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(1/4)*c^(15/4))","A",14,11,26,0.4231,1,"{1584, 457, 288, 321, 329, 297, 1162, 617, 204, 1165, 628}"
209,1,322,0,0.2537565,"\int \frac{x^{19/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(19/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{5 (9 b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{13/4}}-\frac{5 (9 b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{13/4}}+\frac{5 (9 b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{3/4} c^{13/4}}-\frac{5 (9 b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{3/4} c^{13/4}}-\frac{x^{5/2} (9 b B-A c)}{16 b c^2 \left(b+c x^2\right)}+\frac{5 \sqrt{x} (9 b B-A c)}{16 b c^3}-\frac{x^{9/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","\frac{5 (9 b B-A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{13/4}}-\frac{5 (9 b B-A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{3/4} c^{13/4}}+\frac{5 (9 b B-A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{3/4} c^{13/4}}-\frac{5 (9 b B-A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{3/4} c^{13/4}}-\frac{x^{5/2} (9 b B-A c)}{16 b c^2 \left(b+c x^2\right)}+\frac{5 \sqrt{x} (9 b B-A c)}{16 b c^3}-\frac{x^{9/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"(5*(9*b*B - A*c)*Sqrt[x])/(16*b*c^3) - ((b*B - A*c)*x^(9/2))/(4*b*c*(b + c*x^2)^2) - ((9*b*B - A*c)*x^(5/2))/(16*b*c^2*(b + c*x^2)) + (5*(9*b*B - A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(3/4)*c^(13/4)) - (5*(9*b*B - A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(3/4)*c^(13/4)) + (5*(9*b*B - A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(3/4)*c^(13/4)) - (5*(9*b*B - A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(3/4)*c^(13/4))","A",14,11,26,0.4231,1,"{1584, 457, 288, 321, 329, 211, 1165, 628, 1162, 617, 204}"
210,1,293,0,0.2231919,"\int \frac{x^{17/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(17/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{3 (A c+7 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{11/4}}-\frac{3 (A c+7 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{11/4}}-\frac{3 (A c+7 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{5/4} c^{11/4}}+\frac{3 (A c+7 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{5/4} c^{11/4}}-\frac{x^{3/2} (A c+7 b B)}{16 b c^2 \left(b+c x^2\right)}-\frac{x^{7/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","\frac{3 (A c+7 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{11/4}}-\frac{3 (A c+7 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{5/4} c^{11/4}}-\frac{3 (A c+7 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{5/4} c^{11/4}}+\frac{3 (A c+7 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{5/4} c^{11/4}}-\frac{x^{3/2} (A c+7 b B)}{16 b c^2 \left(b+c x^2\right)}-\frac{x^{7/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"-((b*B - A*c)*x^(7/2))/(4*b*c*(b + c*x^2)^2) - ((7*b*B + A*c)*x^(3/2))/(16*b*c^2*(b + c*x^2)) - (3*(7*b*B + A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(5/4)*c^(11/4)) + (3*(7*b*B + A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(5/4)*c^(11/4)) + (3*(7*b*B + A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(5/4)*c^(11/4)) - (3*(7*b*B + A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(5/4)*c^(11/4))","A",13,10,26,0.3846,1,"{1584, 457, 288, 329, 297, 1162, 617, 204, 1165, 628}"
211,1,298,0,0.2358971,"\int \frac{x^{15/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(15/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{(3 A c+5 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{9/4}}+\frac{(3 A c+5 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{9/4}}-\frac{(3 A c+5 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{7/4} c^{9/4}}+\frac{(3 A c+5 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{7/4} c^{9/4}}-\frac{\sqrt{x} (3 A c+5 b B)}{16 b c^2 \left(b+c x^2\right)}-\frac{x^{5/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","-\frac{(3 A c+5 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{9/4}}+\frac{(3 A c+5 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{7/4} c^{9/4}}-\frac{(3 A c+5 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{7/4} c^{9/4}}+\frac{(3 A c+5 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{7/4} c^{9/4}}-\frac{\sqrt{x} (3 A c+5 b B)}{16 b c^2 \left(b+c x^2\right)}-\frac{x^{5/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"-((b*B - A*c)*x^(5/2))/(4*b*c*(b + c*x^2)^2) - ((5*b*B + 3*A*c)*Sqrt[x])/(16*b*c^2*(b + c*x^2)) - ((5*b*B + 3*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(7/4)*c^(9/4)) + ((5*b*B + 3*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(7/4)*c^(9/4)) - ((5*b*B + 3*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(7/4)*c^(9/4)) + ((5*b*B + 3*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(7/4)*c^(9/4))","A",13,10,26,0.3846,1,"{1584, 457, 288, 329, 211, 1165, 628, 1162, 617, 204}"
212,1,298,0,0.22876,"\int \frac{x^{13/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(13/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{(5 A c+3 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{7/4}}-\frac{(5 A c+3 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{7/4}}-\frac{(5 A c+3 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{9/4} c^{7/4}}+\frac{(5 A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{9/4} c^{7/4}}+\frac{x^{3/2} (5 A c+3 b B)}{16 b^2 c \left(b+c x^2\right)}-\frac{x^{3/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","\frac{(5 A c+3 b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{7/4}}-\frac{(5 A c+3 b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{9/4} c^{7/4}}-\frac{(5 A c+3 b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{9/4} c^{7/4}}+\frac{(5 A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{9/4} c^{7/4}}+\frac{x^{3/2} (5 A c+3 b B)}{16 b^2 c \left(b+c x^2\right)}-\frac{x^{3/2} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"-((b*B - A*c)*x^(3/2))/(4*b*c*(b + c*x^2)^2) + ((3*b*B + 5*A*c)*x^(3/2))/(16*b^2*c*(b + c*x^2)) - ((3*b*B + 5*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(9/4)*c^(7/4)) + ((3*b*B + 5*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(9/4)*c^(7/4)) + ((3*b*B + 5*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(9/4)*c^(7/4)) - ((3*b*B + 5*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(9/4)*c^(7/4))","A",13,10,26,0.3846,1,"{1584, 457, 290, 329, 297, 1162, 617, 204, 1165, 628}"
213,1,293,0,0.2305108,"\int \frac{x^{11/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(11/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{3 (7 A c+b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} c^{5/4}}+\frac{3 (7 A c+b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} c^{5/4}}-\frac{3 (7 A c+b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{11/4} c^{5/4}}+\frac{3 (7 A c+b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{11/4} c^{5/4}}+\frac{\sqrt{x} (7 A c+b B)}{16 b^2 c \left(b+c x^2\right)}-\frac{\sqrt{x} (b B-A c)}{4 b c \left(b+c x^2\right)^2}","-\frac{3 (7 A c+b B) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} c^{5/4}}+\frac{3 (7 A c+b B) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{11/4} c^{5/4}}-\frac{3 (7 A c+b B) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{11/4} c^{5/4}}+\frac{3 (7 A c+b B) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{11/4} c^{5/4}}+\frac{\sqrt{x} (7 A c+b B)}{16 b^2 c \left(b+c x^2\right)}-\frac{\sqrt{x} (b B-A c)}{4 b c \left(b+c x^2\right)^2}",1,"-((b*B - A*c)*Sqrt[x])/(4*b*c*(b + c*x^2)^2) + ((b*B + 7*A*c)*Sqrt[x])/(16*b^2*c*(b + c*x^2)) - (3*(b*B + 7*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(11/4)*c^(5/4)) + (3*(b*B + 7*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(11/4)*c^(5/4)) - (3*(b*B + 7*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(11/4)*c^(5/4)) + (3*(b*B + 7*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(11/4)*c^(5/4))","A",13,10,26,0.3846,1,"{1584, 457, 290, 329, 211, 1165, 628, 1162, 617, 204}"
214,1,316,0,0.2559551,"\int \frac{x^{9/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(9/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{5 (b B-9 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4} c^{3/4}}-\frac{5 (b B-9 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4} c^{3/4}}-\frac{5 (b B-9 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{13/4} c^{3/4}}+\frac{5 (b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{13/4} c^{3/4}}-\frac{b B-9 A c}{16 b^2 c \sqrt{x} \left(b+c x^2\right)}+\frac{5 (b B-9 A c)}{16 b^3 c \sqrt{x}}-\frac{b B-A c}{4 b c \sqrt{x} \left(b+c x^2\right)^2}","\frac{5 (b B-9 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4} c^{3/4}}-\frac{5 (b B-9 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{13/4} c^{3/4}}-\frac{5 (b B-9 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{13/4} c^{3/4}}+\frac{5 (b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{13/4} c^{3/4}}-\frac{b B-9 A c}{16 b^2 c \sqrt{x} \left(b+c x^2\right)}+\frac{5 (b B-9 A c)}{16 b^3 c \sqrt{x}}-\frac{b B-A c}{4 b c \sqrt{x} \left(b+c x^2\right)^2}",1,"(5*(b*B - 9*A*c))/(16*b^3*c*Sqrt[x]) - (b*B - A*c)/(4*b*c*Sqrt[x]*(b + c*x^2)^2) - (b*B - 9*A*c)/(16*b^2*c*Sqrt[x]*(b + c*x^2)) - (5*(b*B - 9*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(13/4)*c^(3/4)) + (5*(b*B - 9*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(13/4)*c^(3/4)) + (5*(b*B - 9*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(13/4)*c^(3/4)) - (5*(b*B - 9*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(13/4)*c^(3/4))","A",14,11,26,0.4231,1,"{1584, 457, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
215,1,322,0,0.2506935,"\int \frac{x^{7/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(7/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{3 b B-11 A c}{16 b^2 c x^{3/2} \left(b+c x^2\right)}+\frac{7 (3 b B-11 A c)}{48 b^3 c x^{3/2}}-\frac{7 (3 b B-11 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4} \sqrt[4]{c}}+\frac{7 (3 b B-11 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4} \sqrt[4]{c}}-\frac{7 (3 b B-11 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{15/4} \sqrt[4]{c}}+\frac{7 (3 b B-11 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{15/4} \sqrt[4]{c}}-\frac{b B-A c}{4 b c x^{3/2} \left(b+c x^2\right)^2}","-\frac{3 b B-11 A c}{16 b^2 c x^{3/2} \left(b+c x^2\right)}+\frac{7 (3 b B-11 A c)}{48 b^3 c x^{3/2}}-\frac{7 (3 b B-11 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4} \sqrt[4]{c}}+\frac{7 (3 b B-11 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{15/4} \sqrt[4]{c}}-\frac{7 (3 b B-11 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{15/4} \sqrt[4]{c}}+\frac{7 (3 b B-11 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{15/4} \sqrt[4]{c}}-\frac{b B-A c}{4 b c x^{3/2} \left(b+c x^2\right)^2}",1,"(7*(3*b*B - 11*A*c))/(48*b^3*c*x^(3/2)) - (b*B - A*c)/(4*b*c*x^(3/2)*(b + c*x^2)^2) - (3*b*B - 11*A*c)/(16*b^2*c*x^(3/2)*(b + c*x^2)) - (7*(3*b*B - 11*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(15/4)*c^(1/4)) + (7*(3*b*B - 11*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(15/4)*c^(1/4)) - (7*(3*b*B - 11*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(15/4)*c^(1/4)) + (7*(3*b*B - 11*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(15/4)*c^(1/4))","A",14,11,26,0.4231,1,"{1584, 457, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
216,1,343,0,0.2754407,"\int \frac{x^{5/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(5/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","-\frac{5 b B-13 A c}{16 b^2 c x^{5/2} \left(b+c x^2\right)}+\frac{9 (5 b B-13 A c)}{80 b^3 c x^{5/2}}-\frac{9 (5 b B-13 A c)}{16 b^4 \sqrt{x}}-\frac{9 \sqrt[4]{c} (5 b B-13 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}+\frac{9 \sqrt[4]{c} (5 b B-13 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}+\frac{9 \sqrt[4]{c} (5 b B-13 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{17/4}}-\frac{9 \sqrt[4]{c} (5 b B-13 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{17/4}}-\frac{b B-A c}{4 b c x^{5/2} \left(b+c x^2\right)^2}","-\frac{5 b B-13 A c}{16 b^2 c x^{5/2} \left(b+c x^2\right)}+\frac{9 (5 b B-13 A c)}{80 b^3 c x^{5/2}}-\frac{9 (5 b B-13 A c)}{16 b^4 \sqrt{x}}-\frac{9 \sqrt[4]{c} (5 b B-13 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}+\frac{9 \sqrt[4]{c} (5 b B-13 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{17/4}}+\frac{9 \sqrt[4]{c} (5 b B-13 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{17/4}}-\frac{9 \sqrt[4]{c} (5 b B-13 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{17/4}}-\frac{b B-A c}{4 b c x^{5/2} \left(b+c x^2\right)^2}",1,"(9*(5*b*B - 13*A*c))/(80*b^3*c*x^(5/2)) - (9*(5*b*B - 13*A*c))/(16*b^4*Sqrt[x]) - (b*B - A*c)/(4*b*c*x^(5/2)*(b + c*x^2)^2) - (5*b*B - 13*A*c)/(16*b^2*c*x^(5/2)*(b + c*x^2)) + (9*c^(1/4)*(5*b*B - 13*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(17/4)) - (9*c^(1/4)*(5*b*B - 13*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(17/4)) - (9*c^(1/4)*(5*b*B - 13*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(17/4)) + (9*c^(1/4)*(5*b*B - 13*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(17/4))","A",15,11,26,0.4231,1,"{1584, 457, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
217,1,343,0,0.2776694,"\int \frac{x^{3/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(x^(3/2)*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{11 c^{3/4} (7 b B-15 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}-\frac{11 c^{3/4} (7 b B-15 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}+\frac{11 c^{3/4} (7 b B-15 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{19/4}}-\frac{11 c^{3/4} (7 b B-15 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{19/4}}-\frac{7 b B-15 A c}{16 b^2 c x^{7/2} \left(b+c x^2\right)}-\frac{11 (7 b B-15 A c)}{48 b^4 x^{3/2}}+\frac{11 (7 b B-15 A c)}{112 b^3 c x^{7/2}}-\frac{b B-A c}{4 b c x^{7/2} \left(b+c x^2\right)^2}","\frac{11 c^{3/4} (7 b B-15 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}-\frac{11 c^{3/4} (7 b B-15 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{19/4}}+\frac{11 c^{3/4} (7 b B-15 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{19/4}}-\frac{11 c^{3/4} (7 b B-15 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{19/4}}-\frac{7 b B-15 A c}{16 b^2 c x^{7/2} \left(b+c x^2\right)}-\frac{11 (7 b B-15 A c)}{48 b^4 x^{3/2}}+\frac{11 (7 b B-15 A c)}{112 b^3 c x^{7/2}}-\frac{b B-A c}{4 b c x^{7/2} \left(b+c x^2\right)^2}",1,"(11*(7*b*B - 15*A*c))/(112*b^3*c*x^(7/2)) - (11*(7*b*B - 15*A*c))/(48*b^4*x^(3/2)) - (b*B - A*c)/(4*b*c*x^(7/2)*(b + c*x^2)^2) - (7*b*B - 15*A*c)/(16*b^2*c*x^(7/2)*(b + c*x^2)) + (11*c^(3/4)*(7*b*B - 15*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(19/4)) - (11*c^(3/4)*(7*b*B - 15*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(19/4)) + (11*c^(3/4)*(7*b*B - 15*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(19/4)) - (11*c^(3/4)*(7*b*B - 15*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(19/4))","A",15,11,26,0.4231,1,"{1584, 457, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
218,1,365,0,0.3197219,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(b*x^2 + c*x^4)^3,x]","\frac{13 c^{5/4} (9 b B-17 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}-\frac{13 c^{5/4} (9 b B-17 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}-\frac{13 c^{5/4} (9 b B-17 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{21/4}}+\frac{13 c^{5/4} (9 b B-17 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{21/4}}-\frac{13 (9 b B-17 A c)}{80 b^4 x^{5/2}}-\frac{9 b B-17 A c}{16 b^2 c x^{9/2} \left(b+c x^2\right)}+\frac{13 (9 b B-17 A c)}{144 b^3 c x^{9/2}}+\frac{13 c (9 b B-17 A c)}{16 b^5 \sqrt{x}}-\frac{b B-A c}{4 b c x^{9/2} \left(b+c x^2\right)^2}","\frac{13 c^{5/4} (9 b B-17 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}-\frac{13 c^{5/4} (9 b B-17 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{21/4}}-\frac{13 c^{5/4} (9 b B-17 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{21/4}}+\frac{13 c^{5/4} (9 b B-17 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{21/4}}-\frac{13 (9 b B-17 A c)}{80 b^4 x^{5/2}}-\frac{9 b B-17 A c}{16 b^2 c x^{9/2} \left(b+c x^2\right)}+\frac{13 (9 b B-17 A c)}{144 b^3 c x^{9/2}}+\frac{13 c (9 b B-17 A c)}{16 b^5 \sqrt{x}}-\frac{b B-A c}{4 b c x^{9/2} \left(b+c x^2\right)^2}",1,"(13*(9*b*B - 17*A*c))/(144*b^3*c*x^(9/2)) - (13*(9*b*B - 17*A*c))/(80*b^4*x^(5/2)) + (13*c*(9*b*B - 17*A*c))/(16*b^5*Sqrt[x]) - (b*B - A*c)/(4*b*c*x^(9/2)*(b + c*x^2)^2) - (9*b*B - 17*A*c)/(16*b^2*c*x^(9/2)*(b + c*x^2)) - (13*c^(5/4)*(9*b*B - 17*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(21/4)) + (13*c^(5/4)*(9*b*B - 17*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(21/4)) + (13*c^(5/4)*(9*b*B - 17*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(21/4)) - (13*c^(5/4)*(9*b*B - 17*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(21/4))","A",16,11,26,0.4231,1,"{1584, 457, 290, 325, 329, 297, 1162, 617, 204, 1165, 628}"
219,1,365,0,0.3207268,"\int \frac{A+B x^2}{\sqrt{x} \left(b x^2+c x^4\right)^3} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(b*x^2 + c*x^4)^3),x]","-\frac{15 c^{7/4} (11 b B-19 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}+\frac{15 c^{7/4} (11 b B-19 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}-\frac{15 c^{7/4} (11 b B-19 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{23/4}}+\frac{15 c^{7/4} (11 b B-19 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{23/4}}+\frac{5 c (11 b B-19 A c)}{16 b^5 x^{3/2}}-\frac{15 (11 b B-19 A c)}{112 b^4 x^{7/2}}-\frac{11 b B-19 A c}{16 b^2 c x^{11/2} \left(b+c x^2\right)}+\frac{15 (11 b B-19 A c)}{176 b^3 c x^{11/2}}-\frac{b B-A c}{4 b c x^{11/2} \left(b+c x^2\right)^2}","-\frac{15 c^{7/4} (11 b B-19 A c) \log \left(-\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}+\frac{15 c^{7/4} (11 b B-19 A c) \log \left(\sqrt{2} \sqrt[4]{b} \sqrt[4]{c} \sqrt{x}+\sqrt{b}+\sqrt{c} x\right)}{64 \sqrt{2} b^{23/4}}-\frac{15 c^{7/4} (11 b B-19 A c) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)}{32 \sqrt{2} b^{23/4}}+\frac{15 c^{7/4} (11 b B-19 A c) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}+1\right)}{32 \sqrt{2} b^{23/4}}+\frac{5 c (11 b B-19 A c)}{16 b^5 x^{3/2}}-\frac{15 (11 b B-19 A c)}{112 b^4 x^{7/2}}-\frac{11 b B-19 A c}{16 b^2 c x^{11/2} \left(b+c x^2\right)}+\frac{15 (11 b B-19 A c)}{176 b^3 c x^{11/2}}-\frac{b B-A c}{4 b c x^{11/2} \left(b+c x^2\right)^2}",1,"(15*(11*b*B - 19*A*c))/(176*b^3*c*x^(11/2)) - (15*(11*b*B - 19*A*c))/(112*b^4*x^(7/2)) + (5*c*(11*b*B - 19*A*c))/(16*b^5*x^(3/2)) - (b*B - A*c)/(4*b*c*x^(11/2)*(b + c*x^2)^2) - (11*b*B - 19*A*c)/(16*b^2*c*x^(11/2)*(b + c*x^2)) - (15*c^(7/4)*(11*b*B - 19*A*c)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(23/4)) + (15*c^(7/4)*(11*b*B - 19*A*c)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/b^(1/4)])/(32*Sqrt[2]*b^(23/4)) - (15*c^(7/4)*(11*b*B - 19*A*c)*Log[Sqrt[b] - Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(23/4)) + (15*c^(7/4)*(11*b*B - 19*A*c)*Log[Sqrt[b] + Sqrt[2]*b^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*b^(23/4))","A",16,11,26,0.4231,1,"{1584, 457, 290, 325, 329, 211, 1165, 628, 1162, 617, 204}"
220,1,243,0,0.3903538,"\int x^{5/2} \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^(5/2)*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","\frac{4 b^2 \sqrt{b x^2+c x^4} (3 b B-5 A c)}{231 c^3 \sqrt{x}}-\frac{2 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{3/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{385 c^2}-\frac{2 x^{7/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{55 c}+\frac{2 B x^{3/2} \left(b x^2+c x^4\right)^{3/2}}{15 c}","\frac{4 b^2 \sqrt{b x^2+c x^4} (3 b B-5 A c)}{231 c^3 \sqrt{x}}-\frac{2 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{3/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{385 c^2}-\frac{2 x^{7/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{55 c}+\frac{2 B x^{3/2} \left(b x^2+c x^4\right)^{3/2}}{15 c}",1,"(4*b^2*(3*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(231*c^3*Sqrt[x]) - (4*b*(3*b*B - 5*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(385*c^2) - (2*(3*b*B - 5*A*c)*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(55*c) + (2*B*x^(3/2)*(b*x^2 + c*x^4)^(3/2))/(15*c) - (2*b^(11/4)*(3*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*c^(13/4)*Sqrt[b*x^2 + c*x^4])","A",7,6,28,0.2143,1,"{2039, 2021, 2024, 2032, 329, 220}"
221,1,369,0,0.4356481,"\int x^{3/2} \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[x^(3/2)*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","\frac{4 b^2 x^{3/2} \left(b+c x^2\right) (7 b B-13 A c)}{195 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-13 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-13 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{4 b \sqrt{x} \sqrt{b x^2+c x^4} (7 b B-13 A c)}{585 c^2}-\frac{2 x^{5/2} \sqrt{b x^2+c x^4} (7 b B-13 A c)}{117 c}+\frac{2 B \sqrt{x} \left(b x^2+c x^4\right)^{3/2}}{13 c}","\frac{4 b^2 x^{3/2} \left(b+c x^2\right) (7 b B-13 A c)}{195 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-13 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-13 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{4 b \sqrt{x} \sqrt{b x^2+c x^4} (7 b B-13 A c)}{585 c^2}-\frac{2 x^{5/2} \sqrt{b x^2+c x^4} (7 b B-13 A c)}{117 c}+\frac{2 B \sqrt{x} \left(b x^2+c x^4\right)^{3/2}}{13 c}",1,"(4*b^2*(7*b*B - 13*A*c)*x^(3/2)*(b + c*x^2))/(195*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (4*b*(7*b*B - 13*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(585*c^2) - (2*(7*b*B - 13*A*c)*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(117*c) + (2*B*Sqrt[x]*(b*x^2 + c*x^4)^(3/2))/(13*c) - (4*b^(9/4)*(7*b*B - 13*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[b*x^2 + c*x^4]) + (2*b^(9/4)*(7*b*B - 13*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",8,8,28,0.2857,1,"{2039, 2021, 2024, 2032, 329, 305, 220, 1196}"
222,1,204,0,0.2996797,"\int \sqrt{x} \left(A+B x^2\right) \sqrt{b x^2+c x^4} \, dx","Int[Sqrt[x]*(A + B*x^2)*Sqrt[b*x^2 + c*x^4],x]","\frac{2 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 b \sqrt{b x^2+c x^4} (5 b B-11 A c)}{231 c^2 \sqrt{x}}-\frac{2 x^{3/2} \sqrt{b x^2+c x^4} (5 b B-11 A c)}{77 c}+\frac{2 B \left(b x^2+c x^4\right)^{3/2}}{11 c \sqrt{x}}","\frac{2 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 b \sqrt{b x^2+c x^4} (5 b B-11 A c)}{231 c^2 \sqrt{x}}-\frac{2 x^{3/2} \sqrt{b x^2+c x^4} (5 b B-11 A c)}{77 c}+\frac{2 B \left(b x^2+c x^4\right)^{3/2}}{11 c \sqrt{x}}",1,"(-4*b*(5*b*B - 11*A*c)*Sqrt[b*x^2 + c*x^4])/(231*c^2*Sqrt[x]) - (2*(5*b*B - 11*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(77*c) + (2*B*(b*x^2 + c*x^4)^(3/2))/(11*c*Sqrt[x]) + (2*b^(7/4)*(5*b*B - 11*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2039, 2021, 2024, 2032, 329, 220}"
223,1,326,0,0.3746831,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{\sqrt{x}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/Sqrt[x],x]","-\frac{2 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{4 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{3/2} \left(b+c x^2\right) (b B-3 A c)}{15 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{x} \sqrt{b x^2+c x^4} (b B-3 A c)}{15 c}+\frac{2 B \left(b x^2+c x^4\right)^{3/2}}{9 c x^{3/2}}","-\frac{2 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{4 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{3/2} \left(b+c x^2\right) (b B-3 A c)}{15 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{x} \sqrt{b x^2+c x^4} (b B-3 A c)}{15 c}+\frac{2 B \left(b x^2+c x^4\right)^{3/2}}{9 c x^{3/2}}",1,"(-4*b*(b*B - 3*A*c)*x^(3/2)*(b + c*x^2))/(15*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*(b*B - 3*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(15*c) + (2*B*(b*x^2 + c*x^4)^(3/2))/(9*c*x^(3/2)) + (4*b^(5/4)*(b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[b*x^2 + c*x^4]) - (2*b^(5/4)*(b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2039, 2021, 2032, 329, 305, 220, 1196}"
224,1,165,0,0.2541434,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{3/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(3/2),x]","-\frac{2 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (b B-7 A c)}{21 c \sqrt{x}}+\frac{2 B \left(b x^2+c x^4\right)^{3/2}}{7 c x^{5/2}}","-\frac{2 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (b B-7 A c)}{21 c \sqrt{x}}+\frac{2 B \left(b x^2+c x^4\right)^{3/2}}{7 c x^{5/2}}",1,"(-2*(b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(21*c*Sqrt[x]) + (2*B*(b*x^2 + c*x^4)^(3/2))/(7*c*x^(5/2)) - (2*b^(3/4)*(b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2039, 2021, 2032, 329, 220}"
225,1,323,0,0.3619281,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{5/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(5/2),x]","\frac{2 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 x^{3/2} \left(b+c x^2\right) (5 A c+b B)}{5 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{x} \sqrt{b x^2+c x^4} (5 A c+b B)}{5 b}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{b x^{7/2}}","\frac{2 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 x^{3/2} \left(b+c x^2\right) (5 A c+b B)}{5 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 \sqrt{x} \sqrt{b x^2+c x^4} (5 A c+b B)}{5 b}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{b x^{7/2}}",1,"(4*(b*B + 5*A*c)*x^(3/2)*(b + c*x^2))/(5*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (2*(b*B + 5*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(5*b) - (2*A*(b*x^2 + c*x^4)^(3/2))/(b*x^(7/2)) - (4*b^(1/4)*(b*B + 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[b*x^2 + c*x^4]) + (2*b^(1/4)*(b*B + 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2038, 2021, 2032, 329, 305, 220, 1196}"
226,1,163,0,0.2426259,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{7/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(7/2),x]","\frac{2 \sqrt{b x^2+c x^4} (A c+b B)}{3 b \sqrt{x}}+\frac{2 x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt[4]{c} \sqrt{b x^2+c x^4}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{3 b x^{9/2}}","\frac{2 \sqrt{b x^2+c x^4} (A c+b B)}{3 b \sqrt{x}}+\frac{2 x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} \sqrt[4]{c} \sqrt{b x^2+c x^4}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{3 b x^{9/2}}",1,"(2*(b*B + A*c)*Sqrt[b*x^2 + c*x^4])/(3*b*Sqrt[x]) - (2*A*(b*x^2 + c*x^4)^(3/2))/(3*b*x^(9/2)) + (2*(b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*b^(1/4)*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2038, 2021, 2032, 329, 220}"
227,1,328,0,0.3740053,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{9/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(9/2),x]","\frac{2 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+5 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+5 b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 \sqrt{c} x^{3/2} \left(b+c x^2\right) (A c+5 b B)}{5 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (A c+5 b B)}{5 b x^{3/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{5 b x^{11/2}}","\frac{2 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+5 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{4 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+5 b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{4 \sqrt{c} x^{3/2} \left(b+c x^2\right) (A c+5 b B)}{5 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (A c+5 b B)}{5 b x^{3/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{5 b x^{11/2}}",1,"(4*Sqrt[c]*(5*b*B + A*c)*x^(3/2)*(b + c*x^2))/(5*b*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*(5*b*B + A*c)*Sqrt[b*x^2 + c*x^4])/(5*b*x^(3/2)) - (2*A*(b*x^2 + c*x^4)^(3/2))/(5*b*x^(11/2)) - (4*c^(1/4)*(5*b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^2 + c*x^4]) + (2*c^(1/4)*(5*b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(3/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2038, 2020, 2032, 329, 305, 220, 1196}"
228,1,167,0,0.2503409,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{11/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(11/2),x]","\frac{2 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (7 b B-A c)}{21 b x^{5/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{7 b x^{13/2}}","\frac{2 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (7 b B-A c)}{21 b x^{5/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{7 b x^{13/2}}",1,"(-2*(7*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(21*b*x^(5/2)) - (2*A*(b*x^2 + c*x^4)^(3/2))/(7*b*x^(13/2)) + (2*c^(3/4)*(7*b*B - A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*b^(5/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2038, 2020, 2032, 329, 220}"
229,1,369,0,0.4361706,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{13/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(13/2),x]","\frac{4 c^{3/2} x^{3/2} \left(b+c x^2\right) (3 b B-A c)}{15 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4} (3 b B-A c)}{15 b^2 x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4} (3 b B-A c)}{15 b x^{7/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{9 b x^{15/2}}","\frac{4 c^{3/2} x^{3/2} \left(b+c x^2\right) (3 b B-A c)}{15 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{2 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4} (3 b B-A c)}{15 b^2 x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4} (3 b B-A c)}{15 b x^{7/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{9 b x^{15/2}}",1,"(4*c^(3/2)*(3*b*B - A*c)*x^(3/2)*(b + c*x^2))/(15*b^2*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*(3*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(15*b*x^(7/2)) - (4*c*(3*b*B - A*c)*Sqrt[b*x^2 + c*x^4])/(15*b^2*x^(3/2)) - (2*A*(b*x^2 + c*x^4)^(3/2))/(9*b*x^(15/2)) - (4*c^(5/4)*(3*b*B - A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[b*x^2 + c*x^4]) + (2*c^(5/4)*(3*b*B - A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(7/4)*Sqrt[b*x^2 + c*x^4])","A",8,8,28,0.2857,1,"{2038, 2020, 2025, 2032, 329, 305, 220, 1196}"
230,1,204,0,0.3081422,"\int \frac{\left(A+B x^2\right) \sqrt{b x^2+c x^4}}{x^{15/2}} \, dx","Int[((A + B*x^2)*Sqrt[b*x^2 + c*x^4])/x^(15/2),x]","-\frac{2 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4} (11 b B-5 A c)}{231 b^2 x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4} (11 b B-5 A c)}{77 b x^{9/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{11 b x^{17/2}}","-\frac{2 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 c \sqrt{b x^2+c x^4} (11 b B-5 A c)}{231 b^2 x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4} (11 b B-5 A c)}{77 b x^{9/2}}-\frac{2 A \left(b x^2+c x^4\right)^{3/2}}{11 b x^{17/2}}",1,"(-2*(11*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(77*b*x^(9/2)) - (4*c*(11*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(231*b^2*x^(5/2)) - (2*A*(b*x^2 + c*x^4)^(3/2))/(11*b*x^(17/2)) - (2*c^(7/4)*(11*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*b^(9/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2038, 2020, 2025, 2032, 329, 220}"
231,1,486,0,0.6705108,"\int x^{7/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^(7/2)*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","-\frac{8 b^2 x^{9/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{7735 c^2}+\frac{88 b^3 x^{5/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{69615 c^3}+\frac{88 b^5 x^{3/2} \left(b+c x^2\right) (3 b B-5 A c)}{16575 c^{9/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{88 b^4 \sqrt{x} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{49725 c^4}+\frac{44 b^{21/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{16575 c^{19/4} \sqrt{b x^2+c x^4}}-\frac{88 b^{21/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{16575 c^{19/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{13/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{595 c}-\frac{2 x^{9/2} \left(b x^2+c x^4\right)^{3/2} (3 b B-5 A c)}{105 c}+\frac{2 B x^{5/2} \left(b x^2+c x^4\right)^{5/2}}{25 c}","-\frac{8 b^2 x^{9/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{7735 c^2}+\frac{88 b^3 x^{5/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{69615 c^3}+\frac{88 b^5 x^{3/2} \left(b+c x^2\right) (3 b B-5 A c)}{16575 c^{9/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{88 b^4 \sqrt{x} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{49725 c^4}+\frac{44 b^{21/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{16575 c^{19/4} \sqrt{b x^2+c x^4}}-\frac{88 b^{21/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{16575 c^{19/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{13/2} \sqrt{b x^2+c x^4} (3 b B-5 A c)}{595 c}-\frac{2 x^{9/2} \left(b x^2+c x^4\right)^{3/2} (3 b B-5 A c)}{105 c}+\frac{2 B x^{5/2} \left(b x^2+c x^4\right)^{5/2}}{25 c}",1,"(88*b^5*(3*b*B - 5*A*c)*x^(3/2)*(b + c*x^2))/(16575*c^(9/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (88*b^4*(3*b*B - 5*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(49725*c^4) + (88*b^3*(3*b*B - 5*A*c)*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(69615*c^3) - (8*b^2*(3*b*B - 5*A*c)*x^(9/2)*Sqrt[b*x^2 + c*x^4])/(7735*c^2) - (4*b*(3*b*B - 5*A*c)*x^(13/2)*Sqrt[b*x^2 + c*x^4])/(595*c) - (2*(3*b*B - 5*A*c)*x^(9/2)*(b*x^2 + c*x^4)^(3/2))/(105*c) + (2*B*x^(5/2)*(b*x^2 + c*x^4)^(5/2))/(25*c) - (88*b^(21/4)*(3*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(16575*c^(19/4)*Sqrt[b*x^2 + c*x^4]) + (44*b^(21/4)*(3*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(16575*c^(19/4)*Sqrt[b*x^2 + c*x^4])","A",11,8,28,0.2857,1,"{2039, 2021, 2024, 2032, 329, 305, 220, 1196}"
232,1,321,0,0.4899649,"\int x^{5/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^(5/2)*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","-\frac{8 b^2 x^{7/2} \sqrt{b x^2+c x^4} (13 b B-23 A c)}{24035 c^2}+\frac{72 b^3 x^{3/2} \sqrt{b x^2+c x^4} (13 b B-23 A c)}{168245 c^3}-\frac{24 b^4 \sqrt{b x^2+c x^4} (13 b B-23 A c)}{33649 c^4 \sqrt{x}}+\frac{12 b^{19/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (13 b B-23 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{33649 c^{17/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{11/2} \sqrt{b x^2+c x^4} (13 b B-23 A c)}{2185 c}-\frac{2 x^{7/2} \left(b x^2+c x^4\right)^{3/2} (13 b B-23 A c)}{437 c}+\frac{2 B x^{3/2} \left(b x^2+c x^4\right)^{5/2}}{23 c}","-\frac{8 b^2 x^{7/2} \sqrt{b x^2+c x^4} (13 b B-23 A c)}{24035 c^2}+\frac{72 b^3 x^{3/2} \sqrt{b x^2+c x^4} (13 b B-23 A c)}{168245 c^3}-\frac{24 b^4 \sqrt{b x^2+c x^4} (13 b B-23 A c)}{33649 c^4 \sqrt{x}}+\frac{12 b^{19/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (13 b B-23 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{33649 c^{17/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{11/2} \sqrt{b x^2+c x^4} (13 b B-23 A c)}{2185 c}-\frac{2 x^{7/2} \left(b x^2+c x^4\right)^{3/2} (13 b B-23 A c)}{437 c}+\frac{2 B x^{3/2} \left(b x^2+c x^4\right)^{5/2}}{23 c}",1,"(-24*b^4*(13*b*B - 23*A*c)*Sqrt[b*x^2 + c*x^4])/(33649*c^4*Sqrt[x]) + (72*b^3*(13*b*B - 23*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(168245*c^3) - (8*b^2*(13*b*B - 23*A*c)*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(24035*c^2) - (4*b*(13*b*B - 23*A*c)*x^(11/2)*Sqrt[b*x^2 + c*x^4])/(2185*c) - (2*(13*b*B - 23*A*c)*x^(7/2)*(b*x^2 + c*x^4)^(3/2))/(437*c) + (2*B*x^(3/2)*(b*x^2 + c*x^4)^(5/2))/(23*c) + (12*b^(19/4)*(13*b*B - 23*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(33649*c^(17/4)*Sqrt[b*x^2 + c*x^4])","A",9,6,28,0.2143,1,"{2039, 2021, 2024, 2032, 329, 220}"
233,1,447,0,0.5895579,"\int x^{3/2} \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[x^(3/2)*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","-\frac{8 b^2 x^{5/2} \sqrt{b x^2+c x^4} (11 b B-21 A c)}{13923 c^2}-\frac{8 b^4 x^{3/2} \left(b+c x^2\right) (11 b B-21 A c)}{3315 c^{7/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{8 b^3 \sqrt{x} \sqrt{b x^2+c x^4} (11 b B-21 A c)}{9945 c^3}-\frac{4 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-21 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3315 c^{15/4} \sqrt{b x^2+c x^4}}+\frac{8 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-21 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3315 c^{15/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{9/2} \sqrt{b x^2+c x^4} (11 b B-21 A c)}{1547 c}-\frac{2 x^{5/2} \left(b x^2+c x^4\right)^{3/2} (11 b B-21 A c)}{357 c}+\frac{2 B \sqrt{x} \left(b x^2+c x^4\right)^{5/2}}{21 c}","-\frac{8 b^2 x^{5/2} \sqrt{b x^2+c x^4} (11 b B-21 A c)}{13923 c^2}-\frac{8 b^4 x^{3/2} \left(b+c x^2\right) (11 b B-21 A c)}{3315 c^{7/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{8 b^3 \sqrt{x} \sqrt{b x^2+c x^4} (11 b B-21 A c)}{9945 c^3}-\frac{4 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-21 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3315 c^{15/4} \sqrt{b x^2+c x^4}}+\frac{8 b^{17/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-21 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3315 c^{15/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{9/2} \sqrt{b x^2+c x^4} (11 b B-21 A c)}{1547 c}-\frac{2 x^{5/2} \left(b x^2+c x^4\right)^{3/2} (11 b B-21 A c)}{357 c}+\frac{2 B \sqrt{x} \left(b x^2+c x^4\right)^{5/2}}{21 c}",1,"(-8*b^4*(11*b*B - 21*A*c)*x^(3/2)*(b + c*x^2))/(3315*c^(7/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (8*b^3*(11*b*B - 21*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(9945*c^3) - (8*b^2*(11*b*B - 21*A*c)*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(13923*c^2) - (4*b*(11*b*B - 21*A*c)*x^(9/2)*Sqrt[b*x^2 + c*x^4])/(1547*c) - (2*(11*b*B - 21*A*c)*x^(5/2)*(b*x^2 + c*x^4)^(3/2))/(357*c) + (2*B*Sqrt[x]*(b*x^2 + c*x^4)^(5/2))/(21*c) + (8*b^(17/4)*(11*b*B - 21*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3315*c^(15/4)*Sqrt[b*x^2 + c*x^4]) - (4*b^(17/4)*(11*b*B - 21*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3315*c^(15/4)*Sqrt[b*x^2 + c*x^4])","A",10,8,28,0.2857,1,"{2039, 2021, 2024, 2032, 329, 305, 220, 1196}"
234,1,282,0,0.4248307,"\int \sqrt{x} \left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2} \, dx","Int[Sqrt[x]*(A + B*x^2)*(b*x^2 + c*x^4)^(3/2),x]","\frac{8 b^3 \sqrt{b x^2+c x^4} (9 b B-19 A c)}{4389 c^3 \sqrt{x}}-\frac{8 b^2 x^{3/2} \sqrt{b x^2+c x^4} (9 b B-19 A c)}{7315 c^2}-\frac{4 b^{15/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-19 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4389 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{7/2} \sqrt{b x^2+c x^4} (9 b B-19 A c)}{1045 c}-\frac{2 x^{3/2} \left(b x^2+c x^4\right)^{3/2} (9 b B-19 A c)}{285 c}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{19 c \sqrt{x}}","\frac{8 b^3 \sqrt{b x^2+c x^4} (9 b B-19 A c)}{4389 c^3 \sqrt{x}}-\frac{8 b^2 x^{3/2} \sqrt{b x^2+c x^4} (9 b B-19 A c)}{7315 c^2}-\frac{4 b^{15/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-19 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{4389 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{7/2} \sqrt{b x^2+c x^4} (9 b B-19 A c)}{1045 c}-\frac{2 x^{3/2} \left(b x^2+c x^4\right)^{3/2} (9 b B-19 A c)}{285 c}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{19 c \sqrt{x}}",1,"(8*b^3*(9*b*B - 19*A*c)*Sqrt[b*x^2 + c*x^4])/(4389*c^3*Sqrt[x]) - (8*b^2*(9*b*B - 19*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(7315*c^2) - (4*b*(9*b*B - 19*A*c)*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(1045*c) - (2*(9*b*B - 19*A*c)*x^(3/2)*(b*x^2 + c*x^4)^(3/2))/(285*c) + (2*B*(b*x^2 + c*x^4)^(5/2))/(19*c*Sqrt[x]) - (4*b^(15/4)*(9*b*B - 19*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(4389*c^(13/4)*Sqrt[b*x^2 + c*x^4])","A",8,6,28,0.2143,1,"{2039, 2021, 2024, 2032, 329, 220}"
235,1,408,0,0.5152287,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{\sqrt{x}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/Sqrt[x],x]","\frac{8 b^3 x^{3/2} \left(b+c x^2\right) (7 b B-17 A c)}{1105 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{8 b^2 \sqrt{x} \sqrt{b x^2+c x^4} (7 b B-17 A c)}{3315 c^2}+\frac{4 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-17 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{8 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-17 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{5/2} \sqrt{b x^2+c x^4} (7 b B-17 A c)}{663 c}-\frac{2 \sqrt{x} \left(b x^2+c x^4\right)^{3/2} (7 b B-17 A c)}{221 c}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{17 c x^{3/2}}","\frac{8 b^3 x^{3/2} \left(b+c x^2\right) (7 b B-17 A c)}{1105 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{8 b^2 \sqrt{x} \sqrt{b x^2+c x^4} (7 b B-17 A c)}{3315 c^2}+\frac{4 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-17 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{8 b^{13/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-17 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{1105 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{5/2} \sqrt{b x^2+c x^4} (7 b B-17 A c)}{663 c}-\frac{2 \sqrt{x} \left(b x^2+c x^4\right)^{3/2} (7 b B-17 A c)}{221 c}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{17 c x^{3/2}}",1,"(8*b^3*(7*b*B - 17*A*c)*x^(3/2)*(b + c*x^2))/(1105*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (8*b^2*(7*b*B - 17*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(3315*c^2) - (4*b*(7*b*B - 17*A*c)*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(663*c) - (2*(7*b*B - 17*A*c)*Sqrt[x]*(b*x^2 + c*x^4)^(3/2))/(221*c) + (2*B*(b*x^2 + c*x^4)^(5/2))/(17*c*x^(3/2)) - (8*b^(13/4)*(7*b*B - 17*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(1105*c^(11/4)*Sqrt[b*x^2 + c*x^4]) + (4*b^(13/4)*(7*b*B - 17*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(1105*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",9,8,28,0.2857,1,"{2039, 2021, 2024, 2032, 329, 305, 220, 1196}"
236,1,239,0,0.3693537,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{3/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(3/2),x]","-\frac{8 b^2 \sqrt{b x^2+c x^4} (b B-3 A c)}{231 c^2 \sqrt{x}}+\frac{4 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{3/2} \sqrt{b x^2+c x^4} (b B-3 A c)}{77 c}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (b B-3 A c)}{33 c \sqrt{x}}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{15 c x^{5/2}}","-\frac{8 b^2 \sqrt{b x^2+c x^4} (b B-3 A c)}{231 c^2 \sqrt{x}}+\frac{4 b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{4 b x^{3/2} \sqrt{b x^2+c x^4} (b B-3 A c)}{77 c}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (b B-3 A c)}{33 c \sqrt{x}}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{15 c x^{5/2}}",1,"(-8*b^2*(b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(231*c^2*Sqrt[x]) - (4*b*(b*B - 3*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(77*c) - (2*(b*B - 3*A*c)*(b*x^2 + c*x^4)^(3/2))/(33*c*Sqrt[x]) + (2*B*(b*x^2 + c*x^4)^(5/2))/(15*c*x^(5/2)) + (4*b^(11/4)*(b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",7,6,28,0.2143,1,"{2039, 2021, 2024, 2032, 329, 220}"
237,1,369,0,0.449977,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{5/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(5/2),x]","-\frac{8 b^2 x^{3/2} \left(b+c x^2\right) (3 b B-13 A c)}{195 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-13 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-13 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (3 b B-13 A c)}{117 c x^{3/2}}-\frac{4 b \sqrt{x} \sqrt{b x^2+c x^4} (3 b B-13 A c)}{195 c}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{13 c x^{7/2}}","-\frac{8 b^2 x^{3/2} \left(b+c x^2\right) (3 b B-13 A c)}{195 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{4 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-13 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{8 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-13 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{7/4} \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (3 b B-13 A c)}{117 c x^{3/2}}-\frac{4 b \sqrt{x} \sqrt{b x^2+c x^4} (3 b B-13 A c)}{195 c}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{13 c x^{7/2}}",1,"(-8*b^2*(3*b*B - 13*A*c)*x^(3/2)*(b + c*x^2))/(195*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (4*b*(3*b*B - 13*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(195*c) - (2*(3*b*B - 13*A*c)*(b*x^2 + c*x^4)^(3/2))/(117*c*x^(3/2)) + (2*B*(b*x^2 + c*x^4)^(5/2))/(13*c*x^(7/2)) + (8*b^(9/4)*(3*b*B - 13*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(7/4)*Sqrt[b*x^2 + c*x^4]) - (4*b^(9/4)*(3*b*B - 13*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,28,0.2500,1,"{2039, 2021, 2032, 329, 305, 220, 1196}"
238,1,201,0,0.3115616,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{7/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(7/2),x]","-\frac{4 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (b B-11 A c)}{77 c x^{5/2}}-\frac{4 b \sqrt{b x^2+c x^4} (b B-11 A c)}{77 c \sqrt{x}}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{11 c x^{9/2}}","-\frac{4 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{5/4} \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (b B-11 A c)}{77 c x^{5/2}}-\frac{4 b \sqrt{b x^2+c x^4} (b B-11 A c)}{77 c \sqrt{x}}+\frac{2 B \left(b x^2+c x^4\right)^{5/2}}{11 c x^{9/2}}",1,"(-4*b*(b*B - 11*A*c)*Sqrt[b*x^2 + c*x^4])/(77*c*Sqrt[x]) - (2*(b*B - 11*A*c)*(b*x^2 + c*x^4)^(3/2))/(77*c*x^(5/2)) + (2*B*(b*x^2 + c*x^4)^(5/2))/(11*c*x^(9/2)) - (4*b^(7/4)*(b*B - 11*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(77*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,28,0.1786,1,"{2039, 2021, 2032, 329, 220}"
239,1,356,0,0.4458307,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{9/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(9/2),x]","\frac{4 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 \left(b x^2+c x^4\right)^{3/2} (9 A c+b B)}{9 b x^{3/2}}+\frac{4}{15} \sqrt{x} \sqrt{b x^2+c x^4} (9 A c+b B)+\frac{8 b x^{3/2} \left(b+c x^2\right) (9 A c+b B)}{15 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{b x^{11/2}}","\frac{4 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 \left(b x^2+c x^4\right)^{3/2} (9 A c+b B)}{9 b x^{3/2}}+\frac{4}{15} \sqrt{x} \sqrt{b x^2+c x^4} (9 A c+b B)+\frac{8 b x^{3/2} \left(b+c x^2\right) (9 A c+b B)}{15 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{b x^{11/2}}",1,"(8*b*(b*B + 9*A*c)*x^(3/2)*(b + c*x^2))/(15*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (4*(b*B + 9*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/15 + (2*(b*B + 9*A*c)*(b*x^2 + c*x^4)^(3/2))/(9*b*x^(3/2)) - (2*A*(b*x^2 + c*x^4)^(5/2))/(b*x^(11/2)) - (8*b^(5/4)*(b*B + 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[b*x^2 + c*x^4]) + (4*b^(5/4)*(b*B + 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,28,0.2500,1,"{2038, 2021, 2032, 329, 305, 220, 1196}"
240,1,200,0,0.3221997,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{11/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(11/2),x]","\frac{4 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 A c+3 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{2 \left(b x^2+c x^4\right)^{3/2} (7 A c+3 b B)}{21 b x^{5/2}}+\frac{4 \sqrt{b x^2+c x^4} (7 A c+3 b B)}{21 \sqrt{x}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{3 b x^{13/2}}","\frac{4 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 A c+3 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{c} \sqrt{b x^2+c x^4}}+\frac{2 \left(b x^2+c x^4\right)^{3/2} (7 A c+3 b B)}{21 b x^{5/2}}+\frac{4 \sqrt{b x^2+c x^4} (7 A c+3 b B)}{21 \sqrt{x}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{3 b x^{13/2}}",1,"(4*(3*b*B + 7*A*c)*Sqrt[b*x^2 + c*x^4])/(21*Sqrt[x]) + (2*(3*b*B + 7*A*c)*(b*x^2 + c*x^4)^(3/2))/(21*b*x^(5/2)) - (2*A*(b*x^2 + c*x^4)^(5/2))/(3*b*x^(13/2)) + (4*b^(3/4)*(3*b*B + 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,28,0.1786,1,"{2038, 2021, 2032, 329, 220}"
241,1,354,0,0.4353968,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{13/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(13/2),x]","-\frac{2 \left(b x^2+c x^4\right)^{3/2} (A c+b B)}{b x^{7/2}}+\frac{12 c \sqrt{x} \sqrt{b x^2+c x^4} (A c+b B)}{5 b}+\frac{24 \sqrt{c} x^{3/2} \left(b+c x^2\right) (A c+b B)}{5 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{12 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{24 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{5 b x^{15/2}}","-\frac{2 \left(b x^2+c x^4\right)^{3/2} (A c+b B)}{b x^{7/2}}+\frac{12 c \sqrt{x} \sqrt{b x^2+c x^4} (A c+b B)}{5 b}+\frac{24 \sqrt{c} x^{3/2} \left(b+c x^2\right) (A c+b B)}{5 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{12 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{24 \sqrt[4]{b} \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 \sqrt{b x^2+c x^4}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{5 b x^{15/2}}",1,"(24*Sqrt[c]*(b*B + A*c)*x^(3/2)*(b + c*x^2))/(5*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (12*c*(b*B + A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(5*b) - (2*(b*B + A*c)*(b*x^2 + c*x^4)^(3/2))/(b*x^(7/2)) - (2*A*(b*x^2 + c*x^4)^(5/2))/(5*b*x^(15/2)) - (24*b^(1/4)*c^(1/4)*(b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*Sqrt[b*x^2 + c*x^4]) + (12*b^(1/4)*c^(1/4)*(b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*Sqrt[b*x^2 + c*x^4])","A",8,8,28,0.2857,1,"{2038, 2020, 2021, 2032, 329, 305, 220, 1196}"
242,1,204,0,0.319058,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{15/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(15/2),x]","\frac{4 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 A c+7 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{b} \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (3 A c+7 b B)}{21 b x^{9/2}}+\frac{4 c \sqrt{b x^2+c x^4} (3 A c+7 b B)}{21 b \sqrt{x}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{7 b x^{17/2}}","\frac{4 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 A c+7 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 \sqrt[4]{b} \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (3 A c+7 b B)}{21 b x^{9/2}}+\frac{4 c \sqrt{b x^2+c x^4} (3 A c+7 b B)}{21 b \sqrt{x}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{7 b x^{17/2}}",1,"(4*c*(7*b*B + 3*A*c)*Sqrt[b*x^2 + c*x^4])/(21*b*Sqrt[x]) - (2*(7*b*B + 3*A*c)*(b*x^2 + c*x^4)^(3/2))/(21*b*x^(9/2)) - (2*A*(b*x^2 + c*x^4)^(5/2))/(7*b*x^(17/2)) + (4*c^(3/4)*(7*b*B + 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*b^(1/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2038, 2020, 2021, 2032, 329, 220}"
243,1,364,0,0.4456567,"\int \frac{\left(A+B x^2\right) \left(b x^2+c x^4\right)^{3/2}}{x^{17/2}} \, dx","Int[((A + B*x^2)*(b*x^2 + c*x^4)^(3/2))/x^(17/2),x]","\frac{4 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+9 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+9 b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{8 c^{3/2} x^{3/2} \left(b+c x^2\right) (A c+9 b B)}{15 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (A c+9 b B)}{45 b x^{11/2}}-\frac{4 c \sqrt{b x^2+c x^4} (A c+9 b B)}{15 b x^{3/2}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{9 b x^{19/2}}","\frac{4 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+9 b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}-\frac{8 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+9 b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{3/4} \sqrt{b x^2+c x^4}}+\frac{8 c^{3/2} x^{3/2} \left(b+c x^2\right) (A c+9 b B)}{15 b \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \left(b x^2+c x^4\right)^{3/2} (A c+9 b B)}{45 b x^{11/2}}-\frac{4 c \sqrt{b x^2+c x^4} (A c+9 b B)}{15 b x^{3/2}}-\frac{2 A \left(b x^2+c x^4\right)^{5/2}}{9 b x^{19/2}}",1,"(8*c^(3/2)*(9*b*B + A*c)*x^(3/2)*(b + c*x^2))/(15*b*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (4*c*(9*b*B + A*c)*Sqrt[b*x^2 + c*x^4])/(15*b*x^(3/2)) - (2*(9*b*B + A*c)*(b*x^2 + c*x^4)^(3/2))/(45*b*x^(11/2)) - (2*A*(b*x^2 + c*x^4)^(5/2))/(9*b*x^(19/2)) - (8*c^(5/4)*(9*b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[b*x^2 + c*x^4]) + (4*c^(5/4)*(9*b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(3/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,28,0.2500,1,"{2038, 2020, 2032, 329, 305, 220, 1196}"
244,1,243,0,0.3676418,"\int \frac{x^{13/2} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^(13/2)*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{2 b^2 \sqrt{b x^2+c x^4} (13 b B-15 A c)}{77 c^4 \sqrt{x}}+\frac{b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (13 b B-15 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{17/4} \sqrt{b x^2+c x^4}}-\frac{2 x^{7/2} \sqrt{b x^2+c x^4} (13 b B-15 A c)}{165 c^2}+\frac{6 b x^{3/2} \sqrt{b x^2+c x^4} (13 b B-15 A c)}{385 c^3}+\frac{2 B x^{11/2} \sqrt{b x^2+c x^4}}{15 c}","-\frac{2 b^2 \sqrt{b x^2+c x^4} (13 b B-15 A c)}{77 c^4 \sqrt{x}}+\frac{b^{11/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (13 b B-15 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{77 c^{17/4} \sqrt{b x^2+c x^4}}-\frac{2 x^{7/2} \sqrt{b x^2+c x^4} (13 b B-15 A c)}{165 c^2}+\frac{6 b x^{3/2} \sqrt{b x^2+c x^4} (13 b B-15 A c)}{385 c^3}+\frac{2 B x^{11/2} \sqrt{b x^2+c x^4}}{15 c}",1,"(-2*b^2*(13*b*B - 15*A*c)*Sqrt[b*x^2 + c*x^4])/(77*c^4*Sqrt[x]) + (6*b*(13*b*B - 15*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(385*c^3) - (2*(13*b*B - 15*A*c)*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(165*c^2) + (2*B*x^(11/2)*Sqrt[b*x^2 + c*x^4])/(15*c) + (b^(11/4)*(13*b*B - 15*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(77*c^(17/4)*Sqrt[b*x^2 + c*x^4])","A",7,5,28,0.1786,1,"{2039, 2024, 2032, 329, 220}"
245,1,369,0,0.444791,"\int \frac{x^{11/2} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^(11/2)*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{14 b^2 x^{3/2} \left(b+c x^2\right) (11 b B-13 A c)}{195 c^{7/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{7 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-13 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{15/4} \sqrt{b x^2+c x^4}}+\frac{14 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-13 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{15/4} \sqrt{b x^2+c x^4}}-\frac{2 x^{5/2} \sqrt{b x^2+c x^4} (11 b B-13 A c)}{117 c^2}+\frac{14 b \sqrt{x} \sqrt{b x^2+c x^4} (11 b B-13 A c)}{585 c^3}+\frac{2 B x^{9/2} \sqrt{b x^2+c x^4}}{13 c}","-\frac{14 b^2 x^{3/2} \left(b+c x^2\right) (11 b B-13 A c)}{195 c^{7/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{7 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-13 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{15/4} \sqrt{b x^2+c x^4}}+\frac{14 b^{9/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-13 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{195 c^{15/4} \sqrt{b x^2+c x^4}}-\frac{2 x^{5/2} \sqrt{b x^2+c x^4} (11 b B-13 A c)}{117 c^2}+\frac{14 b \sqrt{x} \sqrt{b x^2+c x^4} (11 b B-13 A c)}{585 c^3}+\frac{2 B x^{9/2} \sqrt{b x^2+c x^4}}{13 c}",1,"(-14*b^2*(11*b*B - 13*A*c)*x^(3/2)*(b + c*x^2))/(195*c^(7/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (14*b*(11*b*B - 13*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(585*c^3) - (2*(11*b*B - 13*A*c)*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(117*c^2) + (2*B*x^(9/2)*Sqrt[b*x^2 + c*x^4])/(13*c) + (14*b^(9/4)*(11*b*B - 13*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(15/4)*Sqrt[b*x^2 + c*x^4]) - (7*b^(9/4)*(11*b*B - 13*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(195*c^(15/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,28,0.2500,1,"{2039, 2024, 2032, 329, 305, 220, 1196}"
246,1,204,0,0.3138294,"\int \frac{x^{9/2} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^(9/2)*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{5 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{2 x^{3/2} \sqrt{b x^2+c x^4} (9 b B-11 A c)}{77 c^2}+\frac{10 b \sqrt{b x^2+c x^4} (9 b B-11 A c)}{231 c^3 \sqrt{x}}+\frac{2 B x^{7/2} \sqrt{b x^2+c x^4}}{11 c}","-\frac{5 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 c^{13/4} \sqrt{b x^2+c x^4}}-\frac{2 x^{3/2} \sqrt{b x^2+c x^4} (9 b B-11 A c)}{77 c^2}+\frac{10 b \sqrt{b x^2+c x^4} (9 b B-11 A c)}{231 c^3 \sqrt{x}}+\frac{2 B x^{7/2} \sqrt{b x^2+c x^4}}{11 c}",1,"(10*b*(9*b*B - 11*A*c)*Sqrt[b*x^2 + c*x^4])/(231*c^3*Sqrt[x]) - (2*(9*b*B - 11*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(77*c^2) + (2*B*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(11*c) - (5*b^(7/4)*(9*b*B - 11*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*c^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,28,0.1786,1,"{2039, 2024, 2032, 329, 220}"
247,1,330,0,0.3766455,"\int \frac{x^{7/2} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^(7/2)*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","\frac{b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{2 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-9 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{2 b x^{3/2} \left(b+c x^2\right) (7 b B-9 A c)}{15 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{x} \sqrt{b x^2+c x^4} (7 b B-9 A c)}{45 c^2}+\frac{2 B x^{5/2} \sqrt{b x^2+c x^4}}{9 c}","\frac{b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{2 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-9 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{2 b x^{3/2} \left(b+c x^2\right) (7 b B-9 A c)}{15 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{x} \sqrt{b x^2+c x^4} (7 b B-9 A c)}{45 c^2}+\frac{2 B x^{5/2} \sqrt{b x^2+c x^4}}{9 c}",1,"(2*b*(7*b*B - 9*A*c)*x^(3/2)*(b + c*x^2))/(15*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*(7*b*B - 9*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(45*c^2) + (2*B*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(9*c) - (2*b^(5/4)*(7*b*B - 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(11/4)*Sqrt[b*x^2 + c*x^4]) + (b^(5/4)*(7*b*B - 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2039, 2024, 2032, 329, 305, 220, 1196}"
248,1,167,0,0.2551777,"\int \frac{x^{5/2} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^(5/2)*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","\frac{b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (5 b B-7 A c)}{21 c^2 \sqrt{x}}+\frac{2 B x^{3/2} \sqrt{b x^2+c x^4}}{7 c}","\frac{b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 c^{9/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (5 b B-7 A c)}{21 c^2 \sqrt{x}}+\frac{2 B x^{3/2} \sqrt{b x^2+c x^4}}{7 c}",1,"(-2*(5*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(21*c^2*Sqrt[x]) + (2*B*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(7*c) + (b^(3/4)*(5*b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2039, 2024, 2032, 329, 220}"
249,1,293,0,0.3112896,"\int \frac{x^{3/2} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(x^(3/2)*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","-\frac{2 x^{3/2} \left(b+c x^2\right) (3 b B-5 A c)}{5 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{\sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{2 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{2 B \sqrt{x} \sqrt{b x^2+c x^4}}{5 c}","-\frac{2 x^{3/2} \left(b+c x^2\right) (3 b B-5 A c)}{5 c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{\sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{2 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{b x^2+c x^4}}+\frac{2 B \sqrt{x} \sqrt{b x^2+c x^4}}{5 c}",1,"(-2*(3*b*B - 5*A*c)*x^(3/2)*(b + c*x^2))/(5*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + (2*B*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(5*c) + (2*b^(1/4)*(3*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(7/4)*Sqrt[b*x^2 + c*x^4]) - (b^(1/4)*(3*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2039, 2032, 329, 305, 220, 1196}"
250,1,130,0,0.1983331,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{\sqrt{b x^2+c x^4}} \, dx","Int[(Sqrt[x]*(A + B*x^2))/Sqrt[b*x^2 + c*x^4],x]","\frac{2 B \sqrt{b x^2+c x^4}}{3 c \sqrt{x}}-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} c^{5/4} \sqrt{b x^2+c x^4}}","\frac{2 B \sqrt{b x^2+c x^4}}{3 c \sqrt{x}}-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{b} c^{5/4} \sqrt{b x^2+c x^4}}",1,"(2*B*Sqrt[b*x^2 + c*x^4])/(3*c*Sqrt[x]) - ((b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*b^(1/4)*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,28,0.1429,1,"{2039, 2032, 329, 220}"
251,1,281,0,0.309211,"\int \frac{A+B x^2}{\sqrt{x} \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(Sqrt[x]*Sqrt[b*x^2 + c*x^4]),x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}-\frac{2 x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 x^{3/2} \left(b+c x^2\right) (A c+b B)}{b \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{b x^2+c x^4}}{b x^{3/2}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}-\frac{2 x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{2 x^{3/2} \left(b+c x^2\right) (A c+b B)}{b \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{b x^2+c x^4}}{b x^{3/2}}",1,"(2*(b*B + A*c)*x^(3/2)*(b + c*x^2))/(b*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*A*Sqrt[b*x^2 + c*x^4])/(b*x^(3/2)) - (2*(b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(3/4)*c^(3/4)*Sqrt[b*x^2 + c*x^4]) + ((b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(3/4)*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2038, 2032, 329, 305, 220, 1196}"
252,1,131,0,0.2037314,"\int \frac{A+B x^2}{x^{3/2} \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^(3/2)*Sqrt[b*x^2 + c*x^4]),x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt[4]{c} \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{b x^2+c x^4}}{3 b x^{5/2}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{3 b^{5/4} \sqrt[4]{c} \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{b x^2+c x^4}}{3 b x^{5/2}}",1,"(-2*A*Sqrt[b*x^2 + c*x^4])/(3*b*x^(5/2)) + ((3*b*B - A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(3*b^(5/4)*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,28,0.1429,1,"{2038, 2032, 329, 220}"
253,1,332,0,0.3780165,"\int \frac{A+B x^2}{x^{5/2} \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^(5/2)*Sqrt[b*x^2 + c*x^4]),x]","\frac{2 \sqrt{c} x^{3/2} \left(b+c x^2\right) (5 b B-3 A c)}{5 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (5 b B-3 A c)}{5 b^2 x^{3/2}}+\frac{\sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-3 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{b x^2+c x^4}}{5 b x^{7/2}}","\frac{2 \sqrt{c} x^{3/2} \left(b+c x^2\right) (5 b B-3 A c)}{5 b^2 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (5 b B-3 A c)}{5 b^2 x^{3/2}}+\frac{\sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-3 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{7/4} \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{b x^2+c x^4}}{5 b x^{7/2}}",1,"(2*Sqrt[c]*(5*b*B - 3*A*c)*x^(3/2)*(b + c*x^2))/(5*b^2*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*A*Sqrt[b*x^2 + c*x^4])/(5*b*x^(7/2)) - (2*(5*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(5*b^2*x^(3/2)) - (2*c^(1/4)*(5*b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[b*x^2 + c*x^4]) + (c^(1/4)*(5*b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(7/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2038, 2025, 2032, 329, 305, 220, 1196}"
254,1,167,0,0.2532391,"\int \frac{A+B x^2}{x^{7/2} \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^(7/2)*Sqrt[b*x^2 + c*x^4]),x]","-\frac{c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (7 b B-5 A c)}{21 b^2 x^{5/2}}-\frac{2 A \sqrt{b x^2+c x^4}}{7 b x^{9/2}}","-\frac{c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{21 b^{9/4} \sqrt{b x^2+c x^4}}-\frac{2 \sqrt{b x^2+c x^4} (7 b B-5 A c)}{21 b^2 x^{5/2}}-\frac{2 A \sqrt{b x^2+c x^4}}{7 b x^{9/2}}",1,"(-2*A*Sqrt[b*x^2 + c*x^4])/(7*b*x^(9/2)) - (2*(7*b*B - 5*A*c)*Sqrt[b*x^2 + c*x^4])/(21*b^2*x^(5/2)) - (c^(3/4)*(7*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(21*b^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2038, 2025, 2032, 329, 220}"
255,1,369,0,0.4409893,"\int \frac{A+B x^2}{x^{9/2} \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^(9/2)*Sqrt[b*x^2 + c*x^4]),x]","-\frac{2 c^{3/2} x^{3/2} \left(b+c x^2\right) (9 b B-7 A c)}{15 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{2 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-7 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{2 c \sqrt{b x^2+c x^4} (9 b B-7 A c)}{15 b^3 x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4} (9 b B-7 A c)}{45 b^2 x^{7/2}}-\frac{2 A \sqrt{b x^2+c x^4}}{9 b x^{11/2}}","-\frac{2 c^{3/2} x^{3/2} \left(b+c x^2\right) (9 b B-7 A c)}{15 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{2 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-7 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{11/4} \sqrt{b x^2+c x^4}}+\frac{2 c \sqrt{b x^2+c x^4} (9 b B-7 A c)}{15 b^3 x^{3/2}}-\frac{2 \sqrt{b x^2+c x^4} (9 b B-7 A c)}{45 b^2 x^{7/2}}-\frac{2 A \sqrt{b x^2+c x^4}}{9 b x^{11/2}}",1,"(-2*c^(3/2)*(9*b*B - 7*A*c)*x^(3/2)*(b + c*x^2))/(15*b^3*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (2*A*Sqrt[b*x^2 + c*x^4])/(9*b*x^(11/2)) - (2*(9*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(45*b^2*x^(7/2)) + (2*c*(9*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(15*b^3*x^(3/2)) + (2*c^(5/4)*(9*b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(11/4)*Sqrt[b*x^2 + c*x^4]) - (c^(5/4)*(9*b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(11/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,28,0.2500,1,"{2038, 2025, 2032, 329, 305, 220, 1196}"
256,1,204,0,0.3112792,"\int \frac{A+B x^2}{x^{11/2} \sqrt{b x^2+c x^4}} \, dx","Int[(A + B*x^2)/(x^(11/2)*Sqrt[b*x^2 + c*x^4]),x]","\frac{5 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{13/4} \sqrt{b x^2+c x^4}}+\frac{10 c \sqrt{b x^2+c x^4} (11 b B-9 A c)}{231 b^3 x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4} (11 b B-9 A c)}{77 b^2 x^{9/2}}-\frac{2 A \sqrt{b x^2+c x^4}}{11 b x^{13/2}}","\frac{5 c^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{231 b^{13/4} \sqrt{b x^2+c x^4}}+\frac{10 c \sqrt{b x^2+c x^4} (11 b B-9 A c)}{231 b^3 x^{5/2}}-\frac{2 \sqrt{b x^2+c x^4} (11 b B-9 A c)}{77 b^2 x^{9/2}}-\frac{2 A \sqrt{b x^2+c x^4}}{11 b x^{13/2}}",1,"(-2*A*Sqrt[b*x^2 + c*x^4])/(11*b*x^(13/2)) - (2*(11*b*B - 9*A*c)*Sqrt[b*x^2 + c*x^4])/(77*b^2*x^(9/2)) + (10*c*(11*b*B - 9*A*c)*Sqrt[b*x^2 + c*x^4])/(231*b^3*x^(5/2)) + (5*c^(7/4)*(11*b*B - 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(231*b^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,28,0.1786,1,"{2038, 2025, 2032, 329, 220}"
257,1,251,0,0.3895877,"\int \frac{x^{17/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(17/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","-\frac{15 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (13 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{154 c^{17/4} \sqrt{b x^2+c x^4}}+\frac{x^{7/2} \sqrt{b x^2+c x^4} (13 b B-11 A c)}{11 b c^2}-\frac{9 x^{3/2} \sqrt{b x^2+c x^4} (13 b B-11 A c)}{77 c^3}+\frac{15 b \sqrt{b x^2+c x^4} (13 b B-11 A c)}{77 c^4 \sqrt{x}}-\frac{x^{15/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","-\frac{15 b^{7/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (13 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{154 c^{17/4} \sqrt{b x^2+c x^4}}+\frac{x^{7/2} \sqrt{b x^2+c x^4} (13 b B-11 A c)}{11 b c^2}-\frac{9 x^{3/2} \sqrt{b x^2+c x^4} (13 b B-11 A c)}{77 c^3}+\frac{15 b \sqrt{b x^2+c x^4} (13 b B-11 A c)}{77 c^4 \sqrt{x}}-\frac{x^{15/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(15/2))/(b*c*Sqrt[b*x^2 + c*x^4])) + (15*b*(13*b*B - 11*A*c)*Sqrt[b*x^2 + c*x^4])/(77*c^4*Sqrt[x]) - (9*(13*b*B - 11*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(77*c^3) + ((13*b*B - 11*A*c)*x^(7/2)*Sqrt[b*x^2 + c*x^4])/(11*b*c^2) - (15*b^(7/4)*(13*b*B - 11*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(154*c^(17/4)*Sqrt[b*x^2 + c*x^4])","A",7,5,28,0.1786,1,"{2037, 2024, 2032, 329, 220}"
258,1,377,0,0.4606161,"\int \frac{x^{15/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(15/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{7 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{30 c^{15/4} \sqrt{b x^2+c x^4}}-\frac{7 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-9 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{15/4} \sqrt{b x^2+c x^4}}+\frac{x^{5/2} \sqrt{b x^2+c x^4} (11 b B-9 A c)}{9 b c^2}+\frac{7 b x^{3/2} \left(b+c x^2\right) (11 b B-9 A c)}{15 c^{7/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{7 \sqrt{x} \sqrt{b x^2+c x^4} (11 b B-9 A c)}{45 c^3}-\frac{x^{13/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{7 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{30 c^{15/4} \sqrt{b x^2+c x^4}}-\frac{7 b^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (11 b B-9 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 c^{15/4} \sqrt{b x^2+c x^4}}+\frac{x^{5/2} \sqrt{b x^2+c x^4} (11 b B-9 A c)}{9 b c^2}+\frac{7 b x^{3/2} \left(b+c x^2\right) (11 b B-9 A c)}{15 c^{7/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{7 \sqrt{x} \sqrt{b x^2+c x^4} (11 b B-9 A c)}{45 c^3}-\frac{x^{13/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(13/2))/(b*c*Sqrt[b*x^2 + c*x^4])) + (7*b*(11*b*B - 9*A*c)*x^(3/2)*(b + c*x^2))/(15*c^(7/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (7*(11*b*B - 9*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(45*c^3) + ((11*b*B - 9*A*c)*x^(5/2)*Sqrt[b*x^2 + c*x^4])/(9*b*c^2) - (7*b^(5/4)*(11*b*B - 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*c^(15/4)*Sqrt[b*x^2 + c*x^4]) + (7*b^(5/4)*(11*b*B - 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(30*c^(15/4)*Sqrt[b*x^2 + c*x^4])","A",8,7,28,0.2500,1,"{2037, 2024, 2032, 329, 305, 220, 1196}"
259,1,214,0,0.3269869,"\int \frac{x^{13/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(13/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{5 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{42 c^{13/4} \sqrt{b x^2+c x^4}}+\frac{x^{3/2} \sqrt{b x^2+c x^4} (9 b B-7 A c)}{7 b c^2}-\frac{5 \sqrt{b x^2+c x^4} (9 b B-7 A c)}{21 c^3 \sqrt{x}}-\frac{x^{11/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{5 b^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{42 c^{13/4} \sqrt{b x^2+c x^4}}+\frac{x^{3/2} \sqrt{b x^2+c x^4} (9 b B-7 A c)}{7 b c^2}-\frac{5 \sqrt{b x^2+c x^4} (9 b B-7 A c)}{21 c^3 \sqrt{x}}-\frac{x^{11/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(11/2))/(b*c*Sqrt[b*x^2 + c*x^4])) - (5*(9*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(21*c^3*Sqrt[x]) + ((9*b*B - 7*A*c)*x^(3/2)*Sqrt[b*x^2 + c*x^4])/(7*b*c^2) + (5*b^(3/4)*(9*b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(42*c^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,5,28,0.1786,1,"{2037, 2024, 2032, 329, 220}"
260,1,340,0,0.3966409,"\int \frac{x^{11/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(11/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","-\frac{3 x^{3/2} \left(b+c x^2\right) (7 b B-5 A c)}{5 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{\sqrt{x} \sqrt{b x^2+c x^4} (7 b B-5 A c)}{5 b c^2}-\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-5 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{x^{9/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","-\frac{3 x^{3/2} \left(b+c x^2\right) (7 b B-5 A c)}{5 c^{5/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{\sqrt{x} \sqrt{b x^2+c x^4} (7 b B-5 A c)}{5 b c^2}-\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 c^{11/4} \sqrt{b x^2+c x^4}}+\frac{3 \sqrt[4]{b} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-5 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 c^{11/4} \sqrt{b x^2+c x^4}}-\frac{x^{9/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(9/2))/(b*c*Sqrt[b*x^2 + c*x^4])) - (3*(7*b*B - 5*A*c)*x^(3/2)*(b + c*x^2))/(5*c^(5/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + ((7*b*B - 5*A*c)*Sqrt[x]*Sqrt[b*x^2 + c*x^4])/(5*b*c^2) + (3*b^(1/4)*(7*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*c^(11/4)*Sqrt[b*x^2 + c*x^4]) - (3*b^(1/4)*(7*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(10*c^(11/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2037, 2024, 2032, 329, 305, 220, 1196}"
261,1,178,0,0.2724655,"\int \frac{x^{9/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(9/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{\sqrt{b x^2+c x^4} (5 b B-3 A c)}{3 b c^2 \sqrt{x}}-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{b} c^{9/4} \sqrt{b x^2+c x^4}}-\frac{x^{7/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{\sqrt{b x^2+c x^4} (5 b B-3 A c)}{3 b c^2 \sqrt{x}}-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 \sqrt[4]{b} c^{9/4} \sqrt{b x^2+c x^4}}-\frac{x^{7/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(7/2))/(b*c*Sqrt[b*x^2 + c*x^4])) + ((5*b*B - 3*A*c)*Sqrt[b*x^2 + c*x^4])/(3*b*c^2*Sqrt[x]) - ((5*b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(6*b^(1/4)*c^(9/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2037, 2024, 2032, 329, 220}"
262,1,299,0,0.3279436,"\int \frac{x^{7/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(7/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{3/4} c^{7/4} \sqrt{b x^2+c x^4}}-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{7/4} \sqrt{b x^2+c x^4}}+\frac{x^{3/2} \left(b+c x^2\right) (3 b B-A c)}{b c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{x^{5/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{3/4} c^{7/4} \sqrt{b x^2+c x^4}}-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{3/4} c^{7/4} \sqrt{b x^2+c x^4}}+\frac{x^{3/2} \left(b+c x^2\right) (3 b B-A c)}{b c^{3/2} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{x^{5/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(5/2))/(b*c*Sqrt[b*x^2 + c*x^4])) + ((3*b*B - A*c)*x^(3/2)*(b + c*x^2))/(b*c^(3/2)*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - ((3*b*B - A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(3/4)*c^(7/4)*Sqrt[b*x^2 + c*x^4]) + ((3*b*B - A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(3/4)*c^(7/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2037, 2032, 329, 305, 220, 1196}"
263,1,137,0,0.2206441,"\int \frac{x^{5/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(5/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{5/4} c^{5/4} \sqrt{b x^2+c x^4}}-\frac{x^{3/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}","\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (A c+b B) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{5/4} c^{5/4} \sqrt{b x^2+c x^4}}-\frac{x^{3/2} (b B-A c)}{b c \sqrt{b x^2+c x^4}}",1,"-(((b*B - A*c)*x^(3/2))/(b*c*Sqrt[b*x^2 + c*x^4])) + ((b*B + A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(5/4)*c^(5/4)*Sqrt[b*x^2 + c*x^4])","A",4,4,28,0.1429,1,"{2037, 2032, 329, 220}"
264,1,318,0,0.3895883,"\int \frac{x^{3/2} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(x^(3/2)*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{7/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{7/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x^{5/2} (b B-3 A c)}{b^2 \sqrt{b x^2+c x^4}}-\frac{x^{3/2} \left(b+c x^2\right) (b B-3 A c)}{b^2 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{x}}{b \sqrt{b x^2+c x^4}}","-\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{2 b^{7/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (b B-3 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{b^{7/4} c^{3/4} \sqrt{b x^2+c x^4}}+\frac{x^{5/2} (b B-3 A c)}{b^2 \sqrt{b x^2+c x^4}}-\frac{x^{3/2} \left(b+c x^2\right) (b B-3 A c)}{b^2 \sqrt{c} \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{2 A \sqrt{x}}{b \sqrt{b x^2+c x^4}}",1,"(-2*A*Sqrt[x])/(b*Sqrt[b*x^2 + c*x^4]) + ((b*B - 3*A*c)*x^(5/2))/(b^2*Sqrt[b*x^2 + c*x^4]) - ((b*B - 3*A*c)*x^(3/2)*(b + c*x^2))/(b^2*Sqrt[c]*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) + ((b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(b^(7/4)*c^(3/4)*Sqrt[b*x^2 + c*x^4]) - ((b*B - 3*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(2*b^(7/4)*c^(3/4)*Sqrt[b*x^2 + c*x^4])","A",7,7,28,0.2500,1,"{2038, 2023, 2032, 329, 305, 220, 1196}"
265,1,167,0,0.2720425,"\int \frac{\sqrt{x} \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(Sqrt[x]*(A + B*x^2))/(b*x^2 + c*x^4)^(3/2),x]","\frac{x^{3/2} (3 b B-5 A c)}{3 b^2 \sqrt{b x^2+c x^4}}+\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt[4]{c} \sqrt{b x^2+c x^4}}-\frac{2 A}{3 b \sqrt{x} \sqrt{b x^2+c x^4}}","\frac{x^{3/2} (3 b B-5 A c)}{3 b^2 \sqrt{b x^2+c x^4}}+\frac{x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (3 b B-5 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{6 b^{9/4} \sqrt[4]{c} \sqrt{b x^2+c x^4}}-\frac{2 A}{3 b \sqrt{x} \sqrt{b x^2+c x^4}}",1,"(-2*A)/(3*b*Sqrt[x]*Sqrt[b*x^2 + c*x^4]) + ((3*b*B - 5*A*c)*x^(3/2))/(3*b^2*Sqrt[b*x^2 + c*x^4]) + ((3*b*B - 5*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(6*b^(9/4)*c^(1/4)*Sqrt[b*x^2 + c*x^4])","A",5,5,28,0.1786,1,"{2038, 2023, 2032, 329, 220}"
266,1,368,0,0.4506569,"\int \frac{A+B x^2}{\sqrt{x} \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(Sqrt[x]*(b*x^2 + c*x^4)^(3/2)),x]","\frac{3 \sqrt{c} x^{3/2} \left(b+c x^2\right) (5 b B-7 A c)}{5 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{\sqrt{x} (5 b B-7 A c)}{5 b^2 \sqrt{b x^2+c x^4}}-\frac{3 \sqrt{b x^2+c x^4} (5 b B-7 A c)}{5 b^3 x^{3/2}}+\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{b x^2+c x^4}}-\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-7 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{b x^2+c x^4}}-\frac{2 A}{5 b x^{3/2} \sqrt{b x^2+c x^4}}","\frac{3 \sqrt{c} x^{3/2} \left(b+c x^2\right) (5 b B-7 A c)}{5 b^3 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}+\frac{\sqrt{x} (5 b B-7 A c)}{5 b^2 \sqrt{b x^2+c x^4}}-\frac{3 \sqrt{b x^2+c x^4} (5 b B-7 A c)}{5 b^3 x^{3/2}}+\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-7 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{10 b^{11/4} \sqrt{b x^2+c x^4}}-\frac{3 \sqrt[4]{c} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (5 b B-7 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{5 b^{11/4} \sqrt{b x^2+c x^4}}-\frac{2 A}{5 b x^{3/2} \sqrt{b x^2+c x^4}}",1,"(-2*A)/(5*b*x^(3/2)*Sqrt[b*x^2 + c*x^4]) + ((5*b*B - 7*A*c)*Sqrt[x])/(5*b^2*Sqrt[b*x^2 + c*x^4]) + (3*Sqrt[c]*(5*b*B - 7*A*c)*x^(3/2)*(b + c*x^2))/(5*b^3*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (3*(5*b*B - 7*A*c)*Sqrt[b*x^2 + c*x^4])/(5*b^3*x^(3/2)) - (3*c^(1/4)*(5*b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(5*b^(11/4)*Sqrt[b*x^2 + c*x^4]) + (3*c^(1/4)*(5*b*B - 7*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(10*b^(11/4)*Sqrt[b*x^2 + c*x^4])","A",8,8,28,0.2857,1,"{2038, 2023, 2025, 2032, 329, 305, 220, 1196}"
267,1,203,0,0.3279385,"\int \frac{A+B x^2}{x^{3/2} \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^(3/2)*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{5 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{42 b^{13/4} \sqrt{b x^2+c x^4}}-\frac{5 \sqrt{b x^2+c x^4} (7 b B-9 A c)}{21 b^3 x^{5/2}}+\frac{7 b B-9 A c}{7 b^2 \sqrt{x} \sqrt{b x^2+c x^4}}-\frac{2 A}{7 b x^{5/2} \sqrt{b x^2+c x^4}}","-\frac{5 c^{3/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (7 b B-9 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{42 b^{13/4} \sqrt{b x^2+c x^4}}-\frac{5 \sqrt{b x^2+c x^4} (7 b B-9 A c)}{21 b^3 x^{5/2}}+\frac{7 b B-9 A c}{7 b^2 \sqrt{x} \sqrt{b x^2+c x^4}}-\frac{2 A}{7 b x^{5/2} \sqrt{b x^2+c x^4}}",1,"(-2*A)/(7*b*x^(5/2)*Sqrt[b*x^2 + c*x^4]) + (7*b*B - 9*A*c)/(7*b^2*Sqrt[x]*Sqrt[b*x^2 + c*x^4]) - (5*(7*b*B - 9*A*c)*Sqrt[b*x^2 + c*x^4])/(21*b^3*x^(5/2)) - (5*c^(3/4)*(7*b*B - 9*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(42*b^(13/4)*Sqrt[b*x^2 + c*x^4])","A",6,6,28,0.2143,1,"{2038, 2023, 2025, 2032, 329, 220}"
268,1,405,0,0.522016,"\int \frac{A+B x^2}{x^{5/2} \left(b x^2+c x^4\right)^{3/2}} \, dx","Int[(A + B*x^2)/(x^(5/2)*(b*x^2 + c*x^4)^(3/2)),x]","-\frac{7 c^{3/2} x^{3/2} \left(b+c x^2\right) (9 b B-11 A c)}{15 b^4 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{7 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{30 b^{15/4} \sqrt{b x^2+c x^4}}+\frac{7 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-11 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{15/4} \sqrt{b x^2+c x^4}}+\frac{7 c \sqrt{b x^2+c x^4} (9 b B-11 A c)}{15 b^4 x^{3/2}}+\frac{9 b B-11 A c}{9 b^2 x^{3/2} \sqrt{b x^2+c x^4}}-\frac{7 \sqrt{b x^2+c x^4} (9 b B-11 A c)}{45 b^3 x^{7/2}}-\frac{2 A}{9 b x^{7/2} \sqrt{b x^2+c x^4}}","-\frac{7 c^{3/2} x^{3/2} \left(b+c x^2\right) (9 b B-11 A c)}{15 b^4 \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{b x^2+c x^4}}-\frac{7 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-11 A c) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{30 b^{15/4} \sqrt{b x^2+c x^4}}+\frac{7 c^{5/4} x \left(\sqrt{b}+\sqrt{c} x\right) \sqrt{\frac{b+c x^2}{\left(\sqrt{b}+\sqrt{c} x\right)^2}} (9 b B-11 A c) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{b}}\right)|\frac{1}{2}\right)}{15 b^{15/4} \sqrt{b x^2+c x^4}}+\frac{7 c \sqrt{b x^2+c x^4} (9 b B-11 A c)}{15 b^4 x^{3/2}}+\frac{9 b B-11 A c}{9 b^2 x^{3/2} \sqrt{b x^2+c x^4}}-\frac{7 \sqrt{b x^2+c x^4} (9 b B-11 A c)}{45 b^3 x^{7/2}}-\frac{2 A}{9 b x^{7/2} \sqrt{b x^2+c x^4}}",1,"(-2*A)/(9*b*x^(7/2)*Sqrt[b*x^2 + c*x^4]) + (9*b*B - 11*A*c)/(9*b^2*x^(3/2)*Sqrt[b*x^2 + c*x^4]) - (7*c^(3/2)*(9*b*B - 11*A*c)*x^(3/2)*(b + c*x^2))/(15*b^4*(Sqrt[b] + Sqrt[c]*x)*Sqrt[b*x^2 + c*x^4]) - (7*(9*b*B - 11*A*c)*Sqrt[b*x^2 + c*x^4])/(45*b^3*x^(7/2)) + (7*c*(9*b*B - 11*A*c)*Sqrt[b*x^2 + c*x^4])/(15*b^4*x^(3/2)) + (7*c^(5/4)*(9*b*B - 11*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(15*b^(15/4)*Sqrt[b*x^2 + c*x^4]) - (7*c^(5/4)*(9*b*B - 11*A*c)*x*(Sqrt[b] + Sqrt[c]*x)*Sqrt[(b + c*x^2)/(Sqrt[b] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/b^(1/4)], 1/2])/(30*b^(15/4)*Sqrt[b*x^2 + c*x^4])","A",9,8,28,0.2857,1,"{2038, 2023, 2025, 2032, 329, 305, 220, 1196}"
269,1,96,0,0.0699623,"\int x^m \left(A+B x^2\right) \left(b x^2+c x^4\right)^3 \, dx","Int[x^m*(A + B*x^2)*(b*x^2 + c*x^4)^3,x]","\frac{b^2 x^{m+9} (3 A c+b B)}{m+9}+\frac{A b^3 x^{m+7}}{m+7}+\frac{c^2 x^{m+13} (A c+3 b B)}{m+13}+\frac{3 b c x^{m+11} (A c+b B)}{m+11}+\frac{B c^3 x^{m+15}}{m+15}","\frac{b^2 x^{m+9} (3 A c+b B)}{m+9}+\frac{A b^3 x^{m+7}}{m+7}+\frac{c^2 x^{m+13} (A c+3 b B)}{m+13}+\frac{3 b c x^{m+11} (A c+b B)}{m+11}+\frac{B c^3 x^{m+15}}{m+15}",1,"(A*b^3*x^(7 + m))/(7 + m) + (b^2*(b*B + 3*A*c)*x^(9 + m))/(9 + m) + (3*b*c*(b*B + A*c)*x^(11 + m))/(11 + m) + (c^2*(3*b*B + A*c)*x^(13 + m))/(13 + m) + (B*c^3*x^(15 + m))/(15 + m)","A",3,2,24,0.08333,1,"{1584, 448}"
270,1,71,0,0.0519871,"\int x^m \left(A+B x^2\right) \left(b x^2+c x^4\right)^2 \, dx","Int[x^m*(A + B*x^2)*(b*x^2 + c*x^4)^2,x]","\frac{A b^2 x^{m+5}}{m+5}+\frac{b x^{m+7} (2 A c+b B)}{m+7}+\frac{c x^{m+9} (A c+2 b B)}{m+9}+\frac{B c^2 x^{m+11}}{m+11}","\frac{A b^2 x^{m+5}}{m+5}+\frac{b x^{m+7} (2 A c+b B)}{m+7}+\frac{c x^{m+9} (A c+2 b B)}{m+9}+\frac{B c^2 x^{m+11}}{m+11}",1,"(A*b^2*x^(5 + m))/(5 + m) + (b*(b*B + 2*A*c)*x^(7 + m))/(7 + m) + (c*(2*b*B + A*c)*x^(9 + m))/(9 + m) + (B*c^2*x^(11 + m))/(11 + m)","A",3,2,24,0.08333,1,"{1584, 448}"
271,1,45,0,0.0298884,"\int x^m \left(A+B x^2\right) \left(b x^2+c x^4\right) \, dx","Int[x^m*(A + B*x^2)*(b*x^2 + c*x^4),x]","\frac{x^{m+5} (A c+b B)}{m+5}+\frac{A b x^{m+3}}{m+3}+\frac{B c x^{m+7}}{m+7}","\frac{x^{m+5} (A c+b B)}{m+5}+\frac{A b x^{m+3}}{m+3}+\frac{B c x^{m+7}}{m+7}",1,"(A*b*x^(3 + m))/(3 + m) + ((b*B + A*c)*x^(5 + m))/(5 + m) + (B*c*x^(7 + m))/(7 + m)","A",3,2,22,0.09091,1,"{1584, 448}"
272,1,71,0,0.0470955,"\int \frac{x^m \left(A+B x^2\right)}{b x^2+c x^4} \, dx","Int[(x^m*(A + B*x^2))/(b*x^2 + c*x^4),x]","\frac{x^{m-1} (b B-A c) \, _2F_1\left(1,\frac{m-1}{2};\frac{m+1}{2};-\frac{c x^2}{b}\right)}{b c (1-m)}-\frac{B x^{m-1}}{c (1-m)}","\frac{x^{m-1} (b B-A c) \, _2F_1\left(1,\frac{m-1}{2};\frac{m+1}{2};-\frac{c x^2}{b}\right)}{b c (1-m)}-\frac{B x^{m-1}}{c (1-m)}",1,"-((B*x^(-1 + m))/(c*(1 - m))) + ((b*B - A*c)*x^(-1 + m)*Hypergeometric2F1[1, (-1 + m)/2, (1 + m)/2, -((c*x^2)/b)])/(b*c*(1 - m))","A",3,3,24,0.1250,1,"{1584, 459, 364}"
273,1,92,0,0.0595799,"\int \frac{x^m \left(A+B x^2\right)}{\left(b x^2+c x^4\right)^2} \, dx","Int[(x^m*(A + B*x^2))/(b*x^2 + c*x^4)^2,x]","\frac{x^{m-3} \left(\frac{b B}{c}-\frac{A (5-m)}{3-m}\right) \, _2F_1\left(1,\frac{m-3}{2};\frac{m-1}{2};-\frac{c x^2}{b}\right)}{2 b^2}-\frac{x^{m-3} (b B-A c)}{2 b c \left(b+c x^2\right)}","\frac{x^{m-3} (b B (3-m)-A c (5-m)) \, _2F_1\left(1,\frac{m-3}{2};\frac{m-1}{2};-\frac{c x^2}{b}\right)}{2 b^2 c (3-m)}-\frac{x^{m-3} (b B-A c)}{2 b c \left(b+c x^2\right)}",1,"-((b*B - A*c)*x^(-3 + m))/(2*b*c*(b + c*x^2)) + (((b*B)/c - (A*(5 - m))/(3 - m))*x^(-3 + m)*Hypergeometric2F1[1, (-3 + m)/2, (-1 + m)/2, -((c*x^2)/b)])/(2*b^2)","A",3,3,24,0.1250,1,"{1584, 457, 364}"
274,1,126,0,0.1366407,"\int x^m \left(A+B x^2\right) \left(b x^2+c x^4\right)^p \, dx","Int[x^m*(A + B*x^2)*(b*x^2 + c*x^4)^p,x]","x^{m+1} \left(\frac{c x^2}{b}+1\right)^{-p} \left(b x^2+c x^4\right)^p \left(\frac{A}{m+2 p+1}-\frac{b B}{c (m+4 p+3)}\right) \, _2F_1\left(-p,\frac{1}{2} (m+2 p+1);\frac{1}{2} (m+2 p+3);-\frac{c x^2}{b}\right)+\frac{B x^{m-1} \left(b x^2+c x^4\right)^{p+1}}{c (m+4 p+3)}","\frac{B x^{m-1} \left(b x^2+c x^4\right)^{p+1}}{c (m+4 p+3)}-\frac{x^{m+1} \left(\frac{c x^2}{b}+1\right)^{-p} \left(b x^2+c x^4\right)^p (b B (m+2 p+1)-A c (m+4 p+3)) \, _2F_1\left(-p,\frac{1}{2} (m+2 p+1);\frac{1}{2} (m+2 p+3);-\frac{c x^2}{b}\right)}{c (m+2 p+1) (m+4 p+3)}",1,"(B*x^(-1 + m)*(b*x^2 + c*x^4)^(1 + p))/(c*(3 + m + 4*p)) + ((A/(1 + m + 2*p) - (b*B)/(c*(3 + m + 4*p)))*x^(1 + m)*(b*x^2 + c*x^4)^p*Hypergeometric2F1[-p, (1 + m + 2*p)/2, (3 + m + 2*p)/2, -((c*x^2)/b)])/(1 + (c*x^2)/b)^p","A",4,4,24,0.1667,1,"{2039, 2032, 365, 364}"
275,1,95,0,0.1561373,"\int x^{-1+n-j p} \left(c+d x^n\right) \left(a x^j+b x^{j+n}\right)^p \, dx","Int[x^(-1 + n - j*p)*(c + d*x^n)*(a*x^j + b*x^(j + n))^p,x]","\frac{d x^{n-j (p+1)} \left(a x^j+b x^{j+n}\right)^{p+1}}{b n (p+2)}-\frac{x^{-j (p+1)} (a d-b c (p+2)) \left(a x^j+b x^{j+n}\right)^{p+1}}{b^2 n (p+1) (p+2)}","\frac{d x^{n-j (p+1)} \left(a x^j+b x^{j+n}\right)^{p+1}}{b n (p+2)}-\frac{x^{-j (p+1)} (a d-b c (p+2)) \left(a x^j+b x^{j+n}\right)^{p+1}}{b^2 n (p+1) (p+2)}",1,"-(((a*d - b*c*(2 + p))*(a*x^j + b*x^(j + n))^(1 + p))/(b^2*n*(1 + p)*(2 + p)*x^(j*(1 + p)))) + (d*x^(n - j*(1 + p))*(a*x^j + b*x^(j + n))^(1 + p))/(b*n*(2 + p))","A",2,2,32,0.06250,1,"{2039, 2014}"
276,1,113,0,0.2238288,"\int (e x)^m \left(c+d x^n\right)^q \left(a x^j+b x^{j+n}\right)^p \, dx","Int[(e*x)^m*(c + d*x^n)^q*(a*x^j + b*x^(j + n))^p,x]","\frac{x (e x)^m \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} \left(a x^j+b x^{j+n}\right)^p F_1\left(\frac{m+j p+1}{n};-p,-q;\frac{m+n+j p+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{j p+m+1}","\frac{x (e x)^m \left(\frac{b x^n}{a}+1\right)^{-p} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} \left(a x^j+b x^{j+n}\right)^p F_1\left(\frac{m+j p+1}{n};-p,-q;\frac{m+n+j p+1}{n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{j p+m+1}",1,"(x*(e*x)^m*(c + d*x^n)^q*(a*x^j + b*x^(j + n))^p*AppellF1[(1 + m + j*p)/n, -p, -q, (1 + m + n + j*p)/n, -((b*x^n)/a), -((d*x^n)/c)])/((1 + m + j*p)*(1 + (b*x^n)/a)^p*(1 + (d*x^n)/c)^q)","A",4,3,30,0.1000,1,"{2042, 511, 510}"
277,1,129,0,0.3567957,"\int (e x)^{7/4} \left(c+d x^n\right)^q \left(a x^j+b x^{j+n}\right)^{5/3} \, dx","Int[(e*x)^(7/4)*(c + d*x^n)^q*(a*x^j + b*x^(j + n))^(5/3),x]","\frac{12 a e (e x)^{3/4} x^{j+2} \left(a x^j+b x^{j+n}\right)^{2/3} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{20 j+33}{12 n};-\frac{5}{3},-q;\frac{20 j+12 n+33}{12 n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{(20 j+33) \left(\frac{b x^n}{a}+1\right)^{2/3}}","\frac{12 a e (e x)^{3/4} x^{j+2} \left(a x^j+b x^{j+n}\right)^{2/3} \left(c+d x^n\right)^q \left(\frac{d x^n}{c}+1\right)^{-q} F_1\left(\frac{20 j+33}{12 n};-\frac{5}{3},-q;\frac{20 j+12 n+33}{12 n};-\frac{b x^n}{a},-\frac{d x^n}{c}\right)}{(20 j+33) \left(\frac{b x^n}{a}+1\right)^{2/3}}",1,"(12*a*e*x^(2 + j)*(e*x)^(3/4)*(c + d*x^n)^q*(a*x^j + b*x^(j + n))^(2/3)*AppellF1[(33 + 20*j)/(12*n), -5/3, -q, (33 + 20*j + 12*n)/(12*n), -((b*x^n)/a), -((d*x^n)/c)])/((33 + 20*j)*(1 + (b*x^n)/a)^(2/3)*(1 + (d*x^n)/c)^q)","A",4,3,34,0.08824,1,"{2042, 511, 510}"
278,1,19,0,0.0257862,"\int \frac{4+3 x^4}{5 x+2 x^5} \, dx","Int[(4 + 3*x^4)/(5*x + 2*x^5),x]","\frac{7}{40} \log \left(2 x^4+5\right)+\frac{4 \log (x)}{5}","\frac{7}{40} \log \left(2 x^4+5\right)+\frac{4 \log (x)}{5}",1,"(4*Log[x])/5 + (7*Log[5 + 2*x^4])/40","A",4,3,19,0.1579,1,"{1593, 446, 72}"
279,1,15,0,0.0219739,"\int \frac{1+x^6}{x-x^7} \, dx","Int[(1 + x^6)/(x - x^7),x]","\log (x)-\frac{1}{3} \log \left(1-x^6\right)","\log (x)-\frac{1}{3} \log \left(1-x^6\right)",1,"Log[x] - Log[1 - x^6]/3","A",4,3,15,0.2000,1,"{1593, 446, 72}"
280,1,17,0,0.025,"\int \frac{8+5 x^{10}}{2 x-x^{11}} \, dx","Int[(8 + 5*x^10)/(2*x - x^11),x]","4 \log (x)-\frac{9}{10} \log \left(2-x^{10}\right)","4 \log (x)-\frac{9}{10} \log \left(2-x^{10}\right)",1,"4*Log[x] - (9*Log[2 - x^10])/10","A",4,3,19,0.1579,1,"{1593, 446, 72}"
281,1,16,0,0.0136957,"\int \frac{-3+2 x}{-x^2+x^3} \, dx","Int[(-3 + 2*x)/(-x^2 + x^3),x]","-\frac{3}{x}-\log (1-x)+\log (x)","-\frac{3}{x}-\log (1-x)+\log (x)",1,"-3/x - Log[1 - x] + Log[x]","A",3,2,17,0.1176,1,"{1593, 77}"
282,1,54,0,0.0497989,"\int \frac{a x^m+b x^n}{c x^m+d x^n} \, dx","Int[(a*x^m + b*x^n)/(c*x^m + d*x^n),x]","\frac{x (b c-a d) \, _2F_1\left(1,\frac{1}{m-n};1+\frac{1}{m-n};-\frac{c x^{m-n}}{d}\right)}{c d}+\frac{a x}{c}","\frac{x (b c-a d) \, _2F_1\left(1,\frac{1}{m-n};1+\frac{1}{m-n};-\frac{c x^{m-n}}{d}\right)}{c d}+\frac{a x}{c}",1,"(a*x)/c + ((b*c - a*d)*x*Hypergeometric2F1[1, (m - n)^(-1), 1 + (m - n)^(-1), -((c*x^(m - n))/d)])/(c*d)","A",4,4,25,0.1600,1,"{1593, 1584, 388, 245}"
283,1,18,0,0.0375639,"\int x^m \left(a+b x^n\right)^p \left(a (1+m+q) x^q+b (1+m+n (1+p)+q) x^{n+q}\right) \, dx","Int[x^m*(a + b*x^n)^p*(a*(1 + m + q)*x^q + b*(1 + m + n*(1 + p) + q)*x^(n + q)),x]","x^{m+q+1} \left(a+b x^n\right)^{p+1}","x^{m+q+1} \left(a+b x^n\right)^{p+1}",1,"x^(1 + m + q)*(a + b*x^n)^(1 + p)","A",2,2,39,0.05128,1,"{1584, 449}"
284,1,64,0,0.0643364,"\int \frac{\left(a+\frac{b}{x}\right)^n x^m}{c+d x} \, dx","Int[((a + b/x)^n*x^m)/(c + d*x),x]","\frac{x^m \left(a+\frac{b}{x}\right)^n \left(\frac{b}{a x}+1\right)^{-n} F_1\left(-m;-n,1;1-m;-\frac{b}{a x},-\frac{c}{d x}\right)}{d m}","\frac{x^m \left(a+\frac{b}{x}\right)^n \left(\frac{b}{a x}+1\right)^{-n} F_1\left(-m;-n,1;1-m;-\frac{b}{a x},-\frac{c}{d x}\right)}{d m}",1,"((a + b/x)^n*x^m*AppellF1[-m, -n, 1, 1 - m, -(b/(a*x)), -(c/(d*x))])/(d*m*(1 + b/(a*x))^n)","A",4,4,20,0.2000,1,"{514, 497, 135, 133}"
285,1,195,0,0.2155863,"\int \frac{\left(a+\frac{b}{x}\right)^n x^2}{c+d x} \, dx","Int[((a + b/x)^n*x^2)/(c + d*x),x]","\frac{\left(a+\frac{b}{x}\right)^{n+1} \left(2 a^2 c^2-2 a b c d n-b^2 d^2 (1-n) n\right) \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{2 a^3 d^3 (n+1)}-\frac{x \left(a+\frac{b}{x}\right)^{n+1} (2 a c+b d (1-n))}{2 a^2 d^2}-\frac{c^3 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^3 (n+1) (a c-b d)}+\frac{x^2 \left(a+\frac{b}{x}\right)^{n+1}}{2 a d}","\frac{\left(a+\frac{b}{x}\right)^{n+1} \left(2 a^2 c^2-2 a b c d n-b^2 d^2 (1-n) n\right) \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{2 a^3 d^3 (n+1)}-\frac{x \left(a+\frac{b}{x}\right)^{n+1} (2 a c+b d (1-n))}{2 a^2 d^2}-\frac{c^3 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^3 (n+1) (a c-b d)}+\frac{x^2 \left(a+\frac{b}{x}\right)^{n+1}}{2 a d}",1,"-((2*a*c + b*d*(1 - n))*(a + b/x)^(1 + n)*x)/(2*a^2*d^2) + ((a + b/x)^(1 + n)*x^2)/(2*a*d) - (c^3*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(d^3*(a*c - b*d)*(1 + n)) + ((2*a^2*c^2 - 2*a*b*c*d*n - b^2*d^2*(1 - n)*n)*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + b/(a*x)])/(2*a^3*d^3*(1 + n))","A",7,7,20,0.3500,1,"{514, 446, 103, 151, 156, 65, 68}"
286,1,131,0,0.0971801,"\int \frac{\left(a+\frac{b}{x}\right)^n x}{c+d x} \, dx","Int[((a + b/x)^n*x)/(c + d*x),x]","-\frac{\left(a+\frac{b}{x}\right)^{n+1} (a c-b d n) \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a^2 d^2 (n+1)}+\frac{c^2 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^2 (n+1) (a c-b d)}+\frac{x \left(a+\frac{b}{x}\right)^{n+1}}{a d}","-\frac{\left(a+\frac{b}{x}\right)^{n+1} (a c-b d n) \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a^2 d^2 (n+1)}+\frac{c^2 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^2 (n+1) (a c-b d)}+\frac{x \left(a+\frac{b}{x}\right)^{n+1}}{a d}",1,"((a + b/x)^(1 + n)*x)/(a*d) + (c^2*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(d^2*(a*c - b*d)*(1 + n)) - ((a*c - b*d*n)*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + b/(a*x)])/(a^2*d^2*(1 + n))","A",6,6,18,0.3333,1,"{514, 375, 103, 156, 65, 68}"
287,1,101,0,0.0555461,"\int \frac{\left(a+\frac{b}{x}\right)^n}{c+d x} \, dx","Int[(a + b/x)^n/(c + d*x),x]","\frac{\left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a d (n+1)}-\frac{c \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d (n+1) (a c-b d)}","\frac{\left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a d (n+1)}-\frac{c \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d (n+1) (a c-b d)}",1,"-((c*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(d*(a*c - b*d)*(1 + n))) + ((a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + b/(a*x)])/(a*d*(1 + n))","A",5,5,17,0.2941,1,"{434, 446, 86, 65, 68}"
288,1,54,0,0.039041,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x (c+d x)} \, dx","Int[(a + b/x)^n/(x*(c + d*x)),x]","\frac{\left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{(n+1) (a c-b d)}","\frac{\left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{(n+1) (a c-b d)}",1,"((a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/((a*c - b*d)*(1 + n))","A",3,3,20,0.1500,1,"{514, 444, 68}"
289,1,84,0,0.0555754,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x^2 (c+d x)} \, dx","Int[(a + b/x)^n/(x^2*(c + d*x)),x]","-\frac{d \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c (n+1) (a c-b d)}-\frac{\left(a+\frac{b}{x}\right)^{n+1}}{b c (n+1)}","-\frac{d \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c (n+1) (a c-b d)}-\frac{\left(a+\frac{b}{x}\right)^{n+1}}{b c (n+1)}",1,"-((a + b/x)^(1 + n)/(b*c*(1 + n))) - (d*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(c*(a*c - b*d)*(1 + n))","A",4,4,20,0.2000,1,"{514, 446, 80, 68}"
290,1,115,0,0.0962083,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x^3 (c+d x)} \, dx","Int[(a + b/x)^n/(x^3*(c + d*x)),x]","\frac{(a c+b d) \left(a+\frac{b}{x}\right)^{n+1}}{b^2 c^2 (n+1)}-\frac{\left(a+\frac{b}{x}\right)^{n+2}}{b^2 c (n+2)}+\frac{d^2 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^2 (n+1) (a c-b d)}","\frac{(a c+b d) \left(a+\frac{b}{x}\right)^{n+1}}{b^2 c^2 (n+1)}-\frac{\left(a+\frac{b}{x}\right)^{n+2}}{b^2 c (n+2)}+\frac{d^2 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^2 (n+1) (a c-b d)}",1,"((a*c + b*d)*(a + b/x)^(1 + n))/(b^2*c^2*(1 + n)) - (a + b/x)^(2 + n)/(b^2*c*(2 + n)) + (d^2*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(c^2*(a*c - b*d)*(1 + n))","A",5,4,20,0.2000,1,"{514, 446, 88, 68}"
291,1,207,0,0.1578292,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x^5 (c+d x)} \, dx","Int[(a + b/x)^n/(x^5*(c + d*x)),x]","\frac{(a c+b d) \left(a^2 c^2+b^2 d^2\right) \left(a+\frac{b}{x}\right)^{n+1}}{b^4 c^4 (n+1)}-\frac{\left(3 a^2 c^2+2 a b c d+b^2 d^2\right) \left(a+\frac{b}{x}\right)^{n+2}}{b^4 c^3 (n+2)}+\frac{(3 a c+b d) \left(a+\frac{b}{x}\right)^{n+3}}{b^4 c^2 (n+3)}-\frac{\left(a+\frac{b}{x}\right)^{n+4}}{b^4 c (n+4)}+\frac{d^4 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^4 (n+1) (a c-b d)}","\frac{(a c+b d) \left(a^2 c^2+b^2 d^2\right) \left(a+\frac{b}{x}\right)^{n+1}}{b^4 c^4 (n+1)}-\frac{\left(3 a^2 c^2+2 a b c d+b^2 d^2\right) \left(a+\frac{b}{x}\right)^{n+2}}{b^4 c^3 (n+2)}+\frac{(3 a c+b d) \left(a+\frac{b}{x}\right)^{n+3}}{b^4 c^2 (n+3)}-\frac{\left(a+\frac{b}{x}\right)^{n+4}}{b^4 c (n+4)}+\frac{d^4 \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^4 (n+1) (a c-b d)}",1,"((a*c + b*d)*(a^2*c^2 + b^2*d^2)*(a + b/x)^(1 + n))/(b^4*c^4*(1 + n)) - ((3*a^2*c^2 + 2*a*b*c*d + b^2*d^2)*(a + b/x)^(2 + n))/(b^4*c^3*(2 + n)) + ((3*a*c + b*d)*(a + b/x)^(3 + n))/(b^4*c^2*(3 + n)) - (a + b/x)^(4 + n)/(b^4*c*(4 + n)) + (d^4*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(c^4*(a*c - b*d)*(1 + n))","A",5,4,20,0.2000,1,"{514, 446, 88, 68}"
292,1,73,0,0.0708469,"\int \frac{\left(a+\frac{b}{x}\right)^n x^m}{(c+d x)^2} \, dx","Int[((a + b/x)^n*x^m)/(c + d*x)^2,x]","-\frac{x^{m-1} \left(a+\frac{b}{x}\right)^n \left(\frac{b}{a x}+1\right)^{-n} F_1\left(1-m;-n,2;2-m;-\frac{b}{a x},-\frac{c}{d x}\right)}{d^2 (1-m)}","-\frac{x^{m-1} \left(a+\frac{b}{x}\right)^n \left(\frac{b}{a x}+1\right)^{-n} F_1\left(1-m;-n,2;2-m;-\frac{b}{a x},-\frac{c}{d x}\right)}{d^2 (1-m)}",1,"-(((a + b/x)^n*x^(-1 + m)*AppellF1[1 - m, -n, 2, 2 - m, -(b/(a*x)), -(c/(d*x))])/(d^2*(1 - m)*(1 + b/(a*x))^n))","A",4,4,20,0.2000,1,"{514, 497, 135, 133}"
293,1,202,0,0.2386041,"\int \frac{\left(a+\frac{b}{x}\right)^n x^2}{(c+d x)^2} \, dx","Int[((a + b/x)^n*x^2)/(c + d*x)^2,x]","-\frac{\left(a+\frac{b}{x}\right)^{n+1} (2 a c-b d n) \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a^2 d^3 (n+1)}+\frac{c^2 \left(a+\frac{b}{x}\right)^{n+1} (2 a c-b d (2-n)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^3 (n+1) (a c-b d)^2}+\frac{c (2 a c-b d) \left(a+\frac{b}{x}\right)^{n+1}}{a d^2 \left(\frac{c}{x}+d\right) (a c-b d)}+\frac{x \left(a+\frac{b}{x}\right)^{n+1}}{a d \left(\frac{c}{x}+d\right)}","-\frac{\left(a+\frac{b}{x}\right)^{n+1} (2 a c-b d n) \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a^2 d^3 (n+1)}+\frac{c^2 \left(a+\frac{b}{x}\right)^{n+1} (2 a c-b d (2-n)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^3 (n+1) (a c-b d)^2}+\frac{c (2 a c-b d) \left(a+\frac{b}{x}\right)^{n+1}}{a d^2 \left(\frac{c}{x}+d\right) (a c-b d)}+\frac{x \left(a+\frac{b}{x}\right)^{n+1}}{a d \left(\frac{c}{x}+d\right)}",1,"(c*(2*a*c - b*d)*(a + b/x)^(1 + n))/(a*d^2*(a*c - b*d)*(d + c/x)) + ((a + b/x)^(1 + n)*x)/(a*d*(d + c/x)) + (c^2*(2*a*c - b*d*(2 - n))*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(d^3*(a*c - b*d)^2*(1 + n)) - ((2*a*c - b*d*n)*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + b/(a*x)])/(a^2*d^3*(1 + n))","A",7,7,20,0.3500,1,"{514, 375, 103, 151, 156, 65, 68}"
294,1,150,0,0.1153102,"\int \frac{\left(a+\frac{b}{x}\right)^n x}{(c+d x)^2} \, dx","Int[((a + b/x)^n*x)/(c + d*x)^2,x]","-\frac{c \left(a+\frac{b}{x}\right)^{n+1} (a c-b d (1-n)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^2 (n+1) (a c-b d)^2}-\frac{c \left(a+\frac{b}{x}\right)^{n+1}}{d \left(\frac{c}{x}+d\right) (a c-b d)}+\frac{\left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a d^2 (n+1)}","-\frac{c \left(a+\frac{b}{x}\right)^{n+1} (a c-b d (1-n)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{d^2 (n+1) (a c-b d)^2}-\frac{c \left(a+\frac{b}{x}\right)^{n+1}}{d \left(\frac{c}{x}+d\right) (a c-b d)}+\frac{\left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(1,n+1;n+2;\frac{b}{a x}+1\right)}{a d^2 (n+1)}",1,"-((c*(a + b/x)^(1 + n))/(d*(a*c - b*d)*(d + c/x))) - (c*(a*c - b*d*(1 - n))*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(d^2*(a*c - b*d)^2*(1 + n)) + ((a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, 1 + b/(a*x)])/(a*d^2*(1 + n))","A",6,6,18,0.3333,1,"{514, 446, 103, 156, 65, 68}"
295,1,56,0,0.0326302,"\int \frac{\left(a+\frac{b}{x}\right)^n}{(c+d x)^2} \, dx","Int[(a + b/x)^n/(c + d*x)^2,x]","-\frac{b \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{(n+1) (a c-b d)^2}","-\frac{b \left(a+\frac{b}{x}\right)^{n+1} \, _2F_1\left(2,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{(n+1) (a c-b d)^2}",1,"-((b*(a + b/x)^(1 + n)*Hypergeometric2F1[2, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/((a*c - b*d)^2*(1 + n)))","A",3,3,17,0.1765,1,"{434, 444, 68}"
296,1,105,0,0.0679815,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x (c+d x)^2} \, dx","Int[(a + b/x)^n/(x*(c + d*x)^2),x]","\frac{\left(a+\frac{b}{x}\right)^{n+1} (a c-b d (n+1)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c (n+1) (a c-b d)^2}-\frac{d \left(a+\frac{b}{x}\right)^{n+1}}{c \left(\frac{c}{x}+d\right) (a c-b d)}","\frac{\left(a+\frac{b}{x}\right)^{n+1} (a c-b d (n+1)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c (n+1) (a c-b d)^2}-\frac{d \left(a+\frac{b}{x}\right)^{n+1}}{c \left(\frac{c}{x}+d\right) (a c-b d)}",1,"-((d*(a + b/x)^(1 + n))/(c*(a*c - b*d)*(d + c/x))) + ((a*c - b*d*(1 + n))*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(c*(a*c - b*d)^2*(1 + n))","A",4,4,20,0.2000,1,"{514, 446, 78, 68}"
297,1,133,0,0.1309789,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x^2 (c+d x)^2} \, dx","Int[(a + b/x)^n/(x^2*(c + d*x)^2),x]","\frac{d^2 \left(a+\frac{b}{x}\right)^{n+1}}{c^2 \left(\frac{c}{x}+d\right) (a c-b d)}-\frac{d \left(a+\frac{b}{x}\right)^{n+1} (2 a c-b d (n+2)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^2 (n+1) (a c-b d)^2}-\frac{\left(a+\frac{b}{x}\right)^{n+1}}{b c^2 (n+1)}","\frac{d^2 \left(a+\frac{b}{x}\right)^{n+1}}{c^2 \left(\frac{c}{x}+d\right) (a c-b d)}-\frac{d \left(a+\frac{b}{x}\right)^{n+1} (2 a c-b d (n+2)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^2 (n+1) (a c-b d)^2}-\frac{\left(a+\frac{b}{x}\right)^{n+1}}{b c^2 (n+1)}",1,"-((a + b/x)^(1 + n)/(b*c^2*(1 + n))) + (d^2*(a + b/x)^(1 + n))/(c^2*(a*c - b*d)*(d + c/x)) - (d*(2*a*c - b*d*(2 + n))*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(c^2*(a*c - b*d)^2*(1 + n))","A",5,5,20,0.2500,1,"{514, 446, 89, 80, 68}"
298,1,217,0,0.2638489,"\int \frac{\left(a+\frac{b}{x}\right)^n}{x^3 (c+d x)^2} \, dx","Int[(a + b/x)^n/(x^3*(c + d*x)^2),x]","-\frac{\left(a+\frac{b}{x}\right)^{n+1} \left(d (b d (n+2) (a c+b d (n+3))-a c (a c+b d (3 n+5)))-\frac{c (a c-b d) (a c+b d (n+3))}{x}\right)}{b^2 c^3 (n+1) (n+2) \left(\frac{c}{x}+d\right) (a c-b d)}+\frac{d^2 \left(a+\frac{b}{x}\right)^{n+1} (3 a c-b d (n+3)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^3 (n+1) (a c-b d)^2}-\frac{\left(a+\frac{b}{x}\right)^{n+1}}{b c (n+2) x^2 \left(\frac{c}{x}+d\right)}","-\frac{\left(a+\frac{b}{x}\right)^{n+1} \left(d (b d (n+2) (a c+b d (n+3))-a c (a c+b d (3 n+5)))-\frac{c (a c-b d) (a c+b d (n+3))}{x}\right)}{b^2 c^3 (n+1) (n+2) \left(\frac{c}{x}+d\right) (a c-b d)}+\frac{d^2 \left(a+\frac{b}{x}\right)^{n+1} (3 a c-b d (n+3)) \, _2F_1\left(1,n+1;n+2;\frac{c \left(a+\frac{b}{x}\right)}{a c-b d}\right)}{c^3 (n+1) (a c-b d)^2}-\frac{\left(a+\frac{b}{x}\right)^{n+1}}{b c (n+2) x^2 \left(\frac{c}{x}+d\right)}",1,"-(((a + b/x)^(1 + n)*(d*(b*d*(2 + n)*(a*c + b*d*(3 + n)) - a*c*(a*c + b*d*(5 + 3*n))) - (c*(a*c - b*d)*(a*c + b*d*(3 + n)))/x))/(b^2*c^3*(a*c - b*d)*(1 + n)*(2 + n)*(d + c/x))) - (a + b/x)^(1 + n)/(b*c*(2 + n)*(d + c/x)*x^2) + (d^2*(3*a*c - b*d*(3 + n))*(a + b/x)^(1 + n)*Hypergeometric2F1[1, 1 + n, 2 + n, (c*(a + b/x))/(a*c - b*d)])/(c^3*(a*c - b*d)^2*(1 + n))","A",5,5,20,0.2500,1,"{514, 446, 100, 146, 68}"