1,1,45,0,0.0207087,"\int x^m (A+B x) \left(b x+c x^2\right) \, dx","Int[x^m*(A + B*x)*(b*x + c*x^2),x]","\frac{x^{m+3} (A c+b B)}{m+3}+\frac{A b x^{m+2}}{m+2}+\frac{B c x^{m+4}}{m+4}","\frac{x^{m+3} (A c+b B)}{m+3}+\frac{A b x^{m+2}}{m+2}+\frac{B c x^{m+4}}{m+4}",1,"(A*b*x^(2 + m))/(2 + m) + ((b*B + A*c)*x^(3 + m))/(3 + m) + (B*c*x^(4 + m))/(4 + m)","A",2,1,18,0.05556,1,"{765}"
2,1,33,0,0.0441337,"\int x^3 (A+B x) \left(b x+c x^2\right) \, dx","Int[x^3*(A + B*x)*(b*x + c*x^2),x]","\frac{1}{6} x^6 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{7} B c x^7","\frac{1}{6} x^6 (A c+b B)+\frac{1}{5} A b x^5+\frac{1}{7} B c x^7",1,"(A*b*x^5)/5 + ((b*B + A*c)*x^6)/6 + (B*c*x^7)/7","A",2,1,18,0.05556,1,"{765}"
3,1,33,0,0.0358081,"\int x^2 (A+B x) \left(b x+c x^2\right) \, dx","Int[x^2*(A + B*x)*(b*x + c*x^2),x]","\frac{1}{5} x^5 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{6} B c x^6","\frac{1}{5} x^5 (A c+b B)+\frac{1}{4} A b x^4+\frac{1}{6} B c x^6",1,"(A*b*x^4)/4 + ((b*B + A*c)*x^5)/5 + (B*c*x^6)/6","A",2,1,18,0.05556,1,"{765}"
4,1,33,0,0.0264801,"\int x (A+B x) \left(b x+c x^2\right) \, dx","Int[x*(A + B*x)*(b*x + c*x^2),x]","\frac{1}{4} x^4 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{5} B c x^5","\frac{1}{4} x^4 (A c+b B)+\frac{1}{3} A b x^3+\frac{1}{5} B c x^5",1,"(A*b*x^3)/3 + ((b*B + A*c)*x^4)/4 + (B*c*x^5)/5","A",2,1,16,0.06250,1,"{765}"
5,1,33,0,0.0186484,"\int (A+B x) \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(b*x + c*x^2),x]","\frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4","\frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4",1,"(A*b*x^2)/2 + ((b*B + A*c)*x^3)/3 + (B*c*x^4)/4","A",2,1,15,0.06667,1,"{631}"
6,1,28,0,0.0182864,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x,x]","\frac{1}{2} x^2 (A c+b B)+A b x+\frac{1}{3} B c x^3","\frac{1}{2} x^2 (A c+b B)+A b x+\frac{1}{3} B c x^3",1,"A*b*x + ((b*B + A*c)*x^2)/2 + (B*c*x^3)/3","A",2,1,18,0.05556,1,"{765}"
7,1,24,0,0.0127155,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^2} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^2,x]","x (A c+b B)+A b \log (x)+\frac{1}{2} B c x^2","x (A c+b B)+A b \log (x)+\frac{1}{2} B c x^2",1,"(b*B + A*c)*x + (B*c*x^2)/2 + A*b*Log[x]","A",2,1,18,0.05556,1,"{765}"
8,1,22,0,0.0158835,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^3} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^3,x]","\log (x) (A c+b B)-\frac{A b}{x}+B c x","\log (x) (A c+b B)-\frac{A b}{x}+B c x",1,"-((A*b)/x) + B*c*x + (b*B + A*c)*Log[x]","A",2,1,18,0.05556,1,"{765}"
9,1,27,0,0.0165446,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^4} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^4,x]","-\frac{A c+b B}{x}-\frac{A b}{2 x^2}+B c \log (x)","-\frac{A c+b B}{x}-\frac{A b}{2 x^2}+B c \log (x)",1,"-(A*b)/(2*x^2) - (b*B + A*c)/x + B*c*Log[x]","A",2,1,18,0.05556,1,"{765}"
10,1,31,0,0.0166305,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^5} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^5,x]","-\frac{A c+b B}{2 x^2}-\frac{A b}{3 x^3}-\frac{B c}{x}","-\frac{A c+b B}{2 x^2}-\frac{A b}{3 x^3}-\frac{B c}{x}",1,"-(A*b)/(3*x^3) - (b*B + A*c)/(2*x^2) - (B*c)/x","A",2,1,18,0.05556,1,"{765}"
11,1,33,0,0.016918,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^6} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^6,x]","-\frac{A c+b B}{3 x^3}-\frac{A b}{4 x^4}-\frac{B c}{2 x^2}","-\frac{A c+b B}{3 x^3}-\frac{A b}{4 x^4}-\frac{B c}{2 x^2}",1,"-(A*b)/(4*x^4) - (b*B + A*c)/(3*x^3) - (B*c)/(2*x^2)","A",2,1,18,0.05556,1,"{765}"
12,1,33,0,0.0166344,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^7} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^7,x]","-\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3}","-\frac{A c+b B}{4 x^4}-\frac{A b}{5 x^5}-\frac{B c}{3 x^3}",1,"-(A*b)/(5*x^5) - (b*B + A*c)/(4*x^4) - (B*c)/(3*x^3)","A",2,1,18,0.05556,1,"{765}"
13,1,33,0,0.0160021,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^8} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^8,x]","-\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4}","-\frac{A c+b B}{5 x^5}-\frac{A b}{6 x^6}-\frac{B c}{4 x^4}",1,"-(A*b)/(6*x^6) - (b*B + A*c)/(5*x^5) - (B*c)/(4*x^4)","A",2,1,18,0.05556,1,"{765}"
14,1,71,0,0.0424106,"\int x^m (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x^m*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{A b^2 x^{m+3}}{m+3}+\frac{b x^{m+4} (2 A c+b B)}{m+4}+\frac{c x^{m+5} (A c+2 b B)}{m+5}+\frac{B c^2 x^{m+6}}{m+6}","\frac{A b^2 x^{m+3}}{m+3}+\frac{b x^{m+4} (2 A c+b B)}{m+4}+\frac{c x^{m+5} (A c+2 b B)}{m+5}+\frac{B c^2 x^{m+6}}{m+6}",1,"(A*b^2*x^(3 + m))/(3 + m) + (b*(b*B + 2*A*c)*x^(4 + m))/(4 + m) + (c*(2*b*B + A*c)*x^(5 + m))/(5 + m) + (B*c^2*x^(6 + m))/(6 + m)","A",2,1,20,0.05000,1,"{765}"
15,1,55,0,0.0616889,"\int x^3 (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x^3*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{6} A b^2 x^6+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{9} B c^2 x^9","\frac{1}{6} A b^2 x^6+\frac{1}{8} c x^8 (A c+2 b B)+\frac{1}{7} b x^7 (2 A c+b B)+\frac{1}{9} B c^2 x^9",1,"(A*b^2*x^6)/6 + (b*(b*B + 2*A*c)*x^7)/7 + (c*(2*b*B + A*c)*x^8)/8 + (B*c^2*x^9)/9","A",2,1,20,0.05000,1,"{765}"
16,1,55,0,0.0558134,"\int x^2 (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x^2*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{5} A b^2 x^5+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{8} B c^2 x^8","\frac{1}{5} A b^2 x^5+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{6} b x^6 (2 A c+b B)+\frac{1}{8} B c^2 x^8",1,"(A*b^2*x^5)/5 + (b*(b*B + 2*A*c)*x^6)/6 + (c*(2*b*B + A*c)*x^7)/7 + (B*c^2*x^8)/8","A",2,1,20,0.05000,1,"{765}"
17,1,55,0,0.0485926,"\int x (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{4} A b^2 x^4+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{7} B c^2 x^7","\frac{1}{4} A b^2 x^4+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{5} b x^5 (2 A c+b B)+\frac{1}{7} B c^2 x^7",1,"(A*b^2*x^4)/4 + (b*(b*B + 2*A*c)*x^5)/5 + (c*(2*b*B + A*c)*x^6)/6 + (B*c^2*x^7)/7","A",2,1,18,0.05556,1,"{765}"
18,1,55,0,0.0340721,"\int (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{3} A b^2 x^3+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{4} b x^4 (2 A c+b B)+\frac{1}{6} B c^2 x^6","\frac{1}{3} A b^2 x^3+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{4} b x^4 (2 A c+b B)+\frac{1}{6} B c^2 x^6",1,"(A*b^2*x^3)/3 + (b*(b*B + 2*A*c)*x^4)/4 + (c*(2*b*B + A*c)*x^5)/5 + (B*c^2*x^6)/6","A",2,1,17,0.05882,1,"{631}"
19,1,55,0,0.0358139,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x,x]","\frac{1}{2} A b^2 x^2+\frac{1}{4} c x^4 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{5} B c^2 x^5","\frac{1}{2} A b^2 x^2+\frac{1}{4} c x^4 (A c+2 b B)+\frac{1}{3} b x^3 (2 A c+b B)+\frac{1}{5} B c^2 x^5",1,"(A*b^2*x^2)/2 + (b*(b*B + 2*A*c)*x^3)/3 + (c*(2*b*B + A*c)*x^4)/4 + (B*c^2*x^5)/5","A",2,1,20,0.05000,1,"{765}"
20,1,38,0,0.027039,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^2,x]","\frac{B (b+c x)^4}{4 c^2}-\frac{(b+c x)^3 (b B-A c)}{3 c^2}","\frac{B (b+c x)^4}{4 c^2}-\frac{(b+c x)^3 (b B-A c)}{3 c^2}",1,"-((b*B - A*c)*(b + c*x)^3)/(3*c^2) + (B*(b + c*x)^4)/(4*c^2)","A",2,1,20,0.05000,1,"{765}"
21,1,46,0,0.0271827,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^3,x]","A b^2 \log (x)+\frac{1}{2} c x^2 (A c+2 b B)+b x (2 A c+b B)+\frac{1}{3} B c^2 x^3","A b^2 \log (x)+\frac{1}{2} c x^2 (A c+2 b B)+b x (2 A c+b B)+\frac{1}{3} B c^2 x^3",1,"b*(b*B + 2*A*c)*x + (c*(2*b*B + A*c)*x^2)/2 + (B*c^2*x^3)/3 + A*b^2*Log[x]","A",2,1,20,0.05000,1,"{765}"
22,1,44,0,0.0315554,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^4,x]","-\frac{A b^2}{x}+c x (A c+2 b B)+b \log (x) (2 A c+b B)+\frac{1}{2} B c^2 x^2","-\frac{A b^2}{x}+c x (A c+2 b B)+b \log (x) (2 A c+b B)+\frac{1}{2} B c^2 x^2",1,"-((A*b^2)/x) + c*(2*b*B + A*c)*x + (B*c^2*x^2)/2 + b*(b*B + 2*A*c)*Log[x]","A",2,1,20,0.05000,1,"{765}"
23,1,44,0,0.0299489,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^5,x]","-\frac{A b^2}{2 x^2}-\frac{b (2 A c+b B)}{x}+c \log (x) (A c+2 b B)+B c^2 x","-\frac{A b^2}{2 x^2}-\frac{b (2 A c+b B)}{x}+c \log (x) (A c+2 b B)+B c^2 x",1,"-(A*b^2)/(2*x^2) - (b*(b*B + 2*A*c))/x + B*c^2*x + c*(2*b*B + A*c)*Log[x]","A",2,1,20,0.05000,1,"{765}"
24,1,49,0,0.0283647,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^6} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^6,x]","-\frac{A b^2}{3 x^3}-\frac{b (2 A c+b B)}{2 x^2}-\frac{c (A c+2 b B)}{x}+B c^2 \log (x)","-\frac{A b^2}{3 x^3}-\frac{b (2 A c+b B)}{2 x^2}-\frac{c (A c+2 b B)}{x}+B c^2 \log (x)",1,"-(A*b^2)/(3*x^3) - (b*(b*B + 2*A*c))/(2*x^2) - (c*(2*b*B + A*c))/x + B*c^2*Log[x]","A",2,1,20,0.05000,1,"{765}"
25,1,53,0,0.0301427,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^7} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^7,x]","-\frac{A b^2}{4 x^4}-\frac{b (2 A c+b B)}{3 x^3}-\frac{c (A c+2 b B)}{2 x^2}-\frac{B c^2}{x}","-\frac{A b^2}{4 x^4}-\frac{b (2 A c+b B)}{3 x^3}-\frac{c (A c+2 b B)}{2 x^2}-\frac{B c^2}{x}",1,"-(A*b^2)/(4*x^4) - (b*(b*B + 2*A*c))/(3*x^3) - (c*(2*b*B + A*c))/(2*x^2) - (B*c^2)/x","A",2,1,20,0.05000,1,"{765}"
26,1,55,0,0.027832,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^8} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^8,x]","-\frac{A b^2}{5 x^5}-\frac{b (2 A c+b B)}{4 x^4}-\frac{c (A c+2 b B)}{3 x^3}-\frac{B c^2}{2 x^2}","-\frac{A b^2}{5 x^5}-\frac{b (2 A c+b B)}{4 x^4}-\frac{c (A c+2 b B)}{3 x^3}-\frac{B c^2}{2 x^2}",1,"-(A*b^2)/(5*x^5) - (b*(b*B + 2*A*c))/(4*x^4) - (c*(2*b*B + A*c))/(3*x^3) - (B*c^2)/(2*x^2)","A",2,1,20,0.05000,1,"{765}"
27,1,96,0,0.0589567,"\int x^m (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x^m*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{b^2 x^{m+5} (3 A c+b B)}{m+5}+\frac{A b^3 x^{m+4}}{m+4}+\frac{c^2 x^{m+7} (A c+3 b B)}{m+7}+\frac{3 b c x^{m+6} (A c+b B)}{m+6}+\frac{B c^3 x^{m+8}}{m+8}","\frac{b^2 x^{m+5} (3 A c+b B)}{m+5}+\frac{A b^3 x^{m+4}}{m+4}+\frac{c^2 x^{m+7} (A c+3 b B)}{m+7}+\frac{3 b c x^{m+6} (A c+b B)}{m+6}+\frac{B c^3 x^{m+8}}{m+8}",1,"(A*b^3*x^(4 + m))/(4 + m) + (b^2*(b*B + 3*A*c)*x^(5 + m))/(5 + m) + (3*b*c*(b*B + A*c)*x^(6 + m))/(6 + m) + (c^2*(3*b*B + A*c)*x^(7 + m))/(7 + m) + (B*c^3*x^(8 + m))/(8 + m)","A",2,1,20,0.05000,1,"{765}"
28,1,75,0,0.081268,"\int x^3 (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x^3*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{8} b^2 x^8 (3 A c+b B)+\frac{1}{7} A b^3 x^7+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{11} B c^3 x^{11}","\frac{1}{8} b^2 x^8 (3 A c+b B)+\frac{1}{7} A b^3 x^7+\frac{1}{10} c^2 x^{10} (A c+3 b B)+\frac{1}{3} b c x^9 (A c+b B)+\frac{1}{11} B c^3 x^{11}",1,"(A*b^3*x^7)/7 + (b^2*(b*B + 3*A*c)*x^8)/8 + (b*c*(b*B + A*c)*x^9)/3 + (c^2*(3*b*B + A*c)*x^10)/10 + (B*c^3*x^11)/11","A",2,1,20,0.05000,1,"{765}"
29,1,75,0,0.0652097,"\int x^2 (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x^2*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{6} A b^3 x^6+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{8} b c x^8 (A c+b B)+\frac{1}{10} B c^3 x^{10}","\frac{1}{7} b^2 x^7 (3 A c+b B)+\frac{1}{6} A b^3 x^6+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{3}{8} b c x^8 (A c+b B)+\frac{1}{10} B c^3 x^{10}",1,"(A*b^3*x^6)/6 + (b^2*(b*B + 3*A*c)*x^7)/7 + (3*b*c*(b*B + A*c)*x^8)/8 + (c^2*(3*b*B + A*c)*x^9)/9 + (B*c^3*x^10)/10","A",2,1,20,0.05000,1,"{765}"
30,1,75,0,0.0573346,"\int x (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{6} b^2 x^6 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{9} B c^3 x^9","\frac{1}{6} b^2 x^6 (3 A c+b B)+\frac{1}{5} A b^3 x^5+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{3}{7} b c x^7 (A c+b B)+\frac{1}{9} B c^3 x^9",1,"(A*b^3*x^5)/5 + (b^2*(b*B + 3*A*c)*x^6)/6 + (3*b*c*(b*B + A*c)*x^7)/7 + (c^2*(3*b*B + A*c)*x^8)/8 + (B*c^3*x^9)/9","A",2,1,18,0.05556,1,"{765}"
31,1,75,0,0.0551682,"\int (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{5} b^2 x^5 (3 A c+b B)+\frac{1}{4} A b^3 x^4+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{2} b c x^6 (A c+b B)+\frac{1}{8} B c^3 x^8","\frac{1}{5} b^2 x^5 (3 A c+b B)+\frac{1}{4} A b^3 x^4+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{2} b c x^6 (A c+b B)+\frac{1}{8} B c^3 x^8",1,"(A*b^3*x^4)/4 + (b^2*(b*B + 3*A*c)*x^5)/5 + (b*c*(b*B + A*c)*x^6)/2 + (c^2*(3*b*B + A*c)*x^7)/7 + (B*c^3*x^8)/8","A",2,1,17,0.05882,1,"{631}"
32,1,75,0,0.0439684,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x,x]","\frac{1}{4} b^2 x^4 (3 A c+b B)+\frac{1}{3} A b^3 x^3+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{7} B c^3 x^7","\frac{1}{4} b^2 x^4 (3 A c+b B)+\frac{1}{3} A b^3 x^3+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{3}{5} b c x^5 (A c+b B)+\frac{1}{7} B c^3 x^7",1,"(A*b^3*x^3)/3 + (b^2*(b*B + 3*A*c)*x^4)/4 + (3*b*c*(b*B + A*c)*x^5)/5 + (c^2*(3*b*B + A*c)*x^6)/6 + (B*c^3*x^7)/7","A",2,1,20,0.05000,1,"{765}"
33,1,62,0,0.0419726,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^2,x]","-\frac{(b+c x)^5 (2 b B-A c)}{5 c^3}+\frac{b (b+c x)^4 (b B-A c)}{4 c^3}+\frac{B (b+c x)^6}{6 c^3}","-\frac{(b+c x)^5 (2 b B-A c)}{5 c^3}+\frac{b (b+c x)^4 (b B-A c)}{4 c^3}+\frac{B (b+c x)^6}{6 c^3}",1,"(b*(b*B - A*c)*(b + c*x)^4)/(4*c^3) - ((2*b*B - A*c)*(b + c*x)^5)/(5*c^3) + (B*(b + c*x)^6)/(6*c^3)","A",2,1,20,0.05000,1,"{765}"
34,1,38,0,0.0200986,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^3,x]","\frac{B (b+c x)^5}{5 c^2}-\frac{(b+c x)^4 (b B-A c)}{4 c^2}","\frac{B (b+c x)^5}{5 c^2}-\frac{(b+c x)^4 (b B-A c)}{4 c^2}",1,"-((b*B - A*c)*(b + c*x)^4)/(4*c^2) + (B*(b + c*x)^5)/(5*c^2)","A",2,1,20,0.05000,1,"{765}"
35,1,66,0,0.0414899,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^4,x]","b^2 x (3 A c+b B)+A b^3 \log (x)+\frac{1}{3} c^2 x^3 (A c+3 b B)+\frac{3}{2} b c x^2 (A c+b B)+\frac{1}{4} B c^3 x^4","b^2 x (3 A c+b B)+A b^3 \log (x)+\frac{1}{3} c^2 x^3 (A c+3 b B)+\frac{3}{2} b c x^2 (A c+b B)+\frac{1}{4} B c^3 x^4",1,"b^2*(b*B + 3*A*c)*x + (3*b*c*(b*B + A*c)*x^2)/2 + (c^2*(3*b*B + A*c)*x^3)/3 + (B*c^3*x^4)/4 + A*b^3*Log[x]","A",2,1,20,0.05000,1,"{765}"
36,1,65,0,0.0466891,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^5,x]","b^2 \log (x) (3 A c+b B)-\frac{A b^3}{x}+\frac{1}{2} c^2 x^2 (A c+3 b B)+3 b c x (A c+b B)+\frac{1}{3} B c^3 x^3","b^2 \log (x) (3 A c+b B)-\frac{A b^3}{x}+\frac{1}{2} c^2 x^2 (A c+3 b B)+3 b c x (A c+b B)+\frac{1}{3} B c^3 x^3",1,"-((A*b^3)/x) + 3*b*c*(b*B + A*c)*x + (c^2*(3*b*B + A*c)*x^2)/2 + (B*c^3*x^3)/3 + b^2*(b*B + 3*A*c)*Log[x]","A",2,1,20,0.05000,1,"{765}"
37,1,65,0,0.0448049,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^6} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^6,x]","-\frac{b^2 (3 A c+b B)}{x}-\frac{A b^3}{2 x^2}+c^2 x (A c+3 b B)+3 b c \log (x) (A c+b B)+\frac{1}{2} B c^3 x^2","-\frac{b^2 (3 A c+b B)}{x}-\frac{A b^3}{2 x^2}+c^2 x (A c+3 b B)+3 b c \log (x) (A c+b B)+\frac{1}{2} B c^3 x^2",1,"-(A*b^3)/(2*x^2) - (b^2*(b*B + 3*A*c))/x + c^2*(3*b*B + A*c)*x + (B*c^3*x^2)/2 + 3*b*c*(b*B + A*c)*Log[x]","A",2,1,20,0.05000,1,"{765}"
38,1,64,0,0.039532,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^7} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^7,x]","-\frac{b^2 (3 A c+b B)}{2 x^2}-\frac{A b^3}{3 x^3}+c^2 \log (x) (A c+3 b B)-\frac{3 b c (A c+b B)}{x}+B c^3 x","-\frac{b^2 (3 A c+b B)}{2 x^2}-\frac{A b^3}{3 x^3}+c^2 \log (x) (A c+3 b B)-\frac{3 b c (A c+b B)}{x}+B c^3 x",1,"-(A*b^3)/(3*x^3) - (b^2*(b*B + 3*A*c))/(2*x^2) - (3*b*c*(b*B + A*c))/x + B*c^3*x + c^2*(3*b*B + A*c)*Log[x]","A",2,1,20,0.05000,1,"{765}"
39,1,69,0,0.0376182,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^8} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^8,x]","-\frac{b^2 (3 A c+b B)}{3 x^3}-\frac{A b^3}{4 x^4}-\frac{c^2 (A c+3 b B)}{x}-\frac{3 b c (A c+b B)}{2 x^2}+B c^3 \log (x)","-\frac{b^2 (3 A c+b B)}{3 x^3}-\frac{A b^3}{4 x^4}-\frac{c^2 (A c+3 b B)}{x}-\frac{3 b c (A c+b B)}{2 x^2}+B c^3 \log (x)",1,"-(A*b^3)/(4*x^4) - (b^2*(b*B + 3*A*c))/(3*x^3) - (3*b*c*(b*B + A*c))/(2*x^2) - (c^2*(3*b*B + A*c))/x + B*c^3*Log[x]","A",2,1,20,0.05000,1,"{765}"
40,1,71,0,0.0398933,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^9} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^9,x]","-\frac{b^2 (3 A c+b B)}{4 x^4}-\frac{A b^3}{5 x^5}-\frac{c^2 (A c+3 b B)}{2 x^2}-\frac{b c (A c+b B)}{x^3}-\frac{B c^3}{x}","-\frac{b^2 (3 A c+b B)}{4 x^4}-\frac{A b^3}{5 x^5}-\frac{c^2 (A c+3 b B)}{2 x^2}-\frac{b c (A c+b B)}{x^3}-\frac{B c^3}{x}",1,"-(A*b^3)/(5*x^5) - (b^2*(b*B + 3*A*c))/(4*x^4) - (b*c*(b*B + A*c))/x^3 - (c^2*(3*b*B + A*c))/(2*x^2) - (B*c^3)/x","A",2,1,20,0.05000,1,"{765}"
41,1,75,0,0.0374368,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{10}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^10,x]","-\frac{b^2 (3 A c+b B)}{5 x^5}-\frac{A b^3}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{3 b c (A c+b B)}{4 x^4}-\frac{B c^3}{2 x^2}","-\frac{b^2 (3 A c+b B)}{5 x^5}-\frac{A b^3}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{3 b c (A c+b B)}{4 x^4}-\frac{B c^3}{2 x^2}",1,"-(A*b^3)/(6*x^6) - (b^2*(b*B + 3*A*c))/(5*x^5) - (3*b*c*(b*B + A*c))/(4*x^4) - (c^2*(3*b*B + A*c))/(3*x^3) - (B*c^3)/(2*x^2)","A",2,1,20,0.05000,1,"{765}"
42,1,75,0,0.0408125,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{11}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^11,x]","-\frac{b^2 (3 A c+b B)}{6 x^6}-\frac{A b^3}{7 x^7}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{3 x^3}","-\frac{b^2 (3 A c+b B)}{6 x^6}-\frac{A b^3}{7 x^7}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{3 b c (A c+b B)}{5 x^5}-\frac{B c^3}{3 x^3}",1,"-(A*b^3)/(7*x^7) - (b^2*(b*B + 3*A*c))/(6*x^6) - (3*b*c*(b*B + A*c))/(5*x^5) - (c^2*(3*b*B + A*c))/(4*x^4) - (B*c^3)/(3*x^3)","A",2,1,20,0.05000,1,"{765}"
43,1,87,0,0.0893381,"\int \frac{x^4 (d+e x)}{b x+c x^2} \, dx","Int[(x^4*(d + e*x))/(b*x + c*x^2),x]","\frac{b^2 x (c d-b e)}{c^4}-\frac{b^3 (c d-b e) \log (b+c x)}{c^5}+\frac{x^3 (c d-b e)}{3 c^2}-\frac{b x^2 (c d-b e)}{2 c^3}+\frac{e x^4}{4 c}","\frac{b^2 x (c d-b e)}{c^4}-\frac{b^3 (c d-b e) \log (b+c x)}{c^5}+\frac{x^3 (c d-b e)}{3 c^2}-\frac{b x^2 (c d-b e)}{2 c^3}+\frac{e x^4}{4 c}",1,"(b^2*(c*d - b*e)*x)/c^4 - (b*(c*d - b*e)*x^2)/(2*c^3) + ((c*d - b*e)*x^3)/(3*c^2) + (e*x^4)/(4*c) - (b^3*(c*d - b*e)*Log[b + c*x])/c^5","A",2,1,20,0.05000,1,"{765}"
44,1,66,0,0.0574302,"\int \frac{x^3 (d+e x)}{b x+c x^2} \, dx","Int[(x^3*(d + e*x))/(b*x + c*x^2),x]","\frac{b^2 (c d-b e) \log (b+c x)}{c^4}+\frac{x^2 (c d-b e)}{2 c^2}-\frac{b x (c d-b e)}{c^3}+\frac{e x^3}{3 c}","\frac{b^2 (c d-b e) \log (b+c x)}{c^4}+\frac{x^2 (c d-b e)}{2 c^2}-\frac{b x (c d-b e)}{c^3}+\frac{e x^3}{3 c}",1,"-((b*(c*d - b*e)*x)/c^3) + ((c*d - b*e)*x^2)/(2*c^2) + (e*x^3)/(3*c) + (b^2*(c*d - b*e)*Log[b + c*x])/c^4","A",2,1,20,0.05000,1,"{765}"
45,1,45,0,0.0404068,"\int \frac{x^2 (d+e x)}{b x+c x^2} \, dx","Int[(x^2*(d + e*x))/(b*x + c*x^2),x]","\frac{x (c d-b e)}{c^2}-\frac{b (c d-b e) \log (b+c x)}{c^3}+\frac{e x^2}{2 c}","\frac{x (c d-b e)}{c^2}-\frac{b (c d-b e) \log (b+c x)}{c^3}+\frac{e x^2}{2 c}",1,"((c*d - b*e)*x)/c^2 + (e*x^2)/(2*c) - (b*(c*d - b*e)*Log[b + c*x])/c^3","A",2,1,20,0.05000,1,"{765}"
46,1,25,0,0.0230134,"\int \frac{x (d+e x)}{b x+c x^2} \, dx","Int[(x*(d + e*x))/(b*x + c*x^2),x]","\frac{(c d-b e) \log (b+c x)}{c^2}+\frac{e x}{c}","\frac{(c d-b e) \log (b+c x)}{c^2}+\frac{e x}{c}",1,"(e*x)/c + ((c*d - b*e)*Log[b + c*x])/c^2","A",2,1,18,0.05556,1,"{765}"
47,1,30,0,0.0200777,"\int \frac{d+e x}{b x+c x^2} \, dx","Int[(d + e*x)/(b*x + c*x^2),x]","\frac{d \log (x)}{b}-\frac{(c d-b e) \log (b+c x)}{b c}","\frac{d \log (x)}{b}-\frac{(c d-b e) \log (b+c x)}{b c}",1,"(d*Log[x])/b - ((c*d - b*e)*Log[b + c*x])/(b*c)","A",2,1,17,0.05882,1,"{631}"
48,1,43,0,0.037177,"\int \frac{d+e x}{x \left(b x+c x^2\right)} \, dx","Int[(d + e*x)/(x*(b*x + c*x^2)),x]","-\frac{\log (x) (c d-b e)}{b^2}+\frac{(c d-b e) \log (b+c x)}{b^2}-\frac{d}{b x}","-\frac{\log (x) (c d-b e)}{b^2}+\frac{(c d-b e) \log (b+c x)}{b^2}-\frac{d}{b x}",1,"-(d/(b*x)) - ((c*d - b*e)*Log[x])/b^2 + ((c*d - b*e)*Log[b + c*x])/b^2","A",2,1,20,0.05000,1,"{765}"
49,1,62,0,0.0483203,"\int \frac{d+e x}{x^2 \left(b x+c x^2\right)} \, dx","Int[(d + e*x)/(x^2*(b*x + c*x^2)),x]","\frac{c d-b e}{b^2 x}+\frac{c \log (x) (c d-b e)}{b^3}-\frac{c (c d-b e) \log (b+c x)}{b^3}-\frac{d}{2 b x^2}","\frac{c d-b e}{b^2 x}+\frac{c \log (x) (c d-b e)}{b^3}-\frac{c (c d-b e) \log (b+c x)}{b^3}-\frac{d}{2 b x^2}",1,"-d/(2*b*x^2) + (c*d - b*e)/(b^2*x) + (c*(c*d - b*e)*Log[x])/b^3 - (c*(c*d - b*e)*Log[b + c*x])/b^3","A",2,1,20,0.05000,1,"{765}"
50,1,86,0,0.0646612,"\int \frac{d+e x}{x^3 \left(b x+c x^2\right)} \, dx","Int[(d + e*x)/(x^3*(b*x + c*x^2)),x]","-\frac{c^2 \log (x) (c d-b e)}{b^4}+\frac{c^2 (c d-b e) \log (b+c x)}{b^4}+\frac{c d-b e}{2 b^2 x^2}-\frac{c (c d-b e)}{b^3 x}-\frac{d}{3 b x^3}","-\frac{c^2 \log (x) (c d-b e)}{b^4}+\frac{c^2 (c d-b e) \log (b+c x)}{b^4}+\frac{c d-b e}{2 b^2 x^2}-\frac{c (c d-b e)}{b^3 x}-\frac{d}{3 b x^3}",1,"-d/(3*b*x^3) + (c*d - b*e)/(2*b^2*x^2) - (c*(c*d - b*e))/(b^3*x) - (c^2*(c*d - b*e)*Log[x])/b^4 + (c^2*(c*d - b*e)*Log[b + c*x])/b^4","A",2,1,20,0.05000,1,"{765}"
51,1,90,0,0.0943529,"\int \frac{x^5 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^5*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{b^3 (c d-b e)}{c^5 (b+c x)}+\frac{b^2 (3 c d-4 b e) \log (b+c x)}{c^5}+\frac{x^2 (c d-2 b e)}{2 c^3}-\frac{b x (2 c d-3 b e)}{c^4}+\frac{e x^3}{3 c^2}","\frac{b^3 (c d-b e)}{c^5 (b+c x)}+\frac{b^2 (3 c d-4 b e) \log (b+c x)}{c^5}+\frac{x^2 (c d-2 b e)}{2 c^3}-\frac{b x (2 c d-3 b e)}{c^4}+\frac{e x^3}{3 c^2}",1,"-((b*(2*c*d - 3*b*e)*x)/c^4) + ((c*d - 2*b*e)*x^2)/(2*c^3) + (e*x^3)/(3*c^2) + (b^3*(c*d - b*e))/(c^5*(b + c*x)) + (b^2*(3*c*d - 4*b*e)*Log[b + c*x])/c^5","A",2,1,20,0.05000,1,"{765}"
52,1,69,0,0.0686247,"\int \frac{x^4 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^4*(d + e*x))/(b*x + c*x^2)^2,x]","-\frac{b^2 (c d-b e)}{c^4 (b+c x)}+\frac{x (c d-2 b e)}{c^3}-\frac{b (2 c d-3 b e) \log (b+c x)}{c^4}+\frac{e x^2}{2 c^2}","-\frac{b^2 (c d-b e)}{c^4 (b+c x)}+\frac{x (c d-2 b e)}{c^3}-\frac{b (2 c d-3 b e) \log (b+c x)}{c^4}+\frac{e x^2}{2 c^2}",1,"((c*d - 2*b*e)*x)/c^3 + (e*x^2)/(2*c^2) - (b^2*(c*d - b*e))/(c^4*(b + c*x)) - (b*(2*c*d - 3*b*e)*Log[b + c*x])/c^4","A",2,1,20,0.05000,1,"{765}"
53,1,45,0,0.0430754,"\int \frac{x^3 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^3*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{b (c d-b e)}{c^3 (b+c x)}+\frac{(c d-2 b e) \log (b+c x)}{c^3}+\frac{e x}{c^2}","\frac{b (c d-b e)}{c^3 (b+c x)}+\frac{(c d-2 b e) \log (b+c x)}{c^3}+\frac{e x}{c^2}",1,"(e*x)/c^2 + (b*(c*d - b*e))/(c^3*(b + c*x)) + ((c*d - 2*b*e)*Log[b + c*x])/c^3","A",2,1,20,0.05000,1,"{765}"
54,1,32,0,0.029932,"\int \frac{x^2 (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^2*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{e \log (b+c x)}{c^2}-\frac{c d-b e}{c^2 (b+c x)}","\frac{e \log (b+c x)}{c^2}-\frac{c d-b e}{c^2 (b+c x)}",1,"-((c*d - b*e)/(c^2*(b + c*x))) + (e*Log[b + c*x])/c^2","A",2,1,20,0.05000,1,"{765}"
55,1,42,0,0.0308703,"\int \frac{x (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x*(d + e*x))/(b*x + c*x^2)^2,x]","-\frac{d \log (b+c x)}{b^2}+\frac{d \log (x)}{b^2}+\frac{c d-b e}{b c (b+c x)}","-\frac{d \log (b+c x)}{b^2}+\frac{d \log (x)}{b^2}+\frac{c d-b e}{b c (b+c x)}",1,"(c*d - b*e)/(b*c*(b + c*x)) + (d*Log[x])/b^2 - (d*Log[b + c*x])/b^2","A",2,1,18,0.05556,1,"{765}"
56,1,65,0,0.049319,"\int \frac{d+e x}{\left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(b*x + c*x^2)^2,x]","-\frac{c d-b e}{b^2 (b+c x)}-\frac{\log (x) (2 c d-b e)}{b^3}+\frac{(2 c d-b e) \log (b+c x)}{b^3}-\frac{d}{b^2 x}","-\frac{c d-b e}{b^2 (b+c x)}-\frac{\log (x) (2 c d-b e)}{b^3}+\frac{(2 c d-b e) \log (b+c x)}{b^3}-\frac{d}{b^2 x}",1,"-(d/(b^2*x)) - (c*d - b*e)/(b^2*(b + c*x)) - ((2*c*d - b*e)*Log[x])/b^3 + ((2*c*d - b*e)*Log[b + c*x])/b^3","A",2,1,17,0.05882,1,"{631}"
57,1,85,0,0.0758893,"\int \frac{d+e x}{x \left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(x*(b*x + c*x^2)^2),x]","\frac{2 c d-b e}{b^3 x}+\frac{c (c d-b e)}{b^3 (b+c x)}+\frac{c \log (x) (3 c d-2 b e)}{b^4}-\frac{c (3 c d-2 b e) \log (b+c x)}{b^4}-\frac{d}{2 b^2 x^2}","\frac{2 c d-b e}{b^3 x}+\frac{c (c d-b e)}{b^3 (b+c x)}+\frac{c \log (x) (3 c d-2 b e)}{b^4}-\frac{c (3 c d-2 b e) \log (b+c x)}{b^4}-\frac{d}{2 b^2 x^2}",1,"-d/(2*b^2*x^2) + (2*c*d - b*e)/(b^3*x) + (c*(c*d - b*e))/(b^3*(b + c*x)) + (c*(3*c*d - 2*b*e)*Log[x])/b^4 - (c*(3*c*d - 2*b*e)*Log[b + c*x])/b^4","A",2,1,20,0.05000,1,"{765}"
58,1,113,0,0.1037209,"\int \frac{d+e x}{x^2 \left(b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(x^2*(b*x + c*x^2)^2),x]","-\frac{c^2 (c d-b e)}{b^4 (b+c x)}-\frac{c^2 \log (x) (4 c d-3 b e)}{b^5}+\frac{c^2 (4 c d-3 b e) \log (b+c x)}{b^5}+\frac{2 c d-b e}{2 b^3 x^2}-\frac{c (3 c d-2 b e)}{b^4 x}-\frac{d}{3 b^2 x^3}","-\frac{c^2 (c d-b e)}{b^4 (b+c x)}-\frac{c^2 \log (x) (4 c d-3 b e)}{b^5}+\frac{c^2 (4 c d-3 b e) \log (b+c x)}{b^5}+\frac{2 c d-b e}{2 b^3 x^2}-\frac{c (3 c d-2 b e)}{b^4 x}-\frac{d}{3 b^2 x^3}",1,"-d/(3*b^2*x^3) + (2*c*d - b*e)/(2*b^3*x^2) - (c*(3*c*d - 2*b*e))/(b^4*x) - (c^2*(c*d - b*e))/(b^4*(b + c*x)) - (c^2*(4*c*d - 3*b*e)*Log[x])/b^5 + (c^2*(4*c*d - 3*b*e)*Log[b + c*x])/b^5","A",2,1,20,0.05000,1,"{765}"
59,1,94,0,0.0988481,"\int \frac{x^6 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^6*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{b^3 (c d-b e)}{2 c^5 (b+c x)^2}-\frac{b^2 (3 c d-4 b e)}{c^5 (b+c x)}+\frac{x (c d-3 b e)}{c^4}-\frac{3 b (c d-2 b e) \log (b+c x)}{c^5}+\frac{e x^2}{2 c^3}","\frac{b^3 (c d-b e)}{2 c^5 (b+c x)^2}-\frac{b^2 (3 c d-4 b e)}{c^5 (b+c x)}+\frac{x (c d-3 b e)}{c^4}-\frac{3 b (c d-2 b e) \log (b+c x)}{c^5}+\frac{e x^2}{2 c^3}",1,"((c*d - 3*b*e)*x)/c^4 + (e*x^2)/(2*c^3) + (b^3*(c*d - b*e))/(2*c^5*(b + c*x)^2) - (b^2*(3*c*d - 4*b*e))/(c^5*(b + c*x)) - (3*b*(c*d - 2*b*e)*Log[b + c*x])/c^5","A",2,1,20,0.05000,1,"{765}"
60,1,71,0,0.0640509,"\int \frac{x^5 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^5*(d + e*x))/(b*x + c*x^2)^3,x]","-\frac{b^2 (c d-b e)}{2 c^4 (b+c x)^2}+\frac{b (2 c d-3 b e)}{c^4 (b+c x)}+\frac{(c d-3 b e) \log (b+c x)}{c^4}+\frac{e x}{c^3}","-\frac{b^2 (c d-b e)}{2 c^4 (b+c x)^2}+\frac{b (2 c d-3 b e)}{c^4 (b+c x)}+\frac{(c d-3 b e) \log (b+c x)}{c^4}+\frac{e x}{c^3}",1,"(e*x)/c^3 - (b^2*(c*d - b*e))/(2*c^4*(b + c*x)^2) + (b*(2*c*d - 3*b*e))/(c^4*(b + c*x)) + ((c*d - 3*b*e)*Log[b + c*x])/c^4","A",2,1,20,0.05000,1,"{765}"
61,1,55,0,0.0466188,"\int \frac{x^4 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^4*(d + e*x))/(b*x + c*x^2)^3,x]","-\frac{c d-2 b e}{c^3 (b+c x)}+\frac{b (c d-b e)}{2 c^3 (b+c x)^2}+\frac{e \log (b+c x)}{c^3}","-\frac{c d-2 b e}{c^3 (b+c x)}+\frac{b (c d-b e)}{2 c^3 (b+c x)^2}+\frac{e \log (b+c x)}{c^3}",1,"(b*(c*d - b*e))/(2*c^3*(b + c*x)^2) - (c*d - 2*b*e)/(c^3*(b + c*x)) + (e*Log[b + c*x])/c^3","A",2,1,20,0.05000,1,"{765}"
62,1,36,0,0.0292562,"\int \frac{x^3 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^3*(d + e*x))/(b*x + c*x^2)^3,x]","-\frac{c d-b e}{2 c^2 (b+c x)^2}-\frac{e}{c^2 (b+c x)}","-\frac{c d-b e}{2 c^2 (b+c x)^2}-\frac{e}{c^2 (b+c x)}",1,"-(c*d - b*e)/(2*c^2*(b + c*x)^2) - e/(c^2*(b + c*x))","A",2,1,20,0.05000,1,"{765}"
63,1,57,0,0.0437102,"\int \frac{x^2 (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^2*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{d}{b^2 (b+c x)}-\frac{d \log (b+c x)}{b^3}+\frac{d \log (x)}{b^3}+\frac{c d-b e}{2 b c (b+c x)^2}","\frac{d}{b^2 (b+c x)}-\frac{d \log (b+c x)}{b^3}+\frac{d \log (x)}{b^3}+\frac{c d-b e}{2 b c (b+c x)^2}",1,"(c*d - b*e)/(2*b*c*(b + c*x)^2) + d/(b^2*(b + c*x)) + (d*Log[x])/b^3 - (d*Log[b + c*x])/b^3","A",2,1,20,0.05000,1,"{765}"
64,1,88,0,0.0748076,"\int \frac{x (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x*(d + e*x))/(b*x + c*x^2)^3,x]","-\frac{2 c d-b e}{b^3 (b+c x)}-\frac{c d-b e}{2 b^2 (b+c x)^2}-\frac{\log (x) (3 c d-b e)}{b^4}+\frac{(3 c d-b e) \log (b+c x)}{b^4}-\frac{d}{b^3 x}","-\frac{2 c d-b e}{b^3 (b+c x)}-\frac{c d-b e}{2 b^2 (b+c x)^2}-\frac{\log (x) (3 c d-b e)}{b^4}+\frac{(3 c d-b e) \log (b+c x)}{b^4}-\frac{d}{b^3 x}",1,"-(d/(b^3*x)) - (c*d - b*e)/(2*b^2*(b + c*x)^2) - (2*c*d - b*e)/(b^3*(b + c*x)) - ((3*c*d - b*e)*Log[x])/b^4 + ((3*c*d - b*e)*Log[b + c*x])/b^4","A",2,1,18,0.05556,1,"{765}"
65,1,110,0,0.0929485,"\int \frac{d+e x}{\left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)/(b*x + c*x^2)^3,x]","\frac{3 c d-b e}{b^4 x}+\frac{c (3 c d-2 b e)}{b^4 (b+c x)}+\frac{c (c d-b e)}{2 b^3 (b+c x)^2}+\frac{3 c \log (x) (2 c d-b e)}{b^5}-\frac{3 c (2 c d-b e) \log (b+c x)}{b^5}-\frac{d}{2 b^3 x^2}","\frac{3 c d-b e}{b^4 x}+\frac{c (3 c d-2 b e)}{b^4 (b+c x)}+\frac{c (c d-b e)}{2 b^3 (b+c x)^2}+\frac{3 c \log (x) (2 c d-b e)}{b^5}-\frac{3 c (2 c d-b e) \log (b+c x)}{b^5}-\frac{d}{2 b^3 x^2}",1,"-d/(2*b^3*x^2) + (3*c*d - b*e)/(b^4*x) + (c*(c*d - b*e))/(2*b^3*(b + c*x)^2) + (c*(3*c*d - 2*b*e))/(b^4*(b + c*x)) + (3*c*(2*c*d - b*e)*Log[x])/b^5 - (3*c*(2*c*d - b*e)*Log[b + c*x])/b^5","A",2,1,17,0.05882,1,"{631}"
66,1,140,0,0.1240811,"\int \frac{d+e x}{x \left(b x+c x^2\right)^3} \, dx","Int[(d + e*x)/(x*(b*x + c*x^2)^3),x]","-\frac{c^2 (4 c d-3 b e)}{b^5 (b+c x)}-\frac{c^2 (c d-b e)}{2 b^4 (b+c x)^2}-\frac{2 c^2 \log (x) (5 c d-3 b e)}{b^6}+\frac{2 c^2 (5 c d-3 b e) \log (b+c x)}{b^6}+\frac{3 c d-b e}{2 b^4 x^2}-\frac{3 c (2 c d-b e)}{b^5 x}-\frac{d}{3 b^3 x^3}","-\frac{c^2 (4 c d-3 b e)}{b^5 (b+c x)}-\frac{c^2 (c d-b e)}{2 b^4 (b+c x)^2}-\frac{2 c^2 \log (x) (5 c d-3 b e)}{b^6}+\frac{2 c^2 (5 c d-3 b e) \log (b+c x)}{b^6}+\frac{3 c d-b e}{2 b^4 x^2}-\frac{3 c (2 c d-b e)}{b^5 x}-\frac{d}{3 b^3 x^3}",1,"-d/(3*b^3*x^3) + (3*c*d - b*e)/(2*b^4*x^2) - (3*c*(2*c*d - b*e))/(b^5*x) - (c^2*(c*d - b*e))/(2*b^4*(b + c*x)^2) - (c^2*(4*c*d - 3*b*e))/(b^5*(b + c*x)) - (2*c^2*(5*c*d - 3*b*e)*Log[x])/b^6 + (2*c^2*(5*c*d - 3*b*e)*Log[b + c*x])/b^6","A",2,1,20,0.05000,1,"{765}"
67,1,200,0,0.1912633,"\int x^3 (A+B x) \sqrt{b x+c x^2} \, dx","Int[x^3*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{7 b^3 (b+2 c x) \sqrt{b x+c x^2} (3 b B-4 A c)}{512 c^5}-\frac{7 b^2 \left(b x+c x^2\right)^{3/2} (3 b B-4 A c)}{192 c^4}-\frac{7 b^5 (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{11/2}}+\frac{7 b x \left(b x+c x^2\right)^{3/2} (3 b B-4 A c)}{160 c^3}-\frac{x^2 \left(b x+c x^2\right)^{3/2} (3 b B-4 A c)}{20 c^2}+\frac{B x^3 \left(b x+c x^2\right)^{3/2}}{6 c}","\frac{7 b^3 (b+2 c x) \sqrt{b x+c x^2} (3 b B-4 A c)}{512 c^5}-\frac{7 b^2 \left(b x+c x^2\right)^{3/2} (3 b B-4 A c)}{192 c^4}-\frac{7 b^5 (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{11/2}}+\frac{7 b x \left(b x+c x^2\right)^{3/2} (3 b B-4 A c)}{160 c^3}-\frac{x^2 \left(b x+c x^2\right)^{3/2} (3 b B-4 A c)}{20 c^2}+\frac{B x^3 \left(b x+c x^2\right)^{3/2}}{6 c}",1,"(7*b^3*(3*b*B - 4*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^5) - (7*b^2*(3*b*B - 4*A*c)*(b*x + c*x^2)^(3/2))/(192*c^4) + (7*b*(3*b*B - 4*A*c)*x*(b*x + c*x^2)^(3/2))/(160*c^3) - ((3*b*B - 4*A*c)*x^2*(b*x + c*x^2)^(3/2))/(20*c^2) + (B*x^3*(b*x + c*x^2)^(3/2))/(6*c) - (7*b^5*(3*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(11/2))","A",7,6,22,0.2727,1,"{794, 670, 640, 612, 620, 206}"
68,1,165,0,0.1598744,"\int x^2 (A+B x) \sqrt{b x+c x^2} \, dx","Int[x^2*(A + B*x)*Sqrt[b*x + c*x^2],x]","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} (7 b B-10 A c)}{128 c^4}+\frac{b^4 (7 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{9/2}}+\frac{b \left(b x+c x^2\right)^{3/2} (7 b B-10 A c)}{48 c^3}-\frac{x \left(b x+c x^2\right)^{3/2} (7 b B-10 A c)}{40 c^2}+\frac{B x^2 \left(b x+c x^2\right)^{3/2}}{5 c}","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} (7 b B-10 A c)}{128 c^4}+\frac{b^4 (7 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{9/2}}+\frac{b \left(b x+c x^2\right)^{3/2} (7 b B-10 A c)}{48 c^3}-\frac{x \left(b x+c x^2\right)^{3/2} (7 b B-10 A c)}{40 c^2}+\frac{B x^2 \left(b x+c x^2\right)^{3/2}}{5 c}",1,"-(b^2*(7*b*B - 10*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^4) + (b*(7*b*B - 10*A*c)*(b*x + c*x^2)^(3/2))/(48*c^3) - ((7*b*B - 10*A*c)*x*(b*x + c*x^2)^(3/2))/(40*c^2) + (B*x^2*(b*x + c*x^2)^(3/2))/(5*c) + (b^4*(7*b*B - 10*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(9/2))","A",6,6,22,0.2727,1,"{794, 670, 640, 612, 620, 206}"
69,1,113,0,0.0496581,"\int x (A+B x) \sqrt{b x+c x^2} \, dx","Int[x*(A + B*x)*Sqrt[b*x + c*x^2],x]","-\frac{b^3 (5 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{7/2}}+\frac{b (b+2 c x) \sqrt{b x+c x^2} (5 b B-8 A c)}{64 c^3}-\frac{\left(b x+c x^2\right)^{3/2} (-8 A c+5 b B-6 B c x)}{24 c^2}","-\frac{b^3 (5 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{7/2}}+\frac{b (b+2 c x) \sqrt{b x+c x^2} (5 b B-8 A c)}{64 c^3}-\frac{\left(b x+c x^2\right)^{3/2} (-8 A c+5 b B-6 B c x)}{24 c^2}",1,"(b*(5*b*B - 8*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^3) - ((5*b*B - 8*A*c - 6*B*c*x)*(b*x + c*x^2)^(3/2))/(24*c^2) - (b^3*(5*b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(7/2))","A",4,4,20,0.2000,1,"{779, 612, 620, 206}"
70,1,97,0,0.0376421,"\int (A+B x) \sqrt{b x+c x^2} \, dx","Int[(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{b^2 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}-\frac{(b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{8 c^2}+\frac{B \left(b x+c x^2\right)^{3/2}}{3 c}","\frac{b^2 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}-\frac{(b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{8 c^2}+\frac{B \left(b x+c x^2\right)^{3/2}}{3 c}",1,"-((b*B - 2*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(8*c^2) + (B*(b*x + c*x^2)^(3/2))/(3*c) + (b^2*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(5/2))","A",4,4,19,0.2105,1,"{640, 612, 620, 206}"
71,1,92,0,0.0724537,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x,x]","-\frac{b (b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{3/2}}-\frac{\sqrt{b x+c x^2} (b B-4 A c)}{4 c}+\frac{B \left(b x+c x^2\right)^{3/2}}{2 c x}","-\frac{b (b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{3/2}}-\frac{\sqrt{b x+c x^2} (b B-4 A c)}{4 c}+\frac{B \left(b x+c x^2\right)^{3/2}}{2 c x}",1,"-((b*B - 4*A*c)*Sqrt[b*x + c*x^2])/(4*c) + (B*(b*x + c*x^2)^(3/2))/(2*c*x) - (b*(b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(3/2))","A",4,4,22,0.1818,1,"{794, 664, 620, 206}"
72,1,83,0,0.0863942,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^2} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^2,x]","\frac{\sqrt{b x+c x^2} (2 A c+b B)}{b}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{b x^2}","\frac{\sqrt{b x+c x^2} (2 A c+b B)}{b}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{b x^2}",1,"((b*B + 2*A*c)*Sqrt[b*x + c*x^2])/b - (2*A*(b*x + c*x^2)^(3/2))/(b*x^2) + ((b*B + 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/Sqrt[c]","A",4,4,22,0.1818,1,"{792, 664, 620, 206}"
73,1,73,0,0.0745639,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^3} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^3,x]","-\frac{2 A \left(b x+c x^2\right)^{3/2}}{3 b x^3}-\frac{2 B \sqrt{b x+c x^2}}{x}+2 B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)","-\frac{2 A \left(b x+c x^2\right)^{3/2}}{3 b x^3}-\frac{2 B \sqrt{b x+c x^2}}{x}+2 B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)",1,"(-2*B*Sqrt[b*x + c*x^2])/x - (2*A*(b*x + c*x^2)^(3/2))/(3*b*x^3) + 2*B*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",4,4,22,0.1818,1,"{792, 662, 620, 206}"
74,1,57,0,0.0450751,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^4} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^4,x]","-\frac{2 \left(b x+c x^2\right)^{3/2} (5 b B-2 A c)}{15 b^2 x^3}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{5 b x^4}","-\frac{2 \left(b x+c x^2\right)^{3/2} (5 b B-2 A c)}{15 b^2 x^3}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{5 b x^4}",1,"(-2*A*(b*x + c*x^2)^(3/2))/(5*b*x^4) - (2*(5*b*B - 2*A*c)*(b*x + c*x^2)^(3/2))/(15*b^2*x^3)","A",2,2,22,0.09091,1,"{792, 650}"
75,1,90,0,0.0870264,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^5} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^5,x]","\frac{4 c \left(b x+c x^2\right)^{3/2} (7 b B-4 A c)}{105 b^3 x^3}-\frac{2 \left(b x+c x^2\right)^{3/2} (7 b B-4 A c)}{35 b^2 x^4}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{7 b x^5}","\frac{4 c \left(b x+c x^2\right)^{3/2} (7 b B-4 A c)}{105 b^3 x^3}-\frac{2 \left(b x+c x^2\right)^{3/2} (7 b B-4 A c)}{35 b^2 x^4}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{7 b x^5}",1,"(-2*A*(b*x + c*x^2)^(3/2))/(7*b*x^5) - (2*(7*b*B - 4*A*c)*(b*x + c*x^2)^(3/2))/(35*b^2*x^4) + (4*c*(7*b*B - 4*A*c)*(b*x + c*x^2)^(3/2))/(105*b^3*x^3)","A",3,3,22,0.1364,1,"{792, 658, 650}"
76,1,125,0,0.1090597,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^6} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^6,x]","-\frac{16 c^2 \left(b x+c x^2\right)^{3/2} (3 b B-2 A c)}{315 b^4 x^3}+\frac{8 c \left(b x+c x^2\right)^{3/2} (3 b B-2 A c)}{105 b^3 x^4}-\frac{2 \left(b x+c x^2\right)^{3/2} (3 b B-2 A c)}{21 b^2 x^5}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{9 b x^6}","-\frac{16 c^2 \left(b x+c x^2\right)^{3/2} (3 b B-2 A c)}{315 b^4 x^3}+\frac{8 c \left(b x+c x^2\right)^{3/2} (3 b B-2 A c)}{105 b^3 x^4}-\frac{2 \left(b x+c x^2\right)^{3/2} (3 b B-2 A c)}{21 b^2 x^5}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{9 b x^6}",1,"(-2*A*(b*x + c*x^2)^(3/2))/(9*b*x^6) - (2*(3*b*B - 2*A*c)*(b*x + c*x^2)^(3/2))/(21*b^2*x^5) + (8*c*(3*b*B - 2*A*c)*(b*x + c*x^2)^(3/2))/(105*b^3*x^4) - (16*c^2*(3*b*B - 2*A*c)*(b*x + c*x^2)^(3/2))/(315*b^4*x^3)","A",4,3,22,0.1364,1,"{792, 658, 650}"
77,1,160,0,0.1573666,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^7} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^7,x]","\frac{32 c^3 \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{3465 b^5 x^3}-\frac{16 c^2 \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{1155 b^4 x^4}+\frac{4 c \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{231 b^3 x^5}-\frac{2 \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{99 b^2 x^6}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{11 b x^7}","\frac{32 c^3 \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{3465 b^5 x^3}-\frac{16 c^2 \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{1155 b^4 x^4}+\frac{4 c \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{231 b^3 x^5}-\frac{2 \left(b x+c x^2\right)^{3/2} (11 b B-8 A c)}{99 b^2 x^6}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{11 b x^7}",1,"(-2*A*(b*x + c*x^2)^(3/2))/(11*b*x^7) - (2*(11*b*B - 8*A*c)*(b*x + c*x^2)^(3/2))/(99*b^2*x^6) + (4*c*(11*b*B - 8*A*c)*(b*x + c*x^2)^(3/2))/(231*b^3*x^5) - (16*c^2*(11*b*B - 8*A*c)*(b*x + c*x^2)^(3/2))/(1155*b^4*x^4) + (32*c^3*(11*b*B - 8*A*c)*(b*x + c*x^2)^(3/2))/(3465*b^5*x^3)","A",5,3,22,0.1364,1,"{792, 658, 650}"
78,1,195,0,0.1953715,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^8} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^8,x]","-\frac{256 c^4 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{45045 b^6 x^3}+\frac{128 c^3 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{15015 b^5 x^4}-\frac{32 c^2 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{3003 b^4 x^5}+\frac{16 c \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{1287 b^3 x^6}-\frac{2 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{143 b^2 x^7}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{13 b x^8}","-\frac{256 c^4 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{45045 b^6 x^3}+\frac{128 c^3 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{15015 b^5 x^4}-\frac{32 c^2 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{3003 b^4 x^5}+\frac{16 c \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{1287 b^3 x^6}-\frac{2 \left(b x+c x^2\right)^{3/2} (13 b B-10 A c)}{143 b^2 x^7}-\frac{2 A \left(b x+c x^2\right)^{3/2}}{13 b x^8}",1,"(-2*A*(b*x + c*x^2)^(3/2))/(13*b*x^8) - (2*(13*b*B - 10*A*c)*(b*x + c*x^2)^(3/2))/(143*b^2*x^7) + (16*c*(13*b*B - 10*A*c)*(b*x + c*x^2)^(3/2))/(1287*b^3*x^6) - (32*c^2*(13*b*B - 10*A*c)*(b*x + c*x^2)^(3/2))/(3003*b^4*x^5) + (128*c^3*(13*b*B - 10*A*c)*(b*x + c*x^2)^(3/2))/(15015*b^5*x^4) - (256*c^4*(13*b*B - 10*A*c)*(b*x + c*x^2)^(3/2))/(45045*b^6*x^3)","A",6,3,22,0.1364,1,"{792, 658, 650}"
79,1,238,0,0.2476687,"\int x^3 (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[x^3*(A + B*x)*(b*x + c*x^2)^(3/2),x]","-\frac{9 b^5 (b+2 c x) \sqrt{b x+c x^2} (11 b B-16 A c)}{16384 c^6}+\frac{3 b^3 (b+2 c x) \left(b x+c x^2\right)^{3/2} (11 b B-16 A c)}{2048 c^5}-\frac{3 b^2 \left(b x+c x^2\right)^{5/2} (11 b B-16 A c)}{640 c^4}+\frac{9 b^7 (11 b B-16 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{13/2}}+\frac{3 b x \left(b x+c x^2\right)^{5/2} (11 b B-16 A c)}{448 c^3}-\frac{x^2 \left(b x+c x^2\right)^{5/2} (11 b B-16 A c)}{112 c^2}+\frac{B x^3 \left(b x+c x^2\right)^{5/2}}{8 c}","-\frac{9 b^5 (b+2 c x) \sqrt{b x+c x^2} (11 b B-16 A c)}{16384 c^6}+\frac{3 b^3 (b+2 c x) \left(b x+c x^2\right)^{3/2} (11 b B-16 A c)}{2048 c^5}-\frac{3 b^2 \left(b x+c x^2\right)^{5/2} (11 b B-16 A c)}{640 c^4}+\frac{9 b^7 (11 b B-16 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{13/2}}+\frac{3 b x \left(b x+c x^2\right)^{5/2} (11 b B-16 A c)}{448 c^3}-\frac{x^2 \left(b x+c x^2\right)^{5/2} (11 b B-16 A c)}{112 c^2}+\frac{B x^3 \left(b x+c x^2\right)^{5/2}}{8 c}",1,"(-9*b^5*(11*b*B - 16*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(16384*c^6) + (3*b^3*(11*b*B - 16*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(2048*c^5) - (3*b^2*(11*b*B - 16*A*c)*(b*x + c*x^2)^(5/2))/(640*c^4) + (3*b*(11*b*B - 16*A*c)*x*(b*x + c*x^2)^(5/2))/(448*c^3) - ((11*b*B - 16*A*c)*x^2*(b*x + c*x^2)^(5/2))/(112*c^2) + (B*x^3*(b*x + c*x^2)^(5/2))/(8*c) + (9*b^7*(11*b*B - 16*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(16384*c^(13/2))","A",8,6,22,0.2727,1,"{794, 670, 640, 612, 620, 206}"
80,1,203,0,0.2012633,"\int x^2 (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[x^2*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{b^4 (b+2 c x) \sqrt{b x+c x^2} (9 b B-14 A c)}{1024 c^5}-\frac{b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (9 b B-14 A c)}{384 c^4}-\frac{b^6 (9 b B-14 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{11/2}}+\frac{b \left(b x+c x^2\right)^{5/2} (9 b B-14 A c)}{120 c^3}-\frac{x \left(b x+c x^2\right)^{5/2} (9 b B-14 A c)}{84 c^2}+\frac{B x^2 \left(b x+c x^2\right)^{5/2}}{7 c}","\frac{b^4 (b+2 c x) \sqrt{b x+c x^2} (9 b B-14 A c)}{1024 c^5}-\frac{b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (9 b B-14 A c)}{384 c^4}-\frac{b^6 (9 b B-14 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{11/2}}+\frac{b \left(b x+c x^2\right)^{5/2} (9 b B-14 A c)}{120 c^3}-\frac{x \left(b x+c x^2\right)^{5/2} (9 b B-14 A c)}{84 c^2}+\frac{B x^2 \left(b x+c x^2\right)^{5/2}}{7 c}",1,"(b^4*(9*b*B - 14*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(1024*c^5) - (b^2*(9*b*B - 14*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(384*c^4) + (b*(9*b*B - 14*A*c)*(b*x + c*x^2)^(5/2))/(120*c^3) - ((9*b*B - 14*A*c)*x*(b*x + c*x^2)^(5/2))/(84*c^2) + (B*x^2*(b*x + c*x^2)^(5/2))/(7*c) - (b^6*(9*b*B - 14*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(1024*c^(11/2))","A",7,6,22,0.2727,1,"{794, 670, 640, 612, 620, 206}"
81,1,151,0,0.0709446,"\int x (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[x*(A + B*x)*(b*x + c*x^2)^(3/2),x]","-\frac{b^3 (b+2 c x) \sqrt{b x+c x^2} (7 b B-12 A c)}{512 c^4}+\frac{b^5 (7 b B-12 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{9/2}}+\frac{b (b+2 c x) \left(b x+c x^2\right)^{3/2} (7 b B-12 A c)}{192 c^3}-\frac{\left(b x+c x^2\right)^{5/2} (-12 A c+7 b B-10 B c x)}{60 c^2}","-\frac{b^3 (b+2 c x) \sqrt{b x+c x^2} (7 b B-12 A c)}{512 c^4}+\frac{b^5 (7 b B-12 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{9/2}}+\frac{b (b+2 c x) \left(b x+c x^2\right)^{3/2} (7 b B-12 A c)}{192 c^3}-\frac{\left(b x+c x^2\right)^{5/2} (-12 A c+7 b B-10 B c x)}{60 c^2}",1,"-(b^3*(7*b*B - 12*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^4) + (b*(7*b*B - 12*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^3) - ((7*b*B - 12*A*c - 10*B*c*x)*(b*x + c*x^2)^(5/2))/(60*c^2) + (b^5*(7*b*B - 12*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(9/2))","A",5,4,20,0.2000,1,"{779, 612, 620, 206}"
82,1,134,0,0.0511963,"\int (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{128 c^3}-\frac{3 b^4 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{16 c^2}+\frac{B \left(b x+c x^2\right)^{5/2}}{5 c}","\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{128 c^3}-\frac{3 b^4 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{16 c^2}+\frac{B \left(b x+c x^2\right)^{5/2}}{5 c}",1,"(3*b^2*(b*B - 2*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^3) - ((b*B - 2*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(16*c^2) + (B*(b*x + c*x^2)^(5/2))/(5*c) - (3*b^4*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(7/2))","A",5,4,19,0.2105,1,"{640, 612, 620, 206}"
83,1,132,0,0.1002008,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x,x]","\frac{b^3 (3 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{5/2}}-\frac{b (b+2 c x) \sqrt{b x+c x^2} (3 b B-8 A c)}{64 c^2}-\frac{\left(b x+c x^2\right)^{3/2} (3 b B-8 A c)}{24 c}+\frac{B \left(b x+c x^2\right)^{5/2}}{4 c x}","\frac{b^3 (3 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{5/2}}-\frac{b (b+2 c x) \sqrt{b x+c x^2} (3 b B-8 A c)}{64 c^2}-\frac{\left(b x+c x^2\right)^{3/2} (3 b B-8 A c)}{24 c}+\frac{B \left(b x+c x^2\right)^{5/2}}{4 c x}",1,"-(b*(3*b*B - 8*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^2) - ((3*b*B - 8*A*c)*(b*x + c*x^2)^(3/2))/(24*c) + (B*(b*x + c*x^2)^(5/2))/(4*c*x) + (b^3*(3*b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(5/2))","A",5,5,22,0.2273,1,"{794, 664, 612, 620, 206}"
84,1,126,0,0.1356717,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^2,x]","-\frac{b^2 (b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{3/2}}+\frac{\left(b x+c x^2\right)^{3/2} (b B-6 A c)}{3 b}+\frac{(b+2 c x) \sqrt{b x+c x^2} (b B-6 A c)}{8 c}+\frac{2 A \left(b x+c x^2\right)^{5/2}}{b x^2}","-\frac{b^2 (b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{3/2}}+\frac{\left(b x+c x^2\right)^{3/2} (b B-6 A c)}{3 b}+\frac{(b+2 c x) \sqrt{b x+c x^2} (b B-6 A c)}{8 c}+\frac{2 A \left(b x+c x^2\right)^{5/2}}{b x^2}",1,"((b*B - 6*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(8*c) + ((b*B - 6*A*c)*(b*x + c*x^2)^(3/2))/(3*b) + (2*A*(b*x + c*x^2)^(5/2))/(b*x^2) - (b^2*(b*B - 6*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(3/2))","A",5,5,22,0.2273,1,"{792, 664, 612, 620, 206}"
85,1,118,0,0.1197125,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^3,x]","\frac{\left(b x+c x^2\right)^{3/2} (4 A c+b B)}{2 b x}+\frac{3}{4} \sqrt{b x+c x^2} (4 A c+b B)+\frac{3 b (4 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 \sqrt{c}}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{b x^3}","\frac{\left(b x+c x^2\right)^{3/2} (4 A c+b B)}{2 b x}+\frac{3}{4} \sqrt{b x+c x^2} (4 A c+b B)+\frac{3 b (4 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 \sqrt{c}}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{b x^3}",1,"(3*(b*B + 4*A*c)*Sqrt[b*x + c*x^2])/4 + ((b*B + 4*A*c)*(b*x + c*x^2)^(3/2))/(2*b*x) - (2*A*(b*x + c*x^2)^(5/2))/(b*x^3) + (3*b*(b*B + 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*Sqrt[c])","A",5,4,22,0.1818,1,"{792, 664, 620, 206}"
86,1,120,0,0.1204546,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^4,x]","-\frac{2 \left(b x+c x^2\right)^{3/2} (2 A c+3 b B)}{3 b x^2}+\frac{c \sqrt{b x+c x^2} (2 A c+3 b B)}{b}+\sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 A \left(b x+c x^2\right)^{5/2}}{3 b x^4}","-\frac{2 \left(b x+c x^2\right)^{3/2} (2 A c+3 b B)}{3 b x^2}+\frac{c \sqrt{b x+c x^2} (2 A c+3 b B)}{b}+\sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 A \left(b x+c x^2\right)^{5/2}}{3 b x^4}",1,"(c*(3*b*B + 2*A*c)*Sqrt[b*x + c*x^2])/b - (2*(3*b*B + 2*A*c)*(b*x + c*x^2)^(3/2))/(3*b*x^2) - (2*A*(b*x + c*x^2)^(5/2))/(3*b*x^4) + Sqrt[c]*(3*b*B + 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",5,5,22,0.2273,1,"{792, 662, 664, 620, 206}"
87,1,95,0,0.1035514,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^5,x]","-\frac{2 A \left(b x+c x^2\right)^{5/2}}{5 b x^5}+2 B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 B \left(b x+c x^2\right)^{3/2}}{3 x^3}-\frac{2 B c \sqrt{b x+c x^2}}{x}","-\frac{2 A \left(b x+c x^2\right)^{5/2}}{5 b x^5}+2 B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 B \left(b x+c x^2\right)^{3/2}}{3 x^3}-\frac{2 B c \sqrt{b x+c x^2}}{x}",1,"(-2*B*c*Sqrt[b*x + c*x^2])/x - (2*B*(b*x + c*x^2)^(3/2))/(3*x^3) - (2*A*(b*x + c*x^2)^(5/2))/(5*b*x^5) + 2*B*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",5,4,22,0.1818,1,"{792, 662, 620, 206}"
88,1,57,0,0.0482936,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^6} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^6,x]","-\frac{2 \left(b x+c x^2\right)^{5/2} (7 b B-2 A c)}{35 b^2 x^5}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{7 b x^6}","-\frac{2 \left(b x+c x^2\right)^{5/2} (7 b B-2 A c)}{35 b^2 x^5}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{7 b x^6}",1,"(-2*A*(b*x + c*x^2)^(5/2))/(7*b*x^6) - (2*(7*b*B - 2*A*c)*(b*x + c*x^2)^(5/2))/(35*b^2*x^5)","A",2,2,22,0.09091,1,"{792, 650}"
89,1,90,0,0.0864704,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^7} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^7,x]","\frac{4 c \left(b x+c x^2\right)^{5/2} (9 b B-4 A c)}{315 b^3 x^5}-\frac{2 \left(b x+c x^2\right)^{5/2} (9 b B-4 A c)}{63 b^2 x^6}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{9 b x^7}","\frac{4 c \left(b x+c x^2\right)^{5/2} (9 b B-4 A c)}{315 b^3 x^5}-\frac{2 \left(b x+c x^2\right)^{5/2} (9 b B-4 A c)}{63 b^2 x^6}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{9 b x^7}",1,"(-2*A*(b*x + c*x^2)^(5/2))/(9*b*x^7) - (2*(9*b*B - 4*A*c)*(b*x + c*x^2)^(5/2))/(63*b^2*x^6) + (4*c*(9*b*B - 4*A*c)*(b*x + c*x^2)^(5/2))/(315*b^3*x^5)","A",3,3,22,0.1364,1,"{792, 658, 650}"
90,1,125,0,0.1182273,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^8} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^8,x]","-\frac{16 c^2 \left(b x+c x^2\right)^{5/2} (11 b B-6 A c)}{3465 b^4 x^5}+\frac{8 c \left(b x+c x^2\right)^{5/2} (11 b B-6 A c)}{693 b^3 x^6}-\frac{2 \left(b x+c x^2\right)^{5/2} (11 b B-6 A c)}{99 b^2 x^7}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{11 b x^8}","-\frac{16 c^2 \left(b x+c x^2\right)^{5/2} (11 b B-6 A c)}{3465 b^4 x^5}+\frac{8 c \left(b x+c x^2\right)^{5/2} (11 b B-6 A c)}{693 b^3 x^6}-\frac{2 \left(b x+c x^2\right)^{5/2} (11 b B-6 A c)}{99 b^2 x^7}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{11 b x^8}",1,"(-2*A*(b*x + c*x^2)^(5/2))/(11*b*x^8) - (2*(11*b*B - 6*A*c)*(b*x + c*x^2)^(5/2))/(99*b^2*x^7) + (8*c*(11*b*B - 6*A*c)*(b*x + c*x^2)^(5/2))/(693*b^3*x^6) - (16*c^2*(11*b*B - 6*A*c)*(b*x + c*x^2)^(5/2))/(3465*b^4*x^5)","A",4,3,22,0.1364,1,"{792, 658, 650}"
91,1,160,0,0.1653695,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^9} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^9,x]","\frac{32 c^3 \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{15015 b^5 x^5}-\frac{16 c^2 \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{3003 b^4 x^6}+\frac{4 c \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{429 b^3 x^7}-\frac{2 \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{143 b^2 x^8}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{13 b x^9}","\frac{32 c^3 \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{15015 b^5 x^5}-\frac{16 c^2 \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{3003 b^4 x^6}+\frac{4 c \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{429 b^3 x^7}-\frac{2 \left(b x+c x^2\right)^{5/2} (13 b B-8 A c)}{143 b^2 x^8}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{13 b x^9}",1,"(-2*A*(b*x + c*x^2)^(5/2))/(13*b*x^9) - (2*(13*b*B - 8*A*c)*(b*x + c*x^2)^(5/2))/(143*b^2*x^8) + (4*c*(13*b*B - 8*A*c)*(b*x + c*x^2)^(5/2))/(429*b^3*x^7) - (16*c^2*(13*b*B - 8*A*c)*(b*x + c*x^2)^(5/2))/(3003*b^4*x^6) + (32*c^3*(13*b*B - 8*A*c)*(b*x + c*x^2)^(5/2))/(15015*b^5*x^5)","A",5,3,22,0.1364,1,"{792, 658, 650}"
92,1,195,0,0.1848236,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{10}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^10,x]","-\frac{256 c^4 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{45045 b^6 x^5}+\frac{128 c^3 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{9009 b^5 x^6}-\frac{32 c^2 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{1287 b^4 x^7}+\frac{16 c \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{429 b^3 x^8}-\frac{2 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{39 b^2 x^9}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{15 b x^{10}}","-\frac{256 c^4 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{45045 b^6 x^5}+\frac{128 c^3 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{9009 b^5 x^6}-\frac{32 c^2 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{1287 b^4 x^7}+\frac{16 c \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{429 b^3 x^8}-\frac{2 \left(b x+c x^2\right)^{5/2} (3 b B-2 A c)}{39 b^2 x^9}-\frac{2 A \left(b x+c x^2\right)^{5/2}}{15 b x^{10}}",1,"(-2*A*(b*x + c*x^2)^(5/2))/(15*b*x^10) - (2*(3*b*B - 2*A*c)*(b*x + c*x^2)^(5/2))/(39*b^2*x^9) + (16*c*(3*b*B - 2*A*c)*(b*x + c*x^2)^(5/2))/(429*b^3*x^8) - (32*c^2*(3*b*B - 2*A*c)*(b*x + c*x^2)^(5/2))/(1287*b^4*x^7) + (128*c^3*(3*b*B - 2*A*c)*(b*x + c*x^2)^(5/2))/(9009*b^5*x^6) - (256*c^4*(3*b*B - 2*A*c)*(b*x + c*x^2)^(5/2))/(45045*b^6*x^5)","A",6,3,22,0.1364,1,"{792, 658, 650}"
93,1,276,0,0.2981659,"\int x^3 (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[x^3*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{11 b^7 (b+2 c x) \sqrt{b x+c x^2} (13 b B-20 A c)}{131072 c^7}-\frac{11 b^5 (b+2 c x) \left(b x+c x^2\right)^{3/2} (13 b B-20 A c)}{49152 c^6}+\frac{11 b^3 (b+2 c x) \left(b x+c x^2\right)^{5/2} (13 b B-20 A c)}{15360 c^5}-\frac{11 b^2 \left(b x+c x^2\right)^{7/2} (13 b B-20 A c)}{4480 c^4}-\frac{11 b^9 (13 b B-20 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{131072 c^{15/2}}+\frac{11 b x \left(b x+c x^2\right)^{7/2} (13 b B-20 A c)}{2880 c^3}-\frac{x^2 \left(b x+c x^2\right)^{7/2} (13 b B-20 A c)}{180 c^2}+\frac{B x^3 \left(b x+c x^2\right)^{7/2}}{10 c}","\frac{11 b^7 (b+2 c x) \sqrt{b x+c x^2} (13 b B-20 A c)}{131072 c^7}-\frac{11 b^5 (b+2 c x) \left(b x+c x^2\right)^{3/2} (13 b B-20 A c)}{49152 c^6}+\frac{11 b^3 (b+2 c x) \left(b x+c x^2\right)^{5/2} (13 b B-20 A c)}{15360 c^5}-\frac{11 b^2 \left(b x+c x^2\right)^{7/2} (13 b B-20 A c)}{4480 c^4}-\frac{11 b^9 (13 b B-20 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{131072 c^{15/2}}+\frac{11 b x \left(b x+c x^2\right)^{7/2} (13 b B-20 A c)}{2880 c^3}-\frac{x^2 \left(b x+c x^2\right)^{7/2} (13 b B-20 A c)}{180 c^2}+\frac{B x^3 \left(b x+c x^2\right)^{7/2}}{10 c}",1,"(11*b^7*(13*b*B - 20*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(131072*c^7) - (11*b^5*(13*b*B - 20*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(49152*c^6) + (11*b^3*(13*b*B - 20*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(15360*c^5) - (11*b^2*(13*b*B - 20*A*c)*(b*x + c*x^2)^(7/2))/(4480*c^4) + (11*b*(13*b*B - 20*A*c)*x*(b*x + c*x^2)^(7/2))/(2880*c^3) - ((13*b*B - 20*A*c)*x^2*(b*x + c*x^2)^(7/2))/(180*c^2) + (B*x^3*(b*x + c*x^2)^(7/2))/(10*c) - (11*b^9*(13*b*B - 20*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(131072*c^(15/2))","A",9,6,22,0.2727,1,"{794, 670, 640, 612, 620, 206}"
94,1,241,0,0.2472175,"\int x^2 (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[x^2*(A + B*x)*(b*x + c*x^2)^(5/2),x]","-\frac{5 b^6 (b+2 c x) \sqrt{b x+c x^2} (11 b B-18 A c)}{32768 c^6}+\frac{5 b^4 (b+2 c x) \left(b x+c x^2\right)^{3/2} (11 b B-18 A c)}{12288 c^5}-\frac{b^2 (b+2 c x) \left(b x+c x^2\right)^{5/2} (11 b B-18 A c)}{768 c^4}+\frac{5 b^8 (11 b B-18 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{32768 c^{13/2}}+\frac{b \left(b x+c x^2\right)^{7/2} (11 b B-18 A c)}{224 c^3}-\frac{x \left(b x+c x^2\right)^{7/2} (11 b B-18 A c)}{144 c^2}+\frac{B x^2 \left(b x+c x^2\right)^{7/2}}{9 c}","-\frac{5 b^6 (b+2 c x) \sqrt{b x+c x^2} (11 b B-18 A c)}{32768 c^6}+\frac{5 b^4 (b+2 c x) \left(b x+c x^2\right)^{3/2} (11 b B-18 A c)}{12288 c^5}-\frac{b^2 (b+2 c x) \left(b x+c x^2\right)^{5/2} (11 b B-18 A c)}{768 c^4}+\frac{5 b^8 (11 b B-18 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{32768 c^{13/2}}+\frac{b \left(b x+c x^2\right)^{7/2} (11 b B-18 A c)}{224 c^3}-\frac{x \left(b x+c x^2\right)^{7/2} (11 b B-18 A c)}{144 c^2}+\frac{B x^2 \left(b x+c x^2\right)^{7/2}}{9 c}",1,"(-5*b^6*(11*b*B - 18*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(32768*c^6) + (5*b^4*(11*b*B - 18*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(12288*c^5) - (b^2*(11*b*B - 18*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(768*c^4) + (b*(11*b*B - 18*A*c)*(b*x + c*x^2)^(7/2))/(224*c^3) - ((11*b*B - 18*A*c)*x*(b*x + c*x^2)^(7/2))/(144*c^2) + (B*x^2*(b*x + c*x^2)^(7/2))/(9*c) + (5*b^8*(11*b*B - 18*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(32768*c^(13/2))","A",8,6,22,0.2727,1,"{794, 670, 640, 612, 620, 206}"
95,1,189,0,0.0866696,"\int x (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[x*(A + B*x)*(b*x + c*x^2)^(5/2),x]","\frac{5 b^5 (b+2 c x) \sqrt{b x+c x^2} (9 b B-16 A c)}{16384 c^5}-\frac{5 b^3 (b+2 c x) \left(b x+c x^2\right)^{3/2} (9 b B-16 A c)}{6144 c^4}-\frac{5 b^7 (9 b B-16 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{b (b+2 c x) \left(b x+c x^2\right)^{5/2} (9 b B-16 A c)}{384 c^3}-\frac{\left(b x+c x^2\right)^{7/2} (-16 A c+9 b B-14 B c x)}{112 c^2}","\frac{5 b^5 (b+2 c x) \sqrt{b x+c x^2} (9 b B-16 A c)}{16384 c^5}-\frac{5 b^3 (b+2 c x) \left(b x+c x^2\right)^{3/2} (9 b B-16 A c)}{6144 c^4}-\frac{5 b^7 (9 b B-16 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{b (b+2 c x) \left(b x+c x^2\right)^{5/2} (9 b B-16 A c)}{384 c^3}-\frac{\left(b x+c x^2\right)^{7/2} (-16 A c+9 b B-14 B c x)}{112 c^2}",1,"(5*b^5*(9*b*B - 16*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(16384*c^5) - (5*b^3*(9*b*B - 16*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(6144*c^4) + (b*(9*b*B - 16*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(384*c^3) - ((9*b*B - 16*A*c - 14*B*c*x)*(b*x + c*x^2)^(7/2))/(112*c^2) - (5*b^7*(9*b*B - 16*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(16384*c^(11/2))","A",6,4,20,0.2000,1,"{779, 612, 620, 206}"
96,1,171,0,0.0666081,"\int (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[(A + B*x)*(b*x + c*x^2)^(5/2),x]","-\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{1024 c^4}+\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}+\frac{5 b^6 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (b B-2 A c)}{24 c^2}+\frac{B \left(b x+c x^2\right)^{7/2}}{7 c}","-\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{1024 c^4}+\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}+\frac{5 b^6 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (b B-2 A c)}{24 c^2}+\frac{B \left(b x+c x^2\right)^{7/2}}{7 c}",1,"(-5*b^4*(b*B - 2*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(1024*c^4) + (5*b^2*(b*B - 2*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(384*c^3) - ((b*B - 2*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(24*c^2) + (B*(b*x + c*x^2)^(7/2))/(7*c) + (5*b^6*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(1024*c^(9/2))","A",6,4,19,0.2105,1,"{640, 612, 620, 206}"
97,1,170,0,0.1291922,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x,x]","\frac{b^3 (b+2 c x) \sqrt{b x+c x^2} (5 b B-12 A c)}{512 c^3}-\frac{b^5 (5 b B-12 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{7/2}}-\frac{b (b+2 c x) \left(b x+c x^2\right)^{3/2} (5 b B-12 A c)}{192 c^2}-\frac{\left(b x+c x^2\right)^{5/2} (5 b B-12 A c)}{60 c}+\frac{B \left(b x+c x^2\right)^{7/2}}{6 c x}","\frac{b^3 (b+2 c x) \sqrt{b x+c x^2} (5 b B-12 A c)}{512 c^3}-\frac{b^5 (5 b B-12 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{512 c^{7/2}}-\frac{b (b+2 c x) \left(b x+c x^2\right)^{3/2} (5 b B-12 A c)}{192 c^2}-\frac{\left(b x+c x^2\right)^{5/2} (5 b B-12 A c)}{60 c}+\frac{B \left(b x+c x^2\right)^{7/2}}{6 c x}",1,"(b^3*(5*b*B - 12*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^3) - (b*(5*b*B - 12*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^2) - ((5*b*B - 12*A*c)*(b*x + c*x^2)^(5/2))/(60*c) + (B*(b*x + c*x^2)^(7/2))/(6*c*x) - (b^5*(5*b*B - 12*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(7/2))","A",6,5,22,0.2273,1,"{794, 664, 612, 620, 206}"
98,1,169,0,0.1699806,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^2,x]","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} (3 b B-10 A c)}{128 c^2}+\frac{b^4 (3 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{5/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (3 b B-10 A c)}{48 c}+\frac{\left(b x+c x^2\right)^{5/2} (3 b B-10 A c)}{15 b}+\frac{2 A \left(b x+c x^2\right)^{7/2}}{3 b x^2}","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} (3 b B-10 A c)}{128 c^2}+\frac{b^4 (3 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{5/2}}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (3 b B-10 A c)}{48 c}+\frac{\left(b x+c x^2\right)^{5/2} (3 b B-10 A c)}{15 b}+\frac{2 A \left(b x+c x^2\right)^{7/2}}{3 b x^2}",1,"-(b^2*(3*b*B - 10*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^2) + ((3*b*B - 10*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(48*c) + ((3*b*B - 10*A*c)*(b*x + c*x^2)^(5/2))/(15*b) + (2*A*(b*x + c*x^2)^(7/2))/(3*b*x^2) + (b^4*(3*b*B - 10*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(5/2))","A",6,5,22,0.2273,1,"{792, 664, 612, 620, 206}"
99,1,155,0,0.1725021,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^3,x]","-\frac{5 b^3 (b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{3/2}}+\frac{\left(b x+c x^2\right)^{5/2} (b B-8 A c)}{4 b x}+\frac{5}{24} \left(b x+c x^2\right)^{3/2} (b B-8 A c)+\frac{5 b (b+2 c x) \sqrt{b x+c x^2} (b B-8 A c)}{64 c}+\frac{2 A \left(b x+c x^2\right)^{7/2}}{b x^3}","-\frac{5 b^3 (b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{3/2}}+\frac{\left(b x+c x^2\right)^{5/2} (b B-8 A c)}{4 b x}+\frac{5}{24} \left(b x+c x^2\right)^{3/2} (b B-8 A c)+\frac{5 b (b+2 c x) \sqrt{b x+c x^2} (b B-8 A c)}{64 c}+\frac{2 A \left(b x+c x^2\right)^{7/2}}{b x^3}",1,"(5*b*(b*B - 8*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c) + (5*(b*B - 8*A*c)*(b*x + c*x^2)^(3/2))/24 + ((b*B - 8*A*c)*(b*x + c*x^2)^(5/2))/(4*b*x) + (2*A*(b*x + c*x^2)^(7/2))/(b*x^3) - (5*b^3*(b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(3/2))","A",6,5,22,0.2273,1,"{792, 664, 612, 620, 206}"
100,1,153,0,0.16711,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^4,x]","\frac{5 b^2 (6 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 \sqrt{c}}+\frac{2 \left(b x+c x^2\right)^{5/2} (6 A c+b B)}{b x^2}-\frac{5 c \left(b x+c x^2\right)^{3/2} (6 A c+b B)}{3 b}-\frac{5}{8} (b+2 c x) \sqrt{b x+c x^2} (6 A c+b B)-\frac{2 A \left(b x+c x^2\right)^{7/2}}{b x^4}","\frac{5 b^2 (6 A c+b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 \sqrt{c}}+\frac{2 \left(b x+c x^2\right)^{5/2} (6 A c+b B)}{b x^2}-\frac{5 c \left(b x+c x^2\right)^{3/2} (6 A c+b B)}{3 b}-\frac{5}{8} (b+2 c x) \sqrt{b x+c x^2} (6 A c+b B)-\frac{2 A \left(b x+c x^2\right)^{7/2}}{b x^4}",1,"(-5*(b*B + 6*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/8 - (5*c*(b*B + 6*A*c)*(b*x + c*x^2)^(3/2))/(3*b) + (2*(b*B + 6*A*c)*(b*x + c*x^2)^(5/2))/(b*x^2) - (2*A*(b*x + c*x^2)^(7/2))/(b*x^4) + (5*b^2*(b*B + 6*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*Sqrt[c])","A",6,6,22,0.2727,1,"{792, 662, 664, 612, 620, 206}"
101,1,157,0,0.1635606,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^5,x]","-\frac{2 \left(b x+c x^2\right)^{5/2} (4 A c+3 b B)}{3 b x^3}+\frac{5 c \left(b x+c x^2\right)^{3/2} (4 A c+3 b B)}{6 b x}+\frac{5}{4} c \sqrt{b x+c x^2} (4 A c+3 b B)+\frac{5}{4} b \sqrt{c} (4 A c+3 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 A \left(b x+c x^2\right)^{7/2}}{3 b x^5}","-\frac{2 \left(b x+c x^2\right)^{5/2} (4 A c+3 b B)}{3 b x^3}+\frac{5 c \left(b x+c x^2\right)^{3/2} (4 A c+3 b B)}{6 b x}+\frac{5}{4} c \sqrt{b x+c x^2} (4 A c+3 b B)+\frac{5}{4} b \sqrt{c} (4 A c+3 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 A \left(b x+c x^2\right)^{7/2}}{3 b x^5}",1,"(5*c*(3*b*B + 4*A*c)*Sqrt[b*x + c*x^2])/4 + (5*c*(3*b*B + 4*A*c)*(b*x + c*x^2)^(3/2))/(6*b*x) - (2*(3*b*B + 4*A*c)*(b*x + c*x^2)^(5/2))/(3*b*x^3) - (2*A*(b*x + c*x^2)^(7/2))/(3*b*x^5) + (5*b*Sqrt[c]*(3*b*B + 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/4","A",6,5,22,0.2273,1,"{792, 662, 664, 620, 206}"
102,1,155,0,0.1627662,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^6} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^6,x]","\frac{c^2 \sqrt{b x+c x^2} (2 A c+5 b B)}{b}+c^{3/2} (2 A c+5 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 \left(b x+c x^2\right)^{5/2} (2 A c+5 b B)}{15 b x^4}-\frac{2 c \left(b x+c x^2\right)^{3/2} (2 A c+5 b B)}{3 b x^2}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{5 b x^6}","\frac{c^2 \sqrt{b x+c x^2} (2 A c+5 b B)}{b}+c^{3/2} (2 A c+5 b B) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 \left(b x+c x^2\right)^{5/2} (2 A c+5 b B)}{15 b x^4}-\frac{2 c \left(b x+c x^2\right)^{3/2} (2 A c+5 b B)}{3 b x^2}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{5 b x^6}",1,"(c^2*(5*b*B + 2*A*c)*Sqrt[b*x + c*x^2])/b - (2*c*(5*b*B + 2*A*c)*(b*x + c*x^2)^(3/2))/(3*b*x^2) - (2*(5*b*B + 2*A*c)*(b*x + c*x^2)^(5/2))/(15*b*x^4) - (2*A*(b*x + c*x^2)^(7/2))/(5*b*x^6) + c^(3/2)*(5*b*B + 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",6,5,22,0.2273,1,"{792, 662, 664, 620, 206}"
103,1,119,0,0.13935,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^7} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^7,x]","-\frac{2 A \left(b x+c x^2\right)^{7/2}}{7 b x^7}-\frac{2 B c^2 \sqrt{b x+c x^2}}{x}+2 B c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 B \left(b x+c x^2\right)^{5/2}}{5 x^5}-\frac{2 B c \left(b x+c x^2\right)^{3/2}}{3 x^3}","-\frac{2 A \left(b x+c x^2\right)^{7/2}}{7 b x^7}-\frac{2 B c^2 \sqrt{b x+c x^2}}{x}+2 B c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)-\frac{2 B \left(b x+c x^2\right)^{5/2}}{5 x^5}-\frac{2 B c \left(b x+c x^2\right)^{3/2}}{3 x^3}",1,"(-2*B*c^2*Sqrt[b*x + c*x^2])/x - (2*B*c*(b*x + c*x^2)^(3/2))/(3*x^3) - (2*B*(b*x + c*x^2)^(5/2))/(5*x^5) - (2*A*(b*x + c*x^2)^(7/2))/(7*b*x^7) + 2*B*c^(5/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]]","A",6,4,22,0.1818,1,"{792, 662, 620, 206}"
104,1,57,0,0.0492487,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^8} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^8,x]","-\frac{2 \left(b x+c x^2\right)^{7/2} (9 b B-2 A c)}{63 b^2 x^7}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{9 b x^8}","-\frac{2 \left(b x+c x^2\right)^{7/2} (9 b B-2 A c)}{63 b^2 x^7}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{9 b x^8}",1,"(-2*A*(b*x + c*x^2)^(7/2))/(9*b*x^8) - (2*(9*b*B - 2*A*c)*(b*x + c*x^2)^(7/2))/(63*b^2*x^7)","A",2,2,22,0.09091,1,"{792, 650}"
105,1,90,0,0.088501,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^9} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^9,x]","\frac{4 c \left(b x+c x^2\right)^{7/2} (11 b B-4 A c)}{693 b^3 x^7}-\frac{2 \left(b x+c x^2\right)^{7/2} (11 b B-4 A c)}{99 b^2 x^8}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{11 b x^9}","\frac{4 c \left(b x+c x^2\right)^{7/2} (11 b B-4 A c)}{693 b^3 x^7}-\frac{2 \left(b x+c x^2\right)^{7/2} (11 b B-4 A c)}{99 b^2 x^8}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{11 b x^9}",1,"(-2*A*(b*x + c*x^2)^(7/2))/(11*b*x^9) - (2*(11*b*B - 4*A*c)*(b*x + c*x^2)^(7/2))/(99*b^2*x^8) + (4*c*(11*b*B - 4*A*c)*(b*x + c*x^2)^(7/2))/(693*b^3*x^7)","A",3,3,22,0.1364,1,"{792, 658, 650}"
106,1,125,0,0.1218921,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{10}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^10,x]","-\frac{16 c^2 \left(b x+c x^2\right)^{7/2} (13 b B-6 A c)}{9009 b^4 x^7}+\frac{8 c \left(b x+c x^2\right)^{7/2} (13 b B-6 A c)}{1287 b^3 x^8}-\frac{2 \left(b x+c x^2\right)^{7/2} (13 b B-6 A c)}{143 b^2 x^9}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{13 b x^{10}}","-\frac{16 c^2 \left(b x+c x^2\right)^{7/2} (13 b B-6 A c)}{9009 b^4 x^7}+\frac{8 c \left(b x+c x^2\right)^{7/2} (13 b B-6 A c)}{1287 b^3 x^8}-\frac{2 \left(b x+c x^2\right)^{7/2} (13 b B-6 A c)}{143 b^2 x^9}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{13 b x^{10}}",1,"(-2*A*(b*x + c*x^2)^(7/2))/(13*b*x^10) - (2*(13*b*B - 6*A*c)*(b*x + c*x^2)^(7/2))/(143*b^2*x^9) + (8*c*(13*b*B - 6*A*c)*(b*x + c*x^2)^(7/2))/(1287*b^3*x^8) - (16*c^2*(13*b*B - 6*A*c)*(b*x + c*x^2)^(7/2))/(9009*b^4*x^7)","A",4,3,22,0.1364,1,"{792, 658, 650}"
107,1,160,0,0.1636954,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{11}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^11,x]","\frac{32 c^3 \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{45045 b^5 x^7}-\frac{16 c^2 \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{6435 b^4 x^8}+\frac{4 c \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{715 b^3 x^9}-\frac{2 \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{195 b^2 x^{10}}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{15 b x^{11}}","\frac{32 c^3 \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{45045 b^5 x^7}-\frac{16 c^2 \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{6435 b^4 x^8}+\frac{4 c \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{715 b^3 x^9}-\frac{2 \left(b x+c x^2\right)^{7/2} (15 b B-8 A c)}{195 b^2 x^{10}}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{15 b x^{11}}",1,"(-2*A*(b*x + c*x^2)^(7/2))/(15*b*x^11) - (2*(15*b*B - 8*A*c)*(b*x + c*x^2)^(7/2))/(195*b^2*x^10) + (4*c*(15*b*B - 8*A*c)*(b*x + c*x^2)^(7/2))/(715*b^3*x^9) - (16*c^2*(15*b*B - 8*A*c)*(b*x + c*x^2)^(7/2))/(6435*b^4*x^8) + (32*c^3*(15*b*B - 8*A*c)*(b*x + c*x^2)^(7/2))/(45045*b^5*x^7)","A",5,3,22,0.1364,1,"{792, 658, 650}"
108,1,195,0,0.206138,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{12}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^12,x]","-\frac{256 c^4 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{765765 b^6 x^7}+\frac{128 c^3 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{109395 b^5 x^8}-\frac{32 c^2 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{12155 b^4 x^9}+\frac{16 c \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{3315 b^3 x^{10}}-\frac{2 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{255 b^2 x^{11}}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{17 b x^{12}}","-\frac{256 c^4 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{765765 b^6 x^7}+\frac{128 c^3 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{109395 b^5 x^8}-\frac{32 c^2 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{12155 b^4 x^9}+\frac{16 c \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{3315 b^3 x^{10}}-\frac{2 \left(b x+c x^2\right)^{7/2} (17 b B-10 A c)}{255 b^2 x^{11}}-\frac{2 A \left(b x+c x^2\right)^{7/2}}{17 b x^{12}}",1,"(-2*A*(b*x + c*x^2)^(7/2))/(17*b*x^12) - (2*(17*b*B - 10*A*c)*(b*x + c*x^2)^(7/2))/(255*b^2*x^11) + (16*c*(17*b*B - 10*A*c)*(b*x + c*x^2)^(7/2))/(3315*b^3*x^10) - (32*c^2*(17*b*B - 10*A*c)*(b*x + c*x^2)^(7/2))/(12155*b^4*x^9) + (128*c^3*(17*b*B - 10*A*c)*(b*x + c*x^2)^(7/2))/(109395*b^5*x^8) - (256*c^4*(17*b*B - 10*A*c)*(b*x + c*x^2)^(7/2))/(765765*b^6*x^7)","A",6,3,22,0.1364,1,"{792, 658, 650}"
109,1,197,0,0.2002747,"\int \frac{x^4 (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x^4*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{7 b^3 \sqrt{b x+c x^2} (9 b B-10 A c)}{128 c^5}-\frac{7 b^2 x \sqrt{b x+c x^2} (9 b B-10 A c)}{192 c^4}-\frac{7 b^4 (9 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{11/2}}+\frac{7 b x^2 \sqrt{b x+c x^2} (9 b B-10 A c)}{240 c^3}-\frac{x^3 \sqrt{b x+c x^2} (9 b B-10 A c)}{40 c^2}+\frac{B x^4 \sqrt{b x+c x^2}}{5 c}","\frac{7 b^3 \sqrt{b x+c x^2} (9 b B-10 A c)}{128 c^5}-\frac{7 b^2 x \sqrt{b x+c x^2} (9 b B-10 A c)}{192 c^4}-\frac{7 b^4 (9 b B-10 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{11/2}}+\frac{7 b x^2 \sqrt{b x+c x^2} (9 b B-10 A c)}{240 c^3}-\frac{x^3 \sqrt{b x+c x^2} (9 b B-10 A c)}{40 c^2}+\frac{B x^4 \sqrt{b x+c x^2}}{5 c}",1,"(7*b^3*(9*b*B - 10*A*c)*Sqrt[b*x + c*x^2])/(128*c^5) - (7*b^2*(9*b*B - 10*A*c)*x*Sqrt[b*x + c*x^2])/(192*c^4) + (7*b*(9*b*B - 10*A*c)*x^2*Sqrt[b*x + c*x^2])/(240*c^3) - ((9*b*B - 10*A*c)*x^3*Sqrt[b*x + c*x^2])/(40*c^2) + (B*x^4*Sqrt[b*x + c*x^2])/(5*c) - (7*b^4*(9*b*B - 10*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(11/2))","A",7,5,22,0.2273,1,"{794, 670, 640, 620, 206}"
110,1,162,0,0.1564913,"\int \frac{x^3 (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x^3*(A + B*x))/Sqrt[b*x + c*x^2],x]","-\frac{5 b^2 \sqrt{b x+c x^2} (7 b B-8 A c)}{64 c^4}+\frac{5 b^3 (7 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{9/2}}+\frac{5 b x \sqrt{b x+c x^2} (7 b B-8 A c)}{96 c^3}-\frac{x^2 \sqrt{b x+c x^2} (7 b B-8 A c)}{24 c^2}+\frac{B x^3 \sqrt{b x+c x^2}}{4 c}","-\frac{5 b^2 \sqrt{b x+c x^2} (7 b B-8 A c)}{64 c^4}+\frac{5 b^3 (7 b B-8 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{64 c^{9/2}}+\frac{5 b x \sqrt{b x+c x^2} (7 b B-8 A c)}{96 c^3}-\frac{x^2 \sqrt{b x+c x^2} (7 b B-8 A c)}{24 c^2}+\frac{B x^3 \sqrt{b x+c x^2}}{4 c}",1,"(-5*b^2*(7*b*B - 8*A*c)*Sqrt[b*x + c*x^2])/(64*c^4) + (5*b*(7*b*B - 8*A*c)*x*Sqrt[b*x + c*x^2])/(96*c^3) - ((7*b*B - 8*A*c)*x^2*Sqrt[b*x + c*x^2])/(24*c^2) + (B*x^3*Sqrt[b*x + c*x^2])/(4*c) + (5*b^3*(7*b*B - 8*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(9/2))","A",6,5,22,0.2273,1,"{794, 670, 640, 620, 206}"
111,1,127,0,0.1179786,"\int \frac{x^2 (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x^2*(A + B*x))/Sqrt[b*x + c*x^2],x]","-\frac{b^2 (5 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{7/2}}+\frac{b \sqrt{b x+c x^2} (5 b B-6 A c)}{8 c^3}-\frac{x \sqrt{b x+c x^2} (5 b B-6 A c)}{12 c^2}+\frac{B x^2 \sqrt{b x+c x^2}}{3 c}","-\frac{b^2 (5 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{7/2}}+\frac{b \sqrt{b x+c x^2} (5 b B-6 A c)}{8 c^3}-\frac{x \sqrt{b x+c x^2} (5 b B-6 A c)}{12 c^2}+\frac{B x^2 \sqrt{b x+c x^2}}{3 c}",1,"(b*(5*b*B - 6*A*c)*Sqrt[b*x + c*x^2])/(8*c^3) - ((5*b*B - 6*A*c)*x*Sqrt[b*x + c*x^2])/(12*c^2) + (B*x^2*Sqrt[b*x + c*x^2])/(3*c) - (b^2*(5*b*B - 6*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(7/2))","A",5,5,22,0.2273,1,"{794, 670, 640, 620, 206}"
112,1,75,0,0.03355,"\int \frac{x (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{b (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{5/2}}-\frac{\sqrt{b x+c x^2} (-4 A c+3 b B-2 B c x)}{4 c^2}","\frac{b (3 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{5/2}}-\frac{\sqrt{b x+c x^2} (-4 A c+3 b B-2 B c x)}{4 c^2}",1,"-((3*b*B - 4*A*c - 2*B*c*x)*Sqrt[b*x + c*x^2])/(4*c^2) + (b*(3*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(5/2))","A",3,3,20,0.1500,1,"{779, 620, 206}"
113,1,55,0,0.0221579,"\int \frac{A+B x}{\sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/Sqrt[b*x + c*x^2],x]","\frac{B \sqrt{b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}","\frac{B \sqrt{b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}",1,"(B*Sqrt[b*x + c*x^2])/c - ((b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,19,0.1579,1,"{640, 620, 206}"
114,1,52,0,0.0348563,"\int \frac{A+B x}{x \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x*Sqrt[b*x + c*x^2]),x]","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}-\frac{2 A \sqrt{b x+c x^2}}{b x}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c}}-\frac{2 A \sqrt{b x+c x^2}}{b x}",1,"(-2*A*Sqrt[b*x + c*x^2])/(b*x) + (2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/Sqrt[c]","A",3,3,22,0.1364,1,"{792, 620, 206}"
115,1,57,0,0.042887,"\int \frac{A+B x}{x^2 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^2*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{b x+c x^2} (3 b B-2 A c)}{3 b^2 x}-\frac{2 A \sqrt{b x+c x^2}}{3 b x^2}","-\frac{2 \sqrt{b x+c x^2} (3 b B-2 A c)}{3 b^2 x}-\frac{2 A \sqrt{b x+c x^2}}{3 b x^2}",1,"(-2*A*Sqrt[b*x + c*x^2])/(3*b*x^2) - (2*(3*b*B - 2*A*c)*Sqrt[b*x + c*x^2])/(3*b^2*x)","A",2,2,22,0.09091,1,"{792, 650}"
116,1,90,0,0.0813891,"\int \frac{A+B x}{x^3 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^3*Sqrt[b*x + c*x^2]),x]","\frac{4 c \sqrt{b x+c x^2} (5 b B-4 A c)}{15 b^3 x}-\frac{2 \sqrt{b x+c x^2} (5 b B-4 A c)}{15 b^2 x^2}-\frac{2 A \sqrt{b x+c x^2}}{5 b x^3}","\frac{4 c \sqrt{b x+c x^2} (5 b B-4 A c)}{15 b^3 x}-\frac{2 \sqrt{b x+c x^2} (5 b B-4 A c)}{15 b^2 x^2}-\frac{2 A \sqrt{b x+c x^2}}{5 b x^3}",1,"(-2*A*Sqrt[b*x + c*x^2])/(5*b*x^3) - (2*(5*b*B - 4*A*c)*Sqrt[b*x + c*x^2])/(15*b^2*x^2) + (4*c*(5*b*B - 4*A*c)*Sqrt[b*x + c*x^2])/(15*b^3*x)","A",3,3,22,0.1364,1,"{792, 658, 650}"
117,1,125,0,0.1094514,"\int \frac{A+B x}{x^4 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^4*Sqrt[b*x + c*x^2]),x]","-\frac{16 c^2 \sqrt{b x+c x^2} (7 b B-6 A c)}{105 b^4 x}+\frac{8 c \sqrt{b x+c x^2} (7 b B-6 A c)}{105 b^3 x^2}-\frac{2 \sqrt{b x+c x^2} (7 b B-6 A c)}{35 b^2 x^3}-\frac{2 A \sqrt{b x+c x^2}}{7 b x^4}","-\frac{16 c^2 \sqrt{b x+c x^2} (7 b B-6 A c)}{105 b^4 x}+\frac{8 c \sqrt{b x+c x^2} (7 b B-6 A c)}{105 b^3 x^2}-\frac{2 \sqrt{b x+c x^2} (7 b B-6 A c)}{35 b^2 x^3}-\frac{2 A \sqrt{b x+c x^2}}{7 b x^4}",1,"(-2*A*Sqrt[b*x + c*x^2])/(7*b*x^4) - (2*(7*b*B - 6*A*c)*Sqrt[b*x + c*x^2])/(35*b^2*x^3) + (8*c*(7*b*B - 6*A*c)*Sqrt[b*x + c*x^2])/(105*b^3*x^2) - (16*c^2*(7*b*B - 6*A*c)*Sqrt[b*x + c*x^2])/(105*b^4*x)","A",4,3,22,0.1364,1,"{792, 658, 650}"
118,1,160,0,0.1425608,"\int \frac{A+B x}{x^5 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^5*Sqrt[b*x + c*x^2]),x]","\frac{32 c^3 \sqrt{b x+c x^2} (9 b B-8 A c)}{315 b^5 x}-\frac{16 c^2 \sqrt{b x+c x^2} (9 b B-8 A c)}{315 b^4 x^2}+\frac{4 c \sqrt{b x+c x^2} (9 b B-8 A c)}{105 b^3 x^3}-\frac{2 \sqrt{b x+c x^2} (9 b B-8 A c)}{63 b^2 x^4}-\frac{2 A \sqrt{b x+c x^2}}{9 b x^5}","\frac{32 c^3 \sqrt{b x+c x^2} (9 b B-8 A c)}{315 b^5 x}-\frac{16 c^2 \sqrt{b x+c x^2} (9 b B-8 A c)}{315 b^4 x^2}+\frac{4 c \sqrt{b x+c x^2} (9 b B-8 A c)}{105 b^3 x^3}-\frac{2 \sqrt{b x+c x^2} (9 b B-8 A c)}{63 b^2 x^4}-\frac{2 A \sqrt{b x+c x^2}}{9 b x^5}",1,"(-2*A*Sqrt[b*x + c*x^2])/(9*b*x^5) - (2*(9*b*B - 8*A*c)*Sqrt[b*x + c*x^2])/(63*b^2*x^4) + (4*c*(9*b*B - 8*A*c)*Sqrt[b*x + c*x^2])/(105*b^3*x^3) - (16*c^2*(9*b*B - 8*A*c)*Sqrt[b*x + c*x^2])/(315*b^4*x^2) + (32*c^3*(9*b*B - 8*A*c)*Sqrt[b*x + c*x^2])/(315*b^5*x)","A",5,3,22,0.1364,1,"{792, 658, 650}"
119,1,195,0,0.1772032,"\int \frac{A+B x}{x^6 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^6*Sqrt[b*x + c*x^2]),x]","-\frac{256 c^4 \sqrt{b x+c x^2} (11 b B-10 A c)}{3465 b^6 x}+\frac{128 c^3 \sqrt{b x+c x^2} (11 b B-10 A c)}{3465 b^5 x^2}-\frac{32 c^2 \sqrt{b x+c x^2} (11 b B-10 A c)}{1155 b^4 x^3}+\frac{16 c \sqrt{b x+c x^2} (11 b B-10 A c)}{693 b^3 x^4}-\frac{2 \sqrt{b x+c x^2} (11 b B-10 A c)}{99 b^2 x^5}-\frac{2 A \sqrt{b x+c x^2}}{11 b x^6}","-\frac{256 c^4 \sqrt{b x+c x^2} (11 b B-10 A c)}{3465 b^6 x}+\frac{128 c^3 \sqrt{b x+c x^2} (11 b B-10 A c)}{3465 b^5 x^2}-\frac{32 c^2 \sqrt{b x+c x^2} (11 b B-10 A c)}{1155 b^4 x^3}+\frac{16 c \sqrt{b x+c x^2} (11 b B-10 A c)}{693 b^3 x^4}-\frac{2 \sqrt{b x+c x^2} (11 b B-10 A c)}{99 b^2 x^5}-\frac{2 A \sqrt{b x+c x^2}}{11 b x^6}",1,"(-2*A*Sqrt[b*x + c*x^2])/(11*b*x^6) - (2*(11*b*B - 10*A*c)*Sqrt[b*x + c*x^2])/(99*b^2*x^5) + (16*c*(11*b*B - 10*A*c)*Sqrt[b*x + c*x^2])/(693*b^3*x^4) - (32*c^2*(11*b*B - 10*A*c)*Sqrt[b*x + c*x^2])/(1155*b^4*x^3) + (128*c^3*(11*b*B - 10*A*c)*Sqrt[b*x + c*x^2])/(3465*b^5*x^2) - (256*c^4*(11*b*B - 10*A*c)*Sqrt[b*x + c*x^2])/(3465*b^6*x)","A",6,3,22,0.1364,1,"{792, 658, 650}"
120,1,170,0,0.1516063,"\int \frac{x^4 (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^4*(A + B*x))/(b*x + c*x^2)^(3/2),x]","-\frac{5 b^2 (7 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{9/2}}+\frac{x^2 \sqrt{b x+c x^2} (7 b B-6 A c)}{3 b c^2}-\frac{5 x \sqrt{b x+c x^2} (7 b B-6 A c)}{12 c^3}+\frac{5 b \sqrt{b x+c x^2} (7 b B-6 A c)}{8 c^4}-\frac{2 x^4 (b B-A c)}{b c \sqrt{b x+c x^2}}","-\frac{5 b^2 (7 b B-6 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{9/2}}+\frac{x^2 \sqrt{b x+c x^2} (7 b B-6 A c)}{3 b c^2}-\frac{5 x \sqrt{b x+c x^2} (7 b B-6 A c)}{12 c^3}+\frac{5 b \sqrt{b x+c x^2} (7 b B-6 A c)}{8 c^4}-\frac{2 x^4 (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^4)/(b*c*Sqrt[b*x + c*x^2]) + (5*b*(7*b*B - 6*A*c)*Sqrt[b*x + c*x^2])/(8*c^4) - (5*(7*b*B - 6*A*c)*x*Sqrt[b*x + c*x^2])/(12*c^3) + ((7*b*B - 6*A*c)*x^2*Sqrt[b*x + c*x^2])/(3*b*c^2) - (5*b^2*(7*b*B - 6*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(9/2))","A",6,5,22,0.2273,1,"{788, 670, 640, 620, 206}"
121,1,135,0,0.116993,"\int \frac{x^3 (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^3*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{x \sqrt{b x+c x^2} (5 b B-4 A c)}{2 b c^2}-\frac{3 \sqrt{b x+c x^2} (5 b B-4 A c)}{4 c^3}+\frac{3 b (5 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{7/2}}-\frac{2 x^3 (b B-A c)}{b c \sqrt{b x+c x^2}}","\frac{x \sqrt{b x+c x^2} (5 b B-4 A c)}{2 b c^2}-\frac{3 \sqrt{b x+c x^2} (5 b B-4 A c)}{4 c^3}+\frac{3 b (5 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{7/2}}-\frac{2 x^3 (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^3)/(b*c*Sqrt[b*x + c*x^2]) - (3*(5*b*B - 4*A*c)*Sqrt[b*x + c*x^2])/(4*c^3) + ((5*b*B - 4*A*c)*x*Sqrt[b*x + c*x^2])/(2*b*c^2) + (3*b*(5*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(7/2))","A",5,5,22,0.2273,1,"{788, 670, 640, 620, 206}"
122,1,99,0,0.0887486,"\int \frac{x^2 (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^2*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{\sqrt{b x+c x^2} (3 b B-2 A c)}{b c^2}-\frac{(3 b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}-\frac{2 x^2 (b B-A c)}{b c \sqrt{b x+c x^2}}","\frac{\sqrt{b x+c x^2} (3 b B-2 A c)}{b c^2}-\frac{(3 b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}-\frac{2 x^2 (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^2)/(b*c*Sqrt[b*x + c*x^2]) + ((3*b*B - 2*A*c)*Sqrt[b*x + c*x^2])/(b*c^2) - ((3*b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",4,4,22,0.1818,1,"{788, 640, 620, 206}"
123,1,60,0,0.0281775,"\int \frac{x (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}-\frac{2 x (b B-A c)}{b c \sqrt{b x+c x^2}}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}-\frac{2 x (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x)/(b*c*Sqrt[b*x + c*x^2]) + (2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,20,0.1500,1,"{777, 620, 206}"
124,1,33,0,0.0093221,"\int \frac{A+B x}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(b*x + c*x^2)^(3/2),x]","-\frac{2 (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}","-\frac{2 (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}",1,"(-2*(A*b - (b*B - 2*A*c)*x))/(b^2*Sqrt[b*x + c*x^2])","A",1,1,19,0.05263,1,"{636}"
125,1,60,0,0.032367,"\int \frac{A+B x}{x \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x*(b*x + c*x^2)^(3/2)),x]","-\frac{2 (b+2 c x) (3 b B-4 A c)}{3 b^3 \sqrt{b x+c x^2}}-\frac{2 A}{3 b x \sqrt{b x+c x^2}}","-\frac{2 (b+2 c x) (3 b B-4 A c)}{3 b^3 \sqrt{b x+c x^2}}-\frac{2 A}{3 b x \sqrt{b x+c x^2}}",1,"(-2*A)/(3*b*x*Sqrt[b*x + c*x^2]) - (2*(3*b*B - 4*A*c)*(b + 2*c*x))/(3*b^3*Sqrt[b*x + c*x^2])","A",2,2,22,0.09091,1,"{792, 613}"
126,1,93,0,0.0837657,"\int \frac{A+B x}{x^2 \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^2*(b*x + c*x^2)^(3/2)),x]","\frac{8 c (b+2 c x) (5 b B-6 A c)}{15 b^4 \sqrt{b x+c x^2}}-\frac{2 (5 b B-6 A c)}{15 b^2 x \sqrt{b x+c x^2}}-\frac{2 A}{5 b x^2 \sqrt{b x+c x^2}}","\frac{8 c (b+2 c x) (5 b B-6 A c)}{15 b^4 \sqrt{b x+c x^2}}-\frac{2 (5 b B-6 A c)}{15 b^2 x \sqrt{b x+c x^2}}-\frac{2 A}{5 b x^2 \sqrt{b x+c x^2}}",1,"(-2*A)/(5*b*x^2*Sqrt[b*x + c*x^2]) - (2*(5*b*B - 6*A*c))/(15*b^2*x*Sqrt[b*x + c*x^2]) + (8*c*(5*b*B - 6*A*c)*(b + 2*c*x))/(15*b^4*Sqrt[b*x + c*x^2])","A",3,3,22,0.1364,1,"{792, 658, 613}"
127,1,128,0,0.1147417,"\int \frac{A+B x}{x^3 \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^3*(b*x + c*x^2)^(3/2)),x]","-\frac{16 c^2 (b+2 c x) (7 b B-8 A c)}{35 b^5 \sqrt{b x+c x^2}}+\frac{4 c (7 b B-8 A c)}{35 b^3 x \sqrt{b x+c x^2}}-\frac{2 (7 b B-8 A c)}{35 b^2 x^2 \sqrt{b x+c x^2}}-\frac{2 A}{7 b x^3 \sqrt{b x+c x^2}}","-\frac{16 c^2 (b+2 c x) (7 b B-8 A c)}{35 b^5 \sqrt{b x+c x^2}}+\frac{4 c (7 b B-8 A c)}{35 b^3 x \sqrt{b x+c x^2}}-\frac{2 (7 b B-8 A c)}{35 b^2 x^2 \sqrt{b x+c x^2}}-\frac{2 A}{7 b x^3 \sqrt{b x+c x^2}}",1,"(-2*A)/(7*b*x^3*Sqrt[b*x + c*x^2]) - (2*(7*b*B - 8*A*c))/(35*b^2*x^2*Sqrt[b*x + c*x^2]) + (4*c*(7*b*B - 8*A*c))/(35*b^3*x*Sqrt[b*x + c*x^2]) - (16*c^2*(7*b*B - 8*A*c)*(b + 2*c*x))/(35*b^5*Sqrt[b*x + c*x^2])","A",4,3,22,0.1364,1,"{792, 658, 613}"
128,1,163,0,0.1438819,"\int \frac{A+B x}{x^4 \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^4*(b*x + c*x^2)^(3/2)),x]","\frac{128 c^3 (b+2 c x) (9 b B-10 A c)}{315 b^6 \sqrt{b x+c x^2}}-\frac{32 c^2 (9 b B-10 A c)}{315 b^4 x \sqrt{b x+c x^2}}+\frac{16 c (9 b B-10 A c)}{315 b^3 x^2 \sqrt{b x+c x^2}}-\frac{2 (9 b B-10 A c)}{63 b^2 x^3 \sqrt{b x+c x^2}}-\frac{2 A}{9 b x^4 \sqrt{b x+c x^2}}","\frac{128 c^3 (b+2 c x) (9 b B-10 A c)}{315 b^6 \sqrt{b x+c x^2}}-\frac{32 c^2 (9 b B-10 A c)}{315 b^4 x \sqrt{b x+c x^2}}+\frac{16 c (9 b B-10 A c)}{315 b^3 x^2 \sqrt{b x+c x^2}}-\frac{2 (9 b B-10 A c)}{63 b^2 x^3 \sqrt{b x+c x^2}}-\frac{2 A}{9 b x^4 \sqrt{b x+c x^2}}",1,"(-2*A)/(9*b*x^4*Sqrt[b*x + c*x^2]) - (2*(9*b*B - 10*A*c))/(63*b^2*x^3*Sqrt[b*x + c*x^2]) + (16*c*(9*b*B - 10*A*c))/(315*b^3*x^2*Sqrt[b*x + c*x^2]) - (32*c^2*(9*b*B - 10*A*c))/(315*b^4*x*Sqrt[b*x + c*x^2]) + (128*c^3*(9*b*B - 10*A*c)*(b + 2*c*x))/(315*b^6*Sqrt[b*x + c*x^2])","A",5,3,22,0.1364,1,"{792, 658, 613}"
129,1,172,0,0.1682294,"\int \frac{x^5 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^5*(A + B*x))/(b*x + c*x^2)^(5/2),x]","-\frac{2 x^3 (7 b B-4 A c)}{3 b c^2 \sqrt{b x+c x^2}}+\frac{5 x \sqrt{b x+c x^2} (7 b B-4 A c)}{6 b c^3}-\frac{5 \sqrt{b x+c x^2} (7 b B-4 A c)}{4 c^4}+\frac{5 b (7 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{9/2}}-\frac{2 x^5 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","-\frac{2 x^3 (7 b B-4 A c)}{3 b c^2 \sqrt{b x+c x^2}}+\frac{5 x \sqrt{b x+c x^2} (7 b B-4 A c)}{6 b c^3}-\frac{5 \sqrt{b x+c x^2} (7 b B-4 A c)}{4 c^4}+\frac{5 b (7 b B-4 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{4 c^{9/2}}-\frac{2 x^5 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^5)/(3*b*c*(b*x + c*x^2)^(3/2)) - (2*(7*b*B - 4*A*c)*x^3)/(3*b*c^2*Sqrt[b*x + c*x^2]) - (5*(7*b*B - 4*A*c)*Sqrt[b*x + c*x^2])/(4*c^4) + (5*(7*b*B - 4*A*c)*x*Sqrt[b*x + c*x^2])/(6*b*c^3) + (5*b*(7*b*B - 4*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(9/2))","A",6,6,22,0.2727,1,"{788, 668, 670, 640, 620, 206}"
130,1,136,0,0.1247062,"\int \frac{x^4 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^4*(A + B*x))/(b*x + c*x^2)^(5/2),x]","-\frac{2 x^2 (5 b B-2 A c)}{3 b c^2 \sqrt{b x+c x^2}}+\frac{\sqrt{b x+c x^2} (5 b B-2 A c)}{b c^3}-\frac{(5 b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{7/2}}-\frac{2 x^4 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","-\frac{2 x^2 (5 b B-2 A c)}{3 b c^2 \sqrt{b x+c x^2}}+\frac{\sqrt{b x+c x^2} (5 b B-2 A c)}{b c^3}-\frac{(5 b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{7/2}}-\frac{2 x^4 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^4)/(3*b*c*(b*x + c*x^2)^(3/2)) - (2*(5*b*B - 2*A*c)*x^2)/(3*b*c^2*Sqrt[b*x + c*x^2]) + ((5*b*B - 2*A*c)*Sqrt[b*x + c*x^2])/(b*c^3) - ((5*b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(7/2)","A",5,5,22,0.2273,1,"{788, 668, 640, 620, 206}"
131,1,84,0,0.084576,"\int \frac{x^3 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^3*(A + B*x))/(b*x + c*x^2)^(5/2),x]","-\frac{2 x^3 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}-\frac{2 B x}{c^2 \sqrt{b x+c x^2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 x^3 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}-\frac{2 B x}{c^2 \sqrt{b x+c x^2}}+\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}",1,"(-2*(b*B - A*c)*x^3)/(3*b*c*(b*x + c*x^2)^(3/2)) - (2*B*x)/(c^2*Sqrt[b*x + c*x^2]) + (2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",4,4,22,0.1818,1,"{788, 652, 620, 206}"
132,1,67,0,0.0542218,"\int \frac{x^2 (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^2*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x (2 A c+b B)}{3 b^2 c \sqrt{b x+c x^2}}-\frac{2 x^2 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{2 x (2 A c+b B)}{3 b^2 c \sqrt{b x+c x^2}}-\frac{2 x^2 (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^2)/(3*b*c*(b*x + c*x^2)^(3/2)) + (2*(b*B + 2*A*c)*x)/(3*b^2*c*Sqrt[b*x + c*x^2])","A",2,2,22,0.09091,1,"{788, 636}"
133,1,70,0,0.0313752,"\int \frac{x (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 (b+2 c x) (b B-4 A c)}{3 b^3 c \sqrt{b x+c x^2}}-\frac{2 x (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{2 (b+2 c x) (b B-4 A c)}{3 b^3 c \sqrt{b x+c x^2}}-\frac{2 x (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x)/(3*b*c*(b*x + c*x^2)^(3/2)) + (2*(b*B - 4*A*c)*(b + 2*c*x))/(3*b^3*c*Sqrt[b*x + c*x^2])","A",2,2,20,0.1000,1,"{777, 613}"
134,1,70,0,0.0184819,"\int \frac{A+B x}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(b*x + c*x^2)^(5/2),x]","-\frac{8 (b+2 c x) (b B-2 A c)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}","-\frac{8 (b+2 c x) (b B-2 A c)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - (b*B - 2*A*c)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) - (8*(b*B - 2*A*c)*(b + 2*c*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,19,0.1053,1,"{638, 613}"
135,1,96,0,0.0675235,"\int \frac{A+B x}{x \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x*(b*x + c*x^2)^(5/2)),x]","\frac{16 c (b+2 c x) (5 b B-8 A c)}{15 b^5 \sqrt{b x+c x^2}}-\frac{2 (b+2 c x) (5 b B-8 A c)}{15 b^3 \left(b x+c x^2\right)^{3/2}}-\frac{2 A}{5 b x \left(b x+c x^2\right)^{3/2}}","\frac{16 c (b+2 c x) (5 b B-8 A c)}{15 b^5 \sqrt{b x+c x^2}}-\frac{2 (b+2 c x) (5 b B-8 A c)}{15 b^3 \left(b x+c x^2\right)^{3/2}}-\frac{2 A}{5 b x \left(b x+c x^2\right)^{3/2}}",1,"(-2*A)/(5*b*x*(b*x + c*x^2)^(3/2)) - (2*(5*b*B - 8*A*c)*(b + 2*c*x))/(15*b^3*(b*x + c*x^2)^(3/2)) + (16*c*(5*b*B - 8*A*c)*(b + 2*c*x))/(15*b^5*Sqrt[b*x + c*x^2])","A",3,3,22,0.1364,1,"{792, 614, 613}"
136,1,131,0,0.1170704,"\int \frac{A+B x}{x^2 \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^2*(b*x + c*x^2)^(5/2)),x]","-\frac{128 c^2 (b+2 c x) (7 b B-10 A c)}{105 b^6 \sqrt{b x+c x^2}}+\frac{16 c (b+2 c x) (7 b B-10 A c)}{105 b^4 \left(b x+c x^2\right)^{3/2}}-\frac{2 (7 b B-10 A c)}{35 b^2 x \left(b x+c x^2\right)^{3/2}}-\frac{2 A}{7 b x^2 \left(b x+c x^2\right)^{3/2}}","-\frac{128 c^2 (b+2 c x) (7 b B-10 A c)}{105 b^6 \sqrt{b x+c x^2}}+\frac{16 c (b+2 c x) (7 b B-10 A c)}{105 b^4 \left(b x+c x^2\right)^{3/2}}-\frac{2 (7 b B-10 A c)}{35 b^2 x \left(b x+c x^2\right)^{3/2}}-\frac{2 A}{7 b x^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*A)/(7*b*x^2*(b*x + c*x^2)^(3/2)) - (2*(7*b*B - 10*A*c))/(35*b^2*x*(b*x + c*x^2)^(3/2)) + (16*c*(7*b*B - 10*A*c)*(b + 2*c*x))/(105*b^4*(b*x + c*x^2)^(3/2)) - (128*c^2*(7*b*B - 10*A*c)*(b + 2*c*x))/(105*b^6*Sqrt[b*x + c*x^2])","A",4,4,22,0.1818,1,"{792, 658, 614, 613}"
137,1,166,0,0.1500523,"\int \frac{A+B x}{x^3 \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^3*(b*x + c*x^2)^(5/2)),x]","\frac{256 c^3 (b+2 c x) (3 b B-4 A c)}{63 b^7 \sqrt{b x+c x^2}}-\frac{32 c^2 (b+2 c x) (3 b B-4 A c)}{63 b^5 \left(b x+c x^2\right)^{3/2}}+\frac{4 c (3 b B-4 A c)}{21 b^3 x \left(b x+c x^2\right)^{3/2}}-\frac{2 (3 b B-4 A c)}{21 b^2 x^2 \left(b x+c x^2\right)^{3/2}}-\frac{2 A}{9 b x^3 \left(b x+c x^2\right)^{3/2}}","\frac{256 c^3 (b+2 c x) (3 b B-4 A c)}{63 b^7 \sqrt{b x+c x^2}}-\frac{32 c^2 (b+2 c x) (3 b B-4 A c)}{63 b^5 \left(b x+c x^2\right)^{3/2}}+\frac{4 c (3 b B-4 A c)}{21 b^3 x \left(b x+c x^2\right)^{3/2}}-\frac{2 (3 b B-4 A c)}{21 b^2 x^2 \left(b x+c x^2\right)^{3/2}}-\frac{2 A}{9 b x^3 \left(b x+c x^2\right)^{3/2}}",1,"(-2*A)/(9*b*x^3*(b*x + c*x^2)^(3/2)) - (2*(3*b*B - 4*A*c))/(21*b^2*x^2*(b*x + c*x^2)^(3/2)) + (4*c*(3*b*B - 4*A*c))/(21*b^3*x*(b*x + c*x^2)^(3/2)) - (32*c^2*(3*b*B - 4*A*c)*(b + 2*c*x))/(63*b^5*(b*x + c*x^2)^(3/2)) + (256*c^3*(3*b*B - 4*A*c)*(b + 2*c*x))/(63*b^7*Sqrt[b*x + c*x^2])","A",5,4,22,0.1818,1,"{792, 658, 614, 613}"
138,1,107,0,0.0313922,"\int \frac{d+e x}{\left(b x+c x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(b*x + c*x^2)^(7/2),x]","-\frac{128 c (b+2 c x) (2 c d-b e)}{15 b^6 \sqrt{b x+c x^2}}+\frac{16 (b+2 c x) (2 c d-b e)}{15 b^4 \left(b x+c x^2\right)^{3/2}}-\frac{2 (x (2 c d-b e)+b d)}{5 b^2 \left(b x+c x^2\right)^{5/2}}","-\frac{128 c (b+2 c x) (2 c d-b e)}{15 b^6 \sqrt{b x+c x^2}}+\frac{16 (b+2 c x) (2 c d-b e)}{15 b^4 \left(b x+c x^2\right)^{3/2}}-\frac{2 (x (2 c d-b e)+b d)}{5 b^2 \left(b x+c x^2\right)^{5/2}}",1,"(-2*(b*d + (2*c*d - b*e)*x))/(5*b^2*(b*x + c*x^2)^(5/2)) + (16*(2*c*d - b*e)*(b + 2*c*x))/(15*b^4*(b*x + c*x^2)^(3/2)) - (128*c*(2*c*d - b*e)*(b + 2*c*x))/(15*b^6*Sqrt[b*x + c*x^2])","A",3,3,19,0.1579,1,"{638, 614, 613}"
139,1,145,0,0.0448613,"\int \frac{d+e x}{\left(b x+c x^2\right)^{9/2}} \, dx","Int[(d + e*x)/(b*x + c*x^2)^(9/2),x]","\frac{1024 c^2 (b+2 c x) (2 c d-b e)}{35 b^8 \sqrt{b x+c x^2}}-\frac{128 c (b+2 c x) (2 c d-b e)}{35 b^6 \left(b x+c x^2\right)^{3/2}}+\frac{24 (b+2 c x) (2 c d-b e)}{35 b^4 \left(b x+c x^2\right)^{5/2}}-\frac{2 (x (2 c d-b e)+b d)}{7 b^2 \left(b x+c x^2\right)^{7/2}}","\frac{1024 c^2 (b+2 c x) (2 c d-b e)}{35 b^8 \sqrt{b x+c x^2}}-\frac{128 c (b+2 c x) (2 c d-b e)}{35 b^6 \left(b x+c x^2\right)^{3/2}}+\frac{24 (b+2 c x) (2 c d-b e)}{35 b^4 \left(b x+c x^2\right)^{5/2}}-\frac{2 (x (2 c d-b e)+b d)}{7 b^2 \left(b x+c x^2\right)^{7/2}}",1,"(-2*(b*d + (2*c*d - b*e)*x))/(7*b^2*(b*x + c*x^2)^(7/2)) + (24*(2*c*d - b*e)*(b + 2*c*x))/(35*b^4*(b*x + c*x^2)^(5/2)) - (128*c*(2*c*d - b*e)*(b + 2*c*x))/(35*b^6*(b*x + c*x^2)^(3/2)) + (1024*c^2*(2*c*d - b*e)*(b + 2*c*x))/(35*b^8*Sqrt[b*x + c*x^2])","A",4,3,19,0.1579,1,"{638, 614, 613}"
140,1,39,0,0.0165459,"\int x^{7/2} (A+B x) \left(b x+c x^2\right) \, dx","Int[x^(7/2)*(A + B*x)*(b*x + c*x^2),x]","\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{11} A b x^{11/2}+\frac{2}{15} B c x^{15/2}","\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{11} A b x^{11/2}+\frac{2}{15} B c x^{15/2}",1,"(2*A*b*x^(11/2))/11 + (2*(b*B + A*c)*x^(13/2))/13 + (2*B*c*x^(15/2))/15","A",2,1,20,0.05000,1,"{765}"
141,1,39,0,0.0165978,"\int x^{5/2} (A+B x) \left(b x+c x^2\right) \, dx","Int[x^(5/2)*(A + B*x)*(b*x + c*x^2),x]","\frac{2}{11} x^{11/2} (A c+b B)+\frac{2}{9} A b x^{9/2}+\frac{2}{13} B c x^{13/2}","\frac{2}{11} x^{11/2} (A c+b B)+\frac{2}{9} A b x^{9/2}+\frac{2}{13} B c x^{13/2}",1,"(2*A*b*x^(9/2))/9 + (2*(b*B + A*c)*x^(11/2))/11 + (2*B*c*x^(13/2))/13","A",2,1,20,0.05000,1,"{765}"
142,1,39,0,0.0163165,"\int x^{3/2} (A+B x) \left(b x+c x^2\right) \, dx","Int[x^(3/2)*(A + B*x)*(b*x + c*x^2),x]","\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{7} A b x^{7/2}+\frac{2}{11} B c x^{11/2}","\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{7} A b x^{7/2}+\frac{2}{11} B c x^{11/2}",1,"(2*A*b*x^(7/2))/7 + (2*(b*B + A*c)*x^(9/2))/9 + (2*B*c*x^(11/2))/11","A",2,1,20,0.05000,1,"{765}"
143,1,39,0,0.0152832,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right) \, dx","Int[Sqrt[x]*(A + B*x)*(b*x + c*x^2),x]","\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{5} A b x^{5/2}+\frac{2}{9} B c x^{9/2}","\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{5} A b x^{5/2}+\frac{2}{9} B c x^{9/2}",1,"(2*A*b*x^(5/2))/5 + (2*(b*B + A*c)*x^(7/2))/7 + (2*B*c*x^(9/2))/9","A",2,1,20,0.05000,1,"{765}"
144,1,39,0,0.0156641,"\int \frac{(A+B x) \left(b x+c x^2\right)}{\sqrt{x}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/Sqrt[x],x]","\frac{2}{5} x^{5/2} (A c+b B)+\frac{2}{3} A b x^{3/2}+\frac{2}{7} B c x^{7/2}","\frac{2}{5} x^{5/2} (A c+b B)+\frac{2}{3} A b x^{3/2}+\frac{2}{7} B c x^{7/2}",1,"(2*A*b*x^(3/2))/3 + (2*(b*B + A*c)*x^(5/2))/5 + (2*B*c*x^(7/2))/7","A",2,1,20,0.05000,1,"{765}"
145,1,37,0,0.0149419,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^(3/2),x]","\frac{2}{3} x^{3/2} (A c+b B)+2 A b \sqrt{x}+\frac{2}{5} B c x^{5/2}","\frac{2}{3} x^{3/2} (A c+b B)+2 A b \sqrt{x}+\frac{2}{5} B c x^{5/2}",1,"2*A*b*Sqrt[x] + (2*(b*B + A*c)*x^(3/2))/3 + (2*B*c*x^(5/2))/5","A",2,1,20,0.05000,1,"{765}"
146,1,35,0,0.0160369,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^(5/2),x]","2 \sqrt{x} (A c+b B)-\frac{2 A b}{\sqrt{x}}+\frac{2}{3} B c x^{3/2}","2 \sqrt{x} (A c+b B)-\frac{2 A b}{\sqrt{x}}+\frac{2}{3} B c x^{3/2}",1,"(-2*A*b)/Sqrt[x] + 2*(b*B + A*c)*Sqrt[x] + (2*B*c*x^(3/2))/3","A",2,1,20,0.05000,1,"{765}"
147,1,35,0,0.0162382,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^(7/2),x]","-\frac{2 (A c+b B)}{\sqrt{x}}-\frac{2 A b}{3 x^{3/2}}+2 B c \sqrt{x}","-\frac{2 (A c+b B)}{\sqrt{x}}-\frac{2 A b}{3 x^{3/2}}+2 B c \sqrt{x}",1,"(-2*A*b)/(3*x^(3/2)) - (2*(b*B + A*c))/Sqrt[x] + 2*B*c*Sqrt[x]","A",2,1,20,0.05000,1,"{765}"
148,1,37,0,0.0169217,"\int \frac{(A+B x) \left(b x+c x^2\right)}{x^{9/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/x^(9/2),x]","-\frac{2 (A c+b B)}{3 x^{3/2}}-\frac{2 A b}{5 x^{5/2}}-\frac{2 B c}{\sqrt{x}}","-\frac{2 (A c+b B)}{3 x^{3/2}}-\frac{2 A b}{5 x^{5/2}}-\frac{2 B c}{\sqrt{x}}",1,"(-2*A*b)/(5*x^(5/2)) - (2*(b*B + A*c))/(3*x^(3/2)) - (2*B*c)/Sqrt[x]","A",2,1,20,0.05000,1,"{765}"
149,1,63,0,0.0333596,"\int x^{7/2} (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x^(7/2)*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2}{13} A b^2 x^{13/2}+\frac{2}{17} c x^{17/2} (A c+2 b B)+\frac{2}{15} b x^{15/2} (2 A c+b B)+\frac{2}{19} B c^2 x^{19/2}","\frac{2}{13} A b^2 x^{13/2}+\frac{2}{17} c x^{17/2} (A c+2 b B)+\frac{2}{15} b x^{15/2} (2 A c+b B)+\frac{2}{19} B c^2 x^{19/2}",1,"(2*A*b^2*x^(13/2))/13 + (2*b*(b*B + 2*A*c)*x^(15/2))/15 + (2*c*(2*b*B + A*c)*x^(17/2))/17 + (2*B*c^2*x^(19/2))/19","A",2,1,22,0.04545,1,"{765}"
150,1,63,0,0.0306611,"\int x^{5/2} (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x^(5/2)*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2}{11} A b^2 x^{11/2}+\frac{2}{15} c x^{15/2} (A c+2 b B)+\frac{2}{13} b x^{13/2} (2 A c+b B)+\frac{2}{17} B c^2 x^{17/2}","\frac{2}{11} A b^2 x^{11/2}+\frac{2}{15} c x^{15/2} (A c+2 b B)+\frac{2}{13} b x^{13/2} (2 A c+b B)+\frac{2}{17} B c^2 x^{17/2}",1,"(2*A*b^2*x^(11/2))/11 + (2*b*(b*B + 2*A*c)*x^(13/2))/13 + (2*c*(2*b*B + A*c)*x^(15/2))/15 + (2*B*c^2*x^(17/2))/17","A",2,1,22,0.04545,1,"{765}"
151,1,63,0,0.0293865,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[x^(3/2)*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2}{9} A b^2 x^{9/2}+\frac{2}{13} c x^{13/2} (A c+2 b B)+\frac{2}{11} b x^{11/2} (2 A c+b B)+\frac{2}{15} B c^2 x^{15/2}","\frac{2}{9} A b^2 x^{9/2}+\frac{2}{13} c x^{13/2} (A c+2 b B)+\frac{2}{11} b x^{11/2} (2 A c+b B)+\frac{2}{15} B c^2 x^{15/2}",1,"(2*A*b^2*x^(9/2))/9 + (2*b*(b*B + 2*A*c)*x^(11/2))/11 + (2*c*(2*b*B + A*c)*x^(13/2))/13 + (2*B*c^2*x^(15/2))/15","A",2,1,22,0.04545,1,"{765}"
152,1,63,0,0.0296317,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^2,x]","\frac{2}{7} A b^2 x^{7/2}+\frac{2}{11} c x^{11/2} (A c+2 b B)+\frac{2}{9} b x^{9/2} (2 A c+b B)+\frac{2}{13} B c^2 x^{13/2}","\frac{2}{7} A b^2 x^{7/2}+\frac{2}{11} c x^{11/2} (A c+2 b B)+\frac{2}{9} b x^{9/2} (2 A c+b B)+\frac{2}{13} B c^2 x^{13/2}",1,"(2*A*b^2*x^(7/2))/7 + (2*b*(b*B + 2*A*c)*x^(9/2))/9 + (2*c*(2*b*B + A*c)*x^(11/2))/11 + (2*B*c^2*x^(13/2))/13","A",2,1,22,0.04545,1,"{765}"
153,1,63,0,0.0299997,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{\sqrt{x}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/Sqrt[x],x]","\frac{2}{5} A b^2 x^{5/2}+\frac{2}{9} c x^{9/2} (A c+2 b B)+\frac{2}{7} b x^{7/2} (2 A c+b B)+\frac{2}{11} B c^2 x^{11/2}","\frac{2}{5} A b^2 x^{5/2}+\frac{2}{9} c x^{9/2} (A c+2 b B)+\frac{2}{7} b x^{7/2} (2 A c+b B)+\frac{2}{11} B c^2 x^{11/2}",1,"(2*A*b^2*x^(5/2))/5 + (2*b*(b*B + 2*A*c)*x^(7/2))/7 + (2*c*(2*b*B + A*c)*x^(9/2))/9 + (2*B*c^2*x^(11/2))/11","A",2,1,22,0.04545,1,"{765}"
154,1,63,0,0.0312946,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^(3/2),x]","\frac{2}{3} A b^2 x^{3/2}+\frac{2}{7} c x^{7/2} (A c+2 b B)+\frac{2}{5} b x^{5/2} (2 A c+b B)+\frac{2}{9} B c^2 x^{9/2}","\frac{2}{3} A b^2 x^{3/2}+\frac{2}{7} c x^{7/2} (A c+2 b B)+\frac{2}{5} b x^{5/2} (2 A c+b B)+\frac{2}{9} B c^2 x^{9/2}",1,"(2*A*b^2*x^(3/2))/3 + (2*b*(b*B + 2*A*c)*x^(5/2))/5 + (2*c*(2*b*B + A*c)*x^(7/2))/7 + (2*B*c^2*x^(9/2))/9","A",2,1,22,0.04545,1,"{765}"
155,1,61,0,0.030016,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^(5/2),x]","2 A b^2 \sqrt{x}+\frac{2}{5} c x^{5/2} (A c+2 b B)+\frac{2}{3} b x^{3/2} (2 A c+b B)+\frac{2}{7} B c^2 x^{7/2}","2 A b^2 \sqrt{x}+\frac{2}{5} c x^{5/2} (A c+2 b B)+\frac{2}{3} b x^{3/2} (2 A c+b B)+\frac{2}{7} B c^2 x^{7/2}",1,"2*A*b^2*Sqrt[x] + (2*b*(b*B + 2*A*c)*x^(3/2))/3 + (2*c*(2*b*B + A*c)*x^(5/2))/5 + (2*B*c^2*x^(7/2))/7","A",2,1,22,0.04545,1,"{765}"
156,1,59,0,0.029797,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^(7/2),x]","-\frac{2 A b^2}{\sqrt{x}}+\frac{2}{3} c x^{3/2} (A c+2 b B)+2 b \sqrt{x} (2 A c+b B)+\frac{2}{5} B c^2 x^{5/2}","-\frac{2 A b^2}{\sqrt{x}}+\frac{2}{3} c x^{3/2} (A c+2 b B)+2 b \sqrt{x} (2 A c+b B)+\frac{2}{5} B c^2 x^{5/2}",1,"(-2*A*b^2)/Sqrt[x] + 2*b*(b*B + 2*A*c)*Sqrt[x] + (2*c*(2*b*B + A*c)*x^(3/2))/3 + (2*B*c^2*x^(5/2))/5","A",2,1,22,0.04545,1,"{765}"
157,1,59,0,0.0301225,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{x^{9/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/x^(9/2),x]","-\frac{2 A b^2}{3 x^{3/2}}-\frac{2 b (2 A c+b B)}{\sqrt{x}}+2 c \sqrt{x} (A c+2 b B)+\frac{2}{3} B c^2 x^{3/2}","-\frac{2 A b^2}{3 x^{3/2}}-\frac{2 b (2 A c+b B)}{\sqrt{x}}+2 c \sqrt{x} (A c+2 b B)+\frac{2}{3} B c^2 x^{3/2}",1,"(-2*A*b^2)/(3*x^(3/2)) - (2*b*(b*B + 2*A*c))/Sqrt[x] + 2*c*(2*b*B + A*c)*Sqrt[x] + (2*B*c^2*x^(3/2))/3","A",2,1,22,0.04545,1,"{765}"
158,1,85,0,0.0475405,"\int x^{7/2} (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x^(7/2)*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2}{17} b^2 x^{17/2} (3 A c+b B)+\frac{2}{15} A b^3 x^{15/2}+\frac{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{6}{19} b c x^{19/2} (A c+b B)+\frac{2}{23} B c^3 x^{23/2}","\frac{2}{17} b^2 x^{17/2} (3 A c+b B)+\frac{2}{15} A b^3 x^{15/2}+\frac{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{6}{19} b c x^{19/2} (A c+b B)+\frac{2}{23} B c^3 x^{23/2}",1,"(2*A*b^3*x^(15/2))/15 + (2*b^2*(b*B + 3*A*c)*x^(17/2))/17 + (6*b*c*(b*B + A*c)*x^(19/2))/19 + (2*c^2*(3*b*B + A*c)*x^(21/2))/21 + (2*B*c^3*x^(23/2))/23","A",2,1,22,0.04545,1,"{765}"
159,1,85,0,0.0453359,"\int x^{5/2} (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x^(5/2)*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{13} A b^3 x^{13/2}+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{21} B c^3 x^{21/2}","\frac{2}{15} b^2 x^{15/2} (3 A c+b B)+\frac{2}{13} A b^3 x^{13/2}+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{6}{17} b c x^{17/2} (A c+b B)+\frac{2}{21} B c^3 x^{21/2}",1,"(2*A*b^3*x^(13/2))/13 + (2*b^2*(b*B + 3*A*c)*x^(15/2))/15 + (6*b*c*(b*B + A*c)*x^(17/2))/17 + (2*c^2*(3*b*B + A*c)*x^(19/2))/19 + (2*B*c^3*x^(21/2))/21","A",2,1,22,0.04545,1,"{765}"
160,1,85,0,0.0418129,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[x^(3/2)*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{11} A b^3 x^{11/2}+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{19} B c^3 x^{19/2}","\frac{2}{13} b^2 x^{13/2} (3 A c+b B)+\frac{2}{11} A b^3 x^{11/2}+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{5} b c x^{15/2} (A c+b B)+\frac{2}{19} B c^3 x^{19/2}",1,"(2*A*b^3*x^(11/2))/11 + (2*b^2*(b*B + 3*A*c)*x^(13/2))/13 + (2*b*c*(b*B + A*c)*x^(15/2))/5 + (2*c^2*(3*b*B + A*c)*x^(17/2))/17 + (2*B*c^3*x^(19/2))/19","A",2,1,22,0.04545,1,"{765}"
161,1,85,0,0.0420168,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^3,x]","\frac{2}{11} b^2 x^{11/2} (3 A c+b B)+\frac{2}{9} A b^3 x^{9/2}+\frac{2}{15} c^2 x^{15/2} (A c+3 b B)+\frac{6}{13} b c x^{13/2} (A c+b B)+\frac{2}{17} B c^3 x^{17/2}","\frac{2}{11} b^2 x^{11/2} (3 A c+b B)+\frac{2}{9} A b^3 x^{9/2}+\frac{2}{15} c^2 x^{15/2} (A c+3 b B)+\frac{6}{13} b c x^{13/2} (A c+b B)+\frac{2}{17} B c^3 x^{17/2}",1,"(2*A*b^3*x^(9/2))/9 + (2*b^2*(b*B + 3*A*c)*x^(11/2))/11 + (6*b*c*(b*B + A*c)*x^(13/2))/13 + (2*c^2*(3*b*B + A*c)*x^(15/2))/15 + (2*B*c^3*x^(17/2))/17","A",2,1,22,0.04545,1,"{765}"
162,1,85,0,0.0405242,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{\sqrt{x}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/Sqrt[x],x]","\frac{2}{9} b^2 x^{9/2} (3 A c+b B)+\frac{2}{7} A b^3 x^{7/2}+\frac{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{6}{11} b c x^{11/2} (A c+b B)+\frac{2}{15} B c^3 x^{15/2}","\frac{2}{9} b^2 x^{9/2} (3 A c+b B)+\frac{2}{7} A b^3 x^{7/2}+\frac{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{6}{11} b c x^{11/2} (A c+b B)+\frac{2}{15} B c^3 x^{15/2}",1,"(2*A*b^3*x^(7/2))/7 + (2*b^2*(b*B + 3*A*c)*x^(9/2))/9 + (6*b*c*(b*B + A*c)*x^(11/2))/11 + (2*c^2*(3*b*B + A*c)*x^(13/2))/13 + (2*B*c^3*x^(15/2))/15","A",2,1,22,0.04545,1,"{765}"
163,1,85,0,0.0442527,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^(3/2),x]","\frac{2}{7} b^2 x^{7/2} (3 A c+b B)+\frac{2}{5} A b^3 x^{5/2}+\frac{2}{11} c^2 x^{11/2} (A c+3 b B)+\frac{2}{3} b c x^{9/2} (A c+b B)+\frac{2}{13} B c^3 x^{13/2}","\frac{2}{7} b^2 x^{7/2} (3 A c+b B)+\frac{2}{5} A b^3 x^{5/2}+\frac{2}{11} c^2 x^{11/2} (A c+3 b B)+\frac{2}{3} b c x^{9/2} (A c+b B)+\frac{2}{13} B c^3 x^{13/2}",1,"(2*A*b^3*x^(5/2))/5 + (2*b^2*(b*B + 3*A*c)*x^(7/2))/7 + (2*b*c*(b*B + A*c)*x^(9/2))/3 + (2*c^2*(3*b*B + A*c)*x^(11/2))/11 + (2*B*c^3*x^(13/2))/13","A",2,1,22,0.04545,1,"{765}"
164,1,85,0,0.0438203,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^(5/2),x]","\frac{2}{5} b^2 x^{5/2} (3 A c+b B)+\frac{2}{3} A b^3 x^{3/2}+\frac{2}{9} c^2 x^{9/2} (A c+3 b B)+\frac{6}{7} b c x^{7/2} (A c+b B)+\frac{2}{11} B c^3 x^{11/2}","\frac{2}{5} b^2 x^{5/2} (3 A c+b B)+\frac{2}{3} A b^3 x^{3/2}+\frac{2}{9} c^2 x^{9/2} (A c+3 b B)+\frac{6}{7} b c x^{7/2} (A c+b B)+\frac{2}{11} B c^3 x^{11/2}",1,"(2*A*b^3*x^(3/2))/3 + (2*b^2*(b*B + 3*A*c)*x^(5/2))/5 + (6*b*c*(b*B + A*c)*x^(7/2))/7 + (2*c^2*(3*b*B + A*c)*x^(9/2))/9 + (2*B*c^3*x^(11/2))/11","A",2,1,22,0.04545,1,"{765}"
165,1,83,0,0.043835,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^(7/2),x]","\frac{2}{3} b^2 x^{3/2} (3 A c+b B)+2 A b^3 \sqrt{x}+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{6}{5} b c x^{5/2} (A c+b B)+\frac{2}{9} B c^3 x^{9/2}","\frac{2}{3} b^2 x^{3/2} (3 A c+b B)+2 A b^3 \sqrt{x}+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{6}{5} b c x^{5/2} (A c+b B)+\frac{2}{9} B c^3 x^{9/2}",1,"2*A*b^3*Sqrt[x] + (2*b^2*(b*B + 3*A*c)*x^(3/2))/3 + (6*b*c*(b*B + A*c)*x^(5/2))/5 + (2*c^2*(3*b*B + A*c)*x^(7/2))/7 + (2*B*c^3*x^(9/2))/9","A",2,1,22,0.04545,1,"{765}"
166,1,79,0,0.0418045,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{9/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^(9/2),x]","2 b^2 \sqrt{x} (3 A c+b B)-\frac{2 A b^3}{\sqrt{x}}+\frac{2}{5} c^2 x^{5/2} (A c+3 b B)+2 b c x^{3/2} (A c+b B)+\frac{2}{7} B c^3 x^{7/2}","2 b^2 \sqrt{x} (3 A c+b B)-\frac{2 A b^3}{\sqrt{x}}+\frac{2}{5} c^2 x^{5/2} (A c+3 b B)+2 b c x^{3/2} (A c+b B)+\frac{2}{7} B c^3 x^{7/2}",1,"(-2*A*b^3)/Sqrt[x] + 2*b^2*(b*B + 3*A*c)*Sqrt[x] + 2*b*c*(b*B + A*c)*x^(3/2) + (2*c^2*(3*b*B + A*c)*x^(5/2))/5 + (2*B*c^3*x^(7/2))/7","A",2,1,22,0.04545,1,"{765}"
167,1,81,0,0.0416227,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{x^{11/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/x^(11/2),x]","-\frac{2 b^2 (3 A c+b B)}{\sqrt{x}}-\frac{2 A b^3}{3 x^{3/2}}+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+6 b c \sqrt{x} (A c+b B)+\frac{2}{5} B c^3 x^{5/2}","-\frac{2 b^2 (3 A c+b B)}{\sqrt{x}}-\frac{2 A b^3}{3 x^{3/2}}+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+6 b c \sqrt{x} (A c+b B)+\frac{2}{5} B c^3 x^{5/2}",1,"(-2*A*b^3)/(3*x^(3/2)) - (2*b^2*(b*B + 3*A*c))/Sqrt[x] + 6*b*c*(b*B + A*c)*Sqrt[x] + (2*c^2*(3*b*B + A*c)*x^(3/2))/3 + (2*B*c^3*x^(5/2))/5","A",2,1,22,0.04545,1,"{765}"
168,1,113,0,0.0712113,"\int \frac{x^{7/2} (A+B x)}{b x+c x^2} \, dx","Int[(x^(7/2)*(A + B*x))/(b*x + c*x^2),x]","-\frac{2 b^2 \sqrt{x} (b B-A c)}{c^4}+\frac{2 b^{5/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{9/2}}-\frac{2 x^{5/2} (b B-A c)}{5 c^2}+\frac{2 b x^{3/2} (b B-A c)}{3 c^3}+\frac{2 B x^{7/2}}{7 c}","-\frac{2 b^2 \sqrt{x} (b B-A c)}{c^4}+\frac{2 b^{5/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{9/2}}-\frac{2 x^{5/2} (b B-A c)}{5 c^2}+\frac{2 b x^{3/2} (b B-A c)}{3 c^3}+\frac{2 B x^{7/2}}{7 c}",1,"(-2*b^2*(b*B - A*c)*Sqrt[x])/c^4 + (2*b*(b*B - A*c)*x^(3/2))/(3*c^3) - (2*(b*B - A*c)*x^(5/2))/(5*c^2) + (2*B*x^(7/2))/(7*c) + (2*b^(5/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(9/2)","A",7,5,22,0.2273,1,"{781, 80, 50, 63, 205}"
169,1,90,0,0.0484572,"\int \frac{x^{5/2} (A+B x)}{b x+c x^2} \, dx","Int[(x^(5/2)*(A + B*x))/(b*x + c*x^2),x]","-\frac{2 b^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 b \sqrt{x} (b B-A c)}{c^3}+\frac{2 B x^{5/2}}{5 c}","-\frac{2 b^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 b \sqrt{x} (b B-A c)}{c^3}+\frac{2 B x^{5/2}}{5 c}",1,"(2*b*(b*B - A*c)*Sqrt[x])/c^3 - (2*(b*B - A*c)*x^(3/2))/(3*c^2) + (2*B*x^(5/2))/(5*c) - (2*b^(3/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(7/2)","A",6,5,22,0.2273,1,"{781, 80, 50, 63, 205}"
170,1,69,0,0.0385251,"\int \frac{x^{3/2} (A+B x)}{b x+c x^2} \, dx","Int[(x^(3/2)*(A + B*x))/(b*x + c*x^2),x]","-\frac{2 \sqrt{x} (b B-A c)}{c^2}+\frac{2 \sqrt{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{5/2}}+\frac{2 B x^{3/2}}{3 c}","-\frac{2 \sqrt{x} (b B-A c)}{c^2}+\frac{2 \sqrt{b} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{5/2}}+\frac{2 B x^{3/2}}{3 c}",1,"(-2*(b*B - A*c)*Sqrt[x])/c^2 + (2*B*x^(3/2))/(3*c) + (2*Sqrt[b]*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(5/2)","A",5,5,22,0.2273,1,"{781, 80, 50, 63, 205}"
171,1,49,0,0.026395,"\int \frac{\sqrt{x} (A+B x)}{b x+c x^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(b*x + c*x^2),x]","\frac{2 B \sqrt{x}}{c}-\frac{2 (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} c^{3/2}}","\frac{2 B \sqrt{x}}{c}-\frac{2 (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} c^{3/2}}",1,"(2*B*Sqrt[x])/c - (2*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*c^(3/2))","A",4,4,22,0.1818,1,"{781, 80, 63, 205}"
172,1,49,0,0.0294378,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)),x]","\frac{2 (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{3/2} \sqrt{c}}-\frac{2 A}{b \sqrt{x}}","\frac{2 (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{3/2} \sqrt{c}}-\frac{2 A}{b \sqrt{x}}",1,"(-2*A)/(b*Sqrt[x]) + (2*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(b^(3/2)*Sqrt[c])","A",4,4,22,0.1818,1,"{781, 78, 63, 205}"
173,1,69,0,0.0417975,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(3/2)*(b*x + c*x^2)),x]","-\frac{2 (b B-A c)}{b^2 \sqrt{x}}-\frac{2 \sqrt{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}-\frac{2 A}{3 b x^{3/2}}","-\frac{2 (b B-A c)}{b^2 \sqrt{x}}-\frac{2 \sqrt{c} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2}}-\frac{2 A}{3 b x^{3/2}}",1,"(-2*A)/(3*b*x^(3/2)) - (2*(b*B - A*c))/(b^2*Sqrt[x]) - (2*Sqrt[c]*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(5/2)","A",5,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
174,1,90,0,0.0534538,"\int \frac{A+B x}{x^{5/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(5/2)*(b*x + c*x^2)),x]","\frac{2 c^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}-\frac{2 (b B-A c)}{3 b^2 x^{3/2}}+\frac{2 c (b B-A c)}{b^3 \sqrt{x}}-\frac{2 A}{5 b x^{5/2}}","\frac{2 c^{3/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}-\frac{2 (b B-A c)}{3 b^2 x^{3/2}}+\frac{2 c (b B-A c)}{b^3 \sqrt{x}}-\frac{2 A}{5 b x^{5/2}}",1,"(-2*A)/(5*b*x^(5/2)) - (2*(b*B - A*c))/(3*b^2*x^(3/2)) + (2*c*(b*B - A*c))/(b^3*Sqrt[x]) + (2*c^(3/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(7/2)","A",6,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
175,1,113,0,0.0676766,"\int \frac{A+B x}{x^{7/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(7/2)*(b*x + c*x^2)),x]","-\frac{2 c^2 (b B-A c)}{b^4 \sqrt{x}}-\frac{2 c^{5/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}+\frac{2 c (b B-A c)}{3 b^3 x^{3/2}}-\frac{2 (b B-A c)}{5 b^2 x^{5/2}}-\frac{2 A}{7 b x^{7/2}}","-\frac{2 c^2 (b B-A c)}{b^4 \sqrt{x}}-\frac{2 c^{5/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}+\frac{2 c (b B-A c)}{3 b^3 x^{3/2}}-\frac{2 (b B-A c)}{5 b^2 x^{5/2}}-\frac{2 A}{7 b x^{7/2}}",1,"(-2*A)/(7*b*x^(7/2)) - (2*(b*B - A*c))/(5*b^2*x^(5/2)) + (2*c*(b*B - A*c))/(3*b^3*x^(3/2)) - (2*c^2*(b*B - A*c))/(b^4*Sqrt[x]) - (2*c^(5/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(9/2)","A",7,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
176,1,136,0,0.0800834,"\int \frac{A+B x}{x^{9/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(9/2)*(b*x + c*x^2)),x]","-\frac{2 c^2 (b B-A c)}{3 b^4 x^{3/2}}+\frac{2 c^3 (b B-A c)}{b^5 \sqrt{x}}+\frac{2 c^{7/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{11/2}}+\frac{2 c (b B-A c)}{5 b^3 x^{5/2}}-\frac{2 (b B-A c)}{7 b^2 x^{7/2}}-\frac{2 A}{9 b x^{9/2}}","-\frac{2 c^2 (b B-A c)}{3 b^4 x^{3/2}}+\frac{2 c^3 (b B-A c)}{b^5 \sqrt{x}}+\frac{2 c^{7/2} (b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{11/2}}+\frac{2 c (b B-A c)}{5 b^3 x^{5/2}}-\frac{2 (b B-A c)}{7 b^2 x^{7/2}}-\frac{2 A}{9 b x^{9/2}}",1,"(-2*A)/(9*b*x^(9/2)) - (2*(b*B - A*c))/(7*b^2*x^(7/2)) + (2*c*(b*B - A*c))/(5*b^3*x^(5/2)) - (2*c^2*(b*B - A*c))/(3*b^4*x^(3/2)) + (2*c^3*(b*B - A*c))/(b^5*Sqrt[x]) + (2*c^(7/2)*(b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(11/2)","A",8,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
177,1,131,0,0.0697185,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^2,x]","-\frac{b^{3/2} (7 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{9/2}}+\frac{x^{5/2} (7 b B-5 A c)}{5 b c^2}-\frac{x^{3/2} (7 b B-5 A c)}{3 c^3}+\frac{b \sqrt{x} (7 b B-5 A c)}{c^4}-\frac{x^{7/2} (b B-A c)}{b c (b+c x)}","-\frac{b^{3/2} (7 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{9/2}}+\frac{x^{5/2} (7 b B-5 A c)}{5 b c^2}-\frac{x^{3/2} (7 b B-5 A c)}{3 c^3}+\frac{b \sqrt{x} (7 b B-5 A c)}{c^4}-\frac{x^{7/2} (b B-A c)}{b c (b+c x)}",1,"(b*(7*b*B - 5*A*c)*Sqrt[x])/c^4 - ((7*b*B - 5*A*c)*x^(3/2))/(3*c^3) + ((7*b*B - 5*A*c)*x^(5/2))/(5*b*c^2) - ((b*B - A*c)*x^(7/2))/(b*c*(b + c*x)) - (b^(3/2)*(7*b*B - 5*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(9/2)","A",7,5,22,0.2273,1,"{781, 78, 50, 63, 205}"
178,1,109,0,0.0557021,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{x^{3/2} (5 b B-3 A c)}{3 b c^2}-\frac{\sqrt{x} (5 b B-3 A c)}{c^3}+\frac{\sqrt{b} (5 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}-\frac{x^{5/2} (b B-A c)}{b c (b+c x)}","\frac{x^{3/2} (5 b B-3 A c)}{3 b c^2}-\frac{\sqrt{x} (5 b B-3 A c)}{c^3}+\frac{\sqrt{b} (5 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{c^{7/2}}-\frac{x^{5/2} (b B-A c)}{b c (b+c x)}",1,"-(((5*b*B - 3*A*c)*Sqrt[x])/c^3) + ((5*b*B - 3*A*c)*x^(3/2))/(3*b*c^2) - ((b*B - A*c)*x^(5/2))/(b*c*(b + c*x)) + (Sqrt[b]*(5*b*B - 3*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/c^(7/2)","A",6,5,22,0.2273,1,"{781, 78, 50, 63, 205}"
179,1,88,0,0.0431694,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{\sqrt{x} (3 b B-A c)}{b c^2}-\frac{(3 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} c^{5/2}}-\frac{x^{3/2} (b B-A c)}{b c (b+c x)}","\frac{\sqrt{x} (3 b B-A c)}{b c^2}-\frac{(3 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{\sqrt{b} c^{5/2}}-\frac{x^{3/2} (b B-A c)}{b c (b+c x)}",1,"((3*b*B - A*c)*Sqrt[x])/(b*c^2) - ((b*B - A*c)*x^(3/2))/(b*c*(b + c*x)) - ((3*b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(Sqrt[b]*c^(5/2))","A",5,5,22,0.2273,1,"{781, 78, 50, 63, 205}"
180,1,64,0,0.0311665,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Int[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{(A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{3/2} c^{3/2}}-\frac{\sqrt{x} (b B-A c)}{b c (b+c x)}","\frac{(A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{3/2} c^{3/2}}-\frac{\sqrt{x} (b B-A c)}{b c (b+c x)}",1,"-(((b*B - A*c)*Sqrt[x])/(b*c*(b + c*x))) + ((b*B + A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(b^(3/2)*c^(3/2))","A",4,4,22,0.1818,1,"{781, 78, 63, 205}"
181,1,85,0,0.0448304,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^2,x]","\frac{b B-3 A c}{b^2 c \sqrt{x}}+\frac{(b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2} \sqrt{c}}-\frac{b B-A c}{b c \sqrt{x} (b+c x)}","\frac{b B-3 A c}{b^2 c \sqrt{x}}+\frac{(b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{5/2} \sqrt{c}}-\frac{b B-A c}{b c \sqrt{x} (b+c x)}",1,"(b*B - 3*A*c)/(b^2*c*Sqrt[x]) - (b*B - A*c)/(b*c*Sqrt[x]*(b + c*x)) + ((b*B - 3*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(b^(5/2)*Sqrt[c])","A",5,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
182,1,110,0,0.0554794,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^2),x]","\frac{3 b B-5 A c}{3 b^2 c x^{3/2}}-\frac{3 b B-5 A c}{b^3 \sqrt{x}}-\frac{\sqrt{c} (3 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}-\frac{b B-A c}{b c x^{3/2} (b+c x)}","\frac{3 b B-5 A c}{3 b^2 c x^{3/2}}-\frac{3 b B-5 A c}{b^3 \sqrt{x}}-\frac{\sqrt{c} (3 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{7/2}}-\frac{b B-A c}{b c x^{3/2} (b+c x)}",1,"(3*b*B - 5*A*c)/(3*b^2*c*x^(3/2)) - (3*b*B - 5*A*c)/(b^3*Sqrt[x]) - (b*B - A*c)/(b*c*x^(3/2)*(b + c*x)) - (Sqrt[c]*(3*b*B - 5*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(7/2)","A",6,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
183,1,130,0,0.0702908,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^2),x]","\frac{c^{3/2} (5 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}-\frac{5 b B-7 A c}{3 b^3 x^{3/2}}+\frac{5 b B-7 A c}{5 b^2 c x^{5/2}}+\frac{c (5 b B-7 A c)}{b^4 \sqrt{x}}-\frac{b B-A c}{b c x^{5/2} (b+c x)}","\frac{c^{3/2} (5 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{9/2}}-\frac{5 b B-7 A c}{3 b^3 x^{3/2}}+\frac{5 b B-7 A c}{5 b^2 c x^{5/2}}+\frac{c (5 b B-7 A c)}{b^4 \sqrt{x}}-\frac{b B-A c}{b c x^{5/2} (b+c x)}",1,"(5*b*B - 7*A*c)/(5*b^2*c*x^(5/2)) - (5*b*B - 7*A*c)/(3*b^3*x^(3/2)) + (c*(5*b*B - 7*A*c))/(b^4*Sqrt[x]) - (b*B - A*c)/(b*c*x^(5/2)*(b + c*x)) + (c^(3/2)*(5*b*B - 7*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(9/2)","A",7,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
184,1,156,0,0.082545,"\int \frac{A+B x}{x^{5/2} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(x^(5/2)*(b*x + c*x^2)^2),x]","-\frac{c^2 (7 b B-9 A c)}{b^5 \sqrt{x}}-\frac{c^{5/2} (7 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{11/2}}+\frac{c (7 b B-9 A c)}{3 b^4 x^{3/2}}-\frac{7 b B-9 A c}{5 b^3 x^{5/2}}+\frac{7 b B-9 A c}{7 b^2 c x^{7/2}}-\frac{b B-A c}{b c x^{7/2} (b+c x)}","-\frac{c^2 (7 b B-9 A c)}{b^5 \sqrt{x}}-\frac{c^{5/2} (7 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{b^{11/2}}+\frac{c (7 b B-9 A c)}{3 b^4 x^{3/2}}-\frac{7 b B-9 A c}{5 b^3 x^{5/2}}+\frac{7 b B-9 A c}{7 b^2 c x^{7/2}}-\frac{b B-A c}{b c x^{7/2} (b+c x)}",1,"(7*b*B - 9*A*c)/(7*b^2*c*x^(7/2)) - (7*b*B - 9*A*c)/(5*b^3*x^(5/2)) + (c*(7*b*B - 9*A*c))/(3*b^4*x^(3/2)) - (c^2*(7*b*B - 9*A*c))/(b^5*Sqrt[x]) - (b*B - A*c)/(b*c*x^(7/2)*(b + c*x)) - (c^(5/2)*(7*b*B - 9*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/b^(11/2)","A",8,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
185,1,169,0,0.0890839,"\int \frac{x^{13/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^(13/2)*(A + B*x))/(b*x + c*x^2)^3,x]","-\frac{7 b^{3/2} (9 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 c^{11/2}}-\frac{x^{7/2} (9 b B-5 A c)}{4 b c^2 (b+c x)}+\frac{7 x^{5/2} (9 b B-5 A c)}{20 b c^3}-\frac{7 x^{3/2} (9 b B-5 A c)}{12 c^4}+\frac{7 b \sqrt{x} (9 b B-5 A c)}{4 c^5}-\frac{x^{9/2} (b B-A c)}{2 b c (b+c x)^2}","-\frac{7 b^{3/2} (9 b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 c^{11/2}}-\frac{x^{7/2} (9 b B-5 A c)}{4 b c^2 (b+c x)}+\frac{7 x^{5/2} (9 b B-5 A c)}{20 b c^3}-\frac{7 x^{3/2} (9 b B-5 A c)}{12 c^4}+\frac{7 b \sqrt{x} (9 b B-5 A c)}{4 c^5}-\frac{x^{9/2} (b B-A c)}{2 b c (b+c x)^2}",1,"(7*b*(9*b*B - 5*A*c)*Sqrt[x])/(4*c^5) - (7*(9*b*B - 5*A*c)*x^(3/2))/(12*c^4) + (7*(9*b*B - 5*A*c)*x^(5/2))/(20*b*c^3) - ((b*B - A*c)*x^(9/2))/(2*b*c*(b + c*x)^2) - ((9*b*B - 5*A*c)*x^(7/2))/(4*b*c^2*(b + c*x)) - (7*b^(3/2)*(9*b*B - 5*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*c^(11/2))","A",8,6,22,0.2727,1,"{781, 78, 47, 50, 63, 205}"
186,1,147,0,0.070526,"\int \frac{x^{11/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^(11/2)*(A + B*x))/(b*x + c*x^2)^3,x]","-\frac{x^{5/2} (7 b B-3 A c)}{4 b c^2 (b+c x)}+\frac{5 x^{3/2} (7 b B-3 A c)}{12 b c^3}-\frac{5 \sqrt{x} (7 b B-3 A c)}{4 c^4}+\frac{5 \sqrt{b} (7 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 c^{9/2}}-\frac{x^{7/2} (b B-A c)}{2 b c (b+c x)^2}","-\frac{x^{5/2} (7 b B-3 A c)}{4 b c^2 (b+c x)}+\frac{5 x^{3/2} (7 b B-3 A c)}{12 b c^3}-\frac{5 \sqrt{x} (7 b B-3 A c)}{4 c^4}+\frac{5 \sqrt{b} (7 b B-3 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 c^{9/2}}-\frac{x^{7/2} (b B-A c)}{2 b c (b+c x)^2}",1,"(-5*(7*b*B - 3*A*c)*Sqrt[x])/(4*c^4) + (5*(7*b*B - 3*A*c)*x^(3/2))/(12*b*c^3) - ((b*B - A*c)*x^(7/2))/(2*b*c*(b + c*x)^2) - ((7*b*B - 3*A*c)*x^(5/2))/(4*b*c^2*(b + c*x)) + (5*Sqrt[b]*(7*b*B - 3*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*c^(9/2))","A",7,6,22,0.2727,1,"{781, 78, 47, 50, 63, 205}"
187,1,126,0,0.0588881,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^3,x]","-\frac{x^{3/2} (5 b B-A c)}{4 b c^2 (b+c x)}+\frac{3 \sqrt{x} (5 b B-A c)}{4 b c^3}-\frac{3 (5 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 \sqrt{b} c^{7/2}}-\frac{x^{5/2} (b B-A c)}{2 b c (b+c x)^2}","-\frac{x^{3/2} (5 b B-A c)}{4 b c^2 (b+c x)}+\frac{3 \sqrt{x} (5 b B-A c)}{4 b c^3}-\frac{3 (5 b B-A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 \sqrt{b} c^{7/2}}-\frac{x^{5/2} (b B-A c)}{2 b c (b+c x)^2}",1,"(3*(5*b*B - A*c)*Sqrt[x])/(4*b*c^3) - ((b*B - A*c)*x^(5/2))/(2*b*c*(b + c*x)^2) - ((5*b*B - A*c)*x^(3/2))/(4*b*c^2*(b + c*x)) - (3*(5*b*B - A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*Sqrt[b]*c^(7/2))","A",6,6,22,0.2727,1,"{781, 78, 47, 50, 63, 205}"
188,1,100,0,0.0491069,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{(A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{3/2} c^{5/2}}-\frac{\sqrt{x} (A c+3 b B)}{4 b c^2 (b+c x)}-\frac{x^{3/2} (b B-A c)}{2 b c (b+c x)^2}","\frac{(A c+3 b B) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{3/2} c^{5/2}}-\frac{\sqrt{x} (A c+3 b B)}{4 b c^2 (b+c x)}-\frac{x^{3/2} (b B-A c)}{2 b c (b+c x)^2}",1,"-((b*B - A*c)*x^(3/2))/(2*b*c*(b + c*x)^2) - ((3*b*B + A*c)*Sqrt[x])/(4*b*c^2*(b + c*x)) + ((3*b*B + A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(3/2)*c^(5/2))","A",5,5,22,0.2273,1,"{781, 78, 47, 63, 205}"
189,1,100,0,0.0479337,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{(3 A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{5/2} c^{3/2}}+\frac{\sqrt{x} (3 A c+b B)}{4 b^2 c (b+c x)}-\frac{\sqrt{x} (b B-A c)}{2 b c (b+c x)^2}","\frac{(3 A c+b B) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{5/2} c^{3/2}}+\frac{\sqrt{x} (3 A c+b B)}{4 b^2 c (b+c x)}-\frac{\sqrt{x} (b B-A c)}{2 b c (b+c x)^2}",1,"-((b*B - A*c)*Sqrt[x])/(2*b*c*(b + c*x)^2) + ((b*B + 3*A*c)*Sqrt[x])/(4*b^2*c*(b + c*x)) + ((b*B + 3*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(5/2)*c^(3/2))","A",5,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
190,1,123,0,0.0580332,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^3,x]","\frac{3 (b B-5 A c)}{4 b^3 c \sqrt{x}}-\frac{b B-5 A c}{4 b^2 c \sqrt{x} (b+c x)}+\frac{3 (b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{7/2} \sqrt{c}}-\frac{b B-A c}{2 b c \sqrt{x} (b+c x)^2}","\frac{3 (b B-5 A c)}{4 b^3 c \sqrt{x}}-\frac{b B-5 A c}{4 b^2 c \sqrt{x} (b+c x)}+\frac{3 (b B-5 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{7/2} \sqrt{c}}-\frac{b B-A c}{2 b c \sqrt{x} (b+c x)^2}",1,"(3*(b*B - 5*A*c))/(4*b^3*c*Sqrt[x]) - (b*B - A*c)/(2*b*c*Sqrt[x]*(b + c*x)^2) - (b*B - 5*A*c)/(4*b^2*c*Sqrt[x]*(b + c*x)) + (3*(b*B - 5*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(7/2)*Sqrt[c])","A",6,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
191,1,147,0,0.0683295,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^3,x]","-\frac{3 b B-7 A c}{4 b^2 c x^{3/2} (b+c x)}+\frac{5 (3 b B-7 A c)}{12 b^3 c x^{3/2}}-\frac{5 (3 b B-7 A c)}{4 b^4 \sqrt{x}}-\frac{5 \sqrt{c} (3 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{9/2}}-\frac{b B-A c}{2 b c x^{3/2} (b+c x)^2}","-\frac{3 b B-7 A c}{4 b^2 c x^{3/2} (b+c x)}+\frac{5 (3 b B-7 A c)}{12 b^3 c x^{3/2}}-\frac{5 (3 b B-7 A c)}{4 b^4 \sqrt{x}}-\frac{5 \sqrt{c} (3 b B-7 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{9/2}}-\frac{b B-A c}{2 b c x^{3/2} (b+c x)^2}",1,"(5*(3*b*B - 7*A*c))/(12*b^3*c*x^(3/2)) - (5*(3*b*B - 7*A*c))/(4*b^4*Sqrt[x]) - (b*B - A*c)/(2*b*c*x^(3/2)*(b + c*x)^2) - (3*b*B - 7*A*c)/(4*b^2*c*x^(3/2)*(b + c*x)) - (5*Sqrt[c]*(3*b*B - 7*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(9/2))","A",7,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
192,1,169,0,0.0873458,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^3),x]","\frac{7 c^{3/2} (5 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{11/2}}-\frac{7 (5 b B-9 A c)}{12 b^4 x^{3/2}}-\frac{5 b B-9 A c}{4 b^2 c x^{5/2} (b+c x)}+\frac{7 (5 b B-9 A c)}{20 b^3 c x^{5/2}}+\frac{7 c (5 b B-9 A c)}{4 b^5 \sqrt{x}}-\frac{b B-A c}{2 b c x^{5/2} (b+c x)^2}","\frac{7 c^{3/2} (5 b B-9 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{11/2}}-\frac{7 (5 b B-9 A c)}{12 b^4 x^{3/2}}-\frac{5 b B-9 A c}{4 b^2 c x^{5/2} (b+c x)}+\frac{7 (5 b B-9 A c)}{20 b^3 c x^{5/2}}+\frac{7 c (5 b B-9 A c)}{4 b^5 \sqrt{x}}-\frac{b B-A c}{2 b c x^{5/2} (b+c x)^2}",1,"(7*(5*b*B - 9*A*c))/(20*b^3*c*x^(5/2)) - (7*(5*b*B - 9*A*c))/(12*b^4*x^(3/2)) + (7*c*(5*b*B - 9*A*c))/(4*b^5*Sqrt[x]) - (b*B - A*c)/(2*b*c*x^(5/2)*(b + c*x)^2) - (5*b*B - 9*A*c)/(4*b^2*c*x^(5/2)*(b + c*x)) + (7*c^(3/2)*(5*b*B - 9*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(11/2))","A",8,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
193,1,193,0,0.1010739,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^3),x]","-\frac{9 c^2 (7 b B-11 A c)}{4 b^6 \sqrt{x}}-\frac{9 c^{5/2} (7 b B-11 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{13/2}}+\frac{3 c (7 b B-11 A c)}{4 b^5 x^{3/2}}-\frac{9 (7 b B-11 A c)}{20 b^4 x^{5/2}}-\frac{7 b B-11 A c}{4 b^2 c x^{7/2} (b+c x)}+\frac{9 (7 b B-11 A c)}{28 b^3 c x^{7/2}}-\frac{b B-A c}{2 b c x^{7/2} (b+c x)^2}","-\frac{9 c^2 (7 b B-11 A c)}{4 b^6 \sqrt{x}}-\frac{9 c^{5/2} (7 b B-11 A c) \tan ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{b}}\right)}{4 b^{13/2}}+\frac{3 c (7 b B-11 A c)}{4 b^5 x^{3/2}}-\frac{9 (7 b B-11 A c)}{20 b^4 x^{5/2}}-\frac{7 b B-11 A c}{4 b^2 c x^{7/2} (b+c x)}+\frac{9 (7 b B-11 A c)}{28 b^3 c x^{7/2}}-\frac{b B-A c}{2 b c x^{7/2} (b+c x)^2}",1,"(9*(7*b*B - 11*A*c))/(28*b^3*c*x^(7/2)) - (9*(7*b*B - 11*A*c))/(20*b^4*x^(5/2)) + (3*c*(7*b*B - 11*A*c))/(4*b^5*x^(3/2)) - (9*c^2*(7*b*B - 11*A*c))/(4*b^6*Sqrt[x]) - (b*B - A*c)/(2*b*c*x^(7/2)*(b + c*x)^2) - (7*b*B - 11*A*c)/(4*b^2*c*x^(7/2)*(b + c*x)) - (9*c^(5/2)*(7*b*B - 11*A*c)*ArcTan[(Sqrt[c]*Sqrt[x])/Sqrt[b]])/(4*b^(13/2))","A",9,5,22,0.2273,1,"{781, 78, 51, 63, 205}"
194,1,207,0,0.194197,"\int x^{7/2} (A+B x) \sqrt{b x+c x^2} \, dx","Int[x^(7/2)*(A + B*x)*Sqrt[b*x + c*x^2],x]","-\frac{256 b^4 \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{45045 c^6 x^{3/2}}+\frac{128 b^3 \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{15015 c^5 \sqrt{x}}-\frac{32 b^2 \sqrt{x} \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{3003 c^4}+\frac{16 b x^{3/2} \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{1287 c^3}-\frac{2 x^{5/2} \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{143 c^2}+\frac{2 B x^{7/2} \left(b x+c x^2\right)^{3/2}}{13 c}","-\frac{256 b^4 \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{45045 c^6 x^{3/2}}+\frac{128 b^3 \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{15015 c^5 \sqrt{x}}-\frac{32 b^2 \sqrt{x} \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{3003 c^4}+\frac{16 b x^{3/2} \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{1287 c^3}-\frac{2 x^{5/2} \left(b x+c x^2\right)^{3/2} (10 b B-13 A c)}{143 c^2}+\frac{2 B x^{7/2} \left(b x+c x^2\right)^{3/2}}{13 c}",1,"(-256*b^4*(10*b*B - 13*A*c)*(b*x + c*x^2)^(3/2))/(45045*c^6*x^(3/2)) + (128*b^3*(10*b*B - 13*A*c)*(b*x + c*x^2)^(3/2))/(15015*c^5*Sqrt[x]) - (32*b^2*(10*b*B - 13*A*c)*Sqrt[x]*(b*x + c*x^2)^(3/2))/(3003*c^4) + (16*b*(10*b*B - 13*A*c)*x^(3/2)*(b*x + c*x^2)^(3/2))/(1287*c^3) - (2*(10*b*B - 13*A*c)*x^(5/2)*(b*x + c*x^2)^(3/2))/(143*c^2) + (2*B*x^(7/2)*(b*x + c*x^2)^(3/2))/(13*c)","A",6,3,24,0.1250,1,"{794, 656, 648}"
195,1,170,0,0.1586239,"\int x^{5/2} (A+B x) \sqrt{b x+c x^2} \, dx","Int[x^(5/2)*(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{32 b^3 \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{3465 c^5 x^{3/2}}-\frac{16 b^2 \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{1155 c^4 \sqrt{x}}+\frac{4 b \sqrt{x} \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{231 c^3}-\frac{2 x^{3/2} \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{99 c^2}+\frac{2 B x^{5/2} \left(b x+c x^2\right)^{3/2}}{11 c}","\frac{32 b^3 \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{3465 c^5 x^{3/2}}-\frac{16 b^2 \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{1155 c^4 \sqrt{x}}+\frac{4 b \sqrt{x} \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{231 c^3}-\frac{2 x^{3/2} \left(b x+c x^2\right)^{3/2} (8 b B-11 A c)}{99 c^2}+\frac{2 B x^{5/2} \left(b x+c x^2\right)^{3/2}}{11 c}",1,"(32*b^3*(8*b*B - 11*A*c)*(b*x + c*x^2)^(3/2))/(3465*c^5*x^(3/2)) - (16*b^2*(8*b*B - 11*A*c)*(b*x + c*x^2)^(3/2))/(1155*c^4*Sqrt[x]) + (4*b*(8*b*B - 11*A*c)*Sqrt[x]*(b*x + c*x^2)^(3/2))/(231*c^3) - (2*(8*b*B - 11*A*c)*x^(3/2)*(b*x + c*x^2)^(3/2))/(99*c^2) + (2*B*x^(5/2)*(b*x + c*x^2)^(3/2))/(11*c)","A",5,3,24,0.1250,1,"{794, 656, 648}"
196,1,133,0,0.0948934,"\int x^{3/2} (A+B x) \sqrt{b x+c x^2} \, dx","Int[x^(3/2)*(A + B*x)*Sqrt[b*x + c*x^2],x]","-\frac{16 b^2 \left(b x+c x^2\right)^{3/2} (2 b B-3 A c)}{315 c^4 x^{3/2}}+\frac{8 b \left(b x+c x^2\right)^{3/2} (2 b B-3 A c)}{105 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \left(b x+c x^2\right)^{3/2} (2 b B-3 A c)}{21 c^2}+\frac{2 B x^{3/2} \left(b x+c x^2\right)^{3/2}}{9 c}","-\frac{16 b^2 \left(b x+c x^2\right)^{3/2} (2 b B-3 A c)}{315 c^4 x^{3/2}}+\frac{8 b \left(b x+c x^2\right)^{3/2} (2 b B-3 A c)}{105 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \left(b x+c x^2\right)^{3/2} (2 b B-3 A c)}{21 c^2}+\frac{2 B x^{3/2} \left(b x+c x^2\right)^{3/2}}{9 c}",1,"(-16*b^2*(2*b*B - 3*A*c)*(b*x + c*x^2)^(3/2))/(315*c^4*x^(3/2)) + (8*b*(2*b*B - 3*A*c)*(b*x + c*x^2)^(3/2))/(105*c^3*Sqrt[x]) - (2*(2*b*B - 3*A*c)*Sqrt[x]*(b*x + c*x^2)^(3/2))/(21*c^2) + (2*B*x^(3/2)*(b*x + c*x^2)^(3/2))/(9*c)","A",4,3,24,0.1250,1,"{794, 656, 648}"
197,1,96,0,0.0761511,"\int \sqrt{x} (A+B x) \sqrt{b x+c x^2} \, dx","Int[Sqrt[x]*(A + B*x)*Sqrt[b*x + c*x^2],x]","-\frac{2 \left(b x+c x^2\right)^{3/2} (4 b B-7 A c)}{35 c^2 \sqrt{x}}+\frac{4 b \left(b x+c x^2\right)^{3/2} (4 b B-7 A c)}{105 c^3 x^{3/2}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{3/2}}{7 c}","-\frac{2 \left(b x+c x^2\right)^{3/2} (4 b B-7 A c)}{35 c^2 \sqrt{x}}+\frac{4 b \left(b x+c x^2\right)^{3/2} (4 b B-7 A c)}{105 c^3 x^{3/2}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{3/2}}{7 c}",1,"(4*b*(4*b*B - 7*A*c)*(b*x + c*x^2)^(3/2))/(105*c^3*x^(3/2)) - (2*(4*b*B - 7*A*c)*(b*x + c*x^2)^(3/2))/(35*c^2*Sqrt[x]) + (2*B*Sqrt[x]*(b*x + c*x^2)^(3/2))/(7*c)","A",3,3,24,0.1250,1,"{794, 656, 648}"
198,1,61,0,0.042698,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{\sqrt{x}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/Sqrt[x],x]","\frac{2 B \left(b x+c x^2\right)^{3/2}}{5 c \sqrt{x}}-\frac{2 \left(b x+c x^2\right)^{3/2} (2 b B-5 A c)}{15 c^2 x^{3/2}}","\frac{2 B \left(b x+c x^2\right)^{3/2}}{5 c \sqrt{x}}-\frac{2 \left(b x+c x^2\right)^{3/2} (2 b B-5 A c)}{15 c^2 x^{3/2}}",1,"(-2*(2*b*B - 5*A*c)*(b*x + c*x^2)^(3/2))/(15*c^2*x^(3/2)) + (2*B*(b*x + c*x^2)^(3/2))/(5*c*Sqrt[x])","A",2,2,24,0.08333,1,"{794, 648}"
199,1,81,0,0.0648041,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{3/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^(3/2),x]","\frac{2 A \sqrt{b x+c x^2}}{\sqrt{x}}-2 A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 B \left(b x+c x^2\right)^{3/2}}{3 c x^{3/2}}","\frac{2 A \sqrt{b x+c x^2}}{\sqrt{x}}-2 A \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 B \left(b x+c x^2\right)^{3/2}}{3 c x^{3/2}}",1,"(2*A*Sqrt[b*x + c*x^2])/Sqrt[x] + (2*B*(b*x + c*x^2)^(3/2))/(3*c*x^(3/2)) - 2*A*Sqrt[b]*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",4,4,24,0.1667,1,"{794, 664, 660, 207}"
200,1,95,0,0.0912353,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{5/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^(5/2),x]","\frac{\sqrt{b x+c x^2} (A c+2 b B)}{b \sqrt{x}}-\frac{(A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{\sqrt{b}}-\frac{A \left(b x+c x^2\right)^{3/2}}{b x^{5/2}}","\frac{\sqrt{b x+c x^2} (A c+2 b B)}{b \sqrt{x}}-\frac{(A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{\sqrt{b}}-\frac{A \left(b x+c x^2\right)^{3/2}}{b x^{5/2}}",1,"((2*b*B + A*c)*Sqrt[b*x + c*x^2])/(b*Sqrt[x]) - (A*(b*x + c*x^2)^(3/2))/(b*x^(5/2)) - ((2*b*B + A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/Sqrt[b]","A",4,4,24,0.1667,1,"{792, 664, 660, 207}"
201,1,105,0,0.0924073,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{7/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^(7/2),x]","-\frac{c (4 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{3/2}}-\frac{\sqrt{b x+c x^2} (4 b B-A c)}{4 b x^{3/2}}-\frac{A \left(b x+c x^2\right)^{3/2}}{2 b x^{7/2}}","-\frac{c (4 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{3/2}}-\frac{\sqrt{b x+c x^2} (4 b B-A c)}{4 b x^{3/2}}-\frac{A \left(b x+c x^2\right)^{3/2}}{2 b x^{7/2}}",1,"-((4*b*B - A*c)*Sqrt[b*x + c*x^2])/(4*b*x^(3/2)) - (A*(b*x + c*x^2)^(3/2))/(2*b*x^(7/2)) - (c*(4*b*B - A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(3/2))","A",4,4,24,0.1667,1,"{792, 662, 660, 207}"
202,1,142,0,0.1195385,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{x^{9/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/x^(9/2),x]","\frac{c^2 (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{5/2}}-\frac{c \sqrt{b x+c x^2} (2 b B-A c)}{8 b^2 x^{3/2}}-\frac{\sqrt{b x+c x^2} (2 b B-A c)}{4 b x^{5/2}}-\frac{A \left(b x+c x^2\right)^{3/2}}{3 b x^{9/2}}","\frac{c^2 (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{5/2}}-\frac{c \sqrt{b x+c x^2} (2 b B-A c)}{8 b^2 x^{3/2}}-\frac{\sqrt{b x+c x^2} (2 b B-A c)}{4 b x^{5/2}}-\frac{A \left(b x+c x^2\right)^{3/2}}{3 b x^{9/2}}",1,"-((2*b*B - A*c)*Sqrt[b*x + c*x^2])/(4*b*x^(5/2)) - (c*(2*b*B - A*c)*Sqrt[b*x + c*x^2])/(8*b^2*x^(3/2)) - (A*(b*x + c*x^2)^(3/2))/(3*b*x^(9/2)) + (c^2*(2*b*B - A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(5/2))","A",5,5,24,0.2083,1,"{792, 662, 672, 660, 207}"
203,1,207,0,0.1530773,"\int x^{5/2} (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[x^(5/2)*(A + B*x)*(b*x + c*x^2)^(3/2),x]","-\frac{256 b^4 \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{45045 c^6 x^{5/2}}+\frac{128 b^3 \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{9009 c^5 x^{3/2}}-\frac{32 b^2 \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{1287 c^4 \sqrt{x}}+\frac{16 b \sqrt{x} \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{429 c^3}-\frac{2 x^{3/2} \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{39 c^2}+\frac{2 B x^{5/2} \left(b x+c x^2\right)^{5/2}}{15 c}","-\frac{256 b^4 \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{45045 c^6 x^{5/2}}+\frac{128 b^3 \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{9009 c^5 x^{3/2}}-\frac{32 b^2 \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{1287 c^4 \sqrt{x}}+\frac{16 b \sqrt{x} \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{429 c^3}-\frac{2 x^{3/2} \left(b x+c x^2\right)^{5/2} (2 b B-3 A c)}{39 c^2}+\frac{2 B x^{5/2} \left(b x+c x^2\right)^{5/2}}{15 c}",1,"(-256*b^4*(2*b*B - 3*A*c)*(b*x + c*x^2)^(5/2))/(45045*c^6*x^(5/2)) + (128*b^3*(2*b*B - 3*A*c)*(b*x + c*x^2)^(5/2))/(9009*c^5*x^(3/2)) - (32*b^2*(2*b*B - 3*A*c)*(b*x + c*x^2)^(5/2))/(1287*c^4*Sqrt[x]) + (16*b*(2*b*B - 3*A*c)*Sqrt[x]*(b*x + c*x^2)^(5/2))/(429*c^3) - (2*(2*b*B - 3*A*c)*x^(3/2)*(b*x + c*x^2)^(5/2))/(39*c^2) + (2*B*x^(5/2)*(b*x + c*x^2)^(5/2))/(15*c)","A",6,3,24,0.1250,1,"{794, 656, 648}"
204,1,170,0,0.1614596,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[x^(3/2)*(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{32 b^3 \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{15015 c^5 x^{5/2}}-\frac{16 b^2 \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{3003 c^4 x^{3/2}}+\frac{4 b \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{429 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{143 c^2}+\frac{2 B x^{3/2} \left(b x+c x^2\right)^{5/2}}{13 c}","\frac{32 b^3 \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{15015 c^5 x^{5/2}}-\frac{16 b^2 \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{3003 c^4 x^{3/2}}+\frac{4 b \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{429 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \left(b x+c x^2\right)^{5/2} (8 b B-13 A c)}{143 c^2}+\frac{2 B x^{3/2} \left(b x+c x^2\right)^{5/2}}{13 c}",1,"(32*b^3*(8*b*B - 13*A*c)*(b*x + c*x^2)^(5/2))/(15015*c^5*x^(5/2)) - (16*b^2*(8*b*B - 13*A*c)*(b*x + c*x^2)^(5/2))/(3003*c^4*x^(3/2)) + (4*b*(8*b*B - 13*A*c)*(b*x + c*x^2)^(5/2))/(429*c^3*Sqrt[x]) - (2*(8*b*B - 13*A*c)*Sqrt[x]*(b*x + c*x^2)^(5/2))/(143*c^2) + (2*B*x^(3/2)*(b*x + c*x^2)^(5/2))/(13*c)","A",5,3,24,0.1250,1,"{794, 656, 648}"
205,1,133,0,0.1109747,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^(3/2),x]","-\frac{16 b^2 \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{3465 c^4 x^{5/2}}-\frac{2 \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{99 c^2 \sqrt{x}}+\frac{8 b \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{693 c^3 x^{3/2}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{5/2}}{11 c}","-\frac{16 b^2 \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{3465 c^4 x^{5/2}}-\frac{2 \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{99 c^2 \sqrt{x}}+\frac{8 b \left(b x+c x^2\right)^{5/2} (6 b B-11 A c)}{693 c^3 x^{3/2}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{5/2}}{11 c}",1,"(-16*b^2*(6*b*B - 11*A*c)*(b*x + c*x^2)^(5/2))/(3465*c^4*x^(5/2)) + (8*b*(6*b*B - 11*A*c)*(b*x + c*x^2)^(5/2))/(693*c^3*x^(3/2)) - (2*(6*b*B - 11*A*c)*(b*x + c*x^2)^(5/2))/(99*c^2*Sqrt[x]) + (2*B*Sqrt[x]*(b*x + c*x^2)^(5/2))/(11*c)","A",4,3,24,0.1250,1,"{794, 656, 648}"
206,1,96,0,0.0791305,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{\sqrt{x}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/Sqrt[x],x]","-\frac{2 \left(b x+c x^2\right)^{5/2} (4 b B-9 A c)}{63 c^2 x^{3/2}}+\frac{4 b \left(b x+c x^2\right)^{5/2} (4 b B-9 A c)}{315 c^3 x^{5/2}}+\frac{2 B \left(b x+c x^2\right)^{5/2}}{9 c \sqrt{x}}","-\frac{2 \left(b x+c x^2\right)^{5/2} (4 b B-9 A c)}{63 c^2 x^{3/2}}+\frac{4 b \left(b x+c x^2\right)^{5/2} (4 b B-9 A c)}{315 c^3 x^{5/2}}+\frac{2 B \left(b x+c x^2\right)^{5/2}}{9 c \sqrt{x}}",1,"(4*b*(4*b*B - 9*A*c)*(b*x + c*x^2)^(5/2))/(315*c^3*x^(5/2)) - (2*(4*b*B - 9*A*c)*(b*x + c*x^2)^(5/2))/(63*c^2*x^(3/2)) + (2*B*(b*x + c*x^2)^(5/2))/(9*c*Sqrt[x])","A",3,3,24,0.1250,1,"{794, 656, 648}"
207,1,61,0,0.0464435,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(3/2),x]","\frac{2 B \left(b x+c x^2\right)^{5/2}}{7 c x^{3/2}}-\frac{2 \left(b x+c x^2\right)^{5/2} (2 b B-7 A c)}{35 c^2 x^{5/2}}","\frac{2 B \left(b x+c x^2\right)^{5/2}}{7 c x^{3/2}}-\frac{2 \left(b x+c x^2\right)^{5/2} (2 b B-7 A c)}{35 c^2 x^{5/2}}",1,"(-2*(2*b*B - 7*A*c)*(b*x + c*x^2)^(5/2))/(35*c^2*x^(5/2)) + (2*B*(b*x + c*x^2)^(5/2))/(7*c*x^(3/2))","A",2,2,24,0.08333,1,"{794, 648}"
208,1,105,0,0.0857289,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(5/2),x]","-2 A b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 A \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}+\frac{2 A b \sqrt{b x+c x^2}}{\sqrt{x}}+\frac{2 B \left(b x+c x^2\right)^{5/2}}{5 c x^{5/2}}","-2 A b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 A \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}+\frac{2 A b \sqrt{b x+c x^2}}{\sqrt{x}}+\frac{2 B \left(b x+c x^2\right)^{5/2}}{5 c x^{5/2}}",1,"(2*A*b*Sqrt[b*x + c*x^2])/Sqrt[x] + (2*A*(b*x + c*x^2)^(3/2))/(3*x^(3/2)) + (2*B*(b*x + c*x^2)^(5/2))/(5*c*x^(5/2)) - 2*A*b^(3/2)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",5,4,24,0.1667,1,"{794, 664, 660, 207}"
209,1,128,0,0.1257913,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(7/2),x]","\frac{\left(b x+c x^2\right)^{3/2} (3 A c+2 b B)}{3 b x^{3/2}}+\frac{\sqrt{b x+c x^2} (3 A c+2 b B)}{\sqrt{x}}-\sqrt{b} (3 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)-\frac{A \left(b x+c x^2\right)^{5/2}}{b x^{7/2}}","\frac{\left(b x+c x^2\right)^{3/2} (3 A c+2 b B)}{3 b x^{3/2}}+\frac{\sqrt{b x+c x^2} (3 A c+2 b B)}{\sqrt{x}}-\sqrt{b} (3 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)-\frac{A \left(b x+c x^2\right)^{5/2}}{b x^{7/2}}",1,"((2*b*B + 3*A*c)*Sqrt[b*x + c*x^2])/Sqrt[x] + ((2*b*B + 3*A*c)*(b*x + c*x^2)^(3/2))/(3*b*x^(3/2)) - (A*(b*x + c*x^2)^(5/2))/(b*x^(7/2)) - Sqrt[b]*(2*b*B + 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",5,4,24,0.1667,1,"{792, 664, 660, 207}"
210,1,137,0,0.1275093,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{9/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(9/2),x]","-\frac{\left(b x+c x^2\right)^{3/2} (A c+4 b B)}{4 b x^{5/2}}+\frac{3 c \sqrt{b x+c x^2} (A c+4 b B)}{4 b \sqrt{x}}-\frac{3 c (A c+4 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 \sqrt{b}}-\frac{A \left(b x+c x^2\right)^{5/2}}{2 b x^{9/2}}","-\frac{\left(b x+c x^2\right)^{3/2} (A c+4 b B)}{4 b x^{5/2}}+\frac{3 c \sqrt{b x+c x^2} (A c+4 b B)}{4 b \sqrt{x}}-\frac{3 c (A c+4 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 \sqrt{b}}-\frac{A \left(b x+c x^2\right)^{5/2}}{2 b x^{9/2}}",1,"(3*c*(4*b*B + A*c)*Sqrt[b*x + c*x^2])/(4*b*Sqrt[x]) - ((4*b*B + A*c)*(b*x + c*x^2)^(3/2))/(4*b*x^(5/2)) - (A*(b*x + c*x^2)^(5/2))/(2*b*x^(9/2)) - (3*c*(4*b*B + A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*Sqrt[b])","A",5,5,24,0.2083,1,"{792, 662, 664, 660, 207}"
211,1,142,0,0.1292404,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{11/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(11/2),x]","-\frac{c^2 (6 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{3/2}}-\frac{\left(b x+c x^2\right)^{3/2} (6 b B-A c)}{12 b x^{7/2}}-\frac{c \sqrt{b x+c x^2} (6 b B-A c)}{8 b x^{3/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{3 b x^{11/2}}","-\frac{c^2 (6 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{3/2}}-\frac{\left(b x+c x^2\right)^{3/2} (6 b B-A c)}{12 b x^{7/2}}-\frac{c \sqrt{b x+c x^2} (6 b B-A c)}{8 b x^{3/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{3 b x^{11/2}}",1,"-(c*(6*b*B - A*c)*Sqrt[b*x + c*x^2])/(8*b*x^(3/2)) - ((6*b*B - A*c)*(b*x + c*x^2)^(3/2))/(12*b*x^(7/2)) - (A*(b*x + c*x^2)^(5/2))/(3*b*x^(11/2)) - (c^2*(6*b*B - A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(3/2))","A",5,4,24,0.1667,1,"{792, 662, 660, 207}"
212,1,179,0,0.1694706,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{13/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(13/2),x]","-\frac{c^2 \sqrt{b x+c x^2} (8 b B-3 A c)}{64 b^2 x^{3/2}}+\frac{c^3 (8 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{5/2}}-\frac{c \sqrt{b x+c x^2} (8 b B-3 A c)}{32 b x^{5/2}}-\frac{\left(b x+c x^2\right)^{3/2} (8 b B-3 A c)}{24 b x^{9/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{4 b x^{13/2}}","-\frac{c^2 \sqrt{b x+c x^2} (8 b B-3 A c)}{64 b^2 x^{3/2}}+\frac{c^3 (8 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{5/2}}-\frac{c \sqrt{b x+c x^2} (8 b B-3 A c)}{32 b x^{5/2}}-\frac{\left(b x+c x^2\right)^{3/2} (8 b B-3 A c)}{24 b x^{9/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{4 b x^{13/2}}",1,"-(c*(8*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(32*b*x^(5/2)) - (c^2*(8*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(64*b^2*x^(3/2)) - ((8*b*B - 3*A*c)*(b*x + c*x^2)^(3/2))/(24*b*x^(9/2)) - (A*(b*x + c*x^2)^(5/2))/(4*b*x^(13/2)) + (c^3*(8*b*B - 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(64*b^(5/2))","A",6,5,24,0.2083,1,"{792, 662, 672, 660, 207}"
213,1,216,0,0.1913312,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{x^{15/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/x^(15/2),x]","\frac{3 c^3 \sqrt{b x+c x^2} (2 b B-A c)}{128 b^3 x^{3/2}}-\frac{c^2 \sqrt{b x+c x^2} (2 b B-A c)}{64 b^2 x^{5/2}}-\frac{3 c^4 (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{128 b^{7/2}}-\frac{c \sqrt{b x+c x^2} (2 b B-A c)}{16 b x^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (2 b B-A c)}{8 b x^{11/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{5 b x^{15/2}}","\frac{3 c^3 \sqrt{b x+c x^2} (2 b B-A c)}{128 b^3 x^{3/2}}-\frac{c^2 \sqrt{b x+c x^2} (2 b B-A c)}{64 b^2 x^{5/2}}-\frac{3 c^4 (2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{128 b^{7/2}}-\frac{c \sqrt{b x+c x^2} (2 b B-A c)}{16 b x^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (2 b B-A c)}{8 b x^{11/2}}-\frac{A \left(b x+c x^2\right)^{5/2}}{5 b x^{15/2}}",1,"-(c*(2*b*B - A*c)*Sqrt[b*x + c*x^2])/(16*b*x^(7/2)) - (c^2*(2*b*B - A*c)*Sqrt[b*x + c*x^2])/(64*b^2*x^(5/2)) + (3*c^3*(2*b*B - A*c)*Sqrt[b*x + c*x^2])/(128*b^3*x^(3/2)) - ((2*b*B - A*c)*(b*x + c*x^2)^(3/2))/(8*b*x^(11/2)) - (A*(b*x + c*x^2)^(5/2))/(5*b*x^(15/2)) - (3*c^4*(2*b*B - A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(128*b^(7/2))","A",7,5,24,0.2083,1,"{792, 662, 672, 660, 207}"
214,1,207,0,0.2033789,"\int x^{3/2} (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[x^(3/2)*(A + B*x)*(b*x + c*x^2)^(5/2),x]","-\frac{256 b^4 \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{765765 c^6 x^{7/2}}+\frac{128 b^3 \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{109395 c^5 x^{5/2}}-\frac{32 b^2 \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{12155 c^4 x^{3/2}}+\frac{16 b \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{3315 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{255 c^2}+\frac{2 B x^{3/2} \left(b x+c x^2\right)^{7/2}}{17 c}","-\frac{256 b^4 \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{765765 c^6 x^{7/2}}+\frac{128 b^3 \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{109395 c^5 x^{5/2}}-\frac{32 b^2 \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{12155 c^4 x^{3/2}}+\frac{16 b \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{3315 c^3 \sqrt{x}}-\frac{2 \sqrt{x} \left(b x+c x^2\right)^{7/2} (10 b B-17 A c)}{255 c^2}+\frac{2 B x^{3/2} \left(b x+c x^2\right)^{7/2}}{17 c}",1,"(-256*b^4*(10*b*B - 17*A*c)*(b*x + c*x^2)^(7/2))/(765765*c^6*x^(7/2)) + (128*b^3*(10*b*B - 17*A*c)*(b*x + c*x^2)^(7/2))/(109395*c^5*x^(5/2)) - (32*b^2*(10*b*B - 17*A*c)*(b*x + c*x^2)^(7/2))/(12155*c^4*x^(3/2)) + (16*b*(10*b*B - 17*A*c)*(b*x + c*x^2)^(7/2))/(3315*c^3*Sqrt[x]) - (2*(10*b*B - 17*A*c)*Sqrt[x]*(b*x + c*x^2)^(7/2))/(255*c^2) + (2*B*x^(3/2)*(b*x + c*x^2)^(7/2))/(17*c)","A",6,3,24,0.1250,1,"{794, 656, 648}"
215,1,170,0,0.1442623,"\int \sqrt{x} (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[Sqrt[x]*(A + B*x)*(b*x + c*x^2)^(5/2),x]","-\frac{16 b^2 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{6435 c^4 x^{5/2}}+\frac{32 b^3 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{45045 c^5 x^{7/2}}-\frac{2 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{195 c^2 \sqrt{x}}+\frac{4 b \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{715 c^3 x^{3/2}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{7/2}}{15 c}","-\frac{16 b^2 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{6435 c^4 x^{5/2}}+\frac{32 b^3 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{45045 c^5 x^{7/2}}-\frac{2 \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{195 c^2 \sqrt{x}}+\frac{4 b \left(b x+c x^2\right)^{7/2} (8 b B-15 A c)}{715 c^3 x^{3/2}}+\frac{2 B \sqrt{x} \left(b x+c x^2\right)^{7/2}}{15 c}",1,"(32*b^3*(8*b*B - 15*A*c)*(b*x + c*x^2)^(7/2))/(45045*c^5*x^(7/2)) - (16*b^2*(8*b*B - 15*A*c)*(b*x + c*x^2)^(7/2))/(6435*c^4*x^(5/2)) + (4*b*(8*b*B - 15*A*c)*(b*x + c*x^2)^(7/2))/(715*c^3*x^(3/2)) - (2*(8*b*B - 15*A*c)*(b*x + c*x^2)^(7/2))/(195*c^2*Sqrt[x]) + (2*B*Sqrt[x]*(b*x + c*x^2)^(7/2))/(15*c)","A",5,3,24,0.1250,1,"{794, 656, 648}"
216,1,133,0,0.111131,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{\sqrt{x}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/Sqrt[x],x]","-\frac{16 b^2 \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{9009 c^4 x^{7/2}}-\frac{2 \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{143 c^2 x^{3/2}}+\frac{8 b \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{1287 c^3 x^{5/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{13 c \sqrt{x}}","-\frac{16 b^2 \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{9009 c^4 x^{7/2}}-\frac{2 \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{143 c^2 x^{3/2}}+\frac{8 b \left(b x+c x^2\right)^{7/2} (6 b B-13 A c)}{1287 c^3 x^{5/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{13 c \sqrt{x}}",1,"(-16*b^2*(6*b*B - 13*A*c)*(b*x + c*x^2)^(7/2))/(9009*c^4*x^(7/2)) + (8*b*(6*b*B - 13*A*c)*(b*x + c*x^2)^(7/2))/(1287*c^3*x^(5/2)) - (2*(6*b*B - 13*A*c)*(b*x + c*x^2)^(7/2))/(143*c^2*x^(3/2)) + (2*B*(b*x + c*x^2)^(7/2))/(13*c*Sqrt[x])","A",4,3,24,0.1250,1,"{794, 656, 648}"
217,1,96,0,0.0889312,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(3/2),x]","-\frac{2 \left(b x+c x^2\right)^{7/2} (4 b B-11 A c)}{99 c^2 x^{5/2}}+\frac{4 b \left(b x+c x^2\right)^{7/2} (4 b B-11 A c)}{693 c^3 x^{7/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{11 c x^{3/2}}","-\frac{2 \left(b x+c x^2\right)^{7/2} (4 b B-11 A c)}{99 c^2 x^{5/2}}+\frac{4 b \left(b x+c x^2\right)^{7/2} (4 b B-11 A c)}{693 c^3 x^{7/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{11 c x^{3/2}}",1,"(4*b*(4*b*B - 11*A*c)*(b*x + c*x^2)^(7/2))/(693*c^3*x^(7/2)) - (2*(4*b*B - 11*A*c)*(b*x + c*x^2)^(7/2))/(99*c^2*x^(5/2)) + (2*B*(b*x + c*x^2)^(7/2))/(11*c*x^(3/2))","A",3,3,24,0.1250,1,"{794, 656, 648}"
218,1,61,0,0.0486153,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(5/2),x]","\frac{2 B \left(b x+c x^2\right)^{7/2}}{9 c x^{5/2}}-\frac{2 \left(b x+c x^2\right)^{7/2} (2 b B-9 A c)}{63 c^2 x^{7/2}}","\frac{2 B \left(b x+c x^2\right)^{7/2}}{9 c x^{5/2}}-\frac{2 \left(b x+c x^2\right)^{7/2} (2 b B-9 A c)}{63 c^2 x^{7/2}}",1,"(-2*(2*b*B - 9*A*c)*(b*x + c*x^2)^(7/2))/(63*c^2*x^(7/2)) + (2*B*(b*x + c*x^2)^(7/2))/(9*c*x^(5/2))","A",2,2,24,0.08333,1,"{794, 648}"
219,1,131,0,0.1158032,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(7/2),x]","\frac{2 A b^2 \sqrt{b x+c x^2}}{\sqrt{x}}-2 A b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 A \left(b x+c x^2\right)^{5/2}}{5 x^{5/2}}+\frac{2 A b \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{7 c x^{7/2}}","\frac{2 A b^2 \sqrt{b x+c x^2}}{\sqrt{x}}-2 A b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{2 A \left(b x+c x^2\right)^{5/2}}{5 x^{5/2}}+\frac{2 A b \left(b x+c x^2\right)^{3/2}}{3 x^{3/2}}+\frac{2 B \left(b x+c x^2\right)^{7/2}}{7 c x^{7/2}}",1,"(2*A*b^2*Sqrt[b*x + c*x^2])/Sqrt[x] + (2*A*b*(b*x + c*x^2)^(3/2))/(3*x^(3/2)) + (2*A*(b*x + c*x^2)^(5/2))/(5*x^(5/2)) + (2*B*(b*x + c*x^2)^(7/2))/(7*c*x^(7/2)) - 2*A*b^(5/2)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",6,4,24,0.1667,1,"{794, 664, 660, 207}"
220,1,160,0,0.1604742,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{9/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(9/2),x]","-b^{3/2} (5 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{\left(b x+c x^2\right)^{5/2} (5 A c+2 b B)}{5 b x^{5/2}}+\frac{\left(b x+c x^2\right)^{3/2} (5 A c+2 b B)}{3 x^{3/2}}+\frac{b \sqrt{b x+c x^2} (5 A c+2 b B)}{\sqrt{x}}-\frac{A \left(b x+c x^2\right)^{7/2}}{b x^{9/2}}","-b^{3/2} (5 A c+2 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)+\frac{\left(b x+c x^2\right)^{5/2} (5 A c+2 b B)}{5 b x^{5/2}}+\frac{\left(b x+c x^2\right)^{3/2} (5 A c+2 b B)}{3 x^{3/2}}+\frac{b \sqrt{b x+c x^2} (5 A c+2 b B)}{\sqrt{x}}-\frac{A \left(b x+c x^2\right)^{7/2}}{b x^{9/2}}",1,"(b*(2*b*B + 5*A*c)*Sqrt[b*x + c*x^2])/Sqrt[x] + ((2*b*B + 5*A*c)*(b*x + c*x^2)^(3/2))/(3*x^(3/2)) + ((2*b*B + 5*A*c)*(b*x + c*x^2)^(5/2))/(5*b*x^(5/2)) - (A*(b*x + c*x^2)^(7/2))/(b*x^(9/2)) - b^(3/2)*(2*b*B + 5*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])]","A",6,4,24,0.1667,1,"{792, 664, 660, 207}"
221,1,172,0,0.1594295,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{11/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(11/2),x]","-\frac{\left(b x+c x^2\right)^{5/2} (3 A c+4 b B)}{4 b x^{7/2}}+\frac{5 c \left(b x+c x^2\right)^{3/2} (3 A c+4 b B)}{12 b x^{3/2}}+\frac{5 c \sqrt{b x+c x^2} (3 A c+4 b B)}{4 \sqrt{x}}-\frac{5}{4} \sqrt{b} c (3 A c+4 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)-\frac{A \left(b x+c x^2\right)^{7/2}}{2 b x^{11/2}}","-\frac{\left(b x+c x^2\right)^{5/2} (3 A c+4 b B)}{4 b x^{7/2}}+\frac{5 c \left(b x+c x^2\right)^{3/2} (3 A c+4 b B)}{12 b x^{3/2}}+\frac{5 c \sqrt{b x+c x^2} (3 A c+4 b B)}{4 \sqrt{x}}-\frac{5}{4} \sqrt{b} c (3 A c+4 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)-\frac{A \left(b x+c x^2\right)^{7/2}}{2 b x^{11/2}}",1,"(5*c*(4*b*B + 3*A*c)*Sqrt[b*x + c*x^2])/(4*Sqrt[x]) + (5*c*(4*b*B + 3*A*c)*(b*x + c*x^2)^(3/2))/(12*b*x^(3/2)) - ((4*b*B + 3*A*c)*(b*x + c*x^2)^(5/2))/(4*b*x^(7/2)) - (A*(b*x + c*x^2)^(7/2))/(2*b*x^(11/2)) - (5*Sqrt[b]*c*(4*b*B + 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/4","A",6,5,24,0.2083,1,"{792, 662, 664, 660, 207}"
222,1,175,0,0.1698797,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{13/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(13/2),x]","\frac{5 c^2 \sqrt{b x+c x^2} (A c+6 b B)}{8 b \sqrt{x}}-\frac{5 c^2 (A c+6 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 \sqrt{b}}-\frac{\left(b x+c x^2\right)^{5/2} (A c+6 b B)}{12 b x^{9/2}}-\frac{5 c \left(b x+c x^2\right)^{3/2} (A c+6 b B)}{24 b x^{5/2}}-\frac{A \left(b x+c x^2\right)^{7/2}}{3 b x^{13/2}}","\frac{5 c^2 \sqrt{b x+c x^2} (A c+6 b B)}{8 b \sqrt{x}}-\frac{5 c^2 (A c+6 b B) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 \sqrt{b}}-\frac{\left(b x+c x^2\right)^{5/2} (A c+6 b B)}{12 b x^{9/2}}-\frac{5 c \left(b x+c x^2\right)^{3/2} (A c+6 b B)}{24 b x^{5/2}}-\frac{A \left(b x+c x^2\right)^{7/2}}{3 b x^{13/2}}",1,"(5*c^2*(6*b*B + A*c)*Sqrt[b*x + c*x^2])/(8*b*Sqrt[x]) - (5*c*(6*b*B + A*c)*(b*x + c*x^2)^(3/2))/(24*b*x^(5/2)) - ((6*b*B + A*c)*(b*x + c*x^2)^(5/2))/(12*b*x^(9/2)) - (A*(b*x + c*x^2)^(7/2))/(3*b*x^(13/2)) - (5*c^2*(6*b*B + A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*Sqrt[b])","A",6,5,24,0.2083,1,"{792, 662, 664, 660, 207}"
223,1,179,0,0.1661585,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{15/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(15/2),x]","-\frac{5 c^3 (8 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{3/2}}-\frac{5 c^2 \sqrt{b x+c x^2} (8 b B-A c)}{64 b x^{3/2}}-\frac{\left(b x+c x^2\right)^{5/2} (8 b B-A c)}{24 b x^{11/2}}-\frac{5 c \left(b x+c x^2\right)^{3/2} (8 b B-A c)}{96 b x^{7/2}}-\frac{A \left(b x+c x^2\right)^{7/2}}{4 b x^{15/2}}","-\frac{5 c^3 (8 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{3/2}}-\frac{5 c^2 \sqrt{b x+c x^2} (8 b B-A c)}{64 b x^{3/2}}-\frac{\left(b x+c x^2\right)^{5/2} (8 b B-A c)}{24 b x^{11/2}}-\frac{5 c \left(b x+c x^2\right)^{3/2} (8 b B-A c)}{96 b x^{7/2}}-\frac{A \left(b x+c x^2\right)^{7/2}}{4 b x^{15/2}}",1,"(-5*c^2*(8*b*B - A*c)*Sqrt[b*x + c*x^2])/(64*b*x^(3/2)) - (5*c*(8*b*B - A*c)*(b*x + c*x^2)^(3/2))/(96*b*x^(7/2)) - ((8*b*B - A*c)*(b*x + c*x^2)^(5/2))/(24*b*x^(11/2)) - (A*(b*x + c*x^2)^(7/2))/(4*b*x^(15/2)) - (5*c^3*(8*b*B - A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(64*b^(3/2))","A",6,4,24,0.1667,1,"{792, 662, 660, 207}"
224,1,216,0,0.2059954,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{x^{17/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/x^(17/2),x]","-\frac{c^3 \sqrt{b x+c x^2} (10 b B-3 A c)}{128 b^2 x^{3/2}}+\frac{c^4 (10 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{128 b^{5/2}}-\frac{c^2 \sqrt{b x+c x^2} (10 b B-3 A c)}{64 b x^{5/2}}-\frac{c \left(b x+c x^2\right)^{3/2} (10 b B-3 A c)}{48 b x^{9/2}}-\frac{\left(b x+c x^2\right)^{5/2} (10 b B-3 A c)}{40 b x^{13/2}}-\frac{A \left(b x+c x^2\right)^{7/2}}{5 b x^{17/2}}","-\frac{c^3 \sqrt{b x+c x^2} (10 b B-3 A c)}{128 b^2 x^{3/2}}+\frac{c^4 (10 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{128 b^{5/2}}-\frac{c^2 \sqrt{b x+c x^2} (10 b B-3 A c)}{64 b x^{5/2}}-\frac{c \left(b x+c x^2\right)^{3/2} (10 b B-3 A c)}{48 b x^{9/2}}-\frac{\left(b x+c x^2\right)^{5/2} (10 b B-3 A c)}{40 b x^{13/2}}-\frac{A \left(b x+c x^2\right)^{7/2}}{5 b x^{17/2}}",1,"-(c^2*(10*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(64*b*x^(5/2)) - (c^3*(10*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(128*b^2*x^(3/2)) - (c*(10*b*B - 3*A*c)*(b*x + c*x^2)^(3/2))/(48*b*x^(9/2)) - ((10*b*B - 3*A*c)*(b*x + c*x^2)^(5/2))/(40*b*x^(13/2)) - (A*(b*x + c*x^2)^(7/2))/(5*b*x^(17/2)) + (c^4*(10*b*B - 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(128*b^(5/2))","A",7,5,24,0.2083,1,"{792, 662, 672, 660, 207}"
225,1,170,0,0.1475826,"\int \frac{x^{7/2} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x^(7/2)*(A + B*x))/Sqrt[b*x + c*x^2],x]","-\frac{16 b^2 \sqrt{x} \sqrt{b x+c x^2} (8 b B-9 A c)}{315 c^4}+\frac{32 b^3 \sqrt{b x+c x^2} (8 b B-9 A c)}{315 c^5 \sqrt{x}}-\frac{2 x^{5/2} \sqrt{b x+c x^2} (8 b B-9 A c)}{63 c^2}+\frac{4 b x^{3/2} \sqrt{b x+c x^2} (8 b B-9 A c)}{105 c^3}+\frac{2 B x^{7/2} \sqrt{b x+c x^2}}{9 c}","-\frac{16 b^2 \sqrt{x} \sqrt{b x+c x^2} (8 b B-9 A c)}{315 c^4}+\frac{32 b^3 \sqrt{b x+c x^2} (8 b B-9 A c)}{315 c^5 \sqrt{x}}-\frac{2 x^{5/2} \sqrt{b x+c x^2} (8 b B-9 A c)}{63 c^2}+\frac{4 b x^{3/2} \sqrt{b x+c x^2} (8 b B-9 A c)}{105 c^3}+\frac{2 B x^{7/2} \sqrt{b x+c x^2}}{9 c}",1,"(32*b^3*(8*b*B - 9*A*c)*Sqrt[b*x + c*x^2])/(315*c^5*Sqrt[x]) - (16*b^2*(8*b*B - 9*A*c)*Sqrt[x]*Sqrt[b*x + c*x^2])/(315*c^4) + (4*b*(8*b*B - 9*A*c)*x^(3/2)*Sqrt[b*x + c*x^2])/(105*c^3) - (2*(8*b*B - 9*A*c)*x^(5/2)*Sqrt[b*x + c*x^2])/(63*c^2) + (2*B*x^(7/2)*Sqrt[b*x + c*x^2])/(9*c)","A",5,3,24,0.1250,1,"{794, 656, 648}"
226,1,133,0,0.1075125,"\int \frac{x^{5/2} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x^(5/2)*(A + B*x))/Sqrt[b*x + c*x^2],x]","-\frac{16 b^2 \sqrt{b x+c x^2} (6 b B-7 A c)}{105 c^4 \sqrt{x}}-\frac{2 x^{3/2} \sqrt{b x+c x^2} (6 b B-7 A c)}{35 c^2}+\frac{8 b \sqrt{x} \sqrt{b x+c x^2} (6 b B-7 A c)}{105 c^3}+\frac{2 B x^{5/2} \sqrt{b x+c x^2}}{7 c}","-\frac{16 b^2 \sqrt{b x+c x^2} (6 b B-7 A c)}{105 c^4 \sqrt{x}}-\frac{2 x^{3/2} \sqrt{b x+c x^2} (6 b B-7 A c)}{35 c^2}+\frac{8 b \sqrt{x} \sqrt{b x+c x^2} (6 b B-7 A c)}{105 c^3}+\frac{2 B x^{5/2} \sqrt{b x+c x^2}}{7 c}",1,"(-16*b^2*(6*b*B - 7*A*c)*Sqrt[b*x + c*x^2])/(105*c^4*Sqrt[x]) + (8*b*(6*b*B - 7*A*c)*Sqrt[x]*Sqrt[b*x + c*x^2])/(105*c^3) - (2*(6*b*B - 7*A*c)*x^(3/2)*Sqrt[b*x + c*x^2])/(35*c^2) + (2*B*x^(5/2)*Sqrt[b*x + c*x^2])/(7*c)","A",4,3,24,0.1250,1,"{794, 656, 648}"
227,1,96,0,0.0787564,"\int \frac{x^{3/2} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(x^(3/2)*(A + B*x))/Sqrt[b*x + c*x^2],x]","-\frac{2 \sqrt{x} \sqrt{b x+c x^2} (4 b B-5 A c)}{15 c^2}+\frac{4 b \sqrt{b x+c x^2} (4 b B-5 A c)}{15 c^3 \sqrt{x}}+\frac{2 B x^{3/2} \sqrt{b x+c x^2}}{5 c}","-\frac{2 \sqrt{x} \sqrt{b x+c x^2} (4 b B-5 A c)}{15 c^2}+\frac{4 b \sqrt{b x+c x^2} (4 b B-5 A c)}{15 c^3 \sqrt{x}}+\frac{2 B x^{3/2} \sqrt{b x+c x^2}}{5 c}",1,"(4*b*(4*b*B - 5*A*c)*Sqrt[b*x + c*x^2])/(15*c^3*Sqrt[x]) - (2*(4*b*B - 5*A*c)*Sqrt[x]*Sqrt[b*x + c*x^2])/(15*c^2) + (2*B*x^(3/2)*Sqrt[b*x + c*x^2])/(5*c)","A",3,3,24,0.1250,1,"{794, 656, 648}"
228,1,61,0,0.0407592,"\int \frac{\sqrt{x} (A+B x)}{\sqrt{b x+c x^2}} \, dx","Int[(Sqrt[x]*(A + B*x))/Sqrt[b*x + c*x^2],x]","\frac{2 B \sqrt{x} \sqrt{b x+c x^2}}{3 c}-\frac{2 \sqrt{b x+c x^2} (2 b B-3 A c)}{3 c^2 \sqrt{x}}","\frac{2 B \sqrt{x} \sqrt{b x+c x^2}}{3 c}-\frac{2 \sqrt{b x+c x^2} (2 b B-3 A c)}{3 c^2 \sqrt{x}}",1,"(-2*(2*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(3*c^2*Sqrt[x]) + (2*B*Sqrt[x]*Sqrt[b*x + c*x^2])/(3*c)","A",2,2,24,0.08333,1,"{794, 648}"
229,1,72,0,0.0611555,"\int \frac{A+B x}{\sqrt{e x} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(Sqrt[e*x]*Sqrt[b*x + c*x^2]),x]","\frac{2 B \sqrt{b x+c x^2}}{c \sqrt{e x}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{b x+c x^2}}{\sqrt{b} \sqrt{e x}}\right)}{\sqrt{b} \sqrt{e}}","\frac{2 B \sqrt{b x+c x^2}}{c \sqrt{e x}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{e} \sqrt{b x+c x^2}}{\sqrt{b} \sqrt{e x}}\right)}{\sqrt{b} \sqrt{e}}",1,"(2*B*Sqrt[b*x + c*x^2])/(c*Sqrt[e*x]) - (2*A*ArcTanh[(Sqrt[e]*Sqrt[b*x + c*x^2])/(Sqrt[b]*Sqrt[e*x])])/(Sqrt[b]*Sqrt[e])","A",3,3,26,0.1154,1,"{794, 660, 208}"
230,1,66,0,0.0511594,"\int \frac{A+B x}{x^{3/2} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^(3/2)*Sqrt[b*x + c*x^2]),x]","-\frac{(2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}-\frac{A \sqrt{b x+c x^2}}{b x^{3/2}}","-\frac{(2 b B-A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}-\frac{A \sqrt{b x+c x^2}}{b x^{3/2}}",1,"-((A*Sqrt[b*x + c*x^2])/(b*x^(3/2))) - ((2*b*B - A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(3/2)","A",3,3,24,0.1250,1,"{792, 660, 207}"
231,1,105,0,0.0861174,"\int \frac{A+B x}{x^{5/2} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^(5/2)*Sqrt[b*x + c*x^2]),x]","-\frac{\sqrt{b x+c x^2} (4 b B-3 A c)}{4 b^2 x^{3/2}}+\frac{c (4 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{5/2}}-\frac{A \sqrt{b x+c x^2}}{2 b x^{5/2}}","-\frac{\sqrt{b x+c x^2} (4 b B-3 A c)}{4 b^2 x^{3/2}}+\frac{c (4 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{5/2}}-\frac{A \sqrt{b x+c x^2}}{2 b x^{5/2}}",1,"-(A*Sqrt[b*x + c*x^2])/(2*b*x^(5/2)) - ((4*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(4*b^2*x^(3/2)) + (c*(4*b*B - 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(5/2))","A",4,4,24,0.1667,1,"{792, 672, 660, 207}"
232,1,142,0,0.1202994,"\int \frac{A+B x}{x^{7/2} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(x^(7/2)*Sqrt[b*x + c*x^2]),x]","-\frac{c^2 (6 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{7/2}}+\frac{c \sqrt{b x+c x^2} (6 b B-5 A c)}{8 b^3 x^{3/2}}-\frac{\sqrt{b x+c x^2} (6 b B-5 A c)}{12 b^2 x^{5/2}}-\frac{A \sqrt{b x+c x^2}}{3 b x^{7/2}}","-\frac{c^2 (6 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{7/2}}+\frac{c \sqrt{b x+c x^2} (6 b B-5 A c)}{8 b^3 x^{3/2}}-\frac{\sqrt{b x+c x^2} (6 b B-5 A c)}{12 b^2 x^{5/2}}-\frac{A \sqrt{b x+c x^2}}{3 b x^{7/2}}",1,"-(A*Sqrt[b*x + c*x^2])/(3*b*x^(7/2)) - ((6*b*B - 5*A*c)*Sqrt[b*x + c*x^2])/(12*b^2*x^(5/2)) + (c*(6*b*B - 5*A*c)*Sqrt[b*x + c*x^2])/(8*b^3*x^(3/2)) - (c^2*(6*b*B - 5*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(7/2))","A",5,4,24,0.1667,1,"{792, 672, 660, 207}"
233,1,178,0,0.1492174,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","-\frac{32 b^2 \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^5 \sqrt{x}}+\frac{2 x^{5/2} \sqrt{b x+c x^2} (8 b B-7 A c)}{7 b c^2}-\frac{12 x^{3/2} \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^3}+\frac{16 b \sqrt{x} \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^4}-\frac{2 x^{9/2} (b B-A c)}{b c \sqrt{b x+c x^2}}","-\frac{32 b^2 \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^5 \sqrt{x}}+\frac{2 x^{5/2} \sqrt{b x+c x^2} (8 b B-7 A c)}{7 b c^2}-\frac{12 x^{3/2} \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^3}+\frac{16 b \sqrt{x} \sqrt{b x+c x^2} (8 b B-7 A c)}{35 c^4}-\frac{2 x^{9/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^(9/2))/(b*c*Sqrt[b*x + c*x^2]) - (32*b^2*(8*b*B - 7*A*c)*Sqrt[b*x + c*x^2])/(35*c^5*Sqrt[x]) + (16*b*(8*b*B - 7*A*c)*Sqrt[x]*Sqrt[b*x + c*x^2])/(35*c^4) - (12*(8*b*B - 7*A*c)*x^(3/2)*Sqrt[b*x + c*x^2])/(35*c^3) + (2*(8*b*B - 7*A*c)*x^(5/2)*Sqrt[b*x + c*x^2])/(7*b*c^2)","A",5,3,24,0.1250,1,"{788, 656, 648}"
234,1,141,0,0.11096,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 x^{3/2} \sqrt{b x+c x^2} (6 b B-5 A c)}{5 b c^2}-\frac{8 \sqrt{x} \sqrt{b x+c x^2} (6 b B-5 A c)}{15 c^3}+\frac{16 b \sqrt{b x+c x^2} (6 b B-5 A c)}{15 c^4 \sqrt{x}}-\frac{2 x^{7/2} (b B-A c)}{b c \sqrt{b x+c x^2}}","\frac{2 x^{3/2} \sqrt{b x+c x^2} (6 b B-5 A c)}{5 b c^2}-\frac{8 \sqrt{x} \sqrt{b x+c x^2} (6 b B-5 A c)}{15 c^3}+\frac{16 b \sqrt{b x+c x^2} (6 b B-5 A c)}{15 c^4 \sqrt{x}}-\frac{2 x^{7/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^(7/2))/(b*c*Sqrt[b*x + c*x^2]) + (16*b*(6*b*B - 5*A*c)*Sqrt[b*x + c*x^2])/(15*c^4*Sqrt[x]) - (8*(6*b*B - 5*A*c)*Sqrt[x]*Sqrt[b*x + c*x^2])/(15*c^3) + (2*(6*b*B - 5*A*c)*x^(3/2)*Sqrt[b*x + c*x^2])/(5*b*c^2)","A",4,3,24,0.1250,1,"{788, 656, 648}"
235,1,106,0,0.080369,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x} \sqrt{b x+c x^2} (4 b B-3 A c)}{3 b c^2}-\frac{4 \sqrt{b x+c x^2} (4 b B-3 A c)}{3 c^3 \sqrt{x}}-\frac{2 x^{5/2} (b B-A c)}{b c \sqrt{b x+c x^2}}","\frac{2 \sqrt{x} \sqrt{b x+c x^2} (4 b B-3 A c)}{3 b c^2}-\frac{4 \sqrt{b x+c x^2} (4 b B-3 A c)}{3 c^3 \sqrt{x}}-\frac{2 x^{5/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^(5/2))/(b*c*Sqrt[b*x + c*x^2]) - (4*(4*b*B - 3*A*c)*Sqrt[b*x + c*x^2])/(3*c^3*Sqrt[x]) + (2*(4*b*B - 3*A*c)*Sqrt[x]*Sqrt[b*x + c*x^2])/(3*b*c^2)","A",3,3,24,0.1250,1,"{788, 656, 648}"
236,1,70,0,0.0450948,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{b x+c x^2} (2 b B-A c)}{b c^2 \sqrt{x}}-\frac{2 x^{3/2} (b B-A c)}{b c \sqrt{b x+c x^2}}","\frac{2 \sqrt{b x+c x^2} (2 b B-A c)}{b c^2 \sqrt{x}}-\frac{2 x^{3/2} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*x^(3/2))/(b*c*Sqrt[b*x + c*x^2]) + (2*(2*b*B - A*c)*Sqrt[b*x + c*x^2])/(b*c^2*Sqrt[x])","A",2,2,24,0.08333,1,"{788, 648}"
237,1,68,0,0.050674,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^(3/2),x]","-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}-\frac{2 \sqrt{x} (b B-A c)}{b c \sqrt{b x+c x^2}}","-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{3/2}}-\frac{2 \sqrt{x} (b B-A c)}{b c \sqrt{b x+c x^2}}",1,"(-2*(b*B - A*c)*Sqrt[x])/(b*c*Sqrt[b*x + c*x^2]) - (2*A*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(3/2)","A",3,3,24,0.1250,1,"{788, 660, 207}"
238,1,97,0,0.0752901,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^(3/2)),x]","\frac{\sqrt{x} (2 b B-3 A c)}{b^2 \sqrt{b x+c x^2}}-\frac{(2 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}-\frac{A}{b \sqrt{x} \sqrt{b x+c x^2}}","\frac{\sqrt{x} (2 b B-3 A c)}{b^2 \sqrt{b x+c x^2}}-\frac{(2 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}-\frac{A}{b \sqrt{x} \sqrt{b x+c x^2}}",1,"-(A/(b*Sqrt[x]*Sqrt[b*x + c*x^2])) + ((2*b*B - 3*A*c)*Sqrt[x])/(b^2*Sqrt[b*x + c*x^2]) - ((2*b*B - 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(5/2)","A",4,4,24,0.1667,1,"{792, 666, 660, 207}"
239,1,140,0,0.1138982,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{3 c \sqrt{x} (4 b B-5 A c)}{4 b^3 \sqrt{b x+c x^2}}-\frac{4 b B-5 A c}{4 b^2 \sqrt{x} \sqrt{b x+c x^2}}+\frac{3 c (4 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{7/2}}-\frac{A}{2 b x^{3/2} \sqrt{b x+c x^2}}","-\frac{3 c \sqrt{x} (4 b B-5 A c)}{4 b^3 \sqrt{b x+c x^2}}-\frac{4 b B-5 A c}{4 b^2 \sqrt{x} \sqrt{b x+c x^2}}+\frac{3 c (4 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{7/2}}-\frac{A}{2 b x^{3/2} \sqrt{b x+c x^2}}",1,"-A/(2*b*x^(3/2)*Sqrt[b*x + c*x^2]) - (4*b*B - 5*A*c)/(4*b^2*Sqrt[x]*Sqrt[b*x + c*x^2]) - (3*c*(4*b*B - 5*A*c)*Sqrt[x])/(4*b^3*Sqrt[b*x + c*x^2]) + (3*c*(4*b*B - 5*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(7/2))","A",5,5,24,0.2083,1,"{792, 672, 666, 660, 207}"
240,1,179,0,0.1524759,"\int \frac{A+B x}{x^{5/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^(5/2)*(b*x + c*x^2)^(3/2)),x]","\frac{5 c^2 \sqrt{x} (6 b B-7 A c)}{8 b^4 \sqrt{b x+c x^2}}-\frac{5 c^2 (6 b B-7 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{9/2}}+\frac{5 c (6 b B-7 A c)}{24 b^3 \sqrt{x} \sqrt{b x+c x^2}}-\frac{6 b B-7 A c}{12 b^2 x^{3/2} \sqrt{b x+c x^2}}-\frac{A}{3 b x^{5/2} \sqrt{b x+c x^2}}","\frac{5 c^2 \sqrt{x} (6 b B-7 A c)}{8 b^4 \sqrt{b x+c x^2}}-\frac{5 c^2 (6 b B-7 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{9/2}}+\frac{5 c (6 b B-7 A c)}{24 b^3 \sqrt{x} \sqrt{b x+c x^2}}-\frac{6 b B-7 A c}{12 b^2 x^{3/2} \sqrt{b x+c x^2}}-\frac{A}{3 b x^{5/2} \sqrt{b x+c x^2}}",1,"-A/(3*b*x^(5/2)*Sqrt[b*x + c*x^2]) - (6*b*B - 7*A*c)/(12*b^2*x^(3/2)*Sqrt[b*x + c*x^2]) + (5*c*(6*b*B - 7*A*c))/(24*b^3*Sqrt[x]*Sqrt[b*x + c*x^2]) + (5*c^2*(6*b*B - 7*A*c)*Sqrt[x])/(8*b^4*Sqrt[b*x + c*x^2]) - (5*c^2*(6*b*B - 7*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(9/2))","A",6,5,24,0.2083,1,"{792, 672, 666, 660, 207}"
241,1,216,0,0.1859571,"\int \frac{A+B x}{x^{7/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^(7/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{35 c^3 \sqrt{x} (8 b B-9 A c)}{64 b^5 \sqrt{b x+c x^2}}-\frac{35 c^2 (8 b B-9 A c)}{192 b^4 \sqrt{x} \sqrt{b x+c x^2}}+\frac{35 c^3 (8 b B-9 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{11/2}}+\frac{7 c (8 b B-9 A c)}{96 b^3 x^{3/2} \sqrt{b x+c x^2}}-\frac{8 b B-9 A c}{24 b^2 x^{5/2} \sqrt{b x+c x^2}}-\frac{A}{4 b x^{7/2} \sqrt{b x+c x^2}}","-\frac{35 c^3 \sqrt{x} (8 b B-9 A c)}{64 b^5 \sqrt{b x+c x^2}}-\frac{35 c^2 (8 b B-9 A c)}{192 b^4 \sqrt{x} \sqrt{b x+c x^2}}+\frac{35 c^3 (8 b B-9 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{64 b^{11/2}}+\frac{7 c (8 b B-9 A c)}{96 b^3 x^{3/2} \sqrt{b x+c x^2}}-\frac{8 b B-9 A c}{24 b^2 x^{5/2} \sqrt{b x+c x^2}}-\frac{A}{4 b x^{7/2} \sqrt{b x+c x^2}}",1,"-A/(4*b*x^(7/2)*Sqrt[b*x + c*x^2]) - (8*b*B - 9*A*c)/(24*b^2*x^(5/2)*Sqrt[b*x + c*x^2]) + (7*c*(8*b*B - 9*A*c))/(96*b^3*x^(3/2)*Sqrt[b*x + c*x^2]) - (35*c^2*(8*b*B - 9*A*c))/(192*b^4*Sqrt[x]*Sqrt[b*x + c*x^2]) - (35*c^3*(8*b*B - 9*A*c)*Sqrt[x])/(64*b^5*Sqrt[b*x + c*x^2]) + (35*c^3*(8*b*B - 9*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(64*b^(11/2))","A",7,5,24,0.2083,1,"{792, 672, 666, 660, 207}"
242,1,180,0,0.1592568,"\int \frac{x^{11/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^(11/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{32 b^2 \sqrt{x} (8 b B-5 A c)}{15 c^5 \sqrt{b x+c x^2}}+\frac{2 x^{7/2} (8 b B-5 A c)}{15 b c^2 \sqrt{b x+c x^2}}-\frac{4 x^{5/2} (8 b B-5 A c)}{15 c^3 \sqrt{b x+c x^2}}+\frac{16 b x^{3/2} (8 b B-5 A c)}{15 c^4 \sqrt{b x+c x^2}}-\frac{2 x^{11/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{32 b^2 \sqrt{x} (8 b B-5 A c)}{15 c^5 \sqrt{b x+c x^2}}+\frac{2 x^{7/2} (8 b B-5 A c)}{15 b c^2 \sqrt{b x+c x^2}}-\frac{4 x^{5/2} (8 b B-5 A c)}{15 c^3 \sqrt{b x+c x^2}}+\frac{16 b x^{3/2} (8 b B-5 A c)}{15 c^4 \sqrt{b x+c x^2}}-\frac{2 x^{11/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^(11/2))/(3*b*c*(b*x + c*x^2)^(3/2)) + (32*b^2*(8*b*B - 5*A*c)*Sqrt[x])/(15*c^5*Sqrt[b*x + c*x^2]) + (16*b*(8*b*B - 5*A*c)*x^(3/2))/(15*c^4*Sqrt[b*x + c*x^2]) - (4*(8*b*B - 5*A*c)*x^(5/2))/(15*c^3*Sqrt[b*x + c*x^2]) + (2*(8*b*B - 5*A*c)*x^(7/2))/(15*b*c^2*Sqrt[b*x + c*x^2])","A",5,3,24,0.1250,1,"{788, 656, 648}"
243,1,143,0,0.1151884,"\int \frac{x^{9/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^(9/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^{5/2} (2 b B-A c)}{3 b c^2 \sqrt{b x+c x^2}}-\frac{8 x^{3/2} (2 b B-A c)}{3 c^3 \sqrt{b x+c x^2}}-\frac{16 b \sqrt{x} (2 b B-A c)}{3 c^4 \sqrt{b x+c x^2}}-\frac{2 x^{9/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{2 x^{5/2} (2 b B-A c)}{3 b c^2 \sqrt{b x+c x^2}}-\frac{8 x^{3/2} (2 b B-A c)}{3 c^3 \sqrt{b x+c x^2}}-\frac{16 b \sqrt{x} (2 b B-A c)}{3 c^4 \sqrt{b x+c x^2}}-\frac{2 x^{9/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^(9/2))/(3*b*c*(b*x + c*x^2)^(3/2)) - (16*b*(2*b*B - A*c)*Sqrt[x])/(3*c^4*Sqrt[b*x + c*x^2]) - (8*(2*b*B - A*c)*x^(3/2))/(3*c^3*Sqrt[b*x + c*x^2]) + (2*(2*b*B - A*c)*x^(5/2))/(3*b*c^2*Sqrt[b*x + c*x^2])","A",4,3,24,0.1250,1,"{788, 656, 648}"
244,1,108,0,0.0896188,"\int \frac{x^{7/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^(7/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 x^{3/2} (4 b B-A c)}{3 b c^2 \sqrt{b x+c x^2}}+\frac{4 \sqrt{x} (4 b B-A c)}{3 c^3 \sqrt{b x+c x^2}}-\frac{2 x^{7/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{2 x^{3/2} (4 b B-A c)}{3 b c^2 \sqrt{b x+c x^2}}+\frac{4 \sqrt{x} (4 b B-A c)}{3 c^3 \sqrt{b x+c x^2}}-\frac{2 x^{7/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^(7/2))/(3*b*c*(b*x + c*x^2)^(3/2)) + (4*(4*b*B - A*c)*Sqrt[x])/(3*c^3*Sqrt[b*x + c*x^2]) + (2*(4*b*B - A*c)*x^(3/2))/(3*b*c^2*Sqrt[b*x + c*x^2])","A",3,3,24,0.1250,1,"{788, 656, 648}"
245,1,73,0,0.0528741,"\int \frac{x^{5/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^(5/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","-\frac{2 \sqrt{x} (A c+2 b B)}{3 b c^2 \sqrt{b x+c x^2}}-\frac{2 x^{5/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","-\frac{2 \sqrt{x} (A c+2 b B)}{3 b c^2 \sqrt{b x+c x^2}}-\frac{2 x^{5/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^(5/2))/(3*b*c*(b*x + c*x^2)^(3/2)) - (2*(2*b*B + A*c)*Sqrt[x])/(3*b*c^2*Sqrt[b*x + c*x^2])","A",2,2,24,0.08333,1,"{788, 648}"
246,1,94,0,0.0766622,"\int \frac{x^{3/2} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(x^(3/2)*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 A \sqrt{x}}{b^2 \sqrt{b x+c x^2}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}-\frac{2 x^{3/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{2 A \sqrt{x}}{b^2 \sqrt{b x+c x^2}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{5/2}}-\frac{2 x^{3/2} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*x^(3/2))/(3*b*c*(b*x + c*x^2)^(3/2)) + (2*A*Sqrt[x])/(b^2*Sqrt[b*x + c*x^2]) - (2*A*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(5/2)","A",4,4,24,0.1667,1,"{788, 666, 660, 207}"
247,1,146,0,0.1185611,"\int \frac{\sqrt{x} (A+B x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(Sqrt[x]*(A + B*x))/(b*x + c*x^2)^(5/2),x]","\frac{\sqrt{x} (2 b B-5 A c)}{b^3 \sqrt{b x+c x^2}}+\frac{2 b B-5 A c}{3 b^2 c \sqrt{x} \sqrt{b x+c x^2}}-\frac{(2 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{7/2}}-\frac{2 \sqrt{x} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}","\frac{\sqrt{x} (2 b B-5 A c)}{b^3 \sqrt{b x+c x^2}}+\frac{2 b B-5 A c}{3 b^2 c \sqrt{x} \sqrt{b x+c x^2}}-\frac{(2 b B-5 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{b^{7/2}}-\frac{2 \sqrt{x} (b B-A c)}{3 b c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(b*B - A*c)*Sqrt[x])/(3*b*c*(b*x + c*x^2)^(3/2)) + (2*b*B - 5*A*c)/(3*b^2*c*Sqrt[x]*Sqrt[b*x + c*x^2]) + ((2*b*B - 5*A*c)*Sqrt[x])/(b^3*Sqrt[b*x + c*x^2]) - ((2*b*B - 5*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/b^(7/2)","A",5,5,24,0.2083,1,"{788, 672, 666, 660, 207}"
248,1,174,0,0.1469509,"\int \frac{A+B x}{\sqrt{x} \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(Sqrt[x]*(b*x + c*x^2)^(5/2)),x]","-\frac{5 c \sqrt{x} (4 b B-7 A c)}{4 b^4 \sqrt{b x+c x^2}}-\frac{5 (4 b B-7 A c)}{12 b^3 \sqrt{x} \sqrt{b x+c x^2}}+\frac{\sqrt{x} (4 b B-7 A c)}{6 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{5 c (4 b B-7 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{9/2}}-\frac{A}{2 b \sqrt{x} \left(b x+c x^2\right)^{3/2}}","-\frac{5 c \sqrt{x} (4 b B-7 A c)}{4 b^4 \sqrt{b x+c x^2}}-\frac{5 (4 b B-7 A c)}{12 b^3 \sqrt{x} \sqrt{b x+c x^2}}+\frac{\sqrt{x} (4 b B-7 A c)}{6 b^2 \left(b x+c x^2\right)^{3/2}}+\frac{5 c (4 b B-7 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{4 b^{9/2}}-\frac{A}{2 b \sqrt{x} \left(b x+c x^2\right)^{3/2}}",1,"-A/(2*b*Sqrt[x]*(b*x + c*x^2)^(3/2)) + ((4*b*B - 7*A*c)*Sqrt[x])/(6*b^2*(b*x + c*x^2)^(3/2)) - (5*(4*b*B - 7*A*c))/(12*b^3*Sqrt[x]*Sqrt[b*x + c*x^2]) - (5*c*(4*b*B - 7*A*c)*Sqrt[x])/(4*b^4*Sqrt[b*x + c*x^2]) + (5*c*(4*b*B - 7*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(4*b^(9/2))","A",6,5,24,0.2083,1,"{792, 666, 672, 660, 207}"
249,1,214,0,0.1831596,"\int \frac{A+B x}{x^{3/2} \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^(3/2)*(b*x + c*x^2)^(5/2)),x]","\frac{35 c^2 \sqrt{x} (2 b B-3 A c)}{8 b^5 \sqrt{b x+c x^2}}-\frac{35 c^2 (2 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{11/2}}+\frac{35 c (2 b B-3 A c)}{24 b^4 \sqrt{x} \sqrt{b x+c x^2}}-\frac{7 c \sqrt{x} (2 b B-3 A c)}{12 b^3 \left(b x+c x^2\right)^{3/2}}-\frac{2 b B-3 A c}{4 b^2 \sqrt{x} \left(b x+c x^2\right)^{3/2}}-\frac{A}{3 b x^{3/2} \left(b x+c x^2\right)^{3/2}}","\frac{35 c^2 \sqrt{x} (2 b B-3 A c)}{8 b^5 \sqrt{b x+c x^2}}-\frac{35 c^2 (2 b B-3 A c) \tanh ^{-1}\left(\frac{\sqrt{b x+c x^2}}{\sqrt{b} \sqrt{x}}\right)}{8 b^{11/2}}+\frac{35 c (2 b B-3 A c)}{24 b^4 \sqrt{x} \sqrt{b x+c x^2}}-\frac{7 c \sqrt{x} (2 b B-3 A c)}{12 b^3 \left(b x+c x^2\right)^{3/2}}-\frac{2 b B-3 A c}{4 b^2 \sqrt{x} \left(b x+c x^2\right)^{3/2}}-\frac{A}{3 b x^{3/2} \left(b x+c x^2\right)^{3/2}}",1,"-A/(3*b*x^(3/2)*(b*x + c*x^2)^(3/2)) - (2*b*B - 3*A*c)/(4*b^2*Sqrt[x]*(b*x + c*x^2)^(3/2)) - (7*c*(2*b*B - 3*A*c)*Sqrt[x])/(12*b^3*(b*x + c*x^2)^(3/2)) + (35*c*(2*b*B - 3*A*c))/(24*b^4*Sqrt[x]*Sqrt[b*x + c*x^2]) + (35*c^2*(2*b*B - 3*A*c)*Sqrt[x])/(8*b^5*Sqrt[b*x + c*x^2]) - (35*c^2*(2*b*B - 3*A*c)*ArcTanh[Sqrt[b*x + c*x^2]/(Sqrt[b]*Sqrt[x])])/(8*b^(11/2))","A",7,5,24,0.2083,1,"{792, 672, 666, 660, 207}"
250,1,24,0,0.011545,"\int x^{1+p} (2 b+3 c x) \left(b x+c x^2\right)^p \, dx","Int[x^(1 + p)*(2*b + 3*c*x)*(b*x + c*x^2)^p,x]","\frac{x^{p+1} \left(b x+c x^2\right)^{p+1}}{p+1}","\frac{x^{p+1} \left(b x+c x^2\right)^{p+1}}{p+1}",1,"(x^(1 + p)*(b*x + c*x^2)^(1 + p))/(1 + p)","A",1,1,25,0.04000,1,"{763}"
251,1,37,0,0.035158,"\int x^3 (A+B x) \left(a+c x^2\right) \, dx","Int[x^3*(A + B*x)*(a + c*x^2),x]","\frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7","\frac{1}{4} a A x^4+\frac{1}{5} a B x^5+\frac{1}{6} A c x^6+\frac{1}{7} B c x^7",1,"(a*A*x^4)/4 + (a*B*x^5)/5 + (A*c*x^6)/6 + (B*c*x^7)/7","A",2,1,16,0.06250,1,"{766}"
252,1,37,0,0.0291948,"\int x^2 (A+B x) \left(a+c x^2\right) \, dx","Int[x^2*(A + B*x)*(a + c*x^2),x]","\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} A c x^5+\frac{1}{6} B c x^6","\frac{1}{3} a A x^3+\frac{1}{4} a B x^4+\frac{1}{5} A c x^5+\frac{1}{6} B c x^6",1,"(a*A*x^3)/3 + (a*B*x^4)/4 + (A*c*x^5)/5 + (B*c*x^6)/6","A",2,1,16,0.06250,1,"{766}"
253,1,37,0,0.0230988,"\int x (A+B x) \left(a+c x^2\right) \, dx","Int[x*(A + B*x)*(a + c*x^2),x]","\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{4} A c x^4+\frac{1}{5} B c x^5","\frac{1}{2} a A x^2+\frac{1}{3} a B x^3+\frac{1}{4} A c x^4+\frac{1}{5} B c x^5",1,"(a*A*x^2)/2 + (a*B*x^3)/3 + (A*c*x^4)/4 + (B*c*x^5)/5","A",2,1,14,0.07143,1,"{766}"
254,1,31,0,0.0064638,"\int (A+B x) \left(a+c x^2\right) \, dx","Int[(A + B*x)*(a + c*x^2),x]","a A x+\frac{B \left(a+c x^2\right)^2}{4 c}+\frac{1}{3} A c x^3","a A x+\frac{B \left(a+c x^2\right)^2}{4 c}+\frac{1}{3} A c x^3",1,"a*A*x + (A*c*x^3)/3 + (B*(a + c*x^2)^2)/(4*c)","A",2,1,13,0.07692,1,"{641}"
255,1,28,0,0.0103621,"\int \frac{(A+B x) \left(a+c x^2\right)}{x} \, dx","Int[((A + B*x)*(a + c*x^2))/x,x]","a A \log (x)+a B x+\frac{1}{2} A c x^2+\frac{1}{3} B c x^3","a A \log (x)+a B x+\frac{1}{2} A c x^2+\frac{1}{3} B c x^3",1,"a*B*x + (A*c*x^2)/2 + (B*c*x^3)/3 + a*A*Log[x]","A",2,1,16,0.06250,1,"{766}"
256,1,26,0,0.0143074,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^2} \, dx","Int[((A + B*x)*(a + c*x^2))/x^2,x]","-\frac{a A}{x}+a B \log (x)+A c x+\frac{1}{2} B c x^2","-\frac{a A}{x}+a B \log (x)+A c x+\frac{1}{2} B c x^2",1,"-((a*A)/x) + A*c*x + (B*c*x^2)/2 + a*B*Log[x]","A",2,1,16,0.06250,1,"{766}"
257,1,26,0,0.0142789,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^3} \, dx","Int[((A + B*x)*(a + c*x^2))/x^3,x]","-\frac{a A}{2 x^2}-\frac{a B}{x}+A c \log (x)+B c x","-\frac{a A}{2 x^2}-\frac{a B}{x}+A c \log (x)+B c x",1,"-(a*A)/(2*x^2) - (a*B)/x + B*c*x + A*c*Log[x]","A",2,1,16,0.06250,1,"{766}"
258,1,65,0,0.0620027,"\int x^3 (A+B x) \left(a+c x^2\right)^2 \, dx","Int[x^3*(A + B*x)*(a + c*x^2)^2,x]","\frac{1}{4} a^2 A x^4+\frac{1}{5} a^2 B x^5+\frac{1}{3} a A c x^6+\frac{2}{7} a B c x^7+\frac{1}{8} A c^2 x^8+\frac{1}{9} B c^2 x^9","\frac{1}{4} a^2 A x^4+\frac{1}{5} a^2 B x^5+\frac{1}{3} a A c x^6+\frac{2}{7} a B c x^7+\frac{1}{8} A c^2 x^8+\frac{1}{9} B c^2 x^9",1,"(a^2*A*x^4)/4 + (a^2*B*x^5)/5 + (a*A*c*x^6)/3 + (2*a*B*c*x^7)/7 + (A*c^2*x^8)/8 + (B*c^2*x^9)/9","A",2,1,18,0.05556,1,"{766}"
259,1,65,0,0.0528254,"\int x^2 (A+B x) \left(a+c x^2\right)^2 \, dx","Int[x^2*(A + B*x)*(a + c*x^2)^2,x]","\frac{1}{3} a^2 A x^3+\frac{1}{4} a^2 B x^4+\frac{2}{5} a A c x^5+\frac{1}{3} a B c x^6+\frac{1}{7} A c^2 x^7+\frac{1}{8} B c^2 x^8","\frac{1}{3} a^2 A x^3+\frac{1}{4} a^2 B x^4+\frac{2}{5} a A c x^5+\frac{1}{3} a B c x^6+\frac{1}{7} A c^2 x^7+\frac{1}{8} B c^2 x^8",1,"(a^2*A*x^3)/3 + (a^2*B*x^4)/4 + (2*a*A*c*x^5)/5 + (a*B*c*x^6)/3 + (A*c^2*x^7)/7 + (B*c^2*x^8)/8","A",2,1,18,0.05556,1,"{766}"
260,1,65,0,0.044207,"\int x (A+B x) \left(a+c x^2\right)^2 \, dx","Int[x*(A + B*x)*(a + c*x^2)^2,x]","\frac{1}{2} a^2 A x^2+\frac{1}{3} a^2 B x^3+\frac{1}{2} a A c x^4+\frac{2}{5} a B c x^5+\frac{1}{6} A c^2 x^6+\frac{1}{7} B c^2 x^7","\frac{1}{2} a^2 A x^2+\frac{1}{3} a^2 B x^3+\frac{1}{2} a A c x^4+\frac{2}{5} a B c x^5+\frac{1}{6} A c^2 x^6+\frac{1}{7} B c^2 x^7",1,"(a^2*A*x^2)/2 + (a^2*B*x^3)/3 + (a*A*c*x^4)/2 + (2*a*B*c*x^5)/5 + (A*c^2*x^6)/6 + (B*c^2*x^7)/7","A",2,1,16,0.06250,1,"{766}"
261,1,45,0,0.0148019,"\int (A+B x) \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(a + c*x^2)^2,x]","a^2 A x+\frac{2}{3} a A c x^3+\frac{B \left(a+c x^2\right)^3}{6 c}+\frac{1}{5} A c^2 x^5","a^2 A x+\frac{2}{3} a A c x^3+\frac{B \left(a+c x^2\right)^3}{6 c}+\frac{1}{5} A c^2 x^5",1,"a^2*A*x + (2*a*A*c*x^3)/3 + (A*c^2*x^5)/5 + (B*(a + c*x^2)^3)/(6*c)","A",3,2,15,0.1333,1,"{641, 194}"
262,1,53,0,0.0209783,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x,x]","a^2 A \log (x)+a^2 B x+a A c x^2+\frac{2}{3} a B c x^3+\frac{1}{4} A c^2 x^4+\frac{1}{5} B c^2 x^5","a^2 A \log (x)+a^2 B x+a A c x^2+\frac{2}{3} a B c x^3+\frac{1}{4} A c^2 x^4+\frac{1}{5} B c^2 x^5",1,"a^2*B*x + a*A*c*x^2 + (2*a*B*c*x^3)/3 + (A*c^2*x^4)/4 + (B*c^2*x^5)/5 + a^2*A*Log[x]","A",2,1,18,0.05556,1,"{766}"
263,1,52,0,0.025836,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^2} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x^2,x]","-\frac{a^2 A}{x}+a^2 B \log (x)+2 a A c x+a B c x^2+\frac{1}{3} A c^2 x^3+\frac{1}{4} B c^2 x^4","-\frac{a^2 A}{x}+a^2 B \log (x)+2 a A c x+a B c x^2+\frac{1}{3} A c^2 x^3+\frac{1}{4} B c^2 x^4",1,"-((a^2*A)/x) + 2*a*A*c*x + a*B*c*x^2 + (A*c^2*x^3)/3 + (B*c^2*x^4)/4 + a^2*B*Log[x]","A",2,1,18,0.05556,1,"{766}"
264,1,56,0,0.025971,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^3} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x^3,x]","-\frac{a^2 A}{2 x^2}-\frac{a^2 B}{x}+2 a A c \log (x)+2 a B c x+\frac{1}{2} A c^2 x^2+\frac{1}{3} B c^2 x^3","-\frac{a^2 A}{2 x^2}-\frac{a^2 B}{x}+2 a A c \log (x)+2 a B c x+\frac{1}{2} A c^2 x^2+\frac{1}{3} B c^2 x^3",1,"-(a^2*A)/(2*x^2) - (a^2*B)/x + 2*a*B*c*x + (A*c^2*x^2)/2 + (B*c^2*x^3)/3 + 2*a*A*c*Log[x]","A",2,1,18,0.05556,1,"{766}"
265,1,93,0,0.1009031,"\int x^3 (A+B x) \left(a+c x^2\right)^3 \, dx","Int[x^3*(A + B*x)*(a + c*x^2)^3,x]","\frac{1}{2} a^2 A c x^6+\frac{1}{4} a^3 A x^4+\frac{3}{7} a^2 B c x^7+\frac{1}{5} a^3 B x^5+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11}","\frac{1}{2} a^2 A c x^6+\frac{1}{4} a^3 A x^4+\frac{3}{7} a^2 B c x^7+\frac{1}{5} a^3 B x^5+\frac{3}{8} a A c^2 x^8+\frac{1}{3} a B c^2 x^9+\frac{1}{10} A c^3 x^{10}+\frac{1}{11} B c^3 x^{11}",1,"(a^3*A*x^4)/4 + (a^3*B*x^5)/5 + (a^2*A*c*x^6)/2 + (3*a^2*B*c*x^7)/7 + (3*a*A*c^2*x^8)/8 + (a*B*c^2*x^9)/3 + (A*c^3*x^10)/10 + (B*c^3*x^11)/11","A",2,1,18,0.05556,1,"{766}"
266,1,93,0,0.088014,"\int x^2 (A+B x) \left(a+c x^2\right)^3 \, dx","Int[x^2*(A + B*x)*(a + c*x^2)^3,x]","\frac{3}{5} a^2 A c x^5+\frac{1}{3} a^3 A x^3+\frac{1}{2} a^2 B c x^6+\frac{1}{4} a^3 B x^4+\frac{3}{7} a A c^2 x^7+\frac{3}{8} a B c^2 x^8+\frac{1}{9} A c^3 x^9+\frac{1}{10} B c^3 x^{10}","\frac{3}{5} a^2 A c x^5+\frac{1}{3} a^3 A x^3+\frac{1}{2} a^2 B c x^6+\frac{1}{4} a^3 B x^4+\frac{3}{7} a A c^2 x^7+\frac{3}{8} a B c^2 x^8+\frac{1}{9} A c^3 x^9+\frac{1}{10} B c^3 x^{10}",1,"(a^3*A*x^3)/3 + (a^3*B*x^4)/4 + (3*a^2*A*c*x^5)/5 + (a^2*B*c*x^6)/2 + (3*a*A*c^2*x^7)/7 + (3*a*B*c^2*x^8)/8 + (A*c^3*x^9)/9 + (B*c^3*x^10)/10","A",2,1,18,0.05556,1,"{766}"
267,1,93,0,0.0792587,"\int x (A+B x) \left(a+c x^2\right)^3 \, dx","Int[x*(A + B*x)*(a + c*x^2)^3,x]","\frac{3}{4} a^2 A c x^4+\frac{1}{2} a^3 A x^2+\frac{3}{5} a^2 B c x^5+\frac{1}{3} a^3 B x^3+\frac{1}{2} a A c^2 x^6+\frac{3}{7} a B c^2 x^7+\frac{1}{8} A c^3 x^8+\frac{1}{9} B c^3 x^9","\frac{3}{4} a^2 A c x^4+\frac{1}{2} a^3 A x^2+\frac{3}{5} a^2 B c x^5+\frac{1}{3} a^3 B x^3+\frac{1}{2} a A c^2 x^6+\frac{3}{7} a B c^2 x^7+\frac{1}{8} A c^3 x^8+\frac{1}{9} B c^3 x^9",1,"(a^3*A*x^2)/2 + (a^3*B*x^3)/3 + (3*a^2*A*c*x^4)/4 + (3*a^2*B*c*x^5)/5 + (a*A*c^2*x^6)/2 + (3*a*B*c^2*x^7)/7 + (A*c^3*x^8)/8 + (B*c^3*x^9)/9","A",2,1,16,0.06250,1,"{766}"
268,1,56,0,0.0205438,"\int (A+B x) \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(a + c*x^2)^3,x]","a^2 A c x^3+a^3 A x+\frac{3}{5} a A c^2 x^5+\frac{B \left(a+c x^2\right)^4}{8 c}+\frac{1}{7} A c^3 x^7","a^2 A c x^3+a^3 A x+\frac{3}{5} a A c^2 x^5+\frac{B \left(a+c x^2\right)^4}{8 c}+\frac{1}{7} A c^3 x^7",1,"a^3*A*x + a^2*A*c*x^3 + (3*a*A*c^2*x^5)/5 + (A*c^3*x^7)/7 + (B*(a + c*x^2)^4)/(8*c)","A",3,2,15,0.1333,1,"{641, 194}"
269,1,81,0,0.0361952,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x,x]","\frac{3}{2} a^2 A c x^2+a^3 A \log (x)+a^2 B c x^3+a^3 B x+\frac{3}{4} a A c^2 x^4+\frac{3}{5} a B c^2 x^5+\frac{1}{6} A c^3 x^6+\frac{1}{7} B c^3 x^7","\frac{3}{2} a^2 A c x^2+a^3 A \log (x)+a^2 B c x^3+a^3 B x+\frac{3}{4} a A c^2 x^4+\frac{3}{5} a B c^2 x^5+\frac{1}{6} A c^3 x^6+\frac{1}{7} B c^3 x^7",1,"a^3*B*x + (3*a^2*A*c*x^2)/2 + a^2*B*c*x^3 + (3*a*A*c^2*x^4)/4 + (3*a*B*c^2*x^5)/5 + (A*c^3*x^6)/6 + (B*c^3*x^7)/7 + a^3*A*Log[x]","A",2,1,18,0.05556,1,"{766}"
270,1,80,0,0.0413895,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^2} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^2,x]","3 a^2 A c x-\frac{a^3 A}{x}+\frac{3}{2} a^2 B c x^2+a^3 B \log (x)+a A c^2 x^3+\frac{3}{4} a B c^2 x^4+\frac{1}{5} A c^3 x^5+\frac{1}{6} B c^3 x^6","3 a^2 A c x-\frac{a^3 A}{x}+\frac{3}{2} a^2 B c x^2+a^3 B \log (x)+a A c^2 x^3+\frac{3}{4} a B c^2 x^4+\frac{1}{5} A c^3 x^5+\frac{1}{6} B c^3 x^6",1,"-((a^3*A)/x) + 3*a^2*A*c*x + (3*a^2*B*c*x^2)/2 + a*A*c^2*x^3 + (3*a*B*c^2*x^4)/4 + (A*c^3*x^5)/5 + (B*c^3*x^6)/6 + a^3*B*Log[x]","A",2,1,18,0.05556,1,"{766}"
271,1,81,0,0.0397865,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^3} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^3,x]","3 a^2 A c \log (x)-\frac{a^3 A}{2 x^2}+3 a^2 B c x-\frac{a^3 B}{x}+\frac{3}{2} a A c^2 x^2+a B c^2 x^3+\frac{1}{4} A c^3 x^4+\frac{1}{5} B c^3 x^5","3 a^2 A c \log (x)-\frac{a^3 A}{2 x^2}+3 a^2 B c x-\frac{a^3 B}{x}+\frac{3}{2} a A c^2 x^2+a B c^2 x^3+\frac{1}{4} A c^3 x^4+\frac{1}{5} B c^3 x^5",1,"-(a^3*A)/(2*x^2) - (a^3*B)/x + 3*a^2*B*c*x + (3*a*A*c^2*x^2)/2 + a*B*c^2*x^3 + (A*c^3*x^4)/4 + (B*c^3*x^5)/5 + 3*a^2*A*c*Log[x]","A",2,1,18,0.05556,1,"{766}"
272,1,121,0,0.1413673,"\int x^3 (A+B x) \left(a+c x^2\right)^4 \, dx","Int[x^3*(A + B*x)*(a + c*x^2)^4,x]","\frac{3}{4} a^2 A c^2 x^8+\frac{2}{3} a^3 A c x^6+\frac{1}{4} a^4 A x^4+\frac{2}{3} a^2 B c^2 x^9+\frac{4}{7} a^3 B c x^7+\frac{1}{5} a^4 B x^5+\frac{2}{5} a A c^3 x^{10}+\frac{4}{11} a B c^3 x^{11}+\frac{1}{12} A c^4 x^{12}+\frac{1}{13} B c^4 x^{13}","\frac{3}{4} a^2 A c^2 x^8+\frac{2}{3} a^3 A c x^6+\frac{1}{4} a^4 A x^4+\frac{2}{3} a^2 B c^2 x^9+\frac{4}{7} a^3 B c x^7+\frac{1}{5} a^4 B x^5+\frac{2}{5} a A c^3 x^{10}+\frac{4}{11} a B c^3 x^{11}+\frac{1}{12} A c^4 x^{12}+\frac{1}{13} B c^4 x^{13}",1,"(a^4*A*x^4)/4 + (a^4*B*x^5)/5 + (2*a^3*A*c*x^6)/3 + (4*a^3*B*c*x^7)/7 + (3*a^2*A*c^2*x^8)/4 + (2*a^2*B*c^2*x^9)/3 + (2*a*A*c^3*x^10)/5 + (4*a*B*c^3*x^11)/11 + (A*c^4*x^12)/12 + (B*c^4*x^13)/13","A",2,1,18,0.05556,1,"{766}"
273,1,121,0,0.123798,"\int x^2 (A+B x) \left(a+c x^2\right)^4 \, dx","Int[x^2*(A + B*x)*(a + c*x^2)^4,x]","\frac{6}{7} a^2 A c^2 x^7+\frac{4}{5} a^3 A c x^5+\frac{1}{3} a^4 A x^3+\frac{3}{4} a^2 B c^2 x^8+\frac{2}{3} a^3 B c x^6+\frac{1}{4} a^4 B x^4+\frac{4}{9} a A c^3 x^9+\frac{2}{5} a B c^3 x^{10}+\frac{1}{11} A c^4 x^{11}+\frac{1}{12} B c^4 x^{12}","\frac{6}{7} a^2 A c^2 x^7+\frac{4}{5} a^3 A c x^5+\frac{1}{3} a^4 A x^3+\frac{3}{4} a^2 B c^2 x^8+\frac{2}{3} a^3 B c x^6+\frac{1}{4} a^4 B x^4+\frac{4}{9} a A c^3 x^9+\frac{2}{5} a B c^3 x^{10}+\frac{1}{11} A c^4 x^{11}+\frac{1}{12} B c^4 x^{12}",1,"(a^4*A*x^3)/3 + (a^4*B*x^4)/4 + (4*a^3*A*c*x^5)/5 + (2*a^3*B*c*x^6)/3 + (6*a^2*A*c^2*x^7)/7 + (3*a^2*B*c^2*x^8)/4 + (4*a*A*c^3*x^9)/9 + (2*a*B*c^3*x^10)/5 + (A*c^4*x^11)/11 + (B*c^4*x^12)/12","A",2,1,18,0.05556,1,"{766}"
274,1,115,0,0.1157339,"\int x (A+B x) \left(a+c x^2\right)^4 \, dx","Int[x*(A + B*x)*(a + c*x^2)^4,x]","a^2 A c^2 x^6+a^3 A c x^4+\frac{1}{2} a^4 A x^2+\frac{6}{7} a^2 B c^2 x^7+\frac{4}{5} a^3 B c x^5+\frac{1}{3} a^4 B x^3+\frac{1}{2} a A c^3 x^8+\frac{4}{9} a B c^3 x^9+\frac{1}{10} A c^4 x^{10}+\frac{1}{11} B c^4 x^{11}","a^2 A c^2 x^6+a^3 A c x^4+\frac{1}{2} a^4 A x^2+\frac{6}{7} a^2 B c^2 x^7+\frac{4}{5} a^3 B c x^5+\frac{1}{3} a^4 B x^3+\frac{1}{2} a A c^3 x^8+\frac{4}{9} a B c^3 x^9+\frac{1}{10} A c^4 x^{10}+\frac{1}{11} B c^4 x^{11}",1,"(a^4*A*x^2)/2 + (a^4*B*x^3)/3 + a^3*A*c*x^4 + (4*a^3*B*c*x^5)/5 + a^2*A*c^2*x^6 + (6*a^2*B*c^2*x^7)/7 + (a*A*c^3*x^8)/2 + (4*a*B*c^3*x^9)/9 + (A*c^4*x^10)/10 + (B*c^4*x^11)/11","A",2,1,16,0.06250,1,"{766}"
275,1,73,0,0.0250958,"\int (A+B x) \left(a+c x^2\right)^4 \, dx","Int[(A + B*x)*(a + c*x^2)^4,x]","\frac{6}{5} a^2 A c^2 x^5+\frac{4}{3} a^3 A c x^3+a^4 A x+\frac{4}{7} a A c^3 x^7+\frac{B \left(a+c x^2\right)^5}{10 c}+\frac{1}{9} A c^4 x^9","\frac{6}{5} a^2 A c^2 x^5+\frac{4}{3} a^3 A c x^3+a^4 A x+\frac{4}{7} a A c^3 x^7+\frac{B \left(a+c x^2\right)^5}{10 c}+\frac{1}{9} A c^4 x^9",1,"a^4*A*x + (4*a^3*A*c*x^3)/3 + (6*a^2*A*c^2*x^5)/5 + (4*a*A*c^3*x^7)/7 + (A*c^4*x^9)/9 + (B*(a + c*x^2)^5)/(10*c)","A",3,2,15,0.1333,1,"{641, 194}"
276,1,110,0,0.052258,"\int \frac{(A+B x) \left(a+c x^2\right)^4}{x} \, dx","Int[((A + B*x)*(a + c*x^2)^4)/x,x]","\frac{3}{2} a^2 A c^2 x^4+2 a^3 A c x^2+a^4 A \log (x)+\frac{6}{5} a^2 B c^2 x^5+\frac{4}{3} a^3 B c x^3+a^4 B x+\frac{2}{3} a A c^3 x^6+\frac{4}{7} a B c^3 x^7+\frac{1}{8} A c^4 x^8+\frac{1}{9} B c^4 x^9","\frac{3}{2} a^2 A c^2 x^4+2 a^3 A c x^2+a^4 A \log (x)+\frac{6}{5} a^2 B c^2 x^5+\frac{4}{3} a^3 B c x^3+a^4 B x+\frac{2}{3} a A c^3 x^6+\frac{4}{7} a B c^3 x^7+\frac{1}{8} A c^4 x^8+\frac{1}{9} B c^4 x^9",1,"a^4*B*x + 2*a^3*A*c*x^2 + (4*a^3*B*c*x^3)/3 + (3*a^2*A*c^2*x^4)/2 + (6*a^2*B*c^2*x^5)/5 + (2*a*A*c^3*x^6)/3 + (4*a*B*c^3*x^7)/7 + (A*c^4*x^8)/8 + (B*c^4*x^9)/9 + a^4*A*Log[x]","A",2,1,18,0.05556,1,"{766}"
277,1,107,0,0.055733,"\int \frac{(A+B x) \left(a+c x^2\right)^4}{x^2} \, dx","Int[((A + B*x)*(a + c*x^2)^4)/x^2,x]","2 a^2 A c^2 x^3+4 a^3 A c x-\frac{a^4 A}{x}+\frac{3}{2} a^2 B c^2 x^4+2 a^3 B c x^2+a^4 B \log (x)+\frac{4}{5} a A c^3 x^5+\frac{2}{3} a B c^3 x^6+\frac{1}{7} A c^4 x^7+\frac{1}{8} B c^4 x^8","2 a^2 A c^2 x^3+4 a^3 A c x-\frac{a^4 A}{x}+\frac{3}{2} a^2 B c^2 x^4+2 a^3 B c x^2+a^4 B \log (x)+\frac{4}{5} a A c^3 x^5+\frac{2}{3} a B c^3 x^6+\frac{1}{7} A c^4 x^7+\frac{1}{8} B c^4 x^8",1,"-((a^4*A)/x) + 4*a^3*A*c*x + 2*a^3*B*c*x^2 + 2*a^2*A*c^2*x^3 + (3*a^2*B*c^2*x^4)/2 + (4*a*A*c^3*x^5)/5 + (2*a*B*c^3*x^6)/3 + (A*c^4*x^7)/7 + (B*c^4*x^8)/8 + a^4*B*Log[x]","A",2,1,18,0.05556,1,"{766}"
278,1,105,0,0.0548459,"\int \frac{(A+B x) \left(a+c x^2\right)^4}{x^3} \, dx","Int[((A + B*x)*(a + c*x^2)^4)/x^3,x]","3 a^2 A c^2 x^2+4 a^3 A c \log (x)-\frac{a^4 A}{2 x^2}+2 a^2 B c^2 x^3+4 a^3 B c x-\frac{a^4 B}{x}+a A c^3 x^4+\frac{4}{5} a B c^3 x^5+\frac{1}{6} A c^4 x^6+\frac{1}{7} B c^4 x^7","3 a^2 A c^2 x^2+4 a^3 A c \log (x)-\frac{a^4 A}{2 x^2}+2 a^2 B c^2 x^3+4 a^3 B c x-\frac{a^4 B}{x}+a A c^3 x^4+\frac{4}{5} a B c^3 x^5+\frac{1}{6} A c^4 x^6+\frac{1}{7} B c^4 x^7",1,"-(a^4*A)/(2*x^2) - (a^4*B)/x + 4*a^3*B*c*x + 3*a^2*A*c^2*x^2 + 2*a^2*B*c^2*x^3 + a*A*c^3*x^4 + (4*a*B*c^3*x^5)/5 + (A*c^4*x^6)/6 + (B*c^4*x^7)/7 + 4*a^3*A*c*Log[x]","A",2,1,18,0.05556,1,"{766}"
279,1,87,0,0.0621743,"\int \frac{x^4 (d+e x)}{a+c x^2} \, dx","Int[(x^4*(d + e*x))/(a + c*x^2),x]","\frac{a^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{5/2}}+\frac{a^2 e \log \left(a+c x^2\right)}{2 c^3}-\frac{a d x}{c^2}-\frac{a e x^2}{2 c^2}+\frac{d x^3}{3 c}+\frac{e x^4}{4 c}","\frac{a^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{5/2}}+\frac{a^2 e \log \left(a+c x^2\right)}{2 c^3}-\frac{a d x}{c^2}-\frac{a e x^2}{2 c^2}+\frac{d x^3}{3 c}+\frac{e x^4}{4 c}",1,"-((a*d*x)/c^2) - (a*e*x^2)/(2*c^2) + (d*x^3)/(3*c) + (e*x^4)/(4*c) + (a^(3/2)*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/c^(5/2) + (a^2*e*Log[a + c*x^2])/(2*c^3)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
280,1,73,0,0.047441,"\int \frac{x^3 (d+e x)}{a+c x^2} \, dx","Int[(x^3*(d + e*x))/(a + c*x^2),x]","\frac{a^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{5/2}}-\frac{a d \log \left(a+c x^2\right)}{2 c^2}-\frac{a e x}{c^2}+\frac{d x^2}{2 c}+\frac{e x^3}{3 c}","\frac{a^{3/2} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{5/2}}-\frac{a d \log \left(a+c x^2\right)}{2 c^2}-\frac{a e x}{c^2}+\frac{d x^2}{2 c}+\frac{e x^3}{3 c}",1,"-((a*e*x)/c^2) + (d*x^2)/(2*c) + (e*x^3)/(3*c) + (a^(3/2)*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/c^(5/2) - (a*d*Log[a + c*x^2])/(2*c^2)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
281,1,61,0,0.0441019,"\int \frac{x^2 (d+e x)}{a+c x^2} \, dx","Int[(x^2*(d + e*x))/(a + c*x^2),x]","-\frac{\sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{3/2}}-\frac{a e \log \left(a+c x^2\right)}{2 c^2}+\frac{d x}{c}+\frac{e x^2}{2 c}","-\frac{\sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{3/2}}-\frac{a e \log \left(a+c x^2\right)}{2 c^2}+\frac{d x}{c}+\frac{e x^2}{2 c}",1,"(d*x)/c + (e*x^2)/(2*c) - (Sqrt[a]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/c^(3/2) - (a*e*Log[a + c*x^2])/(2*c^2)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
282,1,49,0,0.0265298,"\int \frac{x (d+e x)}{a+c x^2} \, dx","Int[(x*(d + e*x))/(a + c*x^2),x]","-\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{3/2}}+\frac{d \log \left(a+c x^2\right)}{2 c}+\frac{e x}{c}","-\frac{\sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{c^{3/2}}+\frac{d \log \left(a+c x^2\right)}{2 c}+\frac{e x}{c}",1,"(e*x)/c - (Sqrt[a]*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/c^(3/2) + (d*Log[a + c*x^2])/(2*c)","A",4,4,16,0.2500,1,"{774, 635, 205, 260}"
283,1,42,0,0.0159209,"\int \frac{d+e x}{a+c x^2} \, dx","Int[(d + e*x)/(a + c*x^2),x]","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{e \log \left(a+c x^2\right)}{2 c}","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{e \log \left(a+c x^2\right)}{2 c}",1,"(d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]) + (e*Log[a + c*x^2])/(2*c)","A",3,3,15,0.2000,1,"{635, 205, 260}"
284,1,49,0,0.0419312,"\int \frac{d+e x}{x \left(a+c x^2\right)} \, dx","Int[(d + e*x)/(x*(a + c*x^2)),x]","-\frac{d \log \left(a+c x^2\right)}{2 a}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{d \log (x)}{a}","-\frac{d \log \left(a+c x^2\right)}{2 a}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{d \log (x)}{a}",1,"(e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]) + (d*Log[x])/a - (d*Log[a + c*x^2])/(2*a)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
285,1,59,0,0.0467175,"\int \frac{d+e x}{x^2 \left(a+c x^2\right)} \, dx","Int[(d + e*x)/(x^2*(a + c*x^2)),x]","-\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{e \log \left(a+c x^2\right)}{2 a}-\frac{d}{a x}+\frac{e \log (x)}{a}","-\frac{\sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{e \log \left(a+c x^2\right)}{2 a}-\frac{d}{a x}+\frac{e \log (x)}{a}",1,"-(d/(a*x)) - (Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/a^(3/2) + (e*Log[x])/a - (e*Log[a + c*x^2])/(2*a)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
286,1,73,0,0.0586117,"\int \frac{d+e x}{x^3 \left(a+c x^2\right)} \, dx","Int[(d + e*x)/(x^3*(a + c*x^2)),x]","\frac{c d \log \left(a+c x^2\right)}{2 a^2}-\frac{c d \log (x)}{a^2}-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{d}{2 a x^2}-\frac{e}{a x}","\frac{c d \log \left(a+c x^2\right)}{2 a^2}-\frac{c d \log (x)}{a^2}-\frac{\sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{3/2}}-\frac{d}{2 a x^2}-\frac{e}{a x}",1,"-d/(2*a*x^2) - e/(a*x) - (Sqrt[c]*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/a^(3/2) - (c*d*Log[x])/a^2 + (c*d*Log[a + c*x^2])/(2*a^2)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
287,1,83,0,0.0577717,"\int \frac{d+e x}{x^4 \left(a+c x^2\right)} \, dx","Int[(d + e*x)/(x^4*(a + c*x^2)),x]","\frac{c^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c d}{a^2 x}+\frac{c e \log \left(a+c x^2\right)}{2 a^2}-\frac{c e \log (x)}{a^2}-\frac{d}{3 a x^3}-\frac{e}{2 a x^2}","\frac{c^{3/2} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{a^{5/2}}+\frac{c d}{a^2 x}+\frac{c e \log \left(a+c x^2\right)}{2 a^2}-\frac{c e \log (x)}{a^2}-\frac{d}{3 a x^3}-\frac{e}{2 a x^2}",1,"-d/(3*a*x^3) - e/(2*a*x^2) + (c*d)/(a^2*x) + (c^(3/2)*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/a^(5/2) - (c*e*Log[x])/a^2 + (c*e*Log[a + c*x^2])/(2*a^2)","A",5,4,18,0.2222,1,"{801, 635, 205, 260}"
288,1,43,0,0.0151123,"\int \frac{d+e x}{a-c x^2} \, dx","Int[(d + e*x)/(a - c*x^2),x]","\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}-\frac{e \log \left(a-c x^2\right)}{2 c}","\frac{d \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}-\frac{e \log \left(a-c x^2\right)}{2 c}",1,"(d*ArcTanh[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]) - (e*Log[a - c*x^2])/(2*c)","A",3,3,16,0.1875,1,"{635, 208, 260}"
289,1,85,0,0.0701616,"\int \frac{x^4 (d+e x)}{\left(a+c x^2\right)^2} \, dx","Int[(x^4*(d + e*x))/(a + c*x^2)^2,x]","-\frac{3 \sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 c^{5/2}}-\frac{a e \log \left(a+c x^2\right)}{c^3}-\frac{x^3 (d+e x)}{2 c \left(a+c x^2\right)}+\frac{3 d x}{2 c^2}+\frac{e x^2}{c^2}","-\frac{3 \sqrt{a} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 c^{5/2}}-\frac{a e \log \left(a+c x^2\right)}{c^3}-\frac{x^3 (d+e x)}{2 c \left(a+c x^2\right)}+\frac{3 d x}{2 c^2}+\frac{e x^2}{c^2}",1,"(3*d*x)/(2*c^2) + (e*x^2)/c^2 - (x^3*(d + e*x))/(2*c*(a + c*x^2)) - (3*Sqrt[a]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*c^(5/2)) - (a*e*Log[a + c*x^2])/c^3","A",6,5,18,0.2778,1,"{819, 801, 635, 205, 260}"
290,1,78,0,0.0448865,"\int \frac{x^3 (d+e x)}{\left(a+c x^2\right)^2} \, dx","Int[(x^3*(d + e*x))/(a + c*x^2)^2,x]","\frac{d \log \left(a+c x^2\right)}{2 c^2}-\frac{3 \sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 c^{5/2}}-\frac{x^2 (d+e x)}{2 c \left(a+c x^2\right)}+\frac{3 e x}{2 c^2}","\frac{d \log \left(a+c x^2\right)}{2 c^2}-\frac{3 \sqrt{a} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 c^{5/2}}-\frac{x^2 (d+e x)}{2 c \left(a+c x^2\right)}+\frac{3 e x}{2 c^2}",1,"(3*e*x)/(2*c^2) - (x^2*(d + e*x))/(2*c*(a + c*x^2)) - (3*Sqrt[a]*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*c^(5/2)) + (d*Log[a + c*x^2])/(2*c^2)","A",5,5,18,0.2778,1,"{819, 774, 635, 205, 260}"
291,1,67,0,0.0307889,"\int \frac{x^2 (d+e x)}{\left(a+c x^2\right)^2} \, dx","Int[(x^2*(d + e*x))/(a + c*x^2)^2,x]","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 \sqrt{a} c^{3/2}}+\frac{e \log \left(a+c x^2\right)}{2 c^2}-\frac{x (d+e x)}{2 c \left(a+c x^2\right)}","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 \sqrt{a} c^{3/2}}+\frac{e \log \left(a+c x^2\right)}{2 c^2}-\frac{x (d+e x)}{2 c \left(a+c x^2\right)}",1,"-(x*(d + e*x))/(2*c*(a + c*x^2)) + (d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*Sqrt[a]*c^(3/2)) + (e*Log[a + c*x^2])/(2*c^2)","A",4,4,18,0.2222,1,"{819, 635, 205, 260}"
292,1,50,0,0.0152033,"\int \frac{x (d+e x)}{\left(a+c x^2\right)^2} \, dx","Int[(x*(d + e*x))/(a + c*x^2)^2,x]","\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 \sqrt{a} c^{3/2}}-\frac{d+e x}{2 c \left(a+c x^2\right)}","\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 \sqrt{a} c^{3/2}}-\frac{d+e x}{2 c \left(a+c x^2\right)}",1,"-(d + e*x)/(2*c*(a + c*x^2)) + (e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*Sqrt[a]*c^(3/2))","A",2,2,16,0.1250,1,"{778, 205}"
293,1,57,0,0.0133848,"\int \frac{d+e x}{\left(a+c x^2\right)^2} \, dx","Int[(d + e*x)/(a + c*x^2)^2,x]","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{a e-c d x}{2 a c \left(a+c x^2\right)}","\frac{d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{a e-c d x}{2 a c \left(a+c x^2\right)}",1,"-(a*e - c*d*x)/(2*a*c*(a + c*x^2)) + (d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c])","A",2,2,15,0.1333,1,"{639, 205}"
294,1,73,0,0.0619373,"\int \frac{d+e x}{x \left(a+c x^2\right)^2} \, dx","Int[(d + e*x)/(x*(a + c*x^2)^2),x]","-\frac{d \log \left(a+c x^2\right)}{2 a^2}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}+\frac{d \log (x)}{a^2}+\frac{d+e x}{2 a \left(a+c x^2\right)}","-\frac{d \log \left(a+c x^2\right)}{2 a^2}+\frac{e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}+\frac{d \log (x)}{a^2}+\frac{d+e x}{2 a \left(a+c x^2\right)}",1,"(d + e*x)/(2*a*(a + c*x^2)) + (e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c]) + (d*Log[x])/a^2 - (d*Log[a + c*x^2])/(2*a^2)","A",6,5,18,0.2778,1,"{823, 801, 635, 205, 260}"
295,1,87,0,0.0680223,"\int \frac{d+e x}{x^2 \left(a+c x^2\right)^2} \, dx","Int[(d + e*x)/(x^2*(a + c*x^2)^2),x]","-\frac{3 \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{e \log \left(a+c x^2\right)}{2 a^2}-\frac{3 d}{2 a^2 x}+\frac{e \log (x)}{a^2}+\frac{d+e x}{2 a x \left(a+c x^2\right)}","-\frac{3 \sqrt{c} d \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{e \log \left(a+c x^2\right)}{2 a^2}-\frac{3 d}{2 a^2 x}+\frac{e \log (x)}{a^2}+\frac{d+e x}{2 a x \left(a+c x^2\right)}",1,"(-3*d)/(2*a^2*x) + (d + e*x)/(2*a*x*(a + c*x^2)) - (3*Sqrt[c]*d*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(5/2)) + (e*Log[x])/a^2 - (e*Log[a + c*x^2])/(2*a^2)","A",6,5,18,0.2778,1,"{823, 801, 635, 205, 260}"
296,1,96,0,0.0836267,"\int \frac{d+e x}{x^3 \left(a+c x^2\right)^2} \, dx","Int[(d + e*x)/(x^3*(a + c*x^2)^2),x]","\frac{c d \log \left(a+c x^2\right)}{a^3}-\frac{2 c d \log (x)}{a^3}-\frac{3 \sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{d}{a^2 x^2}-\frac{3 e}{2 a^2 x}+\frac{d+e x}{2 a x^2 \left(a+c x^2\right)}","\frac{c d \log \left(a+c x^2\right)}{a^3}-\frac{2 c d \log (x)}{a^3}-\frac{3 \sqrt{c} e \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{d}{a^2 x^2}-\frac{3 e}{2 a^2 x}+\frac{d+e x}{2 a x^2 \left(a+c x^2\right)}",1,"-(d/(a^2*x^2)) - (3*e)/(2*a^2*x) + (d + e*x)/(2*a*x^2*(a + c*x^2)) - (3*Sqrt[c]*e*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(5/2)) - (2*c*d*Log[x])/a^3 + (c*d*Log[a + c*x^2])/a^3","A",6,5,18,0.2778,1,"{823, 801, 635, 205, 260}"
297,1,95,0,0.0700957,"\int \frac{x^4 (d+e x)}{a^2-c^2 x^2} \, dx","Int[(x^4*(d + e*x))/(a^2 - c^2*x^2),x]","-\frac{a^3 (a e+c d) \log (a-c x)}{2 c^6}+\frac{a^3 (c d-a e) \log (a+c x)}{2 c^6}-\frac{a^2 d x}{c^4}-\frac{a^2 e x^2}{2 c^4}-\frac{d x^3}{3 c^2}-\frac{e x^4}{4 c^2}","-\frac{a^3 (a e+c d) \log (a-c x)}{2 c^6}+\frac{a^3 (c d-a e) \log (a+c x)}{2 c^6}-\frac{a^2 d x}{c^4}-\frac{a^2 e x^2}{2 c^4}-\frac{d x^3}{3 c^2}-\frac{e x^4}{4 c^2}",1,"-((a^2*d*x)/c^4) - (a^2*e*x^2)/(2*c^4) - (d*x^3)/(3*c^2) - (e*x^4)/(4*c^2) - (a^3*(c*d + a*e)*Log[a - c*x])/(2*c^6) + (a^3*(c*d - a*e)*Log[a + c*x])/(2*c^6)","A",5,3,23,0.1304,1,"{801, 633, 31}"
298,1,81,0,0.0666073,"\int \frac{x^3 (d+e x)}{a^2-c^2 x^2} \, dx","Int[(x^3*(d + e*x))/(a^2 - c^2*x^2),x]","-\frac{a^2 (a e+c d) \log (a-c x)}{2 c^5}-\frac{a^2 (c d-a e) \log (a+c x)}{2 c^5}-\frac{a^2 e x}{c^4}-\frac{d x^2}{2 c^2}-\frac{e x^3}{3 c^2}","-\frac{a^2 (a e+c d) \log (a-c x)}{2 c^5}-\frac{a^2 (c d-a e) \log (a+c x)}{2 c^5}-\frac{a^2 e x}{c^4}-\frac{d x^2}{2 c^2}-\frac{e x^3}{3 c^2}",1,"-((a^2*e*x)/c^4) - (d*x^2)/(2*c^2) - (e*x^3)/(3*c^2) - (a^2*(c*d + a*e)*Log[a - c*x])/(2*c^5) - (a^2*(c*d - a*e)*Log[a + c*x])/(2*c^5)","A",5,3,23,0.1304,1,"{801, 633, 31}"
299,1,63,0,0.0559836,"\int \frac{x^2 (d+e x)}{a^2-c^2 x^2} \, dx","Int[(x^2*(d + e*x))/(a^2 - c^2*x^2),x]","-\frac{a (a e+c d) \log (a-c x)}{2 c^4}+\frac{a (c d-a e) \log (a+c x)}{2 c^4}-\frac{d x}{c^2}-\frac{e x^2}{2 c^2}","-\frac{a (a e+c d) \log (a-c x)}{2 c^4}+\frac{a (c d-a e) \log (a+c x)}{2 c^4}-\frac{d x}{c^2}-\frac{e x^2}{2 c^2}",1,"-((d*x)/c^2) - (e*x^2)/(2*c^2) - (a*(c*d + a*e)*Log[a - c*x])/(2*c^4) + (a*(c*d - a*e)*Log[a + c*x])/(2*c^4)","A",5,3,23,0.1304,1,"{801, 633, 31}"
300,1,50,0,0.0384204,"\int \frac{x (d+e x)}{a^2-c^2 x^2} \, dx","Int[(x*(d + e*x))/(a^2 - c^2*x^2),x]","-\frac{(a e+c d) \log (a-c x)}{2 c^3}-\frac{(c d-a e) \log (a+c x)}{2 c^3}-\frac{e x}{c^2}","-\frac{(a e+c d) \log (a-c x)}{2 c^3}-\frac{(c d-a e) \log (a+c x)}{2 c^3}-\frac{e x}{c^2}",1,"-((e*x)/c^2) - ((c*d + a*e)*Log[a - c*x])/(2*c^3) - ((c*d - a*e)*Log[a + c*x])/(2*c^3)","A",4,3,21,0.1429,1,"{774, 633, 31}"
301,1,46,0,0.0231256,"\int \frac{d+e x}{a^2-c^2 x^2} \, dx","Int[(d + e*x)/(a^2 - c^2*x^2),x]","\frac{\left(\frac{c d}{a}-e\right) \log (a+c x)}{2 c^2}-\frac{\left(\frac{c d}{a}+e\right) \log (a-c x)}{2 c^2}","\frac{\left(\frac{c d}{a}-e\right) \log (a+c x)}{2 c^2}-\frac{\left(\frac{c d}{a}+e\right) \log (a-c x)}{2 c^2}",1,"-(((c*d)/a + e)*Log[a - c*x])/(2*c^2) + (((c*d)/a - e)*Log[a + c*x])/(2*c^2)","A",3,2,20,0.1000,1,"{633, 31}"
302,1,56,0,0.0488401,"\int \frac{d+e x}{x \left(a^2-c^2 x^2\right)} \, dx","Int[(d + e*x)/(x*(a^2 - c^2*x^2)),x]","-\frac{(a e+c d) \log (a-c x)}{2 a^2 c}-\frac{(c d-a e) \log (a+c x)}{2 a^2 c}+\frac{d \log (x)}{a^2}","-\frac{(a e+c d) \log (a-c x)}{2 a^2 c}-\frac{(c d-a e) \log (a+c x)}{2 a^2 c}+\frac{d \log (x)}{a^2}",1,"(d*Log[x])/a^2 - ((c*d + a*e)*Log[a - c*x])/(2*a^2*c) - ((c*d - a*e)*Log[a + c*x])/(2*a^2*c)","A",2,1,23,0.04348,1,"{801}"
303,1,59,0,0.0539944,"\int \frac{d+e x}{x^2 \left(a^2-c^2 x^2\right)} \, dx","Int[(d + e*x)/(x^2*(a^2 - c^2*x^2)),x]","-\frac{(a e+c d) \log (a-c x)}{2 a^3}+\frac{(c d-a e) \log (a+c x)}{2 a^3}-\frac{d}{a^2 x}+\frac{e \log (x)}{a^2}","-\frac{(a e+c d) \log (a-c x)}{2 a^3}+\frac{(c d-a e) \log (a+c x)}{2 a^3}-\frac{d}{a^2 x}+\frac{e \log (x)}{a^2}",1,"-(d/(a^2*x)) + (e*Log[x])/a^2 - ((c*d + a*e)*Log[a - c*x])/(2*a^3) + ((c*d - a*e)*Log[a + c*x])/(2*a^3)","A",2,1,23,0.04348,1,"{801}"
304,1,75,0,0.0661303,"\int \frac{d+e x}{x^3 \left(a^2-c^2 x^2\right)} \, dx","Int[(d + e*x)/(x^3*(a^2 - c^2*x^2)),x]","\frac{c^2 d \log (x)}{a^4}-\frac{c (a e+c d) \log (a-c x)}{2 a^4}-\frac{c (c d-a e) \log (a+c x)}{2 a^4}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}","\frac{c^2 d \log (x)}{a^4}-\frac{c (a e+c d) \log (a-c x)}{2 a^4}-\frac{c (c d-a e) \log (a+c x)}{2 a^4}-\frac{d}{2 a^2 x^2}-\frac{e}{a^2 x}",1,"-d/(2*a^2*x^2) - e/(a^2*x) + (c^2*d*Log[x])/a^4 - (c*(c*d + a*e)*Log[a - c*x])/(2*a^4) - (c*(c*d - a*e)*Log[a + c*x])/(2*a^4)","A",2,1,23,0.04348,1,"{801}"
305,1,93,0,0.0691779,"\int \frac{d+e x}{x^4 \left(a^2-c^2 x^2\right)} \, dx","Int[(d + e*x)/(x^4*(a^2 - c^2*x^2)),x]","-\frac{c^2 (a e+c d) \log (a-c x)}{2 a^5}+\frac{c^2 (c d-a e) \log (a+c x)}{2 a^5}-\frac{c^2 d}{a^4 x}+\frac{c^2 e \log (x)}{a^4}-\frac{d}{3 a^2 x^3}-\frac{e}{2 a^2 x^2}","-\frac{c^2 (a e+c d) \log (a-c x)}{2 a^5}+\frac{c^2 (c d-a e) \log (a+c x)}{2 a^5}-\frac{c^2 d}{a^4 x}+\frac{c^2 e \log (x)}{a^4}-\frac{d}{3 a^2 x^3}-\frac{e}{2 a^2 x^2}",1,"-d/(3*a^2*x^3) - e/(2*a^2*x^2) - (c^2*d)/(a^4*x) + (c^2*e*Log[x])/a^4 - (c^2*(c*d + a*e)*Log[a - c*x])/(2*a^5) + (c^2*(c*d - a*e)*Log[a + c*x])/(2*a^5)","A",2,1,23,0.04348,1,"{801}"
306,1,94,0,0.0988786,"\int \frac{x^4 (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Int[(x^4*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{x^3 (d+e x)}{2 c^2 \left(a^2-c^2 x^2\right)}+\frac{a (4 a e+3 c d) \log (a-c x)}{4 c^6}-\frac{a (3 c d-4 a e) \log (a+c x)}{4 c^6}+\frac{3 d x}{2 c^4}+\frac{e x^2}{c^4}","\frac{x^3 (d+e x)}{2 c^2 \left(a^2-c^2 x^2\right)}+\frac{a (4 a e+3 c d) \log (a-c x)}{4 c^6}-\frac{a (3 c d-4 a e) \log (a+c x)}{4 c^6}+\frac{3 d x}{2 c^4}+\frac{e x^2}{c^4}",1,"(3*d*x)/(2*c^4) + (e*x^2)/c^4 + (x^3*(d + e*x))/(2*c^2*(a^2 - c^2*x^2)) + (a*(3*c*d + 4*a*e)*Log[a - c*x])/(4*c^6) - (a*(3*c*d - 4*a*e)*Log[a + c*x])/(4*c^6)","A",6,4,23,0.1739,1,"{819, 801, 633, 31}"
307,1,84,0,0.0734375,"\int \frac{x^3 (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Int[(x^3*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{x^2 (d+e x)}{2 c^2 \left(a^2-c^2 x^2\right)}+\frac{(3 a e+2 c d) \log (a-c x)}{4 c^5}+\frac{(2 c d-3 a e) \log (a+c x)}{4 c^5}+\frac{3 e x}{2 c^4}","\frac{x^2 (d+e x)}{2 c^2 \left(a^2-c^2 x^2\right)}+\frac{(3 a e+2 c d) \log (a-c x)}{4 c^5}+\frac{(2 c d-3 a e) \log (a+c x)}{4 c^5}+\frac{3 e x}{2 c^4}",1,"(3*e*x)/(2*c^4) + (x^2*(d + e*x))/(2*c^2*(a^2 - c^2*x^2)) + ((2*c*d + 3*a*e)*Log[a - c*x])/(4*c^5) + ((2*c*d - 3*a*e)*Log[a + c*x])/(4*c^5)","A",5,4,23,0.1739,1,"{819, 774, 633, 31}"
308,1,77,0,0.0488583,"\int \frac{x^2 (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Int[(x^2*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{x (d+e x)}{2 c^2 \left(a^2-c^2 x^2\right)}+\frac{(2 a e+c d) \log (a-c x)}{4 a c^4}-\frac{(c d-2 a e) \log (a+c x)}{4 a c^4}","\frac{x (d+e x)}{2 c^2 \left(a^2-c^2 x^2\right)}+\frac{(2 a e+c d) \log (a-c x)}{4 a c^4}-\frac{(c d-2 a e) \log (a+c x)}{4 a c^4}",1,"(x*(d + e*x))/(2*c^2*(a^2 - c^2*x^2)) + ((c*d + 2*a*e)*Log[a - c*x])/(4*a*c^4) - ((c*d - 2*a*e)*Log[a + c*x])/(4*a*c^4)","A",4,3,23,0.1304,1,"{819, 633, 31}"
309,1,45,0,0.0196568,"\int \frac{x (d+e x)}{\left(a^2-c^2 x^2\right)^2} \, dx","Int[(x*(d + e*x))/(a^2 - c^2*x^2)^2,x]","\frac{d+e x}{2 c^2 \left(a^2-c^2 x^2\right)}-\frac{e \tanh ^{-1}\left(\frac{c x}{a}\right)}{2 a c^3}","\frac{d+e x}{2 c^2 \left(a^2-c^2 x^2\right)}-\frac{e \tanh ^{-1}\left(\frac{c x}{a}\right)}{2 a c^3}",1,"(d + e*x)/(2*c^2*(a^2 - c^2*x^2)) - (e*ArcTanh[(c*x)/a])/(2*a*c^3)","A",2,2,21,0.09524,1,"{778, 208}"
310,1,55,0,0.0162884,"\int \frac{d+e x}{\left(a^2-c^2 x^2\right)^2} \, dx","Int[(d + e*x)/(a^2 - c^2*x^2)^2,x]","\frac{a^2 e+c^2 d x}{2 a^2 c^2 \left(a^2-c^2 x^2\right)}+\frac{d \tanh ^{-1}\left(\frac{c x}{a}\right)}{2 a^3 c}","\frac{a^2 e+c^2 d x}{2 a^2 c^2 \left(a^2-c^2 x^2\right)}+\frac{d \tanh ^{-1}\left(\frac{c x}{a}\right)}{2 a^3 c}",1,"(a^2*e + c^2*d*x)/(2*a^2*c^2*(a^2 - c^2*x^2)) + (d*ArcTanh[(c*x)/a])/(2*a^3*c)","A",2,2,20,0.1000,1,"{639, 208}"
311,1,84,0,0.0745372,"\int \frac{d+e x}{x \left(a^2-c^2 x^2\right)^2} \, dx","Int[(d + e*x)/(x*(a^2 - c^2*x^2)^2),x]","\frac{d+e x}{2 a^2 \left(a^2-c^2 x^2\right)}-\frac{(a e+2 c d) \log (a-c x)}{4 a^4 c}-\frac{(2 c d-a e) \log (a+c x)}{4 a^4 c}+\frac{d \log (x)}{a^4}","\frac{d+e x}{2 a^2 \left(a^2-c^2 x^2\right)}-\frac{(a e+2 c d) \log (a-c x)}{4 a^4 c}-\frac{(2 c d-a e) \log (a+c x)}{4 a^4 c}+\frac{d \log (x)}{a^4}",1,"(d + e*x)/(2*a^2*(a^2 - c^2*x^2)) + (d*Log[x])/a^4 - ((2*c*d + a*e)*Log[a - c*x])/(4*a^4*c) - ((2*c*d - a*e)*Log[a + c*x])/(4*a^4*c)","A",3,2,23,0.08696,1,"{823, 801}"
312,1,93,0,0.0948619,"\int \frac{d+e x}{x^2 \left(a^2-c^2 x^2\right)^2} \, dx","Int[(d + e*x)/(x^2*(a^2 - c^2*x^2)^2),x]","\frac{d+e x}{2 a^2 x \left(a^2-c^2 x^2\right)}-\frac{(2 a e+3 c d) \log (a-c x)}{4 a^5}+\frac{(3 c d-2 a e) \log (a+c x)}{4 a^5}-\frac{3 d}{2 a^4 x}+\frac{e \log (x)}{a^4}","\frac{d+e x}{2 a^2 x \left(a^2-c^2 x^2\right)}-\frac{(2 a e+3 c d) \log (a-c x)}{4 a^5}+\frac{(3 c d-2 a e) \log (a+c x)}{4 a^5}-\frac{3 d}{2 a^4 x}+\frac{e \log (x)}{a^4}",1,"(-3*d)/(2*a^4*x) + (d + e*x)/(2*a^2*x*(a^2 - c^2*x^2)) + (e*Log[x])/a^4 - ((3*c*d + 2*a*e)*Log[a - c*x])/(4*a^5) + ((3*c*d - 2*a*e)*Log[a + c*x])/(4*a^5)","A",3,2,23,0.08696,1,"{823, 801}"
313,1,108,0,0.1082927,"\int \frac{d+e x}{x^3 \left(a^2-c^2 x^2\right)^2} \, dx","Int[(d + e*x)/(x^3*(a^2 - c^2*x^2)^2),x]","\frac{d+e x}{2 a^2 x^2 \left(a^2-c^2 x^2\right)}+\frac{2 c^2 d \log (x)}{a^6}-\frac{c (3 a e+4 c d) \log (a-c x)}{4 a^6}-\frac{c (4 c d-3 a e) \log (a+c x)}{4 a^6}-\frac{d}{a^4 x^2}-\frac{3 e}{2 a^4 x}","\frac{d+e x}{2 a^2 x^2 \left(a^2-c^2 x^2\right)}+\frac{2 c^2 d \log (x)}{a^6}-\frac{c (3 a e+4 c d) \log (a-c x)}{4 a^6}-\frac{c (4 c d-3 a e) \log (a+c x)}{4 a^6}-\frac{d}{a^4 x^2}-\frac{3 e}{2 a^4 x}",1,"-(d/(a^4*x^2)) - (3*e)/(2*a^4*x) + (d + e*x)/(2*a^2*x^2*(a^2 - c^2*x^2)) + (2*c^2*d*Log[x])/a^6 - (c*(4*c*d + 3*a*e)*Log[a - c*x])/(4*a^6) - (c*(4*c*d - 3*a*e)*Log[a + c*x])/(4*a^6)","A",3,2,23,0.08696,1,"{823, 801}"
314,1,152,0,0.1285238,"\int x^4 (A+B x) \sqrt{a+c x^2} \, dx","Int[x^4*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{a^2 A x \sqrt{a+c x^2}}{16 c^2}+\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{5/2}}+\frac{a \left(a+c x^2\right)^{3/2} (64 a B-105 A c x)}{840 c^3}+\frac{A x^3 \left(a+c x^2\right)^{3/2}}{6 c}-\frac{4 a B x^2 \left(a+c x^2\right)^{3/2}}{35 c^2}+\frac{B x^4 \left(a+c x^2\right)^{3/2}}{7 c}","\frac{a^2 A x \sqrt{a+c x^2}}{16 c^2}+\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{5/2}}+\frac{a \left(a+c x^2\right)^{3/2} (64 a B-105 A c x)}{840 c^3}+\frac{A x^3 \left(a+c x^2\right)^{3/2}}{6 c}-\frac{4 a B x^2 \left(a+c x^2\right)^{3/2}}{35 c^2}+\frac{B x^4 \left(a+c x^2\right)^{3/2}}{7 c}",1,"(a^2*A*x*Sqrt[a + c*x^2])/(16*c^2) - (4*a*B*x^2*(a + c*x^2)^(3/2))/(35*c^2) + (A*x^3*(a + c*x^2)^(3/2))/(6*c) + (B*x^4*(a + c*x^2)^(3/2))/(7*c) + (a*(64*a*B - 105*A*c*x)*(a + c*x^2)^(3/2))/(840*c^3) + (a^3*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(5/2))","A",7,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
315,1,127,0,0.0809779,"\int x^3 (A+B x) \sqrt{a+c x^2} \, dx","Int[x^3*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{a^2 B x \sqrt{a+c x^2}}{16 c^2}+\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{5/2}}-\frac{a \left(a+c x^2\right)^{3/2} (16 A+15 B x)}{120 c^2}+\frac{A x^2 \left(a+c x^2\right)^{3/2}}{5 c}+\frac{B x^3 \left(a+c x^2\right)^{3/2}}{6 c}","\frac{a^2 B x \sqrt{a+c x^2}}{16 c^2}+\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{5/2}}-\frac{a \left(a+c x^2\right)^{3/2} (16 A+15 B x)}{120 c^2}+\frac{A x^2 \left(a+c x^2\right)^{3/2}}{5 c}+\frac{B x^3 \left(a+c x^2\right)^{3/2}}{6 c}",1,"(a^2*B*x*Sqrt[a + c*x^2])/(16*c^2) + (A*x^2*(a + c*x^2)^(3/2))/(5*c) + (B*x^3*(a + c*x^2)^(3/2))/(6*c) - (a*(16*A + 15*B*x)*(a + c*x^2)^(3/2))/(120*c^2) + (a^3*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(5/2))","A",6,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
316,1,104,0,0.0468163,"\int x^2 (A+B x) \sqrt{a+c x^2} \, dx","Int[x^2*(A + B*x)*Sqrt[a + c*x^2],x]","-\frac{a^2 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}-\frac{\left(a+c x^2\right)^{3/2} (8 a B-15 A c x)}{60 c^2}-\frac{a A x \sqrt{a+c x^2}}{8 c}+\frac{B x^2 \left(a+c x^2\right)^{3/2}}{5 c}","-\frac{a^2 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}-\frac{\left(a+c x^2\right)^{3/2} (8 a B-15 A c x)}{60 c^2}-\frac{a A x \sqrt{a+c x^2}}{8 c}+\frac{B x^2 \left(a+c x^2\right)^{3/2}}{5 c}",1,"-(a*A*x*Sqrt[a + c*x^2])/(8*c) + (B*x^2*(a + c*x^2)^(3/2))/(5*c) - ((8*a*B - 15*A*c*x)*(a + c*x^2)^(3/2))/(60*c^2) - (a^2*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2))","A",5,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
317,1,80,0,0.0255038,"\int x (A+B x) \sqrt{a+c x^2} \, dx","Int[x*(A + B*x)*Sqrt[a + c*x^2],x]","-\frac{a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{\left(a+c x^2\right)^{3/2} (4 A+3 B x)}{12 c}-\frac{a B x \sqrt{a+c x^2}}{8 c}","-\frac{a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{3/2}}+\frac{\left(a+c x^2\right)^{3/2} (4 A+3 B x)}{12 c}-\frac{a B x \sqrt{a+c x^2}}{8 c}",1,"-(a*B*x*Sqrt[a + c*x^2])/(8*c) + ((4*A + 3*B*x)*(a + c*x^2)^(3/2))/(12*c) - (a^2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(3/2))","A",4,4,18,0.2222,1,"{780, 195, 217, 206}"
318,1,67,0,0.0186641,"\int (A+B x) \sqrt{a+c x^2} \, dx","Int[(A + B*x)*Sqrt[a + c*x^2],x]","\frac{1}{2} A x \sqrt{a+c x^2}+\frac{a A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}+\frac{B \left(a+c x^2\right)^{3/2}}{3 c}","\frac{1}{2} A x \sqrt{a+c x^2}+\frac{a A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}+\frac{B \left(a+c x^2\right)^{3/2}}{3 c}",1,"(A*x*Sqrt[a + c*x^2])/2 + (B*(a + c*x^2)^(3/2))/(3*c) + (a*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c])","A",4,4,17,0.2353,1,"{641, 195, 217, 206}"
319,1,79,0,0.0635644,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x,x]","\frac{1}{2} \sqrt{a+c x^2} (2 A+B x)-\sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{a B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}","\frac{1}{2} \sqrt{a+c x^2} (2 A+B x)-\sqrt{a} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{a B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 \sqrt{c}}",1,"((2*A + B*x)*Sqrt[a + c*x^2])/2 + (a*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*Sqrt[c]) - Sqrt[a]*A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",7,7,20,0.3500,1,"{815, 844, 217, 206, 266, 63, 208}"
320,1,75,0,0.0577512,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^2} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x^2,x]","-\frac{\sqrt{a+c x^2} (A-B x)}{x}+A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\sqrt{a} B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)","-\frac{\sqrt{a+c x^2} (A-B x)}{x}+A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\sqrt{a} B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)",1,"-(((A - B*x)*Sqrt[a + c*x^2])/x) + A*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]] - Sqrt[a]*B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",7,7,20,0.3500,1,"{813, 844, 217, 206, 266, 63, 208}"
321,1,80,0,0.0626566,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^3} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x^3,x]","-\frac{\sqrt{a+c x^2} (A+2 B x)}{2 x^2}-\frac{A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}+B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","-\frac{\sqrt{a+c x^2} (A+2 B x)}{2 x^2}-\frac{A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}+B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"-((A + 2*B*x)*Sqrt[a + c*x^2])/(2*x^2) + B*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]] - (A*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*Sqrt[a])","A",7,7,20,0.3500,1,"{811, 844, 217, 206, 266, 63, 208}"
322,1,71,0,0.0407413,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^4} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x^4,x]","-\frac{A \left(a+c x^2\right)^{3/2}}{3 a x^3}-\frac{B \sqrt{a+c x^2}}{2 x^2}-\frac{B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}","-\frac{A \left(a+c x^2\right)^{3/2}}{3 a x^3}-\frac{B \sqrt{a+c x^2}}{2 x^2}-\frac{B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 \sqrt{a}}",1,"-(B*Sqrt[a + c*x^2])/(2*x^2) - (A*(a + c*x^2)^(3/2))/(3*a*x^3) - (B*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*Sqrt[a])","A",5,5,20,0.2500,1,"{807, 266, 47, 63, 208}"
323,1,99,0,0.0617995,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^5} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x^5,x]","\frac{A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{A c \sqrt{a+c x^2}}{8 a x^2}-\frac{A \left(a+c x^2\right)^{3/2}}{4 a x^4}-\frac{B \left(a+c x^2\right)^{3/2}}{3 a x^3}","\frac{A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}+\frac{A c \sqrt{a+c x^2}}{8 a x^2}-\frac{A \left(a+c x^2\right)^{3/2}}{4 a x^4}-\frac{B \left(a+c x^2\right)^{3/2}}{3 a x^3}",1,"(A*c*Sqrt[a + c*x^2])/(8*a*x^2) - (A*(a + c*x^2)^(3/2))/(4*a*x^4) - (B*(a + c*x^2)^(3/2))/(3*a*x^3) + (A*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*a^(3/2))","A",6,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
324,1,122,0,0.0860523,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^6} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x^6,x]","\frac{2 A c \left(a+c x^2\right)^{3/2}}{15 a^2 x^3}+\frac{B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}-\frac{A \left(a+c x^2\right)^{3/2}}{5 a x^5}+\frac{B c \sqrt{a+c x^2}}{8 a x^2}-\frac{B \left(a+c x^2\right)^{3/2}}{4 a x^4}","\frac{2 A c \left(a+c x^2\right)^{3/2}}{15 a^2 x^3}+\frac{B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{3/2}}-\frac{A \left(a+c x^2\right)^{3/2}}{5 a x^5}+\frac{B c \sqrt{a+c x^2}}{8 a x^2}-\frac{B \left(a+c x^2\right)^{3/2}}{4 a x^4}",1,"(B*c*Sqrt[a + c*x^2])/(8*a*x^2) - (A*(a + c*x^2)^(3/2))/(5*a*x^5) - (B*(a + c*x^2)^(3/2))/(4*a*x^4) + (2*A*c*(a + c*x^2)^(3/2))/(15*a^2*x^3) + (B*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*a^(3/2))","A",7,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
325,1,147,0,0.1169139,"\int \frac{(A+B x) \sqrt{a+c x^2}}{x^7} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/x^7,x]","-\frac{A c^2 \sqrt{a+c x^2}}{16 a^2 x^2}-\frac{A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}+\frac{A c \left(a+c x^2\right)^{3/2}}{8 a^2 x^4}+\frac{2 B c \left(a+c x^2\right)^{3/2}}{15 a^2 x^3}-\frac{A \left(a+c x^2\right)^{3/2}}{6 a x^6}-\frac{B \left(a+c x^2\right)^{3/2}}{5 a x^5}","-\frac{A c^2 \sqrt{a+c x^2}}{16 a^2 x^2}-\frac{A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{5/2}}+\frac{A c \left(a+c x^2\right)^{3/2}}{8 a^2 x^4}+\frac{2 B c \left(a+c x^2\right)^{3/2}}{15 a^2 x^3}-\frac{A \left(a+c x^2\right)^{3/2}}{6 a x^6}-\frac{B \left(a+c x^2\right)^{3/2}}{5 a x^5}",1,"-(A*c^2*Sqrt[a + c*x^2])/(16*a^2*x^2) - (A*(a + c*x^2)^(3/2))/(6*a*x^6) - (B*(a + c*x^2)^(3/2))/(5*a*x^5) + (A*c*(a + c*x^2)^(3/2))/(8*a^2*x^4) + (2*B*c*(a + c*x^2)^(3/2))/(15*a^2*x^3) - (A*c^3*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(16*a^(5/2))","A",8,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
326,1,175,0,0.1351074,"\int x^4 (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[x^4*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{3 a^3 A x \sqrt{a+c x^2}}{128 c^2}+\frac{a^2 A x \left(a+c x^2\right)^{3/2}}{64 c^2}+\frac{3 a^4 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}+\frac{a \left(a+c x^2\right)^{5/2} (128 a B-315 A c x)}{5040 c^3}+\frac{A x^3 \left(a+c x^2\right)^{5/2}}{8 c}-\frac{4 a B x^2 \left(a+c x^2\right)^{5/2}}{63 c^2}+\frac{B x^4 \left(a+c x^2\right)^{5/2}}{9 c}","\frac{3 a^3 A x \sqrt{a+c x^2}}{128 c^2}+\frac{a^2 A x \left(a+c x^2\right)^{3/2}}{64 c^2}+\frac{3 a^4 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}+\frac{a \left(a+c x^2\right)^{5/2} (128 a B-315 A c x)}{5040 c^3}+\frac{A x^3 \left(a+c x^2\right)^{5/2}}{8 c}-\frac{4 a B x^2 \left(a+c x^2\right)^{5/2}}{63 c^2}+\frac{B x^4 \left(a+c x^2\right)^{5/2}}{9 c}",1,"(3*a^3*A*x*Sqrt[a + c*x^2])/(128*c^2) + (a^2*A*x*(a + c*x^2)^(3/2))/(64*c^2) - (4*a*B*x^2*(a + c*x^2)^(5/2))/(63*c^2) + (A*x^3*(a + c*x^2)^(5/2))/(8*c) + (B*x^4*(a + c*x^2)^(5/2))/(9*c) + (a*(128*a*B - 315*A*c*x)*(a + c*x^2)^(5/2))/(5040*c^3) + (3*a^4*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(5/2))","A",8,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
327,1,150,0,0.0943001,"\int x^3 (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[x^3*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{3 a^3 B x \sqrt{a+c x^2}}{128 c^2}+\frac{a^2 B x \left(a+c x^2\right)^{3/2}}{64 c^2}+\frac{3 a^4 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}-\frac{a \left(a+c x^2\right)^{5/2} (32 A+35 B x)}{560 c^2}+\frac{A x^2 \left(a+c x^2\right)^{5/2}}{7 c}+\frac{B x^3 \left(a+c x^2\right)^{5/2}}{8 c}","\frac{3 a^3 B x \sqrt{a+c x^2}}{128 c^2}+\frac{a^2 B x \left(a+c x^2\right)^{3/2}}{64 c^2}+\frac{3 a^4 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{5/2}}-\frac{a \left(a+c x^2\right)^{5/2} (32 A+35 B x)}{560 c^2}+\frac{A x^2 \left(a+c x^2\right)^{5/2}}{7 c}+\frac{B x^3 \left(a+c x^2\right)^{5/2}}{8 c}",1,"(3*a^3*B*x*Sqrt[a + c*x^2])/(128*c^2) + (a^2*B*x*(a + c*x^2)^(3/2))/(64*c^2) + (A*x^2*(a + c*x^2)^(5/2))/(7*c) + (B*x^3*(a + c*x^2)^(5/2))/(8*c) - (a*(32*A + 35*B*x)*(a + c*x^2)^(5/2))/(560*c^2) + (3*a^4*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(5/2))","A",7,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
328,1,127,0,0.0574781,"\int x^2 (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[x^2*(A + B*x)*(a + c*x^2)^(3/2),x]","-\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}-\frac{a^2 A x \sqrt{a+c x^2}}{16 c}-\frac{\left(a+c x^2\right)^{5/2} (12 a B-35 A c x)}{210 c^2}-\frac{a A x \left(a+c x^2\right)^{3/2}}{24 c}+\frac{B x^2 \left(a+c x^2\right)^{5/2}}{7 c}","-\frac{a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}-\frac{a^2 A x \sqrt{a+c x^2}}{16 c}-\frac{\left(a+c x^2\right)^{5/2} (12 a B-35 A c x)}{210 c^2}-\frac{a A x \left(a+c x^2\right)^{3/2}}{24 c}+\frac{B x^2 \left(a+c x^2\right)^{5/2}}{7 c}",1,"-(a^2*A*x*Sqrt[a + c*x^2])/(16*c) - (a*A*x*(a + c*x^2)^(3/2))/(24*c) + (B*x^2*(a + c*x^2)^(5/2))/(7*c) - ((12*a*B - 35*A*c*x)*(a + c*x^2)^(5/2))/(210*c^2) - (a^3*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(3/2))","A",6,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
329,1,103,0,0.031254,"\int x (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[x*(A + B*x)*(a + c*x^2)^(3/2),x]","-\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}-\frac{a^2 B x \sqrt{a+c x^2}}{16 c}+\frac{\left(a+c x^2\right)^{5/2} (6 A+5 B x)}{30 c}-\frac{a B x \left(a+c x^2\right)^{3/2}}{24 c}","-\frac{a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 c^{3/2}}-\frac{a^2 B x \sqrt{a+c x^2}}{16 c}+\frac{\left(a+c x^2\right)^{5/2} (6 A+5 B x)}{30 c}-\frac{a B x \left(a+c x^2\right)^{3/2}}{24 c}",1,"-(a^2*B*x*Sqrt[a + c*x^2])/(16*c) - (a*B*x*(a + c*x^2)^(3/2))/(24*c) + ((6*A + 5*B*x)*(a + c*x^2)^(5/2))/(30*c) - (a^3*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*c^(3/2))","A",5,4,18,0.2222,1,"{780, 195, 217, 206}"
330,1,87,0,0.0257915,"\int (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{3 a^2 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{4} A x \left(a+c x^2\right)^{3/2}+\frac{3}{8} a A x \sqrt{a+c x^2}+\frac{B \left(a+c x^2\right)^{5/2}}{5 c}","\frac{3 a^2 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{4} A x \left(a+c x^2\right)^{3/2}+\frac{3}{8} a A x \sqrt{a+c x^2}+\frac{B \left(a+c x^2\right)^{5/2}}{5 c}",1,"(3*a*A*x*Sqrt[a + c*x^2])/8 + (A*x*(a + c*x^2)^(3/2))/4 + (B*(a + c*x^2)^(5/2))/(5*c) + (3*a^2*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*Sqrt[c])","A",5,4,17,0.2353,1,"{641, 195, 217, 206}"
331,1,106,0,0.0888747,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x,x]","-a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{8} a \sqrt{a+c x^2} (8 A+3 B x)+\frac{1}{12} \left(a+c x^2\right)^{3/2} (4 A+3 B x)","-a^{3/2} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 \sqrt{c}}+\frac{1}{8} a \sqrt{a+c x^2} (8 A+3 B x)+\frac{1}{12} \left(a+c x^2\right)^{3/2} (4 A+3 B x)",1,"(a*(8*A + 3*B*x)*Sqrt[a + c*x^2])/8 + ((4*A + 3*B*x)*(a + c*x^2)^(3/2))/12 + (3*a^2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*Sqrt[c]) - a^(3/2)*A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",8,7,20,0.3500,1,"{815, 844, 217, 206, 266, 63, 208}"
332,1,108,0,0.0822563,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^2} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^2,x]","a^{3/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-\frac{\left(a+c x^2\right)^{3/2} (3 A-B x)}{3 x}+\frac{1}{2} \sqrt{a+c x^2} (2 a B+3 A c x)+\frac{3}{2} a A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","a^{3/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-\frac{\left(a+c x^2\right)^{3/2} (3 A-B x)}{3 x}+\frac{1}{2} \sqrt{a+c x^2} (2 a B+3 A c x)+\frac{3}{2} a A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"((2*a*B + 3*A*c*x)*Sqrt[a + c*x^2])/2 - ((3*A - B*x)*(a + c*x^2)^(3/2))/(3*x) + (3*a*A*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/2 - a^(3/2)*B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",8,8,20,0.4000,1,"{813, 815, 844, 217, 206, 266, 63, 208}"
333,1,111,0,0.078875,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^3} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^3,x]","-\frac{\left(a+c x^2\right)^{3/2} (A-B x)}{2 x^2}-\frac{3 \sqrt{a+c x^2} (a B-A c x)}{2 x}-\frac{3}{2} \sqrt{a} A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{3}{2} a B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","-\frac{\left(a+c x^2\right)^{3/2} (A-B x)}{2 x^2}-\frac{3 \sqrt{a+c x^2} (a B-A c x)}{2 x}-\frac{3}{2} \sqrt{a} A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{3}{2} a B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"(-3*(a*B - A*c*x)*Sqrt[a + c*x^2])/(2*x) - ((A - B*x)*(a + c*x^2)^(3/2))/(2*x^2) + (3*a*B*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/2 - (3*Sqrt[a]*A*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/2","A",8,7,20,0.3500,1,"{813, 844, 217, 206, 266, 63, 208}"
334,1,109,0,0.0861821,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^4} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^4,x]","-\frac{c \sqrt{a+c x^2} (2 A-3 B x)}{2 x}-\frac{\left(a+c x^2\right)^{3/2} (2 A+3 B x)}{6 x^3}+A c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\frac{3}{2} \sqrt{a} B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)","-\frac{c \sqrt{a+c x^2} (2 A-3 B x)}{2 x}-\frac{\left(a+c x^2\right)^{3/2} (2 A+3 B x)}{6 x^3}+A c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\frac{3}{2} \sqrt{a} B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)",1,"-(c*(2*A - 3*B*x)*Sqrt[a + c*x^2])/(2*x) - ((2*A + 3*B*x)*(a + c*x^2)^(3/2))/(6*x^3) + A*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]] - (3*Sqrt[a]*B*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/2","A",8,8,20,0.4000,1,"{811, 813, 844, 217, 206, 266, 63, 208}"
335,1,111,0,0.087298,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^5} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^5,x]","-\frac{c \sqrt{a+c x^2} (3 A+8 B x)}{8 x^2}-\frac{\left(a+c x^2\right)^{3/2} (3 A+4 B x)}{12 x^4}-\frac{3 A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}+B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","-\frac{c \sqrt{a+c x^2} (3 A+8 B x)}{8 x^2}-\frac{\left(a+c x^2\right)^{3/2} (3 A+4 B x)}{12 x^4}-\frac{3 A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}+B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"-(c*(3*A + 8*B*x)*Sqrt[a + c*x^2])/(8*x^2) - ((3*A + 4*B*x)*(a + c*x^2)^(3/2))/(12*x^4) + B*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]] - (3*A*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*Sqrt[a])","A",8,7,20,0.3500,1,"{811, 844, 217, 206, 266, 63, 208}"
336,1,93,0,0.0568545,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^6} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^6,x]","-\frac{A \left(a+c x^2\right)^{5/2}}{5 a x^5}-\frac{3 B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{B \left(a+c x^2\right)^{3/2}}{4 x^4}-\frac{3 B c \sqrt{a+c x^2}}{8 x^2}","-\frac{A \left(a+c x^2\right)^{5/2}}{5 a x^5}-\frac{3 B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 \sqrt{a}}-\frac{B \left(a+c x^2\right)^{3/2}}{4 x^4}-\frac{3 B c \sqrt{a+c x^2}}{8 x^2}",1,"(-3*B*c*Sqrt[a + c*x^2])/(8*x^2) - (B*(a + c*x^2)^(3/2))/(4*x^4) - (A*(a + c*x^2)^(5/2))/(5*a*x^5) - (3*B*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*Sqrt[a])","A",6,5,20,0.2500,1,"{807, 266, 47, 63, 208}"
337,1,124,0,0.077989,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^7} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^7,x]","\frac{A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}+\frac{A c^2 \sqrt{a+c x^2}}{16 a x^2}+\frac{A c \left(a+c x^2\right)^{3/2}}{24 a x^4}-\frac{A \left(a+c x^2\right)^{5/2}}{6 a x^6}-\frac{B \left(a+c x^2\right)^{5/2}}{5 a x^5}","\frac{A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}+\frac{A c^2 \sqrt{a+c x^2}}{16 a x^2}+\frac{A c \left(a+c x^2\right)^{3/2}}{24 a x^4}-\frac{A \left(a+c x^2\right)^{5/2}}{6 a x^6}-\frac{B \left(a+c x^2\right)^{5/2}}{5 a x^5}",1,"(A*c^2*Sqrt[a + c*x^2])/(16*a*x^2) + (A*c*(a + c*x^2)^(3/2))/(24*a*x^4) - (A*(a + c*x^2)^(5/2))/(6*a*x^6) - (B*(a + c*x^2)^(5/2))/(5*a*x^5) + (A*c^3*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(16*a^(3/2))","A",7,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
338,1,147,0,0.1052464,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{x^8} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/x^8,x]","\frac{2 A c \left(a+c x^2\right)^{5/2}}{35 a^2 x^5}+\frac{B c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{A \left(a+c x^2\right)^{5/2}}{7 a x^7}+\frac{B c^2 \sqrt{a+c x^2}}{16 a x^2}+\frac{B c \left(a+c x^2\right)^{3/2}}{24 a x^4}-\frac{B \left(a+c x^2\right)^{5/2}}{6 a x^6}","\frac{2 A c \left(a+c x^2\right)^{5/2}}{35 a^2 x^5}+\frac{B c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 a^{3/2}}-\frac{A \left(a+c x^2\right)^{5/2}}{7 a x^7}+\frac{B c^2 \sqrt{a+c x^2}}{16 a x^2}+\frac{B c \left(a+c x^2\right)^{3/2}}{24 a x^4}-\frac{B \left(a+c x^2\right)^{5/2}}{6 a x^6}",1,"(B*c^2*Sqrt[a + c*x^2])/(16*a*x^2) + (B*c*(a + c*x^2)^(3/2))/(24*a*x^4) - (A*(a + c*x^2)^(5/2))/(7*a*x^7) - (B*(a + c*x^2)^(5/2))/(6*a*x^6) + (2*A*c*(a + c*x^2)^(5/2))/(35*a^2*x^5) + (B*c^3*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(16*a^(3/2))","A",8,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
339,1,198,0,0.1512938,"\int x^4 (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[x^4*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{3 a^4 A x \sqrt{a+c x^2}}{256 c^2}+\frac{a^3 A x \left(a+c x^2\right)^{3/2}}{128 c^2}+\frac{a^2 A x \left(a+c x^2\right)^{5/2}}{160 c^2}+\frac{3 a^5 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}+\frac{a \left(a+c x^2\right)^{7/2} (640 a B-2079 A c x)}{55440 c^3}+\frac{A x^3 \left(a+c x^2\right)^{7/2}}{10 c}-\frac{4 a B x^2 \left(a+c x^2\right)^{7/2}}{99 c^2}+\frac{B x^4 \left(a+c x^2\right)^{7/2}}{11 c}","\frac{3 a^4 A x \sqrt{a+c x^2}}{256 c^2}+\frac{a^3 A x \left(a+c x^2\right)^{3/2}}{128 c^2}+\frac{a^2 A x \left(a+c x^2\right)^{5/2}}{160 c^2}+\frac{3 a^5 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}+\frac{a \left(a+c x^2\right)^{7/2} (640 a B-2079 A c x)}{55440 c^3}+\frac{A x^3 \left(a+c x^2\right)^{7/2}}{10 c}-\frac{4 a B x^2 \left(a+c x^2\right)^{7/2}}{99 c^2}+\frac{B x^4 \left(a+c x^2\right)^{7/2}}{11 c}",1,"(3*a^4*A*x*Sqrt[a + c*x^2])/(256*c^2) + (a^3*A*x*(a + c*x^2)^(3/2))/(128*c^2) + (a^2*A*x*(a + c*x^2)^(5/2))/(160*c^2) - (4*a*B*x^2*(a + c*x^2)^(7/2))/(99*c^2) + (A*x^3*(a + c*x^2)^(7/2))/(10*c) + (B*x^4*(a + c*x^2)^(7/2))/(11*c) + (a*(640*a*B - 2079*A*c*x)*(a + c*x^2)^(7/2))/(55440*c^3) + (3*a^5*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(256*c^(5/2))","A",9,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
340,1,173,0,0.1045268,"\int x^3 (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[x^3*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{3 a^4 B x \sqrt{a+c x^2}}{256 c^2}+\frac{a^3 B x \left(a+c x^2\right)^{3/2}}{128 c^2}+\frac{a^2 B x \left(a+c x^2\right)^{5/2}}{160 c^2}+\frac{3 a^5 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}-\frac{a \left(a+c x^2\right)^{7/2} (160 A+189 B x)}{5040 c^2}+\frac{A x^2 \left(a+c x^2\right)^{7/2}}{9 c}+\frac{B x^3 \left(a+c x^2\right)^{7/2}}{10 c}","\frac{3 a^4 B x \sqrt{a+c x^2}}{256 c^2}+\frac{a^3 B x \left(a+c x^2\right)^{3/2}}{128 c^2}+\frac{a^2 B x \left(a+c x^2\right)^{5/2}}{160 c^2}+\frac{3 a^5 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{256 c^{5/2}}-\frac{a \left(a+c x^2\right)^{7/2} (160 A+189 B x)}{5040 c^2}+\frac{A x^2 \left(a+c x^2\right)^{7/2}}{9 c}+\frac{B x^3 \left(a+c x^2\right)^{7/2}}{10 c}",1,"(3*a^4*B*x*Sqrt[a + c*x^2])/(256*c^2) + (a^3*B*x*(a + c*x^2)^(3/2))/(128*c^2) + (a^2*B*x*(a + c*x^2)^(5/2))/(160*c^2) + (A*x^2*(a + c*x^2)^(7/2))/(9*c) + (B*x^3*(a + c*x^2)^(7/2))/(10*c) - (a*(160*A + 189*B*x)*(a + c*x^2)^(7/2))/(5040*c^2) + (3*a^5*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(256*c^(5/2))","A",8,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
341,1,150,0,0.0661778,"\int x^2 (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[x^2*(A + B*x)*(a + c*x^2)^(5/2),x]","-\frac{5 a^4 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}-\frac{5 a^3 A x \sqrt{a+c x^2}}{128 c}-\frac{5 a^2 A x \left(a+c x^2\right)^{3/2}}{192 c}-\frac{\left(a+c x^2\right)^{7/2} (16 a B-63 A c x)}{504 c^2}-\frac{a A x \left(a+c x^2\right)^{5/2}}{48 c}+\frac{B x^2 \left(a+c x^2\right)^{7/2}}{9 c}","-\frac{5 a^4 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}-\frac{5 a^3 A x \sqrt{a+c x^2}}{128 c}-\frac{5 a^2 A x \left(a+c x^2\right)^{3/2}}{192 c}-\frac{\left(a+c x^2\right)^{7/2} (16 a B-63 A c x)}{504 c^2}-\frac{a A x \left(a+c x^2\right)^{5/2}}{48 c}+\frac{B x^2 \left(a+c x^2\right)^{7/2}}{9 c}",1,"(-5*a^3*A*x*Sqrt[a + c*x^2])/(128*c) - (5*a^2*A*x*(a + c*x^2)^(3/2))/(192*c) - (a*A*x*(a + c*x^2)^(5/2))/(48*c) + (B*x^2*(a + c*x^2)^(7/2))/(9*c) - ((16*a*B - 63*A*c*x)*(a + c*x^2)^(7/2))/(504*c^2) - (5*a^4*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(3/2))","A",7,5,20,0.2500,1,"{833, 780, 195, 217, 206}"
342,1,126,0,0.0397593,"\int x (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[x*(A + B*x)*(a + c*x^2)^(5/2),x]","-\frac{5 a^4 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}-\frac{5 a^3 B x \sqrt{a+c x^2}}{128 c}-\frac{5 a^2 B x \left(a+c x^2\right)^{3/2}}{192 c}+\frac{\left(a+c x^2\right)^{7/2} (8 A+7 B x)}{56 c}-\frac{a B x \left(a+c x^2\right)^{5/2}}{48 c}","-\frac{5 a^4 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{128 c^{3/2}}-\frac{5 a^3 B x \sqrt{a+c x^2}}{128 c}-\frac{5 a^2 B x \left(a+c x^2\right)^{3/2}}{192 c}+\frac{\left(a+c x^2\right)^{7/2} (8 A+7 B x)}{56 c}-\frac{a B x \left(a+c x^2\right)^{5/2}}{48 c}",1,"(-5*a^3*B*x*Sqrt[a + c*x^2])/(128*c) - (5*a^2*B*x*(a + c*x^2)^(3/2))/(192*c) - (a*B*x*(a + c*x^2)^(5/2))/(48*c) + ((8*A + 7*B*x)*(a + c*x^2)^(7/2))/(56*c) - (5*a^4*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(128*c^(3/2))","A",6,4,18,0.2222,1,"{780, 195, 217, 206}"
343,1,107,0,0.0342443,"\int (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{5}{16} a^2 A x \sqrt{a+c x^2}+\frac{5 a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{1}{6} A x \left(a+c x^2\right)^{5/2}+\frac{5}{24} a A x \left(a+c x^2\right)^{3/2}+\frac{B \left(a+c x^2\right)^{7/2}}{7 c}","\frac{5}{16} a^2 A x \sqrt{a+c x^2}+\frac{5 a^3 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{1}{6} A x \left(a+c x^2\right)^{5/2}+\frac{5}{24} a A x \left(a+c x^2\right)^{3/2}+\frac{B \left(a+c x^2\right)^{7/2}}{7 c}",1,"(5*a^2*A*x*Sqrt[a + c*x^2])/16 + (5*a*A*x*(a + c*x^2)^(3/2))/24 + (A*x*(a + c*x^2)^(5/2))/6 + (B*(a + c*x^2)^(7/2))/(7*c) + (5*a^3*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*Sqrt[c])","A",6,4,17,0.2353,1,"{641, 195, 217, 206}"
344,1,132,0,0.1219261,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x,x]","\frac{1}{16} a^2 \sqrt{a+c x^2} (16 A+5 B x)-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{5 a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{1}{24} a \left(a+c x^2\right)^{3/2} (8 A+5 B x)+\frac{1}{30} \left(a+c x^2\right)^{5/2} (6 A+5 B x)","\frac{1}{16} a^2 \sqrt{a+c x^2} (16 A+5 B x)-a^{5/2} A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{5 a^3 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{16 \sqrt{c}}+\frac{1}{24} a \left(a+c x^2\right)^{3/2} (8 A+5 B x)+\frac{1}{30} \left(a+c x^2\right)^{5/2} (6 A+5 B x)",1,"(a^2*(16*A + 5*B*x)*Sqrt[a + c*x^2])/16 + (a*(8*A + 5*B*x)*(a + c*x^2)^(3/2))/24 + ((6*A + 5*B*x)*(a + c*x^2)^(5/2))/30 + (5*a^3*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(16*Sqrt[c]) - a^(5/2)*A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",9,7,20,0.3500,1,"{815, 844, 217, 206, 266, 63, 208}"
345,1,136,0,0.1203807,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^2} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^2,x]","\frac{15}{8} a^2 A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)+a^{5/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{1}{8} a \sqrt{a+c x^2} (8 a B+15 A c x)-\frac{\left(a+c x^2\right)^{5/2} (5 A-B x)}{5 x}+\frac{1}{12} \left(a+c x^2\right)^{3/2} (4 a B+15 A c x)","\frac{15}{8} a^2 A \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)+a^{5/2} (-B) \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{1}{8} a \sqrt{a+c x^2} (8 a B+15 A c x)-\frac{\left(a+c x^2\right)^{5/2} (5 A-B x)}{5 x}+\frac{1}{12} \left(a+c x^2\right)^{3/2} (4 a B+15 A c x)",1,"(a*(8*a*B + 15*A*c*x)*Sqrt[a + c*x^2])/8 + ((4*a*B + 15*A*c*x)*(a + c*x^2)^(3/2))/12 - ((5*A - B*x)*(a + c*x^2)^(5/2))/(5*x) + (15*a^2*A*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/8 - a^(5/2)*B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]]","A",9,8,20,0.4000,1,"{813, 815, 844, 217, 206, 266, 63, 208}"
346,1,141,0,0.1179718,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^3} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^3,x]","-\frac{5}{2} a^{3/2} A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{15}{8} a^2 B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\frac{\left(a+c x^2\right)^{5/2} (2 A-B x)}{4 x^2}-\frac{5 \left(a+c x^2\right)^{3/2} (3 a B-2 A c x)}{12 x}+\frac{5}{8} a c \sqrt{a+c x^2} (4 A+3 B x)","-\frac{5}{2} a^{3/2} A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{15}{8} a^2 B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\frac{\left(a+c x^2\right)^{5/2} (2 A-B x)}{4 x^2}-\frac{5 \left(a+c x^2\right)^{3/2} (3 a B-2 A c x)}{12 x}+\frac{5}{8} a c \sqrt{a+c x^2} (4 A+3 B x)",1,"(5*a*c*(4*A + 3*B*x)*Sqrt[a + c*x^2])/8 - (5*(3*a*B - 2*A*c*x)*(a + c*x^2)^(3/2))/(12*x) - ((2*A - B*x)*(a + c*x^2)^(5/2))/(4*x^2) + (15*a^2*B*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/8 - (5*a^(3/2)*A*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/2","A",9,8,20,0.4000,1,"{813, 815, 844, 217, 206, 266, 63, 208}"
347,1,137,0,0.1102496,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^4} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^4,x]","-\frac{5}{2} a^{3/2} B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-\frac{\left(a+c x^2\right)^{5/2} (A-B x)}{3 x^3}-\frac{5 \left(a+c x^2\right)^{3/2} (a B-A c x)}{6 x^2}-\frac{5 a c \sqrt{a+c x^2} (A-B x)}{2 x}+\frac{5}{2} a A c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","-\frac{5}{2} a^{3/2} B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)-\frac{\left(a+c x^2\right)^{5/2} (A-B x)}{3 x^3}-\frac{5 \left(a+c x^2\right)^{3/2} (a B-A c x)}{6 x^2}-\frac{5 a c \sqrt{a+c x^2} (A-B x)}{2 x}+\frac{5}{2} a A c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"(-5*a*c*(A - B*x)*Sqrt[a + c*x^2])/(2*x) - (5*(a*B - A*c*x)*(a + c*x^2)^(3/2))/(6*x^2) - ((A - B*x)*(a + c*x^2)^(5/2))/(3*x^3) + (5*a*A*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/2 - (5*a^(3/2)*B*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/2","A",9,7,20,0.3500,1,"{813, 844, 217, 206, 266, 63, 208}"
348,1,143,0,0.1160931,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^5} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^5,x]","-\frac{\left(a+c x^2\right)^{5/2} (A-2 B x)}{4 x^4}-\frac{5 \left(a+c x^2\right)^{3/2} (4 a B+3 A c x)}{24 x^3}-\frac{5 c \sqrt{a+c x^2} (4 a B-3 A c x)}{8 x}-\frac{15}{8} \sqrt{a} A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{5}{2} a B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","-\frac{\left(a+c x^2\right)^{5/2} (A-2 B x)}{4 x^4}-\frac{5 \left(a+c x^2\right)^{3/2} (4 a B+3 A c x)}{24 x^3}-\frac{5 c \sqrt{a+c x^2} (4 a B-3 A c x)}{8 x}-\frac{15}{8} \sqrt{a} A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)+\frac{5}{2} a B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"(-5*c*(4*a*B - 3*A*c*x)*Sqrt[a + c*x^2])/(8*x) - (5*(4*a*B + 3*A*c*x)*(a + c*x^2)^(3/2))/(24*x^3) - ((A - 2*B*x)*(a + c*x^2)^(5/2))/(4*x^4) + (5*a*B*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/2 - (15*Sqrt[a]*A*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/8","A",9,8,20,0.4000,1,"{813, 811, 844, 217, 206, 266, 63, 208}"
349,1,140,0,0.1183058,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^6} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^6,x]","-\frac{c^2 \sqrt{a+c x^2} (8 A-15 B x)}{8 x}-\frac{c \left(a+c x^2\right)^{3/2} (8 A+15 B x)}{24 x^3}-\frac{\left(a+c x^2\right)^{5/2} (4 A+5 B x)}{20 x^5}+A c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\frac{15}{8} \sqrt{a} B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)","-\frac{c^2 \sqrt{a+c x^2} (8 A-15 B x)}{8 x}-\frac{c \left(a+c x^2\right)^{3/2} (8 A+15 B x)}{24 x^3}-\frac{\left(a+c x^2\right)^{5/2} (4 A+5 B x)}{20 x^5}+A c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)-\frac{15}{8} \sqrt{a} B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)",1,"-(c^2*(8*A - 15*B*x)*Sqrt[a + c*x^2])/(8*x) - (c*(8*A + 15*B*x)*(a + c*x^2)^(3/2))/(24*x^3) - ((4*A + 5*B*x)*(a + c*x^2)^(5/2))/(20*x^5) + A*c^(5/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]] - (15*Sqrt[a]*B*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/8","A",9,8,20,0.4000,1,"{811, 813, 844, 217, 206, 266, 63, 208}"
350,1,140,0,0.1223967,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^7} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^7,x]","-\frac{c^2 \sqrt{a+c x^2} (5 A+16 B x)}{16 x^2}-\frac{c \left(a+c x^2\right)^{3/2} (5 A+8 B x)}{24 x^4}-\frac{\left(a+c x^2\right)^{5/2} (5 A+6 B x)}{30 x^6}-\frac{5 A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}+B c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)","-\frac{c^2 \sqrt{a+c x^2} (5 A+16 B x)}{16 x^2}-\frac{c \left(a+c x^2\right)^{3/2} (5 A+8 B x)}{24 x^4}-\frac{\left(a+c x^2\right)^{5/2} (5 A+6 B x)}{30 x^6}-\frac{5 A c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}+B c^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)",1,"-(c^2*(5*A + 16*B*x)*Sqrt[a + c*x^2])/(16*x^2) - (c*(5*A + 8*B*x)*(a + c*x^2)^(3/2))/(24*x^4) - ((5*A + 6*B*x)*(a + c*x^2)^(5/2))/(30*x^6) + B*c^(5/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]] - (5*A*c^3*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(16*Sqrt[a])","A",9,7,20,0.3500,1,"{811, 844, 217, 206, 266, 63, 208}"
351,1,115,0,0.0725691,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^8} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^8,x]","-\frac{A \left(a+c x^2\right)^{7/2}}{7 a x^7}-\frac{5 B c^2 \sqrt{a+c x^2}}{16 x^2}-\frac{5 B c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{B \left(a+c x^2\right)^{5/2}}{6 x^6}-\frac{5 B c \left(a+c x^2\right)^{3/2}}{24 x^4}","-\frac{A \left(a+c x^2\right)^{7/2}}{7 a x^7}-\frac{5 B c^2 \sqrt{a+c x^2}}{16 x^2}-\frac{5 B c^3 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{16 \sqrt{a}}-\frac{B \left(a+c x^2\right)^{5/2}}{6 x^6}-\frac{5 B c \left(a+c x^2\right)^{3/2}}{24 x^4}",1,"(-5*B*c^2*Sqrt[a + c*x^2])/(16*x^2) - (5*B*c*(a + c*x^2)^(3/2))/(24*x^4) - (B*(a + c*x^2)^(5/2))/(6*x^6) - (A*(a + c*x^2)^(7/2))/(7*a*x^7) - (5*B*c^3*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(16*Sqrt[a])","A",7,5,20,0.2500,1,"{807, 266, 47, 63, 208}"
352,1,149,0,0.0989955,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^9} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^9,x]","\frac{5 A c^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}+\frac{5 A c^3 \sqrt{a+c x^2}}{128 a x^2}+\frac{5 A c^2 \left(a+c x^2\right)^{3/2}}{192 a x^4}+\frac{A c \left(a+c x^2\right)^{5/2}}{48 a x^6}-\frac{A \left(a+c x^2\right)^{7/2}}{8 a x^8}-\frac{B \left(a+c x^2\right)^{7/2}}{7 a x^7}","\frac{5 A c^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}+\frac{5 A c^3 \sqrt{a+c x^2}}{128 a x^2}+\frac{5 A c^2 \left(a+c x^2\right)^{3/2}}{192 a x^4}+\frac{A c \left(a+c x^2\right)^{5/2}}{48 a x^6}-\frac{A \left(a+c x^2\right)^{7/2}}{8 a x^8}-\frac{B \left(a+c x^2\right)^{7/2}}{7 a x^7}",1,"(5*A*c^3*Sqrt[a + c*x^2])/(128*a*x^2) + (5*A*c^2*(a + c*x^2)^(3/2))/(192*a*x^4) + (A*c*(a + c*x^2)^(5/2))/(48*a*x^6) - (A*(a + c*x^2)^(7/2))/(8*a*x^8) - (B*(a + c*x^2)^(7/2))/(7*a*x^7) + (5*A*c^4*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(128*a^(3/2))","A",8,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
353,1,172,0,0.123307,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{x^{10}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/x^10,x]","\frac{2 A c \left(a+c x^2\right)^{7/2}}{63 a^2 x^7}+\frac{5 B c^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}-\frac{A \left(a+c x^2\right)^{7/2}}{9 a x^9}+\frac{5 B c^3 \sqrt{a+c x^2}}{128 a x^2}+\frac{5 B c^2 \left(a+c x^2\right)^{3/2}}{192 a x^4}+\frac{B c \left(a+c x^2\right)^{5/2}}{48 a x^6}-\frac{B \left(a+c x^2\right)^{7/2}}{8 a x^8}","\frac{2 A c \left(a+c x^2\right)^{7/2}}{63 a^2 x^7}+\frac{5 B c^4 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{128 a^{3/2}}-\frac{A \left(a+c x^2\right)^{7/2}}{9 a x^9}+\frac{5 B c^3 \sqrt{a+c x^2}}{128 a x^2}+\frac{5 B c^2 \left(a+c x^2\right)^{3/2}}{192 a x^4}+\frac{B c \left(a+c x^2\right)^{5/2}}{48 a x^6}-\frac{B \left(a+c x^2\right)^{7/2}}{8 a x^8}",1,"(5*B*c^3*Sqrt[a + c*x^2])/(128*a*x^2) + (5*B*c^2*(a + c*x^2)^(3/2))/(192*a*x^4) + (B*c*(a + c*x^2)^(5/2))/(48*a*x^6) - (A*(a + c*x^2)^(7/2))/(9*a*x^9) - (B*(a + c*x^2)^(7/2))/(8*a*x^8) + (2*A*c*(a + c*x^2)^(7/2))/(63*a^2*x^7) + (5*B*c^4*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(128*a^(3/2))","A",9,6,20,0.3000,1,"{835, 807, 266, 47, 63, 208}"
354,1,129,0,0.1065139,"\int \frac{x^4 (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[(x^4*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{3 a^2 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{5/2}}+\frac{a \sqrt{a+c x^2} (64 a B-45 A c x)}{120 c^3}+\frac{A x^3 \sqrt{a+c x^2}}{4 c}-\frac{4 a B x^2 \sqrt{a+c x^2}}{15 c^2}+\frac{B x^4 \sqrt{a+c x^2}}{5 c}","\frac{3 a^2 A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{5/2}}+\frac{a \sqrt{a+c x^2} (64 a B-45 A c x)}{120 c^3}+\frac{A x^3 \sqrt{a+c x^2}}{4 c}-\frac{4 a B x^2 \sqrt{a+c x^2}}{15 c^2}+\frac{B x^4 \sqrt{a+c x^2}}{5 c}",1,"(-4*a*B*x^2*Sqrt[a + c*x^2])/(15*c^2) + (A*x^3*Sqrt[a + c*x^2])/(4*c) + (B*x^4*Sqrt[a + c*x^2])/(5*c) + (a*(64*a*B - 45*A*c*x)*Sqrt[a + c*x^2])/(120*c^3) + (3*a^2*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(5/2))","A",6,4,20,0.2000,1,"{833, 780, 217, 206}"
355,1,104,0,0.0687031,"\int \frac{x^3 (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[(x^3*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{5/2}}-\frac{a \sqrt{a+c x^2} (16 A+9 B x)}{24 c^2}+\frac{A x^2 \sqrt{a+c x^2}}{3 c}+\frac{B x^3 \sqrt{a+c x^2}}{4 c}","\frac{3 a^2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{8 c^{5/2}}-\frac{a \sqrt{a+c x^2} (16 A+9 B x)}{24 c^2}+\frac{A x^2 \sqrt{a+c x^2}}{3 c}+\frac{B x^3 \sqrt{a+c x^2}}{4 c}",1,"(A*x^2*Sqrt[a + c*x^2])/(3*c) + (B*x^3*Sqrt[a + c*x^2])/(4*c) - (a*(16*A + 9*B*x)*Sqrt[a + c*x^2])/(24*c^2) + (3*a^2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(8*c^(5/2))","A",5,4,20,0.2000,1,"{833, 780, 217, 206}"
356,1,81,0,0.0396998,"\int \frac{x^2 (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[(x^2*(A + B*x))/Sqrt[a + c*x^2],x]","-\frac{\sqrt{a+c x^2} (4 a B-3 A c x)}{6 c^2}-\frac{a A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}+\frac{B x^2 \sqrt{a+c x^2}}{3 c}","-\frac{\sqrt{a+c x^2} (4 a B-3 A c x)}{6 c^2}-\frac{a A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}+\frac{B x^2 \sqrt{a+c x^2}}{3 c}",1,"(B*x^2*Sqrt[a + c*x^2])/(3*c) - ((4*a*B - 3*A*c*x)*Sqrt[a + c*x^2])/(6*c^2) - (a*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",4,4,20,0.2000,1,"{833, 780, 217, 206}"
357,1,56,0,0.0177791,"\int \frac{x (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[(x*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{\sqrt{a+c x^2} (2 A+B x)}{2 c}-\frac{a B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}","\frac{\sqrt{a+c x^2} (2 A+B x)}{2 c}-\frac{a B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{3/2}}",1,"((2*A + B*x)*Sqrt[a + c*x^2])/(2*c) - (a*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(3/2))","A",3,3,18,0.1667,1,"{780, 217, 206}"
358,1,43,0,0.0122925,"\int \frac{A+B x}{\sqrt{a+c x^2}} \, dx","Int[(A + B*x)/Sqrt[a + c*x^2],x]","\frac{A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}+\frac{B \sqrt{a+c x^2}}{c}","\frac{A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}+\frac{B \sqrt{a+c x^2}}{c}",1,"(B*Sqrt[a + c*x^2])/c + (A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/Sqrt[c]","A",3,3,17,0.1765,1,"{641, 217, 206}"
359,1,53,0,0.0387258,"\int \frac{A+B x}{x \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(x*Sqrt[a + c*x^2]),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{\sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"(B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/Sqrt[c] - (A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/Sqrt[a]","A",6,6,20,0.3000,1,"{844, 217, 206, 266, 63, 208}"
360,1,47,0,0.0308582,"\int \frac{A+B x}{x^2 \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(x^2*Sqrt[a + c*x^2]),x]","-\frac{A \sqrt{a+c x^2}}{a x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a}}","-\frac{A \sqrt{a+c x^2}}{a x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{\sqrt{a}}",1,"-((A*Sqrt[a + c*x^2])/(a*x)) - (B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/Sqrt[a]","A",4,4,20,0.2000,1,"{807, 266, 63, 208}"
361,1,72,0,0.0513389,"\int \frac{A+B x}{x^3 \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(x^3*Sqrt[a + c*x^2]),x]","\frac{A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+c x^2}}{2 a x^2}-\frac{B \sqrt{a+c x^2}}{a x}","\frac{A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+c x^2}}{2 a x^2}-\frac{B \sqrt{a+c x^2}}{a x}",1,"-(A*Sqrt[a + c*x^2])/(2*a*x^2) - (B*Sqrt[a + c*x^2])/(a*x) + (A*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(3/2))","A",5,5,20,0.2500,1,"{835, 807, 266, 63, 208}"
362,1,97,0,0.0730243,"\int \frac{A+B x}{x^4 \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(x^4*Sqrt[a + c*x^2]),x]","\frac{2 A c \sqrt{a+c x^2}}{3 a^2 x}+\frac{B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+c x^2}}{3 a x^3}-\frac{B \sqrt{a+c x^2}}{2 a x^2}","\frac{2 A c \sqrt{a+c x^2}}{3 a^2 x}+\frac{B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+c x^2}}{3 a x^3}-\frac{B \sqrt{a+c x^2}}{2 a x^2}",1,"-(A*Sqrt[a + c*x^2])/(3*a*x^3) - (B*Sqrt[a + c*x^2])/(2*a*x^2) + (2*A*c*Sqrt[a + c*x^2])/(3*a^2*x) + (B*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(3/2))","A",6,5,20,0.2500,1,"{835, 807, 266, 63, 208}"
363,1,122,0,0.0995186,"\int \frac{A+B x}{x^5 \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(x^5*Sqrt[a + c*x^2]),x]","-\frac{3 A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{3 A c \sqrt{a+c x^2}}{8 a^2 x^2}+\frac{2 B c \sqrt{a+c x^2}}{3 a^2 x}-\frac{A \sqrt{a+c x^2}}{4 a x^4}-\frac{B \sqrt{a+c x^2}}{3 a x^3}","-\frac{3 A c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{3 A c \sqrt{a+c x^2}}{8 a^2 x^2}+\frac{2 B c \sqrt{a+c x^2}}{3 a^2 x}-\frac{A \sqrt{a+c x^2}}{4 a x^4}-\frac{B \sqrt{a+c x^2}}{3 a x^3}",1,"-(A*Sqrt[a + c*x^2])/(4*a*x^4) - (B*Sqrt[a + c*x^2])/(3*a*x^3) + (3*A*c*Sqrt[a + c*x^2])/(8*a^2*x^2) + (2*B*c*Sqrt[a + c*x^2])/(3*a^2*x) - (3*A*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*a^(5/2))","A",7,5,20,0.2500,1,"{835, 807, 266, 63, 208}"
364,1,147,0,0.12864,"\int \frac{A+B x}{x^6 \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(x^6*Sqrt[a + c*x^2]),x]","-\frac{8 A c^2 \sqrt{a+c x^2}}{15 a^3 x}+\frac{4 A c \sqrt{a+c x^2}}{15 a^2 x^3}-\frac{3 B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{3 B c \sqrt{a+c x^2}}{8 a^2 x^2}-\frac{A \sqrt{a+c x^2}}{5 a x^5}-\frac{B \sqrt{a+c x^2}}{4 a x^4}","-\frac{8 A c^2 \sqrt{a+c x^2}}{15 a^3 x}+\frac{4 A c \sqrt{a+c x^2}}{15 a^2 x^3}-\frac{3 B c^2 \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{8 a^{5/2}}+\frac{3 B c \sqrt{a+c x^2}}{8 a^2 x^2}-\frac{A \sqrt{a+c x^2}}{5 a x^5}-\frac{B \sqrt{a+c x^2}}{4 a x^4}",1,"-(A*Sqrt[a + c*x^2])/(5*a*x^5) - (B*Sqrt[a + c*x^2])/(4*a*x^4) + (4*A*c*Sqrt[a + c*x^2])/(15*a^2*x^3) + (3*B*c*Sqrt[a + c*x^2])/(8*a^2*x^2) - (8*A*c^2*Sqrt[a + c*x^2])/(15*a^3*x) - (3*B*c^2*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(8*a^(5/2))","A",8,5,20,0.2500,1,"{835, 807, 266, 63, 208}"
365,1,105,0,0.0714329,"\int \frac{x^4 (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(x^4*(A + B*x))/(a + c*x^2)^(3/2),x]","-\frac{\sqrt{a+c x^2} (16 a B-9 A c x)}{6 c^3}-\frac{x^3 (A+B x)}{c \sqrt{a+c x^2}}-\frac{3 a A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{5/2}}+\frac{4 B x^2 \sqrt{a+c x^2}}{3 c^2}","-\frac{\sqrt{a+c x^2} (16 a B-9 A c x)}{6 c^3}-\frac{x^3 (A+B x)}{c \sqrt{a+c x^2}}-\frac{3 a A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{5/2}}+\frac{4 B x^2 \sqrt{a+c x^2}}{3 c^2}",1,"-((x^3*(A + B*x))/(c*Sqrt[a + c*x^2])) + (4*B*x^2*Sqrt[a + c*x^2])/(3*c^2) - ((16*a*B - 9*A*c*x)*Sqrt[a + c*x^2])/(6*c^3) - (3*a*A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(5/2))","A",5,5,20,0.2500,1,"{819, 833, 780, 217, 206}"
366,1,81,0,0.03984,"\int \frac{x^3 (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(x^3*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{\sqrt{a+c x^2} (4 A+3 B x)}{2 c^2}-\frac{x^2 (A+B x)}{c \sqrt{a+c x^2}}-\frac{3 a B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{5/2}}","\frac{\sqrt{a+c x^2} (4 A+3 B x)}{2 c^2}-\frac{x^2 (A+B x)}{c \sqrt{a+c x^2}}-\frac{3 a B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{2 c^{5/2}}",1,"-((x^2*(A + B*x))/(c*Sqrt[a + c*x^2])) + ((4*A + 3*B*x)*Sqrt[a + c*x^2])/(2*c^2) - (3*a*B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/(2*c^(5/2))","A",4,4,20,0.2000,1,"{819, 780, 217, 206}"
367,1,66,0,0.0339244,"\int \frac{x^2 (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(x^2*(A + B*x))/(a + c*x^2)^(3/2),x]","-\frac{x (A+B x)}{c \sqrt{a+c x^2}}+\frac{A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}+\frac{2 B \sqrt{a+c x^2}}{c^2}","-\frac{x (A+B x)}{c \sqrt{a+c x^2}}+\frac{A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}+\frac{2 B \sqrt{a+c x^2}}{c^2}",1,"-((x*(A + B*x))/(c*Sqrt[a + c*x^2])) + (2*B*Sqrt[a + c*x^2])/c^2 + (A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(3/2)","A",4,4,20,0.2000,1,"{819, 641, 217, 206}"
368,1,48,0,0.0183047,"\int \frac{x (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(x*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{A+B x}{c \sqrt{a+c x^2}}","\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{3/2}}-\frac{A+B x}{c \sqrt{a+c x^2}}",1,"-((A + B*x)/(c*Sqrt[a + c*x^2])) + (B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(3/2)","A",3,3,18,0.1667,1,"{778, 217, 206}"
369,1,28,0,0.0066274,"\int \frac{A+B x}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(a + c*x^2)^(3/2),x]","-\frac{a B-A c x}{a c \sqrt{a+c x^2}}","-\frac{a B-A c x}{a c \sqrt{a+c x^2}}",1,"-((a*B - A*c*x)/(a*c*Sqrt[a + c*x^2]))","A",1,1,17,0.05882,1,"{637}"
370,1,47,0,0.0369784,"\int \frac{A+B x}{x \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x*(a + c*x^2)^(3/2)),x]","\frac{A+B x}{a \sqrt{a+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2}}","\frac{A+B x}{a \sqrt{a+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2}}",1,"(A + B*x)/(a*Sqrt[a + c*x^2]) - (A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/a^(3/2)","A",5,5,20,0.2500,1,"{823, 12, 266, 63, 208}"
371,1,70,0,0.0534567,"\int \frac{A+B x}{x^2 \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^2*(a + c*x^2)^(3/2)),x]","-\frac{2 A \sqrt{a+c x^2}}{a^2 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{A+B x}{a x \sqrt{a+c x^2}}","-\frac{2 A \sqrt{a+c x^2}}{a^2 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{3/2}}+\frac{A+B x}{a x \sqrt{a+c x^2}}",1,"(A + B*x)/(a*x*Sqrt[a + c*x^2]) - (2*A*Sqrt[a + c*x^2])/(a^2*x) - (B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/a^(3/2)","A",5,5,20,0.2500,1,"{823, 807, 266, 63, 208}"
372,1,95,0,0.0795045,"\int \frac{A+B x}{x^3 \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^3*(a + c*x^2)^(3/2)),x]","-\frac{3 A \sqrt{a+c x^2}}{2 a^2 x^2}+\frac{3 A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{2 B \sqrt{a+c x^2}}{a^2 x}+\frac{A+B x}{a x^2 \sqrt{a+c x^2}}","-\frac{3 A \sqrt{a+c x^2}}{2 a^2 x^2}+\frac{3 A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}-\frac{2 B \sqrt{a+c x^2}}{a^2 x}+\frac{A+B x}{a x^2 \sqrt{a+c x^2}}",1,"(A + B*x)/(a*x^2*Sqrt[a + c*x^2]) - (3*A*Sqrt[a + c*x^2])/(2*a^2*x^2) - (2*B*Sqrt[a + c*x^2])/(a^2*x) + (3*A*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(5/2))","A",6,6,20,0.3000,1,"{823, 835, 807, 266, 63, 208}"
373,1,120,0,0.1056445,"\int \frac{A+B x}{x^4 \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^4*(a + c*x^2)^(3/2)),x]","\frac{8 A c \sqrt{a+c x^2}}{3 a^3 x}-\frac{4 A \sqrt{a+c x^2}}{3 a^2 x^3}-\frac{3 B \sqrt{a+c x^2}}{2 a^2 x^2}+\frac{3 B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{A+B x}{a x^3 \sqrt{a+c x^2}}","\frac{8 A c \sqrt{a+c x^2}}{3 a^3 x}-\frac{4 A \sqrt{a+c x^2}}{3 a^2 x^3}-\frac{3 B \sqrt{a+c x^2}}{2 a^2 x^2}+\frac{3 B c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{5/2}}+\frac{A+B x}{a x^3 \sqrt{a+c x^2}}",1,"(A + B*x)/(a*x^3*Sqrt[a + c*x^2]) - (4*A*Sqrt[a + c*x^2])/(3*a^2*x^3) - (3*B*Sqrt[a + c*x^2])/(2*a^2*x^2) + (8*A*c*Sqrt[a + c*x^2])/(3*a^3*x) + (3*B*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(5/2))","A",7,6,20,0.3000,1,"{823, 835, 807, 266, 63, 208}"
374,1,99,0,0.0639875,"\int \frac{x^4 (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(x^4*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{x (3 A+4 B x)}{3 c^2 \sqrt{a+c x^2}}-\frac{x^3 (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}+\frac{8 B \sqrt{a+c x^2}}{3 c^3}","-\frac{x (3 A+4 B x)}{3 c^2 \sqrt{a+c x^2}}-\frac{x^3 (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{A \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}+\frac{8 B \sqrt{a+c x^2}}{3 c^3}",1,"-(x^3*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (x*(3*A + 4*B*x))/(3*c^2*Sqrt[a + c*x^2]) + (8*B*Sqrt[a + c*x^2])/(3*c^3) + (A*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(5/2)","A",5,4,20,0.2000,1,"{819, 641, 217, 206}"
375,1,79,0,0.0411006,"\int \frac{x^3 (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(x^3*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{2 A+3 B x}{3 c^2 \sqrt{a+c x^2}}-\frac{x^2 (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}","-\frac{2 A+3 B x}{3 c^2 \sqrt{a+c x^2}}-\frac{x^2 (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a+c x^2}}\right)}{c^{5/2}}",1,"-(x^2*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (2*A + 3*B*x)/(3*c^2*Sqrt[a + c*x^2]) + (B*ArcTanh[(Sqrt[c]*x)/Sqrt[a + c*x^2]])/c^(5/2)","A",4,4,20,0.2000,1,"{819, 778, 217, 206}"
376,1,53,0,0.020411,"\int \frac{x^2 (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(x^2*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{x^2 (a B-A c x)}{3 a c \left(a+c x^2\right)^{3/2}}-\frac{2 B}{3 c^2 \sqrt{a+c x^2}}","-\frac{x^2 (a B-A c x)}{3 a c \left(a+c x^2\right)^{3/2}}-\frac{2 B}{3 c^2 \sqrt{a+c x^2}}",1,"-(x^2*(a*B - A*c*x))/(3*a*c*(a + c*x^2)^(3/2)) - (2*B)/(3*c^2*Sqrt[a + c*x^2])","A",2,2,20,0.1000,1,"{805, 261}"
377,1,47,0,0.0147285,"\int \frac{x (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(x*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{B x}{3 a c \sqrt{a+c x^2}}-\frac{A+B x}{3 c \left(a+c x^2\right)^{3/2}}","\frac{B x}{3 a c \sqrt{a+c x^2}}-\frac{A+B x}{3 c \left(a+c x^2\right)^{3/2}}",1,"-(A + B*x)/(3*c*(a + c*x^2)^(3/2)) + (B*x)/(3*a*c*Sqrt[a + c*x^2])","A",2,2,18,0.1111,1,"{778, 191}"
378,1,51,0,0.0100937,"\int \frac{A+B x}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(a + c*x^2)^(5/2),x]","\frac{2 A x}{3 a^2 \sqrt{a+c x^2}}-\frac{a B-A c x}{3 a c \left(a+c x^2\right)^{3/2}}","\frac{2 A x}{3 a^2 \sqrt{a+c x^2}}-\frac{a B-A c x}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-(a*B - A*c*x)/(3*a*c*(a + c*x^2)^(3/2)) + (2*A*x)/(3*a^2*Sqrt[a + c*x^2])","A",2,2,17,0.1176,1,"{639, 191}"
379,1,76,0,0.0637584,"\int \frac{A+B x}{x \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x*(a + c*x^2)^(5/2)),x]","\frac{3 A+2 B x}{3 a^2 \sqrt{a+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a \left(a+c x^2\right)^{3/2}}","\frac{3 A+2 B x}{3 a^2 \sqrt{a+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a \left(a+c x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*(a + c*x^2)^(3/2)) + (3*A + 2*B*x)/(3*a^2*Sqrt[a + c*x^2]) - (A*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/a^(5/2)","A",6,5,20,0.2500,1,"{823, 12, 266, 63, 208}"
380,1,104,0,0.0846122,"\int \frac{A+B x}{x^2 \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^2*(a + c*x^2)^(5/2)),x]","\frac{4 A+3 B x}{3 a^2 x \sqrt{a+c x^2}}-\frac{8 A \sqrt{a+c x^2}}{3 a^3 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a x \left(a+c x^2\right)^{3/2}}","\frac{4 A+3 B x}{3 a^2 x \sqrt{a+c x^2}}-\frac{8 A \sqrt{a+c x^2}}{3 a^3 x}-\frac{B \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{a^{5/2}}+\frac{A+B x}{3 a x \left(a+c x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*x*(a + c*x^2)^(3/2)) + (4*A + 3*B*x)/(3*a^2*x*Sqrt[a + c*x^2]) - (8*A*Sqrt[a + c*x^2])/(3*a^3*x) - (B*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/a^(5/2)","A",6,5,20,0.2500,1,"{823, 807, 266, 63, 208}"
381,1,129,0,0.1117295,"\int \frac{A+B x}{x^3 \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^3*(a + c*x^2)^(5/2)),x]","\frac{5 A+4 B x}{3 a^2 x^2 \sqrt{a+c x^2}}-\frac{5 A \sqrt{a+c x^2}}{2 a^3 x^2}+\frac{5 A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{8 B \sqrt{a+c x^2}}{3 a^3 x}+\frac{A+B x}{3 a x^2 \left(a+c x^2\right)^{3/2}}","\frac{5 A+4 B x}{3 a^2 x^2 \sqrt{a+c x^2}}-\frac{5 A \sqrt{a+c x^2}}{2 a^3 x^2}+\frac{5 A c \tanh ^{-1}\left(\frac{\sqrt{a+c x^2}}{\sqrt{a}}\right)}{2 a^{7/2}}-\frac{8 B \sqrt{a+c x^2}}{3 a^3 x}+\frac{A+B x}{3 a x^2 \left(a+c x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*x^2*(a + c*x^2)^(3/2)) + (5*A + 4*B*x)/(3*a^2*x^2*Sqrt[a + c*x^2]) - (5*A*Sqrt[a + c*x^2])/(2*a^3*x^2) - (8*B*Sqrt[a + c*x^2])/(3*a^3*x) + (5*A*c*ArcTanh[Sqrt[a + c*x^2]/Sqrt[a]])/(2*a^(7/2))","A",7,6,20,0.3000,1,"{823, 835, 807, 266, 63, 208}"
382,1,71,0,0.0153587,"\int \frac{d+e x}{\left(a+c x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(a + c*x^2)^(7/2),x]","\frac{8 d x}{15 a^3 \sqrt{a+c x^2}}+\frac{4 d x}{15 a^2 \left(a+c x^2\right)^{3/2}}-\frac{a e-c d x}{5 a c \left(a+c x^2\right)^{5/2}}","\frac{8 d x}{15 a^3 \sqrt{a+c x^2}}+\frac{4 d x}{15 a^2 \left(a+c x^2\right)^{3/2}}-\frac{a e-c d x}{5 a c \left(a+c x^2\right)^{5/2}}",1,"-(a*e - c*d*x)/(5*a*c*(a + c*x^2)^(5/2)) + (4*d*x)/(15*a^2*(a + c*x^2)^(3/2)) + (8*d*x)/(15*a^3*Sqrt[a + c*x^2])","A",3,3,17,0.1765,1,"{639, 192, 191}"
383,1,91,0,0.0211028,"\int \frac{d+e x}{\left(a+c x^2\right)^{9/2}} \, dx","Int[(d + e*x)/(a + c*x^2)^(9/2),x]","\frac{16 d x}{35 a^4 \sqrt{a+c x^2}}+\frac{8 d x}{35 a^3 \left(a+c x^2\right)^{3/2}}+\frac{6 d x}{35 a^2 \left(a+c x^2\right)^{5/2}}-\frac{a e-c d x}{7 a c \left(a+c x^2\right)^{7/2}}","\frac{16 d x}{35 a^4 \sqrt{a+c x^2}}+\frac{8 d x}{35 a^3 \left(a+c x^2\right)^{3/2}}+\frac{6 d x}{35 a^2 \left(a+c x^2\right)^{5/2}}-\frac{a e-c d x}{7 a c \left(a+c x^2\right)^{7/2}}",1,"-(a*e - c*d*x)/(7*a*c*(a + c*x^2)^(7/2)) + (6*d*x)/(35*a^2*(a + c*x^2)^(5/2)) + (8*d*x)/(35*a^3*(a + c*x^2)^(3/2)) + (16*d*x)/(35*a^4*Sqrt[a + c*x^2])","A",4,3,17,0.1765,1,"{639, 192, 191}"
384,1,45,0,0.0122232,"\int x^{7/2} (A+B x) \left(a+c x^2\right) \, dx","Int[x^(7/2)*(A + B*x)*(a + c*x^2),x]","\frac{2}{9} a A x^{9/2}+\frac{2}{11} a B x^{11/2}+\frac{2}{13} A c x^{13/2}+\frac{2}{15} B c x^{15/2}","\frac{2}{9} a A x^{9/2}+\frac{2}{11} a B x^{11/2}+\frac{2}{13} A c x^{13/2}+\frac{2}{15} B c x^{15/2}",1,"(2*a*A*x^(9/2))/9 + (2*a*B*x^(11/2))/11 + (2*A*c*x^(13/2))/13 + (2*B*c*x^(15/2))/15","A",2,1,18,0.05556,1,"{766}"
385,1,45,0,0.0123421,"\int x^{5/2} (A+B x) \left(a+c x^2\right) \, dx","Int[x^(5/2)*(A + B*x)*(a + c*x^2),x]","\frac{2}{7} a A x^{7/2}+\frac{2}{9} a B x^{9/2}+\frac{2}{11} A c x^{11/2}+\frac{2}{13} B c x^{13/2}","\frac{2}{7} a A x^{7/2}+\frac{2}{9} a B x^{9/2}+\frac{2}{11} A c x^{11/2}+\frac{2}{13} B c x^{13/2}",1,"(2*a*A*x^(7/2))/7 + (2*a*B*x^(9/2))/9 + (2*A*c*x^(11/2))/11 + (2*B*c*x^(13/2))/13","A",2,1,18,0.05556,1,"{766}"
386,1,45,0,0.0125184,"\int x^{3/2} (A+B x) \left(a+c x^2\right) \, dx","Int[x^(3/2)*(A + B*x)*(a + c*x^2),x]","\frac{2}{5} a A x^{5/2}+\frac{2}{7} a B x^{7/2}+\frac{2}{9} A c x^{9/2}+\frac{2}{11} B c x^{11/2}","\frac{2}{5} a A x^{5/2}+\frac{2}{7} a B x^{7/2}+\frac{2}{9} A c x^{9/2}+\frac{2}{11} B c x^{11/2}",1,"(2*a*A*x^(5/2))/5 + (2*a*B*x^(7/2))/7 + (2*A*c*x^(9/2))/9 + (2*B*c*x^(11/2))/11","A",2,1,18,0.05556,1,"{766}"
387,1,45,0,0.0123035,"\int \sqrt{x} (A+B x) \left(a+c x^2\right) \, dx","Int[Sqrt[x]*(A + B*x)*(a + c*x^2),x]","\frac{2}{3} a A x^{3/2}+\frac{2}{5} a B x^{5/2}+\frac{2}{7} A c x^{7/2}+\frac{2}{9} B c x^{9/2}","\frac{2}{3} a A x^{3/2}+\frac{2}{5} a B x^{5/2}+\frac{2}{7} A c x^{7/2}+\frac{2}{9} B c x^{9/2}",1,"(2*a*A*x^(3/2))/3 + (2*a*B*x^(5/2))/5 + (2*A*c*x^(7/2))/7 + (2*B*c*x^(9/2))/9","A",2,1,18,0.05556,1,"{766}"
388,1,43,0,0.0121786,"\int \frac{(A+B x) \left(a+c x^2\right)}{\sqrt{x}} \, dx","Int[((A + B*x)*(a + c*x^2))/Sqrt[x],x]","2 a A \sqrt{x}+\frac{2}{3} a B x^{3/2}+\frac{2}{5} A c x^{5/2}+\frac{2}{7} B c x^{7/2}","2 a A \sqrt{x}+\frac{2}{3} a B x^{3/2}+\frac{2}{5} A c x^{5/2}+\frac{2}{7} B c x^{7/2}",1,"2*a*A*Sqrt[x] + (2*a*B*x^(3/2))/3 + (2*A*c*x^(5/2))/5 + (2*B*c*x^(7/2))/7","A",2,1,18,0.05556,1,"{766}"
389,1,41,0,0.0118859,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/x^(3/2),x]","-\frac{2 a A}{\sqrt{x}}+2 a B \sqrt{x}+\frac{2}{3} A c x^{3/2}+\frac{2}{5} B c x^{5/2}","-\frac{2 a A}{\sqrt{x}}+2 a B \sqrt{x}+\frac{2}{3} A c x^{3/2}+\frac{2}{5} B c x^{5/2}",1,"(-2*a*A)/Sqrt[x] + 2*a*B*Sqrt[x] + (2*A*c*x^(3/2))/3 + (2*B*c*x^(5/2))/5","A",2,1,18,0.05556,1,"{766}"
390,1,41,0,0.012395,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/x^(5/2),x]","-\frac{2 a A}{3 x^{3/2}}-\frac{2 a B}{\sqrt{x}}+2 A c \sqrt{x}+\frac{2}{3} B c x^{3/2}","-\frac{2 a A}{3 x^{3/2}}-\frac{2 a B}{\sqrt{x}}+2 A c \sqrt{x}+\frac{2}{3} B c x^{3/2}",1,"(-2*a*A)/(3*x^(3/2)) - (2*a*B)/Sqrt[x] + 2*A*c*Sqrt[x] + (2*B*c*x^(3/2))/3","A",2,1,18,0.05556,1,"{766}"
391,1,41,0,0.0124574,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/x^(7/2),x]","-\frac{2 a A}{5 x^{5/2}}-\frac{2 a B}{3 x^{3/2}}-\frac{2 A c}{\sqrt{x}}+2 B c \sqrt{x}","-\frac{2 a A}{5 x^{5/2}}-\frac{2 a B}{3 x^{3/2}}-\frac{2 A c}{\sqrt{x}}+2 B c \sqrt{x}",1,"(-2*a*A)/(5*x^(5/2)) - (2*a*B)/(3*x^(3/2)) - (2*A*c)/Sqrt[x] + 2*B*c*Sqrt[x]","A",2,1,18,0.05556,1,"{766}"
392,1,43,0,0.0120947,"\int \frac{(A+B x) \left(a+c x^2\right)}{x^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/x^(9/2),x]","-\frac{2 a A}{7 x^{7/2}}-\frac{2 a B}{5 x^{5/2}}-\frac{2 A c}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}}","-\frac{2 a A}{7 x^{7/2}}-\frac{2 a B}{5 x^{5/2}}-\frac{2 A c}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}}",1,"(-2*a*A)/(7*x^(7/2)) - (2*a*B)/(5*x^(5/2)) - (2*A*c)/(3*x^(3/2)) - (2*B*c)/Sqrt[x]","A",2,1,18,0.05556,1,"{766}"
393,1,77,0,0.0245772,"\int x^{7/2} (A+B x) \left(a+c x^2\right)^2 \, dx","Int[x^(7/2)*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{11} a^2 B x^{11/2}+\frac{4}{13} a A c x^{13/2}+\frac{4}{15} a B c x^{15/2}+\frac{2}{17} A c^2 x^{17/2}+\frac{2}{19} B c^2 x^{19/2}","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{11} a^2 B x^{11/2}+\frac{4}{13} a A c x^{13/2}+\frac{4}{15} a B c x^{15/2}+\frac{2}{17} A c^2 x^{17/2}+\frac{2}{19} B c^2 x^{19/2}",1,"(2*a^2*A*x^(9/2))/9 + (2*a^2*B*x^(11/2))/11 + (4*a*A*c*x^(13/2))/13 + (4*a*B*c*x^(15/2))/15 + (2*A*c^2*x^(17/2))/17 + (2*B*c^2*x^(19/2))/19","A",2,1,20,0.05000,1,"{766}"
394,1,77,0,0.0257879,"\int x^{5/2} (A+B x) \left(a+c x^2\right)^2 \, dx","Int[x^(5/2)*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{9} a^2 B x^{9/2}+\frac{4}{11} a A c x^{11/2}+\frac{4}{13} a B c x^{13/2}+\frac{2}{15} A c^2 x^{15/2}+\frac{2}{17} B c^2 x^{17/2}","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{9} a^2 B x^{9/2}+\frac{4}{11} a A c x^{11/2}+\frac{4}{13} a B c x^{13/2}+\frac{2}{15} A c^2 x^{15/2}+\frac{2}{17} B c^2 x^{17/2}",1,"(2*a^2*A*x^(7/2))/7 + (2*a^2*B*x^(9/2))/9 + (4*a*A*c*x^(11/2))/11 + (4*a*B*c*x^(13/2))/13 + (2*A*c^2*x^(15/2))/15 + (2*B*c^2*x^(17/2))/17","A",2,1,20,0.05000,1,"{766}"
395,1,77,0,0.0238589,"\int x^{3/2} (A+B x) \left(a+c x^2\right)^2 \, dx","Int[x^(3/2)*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{7} a^2 B x^{7/2}+\frac{4}{9} a A c x^{9/2}+\frac{4}{11} a B c x^{11/2}+\frac{2}{13} A c^2 x^{13/2}+\frac{2}{15} B c^2 x^{15/2}","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{7} a^2 B x^{7/2}+\frac{4}{9} a A c x^{9/2}+\frac{4}{11} a B c x^{11/2}+\frac{2}{13} A c^2 x^{13/2}+\frac{2}{15} B c^2 x^{15/2}",1,"(2*a^2*A*x^(5/2))/5 + (2*a^2*B*x^(7/2))/7 + (4*a*A*c*x^(9/2))/9 + (4*a*B*c*x^(11/2))/11 + (2*A*c^2*x^(13/2))/13 + (2*B*c^2*x^(15/2))/15","A",2,1,20,0.05000,1,"{766}"
396,1,77,0,0.0240956,"\int \sqrt{x} (A+B x) \left(a+c x^2\right)^2 \, dx","Int[Sqrt[x]*(A + B*x)*(a + c*x^2)^2,x]","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{5} a^2 B x^{5/2}+\frac{4}{7} a A c x^{7/2}+\frac{4}{9} a B c x^{9/2}+\frac{2}{11} A c^2 x^{11/2}+\frac{2}{13} B c^2 x^{13/2}","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{5} a^2 B x^{5/2}+\frac{4}{7} a A c x^{7/2}+\frac{4}{9} a B c x^{9/2}+\frac{2}{11} A c^2 x^{11/2}+\frac{2}{13} B c^2 x^{13/2}",1,"(2*a^2*A*x^(3/2))/3 + (2*a^2*B*x^(5/2))/5 + (4*a*A*c*x^(7/2))/7 + (4*a*B*c*x^(9/2))/9 + (2*A*c^2*x^(11/2))/11 + (2*B*c^2*x^(13/2))/13","A",2,1,20,0.05000,1,"{766}"
397,1,75,0,0.0248111,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{\sqrt{x}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/Sqrt[x],x]","2 a^2 A \sqrt{x}+\frac{2}{3} a^2 B x^{3/2}+\frac{4}{5} a A c x^{5/2}+\frac{4}{7} a B c x^{7/2}+\frac{2}{9} A c^2 x^{9/2}+\frac{2}{11} B c^2 x^{11/2}","2 a^2 A \sqrt{x}+\frac{2}{3} a^2 B x^{3/2}+\frac{4}{5} a A c x^{5/2}+\frac{4}{7} a B c x^{7/2}+\frac{2}{9} A c^2 x^{9/2}+\frac{2}{11} B c^2 x^{11/2}",1,"2*a^2*A*Sqrt[x] + (2*a^2*B*x^(3/2))/3 + (4*a*A*c*x^(5/2))/5 + (4*a*B*c*x^(7/2))/7 + (2*A*c^2*x^(9/2))/9 + (2*B*c^2*x^(11/2))/11","A",2,1,20,0.05000,1,"{766}"
398,1,73,0,0.0246833,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x^(3/2),x]","-\frac{2 a^2 A}{\sqrt{x}}+2 a^2 B \sqrt{x}+\frac{4}{3} a A c x^{3/2}+\frac{4}{5} a B c x^{5/2}+\frac{2}{7} A c^2 x^{7/2}+\frac{2}{9} B c^2 x^{9/2}","-\frac{2 a^2 A}{\sqrt{x}}+2 a^2 B \sqrt{x}+\frac{4}{3} a A c x^{3/2}+\frac{4}{5} a B c x^{5/2}+\frac{2}{7} A c^2 x^{7/2}+\frac{2}{9} B c^2 x^{9/2}",1,"(-2*a^2*A)/Sqrt[x] + 2*a^2*B*Sqrt[x] + (4*a*A*c*x^(3/2))/3 + (4*a*B*c*x^(5/2))/5 + (2*A*c^2*x^(7/2))/7 + (2*B*c^2*x^(9/2))/9","A",2,1,20,0.05000,1,"{766}"
399,1,73,0,0.0235656,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x^(5/2),x]","-\frac{2 a^2 A}{3 x^{3/2}}-\frac{2 a^2 B}{\sqrt{x}}+4 a A c \sqrt{x}+\frac{4}{3} a B c x^{3/2}+\frac{2}{5} A c^2 x^{5/2}+\frac{2}{7} B c^2 x^{7/2}","-\frac{2 a^2 A}{3 x^{3/2}}-\frac{2 a^2 B}{\sqrt{x}}+4 a A c \sqrt{x}+\frac{4}{3} a B c x^{3/2}+\frac{2}{5} A c^2 x^{5/2}+\frac{2}{7} B c^2 x^{7/2}",1,"(-2*a^2*A)/(3*x^(3/2)) - (2*a^2*B)/Sqrt[x] + 4*a*A*c*Sqrt[x] + (4*a*B*c*x^(3/2))/3 + (2*A*c^2*x^(5/2))/5 + (2*B*c^2*x^(7/2))/7","A",2,1,20,0.05000,1,"{766}"
400,1,73,0,0.0255857,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x^(7/2),x]","-\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a^2 B}{3 x^{3/2}}-\frac{4 a A c}{\sqrt{x}}+4 a B c \sqrt{x}+\frac{2}{3} A c^2 x^{3/2}+\frac{2}{5} B c^2 x^{5/2}","-\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a^2 B}{3 x^{3/2}}-\frac{4 a A c}{\sqrt{x}}+4 a B c \sqrt{x}+\frac{2}{3} A c^2 x^{3/2}+\frac{2}{5} B c^2 x^{5/2}",1,"(-2*a^2*A)/(5*x^(5/2)) - (2*a^2*B)/(3*x^(3/2)) - (4*a*A*c)/Sqrt[x] + 4*a*B*c*Sqrt[x] + (2*A*c^2*x^(3/2))/3 + (2*B*c^2*x^(5/2))/5","A",2,1,20,0.05000,1,"{766}"
401,1,73,0,0.0243161,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{x^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/x^(9/2),x]","-\frac{2 a^2 A}{7 x^{7/2}}-\frac{2 a^2 B}{5 x^{5/2}}-\frac{4 a A c}{3 x^{3/2}}-\frac{4 a B c}{\sqrt{x}}+2 A c^2 \sqrt{x}+\frac{2}{3} B c^2 x^{3/2}","-\frac{2 a^2 A}{7 x^{7/2}}-\frac{2 a^2 B}{5 x^{5/2}}-\frac{4 a A c}{3 x^{3/2}}-\frac{4 a B c}{\sqrt{x}}+2 A c^2 \sqrt{x}+\frac{2}{3} B c^2 x^{3/2}",1,"(-2*a^2*A)/(7*x^(7/2)) - (2*a^2*B)/(5*x^(5/2)) - (4*a*A*c)/(3*x^(3/2)) - (4*a*B*c)/Sqrt[x] + 2*A*c^2*Sqrt[x] + (2*B*c^2*x^(3/2))/3","A",2,1,20,0.05000,1,"{766}"
402,1,109,0,0.037606,"\int x^{7/2} (A+B x) \left(a+c x^2\right)^3 \, dx","Int[x^(7/2)*(A + B*x)*(a + c*x^2)^3,x]","\frac{6}{13} a^2 A c x^{13/2}+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{5} a^2 B c x^{15/2}+\frac{2}{11} a^3 B x^{11/2}+\frac{6}{17} a A c^2 x^{17/2}+\frac{6}{19} a B c^2 x^{19/2}+\frac{2}{21} A c^3 x^{21/2}+\frac{2}{23} B c^3 x^{23/2}","\frac{6}{13} a^2 A c x^{13/2}+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{5} a^2 B c x^{15/2}+\frac{2}{11} a^3 B x^{11/2}+\frac{6}{17} a A c^2 x^{17/2}+\frac{6}{19} a B c^2 x^{19/2}+\frac{2}{21} A c^3 x^{21/2}+\frac{2}{23} B c^3 x^{23/2}",1,"(2*a^3*A*x^(9/2))/9 + (2*a^3*B*x^(11/2))/11 + (6*a^2*A*c*x^(13/2))/13 + (2*a^2*B*c*x^(15/2))/5 + (6*a*A*c^2*x^(17/2))/17 + (6*a*B*c^2*x^(19/2))/19 + (2*A*c^3*x^(21/2))/21 + (2*B*c^3*x^(23/2))/23","A",2,1,20,0.05000,1,"{766}"
403,1,109,0,0.0396323,"\int x^{5/2} (A+B x) \left(a+c x^2\right)^3 \, dx","Int[x^(5/2)*(A + B*x)*(a + c*x^2)^3,x]","\frac{6}{11} a^2 A c x^{11/2}+\frac{2}{7} a^3 A x^{7/2}+\frac{6}{13} a^2 B c x^{13/2}+\frac{2}{9} a^3 B x^{9/2}+\frac{2}{5} a A c^2 x^{15/2}+\frac{6}{17} a B c^2 x^{17/2}+\frac{2}{19} A c^3 x^{19/2}+\frac{2}{21} B c^3 x^{21/2}","\frac{6}{11} a^2 A c x^{11/2}+\frac{2}{7} a^3 A x^{7/2}+\frac{6}{13} a^2 B c x^{13/2}+\frac{2}{9} a^3 B x^{9/2}+\frac{2}{5} a A c^2 x^{15/2}+\frac{6}{17} a B c^2 x^{17/2}+\frac{2}{19} A c^3 x^{19/2}+\frac{2}{21} B c^3 x^{21/2}",1,"(2*a^3*A*x^(7/2))/7 + (2*a^3*B*x^(9/2))/9 + (6*a^2*A*c*x^(11/2))/11 + (6*a^2*B*c*x^(13/2))/13 + (2*a*A*c^2*x^(15/2))/5 + (6*a*B*c^2*x^(17/2))/17 + (2*A*c^3*x^(19/2))/19 + (2*B*c^3*x^(21/2))/21","A",2,1,20,0.05000,1,"{766}"
404,1,109,0,0.0368277,"\int x^{3/2} (A+B x) \left(a+c x^2\right)^3 \, dx","Int[x^(3/2)*(A + B*x)*(a + c*x^2)^3,x]","\frac{2}{3} a^2 A c x^{9/2}+\frac{2}{5} a^3 A x^{5/2}+\frac{6}{11} a^2 B c x^{11/2}+\frac{2}{7} a^3 B x^{7/2}+\frac{6}{13} a A c^2 x^{13/2}+\frac{2}{5} a B c^2 x^{15/2}+\frac{2}{17} A c^3 x^{17/2}+\frac{2}{19} B c^3 x^{19/2}","\frac{2}{3} a^2 A c x^{9/2}+\frac{2}{5} a^3 A x^{5/2}+\frac{6}{11} a^2 B c x^{11/2}+\frac{2}{7} a^3 B x^{7/2}+\frac{6}{13} a A c^2 x^{13/2}+\frac{2}{5} a B c^2 x^{15/2}+\frac{2}{17} A c^3 x^{17/2}+\frac{2}{19} B c^3 x^{19/2}",1,"(2*a^3*A*x^(5/2))/5 + (2*a^3*B*x^(7/2))/7 + (2*a^2*A*c*x^(9/2))/3 + (6*a^2*B*c*x^(11/2))/11 + (6*a*A*c^2*x^(13/2))/13 + (2*a*B*c^2*x^(15/2))/5 + (2*A*c^3*x^(17/2))/17 + (2*B*c^3*x^(19/2))/19","A",2,1,20,0.05000,1,"{766}"
405,1,109,0,0.0372586,"\int \sqrt{x} (A+B x) \left(a+c x^2\right)^3 \, dx","Int[Sqrt[x]*(A + B*x)*(a + c*x^2)^3,x]","\frac{6}{7} a^2 A c x^{7/2}+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{3} a^2 B c x^{9/2}+\frac{2}{5} a^3 B x^{5/2}+\frac{6}{11} a A c^2 x^{11/2}+\frac{6}{13} a B c^2 x^{13/2}+\frac{2}{15} A c^3 x^{15/2}+\frac{2}{17} B c^3 x^{17/2}","\frac{6}{7} a^2 A c x^{7/2}+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{3} a^2 B c x^{9/2}+\frac{2}{5} a^3 B x^{5/2}+\frac{6}{11} a A c^2 x^{11/2}+\frac{6}{13} a B c^2 x^{13/2}+\frac{2}{15} A c^3 x^{15/2}+\frac{2}{17} B c^3 x^{17/2}",1,"(2*a^3*A*x^(3/2))/3 + (2*a^3*B*x^(5/2))/5 + (6*a^2*A*c*x^(7/2))/7 + (2*a^2*B*c*x^(9/2))/3 + (6*a*A*c^2*x^(11/2))/11 + (6*a*B*c^2*x^(13/2))/13 + (2*A*c^3*x^(15/2))/15 + (2*B*c^3*x^(17/2))/17","A",2,1,20,0.05000,1,"{766}"
406,1,107,0,0.0390424,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{\sqrt{x}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/Sqrt[x],x]","\frac{6}{5} a^2 A c x^{5/2}+2 a^3 A \sqrt{x}+\frac{6}{7} a^2 B c x^{7/2}+\frac{2}{3} a^3 B x^{3/2}+\frac{2}{3} a A c^2 x^{9/2}+\frac{6}{11} a B c^2 x^{11/2}+\frac{2}{13} A c^3 x^{13/2}+\frac{2}{15} B c^3 x^{15/2}","\frac{6}{5} a^2 A c x^{5/2}+2 a^3 A \sqrt{x}+\frac{6}{7} a^2 B c x^{7/2}+\frac{2}{3} a^3 B x^{3/2}+\frac{2}{3} a A c^2 x^{9/2}+\frac{6}{11} a B c^2 x^{11/2}+\frac{2}{13} A c^3 x^{13/2}+\frac{2}{15} B c^3 x^{15/2}",1,"2*a^3*A*Sqrt[x] + (2*a^3*B*x^(3/2))/3 + (6*a^2*A*c*x^(5/2))/5 + (6*a^2*B*c*x^(7/2))/7 + (2*a*A*c^2*x^(9/2))/3 + (6*a*B*c^2*x^(11/2))/11 + (2*A*c^3*x^(13/2))/13 + (2*B*c^3*x^(15/2))/15","A",2,1,20,0.05000,1,"{766}"
407,1,103,0,0.0378671,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^(3/2),x]","2 a^2 A c x^{3/2}-\frac{2 a^3 A}{\sqrt{x}}+\frac{6}{5} a^2 B c x^{5/2}+2 a^3 B \sqrt{x}+\frac{6}{7} a A c^2 x^{7/2}+\frac{2}{3} a B c^2 x^{9/2}+\frac{2}{11} A c^3 x^{11/2}+\frac{2}{13} B c^3 x^{13/2}","2 a^2 A c x^{3/2}-\frac{2 a^3 A}{\sqrt{x}}+\frac{6}{5} a^2 B c x^{5/2}+2 a^3 B \sqrt{x}+\frac{6}{7} a A c^2 x^{7/2}+\frac{2}{3} a B c^2 x^{9/2}+\frac{2}{11} A c^3 x^{11/2}+\frac{2}{13} B c^3 x^{13/2}",1,"(-2*a^3*A)/Sqrt[x] + 2*a^3*B*Sqrt[x] + 2*a^2*A*c*x^(3/2) + (6*a^2*B*c*x^(5/2))/5 + (6*a*A*c^2*x^(7/2))/7 + (2*a*B*c^2*x^(9/2))/3 + (2*A*c^3*x^(11/2))/11 + (2*B*c^3*x^(13/2))/13","A",2,1,20,0.05000,1,"{766}"
408,1,103,0,0.0372254,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^(5/2),x]","6 a^2 A c \sqrt{x}-\frac{2 a^3 A}{3 x^{3/2}}+2 a^2 B c x^{3/2}-\frac{2 a^3 B}{\sqrt{x}}+\frac{6}{5} a A c^2 x^{5/2}+\frac{6}{7} a B c^2 x^{7/2}+\frac{2}{9} A c^3 x^{9/2}+\frac{2}{11} B c^3 x^{11/2}","6 a^2 A c \sqrt{x}-\frac{2 a^3 A}{3 x^{3/2}}+2 a^2 B c x^{3/2}-\frac{2 a^3 B}{\sqrt{x}}+\frac{6}{5} a A c^2 x^{5/2}+\frac{6}{7} a B c^2 x^{7/2}+\frac{2}{9} A c^3 x^{9/2}+\frac{2}{11} B c^3 x^{11/2}",1,"(-2*a^3*A)/(3*x^(3/2)) - (2*a^3*B)/Sqrt[x] + 6*a^2*A*c*Sqrt[x] + 2*a^2*B*c*x^(3/2) + (6*a*A*c^2*x^(5/2))/5 + (6*a*B*c^2*x^(7/2))/7 + (2*A*c^3*x^(9/2))/9 + (2*B*c^3*x^(11/2))/11","A",2,1,20,0.05000,1,"{766}"
409,1,103,0,0.0388654,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^(7/2),x]","-\frac{6 a^2 A c}{\sqrt{x}}-\frac{2 a^3 A}{5 x^{5/2}}+6 a^2 B c \sqrt{x}-\frac{2 a^3 B}{3 x^{3/2}}+2 a A c^2 x^{3/2}+\frac{6}{5} a B c^2 x^{5/2}+\frac{2}{7} A c^3 x^{7/2}+\frac{2}{9} B c^3 x^{9/2}","-\frac{6 a^2 A c}{\sqrt{x}}-\frac{2 a^3 A}{5 x^{5/2}}+6 a^2 B c \sqrt{x}-\frac{2 a^3 B}{3 x^{3/2}}+2 a A c^2 x^{3/2}+\frac{6}{5} a B c^2 x^{5/2}+\frac{2}{7} A c^3 x^{7/2}+\frac{2}{9} B c^3 x^{9/2}",1,"(-2*a^3*A)/(5*x^(5/2)) - (2*a^3*B)/(3*x^(3/2)) - (6*a^2*A*c)/Sqrt[x] + 6*a^2*B*c*Sqrt[x] + 2*a*A*c^2*x^(3/2) + (6*a*B*c^2*x^(5/2))/5 + (2*A*c^3*x^(7/2))/7 + (2*B*c^3*x^(9/2))/9","A",2,1,20,0.05000,1,"{766}"
410,1,101,0,0.036794,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^(9/2),x]","-\frac{2 a^2 A c}{x^{3/2}}-\frac{2 a^3 A}{7 x^{7/2}}-\frac{6 a^2 B c}{\sqrt{x}}-\frac{2 a^3 B}{5 x^{5/2}}+6 a A c^2 \sqrt{x}+2 a B c^2 x^{3/2}+\frac{2}{5} A c^3 x^{5/2}+\frac{2}{7} B c^3 x^{7/2}","-\frac{2 a^2 A c}{x^{3/2}}-\frac{2 a^3 A}{7 x^{7/2}}-\frac{6 a^2 B c}{\sqrt{x}}-\frac{2 a^3 B}{5 x^{5/2}}+6 a A c^2 \sqrt{x}+2 a B c^2 x^{3/2}+\frac{2}{5} A c^3 x^{5/2}+\frac{2}{7} B c^3 x^{7/2}",1,"(-2*a^3*A)/(7*x^(7/2)) - (2*a^3*B)/(5*x^(5/2)) - (2*a^2*A*c)/x^(3/2) - (6*a^2*B*c)/Sqrt[x] + 6*a*A*c^2*Sqrt[x] + 2*a*B*c^2*x^(3/2) + (2*A*c^3*x^(5/2))/5 + (2*B*c^3*x^(7/2))/7","A",2,1,20,0.05000,1,"{766}"
411,1,103,0,0.0390749,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{x^{11/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/x^(11/2),x]","-\frac{6 a^2 A c}{5 x^{5/2}}-\frac{2 a^3 A}{9 x^{9/2}}-\frac{2 a^2 B c}{x^{3/2}}-\frac{2 a^3 B}{7 x^{7/2}}-\frac{6 a A c^2}{\sqrt{x}}+6 a B c^2 \sqrt{x}+\frac{2}{3} A c^3 x^{3/2}+\frac{2}{5} B c^3 x^{5/2}","-\frac{6 a^2 A c}{5 x^{5/2}}-\frac{2 a^3 A}{9 x^{9/2}}-\frac{2 a^2 B c}{x^{3/2}}-\frac{2 a^3 B}{7 x^{7/2}}-\frac{6 a A c^2}{\sqrt{x}}+6 a B c^2 \sqrt{x}+\frac{2}{3} A c^3 x^{3/2}+\frac{2}{5} B c^3 x^{5/2}",1,"(-2*a^3*A)/(9*x^(9/2)) - (2*a^3*B)/(7*x^(7/2)) - (6*a^2*A*c)/(5*x^(5/2)) - (2*a^2*B*c)/x^(3/2) - (6*a*A*c^2)/Sqrt[x] + 6*a*B*c^2*Sqrt[x] + (2*A*c^3*x^(3/2))/3 + (2*B*c^3*x^(5/2))/5","A",2,1,20,0.05000,1,"{766}"
412,1,292,0,0.3445839,"\int \frac{x^{5/2} (A+B x)}{a+c x^2} \, dx","Int[(x^(5/2)*(A + B*x))/(a + c*x^2),x]","-\frac{a^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}+\frac{a^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}-\frac{a^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} c^{9/4}}+\frac{a^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} c^{9/4}}-\frac{2 a B \sqrt{x}}{c^2}+\frac{2 A x^{3/2}}{3 c}+\frac{2 B x^{5/2}}{5 c}","-\frac{a^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}+\frac{a^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{9/4}}-\frac{a^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} c^{9/4}}+\frac{a^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} c^{9/4}}-\frac{2 a B \sqrt{x}}{c^2}+\frac{2 A x^{3/2}}{3 c}+\frac{2 B x^{5/2}}{5 c}",1,"(-2*a*B*Sqrt[x])/c^2 + (2*A*x^(3/2))/(3*c) + (2*B*x^(5/2))/(5*c) - (a^(3/4)*(Sqrt[a]*B - A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*c^(9/4)) + (a^(3/4)*(Sqrt[a]*B - A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*c^(9/4)) - (a^(3/4)*(Sqrt[a]*B + A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(9/4)) + (a^(3/4)*(Sqrt[a]*B + A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(9/4))","A",13,8,20,0.4000,1,"{825, 827, 1168, 1162, 617, 204, 1165, 628}"
413,1,278,0,0.2719727,"\int \frac{x^{3/2} (A+B x)}{a+c x^2} \, dx","Int[(x^(3/2)*(A + B*x))/(a + c*x^2),x]","-\frac{\sqrt[4]{a} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} c^{7/4}}-\frac{\sqrt[4]{a} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} c^{7/4}}+\frac{2 A \sqrt{x}}{c}+\frac{2 B x^{3/2}}{3 c}","-\frac{\sqrt[4]{a} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} c^{7/4}}+\frac{\sqrt[4]{a} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} c^{7/4}}-\frac{\sqrt[4]{a} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} c^{7/4}}+\frac{2 A \sqrt{x}}{c}+\frac{2 B x^{3/2}}{3 c}",1,"(2*A*Sqrt[x])/c + (2*B*x^(3/2))/(3*c) + (a^(1/4)*(Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*c^(7/4)) - (a^(1/4)*(Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*c^(7/4)) - (a^(1/4)*(Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(7/4)) + (a^(1/4)*(Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*c^(7/4))","A",12,8,20,0.4000,1,"{825, 827, 1168, 1162, 617, 204, 1165, 628}"
414,1,265,0,0.2345677,"\int \frac{\sqrt{x} (A+B x)}{a+c x^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(a + c*x^2),x]","\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{a} c^{5/4}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{a} c^{5/4}}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} c^{5/4}}-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} c^{5/4}}+\frac{2 B \sqrt{x}}{c}","\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{a} c^{5/4}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} \sqrt[4]{a} c^{5/4}}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} \sqrt[4]{a} c^{5/4}}-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} \sqrt[4]{a} c^{5/4}}+\frac{2 B \sqrt{x}}{c}",1,"(2*B*Sqrt[x])/c + ((Sqrt[a]*B - A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*c^(5/4)) - ((Sqrt[a]*B - A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(1/4)*c^(5/4)) + ((Sqrt[a]*B + A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(1/4)*c^(5/4)) - ((Sqrt[a]*B + A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(1/4)*c^(5/4))","A",11,8,20,0.4000,1,"{825, 827, 1168, 1162, 617, 204, 1165, 628}"
415,1,254,0,0.1850141,"\int \frac{A+B x}{\sqrt{x} \left(a+c x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[x]*(a + c*x^2)),x]","\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} c^{3/4}}","\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{3/4} c^{3/4}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{3/4} c^{3/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{3/4} c^{3/4}}",1,"-(((Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*c^(3/4))) + ((Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(3/4)*c^(3/4)) + ((Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(3/4)*c^(3/4)) - ((Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(3/4)*c^(3/4))","A",10,7,20,0.3500,1,"{827, 1168, 1162, 617, 204, 1165, 628}"
416,1,265,0,0.2214665,"\int \frac{A+B x}{x^{3/2} \left(a+c x^2\right)} \, dx","Int[(A + B*x)/(x^(3/2)*(a + c*x^2)),x]","-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{5/4} \sqrt[4]{c}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{5/4} \sqrt[4]{c}}-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} \sqrt[4]{c}}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} \sqrt[4]{c}}-\frac{2 A}{a \sqrt{x}}","-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{5/4} \sqrt[4]{c}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{5/4} \sqrt[4]{c}}-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{5/4} \sqrt[4]{c}}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{5/4} \sqrt[4]{c}}-\frac{2 A}{a \sqrt{x}}",1,"(-2*A)/(a*Sqrt[x]) - ((Sqrt[a]*B - A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*c^(1/4)) + ((Sqrt[a]*B - A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(5/4)*c^(1/4)) - ((Sqrt[a]*B + A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(5/4)*c^(1/4)) + ((Sqrt[a]*B + A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(5/4)*c^(1/4))","A",11,8,20,0.4000,1,"{829, 827, 1168, 1162, 617, 204, 1165, 628}"
417,1,278,0,0.2727345,"\int \frac{A+B x}{x^{5/2} \left(a+c x^2\right)} \, dx","Int[(A + B*x)/(x^(5/2)*(a + c*x^2)),x]","-\frac{\sqrt[4]{c} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{7/4}}+\frac{\sqrt[4]{c} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{7/4}}+\frac{\sqrt[4]{c} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4}}-\frac{\sqrt[4]{c} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4}}-\frac{2 A}{3 a x^{3/2}}-\frac{2 B}{a \sqrt{x}}","-\frac{\sqrt[4]{c} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{7/4}}+\frac{\sqrt[4]{c} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{7/4}}+\frac{\sqrt[4]{c} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{7/4}}-\frac{\sqrt[4]{c} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{7/4}}-\frac{2 A}{3 a x^{3/2}}-\frac{2 B}{a \sqrt{x}}",1,"(-2*A)/(3*a*x^(3/2)) - (2*B)/(a*Sqrt[x]) + ((Sqrt[a]*B + A*Sqrt[c])*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)) - ((Sqrt[a]*B + A*Sqrt[c])*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(7/4)) - ((Sqrt[a]*B - A*Sqrt[c])*c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(7/4)) + ((Sqrt[a]*B - A*Sqrt[c])*c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(7/4))","A",12,8,20,0.4000,1,"{829, 827, 1168, 1162, 617, 204, 1165, 628}"
418,1,292,0,0.3216125,"\int \frac{A+B x}{x^{7/2} \left(a+c x^2\right)} \, dx","Int[(A + B*x)/(x^(7/2)*(a + c*x^2)),x]","\frac{c^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{c^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{9/4}}+\frac{c^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4}}-\frac{c^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4}}+\frac{2 A c}{a^2 \sqrt{x}}-\frac{2 A}{5 a x^{5/2}}-\frac{2 B}{3 a x^{3/2}}","\frac{c^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{9/4}}-\frac{c^{3/4} \left(\sqrt{a} B+A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{9/4}}+\frac{c^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{9/4}}-\frac{c^{3/4} \left(\sqrt{a} B-A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{9/4}}+\frac{2 A c}{a^2 \sqrt{x}}-\frac{2 A}{5 a x^{5/2}}-\frac{2 B}{3 a x^{3/2}}",1,"(-2*A)/(5*a*x^(5/2)) - (2*B)/(3*a*x^(3/2)) + (2*A*c)/(a^2*Sqrt[x]) + ((Sqrt[a]*B - A*Sqrt[c])*c^(3/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)) - ((Sqrt[a]*B - A*Sqrt[c])*c^(3/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(9/4)) + ((Sqrt[a]*B + A*Sqrt[c])*c^(3/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(9/4)) - ((Sqrt[a]*B + A*Sqrt[c])*c^(3/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(9/4))","A",13,8,20,0.4000,1,"{829, 827, 1168, 1162, 617, 204, 1165, 628}"
419,1,306,0,0.3680866,"\int \frac{A+B x}{x^{9/2} \left(a+c x^2\right)} \, dx","Int[(A + B*x)/(x^(9/2)*(a + c*x^2)),x]","\frac{c^{5/4} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{11/4}}-\frac{c^{5/4} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{11/4}}-\frac{c^{5/4} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{11/4}}+\frac{c^{5/4} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{11/4}}+\frac{2 A c}{3 a^2 x^{3/2}}+\frac{2 B c}{a^2 \sqrt{x}}-\frac{2 A}{7 a x^{7/2}}-\frac{2 B}{5 a x^{5/2}}","\frac{c^{5/4} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{11/4}}-\frac{c^{5/4} \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{2 \sqrt{2} a^{11/4}}-\frac{c^{5/4} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{\sqrt{2} a^{11/4}}+\frac{c^{5/4} \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{\sqrt{2} a^{11/4}}+\frac{2 A c}{3 a^2 x^{3/2}}+\frac{2 B c}{a^2 \sqrt{x}}-\frac{2 A}{7 a x^{7/2}}-\frac{2 B}{5 a x^{5/2}}",1,"(-2*A)/(7*a*x^(7/2)) - (2*B)/(5*a*x^(5/2)) + (2*A*c)/(3*a^2*x^(3/2)) + (2*B*c)/(a^2*Sqrt[x]) - ((Sqrt[a]*B + A*Sqrt[c])*c^(5/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(11/4)) + ((Sqrt[a]*B + A*Sqrt[c])*c^(5/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(Sqrt[2]*a^(11/4)) + ((Sqrt[a]*B - A*Sqrt[c])*c^(5/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(11/4)) - ((Sqrt[a]*B - A*Sqrt[c])*c^(5/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(2*Sqrt[2]*a^(11/4))","A",14,8,20,0.4000,1,"{829, 827, 1168, 1162, 617, 204, 1165, 628}"
420,1,304,0,0.3109699,"\int \frac{x^{5/2} (A+B x)}{\left(a+c x^2\right)^2} \, dx","Int[(x^(5/2)*(A + B*x))/(a + c*x^2)^2,x]","\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{a} c^{9/4}}-\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{a} c^{9/4}}+\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} c^{9/4}}-\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} c^{9/4}}-\frac{x^{3/2} (A+B x)}{2 c \left(a+c x^2\right)}+\frac{5 B \sqrt{x}}{2 c^2}","\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{a} c^{9/4}}-\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} \sqrt[4]{a} c^{9/4}}+\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} \sqrt[4]{a} c^{9/4}}-\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} \sqrt[4]{a} c^{9/4}}-\frac{x^{3/2} (A+B x)}{2 c \left(a+c x^2\right)}+\frac{5 B \sqrt{x}}{2 c^2}",1,"(5*B*Sqrt[x])/(2*c^2) - (x^(3/2)*(A + B*x))/(2*c*(a + c*x^2)) + ((5*Sqrt[a]*B - 3*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*c^(9/4)) - ((5*Sqrt[a]*B - 3*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(1/4)*c^(9/4)) + ((5*Sqrt[a]*B + 3*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(1/4)*c^(9/4)) - ((5*Sqrt[a]*B + 3*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(1/4)*c^(9/4))","A",12,9,20,0.4500,1,"{819, 825, 827, 1168, 1162, 617, 204, 1165, 628}"
421,1,289,0,0.2441806,"\int \frac{x^{3/2} (A+B x)}{\left(a+c x^2\right)^2} \, dx","Int[(x^(3/2)*(A + B*x))/(a + c*x^2)^2,x]","\frac{\left(3 \sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\left(3 \sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\left(3 \sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}+\frac{\left(3 \sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\sqrt{x} (A+B x)}{2 c \left(a+c x^2\right)}","\frac{\left(3 \sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\left(3 \sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\left(3 \sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}+\frac{\left(3 \sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{3/4} c^{7/4}}-\frac{\sqrt{x} (A+B x)}{2 c \left(a+c x^2\right)}",1,"-(Sqrt[x]*(A + B*x))/(2*c*(a + c*x^2)) - ((3*Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*c^(7/4)) + ((3*Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(3/4)*c^(7/4)) + ((3*Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(3/4)*c^(7/4)) - ((3*Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(3/4)*c^(7/4))","A",11,8,20,0.4000,1,"{819, 827, 1168, 1162, 617, 204, 1165, 628}"
422,1,292,0,0.226462,"\int \frac{\sqrt{x} (A+B x)}{\left(a+c x^2\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(a + c*x^2)^2,x]","-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{5/4} c^{5/4}}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{5/4} c^{5/4}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} c^{5/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} c^{5/4}}-\frac{\sqrt{x} (a B-A c x)}{2 a c \left(a+c x^2\right)}","-\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{5/4} c^{5/4}}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{5/4} c^{5/4}}-\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{5/4} c^{5/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{5/4} c^{5/4}}-\frac{\sqrt{x} (a B-A c x)}{2 a c \left(a+c x^2\right)}",1,"-(Sqrt[x]*(a*B - A*c*x))/(2*a*c*(a + c*x^2)) - ((Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*c^(5/4)) + ((Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(5/4)*c^(5/4)) - ((Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(5/4)*c^(5/4)) + ((Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(5/4)*c^(5/4))","A",11,8,20,0.4000,1,"{821, 827, 1168, 1162, 617, 204, 1165, 628}"
423,1,287,0,0.2464863,"\int \frac{A+B x}{\sqrt{x} \left(a+c x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[x]*(a + c*x^2)^2),x]","\frac{\left(\sqrt{a} B-3 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} B-3 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(\sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\sqrt{x} (A+B x)}{2 a \left(a+c x^2\right)}","\frac{\left(\sqrt{a} B-3 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} B-3 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{7/4} c^{3/4}}-\frac{\left(\sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\left(\sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{7/4} c^{3/4}}+\frac{\sqrt{x} (A+B x)}{2 a \left(a+c x^2\right)}",1,"(Sqrt[x]*(A + B*x))/(2*a*(a + c*x^2)) - ((Sqrt[a]*B + 3*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*c^(3/4)) + ((Sqrt[a]*B + 3*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(7/4)*c^(3/4)) + ((Sqrt[a]*B - 3*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(7/4)*c^(3/4)) - ((Sqrt[a]*B - 3*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(7/4)*c^(3/4))","A",11,8,20,0.4000,1,"{823, 827, 1168, 1162, 617, 204, 1165, 628}"
424,1,304,0,0.2993079,"\int \frac{A+B x}{x^{3/2} \left(a+c x^2\right)^2} \, dx","Int[(A + B*x)/(x^(3/2)*(a + c*x^2)^2),x]","-\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{9/4} \sqrt[4]{c}}+\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{9/4} \sqrt[4]{c}}-\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} \sqrt[4]{c}}+\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} \sqrt[4]{c}}-\frac{5 A}{2 a^2 \sqrt{x}}+\frac{A+B x}{2 a \sqrt{x} \left(a+c x^2\right)}","-\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{9/4} \sqrt[4]{c}}+\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{9/4} \sqrt[4]{c}}-\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{9/4} \sqrt[4]{c}}+\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{9/4} \sqrt[4]{c}}-\frac{5 A}{2 a^2 \sqrt{x}}+\frac{A+B x}{2 a \sqrt{x} \left(a+c x^2\right)}",1,"(-5*A)/(2*a^2*Sqrt[x]) + (A + B*x)/(2*a*Sqrt[x]*(a + c*x^2)) - ((3*Sqrt[a]*B - 5*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*c^(1/4)) + ((3*Sqrt[a]*B - 5*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(9/4)*c^(1/4)) - ((3*Sqrt[a]*B + 5*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(9/4)*c^(1/4)) + ((3*Sqrt[a]*B + 5*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(9/4)*c^(1/4))","A",12,9,20,0.4500,1,"{823, 829, 827, 1168, 1162, 617, 204, 1165, 628}"
425,1,317,0,0.3495844,"\int \frac{A+B x}{x^{5/2} \left(a+c x^2\right)^2} \, dx","Int[(A + B*x)/(x^(5/2)*(a + c*x^2)^2),x]","-\frac{\sqrt[4]{c} \left(5 \sqrt{a} B-7 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{11/4}}+\frac{\sqrt[4]{c} \left(5 \sqrt{a} B-7 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{11/4}}+\frac{\sqrt[4]{c} \left(5 \sqrt{a} B+7 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4}}-\frac{\sqrt[4]{c} \left(5 \sqrt{a} B+7 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4}}-\frac{7 A}{6 a^2 x^{3/2}}-\frac{5 B}{2 a^2 \sqrt{x}}+\frac{A+B x}{2 a x^{3/2} \left(a+c x^2\right)}","-\frac{\sqrt[4]{c} \left(5 \sqrt{a} B-7 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{11/4}}+\frac{\sqrt[4]{c} \left(5 \sqrt{a} B-7 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{8 \sqrt{2} a^{11/4}}+\frac{\sqrt[4]{c} \left(5 \sqrt{a} B+7 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{4 \sqrt{2} a^{11/4}}-\frac{\sqrt[4]{c} \left(5 \sqrt{a} B+7 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{4 \sqrt{2} a^{11/4}}-\frac{7 A}{6 a^2 x^{3/2}}-\frac{5 B}{2 a^2 \sqrt{x}}+\frac{A+B x}{2 a x^{3/2} \left(a+c x^2\right)}",1,"(-7*A)/(6*a^2*x^(3/2)) - (5*B)/(2*a^2*Sqrt[x]) + (A + B*x)/(2*a*x^(3/2)*(a + c*x^2)) + ((5*Sqrt[a]*B + 7*A*Sqrt[c])*c^(1/4)*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)) - ((5*Sqrt[a]*B + 7*A*Sqrt[c])*c^(1/4)*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(4*Sqrt[2]*a^(11/4)) - ((5*Sqrt[a]*B - 7*A*Sqrt[c])*c^(1/4)*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(11/4)) + ((5*Sqrt[a]*B - 7*A*Sqrt[c])*c^(1/4)*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(8*Sqrt[2]*a^(11/4))","A",13,9,20,0.4500,1,"{823, 829, 827, 1168, 1162, 617, 204, 1165, 628}"
426,1,320,0,0.3061809,"\int \frac{x^{7/2} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Int[(x^(7/2)*(A + B*x))/(a + c*x^2)^3,x]","\frac{\left(21 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{3/4} c^{11/4}}-\frac{\left(21 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{3/4} c^{11/4}}-\frac{\left(21 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{3/4} c^{11/4}}+\frac{\left(21 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{3/4} c^{11/4}}-\frac{\sqrt{x} (5 A+7 B x)}{16 c^2 \left(a+c x^2\right)}-\frac{x^{5/2} (A+B x)}{4 c \left(a+c x^2\right)^2}","\frac{\left(21 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{3/4} c^{11/4}}-\frac{\left(21 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{3/4} c^{11/4}}-\frac{\left(21 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{3/4} c^{11/4}}+\frac{\left(21 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{3/4} c^{11/4}}-\frac{\sqrt{x} (5 A+7 B x)}{16 c^2 \left(a+c x^2\right)}-\frac{x^{5/2} (A+B x)}{4 c \left(a+c x^2\right)^2}",1,"-(x^(5/2)*(A + B*x))/(4*c*(a + c*x^2)^2) - (Sqrt[x]*(5*A + 7*B*x))/(16*c^2*(a + c*x^2)) - ((21*Sqrt[a]*B + 5*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(3/4)*c^(11/4)) + ((21*Sqrt[a]*B + 5*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(3/4)*c^(11/4)) + ((21*Sqrt[a]*B - 5*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(3/4)*c^(11/4)) - ((21*Sqrt[a]*B - 5*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(3/4)*c^(11/4))","A",12,8,20,0.4000,1,"{819, 827, 1168, 1162, 617, 204, 1165, 628}"
427,1,325,0,0.2821176,"\int \frac{x^{5/2} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Int[(x^(5/2)*(A + B*x))/(a + c*x^2)^3,x]","-\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{5/4} c^{9/4}}+\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{5/4} c^{9/4}}-\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{5/4} c^{9/4}}+\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{5/4} c^{9/4}}-\frac{\sqrt{x} (5 a B-3 A c x)}{16 a c^2 \left(a+c x^2\right)}-\frac{x^{3/2} (A+B x)}{4 c \left(a+c x^2\right)^2}","-\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{5/4} c^{9/4}}+\frac{\left(5 \sqrt{a} B-3 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{5/4} c^{9/4}}-\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{5/4} c^{9/4}}+\frac{\left(5 \sqrt{a} B+3 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{5/4} c^{9/4}}-\frac{\sqrt{x} (5 a B-3 A c x)}{16 a c^2 \left(a+c x^2\right)}-\frac{x^{3/2} (A+B x)}{4 c \left(a+c x^2\right)^2}",1,"-(x^(3/2)*(A + B*x))/(4*c*(a + c*x^2)^2) - (Sqrt[x]*(5*a*B - 3*A*c*x))/(16*a*c^2*(a + c*x^2)) - ((5*Sqrt[a]*B + 3*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(5/4)*c^(9/4)) + ((5*Sqrt[a]*B + 3*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(5/4)*c^(9/4)) - ((5*Sqrt[a]*B - 3*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(5/4)*c^(9/4)) + ((5*Sqrt[a]*B - 3*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(5/4)*c^(9/4))","A",12,9,20,0.4500,1,"{819, 821, 827, 1168, 1162, 617, 204, 1165, 628}"
428,1,315,0,0.2800519,"\int \frac{x^{3/2} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Int[(x^(3/2)*(A + B*x))/(a + c*x^2)^3,x]","\frac{3 \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{7/4} c^{7/4}}-\frac{3 \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{7/4} c^{7/4}}-\frac{3 \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{7/4} c^{7/4}}+\frac{3 \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{7/4} c^{7/4}}-\frac{\sqrt{x} (A+B x)}{4 c \left(a+c x^2\right)^2}+\frac{\sqrt{x} (A+3 B x)}{16 a c \left(a+c x^2\right)}","\frac{3 \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{7/4} c^{7/4}}-\frac{3 \left(\sqrt{a} B-A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{7/4} c^{7/4}}-\frac{3 \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{7/4} c^{7/4}}+\frac{3 \left(\sqrt{a} B+A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{7/4} c^{7/4}}-\frac{\sqrt{x} (A+B x)}{4 c \left(a+c x^2\right)^2}+\frac{\sqrt{x} (A+3 B x)}{16 a c \left(a+c x^2\right)}",1,"-(Sqrt[x]*(A + B*x))/(4*c*(a + c*x^2)^2) + (Sqrt[x]*(A + 3*B*x))/(16*a*c*(a + c*x^2)) - (3*(Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(7/4)*c^(7/4)) + (3*(Sqrt[a]*B + A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(7/4)*c^(7/4)) + (3*(Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(7/4)*c^(7/4)) - (3*(Sqrt[a]*B - A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(7/4)*c^(7/4))","A",12,9,20,0.4500,1,"{819, 823, 827, 1168, 1162, 617, 204, 1165, 628}"
429,1,331,0,0.2858141,"\int \frac{\sqrt{x} (A+B x)}{\left(a+c x^2\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x))/(a + c*x^2)^3,x]","-\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{9/4} c^{5/4}}+\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{9/4} c^{5/4}}-\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{9/4} c^{5/4}}+\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{9/4} c^{5/4}}+\frac{\sqrt{x} (a B+5 A c x)}{16 a^2 c \left(a+c x^2\right)}-\frac{\sqrt{x} (a B-A c x)}{4 a c \left(a+c x^2\right)^2}","-\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{9/4} c^{5/4}}+\frac{\left(3 \sqrt{a} B-5 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{9/4} c^{5/4}}-\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{9/4} c^{5/4}}+\frac{\left(3 \sqrt{a} B+5 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{9/4} c^{5/4}}+\frac{\sqrt{x} (a B+5 A c x)}{16 a^2 c \left(a+c x^2\right)}-\frac{\sqrt{x} (a B-A c x)}{4 a c \left(a+c x^2\right)^2}",1,"-(Sqrt[x]*(a*B - A*c*x))/(4*a*c*(a + c*x^2)^2) + (Sqrt[x]*(a*B + 5*A*c*x))/(16*a^2*c*(a + c*x^2)) - ((3*Sqrt[a]*B + 5*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(9/4)*c^(5/4)) + ((3*Sqrt[a]*B + 5*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(9/4)*c^(5/4)) - ((3*Sqrt[a]*B - 5*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(9/4)*c^(5/4)) + ((3*Sqrt[a]*B - 5*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(9/4)*c^(5/4))","A",12,9,20,0.4500,1,"{821, 823, 827, 1168, 1162, 617, 204, 1165, 628}"
430,1,320,0,0.3057588,"\int \frac{A+B x}{\sqrt{x} \left(a+c x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[x]*(a + c*x^2)^3),x]","\frac{\left(5 \sqrt{a} B-21 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}-\frac{\left(5 \sqrt{a} B-21 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}-\frac{\left(5 \sqrt{a} B+21 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\left(5 \sqrt{a} B+21 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\sqrt{x} (7 A+5 B x)}{16 a^2 \left(a+c x^2\right)}+\frac{\sqrt{x} (A+B x)}{4 a \left(a+c x^2\right)^2}","\frac{\left(5 \sqrt{a} B-21 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}-\frac{\left(5 \sqrt{a} B-21 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{11/4} c^{3/4}}-\frac{\left(5 \sqrt{a} B+21 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\left(5 \sqrt{a} B+21 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{11/4} c^{3/4}}+\frac{\sqrt{x} (7 A+5 B x)}{16 a^2 \left(a+c x^2\right)}+\frac{\sqrt{x} (A+B x)}{4 a \left(a+c x^2\right)^2}",1,"(Sqrt[x]*(A + B*x))/(4*a*(a + c*x^2)^2) + (Sqrt[x]*(7*A + 5*B*x))/(16*a^2*(a + c*x^2)) - ((5*Sqrt[a]*B + 21*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(11/4)*c^(3/4)) + ((5*Sqrt[a]*B + 21*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(11/4)*c^(3/4)) + ((5*Sqrt[a]*B - 21*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(11/4)*c^(3/4)) - ((5*Sqrt[a]*B - 21*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(11/4)*c^(3/4))","A",12,8,20,0.4000,1,"{823, 827, 1168, 1162, 617, 204, 1165, 628}"
431,1,333,0,0.3543108,"\int \frac{A+B x}{x^{3/2} \left(a+c x^2\right)^3} \, dx","Int[(A + B*x)/(x^(3/2)*(a + c*x^2)^3),x]","\frac{9 A+7 B x}{16 a^2 \sqrt{x} \left(a+c x^2\right)}-\frac{3 \left(7 \sqrt{a} B+15 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{13/4} \sqrt[4]{c}}+\frac{3 \left(7 \sqrt{a} B+15 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{13/4} \sqrt[4]{c}}-\frac{3 \left(7 \sqrt{a} B-15 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{13/4} \sqrt[4]{c}}+\frac{3 \left(7 \sqrt{a} B-15 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{13/4} \sqrt[4]{c}}-\frac{45 A}{16 a^3 \sqrt{x}}+\frac{A+B x}{4 a \sqrt{x} \left(a+c x^2\right)^2}","\frac{9 A+7 B x}{16 a^2 \sqrt{x} \left(a+c x^2\right)}-\frac{3 \left(7 \sqrt{a} B+15 A \sqrt{c}\right) \log \left(-\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{13/4} \sqrt[4]{c}}+\frac{3 \left(7 \sqrt{a} B+15 A \sqrt{c}\right) \log \left(\sqrt{2} \sqrt[4]{a} \sqrt[4]{c} \sqrt{x}+\sqrt{a}+\sqrt{c} x\right)}{64 \sqrt{2} a^{13/4} \sqrt[4]{c}}-\frac{3 \left(7 \sqrt{a} B-15 A \sqrt{c}\right) \tan ^{-1}\left(1-\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)}{32 \sqrt{2} a^{13/4} \sqrt[4]{c}}+\frac{3 \left(7 \sqrt{a} B-15 A \sqrt{c}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}+1\right)}{32 \sqrt{2} a^{13/4} \sqrt[4]{c}}-\frac{45 A}{16 a^3 \sqrt{x}}+\frac{A+B x}{4 a \sqrt{x} \left(a+c x^2\right)^2}",1,"(-45*A)/(16*a^3*Sqrt[x]) + (A + B*x)/(4*a*Sqrt[x]*(a + c*x^2)^2) + (9*A + 7*B*x)/(16*a^2*Sqrt[x]*(a + c*x^2)) - (3*(7*Sqrt[a]*B - 15*A*Sqrt[c])*ArcTan[1 - (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(13/4)*c^(1/4)) + (3*(7*Sqrt[a]*B - 15*A*Sqrt[c])*ArcTan[1 + (Sqrt[2]*c^(1/4)*Sqrt[x])/a^(1/4)])/(32*Sqrt[2]*a^(13/4)*c^(1/4)) - (3*(7*Sqrt[a]*B + 15*A*Sqrt[c])*Log[Sqrt[a] - Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(13/4)*c^(1/4)) + (3*(7*Sqrt[a]*B + 15*A*Sqrt[c])*Log[Sqrt[a] + Sqrt[2]*a^(1/4)*c^(1/4)*Sqrt[x] + Sqrt[c]*x])/(64*Sqrt[2]*a^(13/4)*c^(1/4))","A",13,9,20,0.4500,1,"{823, 829, 827, 1168, 1162, 617, 204, 1165, 628}"
432,1,45,0,0.0307211,"\int \frac{1-x}{\sqrt{x} \left(1+x^2\right)} \, dx","Int[(1 - x)/(Sqrt[x]*(1 + x^2)),x]","\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}","\frac{\log \left(x+\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}-\frac{\log \left(x-\sqrt{2} \sqrt{x}+1\right)}{\sqrt{2}}",1,"-(Log[1 - Sqrt[2]*Sqrt[x] + x]/Sqrt[2]) + Log[1 + Sqrt[2]*Sqrt[x] + x]/Sqrt[2]","A",4,3,18,0.1667,1,"{827, 1165, 628}"
433,1,427,0,0.5898524,"\int (e x)^{7/2} (A+B x) \sqrt{a+c x^2} \, dx","Int[(e*x)^(7/2)*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{2 a^2 e^3 \sqrt{e x} \sqrt{a+c x^2} (325 A+539 B x)}{15015 c^2}+\frac{2 a^{11/4} e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(539 \sqrt{a} B+325 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15015 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{28 a^3 B e^4 x \sqrt{a+c x^2}}{195 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{28 a^{13/4} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{10 a A e^3 \sqrt{e x} \left(a+c x^2\right)^{3/2}}{77 c^2}+\frac{2 A e (e x)^{5/2} \left(a+c x^2\right)^{3/2}}{11 c}-\frac{14 a B e^2 (e x)^{3/2} \left(a+c x^2\right)^{3/2}}{117 c^2}+\frac{2 B (e x)^{7/2} \left(a+c x^2\right)^{3/2}}{13 c}","\frac{2 a^2 e^3 \sqrt{e x} \sqrt{a+c x^2} (325 A+539 B x)}{15015 c^2}+\frac{2 a^{11/4} e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(539 \sqrt{a} B+325 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15015 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{28 a^3 B e^4 x \sqrt{a+c x^2}}{195 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{28 a^{13/4} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{195 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{10 a A e^3 \sqrt{e x} \left(a+c x^2\right)^{3/2}}{77 c^2}+\frac{2 A e (e x)^{5/2} \left(a+c x^2\right)^{3/2}}{11 c}-\frac{14 a B e^2 (e x)^{3/2} \left(a+c x^2\right)^{3/2}}{117 c^2}+\frac{2 B (e x)^{7/2} \left(a+c x^2\right)^{3/2}}{13 c}",1,"(2*a^2*e^3*Sqrt[e*x]*(325*A + 539*B*x)*Sqrt[a + c*x^2])/(15015*c^2) + (28*a^3*B*e^4*x*Sqrt[a + c*x^2])/(195*c^(5/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (10*a*A*e^3*Sqrt[e*x]*(a + c*x^2)^(3/2))/(77*c^2) - (14*a*B*e^2*(e*x)^(3/2)*(a + c*x^2)^(3/2))/(117*c^2) + (2*A*e*(e*x)^(5/2)*(a + c*x^2)^(3/2))/(11*c) + (2*B*(e*x)^(7/2)*(a + c*x^2)^(3/2))/(13*c) - (28*a^(13/4)*B*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(195*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*a^(11/4)*(539*Sqrt[a]*B + 325*A*Sqrt[c])*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15015*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",10,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
434,1,397,0,0.4887802,"\int (e x)^{5/2} (A+B x) \sqrt{a+c x^2} \, dx","Int[(e*x)^(5/2)*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{2 a^{9/4} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B-77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^2 A e^3 x \sqrt{a+c x^2}}{15 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{4 a^{9/4} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 a e^2 \sqrt{e x} \sqrt{a+c x^2} (25 a B-77 A c x)}{1155 c^2}+\frac{2 A e (e x)^{3/2} \left(a+c x^2\right)^{3/2}}{9 c}-\frac{10 a B e^2 \sqrt{e x} \left(a+c x^2\right)^{3/2}}{77 c^2}+\frac{2 B (e x)^{5/2} \left(a+c x^2\right)^{3/2}}{11 c}","\frac{2 a^{9/4} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B-77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^2 A e^3 x \sqrt{a+c x^2}}{15 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{4 a^{9/4} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 a e^2 \sqrt{e x} \sqrt{a+c x^2} (25 a B-77 A c x)}{1155 c^2}+\frac{2 A e (e x)^{3/2} \left(a+c x^2\right)^{3/2}}{9 c}-\frac{10 a B e^2 \sqrt{e x} \left(a+c x^2\right)^{3/2}}{77 c^2}+\frac{2 B (e x)^{5/2} \left(a+c x^2\right)^{3/2}}{11 c}",1,"(-4*a^2*A*e^3*x*Sqrt[a + c*x^2])/(15*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (2*a*e^2*Sqrt[e*x]*(25*a*B - 77*A*c*x)*Sqrt[a + c*x^2])/(1155*c^2) - (10*a*B*e^2*Sqrt[e*x]*(a + c*x^2)^(3/2))/(77*c^2) + (2*A*e*(e*x)^(3/2)*(a + c*x^2)^(3/2))/(9*c) + (2*B*(e*x)^(5/2)*(a + c*x^2)^(3/2))/(11*c) + (4*a^(9/4)*A*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*a^(9/4)*(25*Sqrt[a]*B - 77*A*Sqrt[c])*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(1155*c^(9/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
435,1,363,0,0.4174434,"\int (e x)^{3/2} (A+B x) \sqrt{a+c x^2} \, dx","Int[(e*x)^(3/2)*(A + B*x)*Sqrt[a + c*x^2],x]","-\frac{2 a^{7/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^2 B e^2 x \sqrt{a+c x^2}}{15 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{4 a^{9/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 a e \sqrt{e x} \sqrt{a+c x^2} (5 A+7 B x)}{105 c}+\frac{2 A e \sqrt{e x} \left(a+c x^2\right)^{3/2}}{7 c}+\frac{2 B (e x)^{3/2} \left(a+c x^2\right)^{3/2}}{9 c}","-\frac{2 a^{7/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^2 B e^2 x \sqrt{a+c x^2}}{15 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{4 a^{9/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 a e \sqrt{e x} \sqrt{a+c x^2} (5 A+7 B x)}{105 c}+\frac{2 A e \sqrt{e x} \left(a+c x^2\right)^{3/2}}{7 c}+\frac{2 B (e x)^{3/2} \left(a+c x^2\right)^{3/2}}{9 c}",1,"(-2*a*e*Sqrt[e*x]*(5*A + 7*B*x)*Sqrt[a + c*x^2])/(105*c) - (4*a^2*B*e^2*x*Sqrt[a + c*x^2])/(15*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (2*A*e*Sqrt[e*x]*(a + c*x^2)^(3/2))/(7*c) + (2*B*(e*x)^(3/2)*(a + c*x^2)^(3/2))/(9*c) + (4*a^(9/4)*B*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (2*a^(7/4)*(7*Sqrt[a]*B + 5*A*Sqrt[c])*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
436,1,328,0,0.3348085,"\int \sqrt{e x} (A+B x) \sqrt{a+c x^2} \, dx","Int[Sqrt[e*x]*(A + B*x)*Sqrt[a + c*x^2],x]","-\frac{2 a^{5/4} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-21 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^{5/4} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{e x} \sqrt{a+c x^2} (5 a B-21 A c x)}{105 c}+\frac{4 a A e x \sqrt{a+c x^2}}{5 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 B \sqrt{e x} \left(a+c x^2\right)^{3/2}}{7 c}","-\frac{2 a^{5/4} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-21 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^{5/4} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{e x} \sqrt{a+c x^2} (5 a B-21 A c x)}{105 c}+\frac{4 a A e x \sqrt{a+c x^2}}{5 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 B \sqrt{e x} \left(a+c x^2\right)^{3/2}}{7 c}",1,"(4*a*A*e*x*Sqrt[a + c*x^2])/(5*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*Sqrt[e*x]*(5*a*B - 21*A*c*x)*Sqrt[a + c*x^2])/(105*c) + (2*B*Sqrt[e*x]*(a + c*x^2)^(3/2))/(7*c) - (4*a^(5/4)*A*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (2*a^(5/4)*(5*Sqrt[a]*B - 21*A*Sqrt[c])*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*c^(5/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
437,1,297,0,0.2718378,"\int \frac{(A+B x) \sqrt{a+c x^2}}{\sqrt{e x}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/Sqrt[e*x],x]","\frac{2 a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^{5/4} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 \sqrt{e x} \sqrt{a+c x^2} (5 A+3 B x)}{15 e}+\frac{4 a B x \sqrt{a+c x^2}}{5 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{2 a^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^{5/4} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 \sqrt{e x} \sqrt{a+c x^2} (5 A+3 B x)}{15 e}+\frac{4 a B x \sqrt{a+c x^2}}{5 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(2*Sqrt[e*x]*(5*A + 3*B*x)*Sqrt[a + c*x^2])/(15*e) + (4*a*B*x*Sqrt[a + c*x^2])/(5*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*a^(5/4)*B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*a^(3/4)*(3*Sqrt[a]*B + 5*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{815, 842, 840, 1198, 220, 1196}"
438,1,300,0,0.2601988,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(3/2),x]","-\frac{2 \sqrt{a+c x^2} (3 A-B x)}{3 e \sqrt{e x}}+\frac{2 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B+3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{4 A \sqrt{c} x \sqrt{a+c x^2}}{e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 \sqrt[4]{a} A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e \sqrt{e x} \sqrt{a+c x^2}}","-\frac{2 \sqrt{a+c x^2} (3 A-B x)}{3 e \sqrt{e x}}+\frac{2 \sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B+3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{4 A \sqrt{c} x \sqrt{a+c x^2}}{e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 \sqrt[4]{a} A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e \sqrt{e x} \sqrt{a+c x^2}}",1,"(-2*(3*A - B*x)*Sqrt[a + c*x^2])/(3*e*Sqrt[e*x]) + (4*A*Sqrt[c]*x*Sqrt[a + c*x^2])/(e*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*a^(1/4)*A*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(e*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*a^(1/4)*(Sqrt[a]*B + 3*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*c^(1/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{813, 842, 840, 1198, 220, 1196}"
439,1,298,0,0.2872718,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{5/2}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(5/2),x]","\frac{2 \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B+A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{a+c x^2} (A+3 B x)}{3 e (e x)^{3/2}}+\frac{4 B \sqrt{c} x \sqrt{a+c x^2}}{e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 \sqrt[4]{a} B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e^2 \sqrt{e x} \sqrt{a+c x^2}}","\frac{2 \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B+A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 \sqrt[4]{a} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{a+c x^2} (A+3 B x)}{3 e (e x)^{3/2}}+\frac{4 B \sqrt{c} x \sqrt{a+c x^2}}{e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 \sqrt[4]{a} B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{e^2 \sqrt{e x} \sqrt{a+c x^2}}",1,"(-2*(A + 3*B*x)*Sqrt[a + c*x^2])/(3*e*(e*x)^(3/2)) + (4*B*Sqrt[c]*x*Sqrt[a + c*x^2])/(e^2*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*a^(1/4)*B*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(e^2*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*(3*Sqrt[a]*B + A*Sqrt[c])*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*a^(1/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{811, 842, 840, 1198, 220, 1196}"
440,1,338,0,0.3497884,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{7/2}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(7/2),x]","\frac{2 c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{a+c x^2} (3 A+5 B x)}{15 e (e x)^{5/2}}+\frac{4 A c^{3/2} x \sqrt{a+c x^2}}{5 a e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 A c \sqrt{a+c x^2}}{5 a e^3 \sqrt{e x}}","\frac{2 c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{3/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{a+c x^2} (3 A+5 B x)}{15 e (e x)^{5/2}}+\frac{4 A c^{3/2} x \sqrt{a+c x^2}}{5 a e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 A c \sqrt{a+c x^2}}{5 a e^3 \sqrt{e x}}",1,"(-4*A*c*Sqrt[a + c*x^2])/(5*a*e^3*Sqrt[e*x]) - (2*(3*A + 5*B*x)*Sqrt[a + c*x^2])/(15*e*(e*x)^(5/2)) + (4*A*c^(3/2)*x*Sqrt[a + c*x^2])/(5*a*e^3*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*A*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(3/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*(5*Sqrt[a]*B + 3*A*Sqrt[c])*c^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*a^(3/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{811, 835, 842, 840, 1198, 220, 1196}"
441,1,368,0,0.4061211,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(e x)^{9/2}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/(e*x)^(9/2),x]","\frac{2 c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(21 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{5/4} e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 B c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{a+c x^2} (5 A+7 B x)}{35 e (e x)^{7/2}}-\frac{4 A c \sqrt{a+c x^2}}{21 a e^3 (e x)^{3/2}}+\frac{4 B c^{3/2} x \sqrt{a+c x^2}}{5 a e^4 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 B c \sqrt{a+c x^2}}{5 a e^4 \sqrt{e x}}","\frac{2 c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(21 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 a^{5/4} e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 B c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{3/4} e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt{a+c x^2} (5 A+7 B x)}{35 e (e x)^{7/2}}-\frac{4 A c \sqrt{a+c x^2}}{21 a e^3 (e x)^{3/2}}+\frac{4 B c^{3/2} x \sqrt{a+c x^2}}{5 a e^4 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{4 B c \sqrt{a+c x^2}}{5 a e^4 \sqrt{e x}}",1,"(-4*A*c*Sqrt[a + c*x^2])/(21*a*e^3*(e*x)^(3/2)) - (4*B*c*Sqrt[a + c*x^2])/(5*a*e^4*Sqrt[e*x]) - (2*(5*A + 7*B*x)*Sqrt[a + c*x^2])/(35*e*(e*x)^(7/2)) + (4*B*c^(3/2)*x*Sqrt[a + c*x^2])/(5*a*e^4*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*B*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(3/4)*e^4*Sqrt[e*x]*Sqrt[a + c*x^2]) + (2*(21*Sqrt[a]*B - 5*A*Sqrt[c])*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*a^(5/4)*e^4*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{811, 835, 842, 840, 1198, 220, 1196}"
442,1,438,0,0.5773023,"\int (e x)^{5/2} (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[(e*x)^(5/2)*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{4 a^2 e^2 \sqrt{e x} \sqrt{a+c x^2} (65 a B-231 A c x)}{15015 c^2}+\frac{4 a^{13/4} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(65 \sqrt{a} B-231 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15015 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^3 A e^3 x \sqrt{a+c x^2}}{65 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{8 a^{13/4} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 a e^2 \sqrt{e x} \left(a+c x^2\right)^{3/2} (13 a B-77 A c x)}{3003 c^2}+\frac{2 A e (e x)^{3/2} \left(a+c x^2\right)^{5/2}}{13 c}-\frac{2 a B e^2 \sqrt{e x} \left(a+c x^2\right)^{5/2}}{33 c^2}+\frac{2 B (e x)^{5/2} \left(a+c x^2\right)^{5/2}}{15 c}","\frac{4 a^2 e^2 \sqrt{e x} \sqrt{a+c x^2} (65 a B-231 A c x)}{15015 c^2}+\frac{4 a^{13/4} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(65 \sqrt{a} B-231 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15015 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^3 A e^3 x \sqrt{a+c x^2}}{65 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{8 a^{13/4} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 a e^2 \sqrt{e x} \left(a+c x^2\right)^{3/2} (13 a B-77 A c x)}{3003 c^2}+\frac{2 A e (e x)^{3/2} \left(a+c x^2\right)^{5/2}}{13 c}-\frac{2 a B e^2 \sqrt{e x} \left(a+c x^2\right)^{5/2}}{33 c^2}+\frac{2 B (e x)^{5/2} \left(a+c x^2\right)^{5/2}}{15 c}",1,"(-8*a^3*A*e^3*x*Sqrt[a + c*x^2])/(65*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (4*a^2*e^2*Sqrt[e*x]*(65*a*B - 231*A*c*x)*Sqrt[a + c*x^2])/(15015*c^2) + (2*a*e^2*Sqrt[e*x]*(13*a*B - 77*A*c*x)*(a + c*x^2)^(3/2))/(3003*c^2) - (2*a*B*e^2*Sqrt[e*x]*(a + c*x^2)^(5/2))/(33*c^2) + (2*A*e*(e*x)^(3/2)*(a + c*x^2)^(5/2))/(13*c) + (2*B*(e*x)^(5/2)*(a + c*x^2)^(5/2))/(15*c) + (8*a^(13/4)*A*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(65*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (4*a^(13/4)*(65*Sqrt[a]*B - 231*A*Sqrt[c])*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15015*c^(9/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",10,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
443,1,400,0,0.4954993,"\int (e x)^{3/2} (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[(e*x)^(3/2)*(A + B*x)*(a + c*x^2)^(3/2),x]","-\frac{4 a^{11/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(77 \sqrt{a} B+65 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^2 e \sqrt{e x} \sqrt{a+c x^2} (65 A+77 B x)}{5005 c}-\frac{8 a^3 B e^2 x \sqrt{a+c x^2}}{65 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{8 a^{13/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 a e \sqrt{e x} \left(a+c x^2\right)^{3/2} (39 A+77 B x)}{3003 c}+\frac{2 A e \sqrt{e x} \left(a+c x^2\right)^{5/2}}{11 c}+\frac{2 B (e x)^{3/2} \left(a+c x^2\right)^{5/2}}{13 c}","-\frac{4 a^{11/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(77 \sqrt{a} B+65 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5005 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 a^2 e \sqrt{e x} \sqrt{a+c x^2} (65 A+77 B x)}{5005 c}-\frac{8 a^3 B e^2 x \sqrt{a+c x^2}}{65 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{8 a^{13/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{65 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 a e \sqrt{e x} \left(a+c x^2\right)^{3/2} (39 A+77 B x)}{3003 c}+\frac{2 A e \sqrt{e x} \left(a+c x^2\right)^{5/2}}{11 c}+\frac{2 B (e x)^{3/2} \left(a+c x^2\right)^{5/2}}{13 c}",1,"(-4*a^2*e*Sqrt[e*x]*(65*A + 77*B*x)*Sqrt[a + c*x^2])/(5005*c) - (8*a^3*B*e^2*x*Sqrt[a + c*x^2])/(65*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*a*e*Sqrt[e*x]*(39*A + 77*B*x)*(a + c*x^2)^(3/2))/(3003*c) + (2*A*e*Sqrt[e*x]*(a + c*x^2)^(5/2))/(11*c) + (2*B*(e*x)^(3/2)*(a + c*x^2)^(5/2))/(13*c) + (8*a^(13/4)*B*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(65*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (4*a^(11/4)*(77*Sqrt[a]*B + 65*A*Sqrt[c])*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5005*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
444,1,366,0,0.4203964,"\int \sqrt{e x} (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[Sqrt[e*x]*(A + B*x)*(a + c*x^2)^(3/2),x]","-\frac{4 a^{9/4} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(15 \sqrt{a} B-77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^{9/4} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{8 a^2 A e x \sqrt{a+c x^2}}{15 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt{e x} \left(a+c x^2\right)^{3/2} (9 a B-77 A c x)}{693 c}-\frac{4 a \sqrt{e x} \sqrt{a+c x^2} (15 a B-77 A c x)}{1155 c}+\frac{2 B \sqrt{e x} \left(a+c x^2\right)^{5/2}}{11 c}","-\frac{4 a^{9/4} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(15 \sqrt{a} B-77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{1155 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^{9/4} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{8 a^2 A e x \sqrt{a+c x^2}}{15 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt{e x} \left(a+c x^2\right)^{3/2} (9 a B-77 A c x)}{693 c}-\frac{4 a \sqrt{e x} \sqrt{a+c x^2} (15 a B-77 A c x)}{1155 c}+\frac{2 B \sqrt{e x} \left(a+c x^2\right)^{5/2}}{11 c}",1,"(8*a^2*A*e*x*Sqrt[a + c*x^2])/(15*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*a*Sqrt[e*x]*(15*a*B - 77*A*c*x)*Sqrt[a + c*x^2])/(1155*c) - (2*Sqrt[e*x]*(9*a*B - 77*A*c*x)*(a + c*x^2)^(3/2))/(693*c) + (2*B*Sqrt[e*x]*(a + c*x^2)^(5/2))/(11*c) - (8*a^(9/4)*A*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (4*a^(9/4)*(15*Sqrt[a]*B - 77*A*Sqrt[c])*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(1155*c^(5/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
445,1,333,0,0.3485019,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{\sqrt{e x}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/Sqrt[e*x],x]","\frac{4 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B+15 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^{9/4} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{8 a^2 B x \sqrt{a+c x^2}}{15 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{4 a \sqrt{e x} \sqrt{a+c x^2} (15 A+7 B x)}{105 e}+\frac{2 \sqrt{e x} \left(a+c x^2\right)^{3/2} (9 A+7 B x)}{63 e}","\frac{4 a^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B+15 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^{9/4} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{8 a^2 B x \sqrt{a+c x^2}}{15 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{4 a \sqrt{e x} \sqrt{a+c x^2} (15 A+7 B x)}{105 e}+\frac{2 \sqrt{e x} \left(a+c x^2\right)^{3/2} (9 A+7 B x)}{63 e}",1,"(4*a*Sqrt[e*x]*(15*A + 7*B*x)*Sqrt[a + c*x^2])/(105*e) + (8*a^2*B*x*Sqrt[a + c*x^2])/(15*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (2*Sqrt[e*x]*(9*A + 7*B*x)*(a + c*x^2)^(3/2))/(63*e) - (8*a^(9/4)*B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (4*a^(7/4)*(7*Sqrt[a]*B + 15*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{815, 842, 840, 1198, 220, 1196}"
446,1,341,0,0.3452201,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(3/2),x]","\frac{4 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+21 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{24 a^{5/4} A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e \sqrt{e x} \sqrt{a+c x^2}}+\frac{4 \sqrt{e x} \sqrt{a+c x^2} (5 a B+21 A c x)}{35 e^2}-\frac{2 \left(a+c x^2\right)^{3/2} (7 A-B x)}{7 e \sqrt{e x}}+\frac{24 a A \sqrt{c} x \sqrt{a+c x^2}}{5 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{4 a^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+21 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{24 a^{5/4} A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e \sqrt{e x} \sqrt{a+c x^2}}+\frac{4 \sqrt{e x} \sqrt{a+c x^2} (5 a B+21 A c x)}{35 e^2}-\frac{2 \left(a+c x^2\right)^{3/2} (7 A-B x)}{7 e \sqrt{e x}}+\frac{24 a A \sqrt{c} x \sqrt{a+c x^2}}{5 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(24*a*A*Sqrt[c]*x*Sqrt[a + c*x^2])/(5*e*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (4*Sqrt[e*x]*(5*a*B + 21*A*c*x)*Sqrt[a + c*x^2])/(35*e^2) - (2*(7*A - B*x)*(a + c*x^2)^(3/2))/(7*e*Sqrt[e*x]) - (24*a^(5/4)*A*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*e*Sqrt[e*x]*Sqrt[a + c*x^2]) + (4*a^(5/4)*(5*Sqrt[a]*B + 21*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(35*c^(1/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{813, 815, 842, 840, 1198, 220, 1196}"
447,1,341,0,0.3194611,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(5/2),x]","\frac{4 a^{3/4} \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(9 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{24 a^{5/4} B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 \sqrt{a+c x^2} (9 a B-5 A c x)}{15 e^2 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{3/2} (5 A-3 B x)}{15 e (e x)^{3/2}}+\frac{24 a B \sqrt{c} x \sqrt{a+c x^2}}{5 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{4 a^{3/4} \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(9 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{24 a^{5/4} B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 \sqrt{a+c x^2} (9 a B-5 A c x)}{15 e^2 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{3/2} (5 A-3 B x)}{15 e (e x)^{3/2}}+\frac{24 a B \sqrt{c} x \sqrt{a+c x^2}}{5 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(24*a*B*Sqrt[c]*x*Sqrt[a + c*x^2])/(5*e^2*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*(9*a*B - 5*A*c*x)*Sqrt[a + c*x^2])/(15*e^2*Sqrt[e*x]) - (2*(5*A - 3*B*x)*(a + c*x^2)^(3/2))/(15*e*(e*x)^(3/2)) - (24*a^(5/4)*B*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]) + (4*a^(3/4)*(9*Sqrt[a]*B + 5*A*Sqrt[c])*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{813, 842, 840, 1198, 220, 1196}"
448,1,339,0,0.3440865,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(7/2),x]","\frac{4 \sqrt[4]{a} c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+9 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 c \sqrt{a+c x^2} (9 A-5 B x)}{15 e^3 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{3/2} (3 A+5 B x)}{15 e (e x)^{5/2}}+\frac{24 A c^{3/2} x \sqrt{a+c x^2}}{5 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{24 \sqrt[4]{a} A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^3 \sqrt{e x} \sqrt{a+c x^2}}","\frac{4 \sqrt[4]{a} c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+9 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 c \sqrt{a+c x^2} (9 A-5 B x)}{15 e^3 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{3/2} (3 A+5 B x)}{15 e (e x)^{5/2}}+\frac{24 A c^{3/2} x \sqrt{a+c x^2}}{5 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{24 \sqrt[4]{a} A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^3 \sqrt{e x} \sqrt{a+c x^2}}",1,"(-4*c*(9*A - 5*B*x)*Sqrt[a + c*x^2])/(15*e^3*Sqrt[e*x]) + (24*A*c^(3/2)*x*Sqrt[a + c*x^2])/(5*e^3*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*(3*A + 5*B*x)*(a + c*x^2)^(3/2))/(15*e*(e*x)^(5/2)) - (24*a^(1/4)*A*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]) + (4*a^(1/4)*(5*Sqrt[a]*B + 9*A*Sqrt[c])*c^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{811, 813, 842, 840, 1198, 220, 1196}"
449,1,339,0,0.3380084,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(e x)^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(e*x)^(9/2),x]","\frac{4 c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(21 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{a} e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 c \sqrt{a+c x^2} (5 A+21 B x)}{35 e^3 (e x)^{3/2}}-\frac{2 \left(a+c x^2\right)^{3/2} (5 A+7 B x)}{35 e (e x)^{7/2}}+\frac{24 B c^{3/2} x \sqrt{a+c x^2}}{5 e^4 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{24 \sqrt[4]{a} B c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^4 \sqrt{e x} \sqrt{a+c x^2}}","\frac{4 c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(21 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{35 \sqrt[4]{a} e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 c \sqrt{a+c x^2} (5 A+21 B x)}{35 e^3 (e x)^{3/2}}-\frac{2 \left(a+c x^2\right)^{3/2} (5 A+7 B x)}{35 e (e x)^{7/2}}+\frac{24 B c^{3/2} x \sqrt{a+c x^2}}{5 e^4 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{24 \sqrt[4]{a} B c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^4 \sqrt{e x} \sqrt{a+c x^2}}",1,"(-4*c*(5*A + 21*B*x)*Sqrt[a + c*x^2])/(35*e^3*(e*x)^(3/2)) + (24*B*c^(3/2)*x*Sqrt[a + c*x^2])/(5*e^4*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*(5*A + 7*B*x)*(a + c*x^2)^(3/2))/(35*e*(e*x)^(7/2)) - (24*a^(1/4)*B*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*e^4*Sqrt[e*x]*Sqrt[a + c*x^2]) + (4*(21*Sqrt[a]*B + 5*A*Sqrt[c])*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(35*a^(1/4)*e^4*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{811, 842, 840, 1198, 220, 1196}"
450,1,437,0,0.5687205,"\int (e x)^{3/2} (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[(e*x)^(3/2)*(A + B*x)*(a + c*x^2)^(5/2),x]","-\frac{8 a^{15/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(231 \sqrt{a} B+221 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{51051 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^3 e \sqrt{e x} \sqrt{a+c x^2} (221 A+231 B x)}{51051 c}-\frac{4 a^2 e \sqrt{e x} \left(a+c x^2\right)^{3/2} (221 A+385 B x)}{51051 c}-\frac{16 a^4 B e^2 x \sqrt{a+c x^2}}{221 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{16 a^{17/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{221 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 a e \sqrt{e x} \left(a+c x^2\right)^{5/2} (221 A+495 B x)}{36465 c}+\frac{2 A e \sqrt{e x} \left(a+c x^2\right)^{7/2}}{15 c}+\frac{2 B (e x)^{3/2} \left(a+c x^2\right)^{7/2}}{17 c}","-\frac{8 a^{15/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(231 \sqrt{a} B+221 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{51051 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^3 e \sqrt{e x} \sqrt{a+c x^2} (221 A+231 B x)}{51051 c}-\frac{4 a^2 e \sqrt{e x} \left(a+c x^2\right)^{3/2} (221 A+385 B x)}{51051 c}-\frac{16 a^4 B e^2 x \sqrt{a+c x^2}}{221 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{16 a^{17/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{221 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 a e \sqrt{e x} \left(a+c x^2\right)^{5/2} (221 A+495 B x)}{36465 c}+\frac{2 A e \sqrt{e x} \left(a+c x^2\right)^{7/2}}{15 c}+\frac{2 B (e x)^{3/2} \left(a+c x^2\right)^{7/2}}{17 c}",1,"(-8*a^3*e*Sqrt[e*x]*(221*A + 231*B*x)*Sqrt[a + c*x^2])/(51051*c) - (16*a^4*B*e^2*x*Sqrt[a + c*x^2])/(221*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*a^2*e*Sqrt[e*x]*(221*A + 385*B*x)*(a + c*x^2)^(3/2))/(51051*c) - (2*a*e*Sqrt[e*x]*(221*A + 495*B*x)*(a + c*x^2)^(5/2))/(36465*c) + (2*A*e*Sqrt[e*x]*(a + c*x^2)^(7/2))/(15*c) + (2*B*(e*x)^(3/2)*(a + c*x^2)^(7/2))/(17*c) + (16*a^(17/4)*B*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(221*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (8*a^(15/4)*(231*Sqrt[a]*B + 221*A*Sqrt[c])*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(51051*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",10,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
451,1,404,0,0.4868705,"\int \sqrt{e x} (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[Sqrt[e*x]*(A + B*x)*(a + c*x^2)^(5/2),x]","-\frac{8 a^{13/4} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(13 \sqrt{a} B-77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3003 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^2 \sqrt{e x} \sqrt{a+c x^2} (13 a B-77 A c x)}{3003 c}-\frac{16 a^{13/4} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{39 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^3 A e x \sqrt{a+c x^2}}{39 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt{e x} \left(a+c x^2\right)^{5/2} (13 a B-165 A c x)}{2145 c}-\frac{4 a \sqrt{e x} \left(a+c x^2\right)^{3/2} (39 a B-385 A c x)}{9009 c}+\frac{2 B \sqrt{e x} \left(a+c x^2\right)^{7/2}}{15 c}","-\frac{8 a^{13/4} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(13 \sqrt{a} B-77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3003 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{8 a^2 \sqrt{e x} \sqrt{a+c x^2} (13 a B-77 A c x)}{3003 c}-\frac{16 a^{13/4} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{39 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^3 A e x \sqrt{a+c x^2}}{39 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt{e x} \left(a+c x^2\right)^{5/2} (13 a B-165 A c x)}{2145 c}-\frac{4 a \sqrt{e x} \left(a+c x^2\right)^{3/2} (39 a B-385 A c x)}{9009 c}+\frac{2 B \sqrt{e x} \left(a+c x^2\right)^{7/2}}{15 c}",1,"(16*a^3*A*e*x*Sqrt[a + c*x^2])/(39*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (8*a^2*Sqrt[e*x]*(13*a*B - 77*A*c*x)*Sqrt[a + c*x^2])/(3003*c) - (4*a*Sqrt[e*x]*(39*a*B - 385*A*c*x)*(a + c*x^2)^(3/2))/(9009*c) - (2*Sqrt[e*x]*(13*a*B - 165*A*c*x)*(a + c*x^2)^(5/2))/(2145*c) + (2*B*Sqrt[e*x]*(a + c*x^2)^(7/2))/(15*c) - (16*a^(13/4)*A*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(39*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (8*a^(13/4)*(13*Sqrt[a]*B - 77*A*Sqrt[c])*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3003*c^(5/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,7,24,0.2917,1,"{833, 815, 842, 840, 1198, 220, 1196}"
452,1,369,0,0.4141194,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{\sqrt{e x}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/Sqrt[e*x],x]","\frac{8 a^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(77 \sqrt{a} B+195 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3003 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{8 a^2 \sqrt{e x} \sqrt{a+c x^2} (195 A+77 B x)}{3003 e}-\frac{16 a^{13/4} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{39 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^3 B x \sqrt{a+c x^2}}{39 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{20 a \sqrt{e x} \left(a+c x^2\right)^{3/2} (117 A+77 B x)}{9009 e}+\frac{2 \sqrt{e x} \left(a+c x^2\right)^{5/2} (13 A+11 B x)}{143 e}","\frac{8 a^{11/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(77 \sqrt{a} B+195 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3003 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{8 a^2 \sqrt{e x} \sqrt{a+c x^2} (195 A+77 B x)}{3003 e}-\frac{16 a^{13/4} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{39 c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^3 B x \sqrt{a+c x^2}}{39 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{20 a \sqrt{e x} \left(a+c x^2\right)^{3/2} (117 A+77 B x)}{9009 e}+\frac{2 \sqrt{e x} \left(a+c x^2\right)^{5/2} (13 A+11 B x)}{143 e}",1,"(8*a^2*Sqrt[e*x]*(195*A + 77*B*x)*Sqrt[a + c*x^2])/(3003*e) + (16*a^3*B*x*Sqrt[a + c*x^2])/(39*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (20*a*Sqrt[e*x]*(117*A + 77*B*x)*(a + c*x^2)^(3/2))/(9009*e) + (2*Sqrt[e*x]*(13*A + 11*B*x)*(a + c*x^2)^(5/2))/(143*e) - (16*a^(13/4)*B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(39*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (8*a^(11/4)*(77*Sqrt[a]*B + 195*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3003*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,6,24,0.2500,1,"{815, 842, 840, 1198, 220, 1196}"
453,1,379,0,0.4137117,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(3/2),x]","\frac{8 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(15 \sqrt{a} B+77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^2 A \sqrt{c} x \sqrt{a+c x^2}}{3 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{16 a^{9/4} A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 e \sqrt{e x} \sqrt{a+c x^2}}+\frac{20 \sqrt{e x} \left(a+c x^2\right)^{3/2} (9 a B+77 A c x)}{693 e^2}+\frac{8 a \sqrt{e x} \sqrt{a+c x^2} (15 a B+77 A c x)}{231 e^2}-\frac{2 \left(a+c x^2\right)^{5/2} (11 A-B x)}{11 e \sqrt{e x}}","\frac{8 a^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(15 \sqrt{a} B+77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{231 \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^2 A \sqrt{c} x \sqrt{a+c x^2}}{3 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{16 a^{9/4} A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 e \sqrt{e x} \sqrt{a+c x^2}}+\frac{20 \sqrt{e x} \left(a+c x^2\right)^{3/2} (9 a B+77 A c x)}{693 e^2}+\frac{8 a \sqrt{e x} \sqrt{a+c x^2} (15 a B+77 A c x)}{231 e^2}-\frac{2 \left(a+c x^2\right)^{5/2} (11 A-B x)}{11 e \sqrt{e x}}",1,"(16*a^2*A*Sqrt[c]*x*Sqrt[a + c*x^2])/(3*e*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (8*a*Sqrt[e*x]*(15*a*B + 77*A*c*x)*Sqrt[a + c*x^2])/(231*e^2) + (20*Sqrt[e*x]*(9*a*B + 77*A*c*x)*(a + c*x^2)^(3/2))/(693*e^2) - (2*(11*A - B*x)*(a + c*x^2)^(5/2))/(11*e*Sqrt[e*x]) - (16*a^(9/4)*A*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*e*Sqrt[e*x]*Sqrt[a + c*x^2]) + (8*a^(9/4)*(15*Sqrt[a]*B + 77*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(231*c^(1/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{813, 815, 842, 840, 1198, 220, 1196}"
454,1,378,0,0.3848941,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(5/2),x]","\frac{8 a^{7/4} \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^2 B \sqrt{c} x \sqrt{a+c x^2}}{3 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{16 a^{9/4} B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{20 \left(a+c x^2\right)^{3/2} (7 a B-3 A c x)}{63 e^2 \sqrt{e x}}+\frac{8 a c \sqrt{e x} \sqrt{a+c x^2} (5 A+7 B x)}{21 e^3}-\frac{2 \left(a+c x^2\right)^{5/2} (3 A-B x)}{9 e (e x)^{3/2}}","\frac{8 a^{7/4} \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{16 a^2 B \sqrt{c} x \sqrt{a+c x^2}}{3 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{16 a^{9/4} B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{20 \left(a+c x^2\right)^{3/2} (7 a B-3 A c x)}{63 e^2 \sqrt{e x}}+\frac{8 a c \sqrt{e x} \sqrt{a+c x^2} (5 A+7 B x)}{21 e^3}-\frac{2 \left(a+c x^2\right)^{5/2} (3 A-B x)}{9 e (e x)^{3/2}}",1,"(8*a*c*Sqrt[e*x]*(5*A + 7*B*x)*Sqrt[a + c*x^2])/(21*e^3) + (16*a^2*B*Sqrt[c]*x*Sqrt[a + c*x^2])/(3*e^2*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (20*(7*a*B - 3*A*c*x)*(a + c*x^2)^(3/2))/(63*e^2*Sqrt[e*x]) - (2*(3*A - B*x)*(a + c*x^2)^(5/2))/(9*e*(e*x)^(3/2)) - (16*a^(9/4)*B*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]) + (8*a^(7/4)*(7*Sqrt[a]*B + 5*A*Sqrt[c])*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(21*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{813, 815, 842, 840, 1198, 220, 1196}"
455,1,376,0,0.4059733,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(7/2),x]","\frac{8 a^{5/4} c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B+63 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{48 a^{5/4} A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 \left(a+c x^2\right)^{3/2} (25 a B-21 A c x)}{105 e^2 (e x)^{3/2}}-\frac{8 a c \sqrt{a+c x^2} (63 A-25 B x)}{105 e^3 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{5/2} (7 A-5 B x)}{35 e (e x)^{5/2}}+\frac{48 a A c^{3/2} x \sqrt{a+c x^2}}{5 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{8 a^{5/4} c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B+63 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{48 a^{5/4} A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 \left(a+c x^2\right)^{3/2} (25 a B-21 A c x)}{105 e^2 (e x)^{3/2}}-\frac{8 a c \sqrt{a+c x^2} (63 A-25 B x)}{105 e^3 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{5/2} (7 A-5 B x)}{35 e (e x)^{5/2}}+\frac{48 a A c^{3/2} x \sqrt{a+c x^2}}{5 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(-8*a*c*(63*A - 25*B*x)*Sqrt[a + c*x^2])/(105*e^3*Sqrt[e*x]) + (48*a*A*c^(3/2)*x*Sqrt[a + c*x^2])/(5*e^3*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*(25*a*B - 21*A*c*x)*(a + c*x^2)^(3/2))/(105*e^2*(e*x)^(3/2)) - (2*(7*A - 5*B*x)*(a + c*x^2)^(5/2))/(35*e*(e*x)^(5/2)) - (48*a^(5/4)*A*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]) + (8*a^(5/4)*(25*Sqrt[a]*B + 63*A*Sqrt[c])*c^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,6,24,0.2500,1,"{813, 842, 840, 1198, 220, 1196}"
456,1,377,0,0.4131663,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(9/2),x]","\frac{8 a^{3/4} c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(63 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{48 a^{5/4} B c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 \left(a+c x^2\right)^{3/2} (21 a B+25 A c x)}{105 e^2 (e x)^{5/2}}-\frac{8 c \sqrt{a+c x^2} (63 a B-25 A c x)}{105 e^4 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{5/2} (5 A-7 B x)}{35 e (e x)^{7/2}}+\frac{48 a B c^{3/2} x \sqrt{a+c x^2}}{5 e^4 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{8 a^{3/4} c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(63 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{48 a^{5/4} B c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 e^4 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 \left(a+c x^2\right)^{3/2} (21 a B+25 A c x)}{105 e^2 (e x)^{5/2}}-\frac{8 c \sqrt{a+c x^2} (63 a B-25 A c x)}{105 e^4 \sqrt{e x}}-\frac{2 \left(a+c x^2\right)^{5/2} (5 A-7 B x)}{35 e (e x)^{7/2}}+\frac{48 a B c^{3/2} x \sqrt{a+c x^2}}{5 e^4 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(48*a*B*c^(3/2)*x*Sqrt[a + c*x^2])/(5*e^4*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (8*c*(63*a*B - 25*A*c*x)*Sqrt[a + c*x^2])/(105*e^4*Sqrt[e*x]) - (4*(21*a*B + 25*A*c*x)*(a + c*x^2)^(3/2))/(105*e^2*(e*x)^(5/2)) - (2*(5*A - 7*B*x)*(a + c*x^2)^(5/2))/(35*e*(e*x)^(7/2)) - (48*a^(5/4)*B*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*e^4*Sqrt[e*x]*Sqrt[a + c*x^2]) + (8*a^(3/4)*(63*Sqrt[a]*B + 25*A*Sqrt[c])*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*e^4*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{813, 811, 842, 840, 1198, 220, 1196}"
457,1,375,0,0.4234791,"\int \frac{(A+B x) \left(a+c x^2\right)^{5/2}}{(e x)^{11/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(5/2))/(e*x)^(11/2),x]","-\frac{8 c^2 \sqrt{a+c x^2} (7 A-5 B x)}{21 e^5 \sqrt{e x}}+\frac{8 \sqrt[4]{a} c^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+7 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 e^5 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 c \left(a+c x^2\right)^{3/2} (7 A+15 B x)}{63 e^3 (e x)^{5/2}}-\frac{2 \left(a+c x^2\right)^{5/2} (7 A+9 B x)}{63 e (e x)^{9/2}}+\frac{16 A c^{5/2} x \sqrt{a+c x^2}}{3 e^5 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{16 \sqrt[4]{a} A c^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 e^5 \sqrt{e x} \sqrt{a+c x^2}}","-\frac{8 c^2 \sqrt{a+c x^2} (7 A-5 B x)}{21 e^5 \sqrt{e x}}+\frac{8 \sqrt[4]{a} c^{7/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+7 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{21 e^5 \sqrt{e x} \sqrt{a+c x^2}}-\frac{4 c \left(a+c x^2\right)^{3/2} (7 A+15 B x)}{63 e^3 (e x)^{5/2}}-\frac{2 \left(a+c x^2\right)^{5/2} (7 A+9 B x)}{63 e (e x)^{9/2}}+\frac{16 A c^{5/2} x \sqrt{a+c x^2}}{3 e^5 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{16 \sqrt[4]{a} A c^{9/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 e^5 \sqrt{e x} \sqrt{a+c x^2}}",1,"(-8*c^2*(7*A - 5*B*x)*Sqrt[a + c*x^2])/(21*e^5*Sqrt[e*x]) + (16*A*c^(5/2)*x*Sqrt[a + c*x^2])/(3*e^5*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (4*c*(7*A + 15*B*x)*(a + c*x^2)^(3/2))/(63*e^3*(e*x)^(5/2)) - (2*(7*A + 9*B*x)*(a + c*x^2)^(5/2))/(63*e*(e*x)^(9/2)) - (16*a^(1/4)*A*c^(9/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*e^5*Sqrt[e*x]*Sqrt[a + c*x^2]) + (8*a^(1/4)*(5*Sqrt[a]*B + 7*A*Sqrt[c])*c^(7/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(21*e^5*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{811, 813, 842, 840, 1198, 220, 1196}"
458,1,388,0,0.4833758,"\int \frac{(e x)^{7/2} (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[((e*x)^(7/2)*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{a^{7/4} e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(49 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{14 a^2 B e^4 x \sqrt{a+c x^2}}{15 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{14 a^{9/4} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{10 a A e^3 \sqrt{e x} \sqrt{a+c x^2}}{21 c^2}+\frac{2 A e (e x)^{5/2} \sqrt{a+c x^2}}{7 c}-\frac{14 a B e^2 (e x)^{3/2} \sqrt{a+c x^2}}{45 c^2}+\frac{2 B (e x)^{7/2} \sqrt{a+c x^2}}{9 c}","\frac{a^{7/4} e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(49 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{14 a^2 B e^4 x \sqrt{a+c x^2}}{15 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{14 a^{9/4} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{10 a A e^3 \sqrt{e x} \sqrt{a+c x^2}}{21 c^2}+\frac{2 A e (e x)^{5/2} \sqrt{a+c x^2}}{7 c}-\frac{14 a B e^2 (e x)^{3/2} \sqrt{a+c x^2}}{45 c^2}+\frac{2 B (e x)^{7/2} \sqrt{a+c x^2}}{9 c}",1,"(-10*a*A*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])/(21*c^2) - (14*a*B*e^2*(e*x)^(3/2)*Sqrt[a + c*x^2])/(45*c^2) + (2*A*e*(e*x)^(5/2)*Sqrt[a + c*x^2])/(7*c) + (2*B*(e*x)^(7/2)*Sqrt[a + c*x^2])/(9*c) + (14*a^2*B*e^4*x*Sqrt[a + c*x^2])/(15*c^(5/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (14*a^(9/4)*B*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (a^(7/4)*(49*Sqrt[a]*B + 25*A*Sqrt[c])*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,6,24,0.2500,1,"{833, 842, 840, 1198, 220, 1196}"
459,1,356,0,0.4050249,"\int \frac{(e x)^{5/2} (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[((e*x)^(5/2)*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{a^{5/4} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B-63 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{6 a^{5/4} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{6 a A e^3 x \sqrt{a+c x^2}}{5 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 A e (e x)^{3/2} \sqrt{a+c x^2}}{5 c}-\frac{10 a B e^2 \sqrt{e x} \sqrt{a+c x^2}}{21 c^2}+\frac{2 B (e x)^{5/2} \sqrt{a+c x^2}}{7 c}","\frac{a^{5/4} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B-63 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{105 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{6 a^{5/4} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{6 a A e^3 x \sqrt{a+c x^2}}{5 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 A e (e x)^{3/2} \sqrt{a+c x^2}}{5 c}-\frac{10 a B e^2 \sqrt{e x} \sqrt{a+c x^2}}{21 c^2}+\frac{2 B (e x)^{5/2} \sqrt{a+c x^2}}{7 c}",1,"(-10*a*B*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])/(21*c^2) + (2*A*e*(e*x)^(3/2)*Sqrt[a + c*x^2])/(5*c) + (2*B*(e*x)^(5/2)*Sqrt[a + c*x^2])/(7*c) - (6*a*A*e^3*x*Sqrt[a + c*x^2])/(5*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (6*a^(5/4)*A*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (a^(5/4)*(25*Sqrt[a]*B - 63*A*Sqrt[c])*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(105*c^(9/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,6,24,0.2500,1,"{833, 842, 840, 1198, 220, 1196}"
460,1,326,0,0.3350526,"\int \frac{(e x)^{3/2} (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[((e*x)^(3/2)*(A + B*x))/Sqrt[a + c*x^2],x]","-\frac{a^{3/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(9 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{6 a^{5/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 A e \sqrt{e x} \sqrt{a+c x^2}}{3 c}-\frac{6 a B e^2 x \sqrt{a+c x^2}}{5 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 B (e x)^{3/2} \sqrt{a+c x^2}}{5 c}","-\frac{a^{3/4} e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(9 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{6 a^{5/4} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 A e \sqrt{e x} \sqrt{a+c x^2}}{3 c}-\frac{6 a B e^2 x \sqrt{a+c x^2}}{5 c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 B (e x)^{3/2} \sqrt{a+c x^2}}{5 c}",1,"(2*A*e*Sqrt[e*x]*Sqrt[a + c*x^2])/(3*c) + (2*B*(e*x)^(3/2)*Sqrt[a + c*x^2])/(5*c) - (6*a*B*e^2*x*Sqrt[a + c*x^2])/(5*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (6*a^(5/4)*B*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (a^(3/4)*(9*Sqrt[a]*B + 5*A*Sqrt[c])*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{833, 842, 840, 1198, 220, 1196}"
461,1,287,0,0.2542883,"\int \frac{\sqrt{e x} (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[(Sqrt[e*x]*(A + B*x))/Sqrt[a + c*x^2],x]","-\frac{\sqrt[4]{a} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt[4]{a} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 A e x \sqrt{a+c x^2}}{\sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 B \sqrt{e x} \sqrt{a+c x^2}}{3 c}","-\frac{\sqrt[4]{a} e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt[4]{a} A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 A e x \sqrt{a+c x^2}}{\sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 B \sqrt{e x} \sqrt{a+c x^2}}{3 c}",1,"(2*B*Sqrt[e*x]*Sqrt[a + c*x^2])/(3*c) + (2*A*e*x*Sqrt[a + c*x^2])/(Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*a^(1/4)*A*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (a^(1/4)*(Sqrt[a]*B - 3*A*Sqrt[c])*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*c^(5/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{833, 842, 840, 1198, 220, 1196}"
462,1,253,0,0.1808833,"\int \frac{A+B x}{\sqrt{e x} \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(Sqrt[e*x]*Sqrt[a + c*x^2]),x]","\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt[4]{a} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 B x \sqrt{a+c x^2}}{\sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 \sqrt[4]{a} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{2 B x \sqrt{a+c x^2}}{\sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(2*B*x*Sqrt[a + c*x^2])/(Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*a^(1/4)*B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (a^(1/4)*(B + (A*Sqrt[c])/Sqrt[a])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",5,5,24,0.2083,1,"{842, 840, 1198, 220, 1196}"
463,1,293,0,0.24781,"\int \frac{A+B x}{(e x)^{3/2} \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/((e*x)^(3/2)*Sqrt[a + c*x^2]),x]","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B+A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 A \sqrt{a+c x^2}}{a e \sqrt{e x}}+\frac{2 A \sqrt{c} x \sqrt{a+c x^2}}{a e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B+A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 A \sqrt{a+c x^2}}{a e \sqrt{e x}}+\frac{2 A \sqrt{c} x \sqrt{a+c x^2}}{a e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(-2*A*Sqrt[a + c*x^2])/(a*e*Sqrt[e*x]) + (2*A*Sqrt[c]*x*Sqrt[a + c*x^2])/(a*e*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*A*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((Sqrt[a]*B + A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*c^(1/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{835, 842, 840, 1198, 220, 1196}"
464,1,327,0,0.317513,"\int \frac{A+B x}{(e x)^{5/2} \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/((e*x)^(5/2)*Sqrt[a + c*x^2]),x]","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 a^{5/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 A \sqrt{a+c x^2}}{3 a e (e x)^{3/2}}-\frac{2 B \sqrt{a+c x^2}}{a e^2 \sqrt{e x}}+\frac{2 B \sqrt{c} x \sqrt{a+c x^2}}{a e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{3 a^{5/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{2 A \sqrt{a+c x^2}}{3 a e (e x)^{3/2}}-\frac{2 B \sqrt{a+c x^2}}{a e^2 \sqrt{e x}}+\frac{2 B \sqrt{c} x \sqrt{a+c x^2}}{a e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(-2*A*Sqrt[a + c*x^2])/(3*a*e*(e*x)^(3/2)) - (2*B*Sqrt[a + c*x^2])/(a*e^2*Sqrt[e*x]) + (2*B*Sqrt[c]*x*Sqrt[a + c*x^2])/(a*e^2*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*B*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((3*Sqrt[a]*B - A*Sqrt[c])*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(3*a^(5/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{835, 842, 840, 1198, 220, 1196}"
465,1,363,0,0.3913113,"\int \frac{A+B x}{(e x)^{7/2} \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/((e*x)^(7/2)*Sqrt[a + c*x^2]),x]","-\frac{c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+9 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{6 A c^{3/2} x \sqrt{a+c x^2}}{5 a^2 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{6 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{6 A c \sqrt{a+c x^2}}{5 a^2 e^3 \sqrt{e x}}-\frac{2 A \sqrt{a+c x^2}}{5 a e (e x)^{5/2}}-\frac{2 B \sqrt{a+c x^2}}{3 a e^2 (e x)^{3/2}}","-\frac{c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+9 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{15 a^{7/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{6 A c^{3/2} x \sqrt{a+c x^2}}{5 a^2 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{6 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{7/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{6 A c \sqrt{a+c x^2}}{5 a^2 e^3 \sqrt{e x}}-\frac{2 A \sqrt{a+c x^2}}{5 a e (e x)^{5/2}}-\frac{2 B \sqrt{a+c x^2}}{3 a e^2 (e x)^{3/2}}",1,"(-2*A*Sqrt[a + c*x^2])/(5*a*e*(e*x)^(5/2)) - (2*B*Sqrt[a + c*x^2])/(3*a*e^2*(e*x)^(3/2)) + (6*A*c*Sqrt[a + c*x^2])/(5*a^2*e^3*Sqrt[e*x]) - (6*A*c^(3/2)*x*Sqrt[a + c*x^2])/(5*a^2*e^3*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (6*A*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(7/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]) - ((5*Sqrt[a]*B + 9*A*Sqrt[c])*c^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(15*a^(7/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,6,24,0.2500,1,"{835, 842, 840, 1198, 220, 1196}"
466,1,360,0,0.4041584,"\int \frac{(e x)^{7/2} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((e*x)^(7/2)*(A + B*x))/(a + c*x^2)^(3/2),x]","-\frac{a^{3/4} e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(63 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{21 a^{5/4} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{5/2} (A+B x)}{c \sqrt{a+c x^2}}+\frac{5 A e^3 \sqrt{e x} \sqrt{a+c x^2}}{3 c^2}-\frac{21 a B e^4 x \sqrt{a+c x^2}}{5 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{7 B e^2 (e x)^{3/2} \sqrt{a+c x^2}}{5 c^2}","-\frac{a^{3/4} e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(63 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{21 a^{5/4} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{5/2} (A+B x)}{c \sqrt{a+c x^2}}+\frac{5 A e^3 \sqrt{e x} \sqrt{a+c x^2}}{3 c^2}-\frac{21 a B e^4 x \sqrt{a+c x^2}}{5 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{7 B e^2 (e x)^{3/2} \sqrt{a+c x^2}}{5 c^2}",1,"-((e*(e*x)^(5/2)*(A + B*x))/(c*Sqrt[a + c*x^2])) + (5*A*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])/(3*c^2) + (7*B*e^2*(e*x)^(3/2)*Sqrt[a + c*x^2])/(5*c^2) - (21*a*B*e^4*x*Sqrt[a + c*x^2])/(5*c^(5/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (21*a^(5/4)*B*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (a^(3/4)*(63*Sqrt[a]*B + 25*A*Sqrt[c])*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(30*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{819, 833, 842, 840, 1198, 220, 1196}"
467,1,326,0,0.3388711,"\int \frac{(e x)^{5/2} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((e*x)^(5/2)*(A + B*x))/(a + c*x^2)^(3/2),x]","-\frac{\sqrt[4]{a} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-9 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{3/2} (A+B x)}{c \sqrt{a+c x^2}}+\frac{3 A e^3 x \sqrt{a+c x^2}}{c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 \sqrt[4]{a} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{5 B e^2 \sqrt{e x} \sqrt{a+c x^2}}{3 c^2}","-\frac{\sqrt[4]{a} e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-9 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{3/2} (A+B x)}{c \sqrt{a+c x^2}}+\frac{3 A e^3 x \sqrt{a+c x^2}}{c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 \sqrt[4]{a} A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{5 B e^2 \sqrt{e x} \sqrt{a+c x^2}}{3 c^2}",1,"-((e*(e*x)^(3/2)*(A + B*x))/(c*Sqrt[a + c*x^2])) + (5*B*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])/(3*c^2) + (3*A*e^3*x*Sqrt[a + c*x^2])/(c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (3*a^(1/4)*A*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (a^(1/4)*(5*Sqrt[a]*B - 9*A*Sqrt[c])*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(6*c^(9/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{819, 833, 842, 840, 1198, 220, 1196}"
468,1,296,0,0.2663852,"\int \frac{(e x)^{3/2} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((e*x)^(3/2)*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B+A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e \sqrt{e x} (A+B x)}{c \sqrt{a+c x^2}}+\frac{3 B e^2 x \sqrt{a+c x^2}}{c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 \sqrt[4]{a} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}","\frac{e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B+A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 \sqrt[4]{a} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e \sqrt{e x} (A+B x)}{c \sqrt{a+c x^2}}+\frac{3 B e^2 x \sqrt{a+c x^2}}{c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 \sqrt[4]{a} B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}",1,"-((e*Sqrt[e*x]*(A + B*x))/(c*Sqrt[a + c*x^2])) + (3*B*e^2*x*Sqrt[a + c*x^2])/(c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (3*a^(1/4)*B*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((3*Sqrt[a]*B + A*Sqrt[c])*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(1/4)*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{819, 842, 840, 1198, 220, 1196}"
469,1,298,0,0.2433686,"\int \frac{\sqrt{e x} (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[(Sqrt[e*x]*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{\sqrt{e x} (a B-A c x)}{a c \sqrt{a+c x^2}}-\frac{A e x \sqrt{a+c x^2}}{a \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{\sqrt{e x} (a B-A c x)}{a c \sqrt{a+c x^2}}-\frac{A e x \sqrt{a+c x^2}}{a \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"-((Sqrt[e*x]*(a*B - A*c*x))/(a*c*Sqrt[a + c*x^2])) - (A*e*x*Sqrt[a + c*x^2])/(a*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (A*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((Sqrt[a]*B - A*Sqrt[c])*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(3/4)*c^(5/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{821, 842, 840, 1198, 220, 1196}"
470,1,290,0,0.2687664,"\int \frac{A+B x}{\sqrt{e x} \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[e*x]*(a + c*x^2)^(3/2)),x]","-\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{5/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{e x} (A+B x)}{a e \sqrt{a+c x^2}}-\frac{B x \sqrt{a+c x^2}}{a \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","-\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{5/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{3/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{e x} (A+B x)}{a e \sqrt{a+c x^2}}-\frac{B x \sqrt{a+c x^2}}{a \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(Sqrt[e*x]*(A + B*x))/(a*e*Sqrt[a + c*x^2]) - (B*x*Sqrt[a + c*x^2])/(a*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(3/4)*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - ((Sqrt[a]*B - A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(5/4)*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",6,6,24,0.2500,1,"{823, 842, 840, 1198, 220, 1196}"
471,1,327,0,0.3356228,"\int \frac{A+B x}{(e x)^{3/2} \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((e*x)^(3/2)*(a + c*x^2)^(3/2)),x]","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B+3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{3 A \sqrt{a+c x^2}}{a^2 e \sqrt{e x}}+\frac{3 A \sqrt{c} x \sqrt{a+c x^2}}{a^2 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{7/4} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{a e \sqrt{e x} \sqrt{a+c x^2}}","\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B+3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{3 A \sqrt{a+c x^2}}{a^2 e \sqrt{e x}}+\frac{3 A \sqrt{c} x \sqrt{a+c x^2}}{a^2 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{7/4} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{a e \sqrt{e x} \sqrt{a+c x^2}}",1,"(A + B*x)/(a*e*Sqrt[e*x]*Sqrt[a + c*x^2]) - (3*A*Sqrt[a + c*x^2])/(a^2*e*Sqrt[e*x]) + (3*A*Sqrt[c]*x*Sqrt[a + c*x^2])/(a^2*e*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (3*A*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(7/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((Sqrt[a]*B + 3*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(7/4)*c^(1/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{823, 835, 842, 840, 1198, 220, 1196}"
472,1,357,0,0.4165125,"\int \frac{A+B x}{(e x)^{5/2} \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((e*x)^(5/2)*(a + c*x^2)^(3/2)),x]","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(9 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{9/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{5 A \sqrt{a+c x^2}}{3 a^2 e (e x)^{3/2}}-\frac{3 B \sqrt{a+c x^2}}{a^2 e^2 \sqrt{e x}}+\frac{3 B \sqrt{c} x \sqrt{a+c x^2}}{a^2 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{7/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{a e (e x)^{3/2} \sqrt{a+c x^2}}","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(9 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{6 a^{9/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}-\frac{5 A \sqrt{a+c x^2}}{3 a^2 e (e x)^{3/2}}-\frac{3 B \sqrt{a+c x^2}}{a^2 e^2 \sqrt{e x}}+\frac{3 B \sqrt{c} x \sqrt{a+c x^2}}{a^2 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{3 B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{a^{7/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{a e (e x)^{3/2} \sqrt{a+c x^2}}",1,"(A + B*x)/(a*e*(e*x)^(3/2)*Sqrt[a + c*x^2]) - (5*A*Sqrt[a + c*x^2])/(3*a^2*e*(e*x)^(3/2)) - (3*B*Sqrt[a + c*x^2])/(a^2*e^2*Sqrt[e*x]) + (3*B*Sqrt[c]*x*Sqrt[a + c*x^2])/(a^2*e^2*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (3*B*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(a^(7/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((9*Sqrt[a]*B - 5*A*Sqrt[c])*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(6*a^(9/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{823, 835, 842, 840, 1198, 220, 1196}"
473,1,393,0,0.5038637,"\int \frac{A+B x}{(e x)^{7/2} \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((e*x)^(7/2)*(a + c*x^2)^(3/2)),x]","-\frac{c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B+63 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 a^{11/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{21 A c^{3/2} x \sqrt{a+c x^2}}{5 a^3 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{21 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{11/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{21 A c \sqrt{a+c x^2}}{5 a^3 e^3 \sqrt{e x}}-\frac{7 A \sqrt{a+c x^2}}{5 a^2 e (e x)^{5/2}}-\frac{5 B \sqrt{a+c x^2}}{3 a^2 e^2 (e x)^{3/2}}+\frac{A+B x}{a e (e x)^{5/2} \sqrt{a+c x^2}}","-\frac{c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B+63 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{30 a^{11/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}-\frac{21 A c^{3/2} x \sqrt{a+c x^2}}{5 a^3 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{21 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{5 a^{11/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{21 A c \sqrt{a+c x^2}}{5 a^3 e^3 \sqrt{e x}}-\frac{7 A \sqrt{a+c x^2}}{5 a^2 e (e x)^{5/2}}-\frac{5 B \sqrt{a+c x^2}}{3 a^2 e^2 (e x)^{3/2}}+\frac{A+B x}{a e (e x)^{5/2} \sqrt{a+c x^2}}",1,"(A + B*x)/(a*e*(e*x)^(5/2)*Sqrt[a + c*x^2]) - (7*A*Sqrt[a + c*x^2])/(5*a^2*e*(e*x)^(5/2)) - (5*B*Sqrt[a + c*x^2])/(3*a^2*e^2*(e*x)^(3/2)) + (21*A*c*Sqrt[a + c*x^2])/(5*a^3*e^3*Sqrt[e*x]) - (21*A*c^(3/2)*x*Sqrt[a + c*x^2])/(5*a^3*e^3*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (21*A*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(5*a^(11/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]) - ((25*Sqrt[a]*B + 63*A*Sqrt[c])*c^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(30*a^(11/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,7,24,0.2917,1,"{823, 835, 842, 840, 1198, 220, 1196}"
474,1,428,0,0.593881,"\int \frac{(e x)^{13/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^(13/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{a^{5/4} e^7 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(325 \sqrt{a} B-539 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{140 c^{17/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{77 a^{5/4} A e^7 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 c^{15/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e^3 (e x)^{7/2} (11 A+13 B x)}{6 c^2 \sqrt{a+c x^2}}-\frac{e (e x)^{11/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}-\frac{77 a A e^7 x \sqrt{a+c x^2}}{10 c^{7/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{77 A e^5 (e x)^{3/2} \sqrt{a+c x^2}}{30 c^3}-\frac{65 a B e^6 \sqrt{e x} \sqrt{a+c x^2}}{14 c^4}+\frac{39 B e^4 (e x)^{5/2} \sqrt{a+c x^2}}{14 c^3}","\frac{a^{5/4} e^7 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(325 \sqrt{a} B-539 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{140 c^{17/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{77 a^{5/4} A e^7 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 c^{15/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e^3 (e x)^{7/2} (11 A+13 B x)}{6 c^2 \sqrt{a+c x^2}}-\frac{e (e x)^{11/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}-\frac{77 a A e^7 x \sqrt{a+c x^2}}{10 c^{7/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{77 A e^5 (e x)^{3/2} \sqrt{a+c x^2}}{30 c^3}-\frac{65 a B e^6 \sqrt{e x} \sqrt{a+c x^2}}{14 c^4}+\frac{39 B e^4 (e x)^{5/2} \sqrt{a+c x^2}}{14 c^3}",1,"-(e*(e*x)^(11/2)*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (e^3*(e*x)^(7/2)*(11*A + 13*B*x))/(6*c^2*Sqrt[a + c*x^2]) - (65*a*B*e^6*Sqrt[e*x]*Sqrt[a + c*x^2])/(14*c^4) + (77*A*e^5*(e*x)^(3/2)*Sqrt[a + c*x^2])/(30*c^3) + (39*B*e^4*(e*x)^(5/2)*Sqrt[a + c*x^2])/(14*c^3) - (77*a*A*e^7*x*Sqrt[a + c*x^2])/(10*c^(7/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (77*a^(5/4)*A*e^7*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(10*c^(15/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + (a^(5/4)*(325*Sqrt[a]*B - 539*A*Sqrt[c])*e^7*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(140*c^(17/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",10,7,24,0.2917,1,"{819, 833, 842, 840, 1198, 220, 1196}"
475,1,398,0,0.4857419,"\int \frac{(e x)^{11/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^(11/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{a^{3/4} e^6 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(77 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 c^{15/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{77 a^{5/4} B e^6 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 c^{15/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e^3 (e x)^{5/2} (9 A+11 B x)}{6 c^2 \sqrt{a+c x^2}}-\frac{e (e x)^{9/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{5 A e^5 \sqrt{e x} \sqrt{a+c x^2}}{2 c^3}-\frac{77 a B e^6 x \sqrt{a+c x^2}}{10 c^{7/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{77 B e^4 (e x)^{3/2} \sqrt{a+c x^2}}{30 c^3}","-\frac{a^{3/4} e^6 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(77 \sqrt{a} B+25 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 c^{15/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{77 a^{5/4} B e^6 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 c^{15/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e^3 (e x)^{5/2} (9 A+11 B x)}{6 c^2 \sqrt{a+c x^2}}-\frac{e (e x)^{9/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{5 A e^5 \sqrt{e x} \sqrt{a+c x^2}}{2 c^3}-\frac{77 a B e^6 x \sqrt{a+c x^2}}{10 c^{7/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{77 B e^4 (e x)^{3/2} \sqrt{a+c x^2}}{30 c^3}",1,"-(e*(e*x)^(9/2)*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (e^3*(e*x)^(5/2)*(9*A + 11*B*x))/(6*c^2*Sqrt[a + c*x^2]) + (5*A*e^5*Sqrt[e*x]*Sqrt[a + c*x^2])/(2*c^3) + (77*B*e^4*(e*x)^(3/2)*Sqrt[a + c*x^2])/(30*c^3) - (77*a*B*e^6*x*Sqrt[a + c*x^2])/(10*c^(7/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (77*a^(5/4)*B*e^6*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(10*c^(15/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (a^(3/4)*(77*Sqrt[a]*B + 25*A*Sqrt[c])*e^6*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(20*c^(15/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,7,24,0.2917,1,"{819, 833, 842, 840, 1198, 220, 1196}"
476,1,368,0,0.4229629,"\int \frac{(e x)^{9/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^(9/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{e^3 (e x)^{3/2} (7 A+9 B x)}{6 c^2 \sqrt{a+c x^2}}-\frac{\sqrt[4]{a} e^5 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-7 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 c^{13/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{7/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{7 A e^5 x \sqrt{a+c x^2}}{2 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 \sqrt[4]{a} A e^5 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{5 B e^4 \sqrt{e x} \sqrt{a+c x^2}}{2 c^3}","-\frac{e^3 (e x)^{3/2} (7 A+9 B x)}{6 c^2 \sqrt{a+c x^2}}-\frac{\sqrt[4]{a} e^5 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-7 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 c^{13/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{7/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{7 A e^5 x \sqrt{a+c x^2}}{2 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 \sqrt[4]{a} A e^5 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{5 B e^4 \sqrt{e x} \sqrt{a+c x^2}}{2 c^3}",1,"-(e*(e*x)^(7/2)*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (e^3*(e*x)^(3/2)*(7*A + 9*B*x))/(6*c^2*Sqrt[a + c*x^2]) + (5*B*e^4*Sqrt[e*x]*Sqrt[a + c*x^2])/(2*c^3) + (7*A*e^5*x*Sqrt[a + c*x^2])/(2*c^(5/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (7*a^(1/4)*A*e^5*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - (a^(1/4)*(5*Sqrt[a]*B - 7*A*Sqrt[c])*e^5*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(4*c^(13/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{819, 833, 842, 840, 1198, 220, 1196}"
477,1,339,0,0.3383799,"\int \frac{(e x)^{7/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^(7/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{e^3 \sqrt{e x} (5 A+7 B x)}{6 c^2 \sqrt{a+c x^2}}+\frac{e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(21 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 \sqrt[4]{a} c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{5/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{7 B e^4 x \sqrt{a+c x^2}}{2 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 \sqrt[4]{a} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}","-\frac{e^3 \sqrt{e x} (5 A+7 B x)}{6 c^2 \sqrt{a+c x^2}}+\frac{e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(21 \sqrt{a} B+5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 \sqrt[4]{a} c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e (e x)^{5/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}+\frac{7 B e^4 x \sqrt{a+c x^2}}{2 c^{5/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 \sqrt[4]{a} B e^4 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 c^{11/4} \sqrt{e x} \sqrt{a+c x^2}}",1,"-(e*(e*x)^(5/2)*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (e^3*Sqrt[e*x]*(5*A + 7*B*x))/(6*c^2*Sqrt[a + c*x^2]) + (7*B*e^4*x*Sqrt[a + c*x^2])/(2*c^(5/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (7*a^(1/4)*B*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((21*Sqrt[a]*B + 5*A*Sqrt[c])*e^4*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(12*a^(1/4)*c^(11/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{819, 842, 840, 1198, 220, 1196}"
478,1,347,0,0.3436069,"\int \frac{(e x)^{5/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^(5/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{3/4} c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e^2 \sqrt{e x} (5 a B-3 A c x)}{6 a c^2 \sqrt{a+c x^2}}-\frac{e (e x)^{3/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}-\frac{A e^3 x \sqrt{a+c x^2}}{2 a c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B-3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{3/4} c^{9/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{A e^3 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{e^2 \sqrt{e x} (5 a B-3 A c x)}{6 a c^2 \sqrt{a+c x^2}}-\frac{e (e x)^{3/2} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}-\frac{A e^3 x \sqrt{a+c x^2}}{2 a c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"-(e*(e*x)^(3/2)*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) - (e^2*Sqrt[e*x]*(5*a*B - 3*A*c*x))/(6*a*c^2*Sqrt[a + c*x^2]) - (A*e^3*x*Sqrt[a + c*x^2])/(2*a*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (A*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(3/4)*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((5*Sqrt[a]*B - 3*A*Sqrt[c])*e^3*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(12*a^(3/4)*c^(9/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{819, 821, 842, 840, 1198, 220, 1196}"
479,1,341,0,0.3456099,"\int \frac{(e x)^{3/2} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^(3/2)*(A + B*x))/(a + c*x^2)^(5/2),x]","-\frac{e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{5/4} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{e \sqrt{e x} (A+3 B x)}{6 a c \sqrt{a+c x^2}}-\frac{e \sqrt{e x} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}-\frac{B e^2 x \sqrt{a+c x^2}}{2 a c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","-\frac{e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B-A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{5/4} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{B e^2 \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{3/4} c^{7/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{e \sqrt{e x} (A+3 B x)}{6 a c \sqrt{a+c x^2}}-\frac{e \sqrt{e x} (A+B x)}{3 c \left(a+c x^2\right)^{3/2}}-\frac{B e^2 x \sqrt{a+c x^2}}{2 a c^{3/2} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"-(e*Sqrt[e*x]*(A + B*x))/(3*c*(a + c*x^2)^(3/2)) + (e*Sqrt[e*x]*(A + 3*B*x))/(6*a*c*Sqrt[a + c*x^2]) - (B*e^2*x*Sqrt[a + c*x^2])/(2*a*c^(3/2)*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (B*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(3/4)*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - ((3*Sqrt[a]*B - A*Sqrt[c])*e^2*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(12*a^(5/4)*c^(7/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{819, 823, 842, 840, 1198, 220, 1196}"
480,1,342,0,0.34599,"\int \frac{\sqrt{e x} (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[(Sqrt[e*x]*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{7/4} c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{e x} (a B+3 A c x)}{6 a^2 c \sqrt{a+c x^2}}+\frac{A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{A e x \sqrt{a+c x^2}}{2 a^2 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt{e x} (a B-A c x)}{3 a c \left(a+c x^2\right)^{3/2}}","\frac{e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{a} B-3 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{7/4} c^{5/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{e x} (a B+3 A c x)}{6 a^2 c \sqrt{a+c x^2}}+\frac{A e \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{A e x \sqrt{a+c x^2}}{2 a^2 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt{e x} (a B-A c x)}{3 a c \left(a+c x^2\right)^{3/2}}",1,"-(Sqrt[e*x]*(a*B - A*c*x))/(3*a*c*(a + c*x^2)^(3/2)) + (Sqrt[e*x]*(a*B + 3*A*c*x))/(6*a^2*c*Sqrt[a + c*x^2]) - (A*e*x*Sqrt[a + c*x^2])/(2*a^2*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (A*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(7/4)*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((Sqrt[a]*B - 3*A*Sqrt[c])*e*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(12*a^(7/4)*c^(5/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,7,24,0.2917,1,"{821, 823, 842, 840, 1198, 220, 1196}"
481,1,335,0,0.3582846,"\int \frac{A+B x}{\sqrt{e x} \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(Sqrt[e*x]*(a + c*x^2)^(5/2)),x]","-\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{9/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{e x} (5 A+3 B x)}{6 a^2 e \sqrt{a+c x^2}}+\frac{B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{B x \sqrt{a+c x^2}}{2 a^2 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{\sqrt{e x} (A+B x)}{3 a e \left(a+c x^2\right)^{3/2}}","-\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(3 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{9/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{e x} (5 A+3 B x)}{6 a^2 e \sqrt{a+c x^2}}+\frac{B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{7/4} c^{3/4} \sqrt{e x} \sqrt{a+c x^2}}-\frac{B x \sqrt{a+c x^2}}{2 a^2 \sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{\sqrt{e x} (A+B x)}{3 a e \left(a+c x^2\right)^{3/2}}",1,"(Sqrt[e*x]*(A + B*x))/(3*a*e*(a + c*x^2)^(3/2)) + (Sqrt[e*x]*(5*A + 3*B*x))/(6*a^2*e*Sqrt[a + c*x^2]) - (B*x*Sqrt[a + c*x^2])/(2*a^2*Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(7/4)*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2]) - ((3*Sqrt[a]*B - 5*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(12*a^(9/4)*c^(3/4)*Sqrt[e*x]*Sqrt[a + c*x^2])","A",7,6,24,0.2500,1,"{823, 842, 840, 1198, 220, 1196}"
482,1,373,0,0.4217695,"\int \frac{A+B x}{(e x)^{3/2} \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((e*x)^(3/2)*(a + c*x^2)^(5/2)),x]","\frac{7 A+5 B x}{6 a^2 e \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+21 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{11/4} \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{7 A \sqrt{a+c x^2}}{2 a^3 e \sqrt{e x}}+\frac{7 A \sqrt{c} x \sqrt{a+c x^2}}{2 a^3 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{11/4} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{3 a e \sqrt{e x} \left(a+c x^2\right)^{3/2}}","\frac{7 A+5 B x}{6 a^2 e \sqrt{e x} \sqrt{a+c x^2}}+\frac{\sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 \sqrt{a} B+21 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{12 a^{11/4} \sqrt[4]{c} e \sqrt{e x} \sqrt{a+c x^2}}-\frac{7 A \sqrt{a+c x^2}}{2 a^3 e \sqrt{e x}}+\frac{7 A \sqrt{c} x \sqrt{a+c x^2}}{2 a^3 e \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 A \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{11/4} e \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{3 a e \sqrt{e x} \left(a+c x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*e*Sqrt[e*x]*(a + c*x^2)^(3/2)) + (7*A + 5*B*x)/(6*a^2*e*Sqrt[e*x]*Sqrt[a + c*x^2]) - (7*A*Sqrt[a + c*x^2])/(2*a^3*e*Sqrt[e*x]) + (7*A*Sqrt[c]*x*Sqrt[a + c*x^2])/(2*a^3*e*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (7*A*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(11/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((5*Sqrt[a]*B + 21*A*Sqrt[c])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(12*a^(11/4)*c^(1/4)*e*Sqrt[e*x]*Sqrt[a + c*x^2])","A",8,7,24,0.2917,1,"{823, 835, 842, 840, 1198, 220, 1196}"
483,1,402,0,0.4983179,"\int \frac{A+B x}{(e x)^{5/2} \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((e*x)^(5/2)*(a + c*x^2)^(5/2)),x]","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{13/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{9 A+7 B x}{6 a^2 e (e x)^{3/2} \sqrt{a+c x^2}}-\frac{5 A \sqrt{a+c x^2}}{2 a^3 e (e x)^{3/2}}-\frac{7 B \sqrt{a+c x^2}}{2 a^3 e^2 \sqrt{e x}}+\frac{7 B \sqrt{c} x \sqrt{a+c x^2}}{2 a^3 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{11/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{3 a e (e x)^{3/2} \left(a+c x^2\right)^{3/2}}","\frac{\sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(7 \sqrt{a} B-5 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{4 a^{13/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{9 A+7 B x}{6 a^2 e (e x)^{3/2} \sqrt{a+c x^2}}-\frac{5 A \sqrt{a+c x^2}}{2 a^3 e (e x)^{3/2}}-\frac{7 B \sqrt{a+c x^2}}{2 a^3 e^2 \sqrt{e x}}+\frac{7 B \sqrt{c} x \sqrt{a+c x^2}}{2 a^3 e^2 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{7 B \sqrt[4]{c} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{2 a^{11/4} e^2 \sqrt{e x} \sqrt{a+c x^2}}+\frac{A+B x}{3 a e (e x)^{3/2} \left(a+c x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*e*(e*x)^(3/2)*(a + c*x^2)^(3/2)) + (9*A + 7*B*x)/(6*a^2*e*(e*x)^(3/2)*Sqrt[a + c*x^2]) - (5*A*Sqrt[a + c*x^2])/(2*a^3*e*(e*x)^(3/2)) - (7*B*Sqrt[a + c*x^2])/(2*a^3*e^2*Sqrt[e*x]) + (7*B*Sqrt[c]*x*Sqrt[a + c*x^2])/(2*a^3*e^2*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (7*B*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(2*a^(11/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2]) + ((7*Sqrt[a]*B - 5*A*Sqrt[c])*c^(1/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(4*a^(13/4)*e^2*Sqrt[e*x]*Sqrt[a + c*x^2])","A",9,7,24,0.2917,1,"{823, 835, 842, 840, 1198, 220, 1196}"
484,1,432,0,0.5789264,"\int \frac{A+B x}{(e x)^{7/2} \left(a+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((e*x)^(7/2)*(a + c*x^2)^(5/2)),x]","-\frac{c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B+77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 a^{15/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{11 A+9 B x}{6 a^2 e (e x)^{5/2} \sqrt{a+c x^2}}-\frac{77 A c^{3/2} x \sqrt{a+c x^2}}{10 a^4 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{77 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{15/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{77 A c \sqrt{a+c x^2}}{10 a^4 e^3 \sqrt{e x}}-\frac{77 A \sqrt{a+c x^2}}{30 a^3 e (e x)^{5/2}}-\frac{5 B \sqrt{a+c x^2}}{2 a^3 e^2 (e x)^{3/2}}+\frac{A+B x}{3 a e (e x)^{5/2} \left(a+c x^2\right)^{3/2}}","-\frac{c^{3/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(25 \sqrt{a} B+77 A \sqrt{c}\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{20 a^{15/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{11 A+9 B x}{6 a^2 e (e x)^{5/2} \sqrt{a+c x^2}}-\frac{77 A c^{3/2} x \sqrt{a+c x^2}}{10 a^4 e^3 \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{77 A c^{5/4} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{2}\right)}{10 a^{15/4} e^3 \sqrt{e x} \sqrt{a+c x^2}}+\frac{77 A c \sqrt{a+c x^2}}{10 a^4 e^3 \sqrt{e x}}-\frac{77 A \sqrt{a+c x^2}}{30 a^3 e (e x)^{5/2}}-\frac{5 B \sqrt{a+c x^2}}{2 a^3 e^2 (e x)^{3/2}}+\frac{A+B x}{3 a e (e x)^{5/2} \left(a+c x^2\right)^{3/2}}",1,"(A + B*x)/(3*a*e*(e*x)^(5/2)*(a + c*x^2)^(3/2)) + (11*A + 9*B*x)/(6*a^2*e*(e*x)^(5/2)*Sqrt[a + c*x^2]) - (77*A*Sqrt[a + c*x^2])/(30*a^3*e*(e*x)^(5/2)) - (5*B*Sqrt[a + c*x^2])/(2*a^3*e^2*(e*x)^(3/2)) + (77*A*c*Sqrt[a + c*x^2])/(10*a^4*e^3*Sqrt[e*x]) - (77*A*c^(3/2)*x*Sqrt[a + c*x^2])/(10*a^4*e^3*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) + (77*A*c^(5/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(10*a^(15/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2]) - ((25*Sqrt[a]*B + 77*A*Sqrt[c])*c^(3/4)*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], 1/2])/(20*a^(15/4)*e^3*Sqrt[e*x]*Sqrt[a + c*x^2])","A",10,7,24,0.2917,1,"{823, 835, 842, 840, 1198, 220, 1196}"
485,1,217,0,0.1651502,"\int (e x)^m (A+B x) \left(a+c x^2\right)^4 \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2)^4,x]","\frac{6 a^2 A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{4 a^3 A c (e x)^{m+3}}{e^3 (m+3)}+\frac{a^4 A (e x)^{m+1}}{e (m+1)}+\frac{6 a^2 B c^2 (e x)^{m+6}}{e^6 (m+6)}+\frac{4 a^3 B c (e x)^{m+4}}{e^4 (m+4)}+\frac{a^4 B (e x)^{m+2}}{e^2 (m+2)}+\frac{4 a A c^3 (e x)^{m+7}}{e^7 (m+7)}+\frac{4 a B c^3 (e x)^{m+8}}{e^8 (m+8)}+\frac{A c^4 (e x)^{m+9}}{e^9 (m+9)}+\frac{B c^4 (e x)^{m+10}}{e^{10} (m+10)}","\frac{6 a^2 A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{4 a^3 A c (e x)^{m+3}}{e^3 (m+3)}+\frac{a^4 A (e x)^{m+1}}{e (m+1)}+\frac{6 a^2 B c^2 (e x)^{m+6}}{e^6 (m+6)}+\frac{4 a^3 B c (e x)^{m+4}}{e^4 (m+4)}+\frac{a^4 B (e x)^{m+2}}{e^2 (m+2)}+\frac{4 a A c^3 (e x)^{m+7}}{e^7 (m+7)}+\frac{4 a B c^3 (e x)^{m+8}}{e^8 (m+8)}+\frac{A c^4 (e x)^{m+9}}{e^9 (m+9)}+\frac{B c^4 (e x)^{m+10}}{e^{10} (m+10)}",1,"(a^4*A*(e*x)^(1 + m))/(e*(1 + m)) + (a^4*B*(e*x)^(2 + m))/(e^2*(2 + m)) + (4*a^3*A*c*(e*x)^(3 + m))/(e^3*(3 + m)) + (4*a^3*B*c*(e*x)^(4 + m))/(e^4*(4 + m)) + (6*a^2*A*c^2*(e*x)^(5 + m))/(e^5*(5 + m)) + (6*a^2*B*c^2*(e*x)^(6 + m))/(e^6*(6 + m)) + (4*a*A*c^3*(e*x)^(7 + m))/(e^7*(7 + m)) + (4*a*B*c^3*(e*x)^(8 + m))/(e^8*(8 + m)) + (A*c^4*(e*x)^(9 + m))/(e^9*(9 + m)) + (B*c^4*(e*x)^(10 + m))/(e^10*(10 + m))","A",2,1,20,0.05000,1,"{766}"
486,1,169,0,0.1024861,"\int (e x)^m (A+B x) \left(a+c x^2\right)^3 \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2)^3,x]","\frac{3 a^2 A c (e x)^{m+3}}{e^3 (m+3)}+\frac{a^3 A (e x)^{m+1}}{e (m+1)}+\frac{3 a^2 B c (e x)^{m+4}}{e^4 (m+4)}+\frac{a^3 B (e x)^{m+2}}{e^2 (m+2)}+\frac{3 a A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{3 a B c^2 (e x)^{m+6}}{e^6 (m+6)}+\frac{A c^3 (e x)^{m+7}}{e^7 (m+7)}+\frac{B c^3 (e x)^{m+8}}{e^8 (m+8)}","\frac{3 a^2 A c (e x)^{m+3}}{e^3 (m+3)}+\frac{a^3 A (e x)^{m+1}}{e (m+1)}+\frac{3 a^2 B c (e x)^{m+4}}{e^4 (m+4)}+\frac{a^3 B (e x)^{m+2}}{e^2 (m+2)}+\frac{3 a A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{3 a B c^2 (e x)^{m+6}}{e^6 (m+6)}+\frac{A c^3 (e x)^{m+7}}{e^7 (m+7)}+\frac{B c^3 (e x)^{m+8}}{e^8 (m+8)}",1,"(a^3*A*(e*x)^(1 + m))/(e*(1 + m)) + (a^3*B*(e*x)^(2 + m))/(e^2*(2 + m)) + (3*a^2*A*c*(e*x)^(3 + m))/(e^3*(3 + m)) + (3*a^2*B*c*(e*x)^(4 + m))/(e^4*(4 + m)) + (3*a*A*c^2*(e*x)^(5 + m))/(e^5*(5 + m)) + (3*a*B*c^2*(e*x)^(6 + m))/(e^6*(6 + m)) + (A*c^3*(e*x)^(7 + m))/(e^7*(7 + m)) + (B*c^3*(e*x)^(8 + m))/(e^8*(8 + m))","A",2,1,20,0.05000,1,"{766}"
487,1,121,0,0.0620844,"\int (e x)^m (A+B x) \left(a+c x^2\right)^2 \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2)^2,x]","\frac{a^2 A (e x)^{m+1}}{e (m+1)}+\frac{a^2 B (e x)^{m+2}}{e^2 (m+2)}+\frac{2 a A c (e x)^{m+3}}{e^3 (m+3)}+\frac{2 a B c (e x)^{m+4}}{e^4 (m+4)}+\frac{A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{B c^2 (e x)^{m+6}}{e^6 (m+6)}","\frac{a^2 A (e x)^{m+1}}{e (m+1)}+\frac{a^2 B (e x)^{m+2}}{e^2 (m+2)}+\frac{2 a A c (e x)^{m+3}}{e^3 (m+3)}+\frac{2 a B c (e x)^{m+4}}{e^4 (m+4)}+\frac{A c^2 (e x)^{m+5}}{e^5 (m+5)}+\frac{B c^2 (e x)^{m+6}}{e^6 (m+6)}",1,"(a^2*A*(e*x)^(1 + m))/(e*(1 + m)) + (a^2*B*(e*x)^(2 + m))/(e^2*(2 + m)) + (2*a*A*c*(e*x)^(3 + m))/(e^3*(3 + m)) + (2*a*B*c*(e*x)^(4 + m))/(e^4*(4 + m)) + (A*c^2*(e*x)^(5 + m))/(e^5*(5 + m)) + (B*c^2*(e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,20,0.05000,1,"{766}"
488,1,73,0,0.0325873,"\int (e x)^m (A+B x) \left(a+c x^2\right) \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2),x]","\frac{a A (e x)^{m+1}}{e (m+1)}+\frac{a B (e x)^{m+2}}{e^2 (m+2)}+\frac{A c (e x)^{m+3}}{e^3 (m+3)}+\frac{B c (e x)^{m+4}}{e^4 (m+4)}","\frac{a A (e x)^{m+1}}{e (m+1)}+\frac{a B (e x)^{m+2}}{e^2 (m+2)}+\frac{A c (e x)^{m+3}}{e^3 (m+3)}+\frac{B c (e x)^{m+4}}{e^4 (m+4)}",1,"(a*A*(e*x)^(1 + m))/(e*(1 + m)) + (a*B*(e*x)^(2 + m))/(e^2*(2 + m)) + (A*c*(e*x)^(3 + m))/(e^3*(3 + m)) + (B*c*(e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,18,0.05556,1,"{766}"
489,1,91,0,0.0421989,"\int \frac{(e x)^m (A+B x)}{a+c x^2} \, dx","Int[((e*x)^m*(A + B*x))/(a + c*x^2),x]","\frac{A (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a e (m+1)}+\frac{B (e x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a e^2 (m+2)}","\frac{A (e x)^{m+1} \, _2F_1\left(1,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a e (m+1)}+\frac{B (e x)^{m+2} \, _2F_1\left(1,\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a e^2 (m+2)}",1,"(A*(e*x)^(1 + m)*Hypergeometric2F1[1, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(a*e*(1 + m)) + (B*(e*x)^(2 + m)*Hypergeometric2F1[1, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(a*e^2*(2 + m))","A",3,2,20,0.1000,1,"{808, 364}"
490,1,91,0,0.039647,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^2} \, dx","Int[((e*x)^m*(A + B*x))/(a + c*x^2)^2,x]","\frac{A (e x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a^2 e (m+1)}+\frac{B (e x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a^2 e^2 (m+2)}","\frac{A (e x)^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a^2 e (m+1)}+\frac{B (e x)^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a^2 e^2 (m+2)}",1,"(A*(e*x)^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(a^2*e*(1 + m)) + (B*(e*x)^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(a^2*e^2*(2 + m))","A",3,2,20,0.1000,1,"{808, 364}"
491,1,91,0,0.0389993,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^3} \, dx","Int[((e*x)^m*(A + B*x))/(a + c*x^2)^3,x]","\frac{A (e x)^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a^3 e (m+1)}+\frac{B (e x)^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a^3 e^2 (m+2)}","\frac{A (e x)^{m+1} \, _2F_1\left(3,\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a^3 e (m+1)}+\frac{B (e x)^{m+2} \, _2F_1\left(3,\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a^3 e^2 (m+2)}",1,"(A*(e*x)^(1 + m)*Hypergeometric2F1[3, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(a^3*e*(1 + m)) + (B*(e*x)^(2 + m)*Hypergeometric2F1[3, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(a^3*e^2*(2 + m))","A",3,2,20,0.1000,1,"{808, 364}"
492,1,145,0,0.0762838,"\int (e x)^m (A+B x) \left(a+c x^2\right)^{5/2} \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2)^(5/2),x]","\frac{a^2 A \sqrt{a+c x^2} (e x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{\frac{c x^2}{a}+1}}+\frac{a^2 B \sqrt{a+c x^2} (e x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{\frac{c x^2}{a}+1}}","\frac{a^2 A \sqrt{a+c x^2} (e x)^{m+1} \, _2F_1\left(-\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{\frac{c x^2}{a}+1}}+\frac{a^2 B \sqrt{a+c x^2} (e x)^{m+2} \, _2F_1\left(-\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{\frac{c x^2}{a}+1}}",1,"(a^2*A*(e*x)^(1 + m)*Sqrt[a + c*x^2]*Hypergeometric2F1[-5/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(e*(1 + m)*Sqrt[1 + (c*x^2)/a]) + (a^2*B*(e*x)^(2 + m)*Sqrt[a + c*x^2]*Hypergeometric2F1[-5/2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(e^2*(2 + m)*Sqrt[1 + (c*x^2)/a])","A",5,3,22,0.1364,1,"{808, 365, 364}"
493,1,141,0,0.0680136,"\int (e x)^m (A+B x) \left(a+c x^2\right)^{3/2} \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2)^(3/2),x]","\frac{a A \sqrt{a+c x^2} (e x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{\frac{c x^2}{a}+1}}+\frac{a B \sqrt{a+c x^2} (e x)^{m+2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{\frac{c x^2}{a}+1}}","\frac{a A \sqrt{a+c x^2} (e x)^{m+1} \, _2F_1\left(-\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{\frac{c x^2}{a}+1}}+\frac{a B \sqrt{a+c x^2} (e x)^{m+2} \, _2F_1\left(-\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{\frac{c x^2}{a}+1}}",1,"(a*A*(e*x)^(1 + m)*Sqrt[a + c*x^2]*Hypergeometric2F1[-3/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(e*(1 + m)*Sqrt[1 + (c*x^2)/a]) + (a*B*(e*x)^(2 + m)*Sqrt[a + c*x^2]*Hypergeometric2F1[-3/2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(e^2*(2 + m)*Sqrt[1 + (c*x^2)/a])","A",5,3,22,0.1364,1,"{808, 365, 364}"
494,1,139,0,0.0646604,"\int (e x)^m (A+B x) \sqrt{a+c x^2} \, dx","Int[(e*x)^m*(A + B*x)*Sqrt[a + c*x^2],x]","\frac{A \sqrt{a+c x^2} (e x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{\frac{c x^2}{a}+1}}+\frac{B \sqrt{a+c x^2} (e x)^{m+2} \, _2F_1\left(-\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{\frac{c x^2}{a}+1}}","\frac{A \sqrt{a+c x^2} (e x)^{m+1} \, _2F_1\left(-\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{\frac{c x^2}{a}+1}}+\frac{B \sqrt{a+c x^2} (e x)^{m+2} \, _2F_1\left(-\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{\frac{c x^2}{a}+1}}",1,"(A*(e*x)^(1 + m)*Sqrt[a + c*x^2]*Hypergeometric2F1[-1/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(e*(1 + m)*Sqrt[1 + (c*x^2)/a]) + (B*(e*x)^(2 + m)*Sqrt[a + c*x^2]*Hypergeometric2F1[-1/2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(e^2*(2 + m)*Sqrt[1 + (c*x^2)/a])","A",5,3,22,0.1364,1,"{808, 365, 364}"
495,1,139,0,0.0631845,"\int \frac{(e x)^m (A+B x)}{\sqrt{a+c x^2}} \, dx","Int[((e*x)^m*(A + B*x))/Sqrt[a + c*x^2],x]","\frac{A \sqrt{\frac{c x^2}{a}+1} (e x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{a+c x^2}}+\frac{B \sqrt{\frac{c x^2}{a}+1} (e x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{a+c x^2}}","\frac{A \sqrt{\frac{c x^2}{a}+1} (e x)^{m+1} \, _2F_1\left(\frac{1}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1) \sqrt{a+c x^2}}+\frac{B \sqrt{\frac{c x^2}{a}+1} (e x)^{m+2} \, _2F_1\left(\frac{1}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2) \sqrt{a+c x^2}}",1,"(A*(e*x)^(1 + m)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(e*(1 + m)*Sqrt[a + c*x^2]) + (B*(e*x)^(2 + m)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[1/2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(e^2*(2 + m)*Sqrt[a + c*x^2])","A",5,3,22,0.1364,1,"{808, 365, 364}"
496,1,145,0,0.0693058,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((e*x)^m*(A + B*x))/(a + c*x^2)^(3/2),x]","\frac{A \sqrt{\frac{c x^2}{a}+1} (e x)^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a e (m+1) \sqrt{a+c x^2}}+\frac{B \sqrt{\frac{c x^2}{a}+1} (e x)^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a e^2 (m+2) \sqrt{a+c x^2}}","\frac{A \sqrt{\frac{c x^2}{a}+1} (e x)^{m+1} \, _2F_1\left(\frac{3}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a e (m+1) \sqrt{a+c x^2}}+\frac{B \sqrt{\frac{c x^2}{a}+1} (e x)^{m+2} \, _2F_1\left(\frac{3}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a e^2 (m+2) \sqrt{a+c x^2}}",1,"(A*(e*x)^(1 + m)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[3/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(a*e*(1 + m)*Sqrt[a + c*x^2]) + (B*(e*x)^(2 + m)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[3/2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(a*e^2*(2 + m)*Sqrt[a + c*x^2])","A",5,3,22,0.1364,1,"{808, 365, 364}"
497,1,145,0,0.0674913,"\int \frac{(e x)^m (A+B x)}{\left(a+c x^2\right)^{5/2}} \, dx","Int[((e*x)^m*(A + B*x))/(a + c*x^2)^(5/2),x]","\frac{A \sqrt{\frac{c x^2}{a}+1} (e x)^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a^2 e (m+1) \sqrt{a+c x^2}}+\frac{B \sqrt{\frac{c x^2}{a}+1} (e x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a^2 e^2 (m+2) \sqrt{a+c x^2}}","\frac{A \sqrt{\frac{c x^2}{a}+1} (e x)^{m+1} \, _2F_1\left(\frac{5}{2},\frac{m+1}{2};\frac{m+3}{2};-\frac{c x^2}{a}\right)}{a^2 e (m+1) \sqrt{a+c x^2}}+\frac{B \sqrt{\frac{c x^2}{a}+1} (e x)^{m+2} \, _2F_1\left(\frac{5}{2},\frac{m+2}{2};\frac{m+4}{2};-\frac{c x^2}{a}\right)}{a^2 e^2 (m+2) \sqrt{a+c x^2}}",1,"(A*(e*x)^(1 + m)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[5/2, (1 + m)/2, (3 + m)/2, -((c*x^2)/a)])/(a^2*e*(1 + m)*Sqrt[a + c*x^2]) + (B*(e*x)^(2 + m)*Sqrt[1 + (c*x^2)/a]*Hypergeometric2F1[5/2, (2 + m)/2, (4 + m)/2, -((c*x^2)/a)])/(a^2*e^2*(2 + m)*Sqrt[a + c*x^2])","A",5,3,22,0.1364,1,"{808, 365, 364}"
498,1,70,0,0.0233617,"\int \frac{x^m (1+a x)}{\left(1-a^2 x^2\right)^2} \, dx","Int[(x^m*(1 + a*x))/(1 - a^2*x^2)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",3,2,21,0.09524,1,"{808, 364}"
499,1,70,0,0.0197647,"\int \frac{x^m}{(1-a x)^2 (1+a x)} \, dx","Int[x^m/((1 - a*x)^2*(1 + a*x)),x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",5,3,19,0.1579,1,"{82, 73, 364}"
500,1,70,0,0.0231833,"\int \left(\frac{x^m}{\left(1-a^2 x^2\right)^2}+\frac{a x^{1+m}}{\left(1-a^2 x^2\right)^2}\right) \, dx","Int[x^m/(1 - a^2*x^2)^2 + (a*x^(1 + m))/(1 - a^2*x^2)^2,x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",3,1,36,0.02778,1,"{364}"
501,1,70,0,0.0343823,"\int \frac{x^m}{(1-a x) \left(1-a^2 x^2\right)} \, dx","Int[x^m/((1 - a*x)*(1 - a^2*x^2)),x]","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}","\frac{x^{m+1} \, _2F_1\left(2,\frac{m+1}{2};\frac{m+3}{2};a^2 x^2\right)}{m+1}+\frac{a x^{m+2} \, _2F_1\left(2,\frac{m+2}{2};\frac{m+4}{2};a^2 x^2\right)}{m+2}",1,"(x^(1 + m)*Hypergeometric2F1[2, (1 + m)/2, (3 + m)/2, a^2*x^2])/(1 + m) + (a*x^(2 + m)*Hypergeometric2F1[2, (2 + m)/2, (4 + m)/2, a^2*x^2])/(2 + m)","A",6,4,24,0.1667,1,"{848, 82, 73, 364}"
502,1,135,0,0.0552938,"\int (e x)^m (A+B x) \left(a+c x^2\right)^p \, dx","Int[(e*x)^m*(A + B*x)*(a + c*x^2)^p,x]","\frac{A (e x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1)}+\frac{B (e x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2)}","\frac{A (e x)^{m+1} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+1}{2},-p;\frac{m+3}{2};-\frac{c x^2}{a}\right)}{e (m+1)}+\frac{B (e x)^{m+2} \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{m+2}{2},-p;\frac{m+4}{2};-\frac{c x^2}{a}\right)}{e^2 (m+2)}",1,"(A*(e*x)^(1 + m)*(a + c*x^2)^p*Hypergeometric2F1[(1 + m)/2, -p, (3 + m)/2, -((c*x^2)/a)])/(e*(1 + m)*(1 + (c*x^2)/a)^p) + (B*(e*x)^(2 + m)*(a + c*x^2)^p*Hypergeometric2F1[(2 + m)/2, -p, (4 + m)/2, -((c*x^2)/a)])/(e^2*(2 + m)*(1 + (c*x^2)/a)^p)","A",5,3,20,0.1500,1,"{808, 365, 364}"
503,1,100,0,0.0609412,"\int x^3 (d+e x) \left(a+c x^2\right)^p \, dx","Int[x^3*(d + e*x)*(a + c*x^2)^p,x]","-\frac{a d \left(a+c x^2\right)^{p+1}}{2 c^2 (p+1)}+\frac{d \left(a+c x^2\right)^{p+2}}{2 c^2 (p+2)}+\frac{1}{5} e x^5 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{c x^2}{a}\right)","-\frac{a d \left(a+c x^2\right)^{p+1}}{2 c^2 (p+1)}+\frac{d \left(a+c x^2\right)^{p+2}}{2 c^2 (p+2)}+\frac{1}{5} e x^5 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{5}{2},-p;\frac{7}{2};-\frac{c x^2}{a}\right)",1,"-(a*d*(a + c*x^2)^(1 + p))/(2*c^2*(1 + p)) + (d*(a + c*x^2)^(2 + p))/(2*c^2*(2 + p)) + (e*x^5*(a + c*x^2)^p*Hypergeometric2F1[5/2, -p, 7/2, -((c*x^2)/a)])/(5*(1 + (c*x^2)/a)^p)","A",6,5,18,0.2778,1,"{764, 266, 43, 365, 364}"
504,1,100,0,0.0604735,"\int x^2 (d+e x) \left(a+c x^2\right)^p \, dx","Int[x^2*(d + e*x)*(a + c*x^2)^p,x]","-\frac{a e \left(a+c x^2\right)^{p+1}}{2 c^2 (p+1)}+\frac{e \left(a+c x^2\right)^{p+2}}{2 c^2 (p+2)}+\frac{1}{3} d x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{c x^2}{a}\right)","-\frac{a e \left(a+c x^2\right)^{p+1}}{2 c^2 (p+1)}+\frac{e \left(a+c x^2\right)^{p+2}}{2 c^2 (p+2)}+\frac{1}{3} d x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{c x^2}{a}\right)",1,"-(a*e*(a + c*x^2)^(1 + p))/(2*c^2*(1 + p)) + (e*(a + c*x^2)^(2 + p))/(2*c^2*(2 + p)) + (d*x^3*(a + c*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((c*x^2)/a)])/(3*(1 + (c*x^2)/a)^p)","A",6,5,18,0.2778,1,"{764, 365, 364, 266, 43}"
505,1,75,0,0.0283265,"\int x (d+e x) \left(a+c x^2\right)^p \, dx","Int[x*(d + e*x)*(a + c*x^2)^p,x]","\frac{d \left(a+c x^2\right)^{p+1}}{2 c (p+1)}+\frac{1}{3} e x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{c x^2}{a}\right)","\frac{d \left(a+c x^2\right)^{p+1}}{2 c (p+1)}+\frac{1}{3} e x^3 \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{3}{2},-p;\frac{5}{2};-\frac{c x^2}{a}\right)",1,"(d*(a + c*x^2)^(1 + p))/(2*c*(1 + p)) + (e*x^3*(a + c*x^2)^p*Hypergeometric2F1[3/2, -p, 5/2, -((c*x^2)/a)])/(3*(1 + (c*x^2)/a)^p)","A",4,4,16,0.2500,1,"{764, 261, 365, 364}"
506,1,70,0,0.0190127,"\int (d+e x) \left(a+c x^2\right)^p \, dx","Int[(d + e*x)*(a + c*x^2)^p,x]","d x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)+\frac{e \left(a+c x^2\right)^{p+1}}{2 c (p+1)}","d x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)+\frac{e \left(a+c x^2\right)^{p+1}}{2 c (p+1)}",1,"(e*(a + c*x^2)^(1 + p))/(2*c*(1 + p)) + (d*x*(a + c*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p","A",3,3,15,0.2000,1,"{641, 246, 245}"
507,1,88,0,0.0453921,"\int \frac{(d+e x) \left(a+c x^2\right)^p}{x} \, dx","Int[((d + e*x)*(a + c*x^2)^p)/x,x]","e x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)-\frac{d \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{c x^2}{a}+1\right)}{2 a (p+1)}","e x \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(\frac{1}{2},-p;\frac{3}{2};-\frac{c x^2}{a}\right)-\frac{d \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{c x^2}{a}+1\right)}{2 a (p+1)}",1,"(e*x*(a + c*x^2)^p*Hypergeometric2F1[1/2, -p, 3/2, -((c*x^2)/a)])/(1 + (c*x^2)/a)^p - (d*(a + c*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (c*x^2)/a])/(2*a*(1 + p))","A",5,5,18,0.2778,1,"{764, 266, 65, 246, 245}"
508,1,91,0,0.047138,"\int \frac{(d+e x) \left(a+c x^2\right)^p}{x^2} \, dx","Int[((d + e*x)*(a + c*x^2)^p)/x^2,x]","-\frac{d \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{c x^2}{a}\right)}{x}-\frac{e \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{c x^2}{a}+1\right)}{2 a (p+1)}","-\frac{d \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{c x^2}{a}\right)}{x}-\frac{e \left(a+c x^2\right)^{p+1} \, _2F_1\left(1,p+1;p+2;\frac{c x^2}{a}+1\right)}{2 a (p+1)}",1,"-((d*(a + c*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((c*x^2)/a)])/(x*(1 + (c*x^2)/a)^p)) - (e*(a + c*x^2)^(1 + p)*Hypergeometric2F1[1, 1 + p, 2 + p, 1 + (c*x^2)/a])/(2*a*(1 + p))","A",5,5,18,0.2778,1,"{764, 365, 364, 266, 65}"
509,1,92,0,0.0503845,"\int \frac{(d+e x) \left(a+c x^2\right)^p}{x^3} \, dx","Int[((d + e*x)*(a + c*x^2)^p)/x^3,x]","\frac{c d \left(a+c x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{c x^2}{a}+1\right)}{2 a^2 (p+1)}-\frac{e \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{c x^2}{a}\right)}{x}","\frac{c d \left(a+c x^2\right)^{p+1} \, _2F_1\left(2,p+1;p+2;\frac{c x^2}{a}+1\right)}{2 a^2 (p+1)}-\frac{e \left(a+c x^2\right)^p \left(\frac{c x^2}{a}+1\right)^{-p} \, _2F_1\left(-\frac{1}{2},-p;\frac{1}{2};-\frac{c x^2}{a}\right)}{x}",1,"-((e*(a + c*x^2)^p*Hypergeometric2F1[-1/2, -p, 1/2, -((c*x^2)/a)])/(x*(1 + (c*x^2)/a)^p)) + (c*d*(a + c*x^2)^(1 + p)*Hypergeometric2F1[2, 1 + p, 2 + p, 1 + (c*x^2)/a])/(2*a^2*(1 + p))","A",5,5,18,0.2778,1,"{764, 266, 65, 365, 364}"
510,1,55,0,0.0483102,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{5} a^2 A x^5+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{6} a x^6 (a B+2 A b)+\frac{1}{8} b^2 B x^8","\frac{1}{5} a^2 A x^5+\frac{1}{7} b x^7 (2 a B+A b)+\frac{1}{6} a x^6 (a B+2 A b)+\frac{1}{8} b^2 B x^8",1,"(a^2*A*x^5)/5 + (a*(2*A*b + a*B)*x^6)/6 + (b*(A*b + 2*a*B)*x^7)/7 + (b^2*B*x^8)/8","A",3,2,25,0.08000,1,"{27, 76}"
511,1,55,0,0.0386783,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{4} a^2 A x^4+\frac{1}{6} b x^6 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{7} b^2 B x^7","\frac{1}{4} a^2 A x^4+\frac{1}{6} b x^6 (2 a B+A b)+\frac{1}{5} a x^5 (a B+2 A b)+\frac{1}{7} b^2 B x^7",1,"(a^2*A*x^4)/4 + (a*(2*A*b + a*B)*x^5)/5 + (b*(A*b + 2*a*B)*x^6)/6 + (b^2*B*x^7)/7","A",3,2,25,0.08000,1,"{27, 76}"
512,1,55,0,0.0317878,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{3} a^2 A x^3+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{6} b^2 B x^6","\frac{1}{3} a^2 A x^3+\frac{1}{5} b x^5 (2 a B+A b)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{6} b^2 B x^6",1,"(a^2*A*x^3)/3 + (a*(2*A*b + a*B)*x^4)/4 + (b*(A*b + 2*a*B)*x^5)/5 + (b^2*B*x^6)/6","A",3,2,25,0.08000,1,"{27, 76}"
513,1,55,0,0.0290921,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{1}{2} a^2 A x^2+\frac{1}{4} b x^4 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{5} b^2 B x^5","\frac{1}{2} a^2 A x^2+\frac{1}{4} b x^4 (2 a B+A b)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{5} b^2 B x^5",1,"(a^2*A*x^2)/2 + (a*(2*A*b + a*B)*x^3)/3 + (b*(A*b + 2*a*B)*x^4)/4 + (b^2*B*x^5)/5","A",3,2,23,0.08696,1,"{27, 76}"
514,1,38,0,0.0209887,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"((A*b - a*B)*(a + b*x)^3)/(3*b^2) + (B*(a + b*x)^4)/(4*b^2)","A",3,2,22,0.09091,1,"{27, 43}"
515,1,40,0,0.0126781,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x,x]","a^2 A \log (x)+2 a A b x+\frac{B (a+b x)^3}{3 b}+\frac{1}{2} A b^2 x^2","a^2 A \log (x)+2 a A b x+\frac{B (a+b x)^3}{3 b}+\frac{1}{2} A b^2 x^2",1,"2*a*A*b*x + (A*b^2*x^2)/2 + (B*(a + b*x)^3)/(3*b) + a^2*A*Log[x]","A",4,3,25,0.1200,1,"{27, 80, 43}"
516,1,44,0,0.026999,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^2,x]","-\frac{a^2 A}{x}+b x (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{2} b^2 B x^2","-\frac{a^2 A}{x}+b x (2 a B+A b)+a \log (x) (a B+2 A b)+\frac{1}{2} b^2 B x^2",1,"-((a^2*A)/x) + b*(A*b + 2*a*B)*x + (b^2*B*x^2)/2 + a*(2*A*b + a*B)*Log[x]","A",3,2,25,0.08000,1,"{27, 76}"
517,1,44,0,0.0244103,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^3,x]","-\frac{a^2 A}{2 x^2}-\frac{a (a B+2 A b)}{x}+b \log (x) (2 a B+A b)+b^2 B x","-\frac{a^2 A}{2 x^2}-\frac{a (a B+2 A b)}{x}+b \log (x) (2 a B+A b)+b^2 B x",1,"-(a^2*A)/(2*x^2) - (a*(2*A*b + a*B))/x + b^2*B*x + b*(A*b + 2*a*B)*Log[x]","A",3,2,25,0.08000,1,"{27, 76}"
518,1,49,0,0.0240986,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^4,x]","-\frac{a^2 A}{3 x^3}-\frac{a (a B+2 A b)}{2 x^2}-\frac{b (2 a B+A b)}{x}+b^2 B \log (x)","-\frac{a^2 A}{3 x^3}-\frac{a (a B+2 A b)}{2 x^2}-\frac{b (2 a B+A b)}{x}+b^2 B \log (x)",1,"-(a^2*A)/(3*x^3) - (a*(2*A*b + a*B))/(2*x^2) - (b*(A*b + 2*a*B))/x + b^2*B*Log[x]","A",3,2,25,0.08000,1,"{27, 76}"
519,1,44,0,0.0113715,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^5,x]","\frac{(a+b x)^3 (A b-4 a B)}{12 a^2 x^3}-\frac{A (a+b x)^3}{4 a x^4}","\frac{(a+b x)^3 (A b-4 a B)}{12 a^2 x^3}-\frac{A (a+b x)^3}{4 a x^4}",1,"-(A*(a + b*x)^3)/(4*a*x^4) + ((A*b - 4*a*B)*(a + b*x)^3)/(12*a^2*x^3)","A",3,3,25,0.1200,1,"{27, 78, 37}"
520,1,55,0,0.0235665,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^6,x]","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{2 x^2}","-\frac{a^2 A}{5 x^5}-\frac{a (a B+2 A b)}{4 x^4}-\frac{b (2 a B+A b)}{3 x^3}-\frac{b^2 B}{2 x^2}",1,"-(a^2*A)/(5*x^5) - (a*(2*A*b + a*B))/(4*x^4) - (b*(A*b + 2*a*B))/(3*x^3) - (b^2*B)/(2*x^2)","A",3,2,25,0.08000,1,"{27, 76}"
521,1,55,0,0.0238052,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^7,x]","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3}","-\frac{a^2 A}{6 x^6}-\frac{a (a B+2 A b)}{5 x^5}-\frac{b (2 a B+A b)}{4 x^4}-\frac{b^2 B}{3 x^3}",1,"-(a^2*A)/(6*x^6) - (a*(2*A*b + a*B))/(5*x^5) - (b*(A*b + 2*a*B))/(4*x^4) - (b^2*B)/(3*x^3)","A",3,2,25,0.08000,1,"{27, 76}"
522,1,55,0,0.0246974,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^8,x]","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{6 x^6}-\frac{b (2 a B+A b)}{5 x^5}-\frac{b^2 B}{4 x^4}","-\frac{a^2 A}{7 x^7}-\frac{a (a B+2 A b)}{6 x^6}-\frac{b (2 a B+A b)}{5 x^5}-\frac{b^2 B}{4 x^4}",1,"-(a^2*A)/(7*x^7) - (a*(2*A*b + a*B))/(6*x^6) - (b*(A*b + 2*a*B))/(5*x^5) - (b^2*B)/(4*x^4)","A",3,2,25,0.08000,1,"{27, 76}"
523,1,99,0,0.0840065,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2}{7} a^2 b x^7 (2 a B+3 A b)+\frac{1}{6} a^3 x^6 (a B+4 A b)+\frac{1}{5} a^4 A x^5+\frac{1}{9} b^3 x^9 (4 a B+A b)+\frac{1}{4} a b^2 x^8 (3 a B+2 A b)+\frac{1}{10} b^4 B x^{10}","\frac{2}{7} a^2 b x^7 (2 a B+3 A b)+\frac{1}{6} a^3 x^6 (a B+4 A b)+\frac{1}{5} a^4 A x^5+\frac{1}{9} b^3 x^9 (4 a B+A b)+\frac{1}{4} a b^2 x^8 (3 a B+2 A b)+\frac{1}{10} b^4 B x^{10}",1,"(a^4*A*x^5)/5 + (a^3*(4*A*b + a*B)*x^6)/6 + (2*a^2*b*(3*A*b + 2*a*B)*x^7)/7 + (a*b^2*(2*A*b + 3*a*B)*x^8)/4 + (b^3*(A*b + 4*a*B)*x^9)/9 + (b^4*B*x^10)/10","A",3,2,27,0.07407,1,"{27, 76}"
524,1,99,0,0.0570259,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{1}{3} a^2 b x^6 (2 a B+3 A b)+\frac{1}{5} a^3 x^5 (a B+4 A b)+\frac{1}{4} a^4 A x^4+\frac{1}{8} b^3 x^8 (4 a B+A b)+\frac{2}{7} a b^2 x^7 (3 a B+2 A b)+\frac{1}{9} b^4 B x^9","\frac{1}{3} a^2 b x^6 (2 a B+3 A b)+\frac{1}{5} a^3 x^5 (a B+4 A b)+\frac{1}{4} a^4 A x^4+\frac{1}{8} b^3 x^8 (4 a B+A b)+\frac{2}{7} a b^2 x^7 (3 a B+2 A b)+\frac{1}{9} b^4 B x^9",1,"(a^4*A*x^4)/4 + (a^3*(4*A*b + a*B)*x^5)/5 + (a^2*b*(3*A*b + 2*a*B)*x^6)/3 + (2*a*b^2*(2*A*b + 3*a*B)*x^7)/7 + (b^3*(A*b + 4*a*B)*x^8)/8 + (b^4*B*x^9)/9","A",3,2,27,0.07407,1,"{27, 76}"
525,1,87,0,0.0529759,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{a^2 (a+b x)^5 (A b-a B)}{5 b^4}+\frac{(a+b x)^7 (A b-3 a B)}{7 b^4}-\frac{a (a+b x)^6 (2 A b-3 a B)}{6 b^4}+\frac{B (a+b x)^8}{8 b^4}","\frac{a^2 (a+b x)^5 (A b-a B)}{5 b^4}+\frac{(a+b x)^7 (A b-3 a B)}{7 b^4}-\frac{a (a+b x)^6 (2 A b-3 a B)}{6 b^4}+\frac{B (a+b x)^8}{8 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x)^5)/(5*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^6)/(6*b^4) + ((A*b - 3*a*B)*(a + b*x)^7)/(7*b^4) + (B*(a + b*x)^8)/(8*b^4)","A",3,2,27,0.07407,1,"{27, 76}"
526,1,61,0,0.0405671,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^6 (A b-2 a B)}{6 b^3}-\frac{a (a+b x)^5 (A b-a B)}{5 b^3}+\frac{B (a+b x)^7}{7 b^3}","\frac{(a+b x)^6 (A b-2 a B)}{6 b^3}-\frac{a (a+b x)^5 (A b-a B)}{5 b^3}+\frac{B (a+b x)^7}{7 b^3}",1,"-(a*(A*b - a*B)*(a + b*x)^5)/(5*b^3) + ((A*b - 2*a*B)*(a + b*x)^6)/(6*b^3) + (B*(a + b*x)^7)/(7*b^3)","A",3,2,25,0.08000,1,"{27, 76}"
527,1,38,0,0.0143632,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2}","\frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2}",1,"((A*b - a*B)*(a + b*x)^5)/(5*b^2) + (B*(a + b*x)^6)/(6*b^2)","A",3,2,24,0.08333,1,"{27, 43}"
528,1,66,0,0.0226127,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x,x]","3 a^2 A b^2 x^2+4 a^3 A b x+a^4 A \log (x)+\frac{4}{3} a A b^3 x^3+\frac{B (a+b x)^5}{5 b}+\frac{1}{4} A b^4 x^4","3 a^2 A b^2 x^2+4 a^3 A b x+a^4 A \log (x)+\frac{4}{3} a A b^3 x^3+\frac{B (a+b x)^5}{5 b}+\frac{1}{4} A b^4 x^4",1,"4*a^3*A*b*x + 3*a^2*A*b^2*x^2 + (4*a*A*b^3*x^3)/3 + (A*b^4*x^4)/4 + (B*(a + b*x)^5)/(5*b) + a^4*A*Log[x]","A",4,3,27,0.1111,1,"{27, 80, 43}"
529,1,86,0,0.0506458,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^2,x]","2 a^2 b x (2 a B+3 A b)+a^3 \log (x) (a B+4 A b)-\frac{a^4 A}{x}+a b^2 x^2 (3 a B+2 A b)+\frac{1}{3} b^3 x^3 (4 a B+A b)+\frac{1}{4} b^4 B x^4","2 a^2 b x (2 a B+3 A b)+a^3 \log (x) (a B+4 A b)-\frac{a^4 A}{x}+a b^2 x^2 (3 a B+2 A b)+\frac{1}{3} b^3 x^3 (4 a B+A b)+\frac{1}{4} b^4 B x^4",1,"-((a^4*A)/x) + 2*a^2*b*(3*A*b + 2*a*B)*x + a*b^2*(2*A*b + 3*a*B)*x^2 + (b^3*(A*b + 4*a*B)*x^3)/3 + (b^4*B*x^4)/4 + a^3*(4*A*b + a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
530,1,90,0,0.0504487,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^3,x]","-\frac{a^3 (a B+4 A b)}{x}+2 a^2 b \log (x) (2 a B+3 A b)-\frac{a^4 A}{2 x^2}+\frac{1}{2} b^3 x^2 (4 a B+A b)+2 a b^2 x (3 a B+2 A b)+\frac{1}{3} b^4 B x^3","-\frac{a^3 (a B+4 A b)}{x}+2 a^2 b \log (x) (2 a B+3 A b)-\frac{a^4 A}{2 x^2}+\frac{1}{2} b^3 x^2 (4 a B+A b)+2 a b^2 x (3 a B+2 A b)+\frac{1}{3} b^4 B x^3",1,"-(a^4*A)/(2*x^2) - (a^3*(4*A*b + a*B))/x + 2*a*b^2*(2*A*b + 3*a*B)*x + (b^3*(A*b + 4*a*B)*x^2)/2 + (b^4*B*x^3)/3 + 2*a^2*b*(3*A*b + 2*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
531,1,89,0,0.0543838,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^4,x]","-\frac{a^3 (a B+4 A b)}{2 x^2}-\frac{2 a^2 b (2 a B+3 A b)}{x}-\frac{a^4 A}{3 x^3}+b^3 x (4 a B+A b)+2 a b^2 \log (x) (3 a B+2 A b)+\frac{1}{2} b^4 B x^2","-\frac{a^3 (a B+4 A b)}{2 x^2}-\frac{2 a^2 b (2 a B+3 A b)}{x}-\frac{a^4 A}{3 x^3}+b^3 x (4 a B+A b)+2 a b^2 \log (x) (3 a B+2 A b)+\frac{1}{2} b^4 B x^2",1,"-(a^4*A)/(3*x^3) - (a^3*(4*A*b + a*B))/(2*x^2) - (2*a^2*b*(3*A*b + 2*a*B))/x + b^3*(A*b + 4*a*B)*x + (b^4*B*x^2)/2 + 2*a*b^2*(2*A*b + 3*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
532,1,86,0,0.0472656,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^5,x]","-\frac{a^3 (a B+4 A b)}{3 x^3}-\frac{a^2 b (2 a B+3 A b)}{x^2}-\frac{a^4 A}{4 x^4}-\frac{2 a b^2 (3 a B+2 A b)}{x}+b^3 \log (x) (4 a B+A b)+b^4 B x","-\frac{a^3 (a B+4 A b)}{3 x^3}-\frac{a^2 b (2 a B+3 A b)}{x^2}-\frac{a^4 A}{4 x^4}-\frac{2 a b^2 (3 a B+2 A b)}{x}+b^3 \log (x) (4 a B+A b)+b^4 B x",1,"-(a^4*A)/(4*x^4) - (a^3*(4*A*b + a*B))/(3*x^3) - (a^2*b*(3*A*b + 2*a*B))/x^2 - (2*a*b^2*(2*A*b + 3*a*B))/x + b^4*B*x + b^3*(A*b + 4*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
533,1,71,0,0.0293582,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^6,x]","-\frac{3 a^2 b^2 B}{x^2}-\frac{4 a^3 b B}{3 x^3}-\frac{a^4 B}{4 x^4}-\frac{A (a+b x)^5}{5 a x^5}-\frac{4 a b^3 B}{x}+b^4 B \log (x)","-\frac{3 a^2 b^2 B}{x^2}-\frac{4 a^3 b B}{3 x^3}-\frac{a^4 B}{4 x^4}-\frac{A (a+b x)^5}{5 a x^5}-\frac{4 a b^3 B}{x}+b^4 B \log (x)",1,"-(a^4*B)/(4*x^4) - (4*a^3*b*B)/(3*x^3) - (3*a^2*b^2*B)/x^2 - (4*a*b^3*B)/x - (A*(a + b*x)^5)/(5*a*x^5) + b^4*B*Log[x]","A",4,3,27,0.1111,1,"{27, 78, 43}"
534,1,44,0,0.012025,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^7,x]","\frac{(a+b x)^5 (A b-6 a B)}{30 a^2 x^5}-\frac{A (a+b x)^5}{6 a x^6}","\frac{(a+b x)^5 (A b-6 a B)}{30 a^2 x^5}-\frac{A (a+b x)^5}{6 a x^6}",1,"-(A*(a + b*x)^5)/(6*a*x^6) + ((A*b - 6*a*B)*(a + b*x)^5)/(30*a^2*x^5)","A",3,3,27,0.1111,1,"{27, 78, 37}"
535,1,99,0,0.0476249,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^8,x]","-\frac{a^3 (a B+4 A b)}{6 x^6}-\frac{2 a^2 b (2 a B+3 A b)}{5 x^5}-\frac{a^4 A}{7 x^7}-\frac{a b^2 (3 a B+2 A b)}{2 x^4}-\frac{b^3 (4 a B+A b)}{3 x^3}-\frac{b^4 B}{2 x^2}","-\frac{a^3 (a B+4 A b)}{6 x^6}-\frac{2 a^2 b (2 a B+3 A b)}{5 x^5}-\frac{a^4 A}{7 x^7}-\frac{a b^2 (3 a B+2 A b)}{2 x^4}-\frac{b^3 (4 a B+A b)}{3 x^3}-\frac{b^4 B}{2 x^2}",1,"-(a^4*A)/(7*x^7) - (a^3*(4*A*b + a*B))/(6*x^6) - (2*a^2*b*(3*A*b + 2*a*B))/(5*x^5) - (a*b^2*(2*A*b + 3*a*B))/(2*x^4) - (b^3*(A*b + 4*a*B))/(3*x^3) - (b^4*B)/(2*x^2)","A",3,2,27,0.07407,1,"{27, 76}"
536,1,99,0,0.0462386,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^9,x]","-\frac{a^3 (a B+4 A b)}{7 x^7}-\frac{a^2 b (2 a B+3 A b)}{3 x^6}-\frac{a^4 A}{8 x^8}-\frac{2 a b^2 (3 a B+2 A b)}{5 x^5}-\frac{b^3 (4 a B+A b)}{4 x^4}-\frac{b^4 B}{3 x^3}","-\frac{a^3 (a B+4 A b)}{7 x^7}-\frac{a^2 b (2 a B+3 A b)}{3 x^6}-\frac{a^4 A}{8 x^8}-\frac{2 a b^2 (3 a B+2 A b)}{5 x^5}-\frac{b^3 (4 a B+A b)}{4 x^4}-\frac{b^4 B}{3 x^3}",1,"-(a^4*A)/(8*x^8) - (a^3*(4*A*b + a*B))/(7*x^7) - (a^2*b*(3*A*b + 2*a*B))/(3*x^6) - (2*a*b^2*(2*A*b + 3*a*B))/(5*x^5) - (b^3*(A*b + 4*a*B))/(4*x^4) - (b^4*B)/(3*x^3)","A",3,2,27,0.07407,1,"{27, 76}"
537,1,99,0,0.0476277,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^10,x]","-\frac{a^3 (a B+4 A b)}{8 x^8}-\frac{2 a^2 b (2 a B+3 A b)}{7 x^7}-\frac{a^4 A}{9 x^9}-\frac{a b^2 (3 a B+2 A b)}{3 x^6}-\frac{b^3 (4 a B+A b)}{5 x^5}-\frac{b^4 B}{4 x^4}","-\frac{a^3 (a B+4 A b)}{8 x^8}-\frac{2 a^2 b (2 a B+3 A b)}{7 x^7}-\frac{a^4 A}{9 x^9}-\frac{a b^2 (3 a B+2 A b)}{3 x^6}-\frac{b^3 (4 a B+A b)}{5 x^5}-\frac{b^4 B}{4 x^4}",1,"-(a^4*A)/(9*x^9) - (a^3*(4*A*b + a*B))/(8*x^8) - (2*a^2*b*(3*A*b + 2*a*B))/(7*x^7) - (a*b^2*(2*A*b + 3*a*B))/(3*x^6) - (b^3*(A*b + 4*a*B))/(5*x^5) - (b^4*B)/(4*x^4)","A",3,2,27,0.07407,1,"{27, 76}"
538,1,99,0,0.049185,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^11,x]","-\frac{a^3 (a B+4 A b)}{9 x^9}-\frac{a^2 b (2 a B+3 A b)}{4 x^8}-\frac{a^4 A}{10 x^{10}}-\frac{2 a b^2 (3 a B+2 A b)}{7 x^7}-\frac{b^3 (4 a B+A b)}{6 x^6}-\frac{b^4 B}{5 x^5}","-\frac{a^3 (a B+4 A b)}{9 x^9}-\frac{a^2 b (2 a B+3 A b)}{4 x^8}-\frac{a^4 A}{10 x^{10}}-\frac{2 a b^2 (3 a B+2 A b)}{7 x^7}-\frac{b^3 (4 a B+A b)}{6 x^6}-\frac{b^4 B}{5 x^5}",1,"-(a^4*A)/(10*x^10) - (a^3*(4*A*b + a*B))/(9*x^9) - (a^2*b*(3*A*b + 2*a*B))/(4*x^8) - (2*a*b^2*(2*A*b + 3*a*B))/(7*x^7) - (b^3*(A*b + 4*a*B))/(6*x^6) - (b^4*B)/(5*x^5)","A",3,2,27,0.07407,1,"{27, 76}"
539,1,143,0,0.1418765,"\int x^5 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^5*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{1}{2} a^2 b^3 x^{10} (4 a B+3 A b)+\frac{5}{9} a^3 b^2 x^9 (3 a B+4 A b)+\frac{3}{8} a^4 b x^8 (2 a B+5 A b)+\frac{1}{7} a^5 x^7 (a B+6 A b)+\frac{1}{6} a^6 A x^6+\frac{1}{12} b^5 x^{12} (6 a B+A b)+\frac{3}{11} a b^4 x^{11} (5 a B+2 A b)+\frac{1}{13} b^6 B x^{13}","\frac{1}{2} a^2 b^3 x^{10} (4 a B+3 A b)+\frac{5}{9} a^3 b^2 x^9 (3 a B+4 A b)+\frac{3}{8} a^4 b x^8 (2 a B+5 A b)+\frac{1}{7} a^5 x^7 (a B+6 A b)+\frac{1}{6} a^6 A x^6+\frac{1}{12} b^5 x^{12} (6 a B+A b)+\frac{3}{11} a b^4 x^{11} (5 a B+2 A b)+\frac{1}{13} b^6 B x^{13}",1,"(a^6*A*x^6)/6 + (a^5*(6*A*b + a*B)*x^7)/7 + (3*a^4*b*(5*A*b + 2*a*B)*x^8)/8 + (5*a^3*b^2*(4*A*b + 3*a*B)*x^9)/9 + (a^2*b^3*(3*A*b + 4*a*B)*x^10)/2 + (3*a*b^4*(2*A*b + 5*a*B)*x^11)/11 + (b^5*(A*b + 6*a*B)*x^12)/12 + (b^6*B*x^13)/13","A",3,2,27,0.07407,1,"{27, 76}"
540,1,139,0,0.0975585,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 a^2 (a+b x)^9 (3 A b-5 a B)}{9 b^6}-\frac{a^3 (a+b x)^8 (4 A b-5 a B)}{8 b^6}+\frac{a^4 (a+b x)^7 (A b-a B)}{7 b^6}+\frac{(a+b x)^{11} (A b-5 a B)}{11 b^6}-\frac{a (a+b x)^{10} (2 A b-5 a B)}{5 b^6}+\frac{B (a+b x)^{12}}{12 b^6}","\frac{2 a^2 (a+b x)^9 (3 A b-5 a B)}{9 b^6}-\frac{a^3 (a+b x)^8 (4 A b-5 a B)}{8 b^6}+\frac{a^4 (a+b x)^7 (A b-a B)}{7 b^6}+\frac{(a+b x)^{11} (A b-5 a B)}{11 b^6}-\frac{a (a+b x)^{10} (2 A b-5 a B)}{5 b^6}+\frac{B (a+b x)^{12}}{12 b^6}",1,"(a^4*(A*b - a*B)*(a + b*x)^7)/(7*b^6) - (a^3*(4*A*b - 5*a*B)*(a + b*x)^8)/(8*b^6) + (2*a^2*(3*A*b - 5*a*B)*(a + b*x)^9)/(9*b^6) - (a*(2*A*b - 5*a*B)*(a + b*x)^10)/(5*b^6) + ((A*b - 5*a*B)*(a + b*x)^11)/(11*b^6) + (B*(a + b*x)^12)/(12*b^6)","A",3,2,27,0.07407,1,"{27, 76}"
541,1,112,0,0.0766769,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{a^2 (a+b x)^8 (3 A b-4 a B)}{8 b^5}-\frac{a^3 (a+b x)^7 (A b-a B)}{7 b^5}+\frac{(a+b x)^{10} (A b-4 a B)}{10 b^5}-\frac{a (a+b x)^9 (A b-2 a B)}{3 b^5}+\frac{B (a+b x)^{11}}{11 b^5}","\frac{a^2 (a+b x)^8 (3 A b-4 a B)}{8 b^5}-\frac{a^3 (a+b x)^7 (A b-a B)}{7 b^5}+\frac{(a+b x)^{10} (A b-4 a B)}{10 b^5}-\frac{a (a+b x)^9 (A b-2 a B)}{3 b^5}+\frac{B (a+b x)^{11}}{11 b^5}",1,"-(a^3*(A*b - a*B)*(a + b*x)^7)/(7*b^5) + (a^2*(3*A*b - 4*a*B)*(a + b*x)^8)/(8*b^5) - (a*(A*b - 2*a*B)*(a + b*x)^9)/(3*b^5) + ((A*b - 4*a*B)*(a + b*x)^10)/(10*b^5) + (B*(a + b*x)^11)/(11*b^5)","A",3,2,27,0.07407,1,"{27, 76}"
542,1,87,0,0.0636993,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{a^2 (a+b x)^7 (A b-a B)}{7 b^4}+\frac{(a+b x)^9 (A b-3 a B)}{9 b^4}-\frac{a (a+b x)^8 (2 A b-3 a B)}{8 b^4}+\frac{B (a+b x)^{10}}{10 b^4}","\frac{a^2 (a+b x)^7 (A b-a B)}{7 b^4}+\frac{(a+b x)^9 (A b-3 a B)}{9 b^4}-\frac{a (a+b x)^8 (2 A b-3 a B)}{8 b^4}+\frac{B (a+b x)^{10}}{10 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x)^7)/(7*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^8)/(8*b^4) + ((A*b - 3*a*B)*(a + b*x)^9)/(9*b^4) + (B*(a + b*x)^10)/(10*b^4)","A",3,2,27,0.07407,1,"{27, 76}"
543,1,61,0,0.0496207,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^8 (A b-2 a B)}{8 b^3}-\frac{a (a+b x)^7 (A b-a B)}{7 b^3}+\frac{B (a+b x)^9}{9 b^3}","\frac{(a+b x)^8 (A b-2 a B)}{8 b^3}-\frac{a (a+b x)^7 (A b-a B)}{7 b^3}+\frac{B (a+b x)^9}{9 b^3}",1,"-(a*(A*b - a*B)*(a + b*x)^7)/(7*b^3) + ((A*b - 2*a*B)*(a + b*x)^8)/(8*b^3) + (B*(a + b*x)^9)/(9*b^3)","A",3,2,25,0.08000,1,"{27, 76}"
544,1,38,0,0.0151013,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^7 (A b-a B)}{7 b^2}+\frac{B (a+b x)^8}{8 b^2}","\frac{(a+b x)^7 (A b-a B)}{7 b^2}+\frac{B (a+b x)^8}{8 b^2}",1,"((A*b - a*B)*(a + b*x)^7)/(7*b^2) + (B*(a + b*x)^8)/(8*b^2)","A",3,2,24,0.08333,1,"{27, 43}"
545,1,96,0,0.0365966,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x,x]","\frac{15}{4} a^2 A b^4 x^4+\frac{20}{3} a^3 A b^3 x^3+\frac{15}{2} a^4 A b^2 x^2+6 a^5 A b x+a^6 A \log (x)+\frac{6}{5} a A b^5 x^5+\frac{B (a+b x)^7}{7 b}+\frac{1}{6} A b^6 x^6","\frac{15}{4} a^2 A b^4 x^4+\frac{20}{3} a^3 A b^3 x^3+\frac{15}{2} a^4 A b^2 x^2+6 a^5 A b x+a^6 A \log (x)+\frac{6}{5} a A b^5 x^5+\frac{B (a+b x)^7}{7 b}+\frac{1}{6} A b^6 x^6",1,"6*a^5*A*b*x + (15*a^4*A*b^2*x^2)/2 + (20*a^3*A*b^3*x^3)/3 + (15*a^2*A*b^4*x^4)/4 + (6*a*A*b^5*x^5)/5 + (A*b^6*x^6)/6 + (B*(a + b*x)^7)/(7*b) + a^6*A*Log[x]","A",4,3,27,0.1111,1,"{27, 80, 43}"
546,1,133,0,0.0766646,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^2,x]","\frac{5}{2} a^3 b^2 x^2 (3 a B+4 A b)+\frac{5}{3} a^2 b^3 x^3 (4 a B+3 A b)+3 a^4 b x (2 a B+5 A b)+a^5 \log (x) (a B+6 A b)-\frac{a^6 A}{x}+\frac{3}{4} a b^4 x^4 (5 a B+2 A b)+\frac{1}{5} b^5 x^5 (6 a B+A b)+\frac{1}{6} b^6 B x^6","\frac{5}{2} a^3 b^2 x^2 (3 a B+4 A b)+\frac{5}{3} a^2 b^3 x^3 (4 a B+3 A b)+3 a^4 b x (2 a B+5 A b)+a^5 \log (x) (a B+6 A b)-\frac{a^6 A}{x}+\frac{3}{4} a b^4 x^4 (5 a B+2 A b)+\frac{1}{5} b^5 x^5 (6 a B+A b)+\frac{1}{6} b^6 B x^6",1,"-((a^6*A)/x) + 3*a^4*b*(5*A*b + 2*a*B)*x + (5*a^3*b^2*(4*A*b + 3*a*B)*x^2)/2 + (5*a^2*b^3*(3*A*b + 4*a*B)*x^3)/3 + (3*a*b^4*(2*A*b + 5*a*B)*x^4)/4 + (b^5*(A*b + 6*a*B)*x^5)/5 + (b^6*B*x^6)/6 + a^5*(6*A*b + a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
547,1,131,0,0.0798859,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^3,x]","\frac{5}{2} a^2 b^3 x^2 (4 a B+3 A b)+5 a^3 b^2 x (3 a B+4 A b)-\frac{a^5 (a B+6 A b)}{x}+3 a^4 b \log (x) (2 a B+5 A b)-\frac{a^6 A}{2 x^2}+a b^4 x^3 (5 a B+2 A b)+\frac{1}{4} b^5 x^4 (6 a B+A b)+\frac{1}{5} b^6 B x^5","\frac{5}{2} a^2 b^3 x^2 (4 a B+3 A b)+5 a^3 b^2 x (3 a B+4 A b)-\frac{a^5 (a B+6 A b)}{x}+3 a^4 b \log (x) (2 a B+5 A b)-\frac{a^6 A}{2 x^2}+a b^4 x^3 (5 a B+2 A b)+\frac{1}{4} b^5 x^4 (6 a B+A b)+\frac{1}{5} b^6 B x^5",1,"-(a^6*A)/(2*x^2) - (a^5*(6*A*b + a*B))/x + 5*a^3*b^2*(4*A*b + 3*a*B)*x + (5*a^2*b^3*(3*A*b + 4*a*B)*x^2)/2 + a*b^4*(2*A*b + 5*a*B)*x^3 + (b^5*(A*b + 6*a*B)*x^4)/4 + (b^6*B*x^5)/5 + 3*a^4*b*(5*A*b + 2*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
548,1,134,0,0.0799055,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^4,x]","5 a^2 b^3 x (4 a B+3 A b)+5 a^3 b^2 \log (x) (3 a B+4 A b)-\frac{a^5 (a B+6 A b)}{2 x^2}-\frac{3 a^4 b (2 a B+5 A b)}{x}-\frac{a^6 A}{3 x^3}+\frac{3}{2} a b^4 x^2 (5 a B+2 A b)+\frac{1}{3} b^5 x^3 (6 a B+A b)+\frac{1}{4} b^6 B x^4","5 a^2 b^3 x (4 a B+3 A b)+5 a^3 b^2 \log (x) (3 a B+4 A b)-\frac{a^5 (a B+6 A b)}{2 x^2}-\frac{3 a^4 b (2 a B+5 A b)}{x}-\frac{a^6 A}{3 x^3}+\frac{3}{2} a b^4 x^2 (5 a B+2 A b)+\frac{1}{3} b^5 x^3 (6 a B+A b)+\frac{1}{4} b^6 B x^4",1,"-(a^6*A)/(3*x^3) - (a^5*(6*A*b + a*B))/(2*x^2) - (3*a^4*b*(5*A*b + 2*a*B))/x + 5*a^2*b^3*(3*A*b + 4*a*B)*x + (3*a*b^4*(2*A*b + 5*a*B)*x^2)/2 + (b^5*(A*b + 6*a*B)*x^3)/3 + (b^6*B*x^4)/4 + 5*a^3*b^2*(4*A*b + 3*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
549,1,134,0,0.0820024,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^5,x]","-\frac{5 a^3 b^2 (3 a B+4 A b)}{x}+5 a^2 b^3 \log (x) (4 a B+3 A b)-\frac{a^5 (a B+6 A b)}{3 x^3}-\frac{3 a^4 b (2 a B+5 A b)}{2 x^2}-\frac{a^6 A}{4 x^4}+\frac{1}{2} b^5 x^2 (6 a B+A b)+3 a b^4 x (5 a B+2 A b)+\frac{1}{3} b^6 B x^3","-\frac{5 a^3 b^2 (3 a B+4 A b)}{x}+5 a^2 b^3 \log (x) (4 a B+3 A b)-\frac{a^5 (a B+6 A b)}{3 x^3}-\frac{3 a^4 b (2 a B+5 A b)}{2 x^2}-\frac{a^6 A}{4 x^4}+\frac{1}{2} b^5 x^2 (6 a B+A b)+3 a b^4 x (5 a B+2 A b)+\frac{1}{3} b^6 B x^3",1,"-(a^6*A)/(4*x^4) - (a^5*(6*A*b + a*B))/(3*x^3) - (3*a^4*b*(5*A*b + 2*a*B))/(2*x^2) - (5*a^3*b^2*(4*A*b + 3*a*B))/x + 3*a*b^4*(2*A*b + 5*a*B)*x + (b^5*(A*b + 6*a*B)*x^2)/2 + (b^6*B*x^3)/3 + 5*a^2*b^3*(3*A*b + 4*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
550,1,131,0,0.0810445,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^6,x]","-\frac{5 a^3 b^2 (3 a B+4 A b)}{2 x^2}-\frac{5 a^2 b^3 (4 a B+3 A b)}{x}-\frac{a^5 (a B+6 A b)}{4 x^4}-\frac{a^4 b (2 a B+5 A b)}{x^3}-\frac{a^6 A}{5 x^5}+b^5 x (6 a B+A b)+3 a b^4 \log (x) (5 a B+2 A b)+\frac{1}{2} b^6 B x^2","-\frac{5 a^3 b^2 (3 a B+4 A b)}{2 x^2}-\frac{5 a^2 b^3 (4 a B+3 A b)}{x}-\frac{a^5 (a B+6 A b)}{4 x^4}-\frac{a^4 b (2 a B+5 A b)}{x^3}-\frac{a^6 A}{5 x^5}+b^5 x (6 a B+A b)+3 a b^4 \log (x) (5 a B+2 A b)+\frac{1}{2} b^6 B x^2",1,"-(a^6*A)/(5*x^5) - (a^5*(6*A*b + a*B))/(4*x^4) - (a^4*b*(5*A*b + 2*a*B))/x^3 - (5*a^3*b^2*(4*A*b + 3*a*B))/(2*x^2) - (5*a^2*b^3*(3*A*b + 4*a*B))/x + b^5*(A*b + 6*a*B)*x + (b^6*B*x^2)/2 + 3*a*b^4*(2*A*b + 5*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
551,1,132,0,0.0762762,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^7,x]","-\frac{5 a^3 b^2 (3 a B+4 A b)}{3 x^3}-\frac{5 a^2 b^3 (4 a B+3 A b)}{2 x^2}-\frac{a^5 (a B+6 A b)}{5 x^5}-\frac{3 a^4 b (2 a B+5 A b)}{4 x^4}-\frac{a^6 A}{6 x^6}-\frac{3 a b^4 (5 a B+2 A b)}{x}+b^5 \log (x) (6 a B+A b)+b^6 B x","-\frac{5 a^3 b^2 (3 a B+4 A b)}{3 x^3}-\frac{5 a^2 b^3 (4 a B+3 A b)}{2 x^2}-\frac{a^5 (a B+6 A b)}{5 x^5}-\frac{3 a^4 b (2 a B+5 A b)}{4 x^4}-\frac{a^6 A}{6 x^6}-\frac{3 a b^4 (5 a B+2 A b)}{x}+b^5 \log (x) (6 a B+A b)+b^6 B x",1,"-(a^6*A)/(6*x^6) - (a^5*(6*A*b + a*B))/(5*x^5) - (3*a^4*b*(5*A*b + 2*a*B))/(4*x^4) - (5*a^3*b^2*(4*A*b + 3*a*B))/(3*x^3) - (5*a^2*b^3*(3*A*b + 4*a*B))/(2*x^2) - (3*a*b^4*(2*A*b + 5*a*B))/x + b^6*B*x + b^5*(A*b + 6*a*B)*Log[x]","A",3,2,27,0.07407,1,"{27, 76}"
552,1,101,0,0.0443396,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^8,x]","-\frac{15 a^2 b^4 B}{2 x^2}-\frac{20 a^3 b^3 B}{3 x^3}-\frac{15 a^4 b^2 B}{4 x^4}-\frac{6 a^5 b B}{5 x^5}-\frac{a^6 B}{6 x^6}-\frac{A (a+b x)^7}{7 a x^7}-\frac{6 a b^5 B}{x}+b^6 B \log (x)","-\frac{15 a^2 b^4 B}{2 x^2}-\frac{20 a^3 b^3 B}{3 x^3}-\frac{15 a^4 b^2 B}{4 x^4}-\frac{6 a^5 b B}{5 x^5}-\frac{a^6 B}{6 x^6}-\frac{A (a+b x)^7}{7 a x^7}-\frac{6 a b^5 B}{x}+b^6 B \log (x)",1,"-(a^6*B)/(6*x^6) - (6*a^5*b*B)/(5*x^5) - (15*a^4*b^2*B)/(4*x^4) - (20*a^3*b^3*B)/(3*x^3) - (15*a^2*b^4*B)/(2*x^2) - (6*a*b^5*B)/x - (A*(a + b*x)^7)/(7*a*x^7) + b^6*B*Log[x]","A",4,3,27,0.1111,1,"{27, 78, 43}"
553,1,44,0,0.012539,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^9,x]","\frac{(a+b x)^7 (A b-8 a B)}{56 a^2 x^7}-\frac{A (a+b x)^7}{8 a x^8}","\frac{(a+b x)^7 (A b-8 a B)}{56 a^2 x^7}-\frac{A (a+b x)^7}{8 a x^8}",1,"-(A*(a + b*x)^7)/(8*a*x^8) + ((A*b - 8*a*B)*(a + b*x)^7)/(56*a^2*x^7)","A",3,3,27,0.1111,1,"{27, 78, 37}"
554,1,72,0,0.0219145,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^10,x]","-\frac{b (a+b x)^7 (2 A b-9 a B)}{504 a^3 x^7}+\frac{(a+b x)^7 (2 A b-9 a B)}{72 a^2 x^8}-\frac{A (a+b x)^7}{9 a x^9}","-\frac{b (a+b x)^7 (2 A b-9 a B)}{504 a^3 x^7}+\frac{(a+b x)^7 (2 A b-9 a B)}{72 a^2 x^8}-\frac{A (a+b x)^7}{9 a x^9}",1,"-(A*(a + b*x)^7)/(9*a*x^9) + ((2*A*b - 9*a*B)*(a + b*x)^7)/(72*a^2*x^8) - (b*(2*A*b - 9*a*B)*(a + b*x)^7)/(504*a^3*x^7)","A",4,4,27,0.1481,1,"{27, 78, 45, 37}"
555,1,143,0,0.0764113,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^11,x]","-\frac{5 a^3 b^2 (3 a B+4 A b)}{7 x^7}-\frac{5 a^2 b^3 (4 a B+3 A b)}{6 x^6}-\frac{a^5 (a B+6 A b)}{9 x^9}-\frac{3 a^4 b (2 a B+5 A b)}{8 x^8}-\frac{a^6 A}{10 x^{10}}-\frac{3 a b^4 (5 a B+2 A b)}{5 x^5}-\frac{b^5 (6 a B+A b)}{4 x^4}-\frac{b^6 B}{3 x^3}","-\frac{5 a^3 b^2 (3 a B+4 A b)}{7 x^7}-\frac{5 a^2 b^3 (4 a B+3 A b)}{6 x^6}-\frac{a^5 (a B+6 A b)}{9 x^9}-\frac{3 a^4 b (2 a B+5 A b)}{8 x^8}-\frac{a^6 A}{10 x^{10}}-\frac{3 a b^4 (5 a B+2 A b)}{5 x^5}-\frac{b^5 (6 a B+A b)}{4 x^4}-\frac{b^6 B}{3 x^3}",1,"-(a^6*A)/(10*x^10) - (a^5*(6*A*b + a*B))/(9*x^9) - (3*a^4*b*(5*A*b + 2*a*B))/(8*x^8) - (5*a^3*b^2*(4*A*b + 3*a*B))/(7*x^7) - (5*a^2*b^3*(3*A*b + 4*a*B))/(6*x^6) - (3*a*b^4*(2*A*b + 5*a*B))/(5*x^5) - (b^5*(A*b + 6*a*B))/(4*x^4) - (b^6*B)/(3*x^3)","A",3,2,27,0.07407,1,"{27, 76}"
556,1,143,0,0.0716047,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{12}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^12,x]","-\frac{5 a^3 b^2 (3 a B+4 A b)}{8 x^8}-\frac{5 a^2 b^3 (4 a B+3 A b)}{7 x^7}-\frac{a^5 (a B+6 A b)}{10 x^{10}}-\frac{a^4 b (2 a B+5 A b)}{3 x^9}-\frac{a^6 A}{11 x^{11}}-\frac{a b^4 (5 a B+2 A b)}{2 x^6}-\frac{b^5 (6 a B+A b)}{5 x^5}-\frac{b^6 B}{4 x^4}","-\frac{5 a^3 b^2 (3 a B+4 A b)}{8 x^8}-\frac{5 a^2 b^3 (4 a B+3 A b)}{7 x^7}-\frac{a^5 (a B+6 A b)}{10 x^{10}}-\frac{a^4 b (2 a B+5 A b)}{3 x^9}-\frac{a^6 A}{11 x^{11}}-\frac{a b^4 (5 a B+2 A b)}{2 x^6}-\frac{b^5 (6 a B+A b)}{5 x^5}-\frac{b^6 B}{4 x^4}",1,"-(a^6*A)/(11*x^11) - (a^5*(6*A*b + a*B))/(10*x^10) - (a^4*b*(5*A*b + 2*a*B))/(3*x^9) - (5*a^3*b^2*(4*A*b + 3*a*B))/(8*x^8) - (5*a^2*b^3*(3*A*b + 4*a*B))/(7*x^7) - (a*b^4*(2*A*b + 5*a*B))/(2*x^6) - (b^5*(A*b + 6*a*B))/(5*x^5) - (b^6*B)/(4*x^4)","A",3,2,27,0.07407,1,"{27, 76}"
557,1,143,0,0.0688152,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{13}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^13,x]","-\frac{5 a^3 b^2 (3 a B+4 A b)}{9 x^9}-\frac{5 a^2 b^3 (4 a B+3 A b)}{8 x^8}-\frac{a^5 (a B+6 A b)}{11 x^{11}}-\frac{3 a^4 b (2 a B+5 A b)}{10 x^{10}}-\frac{a^6 A}{12 x^{12}}-\frac{3 a b^4 (5 a B+2 A b)}{7 x^7}-\frac{b^5 (6 a B+A b)}{6 x^6}-\frac{b^6 B}{5 x^5}","-\frac{5 a^3 b^2 (3 a B+4 A b)}{9 x^9}-\frac{5 a^2 b^3 (4 a B+3 A b)}{8 x^8}-\frac{a^5 (a B+6 A b)}{11 x^{11}}-\frac{3 a^4 b (2 a B+5 A b)}{10 x^{10}}-\frac{a^6 A}{12 x^{12}}-\frac{3 a b^4 (5 a B+2 A b)}{7 x^7}-\frac{b^5 (6 a B+A b)}{6 x^6}-\frac{b^6 B}{5 x^5}",1,"-(a^6*A)/(12*x^12) - (a^5*(6*A*b + a*B))/(11*x^11) - (3*a^4*b*(5*A*b + 2*a*B))/(10*x^10) - (5*a^3*b^2*(4*A*b + 3*a*B))/(9*x^9) - (5*a^2*b^3*(3*A*b + 4*a*B))/(8*x^8) - (3*a*b^4*(2*A*b + 5*a*B))/(7*x^7) - (b^5*(A*b + 6*a*B))/(6*x^6) - (b^6*B)/(5*x^5)","A",3,2,27,0.07407,1,"{27, 76}"
558,1,143,0,0.0709391,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{14}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^14,x]","-\frac{a^3 b^2 (3 a B+4 A b)}{2 x^{10}}-\frac{5 a^2 b^3 (4 a B+3 A b)}{9 x^9}-\frac{a^5 (a B+6 A b)}{12 x^{12}}-\frac{3 a^4 b (2 a B+5 A b)}{11 x^{11}}-\frac{a^6 A}{13 x^{13}}-\frac{3 a b^4 (5 a B+2 A b)}{8 x^8}-\frac{b^5 (6 a B+A b)}{7 x^7}-\frac{b^6 B}{6 x^6}","-\frac{a^3 b^2 (3 a B+4 A b)}{2 x^{10}}-\frac{5 a^2 b^3 (4 a B+3 A b)}{9 x^9}-\frac{a^5 (a B+6 A b)}{12 x^{12}}-\frac{3 a^4 b (2 a B+5 A b)}{11 x^{11}}-\frac{a^6 A}{13 x^{13}}-\frac{3 a b^4 (5 a B+2 A b)}{8 x^8}-\frac{b^5 (6 a B+A b)}{7 x^7}-\frac{b^6 B}{6 x^6}",1,"-(a^6*A)/(13*x^13) - (a^5*(6*A*b + a*B))/(12*x^12) - (3*a^4*b*(5*A*b + 2*a*B))/(11*x^11) - (a^3*b^2*(4*A*b + 3*a*B))/(2*x^10) - (5*a^2*b^3*(3*A*b + 4*a*B))/(9*x^9) - (3*a*b^4*(2*A*b + 5*a*B))/(8*x^8) - (b^5*(A*b + 6*a*B))/(7*x^7) - (b^6*B)/(6*x^6)","A",3,2,27,0.07407,1,"{27, 76}"
559,1,131,0,0.1276744,"\int x^7 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^7*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{18} (x+1)^{18} (d-8 e)-\frac{7}{17} (x+1)^{17} (d-4 e)+\frac{7}{16} (x+1)^{16} (3 d-8 e)-\frac{7}{3} (x+1)^{15} (d-2 e)+\frac{1}{2} (x+1)^{14} (5 d-8 e)-\frac{7}{13} (x+1)^{13} (3 d-4 e)+\frac{1}{12} (x+1)^{12} (7 d-8 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{19} e (x+1)^{19}","\frac{1}{18} (x+1)^{18} (d-8 e)-\frac{7}{17} (x+1)^{17} (d-4 e)+\frac{7}{16} (x+1)^{16} (3 d-8 e)-\frac{7}{3} (x+1)^{15} (d-2 e)+\frac{1}{2} (x+1)^{14} (5 d-8 e)-\frac{7}{13} (x+1)^{13} (3 d-4 e)+\frac{1}{12} (x+1)^{12} (7 d-8 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{19} e (x+1)^{19}",1,"-((d - e)*(1 + x)^11)/11 + ((7*d - 8*e)*(1 + x)^12)/12 - (7*(3*d - 4*e)*(1 + x)^13)/13 + ((5*d - 8*e)*(1 + x)^14)/2 - (7*(d - 2*e)*(1 + x)^15)/3 + (7*(3*d - 8*e)*(1 + x)^16)/16 - (7*(d - 4*e)*(1 + x)^17)/17 + ((d - 8*e)*(1 + x)^18)/18 + (e*(1 + x)^19)/19","A",3,2,19,0.1053,1,"{27, 76}"
560,1,119,0,0.074182,"\int x^6 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^6*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{17} (x+1)^{17} (d-7 e)-\frac{3}{16} (x+1)^{16} (2 d-7 e)+\frac{1}{3} (x+1)^{15} (3 d-7 e)-\frac{5}{14} (x+1)^{14} (4 d-7 e)+\frac{3}{13} (x+1)^{13} (5 d-7 e)-\frac{1}{12} (x+1)^{12} (6 d-7 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{18} e (x+1)^{18}","\frac{1}{17} (x+1)^{17} (d-7 e)-\frac{3}{16} (x+1)^{16} (2 d-7 e)+\frac{1}{3} (x+1)^{15} (3 d-7 e)-\frac{5}{14} (x+1)^{14} (4 d-7 e)+\frac{3}{13} (x+1)^{13} (5 d-7 e)-\frac{1}{12} (x+1)^{12} (6 d-7 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{18} e (x+1)^{18}",1,"((d - e)*(1 + x)^11)/11 - ((6*d - 7*e)*(1 + x)^12)/12 + (3*(5*d - 7*e)*(1 + x)^13)/13 - (5*(4*d - 7*e)*(1 + x)^14)/14 + ((3*d - 7*e)*(1 + x)^15)/3 - (3*(2*d - 7*e)*(1 + x)^16)/16 + ((d - 7*e)*(1 + x)^17)/17 + (e*(1 + x)^18)/18","A",3,2,19,0.1053,1,"{27, 76}"
561,1,99,0,0.0636043,"\int x^5 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^5*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{16} (x+1)^{16} (d-6 e)-\frac{1}{3} (x+1)^{15} (d-3 e)+\frac{5}{7} (x+1)^{14} (d-2 e)-\frac{5}{13} (x+1)^{13} (2 d-3 e)+\frac{1}{12} (x+1)^{12} (5 d-6 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{17} e (x+1)^{17}","\frac{1}{16} (x+1)^{16} (d-6 e)-\frac{1}{3} (x+1)^{15} (d-3 e)+\frac{5}{7} (x+1)^{14} (d-2 e)-\frac{5}{13} (x+1)^{13} (2 d-3 e)+\frac{1}{12} (x+1)^{12} (5 d-6 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{17} e (x+1)^{17}",1,"-((d - e)*(1 + x)^11)/11 + ((5*d - 6*e)*(1 + x)^12)/12 - (5*(2*d - 3*e)*(1 + x)^13)/13 + (5*(d - 2*e)*(1 + x)^14)/7 - ((d - 3*e)*(1 + x)^15)/3 + ((d - 6*e)*(1 + x)^16)/16 + (e*(1 + x)^17)/17","A",3,2,19,0.1053,1,"{27, 76}"
562,1,87,0,0.0567202,"\int x^4 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^4*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{15} (x+1)^{15} (d-5 e)-\frac{1}{7} (x+1)^{14} (2 d-5 e)+\frac{2}{13} (x+1)^{13} (3 d-5 e)-\frac{1}{12} (x+1)^{12} (4 d-5 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{16} e (x+1)^{16}","\frac{1}{15} (x+1)^{15} (d-5 e)-\frac{1}{7} (x+1)^{14} (2 d-5 e)+\frac{2}{13} (x+1)^{13} (3 d-5 e)-\frac{1}{12} (x+1)^{12} (4 d-5 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{16} e (x+1)^{16}",1,"((d - e)*(1 + x)^11)/11 - ((4*d - 5*e)*(1 + x)^12)/12 + (2*(3*d - 5*e)*(1 + x)^13)/13 - ((2*d - 5*e)*(1 + x)^14)/7 + ((d - 5*e)*(1 + x)^15)/15 + (e*(1 + x)^16)/16","A",3,2,19,0.1053,1,"{27, 76}"
563,1,69,0,0.0469993,"\int x^3 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^3*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{14} (x+1)^{14} (d-4 e)-\frac{3}{13} (x+1)^{13} (d-2 e)+\frac{1}{12} (x+1)^{12} (3 d-4 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{15} e (x+1)^{15}","\frac{1}{14} (x+1)^{14} (d-4 e)-\frac{3}{13} (x+1)^{13} (d-2 e)+\frac{1}{12} (x+1)^{12} (3 d-4 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{15} e (x+1)^{15}",1,"-((d - e)*(1 + x)^11)/11 + ((3*d - 4*e)*(1 + x)^12)/12 - (3*(d - 2*e)*(1 + x)^13)/13 + ((d - 4*e)*(1 + x)^14)/14 + (e*(1 + x)^15)/15","A",3,2,19,0.1053,1,"{27, 76}"
564,1,55,0,0.0425917,"\int x^2 (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^2*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{13} (x+1)^{13} (d-3 e)-\frac{1}{12} (x+1)^{12} (2 d-3 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{14} e (x+1)^{14}","\frac{1}{13} (x+1)^{13} (d-3 e)-\frac{1}{12} (x+1)^{12} (2 d-3 e)+\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{14} e (x+1)^{14}",1,"((d - e)*(1 + x)^11)/11 - ((2*d - 3*e)*(1 + x)^12)/12 + ((d - 3*e)*(1 + x)^13)/13 + (e*(1 + x)^14)/14","A",3,2,19,0.1053,1,"{27, 76}"
565,1,39,0,0.0353601,"\int x (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{12} (x+1)^{12} (d-2 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{13} e (x+1)^{13}","\frac{1}{12} (x+1)^{12} (d-2 e)-\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{13} e (x+1)^{13}",1,"-((d - e)*(1 + x)^11)/11 + ((d - 2*e)*(1 + x)^12)/12 + (e*(1 + x)^13)/13","A",3,2,17,0.1176,1,"{27, 76}"
566,1,25,0,0.0085815,"\int (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{12} e (x+1)^{12}","\frac{1}{11} (x+1)^{11} (d-e)+\frac{1}{12} e (x+1)^{12}",1,"((d - e)*(1 + x)^11)/11 + (e*(1 + x)^12)/12","A",3,2,16,0.1250,1,"{27, 43}"
567,1,87,0,0.0217017,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x,x]","\frac{d x^{10}}{10}+\frac{10 d x^9}{9}+\frac{45 d x^8}{8}+\frac{120 d x^7}{7}+35 d x^6+\frac{252 d x^5}{5}+\frac{105 d x^4}{2}+40 d x^3+\frac{45 d x^2}{2}+10 d x+d \log (x)+\frac{1}{11} e (x+1)^{11}","\frac{d x^{10}}{10}+\frac{10 d x^9}{9}+\frac{45 d x^8}{8}+\frac{120 d x^7}{7}+35 d x^6+\frac{252 d x^5}{5}+\frac{105 d x^4}{2}+40 d x^3+\frac{45 d x^2}{2}+10 d x+d \log (x)+\frac{1}{11} e (x+1)^{11}",1,"10*d*x + (45*d*x^2)/2 + 40*d*x^3 + (105*d*x^4)/2 + (252*d*x^5)/5 + 35*d*x^6 + (120*d*x^7)/7 + (45*d*x^8)/8 + (10*d*x^9)/9 + (d*x^10)/10 + (e*(1 + x)^11)/11 + d*Log[x]","A",4,3,19,0.1579,1,"{27, 80, 43}"
568,1,139,0,0.0677171,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^2} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^2,x]","\frac{1}{9} x^9 (d+10 e)+\frac{5}{8} x^8 (2 d+9 e)+\frac{15}{7} x^7 (3 d+8 e)+5 x^6 (4 d+7 e)+\frac{42}{5} x^5 (5 d+6 e)+\frac{21}{2} x^4 (6 d+5 e)+10 x^3 (7 d+4 e)+\frac{15}{2} x^2 (8 d+3 e)+5 x (9 d+2 e)+(10 d+e) \log (x)-\frac{d}{x}+\frac{e x^{10}}{10}","\frac{1}{9} x^9 (d+10 e)+\frac{5}{8} x^8 (2 d+9 e)+\frac{15}{7} x^7 (3 d+8 e)+5 x^6 (4 d+7 e)+\frac{42}{5} x^5 (5 d+6 e)+\frac{21}{2} x^4 (6 d+5 e)+10 x^3 (7 d+4 e)+\frac{15}{2} x^2 (8 d+3 e)+5 x (9 d+2 e)+(10 d+e) \log (x)-\frac{d}{x}+\frac{e x^{10}}{10}",1,"-(d/x) + 5*(9*d + 2*e)*x + (15*(8*d + 3*e)*x^2)/2 + 10*(7*d + 4*e)*x^3 + (21*(6*d + 5*e)*x^4)/2 + (42*(5*d + 6*e)*x^5)/5 + 5*(4*d + 7*e)*x^6 + (15*(3*d + 8*e)*x^7)/7 + (5*(2*d + 9*e)*x^8)/8 + ((d + 10*e)*x^9)/9 + (e*x^10)/10 + (10*d + e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
569,1,138,0,0.0698625,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^3} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^3,x]","\frac{1}{8} x^8 (d+10 e)+\frac{5}{7} x^7 (2 d+9 e)+\frac{5}{2} x^6 (3 d+8 e)+6 x^5 (4 d+7 e)+\frac{21}{2} x^4 (5 d+6 e)+14 x^3 (6 d+5 e)+15 x^2 (7 d+4 e)+15 x (8 d+3 e)-\frac{10 d+e}{x}+5 (9 d+2 e) \log (x)-\frac{d}{2 x^2}+\frac{e x^9}{9}","\frac{1}{8} x^8 (d+10 e)+\frac{5}{7} x^7 (2 d+9 e)+\frac{5}{2} x^6 (3 d+8 e)+6 x^5 (4 d+7 e)+\frac{21}{2} x^4 (5 d+6 e)+14 x^3 (6 d+5 e)+15 x^2 (7 d+4 e)+15 x (8 d+3 e)-\frac{10 d+e}{x}+5 (9 d+2 e) \log (x)-\frac{d}{2 x^2}+\frac{e x^9}{9}",1,"-d/(2*x^2) - (10*d + e)/x + 15*(8*d + 3*e)*x + 15*(7*d + 4*e)*x^2 + 14*(6*d + 5*e)*x^3 + (21*(5*d + 6*e)*x^4)/2 + 6*(4*d + 7*e)*x^5 + (5*(3*d + 8*e)*x^6)/2 + (5*(2*d + 9*e)*x^7)/7 + ((d + 10*e)*x^8)/8 + (e*x^9)/9 + 5*(9*d + 2*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
570,1,138,0,0.0710799,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^4} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^4,x]","\frac{1}{7} x^7 (d+10 e)+\frac{5}{6} x^6 (2 d+9 e)+3 x^5 (3 d+8 e)+\frac{15}{2} x^4 (4 d+7 e)+14 x^3 (5 d+6 e)+21 x^2 (6 d+5 e)-\frac{10 d+e}{2 x^2}+30 x (7 d+4 e)-\frac{5 (9 d+2 e)}{x}+15 (8 d+3 e) \log (x)-\frac{d}{3 x^3}+\frac{e x^8}{8}","\frac{1}{7} x^7 (d+10 e)+\frac{5}{6} x^6 (2 d+9 e)+3 x^5 (3 d+8 e)+\frac{15}{2} x^4 (4 d+7 e)+14 x^3 (5 d+6 e)+21 x^2 (6 d+5 e)-\frac{10 d+e}{2 x^2}+30 x (7 d+4 e)-\frac{5 (9 d+2 e)}{x}+15 (8 d+3 e) \log (x)-\frac{d}{3 x^3}+\frac{e x^8}{8}",1,"-d/(3*x^3) - (10*d + e)/(2*x^2) - (5*(9*d + 2*e))/x + 30*(7*d + 4*e)*x + 21*(6*d + 5*e)*x^2 + 14*(5*d + 6*e)*x^3 + (15*(4*d + 7*e)*x^4)/2 + 3*(3*d + 8*e)*x^5 + (5*(2*d + 9*e)*x^6)/6 + ((d + 10*e)*x^7)/7 + (e*x^8)/8 + 15*(8*d + 3*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
571,1,137,0,0.0683002,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^5} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^5,x]","\frac{1}{6} x^6 (d+10 e)+x^5 (2 d+9 e)+\frac{15}{4} x^4 (3 d+8 e)+10 x^3 (4 d+7 e)+21 x^2 (5 d+6 e)-\frac{5 (9 d+2 e)}{2 x^2}-\frac{10 d+e}{3 x^3}+42 x (6 d+5 e)-\frac{15 (8 d+3 e)}{x}+30 (7 d+4 e) \log (x)-\frac{d}{4 x^4}+\frac{e x^7}{7}","\frac{1}{6} x^6 (d+10 e)+x^5 (2 d+9 e)+\frac{15}{4} x^4 (3 d+8 e)+10 x^3 (4 d+7 e)+21 x^2 (5 d+6 e)-\frac{5 (9 d+2 e)}{2 x^2}-\frac{10 d+e}{3 x^3}+42 x (6 d+5 e)-\frac{15 (8 d+3 e)}{x}+30 (7 d+4 e) \log (x)-\frac{d}{4 x^4}+\frac{e x^7}{7}",1,"-d/(4*x^4) - (10*d + e)/(3*x^3) - (5*(9*d + 2*e))/(2*x^2) - (15*(8*d + 3*e))/x + 42*(6*d + 5*e)*x + 21*(5*d + 6*e)*x^2 + 10*(4*d + 7*e)*x^3 + (15*(3*d + 8*e)*x^4)/4 + (2*d + 9*e)*x^5 + ((d + 10*e)*x^6)/6 + (e*x^7)/7 + 30*(7*d + 4*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
572,1,140,0,0.0706684,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^6} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^6,x]","\frac{1}{5} x^5 (d+10 e)+\frac{5}{4} x^4 (2 d+9 e)+5 x^3 (3 d+8 e)+15 x^2 (4 d+7 e)-\frac{15 (8 d+3 e)}{2 x^2}-\frac{5 (9 d+2 e)}{3 x^3}-\frac{10 d+e}{4 x^4}+42 x (5 d+6 e)-\frac{30 (7 d+4 e)}{x}+42 (6 d+5 e) \log (x)-\frac{d}{5 x^5}+\frac{e x^6}{6}","\frac{1}{5} x^5 (d+10 e)+\frac{5}{4} x^4 (2 d+9 e)+5 x^3 (3 d+8 e)+15 x^2 (4 d+7 e)-\frac{15 (8 d+3 e)}{2 x^2}-\frac{5 (9 d+2 e)}{3 x^3}-\frac{10 d+e}{4 x^4}+42 x (5 d+6 e)-\frac{30 (7 d+4 e)}{x}+42 (6 d+5 e) \log (x)-\frac{d}{5 x^5}+\frac{e x^6}{6}",1,"-d/(5*x^5) - (10*d + e)/(4*x^4) - (5*(9*d + 2*e))/(3*x^3) - (15*(8*d + 3*e))/(2*x^2) - (30*(7*d + 4*e))/x + 42*(5*d + 6*e)*x + 15*(4*d + 7*e)*x^2 + 5*(3*d + 8*e)*x^3 + (5*(2*d + 9*e)*x^4)/4 + ((d + 10*e)*x^5)/5 + (e*x^6)/6 + 42*(6*d + 5*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
573,1,140,0,0.0724965,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^7} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^7,x]","\frac{1}{4} x^4 (d+10 e)+\frac{5}{3} x^3 (2 d+9 e)+\frac{15}{2} x^2 (3 d+8 e)-\frac{15 (7 d+4 e)}{x^2}-\frac{5 (8 d+3 e)}{x^3}-\frac{5 (9 d+2 e)}{4 x^4}-\frac{10 d+e}{5 x^5}+30 x (4 d+7 e)-\frac{42 (6 d+5 e)}{x}+42 (5 d+6 e) \log (x)-\frac{d}{6 x^6}+\frac{e x^5}{5}","\frac{1}{4} x^4 (d+10 e)+\frac{5}{3} x^3 (2 d+9 e)+\frac{15}{2} x^2 (3 d+8 e)-\frac{15 (7 d+4 e)}{x^2}-\frac{5 (8 d+3 e)}{x^3}-\frac{5 (9 d+2 e)}{4 x^4}-\frac{10 d+e}{5 x^5}+30 x (4 d+7 e)-\frac{42 (6 d+5 e)}{x}+42 (5 d+6 e) \log (x)-\frac{d}{6 x^6}+\frac{e x^5}{5}",1,"-d/(6*x^6) - (10*d + e)/(5*x^5) - (5*(9*d + 2*e))/(4*x^4) - (5*(8*d + 3*e))/x^3 - (15*(7*d + 4*e))/x^2 - (42*(6*d + 5*e))/x + 30*(4*d + 7*e)*x + (15*(3*d + 8*e)*x^2)/2 + (5*(2*d + 9*e)*x^3)/3 + ((d + 10*e)*x^4)/4 + (e*x^5)/5 + 42*(5*d + 6*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
574,1,138,0,0.0734573,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^8} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^8,x]","\frac{1}{3} x^3 (d+10 e)+\frac{5}{2} x^2 (2 d+9 e)-\frac{21 (6 d+5 e)}{x^2}-\frac{10 (7 d+4 e)}{x^3}-\frac{15 (8 d+3 e)}{4 x^4}-\frac{9 d+2 e}{x^5}-\frac{10 d+e}{6 x^6}+15 x (3 d+8 e)-\frac{42 (5 d+6 e)}{x}+30 (4 d+7 e) \log (x)-\frac{d}{7 x^7}+\frac{e x^4}{4}","\frac{1}{3} x^3 (d+10 e)+\frac{5}{2} x^2 (2 d+9 e)-\frac{21 (6 d+5 e)}{x^2}-\frac{10 (7 d+4 e)}{x^3}-\frac{15 (8 d+3 e)}{4 x^4}-\frac{9 d+2 e}{x^5}-\frac{10 d+e}{6 x^6}+15 x (3 d+8 e)-\frac{42 (5 d+6 e)}{x}+30 (4 d+7 e) \log (x)-\frac{d}{7 x^7}+\frac{e x^4}{4}",1,"-d/(7*x^7) - (10*d + e)/(6*x^6) - (9*d + 2*e)/x^5 - (15*(8*d + 3*e))/(4*x^4) - (10*(7*d + 4*e))/x^3 - (21*(6*d + 5*e))/x^2 - (42*(5*d + 6*e))/x + 15*(3*d + 8*e)*x + (5*(2*d + 9*e)*x^2)/2 + ((d + 10*e)*x^3)/3 + (e*x^4)/4 + 30*(4*d + 7*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
575,1,138,0,0.0738579,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^9} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^9,x]","\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}-\frac{14 (6 d+5 e)}{x^3}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{3 (8 d+3 e)}{x^5}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{10 d+e}{7 x^7}+5 x (2 d+9 e)-\frac{30 (4 d+7 e)}{x}+15 (3 d+8 e) \log (x)-\frac{d}{8 x^8}+\frac{e x^3}{3}","\frac{1}{2} x^2 (d+10 e)-\frac{21 (5 d+6 e)}{x^2}-\frac{14 (6 d+5 e)}{x^3}-\frac{15 (7 d+4 e)}{2 x^4}-\frac{3 (8 d+3 e)}{x^5}-\frac{5 (9 d+2 e)}{6 x^6}-\frac{10 d+e}{7 x^7}+5 x (2 d+9 e)-\frac{30 (4 d+7 e)}{x}+15 (3 d+8 e) \log (x)-\frac{d}{8 x^8}+\frac{e x^3}{3}",1,"-d/(8*x^8) - (10*d + e)/(7*x^7) - (5*(9*d + 2*e))/(6*x^6) - (3*(8*d + 3*e))/x^5 - (15*(7*d + 4*e))/(2*x^4) - (14*(6*d + 5*e))/x^3 - (21*(5*d + 6*e))/x^2 - (30*(4*d + 7*e))/x + 5*(2*d + 9*e)*x + ((d + 10*e)*x^2)/2 + (e*x^3)/3 + 15*(3*d + 8*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
576,1,137,0,0.079851,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{10}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^10,x]","-\frac{15 (4 d+7 e)}{x^2}-\frac{14 (5 d+6 e)}{x^3}-\frac{21 (6 d+5 e)}{2 x^4}-\frac{6 (7 d+4 e)}{x^5}-\frac{5 (8 d+3 e)}{2 x^6}-\frac{5 (9 d+2 e)}{7 x^7}-\frac{10 d+e}{8 x^8}+x (d+10 e)-\frac{15 (3 d+8 e)}{x}+5 (2 d+9 e) \log (x)-\frac{d}{9 x^9}+\frac{e x^2}{2}","-\frac{15 (4 d+7 e)}{x^2}-\frac{14 (5 d+6 e)}{x^3}-\frac{21 (6 d+5 e)}{2 x^4}-\frac{6 (7 d+4 e)}{x^5}-\frac{5 (8 d+3 e)}{2 x^6}-\frac{5 (9 d+2 e)}{7 x^7}-\frac{10 d+e}{8 x^8}+x (d+10 e)-\frac{15 (3 d+8 e)}{x}+5 (2 d+9 e) \log (x)-\frac{d}{9 x^9}+\frac{e x^2}{2}",1,"-d/(9*x^9) - (10*d + e)/(8*x^8) - (5*(9*d + 2*e))/(7*x^7) - (5*(8*d + 3*e))/(2*x^6) - (6*(7*d + 4*e))/x^5 - (21*(6*d + 5*e))/(2*x^4) - (14*(5*d + 6*e))/x^3 - (15*(4*d + 7*e))/x^2 - (15*(3*d + 8*e))/x + (d + 10*e)*x + (e*x^2)/2 + 5*(2*d + 9*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
577,1,138,0,0.0708308,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{11}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^11,x]","-\frac{15 (3 d+8 e)}{2 x^2}-\frac{10 (4 d+7 e)}{x^3}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{5 (7 d+4 e)}{x^6}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{10 d+e}{9 x^9}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x","-\frac{15 (3 d+8 e)}{2 x^2}-\frac{10 (4 d+7 e)}{x^3}-\frac{21 (5 d+6 e)}{2 x^4}-\frac{42 (6 d+5 e)}{5 x^5}-\frac{5 (7 d+4 e)}{x^6}-\frac{15 (8 d+3 e)}{7 x^7}-\frac{5 (9 d+2 e)}{8 x^8}-\frac{10 d+e}{9 x^9}-\frac{5 (2 d+9 e)}{x}+(d+10 e) \log (x)-\frac{d}{10 x^{10}}+e x",1,"-d/(10*x^10) - (10*d + e)/(9*x^9) - (5*(9*d + 2*e))/(8*x^8) - (15*(8*d + 3*e))/(7*x^7) - (5*(7*d + 4*e))/x^6 - (42*(6*d + 5*e))/(5*x^5) - (21*(5*d + 6*e))/(2*x^4) - (10*(4*d + 7*e))/x^3 - (15*(3*d + 8*e))/(2*x^2) - (5*(2*d + 9*e))/x + e*x + (d + 10*e)*Log[x]","A",3,2,19,0.1053,1,"{27, 76}"
578,1,92,0,0.0316115,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{12}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^12,x]","-\frac{d (x+1)^{11}}{11 x^{11}}-\frac{45 e}{2 x^2}-\frac{40 e}{x^3}-\frac{105 e}{2 x^4}-\frac{252 e}{5 x^5}-\frac{35 e}{x^6}-\frac{120 e}{7 x^7}-\frac{45 e}{8 x^8}-\frac{10 e}{9 x^9}-\frac{e}{10 x^{10}}-\frac{10 e}{x}+e \log (x)","-\frac{d (x+1)^{11}}{11 x^{11}}-\frac{45 e}{2 x^2}-\frac{40 e}{x^3}-\frac{105 e}{2 x^4}-\frac{252 e}{5 x^5}-\frac{35 e}{x^6}-\frac{120 e}{7 x^7}-\frac{45 e}{8 x^8}-\frac{10 e}{9 x^9}-\frac{e}{10 x^{10}}-\frac{10 e}{x}+e \log (x)",1,"-e/(10*x^10) - (10*e)/(9*x^9) - (45*e)/(8*x^8) - (120*e)/(7*x^7) - (35*e)/x^6 - (252*e)/(5*x^5) - (105*e)/(2*x^4) - (40*e)/x^3 - (45*e)/(2*x^2) - (10*e)/x - (d*(1 + x)^11)/(11*x^11) + e*Log[x]","A",4,3,19,0.1579,1,"{27, 78, 43}"
579,1,31,0,0.0064312,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{13}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^13,x]","\frac{(x+1)^{11} (d-12 e)}{132 x^{11}}-\frac{d (x+1)^{11}}{12 x^{12}}","\frac{(x+1)^{11} (d-12 e)}{132 x^{11}}-\frac{d (x+1)^{11}}{12 x^{12}}",1,"-(d*(1 + x)^11)/(12*x^12) + ((d - 12*e)*(1 + x)^11)/(132*x^11)","A",3,3,19,0.1579,1,"{27, 78, 37}"
580,1,52,0,0.0115211,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{14}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^14,x]","-\frac{(x+1)^{11} (2 d-13 e)}{1716 x^{11}}+\frac{(x+1)^{11} (2 d-13 e)}{156 x^{12}}-\frac{d (x+1)^{11}}{13 x^{13}}","-\frac{(x+1)^{11} (2 d-13 e)}{1716 x^{11}}+\frac{(x+1)^{11} (2 d-13 e)}{156 x^{12}}-\frac{d (x+1)^{11}}{13 x^{13}}",1,"-(d*(1 + x)^11)/(13*x^13) + ((2*d - 13*e)*(1 + x)^11)/(156*x^12) - ((2*d - 13*e)*(1 + x)^11)/(1716*x^11)","A",4,4,19,0.2105,1,"{27, 78, 45, 37}"
581,1,71,0,0.0171321,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{15}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^15,x]","\frac{(x+1)^{11} (3 d-14 e)}{12012 x^{11}}-\frac{(x+1)^{11} (3 d-14 e)}{1092 x^{12}}+\frac{(x+1)^{11} (3 d-14 e)}{182 x^{13}}-\frac{d (x+1)^{11}}{14 x^{14}}","\frac{(x+1)^{11} (3 d-14 e)}{12012 x^{11}}-\frac{(x+1)^{11} (3 d-14 e)}{1092 x^{12}}+\frac{(x+1)^{11} (3 d-14 e)}{182 x^{13}}-\frac{d (x+1)^{11}}{14 x^{14}}",1,"-(d*(1 + x)^11)/(14*x^14) + ((3*d - 14*e)*(1 + x)^11)/(182*x^13) - ((3*d - 14*e)*(1 + x)^11)/(1092*x^12) + ((3*d - 14*e)*(1 + x)^11)/(12012*x^11)","A",5,4,19,0.2105,1,"{27, 78, 45, 37}"
582,1,90,0,0.0223859,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{16}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^16,x]","-\frac{(x+1)^{11} (4 d-15 e)}{60060 x^{11}}+\frac{(x+1)^{11} (4 d-15 e)}{5460 x^{12}}-\frac{(x+1)^{11} (4 d-15 e)}{910 x^{13}}+\frac{(x+1)^{11} (4 d-15 e)}{210 x^{14}}-\frac{d (x+1)^{11}}{15 x^{15}}","-\frac{(x+1)^{11} (4 d-15 e)}{60060 x^{11}}+\frac{(x+1)^{11} (4 d-15 e)}{5460 x^{12}}-\frac{(x+1)^{11} (4 d-15 e)}{910 x^{13}}+\frac{(x+1)^{11} (4 d-15 e)}{210 x^{14}}-\frac{d (x+1)^{11}}{15 x^{15}}",1,"-(d*(1 + x)^11)/(15*x^15) + ((4*d - 15*e)*(1 + x)^11)/(210*x^14) - ((4*d - 15*e)*(1 + x)^11)/(910*x^13) + ((4*d - 15*e)*(1 + x)^11)/(5460*x^12) - ((4*d - 15*e)*(1 + x)^11)/(60060*x^11)","A",6,4,19,0.2105,1,"{27, 78, 45, 37}"
583,1,109,0,0.0274371,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{17}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^17,x]","\frac{(x+1)^{11} (5 d-16 e)}{240240 x^{11}}-\frac{(x+1)^{11} (5 d-16 e)}{21840 x^{12}}+\frac{(x+1)^{11} (5 d-16 e)}{3640 x^{13}}-\frac{(x+1)^{11} (5 d-16 e)}{840 x^{14}}+\frac{(x+1)^{11} (5 d-16 e)}{240 x^{15}}-\frac{d (x+1)^{11}}{16 x^{16}}","\frac{(x+1)^{11} (5 d-16 e)}{240240 x^{11}}-\frac{(x+1)^{11} (5 d-16 e)}{21840 x^{12}}+\frac{(x+1)^{11} (5 d-16 e)}{3640 x^{13}}-\frac{(x+1)^{11} (5 d-16 e)}{840 x^{14}}+\frac{(x+1)^{11} (5 d-16 e)}{240 x^{15}}-\frac{d (x+1)^{11}}{16 x^{16}}",1,"-(d*(1 + x)^11)/(16*x^16) + ((5*d - 16*e)*(1 + x)^11)/(240*x^15) - ((5*d - 16*e)*(1 + x)^11)/(840*x^14) + ((5*d - 16*e)*(1 + x)^11)/(3640*x^13) - ((5*d - 16*e)*(1 + x)^11)/(21840*x^12) + ((5*d - 16*e)*(1 + x)^11)/(240240*x^11)","A",7,4,19,0.2105,1,"{27, 78, 45, 37}"
584,1,128,0,0.034437,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{18}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^18,x]","-\frac{(x+1)^{11} (6 d-17 e)}{816816 x^{11}}+\frac{(x+1)^{11} (6 d-17 e)}{74256 x^{12}}-\frac{(x+1)^{11} (6 d-17 e)}{12376 x^{13}}+\frac{(x+1)^{11} (6 d-17 e)}{2856 x^{14}}-\frac{(x+1)^{11} (6 d-17 e)}{816 x^{15}}+\frac{(x+1)^{11} (6 d-17 e)}{272 x^{16}}-\frac{d (x+1)^{11}}{17 x^{17}}","-\frac{(x+1)^{11} (6 d-17 e)}{816816 x^{11}}+\frac{(x+1)^{11} (6 d-17 e)}{74256 x^{12}}-\frac{(x+1)^{11} (6 d-17 e)}{12376 x^{13}}+\frac{(x+1)^{11} (6 d-17 e)}{2856 x^{14}}-\frac{(x+1)^{11} (6 d-17 e)}{816 x^{15}}+\frac{(x+1)^{11} (6 d-17 e)}{272 x^{16}}-\frac{d (x+1)^{11}}{17 x^{17}}",1,"-(d*(1 + x)^11)/(17*x^17) + ((6*d - 17*e)*(1 + x)^11)/(272*x^16) - ((6*d - 17*e)*(1 + x)^11)/(816*x^15) + ((6*d - 17*e)*(1 + x)^11)/(2856*x^14) - ((6*d - 17*e)*(1 + x)^11)/(12376*x^13) + ((6*d - 17*e)*(1 + x)^11)/(74256*x^12) - ((6*d - 17*e)*(1 + x)^11)/(816816*x^11)","A",8,4,19,0.2105,1,"{27, 78, 45, 37}"
585,1,151,0,0.0745416,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{19}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^19,x]","-\frac{d+10 e}{8 x^8}-\frac{5 (2 d+9 e)}{9 x^9}-\frac{3 (3 d+8 e)}{2 x^{10}}-\frac{30 (4 d+7 e)}{11 x^{11}}-\frac{7 (5 d+6 e)}{2 x^{12}}-\frac{42 (6 d+5 e)}{13 x^{13}}-\frac{15 (7 d+4 e)}{7 x^{14}}-\frac{8 d+3 e}{x^{15}}-\frac{5 (9 d+2 e)}{16 x^{16}}-\frac{10 d+e}{17 x^{17}}-\frac{d}{18 x^{18}}-\frac{e}{7 x^7}","-\frac{d+10 e}{8 x^8}-\frac{5 (2 d+9 e)}{9 x^9}-\frac{3 (3 d+8 e)}{2 x^{10}}-\frac{30 (4 d+7 e)}{11 x^{11}}-\frac{7 (5 d+6 e)}{2 x^{12}}-\frac{42 (6 d+5 e)}{13 x^{13}}-\frac{15 (7 d+4 e)}{7 x^{14}}-\frac{8 d+3 e}{x^{15}}-\frac{5 (9 d+2 e)}{16 x^{16}}-\frac{10 d+e}{17 x^{17}}-\frac{d}{18 x^{18}}-\frac{e}{7 x^7}",1,"-d/(18*x^18) - (10*d + e)/(17*x^17) - (5*(9*d + 2*e))/(16*x^16) - (8*d + 3*e)/x^15 - (15*(7*d + 4*e))/(7*x^14) - (42*(6*d + 5*e))/(13*x^13) - (7*(5*d + 6*e))/(2*x^12) - (30*(4*d + 7*e))/(11*x^11) - (3*(3*d + 8*e))/(2*x^10) - (5*(2*d + 9*e))/(9*x^9) - (d + 10*e)/(8*x^8) - e/(7*x^7)","A",3,2,19,0.1053,1,"{27, 76}"
586,1,149,0,0.0664167,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{20}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^20,x]","-\frac{d+10 e}{9 x^9}-\frac{2 d+9 e}{2 x^{10}}-\frac{15 (3 d+8 e)}{11 x^{11}}-\frac{5 (4 d+7 e)}{2 x^{12}}-\frac{42 (5 d+6 e)}{13 x^{13}}-\frac{3 (6 d+5 e)}{x^{14}}-\frac{2 (7 d+4 e)}{x^{15}}-\frac{15 (8 d+3 e)}{16 x^{16}}-\frac{5 (9 d+2 e)}{17 x^{17}}-\frac{10 d+e}{18 x^{18}}-\frac{d}{19 x^{19}}-\frac{e}{8 x^8}","-\frac{d+10 e}{9 x^9}-\frac{2 d+9 e}{2 x^{10}}-\frac{15 (3 d+8 e)}{11 x^{11}}-\frac{5 (4 d+7 e)}{2 x^{12}}-\frac{42 (5 d+6 e)}{13 x^{13}}-\frac{3 (6 d+5 e)}{x^{14}}-\frac{2 (7 d+4 e)}{x^{15}}-\frac{15 (8 d+3 e)}{16 x^{16}}-\frac{5 (9 d+2 e)}{17 x^{17}}-\frac{10 d+e}{18 x^{18}}-\frac{d}{19 x^{19}}-\frac{e}{8 x^8}",1,"-d/(19*x^19) - (10*d + e)/(18*x^18) - (5*(9*d + 2*e))/(17*x^17) - (15*(8*d + 3*e))/(16*x^16) - (2*(7*d + 4*e))/x^15 - (3*(6*d + 5*e))/x^14 - (42*(5*d + 6*e))/(13*x^13) - (5*(4*d + 7*e))/(2*x^12) - (15*(3*d + 8*e))/(11*x^11) - (2*d + 9*e)/(2*x^10) - (d + 10*e)/(9*x^9) - e/(8*x^8)","A",3,2,19,0.1053,1,"{27, 76}"
587,1,151,0,0.0642711,"\int \frac{(d+e x) \left(1+2 x+x^2\right)^5}{x^{21}} \, dx","Int[((d + e*x)*(1 + 2*x + x^2)^5)/x^21,x]","-\frac{d+10 e}{10 x^{10}}-\frac{5 (2 d+9 e)}{11 x^{11}}-\frac{5 (3 d+8 e)}{4 x^{12}}-\frac{30 (4 d+7 e)}{13 x^{13}}-\frac{3 (5 d+6 e)}{x^{14}}-\frac{14 (6 d+5 e)}{5 x^{15}}-\frac{15 (7 d+4 e)}{8 x^{16}}-\frac{15 (8 d+3 e)}{17 x^{17}}-\frac{5 (9 d+2 e)}{18 x^{18}}-\frac{10 d+e}{19 x^{19}}-\frac{d}{20 x^{20}}-\frac{e}{9 x^9}","-\frac{d+10 e}{10 x^{10}}-\frac{5 (2 d+9 e)}{11 x^{11}}-\frac{5 (3 d+8 e)}{4 x^{12}}-\frac{30 (4 d+7 e)}{13 x^{13}}-\frac{3 (5 d+6 e)}{x^{14}}-\frac{14 (6 d+5 e)}{5 x^{15}}-\frac{15 (7 d+4 e)}{8 x^{16}}-\frac{15 (8 d+3 e)}{17 x^{17}}-\frac{5 (9 d+2 e)}{18 x^{18}}-\frac{10 d+e}{19 x^{19}}-\frac{d}{20 x^{20}}-\frac{e}{9 x^9}",1,"-d/(20*x^20) - (10*d + e)/(19*x^19) - (5*(9*d + 2*e))/(18*x^18) - (15*(8*d + 3*e))/(17*x^17) - (15*(7*d + 4*e))/(8*x^16) - (14*(6*d + 5*e))/(5*x^15) - (3*(5*d + 6*e))/x^14 - (30*(4*d + 7*e))/(13*x^13) - (5*(3*d + 8*e))/(4*x^12) - (5*(2*d + 9*e))/(11*x^11) - (d + 10*e)/(10*x^10) - e/(9*x^9)","A",3,2,19,0.1053,1,"{27, 76}"
588,1,83,0,0.0333653,"\int x^{11} (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^11*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{23}}{23}+\frac{x^{22}}{2}+\frac{55 x^{21}}{21}+\frac{33 x^{20}}{4}+\frac{330 x^{19}}{19}+\frac{77 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{165 x^{16}}{8}+11 x^{15}+\frac{55 x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{x^{12}}{12}","\frac{x^{23}}{23}+\frac{x^{22}}{2}+\frac{55 x^{21}}{21}+\frac{33 x^{20}}{4}+\frac{330 x^{19}}{19}+\frac{77 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{165 x^{16}}{8}+11 x^{15}+\frac{55 x^{14}}{14}+\frac{11 x^{13}}{13}+\frac{x^{12}}{12}",1,"x^12/12 + (11*x^13)/13 + (55*x^14)/14 + 11*x^15 + (165*x^16)/8 + (462*x^17)/17 + (77*x^18)/3 + (330*x^19)/19 + (33*x^20)/4 + (55*x^21)/21 + x^22/2 + x^23/23","A",3,2,17,0.1176,1,"{27, 43}"
589,1,83,0,0.0261487,"\int x^{10} (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^10*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11}","\frac{x^{22}}{22}+\frac{11 x^{21}}{21}+\frac{11 x^{20}}{4}+\frac{165 x^{19}}{19}+\frac{55 x^{18}}{3}+\frac{462 x^{17}}{17}+\frac{231 x^{16}}{8}+22 x^{15}+\frac{165 x^{14}}{14}+\frac{55 x^{13}}{13}+\frac{11 x^{12}}{12}+\frac{x^{11}}{11}",1,"x^11/11 + (11*x^12)/12 + (55*x^13)/13 + (165*x^14)/14 + 22*x^15 + (231*x^16)/8 + (462*x^17)/17 + (55*x^18)/3 + (165*x^19)/19 + (11*x^20)/4 + (11*x^21)/21 + x^22/22","A",3,2,17,0.1176,1,"{27, 43}"
590,1,91,0,0.0264048,"\int x^9 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^9*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{21} (x+1)^{21}-\frac{9}{20} (x+1)^{20}+\frac{36}{19} (x+1)^{19}-\frac{14}{3} (x+1)^{18}+\frac{126}{17} (x+1)^{17}-\frac{63}{8} (x+1)^{16}+\frac{28}{5} (x+1)^{15}-\frac{18}{7} (x+1)^{14}+\frac{9}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}","\frac{1}{21} (x+1)^{21}-\frac{9}{20} (x+1)^{20}+\frac{36}{19} (x+1)^{19}-\frac{14}{3} (x+1)^{18}+\frac{126}{17} (x+1)^{17}-\frac{63}{8} (x+1)^{16}+\frac{28}{5} (x+1)^{15}-\frac{18}{7} (x+1)^{14}+\frac{9}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}",1,"-(1 + x)^12/12 + (9*(1 + x)^13)/13 - (18*(1 + x)^14)/7 + (28*(1 + x)^15)/5 - (63*(1 + x)^16)/8 + (126*(1 + x)^17)/17 - (14*(1 + x)^18)/3 + (36*(1 + x)^19)/19 - (9*(1 + x)^20)/20 + (1 + x)^21/21","A",3,2,17,0.1176,1,"{27, 43}"
591,1,80,0,0.0249253,"\int x^8 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^8*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{20} (x+1)^{20}-\frac{8}{19} (x+1)^{19}+\frac{14}{9} (x+1)^{18}-\frac{56}{17} (x+1)^{17}+\frac{35}{8} (x+1)^{16}-\frac{56}{15} (x+1)^{15}+2 (x+1)^{14}-\frac{8}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}","\frac{1}{20} (x+1)^{20}-\frac{8}{19} (x+1)^{19}+\frac{14}{9} (x+1)^{18}-\frac{56}{17} (x+1)^{17}+\frac{35}{8} (x+1)^{16}-\frac{56}{15} (x+1)^{15}+2 (x+1)^{14}-\frac{8}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}",1,"(1 + x)^12/12 - (8*(1 + x)^13)/13 + 2*(1 + x)^14 - (56*(1 + x)^15)/15 + (35*(1 + x)^16)/8 - (56*(1 + x)^17)/17 + (14*(1 + x)^18)/9 - (8*(1 + x)^19)/19 + (1 + x)^20/20","A",3,2,17,0.1176,1,"{27, 43}"
592,1,73,0,0.0230896,"\int x^7 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^7*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{19} (x+1)^{19}-\frac{7}{18} (x+1)^{18}+\frac{21}{17} (x+1)^{17}-\frac{35}{16} (x+1)^{16}+\frac{7}{3} (x+1)^{15}-\frac{3}{2} (x+1)^{14}+\frac{7}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}","\frac{1}{19} (x+1)^{19}-\frac{7}{18} (x+1)^{18}+\frac{21}{17} (x+1)^{17}-\frac{35}{16} (x+1)^{16}+\frac{7}{3} (x+1)^{15}-\frac{3}{2} (x+1)^{14}+\frac{7}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}",1,"-(1 + x)^12/12 + (7*(1 + x)^13)/13 - (3*(1 + x)^14)/2 + (7*(1 + x)^15)/3 - (35*(1 + x)^16)/16 + (21*(1 + x)^17)/17 - (7*(1 + x)^18)/18 + (1 + x)^19/19","A",3,2,17,0.1176,1,"{27, 43}"
593,1,64,0,0.0210965,"\int x^6 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^6*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{18} (x+1)^{18}-\frac{6}{17} (x+1)^{17}+\frac{15}{16} (x+1)^{16}-\frac{4}{3} (x+1)^{15}+\frac{15}{14} (x+1)^{14}-\frac{6}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}","\frac{1}{18} (x+1)^{18}-\frac{6}{17} (x+1)^{17}+\frac{15}{16} (x+1)^{16}-\frac{4}{3} (x+1)^{15}+\frac{15}{14} (x+1)^{14}-\frac{6}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}",1,"(1 + x)^12/12 - (6*(1 + x)^13)/13 + (15*(1 + x)^14)/14 - (4*(1 + x)^15)/3 + (15*(1 + x)^16)/16 - (6*(1 + x)^17)/17 + (1 + x)^18/18","A",3,2,17,0.1176,1,"{27, 43}"
594,1,55,0,0.0194168,"\int x^5 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^5*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{17} (x+1)^{17}-\frac{5}{16} (x+1)^{16}+\frac{2}{3} (x+1)^{15}-\frac{5}{7} (x+1)^{14}+\frac{5}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}","\frac{1}{17} (x+1)^{17}-\frac{5}{16} (x+1)^{16}+\frac{2}{3} (x+1)^{15}-\frac{5}{7} (x+1)^{14}+\frac{5}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}",1,"-(1 + x)^12/12 + (5*(1 + x)^13)/13 - (5*(1 + x)^14)/7 + (2*(1 + x)^15)/3 - (5*(1 + x)^16)/16 + (1 + x)^17/17","A",3,2,17,0.1176,1,"{27, 43}"
595,1,46,0,0.0177084,"\int x^4 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^4*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{16} (x+1)^{16}-\frac{4}{15} (x+1)^{15}+\frac{3}{7} (x+1)^{14}-\frac{4}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}","\frac{1}{16} (x+1)^{16}-\frac{4}{15} (x+1)^{15}+\frac{3}{7} (x+1)^{14}-\frac{4}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}",1,"(1 + x)^12/12 - (4*(1 + x)^13)/13 + (3*(1 + x)^14)/7 - (4*(1 + x)^15)/15 + (1 + x)^16/16","A",3,2,17,0.1176,1,"{27, 43}"
596,1,37,0,0.0162581,"\int x^3 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^3*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{15} (x+1)^{15}-\frac{3}{14} (x+1)^{14}+\frac{3}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}","\frac{1}{15} (x+1)^{15}-\frac{3}{14} (x+1)^{14}+\frac{3}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}",1,"-(1 + x)^12/12 + (3*(1 + x)^13)/13 - (3*(1 + x)^14)/14 + (1 + x)^15/15","A",3,2,17,0.1176,1,"{27, 43}"
597,1,28,0,0.0138082,"\int x^2 (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^2*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{14} (x+1)^{14}-\frac{2}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}","\frac{1}{14} (x+1)^{14}-\frac{2}{13} (x+1)^{13}+\frac{1}{12} (x+1)^{12}",1,"(1 + x)^12/12 - (2*(1 + x)^13)/13 + (1 + x)^14/14","A",3,2,17,0.1176,1,"{27, 43}"
598,1,19,0,0.0054111,"\int x (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}","\frac{1}{13} (x+1)^{13}-\frac{1}{12} (x+1)^{12}",1,"-(1 + x)^12/12 + (1 + x)^13/13","A",3,2,15,0.1333,1,"{27, 43}"
599,1,9,0,0.001211,"\int (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{1}{12} (x+1)^{12}","\frac{1}{12} (x+1)^{12}",1,"(1 + x)^12/12","A",2,2,14,0.1429,1,"{27, 32}"
600,1,72,0,0.0174979,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x,x]","\frac{x^{11}}{11}+\frac{11 x^{10}}{10}+\frac{55 x^9}{9}+\frac{165 x^8}{8}+\frac{330 x^7}{7}+77 x^6+\frac{462 x^5}{5}+\frac{165 x^4}{2}+55 x^3+\frac{55 x^2}{2}+11 x+\log (x)","\frac{x^{11}}{11}+\frac{11 x^{10}}{10}+\frac{55 x^9}{9}+\frac{165 x^8}{8}+\frac{330 x^7}{7}+77 x^6+\frac{462 x^5}{5}+\frac{165 x^4}{2}+55 x^3+\frac{55 x^2}{2}+11 x+\log (x)",1,"11*x + (55*x^2)/2 + 55*x^3 + (165*x^4)/2 + (462*x^5)/5 + 77*x^6 + (330*x^7)/7 + (165*x^8)/8 + (55*x^9)/9 + (11*x^10)/10 + x^11/11 + Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
601,1,72,0,0.0206652,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^2} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^2,x]","\frac{x^{10}}{10}+\frac{11 x^9}{9}+\frac{55 x^8}{8}+\frac{165 x^7}{7}+55 x^6+\frac{462 x^5}{5}+\frac{231 x^4}{2}+110 x^3+\frac{165 x^2}{2}+55 x-\frac{1}{x}+11 \log (x)","\frac{x^{10}}{10}+\frac{11 x^9}{9}+\frac{55 x^8}{8}+\frac{165 x^7}{7}+55 x^6+\frac{462 x^5}{5}+\frac{231 x^4}{2}+110 x^3+\frac{165 x^2}{2}+55 x-\frac{1}{x}+11 \log (x)",1,"-x^(-1) + 55*x + (165*x^2)/2 + 110*x^3 + (231*x^4)/2 + (462*x^5)/5 + 55*x^6 + (165*x^7)/7 + (55*x^8)/8 + (11*x^9)/9 + x^10/10 + 11*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
602,1,70,0,0.0206813,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^3} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^3,x]","\frac{x^9}{9}+\frac{11 x^8}{8}+\frac{55 x^7}{7}+\frac{55 x^6}{2}+66 x^5+\frac{231 x^4}{2}+154 x^3+165 x^2-\frac{1}{2 x^2}+165 x-\frac{11}{x}+55 \log (x)","\frac{x^9}{9}+\frac{11 x^8}{8}+\frac{55 x^7}{7}+\frac{55 x^6}{2}+66 x^5+\frac{231 x^4}{2}+154 x^3+165 x^2-\frac{1}{2 x^2}+165 x-\frac{11}{x}+55 \log (x)",1,"-1/(2*x^2) - 11/x + 165*x + 165*x^2 + 154*x^3 + (231*x^4)/2 + 66*x^5 + (55*x^6)/2 + (55*x^7)/7 + (11*x^8)/8 + x^9/9 + 55*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
603,1,70,0,0.0220666,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^4} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^4,x]","\frac{x^8}{8}+\frac{11 x^7}{7}+\frac{55 x^6}{6}+33 x^5+\frac{165 x^4}{2}+154 x^3+231 x^2-\frac{11}{2 x^2}-\frac{1}{3 x^3}+330 x-\frac{55}{x}+165 \log (x)","\frac{x^8}{8}+\frac{11 x^7}{7}+\frac{55 x^6}{6}+33 x^5+\frac{165 x^4}{2}+154 x^3+231 x^2-\frac{11}{2 x^2}-\frac{1}{3 x^3}+330 x-\frac{55}{x}+165 \log (x)",1,"-1/(3*x^3) - 11/(2*x^2) - 55/x + 330*x + 231*x^2 + 154*x^3 + (165*x^4)/2 + 33*x^5 + (55*x^6)/6 + (11*x^7)/7 + x^8/8 + 165*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
604,1,70,0,0.0217264,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^5} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^5,x]","\frac{x^7}{7}+\frac{11 x^6}{6}+11 x^5+\frac{165 x^4}{4}+110 x^3+231 x^2-\frac{55}{2 x^2}-\frac{11}{3 x^3}-\frac{1}{4 x^4}+462 x-\frac{165}{x}+330 \log (x)","\frac{x^7}{7}+\frac{11 x^6}{6}+11 x^5+\frac{165 x^4}{4}+110 x^3+231 x^2-\frac{55}{2 x^2}-\frac{11}{3 x^3}-\frac{1}{4 x^4}+462 x-\frac{165}{x}+330 \log (x)",1,"-1/(4*x^4) - 11/(3*x^3) - 55/(2*x^2) - 165/x + 462*x + 231*x^2 + 110*x^3 + (165*x^4)/4 + 11*x^5 + (11*x^6)/6 + x^7/7 + 330*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
605,1,72,0,0.0215513,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^6} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^6,x]","\frac{x^6}{6}+\frac{11 x^5}{5}+\frac{55 x^4}{4}+55 x^3+165 x^2-\frac{165}{2 x^2}-\frac{55}{3 x^3}-\frac{11}{4 x^4}-\frac{1}{5 x^5}+462 x-\frac{330}{x}+462 \log (x)","\frac{x^6}{6}+\frac{11 x^5}{5}+\frac{55 x^4}{4}+55 x^3+165 x^2-\frac{165}{2 x^2}-\frac{55}{3 x^3}-\frac{11}{4 x^4}-\frac{1}{5 x^5}+462 x-\frac{330}{x}+462 \log (x)",1,"-1/(5*x^5) - 11/(4*x^4) - 55/(3*x^3) - 165/(2*x^2) - 330/x + 462*x + 165*x^2 + 55*x^3 + (55*x^4)/4 + (11*x^5)/5 + x^6/6 + 462*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
606,1,72,0,0.0216001,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^7} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^7,x]","\frac{x^5}{5}+\frac{11 x^4}{4}+\frac{55 x^3}{3}+\frac{165 x^2}{2}-\frac{165}{x^2}-\frac{55}{x^3}-\frac{55}{4 x^4}-\frac{11}{5 x^5}-\frac{1}{6 x^6}+330 x-\frac{462}{x}+462 \log (x)","\frac{x^5}{5}+\frac{11 x^4}{4}+\frac{55 x^3}{3}+\frac{165 x^2}{2}-\frac{165}{x^2}-\frac{55}{x^3}-\frac{55}{4 x^4}-\frac{11}{5 x^5}-\frac{1}{6 x^6}+330 x-\frac{462}{x}+462 \log (x)",1,"-1/(6*x^6) - 11/(5*x^5) - 55/(4*x^4) - 55/x^3 - 165/x^2 - 462/x + 330*x + (165*x^2)/2 + (55*x^3)/3 + (11*x^4)/4 + x^5/5 + 462*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
607,1,70,0,0.0212897,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^8} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^8,x]","\frac{x^4}{4}+\frac{11 x^3}{3}+\frac{55 x^2}{2}-\frac{231}{x^2}-\frac{110}{x^3}-\frac{165}{4 x^4}-\frac{11}{x^5}-\frac{11}{6 x^6}-\frac{1}{7 x^7}+165 x-\frac{462}{x}+330 \log (x)","\frac{x^4}{4}+\frac{11 x^3}{3}+\frac{55 x^2}{2}-\frac{231}{x^2}-\frac{110}{x^3}-\frac{165}{4 x^4}-\frac{11}{x^5}-\frac{11}{6 x^6}-\frac{1}{7 x^7}+165 x-\frac{462}{x}+330 \log (x)",1,"-1/(7*x^7) - 11/(6*x^6) - 11/x^5 - 165/(4*x^4) - 110/x^3 - 231/x^2 - 462/x + 165*x + (55*x^2)/2 + (11*x^3)/3 + x^4/4 + 330*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
608,1,70,0,0.0214975,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^9} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^9,x]","\frac{x^3}{3}+\frac{11 x^2}{2}-\frac{231}{x^2}-\frac{154}{x^3}-\frac{165}{2 x^4}-\frac{33}{x^5}-\frac{55}{6 x^6}-\frac{11}{7 x^7}-\frac{1}{8 x^8}+55 x-\frac{330}{x}+165 \log (x)","\frac{x^3}{3}+\frac{11 x^2}{2}-\frac{231}{x^2}-\frac{154}{x^3}-\frac{165}{2 x^4}-\frac{33}{x^5}-\frac{55}{6 x^6}-\frac{11}{7 x^7}-\frac{1}{8 x^8}+55 x-\frac{330}{x}+165 \log (x)",1,"-1/(8*x^8) - 11/(7*x^7) - 55/(6*x^6) - 33/x^5 - 165/(2*x^4) - 154/x^3 - 231/x^2 - 330/x + 55*x + (11*x^2)/2 + x^3/3 + 165*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
609,1,70,0,0.0221587,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{10}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^10,x]","\frac{x^2}{2}-\frac{165}{x^2}-\frac{154}{x^3}-\frac{231}{2 x^4}-\frac{66}{x^5}-\frac{55}{2 x^6}-\frac{55}{7 x^7}-\frac{11}{8 x^8}-\frac{1}{9 x^9}+11 x-\frac{165}{x}+55 \log (x)","\frac{x^2}{2}-\frac{165}{x^2}-\frac{154}{x^3}-\frac{231}{2 x^4}-\frac{66}{x^5}-\frac{55}{2 x^6}-\frac{55}{7 x^7}-\frac{11}{8 x^8}-\frac{1}{9 x^9}+11 x-\frac{165}{x}+55 \log (x)",1,"-1/(9*x^9) - 11/(8*x^8) - 55/(7*x^7) - 55/(2*x^6) - 66/x^5 - 231/(2*x^4) - 154/x^3 - 165/x^2 - 165/x + 11*x + x^2/2 + 55*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
610,1,70,0,0.020874,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{11}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^11,x]","-\frac{165}{2 x^2}-\frac{110}{x^3}-\frac{231}{2 x^4}-\frac{462}{5 x^5}-\frac{55}{x^6}-\frac{165}{7 x^7}-\frac{55}{8 x^8}-\frac{11}{9 x^9}-\frac{1}{10 x^{10}}+x-\frac{55}{x}+11 \log (x)","-\frac{165}{2 x^2}-\frac{110}{x^3}-\frac{231}{2 x^4}-\frac{462}{5 x^5}-\frac{55}{x^6}-\frac{165}{7 x^7}-\frac{55}{8 x^8}-\frac{11}{9 x^9}-\frac{1}{10 x^{10}}+x-\frac{55}{x}+11 \log (x)",1,"-1/(10*x^10) - 11/(9*x^9) - 55/(8*x^8) - 165/(7*x^7) - 55/x^6 - 462/(5*x^5) - 231/(2*x^4) - 110/x^3 - 165/(2*x^2) - 55/x + x + 11*Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
611,1,74,0,0.0211485,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{12}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^12,x]","-\frac{55}{2 x^2}-\frac{55}{x^3}-\frac{165}{2 x^4}-\frac{462}{5 x^5}-\frac{77}{x^6}-\frac{330}{7 x^7}-\frac{165}{8 x^8}-\frac{55}{9 x^9}-\frac{11}{10 x^{10}}-\frac{1}{11 x^{11}}-\frac{11}{x}+\log (x)","-\frac{55}{2 x^2}-\frac{55}{x^3}-\frac{165}{2 x^4}-\frac{462}{5 x^5}-\frac{77}{x^6}-\frac{330}{7 x^7}-\frac{165}{8 x^8}-\frac{55}{9 x^9}-\frac{11}{10 x^{10}}-\frac{1}{11 x^{11}}-\frac{11}{x}+\log (x)",1,"-1/(11*x^11) - 11/(10*x^10) - 55/(9*x^9) - 165/(8*x^8) - 330/(7*x^7) - 77/x^6 - 462/(5*x^5) - 165/(2*x^4) - 55/x^3 - 55/(2*x^2) - 11/x + Log[x]","A",3,2,17,0.1176,1,"{27, 43}"
612,1,12,0,0.0015824,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{13}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^13,x]","-\frac{(x+1)^{12}}{12 x^{12}}","-\frac{(x+1)^{12}}{12 x^{12}}",1,"-(1 + x)^12/(12*x^12)","A",2,2,17,0.1176,1,"{27, 37}"
613,1,25,0,0.0032369,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{14}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^14,x]","\frac{(x+1)^{12}}{156 x^{12}}-\frac{(x+1)^{12}}{13 x^{13}}","\frac{(x+1)^{12}}{156 x^{12}}-\frac{(x+1)^{12}}{13 x^{13}}",1,"-(1 + x)^12/(13*x^13) + (1 + x)^12/(156*x^12)","A",3,3,17,0.1765,1,"{27, 45, 37}"
614,1,37,0,0.0052638,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{15}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^15,x]","-\frac{(x+1)^{12}}{1092 x^{12}}+\frac{(x+1)^{12}}{91 x^{13}}-\frac{(x+1)^{12}}{14 x^{14}}","-\frac{(x+1)^{12}}{1092 x^{12}}+\frac{(x+1)^{12}}{91 x^{13}}-\frac{(x+1)^{12}}{14 x^{14}}",1,"-(1 + x)^12/(14*x^14) + (1 + x)^12/(91*x^13) - (1 + x)^12/(1092*x^12)","A",4,3,17,0.1765,1,"{27, 45, 37}"
615,1,49,0,0.0094611,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{16}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^16,x]","\frac{(x+1)^{12}}{5460 x^{12}}-\frac{(x+1)^{12}}{455 x^{13}}+\frac{(x+1)^{12}}{70 x^{14}}-\frac{(x+1)^{12}}{15 x^{15}}","\frac{(x+1)^{12}}{5460 x^{12}}-\frac{(x+1)^{12}}{455 x^{13}}+\frac{(x+1)^{12}}{70 x^{14}}-\frac{(x+1)^{12}}{15 x^{15}}",1,"-(1 + x)^12/(15*x^15) + (1 + x)^12/(70*x^14) - (1 + x)^12/(455*x^13) + (1 + x)^12/(5460*x^12)","A",5,3,17,0.1765,1,"{27, 45, 37}"
616,1,61,0,0.0114299,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{17}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^17,x]","-\frac{(x+1)^{12}}{21840 x^{12}}+\frac{(x+1)^{12}}{1820 x^{13}}-\frac{(x+1)^{12}}{280 x^{14}}+\frac{(x+1)^{12}}{60 x^{15}}-\frac{(x+1)^{12}}{16 x^{16}}","-\frac{(x+1)^{12}}{21840 x^{12}}+\frac{(x+1)^{12}}{1820 x^{13}}-\frac{(x+1)^{12}}{280 x^{14}}+\frac{(x+1)^{12}}{60 x^{15}}-\frac{(x+1)^{12}}{16 x^{16}}",1,"-(1 + x)^12/(16*x^16) + (1 + x)^12/(60*x^15) - (1 + x)^12/(280*x^14) + (1 + x)^12/(1820*x^13) - (1 + x)^12/(21840*x^12)","A",6,3,17,0.1765,1,"{27, 45, 37}"
617,1,73,0,0.0157929,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{18}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^18,x]","\frac{(x+1)^{12}}{74256 x^{12}}-\frac{(x+1)^{12}}{6188 x^{13}}+\frac{(x+1)^{12}}{952 x^{14}}-\frac{(x+1)^{12}}{204 x^{15}}+\frac{5 (x+1)^{12}}{272 x^{16}}-\frac{(x+1)^{12}}{17 x^{17}}","\frac{(x+1)^{12}}{74256 x^{12}}-\frac{(x+1)^{12}}{6188 x^{13}}+\frac{(x+1)^{12}}{952 x^{14}}-\frac{(x+1)^{12}}{204 x^{15}}+\frac{5 (x+1)^{12}}{272 x^{16}}-\frac{(x+1)^{12}}{17 x^{17}}",1,"-(1 + x)^12/(17*x^17) + (5*(1 + x)^12)/(272*x^16) - (1 + x)^12/(204*x^15) + (1 + x)^12/(952*x^14) - (1 + x)^12/(6188*x^13) + (1 + x)^12/(74256*x^12)","A",7,3,17,0.1765,1,"{27, 45, 37}"
618,1,85,0,0.019389,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{19}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^19,x]","-\frac{(x+1)^{12}}{222768 x^{12}}+\frac{(x+1)^{12}}{18564 x^{13}}-\frac{(x+1)^{12}}{2856 x^{14}}+\frac{(x+1)^{12}}{612 x^{15}}-\frac{5 (x+1)^{12}}{816 x^{16}}+\frac{(x+1)^{12}}{51 x^{17}}-\frac{(x+1)^{12}}{18 x^{18}}","-\frac{(x+1)^{12}}{222768 x^{12}}+\frac{(x+1)^{12}}{18564 x^{13}}-\frac{(x+1)^{12}}{2856 x^{14}}+\frac{(x+1)^{12}}{612 x^{15}}-\frac{5 (x+1)^{12}}{816 x^{16}}+\frac{(x+1)^{12}}{51 x^{17}}-\frac{(x+1)^{12}}{18 x^{18}}",1,"-(1 + x)^12/(18*x^18) + (1 + x)^12/(51*x^17) - (5*(1 + x)^12)/(816*x^16) + (1 + x)^12/(612*x^15) - (1 + x)^12/(2856*x^14) + (1 + x)^12/(18564*x^13) - (1 + x)^12/(222768*x^12)","A",8,3,17,0.1765,1,"{27, 45, 37}"
619,1,97,0,0.0268267,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{20}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^20,x]","\frac{(x+1)^{12}}{604656 x^{12}}-\frac{(x+1)^{12}}{50388 x^{13}}+\frac{(x+1)^{12}}{7752 x^{14}}-\frac{7 (x+1)^{12}}{11628 x^{15}}+\frac{35 (x+1)^{12}}{15504 x^{16}}-\frac{7 (x+1)^{12}}{969 x^{17}}+\frac{7 (x+1)^{12}}{342 x^{18}}-\frac{(x+1)^{12}}{19 x^{19}}","\frac{(x+1)^{12}}{604656 x^{12}}-\frac{(x+1)^{12}}{50388 x^{13}}+\frac{(x+1)^{12}}{7752 x^{14}}-\frac{7 (x+1)^{12}}{11628 x^{15}}+\frac{35 (x+1)^{12}}{15504 x^{16}}-\frac{7 (x+1)^{12}}{969 x^{17}}+\frac{7 (x+1)^{12}}{342 x^{18}}-\frac{(x+1)^{12}}{19 x^{19}}",1,"-(1 + x)^12/(19*x^19) + (7*(1 + x)^12)/(342*x^18) - (7*(1 + x)^12)/(969*x^17) + (35*(1 + x)^12)/(15504*x^16) - (7*(1 + x)^12)/(11628*x^15) + (1 + x)^12/(7752*x^14) - (1 + x)^12/(50388*x^13) + (1 + x)^12/(604656*x^12)","A",9,3,17,0.1765,1,"{27, 45, 37}"
620,1,81,0,0.021086,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{21}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^21,x]","-\frac{1}{9 x^9}-\frac{11}{10 x^{10}}-\frac{5}{x^{11}}-\frac{55}{4 x^{12}}-\frac{330}{13 x^{13}}-\frac{33}{x^{14}}-\frac{154}{5 x^{15}}-\frac{165}{8 x^{16}}-\frac{165}{17 x^{17}}-\frac{55}{18 x^{18}}-\frac{11}{19 x^{19}}-\frac{1}{20 x^{20}}","-\frac{1}{9 x^9}-\frac{11}{10 x^{10}}-\frac{5}{x^{11}}-\frac{55}{4 x^{12}}-\frac{330}{13 x^{13}}-\frac{33}{x^{14}}-\frac{154}{5 x^{15}}-\frac{165}{8 x^{16}}-\frac{165}{17 x^{17}}-\frac{55}{18 x^{18}}-\frac{11}{19 x^{19}}-\frac{1}{20 x^{20}}",1,"-1/(20*x^20) - 11/(19*x^19) - 55/(18*x^18) - 165/(17*x^17) - 165/(8*x^16) - 154/(5*x^15) - 33/x^14 - 330/(13*x^13) - 55/(4*x^12) - 5/x^11 - 11/(10*x^10) - 1/(9*x^9)","A",3,2,17,0.1176,1,"{27, 43}"
621,1,83,0,0.0216553,"\int \frac{(1+x) \left(1+2 x+x^2\right)^5}{x^{22}} \, dx","Int[((1 + x)*(1 + 2*x + x^2)^5)/x^22,x]","-\frac{1}{10 x^{10}}-\frac{1}{x^{11}}-\frac{55}{12 x^{12}}-\frac{165}{13 x^{13}}-\frac{165}{7 x^{14}}-\frac{154}{5 x^{15}}-\frac{231}{8 x^{16}}-\frac{330}{17 x^{17}}-\frac{55}{6 x^{18}}-\frac{55}{19 x^{19}}-\frac{11}{20 x^{20}}-\frac{1}{21 x^{21}}","-\frac{1}{10 x^{10}}-\frac{1}{x^{11}}-\frac{55}{12 x^{12}}-\frac{165}{13 x^{13}}-\frac{165}{7 x^{14}}-\frac{154}{5 x^{15}}-\frac{231}{8 x^{16}}-\frac{330}{17 x^{17}}-\frac{55}{6 x^{18}}-\frac{55}{19 x^{19}}-\frac{11}{20 x^{20}}-\frac{1}{21 x^{21}}",1,"-1/(21*x^21) - 11/(20*x^20) - 55/(19*x^19) - 55/(6*x^18) - 330/(17*x^17) - 231/(8*x^16) - 154/(5*x^15) - 165/(7*x^14) - 165/(13*x^13) - 55/(12*x^12) - x^(-11) - 1/(10*x^10)","A",3,2,17,0.1176,1,"{27, 43}"
622,1,134,0,0.1575375,"\int \frac{x^5 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^5*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a^2 x^2 (3 A b-4 a B)}{2 b^5}+\frac{a^5 (A b-a B)}{b^7 (a+b x)}-\frac{a^3 x (4 A b-5 a B)}{b^6}+\frac{a^4 (5 A b-6 a B) \log (a+b x)}{b^7}-\frac{a x^3 (2 A b-3 a B)}{3 b^4}+\frac{x^4 (A b-2 a B)}{4 b^3}+\frac{B x^5}{5 b^2}","\frac{a^2 x^2 (3 A b-4 a B)}{2 b^5}+\frac{a^5 (A b-a B)}{b^7 (a+b x)}-\frac{a^3 x (4 A b-5 a B)}{b^6}+\frac{a^4 (5 A b-6 a B) \log (a+b x)}{b^7}-\frac{a x^3 (2 A b-3 a B)}{3 b^4}+\frac{x^4 (A b-2 a B)}{4 b^3}+\frac{B x^5}{5 b^2}",1,"-((a^3*(4*A*b - 5*a*B)*x)/b^6) + (a^2*(3*A*b - 4*a*B)*x^2)/(2*b^5) - (a*(2*A*b - 3*a*B)*x^3)/(3*b^4) + ((A*b - 2*a*B)*x^4)/(4*b^3) + (B*x^5)/(5*b^2) + (a^5*(A*b - a*B))/(b^7*(a + b*x)) + (a^4*(5*A*b - 6*a*B)*Log[a + b*x])/b^7","A",3,2,27,0.07407,1,"{27, 77}"
623,1,113,0,0.10855,"\int \frac{x^4 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{a^4 (A b-a B)}{b^6 (a+b x)}+\frac{a^2 x (3 A b-4 a B)}{b^5}-\frac{a^3 (4 A b-5 a B) \log (a+b x)}{b^6}-\frac{a x^2 (2 A b-3 a B)}{2 b^4}+\frac{x^3 (A b-2 a B)}{3 b^3}+\frac{B x^4}{4 b^2}","-\frac{a^4 (A b-a B)}{b^6 (a+b x)}+\frac{a^2 x (3 A b-4 a B)}{b^5}-\frac{a^3 (4 A b-5 a B) \log (a+b x)}{b^6}-\frac{a x^2 (2 A b-3 a B)}{2 b^4}+\frac{x^3 (A b-2 a B)}{3 b^3}+\frac{B x^4}{4 b^2}",1,"(a^2*(3*A*b - 4*a*B)*x)/b^5 - (a*(2*A*b - 3*a*B)*x^2)/(2*b^4) + ((A*b - 2*a*B)*x^3)/(3*b^3) + (B*x^4)/(4*b^2) - (a^4*(A*b - a*B))/(b^6*(a + b*x)) - (a^3*(4*A*b - 5*a*B)*Log[a + b*x])/b^6","A",3,2,27,0.07407,1,"{27, 77}"
624,1,90,0,0.0821095,"\int \frac{x^3 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a^3 (A b-a B)}{b^5 (a+b x)}+\frac{a^2 (3 A b-4 a B) \log (a+b x)}{b^5}+\frac{x^2 (A b-2 a B)}{2 b^3}-\frac{a x (2 A b-3 a B)}{b^4}+\frac{B x^3}{3 b^2}","\frac{a^3 (A b-a B)}{b^5 (a+b x)}+\frac{a^2 (3 A b-4 a B) \log (a+b x)}{b^5}+\frac{x^2 (A b-2 a B)}{2 b^3}-\frac{a x (2 A b-3 a B)}{b^4}+\frac{B x^3}{3 b^2}",1,"-((a*(2*A*b - 3*a*B)*x)/b^4) + ((A*b - 2*a*B)*x^2)/(2*b^3) + (B*x^3)/(3*b^2) + (a^3*(A*b - a*B))/(b^5*(a + b*x)) + (a^2*(3*A*b - 4*a*B)*Log[a + b*x])/b^5","A",3,2,27,0.07407,1,"{27, 77}"
625,1,69,0,0.0560725,"\int \frac{x^2 (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{a^2 (A b-a B)}{b^4 (a+b x)}+\frac{x (A b-2 a B)}{b^3}-\frac{a (2 A b-3 a B) \log (a+b x)}{b^4}+\frac{B x^2}{2 b^2}","-\frac{a^2 (A b-a B)}{b^4 (a+b x)}+\frac{x (A b-2 a B)}{b^3}-\frac{a (2 A b-3 a B) \log (a+b x)}{b^4}+\frac{B x^2}{2 b^2}",1,"((A*b - 2*a*B)*x)/b^3 + (B*x^2)/(2*b^2) - (a^2*(A*b - a*B))/(b^4*(a + b*x)) - (a*(2*A*b - 3*a*B)*Log[a + b*x])/b^4","A",3,2,27,0.07407,1,"{27, 77}"
626,1,45,0,0.0362801,"\int \frac{x (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a (A b-a B)}{b^3 (a+b x)}+\frac{(A b-2 a B) \log (a+b x)}{b^3}+\frac{B x}{b^2}","\frac{a (A b-a B)}{b^3 (a+b x)}+\frac{(A b-2 a B) \log (a+b x)}{b^3}+\frac{B x}{b^2}",1,"(B*x)/b^2 + (a*(A*b - a*B))/(b^3*(a + b*x)) + ((A*b - 2*a*B)*Log[a + b*x])/b^3","A",3,2,25,0.08000,1,"{27, 77}"
627,1,32,0,0.0234505,"\int \frac{A+B x}{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)}","\frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)}",1,"-((A*b - a*B)/(b^2*(a + b*x))) + (B*Log[a + b*x])/b^2","A",3,2,24,0.08333,1,"{27, 43}"
628,1,42,0,0.0288124,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{A \log (a+b x)}{a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{a b (a+b x)}","-\frac{A \log (a+b x)}{a^2}+\frac{A \log (x)}{a^2}+\frac{A b-a B}{a b (a+b x)}",1,"(A*b - a*B)/(a*b*(a + b*x)) + (A*Log[x])/a^2 - (A*Log[a + b*x])/a^2","A",3,2,27,0.07407,1,"{27, 77}"
629,1,65,0,0.0505052,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{A b-a B}{a^2 (a+b x)}-\frac{\log (x) (2 A b-a B)}{a^3}+\frac{(2 A b-a B) \log (a+b x)}{a^3}-\frac{A}{a^2 x}","-\frac{A b-a B}{a^2 (a+b x)}-\frac{\log (x) (2 A b-a B)}{a^3}+\frac{(2 A b-a B) \log (a+b x)}{a^3}-\frac{A}{a^2 x}",1,"-(A/(a^2*x)) - (A*b - a*B)/(a^2*(a + b*x)) - ((2*A*b - a*B)*Log[x])/a^3 + ((2*A*b - a*B)*Log[a + b*x])/a^3","A",3,2,27,0.07407,1,"{27, 77}"
630,1,85,0,0.0714481,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{2 A b-a B}{a^3 x}+\frac{b (A b-a B)}{a^3 (a+b x)}+\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{b (3 A b-2 a B) \log (a+b x)}{a^4}-\frac{A}{2 a^2 x^2}","\frac{2 A b-a B}{a^3 x}+\frac{b (A b-a B)}{a^3 (a+b x)}+\frac{b \log (x) (3 A b-2 a B)}{a^4}-\frac{b (3 A b-2 a B) \log (a+b x)}{a^4}-\frac{A}{2 a^2 x^2}",1,"-A/(2*a^2*x^2) + (2*A*b - a*B)/(a^3*x) + (b*(A*b - a*B))/(a^3*(a + b*x)) + (b*(3*A*b - 2*a*B)*Log[x])/a^4 - (b*(3*A*b - 2*a*B)*Log[a + b*x])/a^4","A",3,2,27,0.07407,1,"{27, 77}"
631,1,113,0,0.0920331,"\int \frac{A+B x}{x^4 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^4*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b^2 (A b-a B)}{a^4 (a+b x)}-\frac{b^2 \log (x) (4 A b-3 a B)}{a^5}+\frac{b^2 (4 A b-3 a B) \log (a+b x)}{a^5}+\frac{2 A b-a B}{2 a^3 x^2}-\frac{b (3 A b-2 a B)}{a^4 x}-\frac{A}{3 a^2 x^3}","-\frac{b^2 (A b-a B)}{a^4 (a+b x)}-\frac{b^2 \log (x) (4 A b-3 a B)}{a^5}+\frac{b^2 (4 A b-3 a B) \log (a+b x)}{a^5}+\frac{2 A b-a B}{2 a^3 x^2}-\frac{b (3 A b-2 a B)}{a^4 x}-\frac{A}{3 a^2 x^3}",1,"-A/(3*a^2*x^3) + (2*A*b - a*B)/(2*a^3*x^2) - (b*(3*A*b - 2*a*B))/(a^4*x) - (b^2*(A*b - a*B))/(a^4*(a + b*x)) - (b^2*(4*A*b - 3*a*B)*Log[x])/a^5 + (b^2*(4*A*b - 3*a*B)*Log[a + b*x])/a^5","A",3,2,27,0.07407,1,"{27, 77}"
632,1,133,0,0.1141132,"\int \frac{A+B x}{x^5 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^5*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{b^3 (A b-a B)}{a^5 (a+b x)}+\frac{b^2 (4 A b-3 a B)}{a^5 x}+\frac{b^3 \log (x) (5 A b-4 a B)}{a^6}-\frac{b^3 (5 A b-4 a B) \log (a+b x)}{a^6}-\frac{b (3 A b-2 a B)}{2 a^4 x^2}+\frac{2 A b-a B}{3 a^3 x^3}-\frac{A}{4 a^2 x^4}","\frac{b^3 (A b-a B)}{a^5 (a+b x)}+\frac{b^2 (4 A b-3 a B)}{a^5 x}+\frac{b^3 \log (x) (5 A b-4 a B)}{a^6}-\frac{b^3 (5 A b-4 a B) \log (a+b x)}{a^6}-\frac{b (3 A b-2 a B)}{2 a^4 x^2}+\frac{2 A b-a B}{3 a^3 x^3}-\frac{A}{4 a^2 x^4}",1,"-A/(4*a^2*x^4) + (2*A*b - a*B)/(3*a^3*x^3) - (b*(3*A*b - 2*a*B))/(2*a^4*x^2) + (b^2*(4*A*b - 3*a*B))/(a^5*x) + (b^3*(A*b - a*B))/(a^5*(a + b*x)) + (b^3*(5*A*b - 4*a*B)*Log[x])/a^6 - (b^3*(5*A*b - 4*a*B)*Log[a + b*x])/a^6","A",3,2,27,0.07407,1,"{27, 77}"
633,1,143,0,0.159865,"\int \frac{x^5 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^5*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{a^5 (A b-a B)}{3 b^7 (a+b x)^3}-\frac{a^4 (5 A b-6 a B)}{2 b^7 (a+b x)^2}+\frac{5 a^3 (2 A b-3 a B)}{b^7 (a+b x)}+\frac{10 a^2 (A b-2 a B) \log (a+b x)}{b^7}+\frac{x^2 (A b-4 a B)}{2 b^5}-\frac{2 a x (2 A b-5 a B)}{b^6}+\frac{B x^3}{3 b^4}","\frac{a^5 (A b-a B)}{3 b^7 (a+b x)^3}-\frac{a^4 (5 A b-6 a B)}{2 b^7 (a+b x)^2}+\frac{5 a^3 (2 A b-3 a B)}{b^7 (a+b x)}+\frac{10 a^2 (A b-2 a B) \log (a+b x)}{b^7}+\frac{x^2 (A b-4 a B)}{2 b^5}-\frac{2 a x (2 A b-5 a B)}{b^6}+\frac{B x^3}{3 b^4}",1,"(-2*a*(2*A*b - 5*a*B)*x)/b^6 + ((A*b - 4*a*B)*x^2)/(2*b^5) + (B*x^3)/(3*b^4) + (a^5*(A*b - a*B))/(3*b^7*(a + b*x)^3) - (a^4*(5*A*b - 6*a*B))/(2*b^7*(a + b*x)^2) + (5*a^3*(2*A*b - 3*a*B))/(b^7*(a + b*x)) + (10*a^2*(A*b - 2*a*B)*Log[a + b*x])/b^7","A",3,2,27,0.07407,1,"{27, 77}"
634,1,121,0,0.1234029,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{a^4 (A b-a B)}{3 b^6 (a+b x)^3}+\frac{a^3 (4 A b-5 a B)}{2 b^6 (a+b x)^2}-\frac{2 a^2 (3 A b-5 a B)}{b^6 (a+b x)}+\frac{x (A b-4 a B)}{b^5}-\frac{2 a (2 A b-5 a B) \log (a+b x)}{b^6}+\frac{B x^2}{2 b^4}","-\frac{a^4 (A b-a B)}{3 b^6 (a+b x)^3}+\frac{a^3 (4 A b-5 a B)}{2 b^6 (a+b x)^2}-\frac{2 a^2 (3 A b-5 a B)}{b^6 (a+b x)}+\frac{x (A b-4 a B)}{b^5}-\frac{2 a (2 A b-5 a B) \log (a+b x)}{b^6}+\frac{B x^2}{2 b^4}",1,"((A*b - 4*a*B)*x)/b^5 + (B*x^2)/(2*b^4) - (a^4*(A*b - a*B))/(3*b^6*(a + b*x)^3) + (a^3*(4*A*b - 5*a*B))/(2*b^6*(a + b*x)^2) - (2*a^2*(3*A*b - 5*a*B))/(b^6*(a + b*x)) - (2*a*(2*A*b - 5*a*B)*Log[a + b*x])/b^6","A",3,2,27,0.07407,1,"{27, 77}"
635,1,97,0,0.088243,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{a^3 (A b-a B)}{3 b^5 (a+b x)^3}-\frac{a^2 (3 A b-4 a B)}{2 b^5 (a+b x)^2}+\frac{3 a (A b-2 a B)}{b^5 (a+b x)}+\frac{(A b-4 a B) \log (a+b x)}{b^5}+\frac{B x}{b^4}","\frac{a^3 (A b-a B)}{3 b^5 (a+b x)^3}-\frac{a^2 (3 A b-4 a B)}{2 b^5 (a+b x)^2}+\frac{3 a (A b-2 a B)}{b^5 (a+b x)}+\frac{(A b-4 a B) \log (a+b x)}{b^5}+\frac{B x}{b^4}",1,"(B*x)/b^4 + (a^3*(A*b - a*B))/(3*b^5*(a + b*x)^3) - (a^2*(3*A*b - 4*a*B))/(2*b^5*(a + b*x)^2) + (3*a*(A*b - 2*a*B))/(b^5*(a + b*x)) + ((A*b - 4*a*B)*Log[a + b*x])/b^5","A",3,2,27,0.07407,1,"{27, 77}"
636,1,72,0,0.0329438,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{a^2 B}{2 b^4 (a+b x)^2}+\frac{x^3 (A b-a B)}{3 a b (a+b x)^3}+\frac{2 a B}{b^4 (a+b x)}+\frac{B \log (a+b x)}{b^4}","-\frac{a^2 B}{2 b^4 (a+b x)^2}+\frac{x^3 (A b-a B)}{3 a b (a+b x)^3}+\frac{2 a B}{b^4 (a+b x)}+\frac{B \log (a+b x)}{b^4}",1,"((A*b - a*B)*x^3)/(3*a*b*(a + b*x)^3) - (a^2*B)/(2*b^4*(a + b*x)^2) + (2*a*B)/(b^4*(a + b*x)) + (B*Log[a + b*x])/b^4","A",4,3,27,0.1111,1,"{27, 78, 43}"
637,1,59,0,0.0422136,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{A b-2 a B}{2 b^3 (a+b x)^2}+\frac{a (A b-a B)}{3 b^3 (a+b x)^3}-\frac{B}{b^3 (a+b x)}","-\frac{A b-2 a B}{2 b^3 (a+b x)^2}+\frac{a (A b-a B)}{3 b^3 (a+b x)^3}-\frac{B}{b^3 (a+b x)}",1,"(a*(A*b - a*B))/(3*b^3*(a + b*x)^3) - (A*b - 2*a*B)/(2*b^3*(a + b*x)^2) - B/(b^3*(a + b*x))","A",3,2,25,0.08000,1,"{27, 77}"
638,1,38,0,0.0224458,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{A b-a B}{3 b^2 (a+b x)^3}-\frac{B}{2 b^2 (a+b x)^2}","-\frac{A b-a B}{3 b^2 (a+b x)^3}-\frac{B}{2 b^2 (a+b x)^2}",1,"-(A*b - a*B)/(3*b^2*(a + b*x)^3) - B/(2*b^2*(a + b*x)^2)","A",3,2,24,0.08333,1,"{27, 43}"
639,1,72,0,0.0492757,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{A}{a^3 (a+b x)}+\frac{A}{2 a^2 (a+b x)^2}-\frac{A \log (a+b x)}{a^4}+\frac{A \log (x)}{a^4}+\frac{A b-a B}{3 a b (a+b x)^3}","\frac{A}{a^3 (a+b x)}+\frac{A}{2 a^2 (a+b x)^2}-\frac{A \log (a+b x)}{a^4}+\frac{A \log (x)}{a^4}+\frac{A b-a B}{3 a b (a+b x)^3}",1,"(A*b - a*B)/(3*a*b*(a + b*x)^3) + A/(2*a^2*(a + b*x)^2) + A/(a^3*(a + b*x)) + (A*Log[x])/a^4 - (A*Log[a + b*x])/a^4","A",3,2,27,0.07407,1,"{27, 77}"
640,1,111,0,0.1038003,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{3 A b-a B}{a^4 (a+b x)}-\frac{2 A b-a B}{2 a^3 (a+b x)^2}-\frac{A b-a B}{3 a^2 (a+b x)^3}-\frac{\log (x) (4 A b-a B)}{a^5}+\frac{(4 A b-a B) \log (a+b x)}{a^5}-\frac{A}{a^4 x}","-\frac{3 A b-a B}{a^4 (a+b x)}-\frac{2 A b-a B}{2 a^3 (a+b x)^2}-\frac{A b-a B}{3 a^2 (a+b x)^3}-\frac{\log (x) (4 A b-a B)}{a^5}+\frac{(4 A b-a B) \log (a+b x)}{a^5}-\frac{A}{a^4 x}",1,"-(A/(a^4*x)) - (A*b - a*B)/(3*a^2*(a + b*x)^3) - (2*A*b - a*B)/(2*a^3*(a + b*x)^2) - (3*A*b - a*B)/(a^4*(a + b*x)) - ((4*A*b - a*B)*Log[x])/a^5 + ((4*A*b - a*B)*Log[a + b*x])/a^5","A",3,2,27,0.07407,1,"{27, 77}"
641,1,135,0,0.1213753,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{4 A b-a B}{a^5 x}+\frac{3 b (2 A b-a B)}{a^5 (a+b x)}+\frac{b (3 A b-2 a B)}{2 a^4 (a+b x)^2}+\frac{b (A b-a B)}{3 a^3 (a+b x)^3}+\frac{2 b \log (x) (5 A b-2 a B)}{a^6}-\frac{2 b (5 A b-2 a B) \log (a+b x)}{a^6}-\frac{A}{2 a^4 x^2}","\frac{4 A b-a B}{a^5 x}+\frac{3 b (2 A b-a B)}{a^5 (a+b x)}+\frac{b (3 A b-2 a B)}{2 a^4 (a+b x)^2}+\frac{b (A b-a B)}{3 a^3 (a+b x)^3}+\frac{2 b \log (x) (5 A b-2 a B)}{a^6}-\frac{2 b (5 A b-2 a B) \log (a+b x)}{a^6}-\frac{A}{2 a^4 x^2}",1,"-A/(2*a^4*x^2) + (4*A*b - a*B)/(a^5*x) + (b*(A*b - a*B))/(3*a^3*(a + b*x)^3) + (b*(3*A*b - 2*a*B))/(2*a^4*(a + b*x)^2) + (3*b*(2*A*b - a*B))/(a^5*(a + b*x)) + (2*b*(5*A*b - 2*a*B)*Log[x])/a^6 - (2*b*(5*A*b - 2*a*B)*Log[a + b*x])/a^6","A",3,2,27,0.07407,1,"{27, 77}"
642,1,166,0,0.16872,"\int \frac{A+B x}{x^4 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(x^4*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{2 b^2 (5 A b-3 a B)}{a^6 (a+b x)}-\frac{b^2 (4 A b-3 a B)}{2 a^5 (a+b x)^2}-\frac{b^2 (A b-a B)}{3 a^4 (a+b x)^3}-\frac{10 b^2 \log (x) (2 A b-a B)}{a^7}+\frac{10 b^2 (2 A b-a B) \log (a+b x)}{a^7}+\frac{4 A b-a B}{2 a^5 x^2}-\frac{2 b (5 A b-2 a B)}{a^6 x}-\frac{A}{3 a^4 x^3}","-\frac{2 b^2 (5 A b-3 a B)}{a^6 (a+b x)}-\frac{b^2 (4 A b-3 a B)}{2 a^5 (a+b x)^2}-\frac{b^2 (A b-a B)}{3 a^4 (a+b x)^3}-\frac{10 b^2 \log (x) (2 A b-a B)}{a^7}+\frac{10 b^2 (2 A b-a B) \log (a+b x)}{a^7}+\frac{4 A b-a B}{2 a^5 x^2}-\frac{2 b (5 A b-2 a B)}{a^6 x}-\frac{A}{3 a^4 x^3}",1,"-A/(3*a^4*x^3) + (4*A*b - a*B)/(2*a^5*x^2) - (2*b*(5*A*b - 2*a*B))/(a^6*x) - (b^2*(A*b - a*B))/(3*a^4*(a + b*x)^3) - (b^2*(4*A*b - 3*a*B))/(2*a^5*(a + b*x)^2) - (2*b^2*(5*A*b - 3*a*B))/(a^6*(a + b*x)) - (10*b^2*(2*A*b - a*B)*Log[x])/a^7 + (10*b^2*(2*A*b - a*B)*Log[a + b*x])/a^7","A",3,2,27,0.07407,1,"{27, 77}"
643,1,171,0,0.2163967,"\int \frac{x^6 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^6*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{a^6 (A b-a B)}{5 b^8 (a+b x)^5}+\frac{a^5 (6 A b-7 a B)}{4 b^8 (a+b x)^4}-\frac{a^4 (5 A b-7 a B)}{b^8 (a+b x)^3}+\frac{5 a^3 (4 A b-7 a B)}{2 b^8 (a+b x)^2}-\frac{5 a^2 (3 A b-7 a B)}{b^8 (a+b x)}+\frac{x (A b-6 a B)}{b^7}-\frac{3 a (2 A b-7 a B) \log (a+b x)}{b^8}+\frac{B x^2}{2 b^6}","-\frac{a^6 (A b-a B)}{5 b^8 (a+b x)^5}+\frac{a^5 (6 A b-7 a B)}{4 b^8 (a+b x)^4}-\frac{a^4 (5 A b-7 a B)}{b^8 (a+b x)^3}+\frac{5 a^3 (4 A b-7 a B)}{2 b^8 (a+b x)^2}-\frac{5 a^2 (3 A b-7 a B)}{b^8 (a+b x)}+\frac{x (A b-6 a B)}{b^7}-\frac{3 a (2 A b-7 a B) \log (a+b x)}{b^8}+\frac{B x^2}{2 b^6}",1,"((A*b - 6*a*B)*x)/b^7 + (B*x^2)/(2*b^6) - (a^6*(A*b - a*B))/(5*b^8*(a + b*x)^5) + (a^5*(6*A*b - 7*a*B))/(4*b^8*(a + b*x)^4) - (a^4*(5*A*b - 7*a*B))/(b^8*(a + b*x)^3) + (5*a^3*(4*A*b - 7*a*B))/(2*b^8*(a + b*x)^2) - (5*a^2*(3*A*b - 7*a*B))/(b^8*(a + b*x)) - (3*a*(2*A*b - 7*a*B)*Log[a + b*x])/b^8","A",3,2,27,0.07407,1,"{27, 77}"
644,1,146,0,0.1632009,"\int \frac{x^5 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^5*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{a^5 (A b-a B)}{5 b^7 (a+b x)^5}-\frac{a^4 (5 A b-6 a B)}{4 b^7 (a+b x)^4}+\frac{5 a^3 (2 A b-3 a B)}{3 b^7 (a+b x)^3}-\frac{5 a^2 (A b-2 a B)}{b^7 (a+b x)^2}+\frac{5 a (A b-3 a B)}{b^7 (a+b x)}+\frac{(A b-6 a B) \log (a+b x)}{b^7}+\frac{B x}{b^6}","\frac{a^5 (A b-a B)}{5 b^7 (a+b x)^5}-\frac{a^4 (5 A b-6 a B)}{4 b^7 (a+b x)^4}+\frac{5 a^3 (2 A b-3 a B)}{3 b^7 (a+b x)^3}-\frac{5 a^2 (A b-2 a B)}{b^7 (a+b x)^2}+\frac{5 a (A b-3 a B)}{b^7 (a+b x)}+\frac{(A b-6 a B) \log (a+b x)}{b^7}+\frac{B x}{b^6}",1,"(B*x)/b^6 + (a^5*(A*b - a*B))/(5*b^7*(a + b*x)^5) - (a^4*(5*A*b - 6*a*B))/(4*b^7*(a + b*x)^4) + (5*a^3*(2*A*b - 3*a*B))/(3*b^7*(a + b*x)^3) - (5*a^2*(A*b - 2*a*B))/(b^7*(a + b*x)^2) + (5*a*(A*b - 3*a*B))/(b^7*(a + b*x)) + ((A*b - 6*a*B)*Log[a + b*x])/b^7","A",3,2,27,0.07407,1,"{27, 77}"
645,1,106,0,0.0617757,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{3 a^2 B}{b^6 (a+b x)^2}+\frac{4 a^3 B}{3 b^6 (a+b x)^3}-\frac{a^4 B}{4 b^6 (a+b x)^4}+\frac{x^5 (A b-a B)}{5 a b (a+b x)^5}+\frac{4 a B}{b^6 (a+b x)}+\frac{B \log (a+b x)}{b^6}","-\frac{3 a^2 B}{b^6 (a+b x)^2}+\frac{4 a^3 B}{3 b^6 (a+b x)^3}-\frac{a^4 B}{4 b^6 (a+b x)^4}+\frac{x^5 (A b-a B)}{5 a b (a+b x)^5}+\frac{4 a B}{b^6 (a+b x)}+\frac{B \log (a+b x)}{b^6}",1,"((A*b - a*B)*x^5)/(5*a*b*(a + b*x)^5) - (a^4*B)/(4*b^6*(a + b*x)^4) + (4*a^3*B)/(3*b^6*(a + b*x)^3) - (3*a^2*B)/(b^6*(a + b*x)^2) + (4*a*B)/(b^6*(a + b*x)) + (B*Log[a + b*x])/b^6","A",4,3,27,0.1111,1,"{27, 78, 43}"
646,1,57,0,0.0144524,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^4 (4 a B+A b)}{20 a^2 b (a+b x)^4}+\frac{x^4 (A b-a B)}{5 a b (a+b x)^5}","\frac{x^4 (4 a B+A b)}{20 a^2 b (a+b x)^4}+\frac{x^4 (A b-a B)}{5 a b (a+b x)^5}",1,"((A*b - a*B)*x^4)/(5*a*b*(a + b*x)^5) + ((A*b + 4*a*B)*x^4)/(20*a^2*b*(a + b*x)^4)","A",3,3,27,0.1111,1,"{27, 78, 37}"
647,1,87,0,0.0656881,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{a^2 (A b-a B)}{5 b^4 (a+b x)^5}+\frac{a (2 A b-3 a B)}{4 b^4 (a+b x)^4}-\frac{A b-3 a B}{3 b^4 (a+b x)^3}-\frac{B}{2 b^4 (a+b x)^2}","-\frac{a^2 (A b-a B)}{5 b^4 (a+b x)^5}+\frac{a (2 A b-3 a B)}{4 b^4 (a+b x)^4}-\frac{A b-3 a B}{3 b^4 (a+b x)^3}-\frac{B}{2 b^4 (a+b x)^2}",1,"-(a^2*(A*b - a*B))/(5*b^4*(a + b*x)^5) + (a*(2*A*b - 3*a*B))/(4*b^4*(a + b*x)^4) - (A*b - 3*a*B)/(3*b^4*(a + b*x)^3) - B/(2*b^4*(a + b*x)^2)","A",3,2,27,0.07407,1,"{27, 77}"
648,1,61,0,0.0418753,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{A b-2 a B}{4 b^3 (a+b x)^4}+\frac{a (A b-a B)}{5 b^3 (a+b x)^5}-\frac{B}{3 b^3 (a+b x)^3}","-\frac{A b-2 a B}{4 b^3 (a+b x)^4}+\frac{a (A b-a B)}{5 b^3 (a+b x)^5}-\frac{B}{3 b^3 (a+b x)^3}",1,"(a*(A*b - a*B))/(5*b^3*(a + b*x)^5) - (A*b - 2*a*B)/(4*b^3*(a + b*x)^4) - B/(3*b^3*(a + b*x)^3)","A",3,2,25,0.08000,1,"{27, 77}"
649,1,38,0,0.0231924,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{A b-a B}{5 b^2 (a+b x)^5}-\frac{B}{4 b^2 (a+b x)^4}","-\frac{A b-a B}{5 b^2 (a+b x)^5}-\frac{B}{4 b^2 (a+b x)^4}",1,"-(A*b - a*B)/(5*b^2*(a + b*x)^5) - B/(4*b^2*(a + b*x)^4)","A",3,2,24,0.08333,1,"{27, 43}"
650,1,102,0,0.0742038,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{A}{a^5 (a+b x)}+\frac{A}{2 a^4 (a+b x)^2}+\frac{A}{3 a^3 (a+b x)^3}+\frac{A}{4 a^2 (a+b x)^4}-\frac{A \log (a+b x)}{a^6}+\frac{A \log (x)}{a^6}+\frac{A b-a B}{5 a b (a+b x)^5}","\frac{A}{a^5 (a+b x)}+\frac{A}{2 a^4 (a+b x)^2}+\frac{A}{3 a^3 (a+b x)^3}+\frac{A}{4 a^2 (a+b x)^4}-\frac{A \log (a+b x)}{a^6}+\frac{A \log (x)}{a^6}+\frac{A b-a B}{5 a b (a+b x)^5}",1,"(A*b - a*B)/(5*a*b*(a + b*x)^5) + A/(4*a^2*(a + b*x)^4) + A/(3*a^3*(a + b*x)^3) + A/(2*a^4*(a + b*x)^2) + A/(a^5*(a + b*x)) + (A*Log[x])/a^6 - (A*Log[a + b*x])/a^6","A",3,2,27,0.07407,1,"{27, 77}"
651,1,157,0,0.1645464,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{5 A b-a B}{a^6 (a+b x)}-\frac{4 A b-a B}{2 a^5 (a+b x)^2}-\frac{3 A b-a B}{3 a^4 (a+b x)^3}-\frac{2 A b-a B}{4 a^3 (a+b x)^4}-\frac{A b-a B}{5 a^2 (a+b x)^5}-\frac{\log (x) (6 A b-a B)}{a^7}+\frac{(6 A b-a B) \log (a+b x)}{a^7}-\frac{A}{a^6 x}","-\frac{5 A b-a B}{a^6 (a+b x)}-\frac{4 A b-a B}{2 a^5 (a+b x)^2}-\frac{3 A b-a B}{3 a^4 (a+b x)^3}-\frac{2 A b-a B}{4 a^3 (a+b x)^4}-\frac{A b-a B}{5 a^2 (a+b x)^5}-\frac{\log (x) (6 A b-a B)}{a^7}+\frac{(6 A b-a B) \log (a+b x)}{a^7}-\frac{A}{a^6 x}",1,"-(A/(a^6*x)) - (A*b - a*B)/(5*a^2*(a + b*x)^5) - (2*A*b - a*B)/(4*a^3*(a + b*x)^4) - (3*A*b - a*B)/(3*a^4*(a + b*x)^3) - (4*A*b - a*B)/(2*a^5*(a + b*x)^2) - (5*A*b - a*B)/(a^6*(a + b*x)) - ((6*A*b - a*B)*Log[x])/a^7 + ((6*A*b - a*B)*Log[a + b*x])/a^7","A",3,2,27,0.07407,1,"{27, 77}"
652,1,177,0,0.2029577,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{6 A b-a B}{a^7 x}+\frac{5 b (3 A b-a B)}{a^7 (a+b x)}+\frac{b (5 A b-2 a B)}{a^6 (a+b x)^2}+\frac{b (2 A b-a B)}{a^5 (a+b x)^3}+\frac{b (3 A b-2 a B)}{4 a^4 (a+b x)^4}+\frac{b (A b-a B)}{5 a^3 (a+b x)^5}+\frac{3 b \log (x) (7 A b-2 a B)}{a^8}-\frac{3 b (7 A b-2 a B) \log (a+b x)}{a^8}-\frac{A}{2 a^6 x^2}","\frac{6 A b-a B}{a^7 x}+\frac{5 b (3 A b-a B)}{a^7 (a+b x)}+\frac{b (5 A b-2 a B)}{a^6 (a+b x)^2}+\frac{b (2 A b-a B)}{a^5 (a+b x)^3}+\frac{b (3 A b-2 a B)}{4 a^4 (a+b x)^4}+\frac{b (A b-a B)}{5 a^3 (a+b x)^5}+\frac{3 b \log (x) (7 A b-2 a B)}{a^8}-\frac{3 b (7 A b-2 a B) \log (a+b x)}{a^8}-\frac{A}{2 a^6 x^2}",1,"-A/(2*a^6*x^2) + (6*A*b - a*B)/(a^7*x) + (b*(A*b - a*B))/(5*a^3*(a + b*x)^5) + (b*(3*A*b - 2*a*B))/(4*a^4*(a + b*x)^4) + (b*(2*A*b - a*B))/(a^5*(a + b*x)^3) + (b*(5*A*b - 2*a*B))/(a^6*(a + b*x)^2) + (5*b*(3*A*b - a*B))/(a^7*(a + b*x)) + (3*b*(7*A*b - 2*a*B)*Log[x])/a^8 - (3*b*(7*A*b - 2*a*B)*Log[a + b*x])/a^8","A",3,2,27,0.07407,1,"{27, 77}"
653,1,114,0,0.0670668,"\int x^4 (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^4*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{6 (a+b x)}+\frac{a A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{b B x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}","\frac{x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{6 (a+b x)}+\frac{a A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{b B x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}",1,"(a*A*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + ((A*b + a*B)*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (b*B*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
654,1,114,0,0.0593381,"\int x^3 (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^3*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^5 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{a A x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{b B x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}","\frac{x^5 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{a A x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{b B x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}",1,"(a*A*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + ((A*b + a*B)*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (b*B*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
655,1,114,0,0.0571252,"\int x^2 (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^2*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 (a+b x)}+\frac{a A x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{b B x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","\frac{x^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 (a+b x)}+\frac{a A x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{b B x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(a*A*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + ((A*b + a*B)*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (b*B*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
656,1,114,0,0.0456135,"\int x (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^3 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{a A x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{b B x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}","\frac{x^3 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{a A x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{b B x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}",1,"(a*A*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + ((A*b + a*B)*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (b*B*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x))","A",3,2,27,0.07407,1,"{770, 76}"
657,1,69,0,0.0217286,"\int (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}",1,"((A*b - a*B)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^2) + (B*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(3*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
658,1,105,0,0.0400829,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x,x]","\frac{x \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{a A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}","\frac{x \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{a A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}",1,"((A*b + a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b*B*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
659,1,103,0,0.042111,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^2} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^2,x]","\frac{\log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","\frac{\log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-((a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x))) + (b*B*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + ((A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
660,1,108,0,0.043048,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^3} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^3,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}+\frac{b B \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}+\frac{b B \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - ((A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
661,1,75,0,0.0448886,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^4} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^4,x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 a^2 x^2}-\frac{A \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 a^2 x^3}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 a^2 x^2}-\frac{A \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 a^2 x^3}",1,"((A*b - a*B)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*a^2*x^2) - (A*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(3*a^2*x^3)","A",3,3,29,0.1034,1,"{769, 646, 37}"
662,1,114,0,0.0432004,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^5} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^5,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^3 (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^3 (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}",1,"-(a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - ((A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
663,1,114,0,0.0458225,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^6} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^6,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 x^4 (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 x^4 (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-(a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - ((A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
664,1,114,0,0.0420473,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^7} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^7,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 x^5 (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 x^5 (a+b x)}-\frac{a A \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}",1,"-(a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - ((A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
665,1,210,0,0.1262297,"\int x^5 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^5*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^2 x^9 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{9 (a+b x)}+\frac{3 a b x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{8 (a+b x)}+\frac{a^2 x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{7 (a+b x)}+\frac{a^3 A x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}+\frac{b^3 B x^{10} \sqrt{a^2+2 a b x+b^2 x^2}}{10 (a+b x)}","\frac{b^2 x^9 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{9 (a+b x)}+\frac{3 a b x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{8 (a+b x)}+\frac{a^2 x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{7 (a+b x)}+\frac{a^3 A x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}+\frac{b^3 B x^{10} \sqrt{a^2+2 a b x+b^2 x^2}}{10 (a+b x)}",1,"(a^3*A*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (a^2*(3*A*b + a*B)*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (3*a*b*(A*b + a*B)*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x)) + (b^2*(A*b + 3*a*B)*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (b^3*B*x^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
666,1,210,0,0.092834,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{8 (a+b x)}+\frac{3 a b x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{a^2 x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{6 (a+b x)}+\frac{a^3 A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{b^3 B x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}","\frac{b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{8 (a+b x)}+\frac{3 a b x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{a^2 x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{6 (a+b x)}+\frac{a^3 A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{b^3 B x^9 \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}",1,"(a^3*A*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a^2*(3*A*b + a*B)*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (3*a*b*(A*b + a*B)*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (b^2*(A*b + 3*a*B)*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x)) + (b^3*B*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
667,1,210,0,0.0882991,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^2 x^7 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{7 (a+b x)}+\frac{a b x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{2 (a+b x)}+\frac{a^2 x^5 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 (a+b x)}+\frac{a^3 A x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{b^3 B x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}","\frac{b^2 x^7 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{7 (a+b x)}+\frac{a b x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{2 (a+b x)}+\frac{a^2 x^5 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 (a+b x)}+\frac{a^3 A x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{b^3 B x^8 \sqrt{a^2+2 a b x+b^2 x^2}}{8 (a+b x)}",1,"(a^3*A*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (a^2*(3*A*b + a*B)*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a*b*(A*b + a*B)*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^2*(A*b + 3*a*B)*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (b^3*B*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
668,1,210,0,0.0870089,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^2 x^6 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{6 (a+b x)}+\frac{3 a b x^5 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{a^2 x^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{4 (a+b x)}+\frac{a^3 A x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{b^3 B x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}","\frac{b^2 x^6 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{6 (a+b x)}+\frac{3 a b x^5 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{a^2 x^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{4 (a+b x)}+\frac{a^3 A x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{b^3 B x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}",1,"(a^3*A*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (a^2*(3*A*b + a*B)*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (3*a*b*(A*b + a*B)*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (b^2*(A*b + 3*a*B)*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (b^3*B*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
669,1,121,0,0.068253,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (A b-2 a B)}{5 b^3}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B)}{4 b^3}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (A b-2 a B)}{5 b^3}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B)}{4 b^3}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}",1,"-(a*(A*b - a*B)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^3) + ((A*b - 2*a*B)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^3) + (B*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3)","A",3,2,27,0.07407,1,"{770, 76}"
670,1,69,0,0.0212772,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (A b-a B)}{4 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (A b-a B)}{4 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}",1,"((A*b - a*B)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^2) + (B*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
671,1,182,0,0.0618986,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x,x]","\frac{3 a^2 A b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{3 a A b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{A b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{a^3 A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{B (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 b}","\frac{3 a^2 A b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{3 a A b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}+\frac{A b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{a^3 A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{B (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 b}",1,"(3*a^2*A*b*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (3*a*A*b^2*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (A*b^3*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (B*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b) + (a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",4,3,29,0.1034,1,"{770, 80, 43}"
672,1,200,0,0.0857908,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^2,x]","\frac{3 a b x \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{2 (a+b x)}+\frac{a^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 B x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}","\frac{3 a b x \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{2 (a+b x)}+\frac{a^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 B x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}",1,"-((a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x))) + (3*a*b*(A*b + a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^2*(A*b + 3*a*B)*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^3*B*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
673,1,200,0,0.0884344,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^3,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{x (a+b x)}+\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{a+b x}+\frac{3 a b \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}+\frac{b^3 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{x (a+b x)}+\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{a+b x}+\frac{3 a b \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}+\frac{b^3 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^2*(A*b + 3*a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^3*B*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (3*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
674,1,199,0,0.085728,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^4,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{2 x^2 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x (a+b x)}+\frac{b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}+\frac{b^3 B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{2 x^2 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x (a+b x)}+\frac{b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{a+b x}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}+\frac{b^3 B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (3*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^3*B*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
675,1,187,0,0.0646695,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^5,x]","-\frac{A (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 a x^4}-\frac{a^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{3 a^2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{3 a b^2 B \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 B \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{A (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 a x^4}-\frac{a^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{3 a^2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}-\frac{3 a b^2 B \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^3 B \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (3*a^2*b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (3*a*b^2*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) - (A*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*a*x^4) + (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",4,3,29,0.1034,1,"{770, 78, 43}"
676,1,77,0,0.0456049,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^6,x]","\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{4 a^2 x^4}-\frac{A \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 a^2 x^5}","\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{4 a^2 x^4}-\frac{A \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 a^2 x^5}",1,"((A*b - a*B)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*a^2*x^4) - (A*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*a^2*x^5)","A",3,3,29,0.1034,1,"{769, 646, 37}"
677,1,210,0,0.0789072,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^7,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 x^5 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 x^4 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{3 x^3 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 x^5 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 x^4 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{3 x^3 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (3*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
678,1,210,0,0.0781717,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^8,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{6 x^6 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 x^5 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{4 x^4 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{6 x^6 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 x^5 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{4 x^4 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (3*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
679,1,210,0,0.0807631,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^9,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{7 x^7 (a+b x)}-\frac{a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{2 x^6 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{5 x^5 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{7 x^7 (a+b x)}-\frac{a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{2 x^6 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{5 x^5 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{8 x^8 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^6*(a + b*x)) - (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
680,1,210,0,0.0777503,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^10,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{8 x^8 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 x^7 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{6 x^6 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{8 x^8 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 x^7 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{6 x^6 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (3*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
681,1,210,0,0.0781143,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^11,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{9 x^9 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{8 x^8 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{7 x^7 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{9 x^9 (a+b x)}-\frac{3 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{8 x^8 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{7 x^7 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*x^10*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (3*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
682,1,210,0,0.0786117,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{12}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^12,x]","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{10 x^{10} (a+b x)}-\frac{a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^9 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{8 x^8 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}","-\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{10 x^{10} (a+b x)}-\frac{a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^9 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{8 x^8 (a+b x)}-\frac{a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}",1,"-(a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*x^11*(a + b*x)) - (a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*x^10*(a + b*x)) - (a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^9*(a + b*x)) - (b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
683,1,303,0,0.1767525,"\int x^6 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^6*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^4 x^{12} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{12 (a+b x)}+\frac{5 a b^3 x^{11} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{11 (a+b x)}+\frac{a^2 b^2 x^{10} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{5 a^3 b x^9 \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{9 (a+b x)}+\frac{a^4 x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{8 (a+b x)}+\frac{a^5 A x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{b^5 B x^{13} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}","\frac{b^4 x^{12} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{12 (a+b x)}+\frac{5 a b^3 x^{11} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{11 (a+b x)}+\frac{a^2 b^2 x^{10} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{5 a^3 b x^9 \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{9 (a+b x)}+\frac{a^4 x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{8 (a+b x)}+\frac{a^5 A x^7 \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{b^5 B x^{13} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}",1,"(a^5*A*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (a^4*(5*A*b + a*B)*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x)) + (5*a^3*b*(2*A*b + a*B)*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (a^2*b^2*(A*b + a*B)*x^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a*b^3*(A*b + 2*a*B)*x^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (b^4*(A*b + 5*a*B)*x^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*(a + b*x)) + (b^5*B*x^13*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
684,1,306,0,0.1406781,"\int x^5 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^5*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^4 x^{11} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{11 (a+b x)}+\frac{a b^3 x^{10} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{2 (a+b x)}+\frac{10 a^2 b^2 x^9 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 (a+b x)}+\frac{5 a^3 b x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{8 (a+b x)}+\frac{a^4 x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{7 (a+b x)}+\frac{a^5 A x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}+\frac{b^5 B x^{12} \sqrt{a^2+2 a b x+b^2 x^2}}{12 (a+b x)}","\frac{b^4 x^{11} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{11 (a+b x)}+\frac{a b^3 x^{10} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{2 (a+b x)}+\frac{10 a^2 b^2 x^9 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 (a+b x)}+\frac{5 a^3 b x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{8 (a+b x)}+\frac{a^4 x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{7 (a+b x)}+\frac{a^5 A x^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 (a+b x)}+\frac{b^5 B x^{12} \sqrt{a^2+2 a b x+b^2 x^2}}{12 (a+b x)}",1,"(a^5*A*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (a^4*(5*A*b + a*B)*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (5*a^3*b*(2*A*b + a*B)*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(a + b*x)) + (10*a^2*b^2*(A*b + a*B)*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (a*b^3*(A*b + 2*a*B)*x^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^4*(A*b + 5*a*B)*x^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (b^5*B*x^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
685,1,306,0,0.1270829,"\int x^4 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^4*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^4 x^{10} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{10 (a+b x)}+\frac{5 a b^3 x^9 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{9 (a+b x)}+\frac{5 a^2 b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 (a+b x)}+\frac{5 a^3 b x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{7 (a+b x)}+\frac{a^4 x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{6 (a+b x)}+\frac{a^5 A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{b^5 B x^{11} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}","\frac{b^4 x^{10} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{10 (a+b x)}+\frac{5 a b^3 x^9 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{9 (a+b x)}+\frac{5 a^2 b^2 x^8 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 (a+b x)}+\frac{5 a^3 b x^7 \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{7 (a+b x)}+\frac{a^4 x^6 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{6 (a+b x)}+\frac{a^5 A x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{b^5 B x^{11} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}",1,"(a^5*A*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a^4*(5*A*b + a*B)*x^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(a + b*x)) + (5*a^3*b*(2*A*b + a*B)*x^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (5*a^2*b^2*(A*b + a*B)*x^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (5*a*b^3*(A*b + 2*a*B)*x^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (b^4*(A*b + 5*a*B)*x^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*(a + b*x)) + (b^5*B*x^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
686,1,212,0,0.1189614,"\int x^3 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^3*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (A b-4 a B)}{9 b^5}-\frac{3 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (A b-2 a B)}{8 b^5}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (3 A b-4 a B)}{7 b^5}-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 b^5}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (A b-4 a B)}{9 b^5}-\frac{3 a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (A b-2 a B)}{8 b^5}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (3 A b-4 a B)}{7 b^5}-\frac{a^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 b^5}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}",1,"-(a^3*(A*b - a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^5) + (a^2*(3*A*b - 4*a*B)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) - (3*a*(A*b - 2*a*B)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^5) + ((A*b - 4*a*B)*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^5) + (B*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*b^5)","A",3,2,29,0.06897,1,"{770, 76}"
687,1,167,0,0.102302,"\int x^2 (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^2*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (A b-3 a B)}{8 b^4}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (2 A b-3 a B)}{7 b^4}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 b^4}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (A b-3 a B)}{8 b^4}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (2 A b-3 a B)}{7 b^4}+\frac{a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 b^4}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}",1,"(a^2*(A*b - a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^4) - (a*(2*A*b - 3*a*B)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4) + ((A*b - 3*a*B)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^4) + (B*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^4)","A",3,2,29,0.06897,1,"{770, 76}"
688,1,121,0,0.0757351,"\int x (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (A b-2 a B)}{7 b^3}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 b^3}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (A b-2 a B)}{7 b^3}-\frac{a \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 b^3}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}",1,"-(a*(A*b - a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3) + ((A*b - 2*a*B)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^3) + (B*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^3)","A",3,2,27,0.07407,1,"{770, 76}"
689,1,69,0,0.0213433,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (A b-a B)}{6 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (A b-a B)}{6 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}",1,"((A*b - a*B)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^2) + (B*(a^2 + 2*a*b*x + b^2*x^2)^(7/2))/(7*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
690,1,262,0,0.0771679,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x,x]","\frac{5 a^4 A b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a^3 A b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{10 a^2 A b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{5 a A b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{A b^5 x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a^5 A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{B (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 b}","\frac{5 a^4 A b x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{5 a^3 A b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{10 a^2 A b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{5 a A b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}+\frac{A b^5 x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{a^5 A \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{B (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 b}",1,"(5*a^4*A*b*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a^3*A*b^2*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (10*a^2*A*b^3*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (5*a*A*b^4*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (A*b^5*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (B*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b) + (a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",4,3,29,0.1034,1,"{770, 80, 43}"
691,1,294,0,0.1232888,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^2,x]","\frac{5 a^3 b x \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}+\frac{5 a^2 b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{5 a b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{3 (a+b x)}+\frac{b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{4 (a+b x)}+\frac{a^4 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 B x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","\frac{5 a^3 b x \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}+\frac{5 a^2 b^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{5 a b^3 x^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{3 (a+b x)}+\frac{b^4 x^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{4 (a+b x)}+\frac{a^4 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 B x^5 \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"-((a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x))) + (5*a^3*b*(2*A*b + a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a^2*b^2*(A*b + a*B)*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a*b^3*(A*b + 2*a*B)*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (b^4*(A*b + 5*a*B)*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (b^5*B*x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
692,1,297,0,0.121442,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^3,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{x (a+b x)}+\frac{10 a^2 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{5 a b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{2 (a+b x)}+\frac{b^4 x^3 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{3 (a+b x)}+\frac{5 a^3 b \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}+\frac{b^5 B x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{x (a+b x)}+\frac{10 a^2 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{5 a b^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{2 (a+b x)}+\frac{b^4 x^3 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{3 (a+b x)}+\frac{5 a^3 b \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{2 x^2 (a+b x)}+\frac{b^5 B x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (10*a^2*b^2*(A*b + a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (5*a*b^3*(A*b + 2*a*B)*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^4*(A*b + 5*a*B)*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (b^5*B*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x)) + (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
693,1,297,0,0.1224219,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^4,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{2 x^2 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{x (a+b x)}+\frac{5 a b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}+\frac{b^4 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{2 (a+b x)}+\frac{10 a^2 b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}+\frac{b^5 B x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{2 x^2 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{x (a+b x)}+\frac{5 a b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}+\frac{b^4 x^2 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{2 (a+b x)}+\frac{10 a^2 b^2 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}+\frac{b^5 B x^3 \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (5*a*b^3*(A*b + 2*a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^4*(A*b + 5*a*B)*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (b^5*B*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (10*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
694,1,296,0,0.1285844,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^5,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{3 x^3 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{2 x^2 (a+b x)}-\frac{10 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x (a+b x)}+\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{a+b x}+\frac{5 a b^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}+\frac{b^5 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{3 x^3 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{2 x^2 (a+b x)}-\frac{10 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x (a+b x)}+\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{a+b x}+\frac{5 a b^3 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}+\frac{b^5 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^2*(a + b*x)) - (10*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^4*(A*b + 5*a*B)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^5*B*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + (5*a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
695,1,293,0,0.1161378,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^6,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{4 x^4 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{3 x^3 (a+b x)}-\frac{5 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x^2 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{x (a+b x)}+\frac{b^4 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}+\frac{b^5 B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{4 x^4 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{3 x^3 (a+b x)}-\frac{5 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x^2 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{x (a+b x)}+\frac{b^4 \log (x) \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{a+b x}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}+\frac{b^5 B x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (5*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^2*(a + b*x)) - (5*a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) + (b^5*B*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (b^4*(A*b + 5*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",3,2,29,0.06897,1,"{770, 76}"
696,1,267,0,0.0839709,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^7,x]","-\frac{A (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 a x^6}-\frac{a^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{5 a^4 b B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{10 a^3 b^2 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\frac{5 a b^4 B \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 B \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{A (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 a x^6}-\frac{a^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}-\frac{5 a^4 b B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}-\frac{10 a^3 b^2 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}-\frac{5 a^2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{x^2 (a+b x)}-\frac{5 a b^4 B \sqrt{a^2+2 a b x+b^2 x^2}}{x (a+b x)}+\frac{b^5 B \log (x) \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"-(a^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (5*a^4*b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (10*a^3*b^2*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x)) - (5*a^2*b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^2*(a + b*x)) - (5*a*b^4*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x*(a + b*x)) - (A*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*a*x^6) + (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[x])/(a + b*x)","A",4,3,29,0.1034,1,"{770, 78, 43}"
697,1,77,0,0.0466944,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^8,x]","\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{6 a^2 x^6}-\frac{A \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 a^2 x^7}","\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{6 a^2 x^6}-\frac{A \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 a^2 x^7}",1,"((A*b - a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*a^2*x^6) - (A*(a^2 + 2*a*b*x + b^2*x^2)^(7/2))/(7*a^2*x^7)","A",3,3,29,0.1034,1,"{769, 646, 37}"
698,1,130,0,0.0729824,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^9,x]","-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-4 a B)}{168 a^3 x^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-4 a B)}{28 a^2 x^7}-\frac{A \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{8 a x^8}","-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-4 a B)}{168 a^3 x^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-4 a B)}{28 a^2 x^7}-\frac{A \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{8 a x^8}",1,"-(A*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*a*x^8) + ((A*b - 4*a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(28*a^2*x^7) - (b*(A*b - 4*a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(168*a^3*x^6)","A",4,4,29,0.1379,1,"{770, 78, 45, 37}"
699,1,304,0,0.1169302,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^10,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{8 x^8 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{7 x^7 (a+b x)}-\frac{5 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^6 (a+b x)}-\frac{a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{x^5 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{4 x^4 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{8 x^8 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{7 x^7 (a+b x)}-\frac{5 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^6 (a+b x)}-\frac{a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{x^5 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{4 x^4 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{9 x^9 (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^3 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (5*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^6*(a + b*x)) - (a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^5*(a + b*x)) - (b^4*(A*b + 5*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x)) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^3*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
700,1,306,0,0.1120365,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^11,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{9 x^9 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{8 x^8 (a+b x)}-\frac{10 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 x^7 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{6 x^6 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{5 x^5 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{9 x^9 (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{8 x^8 (a+b x)}-\frac{10 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 x^7 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{6 x^6 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{5 x^5 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{10 x^{10} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 x^4 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*x^10*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (10*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (5*a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (b^4*(A*b + 5*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x)) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^4*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
701,1,306,0,0.1172553,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{12}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^12,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{10 x^{10} (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{9 x^9 (a+b x)}-\frac{5 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 x^8 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{7 x^7 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{6 x^6 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{10 x^{10} (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{9 x^9 (a+b x)}-\frac{5 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{4 x^8 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{7 x^7 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{6 x^6 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{11 x^{11} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^5 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*x^11*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*x^10*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (5*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*x^8*(a + b*x)) - (5*a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (b^4*(A*b + 5*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x)) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^5*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
702,1,306,0,0.1133036,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{13}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^13,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{11 x^{11} (a+b x)}-\frac{a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{2 x^{10} (a+b x)}-\frac{10 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 x^9 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{8 x^8 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{7 x^7 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{12 x^{12} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{11 x^{11} (a+b x)}-\frac{a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{2 x^{10} (a+b x)}-\frac{10 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 x^9 (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{8 x^8 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{7 x^7 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{12 x^{12} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 x^6 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*x^12*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*x^11*(a + b*x)) - (a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*x^10*(a + b*x)) - (10*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (5*a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (b^4*(A*b + 5*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x)) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*x^6*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
703,1,304,0,0.1166205,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{14}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^14,x]","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{12 x^{12} (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{11 x^{11} (a+b x)}-\frac{a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x^{10} (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{9 x^9 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{8 x^8 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{13 x^{13} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}","-\frac{a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{12 x^{12} (a+b x)}-\frac{5 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{11 x^{11} (a+b x)}-\frac{a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x^{10} (a+b x)}-\frac{5 a b^3 \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{9 x^9 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{8 x^8 (a+b x)}-\frac{a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{13 x^{13} (a+b x)}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^7 (a+b x)}",1,"-(a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*x^13*(a + b*x)) - (a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*x^12*(a + b*x)) - (5*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*x^11*(a + b*x)) - (a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^10*(a + b*x)) - (5*a*b^3*(A*b + 2*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*x^9*(a + b*x)) - (b^4*(A*b + 5*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*x^8*(a + b*x)) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^7*(a + b*x))","A",3,2,29,0.06897,1,"{770, 76}"
704,1,258,0,0.1535214,"\int \frac{x^4 (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x^4*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^4 (a+b x) (A b-a B)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^3 (a+b x) (A b-a B)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 x^2 (a+b x) (A b-a B)}{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^3 x (a+b x) (A b-a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^4 (a+b x) (A b-a B) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^5 (a+b x)}{5 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^4 (a+b x) (A b-a B)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^3 (a+b x) (A b-a B)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 x^2 (a+b x) (A b-a B)}{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^3 x (a+b x) (A b-a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^4 (a+b x) (A b-a B) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^5 (a+b x)}{5 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((a^3*(A*b - a*B)*x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (a^2*(A*b - a*B)*x^2*(a + b*x))/(2*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a*(A*b - a*B)*x^3*(a + b*x))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^4*(a + b*x))/(4*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x^5*(a + b*x))/(5*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (a^4*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
705,1,212,0,0.1146334,"\int \frac{x^3 (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x^3*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^3 (a+b x) (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^2 (a+b x) (A b-a B)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 x (a+b x) (A b-a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^3 (a+b x) (A b-a B) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^4 (a+b x)}{4 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^3 (a+b x) (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x^2 (a+b x) (A b-a B)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 x (a+b x) (A b-a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^3 (a+b x) (A b-a B) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^4 (a+b x)}{4 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(a^2*(A*b - a*B)*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a*(A*b - a*B)*x^2*(a + b*x))/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^3*(a + b*x))/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x^4*(a + b*x))/(4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a^3*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
706,1,166,0,0.0897315,"\int \frac{x^2 (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x^2*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^2 (a+b x) (A b-a B)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x (a+b x) (A b-a B)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 (a+b x) (A b-a B) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^3 (a+b x)}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^2 (a+b x) (A b-a B)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a x (a+b x) (A b-a B)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^2 (a+b x) (A b-a B) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^3 (a+b x)}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((a*(A*b - a*B)*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + ((A*b - a*B)*x^2*(a + b*x))/(2*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x^3*(a + b*x))/(3*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (a^2*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
707,1,120,0,0.0609196,"\int \frac{x (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x (a+b x) (A b-a B)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a (a+b x) (A b-a B) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^2 (a+b x)}{2 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x (a+b x) (A b-a B)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a (a+b x) (A b-a B) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^2 (a+b x)}{2 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((A*b - a*B)*x*(a + b*x))/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x^2*(a + b*x))/(2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,27,0.07407,1,"{770, 77}"
708,1,69,0,0.0247329,"\int \frac{A+B x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (A b-a B) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2}}{b^2}","\frac{(a+b x) (A b-a B) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2}}{b^2}",1,"(B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/b^2 + ((A*b - a*B)*(a + b*x)*Log[a + b*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,26,0.1154,1,"{640, 608, 31}"
709,1,80,0,0.0500902,"\int \frac{A+B x}{x \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{A \log (x) (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) (A b-a B) \log (a+b x)}{a b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{A \log (x) (a+b x)}{a \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) (A b-a B) \log (a+b x)}{a b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(A*(a + b*x)*Log[x])/(a*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(a + b*x)*Log[a + b*x])/(a*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 72}"
710,1,113,0,0.0648089,"\int \frac{A+B x}{x^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{\log (x) (a+b x) (A b-a B)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B) \log (a+b x)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A \sqrt{a^2+2 a b x+b^2 x^2}}{a^2 x}","-\frac{\log (x) (a+b x) (A b-a B)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B) \log (a+b x)}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A \sqrt{a^2+2 a b x+b^2 x^2}}{a^2 x}",1,"-((A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a^2*x)) - ((A*b - a*B)*(a + b*x)*Log[x])/(a^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,29,0.1724,1,"{769, 646, 36, 29, 31}"
711,1,162,0,0.0852312,"\int \frac{A+B x}{x^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) (A b-a B)}{a^2 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b \log (x) (a+b x) (A b-a B)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b (a+b x) (A b-a B) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{2 a x^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (A b-a B)}{a^2 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b \log (x) (a+b x) (A b-a B)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b (a+b x) (A b-a B) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{2 a x^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(A*(a + b*x))/(2*a*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x))/(a^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(A*b - a*B)*(a + b*x)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
712,1,211,0,0.1036775,"\int \frac{A+B x}{x^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{b (a+b x) (A b-a B)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B)}{2 a^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^2 \log (x) (a+b x) (A b-a B)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2 (a+b x) (A b-a B) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{3 a x^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{b (a+b x) (A b-a B)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B)}{2 a^2 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^2 \log (x) (a+b x) (A b-a B)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^2 (a+b x) (A b-a B) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{3 a x^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(A*(a + b*x))/(3*a*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x))/(2*a^2*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(A*b - a*B)*(a + b*x))/(a^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^2*(A*b - a*B)*(a + b*x)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
713,1,256,0,0.1203225,"\int \frac{A+B x}{x^5 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{b^2 (a+b x) (A b-a B)}{a^4 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b (a+b x) (A b-a B)}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B)}{3 a^2 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^3 \log (x) (a+b x) (A b-a B)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^3 (a+b x) (A b-a B) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{4 a x^4 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{b^2 (a+b x) (A b-a B)}{a^4 x \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b (a+b x) (A b-a B)}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B)}{3 a^2 x^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b^3 \log (x) (a+b x) (A b-a B)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{b^3 (a+b x) (A b-a B) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{4 a x^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(A*(a + b*x))/(4*a*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x))/(3*a^2*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(A*b - a*B)*(a + b*x))/(2*a^3*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*(A*b - a*B)*(a + b*x))/(a^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^3*(A*b - a*B)*(a + b*x)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^3*(A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
714,1,249,0,0.180792,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{a^4 (A b-a B)}{2 b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^3 (4 A b-5 a B)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a x (a+b x) (A b-2 a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x) (A b-3 a B)}{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^2 (a+b x) (3 A b-5 a B) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^3 (a+b x)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^4 (A b-a B)}{2 b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^3 (4 A b-5 a B)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a x (a+b x) (A b-2 a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^2 (a+b x) (A b-3 a B)}{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^2 (a+b x) (3 A b-5 a B) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^3 (a+b x)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(a^3*(4*A*b - 5*a*B))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a^4*(A*b - a*B))/(2*b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*a*(A*b - 2*a*B)*x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - 3*a*B)*x^2*(a + b*x))/(2*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x^3*(a + b*x))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*a^2*(3*A*b - 5*a*B)*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
715,1,202,0,0.1378251,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{a^3 (A b-a B)}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^2 (3 A b-4 a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x (a+b x) (A b-3 a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a (a+b x) (A b-2 a B) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{a^3 (A b-a B)}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^2 (3 A b-4 a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x (a+b x) (A b-3 a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a (a+b x) (A b-2 a B) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((a^2*(3*A*b - 4*a*B))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (a^3*(A*b - a*B))/(2*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - 3*a*B)*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x^2*(a + b*x))/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*a*(A*b - 2*a*B)*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
716,1,154,0,0.1059336,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{a^2 (A b-a B)}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a (2 A b-3 a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-3 a B) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^2 (A b-a B)}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a (2 A b-3 a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-3 a B) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(a*(2*A*b - 3*a*B))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a^2*(A*b - a*B))/(2*b^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - 3*a*B)*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
717,1,113,0,0.0735174,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{A b-2 a B}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a (A b-a B)}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{A b-2 a B}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a (A b-a B)}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((A*b - 2*a*B)/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (a*(A*b - a*B))/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,27,0.07407,1,"{770, 77}"
718,1,69,0,0.0220015,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{A b-a B}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{A b-a B}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(B/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(2*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,26,0.07692,1,"{640, 607}"
719,1,140,0,0.0885879,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{A b-a B}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A \log (x) (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{A b-a B}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{a^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A \log (x) (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x) \log (a+b x)}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"A/(a^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(2*a*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*(a + b*x)*Log[x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*(a + b*x)*Log[a + b*x])/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
720,1,196,0,0.1357337,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{A b-a B}{2 a^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A b-a B}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\log (x) (a+b x) (3 A b-a B)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 A b-a B) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{A b-a B}{2 a^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A b-a B}{a^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\log (x) (a+b x) (3 A b-a B)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 A b-a B) \log (a+b x)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{a^3 x \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((2*A*b - a*B)/(a^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(2*a^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*(a + b*x))/(a^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((3*A*b - a*B)*(a + b*x)*Log[x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((3*A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
721,1,243,0,0.1613791,"\int \frac{A+B x}{x^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{b (3 A b-2 a B)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 A b-a B)}{a^4 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b (A b-a B)}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b \log (x) (a+b x) (2 A b-a B)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 b (a+b x) (2 A b-a B) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{b (3 A b-2 a B)}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 A b-a B)}{a^4 x \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{b (A b-a B)}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 b \log (x) (a+b x) (2 A b-a B)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 b (a+b x) (2 A b-a B) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{2 a^3 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(b*(3*A*b - 2*a*B))/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(A*b - a*B))/(2*a^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*(a + b*x))/(2*a^3*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((3*A*b - a*B)*(a + b*x))/(a^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*(2*A*b - a*B)*(a + b*x)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b*(2*A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
722,1,245,0,0.1794129,"\int \frac{x^4 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^4*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{a^4 (A b-a B)}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^3 (4 A b-5 a B)}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^2 (3 A b-5 a B)}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a (2 A b-5 a B)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-5 a B) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{a^4 (A b-a B)}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^3 (4 A b-5 a B)}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{a^2 (3 A b-5 a B)}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a (2 A b-5 a B)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-5 a B) \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*a*(2*A*b - 5*a*B))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a^4*(A*b - a*B))/(4*b^6*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (a^3*(4*A*b - 5*a*B))/(3*b^6*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (a^2*(3*A*b - 5*a*B))/(b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - 5*a*B)*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
723,1,188,0,0.0988829,"\int \frac{x^3 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^3*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^4 (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 a B}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a^2 B}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^3 B}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^4 (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 a B}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 a^2 B}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a^3 B}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(3*a*B)/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^4)/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (a^3*B)/(3*b^5*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*a^2*B)/(2*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,29,0.1034,1,"{770, 78, 43}"
724,1,77,0,0.0505231,"\int \frac{x^2 (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^2*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{A x^3}{3 a^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{x^4 (A b-a B)}{4 a^2 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{A x^3}{3 a^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{x^4 (A b-a B)}{4 a^2 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(A*x^3)/(3*a^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - ((A*b - a*B)*x^4)/(4*a^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,29,0.1034,1,"{769, 646, 37}"
725,1,121,0,0.0724546,"\int \frac{x (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{A b-2 a B}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a (A b-a B)}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{A b-2 a B}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{a (A b-a B)}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(a*(A*b - a*B))/(4*b^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - 2*a*B)/(3*b^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - B/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,27,0.07407,1,"{770, 77}"
726,1,71,0,0.0214481,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{A b-a B}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{B}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{A b-a B}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{B}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-B/(3*b^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (A*b - a*B)/(4*b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",2,2,26,0.07692,1,"{640, 607}"
727,1,210,0,0.1203373,"\int \frac{A+B x}{x \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{A b-a B}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{3 a^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A \log (x) (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{A b-a B}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{2 a^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{3 a^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A}{a^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A \log (x) (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x) \log (a+b x)}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"A/(a^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + A/(3*a^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + A/(2*a^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*(a + b*x)*Log[x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*(a + b*x)*Log[a + b*x])/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
728,1,282,0,0.2069469,"\int \frac{A+B x}{x^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{A b-a B}{4 a^2 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 A b-a B}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 A b-a B}{2 a^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A b-a B}{3 a^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\log (x) (a+b x) (5 A b-a B)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (5 A b-a B) \log (a+b x)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{a^5 x \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{A b-a B}{4 a^2 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{4 A b-a B}{a^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 A b-a B}{2 a^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A b-a B}{3 a^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\log (x) (a+b x) (5 A b-a B)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (5 A b-a B) \log (a+b x)}{a^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{A (a+b x)}{a^5 x \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((4*A*b - a*B)/(a^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(4*a^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*A*b - a*B)/(3*a^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*A*b - a*B)/(2*a^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*(a + b*x))/(a^5*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((5*A*b - a*B)*(a + b*x)*Log[x])/(a^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((5*A*b - a*B)*(a + b*x)*Log[a + b*x])/(a^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,29,0.06897,1,"{770, 77}"
729,1,63,0,0.0282857,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{13} b x^{13/2} (2 a B+A b)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{15} b^2 B x^{15/2}",1,"(2*a^2*A*x^(9/2))/9 + (2*a*(2*A*b + a*B)*x^(11/2))/11 + (2*b*(A*b + 2*a*B)*x^(13/2))/13 + (2*b^2*B*x^(15/2))/15","A",3,2,27,0.07407,1,"{27, 76}"
730,1,63,0,0.0284251,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{11} b x^{11/2} (2 a B+A b)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{13} b^2 B x^{13/2}",1,"(2*a^2*A*x^(7/2))/7 + (2*a*(2*A*b + a*B)*x^(9/2))/9 + (2*b*(A*b + 2*a*B)*x^(11/2))/11 + (2*b^2*B*x^(13/2))/13","A",3,2,27,0.07407,1,"{27, 76}"
731,1,63,0,0.0276435,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{11} b^2 B x^{11/2}","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{9} b x^{9/2} (2 a B+A b)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{11} b^2 B x^{11/2}",1,"(2*a^2*A*x^(5/2))/5 + (2*a*(2*A*b + a*B)*x^(7/2))/7 + (2*b*(A*b + 2*a*B)*x^(9/2))/9 + (2*b^2*B*x^(11/2))/11","A",3,2,27,0.07407,1,"{27, 76}"
732,1,63,0,0.0290496,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{7} b x^{7/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{9} b^2 B x^{9/2}","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{7} b x^{7/2} (2 a B+A b)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{9} b^2 B x^{9/2}",1,"(2*a^2*A*x^(3/2))/3 + (2*a*(2*A*b + a*B)*x^(5/2))/5 + (2*b*(A*b + 2*a*B)*x^(7/2))/7 + (2*b^2*B*x^(9/2))/9","A",3,2,27,0.07407,1,"{27, 76}"
733,1,61,0,0.0273857,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{\sqrt{x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/Sqrt[x],x]","2 a^2 A \sqrt{x}+\frac{2}{5} b x^{5/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{7} b^2 B x^{7/2}","2 a^2 A \sqrt{x}+\frac{2}{5} b x^{5/2} (2 a B+A b)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{7} b^2 B x^{7/2}",1,"2*a^2*A*Sqrt[x] + (2*a*(2*A*b + a*B)*x^(3/2))/3 + (2*b*(A*b + 2*a*B)*x^(5/2))/5 + (2*b^2*B*x^(7/2))/7","A",3,2,27,0.07407,1,"{27, 76}"
734,1,59,0,0.027135,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(3/2),x]","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{3} b x^{3/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{5} b^2 B x^{5/2}","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{3} b x^{3/2} (2 a B+A b)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{5} b^2 B x^{5/2}",1,"(-2*a^2*A)/Sqrt[x] + 2*a*(2*A*b + a*B)*Sqrt[x] + (2*b*(A*b + 2*a*B)*x^(3/2))/3 + (2*b^2*B*x^(5/2))/5","A",3,2,27,0.07407,1,"{27, 76}"
735,1,59,0,0.0262727,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(5/2),x]","-\frac{2 a^2 A}{3 x^{3/2}}-\frac{2 a (a B+2 A b)}{\sqrt{x}}+2 b \sqrt{x} (2 a B+A b)+\frac{2}{3} b^2 B x^{3/2}","-\frac{2 a^2 A}{3 x^{3/2}}-\frac{2 a (a B+2 A b)}{\sqrt{x}}+2 b \sqrt{x} (2 a B+A b)+\frac{2}{3} b^2 B x^{3/2}",1,"(-2*a^2*A)/(3*x^(3/2)) - (2*a*(2*A*b + a*B))/Sqrt[x] + 2*b*(A*b + 2*a*B)*Sqrt[x] + (2*b^2*B*x^(3/2))/3","A",3,2,27,0.07407,1,"{27, 76}"
736,1,59,0,0.026495,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(7/2),x]","-\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a (a B+2 A b)}{3 x^{3/2}}-\frac{2 b (2 a B+A b)}{\sqrt{x}}+2 b^2 B \sqrt{x}","-\frac{2 a^2 A}{5 x^{5/2}}-\frac{2 a (a B+2 A b)}{3 x^{3/2}}-\frac{2 b (2 a B+A b)}{\sqrt{x}}+2 b^2 B \sqrt{x}",1,"(-2*a^2*A)/(5*x^(5/2)) - (2*a*(2*A*b + a*B))/(3*x^(3/2)) - (2*b*(A*b + 2*a*B))/Sqrt[x] + 2*b^2*B*Sqrt[x]","A",3,2,27,0.07407,1,"{27, 76}"
737,1,61,0,0.0272062,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{x^{9/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/x^(9/2),x]","-\frac{2 a^2 A}{7 x^{7/2}}-\frac{2 a (a B+2 A b)}{5 x^{5/2}}-\frac{2 b (2 a B+A b)}{3 x^{3/2}}-\frac{2 b^2 B}{\sqrt{x}}","-\frac{2 a^2 A}{7 x^{7/2}}-\frac{2 a (a B+2 A b)}{5 x^{5/2}}-\frac{2 b (2 a B+A b)}{3 x^{3/2}}-\frac{2 b^2 B}{\sqrt{x}}",1,"(-2*a^2*A)/(7*x^(7/2)) - (2*a*(2*A*b + a*B))/(5*x^(5/2)) - (2*b*(A*b + 2*a*B))/(3*x^(3/2)) - (2*b^2*B)/Sqrt[x]","A",3,2,27,0.07407,1,"{27, 76}"
738,1,111,0,0.0575564,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{4}{13} a^2 b x^{13/2} (2 a B+3 A b)+\frac{2}{11} a^3 x^{11/2} (a B+4 A b)+\frac{2}{9} a^4 A x^{9/2}+\frac{2}{17} b^3 x^{17/2} (4 a B+A b)+\frac{4}{15} a b^2 x^{15/2} (3 a B+2 A b)+\frac{2}{19} b^4 B x^{19/2}","\frac{4}{13} a^2 b x^{13/2} (2 a B+3 A b)+\frac{2}{11} a^3 x^{11/2} (a B+4 A b)+\frac{2}{9} a^4 A x^{9/2}+\frac{2}{17} b^3 x^{17/2} (4 a B+A b)+\frac{4}{15} a b^2 x^{15/2} (3 a B+2 A b)+\frac{2}{19} b^4 B x^{19/2}",1,"(2*a^4*A*x^(9/2))/9 + (2*a^3*(4*A*b + a*B)*x^(11/2))/11 + (4*a^2*b*(3*A*b + 2*a*B)*x^(13/2))/13 + (4*a*b^2*(2*A*b + 3*a*B)*x^(15/2))/15 + (2*b^3*(A*b + 4*a*B)*x^(17/2))/17 + (2*b^4*B*x^(19/2))/19","A",3,2,29,0.06897,1,"{27, 76}"
739,1,111,0,0.0552516,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{4}{11} a^2 b x^{11/2} (2 a B+3 A b)+\frac{2}{9} a^3 x^{9/2} (a B+4 A b)+\frac{2}{7} a^4 A x^{7/2}+\frac{2}{15} b^3 x^{15/2} (4 a B+A b)+\frac{4}{13} a b^2 x^{13/2} (3 a B+2 A b)+\frac{2}{17} b^4 B x^{17/2}","\frac{4}{11} a^2 b x^{11/2} (2 a B+3 A b)+\frac{2}{9} a^3 x^{9/2} (a B+4 A b)+\frac{2}{7} a^4 A x^{7/2}+\frac{2}{15} b^3 x^{15/2} (4 a B+A b)+\frac{4}{13} a b^2 x^{13/2} (3 a B+2 A b)+\frac{2}{17} b^4 B x^{17/2}",1,"(2*a^4*A*x^(7/2))/7 + (2*a^3*(4*A*b + a*B)*x^(9/2))/9 + (4*a^2*b*(3*A*b + 2*a*B)*x^(11/2))/11 + (4*a*b^2*(2*A*b + 3*a*B)*x^(13/2))/13 + (2*b^3*(A*b + 4*a*B)*x^(15/2))/15 + (2*b^4*B*x^(17/2))/17","A",3,2,29,0.06897,1,"{27, 76}"
740,1,111,0,0.0522332,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{4}{9} a^2 b x^{9/2} (2 a B+3 A b)+\frac{2}{7} a^3 x^{7/2} (a B+4 A b)+\frac{2}{5} a^4 A x^{5/2}+\frac{2}{13} b^3 x^{13/2} (4 a B+A b)+\frac{4}{11} a b^2 x^{11/2} (3 a B+2 A b)+\frac{2}{15} b^4 B x^{15/2}","\frac{4}{9} a^2 b x^{9/2} (2 a B+3 A b)+\frac{2}{7} a^3 x^{7/2} (a B+4 A b)+\frac{2}{5} a^4 A x^{5/2}+\frac{2}{13} b^3 x^{13/2} (4 a B+A b)+\frac{4}{11} a b^2 x^{11/2} (3 a B+2 A b)+\frac{2}{15} b^4 B x^{15/2}",1,"(2*a^4*A*x^(5/2))/5 + (2*a^3*(4*A*b + a*B)*x^(7/2))/7 + (4*a^2*b*(3*A*b + 2*a*B)*x^(9/2))/9 + (4*a*b^2*(2*A*b + 3*a*B)*x^(11/2))/11 + (2*b^3*(A*b + 4*a*B)*x^(13/2))/13 + (2*b^4*B*x^(15/2))/15","A",3,2,29,0.06897,1,"{27, 76}"
741,1,111,0,0.0540067,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{4}{7} a^2 b x^{7/2} (2 a B+3 A b)+\frac{2}{5} a^3 x^{5/2} (a B+4 A b)+\frac{2}{3} a^4 A x^{3/2}+\frac{2}{11} b^3 x^{11/2} (4 a B+A b)+\frac{4}{9} a b^2 x^{9/2} (3 a B+2 A b)+\frac{2}{13} b^4 B x^{13/2}","\frac{4}{7} a^2 b x^{7/2} (2 a B+3 A b)+\frac{2}{5} a^3 x^{5/2} (a B+4 A b)+\frac{2}{3} a^4 A x^{3/2}+\frac{2}{11} b^3 x^{11/2} (4 a B+A b)+\frac{4}{9} a b^2 x^{9/2} (3 a B+2 A b)+\frac{2}{13} b^4 B x^{13/2}",1,"(2*a^4*A*x^(3/2))/3 + (2*a^3*(4*A*b + a*B)*x^(5/2))/5 + (4*a^2*b*(3*A*b + 2*a*B)*x^(7/2))/7 + (4*a*b^2*(2*A*b + 3*a*B)*x^(9/2))/9 + (2*b^3*(A*b + 4*a*B)*x^(11/2))/11 + (2*b^4*B*x^(13/2))/13","A",3,2,29,0.06897,1,"{27, 76}"
742,1,109,0,0.0554192,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/Sqrt[x],x]","\frac{4}{5} a^2 b x^{5/2} (2 a B+3 A b)+\frac{2}{3} a^3 x^{3/2} (a B+4 A b)+2 a^4 A \sqrt{x}+\frac{2}{9} b^3 x^{9/2} (4 a B+A b)+\frac{4}{7} a b^2 x^{7/2} (3 a B+2 A b)+\frac{2}{11} b^4 B x^{11/2}","\frac{4}{5} a^2 b x^{5/2} (2 a B+3 A b)+\frac{2}{3} a^3 x^{3/2} (a B+4 A b)+2 a^4 A \sqrt{x}+\frac{2}{9} b^3 x^{9/2} (4 a B+A b)+\frac{4}{7} a b^2 x^{7/2} (3 a B+2 A b)+\frac{2}{11} b^4 B x^{11/2}",1,"2*a^4*A*Sqrt[x] + (2*a^3*(4*A*b + a*B)*x^(3/2))/3 + (4*a^2*b*(3*A*b + 2*a*B)*x^(5/2))/5 + (4*a*b^2*(2*A*b + 3*a*B)*x^(7/2))/7 + (2*b^3*(A*b + 4*a*B)*x^(9/2))/9 + (2*b^4*B*x^(11/2))/11","A",3,2,29,0.06897,1,"{27, 76}"
743,1,107,0,0.0510342,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(3/2),x]","\frac{4}{3} a^2 b x^{3/2} (2 a B+3 A b)+2 a^3 \sqrt{x} (a B+4 A b)-\frac{2 a^4 A}{\sqrt{x}}+\frac{2}{7} b^3 x^{7/2} (4 a B+A b)+\frac{4}{5} a b^2 x^{5/2} (3 a B+2 A b)+\frac{2}{9} b^4 B x^{9/2}","\frac{4}{3} a^2 b x^{3/2} (2 a B+3 A b)+2 a^3 \sqrt{x} (a B+4 A b)-\frac{2 a^4 A}{\sqrt{x}}+\frac{2}{7} b^3 x^{7/2} (4 a B+A b)+\frac{4}{5} a b^2 x^{5/2} (3 a B+2 A b)+\frac{2}{9} b^4 B x^{9/2}",1,"(-2*a^4*A)/Sqrt[x] + 2*a^3*(4*A*b + a*B)*Sqrt[x] + (4*a^2*b*(3*A*b + 2*a*B)*x^(3/2))/3 + (4*a*b^2*(2*A*b + 3*a*B)*x^(5/2))/5 + (2*b^3*(A*b + 4*a*B)*x^(7/2))/7 + (2*b^4*B*x^(9/2))/9","A",3,2,29,0.06897,1,"{27, 76}"
744,1,107,0,0.0502736,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(5/2),x]","-\frac{2 a^3 (a B+4 A b)}{\sqrt{x}}+4 a^2 b \sqrt{x} (2 a B+3 A b)-\frac{2 a^4 A}{3 x^{3/2}}+\frac{4}{3} a b^2 x^{3/2} (3 a B+2 A b)+\frac{2}{5} b^3 x^{5/2} (4 a B+A b)+\frac{2}{7} b^4 B x^{7/2}","-\frac{2 a^3 (a B+4 A b)}{\sqrt{x}}+4 a^2 b \sqrt{x} (2 a B+3 A b)-\frac{2 a^4 A}{3 x^{3/2}}+\frac{4}{3} a b^2 x^{3/2} (3 a B+2 A b)+\frac{2}{5} b^3 x^{5/2} (4 a B+A b)+\frac{2}{7} b^4 B x^{7/2}",1,"(-2*a^4*A)/(3*x^(3/2)) - (2*a^3*(4*A*b + a*B))/Sqrt[x] + 4*a^2*b*(3*A*b + 2*a*B)*Sqrt[x] + (4*a*b^2*(2*A*b + 3*a*B)*x^(3/2))/3 + (2*b^3*(A*b + 4*a*B)*x^(5/2))/5 + (2*b^4*B*x^(7/2))/7","A",3,2,29,0.06897,1,"{27, 76}"
745,1,107,0,0.0524969,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(7/2),x]","-\frac{2 a^3 (a B+4 A b)}{3 x^{3/2}}-\frac{4 a^2 b (2 a B+3 A b)}{\sqrt{x}}-\frac{2 a^4 A}{5 x^{5/2}}+\frac{2}{3} b^3 x^{3/2} (4 a B+A b)+4 a b^2 \sqrt{x} (3 a B+2 A b)+\frac{2}{5} b^4 B x^{5/2}","-\frac{2 a^3 (a B+4 A b)}{3 x^{3/2}}-\frac{4 a^2 b (2 a B+3 A b)}{\sqrt{x}}-\frac{2 a^4 A}{5 x^{5/2}}+\frac{2}{3} b^3 x^{3/2} (4 a B+A b)+4 a b^2 \sqrt{x} (3 a B+2 A b)+\frac{2}{5} b^4 B x^{5/2}",1,"(-2*a^4*A)/(5*x^(5/2)) - (2*a^3*(4*A*b + a*B))/(3*x^(3/2)) - (4*a^2*b*(3*A*b + 2*a*B))/Sqrt[x] + 4*a*b^2*(2*A*b + 3*a*B)*Sqrt[x] + (2*b^3*(A*b + 4*a*B)*x^(3/2))/3 + (2*b^4*B*x^(5/2))/5","A",3,2,29,0.06897,1,"{27, 76}"
746,1,107,0,0.0521916,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{x^{9/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/x^(9/2),x]","-\frac{2 a^3 (a B+4 A b)}{5 x^{5/2}}-\frac{4 a^2 b (2 a B+3 A b)}{3 x^{3/2}}-\frac{2 a^4 A}{7 x^{7/2}}-\frac{4 a b^2 (3 a B+2 A b)}{\sqrt{x}}+2 b^3 \sqrt{x} (4 a B+A b)+\frac{2}{3} b^4 B x^{3/2}","-\frac{2 a^3 (a B+4 A b)}{5 x^{5/2}}-\frac{4 a^2 b (2 a B+3 A b)}{3 x^{3/2}}-\frac{2 a^4 A}{7 x^{7/2}}-\frac{4 a b^2 (3 a B+2 A b)}{\sqrt{x}}+2 b^3 \sqrt{x} (4 a B+A b)+\frac{2}{3} b^4 B x^{3/2}",1,"(-2*a^4*A)/(7*x^(7/2)) - (2*a^3*(4*A*b + a*B))/(5*x^(5/2)) - (4*a^2*b*(3*A*b + 2*a*B))/(3*x^(3/2)) - (4*a*b^2*(2*A*b + 3*a*B))/Sqrt[x] + 2*b^3*(A*b + 4*a*B)*Sqrt[x] + (2*b^4*B*x^(3/2))/3","A",3,2,29,0.06897,1,"{27, 76}"
747,1,159,0,0.0895278,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{10}{17} a^2 b^3 x^{17/2} (4 a B+3 A b)+\frac{2}{3} a^3 b^2 x^{15/2} (3 a B+4 A b)+\frac{6}{13} a^4 b x^{13/2} (2 a B+5 A b)+\frac{2}{11} a^5 x^{11/2} (a B+6 A b)+\frac{2}{9} a^6 A x^{9/2}+\frac{2}{21} b^5 x^{21/2} (6 a B+A b)+\frac{6}{19} a b^4 x^{19/2} (5 a B+2 A b)+\frac{2}{23} b^6 B x^{23/2}","\frac{10}{17} a^2 b^3 x^{17/2} (4 a B+3 A b)+\frac{2}{3} a^3 b^2 x^{15/2} (3 a B+4 A b)+\frac{6}{13} a^4 b x^{13/2} (2 a B+5 A b)+\frac{2}{11} a^5 x^{11/2} (a B+6 A b)+\frac{2}{9} a^6 A x^{9/2}+\frac{2}{21} b^5 x^{21/2} (6 a B+A b)+\frac{6}{19} a b^4 x^{19/2} (5 a B+2 A b)+\frac{2}{23} b^6 B x^{23/2}",1,"(2*a^6*A*x^(9/2))/9 + (2*a^5*(6*A*b + a*B)*x^(11/2))/11 + (6*a^4*b*(5*A*b + 2*a*B)*x^(13/2))/13 + (2*a^3*b^2*(4*A*b + 3*a*B)*x^(15/2))/3 + (10*a^2*b^3*(3*A*b + 4*a*B)*x^(17/2))/17 + (6*a*b^4*(2*A*b + 5*a*B)*x^(19/2))/19 + (2*b^5*(A*b + 6*a*B)*x^(21/2))/21 + (2*b^6*B*x^(23/2))/23","A",3,2,29,0.06897,1,"{27, 76}"
748,1,159,0,0.0795575,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2}{3} a^2 b^3 x^{15/2} (4 a B+3 A b)+\frac{10}{13} a^3 b^2 x^{13/2} (3 a B+4 A b)+\frac{6}{11} a^4 b x^{11/2} (2 a B+5 A b)+\frac{2}{9} a^5 x^{9/2} (a B+6 A b)+\frac{2}{7} a^6 A x^{7/2}+\frac{2}{19} b^5 x^{19/2} (6 a B+A b)+\frac{6}{17} a b^4 x^{17/2} (5 a B+2 A b)+\frac{2}{21} b^6 B x^{21/2}","\frac{2}{3} a^2 b^3 x^{15/2} (4 a B+3 A b)+\frac{10}{13} a^3 b^2 x^{13/2} (3 a B+4 A b)+\frac{6}{11} a^4 b x^{11/2} (2 a B+5 A b)+\frac{2}{9} a^5 x^{9/2} (a B+6 A b)+\frac{2}{7} a^6 A x^{7/2}+\frac{2}{19} b^5 x^{19/2} (6 a B+A b)+\frac{6}{17} a b^4 x^{17/2} (5 a B+2 A b)+\frac{2}{21} b^6 B x^{21/2}",1,"(2*a^6*A*x^(7/2))/7 + (2*a^5*(6*A*b + a*B)*x^(9/2))/9 + (6*a^4*b*(5*A*b + 2*a*B)*x^(11/2))/11 + (10*a^3*b^2*(4*A*b + 3*a*B)*x^(13/2))/13 + (2*a^2*b^3*(3*A*b + 4*a*B)*x^(15/2))/3 + (6*a*b^4*(2*A*b + 5*a*B)*x^(17/2))/17 + (2*b^5*(A*b + 6*a*B)*x^(19/2))/19 + (2*b^6*B*x^(21/2))/21","A",3,2,29,0.06897,1,"{27, 76}"
749,1,159,0,0.084969,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{10}{13} a^2 b^3 x^{13/2} (4 a B+3 A b)+\frac{10}{11} a^3 b^2 x^{11/2} (3 a B+4 A b)+\frac{2}{3} a^4 b x^{9/2} (2 a B+5 A b)+\frac{2}{7} a^5 x^{7/2} (a B+6 A b)+\frac{2}{5} a^6 A x^{5/2}+\frac{2}{17} b^5 x^{17/2} (6 a B+A b)+\frac{2}{5} a b^4 x^{15/2} (5 a B+2 A b)+\frac{2}{19} b^6 B x^{19/2}","\frac{10}{13} a^2 b^3 x^{13/2} (4 a B+3 A b)+\frac{10}{11} a^3 b^2 x^{11/2} (3 a B+4 A b)+\frac{2}{3} a^4 b x^{9/2} (2 a B+5 A b)+\frac{2}{7} a^5 x^{7/2} (a B+6 A b)+\frac{2}{5} a^6 A x^{5/2}+\frac{2}{17} b^5 x^{17/2} (6 a B+A b)+\frac{2}{5} a b^4 x^{15/2} (5 a B+2 A b)+\frac{2}{19} b^6 B x^{19/2}",1,"(2*a^6*A*x^(5/2))/5 + (2*a^5*(6*A*b + a*B)*x^(7/2))/7 + (2*a^4*b*(5*A*b + 2*a*B)*x^(9/2))/3 + (10*a^3*b^2*(4*A*b + 3*a*B)*x^(11/2))/11 + (10*a^2*b^3*(3*A*b + 4*a*B)*x^(13/2))/13 + (2*a*b^4*(2*A*b + 5*a*B)*x^(15/2))/5 + (2*b^5*(A*b + 6*a*B)*x^(17/2))/17 + (2*b^6*B*x^(19/2))/19","A",3,2,29,0.06897,1,"{27, 76}"
750,1,159,0,0.0812867,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{10}{11} a^2 b^3 x^{11/2} (4 a B+3 A b)+\frac{10}{9} a^3 b^2 x^{9/2} (3 a B+4 A b)+\frac{6}{7} a^4 b x^{7/2} (2 a B+5 A b)+\frac{2}{5} a^5 x^{5/2} (a B+6 A b)+\frac{2}{3} a^6 A x^{3/2}+\frac{2}{15} b^5 x^{15/2} (6 a B+A b)+\frac{6}{13} a b^4 x^{13/2} (5 a B+2 A b)+\frac{2}{17} b^6 B x^{17/2}","\frac{10}{11} a^2 b^3 x^{11/2} (4 a B+3 A b)+\frac{10}{9} a^3 b^2 x^{9/2} (3 a B+4 A b)+\frac{6}{7} a^4 b x^{7/2} (2 a B+5 A b)+\frac{2}{5} a^5 x^{5/2} (a B+6 A b)+\frac{2}{3} a^6 A x^{3/2}+\frac{2}{15} b^5 x^{15/2} (6 a B+A b)+\frac{6}{13} a b^4 x^{13/2} (5 a B+2 A b)+\frac{2}{17} b^6 B x^{17/2}",1,"(2*a^6*A*x^(3/2))/3 + (2*a^5*(6*A*b + a*B)*x^(5/2))/5 + (6*a^4*b*(5*A*b + 2*a*B)*x^(7/2))/7 + (10*a^3*b^2*(4*A*b + 3*a*B)*x^(9/2))/9 + (10*a^2*b^3*(3*A*b + 4*a*B)*x^(11/2))/11 + (6*a*b^4*(2*A*b + 5*a*B)*x^(13/2))/13 + (2*b^5*(A*b + 6*a*B)*x^(15/2))/15 + (2*b^6*B*x^(17/2))/17","A",3,2,29,0.06897,1,"{27, 76}"
751,1,157,0,0.0798598,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/Sqrt[x],x]","\frac{10}{9} a^2 b^3 x^{9/2} (4 a B+3 A b)+\frac{10}{7} a^3 b^2 x^{7/2} (3 a B+4 A b)+\frac{6}{5} a^4 b x^{5/2} (2 a B+5 A b)+\frac{2}{3} a^5 x^{3/2} (a B+6 A b)+2 a^6 A \sqrt{x}+\frac{2}{13} b^5 x^{13/2} (6 a B+A b)+\frac{6}{11} a b^4 x^{11/2} (5 a B+2 A b)+\frac{2}{15} b^6 B x^{15/2}","\frac{10}{9} a^2 b^3 x^{9/2} (4 a B+3 A b)+\frac{10}{7} a^3 b^2 x^{7/2} (3 a B+4 A b)+\frac{6}{5} a^4 b x^{5/2} (2 a B+5 A b)+\frac{2}{3} a^5 x^{3/2} (a B+6 A b)+2 a^6 A \sqrt{x}+\frac{2}{13} b^5 x^{13/2} (6 a B+A b)+\frac{6}{11} a b^4 x^{11/2} (5 a B+2 A b)+\frac{2}{15} b^6 B x^{15/2}",1,"2*a^6*A*Sqrt[x] + (2*a^5*(6*A*b + a*B)*x^(3/2))/3 + (6*a^4*b*(5*A*b + 2*a*B)*x^(5/2))/5 + (10*a^3*b^2*(4*A*b + 3*a*B)*x^(7/2))/7 + (10*a^2*b^3*(3*A*b + 4*a*B)*x^(9/2))/9 + (6*a*b^4*(2*A*b + 5*a*B)*x^(11/2))/11 + (2*b^5*(A*b + 6*a*B)*x^(13/2))/13 + (2*b^6*B*x^(15/2))/15","A",3,2,29,0.06897,1,"{27, 76}"
752,1,151,0,0.0794442,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(3/2),x]","\frac{10}{7} a^2 b^3 x^{7/2} (4 a B+3 A b)+2 a^3 b^2 x^{5/2} (3 a B+4 A b)+2 a^4 b x^{3/2} (2 a B+5 A b)+2 a^5 \sqrt{x} (a B+6 A b)-\frac{2 a^6 A}{\sqrt{x}}+\frac{2}{11} b^5 x^{11/2} (6 a B+A b)+\frac{2}{3} a b^4 x^{9/2} (5 a B+2 A b)+\frac{2}{13} b^6 B x^{13/2}","\frac{10}{7} a^2 b^3 x^{7/2} (4 a B+3 A b)+2 a^3 b^2 x^{5/2} (3 a B+4 A b)+2 a^4 b x^{3/2} (2 a B+5 A b)+2 a^5 \sqrt{x} (a B+6 A b)-\frac{2 a^6 A}{\sqrt{x}}+\frac{2}{11} b^5 x^{11/2} (6 a B+A b)+\frac{2}{3} a b^4 x^{9/2} (5 a B+2 A b)+\frac{2}{13} b^6 B x^{13/2}",1,"(-2*a^6*A)/Sqrt[x] + 2*a^5*(6*A*b + a*B)*Sqrt[x] + 2*a^4*b*(5*A*b + 2*a*B)*x^(3/2) + 2*a^3*b^2*(4*A*b + 3*a*B)*x^(5/2) + (10*a^2*b^3*(3*A*b + 4*a*B)*x^(7/2))/7 + (2*a*b^4*(2*A*b + 5*a*B)*x^(9/2))/3 + (2*b^5*(A*b + 6*a*B)*x^(11/2))/11 + (2*b^6*B*x^(13/2))/13","A",3,2,29,0.06897,1,"{27, 76}"
753,1,153,0,0.078745,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(5/2),x]","\frac{10}{3} a^3 b^2 x^{3/2} (3 a B+4 A b)+2 a^2 b^3 x^{5/2} (4 a B+3 A b)-\frac{2 a^5 (a B+6 A b)}{\sqrt{x}}+6 a^4 b \sqrt{x} (2 a B+5 A b)-\frac{2 a^6 A}{3 x^{3/2}}+\frac{6}{7} a b^4 x^{7/2} (5 a B+2 A b)+\frac{2}{9} b^5 x^{9/2} (6 a B+A b)+\frac{2}{11} b^6 B x^{11/2}","\frac{10}{3} a^3 b^2 x^{3/2} (3 a B+4 A b)+2 a^2 b^3 x^{5/2} (4 a B+3 A b)-\frac{2 a^5 (a B+6 A b)}{\sqrt{x}}+6 a^4 b \sqrt{x} (2 a B+5 A b)-\frac{2 a^6 A}{3 x^{3/2}}+\frac{6}{7} a b^4 x^{7/2} (5 a B+2 A b)+\frac{2}{9} b^5 x^{9/2} (6 a B+A b)+\frac{2}{11} b^6 B x^{11/2}",1,"(-2*a^6*A)/(3*x^(3/2)) - (2*a^5*(6*A*b + a*B))/Sqrt[x] + 6*a^4*b*(5*A*b + 2*a*B)*Sqrt[x] + (10*a^3*b^2*(4*A*b + 3*a*B)*x^(3/2))/3 + 2*a^2*b^3*(3*A*b + 4*a*B)*x^(5/2) + (6*a*b^4*(2*A*b + 5*a*B)*x^(7/2))/7 + (2*b^5*(A*b + 6*a*B)*x^(9/2))/9 + (2*b^6*B*x^(11/2))/11","A",3,2,29,0.06897,1,"{27, 76}"
754,1,155,0,0.0830776,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(7/2),x]","\frac{10}{3} a^2 b^3 x^{3/2} (4 a B+3 A b)+10 a^3 b^2 \sqrt{x} (3 a B+4 A b)-\frac{2 a^5 (a B+6 A b)}{3 x^{3/2}}-\frac{6 a^4 b (2 a B+5 A b)}{\sqrt{x}}-\frac{2 a^6 A}{5 x^{5/2}}+\frac{6}{5} a b^4 x^{5/2} (5 a B+2 A b)+\frac{2}{7} b^5 x^{7/2} (6 a B+A b)+\frac{2}{9} b^6 B x^{9/2}","\frac{10}{3} a^2 b^3 x^{3/2} (4 a B+3 A b)+10 a^3 b^2 \sqrt{x} (3 a B+4 A b)-\frac{2 a^5 (a B+6 A b)}{3 x^{3/2}}-\frac{6 a^4 b (2 a B+5 A b)}{\sqrt{x}}-\frac{2 a^6 A}{5 x^{5/2}}+\frac{6}{5} a b^4 x^{5/2} (5 a B+2 A b)+\frac{2}{7} b^5 x^{7/2} (6 a B+A b)+\frac{2}{9} b^6 B x^{9/2}",1,"(-2*a^6*A)/(5*x^(5/2)) - (2*a^5*(6*A*b + a*B))/(3*x^(3/2)) - (6*a^4*b*(5*A*b + 2*a*B))/Sqrt[x] + 10*a^3*b^2*(4*A*b + 3*a*B)*Sqrt[x] + (10*a^2*b^3*(3*A*b + 4*a*B)*x^(3/2))/3 + (6*a*b^4*(2*A*b + 5*a*B)*x^(5/2))/5 + (2*b^5*(A*b + 6*a*B)*x^(7/2))/7 + (2*b^6*B*x^(9/2))/9","A",3,2,29,0.06897,1,"{27, 76}"
755,1,151,0,0.0819405,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{9/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(9/2),x]","-\frac{10 a^3 b^2 (3 a B+4 A b)}{\sqrt{x}}+10 a^2 b^3 \sqrt{x} (4 a B+3 A b)-\frac{2 a^5 (a B+6 A b)}{5 x^{5/2}}-\frac{2 a^4 b (2 a B+5 A b)}{x^{3/2}}-\frac{2 a^6 A}{7 x^{7/2}}+2 a b^4 x^{3/2} (5 a B+2 A b)+\frac{2}{5} b^5 x^{5/2} (6 a B+A b)+\frac{2}{7} b^6 B x^{7/2}","-\frac{10 a^3 b^2 (3 a B+4 A b)}{\sqrt{x}}+10 a^2 b^3 \sqrt{x} (4 a B+3 A b)-\frac{2 a^5 (a B+6 A b)}{5 x^{5/2}}-\frac{2 a^4 b (2 a B+5 A b)}{x^{3/2}}-\frac{2 a^6 A}{7 x^{7/2}}+2 a b^4 x^{3/2} (5 a B+2 A b)+\frac{2}{5} b^5 x^{5/2} (6 a B+A b)+\frac{2}{7} b^6 B x^{7/2}",1,"(-2*a^6*A)/(7*x^(7/2)) - (2*a^5*(6*A*b + a*B))/(5*x^(5/2)) - (2*a^4*b*(5*A*b + 2*a*B))/x^(3/2) - (10*a^3*b^2*(4*A*b + 3*a*B))/Sqrt[x] + 10*a^2*b^3*(3*A*b + 4*a*B)*Sqrt[x] + 2*a*b^4*(2*A*b + 5*a*B)*x^(3/2) + (2*b^5*(A*b + 6*a*B)*x^(5/2))/5 + (2*b^6*B*x^(7/2))/7","A",3,2,29,0.06897,1,"{27, 76}"
756,1,155,0,0.080033,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{x^{11/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/x^(11/2),x]","-\frac{10 a^3 b^2 (3 a B+4 A b)}{3 x^{3/2}}-\frac{10 a^2 b^3 (4 a B+3 A b)}{\sqrt{x}}-\frac{2 a^5 (a B+6 A b)}{7 x^{7/2}}-\frac{6 a^4 b (2 a B+5 A b)}{5 x^{5/2}}-\frac{2 a^6 A}{9 x^{9/2}}+\frac{2}{3} b^5 x^{3/2} (6 a B+A b)+6 a b^4 \sqrt{x} (5 a B+2 A b)+\frac{2}{5} b^6 B x^{5/2}","-\frac{10 a^3 b^2 (3 a B+4 A b)}{3 x^{3/2}}-\frac{10 a^2 b^3 (4 a B+3 A b)}{\sqrt{x}}-\frac{2 a^5 (a B+6 A b)}{7 x^{7/2}}-\frac{6 a^4 b (2 a B+5 A b)}{5 x^{5/2}}-\frac{2 a^6 A}{9 x^{9/2}}+\frac{2}{3} b^5 x^{3/2} (6 a B+A b)+6 a b^4 \sqrt{x} (5 a B+2 A b)+\frac{2}{5} b^6 B x^{5/2}",1,"(-2*a^6*A)/(9*x^(9/2)) - (2*a^5*(6*A*b + a*B))/(7*x^(7/2)) - (6*a^4*b*(5*A*b + 2*a*B))/(5*x^(5/2)) - (10*a^3*b^2*(4*A*b + 3*a*B))/(3*x^(3/2)) - (10*a^2*b^3*(3*A*b + 4*a*B))/Sqrt[x] + 6*a*b^4*(2*A*b + 5*a*B)*Sqrt[x] + (2*b^5*(A*b + 6*a*B)*x^(3/2))/3 + (2*b^6*B*x^(5/2))/5","A",3,2,29,0.06897,1,"{27, 76}"
757,1,154,0,0.0833223,"\int \frac{x^{7/2} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a^2 \sqrt{x} (7 A b-9 a B)}{b^5}-\frac{a^{5/2} (7 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}-\frac{x^{7/2} (7 A b-9 a B)}{7 a b^2}+\frac{x^{5/2} (7 A b-9 a B)}{5 b^3}-\frac{a x^{3/2} (7 A b-9 a B)}{3 b^4}+\frac{x^{9/2} (A b-a B)}{a b (a+b x)}","\frac{a^2 \sqrt{x} (7 A b-9 a B)}{b^5}-\frac{a^{5/2} (7 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2}}-\frac{x^{7/2} (7 A b-9 a B)}{7 a b^2}+\frac{x^{5/2} (7 A b-9 a B)}{5 b^3}-\frac{a x^{3/2} (7 A b-9 a B)}{3 b^4}+\frac{x^{9/2} (A b-a B)}{a b (a+b x)}",1,"(a^2*(7*A*b - 9*a*B)*Sqrt[x])/b^5 - (a*(7*A*b - 9*a*B)*x^(3/2))/(3*b^4) + ((7*A*b - 9*a*B)*x^(5/2))/(5*b^3) - ((7*A*b - 9*a*B)*x^(7/2))/(7*a*b^2) + ((A*b - a*B)*x^(9/2))/(a*b*(a + b*x)) - (a^(5/2)*(7*A*b - 9*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(11/2)","A",8,5,29,0.1724,1,"{27, 78, 50, 63, 205}"
758,1,130,0,0.0658589,"\int \frac{x^{5/2} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a^{3/2} (5 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}-\frac{x^{5/2} (5 A b-7 a B)}{5 a b^2}+\frac{x^{3/2} (5 A b-7 a B)}{3 b^3}-\frac{a \sqrt{x} (5 A b-7 a B)}{b^4}+\frac{x^{7/2} (A b-a B)}{a b (a+b x)}","\frac{a^{3/2} (5 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2}}-\frac{x^{5/2} (5 A b-7 a B)}{5 a b^2}+\frac{x^{3/2} (5 A b-7 a B)}{3 b^3}-\frac{a \sqrt{x} (5 A b-7 a B)}{b^4}+\frac{x^{7/2} (A b-a B)}{a b (a+b x)}",1,"-((a*(5*A*b - 7*a*B)*Sqrt[x])/b^4) + ((5*A*b - 7*a*B)*x^(3/2))/(3*b^3) - ((5*A*b - 7*a*B)*x^(5/2))/(5*a*b^2) + ((A*b - a*B)*x^(7/2))/(a*b*(a + b*x)) + (a^(3/2)*(5*A*b - 7*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(9/2)","A",7,5,29,0.1724,1,"{27, 78, 50, 63, 205}"
759,1,108,0,0.0480381,"\int \frac{x^{3/2} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{x^{3/2} (3 A b-5 a B)}{3 a b^2}+\frac{\sqrt{x} (3 A b-5 a B)}{b^3}-\frac{\sqrt{a} (3 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^{5/2} (A b-a B)}{a b (a+b x)}","-\frac{x^{3/2} (3 A b-5 a B)}{3 a b^2}+\frac{\sqrt{x} (3 A b-5 a B)}{b^3}-\frac{\sqrt{a} (3 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2}}+\frac{x^{5/2} (A b-a B)}{a b (a+b x)}",1,"((3*A*b - 5*a*B)*Sqrt[x])/b^3 - ((3*A*b - 5*a*B)*x^(3/2))/(3*a*b^2) + ((A*b - a*B)*x^(5/2))/(a*b*(a + b*x)) - (Sqrt[a]*(3*A*b - 5*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/b^(7/2)","A",6,5,29,0.1724,1,"{27, 78, 50, 63, 205}"
760,1,85,0,0.0371813,"\int \frac{\sqrt{x} (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{\sqrt{x} (A b-3 a B)}{a b^2}+\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{x^{3/2} (A b-a B)}{a b (a+b x)}","-\frac{\sqrt{x} (A b-3 a B)}{a b^2}+\frac{(A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{5/2}}+\frac{x^{3/2} (A b-a B)}{a b (a+b x)}",1,"-(((A*b - 3*a*B)*Sqrt[x])/(a*b^2)) + ((A*b - a*B)*x^(3/2))/(a*b*(a + b*x)) + ((A*b - 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*b^(5/2))","A",5,5,29,0.1724,1,"{27, 78, 50, 63, 205}"
761,1,63,0,0.0251839,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} b^{3/2}}+\frac{\sqrt{x} (A b-a B)}{a b (a+b x)}","\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} b^{3/2}}+\frac{\sqrt{x} (A b-a B)}{a b (a+b x)}",1,"((A*b - a*B)*Sqrt[x])/(a*b*(a + b*x)) + ((A*b + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(3/2)*b^(3/2))","A",4,4,29,0.1379,1,"{27, 78, 63, 205}"
762,1,88,0,0.0373832,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{3 A b-a B}{a^2 b \sqrt{x}}-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b}}+\frac{A b-a B}{a b \sqrt{x} (a+b x)}","-\frac{3 A b-a B}{a^2 b \sqrt{x}}-\frac{(3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2} \sqrt{b}}+\frac{A b-a B}{a b \sqrt{x} (a+b x)}",1,"-((3*A*b - a*B)/(a^2*b*Sqrt[x])) + (A*b - a*B)/(a*b*Sqrt[x]*(a + b*x)) - ((3*A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(5/2)*Sqrt[b])","A",5,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
763,1,107,0,0.04892,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{5 A b-3 a B}{3 a^2 b x^{3/2}}+\frac{5 A b-3 a B}{a^3 \sqrt{x}}+\frac{\sqrt{b} (5 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{A b-a B}{a b x^{3/2} (a+b x)}","-\frac{5 A b-3 a B}{3 a^2 b x^{3/2}}+\frac{5 A b-3 a B}{a^3 \sqrt{x}}+\frac{\sqrt{b} (5 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2}}+\frac{A b-a B}{a b x^{3/2} (a+b x)}",1,"-(5*A*b - 3*a*B)/(3*a^2*b*x^(3/2)) + (5*A*b - 3*a*B)/(a^3*Sqrt[x]) + (A*b - a*B)/(a*b*x^(3/2)*(a + b*x)) + (Sqrt[b]*(5*A*b - 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(7/2)","A",6,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
764,1,131,0,0.0630578,"\int \frac{A+B x}{x^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b^{3/2} (7 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{7 A b-5 a B}{3 a^3 x^{3/2}}-\frac{7 A b-5 a B}{5 a^2 b x^{5/2}}-\frac{b (7 A b-5 a B)}{a^4 \sqrt{x}}+\frac{A b-a B}{a b x^{5/2} (a+b x)}","-\frac{b^{3/2} (7 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2}}+\frac{7 A b-5 a B}{3 a^3 x^{3/2}}-\frac{7 A b-5 a B}{5 a^2 b x^{5/2}}-\frac{b (7 A b-5 a B)}{a^4 \sqrt{x}}+\frac{A b-a B}{a b x^{5/2} (a+b x)}",1,"-(7*A*b - 5*a*B)/(5*a^2*b*x^(5/2)) + (7*A*b - 5*a*B)/(3*a^3*x^(3/2)) - (b*(7*A*b - 5*a*B))/(a^4*Sqrt[x]) + (A*b - a*B)/(a*b*x^(5/2)*(a + b*x)) - (b^(3/2)*(7*A*b - 5*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(9/2)","A",7,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
765,1,153,0,0.0791465,"\int \frac{A+B x}{x^{9/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(x^(9/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{b^2 (9 A b-7 a B)}{a^5 \sqrt{x}}+\frac{b^{5/2} (9 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{11/2}}-\frac{b (9 A b-7 a B)}{3 a^4 x^{3/2}}+\frac{9 A b-7 a B}{5 a^3 x^{5/2}}-\frac{9 A b-7 a B}{7 a^2 b x^{7/2}}+\frac{A b-a B}{a b x^{7/2} (a+b x)}","\frac{b^2 (9 A b-7 a B)}{a^5 \sqrt{x}}+\frac{b^{5/2} (9 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{11/2}}-\frac{b (9 A b-7 a B)}{3 a^4 x^{3/2}}+\frac{9 A b-7 a B}{5 a^3 x^{5/2}}-\frac{9 A b-7 a B}{7 a^2 b x^{7/2}}+\frac{A b-a B}{a b x^{7/2} (a+b x)}",1,"-(9*A*b - 7*a*B)/(7*a^2*b*x^(7/2)) + (9*A*b - 7*a*B)/(5*a^3*x^(5/2)) - (b*(9*A*b - 7*a*B))/(3*a^4*x^(3/2)) + (b^2*(9*A*b - 7*a*B))/(a^5*Sqrt[x]) + (A*b - a*B)/(a*b*x^(7/2)*(a + b*x)) + (b^(5/2)*(9*A*b - 7*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/a^(11/2)","A",8,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
766,1,173,0,0.0783583,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{7/2} (A b-3 a B)}{4 a b^2 (a+b x)^2}+\frac{7 x^{5/2} (A b-3 a B)}{8 a b^3 (a+b x)}-\frac{35 x^{3/2} (A b-3 a B)}{24 a b^4}+\frac{35 \sqrt{x} (A b-3 a B)}{8 b^5}-\frac{35 \sqrt{a} (A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 b^{11/2}}+\frac{x^{9/2} (A b-a B)}{3 a b (a+b x)^3}","\frac{x^{7/2} (A b-3 a B)}{4 a b^2 (a+b x)^2}+\frac{7 x^{5/2} (A b-3 a B)}{8 a b^3 (a+b x)}-\frac{35 x^{3/2} (A b-3 a B)}{24 a b^4}+\frac{35 \sqrt{x} (A b-3 a B)}{8 b^5}-\frac{35 \sqrt{a} (A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 b^{11/2}}+\frac{x^{9/2} (A b-a B)}{3 a b (a+b x)^3}",1,"(35*(A*b - 3*a*B)*Sqrt[x])/(8*b^5) - (35*(A*b - 3*a*B)*x^(3/2))/(24*a*b^4) + ((A*b - a*B)*x^(9/2))/(3*a*b*(a + b*x)^3) + ((A*b - 3*a*B)*x^(7/2))/(4*a*b^2*(a + b*x)^2) + (7*(A*b - 3*a*B)*x^(5/2))/(8*a*b^3*(a + b*x)) - (35*Sqrt[a]*(A*b - 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*b^(11/2))","A",8,6,29,0.2069,1,"{27, 78, 47, 50, 63, 205}"
767,1,153,0,0.0654034,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{5/2} (A b-7 a B)}{12 a b^2 (a+b x)^2}+\frac{5 x^{3/2} (A b-7 a B)}{24 a b^3 (a+b x)}-\frac{5 \sqrt{x} (A b-7 a B)}{8 a b^4}+\frac{5 (A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 \sqrt{a} b^{9/2}}+\frac{x^{7/2} (A b-a B)}{3 a b (a+b x)^3}","\frac{x^{5/2} (A b-7 a B)}{12 a b^2 (a+b x)^2}+\frac{5 x^{3/2} (A b-7 a B)}{24 a b^3 (a+b x)}-\frac{5 \sqrt{x} (A b-7 a B)}{8 a b^4}+\frac{5 (A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 \sqrt{a} b^{9/2}}+\frac{x^{7/2} (A b-a B)}{3 a b (a+b x)^3}",1,"(-5*(A*b - 7*a*B)*Sqrt[x])/(8*a*b^4) + ((A*b - a*B)*x^(7/2))/(3*a*b*(a + b*x)^3) + ((A*b - 7*a*B)*x^(5/2))/(12*a*b^2*(a + b*x)^2) + (5*(A*b - 7*a*B)*x^(3/2))/(24*a*b^3*(a + b*x)) + (5*(A*b - 7*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*Sqrt[a]*b^(9/2))","A",7,6,29,0.2069,1,"{27, 78, 47, 50, 63, 205}"
768,1,130,0,0.0560875,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(5 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{3/2} b^{7/2}}-\frac{x^{3/2} (5 a B+A b)}{12 a b^2 (a+b x)^2}-\frac{\sqrt{x} (5 a B+A b)}{8 a b^3 (a+b x)}+\frac{x^{5/2} (A b-a B)}{3 a b (a+b x)^3}","\frac{(5 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{3/2} b^{7/2}}-\frac{x^{3/2} (5 a B+A b)}{12 a b^2 (a+b x)^2}-\frac{\sqrt{x} (5 a B+A b)}{8 a b^3 (a+b x)}+\frac{x^{5/2} (A b-a B)}{3 a b (a+b x)^3}",1,"((A*b - a*B)*x^(5/2))/(3*a*b*(a + b*x)^3) - ((A*b + 5*a*B)*x^(3/2))/(12*a*b^2*(a + b*x)^2) - ((A*b + 5*a*B)*Sqrt[x])/(8*a*b^3*(a + b*x)) + ((A*b + 5*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*a^(3/2)*b^(7/2))","A",6,5,29,0.1724,1,"{27, 78, 47, 63, 205}"
769,1,127,0,0.0570649,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{\sqrt{x} (a B+A b)}{8 a^2 b^2 (a+b x)}+\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{5/2} b^{5/2}}-\frac{\sqrt{x} (a B+A b)}{4 a b^2 (a+b x)^2}+\frac{x^{3/2} (A b-a B)}{3 a b (a+b x)^3}","\frac{\sqrt{x} (a B+A b)}{8 a^2 b^2 (a+b x)}+\frac{(a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{5/2} b^{5/2}}-\frac{\sqrt{x} (a B+A b)}{4 a b^2 (a+b x)^2}+\frac{x^{3/2} (A b-a B)}{3 a b (a+b x)^3}",1,"((A*b - a*B)*x^(3/2))/(3*a*b*(a + b*x)^3) - ((A*b + a*B)*Sqrt[x])/(4*a*b^2*(a + b*x)^2) + ((A*b + a*B)*Sqrt[x])/(8*a^2*b^2*(a + b*x)) + ((A*b + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*a^(5/2)*b^(5/2))","A",6,6,29,0.2069,1,"{27, 78, 47, 51, 63, 205}"
770,1,130,0,0.0568772,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{(a B+5 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{7/2} b^{3/2}}+\frac{\sqrt{x} (a B+5 A b)}{8 a^3 b (a+b x)}+\frac{\sqrt{x} (a B+5 A b)}{12 a^2 b (a+b x)^2}+\frac{\sqrt{x} (A b-a B)}{3 a b (a+b x)^3}","\frac{(a B+5 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{7/2} b^{3/2}}+\frac{\sqrt{x} (a B+5 A b)}{8 a^3 b (a+b x)}+\frac{\sqrt{x} (a B+5 A b)}{12 a^2 b (a+b x)^2}+\frac{\sqrt{x} (A b-a B)}{3 a b (a+b x)^3}",1,"((A*b - a*B)*Sqrt[x])/(3*a*b*(a + b*x)^3) + ((5*A*b + a*B)*Sqrt[x])/(12*a^2*b*(a + b*x)^2) + ((5*A*b + a*B)*Sqrt[x])/(8*a^3*b*(a + b*x)) + ((5*A*b + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*a^(7/2)*b^(3/2))","A",6,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
771,1,157,0,0.0650374,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{5 (7 A b-a B)}{8 a^4 b \sqrt{x}}+\frac{5 (7 A b-a B)}{24 a^3 b \sqrt{x} (a+b x)}+\frac{7 A b-a B}{12 a^2 b \sqrt{x} (a+b x)^2}-\frac{5 (7 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{9/2} \sqrt{b}}+\frac{A b-a B}{3 a b \sqrt{x} (a+b x)^3}","-\frac{5 (7 A b-a B)}{8 a^4 b \sqrt{x}}+\frac{5 (7 A b-a B)}{24 a^3 b \sqrt{x} (a+b x)}+\frac{7 A b-a B}{12 a^2 b \sqrt{x} (a+b x)^2}-\frac{5 (7 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{9/2} \sqrt{b}}+\frac{A b-a B}{3 a b \sqrt{x} (a+b x)^3}",1,"(-5*(7*A*b - a*B))/(8*a^4*b*Sqrt[x]) + (A*b - a*B)/(3*a*b*Sqrt[x]*(a + b*x)^3) + (7*A*b - a*B)/(12*a^2*b*Sqrt[x]*(a + b*x)^2) + (5*(7*A*b - a*B))/(24*a^3*b*Sqrt[x]*(a + b*x)) - (5*(7*A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*a^(9/2)*Sqrt[b])","A",7,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
772,1,178,0,0.0793817,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{7 (3 A b-a B)}{8 a^3 b x^{3/2} (a+b x)}-\frac{35 (3 A b-a B)}{24 a^4 b x^{3/2}}+\frac{3 A b-a B}{4 a^2 b x^{3/2} (a+b x)^2}+\frac{35 (3 A b-a B)}{8 a^5 \sqrt{x}}+\frac{35 \sqrt{b} (3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{11/2}}+\frac{A b-a B}{3 a b x^{3/2} (a+b x)^3}","\frac{7 (3 A b-a B)}{8 a^3 b x^{3/2} (a+b x)}-\frac{35 (3 A b-a B)}{24 a^4 b x^{3/2}}+\frac{3 A b-a B}{4 a^2 b x^{3/2} (a+b x)^2}+\frac{35 (3 A b-a B)}{8 a^5 \sqrt{x}}+\frac{35 \sqrt{b} (3 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{8 a^{11/2}}+\frac{A b-a B}{3 a b x^{3/2} (a+b x)^3}",1,"(-35*(3*A*b - a*B))/(24*a^4*b*x^(3/2)) + (35*(3*A*b - a*B))/(8*a^5*Sqrt[x]) + (A*b - a*B)/(3*a*b*x^(3/2)*(a + b*x)^3) + (3*A*b - a*B)/(4*a^2*b*x^(3/2)*(a + b*x)^2) + (7*(3*A*b - a*B))/(8*a^3*b*x^(3/2)*(a + b*x)) + (35*Sqrt[b]*(3*A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(8*a^(11/2))","A",8,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
773,1,240,0,0.1171983,"\int \frac{x^{11/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^(11/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{11/2} (3 A b-13 a B)}{40 a b^2 (a+b x)^4}+\frac{11 x^{9/2} (3 A b-13 a B)}{240 a b^3 (a+b x)^3}+\frac{33 x^{7/2} (3 A b-13 a B)}{320 a b^4 (a+b x)^2}+\frac{231 x^{5/2} (3 A b-13 a B)}{640 a b^5 (a+b x)}-\frac{77 x^{3/2} (3 A b-13 a B)}{128 a b^6}+\frac{231 \sqrt{x} (3 A b-13 a B)}{128 b^7}-\frac{231 \sqrt{a} (3 A b-13 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 b^{15/2}}+\frac{x^{13/2} (A b-a B)}{5 a b (a+b x)^5}","\frac{x^{11/2} (3 A b-13 a B)}{40 a b^2 (a+b x)^4}+\frac{11 x^{9/2} (3 A b-13 a B)}{240 a b^3 (a+b x)^3}+\frac{33 x^{7/2} (3 A b-13 a B)}{320 a b^4 (a+b x)^2}+\frac{231 x^{5/2} (3 A b-13 a B)}{640 a b^5 (a+b x)}-\frac{77 x^{3/2} (3 A b-13 a B)}{128 a b^6}+\frac{231 \sqrt{x} (3 A b-13 a B)}{128 b^7}-\frac{231 \sqrt{a} (3 A b-13 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 b^{15/2}}+\frac{x^{13/2} (A b-a B)}{5 a b (a+b x)^5}",1,"(231*(3*A*b - 13*a*B)*Sqrt[x])/(128*b^7) - (77*(3*A*b - 13*a*B)*x^(3/2))/(128*a*b^6) + ((A*b - a*B)*x^(13/2))/(5*a*b*(a + b*x)^5) + ((3*A*b - 13*a*B)*x^(11/2))/(40*a*b^2*(a + b*x)^4) + (11*(3*A*b - 13*a*B)*x^(9/2))/(240*a*b^3*(a + b*x)^3) + (33*(3*A*b - 13*a*B)*x^(7/2))/(320*a*b^4*(a + b*x)^2) + (231*(3*A*b - 13*a*B)*x^(5/2))/(640*a*b^5*(a + b*x)) - (231*Sqrt[a]*(3*A*b - 13*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*b^(15/2))","A",10,6,29,0.2069,1,"{27, 78, 47, 50, 63, 205}"
774,1,213,0,0.095871,"\int \frac{x^{9/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^(9/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{x^{9/2} (A b-11 a B)}{40 a b^2 (a+b x)^4}+\frac{3 x^{7/2} (A b-11 a B)}{80 a b^3 (a+b x)^3}+\frac{21 x^{5/2} (A b-11 a B)}{320 a b^4 (a+b x)^2}+\frac{21 x^{3/2} (A b-11 a B)}{128 a b^5 (a+b x)}-\frac{63 \sqrt{x} (A b-11 a B)}{128 a b^6}+\frac{63 (A b-11 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 \sqrt{a} b^{13/2}}+\frac{x^{11/2} (A b-a B)}{5 a b (a+b x)^5}","\frac{x^{9/2} (A b-11 a B)}{40 a b^2 (a+b x)^4}+\frac{3 x^{7/2} (A b-11 a B)}{80 a b^3 (a+b x)^3}+\frac{21 x^{5/2} (A b-11 a B)}{320 a b^4 (a+b x)^2}+\frac{21 x^{3/2} (A b-11 a B)}{128 a b^5 (a+b x)}-\frac{63 \sqrt{x} (A b-11 a B)}{128 a b^6}+\frac{63 (A b-11 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 \sqrt{a} b^{13/2}}+\frac{x^{11/2} (A b-a B)}{5 a b (a+b x)^5}",1,"(-63*(A*b - 11*a*B)*Sqrt[x])/(128*a*b^6) + ((A*b - a*B)*x^(11/2))/(5*a*b*(a + b*x)^5) + ((A*b - 11*a*B)*x^(9/2))/(40*a*b^2*(a + b*x)^4) + (3*(A*b - 11*a*B)*x^(7/2))/(80*a*b^3*(a + b*x)^3) + (21*(A*b - 11*a*B)*x^(5/2))/(320*a*b^4*(a + b*x)^2) + (21*(A*b - 11*a*B)*x^(3/2))/(128*a*b^5*(a + b*x)) + (63*(A*b - 11*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*Sqrt[a]*b^(13/2))","A",9,6,29,0.2069,1,"{27, 78, 47, 50, 63, 205}"
775,1,190,0,0.0854049,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{7 (9 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{3/2} b^{11/2}}-\frac{x^{7/2} (9 a B+A b)}{40 a b^2 (a+b x)^4}-\frac{7 x^{5/2} (9 a B+A b)}{240 a b^3 (a+b x)^3}-\frac{7 x^{3/2} (9 a B+A b)}{192 a b^4 (a+b x)^2}-\frac{7 \sqrt{x} (9 a B+A b)}{128 a b^5 (a+b x)}+\frac{x^{9/2} (A b-a B)}{5 a b (a+b x)^5}","\frac{7 (9 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{3/2} b^{11/2}}-\frac{x^{7/2} (9 a B+A b)}{40 a b^2 (a+b x)^4}-\frac{7 x^{5/2} (9 a B+A b)}{240 a b^3 (a+b x)^3}-\frac{7 x^{3/2} (9 a B+A b)}{192 a b^4 (a+b x)^2}-\frac{7 \sqrt{x} (9 a B+A b)}{128 a b^5 (a+b x)}+\frac{x^{9/2} (A b-a B)}{5 a b (a+b x)^5}",1,"((A*b - a*B)*x^(9/2))/(5*a*b*(a + b*x)^5) - ((A*b + 9*a*B)*x^(7/2))/(40*a*b^2*(a + b*x)^4) - (7*(A*b + 9*a*B)*x^(5/2))/(240*a*b^3*(a + b*x)^3) - (7*(A*b + 9*a*B)*x^(3/2))/(192*a*b^4*(a + b*x)^2) - (7*(A*b + 9*a*B)*Sqrt[x])/(128*a*b^5*(a + b*x)) + (7*(A*b + 9*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(3/2)*b^(11/2))","A",8,5,29,0.1724,1,"{27, 78, 47, 63, 205}"
776,1,195,0,0.0897173,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{\sqrt{x} (7 a B+3 A b)}{128 a^2 b^4 (a+b x)}+\frac{(7 a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{5/2} b^{9/2}}-\frac{x^{5/2} (7 a B+3 A b)}{40 a b^2 (a+b x)^4}-\frac{x^{3/2} (7 a B+3 A b)}{48 a b^3 (a+b x)^3}-\frac{\sqrt{x} (7 a B+3 A b)}{64 a b^4 (a+b x)^2}+\frac{x^{7/2} (A b-a B)}{5 a b (a+b x)^5}","\frac{\sqrt{x} (7 a B+3 A b)}{128 a^2 b^4 (a+b x)}+\frac{(7 a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{5/2} b^{9/2}}-\frac{x^{5/2} (7 a B+3 A b)}{40 a b^2 (a+b x)^4}-\frac{x^{3/2} (7 a B+3 A b)}{48 a b^3 (a+b x)^3}-\frac{\sqrt{x} (7 a B+3 A b)}{64 a b^4 (a+b x)^2}+\frac{x^{7/2} (A b-a B)}{5 a b (a+b x)^5}",1,"((A*b - a*B)*x^(7/2))/(5*a*b*(a + b*x)^5) - ((3*A*b + 7*a*B)*x^(5/2))/(40*a*b^2*(a + b*x)^4) - ((3*A*b + 7*a*B)*x^(3/2))/(48*a*b^3*(a + b*x)^3) - ((3*A*b + 7*a*B)*Sqrt[x])/(64*a*b^4*(a + b*x)^2) + ((3*A*b + 7*a*B)*Sqrt[x])/(128*a^2*b^4*(a + b*x)) + ((3*A*b + 7*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(5/2)*b^(9/2))","A",8,6,29,0.2069,1,"{27, 78, 47, 51, 63, 205}"
777,1,185,0,0.0925746,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{3 \sqrt{x} (a B+A b)}{128 a^3 b^3 (a+b x)}+\frac{\sqrt{x} (a B+A b)}{64 a^2 b^3 (a+b x)^2}+\frac{3 (a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{7/2} b^{7/2}}-\frac{x^{3/2} (a B+A b)}{8 a b^2 (a+b x)^4}-\frac{\sqrt{x} (a B+A b)}{16 a b^3 (a+b x)^3}+\frac{x^{5/2} (A b-a B)}{5 a b (a+b x)^5}","\frac{3 \sqrt{x} (a B+A b)}{128 a^3 b^3 (a+b x)}+\frac{\sqrt{x} (a B+A b)}{64 a^2 b^3 (a+b x)^2}+\frac{3 (a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{7/2} b^{7/2}}-\frac{x^{3/2} (a B+A b)}{8 a b^2 (a+b x)^4}-\frac{\sqrt{x} (a B+A b)}{16 a b^3 (a+b x)^3}+\frac{x^{5/2} (A b-a B)}{5 a b (a+b x)^5}",1,"((A*b - a*B)*x^(5/2))/(5*a*b*(a + b*x)^5) - ((A*b + a*B)*x^(3/2))/(8*a*b^2*(a + b*x)^4) - ((A*b + a*B)*Sqrt[x])/(16*a*b^3*(a + b*x)^3) + ((A*b + a*B)*Sqrt[x])/(64*a^2*b^3*(a + b*x)^2) + (3*(A*b + a*B)*Sqrt[x])/(128*a^3*b^3*(a + b*x)) + (3*(A*b + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(7/2)*b^(7/2))","A",8,6,29,0.2069,1,"{27, 78, 47, 51, 63, 205}"
778,1,195,0,0.0885511,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{\sqrt{x} (3 a B+7 A b)}{128 a^4 b^2 (a+b x)}+\frac{\sqrt{x} (3 a B+7 A b)}{192 a^3 b^2 (a+b x)^2}+\frac{\sqrt{x} (3 a B+7 A b)}{240 a^2 b^2 (a+b x)^3}+\frac{(3 a B+7 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{9/2} b^{5/2}}-\frac{\sqrt{x} (3 a B+7 A b)}{40 a b^2 (a+b x)^4}+\frac{x^{3/2} (A b-a B)}{5 a b (a+b x)^5}","\frac{\sqrt{x} (3 a B+7 A b)}{128 a^4 b^2 (a+b x)}+\frac{\sqrt{x} (3 a B+7 A b)}{192 a^3 b^2 (a+b x)^2}+\frac{\sqrt{x} (3 a B+7 A b)}{240 a^2 b^2 (a+b x)^3}+\frac{(3 a B+7 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{9/2} b^{5/2}}-\frac{\sqrt{x} (3 a B+7 A b)}{40 a b^2 (a+b x)^4}+\frac{x^{3/2} (A b-a B)}{5 a b (a+b x)^5}",1,"((A*b - a*B)*x^(3/2))/(5*a*b*(a + b*x)^5) - ((7*A*b + 3*a*B)*Sqrt[x])/(40*a*b^2*(a + b*x)^4) + ((7*A*b + 3*a*B)*Sqrt[x])/(240*a^2*b^2*(a + b*x)^3) + ((7*A*b + 3*a*B)*Sqrt[x])/(192*a^3*b^2*(a + b*x)^2) + ((7*A*b + 3*a*B)*Sqrt[x])/(128*a^4*b^2*(a + b*x)) + ((7*A*b + 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(9/2)*b^(5/2))","A",8,6,29,0.2069,1,"{27, 78, 47, 51, 63, 205}"
779,1,190,0,0.0844874,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{7 (a B+9 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{11/2} b^{3/2}}+\frac{7 \sqrt{x} (a B+9 A b)}{128 a^5 b (a+b x)}+\frac{7 \sqrt{x} (a B+9 A b)}{192 a^4 b (a+b x)^2}+\frac{7 \sqrt{x} (a B+9 A b)}{240 a^3 b (a+b x)^3}+\frac{\sqrt{x} (a B+9 A b)}{40 a^2 b (a+b x)^4}+\frac{\sqrt{x} (A b-a B)}{5 a b (a+b x)^5}","\frac{7 (a B+9 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{11/2} b^{3/2}}+\frac{7 \sqrt{x} (a B+9 A b)}{128 a^5 b (a+b x)}+\frac{7 \sqrt{x} (a B+9 A b)}{192 a^4 b (a+b x)^2}+\frac{7 \sqrt{x} (a B+9 A b)}{240 a^3 b (a+b x)^3}+\frac{\sqrt{x} (a B+9 A b)}{40 a^2 b (a+b x)^4}+\frac{\sqrt{x} (A b-a B)}{5 a b (a+b x)^5}",1,"((A*b - a*B)*Sqrt[x])/(5*a*b*(a + b*x)^5) + ((9*A*b + a*B)*Sqrt[x])/(40*a^2*b*(a + b*x)^4) + (7*(9*A*b + a*B)*Sqrt[x])/(240*a^3*b*(a + b*x)^3) + (7*(9*A*b + a*B)*Sqrt[x])/(192*a^4*b*(a + b*x)^2) + (7*(9*A*b + a*B)*Sqrt[x])/(128*a^5*b*(a + b*x)) + (7*(9*A*b + a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(11/2)*b^(3/2))","A",8,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
780,1,219,0,0.0977657,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{63 (11 A b-a B)}{128 a^6 b \sqrt{x}}+\frac{21 (11 A b-a B)}{128 a^5 b \sqrt{x} (a+b x)}+\frac{21 (11 A b-a B)}{320 a^4 b \sqrt{x} (a+b x)^2}+\frac{3 (11 A b-a B)}{80 a^3 b \sqrt{x} (a+b x)^3}+\frac{11 A b-a B}{40 a^2 b \sqrt{x} (a+b x)^4}-\frac{63 (11 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{13/2} \sqrt{b}}+\frac{A b-a B}{5 a b \sqrt{x} (a+b x)^5}","-\frac{63 (11 A b-a B)}{128 a^6 b \sqrt{x}}+\frac{21 (11 A b-a B)}{128 a^5 b \sqrt{x} (a+b x)}+\frac{21 (11 A b-a B)}{320 a^4 b \sqrt{x} (a+b x)^2}+\frac{3 (11 A b-a B)}{80 a^3 b \sqrt{x} (a+b x)^3}+\frac{11 A b-a B}{40 a^2 b \sqrt{x} (a+b x)^4}-\frac{63 (11 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{13/2} \sqrt{b}}+\frac{A b-a B}{5 a b \sqrt{x} (a+b x)^5}",1,"(-63*(11*A*b - a*B))/(128*a^6*b*Sqrt[x]) + (A*b - a*B)/(5*a*b*Sqrt[x]*(a + b*x)^5) + (11*A*b - a*B)/(40*a^2*b*Sqrt[x]*(a + b*x)^4) + (3*(11*A*b - a*B))/(80*a^3*b*Sqrt[x]*(a + b*x)^3) + (21*(11*A*b - a*B))/(320*a^4*b*Sqrt[x]*(a + b*x)^2) + (21*(11*A*b - a*B))/(128*a^5*b*Sqrt[x]*(a + b*x)) - (63*(11*A*b - a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(13/2)*Sqrt[b])","A",9,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
781,1,240,0,0.1160439,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{231 (13 A b-3 a B)}{640 a^5 b x^{3/2} (a+b x)}-\frac{77 (13 A b-3 a B)}{128 a^6 b x^{3/2}}+\frac{33 (13 A b-3 a B)}{320 a^4 b x^{3/2} (a+b x)^2}+\frac{11 (13 A b-3 a B)}{240 a^3 b x^{3/2} (a+b x)^3}+\frac{13 A b-3 a B}{40 a^2 b x^{3/2} (a+b x)^4}+\frac{231 (13 A b-3 a B)}{128 a^7 \sqrt{x}}+\frac{231 \sqrt{b} (13 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{15/2}}+\frac{A b-a B}{5 a b x^{3/2} (a+b x)^5}","\frac{231 (13 A b-3 a B)}{640 a^5 b x^{3/2} (a+b x)}-\frac{77 (13 A b-3 a B)}{128 a^6 b x^{3/2}}+\frac{33 (13 A b-3 a B)}{320 a^4 b x^{3/2} (a+b x)^2}+\frac{11 (13 A b-3 a B)}{240 a^3 b x^{3/2} (a+b x)^3}+\frac{13 A b-3 a B}{40 a^2 b x^{3/2} (a+b x)^4}+\frac{231 (13 A b-3 a B)}{128 a^7 \sqrt{x}}+\frac{231 \sqrt{b} (13 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{128 a^{15/2}}+\frac{A b-a B}{5 a b x^{3/2} (a+b x)^5}",1,"(-77*(13*A*b - 3*a*B))/(128*a^6*b*x^(3/2)) + (231*(13*A*b - 3*a*B))/(128*a^7*Sqrt[x]) + (A*b - a*B)/(5*a*b*x^(3/2)*(a + b*x)^5) + (13*A*b - 3*a*B)/(40*a^2*b*x^(3/2)*(a + b*x)^4) + (11*(13*A*b - 3*a*B))/(240*a^3*b*x^(3/2)*(a + b*x)^3) + (33*(13*A*b - 3*a*B))/(320*a^4*b*x^(3/2)*(a + b*x)^2) + (231*(13*A*b - 3*a*B))/(640*a^5*b*x^(3/2)*(a + b*x)) + (231*Sqrt[b]*(13*A*b - 3*a*B)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(128*a^(15/2))","A",10,5,29,0.1724,1,"{27, 78, 51, 63, 205}"
782,1,120,0,0.0471709,"\int x^{7/2} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^(7/2)*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{11 (a+b x)}+\frac{2 a A x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 b B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}","\frac{2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{11 (a+b x)}+\frac{2 a A x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 b B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}",1,"(2*a*A*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*(A*b + a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (2*b*B*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
783,1,120,0,0.0458809,"\int x^{5/2} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^(5/2)*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 (a+b x)}+\frac{2 a A x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{2 b B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}","\frac{2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 (a+b x)}+\frac{2 a A x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{2 b B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}",1,"(2*a*A*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*(A*b + a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*b*B*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
784,1,120,0,0.0428388,"\int x^{3/2} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[x^(3/2)*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{2 a A x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{2 b B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}","\frac{2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{2 a A x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{2 b B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}",1,"(2*a*A*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*(A*b + a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*b*B*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
785,1,120,0,0.0453983,"\int \sqrt{x} (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[Sqrt[x]*(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{2 a A x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{2 b B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}","\frac{2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{2 a A x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{2 b B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}",1,"(2*a*A*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*(A*b + a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*b*B*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
786,1,118,0,0.042182,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/Sqrt[x],x]","\frac{2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{2 a A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{2 b B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","\frac{2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{2 a A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{2 b B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(2*a*A*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*(A*b + a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*b*B*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
787,1,116,0,0.043068,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{3/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(3/2),x]","\frac{2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}+\frac{2 b B x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}","\frac{2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}+\frac{2 b B x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}",1,"(-2*a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (2*(A*b + a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*b*B*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
788,1,116,0,0.0435198,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{5/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(5/2),x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{\sqrt{x} (a+b x)}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}+\frac{2 b B \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{\sqrt{x} (a+b x)}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}+\frac{2 b B \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(-2*a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (2*b*B*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x)","A",3,2,31,0.06452,1,"{770, 76}"
789,1,118,0,0.0430058,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{7/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(7/2),x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^{3/2} (a+b x)}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}-\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 x^{3/2} (a+b x)}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}-\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}",1,"(-2*a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^(5/2)*(a + b*x)) - (2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (2*b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
790,1,120,0,0.0427632,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{x^{9/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/x^(9/2),x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 x^{5/2} (a+b x)}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^{7/2} (a+b x)}-\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 x^{5/2} (a+b x)}-\frac{2 a A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^{7/2} (a+b x)}-\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}",1,"(-2*a*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^(7/2)*(a + b*x)) - (2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^(5/2)*(a + b*x)) - (2*b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
791,1,220,0,0.0886076,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^2 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{15 (a+b x)}+\frac{6 a b x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{13 (a+b x)}+\frac{2 a^2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{11 (a+b x)}+\frac{2 a^3 A x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 b^3 B x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2}}{17 (a+b x)}","\frac{2 b^2 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{15 (a+b x)}+\frac{6 a b x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{13 (a+b x)}+\frac{2 a^2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{11 (a+b x)}+\frac{2 a^3 A x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 b^3 B x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2}}{17 (a+b x)}",1,"(2*a^3*A*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*a^2*(3*A*b + a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (6*a*b*(A*b + a*B)*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x)) + (2*b^2*(A*b + 3*a*B)*x^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*(a + b*x)) + (2*b^3*B*x^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
792,1,220,0,0.0810922,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^2 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{13 (a+b x)}+\frac{6 a b x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{11 (a+b x)}+\frac{2 a^2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{9 (a+b x)}+\frac{2 a^3 A x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{2 b^3 B x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}{15 (a+b x)}","\frac{2 b^2 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{13 (a+b x)}+\frac{6 a b x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{11 (a+b x)}+\frac{2 a^2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{9 (a+b x)}+\frac{2 a^3 A x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{2 b^3 B x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}{15 (a+b x)}",1,"(2*a^3*A*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*a^2*(3*A*b + a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (6*a*b*(A*b + a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (2*b^2*(A*b + 3*a*B)*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x)) + (2*b^3*B*x^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
793,1,220,0,0.0841359,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{11 (a+b x)}+\frac{2 a b x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{2 a^2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{7 (a+b x)}+\frac{2 a^3 A x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{2 b^3 B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}","\frac{2 b^2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{11 (a+b x)}+\frac{2 a b x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{2 a^2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{7 (a+b x)}+\frac{2 a^3 A x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{2 b^3 B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}",1,"(2*a^3*A*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*a^2*(3*A*b + a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*a*b*(A*b + a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*b^2*(A*b + 3*a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (2*b^3*B*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
794,1,220,0,0.083202,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{9 (a+b x)}+\frac{6 a b x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{2 a^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 (a+b x)}+\frac{2 a^3 A x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{2 b^3 B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}","\frac{2 b^2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{9 (a+b x)}+\frac{6 a b x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{2 a^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 (a+b x)}+\frac{2 a^3 A x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{2 b^3 B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}",1,"(2*a^3*A*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*a^2*(3*A*b + a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (6*a*b*(A*b + a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*b^2*(A*b + 3*a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*b^3*B*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
795,1,218,0,0.0801123,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/Sqrt[x],x]","\frac{2 b^2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{7 (a+b x)}+\frac{6 a b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{2 a^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{3 (a+b x)}+\frac{2 a^3 A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{2 b^3 B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}","\frac{2 b^2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{7 (a+b x)}+\frac{6 a b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{5 (a+b x)}+\frac{2 a^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{3 (a+b x)}+\frac{2 a^3 A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{2 b^3 B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}",1,"(2*a^3*A*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*a^2*(3*A*b + a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (6*a*b*(A*b + a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*b^2*(A*b + 3*a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*b^3*B*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
796,1,214,0,0.0862784,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(3/2),x]","\frac{2 b^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{5 (a+b x)}+\frac{2 a b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{2 a^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{a+b x}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}+\frac{2 b^3 B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}","\frac{2 b^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{5 (a+b x)}+\frac{2 a b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{2 a^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{a+b x}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}+\frac{2 b^3 B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}",1,"(-2*a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (2*a^2*(3*A*b + a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*a*b*(A*b + a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*b^2*(A*b + 3*a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*b^3*B*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
797,1,216,0,0.0834914,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(5/2),x]","-\frac{2 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{\sqrt{x} (a+b x)}+\frac{6 a b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{2 b^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{3 (a+b x)}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}+\frac{2 b^3 B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","-\frac{2 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{\sqrt{x} (a+b x)}+\frac{6 a b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{2 b^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{3 (a+b x)}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}+\frac{2 b^3 B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(-2*a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (2*a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (6*a*b*(A*b + a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*b^2*(A*b + 3*a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*b^3*B*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
798,1,216,0,0.0793051,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(7/2),x]","-\frac{2 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{3 x^{3/2} (a+b x)}-\frac{6 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{\sqrt{x} (a+b x)}+\frac{2 b^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{a+b x}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}+\frac{2 b^3 B x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}","-\frac{2 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{3 x^{3/2} (a+b x)}-\frac{6 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{\sqrt{x} (a+b x)}+\frac{2 b^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{a+b x}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}+\frac{2 b^3 B x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}",1,"(-2*a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^(5/2)*(a + b*x)) - (2*a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (6*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (2*b^2*(A*b + 3*a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*b^3*B*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
799,1,214,0,0.0800435,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{x^{9/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/x^(9/2),x]","-\frac{2 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 x^{5/2} (a+b x)}-\frac{2 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x^{3/2} (a+b x)}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{\sqrt{x} (a+b x)}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^{7/2} (a+b x)}+\frac{2 b^3 B \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}","-\frac{2 a^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+3 A b)}{5 x^{5/2} (a+b x)}-\frac{2 a b \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{x^{3/2} (a+b x)}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (3 a B+A b)}{\sqrt{x} (a+b x)}-\frac{2 a^3 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^{7/2} (a+b x)}+\frac{2 b^3 B \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}",1,"(-2*a^3*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^(7/2)*(a + b*x)) - (2*a^2*(3*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^(5/2)*(a + b*x)) - (2*a*b*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(x^(3/2)*(a + b*x)) - (2*b^2*(A*b + 3*a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (2*b^3*B*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x)","A",3,2,31,0.06452,1,"{770, 76}"
800,1,320,0,0.1342597,"\int x^{7/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^(7/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^4 x^{19/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{19 (a+b x)}+\frac{10 a b^3 x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{17 (a+b x)}+\frac{4 a^2 b^2 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{10 a^3 b x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{13 (a+b x)}+\frac{2 a^4 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{11 (a+b x)}+\frac{2 a^5 A x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 b^5 B x^{21/2} \sqrt{a^2+2 a b x+b^2 x^2}}{21 (a+b x)}","\frac{2 b^4 x^{19/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{19 (a+b x)}+\frac{10 a b^3 x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{17 (a+b x)}+\frac{4 a^2 b^2 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{10 a^3 b x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{13 (a+b x)}+\frac{2 a^4 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{11 (a+b x)}+\frac{2 a^5 A x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}+\frac{2 b^5 B x^{21/2} \sqrt{a^2+2 a b x+b^2 x^2}}{21 (a+b x)}",1,"(2*a^5*A*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*a^4*(5*A*b + a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (10*a^3*b*(2*A*b + a*B)*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x)) + (4*a^2*b^2*(A*b + a*B)*x^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (10*a*b^3*(A*b + 2*a*B)*x^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(19/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(19*(a + b*x)) + (2*b^5*B*x^(21/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(21*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
801,1,320,0,0.121961,"\int x^{5/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^(5/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^4 x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{17 (a+b x)}+\frac{2 a b^3 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{3 (a+b x)}+\frac{20 a^2 b^2 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{13 (a+b x)}+\frac{10 a^3 b x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{11 (a+b x)}+\frac{2 a^4 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{9 (a+b x)}+\frac{2 a^5 A x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{2 b^5 B x^{19/2} \sqrt{a^2+2 a b x+b^2 x^2}}{19 (a+b x)}","\frac{2 b^4 x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{17 (a+b x)}+\frac{2 a b^3 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{3 (a+b x)}+\frac{20 a^2 b^2 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{13 (a+b x)}+\frac{10 a^3 b x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{11 (a+b x)}+\frac{2 a^4 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{9 (a+b x)}+\frac{2 a^5 A x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}+\frac{2 b^5 B x^{19/2} \sqrt{a^2+2 a b x+b^2 x^2}}{19 (a+b x)}",1,"(2*a^5*A*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*a^4*(5*A*b + a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (10*a^3*b*(2*A*b + a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (20*a^2*b^2*(A*b + a*B)*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x)) + (2*a*b^3*(A*b + 2*a*B)*x^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*(a + b*x)) + (2*b^5*B*x^(19/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(19*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
802,1,320,0,0.1204301,"\int x^{3/2} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[x^(3/2)*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^4 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{15 (a+b x)}+\frac{10 a b^3 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{13 (a+b x)}+\frac{20 a^2 b^2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{11 (a+b x)}+\frac{10 a^3 b x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{9 (a+b x)}+\frac{2 a^4 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{7 (a+b x)}+\frac{2 a^5 A x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{2 b^5 B x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2}}{17 (a+b x)}","\frac{2 b^4 x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{15 (a+b x)}+\frac{10 a b^3 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{13 (a+b x)}+\frac{20 a^2 b^2 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{11 (a+b x)}+\frac{10 a^3 b x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{9 (a+b x)}+\frac{2 a^4 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{7 (a+b x)}+\frac{2 a^5 A x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}+\frac{2 b^5 B x^{17/2} \sqrt{a^2+2 a b x+b^2 x^2}}{17 (a+b x)}",1,"(2*a^5*A*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*a^4*(5*A*b + a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (10*a^3*b*(2*A*b + a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (20*a^2*b^2*(A*b + a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (10*a*b^3*(A*b + 2*a*B)*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*(a + b*x)) + (2*b^5*B*x^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
803,1,320,0,0.1195642,"\int \sqrt{x} (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[Sqrt[x]*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^4 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{13 (a+b x)}+\frac{10 a b^3 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{11 (a+b x)}+\frac{20 a^2 b^2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 (a+b x)}+\frac{10 a^3 b x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{7 (a+b x)}+\frac{2 a^4 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{5 (a+b x)}+\frac{2 a^5 A x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{2 b^5 B x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}{15 (a+b x)}","\frac{2 b^4 x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{13 (a+b x)}+\frac{10 a b^3 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{11 (a+b x)}+\frac{20 a^2 b^2 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{9 (a+b x)}+\frac{10 a^3 b x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{7 (a+b x)}+\frac{2 a^4 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{5 (a+b x)}+\frac{2 a^5 A x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}{3 (a+b x)}+\frac{2 b^5 B x^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}{15 (a+b x)}",1,"(2*a^5*A*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*a^4*(5*A*b + a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (10*a^3*b*(2*A*b + a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (20*a^2*b^2*(A*b + a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (10*a*b^3*(A*b + 2*a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x)) + (2*b^5*B*x^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
804,1,316,0,0.1188434,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/Sqrt[x],x]","\frac{2 b^4 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{11 (a+b x)}+\frac{10 a b^3 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{9 (a+b x)}+\frac{20 a^2 b^2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{2 a^3 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}+\frac{2 a^4 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{3 (a+b x)}+\frac{2 a^5 A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{2 b^5 B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}","\frac{2 b^4 x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{11 (a+b x)}+\frac{10 a b^3 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{9 (a+b x)}+\frac{20 a^2 b^2 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{7 (a+b x)}+\frac{2 a^3 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}+\frac{2 a^4 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{3 (a+b x)}+\frac{2 a^5 A \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{2 b^5 B x^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}{13 (a+b x)}",1,"(2*a^5*A*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*a^4*(5*A*b + a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*a^3*b*(2*A*b + a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (20*a^2*b^2*(A*b + a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (10*a*b^3*(A*b + 2*a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x)) + (2*b^5*B*x^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
805,1,314,0,0.1186022,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(3/2),x]","\frac{2 b^4 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{9 (a+b x)}+\frac{10 a b^3 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{7 (a+b x)}+\frac{4 a^2 b^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{10 a^3 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{3 (a+b x)}+\frac{2 a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{a+b x}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}+\frac{2 b^5 B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}","\frac{2 b^4 x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{9 (a+b x)}+\frac{10 a b^3 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{7 (a+b x)}+\frac{4 a^2 b^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{10 a^3 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{3 (a+b x)}+\frac{2 a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{a+b x}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{x} (a+b x)}+\frac{2 b^5 B x^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}{11 (a+b x)}",1,"(-2*a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (2*a^4*(5*A*b + a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (10*a^3*b*(2*A*b + a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (4*a^2*b^2*(A*b + a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (10*a*b^3*(A*b + 2*a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x)) + (2*b^5*B*x^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
806,1,314,0,0.1221873,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(5/2),x]","-\frac{2 a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{\sqrt{x} (a+b x)}+\frac{10 a^3 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}+\frac{20 a^2 b^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{2 a b^3 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}+\frac{2 b^4 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{7 (a+b x)}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}+\frac{2 b^5 B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}","-\frac{2 a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{\sqrt{x} (a+b x)}+\frac{10 a^3 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{a+b x}+\frac{20 a^2 b^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{3 (a+b x)}+\frac{2 a b^3 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}+\frac{2 b^4 x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{7 (a+b x)}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{3 x^{3/2} (a+b x)}+\frac{2 b^5 B x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}{9 (a+b x)}",1,"(-2*a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (2*a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (10*a^3*b*(2*A*b + a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (20*a^2*b^2*(A*b + a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*a*b^3*(A*b + 2*a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*b^4*(A*b + 5*a*B)*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x)) + (2*b^5*B*x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
807,1,316,0,0.1193225,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(7/2),x]","-\frac{2 a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{3 x^{3/2} (a+b x)}-\frac{10 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{\sqrt{x} (a+b x)}+\frac{20 a^2 b^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{10 a b^3 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{3 (a+b x)}+\frac{2 b^4 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{5 (a+b x)}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}+\frac{2 b^5 B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}","-\frac{2 a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{3 x^{3/2} (a+b x)}-\frac{10 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{\sqrt{x} (a+b x)}+\frac{20 a^2 b^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{a+b x}+\frac{10 a b^3 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{3 (a+b x)}+\frac{2 b^4 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{5 (a+b x)}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{5 x^{5/2} (a+b x)}+\frac{2 b^5 B x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}{7 (a+b x)}",1,"(-2*a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^(5/2)*(a + b*x)) - (2*a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (10*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (20*a^2*b^2*(A*b + a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (10*a*b^3*(A*b + 2*a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*b^4*(A*b + 5*a*B)*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x)) + (2*b^5*B*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
808,1,316,0,0.120171,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{x^{9/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/x^(9/2),x]","-\frac{2 a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{5 x^{5/2} (a+b x)}-\frac{10 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{3 x^{3/2} (a+b x)}-\frac{20 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{\sqrt{x} (a+b x)}+\frac{10 a b^3 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}+\frac{2 b^4 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{3 (a+b x)}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^{7/2} (a+b x)}+\frac{2 b^5 B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}","-\frac{2 a^4 \sqrt{a^2+2 a b x+b^2 x^2} (a B+5 A b)}{5 x^{5/2} (a+b x)}-\frac{10 a^3 b \sqrt{a^2+2 a b x+b^2 x^2} (a B+2 A b)}{3 x^{3/2} (a+b x)}-\frac{20 a^2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a B+A b)}{\sqrt{x} (a+b x)}+\frac{10 a b^3 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2} (2 a B+A b)}{a+b x}+\frac{2 b^4 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (5 a B+A b)}{3 (a+b x)}-\frac{2 a^5 A \sqrt{a^2+2 a b x+b^2 x^2}}{7 x^{7/2} (a+b x)}+\frac{2 b^5 B x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}{5 (a+b x)}",1,"(-2*a^5*A*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*x^(7/2)*(a + b*x)) - (2*a^4*(5*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*x^(5/2)*(a + b*x)) - (10*a^3*b*(2*A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*x^(3/2)*(a + b*x)) - (20*a^2*b^2*(A*b + a*B)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(Sqrt[x]*(a + b*x)) + (10*a*b^3*(A*b + 2*a*B)*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + (2*b^4*(A*b + 5*a*B)*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (2*b^5*B*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*(a + b*x))","A",3,2,31,0.06452,1,"{770, 76}"
809,1,286,0,0.1348349,"\int \frac{x^{7/2} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x^(7/2)*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{7/2} (a+b x) (A b-a B)}{7 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a x^{5/2} (a+b x) (A b-a B)}{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^2 x^{3/2} (a+b x) (A b-a B)}{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a^3 \sqrt{x} (a+b x) (A b-a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^{7/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{9/2} (a+b x)}{9 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 x^{7/2} (a+b x) (A b-a B)}{7 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a x^{5/2} (a+b x) (A b-a B)}{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^2 x^{3/2} (a+b x) (A b-a B)}{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a^3 \sqrt{x} (a+b x) (A b-a B)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^{7/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{9/2} (a+b x)}{9 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*a^3*(A*b - a*B)*Sqrt[x]*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*a^2*(A*b - a*B)*x^(3/2)*(a + b*x))/(3*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*a*(A*b - a*B)*x^(5/2)*(a + b*x))/(5*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*x^(7/2)*(a + b*x))/(7*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*x^(9/2)*(a + b*x))/(9*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*a^(7/2)*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,31,0.1613,1,"{770, 80, 50, 63, 205}"
810,1,238,0,0.108314,"\int \frac{x^{5/2} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x^(5/2)*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{5/2} (a+b x) (A b-a B)}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a x^{3/2} (a+b x) (A b-a B)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^2 \sqrt{x} (a+b x) (A b-a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a^{5/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{7/2} (a+b x)}{7 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 x^{5/2} (a+b x) (A b-a B)}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a x^{3/2} (a+b x) (A b-a B)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^2 \sqrt{x} (a+b x) (A b-a B)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a^{5/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{7/2} (a+b x)}{7 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*a^2*(A*b - a*B)*Sqrt[x]*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*a*(A*b - a*B)*x^(3/2)*(a + b*x))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*x^(5/2)*(a + b*x))/(5*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*x^(7/2)*(a + b*x))/(7*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*a^(5/2)*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,31,0.1613,1,"{770, 80, 50, 63, 205}"
811,1,190,0,0.0860083,"\int \frac{x^{3/2} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(x^(3/2)*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 x^{3/2} (a+b x) (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a \sqrt{x} (a+b x) (A b-a B)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^{3/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{5/2} (a+b x)}{5 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 x^{3/2} (a+b x) (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 a \sqrt{x} (a+b x) (A b-a B)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 a^{3/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{5/2} (a+b x)}{5 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*a*(A*b - a*B)*Sqrt[x]*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*x^(3/2)*(a + b*x))/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*x^(5/2)*(a + b*x))/(5*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*a^(3/2)*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,31,0.1613,1,"{770, 80, 50, 63, 205}"
812,1,144,0,0.0703647,"\int \frac{\sqrt{x} (A+B x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(Sqrt[x]*(A + B*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 \sqrt{x} (a+b x) (A b-a B)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 \sqrt{a} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{3/2} (a+b x)}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 \sqrt{x} (a+b x) (A b-a B)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 \sqrt{a} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B x^{3/2} (a+b x)}{3 b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(A*b - a*B)*Sqrt[x]*(a + b*x))/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*x^(3/2)*(a + b*x))/(3*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*Sqrt[a]*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(b^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,31,0.1613,1,"{770, 80, 50, 63, 205}"
813,1,99,0,0.0518154,"\int \frac{A+B x}{\sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B \sqrt{x} (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{\sqrt{a} b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B \sqrt{x} (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*B*Sqrt[x]*(a + b*x))/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(Sqrt[a]*b^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,31,0.1290,1,"{770, 80, 63, 205}"
814,1,99,0,0.0572507,"\int \frac{A+B x}{x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{a \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{2 (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{3/2} \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{a \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*A*(a + b*x))/(a*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(3/2)*Sqrt[b]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,31,0.1290,1,"{770, 78, 63, 205}"
815,1,144,0,0.0749992,"\int \frac{A+B x}{x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) (A b-a B)}{a^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 \sqrt{b} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{3 a x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (A b-a B)}{a^2 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 \sqrt{b} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{3 a x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*A*(a + b*x))/(3*a*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x))/(a^2*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*Sqrt[b]*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
816,1,190,0,0.0938857,"\int \frac{A+B x}{x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 b (a+b x) (A b-a B)}{a^3 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (A b-a B)}{3 a^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b^{3/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{5 a x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{2 b (a+b x) (A b-a B)}{a^3 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (A b-a B)}{3 a^2 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b^{3/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{5 a x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*A*(a + b*x))/(5*a*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x))/(3*a^2*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b*(A*b - a*B)*(a + b*x))/(a^3*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b^(3/2)*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
817,1,238,0,0.1163507,"\int \frac{A+B x}{x^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(x^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 b^2 (a+b x) (A b-a B)}{a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b (a+b x) (A b-a B)}{3 a^3 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (A b-a B)}{5 a^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 b^{5/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{7 a x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 b^2 (a+b x) (A b-a B)}{a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 b (a+b x) (A b-a B)}{3 a^3 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (A b-a B)}{5 a^2 x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 b^{5/2} (a+b x) (A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{a^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 A (a+b x)}{7 a x^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*A*(a + b*x))/(7*a*x^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x))/(5*a^2*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b*(A*b - a*B)*(a + b*x))/(3*a^3*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b^2*(A*b - a*B)*(a + b*x))/(a^4*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b^(5/2)*(A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(a^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
818,1,302,0,0.1505857,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{9/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{7/2} (5 A b-9 a B)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 x^{5/2} (a+b x) (5 A b-9 a B)}{20 a b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 x^{3/2} (a+b x) (5 A b-9 a B)}{12 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 a \sqrt{x} (a+b x) (5 A b-9 a B)}{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 a^{3/2} (a+b x) (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{9/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{7/2} (5 A b-9 a B)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 x^{5/2} (a+b x) (5 A b-9 a B)}{20 a b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 x^{3/2} (a+b x) (5 A b-9 a B)}{12 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 a \sqrt{x} (a+b x) (5 A b-9 a B)}{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 a^{3/2} (a+b x) (5 A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((5*A*b - 9*a*B)*x^(7/2))/(4*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(9/2))/(2*a*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*a*(5*A*b - 9*a*B)*Sqrt[x]*(a + b*x))/(4*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*(5*A*b - 9*a*B)*x^(3/2)*(a + b*x))/(12*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*(5*A*b - 9*a*B)*x^(5/2)*(a + b*x))/(20*a*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*a^(3/2)*(5*A*b - 9*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,6,31,0.1935,1,"{770, 78, 47, 50, 63, 205}"
819,1,255,0,0.1210226,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{7/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{5/2} (3 A b-7 a B)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 x^{3/2} (a+b x) (3 A b-7 a B)}{12 a b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{x} (a+b x) (3 A b-7 a B)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 \sqrt{a} (a+b x) (3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{7/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{5/2} (3 A b-7 a B)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 x^{3/2} (a+b x) (3 A b-7 a B)}{12 a b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{x} (a+b x) (3 A b-7 a B)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 \sqrt{a} (a+b x) (3 A b-7 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((3*A*b - 7*a*B)*x^(5/2))/(4*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(7/2))/(2*a*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*(3*A*b - 7*a*B)*Sqrt[x]*(a + b*x))/(4*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*(3*A*b - 7*a*B)*x^(3/2)*(a + b*x))/(12*a*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*Sqrt[a]*(3*A*b - 7*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,31,0.1935,1,"{770, 78, 47, 50, 63, 205}"
820,1,206,0,0.1112637,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{5/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{3/2} (A b-5 a B)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 \sqrt{x} (a+b x) (A b-5 a B)}{4 a b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 (a+b x) (A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{5/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{3/2} (A b-5 a B)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 \sqrt{x} (a+b x) (A b-5 a B)}{4 a b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 (a+b x) (A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 \sqrt{a} b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((A*b - 5*a*B)*x^(3/2))/(4*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(5/2))/(2*a*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*(A*b - 5*a*B)*Sqrt[x]*(a + b*x))/(4*a*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*(A*b - 5*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*Sqrt[a]*b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,6,31,0.1935,1,"{770, 78, 47, 50, 63, 205}"
821,1,158,0,0.0860282,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{x^{3/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\sqrt{x} (3 a B+A b)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{3/2} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\sqrt{x} (3 a B+A b)}{4 a b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{3/2} b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((A*b + 3*a*B)*Sqrt[x])/(4*a*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(3/2))/(2*a*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b + 3*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(3/2)*b^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,31,0.1613,1,"{770, 78, 47, 63, 205}"
822,1,158,0,0.0861845,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{\sqrt{x} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (a B+3 A b)}{4 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{\sqrt{x} (A b-a B)}{2 a b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (a B+3 A b)}{4 a^2 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{5/2} b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((3*A*b + a*B)*Sqrt[x])/(4*a^2*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*Sqrt[x])/(2*a*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((3*A*b + a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(5/2)*b^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
823,1,209,0,0.108958,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{A b-a B}{2 a b \sqrt{x} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 (a+b x) (5 A b-a B)}{4 a^3 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 A b-a B}{4 a^2 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 (a+b x) (5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2} \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{A b-a B}{2 a b \sqrt{x} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 (a+b x) (5 A b-a B)}{4 a^3 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 A b-a B}{4 a^2 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 (a+b x) (5 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{7/2} \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(5*A*b - a*B)/(4*a^2*b*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(2*a*b*Sqrt[x]*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*(5*A*b - a*B)*(a + b*x))/(4*a^3*b*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*(5*A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(7/2)*Sqrt[b]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
824,1,255,0,0.1294486,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{5 (a+b x) (7 A b-3 a B)}{4 a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 (a+b x) (7 A b-3 a B)}{12 a^3 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 A b-3 a B}{4 a^2 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{2 a b x^{3/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{b} (a+b x) (7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{5 (a+b x) (7 A b-3 a B)}{4 a^4 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 (a+b x) (7 A b-3 a B)}{12 a^3 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 A b-3 a B}{4 a^2 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{2 a b x^{3/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{b} (a+b x) (7 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(7*A*b - 3*a*B)/(4*a^2*b*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(2*a*b*x^(3/2)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*(7*A*b - 3*a*B)*(a + b*x))/(12*a^3*b*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*(7*A*b - 3*a*B)*(a + b*x))/(4*a^4*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*Sqrt[b]*(7*A*b - 3*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
825,1,302,0,0.1461084,"\int \frac{A+B x}{x^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{7 b (a+b x) (9 A b-5 a B)}{4 a^5 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 (a+b x) (9 A b-5 a B)}{12 a^4 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 (a+b x) (9 A b-5 a B)}{20 a^3 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{2 a b x^{5/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{9 A b-5 a B}{4 a^2 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 b^{3/2} (a+b x) (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{7 b (a+b x) (9 A b-5 a B)}{4 a^5 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 (a+b x) (9 A b-5 a B)}{12 a^4 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 (a+b x) (9 A b-5 a B)}{20 a^3 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{2 a b x^{5/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{9 A b-5 a B}{4 a^2 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 b^{3/2} (a+b x) (9 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{4 a^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(9*A*b - 5*a*B)/(4*a^2*b*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(2*a*b*x^(5/2)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*(9*A*b - 5*a*B)*(a + b*x))/(20*a^3*b*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*(9*A*b - 5*a*B)*(a + b*x))/(12*a^4*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*b*(9*A*b - 5*a*B)*(a + b*x))/(4*a^5*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*b^(3/2)*(9*A*b - 5*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(4*a^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
826,1,404,0,0.2021632,"\int \frac{x^{11/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^(11/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{13/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{11/2} (5 A b-13 a B)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{11 x^{9/2} (5 A b-13 a B)}{96 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{33 x^{7/2} (5 A b-13 a B)}{64 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 x^{5/2} (a+b x) (5 A b-13 a B)}{320 a b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{77 x^{3/2} (a+b x) (5 A b-13 a B)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 a \sqrt{x} (a+b x) (5 A b-13 a B)}{64 b^7 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{231 a^{3/2} (a+b x) (5 A b-13 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 b^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{13/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{11/2} (5 A b-13 a B)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{11 x^{9/2} (5 A b-13 a B)}{96 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{33 x^{7/2} (5 A b-13 a B)}{64 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 x^{5/2} (a+b x) (5 A b-13 a B)}{320 a b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{77 x^{3/2} (a+b x) (5 A b-13 a B)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 a \sqrt{x} (a+b x) (5 A b-13 a B)}{64 b^7 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{231 a^{3/2} (a+b x) (5 A b-13 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 b^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(33*(5*A*b - 13*a*B)*x^(7/2))/(64*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(13/2))/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((5*A*b - 13*a*B)*x^(11/2))/(24*a*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (11*(5*A*b - 13*a*B)*x^(9/2))/(96*a*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*a*(5*A*b - 13*a*B)*Sqrt[x]*(a + b*x))/(64*b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (77*(5*A*b - 13*a*B)*x^(3/2)*(a + b*x))/(64*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*(5*A*b - 13*a*B)*x^(5/2)*(a + b*x))/(320*a*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (231*a^(3/2)*(5*A*b - 13*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*b^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,6,31,0.1935,1,"{770, 78, 47, 50, 63, 205}"
827,1,357,0,0.1819593,"\int \frac{x^{9/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^(9/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{11/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{9/2} (3 A b-11 a B)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 x^{7/2} (3 A b-11 a B)}{32 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{21 x^{5/2} (3 A b-11 a B)}{64 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 x^{3/2} (a+b x) (3 A b-11 a B)}{64 a b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{105 \sqrt{x} (a+b x) (3 A b-11 a B)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{105 \sqrt{a} (a+b x) (3 A b-11 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 b^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{11/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{9/2} (3 A b-11 a B)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 x^{7/2} (3 A b-11 a B)}{32 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{21 x^{5/2} (3 A b-11 a B)}{64 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 x^{3/2} (a+b x) (3 A b-11 a B)}{64 a b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{105 \sqrt{x} (a+b x) (3 A b-11 a B)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{105 \sqrt{a} (a+b x) (3 A b-11 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 b^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(21*(3*A*b - 11*a*B)*x^(5/2))/(64*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(11/2))/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((3*A*b - 11*a*B)*x^(9/2))/(24*a*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*(3*A*b - 11*a*B)*x^(7/2))/(32*a*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (105*(3*A*b - 11*a*B)*Sqrt[x]*(a + b*x))/(64*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*(3*A*b - 11*a*B)*x^(3/2)*(a + b*x))/(64*a*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (105*Sqrt[a]*(3*A*b - 11*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*b^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,6,31,0.1935,1,"{770, 78, 47, 50, 63, 205}"
828,1,306,0,0.1502948,"\int \frac{x^{7/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^(7/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{9/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{7/2} (A b-9 a B)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 x^{5/2} (A b-9 a B)}{96 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 x^{3/2} (A b-9 a B)}{192 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 \sqrt{x} (a+b x) (A b-9 a B)}{64 a b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 (a+b x) (A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 \sqrt{a} b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{9/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{x^{7/2} (A b-9 a B)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 x^{5/2} (A b-9 a B)}{96 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 x^{3/2} (A b-9 a B)}{192 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 \sqrt{x} (a+b x) (A b-9 a B)}{64 a b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 (a+b x) (A b-9 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 \sqrt{a} b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(35*(A*b - 9*a*B)*x^(3/2))/(192*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(9/2))/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - 9*a*B)*x^(7/2))/(24*a*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*(A*b - 9*a*B)*x^(5/2))/(96*a*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*(A*b - 9*a*B)*Sqrt[x]*(a + b*x))/(64*a*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*(A*b - 9*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*Sqrt[a]*b^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,6,31,0.1935,1,"{770, 78, 47, 50, 63, 205}"
829,1,258,0,0.1325346,"\int \frac{x^{5/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^(5/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{7/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{x^{5/2} (7 a B+A b)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 x^{3/2} (7 a B+A b)}{96 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 \sqrt{x} (7 a B+A b)}{64 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 (a+b x) (7 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{3/2} b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{7/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{x^{5/2} (7 a B+A b)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 x^{3/2} (7 a B+A b)}{96 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 \sqrt{x} (7 a B+A b)}{64 a b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 (a+b x) (7 a B+A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{3/2} b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-5*(A*b + 7*a*B)*Sqrt[x])/(64*a*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(7/2))/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b + 7*a*B)*x^(5/2))/(24*a*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*(A*b + 7*a*B)*x^(3/2))/(96*a*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*(A*b + 7*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(3/2)*b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,31,0.1613,1,"{770, 78, 47, 63, 205}"
830,1,262,0,0.1473799,"\int \frac{x^{3/2} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(x^(3/2)*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{5/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{x^{3/2} (5 a B+3 A b)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (5 a B+3 A b)}{64 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\sqrt{x} (5 a B+3 A b)}{32 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (5 a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{5/2} b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{5/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{x^{3/2} (5 a B+3 A b)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (5 a B+3 A b)}{64 a^2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\sqrt{x} (5 a B+3 A b)}{32 a b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (5 a B+3 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{5/2} b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((3*A*b + 5*a*B)*Sqrt[x])/(64*a^2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(5/2))/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((3*A*b + 5*a*B)*x^(3/2))/(24*a*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((3*A*b + 5*a*B)*Sqrt[x])/(32*a*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((3*A*b + 5*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(5/2)*b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,31,0.1935,1,"{770, 78, 47, 51, 63, 205}"
831,1,262,0,0.139067,"\int \frac{\sqrt{x} (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(Sqrt[x]*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{x^{3/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (3 a B+5 A b)}{64 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (3 a B+5 A b)}{96 a^2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\sqrt{x} (3 a B+5 A b)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 a B+5 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{7/2} b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{x^{3/2} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (3 a B+5 A b)}{64 a^3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (3 a B+5 A b)}{96 a^2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{\sqrt{x} (3 a B+5 A b)}{24 a b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (3 a B+5 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{7/2} b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((5*A*b + 3*a*B)*Sqrt[x])/(64*a^3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*x^(3/2))/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((5*A*b + 3*a*B)*Sqrt[x])/(24*a*b^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((5*A*b + 3*a*B)*Sqrt[x])/(96*a^2*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((5*A*b + 3*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(7/2)*b^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,31,0.1935,1,"{770, 78, 47, 51, 63, 205}"
832,1,258,0,0.1383649,"\int \frac{A+B x}{\sqrt{x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(Sqrt[x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{\sqrt{x} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{x} (a B+7 A b)}{64 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{x} (a B+7 A b)}{96 a^3 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (a B+7 A b)}{24 a^2 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 (a+b x) (a B+7 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{9/2} b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{\sqrt{x} (A b-a B)}{4 a b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{x} (a B+7 A b)}{64 a^4 b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 \sqrt{x} (a B+7 A b)}{96 a^3 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{\sqrt{x} (a B+7 A b)}{24 a^2 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 (a+b x) (a B+7 A b) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{9/2} b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(5*(7*A*b + a*B)*Sqrt[x])/(64*a^4*b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*Sqrt[x])/(4*a*b*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((7*A*b + a*B)*Sqrt[x])/(24*a^2*b*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*(7*A*b + a*B)*Sqrt[x])/(96*a^3*b*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*(7*A*b + a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(9/2)*b^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
833,1,311,0,0.1583964,"\int \frac{A+B x}{x^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{A b-a B}{4 a b \sqrt{x} (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 (a+b x) (9 A b-a B)}{64 a^5 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 (9 A b-a B)}{192 a^4 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 (9 A b-a B)}{96 a^3 b \sqrt{x} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{9 A b-a B}{24 a^2 b \sqrt{x} (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 (a+b x) (9 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{11/2} \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{A b-a B}{4 a b \sqrt{x} (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 (a+b x) (9 A b-a B)}{64 a^5 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 (9 A b-a B)}{192 a^4 b \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 (9 A b-a B)}{96 a^3 b \sqrt{x} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{9 A b-a B}{24 a^2 b \sqrt{x} (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 (a+b x) (9 A b-a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{11/2} \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(35*(9*A*b - a*B))/(192*a^4*b*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(4*a*b*Sqrt[x]*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (9*A*b - a*B)/(24*a^2*b*Sqrt[x]*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*(9*A*b - a*B))/(96*a^3*b*Sqrt[x]*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*(9*A*b - a*B)*(a + b*x))/(64*a^5*b*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*(9*A*b - a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(11/2)*Sqrt[b]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
834,1,357,0,0.1859626,"\int \frac{A+B x}{x^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","\frac{105 (a+b x) (11 A b-3 a B)}{64 a^6 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 (a+b x) (11 A b-3 a B)}{64 a^5 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 (11 A b-3 a B)}{32 a^3 b x^{3/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{21 (11 A b-3 a B)}{64 a^4 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{11 A b-3 a B}{24 a^2 b x^{3/2} (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{4 a b x^{3/2} (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{105 \sqrt{b} (a+b x) (11 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{105 (a+b x) (11 A b-3 a B)}{64 a^6 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 (a+b x) (11 A b-3 a B)}{64 a^5 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 (11 A b-3 a B)}{32 a^3 b x^{3/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{21 (11 A b-3 a B)}{64 a^4 b x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{11 A b-3 a B}{24 a^2 b x^{3/2} (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{4 a b x^{3/2} (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{105 \sqrt{b} (a+b x) (11 A b-3 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(21*(11*A*b - 3*a*B))/(64*a^4*b*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(4*a*b*x^(3/2)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (11*A*b - 3*a*B)/(24*a^2*b*x^(3/2)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*(11*A*b - 3*a*B))/(32*a^3*b*x^(3/2)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*(11*A*b - 3*a*B)*(a + b*x))/(64*a^5*b*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (105*(11*A*b - 3*a*B)*(a + b*x))/(64*a^6*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (105*Sqrt[b]*(11*A*b - 3*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
835,1,404,0,0.2113773,"\int \frac{A+B x}{x^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{231 b (a+b x) (13 A b-5 a B)}{64 a^7 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{77 (a+b x) (13 A b-5 a B)}{64 a^6 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 (a+b x) (13 A b-5 a B)}{320 a^5 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{11 (13 A b-5 a B)}{96 a^3 b x^{5/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{13 A b-5 a B}{24 a^2 b x^{5/2} (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{33 (13 A b-5 a B)}{64 a^4 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{4 a b x^{5/2} (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 b^{3/2} (a+b x) (13 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{231 b (a+b x) (13 A b-5 a B)}{64 a^7 \sqrt{x} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{77 (a+b x) (13 A b-5 a B)}{64 a^6 x^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 (a+b x) (13 A b-5 a B)}{320 a^5 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{11 (13 A b-5 a B)}{96 a^3 b x^{5/2} (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{13 A b-5 a B}{24 a^2 b x^{5/2} (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{33 (13 A b-5 a B)}{64 a^4 b x^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{A b-a B}{4 a b x^{5/2} (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 b^{3/2} (a+b x) (13 A b-5 a B) \tan ^{-1}\left(\frac{\sqrt{b} \sqrt{x}}{\sqrt{a}}\right)}{64 a^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(33*(13*A*b - 5*a*B))/(64*a^4*b*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (A*b - a*B)/(4*a*b*x^(5/2)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (13*A*b - 5*a*B)/(24*a^2*b*x^(5/2)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (11*(13*A*b - 5*a*B))/(96*a^3*b*x^(5/2)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*(13*A*b - 5*a*B)*(a + b*x))/(320*a^5*b*x^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (77*(13*A*b - 5*a*B)*(a + b*x))/(64*a^6*x^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*b*(13*A*b - 5*a*B)*(a + b*x))/(64*a^7*Sqrt[x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*b^(3/2)*(13*A*b - 5*a*B)*(a + b*x)*ArcTan[(Sqrt[b]*Sqrt[x])/Sqrt[a]])/(64*a^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,5,31,0.1613,1,"{770, 78, 51, 63, 205}"
836,1,179,0,0.1193268,"\int x^m (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[x^m*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{5 a^3 b^2 x^{m+4} (3 a B+4 A b)}{m+4}+\frac{5 a^2 b^3 x^{m+5} (4 a B+3 A b)}{m+5}+\frac{a^5 x^{m+2} (a B+6 A b)}{m+2}+\frac{3 a^4 b x^{m+3} (2 a B+5 A b)}{m+3}+\frac{a^6 A x^{m+1}}{m+1}+\frac{3 a b^4 x^{m+6} (5 a B+2 A b)}{m+6}+\frac{b^5 x^{m+7} (6 a B+A b)}{m+7}+\frac{b^6 B x^{m+8}}{m+8}","\frac{5 a^3 b^2 x^{m+4} (3 a B+4 A b)}{m+4}+\frac{5 a^2 b^3 x^{m+5} (4 a B+3 A b)}{m+5}+\frac{a^5 x^{m+2} (a B+6 A b)}{m+2}+\frac{3 a^4 b x^{m+3} (2 a B+5 A b)}{m+3}+\frac{a^6 A x^{m+1}}{m+1}+\frac{3 a b^4 x^{m+6} (5 a B+2 A b)}{m+6}+\frac{b^5 x^{m+7} (6 a B+A b)}{m+7}+\frac{b^6 B x^{m+8}}{m+8}",1,"(a^6*A*x^(1 + m))/(1 + m) + (a^5*(6*A*b + a*B)*x^(2 + m))/(2 + m) + (3*a^4*b*(5*A*b + 2*a*B)*x^(3 + m))/(3 + m) + (5*a^3*b^2*(4*A*b + 3*a*B)*x^(4 + m))/(4 + m) + (5*a^2*b^3*(3*A*b + 4*a*B)*x^(5 + m))/(5 + m) + (3*a*b^4*(2*A*b + 5*a*B)*x^(6 + m))/(6 + m) + (b^5*(A*b + 6*a*B)*x^(7 + m))/(7 + m) + (b^6*B*x^(8 + m))/(8 + m)","A",3,2,27,0.07407,1,"{27, 76}"
837,1,125,0,0.0736511,"\int x^m (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[x^m*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{a^3 x^{m+2} (a B+4 A b)}{m+2}+\frac{2 a^2 b x^{m+3} (2 a B+3 A b)}{m+3}+\frac{a^4 A x^{m+1}}{m+1}+\frac{2 a b^2 x^{m+4} (3 a B+2 A b)}{m+4}+\frac{b^3 x^{m+5} (4 a B+A b)}{m+5}+\frac{b^4 B x^{m+6}}{m+6}","\frac{a^3 x^{m+2} (a B+4 A b)}{m+2}+\frac{2 a^2 b x^{m+3} (2 a B+3 A b)}{m+3}+\frac{a^4 A x^{m+1}}{m+1}+\frac{2 a b^2 x^{m+4} (3 a B+2 A b)}{m+4}+\frac{b^3 x^{m+5} (4 a B+A b)}{m+5}+\frac{b^4 B x^{m+6}}{m+6}",1,"(a^4*A*x^(1 + m))/(1 + m) + (a^3*(4*A*b + a*B)*x^(2 + m))/(2 + m) + (2*a^2*b*(3*A*b + 2*a*B)*x^(3 + m))/(3 + m) + (2*a*b^2*(2*A*b + 3*a*B)*x^(4 + m))/(4 + m) + (b^3*(A*b + 4*a*B)*x^(5 + m))/(5 + m) + (b^4*B*x^(6 + m))/(6 + m)","A",3,2,27,0.07407,1,"{27, 76}"
838,1,71,0,0.0371273,"\int x^m (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[x^m*(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+2} (a B+2 A b)}{m+2}+\frac{b x^{m+3} (2 a B+A b)}{m+3}+\frac{b^2 B x^{m+4}}{m+4}","\frac{a^2 A x^{m+1}}{m+1}+\frac{a x^{m+2} (a B+2 A b)}{m+2}+\frac{b x^{m+3} (2 a B+A b)}{m+3}+\frac{b^2 B x^{m+4}}{m+4}",1,"(a^2*A*x^(1 + m))/(1 + m) + (a*(2*A*b + a*B)*x^(2 + m))/(2 + m) + (b*(A*b + 2*a*B)*x^(3 + m))/(3 + m) + (b^2*B*x^(4 + m))/(4 + m)","A",3,2,25,0.08000,1,"{27, 76}"
839,1,73,0,0.0296815,"\int \frac{x^m (A+B x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[(x^m*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{x^{m+1} (A b-a B)}{a b (a+b x)}-\frac{x^{m+1} (A b m-a B (m+1)) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a^2 b (m+1)}","\frac{x^{m+1} (A b-a B)}{a b (a+b x)}-\frac{x^{m+1} (A b m-a B (m+1)) \, _2F_1\left(1,m+1;m+2;-\frac{b x}{a}\right)}{a^2 b (m+1)}",1,"((A*b - a*B)*x^(1 + m))/(a*b*(a + b*x)) - ((A*b*m - a*B*(1 + m))*x^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, -((b*x)/a)])/(a^2*b*(1 + m))","A",3,3,27,0.1111,1,"{27, 78, 64}"
840,1,81,0,0.0318195,"\int \frac{x^m (A+B x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(x^m*(A + B*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{x^{m+1} (a B (m+1)+A b (2-m)) \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{3 a^4 b (m+1)}+\frac{x^{m+1} (A b-a B)}{3 a b (a+b x)^3}","\frac{x^{m+1} (a B (m+1)+A b (2-m)) \, _2F_1\left(3,m+1;m+2;-\frac{b x}{a}\right)}{3 a^4 b (m+1)}+\frac{x^{m+1} (A b-a B)}{3 a b (a+b x)^3}",1,"((A*b - a*B)*x^(1 + m))/(3*a*b*(a + b*x)^3) + ((A*b*(2 - m) + a*B*(1 + m))*x^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, -((b*x)/a)])/(3*a^4*b*(1 + m))","A",3,3,27,0.1111,1,"{27, 78, 64}"
841,1,143,0,0.042878,"\int x^m (1+x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^m*(1 + x)*(1 + 2*x + x^2)^5,x]","\frac{x^{m+1}}{m+1}+\frac{11 x^{m+2}}{m+2}+\frac{55 x^{m+3}}{m+3}+\frac{165 x^{m+4}}{m+4}+\frac{330 x^{m+5}}{m+5}+\frac{462 x^{m+6}}{m+6}+\frac{462 x^{m+7}}{m+7}+\frac{330 x^{m+8}}{m+8}+\frac{165 x^{m+9}}{m+9}+\frac{55 x^{m+10}}{m+10}+\frac{11 x^{m+11}}{m+11}+\frac{x^{m+12}}{m+12}","\frac{x^{m+1}}{m+1}+\frac{11 x^{m+2}}{m+2}+\frac{55 x^{m+3}}{m+3}+\frac{165 x^{m+4}}{m+4}+\frac{330 x^{m+5}}{m+5}+\frac{462 x^{m+6}}{m+6}+\frac{462 x^{m+7}}{m+7}+\frac{330 x^{m+8}}{m+8}+\frac{165 x^{m+9}}{m+9}+\frac{55 x^{m+10}}{m+10}+\frac{11 x^{m+11}}{m+11}+\frac{x^{m+12}}{m+12}",1,"x^(1 + m)/(1 + m) + (11*x^(2 + m))/(2 + m) + (55*x^(3 + m))/(3 + m) + (165*x^(4 + m))/(4 + m) + (330*x^(5 + m))/(5 + m) + (462*x^(6 + m))/(6 + m) + (462*x^(7 + m))/(7 + m) + (330*x^(8 + m))/(8 + m) + (165*x^(9 + m))/(9 + m) + (55*x^(10 + m))/(10 + m) + (11*x^(11 + m))/(11 + m) + x^(12 + m)/(12 + m)","A",3,2,17,0.1176,1,"{27, 43}"
842,1,209,0,0.0967435,"\int x^m (d+e x) \left(1+2 x+x^2\right)^5 \, dx","Int[x^m*(d + e*x)*(1 + 2*x + x^2)^5,x]","\frac{(10 d+e) x^{m+2}}{m+2}+\frac{5 (9 d+2 e) x^{m+3}}{m+3}+\frac{15 (8 d+3 e) x^{m+4}}{m+4}+\frac{30 (7 d+4 e) x^{m+5}}{m+5}+\frac{42 (6 d+5 e) x^{m+6}}{m+6}+\frac{42 (5 d+6 e) x^{m+7}}{m+7}+\frac{30 (4 d+7 e) x^{m+8}}{m+8}+\frac{15 (3 d+8 e) x^{m+9}}{m+9}+\frac{5 (2 d+9 e) x^{m+10}}{m+10}+\frac{(d+10 e) x^{m+11}}{m+11}+\frac{d x^{m+1}}{m+1}+\frac{e x^{m+12}}{m+12}","\frac{(10 d+e) x^{m+2}}{m+2}+\frac{5 (9 d+2 e) x^{m+3}}{m+3}+\frac{15 (8 d+3 e) x^{m+4}}{m+4}+\frac{30 (7 d+4 e) x^{m+5}}{m+5}+\frac{42 (6 d+5 e) x^{m+6}}{m+6}+\frac{42 (5 d+6 e) x^{m+7}}{m+7}+\frac{30 (4 d+7 e) x^{m+8}}{m+8}+\frac{15 (3 d+8 e) x^{m+9}}{m+9}+\frac{5 (2 d+9 e) x^{m+10}}{m+10}+\frac{(d+10 e) x^{m+11}}{m+11}+\frac{d x^{m+1}}{m+1}+\frac{e x^{m+12}}{m+12}",1,"(d*x^(1 + m))/(1 + m) + ((10*d + e)*x^(2 + m))/(2 + m) + (5*(9*d + 2*e)*x^(3 + m))/(3 + m) + (15*(8*d + 3*e)*x^(4 + m))/(4 + m) + (30*(7*d + 4*e)*x^(5 + m))/(5 + m) + (42*(6*d + 5*e)*x^(6 + m))/(6 + m) + (42*(5*d + 6*e)*x^(7 + m))/(7 + m) + (30*(4*d + 7*e)*x^(8 + m))/(8 + m) + (15*(3*d + 8*e)*x^(9 + m))/(9 + m) + (5*(2*d + 9*e)*x^(10 + m))/(10 + m) + ((d + 10*e)*x^(11 + m))/(11 + m) + (e*x^(12 + m))/(12 + m)","A",3,2,19,0.1053,1,"{27, 76}"
843,1,47,0,0.0619092,"\int x^3 (A+B x) \left(a+b x+c x^2\right) \, dx","Int[x^3*(A + B*x)*(a + b*x + c*x^2),x]","\frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} x^6 (A c+b B)+\frac{1}{7} B c x^7","\frac{1}{5} x^5 (a B+A b)+\frac{1}{4} a A x^4+\frac{1}{6} x^6 (A c+b B)+\frac{1}{7} B c x^7",1,"(a*A*x^4)/4 + ((A*b + a*B)*x^5)/5 + ((b*B + A*c)*x^6)/6 + (B*c*x^7)/7","A",2,1,19,0.05263,1,"{765}"
844,1,47,0,0.04975,"\int x^2 (A+B x) \left(a+b x+c x^2\right) \, dx","Int[x^2*(A + B*x)*(a + b*x + c*x^2),x]","\frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} x^5 (A c+b B)+\frac{1}{6} B c x^6","\frac{1}{4} x^4 (a B+A b)+\frac{1}{3} a A x^3+\frac{1}{5} x^5 (A c+b B)+\frac{1}{6} B c x^6",1,"(a*A*x^3)/3 + ((A*b + a*B)*x^4)/4 + ((b*B + A*c)*x^5)/5 + (B*c*x^6)/6","A",2,1,19,0.05263,1,"{765}"
845,1,47,0,0.0369795,"\int x (A+B x) \left(a+b x+c x^2\right) \, dx","Int[x*(A + B*x)*(a + b*x + c*x^2),x]","\frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} x^4 (A c+b B)+\frac{1}{5} B c x^5","\frac{1}{3} x^3 (a B+A b)+\frac{1}{2} a A x^2+\frac{1}{4} x^4 (A c+b B)+\frac{1}{5} B c x^5",1,"(a*A*x^2)/2 + ((A*b + a*B)*x^3)/3 + ((b*B + A*c)*x^4)/4 + (B*c*x^5)/5","A",2,1,17,0.05882,1,"{765}"
846,1,42,0,0.0277259,"\int (A+B x) \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(a + b*x + c*x^2),x]","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4",1,"a*A*x + ((A*b + a*B)*x^2)/2 + ((b*B + A*c)*x^3)/3 + (B*c*x^4)/4","A",2,1,16,0.06250,1,"{631}"
847,1,38,0,0.0198945,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x,x]","x (a B+A b)+a A \log (x)+\frac{1}{2} x^2 (A c+b B)+\frac{1}{3} B c x^3","x (a B+A b)+a A \log (x)+\frac{1}{2} x^2 (A c+b B)+\frac{1}{3} B c x^3",1,"(A*b + a*B)*x + ((b*B + A*c)*x^2)/2 + (B*c*x^3)/3 + a*A*Log[x]","A",2,1,19,0.05263,1,"{765}"
848,1,36,0,0.0252918,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^2,x]","\log (x) (a B+A b)-\frac{a A}{x}+x (A c+b B)+\frac{1}{2} B c x^2","\log (x) (a B+A b)-\frac{a A}{x}+x (A c+b B)+\frac{1}{2} B c x^2",1,"-((a*A)/x) + (b*B + A*c)*x + (B*c*x^2)/2 + (A*b + a*B)*Log[x]","A",2,1,19,0.05263,1,"{765}"
849,1,36,0,0.0237494,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^3,x]","-\frac{a B+A b}{x}-\frac{a A}{2 x^2}+\log (x) (A c+b B)+B c x","-\frac{a B+A b}{x}-\frac{a A}{2 x^2}+\log (x) (A c+b B)+B c x",1,"-(a*A)/(2*x^2) - (A*b + a*B)/x + B*c*x + (b*B + A*c)*Log[x]","A",2,1,19,0.05263,1,"{765}"
850,1,41,0,0.0253187,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^4,x]","-\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{A c+b B}{x}+B c \log (x)","-\frac{a B+A b}{2 x^2}-\frac{a A}{3 x^3}-\frac{A c+b B}{x}+B c \log (x)",1,"-(a*A)/(3*x^3) - (A*b + a*B)/(2*x^2) - (b*B + A*c)/x + B*c*Log[x]","A",2,1,19,0.05263,1,"{765}"
851,1,45,0,0.0235477,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^5,x]","-\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{A c+b B}{2 x^2}-\frac{B c}{x}","-\frac{a B+A b}{3 x^3}-\frac{a A}{4 x^4}-\frac{A c+b B}{2 x^2}-\frac{B c}{x}",1,"-(a*A)/(4*x^4) - (A*b + a*B)/(3*x^3) - (b*B + A*c)/(2*x^2) - (B*c)/x","A",2,1,19,0.05263,1,"{765}"
852,1,47,0,0.0243442,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^6,x]","-\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{A c+b B}{3 x^3}-\frac{B c}{2 x^2}","-\frac{a B+A b}{4 x^4}-\frac{a A}{5 x^5}-\frac{A c+b B}{3 x^3}-\frac{B c}{2 x^2}",1,"-(a*A)/(5*x^5) - (A*b + a*B)/(4*x^4) - (b*B + A*c)/(3*x^3) - (B*c)/(2*x^2)","A",2,1,19,0.05263,1,"{765}"
853,1,47,0,0.0234613,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^7,x]","-\frac{a B+A b}{5 x^5}-\frac{a A}{6 x^6}-\frac{A c+b B}{4 x^4}-\frac{B c}{3 x^3}","-\frac{a B+A b}{5 x^5}-\frac{a A}{6 x^6}-\frac{A c+b B}{4 x^4}-\frac{B c}{3 x^3}",1,"-(a*A)/(6*x^6) - (A*b + a*B)/(5*x^5) - (b*B + A*c)/(4*x^4) - (B*c)/(3*x^3)","A",2,1,19,0.05263,1,"{765}"
854,1,47,0,0.0254179,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^8,x]","-\frac{a B+A b}{6 x^6}-\frac{a A}{7 x^7}-\frac{A c+b B}{5 x^5}-\frac{B c}{4 x^4}","-\frac{a B+A b}{6 x^6}-\frac{a A}{7 x^7}-\frac{A c+b B}{5 x^5}-\frac{B c}{4 x^4}",1,"-(a*A)/(7*x^7) - (A*b + a*B)/(6*x^6) - (b*B + A*c)/(5*x^5) - (B*c)/(4*x^4)","A",2,1,19,0.05263,1,"{765}"
855,1,101,0,0.1420875,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[x^2*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{1}{3} a^2 A x^3+\frac{1}{6} x^6 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{5} x^5 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{8} B c^2 x^8","\frac{1}{3} a^2 A x^3+\frac{1}{6} x^6 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{5} x^5 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{4} a x^4 (a B+2 A b)+\frac{1}{7} c x^7 (A c+2 b B)+\frac{1}{8} B c^2 x^8",1,"(a^2*A*x^3)/3 + (a*(2*A*b + a*B)*x^4)/4 + ((2*a*b*B + A*(b^2 + 2*a*c))*x^5)/5 + ((b^2*B + 2*A*b*c + 2*a*B*c)*x^6)/6 + (c*(2*b*B + A*c)*x^7)/7 + (B*c^2*x^8)/8","A",2,1,21,0.04762,1,"{765}"
856,1,101,0,0.1009389,"\int x (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[x*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{1}{2} a^2 A x^2+\frac{1}{5} x^5 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{7} B c^2 x^7","\frac{1}{2} a^2 A x^2+\frac{1}{5} x^5 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{3} a x^3 (a B+2 A b)+\frac{1}{6} c x^6 (A c+2 b B)+\frac{1}{7} B c^2 x^7",1,"(a^2*A*x^2)/2 + (a*(2*A*b + a*B)*x^3)/3 + ((2*a*b*B + A*(b^2 + 2*a*c))*x^4)/4 + ((b^2*B + 2*A*b*c + 2*a*B*c)*x^5)/5 + (c*(2*b*B + A*c)*x^6)/6 + (B*c^2*x^7)/7","A",2,1,19,0.05263,1,"{765}"
857,1,96,0,0.0693599,"\int (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^2,x]","a^2 A x+\frac{1}{4} x^4 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{3} x^3 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{6} B c^2 x^6","a^2 A x+\frac{1}{4} x^4 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{3} x^3 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{6} B c^2 x^6",1,"a^2*A*x + (a*(2*A*b + a*B)*x^2)/2 + ((2*a*b*B + A*(b^2 + 2*a*c))*x^3)/3 + ((b^2*B + 2*A*b*c + 2*a*B*c)*x^4)/4 + (c*(2*b*B + A*c)*x^5)/5 + (B*c^2*x^6)/6","A",2,1,18,0.05556,1,"{631}"
858,1,92,0,0.052385,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x,x]","a^2 A \log (x)+\frac{1}{3} x^3 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{2} x^2 \left(A \left(2 a c+b^2\right)+2 a b B\right)+a x (a B+2 A b)+\frac{1}{4} c x^4 (A c+2 b B)+\frac{1}{5} B c^2 x^5","a^2 A \log (x)+\frac{1}{3} x^3 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{2} x^2 \left(A \left(2 a c+b^2\right)+2 a b B\right)+a x (a B+2 A b)+\frac{1}{4} c x^4 (A c+2 b B)+\frac{1}{5} B c^2 x^5",1,"a*(2*A*b + a*B)*x + ((2*a*b*B + A*(b^2 + 2*a*c))*x^2)/2 + ((b^2*B + 2*A*b*c + 2*a*B*c)*x^3)/3 + (c*(2*b*B + A*c)*x^4)/4 + (B*c^2*x^5)/5 + a^2*A*Log[x]","A",2,1,21,0.04762,1,"{765}"
859,1,90,0,0.0715168,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^2,x]","-\frac{a^2 A}{x}+\frac{1}{2} x^2 \left(2 a B c+2 A b c+b^2 B\right)+x \left(A \left(2 a c+b^2\right)+2 a b B\right)+a \log (x) (a B+2 A b)+\frac{1}{3} c x^3 (A c+2 b B)+\frac{1}{4} B c^2 x^4","-\frac{a^2 A}{x}+\frac{1}{2} x^2 \left(2 a B c+2 A b c+b^2 B\right)+x \left(A \left(2 a c+b^2\right)+2 a b B\right)+a \log (x) (a B+2 A b)+\frac{1}{3} c x^3 (A c+2 b B)+\frac{1}{4} B c^2 x^4",1,"-((a^2*A)/x) + (2*a*b*B + A*(b^2 + 2*a*c))*x + ((b^2*B + 2*A*b*c + 2*a*B*c)*x^2)/2 + (c*(2*b*B + A*c)*x^3)/3 + (B*c^2*x^4)/4 + a*(2*A*b + a*B)*Log[x]","A",2,1,21,0.04762,1,"{765}"
860,1,90,0,0.0671622,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^3,x]","-\frac{a^2 A}{2 x^2}+x \left(2 a B c+2 A b c+b^2 B\right)+\log (x) \left(A \left(2 a c+b^2\right)+2 a b B\right)-\frac{a (a B+2 A b)}{x}+\frac{1}{2} c x^2 (A c+2 b B)+\frac{1}{3} B c^2 x^3","-\frac{a^2 A}{2 x^2}+x \left(2 a B c+2 A b c+b^2 B\right)+\log (x) \left(A \left(2 a c+b^2\right)+2 a b B\right)-\frac{a (a B+2 A b)}{x}+\frac{1}{2} c x^2 (A c+2 b B)+\frac{1}{3} B c^2 x^3",1,"-(a^2*A)/(2*x^2) - (a*(2*A*b + a*B))/x + (b^2*B + 2*A*b*c + 2*a*B*c)*x + (c*(2*b*B + A*c)*x^2)/2 + (B*c^2*x^3)/3 + (2*a*b*B + A*(b^2 + 2*a*c))*Log[x]","A",2,1,21,0.04762,1,"{765}"
861,1,90,0,0.0613583,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^4,x]","-\frac{a^2 A}{3 x^3}-\frac{A \left(2 a c+b^2\right)+2 a b B}{x}+\log (x) \left(2 a B c+2 A b c+b^2 B\right)-\frac{a (a B+2 A b)}{2 x^2}+c x (A c+2 b B)+\frac{1}{2} B c^2 x^2","-\frac{a^2 A}{3 x^3}-\frac{A \left(2 a c+b^2\right)+2 a b B}{x}+\log (x) \left(2 a B c+2 A b c+b^2 B\right)-\frac{a (a B+2 A b)}{2 x^2}+c x (A c+2 b B)+\frac{1}{2} B c^2 x^2",1,"-(a^2*A)/(3*x^3) - (a*(2*A*b + a*B))/(2*x^2) - (2*a*b*B + A*(b^2 + 2*a*c))/x + c*(2*b*B + A*c)*x + (B*c^2*x^2)/2 + (b^2*B + 2*A*b*c + 2*a*B*c)*Log[x]","A",2,1,21,0.04762,1,"{765}"
862,1,90,0,0.0592905,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^5,x]","-\frac{a^2 A}{4 x^4}-\frac{A \left(2 a c+b^2\right)+2 a b B}{2 x^2}-\frac{2 a B c+2 A b c+b^2 B}{x}-\frac{a (a B+2 A b)}{3 x^3}+c \log (x) (A c+2 b B)+B c^2 x","-\frac{a^2 A}{4 x^4}-\frac{A \left(2 a c+b^2\right)+2 a b B}{2 x^2}-\frac{2 a B c+2 A b c+b^2 B}{x}-\frac{a (a B+2 A b)}{3 x^3}+c \log (x) (A c+2 b B)+B c^2 x",1,"-(a^2*A)/(4*x^4) - (a*(2*A*b + a*B))/(3*x^3) - (2*a*b*B + A*(b^2 + 2*a*c))/(2*x^2) - (b^2*B + 2*A*b*c + 2*a*B*c)/x + B*c^2*x + c*(2*b*B + A*c)*Log[x]","A",2,1,21,0.04762,1,"{765}"
863,1,95,0,0.0544118,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^6,x]","-\frac{a^2 A}{5 x^5}-\frac{2 a B c+2 A b c+b^2 B}{2 x^2}-\frac{A \left(2 a c+b^2\right)+2 a b B}{3 x^3}-\frac{a (a B+2 A b)}{4 x^4}-\frac{c (A c+2 b B)}{x}+B c^2 \log (x)","-\frac{a^2 A}{5 x^5}-\frac{2 a B c+2 A b c+b^2 B}{2 x^2}-\frac{A \left(2 a c+b^2\right)+2 a b B}{3 x^3}-\frac{a (a B+2 A b)}{4 x^4}-\frac{c (A c+2 b B)}{x}+B c^2 \log (x)",1,"-(a^2*A)/(5*x^5) - (a*(2*A*b + a*B))/(4*x^4) - (2*a*b*B + A*(b^2 + 2*a*c))/(3*x^3) - (b^2*B + 2*A*b*c + 2*a*B*c)/(2*x^2) - (c*(2*b*B + A*c))/x + B*c^2*Log[x]","A",2,1,21,0.04762,1,"{765}"
864,1,99,0,0.0536574,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^7,x]","-\frac{a^2 A}{6 x^6}-\frac{2 a B c+2 A b c+b^2 B}{3 x^3}-\frac{A \left(2 a c+b^2\right)+2 a b B}{4 x^4}-\frac{a (a B+2 A b)}{5 x^5}-\frac{c (A c+2 b B)}{2 x^2}-\frac{B c^2}{x}","-\frac{a^2 A}{6 x^6}-\frac{2 a B c+2 A b c+b^2 B}{3 x^3}-\frac{A \left(2 a c+b^2\right)+2 a b B}{4 x^4}-\frac{a (a B+2 A b)}{5 x^5}-\frac{c (A c+2 b B)}{2 x^2}-\frac{B c^2}{x}",1,"-(a^2*A)/(6*x^6) - (a*(2*A*b + a*B))/(5*x^5) - (2*a*b*B + A*(b^2 + 2*a*c))/(4*x^4) - (b^2*B + 2*A*b*c + 2*a*B*c)/(3*x^3) - (c*(2*b*B + A*c))/(2*x^2) - (B*c^2)/x","A",2,1,21,0.04762,1,"{765}"
865,1,101,0,0.0528436,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^8,x]","-\frac{a^2 A}{7 x^7}-\frac{2 a B c+2 A b c+b^2 B}{4 x^4}-\frac{A \left(2 a c+b^2\right)+2 a b B}{5 x^5}-\frac{a (a B+2 A b)}{6 x^6}-\frac{c (A c+2 b B)}{3 x^3}-\frac{B c^2}{2 x^2}","-\frac{a^2 A}{7 x^7}-\frac{2 a B c+2 A b c+b^2 B}{4 x^4}-\frac{A \left(2 a c+b^2\right)+2 a b B}{5 x^5}-\frac{a (a B+2 A b)}{6 x^6}-\frac{c (A c+2 b B)}{3 x^3}-\frac{B c^2}{2 x^2}",1,"-(a^2*A)/(7*x^7) - (a*(2*A*b + a*B))/(6*x^6) - (2*a*b*B + A*(b^2 + 2*a*c))/(5*x^5) - (b^2*B + 2*A*b*c + 2*a*B*c)/(4*x^4) - (c*(2*b*B + A*c))/(3*x^3) - (B*c^2)/(2*x^2)","A",2,1,21,0.04762,1,"{765}"
866,1,101,0,0.0523615,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^9} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^9,x]","-\frac{a^2 A}{8 x^8}-\frac{2 a B c+2 A b c+b^2 B}{5 x^5}-\frac{A \left(2 a c+b^2\right)+2 a b B}{6 x^6}-\frac{a (a B+2 A b)}{7 x^7}-\frac{c (A c+2 b B)}{4 x^4}-\frac{B c^2}{3 x^3}","-\frac{a^2 A}{8 x^8}-\frac{2 a B c+2 A b c+b^2 B}{5 x^5}-\frac{A \left(2 a c+b^2\right)+2 a b B}{6 x^6}-\frac{a (a B+2 A b)}{7 x^7}-\frac{c (A c+2 b B)}{4 x^4}-\frac{B c^2}{3 x^3}",1,"-(a^2*A)/(8*x^8) - (a*(2*A*b + a*B))/(7*x^7) - (2*a*b*B + A*(b^2 + 2*a*c))/(6*x^6) - (b^2*B + 2*A*b*c + 2*a*B*c)/(5*x^5) - (c*(2*b*B + A*c))/(4*x^4) - (B*c^2)/(3*x^3)","A",2,1,21,0.04762,1,"{765}"
867,1,166,0,0.2640614,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[x^2*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{7} x^7 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{8} c x^8 \left(a B c+A b c+b^2 B\right)+\frac{1}{6} x^6 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{5} a x^5 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{1}{10} B c^3 x^{10}","\frac{1}{4} a^2 x^4 (a B+3 A b)+\frac{1}{3} a^3 A x^3+\frac{1}{7} x^7 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{8} c x^8 \left(a B c+A b c+b^2 B\right)+\frac{1}{6} x^6 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{5} a x^5 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{9} c^2 x^9 (A c+3 b B)+\frac{1}{10} B c^3 x^{10}",1,"(a^3*A*x^3)/3 + (a^2*(3*A*b + a*B)*x^4)/4 + (3*a*(a*b*B + A*(b^2 + a*c))*x^5)/5 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^6)/6 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^7)/7 + (3*c*(b^2*B + A*b*c + a*B*c)*x^8)/8 + (c^2*(3*b*B + A*c)*x^9)/9 + (B*c^3*x^10)/10","A",2,1,21,0.04762,1,"{765}"
868,1,166,0,0.2025007,"\int x (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[x*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{3} a^2 x^3 (a B+3 A b)+\frac{1}{2} a^3 A x^2+\frac{1}{6} x^6 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{7} c x^7 \left(a B c+A b c+b^2 B\right)+\frac{1}{5} x^5 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{4} a x^4 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{1}{9} B c^3 x^9","\frac{1}{3} a^2 x^3 (a B+3 A b)+\frac{1}{2} a^3 A x^2+\frac{1}{6} x^6 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{7} c x^7 \left(a B c+A b c+b^2 B\right)+\frac{1}{5} x^5 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{4} a x^4 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{8} c^2 x^8 (A c+3 b B)+\frac{1}{9} B c^3 x^9",1,"(a^3*A*x^2)/2 + (a^2*(3*A*b + a*B)*x^3)/3 + (3*a*(a*b*B + A*(b^2 + a*c))*x^4)/4 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^5)/5 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^6)/6 + (3*c*(b^2*B + A*b*c + a*B*c)*x^7)/7 + (c^2*(3*b*B + A*c)*x^8)/8 + (B*c^3*x^9)/9","A",2,1,19,0.05263,1,"{765}"
869,1,158,0,0.1513712,"\int (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{2} a^2 x^2 (a B+3 A b)+a^3 A x+\frac{1}{5} x^5 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{8} B c^3 x^8","\frac{1}{2} a^2 x^2 (a B+3 A b)+a^3 A x+\frac{1}{5} x^5 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{8} B c^3 x^8",1,"a^3*A*x + (a^2*(3*A*b + a*B)*x^2)/2 + a*(a*b*B + A*(b^2 + a*c))*x^3 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^4)/4 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^5)/5 + (c*(b^2*B + A*b*c + a*B*c)*x^6)/2 + (c^2*(3*b*B + A*c)*x^7)/7 + (B*c^3*x^8)/8","A",2,1,18,0.05556,1,"{631}"
870,1,157,0,0.1105665,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x,x]","a^2 x (a B+3 A b)+a^3 A \log (x)+\frac{1}{4} x^4 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{5} c x^5 \left(a B c+A b c+b^2 B\right)+\frac{1}{3} x^3 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{2} a x^2 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{1}{7} B c^3 x^7","a^2 x (a B+3 A b)+a^3 A \log (x)+\frac{1}{4} x^4 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{5} c x^5 \left(a B c+A b c+b^2 B\right)+\frac{1}{3} x^3 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{3}{2} a x^2 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{6} c^2 x^6 (A c+3 b B)+\frac{1}{7} B c^3 x^7",1,"a^2*(3*A*b + a*B)*x + (3*a*(a*b*B + A*(b^2 + a*c))*x^2)/2 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^3)/3 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^4)/4 + (3*c*(b^2*B + A*b*c + a*B*c)*x^5)/5 + (c^2*(3*b*B + A*c)*x^6)/6 + (B*c^3*x^7)/7 + a^3*A*Log[x]","A",2,1,21,0.04762,1,"{765}"
871,1,156,0,0.1079908,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^2,x]","a^2 \log (x) (a B+3 A b)-\frac{a^3 A}{x}+\frac{1}{3} x^3 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{4} c x^4 \left(a B c+A b c+b^2 B\right)+\frac{1}{2} x^2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+3 a x \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{5} c^2 x^5 (A c+3 b B)+\frac{1}{6} B c^3 x^6","a^2 \log (x) (a B+3 A b)-\frac{a^3 A}{x}+\frac{1}{3} x^3 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{4} c x^4 \left(a B c+A b c+b^2 B\right)+\frac{1}{2} x^2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+3 a x \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{5} c^2 x^5 (A c+3 b B)+\frac{1}{6} B c^3 x^6",1,"-((a^3*A)/x) + 3*a*(a*b*B + A*(b^2 + a*c))*x + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^2)/2 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^3)/3 + (3*c*(b^2*B + A*b*c + a*B*c)*x^4)/4 + (c^2*(3*b*B + A*c)*x^5)/5 + (B*c^3*x^6)/6 + a^2*(3*A*b + a*B)*Log[x]","A",2,1,21,0.04762,1,"{765}"
872,1,153,0,0.1245785,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^3,x]","-\frac{a^2 (a B+3 A b)}{x}-\frac{a^3 A}{2 x^2}+\frac{1}{2} x^2 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+c x^3 \left(a B c+A b c+b^2 B\right)+x \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+3 a \log (x) \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{4} c^2 x^4 (A c+3 b B)+\frac{1}{5} B c^3 x^5","-\frac{a^2 (a B+3 A b)}{x}-\frac{a^3 A}{2 x^2}+\frac{1}{2} x^2 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+c x^3 \left(a B c+A b c+b^2 B\right)+x \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+3 a \log (x) \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{4} c^2 x^4 (A c+3 b B)+\frac{1}{5} B c^3 x^5",1,"-(a^3*A)/(2*x^2) - (a^2*(3*A*b + a*B))/x + (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^2)/2 + c*(b^2*B + A*b*c + a*B*c)*x^3 + (c^2*(3*b*B + A*c)*x^4)/4 + (B*c^3*x^5)/5 + 3*a*(a*b*B + A*(b^2 + a*c))*Log[x]","A",2,1,21,0.04762,1,"{765}"
873,1,155,0,0.136451,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^4,x]","-\frac{a^2 (a B+3 A b)}{2 x^2}-\frac{a^3 A}{3 x^3}+x \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{2} c x^2 \left(a B c+A b c+b^2 B\right)-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{x}+\log (x) \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{3} c^2 x^3 (A c+3 b B)+\frac{1}{4} B c^3 x^4","-\frac{a^2 (a B+3 A b)}{2 x^2}-\frac{a^3 A}{3 x^3}+x \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{3}{2} c x^2 \left(a B c+A b c+b^2 B\right)-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{x}+\log (x) \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{1}{3} c^2 x^3 (A c+3 b B)+\frac{1}{4} B c^3 x^4",1,"-(a^3*A)/(3*x^3) - (a^2*(3*A*b + a*B))/(2*x^2) - (3*a*(a*b*B + A*(b^2 + a*c)))/x + (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x + (3*c*(b^2*B + A*b*c + a*B*c)*x^2)/2 + (c^2*(3*b*B + A*c)*x^3)/3 + (B*c^3*x^4)/4 + (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*Log[x]","A",2,1,21,0.04762,1,"{765}"
874,1,156,0,0.1234289,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^5,x]","-\frac{a^2 (a B+3 A b)}{3 x^3}-\frac{a^3 A}{4 x^4}+\log (x) \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{2 x^2}+3 c x \left(a B c+A b c+b^2 B\right)-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{x}+\frac{1}{2} c^2 x^2 (A c+3 b B)+\frac{1}{3} B c^3 x^3","-\frac{a^2 (a B+3 A b)}{3 x^3}-\frac{a^3 A}{4 x^4}+\log (x) \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{2 x^2}+3 c x \left(a B c+A b c+b^2 B\right)-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{x}+\frac{1}{2} c^2 x^2 (A c+3 b B)+\frac{1}{3} B c^3 x^3",1,"-(a^3*A)/(4*x^4) - (a^2*(3*A*b + a*B))/(3*x^3) - (3*a*(a*b*B + A*(b^2 + a*c)))/(2*x^2) - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/x + 3*c*(b^2*B + A*b*c + a*B*c)*x + (c^2*(3*b*B + A*c)*x^2)/2 + (B*c^3*x^3)/3 + (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*Log[x]","A",2,1,21,0.04762,1,"{765}"
875,1,154,0,0.1158292,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^6,x]","-\frac{a^2 (a B+3 A b)}{4 x^4}-\frac{a^3 A}{5 x^5}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{x}-\frac{a \left(A \left(a c+b^2\right)+a b B\right)}{x^3}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{2 x^2}+3 c \log (x) \left(a B c+A b c+b^2 B\right)+c^2 x (A c+3 b B)+\frac{1}{2} B c^3 x^2","-\frac{a^2 (a B+3 A b)}{4 x^4}-\frac{a^3 A}{5 x^5}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{x}-\frac{a \left(A \left(a c+b^2\right)+a b B\right)}{x^3}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{2 x^2}+3 c \log (x) \left(a B c+A b c+b^2 B\right)+c^2 x (A c+3 b B)+\frac{1}{2} B c^3 x^2",1,"-(a^3*A)/(5*x^5) - (a^2*(3*A*b + a*B))/(4*x^4) - (a*(a*b*B + A*(b^2 + a*c)))/x^3 - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/(2*x^2) - (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)/x + c^2*(3*b*B + A*c)*x + (B*c^3*x^2)/2 + 3*c*(b^2*B + A*b*c + a*B*c)*Log[x]","A",2,1,21,0.04762,1,"{765}"
876,1,155,0,0.1091688,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^7,x]","-\frac{a^2 (a B+3 A b)}{5 x^5}-\frac{a^3 A}{6 x^6}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{2 x^2}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{4 x^4}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{3 x^3}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{x}+c^2 \log (x) (A c+3 b B)+B c^3 x","-\frac{a^2 (a B+3 A b)}{5 x^5}-\frac{a^3 A}{6 x^6}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{2 x^2}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{4 x^4}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{3 x^3}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{x}+c^2 \log (x) (A c+3 b B)+B c^3 x",1,"-(a^3*A)/(6*x^6) - (a^2*(3*A*b + a*B))/(5*x^5) - (3*a*(a*b*B + A*(b^2 + a*c)))/(4*x^4) - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/(3*x^3) - (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)/(2*x^2) - (3*c*(b^2*B + A*b*c + a*B*c))/x + B*c^3*x + c^2*(3*b*B + A*c)*Log[x]","A",2,1,21,0.04762,1,"{765}"
877,1,160,0,0.1061108,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^8,x]","-\frac{a^2 (a B+3 A b)}{6 x^6}-\frac{a^3 A}{7 x^7}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{3 x^3}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{5 x^5}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{2 x^2}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{4 x^4}-\frac{c^2 (A c+3 b B)}{x}+B c^3 \log (x)","-\frac{a^2 (a B+3 A b)}{6 x^6}-\frac{a^3 A}{7 x^7}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{3 x^3}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{5 x^5}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{2 x^2}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{4 x^4}-\frac{c^2 (A c+3 b B)}{x}+B c^3 \log (x)",1,"-(a^3*A)/(7*x^7) - (a^2*(3*A*b + a*B))/(6*x^6) - (3*a*(a*b*B + A*(b^2 + a*c)))/(5*x^5) - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/(4*x^4) - (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)/(3*x^3) - (3*c*(b^2*B + A*b*c + a*B*c))/(2*x^2) - (c^2*(3*b*B + A*c))/x + B*c^3*Log[x]","A",2,1,21,0.04762,1,"{765}"
878,1,162,0,0.1049022,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^9} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^9,x]","-\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{a^3 A}{8 x^8}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{4 x^4}-\frac{a \left(A \left(a c+b^2\right)+a b B\right)}{2 x^6}-\frac{c \left(a B c+A b c+b^2 B\right)}{x^3}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{5 x^5}-\frac{c^2 (A c+3 b B)}{2 x^2}-\frac{B c^3}{x}","-\frac{a^2 (a B+3 A b)}{7 x^7}-\frac{a^3 A}{8 x^8}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{4 x^4}-\frac{a \left(A \left(a c+b^2\right)+a b B\right)}{2 x^6}-\frac{c \left(a B c+A b c+b^2 B\right)}{x^3}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{5 x^5}-\frac{c^2 (A c+3 b B)}{2 x^2}-\frac{B c^3}{x}",1,"-(a^3*A)/(8*x^8) - (a^2*(3*A*b + a*B))/(7*x^7) - (a*(a*b*B + A*(b^2 + a*c)))/(2*x^6) - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/(5*x^5) - (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)/(4*x^4) - (c*(b^2*B + A*b*c + a*B*c))/x^3 - (c^2*(3*b*B + A*c))/(2*x^2) - (B*c^3)/x","A",2,1,21,0.04762,1,"{765}"
879,1,166,0,0.1051632,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{10}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^10,x]","-\frac{a^2 (a B+3 A b)}{8 x^8}-\frac{a^3 A}{9 x^9}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{5 x^5}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{7 x^7}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{4 x^4}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{B c^3}{2 x^2}","-\frac{a^2 (a B+3 A b)}{8 x^8}-\frac{a^3 A}{9 x^9}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{5 x^5}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{7 x^7}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{4 x^4}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{6 x^6}-\frac{c^2 (A c+3 b B)}{3 x^3}-\frac{B c^3}{2 x^2}",1,"-(a^3*A)/(9*x^9) - (a^2*(3*A*b + a*B))/(8*x^8) - (3*a*(a*b*B + A*(b^2 + a*c)))/(7*x^7) - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/(6*x^6) - (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)/(5*x^5) - (3*c*(b^2*B + A*b*c + a*B*c))/(4*x^4) - (c^2*(3*b*B + A*c))/(3*x^3) - (B*c^3)/(2*x^2)","A",2,1,21,0.04762,1,"{765}"
880,1,166,0,0.1036329,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{11}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^11,x]","-\frac{a^2 (a B+3 A b)}{9 x^9}-\frac{a^3 A}{10 x^{10}}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{6 x^6}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{8 x^8}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{5 x^5}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{7 x^7}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{B c^3}{3 x^3}","-\frac{a^2 (a B+3 A b)}{9 x^9}-\frac{a^3 A}{10 x^{10}}-\frac{3 a A c^2+6 a b B c+3 A b^2 c+b^3 B}{6 x^6}-\frac{3 a \left(A \left(a c+b^2\right)+a b B\right)}{8 x^8}-\frac{3 c \left(a B c+A b c+b^2 B\right)}{5 x^5}-\frac{A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)}{7 x^7}-\frac{c^2 (A c+3 b B)}{4 x^4}-\frac{B c^3}{3 x^3}",1,"-(a^3*A)/(10*x^10) - (a^2*(3*A*b + a*B))/(9*x^9) - (3*a*(a*b*B + A*(b^2 + a*c)))/(8*x^8) - (3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))/(7*x^7) - (b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)/(6*x^6) - (3*c*(b^2*B + A*b*c + a*B*c))/(5*x^5) - (c^2*(3*b*B + A*c))/(4*x^4) - (B*c^3)/(3*x^3)","A",2,1,21,0.04762,1,"{765}"
881,1,229,0,0.4212583,"\int \frac{x^4 (d+e x)}{a+b x+c x^2} \, dx","Int[(x^4*(d + e*x))/(a + b*x + c*x^2),x]","-\frac{\left(-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right) \log \left(a+b x+c x^2\right)}{2 c^5}-\frac{\left(-5 a^2 b c^2 e+2 a^2 c^3 d-4 a b^2 c^2 d+5 a b^3 c e+b^4 c d+b^5 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \sqrt{b^2-4 a c}}-\frac{x^2 \left(a c e+b^2 (-e)+b c d\right)}{2 c^3}+\frac{x \left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right)}{c^4}+\frac{x^3 (c d-b e)}{3 c^2}+\frac{e x^4}{4 c}","-\frac{\left(-a^2 c^2 e+3 a b^2 c e-2 a b c^2 d+b^3 c d+b^4 (-e)\right) \log \left(a+b x+c x^2\right)}{2 c^5}-\frac{\left(-5 a^2 b c^2 e+2 a^2 c^3 d-4 a b^2 c^2 d+5 a b^3 c e+b^4 c d+b^5 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^5 \sqrt{b^2-4 a c}}-\frac{x^2 \left(a c e+b^2 (-e)+b c d\right)}{2 c^3}+\frac{x \left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right)}{c^4}+\frac{x^3 (c d-b e)}{3 c^2}+\frac{e x^4}{4 c}",1,"((b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e)*x)/c^4 - ((b*c*d - b^2*e + a*c*e)*x^2)/(2*c^3) + ((c*d - b*e)*x^3)/(3*c^2) + (e*x^4)/(4*c) - ((b^4*c*d - 4*a*b^2*c^2*d + 2*a^2*c^3*d - b^5*e + 5*a*b^3*c*e - 5*a^2*b*c^2*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^5*Sqrt[b^2 - 4*a*c]) - ((b^3*c*d - 2*a*b*c^2*d - b^4*e + 3*a*b^2*c*e - a^2*c^2*e)*Log[a + b*x + c*x^2])/(2*c^5)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
882,1,169,0,0.2357101,"\int \frac{x^3 (d+e x)}{a+b x+c x^2} \, dx","Int[(x^3*(d + e*x))/(a + b*x + c*x^2),x]","\frac{\left(-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{\left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \log \left(a+b x+c x^2\right)}{2 c^4}-\frac{x \left(a c e+b^2 (-e)+b c d\right)}{c^3}+\frac{x^2 (c d-b e)}{2 c^2}+\frac{e x^3}{3 c}","\frac{\left(-2 a^2 c^2 e+4 a b^2 c e-3 a b c^2 d+b^3 c d+b^4 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{\left(2 a b c e-a c^2 d+b^2 c d+b^3 (-e)\right) \log \left(a+b x+c x^2\right)}{2 c^4}-\frac{x \left(a c e+b^2 (-e)+b c d\right)}{c^3}+\frac{x^2 (c d-b e)}{2 c^2}+\frac{e x^3}{3 c}",1,"-(((b*c*d - b^2*e + a*c*e)*x)/c^3) + ((c*d - b*e)*x^2)/(2*c^2) + (e*x^3)/(3*c) + ((b^3*c*d - 3*a*b*c^2*d - b^4*e + 4*a*b^2*c*e - 2*a^2*c^2*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*Sqrt[b^2 - 4*a*c]) + ((b^2*c*d - a*c^2*d - b^3*e + 2*a*b*c*e)*Log[a + b*x + c*x^2])/(2*c^4)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
883,1,121,0,0.1481979,"\int \frac{x^2 (d+e x)}{a+b x+c x^2} \, dx","Int[(x^2*(d + e*x))/(a + b*x + c*x^2),x]","-\frac{\left(a c e+b^2 (-e)+b c d\right) \log \left(a+b x+c x^2\right)}{2 c^3}-\frac{\left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{x (c d-b e)}{c^2}+\frac{e x^2}{2 c}","-\frac{\left(a c e+b^2 (-e)+b c d\right) \log \left(a+b x+c x^2\right)}{2 c^3}-\frac{\left(3 a b c e-2 a c^2 d+b^2 c d+b^3 (-e)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{x (c d-b e)}{c^2}+\frac{e x^2}{2 c}",1,"((c*d - b*e)*x)/c^2 + (e*x^2)/(2*c) - ((b^2*c*d - 2*a*c^2*d - b^3*e + 3*a*b*c*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) - ((b*c*d - b^2*e + a*c*e)*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
884,1,85,0,0.0781866,"\int \frac{x (d+e x)}{a+b x+c x^2} \, dx","Int[(x*(d + e*x))/(a + b*x + c*x^2),x]","\frac{\left(2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{(c d-b e) \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{e x}{c}","\frac{\left(2 a c e+b^2 (-e)+b c d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{(c d-b e) \log \left(a+b x+c x^2\right)}{2 c^2}+\frac{e x}{c}",1,"(e*x)/c + ((b*c*d - b^2*e + 2*a*c*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) + ((c*d - b*e)*Log[a + b*x + c*x^2])/(2*c^2)","A",5,5,19,0.2632,1,"{773, 634, 618, 206, 628}"
885,1,66,0,0.0341631,"\int \frac{d+e x}{a+b x+c x^2} \, dx","Int[(d + e*x)/(a + b*x + c*x^2),x]","\frac{e \log \left(a+b x+c x^2\right)}{2 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}","\frac{e \log \left(a+b x+c x^2\right)}{2 c}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}",1,"-(((2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c])) + (e*Log[a + b*x + c*x^2])/(2*c)","A",4,4,18,0.2222,1,"{634, 618, 206, 628}"
886,1,71,0,0.0942628,"\int \frac{d+e x}{x \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)/(x*(a + b*x + c*x^2)),x]","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b x+c x^2\right)}{2 a}+\frac{d \log (x)}{a}","\frac{(b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a \sqrt{b^2-4 a c}}-\frac{d \log \left(a+b x+c x^2\right)}{2 a}+\frac{d \log (x)}{a}",1,"((b*d - 2*a*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a*Sqrt[b^2 - 4*a*c]) + (d*Log[x])/a - (d*Log[a + b*x + c*x^2])/(2*a)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
887,1,104,0,0.1474002,"\int \frac{d+e x}{x^2 \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)/(x^2*(a + b*x + c*x^2)),x]","-\frac{\left(-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c}}+\frac{(b d-a e) \log \left(a+b x+c x^2\right)}{2 a^2}-\frac{\log (x) (b d-a e)}{a^2}-\frac{d}{a x}","-\frac{\left(-a b e-2 a c d+b^2 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \sqrt{b^2-4 a c}}+\frac{(b d-a e) \log \left(a+b x+c x^2\right)}{2 a^2}-\frac{\log (x) (b d-a e)}{a^2}-\frac{d}{a x}",1,"-(d/(a*x)) - ((b^2*d - 2*a*c*d - a*b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^2*Sqrt[b^2 - 4*a*c]) - ((b*d - a*e)*Log[x])/a^2 + ((b*d - a*e)*Log[a + b*x + c*x^2])/(2*a^2)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
888,1,145,0,0.2295217,"\int \frac{d+e x}{x^3 \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)/(x^3*(a + b*x + c*x^2)),x]","-\frac{\left(-a b e-a c d+b^2 d\right) \log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x) \left(-a b e-a c d+b^2 d\right)}{a^3}+\frac{\left(2 a^2 c e-a b^2 e-3 a b c d+b^3 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c}}+\frac{b d-a e}{a^2 x}-\frac{d}{2 a x^2}","-\frac{\left(-a b e-a c d+b^2 d\right) \log \left(a+b x+c x^2\right)}{2 a^3}+\frac{\log (x) \left(-a b e-a c d+b^2 d\right)}{a^3}+\frac{\left(2 a^2 c e-a b^2 e-3 a b c d+b^3 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \sqrt{b^2-4 a c}}+\frac{b d-a e}{a^2 x}-\frac{d}{2 a x^2}",1,"-d/(2*a*x^2) + (b*d - a*e)/(a^2*x) + ((b^3*d - 3*a*b*c*d - a*b^2*e + 2*a^2*c*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*Sqrt[b^2 - 4*a*c]) + ((b^2*d - a*c*d - a*b*e)*Log[x])/a^3 - ((b^2*d - a*c*d - a*b*e)*Log[a + b*x + c*x^2])/(2*a^3)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
889,1,204,0,0.2860725,"\int \frac{d+e x}{x^4 \left(a+b x+c x^2\right)} \, dx","Int[(d + e*x)/(x^4*(a + b*x + c*x^2)),x]","-\frac{\left(3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c}}+\frac{\left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right) \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{-a b e-a c d+b^2 d}{a^3 x}-\frac{\log (x) \left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right)}{a^4}+\frac{b d-a e}{2 a^2 x^2}-\frac{d}{3 a x^3}","-\frac{\left(3 a^2 b c e+2 a^2 c^2 d-4 a b^2 c d-a b^3 e+b^4 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \sqrt{b^2-4 a c}}+\frac{\left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right) \log \left(a+b x+c x^2\right)}{2 a^4}-\frac{-a b e-a c d+b^2 d}{a^3 x}-\frac{\log (x) \left(a^2 c e-a b^2 e-2 a b c d+b^3 d\right)}{a^4}+\frac{b d-a e}{2 a^2 x^2}-\frac{d}{3 a x^3}",1,"-d/(3*a*x^3) + (b*d - a*e)/(2*a^2*x^2) - (b^2*d - a*c*d - a*b*e)/(a^3*x) - ((b^4*d - 4*a*b^2*c*d + 2*a^2*c^2*d - a*b^3*e + 3*a^2*b*c*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*Sqrt[b^2 - 4*a*c]) - ((b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*Log[x])/a^4 + ((b^3*d - 2*a*b*c*d - a*b^2*e + a^2*c*e)*Log[a + b*x + c*x^2])/(2*a^4)","A",6,5,21,0.2381,1,"{800, 634, 618, 206, 628}"
890,1,262,0,0.6382926,"\int \frac{x^4 (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(x^4*(d + e*x))/(a + b*x + c*x^2)^2,x]","-\frac{\left(-30 a^2 b c^2 e+12 a^2 c^3 d-12 a b^2 c^2 d+20 a b^3 c e+2 b^4 c d-3 b^5 e\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{3/2}}-\frac{x^2 \left(8 a c e-3 b^2 e+2 b c d\right)}{2 c^2 \left(b^2-4 a c\right)}-\frac{\left(2 a c e-3 b^2 e+2 b c d\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{x \left(11 a b c e-6 a c^2 d+2 b^2 c d-3 b^3 e\right)}{c^3 \left(b^2-4 a c\right)}+\frac{x^3 \left(x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{\left(-30 a^2 b c^2 e+12 a^2 c^3 d-12 a b^2 c^2 d+20 a b^3 c e+2 b^4 c d-3 b^5 e\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4 \left(b^2-4 a c\right)^{3/2}}-\frac{x^2 \left(8 a c e-3 b^2 e+2 b c d\right)}{2 c^2 \left(b^2-4 a c\right)}-\frac{\left(2 a c e-3 b^2 e+2 b c d\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{x \left(11 a b c e-6 a c^2 d+2 b^2 c d-3 b^3 e\right)}{c^3 \left(b^2-4 a c\right)}+\frac{x^3 \left(x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"((2*b^2*c*d - 6*a*c^2*d - 3*b^3*e + 11*a*b*c*e)*x)/(c^3*(b^2 - 4*a*c)) - ((2*b*c*d - 3*b^2*e + 8*a*c*e)*x^2)/(2*c^2*(b^2 - 4*a*c)) + (x^3*(a*(2*c*d - b*e) + (b*c*d - b^2*e + 2*a*c*e)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) - ((2*b^4*c*d - 12*a*b^2*c^2*d + 12*a^2*c^3*d - 3*b^5*e + 20*a*b^3*c*e - 30*a^2*b*c^2*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*(b^2 - 4*a*c)^(3/2)) - ((2*b*c*d - 3*b^2*e + 2*a*c*e)*Log[a + b*x + c*x^2])/(2*c^4)","A",7,6,21,0.2857,1,"{818, 800, 634, 618, 206, 628}"
891,1,192,0,0.3121778,"\int \frac{x^3 (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(x^3*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{\left(-12 a^2 c^2 e+12 a b^2 c e-6 a b c^2 d+b^3 c d-2 b^4 e\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}-\frac{x \left(6 a c e-2 b^2 e+b c d\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^2 \left(x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{(c d-2 b e) \log \left(a+b x+c x^2\right)}{2 c^3}","\frac{\left(-12 a^2 c^2 e+12 a b^2 c e-6 a b c^2 d+b^3 c d-2 b^4 e\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}-\frac{x \left(6 a c e-2 b^2 e+b c d\right)}{c^2 \left(b^2-4 a c\right)}+\frac{x^2 \left(x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{(c d-2 b e) \log \left(a+b x+c x^2\right)}{2 c^3}",1,"-(((b*c*d - 2*b^2*e + 6*a*c*e)*x)/(c^2*(b^2 - 4*a*c))) + (x^2*(a*(2*c*d - b*e) + (b*c*d - b^2*e + 2*a*c*e)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((b^3*c*d - 6*a*b*c^2*d - 2*b^4*e + 12*a*b^2*c*e - 12*a^2*c^2*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) + ((c*d - 2*b*e)*Log[a + b*x + c*x^2])/(2*c^3)","A",6,6,21,0.2857,1,"{818, 773, 634, 618, 206, 628}"
892,1,132,0,0.1054103,"\int \frac{x^2 (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(x^2*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{\left(2 a c (2 c d-3 b e)+b^3 e\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x \left(x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e \log \left(a+b x+c x^2\right)}{2 c^2}","\frac{\left(2 a c (2 c d-3 b e)+b^3 e\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{x \left(x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e \log \left(a+b x+c x^2\right)}{2 c^2}",1,"(x*(a*(2*c*d - b*e) + (b*c*d - b^2*e + 2*a*c*e)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((b^3*e + 2*a*c*(2*c*d - 3*b*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*(b^2 - 4*a*c)^(3/2)) + (e*Log[a + b*x + c*x^2])/(2*c^2)","A",5,5,21,0.2381,1,"{818, 634, 618, 206, 628}"
893,1,99,0,0.0470867,"\int \frac{x (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(x*(d + e*x))/(a + b*x + c*x^2)^2,x]","\frac{x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 (b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}","\frac{x \left(2 a c e+b^2 (-e)+b c d\right)+a (2 c d-b e)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{2 (b d-2 a e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}",1,"(a*(2*c*d - b*e) + (b*c*d - b^2*e + 2*a*c*e)*x)/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) - (2*(b*d - 2*a*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",3,3,19,0.1579,1,"{777, 618, 206}"
894,1,87,0,0.0384518,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^2,x]","\frac{2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{-2 a e+x (2 c d-b e)+b d}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{-2 a e+x (2 c d-b e)+b d}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((b*d - 2*a*e + (2*c*d - b*e)*x)/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + (2*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",3,3,18,0.1667,1,"{638, 618, 206}"
895,1,135,0,0.1986579,"\int \frac{d+e x}{x \left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(x*(a + b*x + c*x^2)^2),x]","\frac{\left(4 a^2 c e-6 a b c d+b^3 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{d \log \left(a+b x+c x^2\right)}{2 a^2}+\frac{d \log (x)}{a^2}+\frac{c x (b d-2 a e)-a b e-2 a c d+b^2 d}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{\left(4 a^2 c e-6 a b c d+b^3 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^2 \left(b^2-4 a c\right)^{3/2}}-\frac{d \log \left(a+b x+c x^2\right)}{2 a^2}+\frac{d \log (x)}{a^2}+\frac{c x (b d-2 a e)-a b e-2 a c d+b^2 d}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"(b^2*d - 2*a*c*d - a*b*e + c*(b*d - 2*a*e)*x)/(a*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + ((b^3*d - 6*a*b*c*d + 4*a^2*c*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^2*(b^2 - 4*a*c)^(3/2)) + (d*Log[x])/a^2 - (d*Log[a + b*x + c*x^2])/(2*a^2)","A",7,6,21,0.2857,1,"{822, 800, 634, 618, 206, 628}"
896,1,211,0,0.3568301,"\int \frac{d+e x}{x^2 \left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(x^2*(a + b*x + c*x^2)^2),x]","-\frac{\left(6 a^2 b c e+12 a^2 c^2 d-12 a b^2 c d-a b^3 e+2 b^4 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{-a b e-6 a c d+2 b^2 d}{a^2 x \left(b^2-4 a c\right)}+\frac{(2 b d-a e) \log \left(a+b x+c x^2\right)}{2 a^3}-\frac{\log (x) (2 b d-a e)}{a^3}+\frac{c x (b d-2 a e)-a b e-2 a c d+b^2 d}{a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{\left(6 a^2 b c e+12 a^2 c^2 d-12 a b^2 c d-a b^3 e+2 b^4 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^3 \left(b^2-4 a c\right)^{3/2}}-\frac{-a b e-6 a c d+2 b^2 d}{a^2 x \left(b^2-4 a c\right)}+\frac{(2 b d-a e) \log \left(a+b x+c x^2\right)}{2 a^3}-\frac{\log (x) (2 b d-a e)}{a^3}+\frac{c x (b d-2 a e)-a b e-2 a c d+b^2 d}{a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((2*b^2*d - 6*a*c*d - a*b*e)/(a^2*(b^2 - 4*a*c)*x)) + (b^2*d - 2*a*c*d - a*b*e + c*(b*d - 2*a*e)*x)/(a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)) - ((2*b^4*d - 12*a*b^2*c*d + 12*a^2*c^2*d - a*b^3*e + 6*a^2*b*c*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^3*(b^2 - 4*a*c)^(3/2)) - ((2*b*d - a*e)*Log[x])/a^3 + ((2*b*d - a*e)*Log[a + b*x + c*x^2])/(2*a^3)","A",7,6,21,0.2857,1,"{822, 800, 634, 618, 206, 628}"
897,1,283,0,0.6134978,"\int \frac{d+e x}{x^3 \left(a+b x+c x^2\right)^2} \, dx","Int[(d + e*x)/(x^3*(a + b*x + c*x^2)^2),x]","\frac{\left(12 a^2 b^2 c e+30 a^2 b c^2 d-12 a^3 c^2 e-20 a b^3 c d-2 a b^4 e+3 b^5 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{3/2}}-\frac{-2 a b e-8 a c d+3 b^2 d}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\left(-2 a b e-2 a c d+3 b^2 d\right) \log \left(a+b x+c x^2\right)}{2 a^4}+\frac{6 a^2 c e-2 a b^2 e-11 a b c d+3 b^3 d}{a^3 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(-2 a b e-2 a c d+3 b^2 d\right)}{a^4}+\frac{c x (b d-2 a e)-a b e-2 a c d+b^2 d}{a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{\left(12 a^2 b^2 c e+30 a^2 b c^2 d-12 a^3 c^2 e-20 a b^3 c d-2 a b^4 e+3 b^5 d\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a^4 \left(b^2-4 a c\right)^{3/2}}-\frac{-2 a b e-8 a c d+3 b^2 d}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\left(-2 a b e-2 a c d+3 b^2 d\right) \log \left(a+b x+c x^2\right)}{2 a^4}+\frac{6 a^2 c e-2 a b^2 e-11 a b c d+3 b^3 d}{a^3 x \left(b^2-4 a c\right)}+\frac{\log (x) \left(-2 a b e-2 a c d+3 b^2 d\right)}{a^4}+\frac{c x (b d-2 a e)-a b e-2 a c d+b^2 d}{a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(3*b^2*d - 8*a*c*d - 2*a*b*e)/(2*a^2*(b^2 - 4*a*c)*x^2) + (3*b^3*d - 11*a*b*c*d - 2*a*b^2*e + 6*a^2*c*e)/(a^3*(b^2 - 4*a*c)*x) + (b^2*d - 2*a*c*d - a*b*e + c*(b*d - 2*a*e)*x)/(a*(b^2 - 4*a*c)*x^2*(a + b*x + c*x^2)) + ((3*b^5*d - 20*a*b^3*c*d + 30*a^2*b*c^2*d - 2*a*b^4*e + 12*a^2*b^2*c*e - 12*a^3*c^2*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(a^4*(b^2 - 4*a*c)^(3/2)) + ((3*b^2*d - 2*a*c*d - 2*a*b*e)*Log[x])/a^4 - ((3*b^2*d - 2*a*c*d - 2*a*b*e)*Log[a + b*x + c*x^2])/(2*a^4)","A",7,6,21,0.2857,1,"{822, 800, 634, 618, 206, 628}"
898,1,9,0,0.0030123,"\int \frac{5+2 x}{4+5 x+x^2} \, dx","Int[(5 + 2*x)/(4 + 5*x + x^2),x]","\log \left(x^2+5 x+4\right)","\log \left(x^2+5 x+4\right)",1,"Log[4 + 5*x + x^2]","A",1,1,16,0.06250,1,"{628}"
899,1,17,0,0.004653,"\int \frac{7+3 x}{8+6 x+x^2} \, dx","Int[(7 + 3*x)/(8 + 6*x + x^2),x]","\frac{1}{2} \log (x+2)+\frac{5}{2} \log (x+4)","\frac{1}{2} \log (x+2)+\frac{5}{2} \log (x+4)",1,"Log[2 + x]/2 + (5*Log[4 + x])/2","A",3,2,16,0.1250,1,"{632, 31}"
900,1,14,0,0.0108742,"\int \frac{5+2 x}{5+4 x+x^2} \, dx","Int[(5 + 2*x)/(5 + 4*x + x^2),x]","\log \left(x^2+4 x+5\right)+\tan ^{-1}(x+2)","\log \left(x^2+4 x+5\right)+\tan ^{-1}(x+2)",1,"ArcTan[2 + x] + Log[5 + 4*x + x^2]","A",4,4,16,0.2500,1,"{634, 618, 204, 628}"
901,1,33,0,0.0221802,"\int \frac{-2+7 x}{42-16 x+2 x^2} \, dx","Int[(-2 + 7*x)/(42 - 16*x + 2*x^2),x]","\frac{7}{4} \log \left(x^2-8 x+21\right)-\frac{13 \tan ^{-1}\left(\frac{4-x}{\sqrt{5}}\right)}{\sqrt{5}}","\frac{7}{4} \log \left(x^2-8 x+21\right)-\frac{13 \tan ^{-1}\left(\frac{4-x}{\sqrt{5}}\right)}{\sqrt{5}}",1,"(-13*ArcTan[(4 - x)/Sqrt[5]])/Sqrt[5] + (7*Log[21 - 8*x + x^2])/4","A",4,4,18,0.2222,1,"{634, 618, 204, 628}"
902,1,51,0,0.0186711,"\int \frac{3+x}{1+3 x+x^2} \, dx","Int[(3 + x)/(1 + 3*x + x^2),x]","\frac{1}{10} \left(5+3 \sqrt{5}\right) \log \left(2 x-\sqrt{5}+3\right)+\frac{1}{10} \left(5-3 \sqrt{5}\right) \log \left(2 x+\sqrt{5}+3\right)","\frac{1}{10} \left(5+3 \sqrt{5}\right) \log \left(2 x-\sqrt{5}+3\right)+\frac{1}{10} \left(5-3 \sqrt{5}\right) \log \left(2 x+\sqrt{5}+3\right)",1,"((5 + 3*Sqrt[5])*Log[3 - Sqrt[5] + 2*x])/10 + ((5 - 3*Sqrt[5])*Log[3 + Sqrt[5] + 2*x])/10","A",3,2,14,0.1429,1,"{632, 31}"
903,1,49,0,0.0257659,"\int \frac{-1+2 x}{1+8 x+4 x^2} \, dx","Int[(-1 + 2*x)/(1 + 8*x + 4*x^2),x]","\frac{1}{4} \left(1-\sqrt{3}\right) \log \left(2 x-\sqrt{3}+2\right)+\frac{1}{4} \left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+2\right)","\frac{1}{4} \left(1-\sqrt{3}\right) \log \left(2 x-\sqrt{3}+2\right)+\frac{1}{4} \left(1+\sqrt{3}\right) \log \left(2 x+\sqrt{3}+2\right)",1,"((1 - Sqrt[3])*Log[2 - Sqrt[3] + 2*x])/4 + ((1 + Sqrt[3])*Log[2 + Sqrt[3] + 2*x])/4","A",3,2,18,0.1111,1,"{632, 31}"
904,1,16,0,0.0036779,"\int \frac{3+2 x}{\left(13+12 x+4 x^2\right)^2} \, dx","Int[(3 + 2*x)/(13 + 12*x + 4*x^2)^2,x]","-\frac{1}{4 \left(4 x^2+12 x+13\right)}","-\frac{1}{4 \left(4 x^2+12 x+13\right)}",1,"-1/(4*(13 + 12*x + 4*x^2))","A",1,1,18,0.05556,1,"{629}"
905,1,24,0,0.0085993,"\int \frac{4+x}{\left(5+4 x+x^2\right)^2} \, dx","Int[(4 + x)/(5 + 4*x + x^2)^2,x]","\frac{2 x+3}{2 \left(x^2+4 x+5\right)}+\tan ^{-1}(x+2)","\frac{2 x+3}{2 \left(x^2+4 x+5\right)}+\tan ^{-1}(x+2)",1,"(3 + 2*x)/(2*(5 + 4*x + x^2)) + ArcTan[2 + x]","A",3,3,14,0.2143,1,"{638, 618, 204}"
906,1,39,0,0.0131921,"\int \frac{-1+3 x}{\left(1+x+x^2\right)^2} \, dx","Int[(-1 + 3*x)/(1 + x + x^2)^2,x]","-\frac{5 x+7}{3 \left(x^2+x+1\right)}-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}","-\frac{5 x+7}{3 \left(x^2+x+1\right)}-\frac{10 \tan ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"-(7 + 5*x)/(3*(1 + x + x^2)) - (10*ArcTan[(1 + 2*x)/Sqrt[3]])/(3*Sqrt[3])","A",3,3,14,0.2143,1,"{638, 618, 204}"
907,1,58,0,0.0209552,"\int \frac{1+x}{\left(1-x+x^2\right)^3} \, dx","Int[(1 + x)/(1 - x + x^2)^3,x]","-\frac{1-2 x}{2 \left(x^2-x+1\right)}-\frac{1-x}{2 \left(x^2-x+1\right)^2}-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1-2 x}{2 \left(x^2-x+1\right)}-\frac{1-x}{2 \left(x^2-x+1\right)^2}-\frac{2 \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(1 - x)/(2*(1 - x + x^2)^2) - (1 - 2*x)/(2*(1 - x + x^2)) - (2*ArcTan[(1 - 2*x)/Sqrt[3]])/Sqrt[3]","A",4,4,14,0.2857,1,"{638, 614, 618, 204}"
908,1,10,0,0.0016394,"\int \frac{1}{A+B x} \, dx","Int[(A + B*x)^(-1),x]","\frac{\log (A+B x)}{B}","\frac{\log (A+B x)}{B}",1,"Log[A + B*x]/B","A",1,1,7,0.1429,1,"{31}"
909,1,10,0,0.0023645,"\int \frac{A+B x}{A^2+2 A B x+B^2 x^2} \, dx","Int[(A + B*x)/(A^2 + 2*A*B*x + B^2*x^2),x]","\frac{\log (A+B x)}{B}","\frac{\log (A+B x)}{B}",1,"Log[A + B*x]/B","A",2,2,24,0.08333,1,"{27, 31}"
910,1,367,0,0.5080927,"\int x^4 (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[x^4*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(1024 a^2 B c^2-6 c x \left(280 a A c^2-444 a b B c-294 A b^2 c+231 b^3 B\right)+2744 a A b c^2-3276 a b^2 B c-1470 A b^3 c+1155 b^4 B\right)}{13440 c^5}-\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-32 a^2 A c^3+80 a^2 b B c^2+112 a A b^2 c^2-120 a b^3 B c-42 A b^4 c+33 b^5 B\right)}{1024 c^6}+\frac{\left(b^2-4 a c\right) \left(-32 a^2 A c^3+80 a^2 b B c^2+112 a A b^2 c^2-120 a b^3 B c-42 A b^4 c+33 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{13/2}}+\frac{x^2 \left(a+b x+c x^2\right)^{3/2} \left(-32 a B c-42 A b c+33 b^2 B\right)}{280 c^3}-\frac{x^3 \left(a+b x+c x^2\right)^{3/2} (11 b B-14 A c)}{84 c^2}+\frac{B x^4 \left(a+b x+c x^2\right)^{3/2}}{7 c}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(1024 a^2 B c^2-6 c x \left(280 a A c^2-444 a b B c-294 A b^2 c+231 b^3 B\right)+2744 a A b c^2-3276 a b^2 B c-1470 A b^3 c+1155 b^4 B\right)}{13440 c^5}-\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-32 a^2 A c^3+80 a^2 b B c^2+112 a A b^2 c^2-120 a b^3 B c-42 A b^4 c+33 b^5 B\right)}{1024 c^6}+\frac{\left(b^2-4 a c\right) \left(-32 a^2 A c^3+80 a^2 b B c^2+112 a A b^2 c^2-120 a b^3 B c-42 A b^4 c+33 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{13/2}}+\frac{x^2 \left(a+b x+c x^2\right)^{3/2} \left(-32 a B c-42 A b c+33 b^2 B\right)}{280 c^3}-\frac{x^3 \left(a+b x+c x^2\right)^{3/2} (11 b B-14 A c)}{84 c^2}+\frac{B x^4 \left(a+b x+c x^2\right)^{3/2}}{7 c}",1,"-((33*b^5*B - 42*A*b^4*c - 120*a*b^3*B*c + 112*a*A*b^2*c^2 + 80*a^2*b*B*c^2 - 32*a^2*A*c^3)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^6) + ((33*b^2*B - 42*A*b*c - 32*a*B*c)*x^2*(a + b*x + c*x^2)^(3/2))/(280*c^3) - ((11*b*B - 14*A*c)*x^3*(a + b*x + c*x^2)^(3/2))/(84*c^2) + (B*x^4*(a + b*x + c*x^2)^(3/2))/(7*c) + ((1155*b^4*B - 1470*A*b^3*c - 3276*a*b^2*B*c + 2744*a*A*b*c^2 + 1024*a^2*B*c^2 - 6*c*(231*b^3*B - 294*A*b^2*c - 444*a*b*B*c + 280*a*A*c^2)*x)*(a + b*x + c*x^2)^(3/2))/(13440*c^5) + ((b^2 - 4*a*c)*(33*b^5*B - 42*A*b^4*c - 120*a*b^3*B*c + 112*a*A*b^2*c^2 + 80*a^2*b*B*c^2 - 32*a^2*A*c^3)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(13/2))","A",7,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
911,1,280,0,0.3231613,"\int x^3 (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[x^3*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(16 a^2 B c^2+48 a A b c^2-56 a b^2 B c-28 A b^3 c+21 b^4 B\right)}{512 c^5}-\frac{\left(b^2-4 a c\right) \left(16 a^2 B c^2+48 a A b c^2-56 a b^2 B c-28 A b^3 c+21 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{11/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-6 c x \left(-20 a B c-28 A b c+21 b^2 B\right)+128 a A c^2-196 a b B c-140 A b^2 c+105 b^3 B\right)}{960 c^4}-\frac{x^2 \left(a+b x+c x^2\right)^{3/2} (3 b B-4 A c)}{20 c^2}+\frac{B x^3 \left(a+b x+c x^2\right)^{3/2}}{6 c}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(16 a^2 B c^2+48 a A b c^2-56 a b^2 B c-28 A b^3 c+21 b^4 B\right)}{512 c^5}-\frac{\left(b^2-4 a c\right) \left(16 a^2 B c^2+48 a A b c^2-56 a b^2 B c-28 A b^3 c+21 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{11/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-6 c x \left(-20 a B c-28 A b c+21 b^2 B\right)+128 a A c^2-196 a b B c-140 A b^2 c+105 b^3 B\right)}{960 c^4}-\frac{x^2 \left(a+b x+c x^2\right)^{3/2} (3 b B-4 A c)}{20 c^2}+\frac{B x^3 \left(a+b x+c x^2\right)^{3/2}}{6 c}",1,"((21*b^4*B - 28*A*b^3*c - 56*a*b^2*B*c + 48*a*A*b*c^2 + 16*a^2*B*c^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^5) - ((3*b*B - 4*A*c)*x^2*(a + b*x + c*x^2)^(3/2))/(20*c^2) + (B*x^3*(a + b*x + c*x^2)^(3/2))/(6*c) - ((105*b^3*B - 140*A*b^2*c - 196*a*b*B*c + 128*a*A*c^2 - 6*c*(21*b^2*B - 28*A*b*c - 20*a*B*c)*x)*(a + b*x + c*x^2)^(3/2))/(960*c^4) - ((b^2 - 4*a*c)*(21*b^4*B - 28*A*b^3*c - 56*a*b^2*B*c + 48*a*A*b*c^2 + 16*a^2*B*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(11/2))","A",6,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
912,1,205,0,0.1963668,"\int x^2 (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[x^2*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-32 a B c-6 c x (7 b B-10 A c)-50 A b c+35 b^2 B\right)}{240 c^3}-\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(8 a A c^2-12 a b B c-10 A b^2 c+7 b^3 B\right)}{128 c^4}+\frac{\left(b^2-4 a c\right) \left(8 a A c^2-12 a b B c-10 A b^2 c+7 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{9/2}}+\frac{B x^2 \left(a+b x+c x^2\right)^{3/2}}{5 c}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-32 a B c-6 c x (7 b B-10 A c)-50 A b c+35 b^2 B\right)}{240 c^3}-\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(8 a A c^2-12 a b B c-10 A b^2 c+7 b^3 B\right)}{128 c^4}+\frac{\left(b^2-4 a c\right) \left(8 a A c^2-12 a b B c-10 A b^2 c+7 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{9/2}}+\frac{B x^2 \left(a+b x+c x^2\right)^{3/2}}{5 c}",1,"-((7*b^3*B - 10*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^4) + (B*x^2*(a + b*x + c*x^2)^(3/2))/(5*c) + ((35*b^2*B - 50*A*b*c - 32*a*B*c - 6*c*(7*b*B - 10*A*c)*x)*(a + b*x + c*x^2)^(3/2))/(240*c^3) + ((b^2 - 4*a*c)*(7*b^3*B - 10*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(9/2))","A",5,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
913,1,144,0,0.0643105,"\int x (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[x*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a B c-8 A b c+5 b^2 B\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \left(-4 a B c-8 A b c+5 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} (-8 A c+5 b B-6 B c x)}{24 c^2}","\frac{(b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a B c-8 A b c+5 b^2 B\right)}{64 c^3}-\frac{\left(b^2-4 a c\right) \left(-4 a B c-8 A b c+5 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{7/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} (-8 A c+5 b B-6 B c x)}{24 c^2}",1,"((5*b^2*B - 8*A*b*c - 4*a*B*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(64*c^3) - ((5*b*B - 8*A*c - 6*B*c*x)*(a + b*x + c*x^2)^(3/2))/(24*c^2) - ((b^2 - 4*a*c)*(5*b^2*B - 8*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(7/2))","A",4,4,21,0.1905,1,"{779, 612, 621, 206}"
914,1,113,0,0.0458061,"\int (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{\left(b^2-4 a c\right) (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2}}-\frac{(b+2 c x) \sqrt{a+b x+c x^2} (b B-2 A c)}{8 c^2}+\frac{B \left(a+b x+c x^2\right)^{3/2}}{3 c}","\frac{\left(b^2-4 a c\right) (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{5/2}}-\frac{(b+2 c x) \sqrt{a+b x+c x^2} (b B-2 A c)}{8 c^2}+\frac{B \left(a+b x+c x^2\right)^{3/2}}{3 c}",1,"-((b*B - 2*A*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(8*c^2) + (B*(a + b*x + c*x^2)^(3/2))/(3*c) + ((b^2 - 4*a*c)*(b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(5/2))","A",4,4,20,0.2000,1,"{640, 612, 621, 206}"
915,1,129,0,0.1038753,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x,x]","-\frac{\left(-4 a B c-4 A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{3/2}}+\frac{\sqrt{a+b x+c x^2} (4 A c+b B+2 B c x)}{4 c}-\sqrt{a} A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)","-\frac{\left(-4 a B c-4 A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{3/2}}+\frac{\sqrt{a+b x+c x^2} (4 A c+b B+2 B c x)}{4 c}-\sqrt{a} A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)",1,"((b*B + 4*A*c + 2*B*c*x)*Sqrt[a + b*x + c*x^2])/(4*c) - Sqrt[a]*A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])] - ((b^2*B - 4*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(3/2))","A",6,5,23,0.2174,1,"{814, 843, 621, 206, 724}"
916,1,121,0,0.0885888,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^2} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^2,x]","-\frac{(A-B x) \sqrt{a+b x+c x^2}}{x}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a}}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c}}","-\frac{(A-B x) \sqrt{a+b x+c x^2}}{x}-\frac{(2 a B+A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{a}}+\frac{(2 A c+b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 \sqrt{c}}",1,"-(((A - B*x)*Sqrt[a + b*x + c*x^2])/x) - ((A*b + 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[a]) + ((b*B + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*Sqrt[c])","A",6,5,23,0.2174,1,"{812, 843, 621, 206, 724}"
917,1,133,0,0.1019356,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^3} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^3,x]","\frac{\left(-4 a A c-4 a b B+A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{3/2}}-\frac{\sqrt{a+b x+c x^2} (x (4 a B+A b)+2 a A)}{4 a x^2}+B \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)","\frac{\left(-4 a A c-4 a b B+A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{3/2}}-\frac{\sqrt{a+b x+c x^2} (x (4 a B+A b)+2 a A)}{4 a x^2}+B \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)",1,"-((2*a*A + (A*b + 4*a*B)*x)*Sqrt[a + b*x + c*x^2])/(4*a*x^2) + ((A*b^2 - 4*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*a^(3/2)) + B*Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",6,5,23,0.2174,1,"{810, 843, 621, 206, 724}"
918,1,121,0,0.0663229,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^4} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^4,x]","-\frac{\left(b^2-4 a c\right) (A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{5/2}}+\frac{(2 a+b x) (A b-2 a B) \sqrt{a+b x+c x^2}}{8 a^2 x^2}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{3 a x^3}","-\frac{\left(b^2-4 a c\right) (A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{5/2}}+\frac{(2 a+b x) (A b-2 a B) \sqrt{a+b x+c x^2}}{8 a^2 x^2}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{3 a x^3}",1,"((A*b - 2*a*B)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(8*a^2*x^2) - (A*(a + b*x + c*x^2)^(3/2))/(3*a*x^3) - ((A*b - 2*a*B)*(b^2 - 4*a*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*a^(5/2))","A",4,4,23,0.1739,1,"{806, 720, 724, 206}"
919,1,172,0,0.1426985,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^5} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^5,x]","-\frac{(2 a+b x) \sqrt{a+b x+c x^2} \left(-4 a A c-8 a b B+5 A b^2\right)}{64 a^3 x^2}+\frac{\left(b^2-4 a c\right) \left(-4 a A c-8 a b B+5 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{7/2}}+\frac{(5 A b-8 a B) \left(a+b x+c x^2\right)^{3/2}}{24 a^2 x^3}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{4 a x^4}","-\frac{(2 a+b x) \sqrt{a+b x+c x^2} \left(-4 a A c-8 a b B+5 A b^2\right)}{64 a^3 x^2}+\frac{\left(b^2-4 a c\right) \left(-4 a A c-8 a b B+5 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{7/2}}+\frac{(5 A b-8 a B) \left(a+b x+c x^2\right)^{3/2}}{24 a^2 x^3}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{4 a x^4}",1,"-((5*A*b^2 - 8*a*b*B - 4*a*A*c)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(64*a^3*x^2) - (A*(a + b*x + c*x^2)^(3/2))/(4*a*x^4) + ((5*A*b - 8*a*B)*(a + b*x + c*x^2)^(3/2))/(24*a^2*x^3) + ((b^2 - 4*a*c)*(5*A*b^2 - 8*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(128*a^(7/2))","A",5,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
920,1,235,0,0.2699031,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^6} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^6,x]","-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-32 a A c-50 a b B+35 A b^2\right)}{240 a^3 x^3}+\frac{(2 a+b x) \sqrt{a+b x+c x^2} \left(8 a^2 B c-12 a A b c-10 a b^2 B+7 A b^3\right)}{128 a^4 x^2}+\frac{\left(b^2-4 a c\right) \left(2 a B \left(5 b^2-4 a c\right)-A \left(7 b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{9/2}}+\frac{(7 A b-10 a B) \left(a+b x+c x^2\right)^{3/2}}{40 a^2 x^4}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{5 a x^5}","-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-32 a A c-50 a b B+35 A b^2\right)}{240 a^3 x^3}+\frac{(2 a+b x) \sqrt{a+b x+c x^2} \left(8 a^2 B c-12 a A b c-10 a b^2 B+7 A b^3\right)}{128 a^4 x^2}+\frac{\left(b^2-4 a c\right) \left(2 a B \left(5 b^2-4 a c\right)-A \left(7 b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{9/2}}+\frac{(7 A b-10 a B) \left(a+b x+c x^2\right)^{3/2}}{40 a^2 x^4}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{5 a x^5}",1,"((7*A*b^3 - 10*a*b^2*B - 12*a*A*b*c + 8*a^2*B*c)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(128*a^4*x^2) - (A*(a + b*x + c*x^2)^(3/2))/(5*a*x^5) + ((7*A*b - 10*a*B)*(a + b*x + c*x^2)^(3/2))/(40*a^2*x^4) - ((35*A*b^2 - 50*a*b*B - 32*a*A*c)*(a + b*x + c*x^2)^(3/2))/(240*a^3*x^3) + ((b^2 - 4*a*c)*(2*a*B*(5*b^2 - 4*a*c) - A*(7*b^3 - 12*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(256*a^(9/2))","A",6,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
921,1,310,0,0.3571624,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^7} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^7,x]","\frac{(2 a+b x) \sqrt{a+b x+c x^2} \left(4 a b B \left(7 b^2-12 a c\right)-A \left(16 a^2 c^2-56 a b^2 c+21 b^4\right)\right)}{512 a^5 x^2}-\frac{\left(b^2-4 a c\right) \left(4 a b B \left(7 b^2-12 a c\right)-A \left(16 a^2 c^2-56 a b^2 c+21 b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{1024 a^{11/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(128 a^2 B c-196 a A b c-140 a b^2 B+105 A b^3\right)}{960 a^4 x^3}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-20 a A c-28 a b B+21 A b^2\right)}{160 a^3 x^4}+\frac{(3 A b-4 a B) \left(a+b x+c x^2\right)^{3/2}}{20 a^2 x^5}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{6 a x^6}","\frac{(2 a+b x) \sqrt{a+b x+c x^2} \left(4 a b B \left(7 b^2-12 a c\right)-A \left(16 a^2 c^2-56 a b^2 c+21 b^4\right)\right)}{512 a^5 x^2}-\frac{\left(b^2-4 a c\right) \left(4 a b B \left(7 b^2-12 a c\right)-A \left(16 a^2 c^2-56 a b^2 c+21 b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{1024 a^{11/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(128 a^2 B c-196 a A b c-140 a b^2 B+105 A b^3\right)}{960 a^4 x^3}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-20 a A c-28 a b B+21 A b^2\right)}{160 a^3 x^4}+\frac{(3 A b-4 a B) \left(a+b x+c x^2\right)^{3/2}}{20 a^2 x^5}-\frac{A \left(a+b x+c x^2\right)^{3/2}}{6 a x^6}",1,"((4*a*b*B*(7*b^2 - 12*a*c) - A*(21*b^4 - 56*a*b^2*c + 16*a^2*c^2))*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(512*a^5*x^2) - (A*(a + b*x + c*x^2)^(3/2))/(6*a*x^6) + ((3*A*b - 4*a*B)*(a + b*x + c*x^2)^(3/2))/(20*a^2*x^5) - ((21*A*b^2 - 28*a*b*B - 20*a*A*c)*(a + b*x + c*x^2)^(3/2))/(160*a^3*x^4) + ((105*A*b^3 - 140*a*b^2*B - 196*a*A*b*c + 128*a^2*B*c)*(a + b*x + c*x^2)^(3/2))/(960*a^4*x^3) - ((b^2 - 4*a*c)*(4*a*b*B*(7*b^2 - 12*a*c) - A*(21*b^4 - 56*a*b^2*c + 16*a^2*c^2))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(1024*a^(11/2))","A",7,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
922,1,455,0,0.6283154,"\int x^4 (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[x^4*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{\left(a+b x+c x^2\right)^{5/2} \left(2048 a^2 B c^2-10 c x \left(504 a A c^2-748 a b B c-594 A b^2 c+429 b^3 B\right)+6696 a A b c^2-7524 a b^2 B c-4158 A b^3 c+3003 b^4 B\right)}{80640 c^5}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-96 a^2 A c^3+240 a^2 b B c^2+432 a A b^2 c^2-440 a b^3 B c-198 A b^4 c+143 b^5 B\right)}{12288 c^6}+\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-96 a^2 A c^3+240 a^2 b B c^2+432 a A b^2 c^2-440 a b^3 B c-198 A b^4 c+143 b^5 B\right)}{32768 c^7}-\frac{\left(b^2-4 a c\right)^2 \left(-96 a^2 A c^3+240 a^2 b B c^2+432 a A b^2 c^2-440 a b^3 B c-198 A b^4 c+143 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{65536 c^{15/2}}+\frac{x^2 \left(a+b x+c x^2\right)^{5/2} \left(-128 a B c-198 A b c+143 b^2 B\right)}{2016 c^3}-\frac{x^3 \left(a+b x+c x^2\right)^{5/2} (13 b B-18 A c)}{144 c^2}+\frac{B x^4 \left(a+b x+c x^2\right)^{5/2}}{9 c}","\frac{\left(a+b x+c x^2\right)^{5/2} \left(2048 a^2 B c^2-10 c x \left(504 a A c^2-748 a b B c-594 A b^2 c+429 b^3 B\right)+6696 a A b c^2-7524 a b^2 B c-4158 A b^3 c+3003 b^4 B\right)}{80640 c^5}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-96 a^2 A c^3+240 a^2 b B c^2+432 a A b^2 c^2-440 a b^3 B c-198 A b^4 c+143 b^5 B\right)}{12288 c^6}+\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-96 a^2 A c^3+240 a^2 b B c^2+432 a A b^2 c^2-440 a b^3 B c-198 A b^4 c+143 b^5 B\right)}{32768 c^7}-\frac{\left(b^2-4 a c\right)^2 \left(-96 a^2 A c^3+240 a^2 b B c^2+432 a A b^2 c^2-440 a b^3 B c-198 A b^4 c+143 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{65536 c^{15/2}}+\frac{x^2 \left(a+b x+c x^2\right)^{5/2} \left(-128 a B c-198 A b c+143 b^2 B\right)}{2016 c^3}-\frac{x^3 \left(a+b x+c x^2\right)^{5/2} (13 b B-18 A c)}{144 c^2}+\frac{B x^4 \left(a+b x+c x^2\right)^{5/2}}{9 c}",1,"((b^2 - 4*a*c)*(143*b^5*B - 198*A*b^4*c - 440*a*b^3*B*c + 432*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32768*c^7) - ((143*b^5*B - 198*A*b^4*c - 440*a*b^3*B*c + 432*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(12288*c^6) + ((143*b^2*B - 198*A*b*c - 128*a*B*c)*x^2*(a + b*x + c*x^2)^(5/2))/(2016*c^3) - ((13*b*B - 18*A*c)*x^3*(a + b*x + c*x^2)^(5/2))/(144*c^2) + (B*x^4*(a + b*x + c*x^2)^(5/2))/(9*c) + ((3003*b^4*B - 4158*A*b^3*c - 7524*a*b^2*B*c + 6696*a*A*b*c^2 + 2048*a^2*B*c^2 - 10*c*(429*b^3*B - 594*A*b^2*c - 748*a*b*B*c + 504*a*A*c^2)*x)*(a + b*x + c*x^2)^(5/2))/(80640*c^5) - ((b^2 - 4*a*c)^2*(143*b^5*B - 198*A*b^4*c - 440*a*b^3*B*c + 432*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(65536*c^(15/2))","A",8,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
923,1,356,0,0.3969797,"\int x^3 (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[x^3*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(16 a^2 B c^2+64 a A b c^2-72 a b^2 B c-48 A b^3 c+33 b^4 B\right)}{2048 c^5}-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(16 a^2 B c^2+64 a A b c^2-72 a b^2 B c-48 A b^3 c+33 b^4 B\right)}{16384 c^6}+\frac{3 \left(b^2-4 a c\right)^2 \left(16 a^2 B c^2+64 a A b c^2-72 a b^2 B c-48 A b^3 c+33 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{13/2}}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(-10 c x \left(-28 a B c-48 A b c+33 b^2 B\right)+256 a A c^2-372 a b B c-336 A b^2 c+231 b^3 B\right)}{4480 c^4}-\frac{x^2 \left(a+b x+c x^2\right)^{5/2} (11 b B-16 A c)}{112 c^2}+\frac{B x^3 \left(a+b x+c x^2\right)^{5/2}}{8 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(16 a^2 B c^2+64 a A b c^2-72 a b^2 B c-48 A b^3 c+33 b^4 B\right)}{2048 c^5}-\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(16 a^2 B c^2+64 a A b c^2-72 a b^2 B c-48 A b^3 c+33 b^4 B\right)}{16384 c^6}+\frac{3 \left(b^2-4 a c\right)^2 \left(16 a^2 B c^2+64 a A b c^2-72 a b^2 B c-48 A b^3 c+33 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{13/2}}-\frac{\left(a+b x+c x^2\right)^{5/2} \left(-10 c x \left(-28 a B c-48 A b c+33 b^2 B\right)+256 a A c^2-372 a b B c-336 A b^2 c+231 b^3 B\right)}{4480 c^4}-\frac{x^2 \left(a+b x+c x^2\right)^{5/2} (11 b B-16 A c)}{112 c^2}+\frac{B x^3 \left(a+b x+c x^2\right)^{5/2}}{8 c}",1,"(-3*(b^2 - 4*a*c)*(33*b^4*B - 48*A*b^3*c - 72*a*b^2*B*c + 64*a*A*b*c^2 + 16*a^2*B*c^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^6) + ((33*b^4*B - 48*A*b^3*c - 72*a*b^2*B*c + 64*a*A*b*c^2 + 16*a^2*B*c^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(2048*c^5) - ((11*b*B - 16*A*c)*x^2*(a + b*x + c*x^2)^(5/2))/(112*c^2) + (B*x^3*(a + b*x + c*x^2)^(5/2))/(8*c) - ((231*b^3*B - 336*A*b^2*c - 372*a*b*B*c + 256*a*A*c^2 - 10*c*(33*b^2*B - 48*A*b*c - 28*a*B*c)*x)*(a + b*x + c*x^2)^(5/2))/(4480*c^4) + (3*(b^2 - 4*a*c)^2*(33*b^4*B - 48*A*b^3*c - 72*a*b^2*B*c + 64*a*A*b*c^2 + 16*a^2*B*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(13/2))","A",7,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
924,1,269,0,0.248315,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[x^2*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{\left(a+b x+c x^2\right)^{5/2} \left(-48 a B c-10 c x (9 b B-14 A c)-98 A b c+63 b^2 B\right)}{840 c^3}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right)}{384 c^4}+\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right)}{1024 c^5}-\frac{\left(b^2-4 a c\right)^2 \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{11/2}}+\frac{B x^2 \left(a+b x+c x^2\right)^{5/2}}{7 c}","\frac{\left(a+b x+c x^2\right)^{5/2} \left(-48 a B c-10 c x (9 b B-14 A c)-98 A b c+63 b^2 B\right)}{840 c^3}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right)}{384 c^4}+\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right)}{1024 c^5}-\frac{\left(b^2-4 a c\right)^2 \left(8 a A c^2-12 a b B c-14 A b^2 c+9 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{11/2}}+\frac{B x^2 \left(a+b x+c x^2\right)^{5/2}}{7 c}",1,"((b^2 - 4*a*c)*(9*b^3*B - 14*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^5) - ((9*b^3*B - 14*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^4) + (B*x^2*(a + b*x + c*x^2)^(5/2))/(7*c) + ((63*b^2*B - 98*A*b*c - 48*a*B*c - 10*c*(9*b*B - 14*A*c)*x)*(a + b*x + c*x^2)^(5/2))/(840*c^3) - ((b^2 - 4*a*c)^2*(9*b^3*B - 14*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(11/2))","A",6,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
925,1,198,0,0.0948242,"\int x (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[x*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a B c-12 A b c+7 b^2 B\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a B c-12 A b c+7 b^2 B\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 a B c-12 A b c+7 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{\left(a+b x+c x^2\right)^{5/2} (-12 A c+7 b B-10 B c x)}{60 c^2}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a B c-12 A b c+7 b^2 B\right)}{192 c^3}-\frac{\left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a B c-12 A b c+7 b^2 B\right)}{512 c^4}+\frac{\left(b^2-4 a c\right)^2 \left(-4 a B c-12 A b c+7 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{\left(a+b x+c x^2\right)^{5/2} (-12 A c+7 b B-10 B c x)}{60 c^2}",1,"-((b^2 - 4*a*c)*(7*b^2*B - 12*A*b*c - 4*a*B*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(512*c^4) + ((7*b^2*B - 12*A*b*c - 4*a*B*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(192*c^3) - ((7*b*B - 12*A*c - 10*B*c*x)*(a + b*x + c*x^2)^(5/2))/(60*c^2) + ((b^2 - 4*a*c)^2*(7*b^2*B - 12*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(9/2))","A",5,4,21,0.1905,1,"{779, 612, 621, 206}"
926,1,158,0,0.0670433,"\int (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (b B-2 A c)}{128 c^3}-\frac{3 \left(b^2-4 a c\right)^2 (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{7/2}}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} (b B-2 A c)}{16 c^2}+\frac{B \left(a+b x+c x^2\right)^{5/2}}{5 c}","\frac{3 \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (b B-2 A c)}{128 c^3}-\frac{3 \left(b^2-4 a c\right)^2 (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{7/2}}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2} (b B-2 A c)}{16 c^2}+\frac{B \left(a+b x+c x^2\right)^{5/2}}{5 c}",1,"(3*(b^2 - 4*a*c)*(b*B - 2*A*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^3) - ((b*B - 2*A*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(16*c^2) + (B*(a + b*x + c*x^2)^(5/2))/(5*c) - (3*(b^2 - 4*a*c)^2*(b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(7/2))","A",5,4,20,0.2000,1,"{640, 612, 621, 206}"
927,1,218,0,0.2540498,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x,x]","a^{3/2} (-A) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)-\frac{\sqrt{a+b x+c x^2} \left(2 c x \left(-12 a B c-8 A b c+3 b^2 B\right)-64 a A c^2-12 a b B c-8 A b^2 c+3 b^3 B\right)}{64 c^2}+\frac{\left(\left(b^2-4 a c\right) \left(-12 a B c-8 A b c+3 b^2 B\right)+64 a A b c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (8 A c+3 b B+6 B c x)}{24 c}","a^{3/2} (-A) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)-\frac{\sqrt{a+b x+c x^2} \left(2 c x \left(-12 a B c-8 A b c+3 b^2 B\right)-64 a A c^2-12 a b B c-8 A b^2 c+3 b^3 B\right)}{64 c^2}+\frac{\left(\left(b^2-4 a c\right) \left(-12 a B c-8 A b c+3 b^2 B\right)+64 a A b c^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (8 A c+3 b B+6 B c x)}{24 c}",1,"-((3*b^3*B - 8*A*b^2*c - 12*a*b*B*c - 64*a*A*c^2 + 2*c*(3*b^2*B - 8*A*b*c - 12*a*B*c)*x)*Sqrt[a + b*x + c*x^2])/(64*c^2) + ((3*b*B + 8*A*c + 6*B*c*x)*(a + b*x + c*x^2)^(3/2))/(24*c) - a^(3/2)*A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])] + ((64*a*A*b*c^2 + (b^2 - 4*a*c)*(3*b^2*B - 8*A*b*c - 12*a*B*c))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(5/2))","A",7,5,23,0.2174,1,"{814, 843, 621, 206, 724}"
928,1,193,0,0.1767428,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^2,x]","-\frac{\left(-24 a A c^2-12 a b B c-6 A b^2 c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2}}+\frac{\sqrt{a+b x+c x^2} \left(8 a B c+2 c x (6 A c+b B)+18 A b c+b^2 B\right)}{8 c}-\frac{(3 A-B x) \left(a+b x+c x^2\right)^{3/2}}{3 x}-\frac{1}{2} \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)","-\frac{\left(-24 a A c^2-12 a b B c-6 A b^2 c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{3/2}}+\frac{\sqrt{a+b x+c x^2} \left(8 a B c+2 c x (6 A c+b B)+18 A b c+b^2 B\right)}{8 c}-\frac{(3 A-B x) \left(a+b x+c x^2\right)^{3/2}}{3 x}-\frac{1}{2} \sqrt{a} (2 a B+3 A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)",1,"((b^2*B + 18*A*b*c + 8*a*B*c + 2*c*(b*B + 6*A*c)*x)*Sqrt[a + b*x + c*x^2])/(8*c) - ((3*A - B*x)*(a + b*x + c*x^2)^(3/2))/(3*x) - (Sqrt[a]*(3*A*b + 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/2 - ((b^3*B - 6*A*b^2*c - 12*a*b*B*c - 24*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(3/2))","A",7,6,23,0.2609,1,"{812, 814, 843, 621, 206, 724}"
929,1,179,0,0.1665265,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^3,x]","-\frac{3 \left(A \left(4 a c+b^2\right)+4 a b B\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{a}}+\frac{3 \left(4 a B c+4 A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c}}-\frac{(A-B x) \left(a+b x+c x^2\right)^{3/2}}{2 x^2}-\frac{3 \sqrt{a+b x+c x^2} (2 a B-x (2 A c+b B)+A b)}{4 x}","-\frac{3 \left(A \left(4 a c+b^2\right)+4 a b B\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{a}}+\frac{3 \left(4 a B c+4 A b c+b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 \sqrt{c}}-\frac{(A-B x) \left(a+b x+c x^2\right)^{3/2}}{2 x^2}-\frac{3 \sqrt{a+b x+c x^2} (2 a B-x (2 A c+b B)+A b)}{4 x}",1,"(-3*(A*b + 2*a*B - (b*B + 2*A*c)*x)*Sqrt[a + b*x + c*x^2])/(4*x) - ((A - B*x)*(a + b*x + c*x^2)^(3/2))/(2*x^2) - (3*(4*a*b*B + A*(b^2 + 4*a*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[a]) + (3*(b^2*B + 4*A*b*c + 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*Sqrt[c])","A",7,5,23,0.2174,1,"{812, 843, 621, 206, 724}"
930,1,206,0,0.2226764,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^4,x]","-\frac{\left(6 a B \left(4 a c+b^2\right)-A \left(b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{3/2}}+\frac{\sqrt{a+b x+c x^2} \left(2 c x (6 a B+A b)-8 a A c-6 a b B+A b^2\right)}{8 a x}-\frac{\left(a+b x+c x^2\right)^{3/2} (3 x (2 a B+A b)+4 a A)}{12 a x^3}+\frac{1}{2} \sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)","-\frac{\left(6 a B \left(4 a c+b^2\right)-A \left(b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{3/2}}+\frac{\sqrt{a+b x+c x^2} \left(2 c x (6 a B+A b)-8 a A c-6 a b B+A b^2\right)}{8 a x}-\frac{\left(a+b x+c x^2\right)^{3/2} (3 x (2 a B+A b)+4 a A)}{12 a x^3}+\frac{1}{2} \sqrt{c} (2 A c+3 b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)",1,"((A*b^2 - 6*a*b*B - 8*a*A*c + 2*(A*b + 6*a*B)*c*x)*Sqrt[a + b*x + c*x^2])/(8*a*x) - ((4*a*A + 3*(A*b + 2*a*B)*x)*(a + b*x + c*x^2)^(3/2))/(12*a*x^3) - ((6*a*B*(b^2 + 4*a*c) - A*(b^3 - 12*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*a^(3/2)) + (Sqrt[c]*(3*b*B + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/2","A",7,6,23,0.2609,1,"{810, 812, 843, 621, 206, 724}"
931,1,217,0,0.2478308,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^5,x]","-\frac{\sqrt{a+b x+c x^2} \left(x \left(8 a B \left(8 a c+b^2\right)-3 A \left(b^3-4 a b c\right)\right)+2 a \left(8 a b B-3 A \left(b^2-4 a c\right)\right)\right)}{64 a^2 x^2}+\frac{\left(8 a b B \left(b^2-12 a c\right)-3 A \left(b^2-4 a c\right)^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} (x (8 a B+3 A b)+6 a A)}{24 a x^4}+B c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)","-\frac{\sqrt{a+b x+c x^2} \left(x \left(8 a B \left(8 a c+b^2\right)-3 A \left(b^3-4 a b c\right)\right)+2 a \left(8 a b B-3 A \left(b^2-4 a c\right)\right)\right)}{64 a^2 x^2}+\frac{\left(8 a b B \left(b^2-12 a c\right)-3 A \left(b^2-4 a c\right)^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{5/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} (x (8 a B+3 A b)+6 a A)}{24 a x^4}+B c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)",1,"-((2*a*(8*a*b*B - 3*A*(b^2 - 4*a*c)) + (8*a*B*(b^2 + 8*a*c) - 3*A*(b^3 - 4*a*b*c))*x)*Sqrt[a + b*x + c*x^2])/(64*a^2*x^2) - ((6*a*A + (3*A*b + 8*a*B)*x)*(a + b*x + c*x^2)^(3/2))/(24*a*x^4) + ((8*a*b*B*(b^2 - 12*a*c) - 3*A*(b^2 - 4*a*c)^2)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(128*a^(5/2)) + B*c^(3/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",7,5,23,0.2174,1,"{810, 843, 621, 206, 724}"
932,1,170,0,0.0984788,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^6,x]","-\frac{3 \left(b^2-4 a c\right) (2 a+b x) (A b-2 a B) \sqrt{a+b x+c x^2}}{128 a^3 x^2}+\frac{3 \left(b^2-4 a c\right)^2 (A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{7/2}}+\frac{(2 a+b x) (A b-2 a B) \left(a+b x+c x^2\right)^{3/2}}{16 a^2 x^4}-\frac{A \left(a+b x+c x^2\right)^{5/2}}{5 a x^5}","-\frac{3 \left(b^2-4 a c\right) (2 a+b x) (A b-2 a B) \sqrt{a+b x+c x^2}}{128 a^3 x^2}+\frac{3 \left(b^2-4 a c\right)^2 (A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{7/2}}+\frac{(2 a+b x) (A b-2 a B) \left(a+b x+c x^2\right)^{3/2}}{16 a^2 x^4}-\frac{A \left(a+b x+c x^2\right)^{5/2}}{5 a x^5}",1,"(-3*(A*b - 2*a*B)*(b^2 - 4*a*c)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(128*a^3*x^2) + ((A*b - 2*a*B)*(2*a + b*x)*(a + b*x + c*x^2)^(3/2))/(16*a^2*x^4) - (A*(a + b*x + c*x^2)^(5/2))/(5*a*x^5) + (3*(A*b - 2*a*B)*(b^2 - 4*a*c)^2*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(256*a^(7/2))","A",5,4,23,0.1739,1,"{806, 720, 724, 206}"
933,1,230,0,0.2027259,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^7,x]","-\frac{(2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a A c-12 a b B+7 A b^2\right)}{192 a^3 x^4}+\frac{\left(b^2-4 a c\right) (2 a+b x) \sqrt{a+b x+c x^2} \left(-4 a A c-12 a b B+7 A b^2\right)}{512 a^4 x^2}-\frac{\left(b^2-4 a c\right)^2 \left(-4 a A c-12 a b B+7 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{1024 a^{9/2}}+\frac{(7 A b-12 a B) \left(a+b x+c x^2\right)^{5/2}}{60 a^2 x^5}-\frac{A \left(a+b x+c x^2\right)^{5/2}}{6 a x^6}","-\frac{(2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a A c-12 a b B+7 A b^2\right)}{192 a^3 x^4}+\frac{\left(b^2-4 a c\right) (2 a+b x) \sqrt{a+b x+c x^2} \left(-4 a A c-12 a b B+7 A b^2\right)}{512 a^4 x^2}-\frac{\left(b^2-4 a c\right)^2 \left(-4 a A c-12 a b B+7 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{1024 a^{9/2}}+\frac{(7 A b-12 a B) \left(a+b x+c x^2\right)^{5/2}}{60 a^2 x^5}-\frac{A \left(a+b x+c x^2\right)^{5/2}}{6 a x^6}",1,"((b^2 - 4*a*c)*(7*A*b^2 - 12*a*b*B - 4*a*A*c)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(512*a^4*x^2) - ((7*A*b^2 - 12*a*b*B - 4*a*A*c)*(2*a + b*x)*(a + b*x + c*x^2)^(3/2))/(192*a^3*x^4) - (A*(a + b*x + c*x^2)^(5/2))/(6*a*x^6) + ((7*A*b - 12*a*B)*(a + b*x + c*x^2)^(5/2))/(60*a^2*x^5) - ((b^2 - 4*a*c)^2*(7*A*b^2 - 12*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(1024*a^(9/2))","A",6,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
934,1,303,0,0.3858511,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{3/2}}{x^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(3/2))/x^8,x]","-\frac{\left(a+b x+c x^2\right)^{5/2} \left(-48 a A c-98 a b B+63 A b^2\right)}{840 a^3 x^5}+\frac{(2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(8 a^2 B c-12 a A b c-14 a b^2 B+9 A b^3\right)}{384 a^4 x^4}-\frac{\left(b^2-4 a c\right) (2 a+b x) \sqrt{a+b x+c x^2} \left(8 a^2 B c-12 a A b c-14 a b^2 B+9 A b^3\right)}{1024 a^5 x^2}-\frac{\left(b^2-4 a c\right)^2 \left(2 a B \left(7 b^2-4 a c\right)-A \left(9 b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2048 a^{11/2}}+\frac{(9 A b-14 a B) \left(a+b x+c x^2\right)^{5/2}}{84 a^2 x^6}-\frac{A \left(a+b x+c x^2\right)^{5/2}}{7 a x^7}","-\frac{\left(a+b x+c x^2\right)^{5/2} \left(-48 a A c-98 a b B+63 A b^2\right)}{840 a^3 x^5}+\frac{(2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(8 a^2 B c-12 a A b c-14 a b^2 B+9 A b^3\right)}{384 a^4 x^4}-\frac{\left(b^2-4 a c\right) (2 a+b x) \sqrt{a+b x+c x^2} \left(8 a^2 B c-12 a A b c-14 a b^2 B+9 A b^3\right)}{1024 a^5 x^2}-\frac{\left(b^2-4 a c\right)^2 \left(2 a B \left(7 b^2-4 a c\right)-A \left(9 b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2048 a^{11/2}}+\frac{(9 A b-14 a B) \left(a+b x+c x^2\right)^{5/2}}{84 a^2 x^6}-\frac{A \left(a+b x+c x^2\right)^{5/2}}{7 a x^7}",1,"-((b^2 - 4*a*c)*(9*A*b^3 - 14*a*b^2*B - 12*a*A*b*c + 8*a^2*B*c)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(1024*a^5*x^2) + ((9*A*b^3 - 14*a*b^2*B - 12*a*A*b*c + 8*a^2*B*c)*(2*a + b*x)*(a + b*x + c*x^2)^(3/2))/(384*a^4*x^4) - (A*(a + b*x + c*x^2)^(5/2))/(7*a*x^7) + ((9*A*b - 14*a*B)*(a + b*x + c*x^2)^(5/2))/(84*a^2*x^6) - ((63*A*b^2 - 98*a*b*B - 48*a*A*c)*(a + b*x + c*x^2)^(5/2))/(840*a^3*x^5) - ((b^2 - 4*a*c)^2*(2*a*B*(7*b^2 - 4*a*c) - A*(9*b^3 - 12*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2048*a^(11/2))","A",7,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
935,1,543,0,0.7181923,"\int x^4 (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[x^4*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\left(a+b x+c x^2\right)^{7/2} \left(10240 a^2 B c^2-14 c x \left(2376 a A c^2-3380 a b B c-3146 A b^2 c+2145 b^3 B\right)+39688 a A b c^2-42900 a b^2 B c-28314 A b^3 c+19305 b^4 B\right)}{887040 c^5}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right)}{30720 c^6}+\frac{\left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right)}{98304 c^7}-\frac{\left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right)}{262144 c^8}+\frac{\left(b^2-4 a c\right)^3 \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{524288 c^{17/2}}+\frac{x^2 \left(a+b x+c x^2\right)^{7/2} \left(-160 a B c-286 A b c+195 b^2 B\right)}{3960 c^3}-\frac{x^3 \left(a+b x+c x^2\right)^{7/2} (15 b B-22 A c)}{220 c^2}+\frac{B x^4 \left(a+b x+c x^2\right)^{7/2}}{11 c}","\frac{\left(a+b x+c x^2\right)^{7/2} \left(10240 a^2 B c^2-14 c x \left(2376 a A c^2-3380 a b B c-3146 A b^2 c+2145 b^3 B\right)+39688 a A b c^2-42900 a b^2 B c-28314 A b^3 c+19305 b^4 B\right)}{887040 c^5}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right)}{30720 c^6}+\frac{\left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right)}{98304 c^7}-\frac{\left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right)}{262144 c^8}+\frac{\left(b^2-4 a c\right)^3 \left(-96 a^2 A c^3+240 a^2 b B c^2+528 a A b^2 c^2-520 a b^3 B c-286 A b^4 c+195 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{524288 c^{17/2}}+\frac{x^2 \left(a+b x+c x^2\right)^{7/2} \left(-160 a B c-286 A b c+195 b^2 B\right)}{3960 c^3}-\frac{x^3 \left(a+b x+c x^2\right)^{7/2} (15 b B-22 A c)}{220 c^2}+\frac{B x^4 \left(a+b x+c x^2\right)^{7/2}}{11 c}",1,"-((b^2 - 4*a*c)^2*(195*b^5*B - 286*A*b^4*c - 520*a*b^3*B*c + 528*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(262144*c^8) + ((b^2 - 4*a*c)*(195*b^5*B - 286*A*b^4*c - 520*a*b^3*B*c + 528*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(98304*c^7) - ((195*b^5*B - 286*A*b^4*c - 520*a*b^3*B*c + 528*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(30720*c^6) + ((195*b^2*B - 286*A*b*c - 160*a*B*c)*x^2*(a + b*x + c*x^2)^(7/2))/(3960*c^3) - ((15*b*B - 22*A*c)*x^3*(a + b*x + c*x^2)^(7/2))/(220*c^2) + (B*x^4*(a + b*x + c*x^2)^(7/2))/(11*c) + ((19305*b^4*B - 28314*A*b^3*c - 42900*a*b^2*B*c + 39688*a*A*b*c^2 + 10240*a^2*B*c^2 - 14*c*(2145*b^3*B - 3146*A*b^2*c - 3380*a*b*B*c + 2376*a*A*c^2)*x)*(a + b*x + c*x^2)^(7/2))/(887040*c^5) + ((b^2 - 4*a*c)^3*(195*b^5*B - 286*A*b^4*c - 520*a*b^3*B*c + 528*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(524288*c^(17/2))","A",9,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
936,1,432,0,0.485906,"\int x^3 (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[x^3*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right)}{15360 c^5}-\frac{\left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right)}{49152 c^6}+\frac{\left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right)}{131072 c^7}-\frac{\left(b^2-4 a c\right)^3 \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{262144 c^{15/2}}-\frac{\left(a+b x+c x^2\right)^{7/2} \left(-14 c x \left(-108 a B c-220 A b c+143 b^2 B\right)+1280 a A c^2-1804 a b B c-1980 A b^2 c+1287 b^3 B\right)}{40320 c^4}-\frac{x^2 \left(a+b x+c x^2\right)^{7/2} (13 b B-20 A c)}{180 c^2}+\frac{B x^3 \left(a+b x+c x^2\right)^{7/2}}{10 c}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right)}{15360 c^5}-\frac{\left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right)}{49152 c^6}+\frac{\left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right)}{131072 c^7}-\frac{\left(b^2-4 a c\right)^3 \left(48 a^2 B c^2+240 a A b c^2-264 a b^2 B c-220 A b^3 c+143 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{262144 c^{15/2}}-\frac{\left(a+b x+c x^2\right)^{7/2} \left(-14 c x \left(-108 a B c-220 A b c+143 b^2 B\right)+1280 a A c^2-1804 a b B c-1980 A b^2 c+1287 b^3 B\right)}{40320 c^4}-\frac{x^2 \left(a+b x+c x^2\right)^{7/2} (13 b B-20 A c)}{180 c^2}+\frac{B x^3 \left(a+b x+c x^2\right)^{7/2}}{10 c}",1,"((b^2 - 4*a*c)^2*(143*b^4*B - 220*A*b^3*c - 264*a*b^2*B*c + 240*a*A*b*c^2 + 48*a^2*B*c^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(131072*c^7) - ((b^2 - 4*a*c)*(143*b^4*B - 220*A*b^3*c - 264*a*b^2*B*c + 240*a*A*b*c^2 + 48*a^2*B*c^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(49152*c^6) + ((143*b^4*B - 220*A*b^3*c - 264*a*b^2*B*c + 240*a*A*b*c^2 + 48*a^2*B*c^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(15360*c^5) - ((13*b*B - 20*A*c)*x^2*(a + b*x + c*x^2)^(7/2))/(180*c^2) + (B*x^3*(a + b*x + c*x^2)^(7/2))/(10*c) - ((1287*b^3*B - 1980*A*b^2*c - 1804*a*b*B*c + 1280*a*A*c^2 - 14*c*(143*b^2*B - 220*A*b*c - 108*a*B*c)*x)*(a + b*x + c*x^2)^(7/2))/(40320*c^4) - ((b^2 - 4*a*c)^3*(143*b^4*B - 220*A*b^3*c - 264*a*b^2*B*c + 240*a*A*b*c^2 + 48*a^2*B*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(262144*c^(15/2))","A",8,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
937,1,333,0,0.3092552,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[x^2*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{\left(a+b x+c x^2\right)^{7/2} \left(-64 a B c-14 c x (11 b B-18 A c)-162 A b c+99 b^2 B\right)}{2016 c^3}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right)}{768 c^4}+\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right)}{12288 c^5}-\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right)}{32768 c^6}+\frac{5 \left(b^2-4 a c\right)^3 \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{65536 c^{13/2}}+\frac{B x^2 \left(a+b x+c x^2\right)^{7/2}}{9 c}","\frac{\left(a+b x+c x^2\right)^{7/2} \left(-64 a B c-14 c x (11 b B-18 A c)-162 A b c+99 b^2 B\right)}{2016 c^3}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right)}{768 c^4}+\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right)}{12288 c^5}-\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right)}{32768 c^6}+\frac{5 \left(b^2-4 a c\right)^3 \left(8 a A c^2-12 a b B c-18 A b^2 c+11 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{65536 c^{13/2}}+\frac{B x^2 \left(a+b x+c x^2\right)^{7/2}}{9 c}",1,"(-5*(b^2 - 4*a*c)^2*(11*b^3*B - 18*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32768*c^6) + (5*(b^2 - 4*a*c)*(11*b^3*B - 18*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(12288*c^5) - ((11*b^3*B - 18*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(768*c^4) + (B*x^2*(a + b*x + c*x^2)^(7/2))/(9*c) + ((99*b^2*B - 162*A*b*c - 64*a*B*c - 14*c*(11*b*B - 18*A*c)*x)*(a + b*x + c*x^2)^(7/2))/(2016*c^3) + (5*(b^2 - 4*a*c)^3*(11*b^3*B - 18*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(65536*c^(13/2))","A",7,5,23,0.2174,1,"{832, 779, 612, 621, 206}"
938,1,252,0,0.1248237,"\int x (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[x*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 a B c-16 A b c+9 b^2 B\right)}{384 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a B c-16 A b c+9 b^2 B\right)}{6144 c^4}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a B c-16 A b c+9 b^2 B\right)}{16384 c^5}-\frac{5 \left(b^2-4 a c\right)^3 \left(-4 a B c-16 A b c+9 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{11/2}}-\frac{\left(a+b x+c x^2\right)^{7/2} (-16 A c+9 b B-14 B c x)}{112 c^2}","\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 a B c-16 A b c+9 b^2 B\right)}{384 c^3}-\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a B c-16 A b c+9 b^2 B\right)}{6144 c^4}+\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 a B c-16 A b c+9 b^2 B\right)}{16384 c^5}-\frac{5 \left(b^2-4 a c\right)^3 \left(-4 a B c-16 A b c+9 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{32768 c^{11/2}}-\frac{\left(a+b x+c x^2\right)^{7/2} (-16 A c+9 b B-14 B c x)}{112 c^2}",1,"(5*(b^2 - 4*a*c)^2*(9*b^2*B - 16*A*b*c - 4*a*B*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(16384*c^5) - (5*(b^2 - 4*a*c)*(9*b^2*B - 16*A*b*c - 4*a*B*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(6144*c^4) + ((9*b^2*B - 16*A*b*c - 4*a*B*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(384*c^3) - ((9*b*B - 16*A*c - 14*B*c*x)*(a + b*x + c*x^2)^(7/2))/(112*c^2) - (5*(b^2 - 4*a*c)^3*(9*b^2*B - 16*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(32768*c^(11/2))","A",6,4,21,0.1905,1,"{779, 612, 621, 206}"
939,1,203,0,0.095175,"\int (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}-\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (b B-2 A c)}{1024 c^4}+\frac{5 \left(b^2-4 a c\right)^3 (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{9/2}}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} (b B-2 A c)}{24 c^2}+\frac{B \left(a+b x+c x^2\right)^{7/2}}{7 c}","\frac{5 \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}-\frac{5 \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (b B-2 A c)}{1024 c^4}+\frac{5 \left(b^2-4 a c\right)^3 (b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2048 c^{9/2}}-\frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2} (b B-2 A c)}{24 c^2}+\frac{B \left(a+b x+c x^2\right)^{7/2}}{7 c}",1,"(-5*(b^2 - 4*a*c)^2*(b*B - 2*A*c)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(1024*c^4) + (5*(b^2 - 4*a*c)*(b*B - 2*A*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(384*c^3) - ((b*B - 2*A*c)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(24*c^2) + (B*(a + b*x + c*x^2)^(7/2))/(7*c) + (5*(b^2 - 4*a*c)^3*(b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2048*c^(9/2))","A",6,4,20,0.2000,1,"{640, 612, 621, 206}"
940,1,350,0,0.4195114,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x,x]","\frac{\sqrt{a+b x+c x^2} \left(512 a^2 A c^3+2 c x \left(\left(b^2-4 a c\right) \left(-20 a B c-12 A b c+5 b^2 B\right)+64 a A b c^2\right)+b \left(b^2-4 a c\right) \left(-20 a B c-12 A b c+5 b^2 B\right)+64 a A b^2 c^2\right)}{512 c^3}+\frac{\left(512 a^2 A b c^3-\left(b^2-4 a c\right) \left(80 a^2 B c^2+112 a A b c^2-40 a b^2 B c-12 A b^3 c+5 b^4 B\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{7/2}}+a^{5/2} (-A) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)-\frac{\left(a+b x+c x^2\right)^{3/2} \left(2 c x \left(-20 a B c-12 A b c+5 b^2 B\right)-64 a A c^2-20 a b B c-12 A b^2 c+5 b^3 B\right)}{192 c^2}+\frac{\left(a+b x+c x^2\right)^{5/2} (12 A c+5 b B+10 B c x)}{60 c}","\frac{\sqrt{a+b x+c x^2} \left(512 a^2 A c^3+2 c x \left(\left(b^2-4 a c\right) \left(-20 a B c-12 A b c+5 b^2 B\right)+64 a A b c^2\right)+b \left(\left(b^2-4 a c\right) \left(-20 a B c-12 A b c+5 b^2 B\right)+64 a A b c^2\right)\right)}{512 c^3}+\frac{\left(512 a^2 A b c^3-\left(b^2-4 a c\right) \left(80 a^2 B c^2+112 a A b c^2-40 a b^2 B c-12 A b^3 c+5 b^4 B\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{1024 c^{7/2}}+a^{5/2} (-A) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)-\frac{\left(a+b x+c x^2\right)^{3/2} \left(2 c x \left(-20 a B c-12 A b c+5 b^2 B\right)-64 a A c^2-20 a b B c-12 A b^2 c+5 b^3 B\right)}{192 c^2}+\frac{\left(a+b x+c x^2\right)^{5/2} (12 A c+5 b B+10 B c x)}{60 c}",1,"((64*a*A*b^2*c^2 + 512*a^2*A*c^3 + b*(b^2 - 4*a*c)*(5*b^2*B - 12*A*b*c - 20*a*B*c) + 2*c*(64*a*A*b*c^2 + (b^2 - 4*a*c)*(5*b^2*B - 12*A*b*c - 20*a*B*c))*x)*Sqrt[a + b*x + c*x^2])/(512*c^3) - ((5*b^3*B - 12*A*b^2*c - 20*a*b*B*c - 64*a*A*c^2 + 2*c*(5*b^2*B - 12*A*b*c - 20*a*B*c)*x)*(a + b*x + c*x^2)^(3/2))/(192*c^2) + ((5*b*B + 12*A*c + 10*B*c*x)*(a + b*x + c*x^2)^(5/2))/(60*c) - a^(5/2)*A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])] + ((512*a^2*A*b*c^3 - (b^2 - 4*a*c)*(5*b^4*B - 12*A*b^3*c - 40*a*b^2*B*c + 112*a*A*b*c^2 + 80*a^2*B*c^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(1024*c^(7/2))","A",8,5,23,0.2174,1,"{814, 843, 621, 206, 724}"
941,1,310,0,0.3127598,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^2,x]","-\frac{\sqrt{a+b x+c x^2} \left(-128 a^2 B c^2+2 c x \left(-120 a A c^2-28 a b B c-10 A b^2 c+3 b^3 B\right)-440 a A b c^2-28 a b^2 B c-10 A b^3 c+3 b^4 B\right)}{128 c^2}+\frac{\left(480 a^2 A c^3+240 a^2 b B c^2+240 a A b^2 c^2-40 a b^3 B c-10 A b^4 c+3 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{5/2}}-\frac{1}{2} a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)+\frac{\left(a+b x+c x^2\right)^{3/2} \left(16 a B c+6 c x (10 A c+b B)+70 A b c+3 b^2 B\right)}{48 c}-\frac{(5 A-B x) \left(a+b x+c x^2\right)^{5/2}}{5 x}","-\frac{\sqrt{a+b x+c x^2} \left(-128 a^2 B c^2+2 c x \left(-120 a A c^2-28 a b B c-10 A b^2 c+3 b^3 B\right)-440 a A b c^2-28 a b^2 B c-10 A b^3 c+3 b^4 B\right)}{128 c^2}+\frac{\left(480 a^2 A c^3+240 a^2 b B c^2+240 a A b^2 c^2-40 a b^3 B c-10 A b^4 c+3 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{5/2}}-\frac{1}{2} a^{3/2} (2 a B+5 A b) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)+\frac{\left(a+b x+c x^2\right)^{3/2} \left(16 a B c+6 c x (10 A c+b B)+70 A b c+3 b^2 B\right)}{48 c}-\frac{(5 A-B x) \left(a+b x+c x^2\right)^{5/2}}{5 x}",1,"-((3*b^4*B - 10*A*b^3*c - 28*a*b^2*B*c - 440*a*A*b*c^2 - 128*a^2*B*c^2 + 2*c*(3*b^3*B - 10*A*b^2*c - 28*a*b*B*c - 120*a*A*c^2)*x)*Sqrt[a + b*x + c*x^2])/(128*c^2) + ((3*b^2*B + 70*A*b*c + 16*a*B*c + 6*c*(b*B + 10*A*c)*x)*(a + b*x + c*x^2)^(3/2))/(48*c) - ((5*A - B*x)*(a + b*x + c*x^2)^(5/2))/(5*x) - (a^(3/2)*(5*A*b + 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/2 + ((3*b^5*B - 10*A*b^4*c - 40*a*b^3*B*c + 240*a*A*b^2*c^2 + 240*a^2*b*B*c^2 + 480*a^2*A*c^3)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(5/2))","A",8,6,23,0.2609,1,"{812, 814, 843, 621, 206, 724}"
942,1,273,0,0.2589426,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^3,x]","-\frac{5 \left(-48 a^2 B c^2-96 a A b c^2-24 a b^2 B c-8 A b^3 c+b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{3/2}}+\frac{5 \sqrt{a+b x+c x^2} \left(2 c x \left(12 a B c+16 A b c+b^2 B\right)+32 a A c^2+44 a b B c+40 A b^2 c+b^3 B\right)}{64 c}-\frac{5}{8} \sqrt{a} \left(4 a A c+4 a b B+3 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)-\frac{(2 A-B x) \left(a+b x+c x^2\right)^{5/2}}{4 x^2}-\frac{5 \left(a+b x+c x^2\right)^{3/2} (6 (a B+A b)-x (4 A c+b B))}{24 x}","-\frac{5 \left(-48 a^2 B c^2-96 a A b c^2-24 a b^2 B c-8 A b^3 c+b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{3/2}}+\frac{5 \sqrt{a+b x+c x^2} \left(2 c x \left(12 a B c+16 A b c+b^2 B\right)+32 a A c^2+44 a b B c+40 A b^2 c+b^3 B\right)}{64 c}-\frac{5}{8} \sqrt{a} \left(4 a A c+4 a b B+3 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)-\frac{(2 A-B x) \left(a+b x+c x^2\right)^{5/2}}{4 x^2}-\frac{5 \left(a+b x+c x^2\right)^{3/2} (6 (a B+A b)-x (4 A c+b B))}{24 x}",1,"(5*(b^3*B + 40*A*b^2*c + 44*a*b*B*c + 32*a*A*c^2 + 2*c*(b^2*B + 16*A*b*c + 12*a*B*c)*x)*Sqrt[a + b*x + c*x^2])/(64*c) - (5*(6*(A*b + a*B) - (b*B + 4*A*c)*x)*(a + b*x + c*x^2)^(3/2))/(24*x) - ((2*A - B*x)*(a + b*x + c*x^2)^(5/2))/(4*x^2) - (5*Sqrt[a]*(3*A*b^2 + 4*a*b*B + 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/8 - (5*(b^4*B - 8*A*b^3*c - 24*a*b^2*B*c - 96*a*A*b*c^2 - 48*a^2*B*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(3/2))","A",8,6,23,0.2609,1,"{812, 814, 843, 621, 206, 724}"
943,1,255,0,0.3216554,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^4,x]","\frac{5 \left(8 a A c^2+12 a b B c+6 A b^2 c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 \sqrt{c}}-\frac{5 \sqrt{a+b x+c x^2} \left(-x \left(4 a B c+4 A b c+b^2 B\right)+A \left(4 a c+b^2\right)+4 a b B\right)}{8 x}-\frac{5 \left(A \left(12 a b c+b^3\right)+2 a B \left(4 a c+3 b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 \sqrt{a}}-\frac{(A-B x) \left(a+b x+c x^2\right)^{5/2}}{3 x^3}-\frac{5 \left(a+b x+c x^2\right)^{3/2} (2 a B-x (2 A c+b B)+A b)}{12 x^2}","\frac{5 \left(8 a A c^2+12 a b B c+6 A b^2 c+b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 \sqrt{c}}-\frac{5 \sqrt{a+b x+c x^2} \left(-x \left(4 a B c+4 A b c+b^2 B\right)+A \left(4 a c+b^2\right)+4 a b B\right)}{8 x}-\frac{5 \left(A \left(12 a b c+b^3\right)+2 a B \left(4 a c+3 b^2\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 \sqrt{a}}-\frac{(A-B x) \left(a+b x+c x^2\right)^{5/2}}{3 x^3}-\frac{5 \left(a+b x+c x^2\right)^{3/2} (2 a B-x (2 A c+b B)+A b)}{12 x^2}",1,"(-5*(4*a*b*B + A*(b^2 + 4*a*c) - (b^2*B + 4*A*b*c + 4*a*B*c)*x)*Sqrt[a + b*x + c*x^2])/(8*x) - (5*(A*b + 2*a*B - (b*B + 2*A*c)*x)*(a + b*x + c*x^2)^(3/2))/(12*x^2) - ((A - B*x)*(a + b*x + c*x^2)^(5/2))/(3*x^3) - (5*(2*a*B*(3*b^2 + 4*a*c) + A*(b^3 + 12*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*Sqrt[a]) + (5*(b^3*B + 6*A*b^2*c + 12*a*b*B*c + 8*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*Sqrt[c])","A",8,5,23,0.2174,1,"{812, 843, 621, 206, 724}"
944,1,284,0,0.3864301,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^5,x]","-\frac{5 \left(8 a b B \left(12 a c+b^2\right)-A \left(-48 a^2 c^2-24 a b^2 c+b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{3/2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(3 x \left(A \left(4 a c+b^2\right)+8 a b B\right)+4 a (4 a B+A b)\right)}{96 a x^3}-\frac{5 \sqrt{a+b x+c x^2} \left(-2 c x \left(A \left(12 a c+b^2\right)+16 a b B\right)-A \left(b^3-20 a b c\right)+8 a B \left(4 a c+b^2\right)\right)}{64 a x}+\frac{5}{8} \sqrt{c} \left(4 a B c+4 A b c+3 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{(A-2 B x) \left(a+b x+c x^2\right)^{5/2}}{4 x^4}","-\frac{5 \left(8 a b B \left(12 a c+b^2\right)-A \left(-48 a^2 c^2-24 a b^2 c+b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{3/2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(3 x \left(A \left(4 a c+b^2\right)+8 a b B\right)+4 a (4 a B+A b)\right)}{96 a x^3}-\frac{5 \sqrt{a+b x+c x^2} \left(-2 c x \left(A \left(12 a c+b^2\right)+16 a b B\right)-A \left(b^3-20 a b c\right)+8 a B \left(4 a c+b^2\right)\right)}{64 a x}+\frac{5}{8} \sqrt{c} \left(4 a B c+4 A b c+3 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{(A-2 B x) \left(a+b x+c x^2\right)^{5/2}}{4 x^4}",1,"(-5*(8*a*B*(b^2 + 4*a*c) - A*(b^3 - 20*a*b*c) - 2*c*(16*a*b*B + A*(b^2 + 12*a*c))*x)*Sqrt[a + b*x + c*x^2])/(64*a*x) - (5*(4*a*(A*b + 4*a*B) + 3*(8*a*b*B + A*(b^2 + 4*a*c))*x)*(a + b*x + c*x^2)^(3/2))/(96*a*x^3) - ((A - 2*B*x)*(a + b*x + c*x^2)^(5/2))/(4*x^4) - (5*(8*a*b*B*(b^2 + 12*a*c) - A*(b^4 - 24*a*b^2*c - 48*a^2*c^2))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(128*a^(3/2)) + (5*Sqrt[c]*(3*b^2*B + 4*A*b*c + 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/8","A",8,6,23,0.2609,1,"{812, 810, 843, 621, 206, 724}"
945,1,346,0,0.4913844,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^6,x]","\frac{\sqrt{a+b x+c x^2} \left(-A \left(128 a^2 c^2-28 a b^2 c+3 b^4\right)+2 c x \left(10 a B \left(12 a c+b^2\right)-A \left(3 b^3-28 a b c\right)\right)+10 a b B \left(b^2-20 a c\right)\right)}{128 a^2 x}+\frac{\left(10 a B \left(-48 a^2 c^2-24 a b^2 c+b^4\right)-A \left(240 a^2 b c^2-40 a b^3 c+3 b^5\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(4 a \left(-16 a A c-10 a b B+3 A b^2\right)-3 x \left(10 a B \left(4 a c+b^2\right)-A \left(3 b^3-20 a b c\right)\right)\right)}{192 a^2 x^3}+\frac{1}{2} c^{3/2} (2 A c+5 b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{\left(a+b x+c x^2\right)^{5/2} (5 x (2 a B+A b)+8 a A)}{40 a x^5}","\frac{\sqrt{a+b x+c x^2} \left(-A \left(128 a^2 c^2-28 a b^2 c+3 b^4\right)+2 c x \left(10 a B \left(12 a c+b^2\right)-A \left(3 b^3-28 a b c\right)\right)+10 a b B \left(b^2-20 a c\right)\right)}{128 a^2 x}+\frac{\left(10 a B \left(-48 a^2 c^2-24 a b^2 c+b^4\right)-A \left(240 a^2 b c^2-40 a b^3 c+3 b^5\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(4 a \left(-16 a A c-10 a b B+3 A b^2\right)-3 x \left(10 a B \left(4 a c+b^2\right)-A \left(3 b^3-20 a b c\right)\right)\right)}{192 a^2 x^3}+\frac{1}{2} c^{3/2} (2 A c+5 b B) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)-\frac{\left(a+b x+c x^2\right)^{5/2} (5 x (2 a B+A b)+8 a A)}{40 a x^5}",1,"((10*a*b*B*(b^2 - 20*a*c) - A*(3*b^4 - 28*a*b^2*c + 128*a^2*c^2) + 2*c*(10*a*B*(b^2 + 12*a*c) - A*(3*b^3 - 28*a*b*c))*x)*Sqrt[a + b*x + c*x^2])/(128*a^2*x) + ((4*a*(3*A*b^2 - 10*a*b*B - 16*a*A*c) - 3*(10*a*B*(b^2 + 4*a*c) - A*(3*b^3 - 20*a*b*c))*x)*(a + b*x + c*x^2)^(3/2))/(192*a^2*x^3) - ((8*a*A + 5*(A*b + 2*a*B)*x)*(a + b*x + c*x^2)^(5/2))/(40*a*x^5) + ((10*a*B*(b^4 - 24*a*b^2*c - 48*a^2*c^2) - A*(3*b^5 - 40*a*b^3*c + 240*a^2*b*c^2))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(256*a^(5/2)) + (c^(3/2)*(5*b*B + 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/2","A",8,6,23,0.2609,1,"{810, 812, 843, 621, 206, 724}"
946,1,332,0,0.4661066,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^7,x]","\frac{\sqrt{a+b x+c x^2} \left(2 a \left(4 a b B \left(3 b^2-28 a c\right)-5 A \left(b^2-4 a c\right)^2\right)-x \left(5 A b \left(b^2-4 a c\right)^2-4 a B \left(-128 a^2 c^2-28 a b^2 c+3 b^4\right)\right)\right)}{512 a^3 x^2}+\frac{\left(5 A \left(b^2-4 a c\right)^3-4 a b B \left(240 a^2 c^2-40 a b^2 c+3 b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{1024 a^{7/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(x \left(4 a B \left(16 a c+3 b^2\right)-5 A \left(b^3-4 a b c\right)\right)+2 a \left(12 a b B-5 A \left(b^2-4 a c\right)\right)\right)}{192 a^2 x^4}-\frac{\left(a+b x+c x^2\right)^{5/2} (x (12 a B+5 A b)+10 a A)}{60 a x^6}+B c^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)","\frac{\sqrt{a+b x+c x^2} \left(2 a \left(4 a b B \left(3 b^2-28 a c\right)-5 A \left(b^2-4 a c\right)^2\right)-x \left(5 A b \left(b^2-4 a c\right)^2-4 a B \left(-128 a^2 c^2-28 a b^2 c+3 b^4\right)\right)\right)}{512 a^3 x^2}+\frac{\left(5 A \left(b^2-4 a c\right)^3-4 a b B \left(240 a^2 c^2-40 a b^2 c+3 b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{1024 a^{7/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(x \left(4 a B \left(16 a c+3 b^2\right)-5 A \left(b^3-4 a b c\right)\right)+2 a \left(12 a b B-5 A \left(b^2-4 a c\right)\right)\right)}{192 a^2 x^4}-\frac{\left(a+b x+c x^2\right)^{5/2} (x (12 a B+5 A b)+10 a A)}{60 a x^6}+B c^{5/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)",1,"((2*a*(4*a*b*B*(3*b^2 - 28*a*c) - 5*A*(b^2 - 4*a*c)^2) - (5*A*b*(b^2 - 4*a*c)^2 - 4*a*B*(3*b^4 - 28*a*b^2*c - 128*a^2*c^2))*x)*Sqrt[a + b*x + c*x^2])/(512*a^3*x^2) - ((2*a*(12*a*b*B - 5*A*(b^2 - 4*a*c)) + (4*a*B*(3*b^2 + 16*a*c) - 5*A*(b^3 - 4*a*b*c))*x)*(a + b*x + c*x^2)^(3/2))/(192*a^2*x^4) - ((10*a*A + (5*A*b + 12*a*B)*x)*(a + b*x + c*x^2)^(5/2))/(60*a*x^6) + ((5*A*(b^2 - 4*a*c)^3 - 4*a*b*B*(3*b^4 - 40*a*b^2*c + 240*a^2*c^2))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(1024*a^(7/2)) + B*c^(5/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])]","A",8,5,23,0.2174,1,"{810, 843, 621, 206, 724}"
947,1,219,0,0.1343618,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^8,x]","-\frac{5 \left(b^2-4 a c\right) (2 a+b x) (A b-2 a B) \left(a+b x+c x^2\right)^{3/2}}{384 a^3 x^4}+\frac{5 \left(b^2-4 a c\right)^2 (2 a+b x) (A b-2 a B) \sqrt{a+b x+c x^2}}{1024 a^4 x^2}-\frac{5 \left(b^2-4 a c\right)^3 (A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2048 a^{9/2}}+\frac{(2 a+b x) (A b-2 a B) \left(a+b x+c x^2\right)^{5/2}}{24 a^2 x^6}-\frac{A \left(a+b x+c x^2\right)^{7/2}}{7 a x^7}","-\frac{5 \left(b^2-4 a c\right) (2 a+b x) (A b-2 a B) \left(a+b x+c x^2\right)^{3/2}}{384 a^3 x^4}+\frac{5 \left(b^2-4 a c\right)^2 (2 a+b x) (A b-2 a B) \sqrt{a+b x+c x^2}}{1024 a^4 x^2}-\frac{5 \left(b^2-4 a c\right)^3 (A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2048 a^{9/2}}+\frac{(2 a+b x) (A b-2 a B) \left(a+b x+c x^2\right)^{5/2}}{24 a^2 x^6}-\frac{A \left(a+b x+c x^2\right)^{7/2}}{7 a x^7}",1,"(5*(A*b - 2*a*B)*(b^2 - 4*a*c)^2*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(1024*a^4*x^2) - (5*(A*b - 2*a*B)*(b^2 - 4*a*c)*(2*a + b*x)*(a + b*x + c*x^2)^(3/2))/(384*a^3*x^4) + ((A*b - 2*a*B)*(2*a + b*x)*(a + b*x + c*x^2)^(5/2))/(24*a^2*x^6) - (A*(a + b*x + c*x^2)^(7/2))/(7*a*x^7) - (5*(A*b - 2*a*B)*(b^2 - 4*a*c)^3*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2048*a^(9/2))","A",6,4,23,0.1739,1,"{806, 720, 724, 206}"
948,1,288,0,0.2472709,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^9} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^9,x]","-\frac{(2 a+b x) \left(a+b x+c x^2\right)^{5/2} \left(-4 a A c-16 a b B+9 A b^2\right)}{384 a^3 x^6}+\frac{5 \left(b^2-4 a c\right) (2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a A c-16 a b B+9 A b^2\right)}{6144 a^4 x^4}-\frac{5 \left(b^2-4 a c\right)^2 (2 a+b x) \sqrt{a+b x+c x^2} \left(-4 a A c-16 a b B+9 A b^2\right)}{16384 a^5 x^2}+\frac{5 \left(b^2-4 a c\right)^3 \left(-4 a A c-16 a b B+9 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{32768 a^{11/2}}+\frac{(9 A b-16 a B) \left(a+b x+c x^2\right)^{7/2}}{112 a^2 x^7}-\frac{A \left(a+b x+c x^2\right)^{7/2}}{8 a x^8}","-\frac{(2 a+b x) \left(a+b x+c x^2\right)^{5/2} \left(-4 a A c-16 a b B+9 A b^2\right)}{384 a^3 x^6}+\frac{5 \left(b^2-4 a c\right) (2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(-4 a A c-16 a b B+9 A b^2\right)}{6144 a^4 x^4}-\frac{5 \left(b^2-4 a c\right)^2 (2 a+b x) \sqrt{a+b x+c x^2} \left(-4 a A c-16 a b B+9 A b^2\right)}{16384 a^5 x^2}+\frac{5 \left(b^2-4 a c\right)^3 \left(-4 a A c-16 a b B+9 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{32768 a^{11/2}}+\frac{(9 A b-16 a B) \left(a+b x+c x^2\right)^{7/2}}{112 a^2 x^7}-\frac{A \left(a+b x+c x^2\right)^{7/2}}{8 a x^8}",1,"(-5*(b^2 - 4*a*c)^2*(9*A*b^2 - 16*a*b*B - 4*a*A*c)*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(16384*a^5*x^2) + (5*(b^2 - 4*a*c)*(9*A*b^2 - 16*a*b*B - 4*a*A*c)*(2*a + b*x)*(a + b*x + c*x^2)^(3/2))/(6144*a^4*x^4) - ((9*A*b^2 - 16*a*b*B - 4*a*A*c)*(2*a + b*x)*(a + b*x + c*x^2)^(5/2))/(384*a^3*x^6) - (A*(a + b*x + c*x^2)^(7/2))/(8*a*x^8) + ((9*A*b - 16*a*B)*(a + b*x + c*x^2)^(7/2))/(112*a^2*x^7) + (5*(b^2 - 4*a*c)^3*(9*A*b^2 - 16*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(32768*a^(11/2))","A",7,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
949,1,375,0,0.4776553,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^{5/2}}{x^{10}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^(5/2))/x^10,x]","-\frac{\left(a+b x+c x^2\right)^{7/2} \left(-64 a A c-162 a b B+99 A b^2\right)}{2016 a^3 x^7}+\frac{(2 a+b x) \left(a+b x+c x^2\right)^{5/2} \left(8 a^2 B c-12 a A b c-18 a b^2 B+11 A b^3\right)}{768 a^4 x^6}+\frac{5 \left(b^2-4 a c\right) (2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(2 a B \left(9 b^2-4 a c\right)-A \left(11 b^3-12 a b c\right)\right)}{12288 a^5 x^4}-\frac{5 \left(b^2-4 a c\right)^2 (2 a+b x) \sqrt{a+b x+c x^2} \left(2 a B \left(9 b^2-4 a c\right)-A \left(11 b^3-12 a b c\right)\right)}{32768 a^6 x^2}+\frac{5 \left(b^2-4 a c\right)^3 \left(2 a B \left(9 b^2-4 a c\right)-A \left(11 b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{65536 a^{13/2}}+\frac{(11 A b-18 a B) \left(a+b x+c x^2\right)^{7/2}}{144 a^2 x^8}-\frac{A \left(a+b x+c x^2\right)^{7/2}}{9 a x^9}","-\frac{\left(a+b x+c x^2\right)^{7/2} \left(-64 a A c-162 a b B+99 A b^2\right)}{2016 a^3 x^7}+\frac{(2 a+b x) \left(a+b x+c x^2\right)^{5/2} \left(8 a^2 B c-12 a A b c-18 a b^2 B+11 A b^3\right)}{768 a^4 x^6}+\frac{5 \left(b^2-4 a c\right) (2 a+b x) \left(a+b x+c x^2\right)^{3/2} \left(2 a B \left(9 b^2-4 a c\right)-A \left(11 b^3-12 a b c\right)\right)}{12288 a^5 x^4}-\frac{5 \left(b^2-4 a c\right)^2 (2 a+b x) \sqrt{a+b x+c x^2} \left(2 a B \left(9 b^2-4 a c\right)-A \left(11 b^3-12 a b c\right)\right)}{32768 a^6 x^2}+\frac{5 \left(b^2-4 a c\right)^3 \left(2 a B \left(9 b^2-4 a c\right)-A \left(11 b^3-12 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{65536 a^{13/2}}+\frac{(11 A b-18 a B) \left(a+b x+c x^2\right)^{7/2}}{144 a^2 x^8}-\frac{A \left(a+b x+c x^2\right)^{7/2}}{9 a x^9}",1,"(-5*(b^2 - 4*a*c)^2*(2*a*B*(9*b^2 - 4*a*c) - A*(11*b^3 - 12*a*b*c))*(2*a + b*x)*Sqrt[a + b*x + c*x^2])/(32768*a^6*x^2) + (5*(b^2 - 4*a*c)*(2*a*B*(9*b^2 - 4*a*c) - A*(11*b^3 - 12*a*b*c))*(2*a + b*x)*(a + b*x + c*x^2)^(3/2))/(12288*a^5*x^4) + ((11*A*b^3 - 18*a*b^2*B - 12*a*A*b*c + 8*a^2*B*c)*(2*a + b*x)*(a + b*x + c*x^2)^(5/2))/(768*a^4*x^6) - (A*(a + b*x + c*x^2)^(7/2))/(9*a*x^9) + ((11*A*b - 18*a*B)*(a + b*x + c*x^2)^(7/2))/(144*a^2*x^8) - ((99*A*b^2 - 162*a*b*B - 64*a*A*c)*(a + b*x + c*x^2)^(7/2))/(2016*a^3*x^7) + (5*(b^2 - 4*a*c)^3*(2*a*B*(9*b^2 - 4*a*c) - A*(11*b^3 - 12*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(65536*a^(13/2))","A",8,5,23,0.2174,1,"{834, 806, 720, 724, 206}"
950,1,281,0,0.4216436,"\int \frac{x^4 (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Int[(x^4*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(1024 a^2 B c^2-2 c x \left(360 a A c^2-644 a b B c-350 A b^2 c+315 b^3 B\right)+2200 a A b c^2-2940 a b^2 B c-1050 A b^3 c+945 b^4 B\right)}{1920 c^5}-\frac{\left(-96 a^2 A c^3+240 a^2 b B c^2+240 a A b^2 c^2-280 a b^3 B c-70 A b^4 c+63 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{11/2}}+\frac{x^2 \sqrt{a+b x+c x^2} \left(-64 a B c-70 A b c+63 b^2 B\right)}{240 c^3}-\frac{x^3 \sqrt{a+b x+c x^2} (9 b B-10 A c)}{40 c^2}+\frac{B x^4 \sqrt{a+b x+c x^2}}{5 c}","\frac{\sqrt{a+b x+c x^2} \left(1024 a^2 B c^2-2 c x \left(360 a A c^2-644 a b B c-350 A b^2 c+315 b^3 B\right)+2200 a A b c^2-2940 a b^2 B c-1050 A b^3 c+945 b^4 B\right)}{1920 c^5}-\frac{\left(-96 a^2 A c^3+240 a^2 b B c^2+240 a A b^2 c^2-280 a b^3 B c-70 A b^4 c+63 b^5 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{11/2}}+\frac{x^2 \sqrt{a+b x+c x^2} \left(-64 a B c-70 A b c+63 b^2 B\right)}{240 c^3}-\frac{x^3 \sqrt{a+b x+c x^2} (9 b B-10 A c)}{40 c^2}+\frac{B x^4 \sqrt{a+b x+c x^2}}{5 c}",1,"((63*b^2*B - 70*A*b*c - 64*a*B*c)*x^2*Sqrt[a + b*x + c*x^2])/(240*c^3) - ((9*b*B - 10*A*c)*x^3*Sqrt[a + b*x + c*x^2])/(40*c^2) + (B*x^4*Sqrt[a + b*x + c*x^2])/(5*c) + ((945*b^4*B - 1050*A*b^3*c - 2940*a*b^2*B*c + 2200*a*A*b*c^2 + 1024*a^2*B*c^2 - 2*c*(315*b^3*B - 350*A*b^2*c - 644*a*b*B*c + 360*a*A*c^2)*x)*Sqrt[a + b*x + c*x^2])/(1920*c^5) - ((63*b^5*B - 70*A*b^4*c - 280*a*b^3*B*c + 240*a*A*b^2*c^2 + 240*a^2*b*B*c^2 - 96*a^2*A*c^3)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(11/2))","A",6,4,23,0.1739,1,"{832, 779, 621, 206}"
951,1,206,0,0.2431673,"\int \frac{x^3 (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Int[(x^3*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\left(48 a^2 B c^2+96 a A b c^2-120 a b^2 B c-40 A b^3 c+35 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{9/2}}-\frac{\sqrt{a+b x+c x^2} \left(-2 c x \left(-36 a B c-40 A b c+35 b^2 B\right)+128 a A c^2-220 a b B c-120 A b^2 c+105 b^3 B\right)}{192 c^4}-\frac{x^2 \sqrt{a+b x+c x^2} (7 b B-8 A c)}{24 c^2}+\frac{B x^3 \sqrt{a+b x+c x^2}}{4 c}","\frac{\left(48 a^2 B c^2+96 a A b c^2-120 a b^2 B c-40 A b^3 c+35 b^4 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{128 c^{9/2}}-\frac{\sqrt{a+b x+c x^2} \left(-2 c x \left(-36 a B c-40 A b c+35 b^2 B\right)+128 a A c^2-220 a b B c-120 A b^2 c+105 b^3 B\right)}{192 c^4}-\frac{x^2 \sqrt{a+b x+c x^2} (7 b B-8 A c)}{24 c^2}+\frac{B x^3 \sqrt{a+b x+c x^2}}{4 c}",1,"-((7*b*B - 8*A*c)*x^2*Sqrt[a + b*x + c*x^2])/(24*c^2) + (B*x^3*Sqrt[a + b*x + c*x^2])/(4*c) - ((105*b^3*B - 120*A*b^2*c - 220*a*b*B*c + 128*a*A*c^2 - 2*c*(35*b^2*B - 40*A*b*c - 36*a*B*c)*x)*Sqrt[a + b*x + c*x^2])/(192*c^4) + ((35*b^4*B - 40*A*b^3*c - 120*a*b^2*B*c + 96*a*A*b*c^2 + 48*a^2*B*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(9/2))","A",5,4,23,0.1739,1,"{832, 779, 621, 206}"
952,1,143,0,0.1200677,"\int \frac{x^2 (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Int[(x^2*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(-16 a B c-2 c x (5 b B-6 A c)-18 A b c+15 b^2 B\right)}{24 c^3}-\frac{\left(8 a A c^2-12 a b B c-6 A b^2 c+5 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{7/2}}+\frac{B x^2 \sqrt{a+b x+c x^2}}{3 c}","\frac{\sqrt{a+b x+c x^2} \left(-16 a B c-2 c x (5 b B-6 A c)-18 A b c+15 b^2 B\right)}{24 c^3}-\frac{\left(8 a A c^2-12 a b B c-6 A b^2 c+5 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{7/2}}+\frac{B x^2 \sqrt{a+b x+c x^2}}{3 c}",1,"(B*x^2*Sqrt[a + b*x + c*x^2])/(3*c) + ((15*b^2*B - 18*A*b*c - 16*a*B*c - 2*c*(5*b*B - 6*A*c)*x)*Sqrt[a + b*x + c*x^2])/(24*c^3) - ((5*b^3*B - 6*A*b^2*c - 12*a*b*B*c + 8*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(7/2))","A",4,4,23,0.1739,1,"{832, 779, 621, 206}"
953,1,92,0,0.0396828,"\int \frac{x (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Int[(x*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\left(-4 a B c-4 A b c+3 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{5/2}}-\frac{\sqrt{a+b x+c x^2} (-4 A c+3 b B-2 B c x)}{4 c^2}","\frac{\left(-4 a B c-4 A b c+3 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{5/2}}-\frac{\sqrt{a+b x+c x^2} (-4 A c+3 b B-2 B c x)}{4 c^2}",1,"-((3*b*B - 4*A*c - 2*B*c*x)*Sqrt[a + b*x + c*x^2])/(4*c^2) + ((3*b^2*B - 4*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",3,3,21,0.1429,1,"{779, 621, 206}"
954,1,67,0,0.0239877,"\int \frac{A+B x}{\sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/Sqrt[a + b*x + c*x^2],x]","\frac{B \sqrt{a+b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2}}","\frac{B \sqrt{a+b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2}}",1,"(B*Sqrt[a + b*x + c*x^2])/c - ((b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2))","A",3,3,20,0.1500,1,"{640, 621, 206}"
955,1,77,0,0.0475331,"\int \frac{A+B x}{x \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(x*Sqrt[a + b*x + c*x^2]),x]","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a}}","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{\sqrt{a}}",1,"-((A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/Sqrt[a]) + (B*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/Sqrt[c]","A",5,4,23,0.1739,1,"{843, 621, 206, 724}"
956,1,72,0,0.0388087,"\int \frac{A+B x}{x^2 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(x^2*Sqrt[a + b*x + c*x^2]),x]","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+b x+c x^2}}{a x}","\frac{(A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{3/2}}-\frac{A \sqrt{a+b x+c x^2}}{a x}",1,"-((A*Sqrt[a + b*x + c*x^2])/(a*x)) + ((A*b - 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*a^(3/2))","A",3,3,23,0.1304,1,"{806, 724, 206}"
957,1,116,0,0.0893283,"\int \frac{A+B x}{x^3 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(x^3*Sqrt[a + b*x + c*x^2]),x]","-\frac{\left(-4 a A c-4 a b B+3 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{5/2}}+\frac{(3 A b-4 a B) \sqrt{a+b x+c x^2}}{4 a^2 x}-\frac{A \sqrt{a+b x+c x^2}}{2 a x^2}","-\frac{\left(-4 a A c-4 a b B+3 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{5/2}}+\frac{(3 A b-4 a B) \sqrt{a+b x+c x^2}}{4 a^2 x}-\frac{A \sqrt{a+b x+c x^2}}{2 a x^2}",1,"-(A*Sqrt[a + b*x + c*x^2])/(2*a*x^2) + ((3*A*b - 4*a*B)*Sqrt[a + b*x + c*x^2])/(4*a^2*x) - ((3*A*b^2 - 4*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*a^(5/2))","A",4,4,23,0.1739,1,"{834, 806, 724, 206}"
958,1,167,0,0.1618421,"\int \frac{A+B x}{x^4 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(x^4*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{a+b x+c x^2} \left(-16 a A c-18 a b B+15 A b^2\right)}{24 a^3 x}+\frac{\left(8 a^2 B c-12 a A b c-6 a b^2 B+5 A b^3\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{7/2}}+\frac{(5 A b-6 a B) \sqrt{a+b x+c x^2}}{12 a^2 x^2}-\frac{A \sqrt{a+b x+c x^2}}{3 a x^3}","-\frac{\sqrt{a+b x+c x^2} \left(-16 a A c-18 a b B+15 A b^2\right)}{24 a^3 x}+\frac{\left(8 a^2 B c-12 a A b c-6 a b^2 B+5 A b^3\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{7/2}}+\frac{(5 A b-6 a B) \sqrt{a+b x+c x^2}}{12 a^2 x^2}-\frac{A \sqrt{a+b x+c x^2}}{3 a x^3}",1,"-(A*Sqrt[a + b*x + c*x^2])/(3*a*x^3) + ((5*A*b - 6*a*B)*Sqrt[a + b*x + c*x^2])/(12*a^2*x^2) - ((15*A*b^2 - 18*a*b*B - 16*a*A*c)*Sqrt[a + b*x + c*x^2])/(24*a^3*x) + ((5*A*b^3 - 6*a*b^2*B - 12*a*A*b*c + 8*a^2*B*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*a^(7/2))","A",5,4,23,0.1739,1,"{834, 806, 724, 206}"
959,1,231,0,0.2765612,"\int \frac{A+B x}{x^5 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(x^5*Sqrt[a + b*x + c*x^2]),x]","\frac{\left(8 a b B \left(5 b^2-12 a c\right)-A \left(48 a^2 c^2-120 a b^2 c+35 b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{9/2}}+\frac{\sqrt{a+b x+c x^2} \left(128 a^2 B c-220 a A b c-120 a b^2 B+105 A b^3\right)}{192 a^4 x}-\frac{\sqrt{a+b x+c x^2} \left(-36 a A c-40 a b B+35 A b^2\right)}{96 a^3 x^2}+\frac{(7 A b-8 a B) \sqrt{a+b x+c x^2}}{24 a^2 x^3}-\frac{A \sqrt{a+b x+c x^2}}{4 a x^4}","\frac{\left(8 a b B \left(5 b^2-12 a c\right)-A \left(48 a^2 c^2-120 a b^2 c+35 b^4\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{128 a^{9/2}}+\frac{\sqrt{a+b x+c x^2} \left(128 a^2 B c-220 a A b c-120 a b^2 B+105 A b^3\right)}{192 a^4 x}-\frac{\sqrt{a+b x+c x^2} \left(-36 a A c-40 a b B+35 A b^2\right)}{96 a^3 x^2}+\frac{(7 A b-8 a B) \sqrt{a+b x+c x^2}}{24 a^2 x^3}-\frac{A \sqrt{a+b x+c x^2}}{4 a x^4}",1,"-(A*Sqrt[a + b*x + c*x^2])/(4*a*x^4) + ((7*A*b - 8*a*B)*Sqrt[a + b*x + c*x^2])/(24*a^2*x^3) - ((35*A*b^2 - 40*a*b*B - 36*a*A*c)*Sqrt[a + b*x + c*x^2])/(96*a^3*x^2) + ((105*A*b^3 - 120*a*b^2*B - 220*a*A*b*c + 128*a^2*B*c)*Sqrt[a + b*x + c*x^2])/(192*a^4*x) + ((8*a*b*B*(5*b^2 - 12*a*c) - A*(35*b^4 - 120*a*b^2*c + 48*a^2*c^2))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(128*a^(9/2))","A",6,4,23,0.1739,1,"{834, 806, 724, 206}"
960,1,306,0,0.3971917,"\int \frac{A+B x}{x^6 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(x^6*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} \left(50 a b B \left(21 b^2-44 a c\right)-A \left(1024 a^2 c^2-2940 a b^2 c+945 b^4\right)\right)}{1920 a^5 x}-\frac{\left(2 a B \left(48 a^2 c^2-120 a b^2 c+35 b^4\right)-A \left(240 a^2 b c^2-280 a b^3 c+63 b^5\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{11/2}}+\frac{\sqrt{a+b x+c x^2} \left(360 a^2 B c-644 a A b c-350 a b^2 B+315 A b^3\right)}{960 a^4 x^2}-\frac{\sqrt{a+b x+c x^2} \left(-64 a A c-70 a b B+63 A b^2\right)}{240 a^3 x^3}+\frac{(9 A b-10 a B) \sqrt{a+b x+c x^2}}{40 a^2 x^4}-\frac{A \sqrt{a+b x+c x^2}}{5 a x^5}","\frac{\sqrt{a+b x+c x^2} \left(50 a b B \left(21 b^2-44 a c\right)-A \left(1024 a^2 c^2-2940 a b^2 c+945 b^4\right)\right)}{1920 a^5 x}-\frac{\left(2 a B \left(48 a^2 c^2-120 a b^2 c+35 b^4\right)-A \left(240 a^2 b c^2-280 a b^3 c+63 b^5\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{256 a^{11/2}}+\frac{\sqrt{a+b x+c x^2} \left(360 a^2 B c-644 a A b c-350 a b^2 B+315 A b^3\right)}{960 a^4 x^2}-\frac{\sqrt{a+b x+c x^2} \left(-64 a A c-70 a b B+63 A b^2\right)}{240 a^3 x^3}+\frac{(9 A b-10 a B) \sqrt{a+b x+c x^2}}{40 a^2 x^4}-\frac{A \sqrt{a+b x+c x^2}}{5 a x^5}",1,"-(A*Sqrt[a + b*x + c*x^2])/(5*a*x^5) + ((9*A*b - 10*a*B)*Sqrt[a + b*x + c*x^2])/(40*a^2*x^4) - ((63*A*b^2 - 70*a*b*B - 64*a*A*c)*Sqrt[a + b*x + c*x^2])/(240*a^3*x^3) + ((315*A*b^3 - 350*a*b^2*B - 644*a*A*b*c + 360*a^2*B*c)*Sqrt[a + b*x + c*x^2])/(960*a^4*x^2) + ((50*a*b*B*(21*b^2 - 44*a*c) - A*(945*b^4 - 2940*a*b^2*c + 1024*a^2*c^2))*Sqrt[a + b*x + c*x^2])/(1920*a^5*x) - ((2*a*B*(35*b^4 - 120*a*b^2*c + 48*a^2*c^2) - A*(63*b^5 - 280*a*b^3*c + 240*a^2*b*c^2))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(256*a^(11/2))","A",7,4,23,0.1739,1,"{834, 806, 724, 206}"
961,1,280,0,0.2665014,"\int \frac{x^4 (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(x^4*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{\sqrt{a+b x+c x^2} \left(256 a^2 B c^2-2 c x \left(72 a A c^2-116 a b B c-30 A b^2 c+35 b^3 B\right)+312 a A b c^2-460 a b^2 B c-90 A b^3 c+105 b^4 B\right)}{24 c^4 \left(b^2-4 a c\right)}+\frac{x^2 \sqrt{a+b x+c x^2} \left(-16 a B c-6 A b c+7 b^2 B\right)}{3 c^2 \left(b^2-4 a c\right)}-\frac{\left(24 a A c^2-60 a b B c-30 A b^2 c+35 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{9/2}}-\frac{2 x^3 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","\frac{\sqrt{a+b x+c x^2} \left(256 a^2 B c^2-2 c x \left(72 a A c^2-116 a b B c-30 A b^2 c+35 b^3 B\right)+312 a A b c^2-460 a b^2 B c-90 A b^3 c+105 b^4 B\right)}{24 c^4 \left(b^2-4 a c\right)}+\frac{x^2 \sqrt{a+b x+c x^2} \left(-16 a B c-6 A b c+7 b^2 B\right)}{3 c^2 \left(b^2-4 a c\right)}-\frac{\left(24 a A c^2-60 a b B c-30 A b^2 c+35 b^3 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16 c^{9/2}}-\frac{2 x^3 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*x^3*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + ((7*b^2*B - 6*A*b*c - 16*a*B*c)*x^2*Sqrt[a + b*x + c*x^2])/(3*c^2*(b^2 - 4*a*c)) + ((105*b^4*B - 90*A*b^3*c - 460*a*b^2*B*c + 312*a*A*b*c^2 + 256*a^2*B*c^2 - 2*c*(35*b^3*B - 30*A*b^2*c - 116*a*b*B*c + 72*a*A*c^2)*x)*Sqrt[a + b*x + c*x^2])/(24*c^4*(b^2 - 4*a*c)) - ((35*b^3*B - 30*A*b^2*c - 60*a*b*B*c + 24*a*A*c^2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(9/2))","A",5,5,23,0.2174,1,"{818, 832, 779, 621, 206}"
962,1,197,0,0.1350541,"\int \frac{x^3 (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(x^3*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","-\frac{\sqrt{a+b x+c x^2} \left(-2 c x \left(-12 a B c-4 A b c+5 b^2 B\right)+32 a A c^2-52 a b B c-12 A b^2 c+15 b^3 B\right)}{4 c^3 \left(b^2-4 a c\right)}+\frac{3 \left(-4 a B c-4 A b c+5 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{7/2}}-\frac{2 x^2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{\sqrt{a+b x+c x^2} \left(-2 c x \left(-12 a B c-4 A b c+5 b^2 B\right)+32 a A c^2-52 a b B c-12 A b^2 c+15 b^3 B\right)}{4 c^3 \left(b^2-4 a c\right)}+\frac{3 \left(-4 a B c-4 A b c+5 b^2 B\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{8 c^{7/2}}-\frac{2 x^2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*x^2*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) - ((15*b^3*B - 12*A*b^2*c - 52*a*b*B*c + 32*a*A*c^2 - 2*c*(5*b^2*B - 4*A*b*c - 12*a*B*c)*x)*Sqrt[a + b*x + c*x^2])/(4*c^3*(b^2 - 4*a*c)) + (3*(5*b^2*B - 4*A*b*c - 4*a*B*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(7/2))","A",4,4,23,0.1739,1,"{818, 779, 621, 206}"
963,1,153,0,0.1353536,"\int \frac{x^2 (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(x^2*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{\sqrt{a+b x+c x^2} \left(-8 a B c-2 A b c+3 b^2 B\right)}{c^2 \left(b^2-4 a c\right)}-\frac{2 x \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{(3 b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{5/2}}","\frac{\sqrt{a+b x+c x^2} \left(-8 a B c-2 A b c+3 b^2 B\right)}{c^2 \left(b^2-4 a c\right)}-\frac{2 x \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{(3 b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{5/2}}",1,"(-2*x*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + ((3*b^2*B - 2*A*b*c - 8*a*B*c)*Sqrt[a + b*x + c*x^2])/(c^2*(b^2 - 4*a*c)) - ((3*b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(5/2))","A",4,4,23,0.1739,1,"{818, 640, 621, 206}"
964,1,96,0,0.0413259,"\int \frac{x (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(x*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (B*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",3,3,21,0.1429,1,"{777, 621, 206}"
965,1,45,0,0.0111012,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])","A",1,1,20,0.05000,1,"{636}"
966,1,96,0,0.0578137,"\int \frac{A+B x}{x \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{a^{3/2}}","\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{a^{3/2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(a*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) - (A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/a^(3/2)","A",4,4,23,0.1739,1,"{822, 12, 724, 206}"
967,1,158,0,0.1192148,"\int \frac{A+B x}{x^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^2*(a + b*x + c*x^2)^(3/2)),x]","-\frac{\sqrt{a+b x+c x^2} \left(-8 a A c-2 a b B+3 A b^2\right)}{a^2 x \left(b^2-4 a c\right)}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{5/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a x \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{\sqrt{a+b x+c x^2} \left(-8 a A c-2 a b B+3 A b^2\right)}{a^2 x \left(b^2-4 a c\right)}+\frac{(3 A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{5/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a x \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(a*(b^2 - 4*a*c)*x*Sqrt[a + b*x + c*x^2]) - ((3*A*b^2 - 2*a*b*B - 8*a*A*c)*Sqrt[a + b*x + c*x^2])/(a^2*(b^2 - 4*a*c)*x) + ((3*A*b - 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*a^(5/2))","A",4,4,23,0.1739,1,"{822, 806, 724, 206}"
968,1,231,0,0.200162,"\int \frac{A+B x}{x^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^3*(a + b*x + c*x^2)^(3/2)),x]","-\frac{\sqrt{a+b x+c x^2} \left(-12 a A c-4 a b B+5 A b^2\right)}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\sqrt{a+b x+c x^2} \left(4 a B \left(3 b^2-8 a c\right)-A \left(15 b^3-52 a b c\right)\right)}{4 a^3 x \left(b^2-4 a c\right)}-\frac{3 \left(-4 a A c-4 a b B+5 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{7/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a x^2 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{\sqrt{a+b x+c x^2} \left(-12 a A c-4 a b B+5 A b^2\right)}{2 a^2 x^2 \left(b^2-4 a c\right)}-\frac{\sqrt{a+b x+c x^2} \left(4 a B \left(3 b^2-8 a c\right)-A \left(15 b^3-52 a b c\right)\right)}{4 a^3 x \left(b^2-4 a c\right)}-\frac{3 \left(-4 a A c-4 a b B+5 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{7/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a x^2 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(a*(b^2 - 4*a*c)*x^2*Sqrt[a + b*x + c*x^2]) - ((5*A*b^2 - 4*a*b*B - 12*a*A*c)*Sqrt[a + b*x + c*x^2])/(2*a^2*(b^2 - 4*a*c)*x^2) - ((4*a*B*(3*b^2 - 8*a*c) - A*(15*b^3 - 52*a*b*c))*Sqrt[a + b*x + c*x^2])/(4*a^3*(b^2 - 4*a*c)*x) - (3*(5*A*b^2 - 4*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*a^(7/2))","A",5,5,23,0.2174,1,"{822, 834, 806, 724, 206}"
969,1,317,0,0.3878774,"\int \frac{A+B x}{x^4 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(x^4*(a + b*x + c*x^2)^(3/2)),x]","\frac{\sqrt{a+b x+c x^2} \left(6 a b B \left(15 b^2-52 a c\right)-A \left(256 a^2 c^2-460 a b^2 c+105 b^4\right)\right)}{24 a^4 x \left(b^2-4 a c\right)}-\frac{\sqrt{a+b x+c x^2} \left(-16 a A c-6 a b B+7 A b^2\right)}{3 a^2 x^3 \left(b^2-4 a c\right)}-\frac{\sqrt{a+b x+c x^2} \left(6 a B \left(5 b^2-12 a c\right)-A \left(35 b^3-116 a b c\right)\right)}{12 a^3 x^2 \left(b^2-4 a c\right)}-\frac{\left(6 a B \left(5 b^2-4 a c\right)-A \left(35 b^3-60 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{9/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a x^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","\frac{\sqrt{a+b x+c x^2} \left(6 a b B \left(15 b^2-52 a c\right)-A \left(256 a^2 c^2-460 a b^2 c+105 b^4\right)\right)}{24 a^4 x \left(b^2-4 a c\right)}-\frac{\sqrt{a+b x+c x^2} \left(-16 a A c-6 a b B+7 A b^2\right)}{3 a^2 x^3 \left(b^2-4 a c\right)}-\frac{\sqrt{a+b x+c x^2} \left(6 a B \left(5 b^2-12 a c\right)-A \left(35 b^3-116 a b c\right)\right)}{12 a^3 x^2 \left(b^2-4 a c\right)}-\frac{\left(6 a B \left(5 b^2-4 a c\right)-A \left(35 b^3-60 a b c\right)\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{16 a^{9/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a x^3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(a*(b^2 - 4*a*c)*x^3*Sqrt[a + b*x + c*x^2]) - ((7*A*b^2 - 6*a*b*B - 16*a*A*c)*Sqrt[a + b*x + c*x^2])/(3*a^2*(b^2 - 4*a*c)*x^3) - ((6*a*B*(5*b^2 - 12*a*c) - A*(35*b^3 - 116*a*b*c))*Sqrt[a + b*x + c*x^2])/(12*a^3*(b^2 - 4*a*c)*x^2) + ((6*a*b*B*(15*b^2 - 52*a*c) - A*(105*b^4 - 460*a*b^2*c + 256*a^2*c^2))*Sqrt[a + b*x + c*x^2])/(24*a^4*(b^2 - 4*a*c)*x) - ((6*a*B*(5*b^2 - 4*a*c) - A*(35*b^3 - 60*a*b*c))*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(16*a^(9/2))","A",6,5,23,0.2174,1,"{822, 834, 806, 724, 206}"
970,1,285,0,0.2677471,"\int \frac{x^4 (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(x^4*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 x \left(x \left(32 a^2 B c^2+16 a A b c^2-32 a b^2 B c-2 A b^3 c+5 b^4 B\right)+a \left(24 a A c^2-28 a b B c-2 A b^2 c+5 b^3 B\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} \left(128 a^2 B c^2+40 a A b c^2-100 a b^2 B c-6 A b^3 c+15 b^4 B\right)}{3 c^3 \left(b^2-4 a c\right)^2}-\frac{2 x^3 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}-\frac{(5 b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{7/2}}","-\frac{2 x \left(x \left(32 a^2 B c^2+16 a A b c^2-32 a b^2 B c-2 A b^3 c+5 b^4 B\right)+a \left(24 a A c^2-28 a b B c-2 A b^2 c+5 b^3 B\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{\sqrt{a+b x+c x^2} \left(128 a^2 B c^2+40 a A b c^2-100 a b^2 B c-6 A b^3 c+15 b^4 B\right)}{3 c^3 \left(b^2-4 a c\right)^2}-\frac{2 x^3 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}-\frac{(5 b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{7/2}}",1,"(-2*x^3*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*x*(a*(5*b^3*B - 2*A*b^2*c - 28*a*b*B*c + 24*a*A*c^2) + (5*b^4*B - 2*A*b^3*c - 32*a*b^2*B*c + 16*a*A*b*c^2 + 32*a^2*B*c^2)*x))/(3*c^2*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + ((15*b^4*B - 6*A*b^3*c - 100*a*b^2*B*c + 40*a*A*b*c^2 + 128*a^2*B*c^2)*Sqrt[a + b*x + c*x^2])/(3*c^3*(b^2 - 4*a*c)^2) - ((5*b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(7/2))","A",5,4,23,0.1739,1,"{818, 640, 621, 206}"
971,1,189,0,0.1325103,"\int \frac{x^3 (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(x^3*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(x \left(24 a^2 B c^2+8 a A b c^2-22 a b^2 B c+3 b^4 B\right)+a \left(16 a A c^2-20 a b B c+3 b^3 B\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 x^2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 \left(x \left(24 a^2 B c^2+8 a A b c^2-22 a b^2 B c+3 b^4 B\right)+a \left(16 a A c^2-20 a b B c+3 b^3 B\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 x^2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}",1,"(-2*x^2*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*(a*(3*b^3*B - 20*a*b*B*c + 16*a*A*c^2) + (3*b^4*B - 22*a*b^2*B*c + 8*a*A*b*c^2 + 24*a^2*B*c^2)*x))/(3*c^2*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + (B*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(5/2)","A",4,4,23,0.1739,1,"{818, 777, 621, 206}"
972,1,94,0,0.0375209,"\int \frac{x^2 (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(x^2*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{8 (2 a+b x) (A b-2 a B)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 x^2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{8 (2 a+b x) (A b-2 a B)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 x^2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*x^2*(A*b - 2*a*B - (b*B - 2*A*c)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (8*(A*b - 2*a*B)*(2*a + b*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,23,0.08696,1,"{804, 636}"
973,1,114,0,0.04445,"\int \frac{x (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(x*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{2 (b+2 c x) \left(4 a B c-4 A b c+b^2 B\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{2 (b+2 c x) \left(4 a B c-4 A b c+b^2 B\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*(b^2*B - 4*A*b*c + 4*a*B*c)*(b + 2*c*x))/(3*c*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,21,0.09524,1,"{777, 613}"
974,1,90,0,0.0208019,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{8 (b+2 c x) (b B-2 A c)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","-\frac{8 (b+2 c x) (b B-2 A c)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (8*(b*B - 2*A*c)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,20,0.1000,1,"{638, 613}"
975,1,184,0,0.1283447,"\int \frac{A+B x}{x \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x*(a + b*x + c*x^2)^(5/2)),x]","\frac{2 \left(c x \left(16 a^2 B c-20 a A b c+3 A b^3\right)+A \left(24 a^2 c^2-22 a b^2 c+3 b^4\right)+8 a^2 b B c\right)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{a^{5/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{3 a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{2 \left(c x \left(16 a^2 B c-20 a A b c+3 A b^3\right)+A \left(24 a^2 c^2-22 a b^2 c+3 b^4\right)+8 a^2 b B c\right)}{3 a^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{A \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{a^{5/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{3 a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(3*a*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*(8*a^2*b*B*c + A*(3*b^4 - 22*a*b^2*c + 24*a^2*c^2) + c*(3*A*b^3 - 20*a*A*b*c + 16*a^2*B*c)*x))/(3*a^2*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) - (A*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/a^(5/2)","A",5,4,23,0.1739,1,"{822, 12, 724, 206}"
976,1,288,0,0.3124356,"\int \frac{A+B x}{x^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{\sqrt{a+b x+c x^2} \left(2 a b B \left(3 b^2-20 a c\right)-A \left(128 a^2 c^2-100 a b^2 c+15 b^4\right)\right)}{3 a^3 x \left(b^2-4 a c\right)^2}-\frac{2 \left(-c x \left(24 a^2 B c-28 a A b c-2 a b^2 B+5 A b^3\right)-A \left(32 a^2 c^2-32 a b^2 c+5 b^4\right)+2 a b B \left(b^2-8 a c\right)\right)}{3 a^2 x \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{7/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{3 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{\sqrt{a+b x+c x^2} \left(2 a b B \left(3 b^2-20 a c\right)-A \left(128 a^2 c^2-100 a b^2 c+15 b^4\right)\right)}{3 a^3 x \left(b^2-4 a c\right)^2}-\frac{2 \left(-c x \left(24 a^2 B c-28 a A b c-2 a b^2 B+5 A b^3\right)-A \left(32 a^2 c^2-32 a b^2 c+5 b^4\right)+2 a b B \left(b^2-8 a c\right)\right)}{3 a^2 x \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{(5 A b-2 a B) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{2 a^{7/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{3 a x \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(3*a*(b^2 - 4*a*c)*x*(a + b*x + c*x^2)^(3/2)) - (2*(2*a*b*B*(b^2 - 8*a*c) - A*(5*b^4 - 32*a*b^2*c + 32*a^2*c^2) - c*(5*A*b^3 - 2*a*b^2*B - 28*a*A*b*c + 24*a^2*B*c)*x))/(3*a^2*(b^2 - 4*a*c)^2*x*Sqrt[a + b*x + c*x^2]) + ((2*a*b*B*(3*b^2 - 20*a*c) - A*(15*b^4 - 100*a*b^2*c + 128*a^2*c^2))*Sqrt[a + b*x + c*x^2])/(3*a^3*(b^2 - 4*a*c)^2*x) + ((5*A*b - 2*a*B)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(2*a^(7/2))","A",5,4,23,0.1739,1,"{822, 806, 724, 206}"
977,1,381,0,0.461281,"\int \frac{A+B x}{x^3 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(x^3*(a + b*x + c*x^2)^(5/2)),x]","\frac{\sqrt{a+b x+c x^2} \left(4 a b B \left(5 b^2-28 a c\right)-A \left(240 a^2 c^2-216 a b^2 c+35 b^4\right)\right)}{6 a^3 x^2 \left(b^2-4 a c\right)^2}-\frac{\sqrt{a+b x+c x^2} \left(4 a B \left(128 a^2 c^2-100 a b^2 c+15 b^4\right)-A \left(1296 a^2 b c^2-760 a b^3 c+105 b^5\right)\right)}{12 a^4 x \left(b^2-4 a c\right)^2}-\frac{2 \left(-c x \left(32 a^2 B c-36 a A b c-4 a b^2 B+7 A b^3\right)-A \left(40 a^2 c^2-42 a b^2 c+7 b^4\right)+4 a b B \left(b^2-6 a c\right)\right)}{3 a^2 x^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{5 \left(-4 a A c-4 a b B+7 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{9/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{3 a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{\sqrt{a+b x+c x^2} \left(4 a b B \left(5 b^2-28 a c\right)-A \left(240 a^2 c^2-216 a b^2 c+35 b^4\right)\right)}{6 a^3 x^2 \left(b^2-4 a c\right)^2}-\frac{\sqrt{a+b x+c x^2} \left(4 a B \left(128 a^2 c^2-100 a b^2 c+15 b^4\right)-A \left(1296 a^2 b c^2-760 a b^3 c+105 b^5\right)\right)}{12 a^4 x \left(b^2-4 a c\right)^2}-\frac{2 \left(-c x \left(32 a^2 B c-36 a A b c-4 a b^2 B+7 A b^3\right)-A \left(40 a^2 c^2-42 a b^2 c+7 b^4\right)+4 a b B \left(b^2-6 a c\right)\right)}{3 a^2 x^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{5 \left(-4 a A c-4 a b B+7 A b^2\right) \tanh ^{-1}\left(\frac{2 a+b x}{2 \sqrt{a} \sqrt{a+b x+c x^2}}\right)}{8 a^{9/2}}+\frac{2 \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{3 a x^2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(2*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(3*a*(b^2 - 4*a*c)*x^2*(a + b*x + c*x^2)^(3/2)) - (2*(4*a*b*B*(b^2 - 6*a*c) - A*(7*b^4 - 42*a*b^2*c + 40*a^2*c^2) - c*(7*A*b^3 - 4*a*b^2*B - 36*a*A*b*c + 32*a^2*B*c)*x))/(3*a^2*(b^2 - 4*a*c)^2*x^2*Sqrt[a + b*x + c*x^2]) + ((4*a*b*B*(5*b^2 - 28*a*c) - A*(35*b^4 - 216*a*b^2*c + 240*a^2*c^2))*Sqrt[a + b*x + c*x^2])/(6*a^3*(b^2 - 4*a*c)^2*x^2) - ((4*a*B*(15*b^4 - 100*a*b^2*c + 128*a^2*c^2) - A*(105*b^5 - 760*a*b^3*c + 1296*a^2*b*c^2))*Sqrt[a + b*x + c*x^2])/(12*a^4*(b^2 - 4*a*c)^2*x) - (5*(7*A*b^2 - 4*a*b*B - 4*a*A*c)*ArcTanh[(2*a + b*x)/(2*Sqrt[a]*Sqrt[a + b*x + c*x^2])])/(8*a^(9/2))","A",6,5,23,0.2174,1,"{822, 834, 806, 724, 206}"
978,1,135,0,0.0383647,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(7/2),x]","-\frac{128 c (b+2 c x) (2 c d-b e)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}+\frac{16 (b+2 c x) (2 c d-b e)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}","-\frac{128 c (b+2 c x) (2 c d-b e)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}+\frac{16 (b+2 c x) (2 c d-b e)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}",1,"(-2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(5*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) + (16*(2*c*d - b*e)*(b + 2*c*x))/(15*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) - (128*c*(2*c*d - b*e)*(b + 2*c*x))/(15*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",3,3,20,0.1500,1,"{638, 614, 613}"
979,1,181,0,0.0589463,"\int \frac{d+e x}{\left(a+b x+c x^2\right)^{9/2}} \, dx","Int[(d + e*x)/(a + b*x + c*x^2)^(9/2),x]","\frac{1024 c^2 (b+2 c x) (2 c d-b e)}{35 \left(b^2-4 a c\right)^4 \sqrt{a+b x+c x^2}}-\frac{128 c (b+2 c x) (2 c d-b e)}{35 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^{3/2}}+\frac{24 (b+2 c x) (2 c d-b e)}{35 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{5/2}}-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{7 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{7/2}}","\frac{1024 c^2 (b+2 c x) (2 c d-b e)}{35 \left(b^2-4 a c\right)^4 \sqrt{a+b x+c x^2}}-\frac{128 c (b+2 c x) (2 c d-b e)}{35 \left(b^2-4 a c\right)^3 \left(a+b x+c x^2\right)^{3/2}}+\frac{24 (b+2 c x) (2 c d-b e)}{35 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{5/2}}-\frac{2 (-2 a e+x (2 c d-b e)+b d)}{7 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{7/2}}",1,"(-2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(7*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(7/2)) + (24*(2*c*d - b*e)*(b + 2*c*x))/(35*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(5/2)) - (128*c*(2*c*d - b*e)*(b + 2*c*x))/(35*(b^2 - 4*a*c)^3*(a + b*x + c*x^2)^(3/2)) + (1024*c^2*(2*c*d - b*e)*(b + 2*c*x))/(35*(b^2 - 4*a*c)^4*Sqrt[a + b*x + c*x^2])","A",4,3,20,0.1500,1,"{638, 614, 613}"
980,1,19,0,0.0146195,"\int \frac{1-x}{x \sqrt{1+3 x+x^2}} \, dx","Int[(1 - x)/(x*Sqrt[1 + 3*x + x^2]),x]","-2 \tanh ^{-1}\left(\frac{x+1}{\sqrt{x^2+3 x+1}}\right)","-2 \tanh ^{-1}\left(\frac{x+1}{\sqrt{x^2+3 x+1}}\right)",1,"-2*ArcTanh[(1 + x)/Sqrt[1 + 3*x + x^2]]","A",2,2,21,0.09524,1,"{838, 206}"
981,1,55,0,0.0260274,"\int x^{7/2} (A+B x) \left(a+b x+c x^2\right) \, dx","Int[x^(7/2)*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{15} B c x^{15/2}","\frac{2}{11} x^{11/2} (a B+A b)+\frac{2}{9} a A x^{9/2}+\frac{2}{13} x^{13/2} (A c+b B)+\frac{2}{15} B c x^{15/2}",1,"(2*a*A*x^(9/2))/9 + (2*(A*b + a*B)*x^(11/2))/11 + (2*(b*B + A*c)*x^(13/2))/13 + (2*B*c*x^(15/2))/15","A",2,1,21,0.04762,1,"{765}"
982,1,55,0,0.0239771,"\int x^{5/2} (A+B x) \left(a+b x+c x^2\right) \, dx","Int[x^(5/2)*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} x^{11/2} (A c+b B)+\frac{2}{13} B c x^{13/2}","\frac{2}{9} x^{9/2} (a B+A b)+\frac{2}{7} a A x^{7/2}+\frac{2}{11} x^{11/2} (A c+b B)+\frac{2}{13} B c x^{13/2}",1,"(2*a*A*x^(7/2))/7 + (2*(A*b + a*B)*x^(9/2))/9 + (2*(b*B + A*c)*x^(11/2))/11 + (2*B*c*x^(13/2))/13","A",2,1,21,0.04762,1,"{765}"
983,1,55,0,0.0245567,"\int x^{3/2} (A+B x) \left(a+b x+c x^2\right) \, dx","Int[x^(3/2)*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{11} B c x^{11/2}","\frac{2}{7} x^{7/2} (a B+A b)+\frac{2}{5} a A x^{5/2}+\frac{2}{9} x^{9/2} (A c+b B)+\frac{2}{11} B c x^{11/2}",1,"(2*a*A*x^(5/2))/5 + (2*(A*b + a*B)*x^(7/2))/7 + (2*(b*B + A*c)*x^(9/2))/9 + (2*B*c*x^(11/2))/11","A",2,1,21,0.04762,1,"{765}"
984,1,55,0,0.0242031,"\int \sqrt{x} (A+B x) \left(a+b x+c x^2\right) \, dx","Int[Sqrt[x]*(A + B*x)*(a + b*x + c*x^2),x]","\frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{9} B c x^{9/2}","\frac{2}{5} x^{5/2} (a B+A b)+\frac{2}{3} a A x^{3/2}+\frac{2}{7} x^{7/2} (A c+b B)+\frac{2}{9} B c x^{9/2}",1,"(2*a*A*x^(3/2))/3 + (2*(A*b + a*B)*x^(5/2))/5 + (2*(b*B + A*c)*x^(7/2))/7 + (2*B*c*x^(9/2))/9","A",2,1,21,0.04762,1,"{765}"
985,1,53,0,0.0237014,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{\sqrt{x}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/Sqrt[x],x]","\frac{2}{3} x^{3/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{5} x^{5/2} (A c+b B)+\frac{2}{7} B c x^{7/2}","\frac{2}{3} x^{3/2} (a B+A b)+2 a A \sqrt{x}+\frac{2}{5} x^{5/2} (A c+b B)+\frac{2}{7} B c x^{7/2}",1,"2*a*A*Sqrt[x] + (2*(A*b + a*B)*x^(3/2))/3 + (2*(b*B + A*c)*x^(5/2))/5 + (2*B*c*x^(7/2))/7","A",2,1,21,0.04762,1,"{765}"
986,1,51,0,0.024403,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{3/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^(3/2),x]","2 \sqrt{x} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{3} x^{3/2} (A c+b B)+\frac{2}{5} B c x^{5/2}","2 \sqrt{x} (a B+A b)-\frac{2 a A}{\sqrt{x}}+\frac{2}{3} x^{3/2} (A c+b B)+\frac{2}{5} B c x^{5/2}",1,"(-2*a*A)/Sqrt[x] + 2*(A*b + a*B)*Sqrt[x] + (2*(b*B + A*c)*x^(3/2))/3 + (2*B*c*x^(5/2))/5","A",2,1,21,0.04762,1,"{765}"
987,1,51,0,0.0229725,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{5/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^(5/2),x]","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 \sqrt{x} (A c+b B)+\frac{2}{3} B c x^{3/2}","-\frac{2 (a B+A b)}{\sqrt{x}}-\frac{2 a A}{3 x^{3/2}}+2 \sqrt{x} (A c+b B)+\frac{2}{3} B c x^{3/2}",1,"(-2*a*A)/(3*x^(3/2)) - (2*(A*b + a*B))/Sqrt[x] + 2*(b*B + A*c)*Sqrt[x] + (2*B*c*x^(3/2))/3","A",2,1,21,0.04762,1,"{765}"
988,1,51,0,0.0224296,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{7/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^(7/2),x]","-\frac{2 (a B+A b)}{3 x^{3/2}}-\frac{2 a A}{5 x^{5/2}}-\frac{2 (A c+b B)}{\sqrt{x}}+2 B c \sqrt{x}","-\frac{2 (a B+A b)}{3 x^{3/2}}-\frac{2 a A}{5 x^{5/2}}-\frac{2 (A c+b B)}{\sqrt{x}}+2 B c \sqrt{x}",1,"(-2*a*A)/(5*x^(5/2)) - (2*(A*b + a*B))/(3*x^(3/2)) - (2*(b*B + A*c))/Sqrt[x] + 2*B*c*Sqrt[x]","A",2,1,21,0.04762,1,"{765}"
989,1,53,0,0.02865,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{x^{9/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/x^(9/2),x]","-\frac{2 (a B+A b)}{5 x^{5/2}}-\frac{2 a A}{7 x^{7/2}}-\frac{2 (A c+b B)}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}}","-\frac{2 (a B+A b)}{5 x^{5/2}}-\frac{2 a A}{7 x^{7/2}}-\frac{2 (A c+b B)}{3 x^{3/2}}-\frac{2 B c}{\sqrt{x}}",1,"(-2*a*A)/(7*x^(7/2)) - (2*(A*b + a*B))/(5*x^(5/2)) - (2*(b*B + A*c))/(3*x^(3/2)) - (2*B*c)/Sqrt[x]","A",2,1,21,0.04762,1,"{765}"
990,1,113,0,0.0634504,"\int x^{7/2} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[x^(7/2)*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{15} x^{15/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{13} x^{13/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{17} c x^{17/2} (A c+2 b B)+\frac{2}{19} B c^2 x^{19/2}","\frac{2}{9} a^2 A x^{9/2}+\frac{2}{15} x^{15/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{13} x^{13/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{11} a x^{11/2} (a B+2 A b)+\frac{2}{17} c x^{17/2} (A c+2 b B)+\frac{2}{19} B c^2 x^{19/2}",1,"(2*a^2*A*x^(9/2))/9 + (2*a*(2*A*b + a*B)*x^(11/2))/11 + (2*(2*a*b*B + A*(b^2 + 2*a*c))*x^(13/2))/13 + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(15/2))/15 + (2*c*(2*b*B + A*c)*x^(17/2))/17 + (2*B*c^2*x^(19/2))/19","A",2,1,23,0.04348,1,"{765}"
991,1,113,0,0.0596836,"\int x^{5/2} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[x^(5/2)*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{13} x^{13/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{11} x^{11/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{15} c x^{15/2} (A c+2 b B)+\frac{2}{17} B c^2 x^{17/2}","\frac{2}{7} a^2 A x^{7/2}+\frac{2}{13} x^{13/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{11} x^{11/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{9} a x^{9/2} (a B+2 A b)+\frac{2}{15} c x^{15/2} (A c+2 b B)+\frac{2}{17} B c^2 x^{17/2}",1,"(2*a^2*A*x^(7/2))/7 + (2*a*(2*A*b + a*B)*x^(9/2))/9 + (2*(2*a*b*B + A*(b^2 + 2*a*c))*x^(11/2))/11 + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(13/2))/13 + (2*c*(2*b*B + A*c)*x^(15/2))/15 + (2*B*c^2*x^(17/2))/17","A",2,1,23,0.04348,1,"{765}"
992,1,113,0,0.0590619,"\int x^{3/2} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[x^(3/2)*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{11} x^{11/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{9} x^{9/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{13} c x^{13/2} (A c+2 b B)+\frac{2}{15} B c^2 x^{15/2}","\frac{2}{5} a^2 A x^{5/2}+\frac{2}{11} x^{11/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{9} x^{9/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{7} a x^{7/2} (a B+2 A b)+\frac{2}{13} c x^{13/2} (A c+2 b B)+\frac{2}{15} B c^2 x^{15/2}",1,"(2*a^2*A*x^(5/2))/5 + (2*a*(2*A*b + a*B)*x^(7/2))/7 + (2*(2*a*b*B + A*(b^2 + 2*a*c))*x^(9/2))/9 + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(11/2))/11 + (2*c*(2*b*B + A*c)*x^(13/2))/13 + (2*B*c^2*x^(15/2))/15","A",2,1,23,0.04348,1,"{765}"
993,1,113,0,0.057281,"\int \sqrt{x} (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[Sqrt[x]*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{9} x^{9/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{7} x^{7/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{11} c x^{11/2} (A c+2 b B)+\frac{2}{13} B c^2 x^{13/2}","\frac{2}{3} a^2 A x^{3/2}+\frac{2}{9} x^{9/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{7} x^{7/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{5} a x^{5/2} (a B+2 A b)+\frac{2}{11} c x^{11/2} (A c+2 b B)+\frac{2}{13} B c^2 x^{13/2}",1,"(2*a^2*A*x^(3/2))/3 + (2*a*(2*A*b + a*B)*x^(5/2))/5 + (2*(2*a*b*B + A*(b^2 + 2*a*c))*x^(7/2))/7 + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(9/2))/9 + (2*c*(2*b*B + A*c)*x^(11/2))/11 + (2*B*c^2*x^(13/2))/13","A",2,1,23,0.04348,1,"{765}"
994,1,111,0,0.0563842,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{\sqrt{x}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/Sqrt[x],x]","2 a^2 A \sqrt{x}+\frac{2}{7} x^{7/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{5} x^{5/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{9} c x^{9/2} (A c+2 b B)+\frac{2}{11} B c^2 x^{11/2}","2 a^2 A \sqrt{x}+\frac{2}{7} x^{7/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{5} x^{5/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{2}{3} a x^{3/2} (a B+2 A b)+\frac{2}{9} c x^{9/2} (A c+2 b B)+\frac{2}{11} B c^2 x^{11/2}",1,"2*a^2*A*Sqrt[x] + (2*a*(2*A*b + a*B)*x^(3/2))/3 + (2*(2*a*b*B + A*(b^2 + 2*a*c))*x^(5/2))/5 + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(7/2))/7 + (2*c*(2*b*B + A*c)*x^(9/2))/9 + (2*B*c^2*x^(11/2))/11","A",2,1,23,0.04348,1,"{765}"
995,1,109,0,0.0606816,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{3/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^(3/2),x]","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{5} x^{5/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{3} x^{3/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{7} c x^{7/2} (A c+2 b B)+\frac{2}{9} B c^2 x^{9/2}","-\frac{2 a^2 A}{\sqrt{x}}+\frac{2}{5} x^{5/2} \left(2 a B c+2 A b c+b^2 B\right)+\frac{2}{3} x^{3/2} \left(A \left(2 a c+b^2\right)+2 a b B\right)+2 a \sqrt{x} (a B+2 A b)+\frac{2}{7} c x^{7/2} (A c+2 b B)+\frac{2}{9} B c^2 x^{9/2}",1,"(-2*a^2*A)/Sqrt[x] + 2*a*(2*A*b + a*B)*Sqrt[x] + (2*(2*a*b*B + A*(b^2 + 2*a*c))*x^(3/2))/3 + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(5/2))/5 + (2*c*(2*b*B + A*c)*x^(7/2))/7 + (2*B*c^2*x^(9/2))/9","A",2,1,23,0.04348,1,"{765}"
996,1,109,0,0.0552873,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{5/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^(5/2),x]","-\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{3} x^{3/2} \left(2 a B c+2 A b c+b^2 B\right)+2 \sqrt{x} \left(A \left(2 a c+b^2\right)+2 a b B\right)-\frac{2 a (a B+2 A b)}{\sqrt{x}}+\frac{2}{5} c x^{5/2} (A c+2 b B)+\frac{2}{7} B c^2 x^{7/2}","-\frac{2 a^2 A}{3 x^{3/2}}+\frac{2}{3} x^{3/2} \left(2 a B c+2 A b c+b^2 B\right)+2 \sqrt{x} \left(A \left(2 a c+b^2\right)+2 a b B\right)-\frac{2 a (a B+2 A b)}{\sqrt{x}}+\frac{2}{5} c x^{5/2} (A c+2 b B)+\frac{2}{7} B c^2 x^{7/2}",1,"(-2*a^2*A)/(3*x^(3/2)) - (2*a*(2*A*b + a*B))/Sqrt[x] + 2*(2*a*b*B + A*(b^2 + 2*a*c))*Sqrt[x] + (2*(b^2*B + 2*A*b*c + 2*a*B*c)*x^(3/2))/3 + (2*c*(2*b*B + A*c)*x^(5/2))/5 + (2*B*c^2*x^(7/2))/7","A",2,1,23,0.04348,1,"{765}"
997,1,109,0,0.0555632,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{7/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^(7/2),x]","-\frac{2 a^2 A}{5 x^{5/2}}+2 \sqrt{x} \left(2 a B c+2 A b c+b^2 B\right)-\frac{2 \left(A \left(2 a c+b^2\right)+2 a b B\right)}{\sqrt{x}}-\frac{2 a (a B+2 A b)}{3 x^{3/2}}+\frac{2}{3} c x^{3/2} (A c+2 b B)+\frac{2}{5} B c^2 x^{5/2}","-\frac{2 a^2 A}{5 x^{5/2}}+2 \sqrt{x} \left(2 a B c+2 A b c+b^2 B\right)-\frac{2 \left(A \left(2 a c+b^2\right)+2 a b B\right)}{\sqrt{x}}-\frac{2 a (a B+2 A b)}{3 x^{3/2}}+\frac{2}{3} c x^{3/2} (A c+2 b B)+\frac{2}{5} B c^2 x^{5/2}",1,"(-2*a^2*A)/(5*x^(5/2)) - (2*a*(2*A*b + a*B))/(3*x^(3/2)) - (2*(2*a*b*B + A*(b^2 + 2*a*c)))/Sqrt[x] + 2*(b^2*B + 2*A*b*c + 2*a*B*c)*Sqrt[x] + (2*c*(2*b*B + A*c)*x^(3/2))/3 + (2*B*c^2*x^(5/2))/5","A",2,1,23,0.04348,1,"{765}"
998,1,109,0,0.0564041,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{x^{9/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/x^(9/2),x]","-\frac{2 a^2 A}{7 x^{7/2}}-\frac{2 \left(A \left(2 a c+b^2\right)+2 a b B\right)}{3 x^{3/2}}-\frac{2 \left(2 a B c+2 A b c+b^2 B\right)}{\sqrt{x}}-\frac{2 a (a B+2 A b)}{5 x^{5/2}}+2 c \sqrt{x} (A c+2 b B)+\frac{2}{3} B c^2 x^{3/2}","-\frac{2 a^2 A}{7 x^{7/2}}-\frac{2 \left(A \left(2 a c+b^2\right)+2 a b B\right)}{3 x^{3/2}}-\frac{2 \left(2 a B c+2 A b c+b^2 B\right)}{\sqrt{x}}-\frac{2 a (a B+2 A b)}{5 x^{5/2}}+2 c \sqrt{x} (A c+2 b B)+\frac{2}{3} B c^2 x^{3/2}",1,"(-2*a^2*A)/(7*x^(7/2)) - (2*a*(2*A*b + a*B))/(5*x^(5/2)) - (2*(2*a*b*B + A*(b^2 + 2*a*c)))/(3*x^(3/2)) - (2*(b^2*B + 2*A*b*c + 2*a*B*c))/Sqrt[x] + 2*c*(2*b*B + A*c)*Sqrt[x] + (2*B*c^2*x^(3/2))/3","A",2,1,23,0.04348,1,"{765}"
999,1,182,0,0.1248335,"\int x^{7/2} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[x^(7/2)*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{17} x^{17/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{19} c x^{19/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{15} x^{15/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{13} a x^{13/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{2}{23} B c^3 x^{23/2}","\frac{2}{11} a^2 x^{11/2} (a B+3 A b)+\frac{2}{9} a^3 A x^{9/2}+\frac{2}{17} x^{17/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{19} c x^{19/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{15} x^{15/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{13} a x^{13/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{21} c^2 x^{21/2} (A c+3 b B)+\frac{2}{23} B c^3 x^{23/2}",1,"(2*a^3*A*x^(9/2))/9 + (2*a^2*(3*A*b + a*B)*x^(11/2))/11 + (6*a*(a*b*B + A*(b^2 + a*c))*x^(13/2))/13 + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(15/2))/15 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(17/2))/17 + (6*c*(b^2*B + A*b*c + a*B*c)*x^(19/2))/19 + (2*c^2*(3*b*B + A*c)*x^(21/2))/21 + (2*B*c^3*x^(23/2))/23","A",2,1,23,0.04348,1,"{765}"
1000,1,182,0,0.1157156,"\int x^{5/2} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[x^(5/2)*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{7} a^3 A x^{7/2}+\frac{2}{15} x^{15/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{17} c x^{17/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{13} x^{13/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{11} a x^{11/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{2}{21} B c^3 x^{21/2}","\frac{2}{9} a^2 x^{9/2} (a B+3 A b)+\frac{2}{7} a^3 A x^{7/2}+\frac{2}{15} x^{15/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{17} c x^{17/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{13} x^{13/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{11} a x^{11/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{19} c^2 x^{19/2} (A c+3 b B)+\frac{2}{21} B c^3 x^{21/2}",1,"(2*a^3*A*x^(7/2))/7 + (2*a^2*(3*A*b + a*B)*x^(9/2))/9 + (6*a*(a*b*B + A*(b^2 + a*c))*x^(11/2))/11 + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(13/2))/13 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(15/2))/15 + (6*c*(b^2*B + A*b*c + a*B*c)*x^(17/2))/17 + (2*c^2*(3*b*B + A*c)*x^(19/2))/19 + (2*B*c^3*x^(21/2))/21","A",2,1,23,0.04348,1,"{765}"
1001,1,182,0,0.1124825,"\int x^{3/2} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[x^(3/2)*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{13} x^{13/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{2}{5} c x^{15/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{11} x^{11/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{2}{3} a x^{9/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{19} B c^3 x^{19/2}","\frac{2}{7} a^2 x^{7/2} (a B+3 A b)+\frac{2}{5} a^3 A x^{5/2}+\frac{2}{13} x^{13/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{2}{5} c x^{15/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{11} x^{11/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{2}{3} a x^{9/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{17} c^2 x^{17/2} (A c+3 b B)+\frac{2}{19} B c^3 x^{19/2}",1,"(2*a^3*A*x^(5/2))/5 + (2*a^2*(3*A*b + a*B)*x^(7/2))/7 + (2*a*(a*b*B + A*(b^2 + a*c))*x^(9/2))/3 + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(11/2))/11 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(13/2))/13 + (2*c*(b^2*B + A*b*c + a*B*c)*x^(15/2))/5 + (2*c^2*(3*b*B + A*c)*x^(17/2))/17 + (2*B*c^3*x^(19/2))/19","A",2,1,23,0.04348,1,"{765}"
1002,1,182,0,0.1149199,"\int \sqrt{x} (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[Sqrt[x]*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{11} x^{11/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{13} c x^{13/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{9} x^{9/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{7} a x^{7/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{15} c^2 x^{15/2} (A c+3 b B)+\frac{2}{17} B c^3 x^{17/2}","\frac{2}{5} a^2 x^{5/2} (a B+3 A b)+\frac{2}{3} a^3 A x^{3/2}+\frac{2}{11} x^{11/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{13} c x^{13/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{9} x^{9/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{7} a x^{7/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{15} c^2 x^{15/2} (A c+3 b B)+\frac{2}{17} B c^3 x^{17/2}",1,"(2*a^3*A*x^(3/2))/3 + (2*a^2*(3*A*b + a*B)*x^(5/2))/5 + (6*a*(a*b*B + A*(b^2 + a*c))*x^(7/2))/7 + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(9/2))/9 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(11/2))/11 + (6*c*(b^2*B + A*b*c + a*B*c)*x^(13/2))/13 + (2*c^2*(3*b*B + A*c)*x^(15/2))/15 + (2*B*c^3*x^(17/2))/17","A",2,1,23,0.04348,1,"{765}"
1003,1,180,0,0.1110772,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{\sqrt{x}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/Sqrt[x],x]","\frac{2}{3} a^2 x^{3/2} (a B+3 A b)+2 a^3 A \sqrt{x}+\frac{2}{9} x^{9/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{11} c x^{11/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{7} x^{7/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{5} a x^{5/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{2}{15} B c^3 x^{15/2}","\frac{2}{3} a^2 x^{3/2} (a B+3 A b)+2 a^3 A \sqrt{x}+\frac{2}{9} x^{9/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{11} c x^{11/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{7} x^{7/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+\frac{6}{5} a x^{5/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{13} c^2 x^{13/2} (A c+3 b B)+\frac{2}{15} B c^3 x^{15/2}",1,"2*a^3*A*Sqrt[x] + (2*a^2*(3*A*b + a*B)*x^(3/2))/3 + (6*a*(a*b*B + A*(b^2 + a*c))*x^(5/2))/5 + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(7/2))/7 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(9/2))/9 + (6*c*(b^2*B + A*b*c + a*B*c)*x^(11/2))/11 + (2*c^2*(3*b*B + A*c)*x^(13/2))/13 + (2*B*c^3*x^(15/2))/15","A",2,1,23,0.04348,1,"{765}"
1004,1,176,0,0.1174351,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{3/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^(3/2),x]","2 a^2 \sqrt{x} (a B+3 A b)-\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{7} x^{7/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{2}{3} c x^{9/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{5} x^{5/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+2 a x^{3/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{11} c^2 x^{11/2} (A c+3 b B)+\frac{2}{13} B c^3 x^{13/2}","2 a^2 \sqrt{x} (a B+3 A b)-\frac{2 a^3 A}{\sqrt{x}}+\frac{2}{7} x^{7/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{2}{3} c x^{9/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{5} x^{5/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+2 a x^{3/2} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{11} c^2 x^{11/2} (A c+3 b B)+\frac{2}{13} B c^3 x^{13/2}",1,"(-2*a^3*A)/Sqrt[x] + 2*a^2*(3*A*b + a*B)*Sqrt[x] + 2*a*(a*b*B + A*(b^2 + a*c))*x^(3/2) + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(5/2))/5 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(7/2))/7 + (2*c*(b^2*B + A*b*c + a*B*c)*x^(9/2))/3 + (2*c^2*(3*b*B + A*c)*x^(11/2))/11 + (2*B*c^3*x^(13/2))/13","A",2,1,23,0.04348,1,"{765}"
1005,1,178,0,0.1119776,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{5/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^(5/2),x]","-\frac{2 a^2 (a B+3 A b)}{\sqrt{x}}-\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{5} x^{5/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{7} c x^{7/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{3} x^{3/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+6 a \sqrt{x} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{9} c^2 x^{9/2} (A c+3 b B)+\frac{2}{11} B c^3 x^{11/2}","-\frac{2 a^2 (a B+3 A b)}{\sqrt{x}}-\frac{2 a^3 A}{3 x^{3/2}}+\frac{2}{5} x^{5/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{7} c x^{7/2} \left(a B c+A b c+b^2 B\right)+\frac{2}{3} x^{3/2} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+6 a \sqrt{x} \left(A \left(a c+b^2\right)+a b B\right)+\frac{2}{9} c^2 x^{9/2} (A c+3 b B)+\frac{2}{11} B c^3 x^{11/2}",1,"(-2*a^3*A)/(3*x^(3/2)) - (2*a^2*(3*A*b + a*B))/Sqrt[x] + 6*a*(a*b*B + A*(b^2 + a*c))*Sqrt[x] + (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^(3/2))/3 + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(5/2))/5 + (6*c*(b^2*B + A*b*c + a*B*c)*x^(7/2))/7 + (2*c^2*(3*b*B + A*c)*x^(9/2))/9 + (2*B*c^3*x^(11/2))/11","A",2,1,23,0.04348,1,"{765}"
1006,1,178,0,0.1151286,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{7/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^(7/2),x]","-\frac{2 a^2 (a B+3 A b)}{3 x^{3/2}}-\frac{2 a^3 A}{5 x^{5/2}}+\frac{2}{3} x^{3/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{5} c x^{5/2} \left(a B c+A b c+b^2 B\right)+2 \sqrt{x} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)-\frac{6 a \left(A \left(a c+b^2\right)+a b B\right)}{\sqrt{x}}+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{2}{9} B c^3 x^{9/2}","-\frac{2 a^2 (a B+3 A b)}{3 x^{3/2}}-\frac{2 a^3 A}{5 x^{5/2}}+\frac{2}{3} x^{3/2} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{6}{5} c x^{5/2} \left(a B c+A b c+b^2 B\right)+2 \sqrt{x} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)-\frac{6 a \left(A \left(a c+b^2\right)+a b B\right)}{\sqrt{x}}+\frac{2}{7} c^2 x^{7/2} (A c+3 b B)+\frac{2}{9} B c^3 x^{9/2}",1,"(-2*a^3*A)/(5*x^(5/2)) - (2*a^2*(3*A*b + a*B))/(3*x^(3/2)) - (6*a*(a*b*B + A*(b^2 + a*c)))/Sqrt[x] + 2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*Sqrt[x] + (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^(3/2))/3 + (6*c*(b^2*B + A*b*c + a*B*c)*x^(5/2))/5 + (2*c^2*(3*b*B + A*c)*x^(7/2))/7 + (2*B*c^3*x^(9/2))/9","A",2,1,23,0.04348,1,"{765}"
1007,1,174,0,0.1153412,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{9/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^(9/2),x]","-\frac{2 a^2 (a B+3 A b)}{5 x^{5/2}}-\frac{2 a^3 A}{7 x^{7/2}}+2 \sqrt{x} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+2 c x^{3/2} \left(a B c+A b c+b^2 B\right)-\frac{2 a \left(A \left(a c+b^2\right)+a b B\right)}{x^{3/2}}-\frac{2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)}{\sqrt{x}}+\frac{2}{5} c^2 x^{5/2} (A c+3 b B)+\frac{2}{7} B c^3 x^{7/2}","-\frac{2 a^2 (a B+3 A b)}{5 x^{5/2}}-\frac{2 a^3 A}{7 x^{7/2}}+2 \sqrt{x} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+2 c x^{3/2} \left(a B c+A b c+b^2 B\right)-\frac{2 a \left(A \left(a c+b^2\right)+a b B\right)}{x^{3/2}}-\frac{2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)}{\sqrt{x}}+\frac{2}{5} c^2 x^{5/2} (A c+3 b B)+\frac{2}{7} B c^3 x^{7/2}",1,"(-2*a^3*A)/(7*x^(7/2)) - (2*a^2*(3*A*b + a*B))/(5*x^(5/2)) - (2*a*(a*b*B + A*(b^2 + a*c)))/x^(3/2) - (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c)))/Sqrt[x] + 2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*Sqrt[x] + 2*c*(b^2*B + A*b*c + a*B*c)*x^(3/2) + (2*c^2*(3*b*B + A*c)*x^(5/2))/5 + (2*B*c^3*x^(7/2))/7","A",2,1,23,0.04348,1,"{765}"
1008,1,178,0,0.1120421,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{x^{11/2}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/x^(11/2),x]","-\frac{2 a^2 (a B+3 A b)}{7 x^{7/2}}-\frac{2 a^3 A}{9 x^{9/2}}-\frac{2 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)}{\sqrt{x}}-\frac{6 a \left(A \left(a c+b^2\right)+a b B\right)}{5 x^{5/2}}-\frac{2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)}{3 x^{3/2}}+6 c \sqrt{x} \left(a B c+A b c+b^2 B\right)+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+\frac{2}{5} B c^3 x^{5/2}","-\frac{2 a^2 (a B+3 A b)}{7 x^{7/2}}-\frac{2 a^3 A}{9 x^{9/2}}-\frac{2 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)}{\sqrt{x}}-\frac{6 a \left(A \left(a c+b^2\right)+a b B\right)}{5 x^{5/2}}-\frac{2 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)}{3 x^{3/2}}+6 c \sqrt{x} \left(a B c+A b c+b^2 B\right)+\frac{2}{3} c^2 x^{3/2} (A c+3 b B)+\frac{2}{5} B c^3 x^{5/2}",1,"(-2*a^3*A)/(9*x^(9/2)) - (2*a^2*(3*A*b + a*B))/(7*x^(7/2)) - (6*a*(a*b*B + A*(b^2 + a*c)))/(5*x^(5/2)) - (2*(3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c)))/(3*x^(3/2)) - (2*(b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2))/Sqrt[x] + 6*c*(b^2*B + A*b*c + a*B*c)*Sqrt[x] + (2*c^2*(3*b*B + A*c)*x^(3/2))/3 + (2*B*c^3*x^(5/2))/5","A",2,1,23,0.04348,1,"{765}"
1009,1,347,0,4.5447689,"\int \frac{x^{5/2} (A+B x)}{a+b x+c x^2} \, dx","Int[(x^(5/2)*(A + B*x))/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(-\frac{2 a^2 B c^2+3 a A b c^2-4 a b^2 B c-A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+a A c^2-2 a b B c-A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \left(\frac{2 a^2 B c^2+3 a A b c^2-4 a b^2 B c-A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+a A c^2-2 a b B c-A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 \sqrt{x} \left(-a B c-A b c+b^2 B\right)}{c^3}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 B x^{5/2}}{5 c}","-\frac{\sqrt{2} \left(-\frac{2 a^2 B c^2+3 a A b c^2-4 a b^2 B c-A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+a A c^2-2 a b B c-A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^{7/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \left(\frac{2 a^2 B c^2+3 a A b c^2-4 a b^2 B c-A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+a A c^2-2 a b B c-A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{7/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 \sqrt{x} \left(-a B c-A b c+b^2 B\right)}{c^3}-\frac{2 x^{3/2} (b B-A c)}{3 c^2}+\frac{2 B x^{5/2}}{5 c}",1,"(2*(b^2*B - A*b*c - a*B*c)*Sqrt[x])/c^3 - (2*(b*B - A*c)*x^(3/2))/(3*c^2) + (2*B*x^(5/2))/(5*c) - (Sqrt[2]*(b^3*B - A*b^2*c - 2*a*b*B*c + a*A*c^2 - (b^4*B - A*b^3*c - 4*a*b^2*B*c + 3*a*A*b*c^2 + 2*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(c^(7/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*(b^3*B - A*b^2*c - 2*a*b*B*c + a*A*c^2 + (b^4*B - A*b^3*c - 4*a*b^2*B*c + 3*a*A*b*c^2 + 2*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(c^(7/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,4,23,0.1739,1,"{824, 826, 1166, 205}"
1010,1,275,0,1.4811265,"\int \frac{x^{3/2} (A+B x)}{a+b x+c x^2} \, dx","Int[(x^(3/2)*(A + B*x))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(-\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 \sqrt{x} (b B-A c)}{c^2}+\frac{2 B x^{3/2}}{3 c}","\frac{\sqrt{2} \left(-\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(\frac{2 a A c^2-3 a b B c-A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-a B c-A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 \sqrt{x} (b B-A c)}{c^2}+\frac{2 B x^{3/2}}{3 c}",1,"(-2*(b*B - A*c)*Sqrt[x])/c^2 + (2*B*x^(3/2))/(3*c) + (Sqrt[2]*(b^2*B - A*b*c - a*B*c - (b^3*B - A*b^2*c - 3*a*b*B*c + 2*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(c^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*(b^2*B - A*b*c - a*B*c + (b^3*B - A*b^2*c - 3*a*b*B*c + 2*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(c^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,23,0.1739,1,"{824, 826, 1166, 205}"
1011,1,221,0,0.8119029,"\int \frac{\sqrt{x} (A+B x)}{a+b x+c x^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(-\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \left(\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 B \sqrt{x}}{c}","-\frac{\sqrt{2} \left(-\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{c^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \left(\frac{-2 a B c-A b c+b^2 B}{\sqrt{b^2-4 a c}}-A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{c^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 B \sqrt{x}}{c}",1,"(2*B*Sqrt[x])/c - (Sqrt[2]*(b*B - A*c - (b^2*B - A*b*c - 2*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(c^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*(b*B - A*c + (b^2*B - A*b*c - 2*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(c^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,23,0.1739,1,"{824, 826, 1166, 205}"
1012,1,180,0,0.2850881,"\int \frac{A+B x}{\sqrt{x} \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[x]*(a + b*x + c*x^2)),x]","\frac{\sqrt{2} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{2} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{c} \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[2]*(B - (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*(B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",4,3,23,0.1304,1,"{826, 1166, 205}"
1013,1,199,0,0.5456041,"\int \frac{A+B x}{x^{3/2} \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(3/2)*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \left(\frac{A b-2 a B}{\sqrt{b^2-4 a c}}+A\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left(A-\frac{A b-2 a B}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 A}{a \sqrt{x}}","-\frac{\sqrt{2} \sqrt{c} \left(\frac{A b-2 a B}{\sqrt{b^2-4 a c}}+A\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left(A-\frac{A b-2 a B}{\sqrt{b^2-4 a c}}\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 A}{a \sqrt{x}}",1,"(-2*A)/(a*Sqrt[x]) - (Sqrt[2]*Sqrt[c]*(A + (A*b - 2*a*B)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*(A - (A*b - 2*a*B)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(a*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,23,0.1739,1,"{828, 826, 1166, 205}"
1014,1,284,0,0.8056862,"\int \frac{A+B x}{x^{5/2} \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(5/2)*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \left(a B \left(\sqrt{b^2-4 a c}+b\right)-A \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \sqrt{c} \left(a B \left(b-\sqrt{b^2-4 a c}\right)-A \left(-b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 (A b-a B)}{a^2 \sqrt{x}}-\frac{2 A}{3 a x^{3/2}}","-\frac{\sqrt{2} \sqrt{c} \left(a B \left(\sqrt{b^2-4 a c}+b\right)-A \left(b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{2} \sqrt{c} \left(a B \left(b-\sqrt{b^2-4 a c}\right)-A \left(-b \sqrt{b^2-4 a c}-2 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^2 \sqrt{b^2-4 a c} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 (A b-a B)}{a^2 \sqrt{x}}-\frac{2 A}{3 a x^{3/2}}",1,"(-2*A)/(3*a*x^(3/2)) + (2*(A*b - a*B))/(a^2*Sqrt[x]) - (Sqrt[2]*Sqrt[c]*(a*B*(b + Sqrt[b^2 - 4*a*c]) - A*(b^2 - 2*a*c + b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[2]*Sqrt[c]*(a*B*(b - Sqrt[b^2 - 4*a*c]) - A*(b^2 - 2*a*c - b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(a^2*Sqrt[b^2 - 4*a*c]*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,23,0.1739,1,"{828, 826, 1166, 205}"
1015,1,307,0,1.958721,"\int \frac{A+B x}{x^{7/2} \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(7/2)*(a + b*x + c*x^2)),x]","-\frac{2 \left(-a A c-a b B+A b^2\right)}{a^3 \sqrt{x}}-\frac{\sqrt{2} \sqrt{c} \left(-\frac{a B \left(b^2-2 a c\right)-A \left(b^3-3 a b c\right)}{\sqrt{b^2-4 a c}}-a A c-a b B+A b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^3 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left(\frac{a B \left(b^2-2 a c\right)-A \left(b^3-3 a b c\right)}{\sqrt{b^2-4 a c}}-a A c-a b B+A b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^3 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 (A b-a B)}{3 a^2 x^{3/2}}-\frac{2 A}{5 a x^{5/2}}","-\frac{2 \left(-a A c-a b B+A b^2\right)}{a^3 \sqrt{x}}-\frac{\sqrt{2} \sqrt{c} \left(-\frac{a B \left(b^2-2 a c\right)-A \left(b^3-3 a b c\right)}{\sqrt{b^2-4 a c}}-a A c-a b B+A b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^3 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left(\frac{a B \left(b^2-2 a c\right)-A \left(b^3-3 a b c\right)}{\sqrt{b^2-4 a c}}-a A c-a b B+A b^2\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^3 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{2 (A b-a B)}{3 a^2 x^{3/2}}-\frac{2 A}{5 a x^{5/2}}",1,"(-2*A)/(5*a*x^(5/2)) + (2*(A*b - a*B))/(3*a^2*x^(3/2)) - (2*(A*b^2 - a*b*B - a*A*c))/(a^3*Sqrt[x]) - (Sqrt[2]*Sqrt[c]*(A*b^2 - a*b*B - a*A*c - (a*B*(b^2 - 2*a*c) - A*(b^3 - 3*a*b*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a^3*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*(A*b^2 - a*b*B - a*A*c + (a*B*(b^2 - 2*a*c) - A*(b^3 - 3*a*b*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(a^3*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,4,23,0.1739,1,"{828, 826, 1166, 205}"
1016,1,381,0,1.6708685,"\int \frac{A+B x}{x^{9/2} \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/(x^(9/2)*(a + b*x + c*x^2)),x]","-\frac{\sqrt{2} \sqrt{c} \left(\frac{a b B \left(b^2-3 a c\right)-A \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{\sqrt{b^2-4 a c}}-A \left(b^3-2 a b c\right)+a B \left(b^2-a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^4 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left(-\frac{a b B \left(b^2-3 a c\right)-A \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{\sqrt{b^2-4 a c}}-A \left(b^3-2 a b c\right)+a B \left(b^2-a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^4 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 \left(-a A c-a b B+A b^2\right)}{3 a^3 x^{3/2}}-\frac{2 \left(a B \left(b^2-a c\right)-A \left(b^3-2 a b c\right)\right)}{a^4 \sqrt{x}}+\frac{2 (A b-a B)}{5 a^2 x^{5/2}}-\frac{2 A}{7 a x^{7/2}}","-\frac{\sqrt{2} \sqrt{c} \left(\frac{a b B \left(b^2-3 a c\right)-A \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{\sqrt{b^2-4 a c}}-A \left(b^3-2 a b c\right)+a B \left(b^2-a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{a^4 \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{2} \sqrt{c} \left(-\frac{a b B \left(b^2-3 a c\right)-A \left(2 a^2 c^2-4 a b^2 c+b^4\right)}{\sqrt{b^2-4 a c}}-A \left(b^3-2 a b c\right)+a B \left(b^2-a c\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{a^4 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{2 \left(-a A c-a b B+A b^2\right)}{3 a^3 x^{3/2}}-\frac{2 \left(a B \left(b^2-a c\right)-A \left(b^3-2 a b c\right)\right)}{a^4 \sqrt{x}}+\frac{2 (A b-a B)}{5 a^2 x^{5/2}}-\frac{2 A}{7 a x^{7/2}}",1,"(-2*A)/(7*a*x^(7/2)) + (2*(A*b - a*B))/(5*a^2*x^(5/2)) - (2*(A*b^2 - a*b*B - a*A*c))/(3*a^3*x^(3/2)) - (2*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c)))/(a^4*Sqrt[x]) - (Sqrt[2]*Sqrt[c]*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c) + (a*b*B*(b^2 - 3*a*c) - A*(b^4 - 4*a*b^2*c + 2*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(a^4*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[2]*Sqrt[c]*(a*B*(b^2 - a*c) - A*(b^3 - 2*a*b*c) - (a*b*B*(b^2 - 3*a*c) - A*(b^4 - 4*a*b^2*c + 2*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(a^4*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",8,4,23,0.1739,1,"{828, 826, 1166, 205}"
1017,1,411,0,4.1658475,"\int \frac{x^{5/2} (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(x^(5/2)*(A + B*x))/(a + b*x + c*x^2)^2,x]","-\frac{\left(-\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{x} \left(-10 a B c-A b c+3 b^2 B\right)}{c^2 \left(b^2-4 a c\right)}-\frac{x^{3/2} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{\left(-\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\left(\frac{20 a^2 B c^2+8 a A b c^2-19 a b^2 B c-A b^3 c+3 b^4 B}{\sqrt{b^2-4 a c}}+6 a A c^2-13 a b B c-A b^2 c+3 b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{5/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{x} \left(-10 a B c-A b c+3 b^2 B\right)}{c^2 \left(b^2-4 a c\right)}-\frac{x^{3/2} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"((3*b^2*B - A*b*c - 10*a*B*c)*Sqrt[x])/(c^2*(b^2 - 4*a*c)) - (x^(3/2)*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2)) - ((3*b^3*B - A*b^2*c - 13*a*b*B*c + 6*a*A*c^2 - (3*b^4*B - A*b^3*c - 19*a*b^2*B*c + 8*a*A*b*c^2 + 20*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - ((3*b^3*B - A*b^2*c - 13*a*b*B*c + 6*a*A*c^2 + (3*b^4*B - A*b^3*c - 19*a*b^2*B*c + 8*a*A*b*c^2 + 20*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,23,0.2174,1,"{818, 824, 826, 1166, 205}"
1018,1,321,0,1.4305841,"\int \frac{x^{3/2} (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(x^(3/2)*(A + B*x))/(a + b*x + c*x^2)^2,x]","\frac{\left(-\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{x} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","\frac{\left(-\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a A c^2-8 a b B c+A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}-6 a B c+A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} c^{3/2} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{x} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((Sqrt[x]*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(c*(b^2 - 4*a*c)*(a + b*x + c*x^2))) + ((b^2*B + A*b*c - 6*a*B*c - (b^3*B + A*b^2*c - 8*a*b*B*c + 4*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^2*B + A*b*c - 6*a*B*c + (b^3*B + A*b^2*c - 8*a*b*B*c + 4*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,23,0.1739,1,"{818, 826, 1166, 205}"
1019,1,276,0,0.957594,"\int \frac{\sqrt{x} (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[(Sqrt[x]*(A + B*x))/(a + b*x + c*x^2)^2,x]","-\frac{\sqrt{x} (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\left(-\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{\sqrt{x} (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\left(-\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{4 a B c-4 A b c+b^2 B}{\sqrt{b^2-4 a c}}-2 A c+b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} \sqrt{c} \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-((Sqrt[x]*(A*b - 2*a*B - (b*B - 2*A*c)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2))) + ((b*B - 2*A*c - (b^2*B - 4*A*b*c + 4*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b*B - 2*A*c + (b^2*B - 4*A*b*c + 4*a*B*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,23,0.1739,1,"{820, 826, 1166, 205}"
1020,1,304,0,0.8343719,"\int \frac{A+B x}{\sqrt{x} \left(a+b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[x]*(a + b*x + c*x^2)^2),x]","\frac{\sqrt{x} \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\sqrt{c} \left(A \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)+2 a B \left(2 b-\sqrt{b^2-4 a c}\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{-12 a A c+4 a b B+A b^2}{\sqrt{b^2-4 a c}}-2 a B+A b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}","\frac{\sqrt{x} \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{\sqrt{c} \left(A \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)+2 a B \left(2 b-\sqrt{b^2-4 a c}\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{-12 a A c+4 a b B+A b^2}{\sqrt{b^2-4 a c}}-2 a B+A b\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a \left(b^2-4 a c\right) \sqrt{\sqrt{b^2-4 a c}+b}}",1,"(Sqrt[x]*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(a*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (Sqrt[c]*(2*a*B*(2*b - Sqrt[b^2 - 4*a*c]) + A*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(A*b - 2*a*B - (A*b^2 + 4*a*b*B - 12*a*A*c)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a*(b^2 - 4*a*c)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",5,4,23,0.1739,1,"{822, 826, 1166, 205}"
1021,1,406,0,0.9766743,"\int \frac{A+B x}{x^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(x^(3/2)*(a + b*x + c*x^2)^2),x]","-\frac{-10 a A c-a b B+3 A b^2}{a^2 \sqrt{x} \left(b^2-4 a c\right)}+\frac{\sqrt{c} \left(a B \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)-A \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(a B \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right)-A \left(-3 b^2 \sqrt{b^2-4 a c}+10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{c x (A b-2 a B)-2 a A c-a b B+A b^2}{a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{-10 a A c-a b B+3 A b^2}{a^2 \sqrt{x} \left(b^2-4 a c\right)}+\frac{\sqrt{c} \left(a B \left(b \sqrt{b^2-4 a c}-12 a c+b^2\right)-A \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(a B \left(-b \sqrt{b^2-4 a c}-12 a c+b^2\right)-A \left(-3 b^2 \sqrt{b^2-4 a c}+10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^2 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{c x (A b-2 a B)-2 a A c-a b B+A b^2}{a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-((3*A*b^2 - a*b*B - 10*a*A*c)/(a^2*(b^2 - 4*a*c)*Sqrt[x])) + (A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x)/(a*(b^2 - 4*a*c)*Sqrt[x]*(a + b*x + c*x^2)) + (Sqrt[c]*(a*B*(b^2 - 12*a*c + b*Sqrt[b^2 - 4*a*c]) - A*(3*b^3 - 16*a*b*c + 3*b^2*Sqrt[b^2 - 4*a*c] - 10*a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(a*B*(b^2 - 12*a*c - b*Sqrt[b^2 - 4*a*c]) - A*(3*b^3 - 16*a*b*c - 3*b^2*Sqrt[b^2 - 4*a*c] + 10*a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^2*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,23,0.2174,1,"{822, 828, 826, 1166, 205}"
1022,1,521,0,1.555489,"\int \frac{A+B x}{x^{5/2} \left(a+b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(x^(5/2)*(a + b*x + c*x^2)^2),x]","-\frac{\sqrt{c} \left(a B \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2+5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(a B \left(-3 b^2 \sqrt{b^2-4 a c}+10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2-5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c+19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-14 a A c-3 a b B+5 A b^2}{3 a^2 x^{3/2} \left(b^2-4 a c\right)}-\frac{a B \left(3 b^2-10 a c\right)-A \left(5 b^3-19 a b c\right)}{a^3 \sqrt{x} \left(b^2-4 a c\right)}+\frac{c x (A b-2 a B)-2 a A c-a b B+A b^2}{a x^{3/2} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{\sqrt{c} \left(a B \left(3 b^2 \sqrt{b^2-4 a c}-10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2+5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c-19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(a B \left(-3 b^2 \sqrt{b^2-4 a c}+10 a c \sqrt{b^2-4 a c}-16 a b c+3 b^3\right)-A \left(28 a^2 c^2-5 b^3 \sqrt{b^2-4 a c}-29 a b^2 c+19 a b c \sqrt{b^2-4 a c}+5 b^4\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{\sqrt{2} a^3 \left(b^2-4 a c\right)^{3/2} \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{-14 a A c-3 a b B+5 A b^2}{3 a^2 x^{3/2} \left(b^2-4 a c\right)}-\frac{a B \left(3 b^2-10 a c\right)-A \left(5 b^3-19 a b c\right)}{a^3 \sqrt{x} \left(b^2-4 a c\right)}+\frac{c x (A b-2 a B)-2 a A c-a b B+A b^2}{a x^{3/2} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"-(5*A*b^2 - 3*a*b*B - 14*a*A*c)/(3*a^2*(b^2 - 4*a*c)*x^(3/2)) - (a*B*(3*b^2 - 10*a*c) - A*(5*b^3 - 19*a*b*c))/(a^3*(b^2 - 4*a*c)*Sqrt[x]) + (A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x)/(a*(b^2 - 4*a*c)*x^(3/2)*(a + b*x + c*x^2)) - (Sqrt[c]*(a*B*(3*b^3 - 16*a*b*c + 3*b^2*Sqrt[b^2 - 4*a*c] - 10*a*c*Sqrt[b^2 - 4*a*c]) - A*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 + 5*b^3*Sqrt[b^2 - 4*a*c] - 19*a*b*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(a*B*(3*b^3 - 16*a*b*c - 3*b^2*Sqrt[b^2 - 4*a*c] + 10*a*c*Sqrt[b^2 - 4*a*c]) - A*(5*b^4 - 29*a*b^2*c + 28*a^2*c^2 - 5*b^3*Sqrt[b^2 - 4*a*c] + 19*a*b*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(Sqrt[2]*a^3*(b^2 - 4*a*c)^(3/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,5,23,0.2174,1,"{822, 828, 826, 1166, 205}"
1023,1,528,0,9.3191133,"\int \frac{x^{7/2} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[(x^(7/2)*(A + B*x))/(a + b*x + c*x^2)^3,x]","-\frac{\sqrt{x} \left(x \left(28 a^2 B c^2+8 a A b c^2-25 a b^2 B c+A b^3 c+3 b^4 B\right)+a \left(20 a A c^2-24 a b B c+A b^2 c+3 b^3 B\right)\right)}{4 c^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\left(-\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^{5/2} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{\sqrt{x} \left(x \left(28 a^2 B c^2+8 a A b c^2-25 a b^2 B c+A b^3 c+3 b^4 B\right)+a \left(20 a A c^2-24 a b B c+A b^2 c+3 b^3 B\right)\right)}{4 c^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\left(-\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 A c^3+132 a^2 b B c^2-18 a A b^2 c^2-33 a b^3 B c+A b^4 c+3 b^5 B}{\sqrt{b^2-4 a c}}+84 a^2 B c^2-16 a A b c^2-27 a b^2 B c+A b^3 c+3 b^4 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} c^{5/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{x^{5/2} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(x^(5/2)*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(2*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (Sqrt[x]*(a*(3*b^3*B + A*b^2*c - 24*a*b*B*c + 20*a*A*c^2) + (3*b^4*B + A*b^3*c - 25*a*b^2*B*c + 8*a*A*b*c^2 + 28*a^2*B*c^2)*x))/(4*c^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + ((3*b^4*B + A*b^3*c - 27*a*b^2*B*c - 16*a*A*b*c^2 + 84*a^2*B*c^2 - (3*b^5*B + A*b^4*c - 33*a*b^3*B*c - 18*a*A*b^2*c^2 + 132*a^2*b*B*c^2 - 40*a^2*A*c^3)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((3*b^4*B + A*b^3*c - 27*a*b^2*B*c - 16*a*A*b*c^2 + 84*a^2*B*c^2 + (3*b^5*B + A*b^4*c - 33*a*b^3*B*c - 18*a*A*b^2*c^2 + 132*a^2*b*B*c^2 - 40*a^2*A*c^3)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*c^(5/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,23,0.1739,1,"{818, 826, 1166, 205}"
1024,1,459,0,4.6865702,"\int \frac{x^{5/2} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[(x^(5/2)*(A + B*x))/(a + b*x + c*x^2)^3,x]","\frac{\left(-\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{x} \left(a \left(20 a B c-12 A b c+b^2 B\right)-x \left(12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{x^{3/2} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{\left(-\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\left(\frac{-40 a^2 B c^2+36 a A b c^2-18 a b^2 B c+3 A b^3 c+b^4 B}{\sqrt{b^2-4 a c}}+12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{x} \left(a \left(20 a B c-12 A b c+b^2 B\right)-x \left(12 a A c^2-16 a b B c+3 A b^2 c+b^3 B\right)\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{x^{3/2} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(x^(3/2)*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(2*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (Sqrt[x]*(a*(b^2*B - 12*A*b*c + 20*a*B*c) - (b^3*B + 3*A*b^2*c - 16*a*b*B*c + 12*a*A*c^2)*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + ((b^3*B + 3*A*b^2*c - 16*a*b*B*c + 12*a*A*c^2 - (b^4*B + 3*A*b^3*c - 18*a*b^2*B*c + 36*a*A*b*c^2 - 40*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + ((b^3*B + 3*A*b^2*c - 16*a*b*B*c + 12*a*A*c^2 + (b^4*B + 3*A*b^3*c - 18*a*b^2*B*c + 36*a*A*b*c^2 - 40*a^2*B*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,23,0.2174,1,"{818, 820, 826, 1166, 205}"
1025,1,414,0,2.0371659,"\int \frac{x^{3/2} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[(x^(3/2)*(A + B*x))/(a + b*x + c*x^2)^3,x]","\frac{\sqrt{x} \left(3 c x \left(4 a B c-4 A b c+b^2 B\right)+4 a A c^2+4 a b B c-7 A b^2 c+2 b^3 B\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{3 \left(-\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{x} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{\sqrt{x} \left(3 c x \left(4 a B c-4 A b c+b^2 B\right)+4 a A c^2+4 a b B c-7 A b^2 c+2 b^3 B\right)}{4 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{3 \left(-\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{3 \left(\frac{-8 a A c^2+12 a b B c-6 A b^2 c+b^3 B}{\sqrt{b^2-4 a c}}+4 a B c-4 A b c+b^2 B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}-\frac{\sqrt{x} \left(x \left(-2 a B c-A b c+b^2 B\right)+a (b B-2 A c)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-(Sqrt[x]*(a*(b*B - 2*A*c) + (b^2*B - A*b*c - 2*a*B*c)*x))/(2*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (Sqrt[x]*(2*b^3*B - 7*A*b^2*c + 4*a*b*B*c + 4*a*A*c^2 + 3*c*(b^2*B - 4*A*b*c + 4*a*B*c)*x))/(4*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (3*(b^2*B - 4*A*b*c + 4*a*B*c - (b^3*B - 6*A*b^2*c + 12*a*b*B*c - 8*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (3*(b^2*B - 4*A*b*c + 4*a*B*c + (b^3*B - 6*A*b^2*c + 12*a*b*B*c - 8*a*A*c^2)/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,23,0.2174,1,"{818, 822, 826, 1166, 205}"
1026,1,426,0,1.2456248,"\int \frac{\sqrt{x} (A+B x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[(Sqrt[x]*(A + B*x))/(a + b*x + c*x^2)^3,x]","-\frac{\sqrt{x} (-2 a B-x (b B-2 A c)+A b)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{\sqrt{x} \left(c x \left(12 a b B-A \left(20 a c+b^2\right)\right)-A \left(8 a b c+b^3\right)+a B \left(7 b^2-4 a c\right)\right)}{4 a \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\sqrt{c} \left(A \left(b^2 \sqrt{b^2-4 a c}+20 a c \sqrt{b^2-4 a c}-52 a b c+b^3\right)+6 a B \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\frac{A \left(b^3-52 a b c\right)+6 a B \left(4 a c+3 b^2\right)}{\sqrt{b^2-4 a c}}-A \left(20 a c+b^2\right)+12 a b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}","-\frac{\sqrt{x} (-2 a B-x (b B-2 A c)+A b)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{\sqrt{x} \left(c x \left(12 a b B-A \left(20 a c+b^2\right)\right)-A \left(8 a b c+b^3\right)+a B \left(7 b^2-4 a c\right)\right)}{4 a \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\sqrt{c} \left(A \left(b^2 \sqrt{b^2-4 a c}+20 a c \sqrt{b^2-4 a c}-52 a b c+b^3\right)+6 a B \left(-2 b \sqrt{b^2-4 a c}+4 a c+3 b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{\sqrt{c} \left(\frac{A \left(b^3-52 a b c\right)+6 a B \left(4 a c+3 b^2\right)}{\sqrt{b^2-4 a c}}-A \left(20 a c+b^2\right)+12 a b B\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}",1,"-(Sqrt[x]*(A*b - 2*a*B - (b*B - 2*A*c)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (Sqrt[x]*(a*B*(7*b^2 - 4*a*c) - A*(b^3 + 8*a*b*c) + c*(12*a*b*B - A*(b^2 + 20*a*c))*x))/(4*a*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (Sqrt[c]*(6*a*B*(3*b^2 + 4*a*c - 2*b*Sqrt[b^2 - 4*a*c]) + A*(b^3 - 52*a*b*c + b^2*Sqrt[b^2 - 4*a*c] + 20*a*c*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (Sqrt[c]*(12*a*b*B - A*(b^2 + 20*a*c) + (6*a*B*(3*b^2 + 4*a*c) + A*(b^3 - 52*a*b*c))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,5,23,0.2174,1,"{820, 822, 826, 1166, 205}"
1027,1,468,0,1.6602584,"\int \frac{A+B x}{\sqrt{x} \left(a+b x+c x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[x]*(a + b*x + c*x^2)^3),x]","\frac{\sqrt{x} \left(A \left(28 a^2 c^2-25 a b^2 c+3 b^4\right)+c x \left(3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right)+a b B \left(8 a c+b^2\right)\right)}{4 a^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\sqrt{c} \left(\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{x} \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","\frac{\sqrt{x} \left(A \left(28 a^2 c^2-25 a b^2 c+3 b^4\right)+c x \left(3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right)+a b B \left(8 a c+b^2\right)\right)}{4 a^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{\sqrt{c} \left(\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{b-\sqrt{b^2-4 a c}}}+\frac{\sqrt{c} \left(-\frac{3 A \left(56 a^2 c^2-10 a b^2 c+b^4\right)+a b B \left(b^2-52 a c\right)}{\sqrt{b^2-4 a c}}+3 A \left(b^3-8 a b c\right)+a B \left(20 a c+b^2\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a^2 \left(b^2-4 a c\right)^2 \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{\sqrt{x} \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{2 a \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(Sqrt[x]*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(2*a*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (Sqrt[x]*(a*b*B*(b^2 + 8*a*c) + A*(3*b^4 - 25*a*b^2*c + 28*a^2*c^2) + c*(a*B*(b^2 + 20*a*c) + 3*A*(b^3 - 8*a*b*c))*x))/(4*a^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) + (Sqrt[c]*(a*B*(b^2 + 20*a*c) + 3*A*(b^3 - 8*a*b*c) + (a*b*B*(b^2 - 52*a*c) + 3*A*(b^4 - 10*a*b^2*c + 56*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a^2*(b^2 - 4*a*c)^2*Sqrt[b - Sqrt[b^2 - 4*a*c]]) + (Sqrt[c]*(a*B*(b^2 + 20*a*c) + 3*A*(b^3 - 8*a*b*c) - (a*b*B*(b^2 - 52*a*c) + 3*A*(b^4 - 10*a*b^2*c + 56*a^2*c^2))/Sqrt[b^2 - 4*a*c])*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a^2*(b^2 - 4*a*c)^2*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",6,4,23,0.1739,1,"{822, 826, 1166, 205}"
1028,1,664,0,1.7102888,"\int \frac{A+B x}{x^{3/2} \left(a+b x+c x^2\right)^3} \, dx","Int[(A + B*x)/(x^(3/2)*(a + b*x + c*x^2)^3),x]","-\frac{-A \left(36 a^2 c^2-35 a b^2 c+5 b^4\right)+c x \left(a B \left(b^2-28 a c\right)-A \left(5 b^3-32 a b c\right)\right)+a b B \left(b^2-16 a c\right)}{4 a^2 \sqrt{x} \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{3 \left(a b B \left(b^2-8 a c\right)-A \left(60 a^2 c^2-37 a b^2 c+5 b^4\right)\right)}{4 a^3 \sqrt{x} \left(b^2-4 a c\right)^2}+\frac{3 \sqrt{c} \left(a B \left(56 a^2 c^2+b^3 \sqrt{b^2-4 a c}-10 a b^2 c-8 a b c \sqrt{b^2-4 a c}+b^4\right)-A \left(60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2+5 b^4 \sqrt{b^2-4 a c}-47 a b^3 c-37 a b^2 c \sqrt{b^2-4 a c}+5 b^5\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(a B \left(56 a^2 c^2-b^3 \sqrt{b^2-4 a c}-10 a b^2 c+8 a b c \sqrt{b^2-4 a c}+b^4\right)-A \left(-60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2-5 b^4 \sqrt{b^2-4 a c}-47 a b^3 c+37 a b^2 c \sqrt{b^2-4 a c}+5 b^5\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{c x (A b-2 a B)-2 a A c-a b B+A b^2}{2 a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{-A \left(36 a^2 c^2-35 a b^2 c+5 b^4\right)+c x \left(a B \left(b^2-28 a c\right)-A \left(5 b^3-32 a b c\right)\right)+a b B \left(b^2-16 a c\right)}{4 a^2 \sqrt{x} \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{3 \left(a b B \left(b^2-8 a c\right)-A \left(60 a^2 c^2-37 a b^2 c+5 b^4\right)\right)}{4 a^3 \sqrt{x} \left(b^2-4 a c\right)^2}+\frac{3 \sqrt{c} \left(a B \left(56 a^2 c^2+b^3 \sqrt{b^2-4 a c}-10 a b^2 c-8 a b c \sqrt{b^2-4 a c}+b^4\right)-A \left(60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2+5 b^4 \sqrt{b^2-4 a c}-47 a b^3 c-37 a b^2 c \sqrt{b^2-4 a c}+5 b^5\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{b-\sqrt{b^2-4 a c}}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{b-\sqrt{b^2-4 a c}}}-\frac{3 \sqrt{c} \left(a B \left(56 a^2 c^2-b^3 \sqrt{b^2-4 a c}-10 a b^2 c+8 a b c \sqrt{b^2-4 a c}+b^4\right)-A \left(-60 a^2 c^2 \sqrt{b^2-4 a c}+124 a^2 b c^2-5 b^4 \sqrt{b^2-4 a c}-47 a b^3 c+37 a b^2 c \sqrt{b^2-4 a c}+5 b^5\right)\right) \tan ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{x}}{\sqrt{\sqrt{b^2-4 a c}+b}}\right)}{4 \sqrt{2} a^3 \left(b^2-4 a c\right)^{5/2} \sqrt{\sqrt{b^2-4 a c}+b}}+\frac{c x (A b-2 a B)-2 a A c-a b B+A b^2}{2 a \sqrt{x} \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"(3*(a*b*B*(b^2 - 8*a*c) - A*(5*b^4 - 37*a*b^2*c + 60*a^2*c^2)))/(4*a^3*(b^2 - 4*a*c)^2*Sqrt[x]) + (A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x)/(2*a*(b^2 - 4*a*c)*Sqrt[x]*(a + b*x + c*x^2)^2) - (a*b*B*(b^2 - 16*a*c) - A*(5*b^4 - 35*a*b^2*c + 36*a^2*c^2) + c*(a*B*(b^2 - 28*a*c) - A*(5*b^3 - 32*a*b*c))*x)/(4*a^2*(b^2 - 4*a*c)^2*Sqrt[x]*(a + b*x + c*x^2)) + (3*Sqrt[c]*(a*B*(b^4 - 10*a*b^2*c + 56*a^2*c^2 + b^3*Sqrt[b^2 - 4*a*c] - 8*a*b*c*Sqrt[b^2 - 4*a*c]) - A*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 + 5*b^4*Sqrt[b^2 - 4*a*c] - 37*a*b^2*c*Sqrt[b^2 - 4*a*c] + 60*a^2*c^2*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b - Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a^3*(b^2 - 4*a*c)^(5/2)*Sqrt[b - Sqrt[b^2 - 4*a*c]]) - (3*Sqrt[c]*(a*B*(b^4 - 10*a*b^2*c + 56*a^2*c^2 - b^3*Sqrt[b^2 - 4*a*c] + 8*a*b*c*Sqrt[b^2 - 4*a*c]) - A*(5*b^5 - 47*a*b^3*c + 124*a^2*b*c^2 - 5*b^4*Sqrt[b^2 - 4*a*c] + 37*a*b^2*c*Sqrt[b^2 - 4*a*c] - 60*a^2*c^2*Sqrt[b^2 - 4*a*c]))*ArcTan[(Sqrt[2]*Sqrt[c]*Sqrt[x])/Sqrt[b + Sqrt[b^2 - 4*a*c]]])/(4*Sqrt[2]*a^3*(b^2 - 4*a*c)^(5/2)*Sqrt[b + Sqrt[b^2 - 4*a*c]])","A",7,5,23,0.2174,1,"{822, 828, 826, 1166, 205}"
1029,1,454,0,0.5823428,"\int \sqrt{x} (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[Sqrt[x]*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","-\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} \left(5 a B c+3 c x (4 b B-7 A c)-7 A b c+4 b^2 B\right)}{105 c^2}-\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} \left(5 a b B c-2 \left(b^2-3 a c\right) (4 b B-7 A c)\right)}{105 c^{5/2} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-\sqrt{a} \sqrt{c} \left(-10 a B c-7 A b c+4 b^2 B\right)-2 \left(b^2-3 a c\right) (4 b B-7 A c)+5 a b B c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{105 c^{11/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 a b B c-2 \left(b^2-3 a c\right) (4 b B-7 A c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{105 c^{11/4} \sqrt{a+b x+c x^2}}+\frac{2 B \sqrt{x} \left(a+b x+c x^2\right)^{3/2}}{7 c}","-\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} \left(5 a B c+3 c x (4 b B-7 A c)-7 A b c+4 b^2 B\right)}{105 c^2}-\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} \left(5 a b B c-2 \left(b^2-3 a c\right) (4 b B-7 A c)\right)}{105 c^{5/2} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{\sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-\sqrt{a} \sqrt{c} \left(-10 a B c-7 A b c+4 b^2 B\right)-2 \left(b^2-3 a c\right) (4 b B-7 A c)+5 a b B c\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{105 c^{11/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 a b B c-2 \left(b^2-3 a c\right) (4 b B-7 A c)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{105 c^{11/4} \sqrt{a+b x+c x^2}}+\frac{2 B \sqrt{x} \left(a+b x+c x^2\right)^{3/2}}{7 c}",1,"(-2*(5*a*b*B*c - 2*(b^2 - 3*a*c)*(4*b*B - 7*A*c))*Sqrt[x]*Sqrt[a + b*x + c*x^2])/(105*c^(5/2)*(Sqrt[a] + Sqrt[c]*x)) - (2*Sqrt[x]*(4*b^2*B - 7*A*b*c + 5*a*B*c + 3*c*(4*b*B - 7*A*c)*x)*Sqrt[a + b*x + c*x^2])/(105*c^2) + (2*B*Sqrt[x]*(a + b*x + c*x^2)^(3/2))/(7*c) + (2*a^(1/4)*(5*a*b*B*c - 2*(b^2 - 3*a*c)*(4*b*B - 7*A*c))*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(105*c^(11/4)*Sqrt[a + b*x + c*x^2]) - (a^(1/4)*(5*a*b*B*c - 2*(b^2 - 3*a*c)*(4*b*B - 7*A*c) - Sqrt[a]*Sqrt[c]*(4*b^2*B - 7*A*b*c - 10*a*B*c))*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(105*c^(11/4)*Sqrt[a + b*x + c*x^2])","A",6,6,25,0.2400,1,"{832, 814, 839, 1197, 1103, 1195}"
1030,1,373,0,0.3451083,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{\sqrt{x}} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/Sqrt[x],x]","-\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} \left(-6 a B c-5 A b c+2 b^2 B\right)}{15 c^{3/2} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-6 a B c-5 A b c+2 b^2 B\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a+b x+c x^2}}-\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-3 \sqrt{a} B \sqrt{c}-5 A c+2 b B\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} (5 A c+b B+3 B c x)}{15 c}","-\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} \left(-6 a B c-5 A b c+2 b^2 B\right)}{15 c^{3/2} \left(\sqrt{a}+\sqrt{c} x\right)}+\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-6 a B c-5 A b c+2 b^2 B\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a+b x+c x^2}}-\frac{\sqrt[4]{a} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-3 \sqrt{a} B \sqrt{c}-5 A c+2 b B\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 c^{7/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} (5 A c+b B+3 B c x)}{15 c}",1,"(-2*(2*b^2*B - 5*A*b*c - 6*a*B*c)*Sqrt[x]*Sqrt[a + b*x + c*x^2])/(15*c^(3/2)*(Sqrt[a] + Sqrt[c]*x)) + (2*Sqrt[x]*(b*B + 5*A*c + 3*B*c*x)*Sqrt[a + b*x + c*x^2])/(15*c) + (2*a^(1/4)*(2*b^2*B - 5*A*b*c - 6*a*B*c)*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*c^(7/4)*Sqrt[a + b*x + c*x^2]) - (a^(1/4)*(b + 2*Sqrt[a]*Sqrt[c])*(2*b*B - 3*Sqrt[a]*B*Sqrt[c] - 5*A*c)*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*c^(7/4)*Sqrt[a + b*x + c*x^2])","A",5,5,25,0.2000,1,"{814, 839, 1197, 1103, 1195}"
1031,1,341,0,0.315616,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^{3/2}} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^(3/2),x]","\frac{\left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x\right) \left(\sqrt{a} B+3 A \sqrt{c}\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 \sqrt[4]{a} c^{3/4} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} (6 A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{3/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} (6 A c+b B)}{3 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 (3 A-B x) \sqrt{a+b x+c x^2}}{3 \sqrt{x}}","\frac{\left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x\right) \left(\sqrt{a} B+3 A \sqrt{c}\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 \sqrt[4]{a} c^{3/4} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt[4]{a} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} (6 A c+b B) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 c^{3/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{a+b x+c x^2} (6 A c+b B)}{3 \sqrt{c} \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 (3 A-B x) \sqrt{a+b x+c x^2}}{3 \sqrt{x}}",1,"(-2*(3*A - B*x)*Sqrt[a + b*x + c*x^2])/(3*Sqrt[x]) + (2*(b*B + 6*A*c)*Sqrt[x]*Sqrt[a + b*x + c*x^2])/(3*Sqrt[c]*(Sqrt[a] + Sqrt[c]*x)) - (2*a^(1/4)*(b*B + 6*A*c)*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*c^(3/4)*Sqrt[a + b*x + c*x^2]) + ((b + 2*Sqrt[a]*Sqrt[c])*(Sqrt[a]*B + 3*A*Sqrt[c])*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*a^(1/4)*c^(3/4)*Sqrt[a + b*x + c*x^2])","A",5,5,25,0.2000,1,"{812, 839, 1197, 1103, 1195}"
1032,1,353,0,0.3332791,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^{5/2}} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^(5/2),x]","\frac{\left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{c} (6 a B+A b)+\sqrt{a} (2 A c+3 b B)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{3/4} \sqrt[4]{c} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x\right) (6 a B+A b) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{3/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{c} \sqrt{x} (6 a B+A b) \sqrt{a+b x+c x^2}}{3 a \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt{a+b x+c x^2} (x (3 a B+A b)+a A)}{3 a x^{3/2}}","\frac{\left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(\sqrt{c} (6 a B+A b)+\sqrt{a} (2 A c+3 b B)\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{3/4} \sqrt[4]{c} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x\right) (6 a B+A b) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{3 a^{3/4} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{c} \sqrt{x} (6 a B+A b) \sqrt{a+b x+c x^2}}{3 a \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt{a+b x+c x^2} (x (3 a B+A b)+a A)}{3 a x^{3/2}}",1,"(-2*(a*A + (A*b + 3*a*B)*x)*Sqrt[a + b*x + c*x^2])/(3*a*x^(3/2)) + (2*(A*b + 6*a*B)*Sqrt[c]*Sqrt[x]*Sqrt[a + b*x + c*x^2])/(3*a*(Sqrt[a] + Sqrt[c]*x)) - (2*(A*b + 6*a*B)*c^(1/4)*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*a^(3/4)*Sqrt[a + b*x + c*x^2]) + (((A*b + 6*a*B)*Sqrt[c] + Sqrt[a]*(3*b*B + 2*A*c))*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(3*a^(3/4)*c^(1/4)*Sqrt[a + b*x + c*x^2])","A",5,5,25,0.2000,1,"{810, 839, 1197, 1103, 1195}"
1033,1,421,0,0.4386787,"\int \frac{(A+B x) \sqrt{a+b x+c x^2}}{x^{7/2}} \, dx","Int[((A + B*x)*Sqrt[a + b*x + c*x^2])/x^(7/2),x]","\frac{2 \sqrt{a+b x+c x^2} \left(-6 a A c-5 a b B+2 A b^2\right)}{15 a^2 \sqrt{x}}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{a+b x+c x^2} \left(5 a b B-2 A \left(b^2-3 a c\right)\right)}{15 a^2 \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 a b B-2 A \left(b^2-3 a c\right)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 a^{7/4} \sqrt{a+b x+c x^2}}-\frac{\sqrt[4]{c} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-3 \sqrt{a} A \sqrt{c}-5 a B+2 A b\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 a^{7/4} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{a+b x+c x^2} (x (5 a B+A b)+3 a A)}{15 a x^{5/2}}","\frac{2 \sqrt{a+b x+c x^2} \left(-6 a A c-5 a b B+2 A b^2\right)}{15 a^2 \sqrt{x}}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{a+b x+c x^2} \left(5 a b B-2 A \left(b^2-3 a c\right)\right)}{15 a^2 \left(\sqrt{a}+\sqrt{c} x\right)}-\frac{2 \sqrt[4]{c} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(5 a b B-2 A \left(b^2-3 a c\right)\right) E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 a^{7/4} \sqrt{a+b x+c x^2}}-\frac{\sqrt[4]{c} \left(2 \sqrt{a} \sqrt{c}+b\right) \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} \left(-3 \sqrt{a} A \sqrt{c}-5 a B+2 A b\right) F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{15 a^{7/4} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{a+b x+c x^2} (x (5 a B+A b)+3 a A)}{15 a x^{5/2}}",1,"(2*(2*A*b^2 - 5*a*b*B - 6*a*A*c)*Sqrt[a + b*x + c*x^2])/(15*a^2*Sqrt[x]) - (2*(3*a*A + (A*b + 5*a*B)*x)*Sqrt[a + b*x + c*x^2])/(15*a*x^(5/2)) + (2*Sqrt[c]*(5*a*b*B - 2*A*(b^2 - 3*a*c))*Sqrt[x]*Sqrt[a + b*x + c*x^2])/(15*a^2*(Sqrt[a] + Sqrt[c]*x)) - (2*c^(1/4)*(5*a*b*B - 2*A*(b^2 - 3*a*c))*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*a^(7/4)*Sqrt[a + b*x + c*x^2]) - ((b + 2*Sqrt[a]*Sqrt[c])*(2*A*b - 5*a*B - 3*Sqrt[a]*A*Sqrt[c])*c^(1/4)*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(15*a^(7/4)*Sqrt[a + b*x + c*x^2])","A",6,6,25,0.2400,1,"{810, 834, 839, 1197, 1103, 1195}"
1034,1,251,0,0.2010528,"\int (2-5 x) x^{7/2} \sqrt{2+5 x+3 x^2} \, dx","Int[(2 - 5*x)*x^(7/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{10}{39} \left(3 x^2+5 x+2\right)^{3/2} x^{7/2}+\frac{656 \left(3 x^2+5 x+2\right)^{3/2} x^{5/2}}{1287}-\frac{21620 \left(3 x^2+5 x+2\right)^{3/2} x^{3/2}}{34749}+\frac{157160 \left(3 x^2+5 x+2\right)^{3/2} \sqrt{x}}{243243}-\frac{8 (502911 x+397265) \sqrt{3 x^2+5 x+2} \sqrt{x}}{2189187}+\frac{1543648 (3 x+2) \sqrt{x}}{6567561 \sqrt{3 x^2+5 x+2}}+\frac{349240 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2189187 \sqrt{3 x^2+5 x+2}}-\frac{1543648 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{6567561 \sqrt{3 x^2+5 x+2}}","-\frac{10}{39} \left(3 x^2+5 x+2\right)^{3/2} x^{7/2}+\frac{656 \left(3 x^2+5 x+2\right)^{3/2} x^{5/2}}{1287}-\frac{21620 \left(3 x^2+5 x+2\right)^{3/2} x^{3/2}}{34749}+\frac{157160 \left(3 x^2+5 x+2\right)^{3/2} \sqrt{x}}{243243}-\frac{8 (502911 x+397265) \sqrt{3 x^2+5 x+2} \sqrt{x}}{2189187}+\frac{1543648 (3 x+2) \sqrt{x}}{6567561 \sqrt{3 x^2+5 x+2}}+\frac{349240 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2189187 \sqrt{3 x^2+5 x+2}}-\frac{1543648 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{6567561 \sqrt{3 x^2+5 x+2}}",1,"(1543648*Sqrt[x]*(2 + 3*x))/(6567561*Sqrt[2 + 5*x + 3*x^2]) - (8*Sqrt[x]*(397265 + 502911*x)*Sqrt[2 + 5*x + 3*x^2])/2189187 + (157160*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))/243243 - (21620*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2))/34749 + (656*x^(5/2)*(2 + 5*x + 3*x^2)^(3/2))/1287 - (10*x^(7/2)*(2 + 5*x + 3*x^2)^(3/2))/39 - (1543648*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(6567561*Sqrt[2 + 5*x + 3*x^2]) + (349240*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(2189187*Sqrt[2 + 5*x + 3*x^2])","A",9,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1035,1,228,0,0.1730064,"\int (2-5 x) x^{5/2} \sqrt{2+5 x+3 x^2} \, dx","Int[(2 - 5*x)*x^(5/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{10}{33} \left(3 x^2+5 x+2\right)^{3/2} x^{5/2}+\frac{532}{891} \left(3 x^2+5 x+2\right)^{3/2} x^{3/2}-\frac{4420 \left(3 x^2+5 x+2\right)^{3/2} \sqrt{x}}{6237}+\frac{8 (74313 x+57860) \sqrt{3 x^2+5 x+2} \sqrt{x}}{280665}-\frac{261784 (3 x+2) \sqrt{x}}{841995 \sqrt{3 x^2+5 x+2}}-\frac{13016 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{56133 \sqrt{3 x^2+5 x+2}}+\frac{261784 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{841995 \sqrt{3 x^2+5 x+2}}","-\frac{10}{33} \left(3 x^2+5 x+2\right)^{3/2} x^{5/2}+\frac{532}{891} \left(3 x^2+5 x+2\right)^{3/2} x^{3/2}-\frac{4420 \left(3 x^2+5 x+2\right)^{3/2} \sqrt{x}}{6237}+\frac{8 (74313 x+57860) \sqrt{3 x^2+5 x+2} \sqrt{x}}{280665}-\frac{261784 (3 x+2) \sqrt{x}}{841995 \sqrt{3 x^2+5 x+2}}-\frac{13016 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{56133 \sqrt{3 x^2+5 x+2}}+\frac{261784 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{841995 \sqrt{3 x^2+5 x+2}}",1,"(-261784*Sqrt[x]*(2 + 3*x))/(841995*Sqrt[2 + 5*x + 3*x^2]) + (8*Sqrt[x]*(57860 + 74313*x)*Sqrt[2 + 5*x + 3*x^2])/280665 - (4420*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))/6237 + (532*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2))/891 - (10*x^(5/2)*(2 + 5*x + 3*x^2)^(3/2))/33 + (261784*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(841995*Sqrt[2 + 5*x + 3*x^2]) - (13016*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(56133*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1036,1,205,0,0.1471383,"\int (2-5 x) x^{3/2} \sqrt{2+5 x+3 x^2} \, dx","Int[(2 - 5*x)*x^(3/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{10}{27} x^{3/2} \left(3 x^2+5 x+2\right)^{3/2}+\frac{136}{189} \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}-\frac{4 \sqrt{x} (1035 x+779) \sqrt{3 x^2+5 x+2}}{1701}+\frac{2360 \sqrt{x} (3 x+2)}{5103 \sqrt{3 x^2+5 x+2}}+\frac{668 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{1701 \sqrt{3 x^2+5 x+2}}-\frac{2360 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5103 \sqrt{3 x^2+5 x+2}}","-\frac{10}{27} x^{3/2} \left(3 x^2+5 x+2\right)^{3/2}+\frac{136}{189} \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}-\frac{4 \sqrt{x} (1035 x+779) \sqrt{3 x^2+5 x+2}}{1701}+\frac{2360 \sqrt{x} (3 x+2)}{5103 \sqrt{3 x^2+5 x+2}}+\frac{668 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{1701 \sqrt{3 x^2+5 x+2}}-\frac{2360 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5103 \sqrt{3 x^2+5 x+2}}",1,"(2360*Sqrt[x]*(2 + 3*x))/(5103*Sqrt[2 + 5*x + 3*x^2]) - (4*Sqrt[x]*(779 + 1035*x)*Sqrt[2 + 5*x + 3*x^2])/1701 + (136*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))/189 - (10*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2))/27 - (2360*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(5103*Sqrt[2 + 5*x + 3*x^2]) + (668*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(1701*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1037,1,182,0,0.1257057,"\int (2-5 x) \sqrt{x} \sqrt{2+5 x+3 x^2} \, dx","Int[(2 - 5*x)*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{10}{21} \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}+\frac{4}{945} \sqrt{x} (639 x+430) \sqrt{3 x^2+5 x+2}-\frac{2476 \sqrt{x} (3 x+2)}{2835 \sqrt{3 x^2+5 x+2}}-\frac{164 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{189 \sqrt{3 x^2+5 x+2}}+\frac{2476 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2835 \sqrt{3 x^2+5 x+2}}","-\frac{10}{21} \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}+\frac{4}{945} \sqrt{x} (639 x+430) \sqrt{3 x^2+5 x+2}-\frac{2476 \sqrt{x} (3 x+2)}{2835 \sqrt{3 x^2+5 x+2}}-\frac{164 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{189 \sqrt{3 x^2+5 x+2}}+\frac{2476 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2835 \sqrt{3 x^2+5 x+2}}",1,"(-2476*Sqrt[x]*(2 + 3*x))/(2835*Sqrt[2 + 5*x + 3*x^2]) + (4*Sqrt[x]*(430 + 639*x)*Sqrt[2 + 5*x + 3*x^2])/945 - (10*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2))/21 + (2476*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(2835*Sqrt[2 + 5*x + 3*x^2]) - (164*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(189*Sqrt[2 + 5*x + 3*x^2])","A",6,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1038,1,159,0,0.1040312,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{\sqrt{x}} \, dx","Int[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/Sqrt[x],x]","\frac{2}{9} \sqrt{x} \sqrt{3 x^2+5 x+2} (1-9 x)+\frac{88 \sqrt{x} (3 x+2)}{27 \sqrt{3 x^2+5 x+2}}+\frac{34 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}-\frac{88 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}","\frac{2}{9} \sqrt{x} \sqrt{3 x^2+5 x+2} (1-9 x)+\frac{88 \sqrt{x} (3 x+2)}{27 \sqrt{3 x^2+5 x+2}}+\frac{34 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}-\frac{88 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}",1,"(88*Sqrt[x]*(2 + 3*x))/(27*Sqrt[2 + 5*x + 3*x^2]) + (2*(1 - 9*x)*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/9 - (88*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(27*Sqrt[2 + 5*x + 3*x^2]) + (34*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(9*Sqrt[2 + 5*x + 3*x^2])","A",5,5,25,0.2000,1,"{814, 839, 1189, 1100, 1136}"
1039,1,159,0,0.1045995,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{3/2}} \, dx","Int[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(3/2),x]","\frac{22 \sqrt{x} (3 x+2)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 (5 x+6) \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}+\frac{10 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}-\frac{22 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}","\frac{22 \sqrt{x} (3 x+2)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 (5 x+6) \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}+\frac{10 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}-\frac{22 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}",1,"(22*Sqrt[x]*(2 + 3*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (2*(6 + 5*x)*Sqrt[2 + 5*x + 3*x^2])/(3*Sqrt[x]) - (22*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(9*Sqrt[2 + 5*x + 3*x^2]) + (10*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2])","A",5,5,25,0.2000,1,"{812, 839, 1189, 1100, 1136}"
1040,1,157,0,0.09988,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{5/2}} \, dx","Int[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(5/2),x]","-\frac{4 \sqrt{3 x^2+5 x+2} (1-5 x)}{3 x^{3/2}}-\frac{50 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{21 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{50 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","-\frac{4 \sqrt{3 x^2+5 x+2} (1-5 x)}{3 x^{3/2}}-\frac{50 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{21 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{50 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(-50*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (4*(1 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/(3*x^(3/2)) + (50*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) - (21*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",5,5,25,0.2000,1,"{810, 839, 1189, 1100, 1136}"
1041,1,180,0,0.1136242,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{7/2}} \, dx","Int[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(7/2),x]","-\frac{4 \sqrt{3 x^2+5 x+2} (3-10 x)}{15 x^{5/2}}+\frac{139 \sqrt{3 x^2+5 x+2}}{15 \sqrt{x}}-\frac{139 \sqrt{x} (3 x+2)}{15 \sqrt{3 x^2+5 x+2}}-\frac{11 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{139 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{3 x^2+5 x+2}}","-\frac{4 \sqrt{3 x^2+5 x+2} (3-10 x)}{15 x^{5/2}}+\frac{139 \sqrt{3 x^2+5 x+2}}{15 \sqrt{x}}-\frac{139 \sqrt{x} (3 x+2)}{15 \sqrt{3 x^2+5 x+2}}-\frac{11 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{139 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{3 x^2+5 x+2}}",1,"(-139*Sqrt[x]*(2 + 3*x))/(15*Sqrt[2 + 5*x + 3*x^2]) - (4*(3 - 10*x)*Sqrt[2 + 5*x + 3*x^2])/(15*x^(5/2)) + (139*Sqrt[2 + 5*x + 3*x^2])/(15*Sqrt[x]) + (139*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(15*Sqrt[2 + 5*x + 3*x^2]) - (11*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,6,25,0.2400,1,"{810, 834, 839, 1189, 1100, 1136}"
1042,1,205,0,0.1332388,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{9/2}} \, dx","Int[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(9/2),x]","-\frac{4 \sqrt{3 x^2+5 x+2} (1-3 x)}{7 x^{7/2}}-\frac{62 \sqrt{3 x^2+5 x+2}}{21 \sqrt{x}}+\frac{43 \sqrt{3 x^2+5 x+2}}{21 x^{3/2}}+\frac{62 \sqrt{x} (3 x+2)}{21 \sqrt{3 x^2+5 x+2}}+\frac{43 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{7 \sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{62 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{3 x^2+5 x+2}}","-\frac{4 \sqrt{3 x^2+5 x+2} (1-3 x)}{7 x^{7/2}}-\frac{62 \sqrt{3 x^2+5 x+2}}{21 \sqrt{x}}+\frac{43 \sqrt{3 x^2+5 x+2}}{21 x^{3/2}}+\frac{62 \sqrt{x} (3 x+2)}{21 \sqrt{3 x^2+5 x+2}}+\frac{43 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{7 \sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{62 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{3 x^2+5 x+2}}",1,"(62*Sqrt[x]*(2 + 3*x))/(21*Sqrt[2 + 5*x + 3*x^2]) - (4*(1 - 3*x)*Sqrt[2 + 5*x + 3*x^2])/(7*x^(7/2)) + (43*Sqrt[2 + 5*x + 3*x^2])/(21*x^(3/2)) - (62*Sqrt[2 + 5*x + 3*x^2])/(21*Sqrt[x]) - (62*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(21*Sqrt[2 + 5*x + 3*x^2]) + (43*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(7*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{810, 834, 839, 1189, 1100, 1136}"
1043,1,228,0,0.1571513,"\int \frac{(2-5 x) \sqrt{2+5 x+3 x^2}}{x^{11/2}} \, dx","Int[((2 - 5*x)*Sqrt[2 + 5*x + 3*x^2])/x^(11/2),x]","-\frac{4 \sqrt{3 x^2+5 x+2} (7-20 x)}{63 x^{9/2}}+\frac{1331 \sqrt{3 x^2+5 x+2}}{630 \sqrt{x}}-\frac{79 \sqrt{3 x^2+5 x+2}}{63 x^{3/2}}+\frac{97 \sqrt{3 x^2+5 x+2}}{105 x^{5/2}}-\frac{1331 \sqrt{x} (3 x+2)}{630 \sqrt{3 x^2+5 x+2}}-\frac{79 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{1331 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{315 \sqrt{2} \sqrt{3 x^2+5 x+2}}","-\frac{4 \sqrt{3 x^2+5 x+2} (7-20 x)}{63 x^{9/2}}+\frac{1331 \sqrt{3 x^2+5 x+2}}{630 \sqrt{x}}-\frac{79 \sqrt{3 x^2+5 x+2}}{63 x^{3/2}}+\frac{97 \sqrt{3 x^2+5 x+2}}{105 x^{5/2}}-\frac{1331 \sqrt{x} (3 x+2)}{630 \sqrt{3 x^2+5 x+2}}-\frac{79 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{1331 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{315 \sqrt{2} \sqrt{3 x^2+5 x+2}}",1,"(-1331*Sqrt[x]*(2 + 3*x))/(630*Sqrt[2 + 5*x + 3*x^2]) - (4*(7 - 20*x)*Sqrt[2 + 5*x + 3*x^2])/(63*x^(9/2)) + (97*Sqrt[2 + 5*x + 3*x^2])/(105*x^(5/2)) - (79*Sqrt[2 + 5*x + 3*x^2])/(63*x^(3/2)) + (1331*Sqrt[2 + 5*x + 3*x^2])/(630*Sqrt[x]) + (1331*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(315*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2]) - (79*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(21*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{810, 834, 839, 1189, 1100, 1136}"
1044,1,256,0,0.1967853,"\int (2-5 x) x^{5/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(2 - 5*x)*x^(5/2)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2}{9} x^{5/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{136}{351} x^{3/2} \left(3 x^2+5 x+2\right)^{5/2}-\frac{4660 \sqrt{x} \left(3 x^2+5 x+2\right)^{5/2}}{11583}+\frac{8 \sqrt{x} (32921 x+27010) \left(3 x^2+5 x+2\right)^{3/2}}{243243}-\frac{8 \sqrt{x} (205407 x+190465) \sqrt{3 x^2+5 x+2}}{10945935}-\frac{497824 \sqrt{x} (3 x+2)}{32837805 \sqrt{3 x^2+5 x+2}}-\frac{61736 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2189187 \sqrt{3 x^2+5 x+2}}+\frac{497824 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{32837805 \sqrt{3 x^2+5 x+2}}","-\frac{2}{9} x^{5/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{136}{351} x^{3/2} \left(3 x^2+5 x+2\right)^{5/2}-\frac{4660 \sqrt{x} \left(3 x^2+5 x+2\right)^{5/2}}{11583}+\frac{8 \sqrt{x} (32921 x+27010) \left(3 x^2+5 x+2\right)^{3/2}}{243243}-\frac{8 \sqrt{x} (205407 x+190465) \sqrt{3 x^2+5 x+2}}{10945935}-\frac{497824 \sqrt{x} (3 x+2)}{32837805 \sqrt{3 x^2+5 x+2}}-\frac{61736 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2189187 \sqrt{3 x^2+5 x+2}}+\frac{497824 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{32837805 \sqrt{3 x^2+5 x+2}}",1,"(-497824*Sqrt[x]*(2 + 3*x))/(32837805*Sqrt[2 + 5*x + 3*x^2]) - (8*Sqrt[x]*(190465 + 205407*x)*Sqrt[2 + 5*x + 3*x^2])/10945935 + (8*Sqrt[x]*(27010 + 32921*x)*(2 + 5*x + 3*x^2)^(3/2))/243243 - (4660*Sqrt[x]*(2 + 5*x + 3*x^2)^(5/2))/11583 + (136*x^(3/2)*(2 + 5*x + 3*x^2)^(5/2))/351 - (2*x^(5/2)*(2 + 5*x + 3*x^2)^(5/2))/9 + (497824*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(32837805*Sqrt[2 + 5*x + 3*x^2]) - (61736*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(2189187*Sqrt[2 + 5*x + 3*x^2])","A",9,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1045,1,233,0,0.1722425,"\int (2-5 x) x^{3/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(2 - 5*x)*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{10}{39} x^{3/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{556 \sqrt{x} \left(3 x^2+5 x+2\right)^{5/2}}{1287}-\frac{4 \sqrt{x} (8575 x+6959) \left(3 x^2+5 x+2\right)^{3/2}}{27027}+\frac{8 \sqrt{x} (6381 x+6908) \sqrt{3 x^2+5 x+2}}{243243}+\frac{55112 \sqrt{x} (3 x+2)}{729729 \sqrt{3 x^2+5 x+2}}+\frac{25448 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243243 \sqrt{3 x^2+5 x+2}}-\frac{55112 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{729729 \sqrt{3 x^2+5 x+2}}","-\frac{10}{39} x^{3/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{556 \sqrt{x} \left(3 x^2+5 x+2\right)^{5/2}}{1287}-\frac{4 \sqrt{x} (8575 x+6959) \left(3 x^2+5 x+2\right)^{3/2}}{27027}+\frac{8 \sqrt{x} (6381 x+6908) \sqrt{3 x^2+5 x+2}}{243243}+\frac{55112 \sqrt{x} (3 x+2)}{729729 \sqrt{3 x^2+5 x+2}}+\frac{25448 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243243 \sqrt{3 x^2+5 x+2}}-\frac{55112 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{729729 \sqrt{3 x^2+5 x+2}}",1,"(55112*Sqrt[x]*(2 + 3*x))/(729729*Sqrt[2 + 5*x + 3*x^2]) + (8*Sqrt[x]*(6908 + 6381*x)*Sqrt[2 + 5*x + 3*x^2])/243243 - (4*Sqrt[x]*(6959 + 8575*x)*(2 + 5*x + 3*x^2)^(3/2))/27027 + (556*Sqrt[x]*(2 + 5*x + 3*x^2)^(5/2))/1287 - (10*x^(3/2)*(2 + 5*x + 3*x^2)^(5/2))/39 - (55112*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(729729*Sqrt[2 + 5*x + 3*x^2]) + (25448*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(243243*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1046,1,210,0,0.1463277,"\int (2-5 x) \sqrt{x} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(2 - 5*x)*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{10}{33} \sqrt{x} \left(3 x^2+5 x+2\right)^{5/2}+\frac{4}{231} \sqrt{x} (84 x+65) \left(3 x^2+5 x+2\right)^{3/2}-\frac{4}{385} \sqrt{x} (39 x+55) \sqrt{3 x^2+5 x+2}-\frac{424 \sqrt{x} (3 x+2)}{1155 \sqrt{3 x^2+5 x+2}}-\frac{36 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{77 \sqrt{3 x^2+5 x+2}}+\frac{424 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{1155 \sqrt{3 x^2+5 x+2}}","-\frac{10}{33} \sqrt{x} \left(3 x^2+5 x+2\right)^{5/2}+\frac{4}{231} \sqrt{x} (84 x+65) \left(3 x^2+5 x+2\right)^{3/2}-\frac{4}{385} \sqrt{x} (39 x+55) \sqrt{3 x^2+5 x+2}-\frac{424 \sqrt{x} (3 x+2)}{1155 \sqrt{3 x^2+5 x+2}}-\frac{36 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{77 \sqrt{3 x^2+5 x+2}}+\frac{424 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{1155 \sqrt{3 x^2+5 x+2}}",1,"(-424*Sqrt[x]*(2 + 3*x))/(1155*Sqrt[2 + 5*x + 3*x^2]) - (4*Sqrt[x]*(55 + 39*x)*Sqrt[2 + 5*x + 3*x^2])/385 + (4*Sqrt[x]*(65 + 84*x)*(2 + 5*x + 3*x^2)^(3/2))/231 - (10*Sqrt[x]*(2 + 5*x + 3*x^2)^(5/2))/33 + (424*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(1155*Sqrt[2 + 5*x + 3*x^2]) - (36*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(77*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{832, 814, 839, 1189, 1100, 1136}"
1047,1,187,0,0.1201236,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{\sqrt{x}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/Sqrt[x],x]","-\frac{2}{9} \sqrt{x} (5 x+1) \left(3 x^2+5 x+2\right)^{3/2}+\frac{4}{81} \sqrt{x} (45 x+82) \sqrt{3 x^2+5 x+2}+\frac{860 \sqrt{x} (3 x+2)}{243 \sqrt{3 x^2+5 x+2}}+\frac{356 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}-\frac{860 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243 \sqrt{3 x^2+5 x+2}}","-\frac{2}{9} \sqrt{x} (5 x+1) \left(3 x^2+5 x+2\right)^{3/2}+\frac{4}{81} \sqrt{x} (45 x+82) \sqrt{3 x^2+5 x+2}+\frac{860 \sqrt{x} (3 x+2)}{243 \sqrt{3 x^2+5 x+2}}+\frac{356 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}-\frac{860 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243 \sqrt{3 x^2+5 x+2}}",1,"(860*Sqrt[x]*(2 + 3*x))/(243*Sqrt[2 + 5*x + 3*x^2]) + (4*Sqrt[x]*(82 + 45*x)*Sqrt[2 + 5*x + 3*x^2])/81 - (2*Sqrt[x]*(1 + 5*x)*(2 + 5*x + 3*x^2)^(3/2))/9 - (860*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(243*Sqrt[2 + 5*x + 3*x^2]) + (356*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(81*Sqrt[2 + 5*x + 3*x^2])","A",6,5,25,0.2000,1,"{814, 839, 1189, 1100, 1136}"
1048,1,187,0,0.1235541,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{3/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(3/2),x]","-\frac{2 (5 x+14) \left(3 x^2+5 x+2\right)^{3/2}}{7 \sqrt{x}}+\frac{2}{105} \sqrt{x} (531 x+1045) \sqrt{3 x^2+5 x+2}+\frac{5848 \sqrt{x} (3 x+2)}{315 \sqrt{3 x^2+5 x+2}}+\frac{482 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{3 x^2+5 x+2}}-\frac{5848 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{315 \sqrt{3 x^2+5 x+2}}","-\frac{2 (5 x+14) \left(3 x^2+5 x+2\right)^{3/2}}{7 \sqrt{x}}+\frac{2}{105} \sqrt{x} (531 x+1045) \sqrt{3 x^2+5 x+2}+\frac{5848 \sqrt{x} (3 x+2)}{315 \sqrt{3 x^2+5 x+2}}+\frac{482 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{3 x^2+5 x+2}}-\frac{5848 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{315 \sqrt{3 x^2+5 x+2}}",1,"(5848*Sqrt[x]*(2 + 3*x))/(315*Sqrt[2 + 5*x + 3*x^2]) + (2*Sqrt[x]*(1045 + 531*x)*Sqrt[2 + 5*x + 3*x^2])/105 - (2*(14 + 5*x)*(2 + 5*x + 3*x^2)^(3/2))/(7*Sqrt[x]) - (5848*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(315*Sqrt[2 + 5*x + 3*x^2]) + (482*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(21*Sqrt[2 + 5*x + 3*x^2])","A",6,6,25,0.2400,1,"{812, 814, 839, 1189, 1100, 1136}"
1049,1,183,0,0.1220526,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{5/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(5/2),x]","-\frac{2 (3 x+2) \left(3 x^2+5 x+2\right)^{3/2}}{3 x^{3/2}}+\frac{2 (2-x) \sqrt{3 x^2+5 x+2}}{\sqrt{x}}-\frac{34 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{14 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{34 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","-\frac{2 (3 x+2) \left(3 x^2+5 x+2\right)^{3/2}}{3 x^{3/2}}+\frac{2 (2-x) \sqrt{3 x^2+5 x+2}}{\sqrt{x}}-\frac{34 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{14 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{34 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(-34*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (2*(2 - x)*Sqrt[2 + 5*x + 3*x^2])/Sqrt[x] - (2*(2 + 3*x)*(2 + 5*x + 3*x^2)^(3/2))/(3*x^(3/2)) + (34*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) - (14*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,5,25,0.2000,1,"{812, 839, 1189, 1100, 1136}"
1050,1,185,0,0.1210171,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{7/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(7/2),x]","-\frac{4 (3-5 x) \left(3 x^2+5 x+2\right)^{3/2}}{15 x^{5/2}}+\frac{2 (89-35 x) \sqrt{3 x^2+5 x+2}}{5 \sqrt{x}}-\frac{1418 \sqrt{x} (3 x+2)}{15 \sqrt{3 x^2+5 x+2}}-\frac{117 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{1418 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{3 x^2+5 x+2}}","-\frac{4 (3-5 x) \left(3 x^2+5 x+2\right)^{3/2}}{15 x^{5/2}}+\frac{2 (89-35 x) \sqrt{3 x^2+5 x+2}}{5 \sqrt{x}}-\frac{1418 \sqrt{x} (3 x+2)}{15 \sqrt{3 x^2+5 x+2}}-\frac{117 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{1418 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{3 x^2+5 x+2}}",1,"(-1418*Sqrt[x]*(2 + 3*x))/(15*Sqrt[2 + 5*x + 3*x^2]) + (2*(89 - 35*x)*Sqrt[2 + 5*x + 3*x^2])/(5*Sqrt[x]) - (4*(3 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/(15*x^(5/2)) + (1418*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(15*Sqrt[2 + 5*x + 3*x^2]) - (117*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,6,25,0.2400,1,"{810, 812, 839, 1189, 1100, 1136}"
1051,1,187,0,0.1189244,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{9/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(9/2),x]","-\frac{4 (1-2 x) \left(3 x^2+5 x+2\right)^{3/2}}{7 x^{7/2}}+\frac{3 (133 x+22) \sqrt{3 x^2+5 x+2}}{7 x^{3/2}}-\frac{633 \sqrt{x} (3 x+2)}{7 \sqrt{3 x^2+5 x+2}}-\frac{783 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{7 \sqrt{3 x^2+5 x+2}}+\frac{633 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{7 \sqrt{3 x^2+5 x+2}}","-\frac{4 (1-2 x) \left(3 x^2+5 x+2\right)^{3/2}}{7 x^{7/2}}+\frac{3 (133 x+22) \sqrt{3 x^2+5 x+2}}{7 x^{3/2}}-\frac{633 \sqrt{x} (3 x+2)}{7 \sqrt{3 x^2+5 x+2}}-\frac{783 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{7 \sqrt{3 x^2+5 x+2}}+\frac{633 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{7 \sqrt{3 x^2+5 x+2}}",1,"(-633*Sqrt[x]*(2 + 3*x))/(7*Sqrt[2 + 5*x + 3*x^2]) + (3*(22 + 133*x)*Sqrt[2 + 5*x + 3*x^2])/(7*x^(3/2)) - (4*(1 - 2*x)*(2 + 5*x + 3*x^2)^(3/2))/(7*x^(7/2)) + (633*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(7*Sqrt[2 + 5*x + 3*x^2]) - (783*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(7*Sqrt[2 + 5*x + 3*x^2])","A",6,5,25,0.2000,1,"{810, 839, 1189, 1100, 1136}"
1052,1,210,0,0.1321936,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{11/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(11/2),x]","-\frac{4 (7-15 x) \left(3 x^2+5 x+2\right)^{3/2}}{63 x^{9/2}}+\frac{(4055 x+1446) \sqrt{3 x^2+5 x+2}}{315 x^{5/2}}+\frac{5438 \sqrt{3 x^2+5 x+2}}{315 \sqrt{x}}-\frac{5438 \sqrt{x} (3 x+2)}{315 \sqrt{3 x^2+5 x+2}}-\frac{899 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{5438 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{315 \sqrt{3 x^2+5 x+2}}","-\frac{4 (7-15 x) \left(3 x^2+5 x+2\right)^{3/2}}{63 x^{9/2}}+\frac{(4055 x+1446) \sqrt{3 x^2+5 x+2}}{315 x^{5/2}}+\frac{5438 \sqrt{3 x^2+5 x+2}}{315 \sqrt{x}}-\frac{5438 \sqrt{x} (3 x+2)}{315 \sqrt{3 x^2+5 x+2}}-\frac{899 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{21 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{5438 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{315 \sqrt{3 x^2+5 x+2}}",1,"(-5438*Sqrt[x]*(2 + 3*x))/(315*Sqrt[2 + 5*x + 3*x^2]) + (5438*Sqrt[2 + 5*x + 3*x^2])/(315*Sqrt[x]) + ((1446 + 4055*x)*Sqrt[2 + 5*x + 3*x^2])/(315*x^(5/2)) - (4*(7 - 15*x)*(2 + 5*x + 3*x^2)^(3/2))/(63*x^(9/2)) + (5438*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(315*Sqrt[2 + 5*x + 3*x^2]) - (899*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(21*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{810, 834, 839, 1189, 1100, 1136}"
1053,1,233,0,0.1520559,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{13/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(13/2),x]","-\frac{4 (9-20 x) \left(3 x^2+5 x+2\right)^{3/2}}{99 x^{11/2}}+\frac{(1367 x+634) \sqrt{3 x^2+5 x+2}}{231 x^{7/2}}-\frac{3229 \sqrt{3 x^2+5 x+2}}{1386 \sqrt{x}}+\frac{1357 \sqrt{3 x^2+5 x+2}}{693 x^{3/2}}+\frac{3229 \sqrt{x} (3 x+2)}{1386 \sqrt{3 x^2+5 x+2}}+\frac{1357 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{231 \sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{3229 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{693 \sqrt{2} \sqrt{3 x^2+5 x+2}}","-\frac{4 (9-20 x) \left(3 x^2+5 x+2\right)^{3/2}}{99 x^{11/2}}+\frac{(1367 x+634) \sqrt{3 x^2+5 x+2}}{231 x^{7/2}}-\frac{3229 \sqrt{3 x^2+5 x+2}}{1386 \sqrt{x}}+\frac{1357 \sqrt{3 x^2+5 x+2}}{693 x^{3/2}}+\frac{3229 \sqrt{x} (3 x+2)}{1386 \sqrt{3 x^2+5 x+2}}+\frac{1357 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{231 \sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{3229 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{693 \sqrt{2} \sqrt{3 x^2+5 x+2}}",1,"(3229*Sqrt[x]*(2 + 3*x))/(1386*Sqrt[2 + 5*x + 3*x^2]) + (1357*Sqrt[2 + 5*x + 3*x^2])/(693*x^(3/2)) - (3229*Sqrt[2 + 5*x + 3*x^2])/(1386*Sqrt[x]) + ((634 + 1367*x)*Sqrt[2 + 5*x + 3*x^2])/(231*x^(7/2)) - (4*(9 - 20*x)*(2 + 5*x + 3*x^2)^(3/2))/(99*x^(11/2)) - (3229*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(693*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2]) + (1357*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(231*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{810, 834, 839, 1189, 1100, 1136}"
1054,1,256,0,0.1792042,"\int \frac{(2-5 x) \left(2+5 x+3 x^2\right)^{3/2}}{x^{15/2}} \, dx","Int[((2 - 5*x)*(2 + 5*x + 3*x^2)^(3/2))/x^(15/2),x]","-\frac{4 (11-25 x) \left(3 x^2+5 x+2\right)^{3/2}}{143 x^{13/2}}+\frac{(3445 x+1834) \sqrt{3 x^2+5 x+2}}{1001 x^{9/2}}+\frac{6907 \sqrt{3 x^2+5 x+2}}{10010 \sqrt{x}}-\frac{1231 \sqrt{3 x^2+5 x+2}}{2002 x^{3/2}}+\frac{204 \sqrt{3 x^2+5 x+2}}{385 x^{5/2}}-\frac{6907 \sqrt{x} (3 x+2)}{10010 \sqrt{3 x^2+5 x+2}}-\frac{3693 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2002 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{6907 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5005 \sqrt{2} \sqrt{3 x^2+5 x+2}}","-\frac{4 (11-25 x) \left(3 x^2+5 x+2\right)^{3/2}}{143 x^{13/2}}+\frac{(3445 x+1834) \sqrt{3 x^2+5 x+2}}{1001 x^{9/2}}+\frac{6907 \sqrt{3 x^2+5 x+2}}{10010 \sqrt{x}}-\frac{1231 \sqrt{3 x^2+5 x+2}}{2002 x^{3/2}}+\frac{204 \sqrt{3 x^2+5 x+2}}{385 x^{5/2}}-\frac{6907 \sqrt{x} (3 x+2)}{10010 \sqrt{3 x^2+5 x+2}}-\frac{3693 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2002 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{6907 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5005 \sqrt{2} \sqrt{3 x^2+5 x+2}}",1,"(-6907*Sqrt[x]*(2 + 3*x))/(10010*Sqrt[2 + 5*x + 3*x^2]) + (204*Sqrt[2 + 5*x + 3*x^2])/(385*x^(5/2)) - (1231*Sqrt[2 + 5*x + 3*x^2])/(2002*x^(3/2)) + (6907*Sqrt[2 + 5*x + 3*x^2])/(10010*Sqrt[x]) + ((1834 + 3445*x)*Sqrt[2 + 5*x + 3*x^2])/(1001*x^(9/2)) - (4*(11 - 25*x)*(2 + 5*x + 3*x^2)^(3/2))/(143*x^(13/2)) + (6907*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(5005*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2]) - (3693*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(2002*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,25,0.2400,1,"{810, 834, 839, 1189, 1100, 1136}"
1055,1,300,0,0.2188725,"\int \frac{A+B x}{\sqrt{e x} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(Sqrt[e*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt[4]{a} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{e x} \sqrt{a+b x+c x^2}}+\frac{2 B x \sqrt{a+b x+c x^2}}{\sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}","\frac{\sqrt[4]{a} \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} F\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt[4]{a} B \sqrt{x} \left(\sqrt{a}+\sqrt{c} x\right) \sqrt{\frac{a+b x+c x^2}{\left(\sqrt{a}+\sqrt{c} x\right)^2}} E\left(2 \tan ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{x}}{\sqrt[4]{a}}\right)|\frac{1}{4} \left(2-\frac{b}{\sqrt{a} \sqrt{c}}\right)\right)}{c^{3/4} \sqrt{e x} \sqrt{a+b x+c x^2}}+\frac{2 B x \sqrt{a+b x+c x^2}}{\sqrt{c} \sqrt{e x} \left(\sqrt{a}+\sqrt{c} x\right)}",1,"(2*B*x*Sqrt[a + b*x + c*x^2])/(Sqrt[c]*Sqrt[e*x]*(Sqrt[a] + Sqrt[c]*x)) - (2*a^(1/4)*B*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticE[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(3/4)*Sqrt[e*x]*Sqrt[a + b*x + c*x^2]) + (a^(1/4)*(B + (A*Sqrt[c])/Sqrt[a])*Sqrt[x]*(Sqrt[a] + Sqrt[c]*x)*Sqrt[(a + b*x + c*x^2)/(Sqrt[a] + Sqrt[c]*x)^2]*EllipticF[2*ArcTan[(c^(1/4)*Sqrt[x])/a^(1/4)], (2 - b/(Sqrt[a]*Sqrt[c]))/4])/(c^(3/4)*Sqrt[e*x]*Sqrt[a + b*x + c*x^2])","A",5,5,27,0.1852,1,"{841, 839, 1197, 1103, 1195}"
1056,1,223,0,0.1626159,"\int \frac{(2-5 x) x^{7/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((2 - 5*x)*x^(7/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{10}{27} \sqrt{3 x^2+5 x+2} x^{7/2}+\frac{508}{567} \sqrt{3 x^2+5 x+2} x^{5/2}-\frac{820}{567} \sqrt{3 x^2+5 x+2} x^{3/2}+\frac{11320 \sqrt{3 x^2+5 x+2} \sqrt{x}}{5103}-\frac{68920 (3 x+2) \sqrt{x}}{15309 \sqrt{3 x^2+5 x+2}}-\frac{11320 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5103 \sqrt{3 x^2+5 x+2}}+\frac{68920 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15309 \sqrt{3 x^2+5 x+2}}","-\frac{10}{27} \sqrt{3 x^2+5 x+2} x^{7/2}+\frac{508}{567} \sqrt{3 x^2+5 x+2} x^{5/2}-\frac{820}{567} \sqrt{3 x^2+5 x+2} x^{3/2}+\frac{11320 \sqrt{3 x^2+5 x+2} \sqrt{x}}{5103}-\frac{68920 (3 x+2) \sqrt{x}}{15309 \sqrt{3 x^2+5 x+2}}-\frac{11320 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5103 \sqrt{3 x^2+5 x+2}}+\frac{68920 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15309 \sqrt{3 x^2+5 x+2}}",1,"(-68920*Sqrt[x]*(2 + 3*x))/(15309*Sqrt[2 + 5*x + 3*x^2]) + (11320*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/5103 - (820*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])/567 + (508*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])/567 - (10*x^(7/2)*Sqrt[2 + 5*x + 3*x^2])/27 + (68920*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(15309*Sqrt[2 + 5*x + 3*x^2]) - (11320*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(5103*Sqrt[2 + 5*x + 3*x^2])","A",8,5,25,0.2000,1,"{832, 839, 1189, 1100, 1136}"
1057,1,200,0,0.1431268,"\int \frac{(2-5 x) x^{5/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((2 - 5*x)*x^(5/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{10}{21} \sqrt{3 x^2+5 x+2} x^{5/2}+\frac{128}{105} \sqrt{3 x^2+5 x+2} x^{3/2}-\frac{412}{189} \sqrt{3 x^2+5 x+2} \sqrt{x}+\frac{13688 (3 x+2) \sqrt{x}}{2835 \sqrt{3 x^2+5 x+2}}+\frac{412 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{189 \sqrt{3 x^2+5 x+2}}-\frac{13688 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2835 \sqrt{3 x^2+5 x+2}}","-\frac{10}{21} \sqrt{3 x^2+5 x+2} x^{5/2}+\frac{128}{105} \sqrt{3 x^2+5 x+2} x^{3/2}-\frac{412}{189} \sqrt{3 x^2+5 x+2} \sqrt{x}+\frac{13688 (3 x+2) \sqrt{x}}{2835 \sqrt{3 x^2+5 x+2}}+\frac{412 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{189 \sqrt{3 x^2+5 x+2}}-\frac{13688 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2835 \sqrt{3 x^2+5 x+2}}",1,"(13688*Sqrt[x]*(2 + 3*x))/(2835*Sqrt[2 + 5*x + 3*x^2]) - (412*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/189 + (128*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])/105 - (10*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])/21 - (13688*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(2835*Sqrt[2 + 5*x + 3*x^2]) + (412*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(189*Sqrt[2 + 5*x + 3*x^2])","A",7,5,25,0.2000,1,"{832, 839, 1189, 1100, 1136}"
1058,1,177,0,0.1203297,"\int \frac{(2-5 x) x^{3/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((2 - 5*x)*x^(3/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{3} \sqrt{3 x^2+5 x+2} x^{3/2}+\frac{52}{27} \sqrt{3 x^2+5 x+2} \sqrt{x}-\frac{412 (3 x+2) \sqrt{x}}{81 \sqrt{3 x^2+5 x+2}}-\frac{52 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}+\frac{412 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}","-\frac{2}{3} \sqrt{3 x^2+5 x+2} x^{3/2}+\frac{52}{27} \sqrt{3 x^2+5 x+2} \sqrt{x}-\frac{412 (3 x+2) \sqrt{x}}{81 \sqrt{3 x^2+5 x+2}}-\frac{52 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}+\frac{412 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}",1,"(-412*Sqrt[x]*(2 + 3*x))/(81*Sqrt[2 + 5*x + 3*x^2]) + (52*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/27 - (2*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])/3 + (412*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(81*Sqrt[2 + 5*x + 3*x^2]) - (52*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(27*Sqrt[2 + 5*x + 3*x^2])","A",6,5,25,0.2000,1,"{832, 839, 1189, 1100, 1136}"
1059,1,154,0,0.0986726,"\int \frac{(2-5 x) \sqrt{x}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((2 - 5*x)*Sqrt[x])/Sqrt[2 + 5*x + 3*x^2],x]","\frac{136 \sqrt{x} (3 x+2)}{27 \sqrt{3 x^2+5 x+2}}-\frac{10}{9} \sqrt{x} \sqrt{3 x^2+5 x+2}+\frac{10 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}-\frac{136 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}","\frac{136 \sqrt{x} (3 x+2)}{27 \sqrt{3 x^2+5 x+2}}-\frac{10}{9} \sqrt{x} \sqrt{3 x^2+5 x+2}+\frac{10 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}-\frac{136 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}",1,"(136*Sqrt[x]*(2 + 3*x))/(27*Sqrt[2 + 5*x + 3*x^2]) - (10*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/9 - (136*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(27*Sqrt[2 + 5*x + 3*x^2]) + (10*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(9*Sqrt[2 + 5*x + 3*x^2])","A",5,5,25,0.2000,1,"{832, 839, 1189, 1100, 1136}"
1060,1,129,0,0.0797963,"\int \frac{2-5 x}{\sqrt{x} \sqrt{2+5 x+3 x^2}} \, dx","Int[(2 - 5*x)/(Sqrt[x]*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{10 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{10 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","-\frac{10 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{10 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(-10*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (10*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) + (2*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",4,4,25,0.1600,1,"{839, 1189, 1100, 1136}"
1061,1,146,0,0.0915021,"\int \frac{2-5 x}{x^{3/2} \sqrt{2+5 x+3 x^2}} \, dx","Int[(2 - 5*x)/(x^(3/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{2 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{3 x^2+5 x+2}}{\sqrt{x}}-\frac{5 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}","\frac{2 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{3 x^2+5 x+2}}{\sqrt{x}}-\frac{5 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}",1,"(2*Sqrt[x]*(2 + 3*x))/Sqrt[2 + 5*x + 3*x^2] - (2*Sqrt[2 + 5*x + 3*x^2])/Sqrt[x] - (2*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2] - (5*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",5,5,25,0.2000,1,"{834, 839, 1189, 1100, 1136}"
1062,1,175,0,0.1123554,"\int \frac{2-5 x}{x^{5/2} \sqrt{2+5 x+3 x^2}} \, dx","Int[(2 - 5*x)/(x^(5/2)*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{25 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{25 \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}-\frac{2 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}-\frac{\sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{25 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","-\frac{25 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{25 \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}-\frac{2 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}-\frac{\sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{25 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(-25*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (2*Sqrt[2 + 5*x + 3*x^2])/(3*x^(3/2)) + (25*Sqrt[2 + 5*x + 3*x^2])/(3*Sqrt[x]) + (25*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) - (Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,5,25,0.2000,1,"{834, 839, 1189, 1100, 1136}"
1063,1,196,0,0.1355234,"\int \frac{2-5 x}{x^{7/2} \sqrt{2+5 x+3 x^2}} \, dx","Int[(2 - 5*x)/(x^(7/2)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{66 \sqrt{x} (3 x+2)}{5 \sqrt{3 x^2+5 x+2}}-\frac{66 \sqrt{3 x^2+5 x+2}}{5 \sqrt{x}}+\frac{3 \sqrt{3 x^2+5 x+2}}{x^{3/2}}-\frac{2 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}+\frac{9 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{66 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5 \sqrt{3 x^2+5 x+2}}","\frac{66 \sqrt{x} (3 x+2)}{5 \sqrt{3 x^2+5 x+2}}-\frac{66 \sqrt{3 x^2+5 x+2}}{5 \sqrt{x}}+\frac{3 \sqrt{3 x^2+5 x+2}}{x^{3/2}}-\frac{2 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}+\frac{9 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{66 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5 \sqrt{3 x^2+5 x+2}}",1,"(66*Sqrt[x]*(2 + 3*x))/(5*Sqrt[2 + 5*x + 3*x^2]) - (2*Sqrt[2 + 5*x + 3*x^2])/(5*x^(5/2)) + (3*Sqrt[2 + 5*x + 3*x^2])/x^(3/2) - (66*Sqrt[2 + 5*x + 3*x^2])/(5*Sqrt[x]) - (66*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(5*Sqrt[2 + 5*x + 3*x^2]) + (9*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",7,5,25,0.2000,1,"{834, 839, 1189, 1100, 1136}"
1064,1,197,0,0.1400854,"\int \frac{(2-5 x) x^{7/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((2 - 5*x)*x^(7/2))/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{2 (95 x+74) x^{5/2}}{3 \sqrt{3 x^2+5 x+2}}-\frac{64}{3} \sqrt{3 x^2+5 x+2} x^{3/2}+20 \sqrt{3 x^2+5 x+2} \sqrt{x}-\frac{24 (3 x+2) \sqrt{x}}{\sqrt{3 x^2+5 x+2}}-\frac{20 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{24 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{5/2}}{3 \sqrt{3 x^2+5 x+2}}-\frac{64}{3} \sqrt{3 x^2+5 x+2} x^{3/2}+20 \sqrt{3 x^2+5 x+2} \sqrt{x}-\frac{24 (3 x+2) \sqrt{x}}{\sqrt{3 x^2+5 x+2}}-\frac{20 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{24 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}",1,"(-24*Sqrt[x]*(2 + 3*x))/Sqrt[2 + 5*x + 3*x^2] + (2*x^(5/2)*(74 + 95*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + 20*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2] - (64*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])/3 + (24*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2] - (20*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",7,6,25,0.2400,1,"{818, 832, 839, 1189, 1100, 1136}"
1065,1,182,0,0.1201609,"\int \frac{(2-5 x) x^{5/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((2 - 5*x)*x^(5/2))/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{2 (95 x+74) x^{3/2}}{3 \sqrt{3 x^2+5 x+2}}-\frac{580}{27} \sqrt{3 x^2+5 x+2} \sqrt{x}+\frac{1804 (3 x+2) \sqrt{x}}{81 \sqrt{3 x^2+5 x+2}}+\frac{580 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}-\frac{1804 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{3/2}}{3 \sqrt{3 x^2+5 x+2}}-\frac{580}{27} \sqrt{3 x^2+5 x+2} \sqrt{x}+\frac{1804 (3 x+2) \sqrt{x}}{81 \sqrt{3 x^2+5 x+2}}+\frac{580 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}-\frac{1804 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}",1,"(1804*Sqrt[x]*(2 + 3*x))/(81*Sqrt[2 + 5*x + 3*x^2]) + (2*x^(3/2)*(74 + 95*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (580*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/27 - (1804*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(81*Sqrt[2 + 5*x + 3*x^2]) + (580*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(27*Sqrt[2 + 5*x + 3*x^2])","A",6,6,25,0.2400,1,"{818, 832, 839, 1189, 1100, 1136}"
1066,1,159,0,0.0998932,"\int \frac{(2-5 x) x^{3/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((2 - 5*x)*x^(3/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{200 \sqrt{x} (3 x+2)}{9 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (95 x+74)}{3 \sqrt{3 x^2+5 x+2}}-\frac{74 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}+\frac{200 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}","-\frac{200 \sqrt{x} (3 x+2)}{9 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (95 x+74)}{3 \sqrt{3 x^2+5 x+2}}-\frac{74 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}+\frac{200 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}",1,"(-200*Sqrt[x]*(2 + 3*x))/(9*Sqrt[2 + 5*x + 3*x^2]) + (2*Sqrt[x]*(74 + 95*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (200*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(9*Sqrt[2 + 5*x + 3*x^2]) - (74*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2])","A",5,5,25,0.2000,1,"{818, 839, 1189, 1100, 1136}"
1067,1,155,0,0.1012861,"\int \frac{(2-5 x) \sqrt{x}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((2 - 5*x)*Sqrt[x])/(2 + 5*x + 3*x^2)^(3/2),x]","\frac{74 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{x} (37 x+30)}{\sqrt{3 x^2+5 x+2}}+\frac{30 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{74 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","\frac{74 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{x} (37 x+30)}{\sqrt{3 x^2+5 x+2}}+\frac{30 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{74 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(74*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (2*Sqrt[x]*(30 + 37*x))/Sqrt[2 + 5*x + 3*x^2] - (74*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) + (30*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",5,5,25,0.2000,1,"{820, 839, 1189, 1100, 1136}"
1068,1,151,0,0.090641,"\int \frac{2-5 x}{\sqrt{x} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(2 - 5*x)/(Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{30 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (45 x+38)}{\sqrt{3 x^2+5 x+2}}-\frac{37 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{30 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}","-\frac{30 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (45 x+38)}{\sqrt{3 x^2+5 x+2}}-\frac{37 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{30 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}",1,"(-30*Sqrt[x]*(2 + 3*x))/Sqrt[2 + 5*x + 3*x^2] + (2*Sqrt[x]*(38 + 45*x))/Sqrt[2 + 5*x + 3*x^2] + (30*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2] - (37*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",5,5,25,0.2000,1,"{822, 839, 1189, 1100, 1136}"
1069,1,172,0,0.1021679,"\int \frac{2-5 x}{x^{3/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(2 - 5*x)/(x^(3/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{39 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}-\frac{39 \sqrt{3 x^2+5 x+2}}{\sqrt{x}}+\frac{2 (45 x+38)}{\sqrt{x} \sqrt{3 x^2+5 x+2}}+\frac{45 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{39 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}","\frac{39 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}-\frac{39 \sqrt{3 x^2+5 x+2}}{\sqrt{x}}+\frac{2 (45 x+38)}{\sqrt{x} \sqrt{3 x^2+5 x+2}}+\frac{45 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{39 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}",1,"(39*Sqrt[x]*(2 + 3*x))/Sqrt[2 + 5*x + 3*x^2] + (2*(38 + 45*x))/(Sqrt[x]*Sqrt[2 + 5*x + 3*x^2]) - (39*Sqrt[2 + 5*x + 3*x^2])/Sqrt[x] - (39*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2] + (45*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,6,25,0.2400,1,"{822, 834, 839, 1189, 1100, 1136}"
1070,1,201,0,0.1223045,"\int \frac{2-5 x}{x^{5/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(2 - 5*x)/(x^(5/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{170 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{170 \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}-\frac{115 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}+\frac{2 (45 x+38)}{x^{3/2} \sqrt{3 x^2+5 x+2}}-\frac{115 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{170 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","-\frac{170 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{170 \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}-\frac{115 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}+\frac{2 (45 x+38)}{x^{3/2} \sqrt{3 x^2+5 x+2}}-\frac{115 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{170 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(-170*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (2*(38 + 45*x))/(x^(3/2)*Sqrt[2 + 5*x + 3*x^2]) - (115*Sqrt[2 + 5*x + 3*x^2])/(3*x^(3/2)) + (170*Sqrt[2 + 5*x + 3*x^2])/(3*Sqrt[x]) + (170*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) - (115*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{822, 834, 839, 1189, 1100, 1136}"
1071,1,224,0,0.1438889,"\int \frac{2-5 x}{x^{7/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(2 - 5*x)/(x^(7/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{2693 \sqrt{x} (3 x+2)}{30 \sqrt{3 x^2+5 x+2}}-\frac{2693 \sqrt{3 x^2+5 x+2}}{30 \sqrt{x}}+\frac{157 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}-\frac{191 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}+\frac{2 (45 x+38)}{x^{5/2} \sqrt{3 x^2+5 x+2}}+\frac{157 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{2693 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{2} \sqrt{3 x^2+5 x+2}}","\frac{2693 \sqrt{x} (3 x+2)}{30 \sqrt{3 x^2+5 x+2}}-\frac{2693 \sqrt{3 x^2+5 x+2}}{30 \sqrt{x}}+\frac{157 \sqrt{3 x^2+5 x+2}}{3 x^{3/2}}-\frac{191 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}+\frac{2 (45 x+38)}{x^{5/2} \sqrt{3 x^2+5 x+2}}+\frac{157 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{2693 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{2} \sqrt{3 x^2+5 x+2}}",1,"(2693*Sqrt[x]*(2 + 3*x))/(30*Sqrt[2 + 5*x + 3*x^2]) + (2*(38 + 45*x))/(x^(5/2)*Sqrt[2 + 5*x + 3*x^2]) - (191*Sqrt[2 + 5*x + 3*x^2])/(5*x^(5/2)) + (157*Sqrt[2 + 5*x + 3*x^2])/(3*x^(3/2)) - (2693*Sqrt[2 + 5*x + 3*x^2])/(30*Sqrt[x]) - (2693*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(15*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2]) + (157*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{822, 834, 839, 1189, 1100, 1136}"
1072,1,256,0,0.18789,"\int \frac{(2-5 x) x^{13/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*x^(13/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 (95 x+74) x^{11/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{4 (1685 x+1484) x^{7/2}}{27 \sqrt{3 x^2+5 x+2}}+\frac{45820}{567} \sqrt{3 x^2+5 x+2} x^{5/2}-\frac{167336 \sqrt{3 x^2+5 x+2} x^{3/2}}{2835}+\frac{211144 \sqrt{3 x^2+5 x+2} \sqrt{x}}{5103}-\frac{1521056 (3 x+2) \sqrt{x}}{76545 \sqrt{3 x^2+5 x+2}}-\frac{211144 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5103 \sqrt{3 x^2+5 x+2}}+\frac{1521056 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{76545 \sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{11/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{4 (1685 x+1484) x^{7/2}}{27 \sqrt{3 x^2+5 x+2}}+\frac{45820}{567} \sqrt{3 x^2+5 x+2} x^{5/2}-\frac{167336 \sqrt{3 x^2+5 x+2} x^{3/2}}{2835}+\frac{211144 \sqrt{3 x^2+5 x+2} \sqrt{x}}{5103}-\frac{1521056 (3 x+2) \sqrt{x}}{76545 \sqrt{3 x^2+5 x+2}}-\frac{211144 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{5103 \sqrt{3 x^2+5 x+2}}+\frac{1521056 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{76545 \sqrt{3 x^2+5 x+2}}",1,"(2*x^(11/2)*(74 + 95*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) - (1521056*Sqrt[x]*(2 + 3*x))/(76545*Sqrt[2 + 5*x + 3*x^2]) - (4*x^(7/2)*(1484 + 1685*x))/(27*Sqrt[2 + 5*x + 3*x^2]) + (211144*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/5103 - (167336*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])/2835 + (45820*x^(5/2)*Sqrt[2 + 5*x + 3*x^2])/567 + (1521056*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(76545*Sqrt[2 + 5*x + 3*x^2]) - (211144*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(5103*Sqrt[2 + 5*x + 3*x^2])","A",9,6,25,0.2400,1,"{818, 832, 839, 1189, 1100, 1136}"
1073,1,233,0,0.1635976,"\int \frac{(2-5 x) x^{11/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*x^(11/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 (95 x+74) x^{9/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{8 (905 x+773) x^{5/2}}{27 \sqrt{3 x^2+5 x+2}}+\frac{2348}{27} \sqrt{3 x^2+5 x+2} x^{3/2}-\frac{16040}{243} \sqrt{3 x^2+5 x+2} \sqrt{x}+\frac{33608 (3 x+2) \sqrt{x}}{729 \sqrt{3 x^2+5 x+2}}+\frac{16040 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243 \sqrt{3 x^2+5 x+2}}-\frac{33608 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{729 \sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{9/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{8 (905 x+773) x^{5/2}}{27 \sqrt{3 x^2+5 x+2}}+\frac{2348}{27} \sqrt{3 x^2+5 x+2} x^{3/2}-\frac{16040}{243} \sqrt{3 x^2+5 x+2} \sqrt{x}+\frac{33608 (3 x+2) \sqrt{x}}{729 \sqrt{3 x^2+5 x+2}}+\frac{16040 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243 \sqrt{3 x^2+5 x+2}}-\frac{33608 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{729 \sqrt{3 x^2+5 x+2}}",1,"(2*x^(9/2)*(74 + 95*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (33608*Sqrt[x]*(2 + 3*x))/(729*Sqrt[2 + 5*x + 3*x^2]) - (8*x^(5/2)*(773 + 905*x))/(27*Sqrt[2 + 5*x + 3*x^2]) - (16040*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/243 + (2348*x^(3/2)*Sqrt[2 + 5*x + 3*x^2])/27 - (33608*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(729*Sqrt[2 + 5*x + 3*x^2]) + (16040*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(243*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{818, 832, 839, 1189, 1100, 1136}"
1074,1,210,0,0.1473355,"\int \frac{(2-5 x) x^{9/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*x^(9/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 (95 x+74) x^{7/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{4 (645 x+536) x^{3/2}}{9 \sqrt{3 x^2+5 x+2}}+\frac{7540}{81} \sqrt{3 x^2+5 x+2} \sqrt{x}-\frac{17512 (3 x+2) \sqrt{x}}{243 \sqrt{3 x^2+5 x+2}}-\frac{7540 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}+\frac{17512 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243 \sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{7/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{4 (645 x+536) x^{3/2}}{9 \sqrt{3 x^2+5 x+2}}+\frac{7540}{81} \sqrt{3 x^2+5 x+2} \sqrt{x}-\frac{17512 (3 x+2) \sqrt{x}}{243 \sqrt{3 x^2+5 x+2}}-\frac{7540 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}+\frac{17512 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{243 \sqrt{3 x^2+5 x+2}}",1,"(2*x^(7/2)*(74 + 95*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) - (17512*Sqrt[x]*(2 + 3*x))/(243*Sqrt[2 + 5*x + 3*x^2]) - (4*x^(3/2)*(536 + 645*x))/(9*Sqrt[2 + 5*x + 3*x^2]) + (7540*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2])/81 + (17512*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(243*Sqrt[2 + 5*x + 3*x^2]) - (7540*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(81*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{818, 832, 839, 1189, 1100, 1136}"
1075,1,187,0,0.1218062,"\int \frac{(2-5 x) x^{7/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*x^(7/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 (95 x+74) x^{5/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{8020 (3 x+2) \sqrt{x}}{81 \sqrt{3 x^2+5 x+2}}-\frac{40 (206 x+167) \sqrt{x}}{27 \sqrt{3 x^2+5 x+2}}+\frac{3340 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}-\frac{8020 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{5/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{8020 (3 x+2) \sqrt{x}}{81 \sqrt{3 x^2+5 x+2}}-\frac{40 (206 x+167) \sqrt{x}}{27 \sqrt{3 x^2+5 x+2}}+\frac{3340 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}-\frac{8020 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{81 \sqrt{3 x^2+5 x+2}}",1,"(2*x^(5/2)*(74 + 95*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (8020*Sqrt[x]*(2 + 3*x))/(81*Sqrt[2 + 5*x + 3*x^2]) - (40*Sqrt[x]*(167 + 206*x))/(27*Sqrt[2 + 5*x + 3*x^2]) - (8020*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(81*Sqrt[2 + 5*x + 3*x^2]) + (3340*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(27*Sqrt[2 + 5*x + 3*x^2])","A",6,5,25,0.2000,1,"{818, 839, 1189, 1100, 1136}"
1076,1,187,0,0.1210587,"\int \frac{(2-5 x) x^{5/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*x^(5/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{2 (95 x+74) x^{3/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{3464 (3 x+2) \sqrt{x}}{27 \sqrt{3 x^2+5 x+2}}+\frac{4 (866 x+715) \sqrt{x}}{9 \sqrt{3 x^2+5 x+2}}-\frac{1430 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}+\frac{3464 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}","\frac{2 (95 x+74) x^{3/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{3464 (3 x+2) \sqrt{x}}{27 \sqrt{3 x^2+5 x+2}}+\frac{4 (866 x+715) \sqrt{x}}{9 \sqrt{3 x^2+5 x+2}}-\frac{1430 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}+\frac{3464 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{27 \sqrt{3 x^2+5 x+2}}",1,"(2*x^(3/2)*(74 + 95*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) - (3464*Sqrt[x]*(2 + 3*x))/(27*Sqrt[2 + 5*x + 3*x^2]) + (4*Sqrt[x]*(715 + 866*x))/(9*Sqrt[2 + 5*x + 3*x^2]) + (3464*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(27*Sqrt[2 + 5*x + 3*x^2]) - (1430*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(9*Sqrt[2 + 5*x + 3*x^2])","A",6,6,25,0.2400,1,"{818, 820, 839, 1189, 1100, 1136}"
1077,1,187,0,0.1101483,"\int \frac{(2-5 x) x^{3/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*x^(3/2))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{1450 \sqrt{x} (3 x+2)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{x} (2175 x+1831)}{9 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (95 x+74)}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{598 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}-\frac{1450 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}","\frac{1450 \sqrt{x} (3 x+2)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{x} (2175 x+1831)}{9 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (95 x+74)}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{598 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}-\frac{1450 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{9 \sqrt{3 x^2+5 x+2}}",1,"(2*Sqrt[x]*(74 + 95*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (1450*Sqrt[x]*(2 + 3*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (2*Sqrt[x]*(1831 + 2175*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (1450*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(9*Sqrt[2 + 5*x + 3*x^2]) + (598*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2])","A",6,6,25,0.2400,1,"{818, 822, 839, 1189, 1100, 1136}"
1078,1,179,0,0.1126934,"\int \frac{(2-5 x) \sqrt{x}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((2 - 5*x)*Sqrt[x])/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{198 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (297 x+250)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{x} (37 x+30)}{3 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{245 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{198 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}","-\frac{198 \sqrt{x} (3 x+2)}{\sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (297 x+250)}{\sqrt{3 x^2+5 x+2}}-\frac{2 \sqrt{x} (37 x+30)}{3 \left(3 x^2+5 x+2\right)^{3/2}}-\frac{245 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}+\frac{198 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[x]*(30 + 37*x))/(3*(2 + 5*x + 3*x^2)^(3/2)) - (198*Sqrt[x]*(2 + 3*x))/Sqrt[2 + 5*x + 3*x^2] + (2*Sqrt[x]*(250 + 297*x))/Sqrt[2 + 5*x + 3*x^2] + (198*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2] - (245*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,6,25,0.2400,1,"{820, 822, 839, 1189, 1100, 1136}"
1079,1,185,0,0.110436,"\int \frac{2-5 x}{\sqrt{x} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(2 - 5*x)/(Sqrt[x]*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{715 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{5 \sqrt{x} (429 x+361)}{3 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (45 x+38)}{3 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{295 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{715 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","\frac{715 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}-\frac{5 \sqrt{x} (429 x+361)}{3 \sqrt{3 x^2+5 x+2}}+\frac{2 \sqrt{x} (45 x+38)}{3 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{295 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{3 x^2+5 x+2}}-\frac{715 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(2*Sqrt[x]*(38 + 45*x))/(3*(2 + 5*x + 3*x^2)^(3/2)) + (715*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (5*Sqrt[x]*(361 + 429*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (715*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) + (295*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/Sqrt[2 + 5*x + 3*x^2]","A",6,5,25,0.2000,1,"{822, 839, 1189, 1100, 1136}"
1080,1,208,0,0.1235277,"\int \frac{2-5 x}{x^{3/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(2 - 5*x)/(x^(3/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{838 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{838 \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}-\frac{2085 x+1717}{3 \sqrt{x} \sqrt{3 x^2+5 x+2}}+\frac{2 (45 x+38)}{3 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}-\frac{695 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{838 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}","-\frac{838 \sqrt{x} (3 x+2)}{3 \sqrt{3 x^2+5 x+2}}+\frac{838 \sqrt{3 x^2+5 x+2}}{3 \sqrt{x}}-\frac{2085 x+1717}{3 \sqrt{x} \sqrt{3 x^2+5 x+2}}+\frac{2 (45 x+38)}{3 \sqrt{x} \left(3 x^2+5 x+2\right)^{3/2}}-\frac{695 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{838 \sqrt{2} (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{3 \sqrt{3 x^2+5 x+2}}",1,"(2*(38 + 45*x))/(3*Sqrt[x]*(2 + 5*x + 3*x^2)^(3/2)) - (838*Sqrt[x]*(2 + 3*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (1717 + 2085*x)/(3*Sqrt[x]*Sqrt[2 + 5*x + 3*x^2]) + (838*Sqrt[2 + 5*x + 3*x^2])/(3*Sqrt[x]) + (838*Sqrt[2]*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(3*Sqrt[2 + 5*x + 3*x^2]) - (695*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,25,0.2400,1,"{822, 834, 839, 1189, 1100, 1136}"
1081,1,225,0,0.1446988,"\int \frac{2-5 x}{x^{5/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(2 - 5*x)/(x^(5/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","\frac{625 \sqrt{x} (3 x+2)}{2 \sqrt{3 x^2+5 x+2}}-\frac{625 \sqrt{3 x^2+5 x+2}}{2 \sqrt{x}}+\frac{265 \sqrt{3 x^2+5 x+2}}{x^{3/2}}-\frac{3 (225 x+181)}{x^{3/2} \sqrt{3 x^2+5 x+2}}+\frac{2 (45 x+38)}{3 x^{3/2} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{795 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{625 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}","\frac{625 \sqrt{x} (3 x+2)}{2 \sqrt{3 x^2+5 x+2}}-\frac{625 \sqrt{3 x^2+5 x+2}}{2 \sqrt{x}}+\frac{265 \sqrt{3 x^2+5 x+2}}{x^{3/2}}-\frac{3 (225 x+181)}{x^{3/2} \sqrt{3 x^2+5 x+2}}+\frac{2 (45 x+38)}{3 x^{3/2} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{795 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}-\frac{625 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{\sqrt{2} \sqrt{3 x^2+5 x+2}}",1,"(2*(38 + 45*x))/(3*x^(3/2)*(2 + 5*x + 3*x^2)^(3/2)) + (625*Sqrt[x]*(2 + 3*x))/(2*Sqrt[2 + 5*x + 3*x^2]) - (3*(181 + 225*x))/(x^(3/2)*Sqrt[2 + 5*x + 3*x^2]) + (265*Sqrt[2 + 5*x + 3*x^2])/x^(3/2) - (625*Sqrt[2 + 5*x + 3*x^2])/(2*Sqrt[x]) - (625*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2]) + (795*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,25,0.2400,1,"{822, 834, 839, 1189, 1100, 1136}"
1082,1,256,0,0.1674112,"\int \frac{2-5 x}{x^{7/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(2 - 5*x)/(x^(7/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{9521 \sqrt{x} (3 x+2)}{30 \sqrt{3 x^2+5 x+2}}+\frac{9521 \sqrt{3 x^2+5 x+2}}{30 \sqrt{x}}-\frac{1733 \sqrt{3 x^2+5 x+2}}{6 x^{3/2}}+\frac{1252 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}-\frac{1965 x+1541}{3 x^{5/2} \sqrt{3 x^2+5 x+2}}+\frac{2 (45 x+38)}{3 x^{5/2} \left(3 x^2+5 x+2\right)^{3/2}}-\frac{1733 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{9521 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{2} \sqrt{3 x^2+5 x+2}}","-\frac{9521 \sqrt{x} (3 x+2)}{30 \sqrt{3 x^2+5 x+2}}+\frac{9521 \sqrt{3 x^2+5 x+2}}{30 \sqrt{x}}-\frac{1733 \sqrt{3 x^2+5 x+2}}{6 x^{3/2}}+\frac{1252 \sqrt{3 x^2+5 x+2}}{5 x^{5/2}}-\frac{1965 x+1541}{3 x^{5/2} \sqrt{3 x^2+5 x+2}}+\frac{2 (45 x+38)}{3 x^{5/2} \left(3 x^2+5 x+2\right)^{3/2}}-\frac{1733 (x+1) \sqrt{\frac{3 x+2}{x+1}} F\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{2 \sqrt{2} \sqrt{3 x^2+5 x+2}}+\frac{9521 (x+1) \sqrt{\frac{3 x+2}{x+1}} E\left(\tan ^{-1}\left(\sqrt{x}\right)|-\frac{1}{2}\right)}{15 \sqrt{2} \sqrt{3 x^2+5 x+2}}",1,"(2*(38 + 45*x))/(3*x^(5/2)*(2 + 5*x + 3*x^2)^(3/2)) - (9521*Sqrt[x]*(2 + 3*x))/(30*Sqrt[2 + 5*x + 3*x^2]) - (1541 + 1965*x)/(3*x^(5/2)*Sqrt[2 + 5*x + 3*x^2]) + (1252*Sqrt[2 + 5*x + 3*x^2])/(5*x^(5/2)) - (1733*Sqrt[2 + 5*x + 3*x^2])/(6*x^(3/2)) + (9521*Sqrt[2 + 5*x + 3*x^2])/(30*Sqrt[x]) + (9521*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticE[ArcTan[Sqrt[x]], -1/2])/(15*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2]) - (1733*(1 + x)*Sqrt[(2 + 3*x)/(1 + x)]*EllipticF[ArcTan[Sqrt[x]], -1/2])/(2*Sqrt[2]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,25,0.2400,1,"{822, 834, 839, 1189, 1100, 1136}"
1083,1,240,0,0.1899548,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{a^2 (e x)^{m+2} (a B+3 A b)}{e^2 (m+2)}+\frac{a^3 A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+5} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)}{e^5 (m+5)}+\frac{3 a (e x)^{m+3} \left(A \left(a c+b^2\right)+a b B\right)}{e^3 (m+3)}+\frac{(e x)^{m+4} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)}{e^4 (m+4)}+\frac{3 c (e x)^{m+6} \left(a B c+A b c+b^2 B\right)}{e^6 (m+6)}+\frac{c^2 (e x)^{m+7} (A c+3 b B)}{e^7 (m+7)}+\frac{B c^3 (e x)^{m+8}}{e^8 (m+8)}","\frac{a^2 (e x)^{m+2} (a B+3 A b)}{e^2 (m+2)}+\frac{a^3 A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+5} \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)}{e^5 (m+5)}+\frac{3 a (e x)^{m+3} \left(A \left(a c+b^2\right)+a b B\right)}{e^3 (m+3)}+\frac{(e x)^{m+4} \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)}{e^4 (m+4)}+\frac{3 c (e x)^{m+6} \left(a B c+A b c+b^2 B\right)}{e^6 (m+6)}+\frac{c^2 (e x)^{m+7} (A c+3 b B)}{e^7 (m+7)}+\frac{B c^3 (e x)^{m+8}}{e^8 (m+8)}",1,"(a^3*A*(e*x)^(1 + m))/(e*(1 + m)) + (a^2*(3*A*b + a*B)*(e*x)^(2 + m))/(e^2*(2 + m)) + (3*a*(a*b*B + A*(b^2 + a*c))*(e*x)^(3 + m))/(e^3*(3 + m)) + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*(e*x)^(4 + m))/(e^4*(4 + m)) + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*(e*x)^(5 + m))/(e^5*(5 + m)) + (3*c*(b^2*B + A*b*c + a*B*c)*(e*x)^(6 + m))/(e^6*(6 + m)) + (c^2*(3*b*B + A*c)*(e*x)^(7 + m))/(e^7*(7 + m)) + (B*c^3*(e*x)^(8 + m))/(e^8*(8 + m))","A",2,1,23,0.04348,1,"{765}"
1084,1,155,0,0.0974905,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^2,x]","\frac{a^2 A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+3} \left(A \left(2 a c+b^2\right)+2 a b B\right)}{e^3 (m+3)}+\frac{(e x)^{m+4} \left(2 a B c+2 A b c+b^2 B\right)}{e^4 (m+4)}+\frac{a (e x)^{m+2} (a B+2 A b)}{e^2 (m+2)}+\frac{c (e x)^{m+5} (A c+2 b B)}{e^5 (m+5)}+\frac{B c^2 (e x)^{m+6}}{e^6 (m+6)}","\frac{a^2 A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+3} \left(A \left(2 a c+b^2\right)+2 a b B\right)}{e^3 (m+3)}+\frac{(e x)^{m+4} \left(2 a B c+2 A b c+b^2 B\right)}{e^4 (m+4)}+\frac{a (e x)^{m+2} (a B+2 A b)}{e^2 (m+2)}+\frac{c (e x)^{m+5} (A c+2 b B)}{e^5 (m+5)}+\frac{B c^2 (e x)^{m+6}}{e^6 (m+6)}",1,"(a^2*A*(e*x)^(1 + m))/(e*(1 + m)) + (a*(2*A*b + a*B)*(e*x)^(2 + m))/(e^2*(2 + m)) + ((2*a*b*B + A*(b^2 + 2*a*c))*(e*x)^(3 + m))/(e^3*(3 + m)) + ((b^2*B + 2*A*b*c + 2*a*B*c)*(e*x)^(4 + m))/(e^4*(4 + m)) + (c*(2*b*B + A*c)*(e*x)^(5 + m))/(e^5*(5 + m)) + (B*c^2*(e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,23,0.04348,1,"{765}"
1085,1,83,0,0.0424643,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right) \, dx","Int[(e*x)^m*(A + B*x)*(a + b*x + c*x^2),x]","\frac{(e x)^{m+2} (a B+A b)}{e^2 (m+2)}+\frac{a A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+3} (A c+b B)}{e^3 (m+3)}+\frac{B c (e x)^{m+4}}{e^4 (m+4)}","\frac{(e x)^{m+2} (a B+A b)}{e^2 (m+2)}+\frac{a A (e x)^{m+1}}{e (m+1)}+\frac{(e x)^{m+3} (A c+b B)}{e^3 (m+3)}+\frac{B c (e x)^{m+4}}{e^4 (m+4)}",1,"(a*A*(e*x)^(1 + m))/(e*(1 + m)) + ((A*b + a*B)*(e*x)^(2 + m))/(e^2*(2 + m)) + ((b*B + A*c)*(e*x)^(3 + m))/(e^3*(3 + m)) + (B*c*(e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,21,0.04762,1,"{765}"
1086,1,172,0,0.3051223,"\int \frac{(e x)^m (A+B x)}{a+b x+c x^2} \, dx","Int[((e*x)^m*(A + B*x))/(a + b*x + c*x^2),x]","\frac{(e x)^{m+1} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(e x)^{m+1} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(\sqrt{b^2-4 a c}+b\right)}","\frac{(e x)^{m+1} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(b-\sqrt{b^2-4 a c}\right)}+\frac{(e x)^{m+1} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(\sqrt{b^2-4 a c}+b\right)}",1,"((B - (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*(e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/((b - Sqrt[b^2 - 4*a*c])*e*(1 + m)) + ((B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*(e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/((b + Sqrt[b^2 - 4*a*c])*e*(1 + m))","A",4,2,23,0.08696,1,"{830, 64}"
1087,1,317,0,0.8825178,"\int \frac{(e x)^m (A+B x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[((e*x)^m*(A + B*x))/(a + b*x + c*x^2)^2,x]","-\frac{c (e x)^{m+1} \left(A b m \left(\sqrt{b^2-4 a c}+b\right)-2 a \left(B m \sqrt{b^2-4 a c}-2 A c (1-m)+b B\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{a e (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (e x)^{m+1} \left(\frac{-4 a A c (1-m)+2 a b B-A b^2 m}{\sqrt{b^2-4 a c}}+m (A b-2 a B)\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{a e (m+1) \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(e x)^{m+1} \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a e \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}","-\frac{c (e x)^{m+1} \left(A b m \left(\sqrt{b^2-4 a c}+b\right)-2 a \left(B m \sqrt{b^2-4 a c}-2 A c (1-m)+b B\right)\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}}\right)}{a e (m+1) \left(b^2-4 a c\right)^{3/2} \left(b-\sqrt{b^2-4 a c}\right)}-\frac{c (e x)^{m+1} \left(\frac{2 a (b B-2 A c (1-m))-A b^2 m}{\sqrt{b^2-4 a c}}+m (A b-2 a B)\right) \, _2F_1\left(1,m+1;m+2;-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{a e (m+1) \left(b^2-4 a c\right) \left(\sqrt{b^2-4 a c}+b\right)}+\frac{(e x)^{m+1} \left(c x (A b-2 a B)-2 a A c-a b B+A b^2\right)}{a e \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}",1,"((e*x)^(1 + m)*(A*b^2 - a*b*B - 2*a*A*c + (A*b - 2*a*B)*c*x))/(a*(b^2 - 4*a*c)*e*(a + b*x + c*x^2)) - (c*(A*b*(b + Sqrt[b^2 - 4*a*c])*m - 2*a*(b*B - 2*A*c*(1 - m) + B*Sqrt[b^2 - 4*a*c]*m))*(e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c])])/(a*(b^2 - 4*a*c)^(3/2)*(b - Sqrt[b^2 - 4*a*c])*e*(1 + m)) - (c*((A*b - 2*a*B)*m + (2*a*b*B - 4*a*A*c*(1 - m) - A*b^2*m)/Sqrt[b^2 - 4*a*c])*(e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(a*(b^2 - 4*a*c)*(b + Sqrt[b^2 - 4*a*c])*e*(1 + m))","A",5,3,23,0.1304,1,"{822, 830, 64}"
1088,1,281,0,0.5480724,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{A (e x)^{m+1} \left(a+b x+c x^2\right)^{5/2} F_1\left(m+1;-\frac{5}{2},-\frac{5}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2}}+\frac{B (e x)^{m+2} \left(a+b x+c x^2\right)^{5/2} F_1\left(m+2;-\frac{5}{2},-\frac{5}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2}}","\frac{A (e x)^{m+1} \left(a+b x+c x^2\right)^{5/2} F_1\left(m+1;-\frac{5}{2},-\frac{5}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2}}+\frac{B (e x)^{m+2} \left(a+b x+c x^2\right)^{5/2} F_1\left(m+2;-\frac{5}{2},-\frac{5}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2}}",1,"(A*(e*x)^(1 + m)*(a + b*x + c*x^2)^(5/2)*AppellF1[1 + m, -5/2, -5/2, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(5/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(5/2)) + (B*(e*x)^(2 + m)*(a + b*x + c*x^2)^(5/2)*AppellF1[2 + m, -5/2, -5/2, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(5/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(5/2))","A",5,3,25,0.1200,1,"{843, 759, 133}"
1089,1,281,0,0.4142251,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{A (e x)^{m+1} \left(a+b x+c x^2\right)^{3/2} F_1\left(m+1;-\frac{3}{2},-\frac{3}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2}}+\frac{B (e x)^{m+2} \left(a+b x+c x^2\right)^{3/2} F_1\left(m+2;-\frac{3}{2},-\frac{3}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2}}","\frac{A (e x)^{m+1} \left(a+b x+c x^2\right)^{3/2} F_1\left(m+1;-\frac{3}{2},-\frac{3}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2}}+\frac{B (e x)^{m+2} \left(a+b x+c x^2\right)^{3/2} F_1\left(m+2;-\frac{3}{2},-\frac{3}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2}}",1,"(A*(e*x)^(1 + m)*(a + b*x + c*x^2)^(3/2)*AppellF1[1 + m, -3/2, -3/2, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(3/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(3/2)) + (B*(e*x)^(2 + m)*(a + b*x + c*x^2)^(3/2)*AppellF1[2 + m, -3/2, -3/2, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(3/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(3/2))","A",5,3,25,0.1200,1,"{843, 759, 133}"
1090,1,281,0,0.4127019,"\int (e x)^m (A+B x) \sqrt{a+b x+c x^2} \, dx","Int[(e*x)^m*(A + B*x)*Sqrt[a + b*x + c*x^2],x]","\frac{A (e x)^{m+1} \sqrt{a+b x+c x^2} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1}}+\frac{B (e x)^{m+2} \sqrt{a+b x+c x^2} F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1}}","\frac{A (e x)^{m+1} \sqrt{a+b x+c x^2} F_1\left(m+1;-\frac{1}{2},-\frac{1}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1}}+\frac{B (e x)^{m+2} \sqrt{a+b x+c x^2} F_1\left(m+2;-\frac{1}{2},-\frac{1}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1}}",1,"(A*(e*x)^(1 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[1 + m, -1/2, -1/2, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*Sqrt[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])]) + (B*(e*x)^(2 + m)*Sqrt[a + b*x + c*x^2]*AppellF1[2 + m, -1/2, -1/2, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*Sqrt[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])])","A",5,3,25,0.1200,1,"{843, 759, 133}"
1091,1,281,0,0.4068885,"\int \frac{(e x)^m (A+B x)}{\sqrt{a+b x+c x^2}} \, dx","Int[((e*x)^m*(A + B*x))/Sqrt[a + b*x + c*x^2],x]","\frac{A (e x)^{m+1} \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \sqrt{a+b x+c x^2}}+\frac{B (e x)^{m+2} \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \sqrt{a+b x+c x^2}}","\frac{A (e x)^{m+1} \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1} F_1\left(m+1;\frac{1}{2},\frac{1}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \sqrt{a+b x+c x^2}}+\frac{B (e x)^{m+2} \sqrt{\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1} \sqrt{\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1} F_1\left(m+2;\frac{1}{2},\frac{1}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \sqrt{a+b x+c x^2}}",1,"(A*(e*x)^(1 + m)*Sqrt[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[1 + m, 1/2, 1/2, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*Sqrt[a + b*x + c*x^2]) + (B*(e*x)^(2 + m)*Sqrt[1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c])]*Sqrt[1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c])]*AppellF1[2 + m, 1/2, 1/2, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*Sqrt[a + b*x + c*x^2])","A",5,3,25,0.1200,1,"{843, 759, 133}"
1092,1,281,0,0.406844,"\int \frac{(e x)^m (A+B x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((e*x)^m*(A + B*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{A (e x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(a+b x+c x^2\right)^{3/2}}+\frac{B (e x)^{m+2} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2} F_1\left(m+2;\frac{3}{2},\frac{3}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(a+b x+c x^2\right)^{3/2}}","\frac{A (e x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2} F_1\left(m+1;\frac{3}{2},\frac{3}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(a+b x+c x^2\right)^{3/2}}+\frac{B (e x)^{m+2} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{3/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{3/2} F_1\left(m+2;\frac{3}{2},\frac{3}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(a+b x+c x^2\right)^{3/2}}",1,"(A*(e*x)^(1 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(3/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(3/2)*AppellF1[1 + m, 3/2, 3/2, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*(a + b*x + c*x^2)^(3/2)) + (B*(e*x)^(2 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(3/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(3/2)*AppellF1[2 + m, 3/2, 3/2, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*(a + b*x + c*x^2)^(3/2))","A",5,3,25,0.1200,1,"{843, 759, 133}"
1093,1,281,0,0.4112759,"\int \frac{(e x)^m (A+B x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((e*x)^m*(A + B*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{A (e x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2} F_1\left(m+1;\frac{5}{2},\frac{5}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(a+b x+c x^2\right)^{5/2}}+\frac{B (e x)^{m+2} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2} F_1\left(m+2;\frac{5}{2},\frac{5}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(a+b x+c x^2\right)^{5/2}}","\frac{A (e x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2} F_1\left(m+1;\frac{5}{2},\frac{5}{2};m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1) \left(a+b x+c x^2\right)^{5/2}}+\frac{B (e x)^{m+2} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{5/2} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{5/2} F_1\left(m+2;\frac{5}{2},\frac{5}{2};m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2) \left(a+b x+c x^2\right)^{5/2}}",1,"(A*(e*x)^(1 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(5/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(5/2)*AppellF1[1 + m, 5/2, 5/2, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*(a + b*x + c*x^2)^(5/2)) + (B*(e*x)^(2 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^(5/2)*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^(5/2)*AppellF1[2 + m, 5/2, 5/2, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*(a + b*x + c*x^2)^(5/2))","A",5,3,25,0.1200,1,"{843, 759, 133}"
1094,1,277,0,0.4044508,"\int (e x)^m (A+B x) \left(a+b x+c x^2\right)^p \, dx","Int[(e*x)^m*(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{A (e x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(m+1;-p,-p;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1)}+\frac{B (e x)^{m+2} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(m+2;-p,-p;m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2)}","\frac{A (e x)^{m+1} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(m+1;-p,-p;m+2;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e (m+1)}+\frac{B (e x)^{m+2} \left(\frac{2 c x}{b-\sqrt{b^2-4 a c}}+1\right)^{-p} \left(\frac{2 c x}{\sqrt{b^2-4 a c}+b}+1\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(m+2;-p,-p;m+3;-\frac{2 c x}{b-\sqrt{b^2-4 a c}},-\frac{2 c x}{b+\sqrt{b^2-4 a c}}\right)}{e^2 (m+2)}",1,"(A*(e*x)^(1 + m)*(a + b*x + c*x^2)^p*AppellF1[1 + m, -p, -p, 2 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e*(1 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p) + (B*(e*x)^(2 + m)*(a + b*x + c*x^2)^p*AppellF1[2 + m, -p, -p, 3 + m, (-2*c*x)/(b - Sqrt[b^2 - 4*a*c]), (-2*c*x)/(b + Sqrt[b^2 - 4*a*c])])/(e^2*(2 + m)*(1 + (2*c*x)/(b - Sqrt[b^2 - 4*a*c]))^p*(1 + (2*c*x)/(b + Sqrt[b^2 - 4*a*c]))^p)","A",5,3,23,0.1304,1,"{843, 759, 133}"
1095,1,442,0,0.7428933,"\int x^3 (A+B x) \left(a+b x+c x^2\right)^p \, dx","Int[x^3*(A + B*x)*(a + b*x + c*x^2)^p,x]","-\frac{2^{p-1} \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(12 a^2 B c^2+6 a A b c^2 (2 p+5)-12 a b^2 B c (p+3)-A b^3 c \left(2 p^2+11 p+15\right)+b^4 B \left(p^2+7 p+12\right)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^4 (p+1) (2 p+3) (2 p+5) \sqrt{b^2-4 a c}}+\frac{\left(a+b x+c x^2\right)^{p+1} \left(-2 c (p+1) x \left(6 a B c (p+2)+A b c \left(2 p^2+11 p+15\right)+b^2 (-B) \left(p^2+7 p+12\right)\right)+b (p+2) \left(6 a B c (p+2)+A b c \left(2 p^2+11 p+15\right)+b^2 (-B) \left(p^2+7 p+12\right)\right)+2 a c (2 p+3) (b B (p+4)-A c (2 p+5))\right)}{4 c^4 (p+1) (p+2) (2 p+3) (2 p+5)}-\frac{x^2 \left(a+b x+c x^2\right)^{p+1} (b B (p+4)-A c (2 p+5))}{2 c^2 (p+2) (2 p+5)}+\frac{B x^3 \left(a+b x+c x^2\right)^{p+1}}{c (2 p+5)}","-\frac{2^{p-1} \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(12 a^2 B c^2+6 a A b c^2 (2 p+5)-12 a b^2 B c (p+3)-A b^3 c \left(2 p^2+11 p+15\right)+b^4 B \left(p^2+7 p+12\right)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^4 (p+1) (2 p+3) (2 p+5) \sqrt{b^2-4 a c}}+\frac{\left(a+b x+c x^2\right)^{p+1} \left(-2 c (p+1) x \left(6 a B c (p+2)+A b c \left(2 p^2+11 p+15\right)+b^2 (-B) \left(p^2+7 p+12\right)\right)+b (p+2) \left(6 a B c (p+2)+A b c \left(2 p^2+11 p+15\right)+b^2 (-B) \left(p^2+7 p+12\right)\right)+2 a c (2 p+3) (b B (p+4)-A c (2 p+5))\right)}{4 c^4 (p+1) (p+2) (2 p+3) (2 p+5)}-\frac{x^2 \left(a+b x+c x^2\right)^{p+1} (b B (p+4)-A c (2 p+5))}{2 c^2 (p+2) (2 p+5)}+\frac{B x^3 \left(a+b x+c x^2\right)^{p+1}}{c (2 p+5)}",1,"-((b*B*(4 + p) - A*c*(5 + 2*p))*x^2*(a + b*x + c*x^2)^(1 + p))/(2*c^2*(2 + p)*(5 + 2*p)) + (B*x^3*(a + b*x + c*x^2)^(1 + p))/(c*(5 + 2*p)) + ((2*a*c*(3 + 2*p)*(b*B*(4 + p) - A*c*(5 + 2*p)) + b*(2 + p)*(6*a*B*c*(2 + p) - b^2*B*(12 + 7*p + p^2) + A*b*c*(15 + 11*p + 2*p^2)) - 2*c*(1 + p)*(6*a*B*c*(2 + p) - b^2*B*(12 + 7*p + p^2) + A*b*c*(15 + 11*p + 2*p^2))*x)*(a + b*x + c*x^2)^(1 + p))/(4*c^4*(1 + p)*(2 + p)*(3 + 2*p)*(5 + 2*p)) - (2^(-1 + p)*(12*a^2*B*c^2 - 12*a*b^2*B*c*(3 + p) + 6*a*A*b*c^2*(5 + 2*p) + b^4*B*(12 + 7*p + p^2) - A*b^3*c*(15 + 11*p + 2*p^2))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c^4*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p)*(5 + 2*p))","A",4,3,21,0.1429,1,"{832, 779, 624}"
1096,1,287,0,0.2866221,"\int x^2 (A+B x) \left(a+b x+c x^2\right)^p \, dx","Int[x^2*(A + B*x)*(a + b*x + c*x^2)^p,x]","-\frac{2^{p-1} \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(-4 a A c^2+6 a b B c+2 A b^2 c (p+2)+b^3 (-B) (p+3)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^3 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{\left(a+b x+c x^2\right)^{p+1} (2 a B c (2 p+3)-2 c (p+1) x (2 A c (p+2)-b B (p+3))+b (p+2) (2 A c (p+2)-b B (p+3)))}{4 c^3 (p+1) (p+2) (2 p+3)}+\frac{B x^2 \left(a+b x+c x^2\right)^{p+1}}{2 c (p+2)}","-\frac{2^{p-1} \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(-4 a A c^2+6 a b B c+2 A b^2 c (p+2)+b^3 (-B) (p+3)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^3 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{\left(a+b x+c x^2\right)^{p+1} (2 a B c (2 p+3)-2 c (p+1) x (2 A c (p+2)-b B (p+3))+b (p+2) (2 A c (p+2)-b B (p+3)))}{4 c^3 (p+1) (p+2) (2 p+3)}+\frac{B x^2 \left(a+b x+c x^2\right)^{p+1}}{2 c (p+2)}",1,"(B*x^2*(a + b*x + c*x^2)^(1 + p))/(2*c*(2 + p)) - ((2*a*B*c*(3 + 2*p) + b*(2 + p)*(2*A*c*(2 + p) - b*B*(3 + p)) - 2*c*(1 + p)*(2*A*c*(2 + p) - b*B*(3 + p))*x)*(a + b*x + c*x^2)^(1 + p))/(4*c^3*(1 + p)*(2 + p)*(3 + 2*p)) - (2^(-1 + p)*(6*a*b*B*c - 4*a*A*c^2 + 2*A*b^2*c*(2 + p) - b^3*B*(3 + p))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c^3*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",3,3,21,0.1429,1,"{832, 779, 624}"
1097,1,211,0,0.0893853,"\int x (A+B x) \left(a+b x+c x^2\right)^p \, dx","Int[x*(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{2^p \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \left(2 a B c+A b c (2 p+3)+b^2 (-B) (p+2)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{\left(a+b x+c x^2\right)^{p+1} (-A c (2 p+3)+b B (p+2)-2 B c (p+1) x)}{2 c^2 (p+1) (2 p+3)}","\frac{2^p \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \left(2 a B c+A b c (2 p+3)+b^2 (-B) (p+2)\right) \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c^2 (p+1) (2 p+3) \sqrt{b^2-4 a c}}-\frac{\left(a+b x+c x^2\right)^{p+1} (-A c (2 p+3)+b B (p+2)-2 B c (p+1) x)}{2 c^2 (p+1) (2 p+3)}",1,"-((b*B*(2 + p) - A*c*(3 + 2*p) - 2*B*c*(1 + p)*x)*(a + b*x + c*x^2)^(1 + p))/(2*c^2*(1 + p)*(3 + 2*p)) + (2^p*(2*a*B*c - b^2*B*(2 + p) + A*b*c*(3 + 2*p))*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c^2*Sqrt[b^2 - 4*a*c]*(1 + p)*(3 + 2*p))","A",2,2,19,0.1053,1,"{779, 624}"
1098,1,158,0,0.0492388,"\int (A+B x) \left(a+b x+c x^2\right)^p \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^p,x]","\frac{2^p (b B-2 A c) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c (p+1) \sqrt{b^2-4 a c}}+\frac{B \left(a+b x+c x^2\right)^{p+1}}{2 c (p+1)}","\frac{2^p (b B-2 A c) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{c (p+1) \sqrt{b^2-4 a c}}+\frac{B \left(a+b x+c x^2\right)^{p+1}}{2 c (p+1)}",1,"(B*(a + b*x + c*x^2)^(1 + p))/(2*c*(1 + p)) + (2^p*(b*B - 2*A*c)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(c*Sqrt[b^2 - 4*a*c]*(1 + p))","A",2,2,18,0.1111,1,"{640, 624}"
1099,1,273,0,0.1481021,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^p}{x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^p)/x,x]","\frac{A 2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x},-\frac{b+\sqrt{b^2-4 a c}}{2 c x}\right)}{p}-\frac{B 2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}","\frac{A 2^{2 p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x},-\frac{b+\sqrt{b^2-4 a c}}{2 c x}\right)}{p}-\frac{B 2^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \left(a+b x+c x^2\right)^{p+1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{(p+1) \sqrt{b^2-4 a c}}",1,"(2^(-1 + 2*p)*A*(a + b*x + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x)])/(p*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p) - (2^(1 + p)*B*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(Sqrt[b^2 - 4*a*c]*(1 + p))","A",4,4,21,0.1905,1,"{843, 624, 758, 133}"
1100,1,315,0,0.2034004,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^p}{x^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^p)/x^2,x]","\frac{2^{2 p-1} (a B+A b p) \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x},-\frac{b+\sqrt{b^2-4 a c}}{2 c x}\right)}{a p}-\frac{A c 2^{p+1} (2 p+1) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{a (p+1) \sqrt{b^2-4 a c}}-\frac{A \left(a+b x+c x^2\right)^{p+1}}{a x}","\frac{2^{2 p-1} (a B+A b p) \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(a+b x+c x^2\right)^p F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x},-\frac{b+\sqrt{b^2-4 a c}}{2 c x}\right)}{a p}-\frac{A c 2^{p+1} (2 p+1) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{a (p+1) \sqrt{b^2-4 a c}}-\frac{A \left(a+b x+c x^2\right)^{p+1}}{a x}",1,"-((A*(a + b*x + c*x^2)^(1 + p))/(a*x)) + (2^(-1 + 2*p)*(a*B + A*b*p)*(a + b*x + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x)])/(a*p*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p) - (2^(1 + p)*A*c*(1 + 2*p)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(a*Sqrt[b^2 - 4*a*c]*(1 + p))","A",5,5,21,0.2381,1,"{834, 843, 624, 758, 133}"
1101,1,375,0,0.3557225,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^p}{x^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^p)/x^3,x]","\frac{4^{p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(a+b x+c x^2\right)^p \left(2 a A c+2 a b B-A b^2 (1-p)\right) F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x},-\frac{b+\sqrt{b^2-4 a c}}{2 c x}\right)}{a^2}-\frac{c 2^p (2 p+1) (2 a B-A b (1-p)) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{a^2 (p+1) \sqrt{b^2-4 a c}}-\frac{(2 a B-A b (1-p)) \left(a+b x+c x^2\right)^{p+1}}{2 a^2 x}-\frac{A \left(a+b x+c x^2\right)^{p+1}}{2 a x^2}","\frac{4^{p-1} \left(\frac{-\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(\frac{\sqrt{b^2-4 a c}+b+2 c x}{c x}\right)^{-p} \left(a+b x+c x^2\right)^p \left(A \left(2 a c-b^2 (1-p)\right)+2 a b B\right) F_1\left(-2 p;-p,-p;1-2 p;-\frac{b-\sqrt{b^2-4 a c}}{2 c x},-\frac{b+\sqrt{b^2-4 a c}}{2 c x}\right)}{a^2}-\frac{c 2^p (2 p+1) (2 a B-A b (1-p)) \left(a+b x+c x^2\right)^{p+1} \left(-\frac{-\sqrt{b^2-4 a c}+b+2 c x}{\sqrt{b^2-4 a c}}\right)^{-p-1} \, _2F_1\left(-p,p+1;p+2;\frac{b+2 c x+\sqrt{b^2-4 a c}}{2 \sqrt{b^2-4 a c}}\right)}{a^2 (p+1) \sqrt{b^2-4 a c}}-\frac{(2 a B-A b (1-p)) \left(a+b x+c x^2\right)^{p+1}}{2 a^2 x}-\frac{A \left(a+b x+c x^2\right)^{p+1}}{2 a x^2}",1,"-(A*(a + b*x + c*x^2)^(1 + p))/(2*a*x^2) - ((2*a*B - A*b*(1 - p))*(a + b*x + c*x^2)^(1 + p))/(2*a^2*x) + (4^(-1 + p)*(2*a*b*B + 2*a*A*c - A*b^2*(1 - p))*(a + b*x + c*x^2)^p*AppellF1[-2*p, -p, -p, 1 - 2*p, -(b - Sqrt[b^2 - 4*a*c])/(2*c*x), -(b + Sqrt[b^2 - 4*a*c])/(2*c*x)])/(a^2*((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p*((b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(c*x))^p) - (2^p*c*(2*a*B - A*b*(1 - p))*(1 + 2*p)*(-((b - Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]))^(-1 - p)*(a + b*x + c*x^2)^(1 + p)*Hypergeometric2F1[-p, 1 + p, 2 + p, (b + Sqrt[b^2 - 4*a*c] + 2*c*x)/(2*Sqrt[b^2 - 4*a*c])])/(a^2*Sqrt[b^2 - 4*a*c]*(1 + p))","A",6,5,21,0.2381,1,"{834, 843, 624, 758, 133}"
1102,1,136,0,0.0979955,"\int (A+B x) (d+e x)^m \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^m*(b*x + c*x^2),x]","-\frac{d (B d-A e) (c d-b e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(d+e x)^{m+2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4 (m+2)}-\frac{(d+e x)^{m+3} (-A c e-b B e+3 B c d)}{e^4 (m+3)}+\frac{B c (d+e x)^{m+4}}{e^4 (m+4)}","-\frac{d (B d-A e) (c d-b e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(d+e x)^{m+2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4 (m+2)}-\frac{(d+e x)^{m+3} (-A c e-b B e+3 B c d)}{e^4 (m+3)}+\frac{B c (d+e x)^{m+4}}{e^4 (m+4)}",1,"-((d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^4*(2 + m)) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (B*c*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,22,0.04545,1,"{771}"
1103,1,118,0,0.1750771,"\int (A+B x) (d+e x)^4 \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^4*(b*x + c*x^2),x]","-\frac{(d+e x)^7 (-A c e-b B e+3 B c d)}{7 e^4}+\frac{(d+e x)^6 (B d (3 c d-2 b e)-A e (2 c d-b e))}{6 e^4}-\frac{d (d+e x)^5 (B d-A e) (c d-b e)}{5 e^4}+\frac{B c (d+e x)^8}{8 e^4}","-\frac{(d+e x)^7 (-A c e-b B e+3 B c d)}{7 e^4}+\frac{(d+e x)^6 (B d (3 c d-2 b e)-A e (2 c d-b e))}{6 e^4}-\frac{d (d+e x)^5 (B d-A e) (c d-b e)}{5 e^4}+\frac{B c (d+e x)^8}{8 e^4}",1,"-(d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^5)/(5*e^4) + ((B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^6)/(6*e^4) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^7)/(7*e^4) + (B*c*(d + e*x)^8)/(8*e^4)","A",2,1,22,0.04545,1,"{771}"
1104,1,118,0,0.136868,"\int (A+B x) (d+e x)^3 \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^3*(b*x + c*x^2),x]","-\frac{(d+e x)^6 (-A c e-b B e+3 B c d)}{6 e^4}+\frac{(d+e x)^5 (B d (3 c d-2 b e)-A e (2 c d-b e))}{5 e^4}-\frac{d (d+e x)^4 (B d-A e) (c d-b e)}{4 e^4}+\frac{B c (d+e x)^7}{7 e^4}","-\frac{(d+e x)^6 (-A c e-b B e+3 B c d)}{6 e^4}+\frac{(d+e x)^5 (B d (3 c d-2 b e)-A e (2 c d-b e))}{5 e^4}-\frac{d (d+e x)^4 (B d-A e) (c d-b e)}{4 e^4}+\frac{B c (d+e x)^7}{7 e^4}",1,"-(d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^4)/(4*e^4) + ((B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^5)/(5*e^4) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^6)/(6*e^4) + (B*c*(d + e*x)^7)/(7*e^4)","A",2,1,22,0.04545,1,"{771}"
1105,1,99,0,0.1010152,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^2*(b*x + c*x^2),x]","\frac{1}{5} e x^5 (A c e+b B e+2 B c d)+\frac{1}{4} x^4 (A e (b e+2 c d)+B d (2 b e+c d))+\frac{1}{3} d x^3 (2 A b e+A c d+b B d)+\frac{1}{2} A b d^2 x^2+\frac{1}{6} B c e^2 x^6","\frac{1}{5} e x^5 (A c e+b B e+2 B c d)+\frac{1}{4} x^4 (A e (b e+2 c d)+B d (2 b e+c d))+\frac{1}{3} d x^3 (2 A b e+A c d+b B d)+\frac{1}{2} A b d^2 x^2+\frac{1}{6} B c e^2 x^6",1,"(A*b*d^2*x^2)/2 + (d*(b*B*d + A*c*d + 2*A*b*e)*x^3)/3 + ((A*e*(2*c*d + b*e) + B*d*(c*d + 2*b*e))*x^4)/4 + (e*(2*B*c*d + b*B*e + A*c*e)*x^5)/5 + (B*c*e^2*x^6)/6","A",2,1,22,0.04545,1,"{771}"
1106,1,61,0,0.0629858,"\int (A+B x) (d+e x) \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)*(b*x + c*x^2),x]","\frac{1}{4} x^4 (A c e+b B e+B c d)+\frac{1}{3} x^3 (A b e+A c d+b B d)+\frac{1}{2} A b d x^2+\frac{1}{5} B c e x^5","\frac{1}{4} x^4 (A c e+b B e+B c d)+\frac{1}{3} x^3 (A b e+A c d+b B d)+\frac{1}{2} A b d x^2+\frac{1}{5} B c e x^5",1,"(A*b*d*x^2)/2 + ((b*B*d + A*c*d + A*b*e)*x^3)/3 + ((B*c*d + b*B*e + A*c*e)*x^4)/4 + (B*c*e*x^5)/5","A",2,1,20,0.05000,1,"{771}"
1107,1,33,0,0.0227114,"\int (A+B x) \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(b*x + c*x^2),x]","\frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4","\frac{1}{3} x^3 (A c+b B)+\frac{1}{2} A b x^2+\frac{1}{4} B c x^4",1,"(A*b*x^2)/2 + ((b*B + A*c)*x^3)/3 + (B*c*x^4)/4","A",2,1,15,0.06667,1,"{631}"
1108,1,87,0,0.0978763,"\int \frac{(A+B x) \left(b x+c x^2\right)}{d+e x} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x),x]","-\frac{x^2 (-A c e-b B e+B c d)}{2 e^2}+\frac{x (B d-A e) (c d-b e)}{e^3}-\frac{d (B d-A e) (c d-b e) \log (d+e x)}{e^4}+\frac{B c x^3}{3 e}","-\frac{x^2 (-A c e-b B e+B c d)}{2 e^2}+\frac{x (B d-A e) (c d-b e)}{e^3}-\frac{d (B d-A e) (c d-b e) \log (d+e x)}{e^4}+\frac{B c x^3}{3 e}",1,"((B*d - A*e)*(c*d - b*e)*x)/e^3 - ((B*c*d - b*B*e - A*c*e)*x^2)/(2*e^2) + (B*c*x^3)/(3*e) - (d*(B*d - A*e)*(c*d - b*e)*Log[d + e*x])/e^4","A",2,1,22,0.04545,1,"{771}"
1109,1,99,0,0.1145046,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^2} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^2,x]","-\frac{x (-A c e-b B e+2 B c d)}{e^3}+\frac{d (B d-A e) (c d-b e)}{e^4 (d+e x)}+\frac{\log (d+e x) (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4}+\frac{B c x^2}{2 e^2}","-\frac{x (-A c e-b B e+2 B c d)}{e^3}+\frac{d (B d-A e) (c d-b e)}{e^4 (d+e x)}+\frac{\log (d+e x) (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4}+\frac{B c x^2}{2 e^2}",1,"-(((2*B*c*d - b*B*e - A*c*e)*x)/e^3) + (B*c*x^2)/(2*e^2) + (d*(B*d - A*e)*(c*d - b*e))/(e^4*(d + e*x)) + ((B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*Log[d + e*x])/e^4","A",2,1,22,0.04545,1,"{771}"
1110,1,104,0,0.1073331,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^3} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^3,x]","\frac{d (B d-A e) (c d-b e)}{2 e^4 (d+e x)^2}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{e^4 (d+e x)}-\frac{\log (d+e x) (-A c e-b B e+3 B c d)}{e^4}+\frac{B c x}{e^3}","\frac{d (B d-A e) (c d-b e)}{2 e^4 (d+e x)^2}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{e^4 (d+e x)}-\frac{\log (d+e x) (-A c e-b B e+3 B c d)}{e^4}+\frac{B c x}{e^3}",1,"(B*c*x)/e^3 + (d*(B*d - A*e)*(c*d - b*e))/(2*e^4*(d + e*x)^2) - (B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))/(e^4*(d + e*x)) - ((3*B*c*d - b*B*e - A*c*e)*Log[d + e*x])/e^4","A",2,1,22,0.04545,1,"{771}"
1111,1,111,0,0.105651,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^4} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^4,x]","\frac{d (B d-A e) (c d-b e)}{3 e^4 (d+e x)^3}+\frac{-A c e-b B e+3 B c d}{e^4 (d+e x)}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{2 e^4 (d+e x)^2}+\frac{B c \log (d+e x)}{e^4}","\frac{d (B d-A e) (c d-b e)}{3 e^4 (d+e x)^3}+\frac{-A c e-b B e+3 B c d}{e^4 (d+e x)}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{2 e^4 (d+e x)^2}+\frac{B c \log (d+e x)}{e^4}",1,"(d*(B*d - A*e)*(c*d - b*e))/(3*e^4*(d + e*x)^3) - (B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))/(2*e^4*(d + e*x)^2) + (3*B*c*d - b*B*e - A*c*e)/(e^4*(d + e*x)) + (B*c*Log[d + e*x])/e^4","A",2,1,22,0.04545,1,"{771}"
1112,1,116,0,0.0985844,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^5} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^5,x]","\frac{-A c e-b B e+3 B c d}{2 e^4 (d+e x)^2}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{3 e^4 (d+e x)^3}+\frac{d (B d-A e) (c d-b e)}{4 e^4 (d+e x)^4}-\frac{B c}{e^4 (d+e x)}","\frac{-A c e-b B e+3 B c d}{2 e^4 (d+e x)^2}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{3 e^4 (d+e x)^3}+\frac{d (B d-A e) (c d-b e)}{4 e^4 (d+e x)^4}-\frac{B c}{e^4 (d+e x)}",1,"(d*(B*d - A*e)*(c*d - b*e))/(4*e^4*(d + e*x)^4) - (B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))/(3*e^4*(d + e*x)^3) + (3*B*c*d - b*B*e - A*c*e)/(2*e^4*(d + e*x)^2) - (B*c)/(e^4*(d + e*x))","A",2,1,22,0.04545,1,"{771}"
1113,1,118,0,0.1003027,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^6} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^6,x]","\frac{-A c e-b B e+3 B c d}{3 e^4 (d+e x)^3}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{4 e^4 (d+e x)^4}+\frac{d (B d-A e) (c d-b e)}{5 e^4 (d+e x)^5}-\frac{B c}{2 e^4 (d+e x)^2}","\frac{-A c e-b B e+3 B c d}{3 e^4 (d+e x)^3}-\frac{B d (3 c d-2 b e)-A e (2 c d-b e)}{4 e^4 (d+e x)^4}+\frac{d (B d-A e) (c d-b e)}{5 e^4 (d+e x)^5}-\frac{B c}{2 e^4 (d+e x)^2}",1,"(d*(B*d - A*e)*(c*d - b*e))/(5*e^4*(d + e*x)^5) - (B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))/(4*e^4*(d + e*x)^4) + (3*B*c*d - b*B*e - A*c*e)/(3*e^4*(d + e*x)^3) - (B*c)/(2*e^4*(d + e*x)^2)","A",2,1,22,0.04545,1,"{771}"
1114,1,282,0,0.2270592,"\int (A+B x) (d+e x)^m \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^m*(b*x + c*x^2)^2,x]","\frac{(d+e x)^{m+3} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6 (m+3)}-\frac{(d+e x)^{m+4} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{e^6 (m+4)}-\frac{d^2 (B d-A e) (c d-b e)^2 (d+e x)^{m+1}}{e^6 (m+1)}+\frac{d (c d-b e) (d+e x)^{m+2} (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6 (m+2)}-\frac{c (d+e x)^{m+5} (-A c e-2 b B e+5 B c d)}{e^6 (m+5)}+\frac{B c^2 (d+e x)^{m+6}}{e^6 (m+6)}","\frac{(d+e x)^{m+3} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6 (m+3)}-\frac{(d+e x)^{m+4} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{e^6 (m+4)}-\frac{d^2 (B d-A e) (c d-b e)^2 (d+e x)^{m+1}}{e^6 (m+1)}+\frac{d (c d-b e) (d+e x)^{m+2} (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6 (m+2)}-\frac{c (d+e x)^{m+5} (-A c e-2 b B e+5 B c d)}{e^6 (m+5)}+\frac{B c^2 (d+e x)^{m+6}}{e^6 (m+6)}",1,"-((d^2*(B*d - A*e)*(c*d - b*e)^2*(d + e*x)^(1 + m))/(e^6*(1 + m))) + (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^6*(2 + m)) + ((A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(3 + m))/(e^6*(3 + m)) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (B*c^2*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,24,0.04167,1,"{771}"
1115,1,228,0,0.2478097,"\int (A+B x) (d+e x)^3 \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^3*(b*x + c*x^2)^2,x]","\frac{1}{7} e x^7 \left(A c e (2 b e+3 c d)+B \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)\right)+\frac{1}{6} x^6 \left(A e \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)+B d \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)\right)+\frac{1}{5} d x^5 \left(3 b^2 e (A e+B d)+2 b c d (3 A e+B d)+A c^2 d^2\right)+\frac{1}{3} A b^2 d^3 x^3+\frac{1}{4} b d^2 x^4 (3 A b e+2 A c d+b B d)+\frac{1}{8} c e^2 x^8 (A c e+2 b B e+3 B c d)+\frac{1}{9} B c^2 e^3 x^9","\frac{1}{7} e x^7 \left(A c e (2 b e+3 c d)+B \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)\right)+\frac{1}{6} x^6 \left(A e \left(b^2 e^2+6 b c d e+3 c^2 d^2\right)+B d \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)\right)+\frac{1}{5} d x^5 \left(3 b^2 e (A e+B d)+2 b c d (3 A e+B d)+A c^2 d^2\right)+\frac{1}{3} A b^2 d^3 x^3+\frac{1}{4} b d^2 x^4 (3 A b e+2 A c d+b B d)+\frac{1}{8} c e^2 x^8 (A c e+2 b B e+3 B c d)+\frac{1}{9} B c^2 e^3 x^9",1,"(A*b^2*d^3*x^3)/3 + (b*d^2*(b*B*d + 2*A*c*d + 3*A*b*e)*x^4)/4 + (d*(A*c^2*d^2 + 3*b^2*e*(B*d + A*e) + 2*b*c*d*(B*d + 3*A*e))*x^5)/5 + ((A*e*(3*c^2*d^2 + 6*b*c*d*e + b^2*e^2) + B*d*(c^2*d^2 + 6*b*c*d*e + 3*b^2*e^2))*x^6)/6 + (e*(A*c*e*(3*c*d + 2*b*e) + B*(3*c^2*d^2 + 6*b*c*d*e + b^2*e^2))*x^7)/7 + (c*e^2*(3*B*c*d + 2*b*B*e + A*c*e)*x^8)/8 + (B*c^2*e^3*x^9)/9","A",2,1,24,0.04167,1,"{771}"
1116,1,162,0,0.2239126,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^2,x]","\frac{1}{6} x^6 \left(2 A c e (b e+c d)+B \left(b^2 e^2+4 b c d e+c^2 d^2\right)\right)+\frac{1}{5} x^5 \left(b^2 e (A e+2 B d)+2 b c d (2 A e+B d)+A c^2 d^2\right)+\frac{1}{3} A b^2 d^2 x^3+\frac{1}{7} c e x^7 (A c e+2 B (b e+c d))+\frac{1}{4} b d x^4 (2 A b e+2 A c d+b B d)+\frac{1}{8} B c^2 e^2 x^8","\frac{1}{6} x^6 \left(2 A c e (b e+c d)+B \left(b^2 e^2+4 b c d e+c^2 d^2\right)\right)+\frac{1}{5} x^5 \left(b^2 e (A e+2 B d)+2 b c d (2 A e+B d)+A c^2 d^2\right)+\frac{1}{3} A b^2 d^2 x^3+\frac{1}{7} c e x^7 (A c e+2 B (b e+c d))+\frac{1}{4} b d x^4 (2 A b e+2 A c d+b B d)+\frac{1}{8} B c^2 e^2 x^8",1,"(A*b^2*d^2*x^3)/3 + (b*d*(b*B*d + 2*A*c*d + 2*A*b*e)*x^4)/4 + ((A*c^2*d^2 + b^2*e*(2*B*d + A*e) + 2*b*c*d*(B*d + 2*A*e))*x^5)/5 + ((2*A*c*e*(c*d + b*e) + B*(c^2*d^2 + 4*b*c*d*e + b^2*e^2))*x^6)/6 + (c*e*(A*c*e + 2*B*(c*d + b*e))*x^7)/7 + (B*c^2*e^2*x^8)/8","A",2,1,24,0.04167,1,"{771}"
1117,1,100,0,0.1119952,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)*(b*x + c*x^2)^2,x]","\frac{1}{5} x^5 \left(2 b c (A e+B d)+A c^2 d+b^2 B e\right)+\frac{1}{3} A b^2 d x^3+\frac{1}{6} c x^6 (A c e+2 b B e+B c d)+\frac{1}{4} b x^4 (A b e+2 A c d+b B d)+\frac{1}{7} B c^2 e x^7","\frac{1}{5} x^5 \left(2 b c (A e+B d)+A c^2 d+b^2 B e\right)+\frac{1}{3} A b^2 d x^3+\frac{1}{6} c x^6 (A c e+2 b B e+B c d)+\frac{1}{4} b x^4 (A b e+2 A c d+b B d)+\frac{1}{7} B c^2 e x^7",1,"(A*b^2*d*x^3)/3 + (b*(b*B*d + 2*A*c*d + A*b*e)*x^4)/4 + ((A*c^2*d + b^2*B*e + 2*b*c*(B*d + A*e))*x^5)/5 + (c*(B*c*d + 2*b*B*e + A*c*e)*x^6)/6 + (B*c^2*e*x^7)/7","A",2,1,22,0.04545,1,"{771}"
1118,1,55,0,0.0441635,"\int (A+B x) \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(b*x + c*x^2)^2,x]","\frac{1}{3} A b^2 x^3+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{4} b x^4 (2 A c+b B)+\frac{1}{6} B c^2 x^6","\frac{1}{3} A b^2 x^3+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{4} b x^4 (2 A c+b B)+\frac{1}{6} B c^2 x^6",1,"(A*b^2*x^3)/3 + (b*(b*B + 2*A*c)*x^4)/4 + (c*(2*b*B + A*c)*x^5)/5 + (B*c^2*x^6)/6","A",2,1,17,0.05882,1,"{631}"
1119,1,161,0,0.2256908,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{d+e x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x),x]","-\frac{d^2 (B d-A e) (c d-b e)^2 \log (d+e x)}{e^6}-\frac{c x^4 (-A c e-2 b B e+B c d)}{4 e^2}-\frac{x^3 \left(A c e (c d-2 b e)-B (c d-b e)^2\right)}{3 e^3}-\frac{x^2 (B d-A e) (c d-b e)^2}{2 e^4}+\frac{d x (B d-A e) (c d-b e)^2}{e^5}+\frac{B c^2 x^5}{5 e}","-\frac{d^2 (B d-A e) (c d-b e)^2 \log (d+e x)}{e^6}-\frac{c x^4 (-A c e-2 b B e+B c d)}{4 e^2}-\frac{x^3 \left(A c e (c d-2 b e)-B (c d-b e)^2\right)}{3 e^3}-\frac{x^2 (B d-A e) (c d-b e)^2}{2 e^4}+\frac{d x (B d-A e) (c d-b e)^2}{e^5}+\frac{B c^2 x^5}{5 e}",1,"(d*(B*d - A*e)*(c*d - b*e)^2*x)/e^5 - ((B*d - A*e)*(c*d - b*e)^2*x^2)/(2*e^4) - ((A*c*e*(c*d - 2*b*e) - B*(c*d - b*e)^2)*x^3)/(3*e^3) - (c*(B*c*d - 2*b*B*e - A*c*e)*x^4)/(4*e^2) + (B*c^2*x^5)/(5*e) - (d^2*(B*d - A*e)*(c*d - b*e)^2*Log[d + e*x])/e^6","A",2,1,24,0.04167,1,"{771}"
1120,1,194,0,0.2782302,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^2,x]","\frac{d^2 (B d-A e) (c d-b e)^2}{e^6 (d+e x)}-\frac{c x^3 (-A c e-2 b B e+2 B c d)}{3 e^3}+\frac{x^2 (c d-b e) (-2 A c e-b B e+3 B c d)}{2 e^4}-\frac{x (c d-b e) (2 B d (2 c d-b e)-A e (3 c d-b e))}{e^5}+\frac{d (c d-b e) \log (d+e x) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6}+\frac{B c^2 x^4}{4 e^2}","\frac{d^2 (B d-A e) (c d-b e)^2}{e^6 (d+e x)}-\frac{c x^3 (-A c e-2 b B e+2 B c d)}{3 e^3}+\frac{x^2 (c d-b e) (-2 A c e-b B e+3 B c d)}{2 e^4}-\frac{x (c d-b e) (2 B d (2 c d-b e)-A e (3 c d-b e))}{e^5}+\frac{d (c d-b e) \log (d+e x) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6}+\frac{B c^2 x^4}{4 e^2}",1,"-(((c*d - b*e)*(2*B*d*(2*c*d - b*e) - A*e*(3*c*d - b*e))*x)/e^5) + ((c*d - b*e)*(3*B*c*d - b*B*e - 2*A*c*e)*x^2)/(2*e^4) - (c*(2*B*c*d - 2*b*B*e - A*c*e)*x^3)/(3*e^3) + (B*c^2*x^4)/(4*e^2) + (d^2*(B*d - A*e)*(c*d - b*e)^2)/(e^6*(d + e*x)) + (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*Log[d + e*x])/e^6","A",2,1,24,0.04167,1,"{771}"
1121,1,232,0,0.3205759,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^3,x]","-\frac{x \left(A c e (3 c d-2 b e)-B \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)\right)}{e^5}+\frac{\log (d+e x) \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6}+\frac{d^2 (B d-A e) (c d-b e)^2}{2 e^6 (d+e x)^2}-\frac{c x^2 (-A c e-2 b B e+3 B c d)}{2 e^4}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6 (d+e x)}+\frac{B c^2 x^3}{3 e^3}","-\frac{x \left(A c e (3 c d-2 b e)-B \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)\right)}{e^5}+\frac{\log (d+e x) \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6}+\frac{d^2 (B d-A e) (c d-b e)^2}{2 e^6 (d+e x)^2}-\frac{c x^2 (-A c e-2 b B e+3 B c d)}{2 e^4}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6 (d+e x)}+\frac{B c^2 x^3}{3 e^3}",1,"-(((A*c*e*(3*c*d - 2*b*e) - B*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2))*x)/e^5) - (c*(3*B*c*d - 2*b*B*e - A*c*e)*x^2)/(2*e^4) + (B*c^2*x^3)/(3*e^3) + (d^2*(B*d - A*e)*(c*d - b*e)^2)/(2*e^6*(d + e*x)^2) - (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(e^6*(d + e*x)) + ((A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*Log[d + e*x])/e^6","A",2,1,24,0.04167,1,"{771}"
1122,1,238,0,0.2999408,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^4,x]","-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{e^6 (d+e x)}-\frac{\log (d+e x) \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{e^6}+\frac{d^2 (B d-A e) (c d-b e)^2}{3 e^6 (d+e x)^3}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{2 e^6 (d+e x)^2}-\frac{c x (-A c e-2 b B e+4 B c d)}{e^5}+\frac{B c^2 x^2}{2 e^4}","-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{e^6 (d+e x)}-\frac{\log (d+e x) \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{e^6}+\frac{d^2 (B d-A e) (c d-b e)^2}{3 e^6 (d+e x)^3}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{2 e^6 (d+e x)^2}-\frac{c x (-A c e-2 b B e+4 B c d)}{e^5}+\frac{B c^2 x^2}{2 e^4}",1,"-((c*(4*B*c*d - 2*b*B*e - A*c*e)*x)/e^5) + (B*c^2*x^2)/(2*e^4) + (d^2*(B*d - A*e)*(c*d - b*e)^2)/(3*e^6*(d + e*x)^3) - (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(2*e^6*(d + e*x)^2) - (A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))/(e^6*(d + e*x)) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*Log[d + e*x])/e^6","A",2,1,24,0.04167,1,"{771}"
1123,1,240,0,0.281976,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^5,x]","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{e^6 (d+e x)}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}+\frac{d^2 (B d-A e) (c d-b e)^2}{4 e^6 (d+e x)^4}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{3 e^6 (d+e x)^3}-\frac{c \log (d+e x) (-A c e-2 b B e+5 B c d)}{e^6}+\frac{B c^2 x}{e^5}","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{e^6 (d+e x)}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}+\frac{d^2 (B d-A e) (c d-b e)^2}{4 e^6 (d+e x)^4}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{3 e^6 (d+e x)^3}-\frac{c \log (d+e x) (-A c e-2 b B e+5 B c d)}{e^6}+\frac{B c^2 x}{e^5}",1,"(B*c^2*x)/e^5 + (d^2*(B*d - A*e)*(c*d - b*e)^2)/(4*e^6*(d + e*x)^4) - (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(3*e^6*(d + e*x)^3) - (A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))/(2*e^6*(d + e*x)^2) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))/(e^6*(d + e*x)) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*Log[d + e*x])/e^6","A",2,1,24,0.04167,1,"{771}"
1124,1,248,0,0.2399038,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^6} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^6,x]","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{d^2 (B d-A e) (c d-b e)^2}{5 e^6 (d+e x)^5}+\frac{c (-A c e-2 b B e+5 B c d)}{e^6 (d+e x)}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{4 e^6 (d+e x)^4}+\frac{B c^2 \log (d+e x)}{e^6}","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{d^2 (B d-A e) (c d-b e)^2}{5 e^6 (d+e x)^5}+\frac{c (-A c e-2 b B e+5 B c d)}{e^6 (d+e x)}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{4 e^6 (d+e x)^4}+\frac{B c^2 \log (d+e x)}{e^6}",1,"(d^2*(B*d - A*e)*(c*d - b*e)^2)/(5*e^6*(d + e*x)^5) - (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(4*e^6*(d + e*x)^4) - (A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))/(3*e^6*(d + e*x)^3) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))/(2*e^6*(d + e*x)^2) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(e^6*(d + e*x)) + (B*c^2*Log[d + e*x])/e^6","A",2,1,24,0.04167,1,"{771}"
1125,1,253,0,0.2266526,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^7} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^7,x]","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{3 e^6 (d+e x)^3}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{4 e^6 (d+e x)^4}+\frac{d^2 (B d-A e) (c d-b e)^2}{6 e^6 (d+e x)^6}+\frac{c (-A c e-2 b B e+5 B c d)}{2 e^6 (d+e x)^2}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{5 e^6 (d+e x)^5}-\frac{B c^2}{e^6 (d+e x)}","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{3 e^6 (d+e x)^3}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{4 e^6 (d+e x)^4}+\frac{d^2 (B d-A e) (c d-b e)^2}{6 e^6 (d+e x)^6}+\frac{c (-A c e-2 b B e+5 B c d)}{2 e^6 (d+e x)^2}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{5 e^6 (d+e x)^5}-\frac{B c^2}{e^6 (d+e x)}",1,"(d^2*(B*d - A*e)*(c*d - b*e)^2)/(6*e^6*(d + e*x)^6) - (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(5*e^6*(d + e*x)^5) - (A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))/(4*e^6*(d + e*x)^4) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))/(3*e^6*(d + e*x)^3) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(2*e^6*(d + e*x)^2) - (B*c^2)/(e^6*(d + e*x))","A",2,1,24,0.04167,1,"{771}"
1126,1,255,0,0.2236287,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^8} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^8,x]","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{4 e^6 (d+e x)^4}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{5 e^6 (d+e x)^5}+\frac{d^2 (B d-A e) (c d-b e)^2}{7 e^6 (d+e x)^7}+\frac{c (-A c e-2 b B e+5 B c d)}{3 e^6 (d+e x)^3}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{6 e^6 (d+e x)^6}-\frac{B c^2}{2 e^6 (d+e x)^2}","\frac{2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)}{4 e^6 (d+e x)^4}-\frac{A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)}{5 e^6 (d+e x)^5}+\frac{d^2 (B d-A e) (c d-b e)^2}{7 e^6 (d+e x)^7}+\frac{c (-A c e-2 b B e+5 B c d)}{3 e^6 (d+e x)^3}-\frac{d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{6 e^6 (d+e x)^6}-\frac{B c^2}{2 e^6 (d+e x)^2}",1,"(d^2*(B*d - A*e)*(c*d - b*e)^2)/(7*e^6*(d + e*x)^7) - (d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(6*e^6*(d + e*x)^6) - (A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))/(5*e^6*(d + e*x)^5) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))/(4*e^6*(d + e*x)^4) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(3*e^6*(d + e*x)^3) - (B*c^2)/(2*e^6*(d + e*x)^2)","A",2,1,24,0.04167,1,"{771}"
1127,1,484,0,0.407169,"\int (A+B x) (d+e x)^m \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^m*(b*x + c*x^2)^3,x]","\frac{3 d (c d-b e) (d+e x)^{m+3} \left(A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)\right)}{e^8 (m+3)}+\frac{(d+e x)^{m+4} \left(B d \left(30 b^2 c d e^2-4 b^3 e^3-60 b c^2 d^2 e+35 c^3 d^3\right)-A e \left(12 b^2 c d e^2-b^3 e^3-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^8 (m+4)}+\frac{(d+e x)^{m+5} \left(3 A c e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B \left(15 b^2 c d e^2-b^3 e^3-45 b c^2 d^2 e+35 c^3 d^3\right)\right)}{e^8 (m+5)}-\frac{3 c (d+e x)^{m+6} \left(A c e (2 c d-b e)-B \left(b^2 e^2-6 b c d e+7 c^2 d^2\right)\right)}{e^8 (m+6)}-\frac{c^2 (d+e x)^{m+7} (-A c e-3 b B e+7 B c d)}{e^8 (m+7)}-\frac{d^3 (B d-A e) (c d-b e)^3 (d+e x)^{m+1}}{e^8 (m+1)}+\frac{d^2 (c d-b e)^2 (d+e x)^{m+2} (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{e^8 (m+2)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)}","\frac{3 d (c d-b e) (d+e x)^{m+3} \left(A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)\right)}{e^8 (m+3)}+\frac{(d+e x)^{m+4} \left(B d \left(30 b^2 c d e^2-4 b^3 e^3-60 b c^2 d^2 e+35 c^3 d^3\right)-A e \left(12 b^2 c d e^2-b^3 e^3-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^8 (m+4)}+\frac{(d+e x)^{m+5} \left(3 A c e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B \left(15 b^2 c d e^2-b^3 e^3-45 b c^2 d^2 e+35 c^3 d^3\right)\right)}{e^8 (m+5)}-\frac{3 c (d+e x)^{m+6} \left(A c e (2 c d-b e)-B \left(b^2 e^2-6 b c d e+7 c^2 d^2\right)\right)}{e^8 (m+6)}-\frac{c^2 (d+e x)^{m+7} (-A c e-3 b B e+7 B c d)}{e^8 (m+7)}-\frac{d^3 (B d-A e) (c d-b e)^3 (d+e x)^{m+1}}{e^8 (m+1)}+\frac{d^2 (c d-b e)^2 (d+e x)^{m+2} (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{e^8 (m+2)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)}",1,"-((d^3*(B*d - A*e)*(c*d - b*e)^3*(d + e*x)^(1 + m))/(e^8*(1 + m))) + (d^2*(c*d - b*e)^2*(B*d*(7*c*d - 4*b*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^8*(2 + m)) + (3*d*(c*d - b*e)*(A*e*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2) - B*d*(7*c^2*d^2 - 8*b*c*d*e + 2*b^2*e^2))*(d + e*x)^(3 + m))/(e^8*(3 + m)) + ((B*d*(35*c^3*d^3 - 60*b*c^2*d^2*e + 30*b^2*c*d*e^2 - 4*b^3*e^3) - A*e*(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 - b^3*e^3))*(d + e*x)^(4 + m))/(e^8*(4 + m)) + ((3*A*c*e*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2) - B*(35*c^3*d^3 - 45*b*c^2*d^2*e + 15*b^2*c*d*e^2 - b^3*e^3))*(d + e*x)^(5 + m))/(e^8*(5 + m)) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 - 6*b*c*d*e + b^2*e^2))*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (B*c^3*(d + e*x)^(8 + m))/(e^8*(8 + m))","A",2,1,24,0.04167,1,"{771}"
1128,1,412,0,0.5099985,"\int (A+B x) (d+e x)^4 \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^4*(b*x + c*x^2)^3,x]","\frac{1}{10} c e^2 x^{10} \left(A c e (3 b e+4 c d)+3 B \left(b^2 e^2+4 b c d e+2 c^2 d^2\right)\right)+\frac{1}{9} e x^9 \left(3 A c e \left(b^2 e^2+4 b c d e+2 c^2 d^2\right)+B \left(12 b^2 c d e^2+b^3 e^3+18 b c^2 d^2 e+4 c^3 d^3\right)\right)+\frac{1}{8} x^8 \left(A e \left(12 b^2 c d e^2+b^3 e^3+18 b c^2 d^2 e+4 c^3 d^3\right)+B d \left(18 b^2 c d e^2+4 b^3 e^3+12 b c^2 d^2 e+c^3 d^3\right)\right)+\frac{1}{7} d x^7 \left(6 b^2 c d e (3 A e+2 B d)+2 b^3 e^2 (2 A e+3 B d)+3 b c^2 d^2 (4 A e+B d)+A c^3 d^3\right)+\frac{1}{6} b d^2 x^6 \left(2 b^2 e (3 A e+2 B d)+3 b c d (4 A e+B d)+3 A c^2 d^2\right)+\frac{1}{5} b^2 d^3 x^5 (4 A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d^4 x^4+\frac{1}{11} c^2 e^3 x^{11} (A c e+3 b B e+4 B c d)+\frac{1}{12} B c^3 e^4 x^{12}","\frac{1}{10} c e^2 x^{10} \left(A c e (3 b e+4 c d)+3 B \left(b^2 e^2+4 b c d e+2 c^2 d^2\right)\right)+\frac{1}{9} e x^9 \left(3 A c e \left(b^2 e^2+4 b c d e+2 c^2 d^2\right)+B \left(12 b^2 c d e^2+b^3 e^3+18 b c^2 d^2 e+4 c^3 d^3\right)\right)+\frac{1}{8} x^8 \left(A e \left(12 b^2 c d e^2+b^3 e^3+18 b c^2 d^2 e+4 c^3 d^3\right)+B d \left(18 b^2 c d e^2+4 b^3 e^3+12 b c^2 d^2 e+c^3 d^3\right)\right)+\frac{1}{7} d x^7 \left(6 b^2 c d e (3 A e+2 B d)+2 b^3 e^2 (2 A e+3 B d)+3 b c^2 d^2 (4 A e+B d)+A c^3 d^3\right)+\frac{1}{6} b d^2 x^6 \left(2 b^2 e (3 A e+2 B d)+3 b c d (4 A e+B d)+3 A c^2 d^2\right)+\frac{1}{5} b^2 d^3 x^5 (4 A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d^4 x^4+\frac{1}{11} c^2 e^3 x^{11} (A c e+3 b B e+4 B c d)+\frac{1}{12} B c^3 e^4 x^{12}",1,"(A*b^3*d^4*x^4)/4 + (b^2*d^3*(b*B*d + 3*A*c*d + 4*A*b*e)*x^5)/5 + (b*d^2*(3*A*c^2*d^2 + 2*b^2*e*(2*B*d + 3*A*e) + 3*b*c*d*(B*d + 4*A*e))*x^6)/6 + (d*(A*c^3*d^3 + 2*b^3*e^2*(3*B*d + 2*A*e) + 6*b^2*c*d*e*(2*B*d + 3*A*e) + 3*b*c^2*d^2*(B*d + 4*A*e))*x^7)/7 + ((A*e*(4*c^3*d^3 + 18*b*c^2*d^2*e + 12*b^2*c*d*e^2 + b^3*e^3) + B*d*(c^3*d^3 + 12*b*c^2*d^2*e + 18*b^2*c*d*e^2 + 4*b^3*e^3))*x^8)/8 + (e*(3*A*c*e*(2*c^2*d^2 + 4*b*c*d*e + b^2*e^2) + B*(4*c^3*d^3 + 18*b*c^2*d^2*e + 12*b^2*c*d*e^2 + b^3*e^3))*x^9)/9 + (c*e^2*(A*c*e*(4*c*d + 3*b*e) + 3*B*(2*c^2*d^2 + 4*b*c*d*e + b^2*e^2))*x^10)/10 + (c^2*e^3*(4*B*c*d + 3*b*B*e + A*c*e)*x^11)/11 + (B*c^3*e^4*x^12)/12","A",2,1,24,0.04167,1,"{771}"
1129,1,305,0,0.4752489,"\int (A+B x) (d+e x)^3 \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^3*(b*x + c*x^2)^3,x]","\frac{1}{3} c e x^9 \left(A c e (b e+c d)+B \left(b^2 e^2+3 b c d e+c^2 d^2\right)\right)+\frac{1}{8} x^8 \left(3 A c e \left(b^2 e^2+3 b c d e+c^2 d^2\right)+B \left(9 b^2 c d e^2+b^3 e^3+9 b c^2 d^2 e+c^3 d^3\right)\right)+\frac{1}{7} x^7 \left(9 b^2 c d e (A e+B d)+b^3 e^2 (A e+3 B d)+3 b c^2 d^2 (3 A e+B d)+A c^3 d^3\right)+\frac{1}{2} b d x^6 \left(b^2 e (A e+B d)+b c d (3 A e+B d)+A c^2 d^2\right)+\frac{1}{5} b^2 d^2 x^5 (3 A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d^3 x^4+\frac{1}{10} c^2 e^2 x^{10} (A c e+3 B (b e+c d))+\frac{1}{11} B c^3 e^3 x^{11}","\frac{1}{3} c e x^9 \left(A c e (b e+c d)+B \left(b^2 e^2+3 b c d e+c^2 d^2\right)\right)+\frac{1}{8} x^8 \left(3 A c e \left(b^2 e^2+3 b c d e+c^2 d^2\right)+B \left(9 b^2 c d e^2+b^3 e^3+9 b c^2 d^2 e+c^3 d^3\right)\right)+\frac{1}{7} x^7 \left(9 b^2 c d e (A e+B d)+b^3 e^2 (A e+3 B d)+3 b c^2 d^2 (3 A e+B d)+A c^3 d^3\right)+\frac{1}{2} b d x^6 \left(b^2 e (A e+B d)+b c d (3 A e+B d)+A c^2 d^2\right)+\frac{1}{5} b^2 d^2 x^5 (3 A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d^3 x^4+\frac{1}{10} c^2 e^2 x^{10} (A c e+3 B (b e+c d))+\frac{1}{11} B c^3 e^3 x^{11}",1,"(A*b^3*d^3*x^4)/4 + (b^2*d^2*(b*B*d + 3*A*c*d + 3*A*b*e)*x^5)/5 + (b*d*(A*c^2*d^2 + b^2*e*(B*d + A*e) + b*c*d*(B*d + 3*A*e))*x^6)/2 + ((A*c^3*d^3 + 9*b^2*c*d*e*(B*d + A*e) + b^3*e^2*(3*B*d + A*e) + 3*b*c^2*d^2*(B*d + 3*A*e))*x^7)/7 + ((3*A*c*e*(c^2*d^2 + 3*b*c*d*e + b^2*e^2) + B*(c^3*d^3 + 9*b*c^2*d^2*e + 9*b^2*c*d*e^2 + b^3*e^3))*x^8)/8 + (c*e*(A*c*e*(c*d + b*e) + B*(c^2*d^2 + 3*b*c*d*e + b^2*e^2))*x^9)/3 + (c^2*e^2*(A*c*e + 3*B*(c*d + b*e))*x^10)/10 + (B*c^3*e^3*x^11)/11","A",2,1,24,0.04167,1,"{771}"
1130,1,225,0,0.2980262,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^3,x]","\frac{1}{8} c x^8 \left(A c e (3 b e+2 c d)+B \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)\right)+\frac{1}{7} x^7 \left(3 b^2 c e (A e+2 B d)+3 b c^2 d (2 A e+B d)+A c^3 d^2+b^3 B e^2\right)+\frac{1}{6} b x^6 \left(b^2 e (A e+2 B d)+3 b c d (2 A e+B d)+3 A c^2 d^2\right)+\frac{1}{5} b^2 d x^5 (2 A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d^2 x^4+\frac{1}{9} c^2 e x^9 (A c e+3 b B e+2 B c d)+\frac{1}{10} B c^3 e^2 x^{10}","\frac{1}{8} c x^8 \left(A c e (3 b e+2 c d)+B \left(3 b^2 e^2+6 b c d e+c^2 d^2\right)\right)+\frac{1}{7} x^7 \left(3 b^2 c e (A e+2 B d)+3 b c^2 d (2 A e+B d)+A c^3 d^2+b^3 B e^2\right)+\frac{1}{6} b x^6 \left(b^2 e (A e+2 B d)+3 b c d (2 A e+B d)+3 A c^2 d^2\right)+\frac{1}{5} b^2 d x^5 (2 A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d^2 x^4+\frac{1}{9} c^2 e x^9 (A c e+3 b B e+2 B c d)+\frac{1}{10} B c^3 e^2 x^{10}",1,"(A*b^3*d^2*x^4)/4 + (b^2*d*(b*B*d + 3*A*c*d + 2*A*b*e)*x^5)/5 + (b*(3*A*c^2*d^2 + b^2*e*(2*B*d + A*e) + 3*b*c*d*(B*d + 2*A*e))*x^6)/6 + ((A*c^3*d^2 + b^3*B*e^2 + 3*b^2*c*e*(2*B*d + A*e) + 3*b*c^2*d*(B*d + 2*A*e))*x^7)/7 + (c*(A*c*e*(2*c*d + 3*b*e) + B*(c^2*d^2 + 6*b*c*d*e + 3*b^2*e^2))*x^8)/8 + (c^2*e*(2*B*c*d + 3*b*B*e + A*c*e)*x^9)/9 + (B*c^3*e^2*x^10)/10","A",2,1,24,0.04167,1,"{771}"
1131,1,139,0,0.1625425,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)*(b*x + c*x^2)^3,x]","\frac{1}{7} c x^7 \left(3 b c (A e+B d)+A c^2 d+3 b^2 B e\right)+\frac{1}{6} b x^6 \left(3 b c (A e+B d)+3 A c^2 d+b^2 B e\right)+\frac{1}{5} b^2 x^5 (A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d x^4+\frac{1}{8} c^2 x^8 (A c e+3 b B e+B c d)+\frac{1}{9} B c^3 e x^9","\frac{1}{7} c x^7 \left(3 b c (A e+B d)+A c^2 d+3 b^2 B e\right)+\frac{1}{6} b x^6 \left(3 b c (A e+B d)+3 A c^2 d+b^2 B e\right)+\frac{1}{5} b^2 x^5 (A b e+3 A c d+b B d)+\frac{1}{4} A b^3 d x^4+\frac{1}{8} c^2 x^8 (A c e+3 b B e+B c d)+\frac{1}{9} B c^3 e x^9",1,"(A*b^3*d*x^4)/4 + (b^2*(b*B*d + 3*A*c*d + A*b*e)*x^5)/5 + (b*(3*A*c^2*d + b^2*B*e + 3*b*c*(B*d + A*e))*x^6)/6 + (c*(A*c^2*d + 3*b^2*B*e + 3*b*c*(B*d + A*e))*x^7)/7 + (c^2*(B*c*d + 3*b*B*e + A*c*e)*x^8)/8 + (B*c^3*e*x^9)/9","A",2,1,22,0.04545,1,"{771}"
1132,1,75,0,0.0735677,"\int (A+B x) \left(b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(b*x + c*x^2)^3,x]","\frac{1}{5} b^2 x^5 (3 A c+b B)+\frac{1}{4} A b^3 x^4+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{2} b c x^6 (A c+b B)+\frac{1}{8} B c^3 x^8","\frac{1}{5} b^2 x^5 (3 A c+b B)+\frac{1}{4} A b^3 x^4+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{2} b c x^6 (A c+b B)+\frac{1}{8} B c^3 x^8",1,"(A*b^3*x^4)/4 + (b^2*(b*B + 3*A*c)*x^5)/5 + (b*c*(b*B + A*c)*x^6)/2 + (c^2*(3*b*B + A*c)*x^7)/7 + (B*c^3*x^8)/8","A",2,1,17,0.05882,1,"{631}"
1133,1,257,0,0.4486465,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{d+e x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x),x]","-\frac{c x^5 \left(A c e (c d-3 b e)-B \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)\right)}{5 e^3}-\frac{x^4 \left(B (c d-b e)^3-A c e \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)\right)}{4 e^4}-\frac{c^2 x^6 (-A c e-3 b B e+B c d)}{6 e^2}+\frac{d^2 x (B d-A e) (c d-b e)^3}{e^7}-\frac{d^3 (B d-A e) (c d-b e)^3 \log (d+e x)}{e^8}+\frac{x^3 (B d-A e) (c d-b e)^3}{3 e^5}-\frac{d x^2 (B d-A e) (c d-b e)^3}{2 e^6}+\frac{B c^3 x^7}{7 e}","-\frac{c x^5 \left(A c e (c d-3 b e)-B \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)\right)}{5 e^3}-\frac{x^4 \left(B (c d-b e)^3-A c e \left(3 b^2 e^2-3 b c d e+c^2 d^2\right)\right)}{4 e^4}-\frac{c^2 x^6 (-A c e-3 b B e+B c d)}{6 e^2}+\frac{d^2 x (B d-A e) (c d-b e)^3}{e^7}-\frac{d^3 (B d-A e) (c d-b e)^3 \log (d+e x)}{e^8}+\frac{x^3 (B d-A e) (c d-b e)^3}{3 e^5}-\frac{d x^2 (B d-A e) (c d-b e)^3}{2 e^6}+\frac{B c^3 x^7}{7 e}",1,"(d^2*(B*d - A*e)*(c*d - b*e)^3*x)/e^7 - (d*(B*d - A*e)*(c*d - b*e)^3*x^2)/(2*e^6) + ((B*d - A*e)*(c*d - b*e)^3*x^3)/(3*e^5) - ((B*(c*d - b*e)^3 - A*c*e*(c^2*d^2 - 3*b*c*d*e + 3*b^2*e^2))*x^4)/(4*e^4) - (c*(A*c*e*(c*d - 3*b*e) - B*(c^2*d^2 - 3*b*c*d*e + 3*b^2*e^2))*x^5)/(5*e^3) - (c^2*(B*c*d - 3*b*B*e - A*c*e)*x^6)/(6*e^2) + (B*c^3*x^7)/(7*e) - (d^3*(B*d - A*e)*(c*d - b*e)^3*Log[d + e*x])/e^8","A",2,1,24,0.04167,1,"{771}"
1134,1,287,0,0.5454039,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{(d+e x)^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x)^2,x]","-\frac{c^2 x^5 (-A c e-3 b B e+2 B c d)}{5 e^3}+\frac{d^3 (B d-A e) (c d-b e)^3}{e^8 (d+e x)}+\frac{d^2 (c d-b e)^2 \log (d+e x) (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{e^8}-\frac{c x^4 \left(A c e (2 c d-3 b e)-3 B (c d-b e)^2\right)}{4 e^4}-\frac{x^3 (c d-b e)^2 (-3 A c e-b B e+4 B c d)}{3 e^5}+\frac{x^2 (c d-b e)^2 (B d (5 c d-2 b e)-A e (4 c d-b e))}{2 e^6}+\frac{d x (c d-b e)^2 (A e (5 c d-2 b e)-3 B d (2 c d-b e))}{e^7}+\frac{B c^3 x^6}{6 e^2}","-\frac{c^2 x^5 (-A c e-3 b B e+2 B c d)}{5 e^3}+\frac{d^3 (B d-A e) (c d-b e)^3}{e^8 (d+e x)}+\frac{d^2 (c d-b e)^2 \log (d+e x) (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{e^8}-\frac{c x^4 \left(A c e (2 c d-3 b e)-3 B (c d-b e)^2\right)}{4 e^4}-\frac{x^3 (c d-b e)^2 (-3 A c e-b B e+4 B c d)}{3 e^5}+\frac{x^2 (c d-b e)^2 (B d (5 c d-2 b e)-A e (4 c d-b e))}{2 e^6}+\frac{d x (c d-b e)^2 (A e (5 c d-2 b e)-3 B d (2 c d-b e))}{e^7}+\frac{B c^3 x^6}{6 e^2}",1,"(d*(c*d - b*e)^2*(A*e*(5*c*d - 2*b*e) - 3*B*d*(2*c*d - b*e))*x)/e^7 + ((c*d - b*e)^2*(B*d*(5*c*d - 2*b*e) - A*e*(4*c*d - b*e))*x^2)/(2*e^6) - ((c*d - b*e)^2*(4*B*c*d - b*B*e - 3*A*c*e)*x^3)/(3*e^5) - (c*(A*c*e*(2*c*d - 3*b*e) - 3*B*(c*d - b*e)^2)*x^4)/(4*e^4) - (c^2*(2*B*c*d - 3*b*B*e - A*c*e)*x^5)/(5*e^3) + (B*c^3*x^6)/(6*e^2) + (d^3*(B*d - A*e)*(c*d - b*e)^3)/(e^8*(d + e*x)) + (d^2*(c*d - b*e)^2*(B*d*(7*c*d - 4*b*e) - 3*A*e*(2*c*d - b*e))*Log[d + e*x])/e^8","A",2,1,24,0.04167,1,"{771}"
1135,1,359,0,0.5828007,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{(d+e x)^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x)^3,x]","\frac{x^2 (c d-b e) \left(3 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{2 e^6}-\frac{x (c d-b e) \left(A e \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)-3 B d \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)\right)}{e^7}+\frac{3 d (c d-b e) \log (d+e x) \left(A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)\right)}{e^8}-\frac{c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}-\frac{d^2 (c d-b e)^2 (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{e^8 (d+e x)}+\frac{d^3 (B d-A e) (c d-b e)^3}{2 e^8 (d+e x)^2}+\frac{c x^3 (c d-b e) (-A c e-b B e+2 B c d)}{e^5}+\frac{B c^3 x^5}{5 e^3}","\frac{x^2 (c d-b e) \left(3 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{2 e^6}-\frac{x (c d-b e) \left(A e \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)-3 B d \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)\right)}{e^7}+\frac{3 d (c d-b e) \log (d+e x) \left(A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)\right)}{e^8}-\frac{c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}-\frac{d^2 (c d-b e)^2 (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{e^8 (d+e x)}+\frac{d^3 (B d-A e) (c d-b e)^3}{2 e^8 (d+e x)^2}+\frac{c x^3 (c d-b e) (-A c e-b B e+2 B c d)}{e^5}+\frac{B c^3 x^5}{5 e^3}",1,"-(((c*d - b*e)*(A*e*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2) - 3*B*d*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2))*x)/e^7) + ((c*d - b*e)*(3*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*x^2)/(2*e^6) + (c*(c*d - b*e)*(2*B*c*d - b*B*e - A*c*e)*x^3)/e^5 - (c^2*(3*B*c*d - 3*b*B*e - A*c*e)*x^4)/(4*e^4) + (B*c^3*x^5)/(5*e^3) + (d^3*(B*d - A*e)*(c*d - b*e)^3)/(2*e^8*(d + e*x)^2) - (d^2*(c*d - b*e)^2*(B*d*(7*c*d - 4*b*e) - 3*A*e*(2*c*d - b*e)))/(e^8*(d + e*x)) + (3*d*(c*d - b*e)*(A*e*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2) - B*d*(7*c^2*d^2 - 8*b*c*d*e + 2*b^2*e^2))*Log[d + e*x])/e^8","A",2,1,24,0.04167,1,"{771}"
1136,1,422,0,0.6355388,"\int \frac{(A+B x) \left(b x+c x^2\right)^3}{(d+e x)^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^3)/(d + e*x)^4,x]","-\frac{c x^2 \left(A c e (4 c d-3 b e)-B \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{2 e^6}+\frac{x \left(A c e \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)-B \left(12 b^2 c d e^2-b^3 e^3-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^7}-\frac{3 d (c d-b e) \left(A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)\right)}{e^8 (d+e x)}+\frac{\log (d+e x) \left(B d \left(30 b^2 c d e^2-4 b^3 e^3-60 b c^2 d^2 e+35 c^3 d^3\right)-A e \left(12 b^2 c d e^2-b^3 e^3-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^8}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}-\frac{d^2 (c d-b e)^2 (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{2 e^8 (d+e x)^2}+\frac{d^3 (B d-A e) (c d-b e)^3}{3 e^8 (d+e x)^3}+\frac{B c^3 x^4}{4 e^4}","-\frac{c x^2 \left(A c e (4 c d-3 b e)-B \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{2 e^6}+\frac{x \left(A c e \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)-B \left(12 b^2 c d e^2-b^3 e^3-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^7}-\frac{3 d (c d-b e) \left(A e \left(b^2 e^2-5 b c d e+5 c^2 d^2\right)-B d \left(2 b^2 e^2-8 b c d e+7 c^2 d^2\right)\right)}{e^8 (d+e x)}+\frac{\log (d+e x) \left(B d \left(30 b^2 c d e^2-4 b^3 e^3-60 b c^2 d^2 e+35 c^3 d^3\right)-A e \left(12 b^2 c d e^2-b^3 e^3-30 b c^2 d^2 e+20 c^3 d^3\right)\right)}{e^8}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}-\frac{d^2 (c d-b e)^2 (B d (7 c d-4 b e)-3 A e (2 c d-b e))}{2 e^8 (d+e x)^2}+\frac{d^3 (B d-A e) (c d-b e)^3}{3 e^8 (d+e x)^3}+\frac{B c^3 x^4}{4 e^4}",1,"((A*c*e*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2) - B*(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 - b^3*e^3))*x)/e^7 - (c*(A*c*e*(4*c*d - 3*b*e) - B*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*x^2)/(2*e^6) - (c^2*(4*B*c*d - 3*b*B*e - A*c*e)*x^3)/(3*e^5) + (B*c^3*x^4)/(4*e^4) + (d^3*(B*d - A*e)*(c*d - b*e)^3)/(3*e^8*(d + e*x)^3) - (d^2*(c*d - b*e)^2*(B*d*(7*c*d - 4*b*e) - 3*A*e*(2*c*d - b*e)))/(2*e^8*(d + e*x)^2) - (3*d*(c*d - b*e)*(A*e*(5*c^2*d^2 - 5*b*c*d*e + b^2*e^2) - B*d*(7*c^2*d^2 - 8*b*c*d*e + 2*b^2*e^2)))/(e^8*(d + e*x)) + ((B*d*(35*c^3*d^3 - 60*b*c^2*d^2*e + 30*b^2*c*d*e^2 - 4*b^3*e^3) - A*e*(20*c^3*d^3 - 30*b*c^2*d^2*e + 12*b^2*c*d*e^2 - b^3*e^3))*Log[d + e*x])/e^8","A",2,1,24,0.04167,1,"{771}"
1137,1,207,0,0.2625974,"\int \frac{(A+B x) (d+e x)^4}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2),x]","\frac{e^2 x^2 \left(A c e (4 c d-b e)+B \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)\right)}{2 c^3}+\frac{e x \left(A c e \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)+B \left(4 b^2 c d e^2-b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{c^4}+\frac{e^3 x^3 (A c e-b B e+4 B c d)}{3 c^2}+\frac{(b B-A c) (c d-b e)^4 \log (b+c x)}{b c^5}+\frac{A d^4 \log (x)}{b}+\frac{B e^4 x^4}{4 c}","\frac{e^2 x^2 \left(A c e (4 c d-b e)+B \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)\right)}{2 c^3}+\frac{e x \left(A c e \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)+B \left(4 b^2 c d e^2-b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{c^4}+\frac{e^3 x^3 (A c e-b B e+4 B c d)}{3 c^2}+\frac{(b B-A c) (c d-b e)^4 \log (b+c x)}{b c^5}+\frac{A d^4 \log (x)}{b}+\frac{B e^4 x^4}{4 c}",1,"(e*(A*c*e*(6*c^2*d^2 - 4*b*c*d*e + b^2*e^2) + B*(4*c^3*d^3 - 6*b*c^2*d^2*e + 4*b^2*c*d*e^2 - b^3*e^3))*x)/c^4 + (e^2*(A*c*e*(4*c*d - b*e) + B*(6*c^2*d^2 - 4*b*c*d*e + b^2*e^2))*x^2)/(2*c^3) + (e^3*(4*B*c*d - b*B*e + A*c*e)*x^3)/(3*c^2) + (B*e^4*x^4)/(4*c) + (A*d^4*Log[x])/b + ((b*B - A*c)*(c*d - b*e)^4*Log[b + c*x])/(b*c^5)","A",2,1,24,0.04167,1,"{771}"
1138,1,128,0,0.1562394,"\int \frac{(A+B x) (d+e x)^3}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2),x]","\frac{e x \left(A c e (3 c d-b e)+B \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{c^3}+\frac{e^2 x^2 (A c e-b B e+3 B c d)}{2 c^2}+\frac{(b B-A c) (c d-b e)^3 \log (b+c x)}{b c^4}+\frac{A d^3 \log (x)}{b}+\frac{B e^3 x^3}{3 c}","\frac{e x \left(A c e (3 c d-b e)+B \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{c^3}+\frac{e^2 x^2 (A c e-b B e+3 B c d)}{2 c^2}+\frac{(b B-A c) (c d-b e)^3 \log (b+c x)}{b c^4}+\frac{A d^3 \log (x)}{b}+\frac{B e^3 x^3}{3 c}",1,"(e*(A*c*e*(3*c*d - b*e) + B*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2))*x)/c^3 + (e^2*(3*B*c*d - b*B*e + A*c*e)*x^2)/(2*c^2) + (B*e^3*x^3)/(3*c) + (A*d^3*Log[x])/b + ((b*B - A*c)*(c*d - b*e)^3*Log[b + c*x])/(b*c^4)","A",2,1,24,0.04167,1,"{771}"
1139,1,77,0,0.0863375,"\int \frac{(A+B x) (d+e x)^2}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2),x]","\frac{e x (A c e-b B e+2 B c d)}{c^2}+\frac{(b B-A c) (c d-b e)^2 \log (b+c x)}{b c^3}+\frac{A d^2 \log (x)}{b}+\frac{B e^2 x^2}{2 c}","\frac{e x (A c e-b B e+2 B c d)}{c^2}+\frac{(b B-A c) (c d-b e)^2 \log (b+c x)}{b c^3}+\frac{A d^2 \log (x)}{b}+\frac{B e^2 x^2}{2 c}",1,"(e*(2*B*c*d - b*B*e + A*c*e)*x)/c^2 + (B*e^2*x^2)/(2*c) + (A*d^2*Log[x])/b + ((b*B - A*c)*(c*d - b*e)^2*Log[b + c*x])/(b*c^3)","A",2,1,24,0.04167,1,"{771}"
1140,1,45,0,0.0447597,"\int \frac{(A+B x) (d+e x)}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x))/(b*x + c*x^2),x]","\frac{(b B-A c) (c d-b e) \log (b+c x)}{b c^2}+\frac{A d \log (x)}{b}+\frac{B e x}{c}","\frac{(b B-A c) (c d-b e) \log (b+c x)}{b c^2}+\frac{A d \log (x)}{b}+\frac{B e x}{c}",1,"(B*e*x)/c + (A*d*Log[x])/b + ((b*B - A*c)*(c*d - b*e)*Log[b + c*x])/(b*c^2)","A",2,1,22,0.04545,1,"{771}"
1141,1,29,0,0.0204292,"\int \frac{A+B x}{b x+c x^2} \, dx","Int[(A + B*x)/(b*x + c*x^2),x]","\frac{(b B-A c) \log (b+c x)}{b c}+\frac{A \log (x)}{b}","\frac{(b B-A c) \log (b+c x)}{b c}+\frac{A \log (x)}{b}",1,"(A*Log[x])/b + ((b*B - A*c)*Log[b + c*x])/(b*c)","A",2,1,17,0.05882,1,"{631}"
1142,1,68,0,0.0727457,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)*(b*x + c*x^2)),x]","\frac{(b B-A c) \log (b+c x)}{b (c d-b e)}-\frac{(B d-A e) \log (d+e x)}{d (c d-b e)}+\frac{A \log (x)}{b d}","\frac{(b B-A c) \log (b+c x)}{b (c d-b e)}-\frac{(B d-A e) \log (d+e x)}{d (c d-b e)}+\frac{A \log (x)}{b d}",1,"(A*Log[x])/(b*d) + ((b*B - A*c)*Log[b + c*x])/(b*(c*d - b*e)) - ((B*d - A*e)*Log[d + e*x])/(d*(c*d - b*e))","A",2,1,24,0.04167,1,"{771}"
1143,1,110,0,0.1340211,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)),x]","-\frac{\log (d+e x) \left(B c d^2-A e (2 c d-b e)\right)}{d^2 (c d-b e)^2}+\frac{B d-A e}{d (d+e x) (c d-b e)}+\frac{c (b B-A c) \log (b+c x)}{b (c d-b e)^2}+\frac{A \log (x)}{b d^2}","-\frac{\log (d+e x) \left(B c d^2-A e (2 c d-b e)\right)}{d^2 (c d-b e)^2}+\frac{B d-A e}{d (d+e x) (c d-b e)}+\frac{c (b B-A c) \log (b+c x)}{b (c d-b e)^2}+\frac{A \log (x)}{b d^2}",1,"(B*d - A*e)/(d*(c*d - b*e)*(d + e*x)) + (A*Log[x])/(b*d^2) + (c*(b*B - A*c)*Log[b + c*x])/(b*(c*d - b*e)^2) - ((B*c*d^2 - A*e*(2*c*d - b*e))*Log[d + e*x])/(d^2*(c*d - b*e)^2)","A",2,1,24,0.04167,1,"{771}"
1144,1,171,0,0.2251223,"\int \frac{A+B x}{(d+e x)^3 \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^3*(b*x + c*x^2)),x]","-\frac{\log (d+e x) \left(B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{d^3 (c d-b e)^3}+\frac{c^2 (b B-A c) \log (b+c x)}{b (c d-b e)^3}+\frac{B c d^2-A e (2 c d-b e)}{d^2 (d+e x) (c d-b e)^2}+\frac{B d-A e}{2 d (d+e x)^2 (c d-b e)}+\frac{A \log (x)}{b d^3}","-\frac{\log (d+e x) \left(B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{d^3 (c d-b e)^3}+\frac{c^2 (b B-A c) \log (b+c x)}{b (c d-b e)^3}+\frac{B c d^2-A e (2 c d-b e)}{d^2 (d+e x) (c d-b e)^2}+\frac{B d-A e}{2 d (d+e x)^2 (c d-b e)}+\frac{A \log (x)}{b d^3}",1,"(B*d - A*e)/(2*d*(c*d - b*e)*(d + e*x)^2) + (B*c*d^2 - A*e*(2*c*d - b*e))/(d^2*(c*d - b*e)^2*(d + e*x)) + (A*Log[x])/(b*d^3) + (c^2*(b*B - A*c)*Log[b + c*x])/(b*(c*d - b*e)^3) - ((B*c^2*d^3 - A*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2))*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",2,1,24,0.04167,1,"{771}"
1145,1,245,0,0.3018613,"\int \frac{A+B x}{(d+e x)^4 \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^4*(b*x + c*x^2)),x]","\frac{B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)}{d^3 (d+e x) (c d-b e)^3}-\frac{\log (d+e x) \left(B c^3 d^4-A e \left(4 b^2 c d e^2-b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{d^4 (c d-b e)^4}+\frac{c^3 (b B-A c) \log (b+c x)}{b (c d-b e)^4}+\frac{B c d^2-A e (2 c d-b e)}{2 d^2 (d+e x)^2 (c d-b e)^2}+\frac{B d-A e}{3 d (d+e x)^3 (c d-b e)}+\frac{A \log (x)}{b d^4}","\frac{B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)}{d^3 (d+e x) (c d-b e)^3}-\frac{\log (d+e x) \left(B c^3 d^4-A e \left(4 b^2 c d e^2-b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{d^4 (c d-b e)^4}+\frac{c^3 (b B-A c) \log (b+c x)}{b (c d-b e)^4}+\frac{B c d^2-A e (2 c d-b e)}{2 d^2 (d+e x)^2 (c d-b e)^2}+\frac{B d-A e}{3 d (d+e x)^3 (c d-b e)}+\frac{A \log (x)}{b d^4}",1,"(B*d - A*e)/(3*d*(c*d - b*e)*(d + e*x)^3) + (B*c*d^2 - A*e*(2*c*d - b*e))/(2*d^2*(c*d - b*e)^2*(d + e*x)^2) + (B*c^2*d^3 - A*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2))/(d^3*(c*d - b*e)^3*(d + e*x)) + (A*Log[x])/(b*d^4) + (c^3*(b*B - A*c)*Log[b + c*x])/(b*(c*d - b*e)^4) - ((B*c^3*d^4 - A*e*(4*c^3*d^3 - 6*b*c^2*d^2*e + 4*b^2*c*d*e^2 - b^3*e^3))*Log[d + e*x])/(d^4*(c*d - b*e)^4)","A",2,1,24,0.04167,1,"{771}"
1146,1,156,0,0.2253191,"\int \frac{(A+B x) (d+e x)^4}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2)^2,x]","\frac{(b B-A c) (c d-b e)^4}{b^2 c^4 (b+c x)}+\frac{(c d-b e)^3 \log (b+c x) \left(-b c (B d-2 A e)+2 A c^2 d-3 b^2 B e\right)}{b^3 c^4}+\frac{d^3 \log (x) (4 A b e-2 A c d+b B d)}{b^3}-\frac{A d^4}{b^2 x}+\frac{e^3 x (A c e-2 b B e+4 B c d)}{c^3}+\frac{B e^4 x^2}{2 c^2}","\frac{(b B-A c) (c d-b e)^4}{b^2 c^4 (b+c x)}+\frac{(c d-b e)^3 \log (b+c x) \left(-b c (B d-2 A e)+2 A c^2 d-3 b^2 B e\right)}{b^3 c^4}+\frac{d^3 \log (x) (4 A b e-2 A c d+b B d)}{b^3}-\frac{A d^4}{b^2 x}+\frac{e^3 x (A c e-2 b B e+4 B c d)}{c^3}+\frac{B e^4 x^2}{2 c^2}",1,"-((A*d^4)/(b^2*x)) + (e^3*(4*B*c*d - 2*b*B*e + A*c*e)*x)/c^3 + (B*e^4*x^2)/(2*c^2) + ((b*B - A*c)*(c*d - b*e)^4)/(b^2*c^4*(b + c*x)) + (d^3*(b*B*d - 2*A*c*d + 4*A*b*e)*Log[x])/b^3 + ((c*d - b*e)^3*(2*A*c^2*d - 3*b^2*B*e - b*c*(B*d - 2*A*e))*Log[b + c*x])/(b^3*c^4)","A",2,1,24,0.04167,1,"{771}"
1147,1,128,0,0.1586711,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^2,x]","\frac{(b B-A c) (c d-b e)^3}{b^2 c^3 (b+c x)}+\frac{(c d-b e)^2 \log (b+c x) \left(-b c (B d-A e)+2 A c^2 d-2 b^2 B e\right)}{b^3 c^3}+\frac{d^2 \log (x) (3 A b e-2 A c d+b B d)}{b^3}-\frac{A d^3}{b^2 x}+\frac{B e^3 x}{c^2}","\frac{(b B-A c) (c d-b e)^3}{b^2 c^3 (b+c x)}+\frac{(c d-b e)^2 \log (b+c x) \left(-b c (B d-A e)+2 A c^2 d-2 b^2 B e\right)}{b^3 c^3}+\frac{d^2 \log (x) (3 A b e-2 A c d+b B d)}{b^3}-\frac{A d^3}{b^2 x}+\frac{B e^3 x}{c^2}",1,"-((A*d^3)/(b^2*x)) + (B*e^3*x)/c^2 + ((b*B - A*c)*(c*d - b*e)^3)/(b^2*c^3*(b + c*x)) + (d^2*(b*B*d - 2*A*c*d + 3*A*b*e)*Log[x])/b^3 + ((c*d - b*e)^2*(2*A*c^2*d - 2*b^2*B*e - b*c*(B*d - A*e))*Log[b + c*x])/(b^3*c^3)","A",2,1,24,0.04167,1,"{771}"
1148,1,108,0,0.1207822,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^2,x]","\frac{(b B-A c) (c d-b e)^2}{b^2 c^2 (b+c x)}-\frac{(c d-b e) \log (b+c x) \left(-2 A c^2 d+b^2 B e+b B c d\right)}{b^3 c^2}+\frac{d \log (x) (2 A b e-2 A c d+b B d)}{b^3}-\frac{A d^2}{b^2 x}","\frac{(b B-A c) (c d-b e)^2}{b^2 c^2 (b+c x)}-\frac{(c d-b e) \log (b+c x) \left(-2 A c^2 d+b^2 B e+b B c d\right)}{b^3 c^2}+\frac{d \log (x) (2 A b e-2 A c d+b B d)}{b^3}-\frac{A d^2}{b^2 x}",1,"-((A*d^2)/(b^2*x)) + ((b*B - A*c)*(c*d - b*e)^2)/(b^2*c^2*(b + c*x)) + (d*(b*B*d - 2*A*c*d + 2*A*b*e)*Log[x])/b^3 - ((c*d - b*e)*(b*B*c*d - 2*A*c^2*d + b^2*B*e)*Log[b + c*x])/(b^3*c^2)","A",2,1,24,0.04167,1,"{771}"
1149,1,86,0,0.0816473,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x))/(b*x + c*x^2)^2,x]","\frac{(b B-A c) (c d-b e)}{b^2 c (b+c x)}+\frac{\log (x) (A b e-2 A c d+b B d)}{b^3}-\frac{\log (b+c x) (A b e-2 A c d+b B d)}{b^3}-\frac{A d}{b^2 x}","\frac{(b B-A c) (c d-b e)}{b^2 c (b+c x)}+\frac{\log (x) (A b e-2 A c d+b B d)}{b^3}-\frac{\log (b+c x) (A b e-2 A c d+b B d)}{b^3}-\frac{A d}{b^2 x}",1,"-((A*d)/(b^2*x)) + ((b*B - A*c)*(c*d - b*e))/(b^2*c*(b + c*x)) + ((b*B*d - 2*A*c*d + A*b*e)*Log[x])/b^3 - ((b*B*d - 2*A*c*d + A*b*e)*Log[b + c*x])/b^3","A",2,1,22,0.04545,1,"{771}"
1150,1,62,0,0.0501146,"\int \frac{A+B x}{\left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(b*x + c*x^2)^2,x]","\frac{b B-A c}{b^2 (b+c x)}+\frac{\log (x) (b B-2 A c)}{b^3}-\frac{(b B-2 A c) \log (b+c x)}{b^3}-\frac{A}{b^2 x}","\frac{b B-A c}{b^2 (b+c x)}+\frac{\log (x) (b B-2 A c)}{b^3}-\frac{(b B-2 A c) \log (b+c x)}{b^3}-\frac{A}{b^2 x}",1,"-(A/(b^2*x)) + (b*B - A*c)/(b^2*(b + c*x)) + ((b*B - 2*A*c)*Log[x])/b^3 - ((b*B - 2*A*c)*Log[b + c*x])/b^3","A",2,1,17,0.05882,1,"{631}"
1151,1,147,0,0.1988911,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)*(b*x + c*x^2)^2),x]","\frac{c \log (b+c x) \left(-b c (3 A e+B d)+2 A c^2 d+2 b^2 B e\right)}{b^3 (c d-b e)^2}+\frac{\log (x) (-A b e-2 A c d+b B d)}{b^3 d^2}+\frac{c (b B-A c)}{b^2 (b+c x) (c d-b e)}-\frac{A}{b^2 d x}-\frac{e^2 (B d-A e) \log (d+e x)}{d^2 (c d-b e)^2}","\frac{c \log (b+c x) \left(-b c (3 A e+B d)+2 A c^2 d+2 b^2 B e\right)}{b^3 (c d-b e)^2}+\frac{\log (x) (-A b e-2 A c d+b B d)}{b^3 d^2}+\frac{c (b B-A c)}{b^2 (b+c x) (c d-b e)}-\frac{A}{b^2 d x}-\frac{e^2 (B d-A e) \log (d+e x)}{d^2 (c d-b e)^2}",1,"-(A/(b^2*d*x)) + (c*(b*B - A*c))/(b^2*(c*d - b*e)*(b + c*x)) + ((b*B*d - 2*A*c*d - A*b*e)*Log[x])/(b^3*d^2) + (c*(2*A*c^2*d + 2*b^2*B*e - b*c*(B*d + 3*A*e))*Log[b + c*x])/(b^3*(c*d - b*e)^2) - (e^2*(B*d - A*e)*Log[d + e*x])/(d^2*(c*d - b*e)^2)","A",2,1,24,0.04167,1,"{771}"
1152,1,201,0,0.3305453,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^2),x]","\frac{c^2 (b B-A c)}{b^2 (b+c x) (c d-b e)^2}+\frac{c^2 \log (b+c x) \left(-b c (4 A e+B d)+2 A c^2 d+3 b^2 B e\right)}{b^3 (c d-b e)^3}+\frac{\log (x) (-2 A b e-2 A c d+b B d)}{b^3 d^3}-\frac{A}{b^2 d^2 x}+\frac{e^2 (B d-A e)}{d^2 (d+e x) (c d-b e)^2}+\frac{e^2 \log (d+e x) (2 A e (2 c d-b e)-B d (3 c d-b e))}{d^3 (c d-b e)^3}","\frac{c^2 (b B-A c)}{b^2 (b+c x) (c d-b e)^2}+\frac{c^2 \log (b+c x) \left(-b c (4 A e+B d)+2 A c^2 d+3 b^2 B e\right)}{b^3 (c d-b e)^3}+\frac{\log (x) (-2 A b e-2 A c d+b B d)}{b^3 d^3}-\frac{A}{b^2 d^2 x}+\frac{e^2 (B d-A e)}{d^2 (d+e x) (c d-b e)^2}+\frac{e^2 \log (d+e x) (2 A e (2 c d-b e)-B d (3 c d-b e))}{d^3 (c d-b e)^3}",1,"-(A/(b^2*d^2*x)) + (c^2*(b*B - A*c))/(b^2*(c*d - b*e)^2*(b + c*x)) + (e^2*(B*d - A*e))/(d^2*(c*d - b*e)^2*(d + e*x)) + ((b*B*d - 2*A*c*d - 2*A*b*e)*Log[x])/(b^3*d^3) + (c^2*(2*A*c^2*d + 3*b^2*B*e - b*c*(B*d + 4*A*e))*Log[b + c*x])/(b^3*(c*d - b*e)^3) + (e^2*(2*A*e*(2*c*d - b*e) - B*d*(3*c*d - b*e))*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",2,1,24,0.04167,1,"{771}"
1153,1,283,0,0.4619931,"\int \frac{A+B x}{(d+e x)^3 \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^3*(b*x + c*x^2)^2),x]","-\frac{e^2 \log (d+e x) \left(B d \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)-A e \left(3 b^2 e^2-10 b c d e+10 c^2 d^2\right)\right)}{d^4 (c d-b e)^4}+\frac{c^3 (b B-A c)}{b^2 (b+c x) (c d-b e)^3}+\frac{c^3 \log (b+c x) \left(-b c (5 A e+B d)+2 A c^2 d+4 b^2 B e\right)}{b^3 (c d-b e)^4}+\frac{\log (x) (-3 A b e-2 A c d+b B d)}{b^3 d^4}-\frac{A}{b^2 d^3 x}-\frac{e^2 (2 A e (2 c d-b e)-B d (3 c d-b e))}{d^3 (d+e x) (c d-b e)^3}+\frac{e^2 (B d-A e)}{2 d^2 (d+e x)^2 (c d-b e)^2}","-\frac{e^2 \log (d+e x) \left(B d \left(b^2 e^2-4 b c d e+6 c^2 d^2\right)-A e \left(3 b^2 e^2-10 b c d e+10 c^2 d^2\right)\right)}{d^4 (c d-b e)^4}+\frac{c^3 (b B-A c)}{b^2 (b+c x) (c d-b e)^3}+\frac{c^3 \log (b+c x) \left(-b c (5 A e+B d)+2 A c^2 d+4 b^2 B e\right)}{b^3 (c d-b e)^4}+\frac{\log (x) (-3 A b e-2 A c d+b B d)}{b^3 d^4}-\frac{A}{b^2 d^3 x}-\frac{e^2 (2 A e (2 c d-b e)-B d (3 c d-b e))}{d^3 (d+e x) (c d-b e)^3}+\frac{e^2 (B d-A e)}{2 d^2 (d+e x)^2 (c d-b e)^2}",1,"-(A/(b^2*d^3*x)) + (c^3*(b*B - A*c))/(b^2*(c*d - b*e)^3*(b + c*x)) + (e^2*(B*d - A*e))/(2*d^2*(c*d - b*e)^2*(d + e*x)^2) - (e^2*(2*A*e*(2*c*d - b*e) - B*d*(3*c*d - b*e)))/(d^3*(c*d - b*e)^3*(d + e*x)) + ((b*B*d - 2*A*c*d - 3*A*b*e)*Log[x])/(b^3*d^4) + (c^3*(2*A*c^2*d + 4*b^2*B*e - b*c*(B*d + 5*A*e))*Log[b + c*x])/(b^3*(c*d - b*e)^4) - (e^2*(B*d*(6*c^2*d^2 - 4*b*c*d*e + b^2*e^2) - A*e*(10*c^2*d^2 - 10*b*c*d*e + 3*b^2*e^2))*Log[d + e*x])/(d^4*(c*d - b*e)^4)","A",2,1,24,0.04167,1,"{771}"
1154,1,257,0,0.4278515,"\int \frac{(A+B x) (d+e x)^5}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^5)/(b*x + c*x^2)^3,x]","-\frac{(c d-b e)^3 \log (b+c x) \left(-b^2 c e (4 B d-A e)-3 b c^2 d (B d-A e)+6 A c^3 d^2-3 b^3 B e^2\right)}{b^5 c^4}+\frac{d^3 \log (x) \left(5 b^2 e (2 A e+B d)-3 b c d (5 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{(c d-b e)^4 \left(-2 A b c e-3 A c^2 d+3 b^2 B e+2 b B c d\right)}{b^4 c^4 (b+c x)}-\frac{(b B-A c) (c d-b e)^5}{2 b^3 c^4 (b+c x)^2}-\frac{d^4 (5 A b e-3 A c d+b B d)}{b^4 x}-\frac{A d^5}{2 b^3 x^2}+\frac{B e^5 x}{c^3}","-\frac{(c d-b e)^3 \log (b+c x) \left(-b^2 c e (4 B d-A e)-3 b c^2 d (B d-A e)+6 A c^3 d^2-3 b^3 B e^2\right)}{b^5 c^4}+\frac{d^3 \log (x) \left(5 b^2 e (2 A e+B d)-3 b c d (5 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{(c d-b e)^4 \left(-2 A b c e-3 A c^2 d+3 b^2 B e+2 b B c d\right)}{b^4 c^4 (b+c x)}-\frac{(b B-A c) (c d-b e)^5}{2 b^3 c^4 (b+c x)^2}-\frac{d^4 (5 A b e-3 A c d+b B d)}{b^4 x}-\frac{A d^5}{2 b^3 x^2}+\frac{B e^5 x}{c^3}",1,"-(A*d^5)/(2*b^3*x^2) - (d^4*(b*B*d - 3*A*c*d + 5*A*b*e))/(b^4*x) + (B*e^5*x)/c^3 - ((b*B - A*c)*(c*d - b*e)^5)/(2*b^3*c^4*(b + c*x)^2) - ((c*d - b*e)^4*(2*b*B*c*d - 3*A*c^2*d + 3*b^2*B*e - 2*A*b*c*e))/(b^4*c^4*(b + c*x)) + (d^3*(6*A*c^2*d^2 + 5*b^2*e*(B*d + 2*A*e) - 3*b*c*d*(B*d + 5*A*e))*Log[x])/b^5 - ((c*d - b*e)^3*(6*A*c^3*d^2 - 3*b^3*B*e^2 - 3*b*c^2*d*(B*d - A*e) - b^2*c*e*(4*B*d - A*e))*Log[b + c*x])/(b^5*c^4)","A",2,1,24,0.04167,1,"{771}"
1155,1,235,0,0.3319142,"\int \frac{(A+B x) (d+e x)^4}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2)^3,x]","\frac{(c d-b e)^2 \log (b+c x) \left(-6 A c^3 d^2+2 b^2 B c d e+b^3 B e^2+3 b B c^2 d^2\right)}{b^5 c^3}+\frac{d^2 \log (x) \left(2 b^2 e (3 A e+2 B d)-3 b c d (4 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{(c d-b e)^3 \left(-A b c e-3 A c^2 d+2 b^2 B e+2 b B c d\right)}{b^4 c^3 (b+c x)}-\frac{(b B-A c) (c d-b e)^4}{2 b^3 c^3 (b+c x)^2}-\frac{d^3 (4 A b e-3 A c d+b B d)}{b^4 x}-\frac{A d^4}{2 b^3 x^2}","\frac{(c d-b e)^2 \log (b+c x) \left(-6 A c^3 d^2+2 b^2 B c d e+b^3 B e^2+3 b B c^2 d^2\right)}{b^5 c^3}+\frac{d^2 \log (x) \left(2 b^2 e (3 A e+2 B d)-3 b c d (4 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{(c d-b e)^3 \left(-A b c e-3 A c^2 d+2 b^2 B e+2 b B c d\right)}{b^4 c^3 (b+c x)}-\frac{(b B-A c) (c d-b e)^4}{2 b^3 c^3 (b+c x)^2}-\frac{d^3 (4 A b e-3 A c d+b B d)}{b^4 x}-\frac{A d^4}{2 b^3 x^2}",1,"-(A*d^4)/(2*b^3*x^2) - (d^3*(b*B*d - 3*A*c*d + 4*A*b*e))/(b^4*x) - ((b*B - A*c)*(c*d - b*e)^4)/(2*b^3*c^3*(b + c*x)^2) - ((c*d - b*e)^3*(2*b*B*c*d - 3*A*c^2*d + 2*b^2*B*e - A*b*c*e))/(b^4*c^3*(b + c*x)) + (d^2*(6*A*c^2*d^2 + 2*b^2*e*(2*B*d + 3*A*e) - 3*b*c*d*(B*d + 4*A*e))*Log[x])/b^5 + ((c*d - b*e)^2*(3*b*B*c^2*d^2 - 6*A*c^3*d^2 + 2*b^2*B*c*d*e + b^3*B*e^2)*Log[b + c*x])/(b^5*c^3)","A",2,1,24,0.04167,1,"{771}"
1156,1,185,0,0.2460132,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^3,x]","-\frac{(c d-b e)^2 \left(-3 A c^2 d+b^2 B e+2 b B c d\right)}{b^4 c^2 (b+c x)}-\frac{(b B-A c) (c d-b e)^3}{2 b^3 c^2 (b+c x)^2}-\frac{d^2 (3 A b e-3 A c d+b B d)}{b^4 x}-\frac{3 d \log (x) (c d-b e) (A b e-2 A c d+b B d)}{b^5}+\frac{3 d (c d-b e) \log (b+c x) (A b e-2 A c d+b B d)}{b^5}-\frac{A d^3}{2 b^3 x^2}","-\frac{(c d-b e)^2 \left(-3 A c^2 d+b^2 B e+2 b B c d\right)}{b^4 c^2 (b+c x)}-\frac{(b B-A c) (c d-b e)^3}{2 b^3 c^2 (b+c x)^2}-\frac{d^2 (3 A b e-3 A c d+b B d)}{b^4 x}-\frac{3 d \log (x) (c d-b e) (A b e-2 A c d+b B d)}{b^5}+\frac{3 d (c d-b e) \log (b+c x) (A b e-2 A c d+b B d)}{b^5}-\frac{A d^3}{2 b^3 x^2}",1,"-(A*d^3)/(2*b^3*x^2) - (d^2*(b*B*d - 3*A*c*d + 3*A*b*e))/(b^4*x) - ((b*B - A*c)*(c*d - b*e)^3)/(2*b^3*c^2*(b + c*x)^2) - ((c*d - b*e)^2*(2*b*B*c*d - 3*A*c^2*d + b^2*B*e))/(b^4*c^2*(b + c*x)) - (3*d*(c*d - b*e)*(b*B*d - 2*A*c*d + A*b*e)*Log[x])/b^5 + (3*d*(c*d - b*e)*(b*B*d - 2*A*c*d + A*b*e)*Log[b + c*x])/b^5","A",2,1,24,0.04167,1,"{771}"
1157,1,198,0,0.2448631,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^3,x]","\frac{\log (x) \left(b^2 e (A e+2 B d)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{\log (b+c x) \left(b^2 e (A e+2 B d)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{d (2 A b e-3 A c d+b B d)}{b^4 x}-\frac{(c d-b e) (A b e-3 A c d+2 b B d)}{b^4 (b+c x)}-\frac{(b B-A c) (c d-b e)^2}{2 b^3 c (b+c x)^2}-\frac{A d^2}{2 b^3 x^2}","\frac{\log (x) \left(b^2 e (A e+2 B d)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{\log (b+c x) \left(b^2 e (A e+2 B d)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{b^5}-\frac{d (2 A b e-3 A c d+b B d)}{b^4 x}-\frac{(c d-b e) (A b e-3 A c d+2 b B d)}{b^4 (b+c x)}-\frac{(b B-A c) (c d-b e)^2}{2 b^3 c (b+c x)^2}-\frac{A d^2}{2 b^3 x^2}",1,"-(A*d^2)/(2*b^3*x^2) - (d*(b*B*d - 3*A*c*d + 2*A*b*e))/(b^4*x) - ((b*B - A*c)*(c*d - b*e)^2)/(2*b^3*c*(b + c*x)^2) - ((c*d - b*e)*(2*b*B*d - 3*A*c*d + A*b*e))/(b^4*(b + c*x)) + ((6*A*c^2*d^2 + b^2*e*(2*B*d + A*e) - 3*b*c*d*(B*d + 2*A*e))*Log[x])/b^5 - ((6*A*c^2*d^2 + b^2*e*(2*B*d + A*e) - 3*b*c*d*(B*d + 2*A*e))*Log[b + c*x])/b^5","A",2,1,24,0.04167,1,"{771}"
1158,1,168,0,0.2099314,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x))/(b*x + c*x^2)^3,x]","\frac{-2 b c (A e+B d)+3 A c^2 d+b^2 B e}{b^4 (b+c x)}+\frac{\log (x) \left(-3 b c (A e+B d)+6 A c^2 d+b^2 B e\right)}{b^5}-\frac{\log (b+c x) \left(-3 b c (A e+B d)+6 A c^2 d+b^2 B e\right)}{b^5}-\frac{A b e-3 A c d+b B d}{b^4 x}-\frac{(b B-A c) (c d-b e)}{2 b^3 (b+c x)^2}-\frac{A d}{2 b^3 x^2}","\frac{-2 b c (A e+B d)+3 A c^2 d+b^2 B e}{b^4 (b+c x)}+\frac{\log (x) \left(-3 b c (A e+B d)+6 A c^2 d+b^2 B e\right)}{b^5}-\frac{\log (b+c x) \left(-3 b c (A e+B d)+6 A c^2 d+b^2 B e\right)}{b^5}-\frac{A b e-3 A c d+b B d}{b^4 x}-\frac{(b B-A c) (c d-b e)}{2 b^3 (b+c x)^2}-\frac{A d}{2 b^3 x^2}",1,"-(A*d)/(2*b^3*x^2) - (b*B*d - 3*A*c*d + A*b*e)/(b^4*x) - ((b*B - A*c)*(c*d - b*e))/(2*b^3*(b + c*x)^2) + (3*A*c^2*d + b^2*B*e - 2*b*c*(B*d + A*e))/(b^4*(b + c*x)) + ((6*A*c^2*d + b^2*B*e - 3*b*c*(B*d + A*e))*Log[x])/b^5 - ((6*A*c^2*d + b^2*B*e - 3*b*c*(B*d + A*e))*Log[b + c*x])/b^5","A",2,1,22,0.04545,1,"{771}"
1159,1,109,0,0.0986541,"\int \frac{A+B x}{\left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/(b*x + c*x^2)^3,x]","-\frac{b B-3 A c}{b^4 x}-\frac{c (2 b B-3 A c)}{b^4 (b+c x)}-\frac{c (b B-A c)}{2 b^3 (b+c x)^2}-\frac{3 c \log (x) (b B-2 A c)}{b^5}+\frac{3 c (b B-2 A c) \log (b+c x)}{b^5}-\frac{A}{2 b^3 x^2}","-\frac{b B-3 A c}{b^4 x}-\frac{c (2 b B-3 A c)}{b^4 (b+c x)}-\frac{c (b B-A c)}{2 b^3 (b+c x)^2}-\frac{3 c \log (x) (b B-2 A c)}{b^5}+\frac{3 c (b B-2 A c) \log (b+c x)}{b^5}-\frac{A}{2 b^3 x^2}",1,"-A/(2*b^3*x^2) - (b*B - 3*A*c)/(b^4*x) - (c*(b*B - A*c))/(2*b^3*(b + c*x)^2) - (c*(2*b*B - 3*A*c))/(b^4*(b + c*x)) - (3*c*(b*B - 2*A*c)*Log[x])/b^5 + (3*c*(b*B - 2*A*c)*Log[b + c*x])/b^5","A",2,1,17,0.05882,1,"{631}"
1160,1,279,0,0.502389,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)*(b*x + c*x^2)^3),x]","-\frac{c^2 \log (b+c x) \left(2 b^2 c e (5 A e+4 B d)-3 b c^2 d (5 A e+B d)+6 A c^3 d^2-6 b^3 B e^2\right)}{b^5 (c d-b e)^3}+\frac{\log (x) \left(b^2 (-e) (B d-A e)-3 b c d (B d-A e)+6 A c^2 d^2\right)}{b^5 d^3}+\frac{c^2 \left(-2 b c (2 A e+B d)+3 A c^2 d+3 b^2 B e\right)}{b^4 (b+c x) (c d-b e)^2}-\frac{c^2 (b B-A c)}{2 b^3 (b+c x)^2 (c d-b e)}-\frac{-A b e-3 A c d+b B d}{b^4 d^2 x}-\frac{A}{2 b^3 d x^2}-\frac{e^4 (B d-A e) \log (d+e x)}{d^3 (c d-b e)^3}","-\frac{c^2 \log (b+c x) \left(2 b^2 c e (5 A e+4 B d)-3 b c^2 d (5 A e+B d)+6 A c^3 d^2-6 b^3 B e^2\right)}{b^5 (c d-b e)^3}+\frac{\log (x) \left(b^2 (-e) (B d-A e)-3 b c d (B d-A e)+6 A c^2 d^2\right)}{b^5 d^3}+\frac{c^2 \left(-2 b c (2 A e+B d)+3 A c^2 d+3 b^2 B e\right)}{b^4 (b+c x) (c d-b e)^2}-\frac{c^2 (b B-A c)}{2 b^3 (b+c x)^2 (c d-b e)}-\frac{-A b e-3 A c d+b B d}{b^4 d^2 x}-\frac{A}{2 b^3 d x^2}-\frac{e^4 (B d-A e) \log (d+e x)}{d^3 (c d-b e)^3}",1,"-A/(2*b^3*d*x^2) - (b*B*d - 3*A*c*d - A*b*e)/(b^4*d^2*x) - (c^2*(b*B - A*c))/(2*b^3*(c*d - b*e)*(b + c*x)^2) + (c^2*(3*A*c^2*d + 3*b^2*B*e - 2*b*c*(B*d + 2*A*e)))/(b^4*(c*d - b*e)^2*(b + c*x)) + ((6*A*c^2*d^2 - 3*b*c*d*(B*d - A*e) - b^2*e*(B*d - A*e))*Log[x])/(b^5*d^3) - (c^2*(6*A*c^3*d^2 - 6*b^3*B*e^2 - 3*b*c^2*d*(B*d + 5*A*e) + 2*b^2*c*e*(4*B*d + 5*A*e))*Log[b + c*x])/(b^5*(c*d - b*e)^3) - (e^4*(B*d - A*e)*Log[d + e*x])/(d^3*(c*d - b*e)^3)","A",2,1,24,0.04167,1,"{771}"
1161,1,331,0,0.6720278,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^3),x]","-\frac{c^3 \log (b+c x) \left(5 b^2 c e (3 A e+2 B d)-3 b c^2 d (6 A e+B d)+6 A c^3 d^2-10 b^3 B e^2\right)}{b^5 (c d-b e)^4}+\frac{\log (x) \left(b^2 (-e) (2 B d-3 A e)-3 b c d (B d-2 A e)+6 A c^2 d^2\right)}{b^5 d^4}-\frac{c^3 \left(5 A b c e-3 A c^2 d-4 b^2 B e+2 b B c d\right)}{b^4 (b+c x) (c d-b e)^3}-\frac{c^3 (b B-A c)}{2 b^3 (b+c x)^2 (c d-b e)^2}-\frac{-2 A b e-3 A c d+b B d}{b^4 d^3 x}-\frac{A}{2 b^3 d^2 x^2}+\frac{e^4 (B d-A e)}{d^3 (d+e x) (c d-b e)^3}-\frac{e^4 \log (d+e x) (B d (5 c d-2 b e)-3 A e (2 c d-b e))}{d^4 (c d-b e)^4}","-\frac{c^3 \log (b+c x) \left(5 b^2 c e (3 A e+2 B d)-3 b c^2 d (6 A e+B d)+6 A c^3 d^2-10 b^3 B e^2\right)}{b^5 (c d-b e)^4}+\frac{\log (x) \left(b^2 (-e) (2 B d-3 A e)-3 b c d (B d-2 A e)+6 A c^2 d^2\right)}{b^5 d^4}-\frac{c^3 \left(5 A b c e-3 A c^2 d-4 b^2 B e+2 b B c d\right)}{b^4 (b+c x) (c d-b e)^3}-\frac{c^3 (b B-A c)}{2 b^3 (b+c x)^2 (c d-b e)^2}-\frac{-2 A b e-3 A c d+b B d}{b^4 d^3 x}-\frac{A}{2 b^3 d^2 x^2}+\frac{e^4 (B d-A e)}{d^3 (d+e x) (c d-b e)^3}-\frac{e^4 \log (d+e x) (B d (5 c d-2 b e)-3 A e (2 c d-b e))}{d^4 (c d-b e)^4}",1,"-A/(2*b^3*d^2*x^2) - (b*B*d - 3*A*c*d - 2*A*b*e)/(b^4*d^3*x) - (c^3*(b*B - A*c))/(2*b^3*(c*d - b*e)^2*(b + c*x)^2) - (c^3*(2*b*B*c*d - 3*A*c^2*d - 4*b^2*B*e + 5*A*b*c*e))/(b^4*(c*d - b*e)^3*(b + c*x)) + (e^4*(B*d - A*e))/(d^3*(c*d - b*e)^3*(d + e*x)) + ((6*A*c^2*d^2 - b^2*e*(2*B*d - 3*A*e) - 3*b*c*d*(B*d - 2*A*e))*Log[x])/(b^5*d^4) - (c^3*(6*A*c^3*d^2 - 10*b^3*B*e^2 + 5*b^2*c*e*(2*B*d + 3*A*e) - 3*b*c^2*d*(B*d + 6*A*e))*Log[b + c*x])/(b^5*(c*d - b*e)^4) - (e^4*(B*d*(5*c*d - 2*b*e) - 3*A*e*(2*c*d - b*e))*Log[d + e*x])/(d^4*(c*d - b*e)^4)","A",2,1,24,0.04167,1,"{771}"
1162,1,404,0,0.5472297,"\int (A+B x) (d+e x)^3 \sqrt{b x+c x^2} \, dx","Int[(A + B*x)*(d + e*x)^3*Sqrt[b*x + c*x^2],x]","\frac{\left(b x+c x^2\right)^{3/2} \left(6 c e x \left(28 A c e (2 c d-b e)+B \left(21 b^2 e^2-36 b c d e+8 c^2 d^2\right)\right)+4 A c e \left(35 b^2 e^2-150 b c d e+192 c^2 d^2\right)+B \left(420 b^2 c d e^2-105 b^3 e^3-456 b c^2 d^2 e+64 c^3 d^3\right)\right)}{960 c^4}+\frac{(b+2 c x) \sqrt{b x+c x^2} \left(120 b^2 c^2 d e (A e+B d)-28 b^3 c e^2 (A e+3 B d)-64 b c^3 d^2 (3 A e+B d)+128 A c^4 d^3+21 b^4 B e^3\right)}{512 c^5}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(120 b^2 c^2 d e (A e+B d)-28 b^3 c e^2 (A e+3 B d)-64 b c^3 d^2 (3 A e+B d)+128 A c^4 d^3+21 b^4 B e^3\right)}{512 c^{11/2}}+\frac{\left(b x+c x^2\right)^{3/2} (d+e x)^2 (4 A c e-3 b B e+2 B c d)}{20 c^2}+\frac{B \left(b x+c x^2\right)^{3/2} (d+e x)^3}{6 c}","\frac{\left(b x+c x^2\right)^{3/2} \left(6 c e x \left(28 A c e (2 c d-b e)+B \left(21 b^2 e^2-36 b c d e+8 c^2 d^2\right)\right)+4 A c e \left(35 b^2 e^2-150 b c d e+192 c^2 d^2\right)+B \left(420 b^2 c d e^2-105 b^3 e^3-456 b c^2 d^2 e+64 c^3 d^3\right)\right)}{960 c^4}+\frac{(b+2 c x) \sqrt{b x+c x^2} \left(120 b^2 c^2 d e (A e+B d)-28 b^3 c e^2 (A e+3 B d)-64 b c^3 d^2 (3 A e+B d)+128 A c^4 d^3+21 b^4 B e^3\right)}{512 c^5}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(120 b^2 c^2 d e (A e+B d)-28 b^3 c e^2 (A e+3 B d)-64 b c^3 d^2 (3 A e+B d)+128 A c^4 d^3+21 b^4 B e^3\right)}{512 c^{11/2}}+\frac{\left(b x+c x^2\right)^{3/2} (d+e x)^2 (4 A c e-3 b B e+2 B c d)}{20 c^2}+\frac{B \left(b x+c x^2\right)^{3/2} (d+e x)^3}{6 c}",1,"((128*A*c^4*d^3 + 21*b^4*B*e^3 + 120*b^2*c^2*d*e*(B*d + A*e) - 28*b^3*c*e^2*(3*B*d + A*e) - 64*b*c^3*d^2*(B*d + 3*A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^5) + ((2*B*c*d - 3*b*B*e + 4*A*c*e)*(d + e*x)^2*(b*x + c*x^2)^(3/2))/(20*c^2) + (B*(d + e*x)^3*(b*x + c*x^2)^(3/2))/(6*c) + ((4*A*c*e*(192*c^2*d^2 - 150*b*c*d*e + 35*b^2*e^2) + B*(64*c^3*d^3 - 456*b*c^2*d^2*e + 420*b^2*c*d*e^2 - 105*b^3*e^3) + 6*c*e*(28*A*c*e*(2*c*d - b*e) + B*(8*c^2*d^2 - 36*b*c*d*e + 21*b^2*e^2))*x)*(b*x + c*x^2)^(3/2))/(960*c^4) - (b^2*(128*A*c^4*d^3 + 21*b^4*B*e^3 + 120*b^2*c^2*d*e*(B*d + A*e) - 28*b^3*c*e^2*(3*B*d + A*e) - 64*b*c^3*d^2*(B*d + 3*A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(11/2))","A",6,5,26,0.1923,1,"{832, 779, 612, 620, 206}"
1163,1,267,0,0.2740543,"\int (A+B x) (d+e x)^2 \sqrt{b x+c x^2} \, dx","Int[(A + B*x)*(d + e*x)^2*Sqrt[b*x + c*x^2],x]","\frac{\left(b x+c x^2\right)^{3/2} \left(6 c e x (10 A c e-7 b B e+4 B c d)+10 A c e (16 c d-5 b e)+B \left(35 b^2 e^2-100 b c d e+32 c^2 d^2\right)\right)}{240 c^3}+\frac{(b+2 c x) \sqrt{b x+c x^2} \left(10 b^2 c e (A e+2 B d)-16 b c^2 d (2 A e+B d)+32 A c^3 d^2-7 b^3 B e^2\right)}{128 c^4}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(10 b^2 c e (A e+2 B d)-16 b c^2 d (2 A e+B d)+32 A c^3 d^2-7 b^3 B e^2\right)}{128 c^{9/2}}+\frac{B \left(b x+c x^2\right)^{3/2} (d+e x)^2}{5 c}","\frac{\left(b x+c x^2\right)^{3/2} \left(6 c e x (10 A c e-7 b B e+4 B c d)+10 A c e (16 c d-5 b e)+B \left(35 b^2 e^2-100 b c d e+32 c^2 d^2\right)\right)}{240 c^3}+\frac{(b+2 c x) \sqrt{b x+c x^2} \left(10 b^2 c e (A e+2 B d)-16 b c^2 d (2 A e+B d)+32 A c^3 d^2-7 b^3 B e^2\right)}{128 c^4}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(10 b^2 c e (A e+2 B d)-16 b c^2 d (2 A e+B d)+32 A c^3 d^2-7 b^3 B e^2\right)}{128 c^{9/2}}+\frac{B \left(b x+c x^2\right)^{3/2} (d+e x)^2}{5 c}",1,"((32*A*c^3*d^2 - 7*b^3*B*e^2 + 10*b^2*c*e*(2*B*d + A*e) - 16*b*c^2*d*(B*d + 2*A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^4) + (B*(d + e*x)^2*(b*x + c*x^2)^(3/2))/(5*c) + ((10*A*c*e*(16*c*d - 5*b*e) + B*(32*c^2*d^2 - 100*b*c*d*e + 35*b^2*e^2) + 6*c*e*(4*B*c*d - 7*b*B*e + 10*A*c*e)*x)*(b*x + c*x^2)^(3/2))/(240*c^3) - (b^2*(32*A*c^3*d^2 - 7*b^3*B*e^2 + 10*b^2*c*e*(2*B*d + A*e) - 16*b*c^2*d*(B*d + 2*A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(9/2))","A",5,5,26,0.1923,1,"{832, 779, 612, 620, 206}"
1164,1,154,0,0.1407697,"\int (A+B x) (d+e x) \sqrt{b x+c x^2} \, dx","Int[(A + B*x)*(d + e*x)*Sqrt[b*x + c*x^2],x]","\frac{(b+2 c x) \sqrt{b x+c x^2} \left(-8 b c (A e+B d)+16 A c^2 d+5 b^2 B e\right)}{64 c^3}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-8 b c (A e+B d)+16 A c^2 d+5 b^2 B e\right)}{64 c^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (-8 c (A e+B d)+5 b B e-6 B c e x)}{24 c^2}","\frac{(b+2 c x) \sqrt{b x+c x^2} \left(-8 b c (A e+B d)+16 A c^2 d+5 b^2 B e\right)}{64 c^3}-\frac{b^2 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-8 b c (A e+B d)+16 A c^2 d+5 b^2 B e\right)}{64 c^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (-8 c (A e+B d)+5 b B e-6 B c e x)}{24 c^2}",1,"((16*A*c^2*d + 5*b^2*B*e - 8*b*c*(B*d + A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(64*c^3) - ((5*b*B*e - 8*c*(B*d + A*e) - 6*B*c*e*x)*(b*x + c*x^2)^(3/2))/(24*c^2) - (b^2*(16*A*c^2*d + 5*b^2*B*e - 8*b*c*(B*d + A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(7/2))","A",4,4,24,0.1667,1,"{779, 612, 620, 206}"
1165,1,97,0,0.0392168,"\int (A+B x) \sqrt{b x+c x^2} \, dx","Int[(A + B*x)*Sqrt[b*x + c*x^2],x]","\frac{b^2 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}-\frac{(b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{8 c^2}+\frac{B \left(b x+c x^2\right)^{3/2}}{3 c}","\frac{b^2 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{8 c^{5/2}}-\frac{(b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{8 c^2}+\frac{B \left(b x+c x^2\right)^{3/2}}{3 c}",1,"-((b*B - 2*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(8*c^2) + (B*(b*x + c*x^2)^(3/2))/(3*c) + (b^2*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(5/2))","A",4,4,19,0.2105,1,"{640, 612, 620, 206}"
1166,1,200,0,0.2762654,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{d+e x} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x),x]","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)-B \left(-b^2 e^2-4 b c d e+8 c^2 d^2\right)\right)}{4 c^{3/2} e^3}-\frac{\sqrt{b x+c x^2} (-4 A c e-b B e+4 B c d-2 B c e x)}{4 c e^2}-\frac{\sqrt{d} (B d-A e) \sqrt{c d-b e} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^3}","-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)-B \left(-b^2 e^2-4 b c d e+8 c^2 d^2\right)\right)}{4 c^{3/2} e^3}-\frac{\sqrt{b x+c x^2} (-4 A c e-b B e+4 B c d-2 B c e x)}{4 c e^2}-\frac{\sqrt{d} (B d-A e) \sqrt{c d-b e} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^3}",1,"-((4*B*c*d - b*B*e - 4*A*c*e - 2*B*c*e*x)*Sqrt[b*x + c*x^2])/(4*c*e^2) - ((4*A*c*e*(2*c*d - b*e) - B*(8*c^2*d^2 - 4*b*c*d*e - b^2*e^2))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(3/2)*e^3) - (Sqrt[d]*(B*d - A*e)*Sqrt[c*d - b*e]*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/e^3","A",6,5,26,0.1923,1,"{814, 843, 620, 206, 724}"
1167,1,185,0,0.1856009,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^2} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^2,x]","\frac{\sqrt{b x+c x^2} (-A e+2 B d+B e x)}{e^2 (d+e x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (-2 A c e-b B e+4 B c d)}{\sqrt{c} e^3}+\frac{(B d (4 c d-3 b e)-A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 \sqrt{d} e^3 \sqrt{c d-b e}}","\frac{\sqrt{b x+c x^2} (-A e+2 B d+B e x)}{e^2 (d+e x)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (-2 A c e-b B e+4 B c d)}{\sqrt{c} e^3}+\frac{(B d (4 c d-3 b e)-A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 \sqrt{d} e^3 \sqrt{c d-b e}}",1,"((2*B*d - A*e + B*e*x)*Sqrt[b*x + c*x^2])/(e^2*(d + e*x)) - ((4*B*c*d - b*B*e - 2*A*c*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(Sqrt[c]*e^3) + ((B*d*(4*c*d - 3*b*e) - A*e*(2*c*d - b*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*Sqrt[d]*e^3*Sqrt[c*d - b*e])","A",6,5,26,0.1923,1,"{812, 843, 620, 206, 724}"
1168,1,235,0,0.3226176,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^3} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^3,x]","-\frac{\left(A b^2 e^3+B d \left(3 b^2 e^2-12 b c d e+8 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{3/2} e^3 (c d-b e)^{3/2}}+\frac{\sqrt{b x+c x^2} \left(d \left(A b e^2-B d (4 c d-3 b e)\right)-e x (B d (6 c d-5 b e)-A e (2 c d-b e))\right)}{4 d e^2 (d+e x)^2 (c d-b e)}+\frac{2 B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^3}","-\frac{\left(A b^2 e^3+B d \left(3 b^2 e^2-12 b c d e+8 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{3/2} e^3 (c d-b e)^{3/2}}+\frac{\sqrt{b x+c x^2} \left(d \left(A b e^2-B d (4 c d-3 b e)\right)-e x (B d (6 c d-5 b e)-A e (2 c d-b e))\right)}{4 d e^2 (d+e x)^2 (c d-b e)}+\frac{2 B \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^3}",1,"((d*(A*b*e^2 - B*d*(4*c*d - 3*b*e)) - e*(B*d*(6*c*d - 5*b*e) - A*e*(2*c*d - b*e))*x)*Sqrt[b*x + c*x^2])/(4*d*e^2*(c*d - b*e)*(d + e*x)^2) + (2*B*Sqrt[c]*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/e^3 - ((A*b^2*e^3 + B*d*(8*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*d^(3/2)*e^3*(c*d - b*e)^(3/2))","A",6,5,26,0.1923,1,"{810, 843, 620, 206, 724}"
1169,1,200,0,0.1807793,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^4} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^4,x]","\frac{b^2 (A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{5/2} (c d-b e)^{5/2}}-\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{8 d^2 (d+e x)^2 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{3/2} (B d-A e)}{3 d (d+e x)^3 (c d-b e)}","\frac{b^2 (A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{5/2} (c d-b e)^{5/2}}-\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{8 d^2 (d+e x)^2 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{3/2} (B d-A e)}{3 d (d+e x)^3 (c d-b e)}",1,"-((b*B*d - 2*A*c*d + A*b*e)*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(8*d^2*(c*d - b*e)^2*(d + e*x)^2) + ((B*d - A*e)*(b*x + c*x^2)^(3/2))/(3*d*(c*d - b*e)*(d + e*x)^3) + (b^2*(b*B*d - 2*A*c*d + A*b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(16*d^(5/2)*(c*d - b*e)^(5/2))","A",4,4,26,0.1538,1,"{806, 720, 724, 206}"
1170,1,310,0,0.4053854,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^5} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^5,x]","\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(b^2 e (5 A e+3 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right)}{64 d^3 (d+e x)^2 (c d-b e)^3}-\frac{b^2 \left(b^2 e (5 A e+3 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{7/2} (c d-b e)^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (5 A e (2 c d-b e)-B d (3 b e+2 c d))}{24 d^2 (d+e x)^3 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{3/2} (B d-A e)}{4 d (d+e x)^4 (c d-b e)}","\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(b^2 e (5 A e+3 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right)}{64 d^3 (d+e x)^2 (c d-b e)^3}-\frac{b^2 \left(b^2 e (5 A e+3 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{7/2} (c d-b e)^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (5 A e (2 c d-b e)-B d (3 b e+2 c d))}{24 d^2 (d+e x)^3 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{3/2} (B d-A e)}{4 d (d+e x)^4 (c d-b e)}",1,"((16*A*c^2*d^2 - 8*b*c*d*(B*d + 2*A*e) + b^2*e*(3*B*d + 5*A*e))*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(64*d^3*(c*d - b*e)^3*(d + e*x)^2) + ((B*d - A*e)*(b*x + c*x^2)^(3/2))/(4*d*(c*d - b*e)*(d + e*x)^4) - ((5*A*e*(2*c*d - b*e) - B*d*(2*c*d + 3*b*e))*(b*x + c*x^2)^(3/2))/(24*d^2*(c*d - b*e)^2*(d + e*x)^3) - (b^2*(16*A*c^2*d^2 - 8*b*c*d*(B*d + 2*A*e) + b^2*e*(3*B*d + 5*A*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(128*d^(7/2)*(c*d - b*e)^(7/2))","A",5,5,26,0.1923,1,"{834, 806, 720, 724, 206}"
1171,1,449,0,0.7816273,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^6} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^6,x]","\frac{\left(b x+c x^2\right)^{3/2} \left(B d \left(-15 b^2 e^2+42 b c d e+8 c^2 d^2\right)-A e \left(35 b^2 e^2-108 b c d e+108 c^2 d^2\right)\right)}{240 d^3 (d+e x)^3 (c d-b e)^3}+\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(6 b^2 c d e (5 A e+2 B d)+b^3 \left(-e^2\right) (7 A e+3 B d)-16 b c^2 d^2 (3 A e+B d)+32 A c^3 d^3\right)}{128 d^4 (d+e x)^2 (c d-b e)^4}-\frac{b^2 \left(6 b^2 c d e (5 A e+2 B d)+b^3 \left(-e^2\right) (7 A e+3 B d)-16 b c^2 d^2 (3 A e+B d)+32 A c^3 d^3\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{256 d^{9/2} (c d-b e)^{9/2}}-\frac{\left(b x+c x^2\right)^{3/2} (7 A e (2 c d-b e)-B d (3 b e+4 c d))}{40 d^2 (d+e x)^4 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{3/2} (B d-A e)}{5 d (d+e x)^5 (c d-b e)}","\frac{\left(b x+c x^2\right)^{3/2} \left(B d \left(-15 b^2 e^2+42 b c d e+8 c^2 d^2\right)-A e \left(35 b^2 e^2-108 b c d e+108 c^2 d^2\right)\right)}{240 d^3 (d+e x)^3 (c d-b e)^3}+\frac{\sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(6 b^2 c d e (5 A e+2 B d)+b^3 \left(-e^2\right) (7 A e+3 B d)-16 b c^2 d^2 (3 A e+B d)+32 A c^3 d^3\right)}{128 d^4 (d+e x)^2 (c d-b e)^4}-\frac{b^2 \left(6 b^2 c d e (5 A e+2 B d)+b^3 \left(-e^2\right) (7 A e+3 B d)-16 b c^2 d^2 (3 A e+B d)+32 A c^3 d^3\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{256 d^{9/2} (c d-b e)^{9/2}}-\frac{\left(b x+c x^2\right)^{3/2} (7 A e (2 c d-b e)-B d (3 b e+4 c d))}{40 d^2 (d+e x)^4 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{3/2} (B d-A e)}{5 d (d+e x)^5 (c d-b e)}",1,"((32*A*c^3*d^3 - 16*b*c^2*d^2*(B*d + 3*A*e) + 6*b^2*c*d*e*(2*B*d + 5*A*e) - b^3*e^2*(3*B*d + 7*A*e))*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(128*d^4*(c*d - b*e)^4*(d + e*x)^2) + ((B*d - A*e)*(b*x + c*x^2)^(3/2))/(5*d*(c*d - b*e)*(d + e*x)^5) - ((7*A*e*(2*c*d - b*e) - B*d*(4*c*d + 3*b*e))*(b*x + c*x^2)^(3/2))/(40*d^2*(c*d - b*e)^2*(d + e*x)^4) + ((B*d*(8*c^2*d^2 + 42*b*c*d*e - 15*b^2*e^2) - A*e*(108*c^2*d^2 - 108*b*c*d*e + 35*b^2*e^2))*(b*x + c*x^2)^(3/2))/(240*d^3*(c*d - b*e)^3*(d + e*x)^3) - (b^2*(32*A*c^3*d^3 - 16*b*c^2*d^2*(B*d + 3*A*e) + 6*b^2*c*d*e*(2*B*d + 5*A*e) - b^3*e^2*(3*B*d + 7*A*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(256*d^(9/2)*(c*d - b*e)^(9/2))","A",6,5,26,0.1923,1,"{834, 806, 720, 724, 206}"
1172,1,345,0,0.3366633,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^(3/2),x]","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} \left(14 b^2 c e (A e+2 B d)-24 b c^2 d (2 A e+B d)+48 A c^3 d^2-9 b^3 B e^2\right)}{1024 c^5}+\frac{\left(b x+c x^2\right)^{5/2} \left(10 c e x (14 A c e-9 b B e+4 B c d)+14 A c e (24 c d-7 b e)+B \left(63 b^2 e^2-196 b c d e+48 c^2 d^2\right)\right)}{840 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} \left(14 b^2 c e (A e+2 B d)-24 b c^2 d (2 A e+B d)+48 A c^3 d^2-9 b^3 B e^2\right)}{384 c^4}+\frac{b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(14 b^2 c e (A e+2 B d)-24 b c^2 d (2 A e+B d)+48 A c^3 d^2-9 b^3 B e^2\right)}{1024 c^{11/2}}+\frac{B \left(b x+c x^2\right)^{5/2} (d+e x)^2}{7 c}","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} \left(14 b^2 c e (A e+2 B d)-24 b c^2 d (2 A e+B d)+48 A c^3 d^2-9 b^3 B e^2\right)}{1024 c^5}+\frac{\left(b x+c x^2\right)^{5/2} \left(10 c e x (14 A c e-9 b B e+4 B c d)+14 A c e (24 c d-7 b e)+B \left(63 b^2 e^2-196 b c d e+48 c^2 d^2\right)\right)}{840 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} \left(14 b^2 c e (A e+2 B d)-24 b c^2 d (2 A e+B d)+48 A c^3 d^2-9 b^3 B e^2\right)}{384 c^4}+\frac{b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(14 b^2 c e (A e+2 B d)-24 b c^2 d (2 A e+B d)+48 A c^3 d^2-9 b^3 B e^2\right)}{1024 c^{11/2}}+\frac{B \left(b x+c x^2\right)^{5/2} (d+e x)^2}{7 c}",1,"-(b^2*(48*A*c^3*d^2 - 9*b^3*B*e^2 + 14*b^2*c*e*(2*B*d + A*e) - 24*b*c^2*d*(B*d + 2*A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(1024*c^5) + ((48*A*c^3*d^2 - 9*b^3*B*e^2 + 14*b^2*c*e*(2*B*d + A*e) - 24*b*c^2*d*(B*d + 2*A*e))*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(384*c^4) + (B*(d + e*x)^2*(b*x + c*x^2)^(5/2))/(7*c) + ((14*A*c*e*(24*c*d - 7*b*e) + B*(48*c^2*d^2 - 196*b*c*d*e + 63*b^2*e^2) + 10*c*e*(4*B*c*d - 9*b*B*e + 14*A*c*e)*x)*(b*x + c*x^2)^(5/2))/(840*c^3) + (b^4*(48*A*c^3*d^2 - 9*b^3*B*e^2 + 14*b^2*c*e*(2*B*d + A*e) - 24*b*c^2*d*(B*d + 2*A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(1024*c^(11/2))","A",6,5,26,0.1923,1,"{832, 779, 612, 620, 206}"
1173,1,209,0,0.1907851,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)*(b*x + c*x^2)^(3/2),x]","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{512 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{192 c^3}+\frac{b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{512 c^{9/2}}-\frac{\left(b x+c x^2\right)^{5/2} (-12 c (A e+B d)+7 b B e-10 B c e x)}{60 c^2}","-\frac{b^2 (b+2 c x) \sqrt{b x+c x^2} \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{512 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{192 c^3}+\frac{b^4 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-12 b c (A e+B d)+24 A c^2 d+7 b^2 B e\right)}{512 c^{9/2}}-\frac{\left(b x+c x^2\right)^{5/2} (-12 c (A e+B d)+7 b B e-10 B c e x)}{60 c^2}",1,"-(b^2*(24*A*c^2*d + 7*b^2*B*e - 12*b*c*(B*d + A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(512*c^4) + ((24*A*c^2*d + 7*b^2*B*e - 12*b*c*(B*d + A*e))*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(192*c^3) - ((7*b*B*e - 12*c*(B*d + A*e) - 10*B*c*e*x)*(b*x + c*x^2)^(5/2))/(60*c^2) + (b^4*(24*A*c^2*d + 7*b^2*B*e - 12*b*c*(B*d + A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(9/2))","A",5,4,24,0.1667,1,"{779, 612, 620, 206}"
1174,1,134,0,0.0534346,"\int (A+B x) \left(b x+c x^2\right)^{3/2} \, dx","Int[(A + B*x)*(b*x + c*x^2)^(3/2),x]","\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{128 c^3}-\frac{3 b^4 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{16 c^2}+\frac{B \left(b x+c x^2\right)^{5/2}}{5 c}","\frac{3 b^2 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{128 c^3}-\frac{3 b^4 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{128 c^{7/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{16 c^2}+\frac{B \left(b x+c x^2\right)^{5/2}}{5 c}",1,"(3*b^2*(b*B - 2*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(128*c^3) - ((b*B - 2*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(16*c^2) + (B*(b*x + c*x^2)^(5/2))/(5*c) - (3*b^4*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(7/2))","A",5,4,19,0.2105,1,"{640, 612, 620, 206}"
1175,1,392,0,0.5902334,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x),x]","\frac{\sqrt{b x+c x^2} \left(-2 c e x \left(8 A c e (2 c d-b e)-B \left(-3 b^2 e^2-8 b c d e+16 c^2 d^2\right)\right)+8 A c e \left(b^2 e^2-10 b c d e+8 c^2 d^2\right)-B \left(8 b^2 c d e^2+3 b^3 e^3-80 b c^2 d^2 e+64 c^3 d^3\right)\right)}{64 c^2 e^4}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(8 A c e \left(6 b^2 c d e^2+b^3 e^3-24 b c^2 d^2 e+16 c^3 d^3\right)-B \left(48 b^2 c^2 d^2 e^2+8 b^3 c d e^3+3 b^4 e^4-192 b c^3 d^3 e+128 c^4 d^4\right)\right)}{64 c^{5/2} e^5}-\frac{d^{3/2} (B d-A e) (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^5}-\frac{\left(b x+c x^2\right)^{3/2} (-8 A c e-3 b B e+8 B c d-6 B c e x)}{24 c e^2}","\frac{\sqrt{b x+c x^2} \left(-2 c e x \left(8 A c e (2 c d-b e)-B \left(-3 b^2 e^2-8 b c d e+16 c^2 d^2\right)\right)+8 A c e \left(b^2 e^2-10 b c d e+8 c^2 d^2\right)-B \left(8 b^2 c d e^2+3 b^3 e^3-80 b c^2 d^2 e+64 c^3 d^3\right)\right)}{64 c^2 e^4}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(8 A c e \left(6 b^2 c d e^2+b^3 e^3-24 b c^2 d^2 e+16 c^3 d^3\right)-B \left(48 b^2 c^2 d^2 e^2+8 b^3 c d e^3+3 b^4 e^4-192 b c^3 d^3 e+128 c^4 d^4\right)\right)}{64 c^{5/2} e^5}-\frac{d^{3/2} (B d-A e) (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^5}-\frac{\left(b x+c x^2\right)^{3/2} (-8 A c e-3 b B e+8 B c d-6 B c e x)}{24 c e^2}",1,"((8*A*c*e*(8*c^2*d^2 - 10*b*c*d*e + b^2*e^2) - B*(64*c^3*d^3 - 80*b*c^2*d^2*e + 8*b^2*c*d*e^2 + 3*b^3*e^3) - 2*c*e*(8*A*c*e*(2*c*d - b*e) - B*(16*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(64*c^2*e^4) - ((8*B*c*d - 3*b*B*e - 8*A*c*e - 6*B*c*e*x)*(b*x + c*x^2)^(3/2))/(24*c*e^2) - ((8*A*c*e*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3) - B*(128*c^4*d^4 - 192*b*c^3*d^3*e + 48*b^2*c^2*d^2*e^2 + 8*b^3*c*d*e^3 + 3*b^4*e^4))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(5/2)*e^5) - (d^(3/2)*(B*d - A*e)*(c*d - b*e)^(3/2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/e^5","A",7,5,26,0.1923,1,"{814, 843, 620, 206, 724}"
1176,1,323,0,0.424148,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^2,x]","-\frac{\sqrt{b x+c x^2} \left(2 c e x (-6 A c e-b B e+8 B c d)+6 A c e (4 c d-3 b e)-B \left(b^2 e^2-28 b c d e+32 c^2 d^2\right)\right)}{8 c e^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 b c e (4 B d-3 A e) (2 c d-b e)-\left(-b^2 e^2-4 b c d e+8 c^2 d^2\right) (-6 A c e-b B e+8 B c d)\right)}{8 c^{3/2} e^5}+\frac{\left(b x+c x^2\right)^{3/2} (-3 A e+4 B d+B e x)}{3 e^2 (d+e x)}+\frac{\sqrt{d} \sqrt{c d-b e} (B d (8 c d-5 b e)-3 A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^5}","-\frac{\sqrt{b x+c x^2} \left(2 c e x (-6 A c e-b B e+8 B c d)+6 A c e (4 c d-3 b e)-B \left(b^2 e^2-28 b c d e+32 c^2 d^2\right)\right)}{8 c e^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 b c e (4 B d-3 A e) (2 c d-b e)-\left(-b^2 e^2-4 b c d e+8 c^2 d^2\right) (-6 A c e-b B e+8 B c d)\right)}{8 c^{3/2} e^5}+\frac{\left(b x+c x^2\right)^{3/2} (-3 A e+4 B d+B e x)}{3 e^2 (d+e x)}+\frac{\sqrt{d} \sqrt{c d-b e} (B d (8 c d-5 b e)-3 A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^5}",1,"-((6*A*c*e*(4*c*d - 3*b*e) - B*(32*c^2*d^2 - 28*b*c*d*e + b^2*e^2) + 2*c*e*(8*B*c*d - b*B*e - 6*A*c*e)*x)*Sqrt[b*x + c*x^2])/(8*c*e^4) + ((4*B*d - 3*A*e + B*e*x)*(b*x + c*x^2)^(3/2))/(3*e^2*(d + e*x)) + ((4*b*c*e*(4*B*d - 3*A*e)*(2*c*d - b*e) - (8*B*c*d - b*B*e - 6*A*c*e)*(8*c^2*d^2 - 4*b*c*d*e - b^2*e^2))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(3/2)*e^5) + (Sqrt[d]*Sqrt[c*d - b*e]*(B*d*(8*c*d - 5*b*e) - 3*A*e*(2*c*d - b*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*e^5)","A",7,6,26,0.2308,1,"{812, 814, 843, 620, 206, 724}"
1177,1,314,0,0.4268193,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^3,x]","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)-B \left(b^2 e^2-12 b c d e+16 c^2 d^2\right)\right)}{4 \sqrt{c} e^5}+\frac{3 \left(A e \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)-B d \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 \sqrt{d} e^5 \sqrt{c d-b e}}+\frac{\left(b x+c x^2\right)^{3/2} (-A e+2 B d+B e x)}{2 e^2 (d+e x)^2}-\frac{3 \sqrt{b x+c x^2} (e x (-2 A c e-b B e+4 B c d)-A e (4 c d-b e)+4 B d (2 c d-b e))}{4 e^4 (d+e x)}","-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)-B \left(b^2 e^2-12 b c d e+16 c^2 d^2\right)\right)}{4 \sqrt{c} e^5}+\frac{3 \left(A e \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)-B d \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 \sqrt{d} e^5 \sqrt{c d-b e}}+\frac{\left(b x+c x^2\right)^{3/2} (-A e+2 B d+B e x)}{2 e^2 (d+e x)^2}-\frac{3 \sqrt{b x+c x^2} (e x (-2 A c e-b B e+4 B c d)-A e (4 c d-b e)+4 B d (2 c d-b e))}{4 e^4 (d+e x)}",1,"(-3*(4*B*d*(2*c*d - b*e) - A*e*(4*c*d - b*e) + e*(4*B*c*d - b*B*e - 2*A*c*e)*x)*Sqrt[b*x + c*x^2])/(4*e^4*(d + e*x)) + ((2*B*d - A*e + B*e*x)*(b*x + c*x^2)^(3/2))/(2*e^2*(d + e*x)^2) - (3*(4*A*c*e*(2*c*d - b*e) - B*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*Sqrt[c]*e^5) + (3*(A*e*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2) - B*d*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*Sqrt[d]*e^5*Sqrt[c*d - b*e])","A",7,5,26,0.1923,1,"{812, 843, 620, 206, 724}"
1178,1,426,0,0.5298574,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^4,x]","-\frac{\sqrt{b x+c x^2} \left(A e \left(-b^2 e^2-6 b c d e+8 c^2 d^2\right)-2 c e x (B d (8 c d-7 b e)-A e (2 c d-b e))-B d \left(5 b^2 e^2-36 b c d e+32 c^2 d^2\right)\right)}{8 d e^4 (d+e x) (c d-b e)}+\frac{\left(B d \left(60 b^2 c d e^2-5 b^3 e^3-120 b c^2 d^2 e+64 c^3 d^3\right)-A e \left(6 b^2 c d e^2+b^3 e^3-24 b c^2 d^2 e+16 c^3 d^3\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{3/2} e^5 (c d-b e)^{3/2}}-\frac{\left(b x+c x^2\right)^{3/2} (3 e x (B d (4 c d-3 b e)-A e (2 c d-b e))+d (B d (8 c d-5 b e)-A e (b e+2 c d)))}{12 d e^2 (d+e x)^3 (c d-b e)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (-2 A c e-3 b B e+8 B c d)}{e^5}","-\frac{\sqrt{b x+c x^2} \left(A e \left(-b^2 e^2-6 b c d e+8 c^2 d^2\right)-2 c e x (B d (8 c d-7 b e)-A e (2 c d-b e))-B d \left(5 b^2 e^2-36 b c d e+32 c^2 d^2\right)\right)}{8 d e^4 (d+e x) (c d-b e)}+\frac{\left(B d \left(60 b^2 c d e^2-5 b^3 e^3-120 b c^2 d^2 e+64 c^3 d^3\right)-A e \left(6 b^2 c d e^2+b^3 e^3-24 b c^2 d^2 e+16 c^3 d^3\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{3/2} e^5 (c d-b e)^{3/2}}-\frac{\left(b x+c x^2\right)^{3/2} (3 e x (B d (4 c d-3 b e)-A e (2 c d-b e))+d (B d (8 c d-5 b e)-A e (b e+2 c d)))}{12 d e^2 (d+e x)^3 (c d-b e)}-\frac{\sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (-2 A c e-3 b B e+8 B c d)}{e^5}",1,"-((A*e*(8*c^2*d^2 - 6*b*c*d*e - b^2*e^2) - B*d*(32*c^2*d^2 - 36*b*c*d*e + 5*b^2*e^2) - 2*c*e*(B*d*(8*c*d - 7*b*e) - A*e*(2*c*d - b*e))*x)*Sqrt[b*x + c*x^2])/(8*d*e^4*(c*d - b*e)*(d + e*x)) - ((d*(B*d*(8*c*d - 5*b*e) - A*e*(2*c*d + b*e)) + 3*e*(B*d*(4*c*d - 3*b*e) - A*e*(2*c*d - b*e))*x)*(b*x + c*x^2)^(3/2))/(12*d*e^2*(c*d - b*e)*(d + e*x)^3) - (Sqrt[c]*(8*B*c*d - 3*b*B*e - 2*A*c*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/e^5 + ((B*d*(64*c^3*d^3 - 120*b*c^2*d^2*e + 60*b^2*c*d*e^2 - 5*b^3*e^3) - A*e*(16*c^3*d^3 - 24*b*c^2*d^2*e + 6*b^2*c*d*e^2 + b^3*e^3))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(16*d^(3/2)*e^5*(c*d - b*e)^(3/2))","A",7,6,26,0.2308,1,"{810, 812, 843, 620, 206, 724}"
1179,1,421,0,0.5385374,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^5,x]","-\frac{\sqrt{b x+c x^2} \left(e x \left(3 A b^2 e^3 (2 c d-b e)+B d \left(98 b^2 c d e^2-5 b^3 e^3-192 b c^2 d^2 e+96 c^3 d^3\right)\right)+d \left(3 A b^3 e^4+B d \left(40 b^2 c d e^2+5 b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)\right)\right)}{64 d^2 e^4 (d+e x)^2 (c d-b e)^2}+\frac{\left(3 A b^4 e^5-B d \left(240 b^2 c^2 d^2 e^2-40 b^3 c d e^3-5 b^4 e^4-320 b c^3 d^3 e+128 c^4 d^4\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{5/2} e^5 (c d-b e)^{5/2}}+\frac{\left(b x+c x^2\right)^{3/2} \left(d \left(3 A b e^2-B d (8 c d-5 b e)\right)-e x (B d (14 c d-11 b e)-3 A e (2 c d-b e))\right)}{24 d e^2 (d+e x)^4 (c d-b e)}+\frac{2 B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^5}","-\frac{\sqrt{b x+c x^2} \left(e x \left(3 A b^2 e^3 (2 c d-b e)+B d \left(98 b^2 c d e^2-5 b^3 e^3-192 b c^2 d^2 e+96 c^3 d^3\right)\right)+d \left(3 A b^3 e^4+B d \left(40 b^2 c d e^2+5 b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)\right)\right)}{64 d^2 e^4 (d+e x)^2 (c d-b e)^2}+\frac{\left(3 A b^4 e^5-B d \left(240 b^2 c^2 d^2 e^2-40 b^3 c d e^3-5 b^4 e^4-320 b c^3 d^3 e+128 c^4 d^4\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{5/2} e^5 (c d-b e)^{5/2}}+\frac{\left(b x+c x^2\right)^{3/2} \left(d \left(3 A b e^2-B d (8 c d-5 b e)\right)-e x (B d (14 c d-11 b e)-3 A e (2 c d-b e))\right)}{24 d e^2 (d+e x)^4 (c d-b e)}+\frac{2 B c^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{e^5}",1,"-((d*(3*A*b^3*e^4 + B*d*(64*c^3*d^3 - 112*b*c^2*d^2*e + 40*b^2*c*d*e^2 + 5*b^3*e^3)) + e*(3*A*b^2*e^3*(2*c*d - b*e) + B*d*(96*c^3*d^3 - 192*b*c^2*d^2*e + 98*b^2*c*d*e^2 - 5*b^3*e^3))*x)*Sqrt[b*x + c*x^2])/(64*d^2*e^4*(c*d - b*e)^2*(d + e*x)^2) + ((d*(3*A*b*e^2 - B*d*(8*c*d - 5*b*e)) - e*(B*d*(14*c*d - 11*b*e) - 3*A*e*(2*c*d - b*e))*x)*(b*x + c*x^2)^(3/2))/(24*d*e^2*(c*d - b*e)*(d + e*x)^4) + (2*B*c^(3/2)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/e^5 + ((3*A*b^4*e^5 - B*d*(128*c^4*d^4 - 320*b*c^3*d^3*e + 240*b^2*c^2*d^2*e^2 - 40*b^3*c*d*e^3 - 5*b^4*e^4))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(128*d^(5/2)*e^5*(c*d - b*e)^(5/2))","A",7,5,26,0.1923,1,"{810, 843, 620, 206, 724}"
1180,1,269,0,0.2312351,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^6,x]","\frac{3 b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{128 d^3 (d+e x)^2 (c d-b e)^3}-\frac{3 b^4 (A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{256 d^{7/2} (c d-b e)^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{16 d^2 (d+e x)^4 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{5/2} (B d-A e)}{5 d (d+e x)^5 (c d-b e)}","\frac{3 b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{128 d^3 (d+e x)^2 (c d-b e)^3}-\frac{3 b^4 (A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{256 d^{7/2} (c d-b e)^{7/2}}-\frac{\left(b x+c x^2\right)^{3/2} (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{16 d^2 (d+e x)^4 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{5/2} (B d-A e)}{5 d (d+e x)^5 (c d-b e)}",1,"(3*b^2*(b*B*d - 2*A*c*d + A*b*e)*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(128*d^3*(c*d - b*e)^3*(d + e*x)^2) - ((b*B*d - 2*A*c*d + A*b*e)*(b*d + (2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(16*d^2*(c*d - b*e)^2*(d + e*x)^4) + ((B*d - A*e)*(b*x + c*x^2)^(5/2))/(5*d*(c*d - b*e)*(d + e*x)^5) - (3*b^4*(b*B*d - 2*A*c*d + A*b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(256*d^(7/2)*(c*d - b*e)^(7/2))","A",5,4,26,0.1538,1,"{806, 720, 724, 206}"
1181,1,402,0,0.5777448,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^7,x]","-\frac{b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(b^2 e (7 A e+5 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right)}{512 d^4 (d+e x)^2 (c d-b e)^4}+\frac{\left(b x+c x^2\right)^{3/2} (x (2 c d-b e)+b d) \left(b^2 e (7 A e+5 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right)}{192 d^3 (d+e x)^4 (c d-b e)^3}+\frac{b^4 \left(b^2 e (7 A e+5 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{1024 d^{9/2} (c d-b e)^{9/2}}-\frac{\left(b x+c x^2\right)^{5/2} (7 A e (2 c d-b e)-B d (5 b e+2 c d))}{60 d^2 (d+e x)^5 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{5/2} (B d-A e)}{6 d (d+e x)^6 (c d-b e)}","-\frac{b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(b^2 e (7 A e+5 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right)}{512 d^4 (d+e x)^2 (c d-b e)^4}+\frac{\left(b x+c x^2\right)^{3/2} (x (2 c d-b e)+b d) \left(b^2 e (7 A e+5 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right)}{192 d^3 (d+e x)^4 (c d-b e)^3}+\frac{b^4 \left(b^2 e (7 A e+5 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{1024 d^{9/2} (c d-b e)^{9/2}}-\frac{\left(b x+c x^2\right)^{5/2} (7 A e (2 c d-b e)-B d (5 b e+2 c d))}{60 d^2 (d+e x)^5 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{5/2} (B d-A e)}{6 d (d+e x)^6 (c d-b e)}",1,"-(b^2*(24*A*c^2*d^2 - 12*b*c*d*(B*d + 2*A*e) + b^2*e*(5*B*d + 7*A*e))*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(512*d^4*(c*d - b*e)^4*(d + e*x)^2) + ((24*A*c^2*d^2 - 12*b*c*d*(B*d + 2*A*e) + b^2*e*(5*B*d + 7*A*e))*(b*d + (2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(192*d^3*(c*d - b*e)^3*(d + e*x)^4) + ((B*d - A*e)*(b*x + c*x^2)^(5/2))/(6*d*(c*d - b*e)*(d + e*x)^6) - ((7*A*e*(2*c*d - b*e) - B*d*(2*c*d + 5*b*e))*(b*x + c*x^2)^(5/2))/(60*d^2*(c*d - b*e)^2*(d + e*x)^5) + (b^4*(24*A*c^2*d^2 - 12*b*c*d*(B*d + 2*A*e) + b^2*e*(5*B*d + 7*A*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(1024*d^(9/2)*(c*d - b*e)^(9/2))","A",6,5,26,0.1923,1,"{834, 806, 720, 724, 206}"
1182,1,565,0,1.0149039,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^8} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^8,x]","-\frac{b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(2 b^2 c d e (21 A e+10 B d)+b^3 \left(-e^2\right) (9 A e+5 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right)}{1024 d^5 (d+e x)^2 (c d-b e)^5}+\frac{\left(b x+c x^2\right)^{5/2} \left(B d \left(-35 b^2 e^2+90 b c d e+8 c^2 d^2\right)-3 A e \left(21 b^2 e^2-68 b c d e+68 c^2 d^2\right)\right)}{840 d^3 (d+e x)^5 (c d-b e)^3}+\frac{\left(b x+c x^2\right)^{3/2} (x (2 c d-b e)+b d) \left(2 b^2 c d e (21 A e+10 B d)+b^3 \left(-e^2\right) (9 A e+5 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right)}{384 d^4 (d+e x)^4 (c d-b e)^4}+\frac{b^4 \left(2 b^2 c d e (21 A e+10 B d)+b^3 \left(-e^2\right) (9 A e+5 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2048 d^{11/2} (c d-b e)^{11/2}}-\frac{\left(b x+c x^2\right)^{5/2} (9 A e (2 c d-b e)-B d (5 b e+4 c d))}{84 d^2 (d+e x)^6 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{5/2} (B d-A e)}{7 d (d+e x)^7 (c d-b e)}","-\frac{b^2 \sqrt{b x+c x^2} (x (2 c d-b e)+b d) \left(2 b^2 c d e (21 A e+10 B d)+b^3 \left(-e^2\right) (9 A e+5 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right)}{1024 d^5 (d+e x)^2 (c d-b e)^5}+\frac{\left(b x+c x^2\right)^{5/2} \left(B d \left(-35 b^2 e^2+90 b c d e+8 c^2 d^2\right)-3 A e \left(21 b^2 e^2-68 b c d e+68 c^2 d^2\right)\right)}{840 d^3 (d+e x)^5 (c d-b e)^3}+\frac{\left(b x+c x^2\right)^{3/2} (x (2 c d-b e)+b d) \left(2 b^2 c d e (21 A e+10 B d)+b^3 \left(-e^2\right) (9 A e+5 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right)}{384 d^4 (d+e x)^4 (c d-b e)^4}+\frac{b^4 \left(2 b^2 c d e (21 A e+10 B d)+b^3 \left(-e^2\right) (9 A e+5 B d)-24 b c^2 d^2 (3 A e+B d)+48 A c^3 d^3\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2048 d^{11/2} (c d-b e)^{11/2}}-\frac{\left(b x+c x^2\right)^{5/2} (9 A e (2 c d-b e)-B d (5 b e+4 c d))}{84 d^2 (d+e x)^6 (c d-b e)^2}+\frac{\left(b x+c x^2\right)^{5/2} (B d-A e)}{7 d (d+e x)^7 (c d-b e)}",1,"-(b^2*(48*A*c^3*d^3 - 24*b*c^2*d^2*(B*d + 3*A*e) - b^3*e^2*(5*B*d + 9*A*e) + 2*b^2*c*d*e*(10*B*d + 21*A*e))*(b*d + (2*c*d - b*e)*x)*Sqrt[b*x + c*x^2])/(1024*d^5*(c*d - b*e)^5*(d + e*x)^2) + ((48*A*c^3*d^3 - 24*b*c^2*d^2*(B*d + 3*A*e) - b^3*e^2*(5*B*d + 9*A*e) + 2*b^2*c*d*e*(10*B*d + 21*A*e))*(b*d + (2*c*d - b*e)*x)*(b*x + c*x^2)^(3/2))/(384*d^4*(c*d - b*e)^4*(d + e*x)^4) + ((B*d - A*e)*(b*x + c*x^2)^(5/2))/(7*d*(c*d - b*e)*(d + e*x)^7) - ((9*A*e*(2*c*d - b*e) - B*d*(4*c*d + 5*b*e))*(b*x + c*x^2)^(5/2))/(84*d^2*(c*d - b*e)^2*(d + e*x)^6) + ((B*d*(8*c^2*d^2 + 90*b*c*d*e - 35*b^2*e^2) - 3*A*e*(68*c^2*d^2 - 68*b*c*d*e + 21*b^2*e^2))*(b*x + c*x^2)^(5/2))/(840*d^3*(c*d - b*e)^3*(d + e*x)^5) + (b^4*(48*A*c^3*d^3 - 24*b*c^2*d^2*(B*d + 3*A*e) - b^3*e^2*(5*B*d + 9*A*e) + 2*b^2*c*d*e*(10*B*d + 21*A*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2048*d^(11/2)*(c*d - b*e)^(11/2))","A",7,5,26,0.1923,1,"{834, 806, 720, 724, 206}"
1183,1,423,0,0.4332987,"\int (A+B x) (d+e x)^2 \left(b x+c x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^2*(b*x + c*x^2)^(5/2),x]","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{32768 c^6}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{12288 c^5}+\frac{\left(b x+c x^2\right)^{7/2} \left(14 c e x (18 A c e-11 b B e+4 B c d)+18 A c e (32 c d-9 b e)+B \left(99 b^2 e^2-324 b c d e+64 c^2 d^2\right)\right)}{2016 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{768 c^4}-\frac{5 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{32768 c^{13/2}}+\frac{B \left(b x+c x^2\right)^{7/2} (d+e x)^2}{9 c}","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{32768 c^6}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{12288 c^5}+\frac{\left(b x+c x^2\right)^{7/2} \left(14 c e x (18 A c e-11 b B e+4 B c d)+18 A c e (32 c d-9 b e)+B \left(99 b^2 e^2-324 b c d e+64 c^2 d^2\right)\right)}{2016 c^3}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{768 c^4}-\frac{5 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(18 b^2 c e (A e+2 B d)-32 b c^2 d (2 A e+B d)+64 A c^3 d^2-11 b^3 B e^2\right)}{32768 c^{13/2}}+\frac{B \left(b x+c x^2\right)^{7/2} (d+e x)^2}{9 c}",1,"(5*b^4*(64*A*c^3*d^2 - 11*b^3*B*e^2 + 18*b^2*c*e*(2*B*d + A*e) - 32*b*c^2*d*(B*d + 2*A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(32768*c^6) - (5*b^2*(64*A*c^3*d^2 - 11*b^3*B*e^2 + 18*b^2*c*e*(2*B*d + A*e) - 32*b*c^2*d*(B*d + 2*A*e))*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(12288*c^5) + ((64*A*c^3*d^2 - 11*b^3*B*e^2 + 18*b^2*c*e*(2*B*d + A*e) - 32*b*c^2*d*(B*d + 2*A*e))*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(768*c^4) + (B*(d + e*x)^2*(b*x + c*x^2)^(7/2))/(9*c) + ((18*A*c*e*(32*c*d - 9*b*e) + B*(64*c^2*d^2 - 324*b*c*d*e + 99*b^2*e^2) + 14*c*e*(4*B*c*d - 11*b*B*e + 18*A*c*e)*x)*(b*x + c*x^2)^(7/2))/(2016*c^3) - (5*b^6*(64*A*c^3*d^2 - 11*b^3*B*e^2 + 18*b^2*c*e*(2*B*d + A*e) - 32*b*c^2*d*(B*d + 2*A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(32768*c^(13/2))","A",7,5,26,0.1923,1,"{832, 779, 612, 620, 206}"
1184,1,264,0,0.2499381,"\int (A+B x) (d+e x) \left(b x+c x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)*(b*x + c*x^2)^(5/2),x]","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{16384 c^5}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{6144 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{384 c^3}-\frac{5 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{16384 c^{11/2}}-\frac{\left(b x+c x^2\right)^{7/2} (-16 c (A e+B d)+9 b B e-14 B c e x)}{112 c^2}","\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{16384 c^5}-\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{6144 c^4}+\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{384 c^3}-\frac{5 b^6 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-16 b c (A e+B d)+32 A c^2 d+9 b^2 B e\right)}{16384 c^{11/2}}-\frac{\left(b x+c x^2\right)^{7/2} (-16 c (A e+B d)+9 b B e-14 B c e x)}{112 c^2}",1,"(5*b^4*(32*A*c^2*d + 9*b^2*B*e - 16*b*c*(B*d + A*e))*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(16384*c^5) - (5*b^2*(32*A*c^2*d + 9*b^2*B*e - 16*b*c*(B*d + A*e))*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(6144*c^4) + ((32*A*c^2*d + 9*b^2*B*e - 16*b*c*(B*d + A*e))*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(384*c^3) - ((9*b*B*e - 16*c*(B*d + A*e) - 14*B*c*e*x)*(b*x + c*x^2)^(7/2))/(112*c^2) - (5*b^6*(32*A*c^2*d + 9*b^2*B*e - 16*b*c*(B*d + A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(16384*c^(11/2))","A",6,4,24,0.1667,1,"{779, 612, 620, 206}"
1185,1,171,0,0.0729027,"\int (A+B x) \left(b x+c x^2\right)^{5/2} \, dx","Int[(A + B*x)*(b*x + c*x^2)^(5/2),x]","-\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{1024 c^4}+\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}+\frac{5 b^6 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (b B-2 A c)}{24 c^2}+\frac{B \left(b x+c x^2\right)^{7/2}}{7 c}","-\frac{5 b^4 (b+2 c x) \sqrt{b x+c x^2} (b B-2 A c)}{1024 c^4}+\frac{5 b^2 (b+2 c x) \left(b x+c x^2\right)^{3/2} (b B-2 A c)}{384 c^3}+\frac{5 b^6 (b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{1024 c^{9/2}}-\frac{(b+2 c x) \left(b x+c x^2\right)^{5/2} (b B-2 A c)}{24 c^2}+\frac{B \left(b x+c x^2\right)^{7/2}}{7 c}",1,"(-5*b^4*(b*B - 2*A*c)*(b + 2*c*x)*Sqrt[b*x + c*x^2])/(1024*c^4) + (5*b^2*(b*B - 2*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(3/2))/(384*c^3) - ((b*B - 2*A*c)*(b + 2*c*x)*(b*x + c*x^2)^(5/2))/(24*c^2) + (B*(b*x + c*x^2)^(7/2))/(7*c) + (5*b^6*(b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(1024*c^(9/2))","A",6,4,19,0.2105,1,"{640, 612, 620, 206}"
1186,1,703,0,1.1249551,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{d+e x} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x),x]","\frac{\left(b x+c x^2\right)^{3/2} \left(-2 c e x \left(12 A c e (2 c d-b e)-B \left(-5 b^2 e^2-12 b c d e+24 c^2 d^2\right)\right)+4 A c e \left(3 b^2 e^2-22 b c d e+16 c^2 d^2\right)-B \left(12 b^2 c d e^2+5 b^3 e^3-88 b c^2 d^2 e+64 c^3 d^3\right)\right)}{192 c^2 e^4}+\frac{\sqrt{b x+c x^2} \left(3 \left(4 A c e \left(176 b^2 c^2 d^2 e^2-10 b^3 c d e^3-3 b^4 e^4-288 b c^3 d^3 e+128 c^4 d^4\right)-B \left(704 b^2 c^3 d^3 e^2-40 b^3 c^2 d^2 e^3-12 b^4 c d e^4-5 b^5 e^5-1152 b c^4 d^4 e+512 c^5 d^5\right)\right)-2 c e x \left(\left(-3 b^2 e^2-8 b c d e+16 c^2 d^2\right) \left(12 A c e (2 c d-b e)-B \left(-5 b^2 e^2-12 b c d e+24 c^2 d^2\right)\right)+8 b c d e (2 c d-b e) (-12 A c e-5 b B e+12 B c d)\right)\right)}{1536 c^3 e^6}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e \left(480 b^2 c^3 d^3 e^2-80 b^3 c^2 d^2 e^3-10 b^4 c d e^4-3 b^5 e^5-640 b c^4 d^4 e+256 c^5 d^5\right)-B \left(1920 b^2 c^4 d^4 e^2-320 b^3 c^3 d^3 e^3-40 b^4 c^2 d^2 e^4-12 b^5 c d e^5-5 b^6 e^6-2560 b c^5 d^5 e+1024 c^6 d^6\right)\right)}{512 c^{7/2} e^7}-\frac{d^{5/2} (B d-A e) (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^7}-\frac{\left(b x+c x^2\right)^{5/2} (-12 A c e-5 b B e+12 B c d-10 B c e x)}{60 c e^2}","\frac{\left(b x+c x^2\right)^{3/2} \left(-2 c e x \left(12 A c e (2 c d-b e)-B \left(-5 b^2 e^2-12 b c d e+24 c^2 d^2\right)\right)+4 A c e \left(3 b^2 e^2-22 b c d e+16 c^2 d^2\right)-B \left(12 b^2 c d e^2+5 b^3 e^3-88 b c^2 d^2 e+64 c^3 d^3\right)\right)}{192 c^2 e^4}+\frac{\sqrt{b x+c x^2} \left(3 \left(4 A c e \left(176 b^2 c^2 d^2 e^2-10 b^3 c d e^3-3 b^4 e^4-288 b c^3 d^3 e+128 c^4 d^4\right)-B \left(704 b^2 c^3 d^3 e^2-40 b^3 c^2 d^2 e^3-12 b^4 c d e^4-5 b^5 e^5-1152 b c^4 d^4 e+512 c^5 d^5\right)\right)-2 c e x \left(\left(-3 b^2 e^2-8 b c d e+16 c^2 d^2\right) \left(12 A c e (2 c d-b e)-B \left(-5 b^2 e^2-12 b c d e+24 c^2 d^2\right)\right)+8 b c d e (2 c d-b e) (-12 A c e-5 b B e+12 B c d)\right)\right)}{1536 c^3 e^6}-\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e \left(480 b^2 c^3 d^3 e^2-80 b^3 c^2 d^2 e^3-10 b^4 c d e^4-3 b^5 e^5-640 b c^4 d^4 e+256 c^5 d^5\right)-B \left(1920 b^2 c^4 d^4 e^2-320 b^3 c^3 d^3 e^3-40 b^4 c^2 d^2 e^4-12 b^5 c d e^5-5 b^6 e^6-2560 b c^5 d^5 e+1024 c^6 d^6\right)\right)}{512 c^{7/2} e^7}-\frac{d^{5/2} (B d-A e) (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{e^7}-\frac{\left(b x+c x^2\right)^{5/2} (-12 A c e-5 b B e+12 B c d-10 B c e x)}{60 c e^2}",1,"((3*(4*A*c*e*(128*c^4*d^4 - 288*b*c^3*d^3*e + 176*b^2*c^2*d^2*e^2 - 10*b^3*c*d*e^3 - 3*b^4*e^4) - B*(512*c^5*d^5 - 1152*b*c^4*d^4*e + 704*b^2*c^3*d^3*e^2 - 40*b^3*c^2*d^2*e^3 - 12*b^4*c*d*e^4 - 5*b^5*e^5)) - 2*c*e*(8*b*c*d*e*(2*c*d - b*e)*(12*B*c*d - 5*b*B*e - 12*A*c*e) + (16*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2)*(12*A*c*e*(2*c*d - b*e) - B*(24*c^2*d^2 - 12*b*c*d*e - 5*b^2*e^2)))*x)*Sqrt[b*x + c*x^2])/(1536*c^3*e^6) + ((4*A*c*e*(16*c^2*d^2 - 22*b*c*d*e + 3*b^2*e^2) - B*(64*c^3*d^3 - 88*b*c^2*d^2*e + 12*b^2*c*d*e^2 + 5*b^3*e^3) - 2*c*e*(12*A*c*e*(2*c*d - b*e) - B*(24*c^2*d^2 - 12*b*c*d*e - 5*b^2*e^2))*x)*(b*x + c*x^2)^(3/2))/(192*c^2*e^4) - ((12*B*c*d - 5*b*B*e - 12*A*c*e - 10*B*c*e*x)*(b*x + c*x^2)^(5/2))/(60*c*e^2) - ((4*A*c*e*(256*c^5*d^5 - 640*b*c^4*d^4*e + 480*b^2*c^3*d^3*e^2 - 80*b^3*c^2*d^2*e^3 - 10*b^4*c*d*e^4 - 3*b^5*e^5) - B*(1024*c^6*d^6 - 2560*b*c^5*d^5*e + 1920*b^2*c^4*d^4*e^2 - 320*b^3*c^3*d^3*e^3 - 40*b^4*c^2*d^2*e^4 - 12*b^5*c*d*e^5 - 5*b^6*e^6))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(512*c^(7/2)*e^7) - (d^(5/2)*(B*d - A*e)*(c*d - b*e)^(5/2)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/e^7","A",8,5,26,0.1923,1,"{814, 843, 620, 206, 724}"
1187,1,574,0,0.9275765,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^2,x]","-\frac{\left(b x+c x^2\right)^{3/2} \left(6 c e x (-10 A c e-b B e+12 B c d)+10 A c e (8 c d-7 b e)-B \left(3 b^2 e^2-92 b c d e+96 c^2 d^2\right)\right)}{48 c e^4}-\frac{\sqrt{b x+c x^2} \left(-2 c e x \left(8 b c e (6 B d-5 A e) (2 c d-b e)-\left(-3 b^2 e^2-8 b c d e+16 c^2 d^2\right) (-10 A c e-b B e+12 B c d)\right)+10 A c e \left(48 b^2 c d e^2-b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)-B \left(656 b^2 c^2 d^2 e^2-20 b^3 c d e^3-3 b^4 e^4-1408 b c^3 d^3 e+768 c^4 d^4\right)\right)}{128 c^2 e^6}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(10 A c e \left(144 b^2 c^2 d^2 e^2-16 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right)-B \left(1920 b^2 c^3 d^3 e^2-240 b^3 c^2 d^2 e^3-20 b^4 c d e^4-3 b^5 e^5-3200 b c^4 d^4 e+1536 c^5 d^5\right)\right)}{128 c^{5/2} e^7}+\frac{d^{3/2} (c d-b e)^{3/2} (B d (12 c d-7 b e)-5 A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^7}+\frac{\left(b x+c x^2\right)^{5/2} (-5 A e+6 B d+B e x)}{5 e^2 (d+e x)}","-\frac{\left(b x+c x^2\right)^{3/2} \left(6 c e x (-10 A c e-b B e+12 B c d)+10 A c e (8 c d-7 b e)-B \left(3 b^2 e^2-92 b c d e+96 c^2 d^2\right)\right)}{48 c e^4}-\frac{\sqrt{b x+c x^2} \left(-2 c e x \left(8 b c e (6 B d-5 A e) (2 c d-b e)-\left(-3 b^2 e^2-8 b c d e+16 c^2 d^2\right) (-10 A c e-b B e+12 B c d)\right)+10 A c e \left(48 b^2 c d e^2-b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)-B \left(656 b^2 c^2 d^2 e^2-20 b^3 c d e^3-3 b^4 e^4-1408 b c^3 d^3 e+768 c^4 d^4\right)\right)}{128 c^2 e^6}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(10 A c e \left(144 b^2 c^2 d^2 e^2-16 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right)-B \left(1920 b^2 c^3 d^3 e^2-240 b^3 c^2 d^2 e^3-20 b^4 c d e^4-3 b^5 e^5-3200 b c^4 d^4 e+1536 c^5 d^5\right)\right)}{128 c^{5/2} e^7}+\frac{d^{3/2} (c d-b e)^{3/2} (B d (12 c d-7 b e)-5 A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 e^7}+\frac{\left(b x+c x^2\right)^{5/2} (-5 A e+6 B d+B e x)}{5 e^2 (d+e x)}",1,"-((10*A*c*e*(64*c^3*d^3 - 112*b*c^2*d^2*e + 48*b^2*c*d*e^2 - b^3*e^3) - B*(768*c^4*d^4 - 1408*b*c^3*d^3*e + 656*b^2*c^2*d^2*e^2 - 20*b^3*c*d*e^3 - 3*b^4*e^4) - 2*c*e*(8*b*c*e*(6*B*d - 5*A*e)*(2*c*d - b*e) - (12*B*c*d - b*B*e - 10*A*c*e)*(16*c^2*d^2 - 8*b*c*d*e - 3*b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(128*c^2*e^6) - ((10*A*c*e*(8*c*d - 7*b*e) - B*(96*c^2*d^2 - 92*b*c*d*e + 3*b^2*e^2) + 6*c*e*(12*B*c*d - b*B*e - 10*A*c*e)*x)*(b*x + c*x^2)^(3/2))/(48*c*e^4) + ((6*B*d - 5*A*e + B*e*x)*(b*x + c*x^2)^(5/2))/(5*e^2*(d + e*x)) + ((10*A*c*e*(128*c^4*d^4 - 256*b*c^3*d^3*e + 144*b^2*c^2*d^2*e^2 - 16*b^3*c*d*e^3 - b^4*e^4) - B*(1536*c^5*d^5 - 3200*b*c^4*d^4*e + 1920*b^2*c^3*d^3*e^2 - 240*b^3*c^2*d^2*e^3 - 20*b^4*c*d*e^4 - 3*b^5*e^5))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(128*c^(5/2)*e^7) + (d^(3/2)*(c*d - b*e)^(3/2)*(B*d*(12*c*d - 7*b*e) - 5*A*e*(2*c*d - b*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*e^7)","A",8,6,26,0.2308,1,"{812, 814, 843, 620, 206, 724}"
1188,1,508,0,0.7476491,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^3,x]","\frac{5 \sqrt{b x+c x^2} \left(-2 c e x \left(16 A c e (2 c d-b e)-B \left(b^2 e^2-32 b c d e+48 c^2 d^2\right)\right)+8 A c e \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right)-B \left(88 b^2 c d e^2-b^3 e^3-272 b c^2 d^2 e+192 c^3 d^3\right)\right)}{64 c e^6}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(8 A c e \left(18 b^2 c d e^2-b^3 e^3-48 b c^2 d^2 e+32 c^3 d^3\right)-B \left(288 b^2 c^2 d^2 e^2-24 b^3 c d e^3-b^4 e^4-640 b c^3 d^3 e+384 c^4 d^4\right)\right)}{64 c^{3/2} e^7}+\frac{5 \sqrt{d} \sqrt{c d-b e} \left(A e \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(7 b^2 e^2-28 b c d e+24 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 e^7}+\frac{\left(b x+c x^2\right)^{5/2} (-2 A e+3 B d+B e x)}{4 e^2 (d+e x)^2}-\frac{5 \left(b x+c x^2\right)^{3/2} (e x (-4 A c e-b B e+6 B c d)-2 A e (8 c d-3 b e)+B d (24 c d-13 b e))}{24 e^4 (d+e x)}","\frac{5 \sqrt{b x+c x^2} \left(-2 c e x \left(16 A c e (2 c d-b e)-B \left(b^2 e^2-32 b c d e+48 c^2 d^2\right)\right)+8 A c e \left(5 b^2 e^2-20 b c d e+16 c^2 d^2\right)-B \left(88 b^2 c d e^2-b^3 e^3-272 b c^2 d^2 e+192 c^3 d^3\right)\right)}{64 c e^6}-\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(8 A c e \left(18 b^2 c d e^2-b^3 e^3-48 b c^2 d^2 e+32 c^3 d^3\right)-B \left(288 b^2 c^2 d^2 e^2-24 b^3 c d e^3-b^4 e^4-640 b c^3 d^3 e+384 c^4 d^4\right)\right)}{64 c^{3/2} e^7}+\frac{5 \sqrt{d} \sqrt{c d-b e} \left(A e \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(7 b^2 e^2-28 b c d e+24 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 e^7}+\frac{\left(b x+c x^2\right)^{5/2} (-2 A e+3 B d+B e x)}{4 e^2 (d+e x)^2}-\frac{5 \left(b x+c x^2\right)^{3/2} (e x (-4 A c e-b B e+6 B c d)-2 A e (8 c d-3 b e)+B d (24 c d-13 b e))}{24 e^4 (d+e x)}",1,"(5*(8*A*c*e*(16*c^2*d^2 - 20*b*c*d*e + 5*b^2*e^2) - B*(192*c^3*d^3 - 272*b*c^2*d^2*e + 88*b^2*c*d*e^2 - b^3*e^3) - 2*c*e*(16*A*c*e*(2*c*d - b*e) - B*(48*c^2*d^2 - 32*b*c*d*e + b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(64*c*e^6) - (5*(B*d*(24*c*d - 13*b*e) - 2*A*e*(8*c*d - 3*b*e) + e*(6*B*c*d - b*B*e - 4*A*c*e)*x)*(b*x + c*x^2)^(3/2))/(24*e^4*(d + e*x)) + ((3*B*d - 2*A*e + B*e*x)*(b*x + c*x^2)^(5/2))/(4*e^2*(d + e*x)^2) - (5*(8*A*c*e*(32*c^3*d^3 - 48*b*c^2*d^2*e + 18*b^2*c*d*e^2 - b^3*e^3) - B*(384*c^4*d^4 - 640*b*c^3*d^3*e + 288*b^2*c^2*d^2*e^2 - 24*b^3*c*d*e^3 - b^4*e^4))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(3/2)*e^7) + (5*Sqrt[d]*Sqrt[c*d - b*e]*(A*e*(16*c^2*d^2 - 16*b*c*d*e + 3*b^2*e^2) - B*d*(24*c^2*d^2 - 28*b*c*d*e + 7*b^2*e^2))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*e^7)","A",8,6,26,0.2308,1,"{812, 814, 843, 620, 206, 724}"
1189,1,495,0,0.6621048,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{5 \sqrt{b x+c x^2} \left(e x \left(4 A c e (2 c d-b e)-B \left(b^2 e^2-12 b c d e+16 c^2 d^2\right)\right)+A e \left(b^2 e^2-12 b c d e+16 c^2 d^2\right)-2 B d \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)\right)}{8 e^6 (d+e x)}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(2 A c e \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)-B \left(24 b^2 c d e^2-b^3 e^3-80 b c^2 d^2 e+64 c^3 d^3\right)\right)}{8 \sqrt{c} e^7}+\frac{5 \left(B d \left(56 b^2 c d e^2-7 b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)-A e \left(18 b^2 c d e^2-b^3 e^3-48 b c^2 d^2 e+32 c^3 d^3\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 \sqrt{d} e^7 \sqrt{c d-b e}}+\frac{\left(b x+c x^2\right)^{5/2} (-A e+2 B d+B e x)}{3 e^2 (d+e x)^3}-\frac{5 \left(b x+c x^2\right)^{3/2} (e x (-2 A c e-b B e+4 B c d)-A e (4 c d-b e)+4 B d (2 c d-b e))}{12 e^4 (d+e x)^2}","-\frac{5 \sqrt{b x+c x^2} \left(e x \left(4 A c e (2 c d-b e)-B \left(b^2 e^2-12 b c d e+16 c^2 d^2\right)\right)+A e \left(b^2 e^2-12 b c d e+16 c^2 d^2\right)-2 B d \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)\right)}{8 e^6 (d+e x)}+\frac{5 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(2 A c e \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)-B \left(24 b^2 c d e^2-b^3 e^3-80 b c^2 d^2 e+64 c^3 d^3\right)\right)}{8 \sqrt{c} e^7}+\frac{5 \left(B d \left(56 b^2 c d e^2-7 b^3 e^3-112 b c^2 d^2 e+64 c^3 d^3\right)-A e \left(18 b^2 c d e^2-b^3 e^3-48 b c^2 d^2 e+32 c^3 d^3\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 \sqrt{d} e^7 \sqrt{c d-b e}}+\frac{\left(b x+c x^2\right)^{5/2} (-A e+2 B d+B e x)}{3 e^2 (d+e x)^3}-\frac{5 \left(b x+c x^2\right)^{3/2} (e x (-2 A c e-b B e+4 B c d)-A e (4 c d-b e)+4 B d (2 c d-b e))}{12 e^4 (d+e x)^2}",1,"(-5*(A*e*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2) - 2*B*d*(16*c^2*d^2 - 16*b*c*d*e + 3*b^2*e^2) + e*(4*A*c*e*(2*c*d - b*e) - B*(16*c^2*d^2 - 12*b*c*d*e + b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(8*e^6*(d + e*x)) - (5*(4*B*d*(2*c*d - b*e) - A*e*(4*c*d - b*e) + e*(4*B*c*d - b*B*e - 2*A*c*e)*x)*(b*x + c*x^2)^(3/2))/(12*e^4*(d + e*x)^2) + ((2*B*d - A*e + B*e*x)*(b*x + c*x^2)^(5/2))/(3*e^2*(d + e*x)^3) + (5*(2*A*c*e*(16*c^2*d^2 - 16*b*c*d*e + 3*b^2*e^2) - B*(64*c^3*d^3 - 80*b*c^2*d^2*e + 24*b^2*c*d*e^2 - b^3*e^3))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*Sqrt[c]*e^7) + (5*(B*d*(64*c^3*d^3 - 112*b*c^2*d^2*e + 56*b^2*c*d*e^2 - 7*b^3*e^3) - A*e*(32*c^3*d^3 - 48*b*c^2*d^2*e + 18*b^2*c*d*e^2 - b^3*e^3))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(16*Sqrt[d]*e^7*Sqrt[c*d - b*e])","A",8,5,26,0.1923,1,"{812, 843, 620, 206, 724}"
1190,1,633,0,0.9023759,"\int \frac{(A+B x) \left(b x+c x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(5/2))/(d + e*x)^5,x]","-\frac{5 \left(b x+c x^2\right)^{3/2} \left(3 e x \left(A e \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)-B d \left(9 b^2 e^2-32 b c d e+24 c^2 d^2\right)\right)+d \left(A e \left(-b^2 e^2-12 b c d e+16 c^2 d^2\right)-B d \left(7 b^2 e^2-52 b c d e+48 c^2 d^2\right)\right)\right)}{96 d e^4 (d+e x)^3 (c d-b e)}-\frac{5 \sqrt{b x+c x^2} \left(-2 c e x \left(A e \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(17 b^2 e^2-64 b c d e+48 c^2 d^2\right)\right)-A e \left(16 b^2 c d e^2+b^3 e^3-80 b c^2 d^2 e+64 c^3 d^3\right)+B d \left(120 b^2 c d e^2-7 b^3 e^3-304 b c^2 d^2 e+192 c^3 d^3\right)\right)}{64 d e^6 (d+e x) (c d-b e)}-\frac{5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)-B \left(3 b^2 e^2-20 b c d e+24 c^2 d^2\right)\right)}{4 e^7}+\frac{5 \left(A e \left(144 b^2 c^2 d^2 e^2-16 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right)-B d \left(672 b^2 c^2 d^2 e^2-168 b^3 c d e^3+7 b^4 e^4-896 b c^3 d^3 e+384 c^4 d^4\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{3/2} e^7 (c d-b e)^{3/2}}+\frac{\left(b x+c x^2\right)^{5/2} (-A e+3 B d+2 B e x)}{4 e^2 (d+e x)^4}","-\frac{5 \left(b x+c x^2\right)^{3/2} \left(3 e x \left(A e \left(b^2 e^2-8 b c d e+8 c^2 d^2\right)-B d \left(9 b^2 e^2-32 b c d e+24 c^2 d^2\right)\right)+d \left(A e \left(-b^2 e^2-12 b c d e+16 c^2 d^2\right)-B d \left(7 b^2 e^2-52 b c d e+48 c^2 d^2\right)\right)\right)}{96 d e^4 (d+e x)^3 (c d-b e)}-\frac{5 \sqrt{b x+c x^2} \left(-2 c e x \left(A e \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(17 b^2 e^2-64 b c d e+48 c^2 d^2\right)\right)-A e \left(16 b^2 c d e^2+b^3 e^3-80 b c^2 d^2 e+64 c^3 d^3\right)+B d \left(120 b^2 c d e^2-7 b^3 e^3-304 b c^2 d^2 e+192 c^3 d^3\right)\right)}{64 d e^6 (d+e x) (c d-b e)}-\frac{5 \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)-B \left(3 b^2 e^2-20 b c d e+24 c^2 d^2\right)\right)}{4 e^7}+\frac{5 \left(A e \left(144 b^2 c^2 d^2 e^2-16 b^3 c d e^3-b^4 e^4-256 b c^3 d^3 e+128 c^4 d^4\right)-B d \left(672 b^2 c^2 d^2 e^2-168 b^3 c d e^3+7 b^4 e^4-896 b c^3 d^3 e+384 c^4 d^4\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{128 d^{3/2} e^7 (c d-b e)^{3/2}}+\frac{\left(b x+c x^2\right)^{5/2} (-A e+3 B d+2 B e x)}{4 e^2 (d+e x)^4}",1,"(-5*(B*d*(192*c^3*d^3 - 304*b*c^2*d^2*e + 120*b^2*c*d*e^2 - 7*b^3*e^3) - A*e*(64*c^3*d^3 - 80*b*c^2*d^2*e + 16*b^2*c*d*e^2 + b^3*e^3) - 2*c*e*(A*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2) - B*d*(48*c^2*d^2 - 64*b*c*d*e + 17*b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(64*d*e^6*(c*d - b*e)*(d + e*x)) - (5*(d*(A*e*(16*c^2*d^2 - 12*b*c*d*e - b^2*e^2) - B*d*(48*c^2*d^2 - 52*b*c*d*e + 7*b^2*e^2)) + 3*e*(A*e*(8*c^2*d^2 - 8*b*c*d*e + b^2*e^2) - B*d*(24*c^2*d^2 - 32*b*c*d*e + 9*b^2*e^2))*x)*(b*x + c*x^2)^(3/2))/(96*d*e^4*(c*d - b*e)*(d + e*x)^3) + ((3*B*d - A*e + 2*B*e*x)*(b*x + c*x^2)^(5/2))/(4*e^2*(d + e*x)^4) - (5*Sqrt[c]*(4*A*c*e*(2*c*d - b*e) - B*(24*c^2*d^2 - 20*b*c*d*e + 3*b^2*e^2))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*e^7) + (5*(A*e*(128*c^4*d^4 - 256*b*c^3*d^3*e + 144*b^2*c^2*d^2*e^2 - 16*b^3*c*d*e^3 - b^4*e^4) - B*d*(384*c^4*d^4 - 896*b*c^3*d^3*e + 672*b^2*c^2*d^2*e^2 - 168*b^3*c*d*e^3 + 7*b^4*e^4))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(128*d^(3/2)*e^7*(c*d - b*e)^(3/2))","A",8,6,26,0.2308,1,"{812, 810, 843, 620, 206, 724}"
1191,1,305,0,0.4425334,"\int \frac{(A+B x) (d+e x)^3}{\sqrt{b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{b x+c x^2} \left(2 c e x \left(40 A c e (2 c d-b e)+B \left(35 b^2 e^2-64 b c d e+24 c^2 d^2\right)\right)+8 A c e \left(15 b^2 e^2-54 b c d e+64 c^2 d^2\right)+B \left(360 b^2 c d e^2-105 b^3 e^3-376 b c^2 d^2 e+96 c^3 d^3\right)\right)}{192 c^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(144 b^2 c^2 d e (A e+B d)-40 b^3 c e^2 (A e+3 B d)-64 b c^3 d^2 (3 A e+B d)+128 A c^4 d^3+35 b^4 B e^3\right)}{64 c^{9/2}}+\frac{\sqrt{b x+c x^2} (d+e x)^2 (8 A c e-7 b B e+6 B c d)}{24 c^2}+\frac{B \sqrt{b x+c x^2} (d+e x)^3}{4 c}","\frac{\sqrt{b x+c x^2} \left(2 c e x \left(40 A c e (2 c d-b e)+B \left(35 b^2 e^2-64 b c d e+24 c^2 d^2\right)\right)+8 A c e \left(15 b^2 e^2-54 b c d e+64 c^2 d^2\right)+B \left(360 b^2 c d e^2-105 b^3 e^3-376 b c^2 d^2 e+96 c^3 d^3\right)\right)}{192 c^4}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(144 b^2 c^2 d e (A e+B d)-40 b^3 c e^2 (A e+3 B d)-64 b c^3 d^2 (3 A e+B d)+128 A c^4 d^3+35 b^4 B e^3\right)}{64 c^{9/2}}+\frac{\sqrt{b x+c x^2} (d+e x)^2 (8 A c e-7 b B e+6 B c d)}{24 c^2}+\frac{B \sqrt{b x+c x^2} (d+e x)^3}{4 c}",1,"((6*B*c*d - 7*b*B*e + 8*A*c*e)*(d + e*x)^2*Sqrt[b*x + c*x^2])/(24*c^2) + (B*(d + e*x)^3*Sqrt[b*x + c*x^2])/(4*c) + ((8*A*c*e*(64*c^2*d^2 - 54*b*c*d*e + 15*b^2*e^2) + B*(96*c^3*d^3 - 376*b*c^2*d^2*e + 360*b^2*c*d*e^2 - 105*b^3*e^3) + 2*c*e*(40*A*c*e*(2*c*d - b*e) + B*(24*c^2*d^2 - 64*b*c*d*e + 35*b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(192*c^4) + ((128*A*c^4*d^3 + 35*b^4*B*e^3 + 144*b^2*c^2*d*e*(B*d + A*e) - 40*b^3*c*e^2*(3*B*d + A*e) - 64*b*c^3*d^2*(B*d + 3*A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(64*c^(9/2))","A",5,4,26,0.1538,1,"{832, 779, 620, 206}"
1192,1,189,0,0.1904465,"\int \frac{(A+B x) (d+e x)^2}{\sqrt{b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/Sqrt[b*x + c*x^2],x]","\frac{\sqrt{b x+c x^2} \left(2 c e x (6 A c e-5 b B e+4 B c d)+6 A c e (8 c d-3 b e)+B \left(15 b^2 e^2-36 b c d e+16 c^2 d^2\right)\right)}{24 c^3}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(6 b^2 c e (A e+2 B d)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2-5 b^3 B e^2\right)}{8 c^{7/2}}+\frac{B \sqrt{b x+c x^2} (d+e x)^2}{3 c}","\frac{\sqrt{b x+c x^2} \left(2 c e x (6 A c e-5 b B e+4 B c d)+6 A c e (8 c d-3 b e)+B \left(15 b^2 e^2-36 b c d e+16 c^2 d^2\right)\right)}{24 c^3}+\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(6 b^2 c e (A e+2 B d)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2-5 b^3 B e^2\right)}{8 c^{7/2}}+\frac{B \sqrt{b x+c x^2} (d+e x)^2}{3 c}",1,"(B*(d + e*x)^2*Sqrt[b*x + c*x^2])/(3*c) + ((6*A*c*e*(8*c*d - 3*b*e) + B*(16*c^2*d^2 - 36*b*c*d*e + 15*b^2*e^2) + 2*c*e*(4*B*c*d - 5*b*B*e + 6*A*c*e)*x)*Sqrt[b*x + c*x^2])/(24*c^3) + ((16*A*c^3*d^2 - 5*b^3*B*e^2 + 6*b^2*c*e*(2*B*d + A*e) - 8*b*c^2*d*(B*d + 2*A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(8*c^(7/2))","A",4,4,26,0.1538,1,"{832, 779, 620, 206}"
1193,1,99,0,0.075848,"\int \frac{(A+B x) (d+e x)}{\sqrt{b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x))/Sqrt[b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-4 b c (A e+B d)+8 A c^2 d+3 b^2 B e\right)}{4 c^{5/2}}-\frac{\sqrt{b x+c x^2} (-4 c (A e+B d)+3 b B e-2 B c e x)}{4 c^2}","\frac{\tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(-4 b c (A e+B d)+8 A c^2 d+3 b^2 B e\right)}{4 c^{5/2}}-\frac{\sqrt{b x+c x^2} (-4 c (A e+B d)+3 b B e-2 B c e x)}{4 c^2}",1,"-((3*b*B*e - 4*c*(B*d + A*e) - 2*B*c*e*x)*Sqrt[b*x + c*x^2])/(4*c^2) + ((8*A*c^2*d + 3*b^2*B*e - 4*b*c*(B*d + A*e))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(5/2))","A",3,3,24,0.1250,1,"{779, 620, 206}"
1194,1,55,0,0.0332168,"\int \frac{A+B x}{\sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/Sqrt[b*x + c*x^2],x]","\frac{B \sqrt{b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}","\frac{B \sqrt{b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}",1,"(B*Sqrt[b*x + c*x^2])/c - ((b*B - 2*A*c)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,19,0.1579,1,"{640, 620, 206}"
1195,1,113,0,0.0816045,"\int \frac{A+B x}{(d+e x) \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)*Sqrt[b*x + c*x^2]),x]","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c} e}-\frac{(B d-A e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{\sqrt{d} e \sqrt{c d-b e}}","\frac{2 B \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{\sqrt{c} e}-\frac{(B d-A e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{\sqrt{d} e \sqrt{c d-b e}}",1,"(2*B*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(Sqrt[c]*e) - ((B*d - A*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(Sqrt[d]*e*Sqrt[c*d - b*e])","A",5,4,26,0.1538,1,"{843, 620, 206, 724}"
1196,1,128,0,0.0848131,"\int \frac{A+B x}{(d+e x)^2 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^2*Sqrt[b*x + c*x^2]),x]","\frac{\sqrt{b x+c x^2} (B d-A e)}{d (d+e x) (c d-b e)}-\frac{(A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{3/2} (c d-b e)^{3/2}}","\frac{\sqrt{b x+c x^2} (B d-A e)}{d (d+e x) (c d-b e)}-\frac{(A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{3/2} (c d-b e)^{3/2}}",1,"((B*d - A*e)*Sqrt[b*x + c*x^2])/(d*(c*d - b*e)*(d + e*x)) - ((b*B*d - 2*A*c*d + A*b*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*d^(3/2)*(c*d - b*e)^(3/2))","A",3,3,26,0.1154,1,"{806, 724, 206}"
1197,1,216,0,0.2632831,"\int \frac{A+B x}{(d+e x)^3 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^3*Sqrt[b*x + c*x^2]),x]","\frac{\left(b^2 e (3 A e+B d)-4 b c d (2 A e+B d)+8 A c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{5/2} (c d-b e)^{5/2}}-\frac{\sqrt{b x+c x^2} (3 A e (2 c d-b e)-B d (b e+2 c d))}{4 d^2 (d+e x) (c d-b e)^2}+\frac{\sqrt{b x+c x^2} (B d-A e)}{2 d (d+e x)^2 (c d-b e)}","\frac{\left(b^2 e (3 A e+B d)-4 b c d (2 A e+B d)+8 A c^2 d^2\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{5/2} (c d-b e)^{5/2}}-\frac{\sqrt{b x+c x^2} (3 A e (2 c d-b e)-B d (b e+2 c d))}{4 d^2 (d+e x) (c d-b e)^2}+\frac{\sqrt{b x+c x^2} (B d-A e)}{2 d (d+e x)^2 (c d-b e)}",1,"((B*d - A*e)*Sqrt[b*x + c*x^2])/(2*d*(c*d - b*e)*(d + e*x)^2) - ((3*A*e*(2*c*d - b*e) - B*d*(2*c*d + b*e))*Sqrt[b*x + c*x^2])/(4*d^2*(c*d - b*e)^2*(d + e*x)) + ((8*A*c^2*d^2 - 4*b*c*d*(B*d + 2*A*e) + b^2*e*(B*d + 3*A*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*d^(5/2)*(c*d - b*e)^(5/2))","A",4,4,26,0.1538,1,"{834, 806, 724, 206}"
1198,1,331,0,0.4974108,"\int \frac{A+B x}{(d+e x)^4 \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^4*Sqrt[b*x + c*x^2]),x]","\frac{\sqrt{b x+c x^2} \left(B d \left(-3 b^2 e^2+10 b c d e+8 c^2 d^2\right)-A e \left(15 b^2 e^2-44 b c d e+44 c^2 d^2\right)\right)}{24 d^3 (d+e x) (c d-b e)^3}+\frac{\left(2 b^2 c d e (9 A e+2 B d)+b^3 \left(-e^2\right) (5 A e+B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{7/2} (c d-b e)^{7/2}}-\frac{\sqrt{b x+c x^2} (5 A e (2 c d-b e)-B d (b e+4 c d))}{12 d^2 (d+e x)^2 (c d-b e)^2}+\frac{\sqrt{b x+c x^2} (B d-A e)}{3 d (d+e x)^3 (c d-b e)}","\frac{\sqrt{b x+c x^2} \left(B d \left(-3 b^2 e^2+10 b c d e+8 c^2 d^2\right)-A e \left(15 b^2 e^2-44 b c d e+44 c^2 d^2\right)\right)}{24 d^3 (d+e x) (c d-b e)^3}+\frac{\left(2 b^2 c d e (9 A e+2 B d)+b^3 \left(-e^2\right) (5 A e+B d)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{16 d^{7/2} (c d-b e)^{7/2}}-\frac{\sqrt{b x+c x^2} (5 A e (2 c d-b e)-B d (b e+4 c d))}{12 d^2 (d+e x)^2 (c d-b e)^2}+\frac{\sqrt{b x+c x^2} (B d-A e)}{3 d (d+e x)^3 (c d-b e)}",1,"((B*d - A*e)*Sqrt[b*x + c*x^2])/(3*d*(c*d - b*e)*(d + e*x)^3) - ((5*A*e*(2*c*d - b*e) - B*d*(4*c*d + b*e))*Sqrt[b*x + c*x^2])/(12*d^2*(c*d - b*e)^2*(d + e*x)^2) + ((B*d*(8*c^2*d^2 + 10*b*c*d*e - 3*b^2*e^2) - A*e*(44*c^2*d^2 - 44*b*c*d*e + 15*b^2*e^2))*Sqrt[b*x + c*x^2])/(24*d^3*(c*d - b*e)^3*(d + e*x)) + ((16*A*c^3*d^3 - 8*b*c^2*d^2*(B*d + 3*A*e) - b^3*e^2*(B*d + 5*A*e) + 2*b^2*c*d*e*(2*B*d + 9*A*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(16*d^(7/2)*(c*d - b*e)^(7/2))","A",5,4,26,0.1538,1,"{834, 806, 724, 206}"
1199,1,238,0,0.2150597,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^(3/2),x]","\frac{e \sqrt{b x+c x^2} \left(2 c e x \left(-4 b c (A e+B d)+8 A c^2 d+5 b^2 B e\right)+12 b^2 c e (A e+3 B d)-8 b c^2 d (3 A e+2 B d)+32 A c^3 d^2-15 b^3 B e^2\right)}{4 b^2 c^3}+\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)+B \left(5 b^2 e^2-12 b c d e+8 c^2 d^2\right)\right)}{4 c^{7/2}}-\frac{2 (d+e x)^2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}","\frac{e \sqrt{b x+c x^2} \left(2 c e x \left(-4 b c (A e+B d)+8 A c^2 d+5 b^2 B e\right)+12 b^2 c e (A e+3 B d)-8 b c^2 d (3 A e+2 B d)+32 A c^3 d^2-15 b^3 B e^2\right)}{4 b^2 c^3}+\frac{3 e \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) \left(4 A c e (2 c d-b e)+B \left(5 b^2 e^2-12 b c d e+8 c^2 d^2\right)\right)}{4 c^{7/2}}-\frac{2 (d+e x)^2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}",1,"(-2*(d + e*x)^2*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*Sqrt[b*x + c*x^2]) + (e*(32*A*c^3*d^2 - 15*b^3*B*e^2 + 12*b^2*c*e*(3*B*d + A*e) - 8*b*c^2*d*(2*B*d + 3*A*e) + 2*c*e*(8*A*c^2*d + 5*b^2*B*e - 4*b*c*(B*d + A*e))*x)*Sqrt[b*x + c*x^2])/(4*b^2*c^3) + (3*e*(4*A*c*e*(2*c*d - b*e) + B*(8*c^2*d^2 - 12*b*c*d*e + 5*b^2*e^2))*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/(4*c^(7/2))","A",4,4,26,0.1538,1,"{818, 779, 620, 206}"
1200,1,151,0,0.149722,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^(3/2),x]","\frac{e \sqrt{b x+c x^2} \left(-2 b c (A e+B d)+4 A c^2 d+3 b^2 B e\right)}{b^2 c^2}-\frac{2 (d+e x) \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (2 A c e-3 b B e+4 B c d)}{c^{5/2}}","\frac{e \sqrt{b x+c x^2} \left(-2 b c (A e+B d)+4 A c^2 d+3 b^2 B e\right)}{b^2 c^2}-\frac{2 (d+e x) \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{e \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (2 A c e-3 b B e+4 B c d)}{c^{5/2}}",1,"(-2*(d + e*x)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*Sqrt[b*x + c*x^2]) + (e*(4*A*c^2*d + 3*b^2*B*e - 2*b*c*(B*d + A*e))*Sqrt[b*x + c*x^2])/(b^2*c^2) + (e*(4*B*c*d - 3*b*B*e + 2*A*c*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",4,4,26,0.1538,1,"{818, 640, 620, 206}"
1201,1,85,0,0.038459,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x))/(b*x + c*x^2)^(3/2),x]","\frac{2 B e \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}-\frac{2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}","\frac{2 B e \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{3/2}}-\frac{2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}",1,"(-2*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*Sqrt[b*x + c*x^2]) + (2*B*e*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(3/2)","A",3,3,24,0.1250,1,"{777, 620, 206}"
1202,1,33,0,0.0099222,"\int \frac{A+B x}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(b*x + c*x^2)^(3/2),x]","-\frac{2 (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}","-\frac{2 (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}",1,"(-2*(A*b - (b*B - 2*A*c)*x))/(b^2*Sqrt[b*x + c*x^2])","A",1,1,19,0.05263,1,"{636}"
1203,1,141,0,0.1211394,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)*(b*x + c*x^2)^(3/2)),x]","-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}-\frac{e (B d-A e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{3/2} (c d-b e)^{3/2}}","-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}-\frac{e (B d-A e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{3/2} (c d-b e)^{3/2}}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*Sqrt[b*x + c*x^2]) - (e*(B*d - A*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(d^(3/2)*(c*d - b*e)^(3/2))","A",4,4,26,0.1538,1,"{822, 12, 724, 206}"
1204,1,245,0,0.3125623,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-3 A e)-2 b c d (2 A e+B d)+4 A c^2 d^2\right)}{b^2 d^2 (d+e x) (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x) (c d-b e)}+\frac{e (3 A e (2 c d-b e)-B d (4 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{5/2} (c d-b e)^{5/2}}","-\frac{e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-3 A e)-2 b c d (2 A e+B d)+4 A c^2 d^2\right)}{b^2 d^2 (d+e x) (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x) (c d-b e)}+\frac{e (3 A e (2 c d-b e)-B d (4 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{5/2} (c d-b e)^{5/2}}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*(d + e*x)*Sqrt[b*x + c*x^2]) - (e*(4*A*c^2*d^2 - b^2*e*(B*d - 3*A*e) - 2*b*c*d*(B*d + 2*A*e))*Sqrt[b*x + c*x^2])/(b^2*d^2*(c*d - b*e)^2*(d + e*x)) + (e*(3*A*e*(2*c*d - b*e) - B*d*(4*c*d - b*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*d^(5/2)*(c*d - b*e)^(5/2))","A",4,4,26,0.1538,1,"{822, 806, 724, 206}"
1205,1,374,0,0.5895814,"\int \frac{A+B x}{(d+e x)^3 \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^3*(b*x + c*x^2)^(3/2)),x]","-\frac{e \sqrt{b x+c x^2} \left(-2 b^2 c d e (5 B d-19 A e)+3 b^3 e^2 (B d-5 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)}{4 b^2 d^3 (d+e x) (c d-b e)^3}-\frac{3 e \left(B d \left(b^2 e^2-4 b c d e+8 c^2 d^2\right)-A e \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{7/2} (c d-b e)^{7/2}}-\frac{e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-5 A e)-4 b c d (2 A e+B d)+8 A c^2 d^2\right)}{2 b^2 d^2 (d+e x)^2 (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^2 (c d-b e)}","-\frac{e \sqrt{b x+c x^2} \left(-2 b^2 c d e (5 B d-19 A e)+3 b^3 e^2 (B d-5 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)}{4 b^2 d^3 (d+e x) (c d-b e)^3}-\frac{3 e \left(B d \left(b^2 e^2-4 b c d e+8 c^2 d^2\right)-A e \left(5 b^2 e^2-16 b c d e+16 c^2 d^2\right)\right) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{8 d^{7/2} (c d-b e)^{7/2}}-\frac{e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-5 A e)-4 b c d (2 A e+B d)+8 A c^2 d^2\right)}{2 b^2 d^2 (d+e x)^2 (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^2 (c d-b e)}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*(d + e*x)^2*Sqrt[b*x + c*x^2]) - (e*(8*A*c^2*d^2 - b^2*e*(B*d - 5*A*e) - 4*b*c*d*(B*d + 2*A*e))*Sqrt[b*x + c*x^2])/(2*b^2*d^2*(c*d - b*e)^2*(d + e*x)^2) - (e*(16*A*c^3*d^3 - 2*b^2*c*d*e*(5*B*d - 19*A*e) + 3*b^3*e^2*(B*d - 5*A*e) - 8*b*c^2*d^2*(B*d + 3*A*e))*Sqrt[b*x + c*x^2])/(4*b^2*d^3*(c*d - b*e)^3*(d + e*x)) - (3*e*(B*d*(8*c^2*d^2 - 4*b*c*d*e + b^2*e^2) - A*e*(16*c^2*d^2 - 16*b*c*d*e + 5*b^2*e^2))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(8*d^(7/2)*(c*d - b*e)^(7/2))","A",5,5,26,0.1923,1,"{822, 834, 806, 724, 206}"
1206,1,341,0,0.4578712,"\int \frac{(A+B x) (d+e x)^4}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^4)/(b*x + c*x^2)^(5/2),x]","-\frac{e \sqrt{b x+c x^2} \left(4 b^2 c^2 d e (A e+2 B d)+2 b^3 c e^2 (3 A e+7 B d)-16 b c^3 d^2 (3 A e+B d)+32 A c^4 d^3-15 b^4 B e^3\right)}{3 b^4 c^3}-\frac{2 (d+e x) \left(b c d^2 \left(10 A b c e-8 A c^2 d+b^2 (-B) e+4 b B c d\right)-x \left(4 b^2 c^2 d e (A e+B d)+2 b^3 c e^2 (A e+3 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3-5 b^4 B e^3\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}-\frac{2 (d+e x)^3 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}+\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (2 A c e-5 b B e+8 B c d)}{c^{7/2}}","-\frac{e \sqrt{b x+c x^2} \left(4 b^2 c^2 d e (A e+2 B d)+2 b^3 c e^2 (3 A e+7 B d)-16 b c^3 d^2 (3 A e+B d)+32 A c^4 d^3-15 b^4 B e^3\right)}{3 b^4 c^3}-\frac{2 (d+e x) \left(b c d^2 \left(10 A b c e-8 A c^2 d+b^2 (-B) e+4 b B c d\right)-x \left(4 b^2 c^2 d e (A e+B d)+2 b^3 c e^2 (A e+3 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3-5 b^4 B e^3\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}-\frac{2 (d+e x)^3 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}+\frac{e^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right) (2 A c e-5 b B e+8 B c d)}{c^{7/2}}",1,"(-2*(d + e*x)^3*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(3*b^2*c*(b*x + c*x^2)^(3/2)) - (2*(d + e*x)*(b*c*d^2*(4*b*B*c*d - 8*A*c^2*d - b^2*B*e + 10*A*b*c*e) - (16*A*c^4*d^3 - 5*b^4*B*e^3 + 4*b^2*c^2*d*e*(B*d + A*e) + 2*b^3*c*e^2*(3*B*d + A*e) - 8*b*c^3*d^2*(B*d + 3*A*e))*x))/(3*b^4*c^2*Sqrt[b*x + c*x^2]) - (e*(32*A*c^4*d^3 - 15*b^4*B*e^3 + 4*b^2*c^2*d*e*(2*B*d + A*e) - 16*b*c^3*d^2*(B*d + 3*A*e) + 2*b^3*c*e^2*(7*B*d + 3*A*e))*Sqrt[b*x + c*x^2])/(3*b^4*c^3) + (e^3*(8*B*c*d - 5*b*B*e + 2*A*c*e)*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(7/2)","A",5,4,26,0.1538,1,"{818, 640, 620, 206}"
1207,1,220,0,0.2028308,"\int \frac{(A+B x) (d+e x)^3}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(b*x + c*x^2)^(5/2),x]","\frac{2 \left(x \left(2 b^2 c^2 d e (4 A e+3 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3+2 b^3 B c d e^2-3 b^4 B e^3\right)+b c d^2 \left(-4 b c (2 A e+B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}-\frac{2 (d+e x)^2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}+\frac{2 B e^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}","\frac{2 \left(x \left(2 b^2 c^2 d e (4 A e+3 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3+2 b^3 B c d e^2-3 b^4 B e^3\right)+b c d^2 \left(-4 b c (2 A e+B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}-\frac{2 (d+e x)^2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}+\frac{2 B e^3 \tanh ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{b x+c x^2}}\right)}{c^{5/2}}",1,"(-2*(d + e*x)^2*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(3*b^2*c*(b*x + c*x^2)^(3/2)) + (2*(b*c*d^2*(8*A*c^2*d + b^2*B*e - 4*b*c*(B*d + 2*A*e)) + (16*A*c^4*d^3 + 2*b^3*B*c*d*e^2 - 3*b^4*B*e^3 - 8*b*c^3*d^2*(B*d + 3*A*e) + 2*b^2*c^2*d*e*(3*B*d + 4*A*e))*x))/(3*b^4*c^2*Sqrt[b*x + c*x^2]) + (2*B*e^3*ArcTanh[(Sqrt[c]*x)/Sqrt[b*x + c*x^2]])/c^(5/2)","A",4,4,26,0.1538,1,"{818, 777, 620, 206}"
1208,1,92,0,0.0518084,"\int \frac{(A+B x) (d+e x)^2}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(b*x + c*x^2)^(5/2),x]","-\frac{2 (d+e x)^2 (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}-\frac{8 (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{3 b^4 \sqrt{b x+c x^2}}","-\frac{2 (d+e x)^2 (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}-\frac{8 (x (2 c d-b e)+b d) (A b e-2 A c d+b B d)}{3 b^4 \sqrt{b x+c x^2}}",1,"(-2*(A*b - (b*B - 2*A*c)*x)*(d + e*x)^2)/(3*b^2*(b*x + c*x^2)^(3/2)) - (8*(b*B*d - 2*A*c*d + A*b*e)*(b*d + (2*c*d - b*e)*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,26,0.07692,1,"{804, 636}"
1209,1,111,0,0.0979879,"\int \frac{(A+B x) (d+e x)}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x))/(b*x + c*x^2)^(5/2),x]","\frac{2 (b+2 c x) \left(-4 b c (A e+B d)+8 A c^2 d+b^2 B e\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}","\frac{2 (b+2 c x) \left(-4 b c (A e+B d)+8 A c^2 d+b^2 B e\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(3*b^2*c*(b*x + c*x^2)^(3/2)) + (2*(8*A*c^2*d + b^2*B*e - 4*b*c*(B*d + A*e))*(b + 2*c*x))/(3*b^4*c*Sqrt[b*x + c*x^2])","A",2,2,24,0.08333,1,"{777, 613}"
1210,1,70,0,0.0215591,"\int \frac{A+B x}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(b*x + c*x^2)^(5/2),x]","-\frac{8 (b+2 c x) (b B-2 A c)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}","-\frac{8 (b+2 c x) (b B-2 A c)}{3 b^4 \sqrt{b x+c x^2}}-\frac{2 (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - (b*B - 2*A*c)*x))/(3*b^2*(b*x + c*x^2)^(3/2)) - (8*(b*B - 2*A*c)*(b + 2*c*x))/(3*b^4*Sqrt[b*x + c*x^2])","A",2,2,19,0.1053,1,"{638, 613}"
1211,1,287,0,0.3542284,"\int \frac{A+B x}{(d+e x) \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)*(b*x + c*x^2)^(5/2)),x]","\frac{2 \left(c x \left(2 b^2 c d e (A e+7 B d)-3 b^3 e^2 (B d-A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)+b (c d-b e) \left(3 b^2 e (B d-A e)-4 b c d (A e+B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}-\frac{e^3 (B d-A e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{5/2} (c d-b e)^{5/2}}","\frac{2 \left(c x \left(2 b^2 c d e (A e+7 B d)-3 b^3 e^2 (B d-A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)+b (c d-b e) \left(3 b^2 e (B d-A e)-4 b c d (A e+B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}-\frac{e^3 (B d-A e) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{d^{5/2} (c d-b e)^{5/2}}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(3*b^2*d*(c*d - b*e)*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*A*c^2*d^2 + 3*b^2*e*(B*d - A*e) - 4*b*c*d*(B*d + A*e)) + c*(16*A*c^3*d^3 - 3*b^3*e^2*(B*d - A*e) + 2*b^2*c*d*e*(7*B*d + A*e) - 8*b*c^2*d^2*(B*d + 3*A*e))*x))/(3*b^4*d^2*(c*d - b*e)^2*Sqrt[b*x + c*x^2]) - (e^3*(B*d - A*e)*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(d^(5/2)*(c*d - b*e)^(5/2))","A",5,4,26,0.1538,1,"{822, 12, 724, 206}"
1212,1,449,0,0.7200081,"\int \frac{A+B x}{(d+e x)^2 \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^2*(b*x + c*x^2)^(5/2)),x]","\frac{e \sqrt{b x+c x^2} \left(4 b^2 c^2 d^2 e (3 A e+10 B d)-2 b^3 c d e^2 (9 B d-10 A e)+3 b^4 e^3 (3 B d-5 A e)-16 b c^3 d^3 (4 A e+B d)+32 A c^4 d^4\right)}{3 b^4 d^3 (d+e x) (c d-b e)^3}+\frac{2 \left(c x \left(2 b^2 c d e (8 B d-A e)+b^3 \left(-e^2\right) (3 B d-5 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (3 B d-5 A e)-2 b c d (A e+2 B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (d+e x) (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (d+e x) (c d-b e)}-\frac{e^3 (B d (8 c d-3 b e)-5 A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{7/2} (c d-b e)^{7/2}}","\frac{e \sqrt{b x+c x^2} \left(4 b^2 c^2 d^2 e (3 A e+10 B d)-2 b^3 c d e^2 (9 B d-10 A e)+3 b^4 e^3 (3 B d-5 A e)-16 b c^3 d^3 (4 A e+B d)+32 A c^4 d^4\right)}{3 b^4 d^3 (d+e x) (c d-b e)^3}+\frac{2 \left(c x \left(2 b^2 c d e (8 B d-A e)+b^3 \left(-e^2\right) (3 B d-5 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (3 B d-5 A e)-2 b c d (A e+2 B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (d+e x) (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (d+e x) (c d-b e)}-\frac{e^3 (B d (8 c d-3 b e)-5 A e (2 c d-b e)) \tanh ^{-1}\left(\frac{x (2 c d-b e)+b d}{2 \sqrt{d} \sqrt{b x+c x^2} \sqrt{c d-b e}}\right)}{2 d^{7/2} (c d-b e)^{7/2}}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(3*b^2*d*(c*d - b*e)*(d + e*x)*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*A*c^2*d^2 + b^2*e*(3*B*d - 5*A*e) - 2*b*c*d*(2*B*d + A*e)) + c*(16*A*c^3*d^3 - b^3*e^2*(3*B*d - 5*A*e) + 2*b^2*c*d*e*(8*B*d - A*e) - 8*b*c^2*d^2*(B*d + 3*A*e))*x))/(3*b^4*d^2*(c*d - b*e)^2*(d + e*x)*Sqrt[b*x + c*x^2]) + (e*(32*A*c^4*d^4 - 2*b^3*c*d*e^2*(9*B*d - 10*A*e) + 3*b^4*e^3*(3*B*d - 5*A*e) + 4*b^2*c^2*d^2*e*(10*B*d + 3*A*e) - 16*b*c^3*d^3*(B*d + 4*A*e))*Sqrt[b*x + c*x^2])/(3*b^4*d^3*(c*d - b*e)^3*(d + e*x)) - (e^3*(B*d*(8*c*d - 3*b*e) - 5*A*e*(2*c*d - b*e))*ArcTanh[(b*d + (2*c*d - b*e)*x)/(2*Sqrt[d]*Sqrt[c*d - b*e]*Sqrt[b*x + c*x^2])])/(2*d^(7/2)*(c*d - b*e)^(7/2))","A",5,4,26,0.1538,1,"{822, 806, 724, 206}"
1213,1,126,0,0.0885321,"\int (A+B x) (d+e x)^{7/2} \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{13/2} (-A c e-b B e+3 B c d)}{13 e^4}+\frac{2 (d+e x)^{11/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{11 e^4}-\frac{2 d (d+e x)^{9/2} (B d-A e) (c d-b e)}{9 e^4}+\frac{2 B c (d+e x)^{15/2}}{15 e^4}","-\frac{2 (d+e x)^{13/2} (-A c e-b B e+3 B c d)}{13 e^4}+\frac{2 (d+e x)^{11/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{11 e^4}-\frac{2 d (d+e x)^{9/2} (B d-A e) (c d-b e)}{9 e^4}+\frac{2 B c (d+e x)^{15/2}}{15 e^4}",1,"(-2*d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^(9/2))/(9*e^4) + (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^(11/2))/(11*e^4) - (2*(3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(13/2))/(13*e^4) + (2*B*c*(d + e*x)^(15/2))/(15*e^4)","A",2,1,24,0.04167,1,"{771}"
1214,1,126,0,0.0787755,"\int (A+B x) (d+e x)^{5/2} \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{11/2} (-A c e-b B e+3 B c d)}{11 e^4}+\frac{2 (d+e x)^{9/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{9 e^4}-\frac{2 d (d+e x)^{7/2} (B d-A e) (c d-b e)}{7 e^4}+\frac{2 B c (d+e x)^{13/2}}{13 e^4}","-\frac{2 (d+e x)^{11/2} (-A c e-b B e+3 B c d)}{11 e^4}+\frac{2 (d+e x)^{9/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{9 e^4}-\frac{2 d (d+e x)^{7/2} (B d-A e) (c d-b e)}{7 e^4}+\frac{2 B c (d+e x)^{13/2}}{13 e^4}",1,"(-2*d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^(7/2))/(7*e^4) + (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^(9/2))/(9*e^4) - (2*(3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(11/2))/(11*e^4) + (2*B*c*(d + e*x)^(13/2))/(13*e^4)","A",2,1,24,0.04167,1,"{771}"
1215,1,126,0,0.0732722,"\int (A+B x) (d+e x)^{3/2} \left(b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{9/2} (-A c e-b B e+3 B c d)}{9 e^4}+\frac{2 (d+e x)^{7/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{7 e^4}-\frac{2 d (d+e x)^{5/2} (B d-A e) (c d-b e)}{5 e^4}+\frac{2 B c (d+e x)^{11/2}}{11 e^4}","-\frac{2 (d+e x)^{9/2} (-A c e-b B e+3 B c d)}{9 e^4}+\frac{2 (d+e x)^{7/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{7 e^4}-\frac{2 d (d+e x)^{5/2} (B d-A e) (c d-b e)}{5 e^4}+\frac{2 B c (d+e x)^{11/2}}{11 e^4}",1,"(-2*d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^(5/2))/(5*e^4) + (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^(7/2))/(7*e^4) - (2*(3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(9/2))/(9*e^4) + (2*B*c*(d + e*x)^(11/2))/(11*e^4)","A",2,1,24,0.04167,1,"{771}"
1216,1,126,0,0.07656,"\int (A+B x) \sqrt{d+e x} \left(b x+c x^2\right) \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(b*x + c*x^2),x]","-\frac{2 (d+e x)^{7/2} (-A c e-b B e+3 B c d)}{7 e^4}+\frac{2 (d+e x)^{5/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{5 e^4}-\frac{2 d (d+e x)^{3/2} (B d-A e) (c d-b e)}{3 e^4}+\frac{2 B c (d+e x)^{9/2}}{9 e^4}","-\frac{2 (d+e x)^{7/2} (-A c e-b B e+3 B c d)}{7 e^4}+\frac{2 (d+e x)^{5/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{5 e^4}-\frac{2 d (d+e x)^{3/2} (B d-A e) (c d-b e)}{3 e^4}+\frac{2 B c (d+e x)^{9/2}}{9 e^4}",1,"(-2*d*(B*d - A*e)*(c*d - b*e)*(d + e*x)^(3/2))/(3*e^4) + (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^(5/2))/(5*e^4) - (2*(3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(7/2))/(7*e^4) + (2*B*c*(d + e*x)^(9/2))/(9*e^4)","A",2,1,24,0.04167,1,"{771}"
1217,1,124,0,0.0764481,"\int \frac{(A+B x) \left(b x+c x^2\right)}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/Sqrt[d + e*x],x]","-\frac{2 (d+e x)^{5/2} (-A c e-b B e+3 B c d)}{5 e^4}+\frac{2 (d+e x)^{3/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{3 e^4}-\frac{2 d \sqrt{d+e x} (B d-A e) (c d-b e)}{e^4}+\frac{2 B c (d+e x)^{7/2}}{7 e^4}","-\frac{2 (d+e x)^{5/2} (-A c e-b B e+3 B c d)}{5 e^4}+\frac{2 (d+e x)^{3/2} (B d (3 c d-2 b e)-A e (2 c d-b e))}{3 e^4}-\frac{2 d \sqrt{d+e x} (B d-A e) (c d-b e)}{e^4}+\frac{2 B c (d+e x)^{7/2}}{7 e^4}",1,"(-2*d*(B*d - A*e)*(c*d - b*e)*Sqrt[d + e*x])/e^4 + (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*(d + e*x)^(3/2))/(3*e^4) - (2*(3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(5/2))/(5*e^4) + (2*B*c*(d + e*x)^(7/2))/(7*e^4)","A",2,1,24,0.04167,1,"{771}"
1218,1,122,0,0.0759785,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^(3/2),x]","-\frac{2 (d+e x)^{3/2} (-A c e-b B e+3 B c d)}{3 e^4}+\frac{2 \sqrt{d+e x} (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4}+\frac{2 d (B d-A e) (c d-b e)}{e^4 \sqrt{d+e x}}+\frac{2 B c (d+e x)^{5/2}}{5 e^4}","-\frac{2 (d+e x)^{3/2} (-A c e-b B e+3 B c d)}{3 e^4}+\frac{2 \sqrt{d+e x} (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4}+\frac{2 d (B d-A e) (c d-b e)}{e^4 \sqrt{d+e x}}+\frac{2 B c (d+e x)^{5/2}}{5 e^4}",1,"(2*d*(B*d - A*e)*(c*d - b*e))/(e^4*Sqrt[d + e*x]) + (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e))*Sqrt[d + e*x])/e^4 - (2*(3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(3/2))/(3*e^4) + (2*B*c*(d + e*x)^(5/2))/(5*e^4)","A",2,1,24,0.04167,1,"{771}"
1219,1,122,0,0.0744253,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{d+e x} (-A c e-b B e+3 B c d)}{e^4}-\frac{2 (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4 \sqrt{d+e x}}+\frac{2 d (B d-A e) (c d-b e)}{3 e^4 (d+e x)^{3/2}}+\frac{2 B c (d+e x)^{3/2}}{3 e^4}","-\frac{2 \sqrt{d+e x} (-A c e-b B e+3 B c d)}{e^4}-\frac{2 (B d (3 c d-2 b e)-A e (2 c d-b e))}{e^4 \sqrt{d+e x}}+\frac{2 d (B d-A e) (c d-b e)}{3 e^4 (d+e x)^{3/2}}+\frac{2 B c (d+e x)^{3/2}}{3 e^4}",1,"(2*d*(B*d - A*e)*(c*d - b*e))/(3*e^4*(d + e*x)^(3/2)) - (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e)))/(e^4*Sqrt[d + e*x]) - (2*(3*B*c*d - b*B*e - A*c*e)*Sqrt[d + e*x])/e^4 + (2*B*c*(d + e*x)^(3/2))/(3*e^4)","A",2,1,24,0.04167,1,"{771}"
1220,1,122,0,0.074826,"\int \frac{(A+B x) \left(b x+c x^2\right)}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2))/(d + e*x)^(7/2),x]","\frac{2 (-A c e-b B e+3 B c d)}{e^4 \sqrt{d+e x}}-\frac{2 (B d (3 c d-2 b e)-A e (2 c d-b e))}{3 e^4 (d+e x)^{3/2}}+\frac{2 d (B d-A e) (c d-b e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 B c \sqrt{d+e x}}{e^4}","\frac{2 (-A c e-b B e+3 B c d)}{e^4 \sqrt{d+e x}}-\frac{2 (B d (3 c d-2 b e)-A e (2 c d-b e))}{3 e^4 (d+e x)^{3/2}}+\frac{2 d (B d-A e) (c d-b e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 B c \sqrt{d+e x}}{e^4}",1,"(2*d*(B*d - A*e)*(c*d - b*e))/(5*e^4*(d + e*x)^(5/2)) - (2*(B*d*(3*c*d - 2*b*e) - A*e*(2*c*d - b*e)))/(3*e^4*(d + e*x)^(3/2)) + (2*(3*B*c*d - b*B*e - A*c*e))/(e^4*Sqrt[d + e*x]) + (2*B*c*Sqrt[d + e*x])/e^4","A",2,1,24,0.04167,1,"{771}"
1221,1,267,0,0.2139619,"\int (A+B x) (d+e x)^{7/2} \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(b*x + c*x^2)^2,x]","-\frac{2 (d+e x)^{15/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{15 e^6}+\frac{2 (d+e x)^{13/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{13 e^6}-\frac{2 d^2 (d+e x)^{9/2} (B d-A e) (c d-b e)^2}{9 e^6}-\frac{2 c (d+e x)^{17/2} (-A c e-2 b B e+5 B c d)}{17 e^6}+\frac{2 d (d+e x)^{11/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{11 e^6}+\frac{2 B c^2 (d+e x)^{19/2}}{19 e^6}","-\frac{2 (d+e x)^{15/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{15 e^6}+\frac{2 (d+e x)^{13/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{13 e^6}-\frac{2 d^2 (d+e x)^{9/2} (B d-A e) (c d-b e)^2}{9 e^6}-\frac{2 c (d+e x)^{17/2} (-A c e-2 b B e+5 B c d)}{17 e^6}+\frac{2 d (d+e x)^{11/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{11 e^6}+\frac{2 B c^2 (d+e x)^{19/2}}{19 e^6}",1,"(-2*d^2*(B*d - A*e)*(c*d - b*e)^2*(d + e*x)^(9/2))/(9*e^6) + (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(11/2))/(11*e^6) + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(13/2))/(13*e^6) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(15/2))/(15*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(17/2))/(17*e^6) + (2*B*c^2*(d + e*x)^(19/2))/(19*e^6)","A",2,1,26,0.03846,1,"{771}"
1222,1,267,0,0.1520866,"\int (A+B x) (d+e x)^{5/2} \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(b*x + c*x^2)^2,x]","-\frac{2 (d+e x)^{13/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{13 e^6}+\frac{2 (d+e x)^{11/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{11 e^6}-\frac{2 d^2 (d+e x)^{7/2} (B d-A e) (c d-b e)^2}{7 e^6}-\frac{2 c (d+e x)^{15/2} (-A c e-2 b B e+5 B c d)}{15 e^6}+\frac{2 d (d+e x)^{9/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{9 e^6}+\frac{2 B c^2 (d+e x)^{17/2}}{17 e^6}","-\frac{2 (d+e x)^{13/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{13 e^6}+\frac{2 (d+e x)^{11/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{11 e^6}-\frac{2 d^2 (d+e x)^{7/2} (B d-A e) (c d-b e)^2}{7 e^6}-\frac{2 c (d+e x)^{15/2} (-A c e-2 b B e+5 B c d)}{15 e^6}+\frac{2 d (d+e x)^{9/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{9 e^6}+\frac{2 B c^2 (d+e x)^{17/2}}{17 e^6}",1,"(-2*d^2*(B*d - A*e)*(c*d - b*e)^2*(d + e*x)^(7/2))/(7*e^6) + (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(9/2))/(9*e^6) + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(11/2))/(11*e^6) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(13/2))/(13*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(15/2))/(15*e^6) + (2*B*c^2*(d + e*x)^(17/2))/(17*e^6)","A",2,1,26,0.03846,1,"{771}"
1223,1,267,0,0.1583419,"\int (A+B x) (d+e x)^{3/2} \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(b*x + c*x^2)^2,x]","-\frac{2 (d+e x)^{11/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{11 e^6}+\frac{2 (d+e x)^{9/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{9 e^6}-\frac{2 d^2 (d+e x)^{5/2} (B d-A e) (c d-b e)^2}{5 e^6}-\frac{2 c (d+e x)^{13/2} (-A c e-2 b B e+5 B c d)}{13 e^6}+\frac{2 d (d+e x)^{7/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{7 e^6}+\frac{2 B c^2 (d+e x)^{15/2}}{15 e^6}","-\frac{2 (d+e x)^{11/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{11 e^6}+\frac{2 (d+e x)^{9/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{9 e^6}-\frac{2 d^2 (d+e x)^{5/2} (B d-A e) (c d-b e)^2}{5 e^6}-\frac{2 c (d+e x)^{13/2} (-A c e-2 b B e+5 B c d)}{13 e^6}+\frac{2 d (d+e x)^{7/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{7 e^6}+\frac{2 B c^2 (d+e x)^{15/2}}{15 e^6}",1,"(-2*d^2*(B*d - A*e)*(c*d - b*e)^2*(d + e*x)^(5/2))/(5*e^6) + (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(7/2))/(7*e^6) + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(9/2))/(9*e^6) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(11/2))/(11*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(13/2))/(13*e^6) + (2*B*c^2*(d + e*x)^(15/2))/(15*e^6)","A",2,1,26,0.03846,1,"{771}"
1224,1,267,0,0.152945,"\int (A+B x) \sqrt{d+e x} \left(b x+c x^2\right)^2 \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(b*x + c*x^2)^2,x]","-\frac{2 (d+e x)^{9/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{9 e^6}+\frac{2 (d+e x)^{7/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{7 e^6}-\frac{2 d^2 (d+e x)^{3/2} (B d-A e) (c d-b e)^2}{3 e^6}-\frac{2 c (d+e x)^{11/2} (-A c e-2 b B e+5 B c d)}{11 e^6}+\frac{2 d (d+e x)^{5/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{5 e^6}+\frac{2 B c^2 (d+e x)^{13/2}}{13 e^6}","-\frac{2 (d+e x)^{9/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{9 e^6}+\frac{2 (d+e x)^{7/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{7 e^6}-\frac{2 d^2 (d+e x)^{3/2} (B d-A e) (c d-b e)^2}{3 e^6}-\frac{2 c (d+e x)^{11/2} (-A c e-2 b B e+5 B c d)}{11 e^6}+\frac{2 d (d+e x)^{5/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{5 e^6}+\frac{2 B c^2 (d+e x)^{13/2}}{13 e^6}",1,"(-2*d^2*(B*d - A*e)*(c*d - b*e)^2*(d + e*x)^(3/2))/(3*e^6) + (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(5/2))/(5*e^6) + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(7/2))/(7*e^6) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(9/2))/(9*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(11/2))/(11*e^6) + (2*B*c^2*(d + e*x)^(13/2))/(13*e^6)","A",2,1,26,0.03846,1,"{771}"
1225,1,265,0,0.1584871,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/Sqrt[d + e*x],x]","-\frac{2 (d+e x)^{7/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{7 e^6}+\frac{2 (d+e x)^{5/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{5 e^6}-\frac{2 d^2 \sqrt{d+e x} (B d-A e) (c d-b e)^2}{e^6}-\frac{2 c (d+e x)^{9/2} (-A c e-2 b B e+5 B c d)}{9 e^6}+\frac{2 d (d+e x)^{3/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{3 e^6}+\frac{2 B c^2 (d+e x)^{11/2}}{11 e^6}","-\frac{2 (d+e x)^{7/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{7 e^6}+\frac{2 (d+e x)^{5/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{5 e^6}-\frac{2 d^2 \sqrt{d+e x} (B d-A e) (c d-b e)^2}{e^6}-\frac{2 c (d+e x)^{9/2} (-A c e-2 b B e+5 B c d)}{9 e^6}+\frac{2 d (d+e x)^{3/2} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{3 e^6}+\frac{2 B c^2 (d+e x)^{11/2}}{11 e^6}",1,"(-2*d^2*(B*d - A*e)*(c*d - b*e)^2*Sqrt[d + e*x])/e^6 + (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(3/2))/(3*e^6) + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(5/2))/(5*e^6) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(7/2))/(7*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(9/2))/(9*e^6) + (2*B*c^2*(d + e*x)^(11/2))/(11*e^6)","A",2,1,26,0.03846,1,"{771}"
1226,1,263,0,0.1594556,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^(3/2),x]","-\frac{2 (d+e x)^{5/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{5 e^6}+\frac{2 (d+e x)^{3/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{3 e^6}+\frac{2 d^2 (B d-A e) (c d-b e)^2}{e^6 \sqrt{d+e x}}-\frac{2 c (d+e x)^{7/2} (-A c e-2 b B e+5 B c d)}{7 e^6}+\frac{2 d \sqrt{d+e x} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6}+\frac{2 B c^2 (d+e x)^{9/2}}{9 e^6}","-\frac{2 (d+e x)^{5/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{5 e^6}+\frac{2 (d+e x)^{3/2} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{3 e^6}+\frac{2 d^2 (B d-A e) (c d-b e)^2}{e^6 \sqrt{d+e x}}-\frac{2 c (d+e x)^{7/2} (-A c e-2 b B e+5 B c d)}{7 e^6}+\frac{2 d \sqrt{d+e x} (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6}+\frac{2 B c^2 (d+e x)^{9/2}}{9 e^6}",1,"(2*d^2*(B*d - A*e)*(c*d - b*e)^2)/(e^6*Sqrt[d + e*x]) + (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e))*Sqrt[d + e*x])/e^6 + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*(d + e*x)^(3/2))/(3*e^6) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(5/2))/(5*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(7/2))/(7*e^6) + (2*B*c^2*(d + e*x)^(9/2))/(9*e^6)","A",2,1,26,0.03846,1,"{771}"
1227,1,263,0,0.1535397,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^(5/2),x]","-\frac{2 (d+e x)^{3/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{3 e^6}+\frac{2 \sqrt{d+e x} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6}+\frac{2 d^2 (B d-A e) (c d-b e)^2}{3 e^6 (d+e x)^{3/2}}-\frac{2 c (d+e x)^{5/2} (-A c e-2 b B e+5 B c d)}{5 e^6}-\frac{2 d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6 \sqrt{d+e x}}+\frac{2 B c^2 (d+e x)^{7/2}}{7 e^6}","-\frac{2 (d+e x)^{3/2} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{3 e^6}+\frac{2 \sqrt{d+e x} \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6}+\frac{2 d^2 (B d-A e) (c d-b e)^2}{3 e^6 (d+e x)^{3/2}}-\frac{2 c (d+e x)^{5/2} (-A c e-2 b B e+5 B c d)}{5 e^6}-\frac{2 d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{e^6 \sqrt{d+e x}}+\frac{2 B c^2 (d+e x)^{7/2}}{7 e^6}",1,"(2*d^2*(B*d - A*e)*(c*d - b*e)^2)/(3*e^6*(d + e*x)^(3/2)) - (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(e^6*Sqrt[d + e*x]) + (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2))*Sqrt[d + e*x])/e^6 - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*(d + e*x)^(3/2))/(3*e^6) - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(5/2))/(5*e^6) + (2*B*c^2*(d + e*x)^(7/2))/(7*e^6)","A",2,1,26,0.03846,1,"{771}"
1228,1,263,0,0.1567022,"\int \frac{(A+B x) \left(b x+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^2)/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{d+e x} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{e^6}-\frac{2 \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6 \sqrt{d+e x}}+\frac{2 d^2 (B d-A e) (c d-b e)^2}{5 e^6 (d+e x)^{5/2}}-\frac{2 c (d+e x)^{3/2} (-A c e-2 b B e+5 B c d)}{3 e^6}-\frac{2 d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{3 e^6 (d+e x)^{3/2}}+\frac{2 B c^2 (d+e x)^{5/2}}{5 e^6}","-\frac{2 \sqrt{d+e x} \left(2 A c e (2 c d-b e)-B \left(b^2 e^2-8 b c d e+10 c^2 d^2\right)\right)}{e^6}-\frac{2 \left(A e \left(b^2 e^2-6 b c d e+6 c^2 d^2\right)-B d \left(3 b^2 e^2-12 b c d e+10 c^2 d^2\right)\right)}{e^6 \sqrt{d+e x}}+\frac{2 d^2 (B d-A e) (c d-b e)^2}{5 e^6 (d+e x)^{5/2}}-\frac{2 c (d+e x)^{3/2} (-A c e-2 b B e+5 B c d)}{3 e^6}-\frac{2 d (c d-b e) (B d (5 c d-3 b e)-2 A e (2 c d-b e))}{3 e^6 (d+e x)^{3/2}}+\frac{2 B c^2 (d+e x)^{5/2}}{5 e^6}",1,"(2*d^2*(B*d - A*e)*(c*d - b*e)^2)/(5*e^6*(d + e*x)^(5/2)) - (2*d*(c*d - b*e)*(B*d*(5*c*d - 3*b*e) - 2*A*e*(2*c*d - b*e)))/(3*e^6*(d + e*x)^(3/2)) - (2*(A*e*(6*c^2*d^2 - 6*b*c*d*e + b^2*e^2) - B*d*(10*c^2*d^2 - 12*b*c*d*e + 3*b^2*e^2)))/(e^6*Sqrt[d + e*x]) - (2*(2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 - 8*b*c*d*e + b^2*e^2))*Sqrt[d + e*x])/e^6 - (2*c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(3/2))/(3*e^6) + (2*B*c^2*(d + e*x)^(5/2))/(5*e^6)","A",2,1,26,0.03846,1,"{771}"
1229,1,228,0,0.5609632,"\int \frac{(A+B x) (d+e x)^{7/2}}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2),x]","\frac{2 \sqrt{d+e x} \left(A c e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)+B (c d-b e)^3\right)}{c^4}+\frac{2 (d+e x)^{5/2} (A c e-b B e+B c d)}{5 c^2}+\frac{2 (d+e x)^{3/2} \left(A c e (2 c d-b e)+B (c d-b e)^2\right)}{3 c^3}-\frac{2 (b B-A c) (c d-b e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{9/2}}-\frac{2 A d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B (d+e x)^{7/2}}{7 c}","\frac{2 \sqrt{d+e x} \left(A c e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)+B (c d-b e)^3\right)}{c^4}+\frac{2 (d+e x)^{5/2} (A c e-b B e+B c d)}{5 c^2}+\frac{2 (d+e x)^{3/2} \left(A c e (2 c d-b e)+B (c d-b e)^2\right)}{3 c^3}-\frac{2 (b B-A c) (c d-b e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{9/2}}-\frac{2 A d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B (d+e x)^{7/2}}{7 c}",1,"(2*(B*(c*d - b*e)^3 + A*c*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2))*Sqrt[d + e*x])/c^4 + (2*(B*(c*d - b*e)^2 + A*c*e*(2*c*d - b*e))*(d + e*x)^(3/2))/(3*c^3) + (2*(B*c*d - b*B*e + A*c*e)*(d + e*x)^(5/2))/(5*c^2) + (2*B*(d + e*x)^(7/2))/(7*c) - (2*A*d^(7/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b - (2*(b*B - A*c)*(c*d - b*e)^(7/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(9/2))","A",8,4,26,0.1538,1,"{824, 826, 1166, 208}"
1230,1,173,0,0.362408,"\int \frac{(A+B x) (d+e x)^{5/2}}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2),x]","\frac{2 (d+e x)^{3/2} (A c e-b B e+B c d)}{3 c^2}+\frac{2 \sqrt{d+e x} \left(A c e (2 c d-b e)+B (c d-b e)^2\right)}{c^3}-\frac{2 (b B-A c) (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{7/2}}-\frac{2 A d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B (d+e x)^{5/2}}{5 c}","\frac{2 (d+e x)^{3/2} (A c e-b B e+B c d)}{3 c^2}+\frac{2 \sqrt{d+e x} \left(A c e (2 c d-b e)+B (c d-b e)^2\right)}{c^3}-\frac{2 (b B-A c) (c d-b e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{7/2}}-\frac{2 A d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B (d+e x)^{5/2}}{5 c}",1,"(2*(B*(c*d - b*e)^2 + A*c*e*(2*c*d - b*e))*Sqrt[d + e*x])/c^3 + (2*(B*c*d - b*B*e + A*c*e)*(d + e*x)^(3/2))/(3*c^2) + (2*B*(d + e*x)^(5/2))/(5*c) - (2*A*d^(5/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b - (2*(b*B - A*c)*(c*d - b*e)^(5/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(7/2))","A",7,4,26,0.1538,1,"{824, 826, 1166, 208}"
1231,1,131,0,0.2958193,"\int \frac{(A+B x) (d+e x)^{3/2}}{b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2),x]","\frac{2 \sqrt{d+e x} (A c e-b B e+B c d)}{c^2}-\frac{2 (b B-A c) (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{5/2}}-\frac{2 A d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B (d+e x)^{3/2}}{3 c}","\frac{2 \sqrt{d+e x} (A c e-b B e+B c d)}{c^2}-\frac{2 (b B-A c) (c d-b e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{5/2}}-\frac{2 A d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B (d+e x)^{3/2}}{3 c}",1,"(2*(B*c*d - b*B*e + A*c*e)*Sqrt[d + e*x])/c^2 + (2*B*(d + e*x)^(3/2))/(3*c) - (2*A*d^(3/2)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b - (2*(b*B - A*c)*(c*d - b*e)^(3/2)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(5/2))","A",6,4,26,0.1538,1,"{824, 826, 1166, 208}"
1232,1,101,0,0.1751309,"\int \frac{(A+B x) \sqrt{d+e x}}{b x+c x^2} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2),x]","-\frac{2 (b B-A c) \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{3/2}}-\frac{2 A \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B \sqrt{d+e x}}{c}","-\frac{2 (b B-A c) \sqrt{c d-b e} \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b c^{3/2}}-\frac{2 A \sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b}+\frac{2 B \sqrt{d+e x}}{c}",1,"(2*B*Sqrt[d + e*x])/c - (2*A*Sqrt[d]*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b - (2*(b*B - A*c)*Sqrt[c*d - b*e]*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*c^(3/2))","A",5,4,26,0.1538,1,"{824, 826, 1166, 208}"
1233,1,86,0,0.1800736,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)),x]","-\frac{2 (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b \sqrt{c} \sqrt{c d-b e}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b \sqrt{d}}","-\frac{2 (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b \sqrt{c} \sqrt{c d-b e}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b \sqrt{d}}",1,"(-2*A*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*Sqrt[d]) - (2*(b*B - A*c)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*Sqrt[c]*Sqrt[c*d - b*e])","A",4,3,26,0.1154,1,"{826, 1166, 208}"
1234,1,118,0,0.3019362,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)),x]","\frac{2 (B d-A e)}{d \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{c} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{3/2}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{3/2}}","\frac{2 (B d-A e)}{d \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{c} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{3/2}}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{3/2}}",1,"(2*(B*d - A*e))/(d*(c*d - b*e)*Sqrt[d + e*x]) - (2*A*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(3/2)) - (2*Sqrt[c]*(b*B - A*c)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(3/2))","A",5,4,26,0.1538,1,"{828, 826, 1166, 208}"
1235,1,164,0,0.3247185,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)),x]","-\frac{2 c^{3/2} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{5/2}}+\frac{2 \left(B c d^2-A e (2 c d-b e)\right)}{d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{2 (B d-A e)}{3 d (d+e x)^{3/2} (c d-b e)}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{5/2}}","-\frac{2 c^{3/2} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{5/2}}+\frac{2 \left(B c d^2-A e (2 c d-b e)\right)}{d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{2 (B d-A e)}{3 d (d+e x)^{3/2} (c d-b e)}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{5/2}}",1,"(2*(B*d - A*e))/(3*d*(c*d - b*e)*(d + e*x)^(3/2)) + (2*(B*c*d^2 - A*e*(2*c*d - b*e)))/(d^2*(c*d - b*e)^2*Sqrt[d + e*x]) - (2*A*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(5/2)) - (2*c^(3/2)*(b*B - A*c)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(5/2))","A",6,4,26,0.1538,1,"{828, 826, 1166, 208}"
1236,1,225,0,0.4495278,"\int \frac{A+B x}{(d+e x)^{7/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)),x]","\frac{2 \left(B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{2 c^{5/2} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{7/2}}+\frac{2 \left(B c d^2-A e (2 c d-b e)\right)}{3 d^2 (d+e x)^{3/2} (c d-b e)^2}+\frac{2 (B d-A e)}{5 d (d+e x)^{5/2} (c d-b e)}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{7/2}}","\frac{2 \left(B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{2 c^{5/2} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{7/2}}+\frac{2 \left(B c d^2-A e (2 c d-b e)\right)}{3 d^2 (d+e x)^{3/2} (c d-b e)^2}+\frac{2 (B d-A e)}{5 d (d+e x)^{5/2} (c d-b e)}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{7/2}}",1,"(2*(B*d - A*e))/(5*d*(c*d - b*e)*(d + e*x)^(5/2)) + (2*(B*c*d^2 - A*e*(2*c*d - b*e)))/(3*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) + (2*(B*c^2*d^3 - A*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2)))/(d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (2*A*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(7/2)) - (2*c^(5/2)*(b*B - A*c)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(7/2))","A",7,4,26,0.1538,1,"{828, 826, 1166, 208}"
1237,1,301,0,0.5516131,"\int \frac{A+B x}{(d+e x)^{9/2} \left(b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(9/2)*(b*x + c*x^2)),x]","\frac{2 \left(B c^3 d^4-A e \left(4 b^2 c d e^2-b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{d^4 \sqrt{d+e x} (c d-b e)^4}+\frac{2 \left(B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{3 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac{2 c^{7/2} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{9/2}}+\frac{2 \left(B c d^2-A e (2 c d-b e)\right)}{5 d^2 (d+e x)^{5/2} (c d-b e)^2}+\frac{2 (B d-A e)}{7 d (d+e x)^{7/2} (c d-b e)}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{9/2}}","\frac{2 \left(B c^3 d^4-A e \left(4 b^2 c d e^2-b^3 e^3-6 b c^2 d^2 e+4 c^3 d^3\right)\right)}{d^4 \sqrt{d+e x} (c d-b e)^4}+\frac{2 \left(B c^2 d^3-A e \left(b^2 e^2-3 b c d e+3 c^2 d^2\right)\right)}{3 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac{2 c^{7/2} (b B-A c) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b (c d-b e)^{9/2}}+\frac{2 \left(B c d^2-A e (2 c d-b e)\right)}{5 d^2 (d+e x)^{5/2} (c d-b e)^2}+\frac{2 (B d-A e)}{7 d (d+e x)^{7/2} (c d-b e)}-\frac{2 A \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right)}{b d^{9/2}}",1,"(2*(B*d - A*e))/(7*d*(c*d - b*e)*(d + e*x)^(7/2)) + (2*(B*c*d^2 - A*e*(2*c*d - b*e)))/(5*d^2*(c*d - b*e)^2*(d + e*x)^(5/2)) + (2*(B*c^2*d^3 - A*e*(3*c^2*d^2 - 3*b*c*d*e + b^2*e^2)))/(3*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) + (2*(B*c^3*d^4 - A*e*(4*c^3*d^3 - 6*b*c^2*d^2*e + 4*b^2*c*d*e^2 - b^3*e^3)))/(d^4*(c*d - b*e)^4*Sqrt[d + e*x]) - (2*A*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b*d^(9/2)) - (2*c^(7/2)*(b*B - A*c)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b*(c*d - b*e)^(9/2))","A",8,4,26,0.1538,1,"{828, 826, 1166, 208}"
1238,1,386,0,1.1937004,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(9/2))/(b*x + c*x^2)^2,x]","\frac{e (d+e x)^{3/2} \left(b^2 c e (5 A e+12 B d)-3 b c^2 d (2 A e+B d)+6 A c^3 d^2-7 b^3 B e^2\right)}{3 b^2 c^3}+\frac{e \sqrt{d+e x} \left(b^2 c^2 d e (11 A e+15 B d)-b^3 c e^2 (5 A e+19 B d)-b c^3 d^2 (3 A e+B d)+2 A c^4 d^3+7 b^4 B e^3\right)}{b^2 c^4}-\frac{(d+e x)^{7/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}+\frac{e (d+e x)^{5/2} \left(-5 b c (A e+B d)+10 A c^2 d+7 b^2 B e\right)}{5 b^2 c^2}-\frac{(c d-b e)^{7/2} \left(-b c (2 B d-5 A e)+4 A c^2 d-7 b^2 B e\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{9/2}}-\frac{d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (9 A b e-4 A c d+2 b B d)}{b^3}","\frac{e (d+e x)^{3/2} \left(b^2 c e (5 A e+12 B d)-3 b c^2 d (2 A e+B d)+6 A c^3 d^2-7 b^3 B e^2\right)}{3 b^2 c^3}+\frac{e \sqrt{d+e x} \left(b^2 c^2 d e (11 A e+15 B d)-b^3 c e^2 (5 A e+19 B d)-b c^3 d^2 (3 A e+B d)+2 A c^4 d^3+7 b^4 B e^3\right)}{b^2 c^4}-\frac{(d+e x)^{7/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}+\frac{e (d+e x)^{5/2} \left(-5 b c (A e+B d)+10 A c^2 d+7 b^2 B e\right)}{5 b^2 c^2}-\frac{(c d-b e)^{7/2} \left(-b c (2 B d-5 A e)+4 A c^2 d-7 b^2 B e\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{9/2}}-\frac{d^{7/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (9 A b e-4 A c d+2 b B d)}{b^3}",1,"(e*(2*A*c^4*d^3 + 7*b^4*B*e^3 - b*c^3*d^2*(B*d + 3*A*e) - b^3*c*e^2*(19*B*d + 5*A*e) + b^2*c^2*d*e*(15*B*d + 11*A*e))*Sqrt[d + e*x])/(b^2*c^4) + (e*(6*A*c^3*d^2 - 7*b^3*B*e^2 - 3*b*c^2*d*(B*d + 2*A*e) + b^2*c*e*(12*B*d + 5*A*e))*(d + e*x)^(3/2))/(3*b^2*c^3) + (e*(10*A*c^2*d + 7*b^2*B*e - 5*b*c*(B*d + A*e))*(d + e*x)^(5/2))/(5*b^2*c^2) - ((d + e*x)^(7/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*(b*x + c*x^2)) - (d^(7/2)*(2*b*B*d - 4*A*c*d + 9*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - ((c*d - b*e)^(7/2)*(4*A*c^2*d - 7*b^2*B*e - b*c*(2*B*d - 5*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(9/2))","A",8,5,26,0.1923,1,"{818, 824, 826, 1166, 208}"
1239,1,292,0,0.8820681,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^2,x]","\frac{e \sqrt{d+e x} \left(b^2 c e (3 A e+8 B d)-b c^2 d (2 A e+B d)+2 A c^3 d^2-5 b^3 B e^2\right)}{b^2 c^3}-\frac{(d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}+\frac{e (d+e x)^{3/2} \left(-3 b c (A e+B d)+6 A c^2 d+5 b^2 B e\right)}{3 b^2 c^2}+\frac{(c d-b e)^{5/2} \left(-3 A b c e-4 A c^2 d+5 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{7/2}}-\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (7 A b e-4 A c d+2 b B d)}{b^3}","\frac{e \sqrt{d+e x} \left(b^2 c e (3 A e+8 B d)-b c^2 d (2 A e+B d)+2 A c^3 d^2-5 b^3 B e^2\right)}{b^2 c^3}-\frac{(d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}+\frac{e (d+e x)^{3/2} \left(-3 b c (A e+B d)+6 A c^2 d+5 b^2 B e\right)}{3 b^2 c^2}+\frac{(c d-b e)^{5/2} \left(-3 A b c e-4 A c^2 d+5 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{7/2}}-\frac{d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (7 A b e-4 A c d+2 b B d)}{b^3}",1,"(e*(2*A*c^3*d^2 - 5*b^3*B*e^2 - b*c^2*d*(B*d + 2*A*e) + b^2*c*e*(8*B*d + 3*A*e))*Sqrt[d + e*x])/(b^2*c^3) + (e*(6*A*c^2*d + 5*b^2*B*e - 3*b*c*(B*d + A*e))*(d + e*x)^(3/2))/(3*b^2*c^2) - ((d + e*x)^(5/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*(b*x + c*x^2)) - (d^(5/2)*(2*b*B*d - 4*A*c*d + 7*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 + ((c*d - b*e)^(5/2)*(2*b*B*c*d - 4*A*c^2*d + 5*b^2*B*e - 3*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(7/2))","A",7,5,26,0.1923,1,"{818, 824, 826, 1166, 208}"
1240,1,225,0,0.5820951,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^2,x]","-\frac{(d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}+\frac{e \sqrt{d+e x} \left(-b c (A e+B d)+2 A c^2 d+3 b^2 B e\right)}{b^2 c^2}-\frac{(c d-b e)^{3/2} \left(-b c (2 B d-A e)+4 A c^2 d-3 b^2 B e\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{5/2}}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (5 A b e-4 A c d+2 b B d)}{b^3}","-\frac{(d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}+\frac{e \sqrt{d+e x} \left(-b c (A e+B d)+2 A c^2 d+3 b^2 B e\right)}{b^2 c^2}-\frac{(c d-b e)^{3/2} \left(-b c (2 B d-A e)+4 A c^2 d-3 b^2 B e\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{5/2}}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (5 A b e-4 A c d+2 b B d)}{b^3}",1,"(e*(2*A*c^2*d + 3*b^2*B*e - b*c*(B*d + A*e))*Sqrt[d + e*x])/(b^2*c^2) - ((d + e*x)^(3/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*(b*x + c*x^2)) - (d^(3/2)*(2*b*B*d - 4*A*c*d + 5*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - ((c*d - b*e)^(3/2)*(4*A*c^2*d - 3*b^2*B*e - b*c*(2*B*d - A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(5/2))","A",6,5,26,0.1923,1,"{818, 824, 826, 1166, 208}"
1241,1,181,0,0.3370437,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^2,x]","-\frac{\sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}-\frac{\sqrt{c d-b e} \left(-b c (A e+2 B d)+4 A c^2 d+b^2 (-B) e\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{3/2}}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (3 A b e-4 A c d+2 b B d)}{b^3}","-\frac{\sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \left(b x+c x^2\right)}-\frac{\sqrt{c d-b e} \left(-b c (A e+2 B d)+4 A c^2 d+b^2 (-B) e\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 c^{3/2}}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (3 A b e-4 A c d+2 b B d)}{b^3}",1,"-((Sqrt[d + e*x]*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*(b*x + c*x^2))) - (Sqrt[d]*(2*b*B*d - 4*A*c*d + 3*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/b^3 - (Sqrt[c*d - b*e]*(4*A*c^2*d - b^2*B*e - b*c*(2*B*d + A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*c^(3/2))","A",5,4,26,0.1538,1,"{818, 826, 1166, 208}"
1242,1,158,0,0.3138632,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^2} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^2,x]","\frac{\left(3 A b c e-4 A c^2 d+b^2 (-B) e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 \sqrt{c} \sqrt{c d-b e}}-\frac{\sqrt{d+e x} (A b-x (b B-2 A c))}{b^2 \left(b x+c x^2\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (A b e-4 A c d+2 b B d)}{b^3 \sqrt{d}}","\frac{\left(3 A b c e-4 A c^2 d+b^2 (-B) e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 \sqrt{c} \sqrt{c d-b e}}-\frac{\sqrt{d+e x} (A b-x (b B-2 A c))}{b^2 \left(b x+c x^2\right)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (A b e-4 A c d+2 b B d)}{b^3 \sqrt{d}}",1,"-(((A*b - (b*B - 2*A*c)*x)*Sqrt[d + e*x])/(b^2*(b*x + c*x^2))) - ((2*b*B*d - 4*A*c*d + A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*Sqrt[d]) + ((2*b*B*c*d - 4*A*c^2*d - b^2*B*e + 3*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*Sqrt[c]*Sqrt[c*d - b*e])","A",5,4,26,0.1538,1,"{820, 826, 1166, 208}"
1243,1,188,0,0.3386039,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^2),x]","\frac{\sqrt{c} \left(5 A b c e-4 A c^2 d-3 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-A b e-4 A c d+2 b B d)}{b^3 d^{3/2}}-\frac{\sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \left(b x+c x^2\right) (c d-b e)}","\frac{\sqrt{c} \left(5 A b c e-4 A c^2 d-3 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{3/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-A b e-4 A c d+2 b B d)}{b^3 d^{3/2}}-\frac{\sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \left(b x+c x^2\right) (c d-b e)}",1,"-((Sqrt[d + e*x]*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*(b*x + c*x^2))) - ((2*b*B*d - 4*A*c*d - A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(3/2)) + (Sqrt[c]*(2*b*B*c*d - 4*A*c^2*d - 3*b^2*B*e + 5*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(3/2))","A",5,4,26,0.1538,1,"{822, 826, 1166, 208}"
1244,1,254,0,0.5558347,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^2),x]","-\frac{e \left(b^2 (-e) (2 B d-3 A e)-b c d (2 A e+B d)+2 A c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{c^{3/2} \left(7 A b c e-4 A c^2 d-5 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-3 A b e-4 A c d+2 b B d)}{b^3 d^{5/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)}","-\frac{e \left(b^2 (-e) (2 B d-3 A e)-b c d (2 A e+B d)+2 A c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{c^{3/2} \left(7 A b c e-4 A c^2 d-5 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-3 A b e-4 A c d+2 b B d)}{b^3 d^{5/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)}",1,"-((e*(2*A*c^2*d^2 - b^2*e*(2*B*d - 3*A*e) - b*c*d*(B*d + 2*A*e)))/(b^2*d^2*(c*d - b*e)^2*Sqrt[d + e*x])) - (A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x)/(b^2*d*(c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)) - ((2*b*B*d - 4*A*c*d - 3*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(5/2)) + (c^(3/2)*(2*b*B*c*d - 4*A*c^2*d - 5*b^2*B*e + 7*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(5/2))","A",6,5,26,0.1923,1,"{822, 828, 826, 1166, 208}"
1245,1,344,0,0.9170874,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)^2),x]","-\frac{e \left(-b^2 c d e (6 B d-11 A e)+b^3 e^2 (2 B d-5 A e)-b c^2 d^2 (3 A e+B d)+2 A c^3 d^3\right)}{b^2 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{e \left(b^2 (-e) (2 B d-5 A e)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}+\frac{c^{5/2} \left(9 A b c e-4 A c^2 d-7 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-5 A b e-4 A c d+2 b B d)}{b^3 d^{7/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)}","-\frac{e \left(-b^2 c d e (6 B d-11 A e)+b^3 e^2 (2 B d-5 A e)-b c^2 d^2 (3 A e+B d)+2 A c^3 d^3\right)}{b^2 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{e \left(b^2 (-e) (2 B d-5 A e)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}+\frac{c^{5/2} \left(9 A b c e-4 A c^2 d-7 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{7/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-5 A b e-4 A c d+2 b B d)}{b^3 d^{7/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)}",1,"-(e*(6*A*c^2*d^2 - b^2*e*(2*B*d - 5*A*e) - 3*b*c*d*(B*d + 2*A*e)))/(3*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (e*(2*A*c^3*d^3 - b^2*c*d*e*(6*B*d - 11*A*e) + b^3*e^2*(2*B*d - 5*A*e) - b*c^2*d^2*(B*d + 3*A*e)))/(b^2*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*(b*x + c*x^2)) - ((2*b*B*d - 4*A*c*d - 5*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(7/2)) + (c^(5/2)*(2*b*B*c*d - 4*A*c^2*d - 7*b^2*B*e + 9*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(7/2))","A",7,5,26,0.1923,1,"{822, 828, 826, 1166, 208}"
1246,1,457,0,1.2827146,"\int \frac{A+B x}{(d+e x)^{7/2} \left(b x+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(b*x + c*x^2)^2),x]","-\frac{e \left(-2 b^2 c^2 d^2 e (6 B d-13 A e)+8 b^3 c d e^2 (B d-3 A e)+b^4 \left(-e^3\right) (2 B d-7 A e)-b c^3 d^3 (4 A e+B d)+2 A c^4 d^4\right)}{b^2 d^4 \sqrt{d+e x} (c d-b e)^4}-\frac{e \left(-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right)}{3 b^2 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac{e \left(b^2 (-e) (2 B d-7 A e)-5 b c d (2 A e+B d)+10 A c^2 d^2\right)}{5 b^2 d^2 (d+e x)^{5/2} (c d-b e)^2}+\frac{c^{7/2} \left(11 A b c e-4 A c^2 d-9 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-7 A b e-4 A c d+2 b B d)}{b^3 d^{9/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{5/2} (c d-b e)}","-\frac{e \left(-2 b^2 c^2 d^2 e (6 B d-13 A e)+8 b^3 c d e^2 (B d-3 A e)+b^4 \left(-e^3\right) (2 B d-7 A e)-b c^3 d^3 (4 A e+B d)+2 A c^4 d^4\right)}{b^2 d^4 \sqrt{d+e x} (c d-b e)^4}-\frac{e \left(-b^2 c d e (6 B d-17 A e)+b^3 e^2 (2 B d-7 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right)}{3 b^2 d^3 (d+e x)^{3/2} (c d-b e)^3}-\frac{e \left(b^2 (-e) (2 B d-7 A e)-5 b c d (2 A e+B d)+10 A c^2 d^2\right)}{5 b^2 d^2 (d+e x)^{5/2} (c d-b e)^2}+\frac{c^{7/2} \left(11 A b c e-4 A c^2 d-9 b^2 B e+2 b B c d\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{b^3 (c d-b e)^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) (-7 A b e-4 A c d+2 b B d)}{b^3 d^{9/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{b^2 d \left(b x+c x^2\right) (d+e x)^{5/2} (c d-b e)}",1,"-(e*(10*A*c^2*d^2 - b^2*e*(2*B*d - 7*A*e) - 5*b*c*d*(B*d + 2*A*e)))/(5*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(5/2)) - (e*(6*A*c^3*d^3 - b^2*c*d*e*(6*B*d - 17*A*e) + b^3*e^2*(2*B*d - 7*A*e) - 3*b*c^2*d^2*(B*d + 3*A*e)))/(3*b^2*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) - (e*(2*A*c^4*d^4 - 2*b^2*c^2*d^2*e*(6*B*d - 13*A*e) - b^4*e^3*(2*B*d - 7*A*e) + 8*b^3*c*d*e^2*(B*d - 3*A*e) - b*c^3*d^3*(B*d + 4*A*e)))/(b^2*d^4*(c*d - b*e)^4*Sqrt[d + e*x]) - (A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x)/(b^2*d*(c*d - b*e)*(d + e*x)^(5/2)*(b*x + c*x^2)) - ((2*b*B*d - 4*A*c*d - 7*A*b*e)*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(b^3*d^(9/2)) + (c^(7/2)*(2*b*B*c*d - 4*A*c^2*d - 9*b^2*B*e + 11*A*b*c*e)*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(b^3*(c*d - b*e)^(9/2))","A",8,5,26,0.1923,1,"{822, 828, 826, 1166, 208}"
1247,1,461,0,1.2151267,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(9/2))/(b*x + c*x^2)^3,x]","\frac{(d+e x)^{3/2} \left(x \left(b^2 c^2 d e (10 A e+9 B d)+b^3 c e^2 (A e+4 B d)-12 b c^3 d^2 (3 A e+B d)+24 A c^4 d^3-5 b^4 B e^3\right)+b c d^2 \left(-b c (13 A e+6 B d)+12 A c^2 d+2 b^2 B e\right)\right)}{4 b^4 c^2 \left(b x+c x^2\right)}-\frac{3 e \sqrt{d+e x} \left(b^2 c^2 d e (2 A e+3 B d)+b^3 c e^2 (A e+2 B d)-4 b c^3 d^2 (3 A e+B d)+8 A c^4 d^3-5 b^4 B e^3\right)}{4 b^4 c^3}+\frac{3 (c d-b e)^{5/2} \left(-b^2 c e (8 B d-A e)-4 b c^2 d (2 B d-A e)+16 A c^3 d^2-5 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{7/2}}-\frac{3 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(3 b^2 e (7 A e+4 B d)-4 b c d (9 A e+2 B d)+16 A c^2 d^2\right)}{4 b^5}-\frac{(d+e x)^{7/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}","\frac{(d+e x)^{3/2} \left(x \left(b^2 c^2 d e (10 A e+9 B d)+b^3 c e^2 (A e+4 B d)-12 b c^3 d^2 (3 A e+B d)+24 A c^4 d^3-5 b^4 B e^3\right)+b c d^2 \left(-b c (13 A e+6 B d)+12 A c^2 d+2 b^2 B e\right)\right)}{4 b^4 c^2 \left(b x+c x^2\right)}-\frac{3 e \sqrt{d+e x} \left(b^2 c^2 d e (2 A e+3 B d)+b^3 c e^2 (A e+2 B d)-4 b c^3 d^2 (3 A e+B d)+8 A c^4 d^3-5 b^4 B e^3\right)}{4 b^4 c^3}+\frac{3 (c d-b e)^{5/2} \left(-b^2 c e (8 B d-A e)-4 b c^2 d (2 B d-A e)+16 A c^3 d^2-5 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{7/2}}-\frac{3 d^{5/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(3 b^2 e (7 A e+4 B d)-4 b c d (9 A e+2 B d)+16 A c^2 d^2\right)}{4 b^5}-\frac{(d+e x)^{7/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}",1,"(-3*e*(8*A*c^4*d^3 - 5*b^4*B*e^3 + b^3*c*e^2*(2*B*d + A*e) + b^2*c^2*d*e*(3*B*d + 2*A*e) - 4*b*c^3*d^2*(B*d + 3*A*e))*Sqrt[d + e*x])/(4*b^4*c^3) - ((d + e*x)^(7/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(2*b^2*c*(b*x + c*x^2)^2) + ((d + e*x)^(3/2)*(b*c*d^2*(12*A*c^2*d + 2*b^2*B*e - b*c*(6*B*d + 13*A*e)) + (24*A*c^4*d^3 - 5*b^4*B*e^3 + b^3*c*e^2*(4*B*d + A*e) - 12*b*c^3*d^2*(B*d + 3*A*e) + b^2*c^2*d*e*(9*B*d + 10*A*e))*x))/(4*b^4*c^2*(b*x + c*x^2)) - (3*d^(5/2)*(16*A*c^2*d^2 + 3*b^2*e*(4*B*d + 7*A*e) - 4*b*c*d*(2*B*d + 9*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5) + (3*(c*d - b*e)^(5/2)*(16*A*c^3*d^2 - 5*b^3*B*e^2 - 4*b*c^2*d*(2*B*d - A*e) - b^2*c*e*(8*B*d - A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*c^(7/2))","A",7,5,26,0.1923,1,"{818, 824, 826, 1166, 208}"
1248,1,363,0,0.826888,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^3,x]","\frac{\sqrt{d+e x} \left(x \left(b^2 c^2 d e (14 A e+11 B d)-A b^3 c e^3-12 b c^3 d^2 (3 A e+B d)+24 A c^4 d^3-3 b^4 B e^3\right)+b c d^2 \left(-b c (11 A e+6 B d)+12 A c^2 d+2 b^2 B e\right)\right)}{4 b^4 c^2 \left(b x+c x^2\right)}+\frac{(c d-b e)^{3/2} \left(-b^2 c e (A e+8 B d)-12 b c^2 d (A e+2 B d)+48 A c^3 d^2-3 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{5/2}}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(7 b^2 e (5 A e+4 B d)-12 b c d (7 A e+2 B d)+48 A c^2 d^2\right)}{4 b^5}-\frac{(d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}","\frac{\sqrt{d+e x} \left(x \left(b^2 c^2 d e (14 A e+11 B d)-A b^3 c e^3-12 b c^3 d^2 (3 A e+B d)+24 A c^4 d^3-3 b^4 B e^3\right)+b c d^2 \left(-b c (11 A e+6 B d)+12 A c^2 d+2 b^2 B e\right)\right)}{4 b^4 c^2 \left(b x+c x^2\right)}+\frac{(c d-b e)^{3/2} \left(-b^2 c e (A e+8 B d)-12 b c^2 d (A e+2 B d)+48 A c^3 d^2-3 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{5/2}}-\frac{d^{3/2} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(7 b^2 e (5 A e+4 B d)-12 b c d (7 A e+2 B d)+48 A c^2 d^2\right)}{4 b^5}-\frac{(d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}",1,"-((d + e*x)^(5/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(2*b^2*c*(b*x + c*x^2)^2) + (Sqrt[d + e*x]*(b*c*d^2*(12*A*c^2*d + 2*b^2*B*e - b*c*(6*B*d + 11*A*e)) + (24*A*c^4*d^3 - 3*b^4*B*e^3 - A*b^3*c*e^3 - 12*b*c^3*d^2*(B*d + 3*A*e) + b^2*c^2*d*e*(11*B*d + 14*A*e))*x))/(4*b^4*c^2*(b*x + c*x^2)) - (d^(3/2)*(48*A*c^2*d^2 + 7*b^2*e*(4*B*d + 5*A*e) - 12*b*c*d*(2*B*d + 7*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5) + ((c*d - b*e)^(3/2)*(48*A*c^3*d^2 - 3*b^3*B*e^2 - 12*b*c^2*d*(2*B*d + A*e) - b^2*c*e*(8*B*d + A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*c^(5/2))","A",6,4,26,0.1538,1,"{818, 826, 1166, 208}"
1249,1,344,0,0.697501,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^3,x]","-\frac{\sqrt{d+e x} \left(b d \left(9 A b c e-12 A c^2 d-2 b^2 B e+6 b B c d\right)-x \left(b^2 c e (3 A e+7 B d)-12 b c^2 d (2 A e+B d)+24 A c^3 d^2+b^3 B e^2\right)\right)}{4 b^4 c \left(b x+c x^2\right)}+\frac{\sqrt{c d-b e} \left(b^2 c e (3 A e+8 B d)-12 b c^2 d (3 A e+2 B d)+48 A c^3 d^2+b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{3/2}}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(5 b^2 e (3 A e+4 B d)-12 b c d (5 A e+2 B d)+48 A c^2 d^2\right)}{4 b^5}-\frac{(d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}","-\frac{\sqrt{d+e x} \left(b d \left(9 A b c e-12 A c^2 d-2 b^2 B e+6 b B c d\right)-x \left(b^2 c e (3 A e+7 B d)-12 b c^2 d (2 A e+B d)+24 A c^3 d^2+b^3 B e^2\right)\right)}{4 b^4 c \left(b x+c x^2\right)}+\frac{\sqrt{c d-b e} \left(b^2 c e (3 A e+8 B d)-12 b c^2 d (3 A e+2 B d)+48 A c^3 d^2+b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 c^{3/2}}-\frac{\sqrt{d} \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(5 b^2 e (3 A e+4 B d)-12 b c d (5 A e+2 B d)+48 A c^2 d^2\right)}{4 b^5}-\frac{(d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}",1,"-((d + e*x)^(3/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(2*b^2*c*(b*x + c*x^2)^2) - (Sqrt[d + e*x]*(b*d*(6*b*B*c*d - 12*A*c^2*d - 2*b^2*B*e + 9*A*b*c*e) - (24*A*c^3*d^2 + b^3*B*e^2 - 12*b*c^2*d*(B*d + 2*A*e) + b^2*c*e*(7*B*d + 3*A*e))*x))/(4*b^4*c*(b*x + c*x^2)) - (Sqrt[d]*(48*A*c^2*d^2 + 5*b^2*e*(4*B*d + 3*A*e) - 12*b*c*d*(2*B*d + 5*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5) + (Sqrt[c*d - b*e]*(48*A*c^3*d^2 + b^3*B*e^2 - 12*b*c^2*d*(2*B*d + 3*A*e) + b^2*c*e*(8*B*d + 3*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*c^(3/2))","A",6,5,26,0.1923,1,"{818, 820, 826, 1166, 208}"
1250,1,346,0,0.8687461,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^3,x]","\frac{3 \left(b^2 c e (5 A e+8 B d)-4 b c^2 d (5 A e+2 B d)+16 A c^3 d^2+b^3 (-B) e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 \sqrt{c} \sqrt{c d-b e}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 e (A e+4 B d)-4 b c d (3 A e+2 B d)+16 A c^2 d^2\right)}{4 b^5 \sqrt{d}}-\frac{\sqrt{d+e x} \left(b (c d-b e) \left(7 A b c e-12 A c^2 d-2 b^2 B e+6 b B c d\right)-3 c x (c d-b e) \left(-4 b c (A e+B d)+8 A c^2 d+b^2 B e\right)\right)}{4 b^4 c \left(b x+c x^2\right) (c d-b e)}-\frac{\sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}","\frac{3 \left(b^2 c e (5 A e+8 B d)-4 b c^2 d (5 A e+2 B d)+16 A c^3 d^2+b^3 (-B) e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 \sqrt{c} \sqrt{c d-b e}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 e (A e+4 B d)-4 b c d (3 A e+2 B d)+16 A c^2 d^2\right)}{4 b^5 \sqrt{d}}-\frac{\sqrt{d+e x} \left(b (c d-b e) \left(7 A b c e-12 A c^2 d-2 b^2 B e+6 b B c d\right)-3 c x (c d-b e) \left(-4 b c (A e+B d)+8 A c^2 d+b^2 B e\right)\right)}{4 b^4 c \left(b x+c x^2\right) (c d-b e)}-\frac{\sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{2 b^2 c \left(b x+c x^2\right)^2}",1,"-(Sqrt[d + e*x]*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(2*b^2*c*(b*x + c*x^2)^2) - (Sqrt[d + e*x]*(b*(c*d - b*e)*(6*b*B*c*d - 12*A*c^2*d - 2*b^2*B*e + 7*A*b*c*e) - 3*c*(c*d - b*e)*(8*A*c^2*d + b^2*B*e - 4*b*c*(B*d + A*e))*x))/(4*b^4*c*(c*d - b*e)*(b*x + c*x^2)) - (3*(16*A*c^2*d^2 + b^2*e*(4*B*d + A*e) - 4*b*c*d*(2*B*d + 3*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*Sqrt[d]) + (3*(16*A*c^3*d^2 - b^3*B*e^2 - 4*b*c^2*d*(2*B*d + 5*A*e) + b^2*c*e*(8*B*d + 5*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*Sqrt[c]*Sqrt[c*d - b*e])","A",6,5,26,0.1923,1,"{818, 822, 826, 1166, 208}"
1251,1,317,0,0.6996562,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^3} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^3,x]","\frac{\sqrt{c} \left(5 b^2 c e (7 A e+8 B d)-12 b c^2 d (7 A e+2 B d)+48 A c^3 d^2-15 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{3/2}}-\frac{\sqrt{d+e x} \left(b (c d-b e) (A b e-12 A c d+6 b B d)-c x \left(b^2 e (A e+11 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right)\right)}{4 b^4 d \left(b x+c x^2\right) (c d-b e)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 e (4 B d-A e)-12 b c d (A e+2 B d)+48 A c^2 d^2\right)}{4 b^5 d^{3/2}}-\frac{\sqrt{d+e x} (A b-x (b B-2 A c))}{2 b^2 \left(b x+c x^2\right)^2}","\frac{\sqrt{c} \left(5 b^2 c e (7 A e+8 B d)-12 b c^2 d (7 A e+2 B d)+48 A c^3 d^2-15 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{3/2}}-\frac{\sqrt{d+e x} \left(b (c d-b e) (A b e-12 A c d+6 b B d)-c x \left(b^2 e (A e+11 B d)-12 b c d (2 A e+B d)+24 A c^2 d^2\right)\right)}{4 b^4 d \left(b x+c x^2\right) (c d-b e)}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 e (4 B d-A e)-12 b c d (A e+2 B d)+48 A c^2 d^2\right)}{4 b^5 d^{3/2}}-\frac{\sqrt{d+e x} (A b-x (b B-2 A c))}{2 b^2 \left(b x+c x^2\right)^2}",1,"-((A*b - (b*B - 2*A*c)*x)*Sqrt[d + e*x])/(2*b^2*(b*x + c*x^2)^2) - (Sqrt[d + e*x]*(b*(c*d - b*e)*(6*b*B*d - 12*A*c*d + A*b*e) - c*(24*A*c^2*d^2 + b^2*e*(11*B*d + A*e) - 12*b*c*d*(B*d + 2*A*e))*x))/(4*b^4*d*(c*d - b*e)*(b*x + c*x^2)) - ((48*A*c^2*d^2 + b^2*e*(4*B*d - A*e) - 12*b*c*d*(2*B*d + A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(3/2)) + (Sqrt[c]*(48*A*c^3*d^2 - 15*b^3*B*e^2 - 12*b*c^2*d*(2*B*d + 7*A*e) + 5*b^2*c*e*(8*B*d + 7*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(3/2))","A",6,5,26,0.1923,1,"{820, 822, 826, 1166, 208}"
1252,1,394,0,0.900164,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^3),x]","\frac{\sqrt{d+e x} \left(c x \left(b^2 c d e (6 A e+19 B d)+b^3 \left(-e^2\right) (4 B d-3 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (4 B d-3 A e)-b c d (7 A e+6 B d)+12 A c^2 d^2\right)\right)}{4 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}+\frac{c^{3/2} \left(7 b^2 c e (9 A e+8 B d)-12 b c^2 d (9 A e+2 B d)+48 A c^3 d^2-35 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 (-e) (4 B d-3 A e)-12 b c d (2 B d-A e)+48 A c^2 d^2\right)}{4 b^5 d^{5/2}}-\frac{\sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{2 b^2 d \left(b x+c x^2\right)^2 (c d-b e)}","\frac{\sqrt{d+e x} \left(c x \left(b^2 c d e (6 A e+19 B d)+b^3 \left(-e^2\right) (4 B d-3 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (4 B d-3 A e)-b c d (7 A e+6 B d)+12 A c^2 d^2\right)\right)}{4 b^4 d^2 \left(b x+c x^2\right) (c d-b e)^2}+\frac{c^{3/2} \left(7 b^2 c e (9 A e+8 B d)-12 b c^2 d (9 A e+2 B d)+48 A c^3 d^2-35 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{5/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 (-e) (4 B d-3 A e)-12 b c d (2 B d-A e)+48 A c^2 d^2\right)}{4 b^5 d^{5/2}}-\frac{\sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{2 b^2 d \left(b x+c x^2\right)^2 (c d-b e)}",1,"-(Sqrt[d + e*x]*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(2*b^2*d*(c*d - b*e)*(b*x + c*x^2)^2) + (Sqrt[d + e*x]*(b*(c*d - b*e)*(12*A*c^2*d^2 + b^2*e*(4*B*d - 3*A*e) - b*c*d*(6*B*d + 7*A*e)) + c*(24*A*c^3*d^3 - b^3*e^2*(4*B*d - 3*A*e) - 12*b*c^2*d^2*(B*d + 3*A*e) + b^2*c*d*e*(19*B*d + 6*A*e))*x))/(4*b^4*d^2*(c*d - b*e)^2*(b*x + c*x^2)) - ((48*A*c^2*d^2 - b^2*e*(4*B*d - 3*A*e) - 12*b*c*d*(2*B*d - A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(5/2)) + (c^(3/2)*(48*A*c^3*d^2 - 35*b^3*B*e^2 - 12*b*c^2*d*(2*B*d + 9*A*e) + 7*b^2*c*e*(8*B*d + 9*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(5/2))","A",6,4,26,0.1538,1,"{822, 826, 1166, 208}"
1253,1,506,0,1.4510714,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^3),x]","\frac{c x \left(b^2 c d e (2 A e+21 B d)+b^3 \left(-e^2\right) (4 B d-5 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (4 B d-5 A e)-b c d (5 A e+6 B d)+12 A c^2 d^2\right)}{4 b^4 d^2 \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)^2}+\frac{3 e \left(b^2 c^2 d^2 e (5 A e+9 B d)-b^3 c d e^2 (4 B d-3 A e)+b^4 e^3 (4 B d-5 A e)-4 b c^3 d^3 (4 A e+B d)+8 A c^4 d^4\right)}{4 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{3 c^{5/2} \left(3 b^2 c e (11 A e+8 B d)-4 b c^2 d (11 A e+2 B d)+16 A c^3 d^2-21 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{7/2}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 (-e) (4 B d-5 A e)-4 b c d (2 B d-3 A e)+16 A c^2 d^2\right)}{4 b^5 d^{7/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 \sqrt{d+e x} (c d-b e)}","\frac{c x \left(b^2 c d e (2 A e+21 B d)+b^3 \left(-e^2\right) (4 B d-5 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (4 B d-5 A e)-b c d (5 A e+6 B d)+12 A c^2 d^2\right)}{4 b^4 d^2 \left(b x+c x^2\right) \sqrt{d+e x} (c d-b e)^2}+\frac{3 e \left(b^2 c^2 d^2 e (5 A e+9 B d)-b^3 c d e^2 (4 B d-3 A e)+b^4 e^3 (4 B d-5 A e)-4 b c^3 d^3 (4 A e+B d)+8 A c^4 d^4\right)}{4 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{3 c^{5/2} \left(3 b^2 c e (11 A e+8 B d)-4 b c^2 d (11 A e+2 B d)+16 A c^3 d^2-21 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{7/2}}-\frac{3 \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(b^2 (-e) (4 B d-5 A e)-4 b c d (2 B d-3 A e)+16 A c^2 d^2\right)}{4 b^5 d^{7/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 \sqrt{d+e x} (c d-b e)}",1,"(3*e*(8*A*c^4*d^4 + b^4*e^3*(4*B*d - 5*A*e) - b^3*c*d*e^2*(4*B*d - 3*A*e) - 4*b*c^3*d^3*(B*d + 4*A*e) + b^2*c^2*d^2*e*(9*B*d + 5*A*e)))/(4*b^4*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x)/(2*b^2*d*(c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)^2) + (b*(c*d - b*e)*(12*A*c^2*d^2 + b^2*e*(4*B*d - 5*A*e) - b*c*d*(6*B*d + 5*A*e)) + c*(24*A*c^3*d^3 - b^3*e^2*(4*B*d - 5*A*e) + b^2*c*d*e*(21*B*d + 2*A*e) - 12*b*c^2*d^2*(B*d + 3*A*e))*x)/(4*b^4*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*(b*x + c*x^2)) - (3*(16*A*c^2*d^2 - b^2*e*(4*B*d - 5*A*e) - 4*b*c*d*(2*B*d - 3*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(7/2)) + (3*c^(5/2)*(16*A*c^3*d^2 - 21*b^3*B*e^2 - 4*b*c^2*d*(2*B*d + 11*A*e) + 3*b^2*c*e*(8*B*d + 11*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(7/2))","A",7,5,26,0.1923,1,"{822, 828, 826, 1166, 208}"
1254,1,644,0,1.7905851,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)^3),x]","\frac{c x \left(b^2 c d e (23 B d-2 A e)+b^3 \left(-e^2\right) (4 B d-7 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (4 B d-7 A e)-3 b c d (A e+2 B d)+12 A c^2 d^2\right)}{4 b^4 d^2 \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)^2}+\frac{e \left(-6 b^3 c^2 d^2 e^2 (4 B d-3 A e)+7 b^2 c^3 d^3 e (4 A e+5 B d)+8 b^4 c d e^3 (7 B d-10 A e)-5 b^5 e^4 (4 B d-7 A e)-12 b c^4 d^4 (5 A e+B d)+24 A c^5 d^5\right)}{4 b^4 d^4 \sqrt{d+e x} (c d-b e)^4}+\frac{e \left(3 b^2 c^2 d^2 e (9 A e+29 B d)-9 b^3 c d e^2 (4 B d-5 A e)+5 b^4 e^3 (4 B d-7 A e)-36 b c^3 d^3 (4 A e+B d)+72 A c^4 d^4\right)}{12 b^4 d^3 (d+e x)^{3/2} (c d-b e)^3}+\frac{c^{7/2} \left(11 b^2 c e (13 A e+8 B d)-12 b c^2 d (13 A e+2 B d)+48 A c^3 d^2-99 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(-5 b^2 e (4 B d-7 A e)-12 b c d (2 B d-5 A e)+48 A c^2 d^2\right)}{4 b^5 d^{9/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 (d+e x)^{3/2} (c d-b e)}","\frac{c x \left(b^2 c d e (23 B d-2 A e)+b^3 \left(-e^2\right) (4 B d-7 A e)-12 b c^2 d^2 (3 A e+B d)+24 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (4 B d-7 A e)-3 b c d (A e+2 B d)+12 A c^2 d^2\right)}{4 b^4 d^2 \left(b x+c x^2\right) (d+e x)^{3/2} (c d-b e)^2}+\frac{e \left(-6 b^3 c^2 d^2 e^2 (4 B d-3 A e)+7 b^2 c^3 d^3 e (4 A e+5 B d)+8 b^4 c d e^3 (7 B d-10 A e)-5 b^5 e^4 (4 B d-7 A e)-12 b c^4 d^4 (5 A e+B d)+24 A c^5 d^5\right)}{4 b^4 d^4 \sqrt{d+e x} (c d-b e)^4}+\frac{e \left(3 b^2 c^2 d^2 e (9 A e+29 B d)-9 b^3 c d e^2 (4 B d-5 A e)+5 b^4 e^3 (4 B d-7 A e)-36 b c^3 d^3 (4 A e+B d)+72 A c^4 d^4\right)}{12 b^4 d^3 (d+e x)^{3/2} (c d-b e)^3}+\frac{c^{7/2} \left(11 b^2 c e (13 A e+8 B d)-12 b c^2 d (13 A e+2 B d)+48 A c^3 d^2-99 b^3 B e^2\right) \tanh ^{-1}\left(\frac{\sqrt{c} \sqrt{d+e x}}{\sqrt{c d-b e}}\right)}{4 b^5 (c d-b e)^{9/2}}-\frac{\tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d}}\right) \left(-5 b^2 e (4 B d-7 A e)-12 b c d (2 B d-5 A e)+48 A c^2 d^2\right)}{4 b^5 d^{9/2}}-\frac{c x (2 A c d-b (A e+B d))+A b (c d-b e)}{2 b^2 d \left(b x+c x^2\right)^2 (d+e x)^{3/2} (c d-b e)}",1,"(e*(72*A*c^4*d^4 + 5*b^4*e^3*(4*B*d - 7*A*e) - 9*b^3*c*d*e^2*(4*B*d - 5*A*e) - 36*b*c^3*d^3*(B*d + 4*A*e) + 3*b^2*c^2*d^2*e*(29*B*d + 9*A*e)))/(12*b^4*d^3*(c*d - b*e)^3*(d + e*x)^(3/2)) + (e*(24*A*c^5*d^5 + 8*b^4*c*d*e^3*(7*B*d - 10*A*e) - 5*b^5*e^4*(4*B*d - 7*A*e) - 6*b^3*c^2*d^2*e^2*(4*B*d - 3*A*e) + 7*b^2*c^3*d^3*e*(5*B*d + 4*A*e) - 12*b*c^4*d^4*(B*d + 5*A*e)))/(4*b^4*d^4*(c*d - b*e)^4*Sqrt[d + e*x]) - (A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x)/(2*b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*(b*x + c*x^2)^2) + (b*(c*d - b*e)*(12*A*c^2*d^2 + b^2*e*(4*B*d - 7*A*e) - 3*b*c*d*(2*B*d + A*e)) + c*(24*A*c^3*d^3 - b^3*e^2*(4*B*d - 7*A*e) + b^2*c*d*e*(23*B*d - 2*A*e) - 12*b*c^2*d^2*(B*d + 3*A*e))*x)/(4*b^4*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)*(b*x + c*x^2)) - ((48*A*c^2*d^2 - 5*b^2*e*(4*B*d - 7*A*e) - 12*b*c*d*(2*B*d - 5*A*e))*ArcTanh[Sqrt[d + e*x]/Sqrt[d]])/(4*b^5*d^(9/2)) + (c^(7/2)*(48*A*c^3*d^2 - 99*b^3*B*e^2 - 12*b*c^2*d*(2*B*d + 13*A*e) + 11*b^2*c*e*(8*B*d + 13*A*e))*ArcTanh[(Sqrt[c]*Sqrt[d + e*x])/Sqrt[c*d - b*e]])/(4*b^5*(c*d - b*e)^(9/2))","A",8,5,26,0.1923,1,"{822, 828, 826, 1166, 208}"
1255,1,433,0,0.6040684,"\int (A+B x) \sqrt{d+e x} \sqrt{b x+c x^2} \, dx","Int[(A + B*x)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(3 c e x (7 A c e-4 b B e+B c d)+7 A c e (b e+c d)-B \left(4 b^2 e^2-2 b c d e+4 c^2 d^2\right)\right)}{105 c^2 e^2}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(7 A c e (2 c d-b e)-B \left(-4 b^2 e^2-b c d e+8 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(\left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right) (7 A c e-4 b B e+B c d)+5 c d e (3 b B-7 A c) (2 c d-b e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 B \left(b x+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(3 c e x (7 A c e-4 b B e+B c d)+7 A c e (b e+c d)-B \left(4 b^2 e^2-2 b c d e+4 c^2 d^2\right)\right)}{105 c^2 e^2}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(7 A c e (2 c d-b e)-B \left(-4 b^2 e^2-b c d e+8 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(\left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right) (7 A c e-4 b B e+B c d)+5 c d e (3 b B-7 A c) (2 c d-b e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{5/2} e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 B \left(b x+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}",1,"(2*Sqrt[d + e*x]*(7*A*c*e*(c*d + b*e) - B*(4*c^2*d^2 - 2*b*c*d*e + 4*b^2*e^2) + 3*c*e*(B*c*d - 4*b*B*e + 7*A*c*e)*x)*Sqrt[b*x + c*x^2])/(105*c^2*e^2) + (2*B*Sqrt[d + e*x]*(b*x + c*x^2)^(3/2))/(7*c) + (2*Sqrt[-b]*(5*c*(3*b*B - 7*A*c)*d*e*(2*c*d - b*e) + (B*c*d - 4*b*B*e + 7*A*c*e)*(8*c^2*d^2 - 3*b*c*d*e - 2*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(5/2)*e^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*d*(c*d - b*e)*(7*A*c*e*(2*c*d - b*e) - B*(8*c^2*d^2 - b*c*d*e - 4*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(5/2)*e^3*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{832, 814, 843, 715, 112, 110, 117, 116}"
1256,1,318,0,0.3293674,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/Sqrt[d + e*x],x]","-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(5 A c e (2 c d-b e)-B \left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (-10 A c e+b B e+8 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (-5 A c e-b B e+4 B c d-3 B c e x)}{15 c e^2}","-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(5 A c e (2 c d-b e)-B \left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (-10 A c e+b B e+8 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{3/2} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (-5 A c e-b B e+4 B c d-3 B c e x)}{15 c e^2}",1,"(-2*Sqrt[d + e*x]*(4*B*c*d - b*B*e - 5*A*c*e - 3*B*c*e*x)*Sqrt[b*x + c*x^2])/(15*c*e^2) - (2*Sqrt[-b]*(5*A*c*e*(2*c*d - b*e) - B*(8*c^2*d^2 - 3*b*c*d*e - 2*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(3/2)*e^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*(8*B*c*d + b*B*e - 10*A*c*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(3/2)*e^3*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{814, 843, 715, 112, 110, 117, 116}"
1257,1,283,0,0.287848,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^(3/2),x]","\frac{2 \sqrt{b x+c x^2} (-3 A e+4 B d+B e x)}{3 e^2 \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (B d (8 c d-5 b e)-3 A e (2 c d-b e)) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (-6 A c e-b B e+8 B c d) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","\frac{2 \sqrt{b x+c x^2} (-3 A e+4 B d+B e x)}{3 e^2 \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (B d (8 c d-5 b e)-3 A e (2 c d-b e)) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (-6 A c e-b B e+8 B c d) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(2*(4*B*d - 3*A*e + B*e*x)*Sqrt[b*x + c*x^2])/(3*e^2*Sqrt[d + e*x]) - (2*Sqrt[-b]*(8*B*c*d - b*B*e - 6*A*c*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*Sqrt[c]*e^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*(B*d*(8*c*d - 5*b*e) - 3*A*e*(2*c*d - b*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*Sqrt[c]*e^3*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{812, 843, 715, 112, 110, 117, 116}"
1258,1,346,0,0.3800079,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{b x+c x^2} \left(d^2 (-A c e-3 b B e+4 B c d)+e x (B d (5 c d-4 b e)-A e (2 c d-b e))\right)}{3 d e^2 (d+e x)^{3/2} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (-2 A c e-3 b B e+8 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (B d (8 c d-7 b e)-A e (2 c d-b e)) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}","-\frac{2 \sqrt{b x+c x^2} \left(d^2 (-A c e-3 b B e+4 B c d)+e x (B d (5 c d-4 b e)-A e (2 c d-b e))\right)}{3 d e^2 (d+e x)^{3/2} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (-2 A c e-3 b B e+8 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 \sqrt{c} e^3 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (B d (8 c d-7 b e)-A e (2 c d-b e)) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}",1,"(-2*(d^2*(4*B*c*d - 3*b*B*e - A*c*e) + e*(B*d*(5*c*d - 4*b*e) - A*e*(2*c*d - b*e))*x)*Sqrt[b*x + c*x^2])/(3*d*e^2*(c*d - b*e)*(d + e*x)^(3/2)) + (2*Sqrt[-b]*Sqrt[c]*(B*d*(8*c*d - 7*b*e) - A*e*(2*c*d - b*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*d*e^3*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*(8*B*c*d - 3*b*B*e - 2*A*c*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*Sqrt[c]*e^3*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{810, 843, 715, 112, 110, 117, 116}"
1259,1,494,0,0.637924,"\int \frac{(A+B x) \sqrt{b x+c x^2}}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*Sqrt[b*x + c*x^2])/(d + e*x)^(7/2),x]","\frac{2 \sqrt{b x+c x^2} \left(2 A e \left(b^2 e^2-b c d e+c^2 d^2\right)+B d \left(3 b^2 e^2-13 b c d e+8 c^2 d^2\right)\right)}{15 d^2 e^2 \sqrt{d+e x} (c d-b e)^2}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(2 A e \left(b^2 e^2-b c d e+c^2 d^2\right)+B d \left(3 b^2 e^2-13 b c d e+8 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \sqrt{b x+c x^2} (e x (B d (7 c d-6 b e)-A e (2 c d-b e))+d (A e (c d-2 b e)+B d (4 c d-3 b e)))}{15 d e^2 (d+e x)^{5/2} (c d-b e)}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (A e (2 c d-b e)+B d (8 c d-9 b e)) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d e^3 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}","\frac{2 \sqrt{b x+c x^2} \left(2 A e \left(b^2 e^2-b c d e+c^2 d^2\right)+B d \left(3 b^2 e^2-13 b c d e+8 c^2 d^2\right)\right)}{15 d^2 e^2 \sqrt{d+e x} (c d-b e)^2}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(2 A e \left(b^2 e^2-b c d e+c^2 d^2\right)+B d \left(3 b^2 e^2-13 b c d e+8 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 e^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 \sqrt{b x+c x^2} (e x (B d (7 c d-6 b e)-A e (2 c d-b e))+d (A e (c d-2 b e)+B d (4 c d-3 b e)))}{15 d e^2 (d+e x)^{5/2} (c d-b e)}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (A e (2 c d-b e)+B d (8 c d-9 b e)) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d e^3 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}",1,"(2*(2*A*e*(c^2*d^2 - b*c*d*e + b^2*e^2) + B*d*(8*c^2*d^2 - 13*b*c*d*e + 3*b^2*e^2))*Sqrt[b*x + c*x^2])/(15*d^2*e^2*(c*d - b*e)^2*Sqrt[d + e*x]) - (2*(d*(B*d*(4*c*d - 3*b*e) + A*e*(c*d - 2*b*e)) + e*(B*d*(7*c*d - 6*b*e) - A*e*(2*c*d - b*e))*x)*Sqrt[b*x + c*x^2])/(15*d*e^2*(c*d - b*e)*(d + e*x)^(5/2)) - (2*Sqrt[-b]*Sqrt[c]*(2*A*e*(c^2*d^2 - b*c*d*e + b^2*e^2) + B*d*(8*c^2*d^2 - 13*b*c*d*e + 3*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d^2*e^3*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*Sqrt[c]*(B*d*(8*c*d - 9*b*e) + A*e*(2*c*d - b*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d*e^3*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{810, 834, 843, 715, 112, 110, 117, 116}"
1260,1,574,0,0.7820019,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x \left(9 A c e (2 c d-b e)-B \left(-4 b^2 e^2-7 b c d e+16 c^2 d^2\right)\right)+9 A c e \left(b^2 e^2-11 b c d e+8 c^2 d^2\right)-2 B \left(3 b^2 c d e^2+2 b^3 e^3-42 b c^2 d^2 e+32 c^3 d^3\right)\right)}{315 c^2 e^4}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(9 A c e \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right)-B \left(-9 b^2 c d e^2-4 b^3 e^3-120 b c^2 d^2 e+128 c^3 d^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(\left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right) \left(9 A c e (2 c d-b e)-B \left(-4 b^2 e^2-7 b c d e+16 c^2 d^2\right)\right)+5 b c d e (2 c d-b e) (-9 A c e-3 b B e+8 B c d)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (-9 A c e-3 b B e+8 B c d-7 B c e x)}{63 c e^2}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 c e x \left(9 A c e (2 c d-b e)-B \left(-4 b^2 e^2-7 b c d e+16 c^2 d^2\right)\right)+9 A c e \left(b^2 e^2-11 b c d e+8 c^2 d^2\right)-2 B \left(3 b^2 c d e^2+2 b^3 e^3-42 b c^2 d^2 e+32 c^3 d^3\right)\right)}{315 c^2 e^4}+\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(9 A c e \left(-b^2 e^2-16 b c d e+16 c^2 d^2\right)-B \left(-9 b^2 c d e^2-4 b^3 e^3-120 b c^2 d^2 e+128 c^3 d^3\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(\left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right) \left(9 A c e (2 c d-b e)-B \left(-4 b^2 e^2-7 b c d e+16 c^2 d^2\right)\right)+5 b c d e (2 c d-b e) (-9 A c e-3 b B e+8 B c d)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{315 c^{5/2} e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (-9 A c e-3 b B e+8 B c d-7 B c e x)}{63 c e^2}",1,"(2*Sqrt[d + e*x]*(9*A*c*e*(8*c^2*d^2 - 11*b*c*d*e + b^2*e^2) - 2*B*(32*c^3*d^3 - 42*b*c^2*d^2*e + 3*b^2*c*d*e^2 + 2*b^3*e^3) - 3*c*e*(9*A*c*e*(2*c*d - b*e) - B*(16*c^2*d^2 - 7*b*c*d*e - 4*b^2*e^2))*x)*Sqrt[b*x + c*x^2])/(315*c^2*e^4) - (2*Sqrt[d + e*x]*(8*B*c*d - 3*b*B*e - 9*A*c*e - 7*B*c*e*x)*(b*x + c*x^2)^(3/2))/(63*c*e^2) - (2*Sqrt[-b]*(5*b*c*d*e*(2*c*d - b*e)*(8*B*c*d - 3*b*B*e - 9*A*c*e) + (8*c^2*d^2 - 3*b*c*d*e - 2*b^2*e^2)*(9*A*c*e*(2*c*d - b*e) - B*(16*c^2*d^2 - 7*b*c*d*e - 4*b^2*e^2)))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(315*c^(5/2)*e^5*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*d*(c*d - b*e)*(9*A*c*e*(16*c^2*d^2 - 16*b*c*d*e - b^2*e^2) - B*(128*c^3*d^3 - 120*b*c^2*d^2*e - 9*b^2*c*d*e^2 - 4*b^3*e^3))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(315*c^(5/2)*e^5*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,7,28,0.2500,1,"{814, 843, 715, 112, 110, 117, 116}"
1261,1,449,0,0.5686598,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^(3/2),x]","-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(3 c e x (-14 A c e-b B e+16 B c d)+7 A c e (8 c d-7 b e)-B \left(b^2 e^2-60 b c d e+64 c^2 d^2\right)\right)}{35 c e^4}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(56 A c e (2 c d-b e)-B \left(-b^2 e^2-72 b c d e+128 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(5 b c e (8 B d-7 A e) (2 c d-b e)-\left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right) (-14 A c e-b B e+16 B c d)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (-7 A e+8 B d+B e x)}{7 e^2 \sqrt{d+e x}}","-\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(3 c e x (-14 A c e-b B e+16 B c d)+7 A c e (8 c d-7 b e)-B \left(b^2 e^2-60 b c d e+64 c^2 d^2\right)\right)}{35 c e^4}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(56 A c e (2 c d-b e)-B \left(-b^2 e^2-72 b c d e+128 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(5 b c e (8 B d-7 A e) (2 c d-b e)-\left(-2 b^2 e^2-3 b c d e+8 c^2 d^2\right) (-14 A c e-b B e+16 B c d)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{35 c^{3/2} e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (-7 A e+8 B d+B e x)}{7 e^2 \sqrt{d+e x}}",1,"(-2*Sqrt[d + e*x]*(7*A*c*e*(8*c*d - 7*b*e) - B*(64*c^2*d^2 - 60*b*c*d*e + b^2*e^2) + 3*c*e*(16*B*c*d - b*B*e - 14*A*c*e)*x)*Sqrt[b*x + c*x^2])/(35*c*e^4) + (2*(8*B*d - 7*A*e + B*e*x)*(b*x + c*x^2)^(3/2))/(7*e^2*Sqrt[d + e*x]) + (2*Sqrt[-b]*(5*b*c*e*(8*B*d - 7*A*e)*(2*c*d - b*e) - (16*B*c*d - b*B*e - 14*A*c*e)*(8*c^2*d^2 - 3*b*c*d*e - 2*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(35*c^(3/2)*e^5*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*(56*A*c*e*(2*c*d - b*e) - B*(128*c^2*d^2 - 72*b*c*d*e - b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(35*c^(3/2)*e^5*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{812, 814, 843, 715, 112, 110, 117, 116}"
1262,1,413,0,0.5018748,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(5 A e \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(39 b^2 e^2-152 b c d e+128 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(40 A c e (2 c d-b e)-B \left(3 b^2 e^2-88 b c d e+128 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (-5 A e+8 B d+3 B e x)}{15 e^2 (d+e x)^{3/2}}-\frac{2 \sqrt{b x+c x^2} (e x (-10 A c e-3 b B e+16 B c d)-5 A e (8 c d-3 b e)+4 B d (16 c d-9 b e))}{15 e^4 \sqrt{d+e x}}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(5 A e \left(3 b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(39 b^2 e^2-152 b c d e+128 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(40 A c e (2 c d-b e)-B \left(3 b^2 e^2-88 b c d e+128 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \left(b x+c x^2\right)^{3/2} (-5 A e+8 B d+3 B e x)}{15 e^2 (d+e x)^{3/2}}-\frac{2 \sqrt{b x+c x^2} (e x (-10 A c e-3 b B e+16 B c d)-5 A e (8 c d-3 b e)+4 B d (16 c d-9 b e))}{15 e^4 \sqrt{d+e x}}",1,"(-2*(4*B*d*(16*c*d - 9*b*e) - 5*A*e*(8*c*d - 3*b*e) + e*(16*B*c*d - 3*b*B*e - 10*A*c*e)*x)*Sqrt[b*x + c*x^2])/(15*e^4*Sqrt[d + e*x]) + (2*(8*B*d - 5*A*e + 3*B*e*x)*(b*x + c*x^2)^(3/2))/(15*e^2*(d + e*x)^(3/2)) - (2*Sqrt[-b]*(40*A*c*e*(2*c*d - b*e) - B*(128*c^2*d^2 - 88*b*c*d*e + 3*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*Sqrt[c]*e^5*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*(5*A*e*(16*c^2*d^2 - 16*b*c*d*e + 3*b^2*e^2) - B*d*(128*c^2*d^2 - 152*b*c*d*e + 39*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*Sqrt[c]*e^5*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,7,28,0.2500,1,"{812, 843, 715, 112, 110, 117, 116}"
1263,1,516,0,0.6661913,"\int \frac{(A+B x) \left(b x+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(b*x + c*x^2)^(3/2))/(d + e*x)^(7/2),x]","-\frac{2 \sqrt{b x+c x^2} \left(d \left(3 A c e (8 c d-7 b e)-B \left(15 b^2 e^2-76 b c d e+64 c^2 d^2\right)\right)-c e x (B d (16 c d-13 b e)-3 A e (2 c d-b e))\right)}{15 d e^4 \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(24 A c e (2 c d-b e)-B \left(15 b^2 e^2-104 b c d e+128 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(3 A e \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(43 b^2 e^2-168 b c d e+128 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 \left(b x+c x^2\right)^{3/2} \left(d^2 (-3 A c e-5 b B e+8 B c d)+e x (B d (11 c d-8 b e)-3 A e (2 c d-b e))\right)}{15 d e^2 (d+e x)^{5/2} (c d-b e)}","-\frac{2 \sqrt{b x+c x^2} \left(d \left(3 A c e (8 c d-7 b e)-B \left(15 b^2 e^2-76 b c d e+64 c^2 d^2\right)\right)-c e x (B d (16 c d-13 b e)-3 A e (2 c d-b e))\right)}{15 d e^4 \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(24 A c e (2 c d-b e)-B \left(15 b^2 e^2-104 b c d e+128 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 \sqrt{c} e^5 \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(3 A e \left(b^2 e^2-16 b c d e+16 c^2 d^2\right)-B d \left(43 b^2 e^2-168 b c d e+128 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d e^5 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}-\frac{2 \left(b x+c x^2\right)^{3/2} \left(d^2 (-3 A c e-5 b B e+8 B c d)+e x (B d (11 c d-8 b e)-3 A e (2 c d-b e))\right)}{15 d e^2 (d+e x)^{5/2} (c d-b e)}",1,"(-2*(d*(3*A*c*e*(8*c*d - 7*b*e) - B*(64*c^2*d^2 - 76*b*c*d*e + 15*b^2*e^2)) - c*e*(B*d*(16*c*d - 13*b*e) - 3*A*e*(2*c*d - b*e))*x)*Sqrt[b*x + c*x^2])/(15*d*e^4*(c*d - b*e)*Sqrt[d + e*x]) - (2*(d^2*(8*B*c*d - 5*b*B*e - 3*A*c*e) + e*(B*d*(11*c*d - 8*b*e) - 3*A*e*(2*c*d - b*e))*x)*(b*x + c*x^2)^(3/2))/(15*d*e^2*(c*d - b*e)*(d + e*x)^(5/2)) + (2*Sqrt[-b]*Sqrt[c]*(3*A*e*(16*c^2*d^2 - 16*b*c*d*e + b^2*e^2) - B*d*(128*c^2*d^2 - 168*b*c*d*e + 43*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d*e^5*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*(24*A*c*e*(2*c*d - b*e) - B*(128*c^2*d^2 - 104*b*c*d*e + 15*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*Sqrt[c]*e^5*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{810, 812, 843, 715, 112, 110, 117, 116}"
1264,1,460,0,0.7656605,"\int \frac{(A+B x) (d+e x)^{5/2}}{\sqrt{b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(28 A c e (2 c d-b e)+B \left(24 b^2 e^2-43 b c d e+15 c^2 d^2\right)\right)}{105 c^3}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(28 A c e (2 c d-b e)+B \left(24 b^2 e^2-43 b c d e+15 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} e \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(7 A c e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)+B \left(128 b^2 c d e^2-48 b^3 e^3-103 b c^2 d^2 e+15 c^3 d^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{b x+c x^2} (d+e x)^{3/2} (7 A c e-6 b B e+5 B c d)}{35 c^2}+\frac{2 B \sqrt{b x+c x^2} (d+e x)^{5/2}}{7 c}","\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} \left(28 A c e (2 c d-b e)+B \left(24 b^2 e^2-43 b c d e+15 c^2 d^2\right)\right)}{105 c^3}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(28 A c e (2 c d-b e)+B \left(24 b^2 e^2-43 b c d e+15 c^2 d^2\right)\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} e \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(7 A c e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)+B \left(128 b^2 c d e^2-48 b^3 e^3-103 b c^2 d^2 e+15 c^3 d^3\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{105 c^{7/2} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{b x+c x^2} (d+e x)^{3/2} (7 A c e-6 b B e+5 B c d)}{35 c^2}+\frac{2 B \sqrt{b x+c x^2} (d+e x)^{5/2}}{7 c}",1,"(2*(28*A*c*e*(2*c*d - b*e) + B*(15*c^2*d^2 - 43*b*c*d*e + 24*b^2*e^2))*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(105*c^3) + (2*(5*B*c*d - 6*b*B*e + 7*A*c*e)*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(35*c^2) + (2*B*(d + e*x)^(5/2)*Sqrt[b*x + c*x^2])/(7*c) + (2*Sqrt[-b]*(7*A*c*e*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2) + B*(15*c^3*d^3 - 103*b*c^2*d^2*e + 128*b^2*c*d*e^2 - 48*b^3*e^3))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(7/2)*e*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*(28*A*c*e*(2*c*d - b*e) + B*(15*c^2*d^2 - 43*b*c*d*e + 24*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(105*c^(7/2)*e*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,7,28,0.2500,1,"{832, 843, 715, 112, 110, 117, 116}"
1265,1,339,0,0.4778886,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(10 A c e (2 c d-b e)+B \left(8 b^2 e^2-13 b c d e+3 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (5 A c e-4 b B e+3 B c d)}{15 c^2}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (5 A c e-4 b B e+3 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} e \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 B \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 c}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(10 A c e (2 c d-b e)+B \left(8 b^2 e^2-13 b c d e+3 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 \sqrt{b x+c x^2} \sqrt{d+e x} (5 A c e-4 b B e+3 B c d)}{15 c^2}-\frac{2 \sqrt{-b} d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) (5 A c e-4 b B e+3 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 c^{5/2} e \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 B \sqrt{b x+c x^2} (d+e x)^{3/2}}{5 c}",1,"(2*(3*B*c*d - 4*b*B*e + 5*A*c*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(15*c^2) + (2*B*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(5*c) + (2*Sqrt[-b]*(10*A*c*e*(2*c*d - b*e) + B*(3*c^2*d^2 - 13*b*c*d*e + 8*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(5/2)*e*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*d*(c*d - b*e)*(3*B*c*d - 4*b*B*e + 5*A*c*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*c^(5/2)*e*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,7,28,0.2500,1,"{832, 843, 715, 112, 110, 117, 116}"
1266,1,254,0,0.2834936,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{b x+c x^2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/Sqrt[b*x + c*x^2],x]","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (3 A c e-2 b B e+B c d) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{-b} B d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} e \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 B \sqrt{b x+c x^2} \sqrt{d+e x}}{3 c}","\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (3 A c e-2 b B e+B c d) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{-b} B d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 c^{3/2} e \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 B \sqrt{b x+c x^2} \sqrt{d+e x}}{3 c}",1,"(2*B*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(3*c) + (2*Sqrt[-b]*(B*c*d - 2*b*B*e + 3*A*c*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*c^(3/2)*e*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*B*d*(c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*c^(3/2)*e*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{832, 843, 715, 112, 110, 117, 116}"
1267,1,204,0,0.1202051,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{-b} B \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (B d-A e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{-b} B \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 \sqrt{-b} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (B d-A e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(2*Sqrt[-b]*B*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(Sqrt[c]*e*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*(B*d - A*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(Sqrt[c]*e*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",7,6,28,0.2143,1,"{843, 715, 112, 110, 117, 116}"
1268,1,262,0,0.2525091,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{b x+c x^2} (B d-A e)}{d \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (B d-A e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{d e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}+\frac{2 \sqrt{-b} B \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{b x+c x^2} (B d-A e)}{d \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (B d-A e) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{d e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}+\frac{2 \sqrt{-b} B \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{\sqrt{c} e \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(2*(B*d - A*e)*Sqrt[b*x + c*x^2])/(d*(c*d - b*e)*Sqrt[d + e*x]) - (2*Sqrt[-b]*Sqrt[c]*(B*d - A*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(d*e*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*B*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(Sqrt[c]*e*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{834, 843, 715, 112, 110, 117, 116}"
1269,1,369,0,0.4784018,"\int \frac{A+B x}{(d+e x)^{5/2} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*Sqrt[b*x + c*x^2]),x]","-\frac{2 \sqrt{b x+c x^2} (2 A e (2 c d-b e)-B d (b e+c d))}{3 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 A e (2 c d-b e)-B d (b e+c d)) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d^2 e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}+\frac{2 \sqrt{b x+c x^2} (B d-A e)}{3 d (d+e x)^{3/2} (c d-b e)}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (B d-A e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d e \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}","-\frac{2 \sqrt{b x+c x^2} (2 A e (2 c d-b e)-B d (b e+c d))}{3 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (2 A e (2 c d-b e)-B d (b e+c d)) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d^2 e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}+\frac{2 \sqrt{b x+c x^2} (B d-A e)}{3 d (d+e x)^{3/2} (c d-b e)}+\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (B d-A e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 d e \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}",1,"(2*(B*d - A*e)*Sqrt[b*x + c*x^2])/(3*d*(c*d - b*e)*(d + e*x)^(3/2)) - (2*(2*A*e*(2*c*d - b*e) - B*d*(c*d + b*e))*Sqrt[b*x + c*x^2])/(3*d^2*(c*d - b*e)^2*Sqrt[d + e*x]) + (2*Sqrt[-b]*Sqrt[c]*(2*A*e*(2*c*d - b*e) - B*d*(c*d + b*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*d^2*e*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[-b]*Sqrt[c]*(B*d - A*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*d*e*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,7,28,0.2500,1,"{834, 843, 715, 112, 110, 117, 116}"
1270,1,510,0,0.8008029,"\int \frac{A+B x}{(d+e x)^{7/2} \sqrt{b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*Sqrt[b*x + c*x^2]),x]","\frac{2 \sqrt{b x+c x^2} \left(B d \left(-2 b^2 e^2+7 b c d e+3 c^2 d^2\right)-A e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)\right)}{15 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(B d \left(-2 b^2 e^2+7 b c d e+3 c^2 d^2\right)-A e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^3 e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 \sqrt{b x+c x^2} (4 A e (2 c d-b e)-B d (b e+3 c d))}{15 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (4 A e (2 c d-b e)-B d (b e+3 c d)) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 e \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{b x+c x^2} (B d-A e)}{5 d (d+e x)^{5/2} (c d-b e)}","\frac{2 \sqrt{b x+c x^2} \left(B d \left(-2 b^2 e^2+7 b c d e+3 c^2 d^2\right)-A e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)\right)}{15 d^3 \sqrt{d+e x} (c d-b e)^3}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(B d \left(-2 b^2 e^2+7 b c d e+3 c^2 d^2\right)-A e \left(8 b^2 e^2-23 b c d e+23 c^2 d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^3 e \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 \sqrt{b x+c x^2} (4 A e (2 c d-b e)-B d (b e+3 c d))}{15 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 \sqrt{-b} \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (4 A e (2 c d-b e)-B d (b e+3 c d)) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 d^2 e \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{b x+c x^2} (B d-A e)}{5 d (d+e x)^{5/2} (c d-b e)}",1,"(2*(B*d - A*e)*Sqrt[b*x + c*x^2])/(5*d*(c*d - b*e)*(d + e*x)^(5/2)) - (2*(4*A*e*(2*c*d - b*e) - B*d*(3*c*d + b*e))*Sqrt[b*x + c*x^2])/(15*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) + (2*(B*d*(3*c^2*d^2 + 7*b*c*d*e - 2*b^2*e^2) - A*e*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2))*Sqrt[b*x + c*x^2])/(15*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (2*Sqrt[-b]*Sqrt[c]*(B*d*(3*c^2*d^2 + 7*b*c*d*e - 2*b^2*e^2) - A*e*(23*c^2*d^2 - 23*b*c*d*e + 8*b^2*e^2))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d^3*e*(c*d - b*e)^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[-b]*Sqrt[c]*(4*A*e*(2*c*d - b*e) - B*d*(3*c*d + b*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*d^2*e*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,7,28,0.2500,1,"{834, 843, 715, 112, 110, 117, 116}"
1271,1,527,0,0.9066692,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^(3/2),x]","\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(b^2 c e (20 A e+43 B d)-15 b c^2 d (2 A e+B d)+30 A c^3 d^2-24 b^3 B e^2\right)}{15 b^2 c^3}-\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(b^2 c e (20 A e+43 B d)-15 b c^2 d (2 A e+B d)+30 A c^3 d^2-24 b^3 B e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 (-b)^{3/2} c^{7/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c^2 d e (95 A e+103 B d)-8 b^3 c e^2 (5 A e+16 B d)-15 b c^3 d^2 (3 A e+B d)+30 A c^4 d^3+48 b^4 B e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 (-b)^{3/2} c^{7/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{3/2} \left(-5 b c (A e+B d)+10 A c^2 d+6 b^2 B e\right)}{5 b^2 c^2}","\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(b^2 c e (20 A e+43 B d)-15 b c^2 d (2 A e+B d)+30 A c^3 d^2-24 b^3 B e^2\right)}{15 b^2 c^3}-\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(b^2 c e (20 A e+43 B d)-15 b c^2 d (2 A e+B d)+30 A c^3 d^2-24 b^3 B e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 (-b)^{3/2} c^{7/2} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c^2 d e (95 A e+103 B d)-8 b^3 c e^2 (5 A e+16 B d)-15 b c^3 d^2 (3 A e+B d)+30 A c^4 d^3+48 b^4 B e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{15 (-b)^{3/2} c^{7/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} (d+e x)^{3/2} \left(-5 b c (A e+B d)+10 A c^2 d+6 b^2 B e\right)}{5 b^2 c^2}",1,"(-2*(d + e*x)^(5/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*Sqrt[b*x + c*x^2]) + (2*e*(30*A*c^3*d^2 - 24*b^3*B*e^2 - 15*b*c^2*d*(B*d + 2*A*e) + b^2*c*e*(43*B*d + 20*A*e))*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(15*b^2*c^3) + (2*e*(10*A*c^2*d + 6*b^2*B*e - 5*b*c*(B*d + A*e))*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2])/(5*b^2*c^2) + (2*(30*A*c^4*d^3 + 48*b^4*B*e^3 - 15*b*c^3*d^2*(B*d + 3*A*e) - 8*b^3*c*e^2*(16*B*d + 5*A*e) + b^2*c^2*d*e*(103*B*d + 95*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*(-b)^(3/2)*c^(7/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*d*(c*d - b*e)*(30*A*c^3*d^2 - 24*b^3*B*e^2 - 15*b*c^2*d*(B*d + 2*A*e) + b^2*c*e*(43*B*d + 20*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(15*(-b)^(3/2)*c^(7/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,28,0.2857,1,"{818, 832, 843, 715, 112, 110, 117, 116}"
1272,1,399,0,0.5479671,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c e (6 A e+13 B d)-3 b c^2 d (2 A e+B d)+6 A c^3 d^2-8 b^3 B e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 b c (A e+B d)+6 A c^2 d+4 b^2 B e\right)}{3 b^2 c^2}-\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-3 b c (A e+B d)+6 A c^2 d+4 b^2 B e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c e (6 A e+13 B d)-3 b c^2 d (2 A e+B d)+6 A c^3 d^2-8 b^3 B e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{2 e \sqrt{b x+c x^2} \sqrt{d+e x} \left(-3 b c (A e+B d)+6 A c^2 d+4 b^2 B e\right)}{3 b^2 c^2}-\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-3 b c (A e+B d)+6 A c^2 d+4 b^2 B e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(-2*(d + e*x)^(3/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*Sqrt[b*x + c*x^2]) + (2*e*(6*A*c^2*d + 4*b^2*B*e - 3*b*c*(B*d + A*e))*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])/(3*b^2*c^2) + (2*(6*A*c^3*d^2 - 8*b^3*B*e^2 - 3*b*c^2*d*(B*d + 2*A*e) + b^2*c*e*(13*B*d + 6*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*c^(5/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*d*(c*d - b*e)*(6*A*c^2*d + 4*b^2*B*e - 3*b*c*(B*d + A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*c^(5/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{818, 832, 843, 715, 112, 110, 117, 116}"
1273,1,295,0,0.311367,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(-b c (A e+B d)+2 A c^2 d+2 b^2 B e\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (b B-2 A c) (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}","-\frac{2 \sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{b^2 c \sqrt{b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(-b c (A e+B d)+2 A c^2 d+2 b^2 B e\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (b B-2 A c) (c d-b e) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(-2*Sqrt[d + e*x]*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(b^2*c*Sqrt[b*x + c*x^2]) + (2*(2*A*c^2*d + 2*b^2*B*e - b*c*(B*d + A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*c^(3/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*(b*B - 2*A*c)*d*(c*d - b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*c^(3/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{818, 843, 715, 112, 110, 117, 116}"
1274,1,253,0,0.2182623,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{d+e x} (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (b B-2 A c) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","-\frac{2 \sqrt{d+e x} (A b-x (b B-2 A c))}{b^2 \sqrt{b x+c x^2}}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (b B-2 A c) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(-2*(A*b - (b*B - 2*A*c)*x)*Sqrt[d + e*x])/(b^2*Sqrt[b*x + c*x^2]) - (2*(b*B - 2*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[c]*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*(b*B*d - 2*A*c*d + A*b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{820, 843, 715, 112, 110, 117, 116}"
1275,1,295,0,0.2879189,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^(3/2)),x]","-\frac{2 \sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (b B-2 A c) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (A b e-2 A c d+b B d) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}","-\frac{2 \sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (c d-b e)}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (b B-2 A c) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} (A b e-2 A c d+b B d) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}",1,"(-2*Sqrt[d + e*x]*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*Sqrt[b*x + c*x^2]) - (2*Sqrt[c]*(b*B*d - 2*A*c*d + A*b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*d*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*(b*B - 2*A*c)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",8,7,28,0.2500,1,"{822, 843, 715, 112, 110, 117, 116}"
1276,1,415,0,0.5441412,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{2 e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-2 A e)-b c d (2 A e+B d)+2 A c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 (-e) (B d-2 A e)-b c d (2 A e+B d)+2 A c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}","-\frac{2 e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-2 A e)-b c d (2 A e+B d)+2 A c^2 d^2\right)}{b^2 d^2 \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 (-e) (B d-2 A e)-b c d (2 A e+B d)+2 A c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{(-b)^{3/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2]) - (2*e*(2*A*c^2*d^2 - b^2*e*(B*d - 2*A*e) - b*c*d*(B*d + 2*A*e))*Sqrt[b*x + c*x^2])/(b^2*d^2*(c*d - b*e)^2*Sqrt[d + e*x]) + (2*Sqrt[c]*(2*A*c^2*d^2 - b^2*e*(B*d - 2*A*e) - b*c*d*(B*d + 2*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*d^2*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[c]*(b*B*d - 2*A*c*d + A*b*e)*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/((-b)^(3/2)*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{822, 834, 843, 715, 112, 110, 117, 116}"
1277,1,570,0,0.9870873,"\int \frac{A+B x}{(d+e x)^{5/2} \left(b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(b*x + c*x^2)^(3/2)),x]","-\frac{2 e \sqrt{b x+c x^2} \left(-b^2 c d e (7 B d-19 A e)+2 b^3 e^2 (B d-4 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right)}{3 b^2 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(-b^2 c d e (7 B d-19 A e)+2 b^3 e^2 (B d-4 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-4 A e)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^2 (-e) (B d-4 A e)-3 b c d (2 A e+B d)+6 A c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^{3/2} (c d-b e)}","-\frac{2 e \sqrt{b x+c x^2} \left(-b^2 c d e (7 B d-19 A e)+2 b^3 e^2 (B d-4 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right)}{3 b^2 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(-b^2 c d e (7 B d-19 A e)+2 b^3 e^2 (B d-4 A e)-3 b c^2 d^2 (3 A e+B d)+6 A c^3 d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 e \sqrt{b x+c x^2} \left(b^2 (-e) (B d-4 A e)-3 b c d (2 A e+B d)+6 A c^2 d^2\right)}{3 b^2 d^2 (d+e x)^{3/2} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^2 (-e) (B d-4 A e)-3 b c d (2 A e+B d)+6 A c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{3/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{b^2 d \sqrt{b x+c x^2} (d+e x)^{3/2} (c d-b e)}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(b^2*d*(c*d - b*e)*(d + e*x)^(3/2)*Sqrt[b*x + c*x^2]) - (2*e*(6*A*c^2*d^2 - b^2*e*(B*d - 4*A*e) - 3*b*c*d*(B*d + 2*A*e))*Sqrt[b*x + c*x^2])/(3*b^2*d^2*(c*d - b*e)^2*(d + e*x)^(3/2)) - (2*e*(6*A*c^3*d^3 - b^2*c*d*e*(7*B*d - 19*A*e) + 2*b^3*e^2*(B*d - 4*A*e) - 3*b*c^2*d^2*(B*d + 3*A*e))*Sqrt[b*x + c*x^2])/(3*b^2*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) + (2*Sqrt[c]*(6*A*c^3*d^3 - b^2*c*d*e*(7*B*d - 19*A*e) + 2*b^3*e^2*(B*d - 4*A*e) - 3*b*c^2*d^2*(B*d + 3*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*d^3*(c*d - b*e)^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) - (2*Sqrt[c]*(6*A*c^2*d^2 - b^2*e*(B*d - 4*A*e) - 3*b*c*d*(B*d + 2*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(3/2)*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,28,0.2857,1,"{822, 834, 843, 715, 112, 110, 117, 116}"
1278,1,524,0,0.7287528,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(x \left(b^2 c^2 d e (6 A e+5 B d)+b^3 c e^2 (A e+4 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3-4 b^4 B e^3\right)+b c d^2 \left(-b c (9 A e+4 B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(b^2 c e (B d-A e)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2+4 b^3 B e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c^2 d e (4 A e+5 B d)+b^3 c e^2 (2 A e+5 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3-8 b^4 B e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}","\frac{2 \sqrt{d+e x} \left(x \left(b^2 c^2 d e (6 A e+5 B d)+b^3 c e^2 (A e+4 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3-4 b^4 B e^3\right)+b c d^2 \left(-b c (9 A e+4 B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c^2 \sqrt{b x+c x^2}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(b^2 c e (B d-A e)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2+4 b^3 B e^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c^2 d e (4 A e+5 B d)+b^3 c e^2 (2 A e+5 B d)-8 b c^3 d^2 (3 A e+B d)+16 A c^4 d^3-8 b^4 B e^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{5/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{5/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(5/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(3*b^2*c*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*c*d^2*(8*A*c^2*d + b^2*B*e - b*c*(4*B*d + 9*A*e)) + (16*A*c^4*d^3 - 4*b^4*B*e^3 + b^3*c*e^2*(4*B*d + A*e) - 8*b*c^3*d^2*(B*d + 3*A*e) + b^2*c^2*d*e*(5*B*d + 6*A*e))*x))/(3*b^4*c^2*Sqrt[b*x + c*x^2]) - (2*(16*A*c^4*d^3 - 8*b^4*B*e^3 + b^3*c*e^2*(5*B*d + 2*A*e) - 8*b*c^3*d^2*(B*d + 3*A*e) + b^2*c^2*d*e*(5*B*d + 4*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(5/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*d*(c*d - b*e)*(16*A*c^3*d^2 + 4*b^3*B*e^2 + b^2*c*e*(B*d - A*e) - 8*b*c^2*d*(B*d + 2*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(5/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,7,28,0.2500,1,"{818, 843, 715, 112, 110, 117, 116}"
1279,1,454,0,0.5614336,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} \left(x \left(b^2 c e (A e+3 B d)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2+2 b^3 B e^2\right)+b d \left(-b c (7 A e+4 B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c e (A e+3 B d)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2+2 b^3 B e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-8 b c (A e+B d)+16 A c^2 d+b^2 (-B) e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \left(x \left(b^2 c e (A e+3 B d)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2+2 b^3 B e^2\right)+b d \left(-b c (7 A e+4 B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c e (A e+3 B d)-8 b c^2 d (2 A e+B d)+16 A c^3 d^2+2 b^3 B e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}-\frac{2 (d+e x)^{3/2} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}+\frac{2 d \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} (c d-b e) \left(-8 b c (A e+B d)+16 A c^2 d+b^2 (-B) e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} c^{3/2} \sqrt{b x+c x^2} \sqrt{d+e x}}",1,"(-2*(d + e*x)^(3/2)*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(3*b^2*c*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*d*(8*A*c^2*d + b^2*B*e - b*c*(4*B*d + 7*A*e)) + (16*A*c^3*d^2 + 2*b^3*B*e^2 + b^2*c*e*(3*B*d + A*e) - 8*b*c^2*d*(B*d + 2*A*e))*x))/(3*b^4*c*Sqrt[b*x + c*x^2]) - (2*(16*A*c^3*d^2 + 2*b^3*B*e^2 + b^2*c*e*(3*B*d + A*e) - 8*b*c^2*d*(B*d + 2*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(3/2)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*d*(c*d - b*e)*(16*A*c^2*d - b^2*B*e - 8*b*c*(B*d + A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*c^(3/2)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{818, 820, 843, 715, 112, 110, 117, 116}"
1280,1,410,0,0.5858372,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(b*x + c*x^2)^(5/2),x]","\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^2 e (3 A e+5 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(c x \left(-8 b c (A e+B d)+16 A c^2 d+b^2 B e\right)+b \left(-b c (5 A e+4 B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 \sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(-8 b c (A e+B d)+16 A c^2 d+b^2 B e\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}","\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^2 e (3 A e+5 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{d+e x} \left(c x \left(-8 b c (A e+B d)+16 A c^2 d+b^2 B e\right)+b \left(-b c (5 A e+4 B d)+8 A c^2 d+b^2 B e\right)\right)}{3 b^4 c \sqrt{b x+c x^2}}-\frac{2 \sqrt{d+e x} \left(x \left(-b c (A e+B d)+2 A c^2 d+b^2 B e\right)+A b c d\right)}{3 b^2 c \left(b x+c x^2\right)^{3/2}}-\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(-8 b c (A e+B d)+16 A c^2 d+b^2 B e\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1}}",1,"(-2*Sqrt[d + e*x]*(A*b*c*d + (2*A*c^2*d + b^2*B*e - b*c*(B*d + A*e))*x))/(3*b^2*c*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*(8*A*c^2*d + b^2*B*e - b*c*(4*B*d + 5*A*e)) + c*(16*A*c^2*d + b^2*B*e - 8*b*c*(B*d + A*e))*x))/(3*b^4*c*Sqrt[b*x + c*x^2]) - (2*(16*A*c^2*d + b^2*B*e - 8*b*c*(B*d + A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[c]*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*(16*A*c^2*d^2 - 8*b*c*d*(B*d + 2*A*e) + b^2*e*(5*B*d + 3*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{818, 822, 843, 715, 112, 110, 117, 116}"
1281,1,420,0,0.5463801,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(b*x + c*x^2)^(5/2),x]","-\frac{2 \sqrt{d+e x} \left(b (c d-b e) (A b e-8 A c d+4 b B d)-c x \left(b^2 e (A e+7 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right)\right)}{3 b^4 d \sqrt{b x+c x^2} (c d-b e)}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e (A e+7 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(-8 b c (A e+B d)+16 A c^2 d+3 b^2 B e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}","-\frac{2 \sqrt{d+e x} \left(b (c d-b e) (A b e-8 A c d+4 b B d)-c x \left(b^2 e (A e+7 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right)\right)}{3 b^4 d \sqrt{b x+c x^2} (c d-b e)}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 e (A e+7 B d)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)}+\frac{2 \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(-8 b c (A e+B d)+16 A c^2 d+3 b^2 B e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} \sqrt{c} \sqrt{b x+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} (A b-x (b B-2 A c))}{3 b^2 \left(b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - (b*B - 2*A*c)*x)*Sqrt[d + e*x])/(3*b^2*(b*x + c*x^2)^(3/2)) - (2*Sqrt[d + e*x]*(b*(c*d - b*e)*(4*b*B*d - 8*A*c*d + A*b*e) - c*(16*A*c^2*d^2 + b^2*e*(7*B*d + A*e) - 8*b*c*d*(B*d + 2*A*e))*x))/(3*b^4*d*(c*d - b*e)*Sqrt[b*x + c*x^2]) - (2*Sqrt[c]*(16*A*c^2*d^2 + b^2*e*(7*B*d + A*e) - 8*b*c*d*(B*d + 2*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d*(c*d - b*e)*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*(16*A*c^2*d + 3*b^2*B*e - 8*b*c*(B*d + A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*Sqrt[c]*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,8,28,0.2857,1,"{820, 822, 843, 715, 112, 110, 117, 116}"
1282,1,543,0,0.7556954,"\int \frac{A+B x}{\sqrt{d+e x} \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(b*x + c*x^2)^(5/2)),x]","\frac{2 \sqrt{d+e x} \left(c x \left(b^2 c d e (4 A e+13 B d)+b^3 \left(-e^2\right) (3 B d-2 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (3 B d-2 A e)-b c d (5 A e+4 B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c d e (4 A e+13 B d)+b^3 \left(-e^2\right) (3 B d-2 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^2 e (9 B d-A e)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}","\frac{2 \sqrt{d+e x} \left(c x \left(b^2 c d e (4 A e+13 B d)+b^3 \left(-e^2\right) (3 B d-2 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right)+b (c d-b e) \left(b^2 e (3 B d-2 A e)-b c d (5 A e+4 B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c d e (4 A e+13 B d)+b^3 \left(-e^2\right) (3 B d-2 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^2 e (9 B d-A e)-8 b c d (2 A e+B d)+16 A c^2 d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)}-\frac{2 \sqrt{d+e x} (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} (c d-b e)}",1,"(-2*Sqrt[d + e*x]*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(3*b^2*d*(c*d - b*e)*(b*x + c*x^2)^(3/2)) + (2*Sqrt[d + e*x]*(b*(c*d - b*e)*(8*A*c^2*d^2 + b^2*e*(3*B*d - 2*A*e) - b*c*d*(4*B*d + 5*A*e)) + c*(16*A*c^3*d^3 - b^3*e^2*(3*B*d - 2*A*e) - 8*b*c^2*d^2*(B*d + 3*A*e) + b^2*c*d*e*(13*B*d + 4*A*e))*x))/(3*b^4*d^2*(c*d - b*e)^2*Sqrt[b*x + c*x^2]) - (2*Sqrt[c]*(16*A*c^3*d^3 - b^3*e^2*(3*B*d - 2*A*e) - 8*b*c^2*d^2*(B*d + 3*A*e) + b^2*c*d*e*(13*B*d + 4*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d^2*(c*d - b*e)^2*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[c]*(16*A*c^2*d^2 + b^2*e*(9*B*d - A*e) - 8*b*c*d*(B*d + 2*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d*(c*d - b*e)*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",9,7,28,0.2500,1,"{822, 843, 715, 112, 110, 117, 116}"
1283,1,706,0,1.1935905,"\int \frac{A+B x}{(d+e x)^{3/2} \left(b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(b*x + c*x^2)^(5/2)),x]","\frac{2 e \sqrt{b x+c x^2} \left(b^2 c^2 d^2 e (9 A e+19 B d)-b^3 c d e^2 (9 B d-7 A e)+b^4 \left(6 B d e^3-8 A e^4\right)-8 b c^3 d^3 (4 A e+B d)+16 A c^4 d^4\right)}{3 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \left(c x \left(b^3 \left(-e^2\right) (3 B d-4 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3+15 b^2 B c d^2 e\right)+b (c d-b e) \left(b^2 e (3 B d-4 A e)-b c d (3 A e+4 B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^3 \left(-e^2\right) (3 B d-4 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3+15 b^2 B c d^2 e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c^2 d^2 e (9 A e+19 B d)-b^3 c d e^2 (9 B d-7 A e)+2 b^4 e^3 (3 B d-4 A e)-8 b c^3 d^3 (4 A e+B d)+16 A c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (c d-b e)}","\frac{2 e \sqrt{b x+c x^2} \left(b^2 c^2 d^2 e (9 A e+19 B d)-b^3 c d e^2 (9 B d-7 A e)+b^4 \left(6 B d e^3-8 A e^4\right)-8 b c^3 d^3 (4 A e+B d)+16 A c^4 d^4\right)}{3 b^4 d^3 \sqrt{d+e x} (c d-b e)^3}+\frac{2 \left(c x \left(b^3 \left(-e^2\right) (3 B d-4 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3+15 b^2 B c d^2 e\right)+b (c d-b e) \left(b^2 e (3 B d-4 A e)-b c d (3 A e+4 B d)+8 A c^2 d^2\right)\right)}{3 b^4 d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}+\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{\frac{e x}{d}+1} \left(b^3 \left(-e^2\right) (3 B d-4 A e)-8 b c^2 d^2 (3 A e+B d)+16 A c^3 d^3+15 b^2 B c d^2 e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^2 \sqrt{b x+c x^2} \sqrt{d+e x} (c d-b e)^2}-\frac{2 \sqrt{c} \sqrt{x} \sqrt{\frac{c x}{b}+1} \sqrt{d+e x} \left(b^2 c^2 d^2 e (9 A e+19 B d)-b^3 c d e^2 (9 B d-7 A e)+2 b^4 e^3 (3 B d-4 A e)-8 b c^3 d^3 (4 A e+B d)+16 A c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{c} \sqrt{x}}{\sqrt{-b}}\right)|\frac{b e}{c d}\right)}{3 (-b)^{7/2} d^3 \sqrt{b x+c x^2} \sqrt{\frac{e x}{d}+1} (c d-b e)^3}-\frac{2 (c x (2 A c d-b (A e+B d))+A b (c d-b e))}{3 b^2 d \left(b x+c x^2\right)^{3/2} \sqrt{d+e x} (c d-b e)}",1,"(-2*(A*b*(c*d - b*e) + c*(2*A*c*d - b*(B*d + A*e))*x))/(3*b^2*d*(c*d - b*e)*Sqrt[d + e*x]*(b*x + c*x^2)^(3/2)) + (2*(b*(c*d - b*e)*(8*A*c^2*d^2 + b^2*e*(3*B*d - 4*A*e) - b*c*d*(4*B*d + 3*A*e)) + c*(16*A*c^3*d^3 + 15*b^2*B*c*d^2*e - b^3*e^2*(3*B*d - 4*A*e) - 8*b*c^2*d^2*(B*d + 3*A*e))*x))/(3*b^4*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2]) + (2*e*(16*A*c^4*d^4 - b^3*c*d*e^2*(9*B*d - 7*A*e) - 8*b*c^3*d^3*(B*d + 4*A*e) + b^2*c^2*d^2*e*(19*B*d + 9*A*e) + b^4*(6*B*d*e^3 - 8*A*e^4))*Sqrt[b*x + c*x^2])/(3*b^4*d^3*(c*d - b*e)^3*Sqrt[d + e*x]) - (2*Sqrt[c]*(16*A*c^4*d^4 - b^3*c*d*e^2*(9*B*d - 7*A*e) + 2*b^4*e^3*(3*B*d - 4*A*e) - 8*b*c^3*d^3*(B*d + 4*A*e) + b^2*c^2*d^2*e*(19*B*d + 9*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[d + e*x]*EllipticE[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d^3*(c*d - b*e)^3*Sqrt[1 + (e*x)/d]*Sqrt[b*x + c*x^2]) + (2*Sqrt[c]*(16*A*c^3*d^3 + 15*b^2*B*c*d^2*e - b^3*e^2*(3*B*d - 4*A*e) - 8*b*c^2*d^2*(B*d + 3*A*e))*Sqrt[x]*Sqrt[1 + (c*x)/b]*Sqrt[1 + (e*x)/d]*EllipticF[ArcSin[(Sqrt[c]*Sqrt[x])/Sqrt[-b]], (b*e)/(c*d)])/(3*(-b)^(7/2)*d^2*(c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[b*x + c*x^2])","A",10,8,28,0.2857,1,"{822, 834, 843, 715, 112, 110, 117, 116}"
1284,1,108,0,0.1764889,"\int (A+B x) (d+e x)^5 \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^5*(a + c*x^2),x]","\frac{(d+e x)^7 \left(a B e^2-2 A c d e+3 B c d^2\right)}{7 e^4}-\frac{(d+e x)^6 \left(a e^2+c d^2\right) (B d-A e)}{6 e^4}-\frac{c (d+e x)^8 (3 B d-A e)}{8 e^4}+\frac{B c (d+e x)^9}{9 e^4}","\frac{(d+e x)^7 \left(a B e^2-2 A c d e+3 B c d^2\right)}{7 e^4}-\frac{(d+e x)^6 \left(a e^2+c d^2\right) (B d-A e)}{6 e^4}-\frac{c (d+e x)^8 (3 B d-A e)}{8 e^4}+\frac{B c (d+e x)^9}{9 e^4}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^6)/(6*e^4) + ((3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^7)/(7*e^4) - (c*(3*B*d - A*e)*(d + e*x)^8)/(8*e^4) + (B*c*(d + e*x)^9)/(9*e^4)","A",2,1,20,0.05000,1,"{772}"
1285,1,108,0,0.1377433,"\int (A+B x) (d+e x)^4 \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^4*(a + c*x^2),x]","\frac{(d+e x)^6 \left(a B e^2-2 A c d e+3 B c d^2\right)}{6 e^4}-\frac{(d+e x)^5 \left(a e^2+c d^2\right) (B d-A e)}{5 e^4}-\frac{c (d+e x)^7 (3 B d-A e)}{7 e^4}+\frac{B c (d+e x)^8}{8 e^4}","\frac{(d+e x)^6 \left(a B e^2-2 A c d e+3 B c d^2\right)}{6 e^4}-\frac{(d+e x)^5 \left(a e^2+c d^2\right) (B d-A e)}{5 e^4}-\frac{c (d+e x)^7 (3 B d-A e)}{7 e^4}+\frac{B c (d+e x)^8}{8 e^4}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^5)/(5*e^4) + ((3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^6)/(6*e^4) - (c*(3*B*d - A*e)*(d + e*x)^7)/(7*e^4) + (B*c*(d + e*x)^8)/(8*e^4)","A",2,1,20,0.05000,1,"{772}"
1286,1,108,0,0.1143925,"\int (A+B x) (d+e x)^3 \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^3*(a + c*x^2),x]","\frac{(d+e x)^5 \left(a B e^2-2 A c d e+3 B c d^2\right)}{5 e^4}-\frac{(d+e x)^4 \left(a e^2+c d^2\right) (B d-A e)}{4 e^4}-\frac{c (d+e x)^6 (3 B d-A e)}{6 e^4}+\frac{B c (d+e x)^7}{7 e^4}","\frac{(d+e x)^5 \left(a B e^2-2 A c d e+3 B c d^2\right)}{5 e^4}-\frac{(d+e x)^4 \left(a e^2+c d^2\right) (B d-A e)}{4 e^4}-\frac{c (d+e x)^6 (3 B d-A e)}{6 e^4}+\frac{B c (d+e x)^7}{7 e^4}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^4)/(4*e^4) + ((3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^5)/(5*e^4) - (c*(3*B*d - A*e)*(d + e*x)^6)/(6*e^4) + (B*c*(d + e*x)^7)/(7*e^4)","A",2,1,20,0.05000,1,"{772}"
1287,1,108,0,0.0851988,"\int (A+B x) (d+e x)^2 \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^2*(a + c*x^2),x]","\frac{(d+e x)^4 \left(a B e^2-2 A c d e+3 B c d^2\right)}{4 e^4}-\frac{(d+e x)^3 \left(a e^2+c d^2\right) (B d-A e)}{3 e^4}-\frac{c (d+e x)^5 (3 B d-A e)}{5 e^4}+\frac{B c (d+e x)^6}{6 e^4}","\frac{(d+e x)^4 \left(a B e^2-2 A c d e+3 B c d^2\right)}{4 e^4}-\frac{(d+e x)^3 \left(a e^2+c d^2\right) (B d-A e)}{3 e^4}-\frac{c (d+e x)^5 (3 B d-A e)}{5 e^4}+\frac{B c (d+e x)^6}{6 e^4}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^3)/(3*e^4) + ((3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^4)/(4*e^4) - (c*(3*B*d - A*e)*(d + e*x)^5)/(5*e^4) + (B*c*(d + e*x)^6)/(6*e^4)","A",2,1,20,0.05000,1,"{772}"
1288,1,62,0,0.0584914,"\int (A+B x) (d+e x) \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)*(a + c*x^2),x]","\frac{1}{3} x^3 (a B e+A c d)+\frac{1}{2} a x^2 (A e+B d)+a A d x+\frac{1}{4} c x^4 (A e+B d)+\frac{1}{5} B c e x^5","\frac{1}{3} x^3 (a B e+A c d)+\frac{1}{2} a x^2 (A e+B d)+a A d x+\frac{1}{4} c x^4 (A e+B d)+\frac{1}{5} B c e x^5",1,"a*A*d*x + (a*(B*d + A*e)*x^2)/2 + ((A*c*d + a*B*e)*x^3)/3 + (c*(B*d + A*e)*x^4)/4 + (B*c*e*x^5)/5","A",2,1,18,0.05556,1,"{772}"
1289,1,31,0,0.0067756,"\int (A+B x) \left(a+c x^2\right) \, dx","Int[(A + B*x)*(a + c*x^2),x]","a A x+\frac{B \left(a+c x^2\right)^2}{4 c}+\frac{1}{3} A c x^3","a A x+\frac{B \left(a+c x^2\right)^2}{4 c}+\frac{1}{3} A c x^3",1,"a*A*x + (A*c*x^3)/3 + (B*(a + c*x^2)^2)/(4*c)","A",2,1,13,0.07692,1,"{641}"
1290,1,86,0,0.0758643,"\int \frac{(A+B x) \left(a+c x^2\right)}{d+e x} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x),x]","\frac{x \left(a B e^2-A c d e+B c d^2\right)}{e^3}-\frac{\left(a e^2+c d^2\right) (B d-A e) \log (d+e x)}{e^4}-\frac{c x^2 (B d-A e)}{2 e^2}+\frac{B c x^3}{3 e}","\frac{x \left(a B e^2-A c d e+B c d^2\right)}{e^3}-\frac{\left(a e^2+c d^2\right) (B d-A e) \log (d+e x)}{e^4}-\frac{c x^2 (B d-A e)}{2 e^2}+\frac{B c x^3}{3 e}",1,"((B*c*d^2 - A*c*d*e + a*B*e^2)*x)/e^3 - (c*(B*d - A*e)*x^2)/(2*e^2) + (B*c*x^3)/(3*e) - ((B*d - A*e)*(c*d^2 + a*e^2)*Log[d + e*x])/e^4","A",2,1,20,0.05000,1,"{772}"
1291,1,89,0,0.0777694,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^2} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^2,x]","\frac{\left(a e^2+c d^2\right) (B d-A e)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4}-\frac{c x (2 B d-A e)}{e^3}+\frac{B c x^2}{2 e^2}","\frac{\left(a e^2+c d^2\right) (B d-A e)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4}-\frac{c x (2 B d-A e)}{e^3}+\frac{B c x^2}{2 e^2}",1,"-((c*(2*B*d - A*e)*x)/e^3) + (B*c*x^2)/(2*e^2) + ((B*d - A*e)*(c*d^2 + a*e^2))/(e^4*(d + e*x)) + ((3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Log[d + e*x])/e^4","A",2,1,20,0.05000,1,"{772}"
1292,1,94,0,0.0720507,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^3} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^3,x]","\frac{\left(a e^2+c d^2\right) (B d-A e)}{2 e^4 (d+e x)^2}-\frac{a B e^2-2 A c d e+3 B c d^2}{e^4 (d+e x)}-\frac{c (3 B d-A e) \log (d+e x)}{e^4}+\frac{B c x}{e^3}","\frac{\left(a e^2+c d^2\right) (B d-A e)}{2 e^4 (d+e x)^2}-\frac{a B e^2-2 A c d e+3 B c d^2}{e^4 (d+e x)}-\frac{c (3 B d-A e) \log (d+e x)}{e^4}+\frac{B c x}{e^3}",1,"(B*c*x)/e^3 + ((B*d - A*e)*(c*d^2 + a*e^2))/(2*e^4*(d + e*x)^2) - (3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)/(e^4*(d + e*x)) - (c*(3*B*d - A*e)*Log[d + e*x])/e^4","A",2,1,20,0.05000,1,"{772}"
1293,1,101,0,0.072604,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^4} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^4,x]","-\frac{a B e^2-2 A c d e+3 B c d^2}{2 e^4 (d+e x)^2}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{3 e^4 (d+e x)^3}+\frac{c (3 B d-A e)}{e^4 (d+e x)}+\frac{B c \log (d+e x)}{e^4}","-\frac{a B e^2-2 A c d e+3 B c d^2}{2 e^4 (d+e x)^2}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{3 e^4 (d+e x)^3}+\frac{c (3 B d-A e)}{e^4 (d+e x)}+\frac{B c \log (d+e x)}{e^4}",1,"((B*d - A*e)*(c*d^2 + a*e^2))/(3*e^4*(d + e*x)^3) - (3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)/(2*e^4*(d + e*x)^2) + (c*(3*B*d - A*e))/(e^4*(d + e*x)) + (B*c*Log[d + e*x])/e^4","A",2,1,20,0.05000,1,"{772}"
1294,1,106,0,0.0691662,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^5} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^5,x]","-\frac{a B e^2-2 A c d e+3 B c d^2}{3 e^4 (d+e x)^3}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{4 e^4 (d+e x)^4}+\frac{c (3 B d-A e)}{2 e^4 (d+e x)^2}-\frac{B c}{e^4 (d+e x)}","-\frac{a B e^2-2 A c d e+3 B c d^2}{3 e^4 (d+e x)^3}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{4 e^4 (d+e x)^4}+\frac{c (3 B d-A e)}{2 e^4 (d+e x)^2}-\frac{B c}{e^4 (d+e x)}",1,"((B*d - A*e)*(c*d^2 + a*e^2))/(4*e^4*(d + e*x)^4) - (3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)/(3*e^4*(d + e*x)^3) + (c*(3*B*d - A*e))/(2*e^4*(d + e*x)^2) - (B*c)/(e^4*(d + e*x))","A",2,1,20,0.05000,1,"{772}"
1295,1,108,0,0.0706327,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^6} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^6,x]","-\frac{a B e^2-2 A c d e+3 B c d^2}{4 e^4 (d+e x)^4}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{5 e^4 (d+e x)^5}+\frac{c (3 B d-A e)}{3 e^4 (d+e x)^3}-\frac{B c}{2 e^4 (d+e x)^2}","-\frac{a B e^2-2 A c d e+3 B c d^2}{4 e^4 (d+e x)^4}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{5 e^4 (d+e x)^5}+\frac{c (3 B d-A e)}{3 e^4 (d+e x)^3}-\frac{B c}{2 e^4 (d+e x)^2}",1,"((B*d - A*e)*(c*d^2 + a*e^2))/(5*e^4*(d + e*x)^5) - (3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)/(4*e^4*(d + e*x)^4) + (c*(3*B*d - A*e))/(3*e^4*(d + e*x)^3) - (B*c)/(2*e^4*(d + e*x)^2)","A",2,1,20,0.05000,1,"{772}"
1296,1,108,0,0.0679083,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^7} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^7,x]","-\frac{a B e^2-2 A c d e+3 B c d^2}{5 e^4 (d+e x)^5}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{6 e^4 (d+e x)^6}+\frac{c (3 B d-A e)}{4 e^4 (d+e x)^4}-\frac{B c}{3 e^4 (d+e x)^3}","-\frac{a B e^2-2 A c d e+3 B c d^2}{5 e^4 (d+e x)^5}+\frac{\left(a e^2+c d^2\right) (B d-A e)}{6 e^4 (d+e x)^6}+\frac{c (3 B d-A e)}{4 e^4 (d+e x)^4}-\frac{B c}{3 e^4 (d+e x)^3}",1,"((B*d - A*e)*(c*d^2 + a*e^2))/(6*e^4*(d + e*x)^6) - (3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)/(5*e^4*(d + e*x)^5) + (c*(3*B*d - A*e))/(4*e^4*(d + e*x)^4) - (B*c)/(3*e^4*(d + e*x)^3)","A",2,1,20,0.05000,1,"{772}"
1297,1,206,0,0.3912141,"\int (A+B x) (d+e x)^5 \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^5*(a + c*x^2)^2,x]","\frac{2 c (d+e x)^9 \left(a B e^2-2 A c d e+5 B c d^2\right)}{9 e^6}-\frac{c (d+e x)^8 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{4 e^6}+\frac{(d+e x)^7 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{7 e^6}-\frac{(d+e x)^6 \left(a e^2+c d^2\right)^2 (B d-A e)}{6 e^6}-\frac{c^2 (d+e x)^{10} (5 B d-A e)}{10 e^6}+\frac{B c^2 (d+e x)^{11}}{11 e^6}","\frac{2 c (d+e x)^9 \left(a B e^2-2 A c d e+5 B c d^2\right)}{9 e^6}-\frac{c (d+e x)^8 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{4 e^6}+\frac{(d+e x)^7 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{7 e^6}-\frac{(d+e x)^6 \left(a e^2+c d^2\right)^2 (B d-A e)}{6 e^6}-\frac{c^2 (d+e x)^{10} (5 B d-A e)}{10 e^6}+\frac{B c^2 (d+e x)^{11}}{11 e^6}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^2*(d + e*x)^6)/(6*e^6) + ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^7)/(7*e^6) - (c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^8)/(4*e^6) + (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^9)/(9*e^6) - (c^2*(5*B*d - A*e)*(d + e*x)^10)/(10*e^6) + (B*c^2*(d + e*x)^11)/(11*e^6)","A",2,1,22,0.04545,1,"{772}"
1298,1,206,0,0.2734896,"\int (A+B x) (d+e x)^4 \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^4*(a + c*x^2)^2,x]","\frac{c (d+e x)^8 \left(a B e^2-2 A c d e+5 B c d^2\right)}{4 e^6}-\frac{2 c (d+e x)^7 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{7 e^6}+\frac{(d+e x)^6 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{6 e^6}-\frac{(d+e x)^5 \left(a e^2+c d^2\right)^2 (B d-A e)}{5 e^6}-\frac{c^2 (d+e x)^9 (5 B d-A e)}{9 e^6}+\frac{B c^2 (d+e x)^{10}}{10 e^6}","\frac{c (d+e x)^8 \left(a B e^2-2 A c d e+5 B c d^2\right)}{4 e^6}-\frac{2 c (d+e x)^7 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{7 e^6}+\frac{(d+e x)^6 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{6 e^6}-\frac{(d+e x)^5 \left(a e^2+c d^2\right)^2 (B d-A e)}{5 e^6}-\frac{c^2 (d+e x)^9 (5 B d-A e)}{9 e^6}+\frac{B c^2 (d+e x)^{10}}{10 e^6}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^2*(d + e*x)^5)/(5*e^6) + ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^6)/(6*e^6) - (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^7)/(7*e^6) + (c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^8)/(4*e^6) - (c^2*(5*B*d - A*e)*(d + e*x)^9)/(9*e^6) + (B*c^2*(d + e*x)^10)/(10*e^6)","A",2,1,22,0.04545,1,"{772}"
1299,1,206,0,0.2169893,"\int (A+B x) (d+e x)^3 \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^3*(a + c*x^2)^2,x]","\frac{2 c (d+e x)^7 \left(a B e^2-2 A c d e+5 B c d^2\right)}{7 e^6}-\frac{c (d+e x)^6 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6}+\frac{(d+e x)^5 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6}-\frac{(d+e x)^4 \left(a e^2+c d^2\right)^2 (B d-A e)}{4 e^6}-\frac{c^2 (d+e x)^8 (5 B d-A e)}{8 e^6}+\frac{B c^2 (d+e x)^9}{9 e^6}","\frac{2 c (d+e x)^7 \left(a B e^2-2 A c d e+5 B c d^2\right)}{7 e^6}-\frac{c (d+e x)^6 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6}+\frac{(d+e x)^5 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6}-\frac{(d+e x)^4 \left(a e^2+c d^2\right)^2 (B d-A e)}{4 e^6}-\frac{c^2 (d+e x)^8 (5 B d-A e)}{8 e^6}+\frac{B c^2 (d+e x)^9}{9 e^6}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^2*(d + e*x)^4)/(4*e^6) + ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^5)/(5*e^6) - (c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^6)/(3*e^6) + (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^7)/(7*e^6) - (c^2*(5*B*d - A*e)*(d + e*x)^8)/(8*e^6) + (B*c^2*(d + e*x)^9)/(9*e^6)","A",2,1,22,0.04545,1,"{772}"
1300,1,206,0,0.1708314,"\int (A+B x) (d+e x)^2 \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^2*(a + c*x^2)^2,x]","\frac{c (d+e x)^6 \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6}-\frac{2 c (d+e x)^5 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{5 e^6}+\frac{(d+e x)^4 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{4 e^6}-\frac{(d+e x)^3 \left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6}-\frac{c^2 (d+e x)^7 (5 B d-A e)}{7 e^6}+\frac{B c^2 (d+e x)^8}{8 e^6}","\frac{c (d+e x)^6 \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6}-\frac{2 c (d+e x)^5 \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{5 e^6}+\frac{(d+e x)^4 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{4 e^6}-\frac{(d+e x)^3 \left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6}-\frac{c^2 (d+e x)^7 (5 B d-A e)}{7 e^6}+\frac{B c^2 (d+e x)^8}{8 e^6}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^2*(d + e*x)^3)/(3*e^6) + ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^4)/(4*e^6) - (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^5)/(5*e^6) + (c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^6)/(3*e^6) - (c^2*(5*B*d - A*e)*(d + e*x)^7)/(7*e^6) + (B*c^2*(d + e*x)^8)/(8*e^6)","A",2,1,22,0.04545,1,"{772}"
1301,1,106,0,0.1280921,"\int (A+B x) (d+e x) \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)*(a + c*x^2)^2,x]","\frac{1}{2} a^2 x^2 (A e+B d)+a^2 A d x+\frac{1}{5} c x^5 (2 a B e+A c d)+\frac{1}{2} a c x^4 (A e+B d)+\frac{1}{3} a x^3 (a B e+2 A c d)+\frac{1}{6} c^2 x^6 (A e+B d)+\frac{1}{7} B c^2 e x^7","\frac{1}{2} a^2 x^2 (A e+B d)+a^2 A d x+\frac{1}{5} c x^5 (2 a B e+A c d)+\frac{1}{2} a c x^4 (A e+B d)+\frac{1}{3} a x^3 (a B e+2 A c d)+\frac{1}{6} c^2 x^6 (A e+B d)+\frac{1}{7} B c^2 e x^7",1,"a^2*A*d*x + (a^2*(B*d + A*e)*x^2)/2 + (a*(2*A*c*d + a*B*e)*x^3)/3 + (a*c*(B*d + A*e)*x^4)/2 + (c*(A*c*d + 2*a*B*e)*x^5)/5 + (c^2*(B*d + A*e)*x^6)/6 + (B*c^2*e*x^7)/7","A",2,1,20,0.05000,1,"{772}"
1302,1,45,0,0.0155965,"\int (A+B x) \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(a + c*x^2)^2,x]","a^2 A x+\frac{2}{3} a A c x^3+\frac{B \left(a+c x^2\right)^3}{6 c}+\frac{1}{5} A c^2 x^5","a^2 A x+\frac{2}{3} a A c x^3+\frac{B \left(a+c x^2\right)^3}{6 c}+\frac{1}{5} A c^2 x^5",1,"a^2*A*x + (2*a*A*c*x^3)/3 + (A*c^2*x^5)/5 + (B*(a + c*x^2)^3)/(6*c)","A",3,2,15,0.1333,1,"{641, 194}"
1303,1,169,0,0.1919671,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{d+e x} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x),x]","\frac{c x^3 \left(2 a B e^2-A c d e+B c d^2\right)}{3 e^3}-\frac{c x^2 \left(2 a e^2+c d^2\right) (B d-A e)}{2 e^4}+\frac{x \left(B \left(a e^2+c d^2\right)^2-A c d e \left(2 a e^2+c d^2\right)\right)}{e^5}-\frac{\left(a e^2+c d^2\right)^2 (B d-A e) \log (d+e x)}{e^6}-\frac{c^2 x^4 (B d-A e)}{4 e^2}+\frac{B c^2 x^5}{5 e}","\frac{c x^3 \left(2 a B e^2-A c d e+B c d^2\right)}{3 e^3}-\frac{c x^2 \left(2 a e^2+c d^2\right) (B d-A e)}{2 e^4}+\frac{x \left(B \left(a e^2+c d^2\right)^2-A c d e \left(2 a e^2+c d^2\right)\right)}{e^5}-\frac{\left(a e^2+c d^2\right)^2 (B d-A e) \log (d+e x)}{e^6}-\frac{c^2 x^4 (B d-A e)}{4 e^2}+\frac{B c^2 x^5}{5 e}",1,"((B*(c*d^2 + a*e^2)^2 - A*c*d*e*(c*d^2 + 2*a*e^2))*x)/e^5 - (c*(B*d - A*e)*(c*d^2 + 2*a*e^2)*x^2)/(2*e^4) + (c*(B*c*d^2 - A*c*d*e + 2*a*B*e^2)*x^3)/(3*e^3) - (c^2*(B*d - A*e)*x^4)/(4*e^2) + (B*c^2*x^5)/(5*e) - ((B*d - A*e)*(c*d^2 + a*e^2)^2*Log[d + e*x])/e^6","A",2,1,22,0.04545,1,"{772}"
1304,1,180,0,0.215351,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^2} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^2,x]","\frac{c x^2 \left(2 a B e^2-2 A c d e+3 B c d^2\right)}{2 e^4}-\frac{c x \left(-2 a A e^3+4 a B d e^2-3 A c d^2 e+4 B c d^3\right)}{e^5}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{e^6 (d+e x)}+\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6}-\frac{c^2 x^3 (2 B d-A e)}{3 e^3}+\frac{B c^2 x^4}{4 e^2}","\frac{c x^2 \left(2 a B e^2-2 A c d e+3 B c d^2\right)}{2 e^4}-\frac{c x \left(-2 a A e^3+4 a B d e^2-3 A c d^2 e+4 B c d^3\right)}{e^5}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{e^6 (d+e x)}+\frac{\left(a e^2+c d^2\right) \log (d+e x) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6}-\frac{c^2 x^3 (2 B d-A e)}{3 e^3}+\frac{B c^2 x^4}{4 e^2}",1,"-((c*(4*B*c*d^3 - 3*A*c*d^2*e + 4*a*B*d*e^2 - 2*a*A*e^3)*x)/e^5) + (c*(3*B*c*d^2 - 2*A*c*d*e + 2*a*B*e^2)*x^2)/(2*e^4) - (c^2*(2*B*d - A*e)*x^3)/(3*e^3) + (B*c^2*x^4)/(4*e^2) + ((B*d - A*e)*(c*d^2 + a*e^2)^2)/(e^6*(d + e*x)) + ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*Log[d + e*x])/e^6","A",2,1,22,0.04545,1,"{772}"
1305,1,185,0,0.198817,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^3} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^3,x]","\frac{c x \left(2 a B e^2-3 A c d e+6 B c d^2\right)}{e^5}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6 (d+e x)}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{2 e^6 (d+e x)^2}-\frac{2 c \log (d+e x) \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6}-\frac{c^2 x^2 (3 B d-A e)}{2 e^4}+\frac{B c^2 x^3}{3 e^3}","\frac{c x \left(2 a B e^2-3 A c d e+6 B c d^2\right)}{e^5}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6 (d+e x)}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{2 e^6 (d+e x)^2}-\frac{2 c \log (d+e x) \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6}-\frac{c^2 x^2 (3 B d-A e)}{2 e^4}+\frac{B c^2 x^3}{3 e^3}",1,"(c*(6*B*c*d^2 - 3*A*c*d*e + 2*a*B*e^2)*x)/e^5 - (c^2*(3*B*d - A*e)*x^2)/(2*e^4) + (B*c^2*x^3)/(3*e^3) + ((B*d - A*e)*(c*d^2 + a*e^2)^2)/(2*e^6*(d + e*x)^2) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(e^6*(d + e*x)) - (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*Log[d + e*x])/e^6","A",2,1,22,0.04545,1,"{772}"
1306,1,189,0,0.1901208,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^4} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^4,x]","\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 (d+e x)}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{2 e^6 (d+e x)^2}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6 (d+e x)^3}+\frac{2 c \log (d+e x) \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6}-\frac{c^2 x (4 B d-A e)}{e^5}+\frac{B c^2 x^2}{2 e^4}","\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 (d+e x)}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{2 e^6 (d+e x)^2}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6 (d+e x)^3}+\frac{2 c \log (d+e x) \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6}-\frac{c^2 x (4 B d-A e)}{e^5}+\frac{B c^2 x^2}{2 e^4}",1,"-((c^2*(4*B*d - A*e)*x)/e^5) + (B*c^2*x^2)/(2*e^4) + ((B*d - A*e)*(c*d^2 + a*e^2)^2)/(3*e^6*(d + e*x)^3) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(2*e^6*(d + e*x)^2) + (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^6*(d + e*x)) + (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Log[d + e*x])/e^6","A",2,1,22,0.04545,1,"{772}"
1307,1,189,0,0.1676425,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^5} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^5,x]","-\frac{2 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (d+e x)}+\frac{c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 (d+e x)^2}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^3}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{4 e^6 (d+e x)^4}-\frac{c^2 (5 B d-A e) \log (d+e x)}{e^6}+\frac{B c^2 x}{e^5}","-\frac{2 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (d+e x)}+\frac{c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 (d+e x)^2}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^3}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{4 e^6 (d+e x)^4}-\frac{c^2 (5 B d-A e) \log (d+e x)}{e^6}+\frac{B c^2 x}{e^5}",1,"(B*c^2*x)/e^5 + ((B*d - A*e)*(c*d^2 + a*e^2)^2)/(4*e^6*(d + e*x)^4) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(3*e^6*(d + e*x)^3) + (c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^6*(d + e*x)^2) - (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(e^6*(d + e*x)) - (c^2*(5*B*d - A*e)*Log[d + e*x])/e^6","A",2,1,22,0.04545,1,"{772}"
1308,1,197,0,0.1516556,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^6} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^6,x]","-\frac{c \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (d+e x)^2}+\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6 (d+e x)^3}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{4 e^6 (d+e x)^4}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{5 e^6 (d+e x)^5}+\frac{c^2 (5 B d-A e)}{e^6 (d+e x)}+\frac{B c^2 \log (d+e x)}{e^6}","-\frac{c \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (d+e x)^2}+\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6 (d+e x)^3}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{4 e^6 (d+e x)^4}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{5 e^6 (d+e x)^5}+\frac{c^2 (5 B d-A e)}{e^6 (d+e x)}+\frac{B c^2 \log (d+e x)}{e^6}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^2)/(5*e^6*(d + e*x)^5) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(4*e^6*(d + e*x)^4) + (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(3*e^6*(d + e*x)^3) - (c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(e^6*(d + e*x)^2) + (c^2*(5*B*d - A*e))/(e^6*(d + e*x)) + (B*c^2*Log[d + e*x])/e^6","A",2,1,22,0.04545,1,"{772}"
1309,1,204,0,0.1412666,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^7} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^7,x]","-\frac{2 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^3}+\frac{c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{2 e^6 (d+e x)^4}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6 (d+e x)^5}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{6 e^6 (d+e x)^6}+\frac{c^2 (5 B d-A e)}{2 e^6 (d+e x)^2}-\frac{B c^2}{e^6 (d+e x)}","-\frac{2 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^3}+\frac{c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{2 e^6 (d+e x)^4}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6 (d+e x)^5}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{6 e^6 (d+e x)^6}+\frac{c^2 (5 B d-A e)}{2 e^6 (d+e x)^2}-\frac{B c^2}{e^6 (d+e x)}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^2)/(6*e^6*(d + e*x)^6) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(5*e^6*(d + e*x)^5) + (c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(2*e^6*(d + e*x)^4) - (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(3*e^6*(d + e*x)^3) + (c^2*(5*B*d - A*e))/(2*e^6*(d + e*x)^2) - (B*c^2)/(e^6*(d + e*x))","A",2,1,22,0.04545,1,"{772}"
1310,1,206,0,0.1390451,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^8} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^8,x]","-\frac{c \left(a B e^2-2 A c d e+5 B c d^2\right)}{2 e^6 (d+e x)^4}+\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{5 e^6 (d+e x)^5}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{6 e^6 (d+e x)^6}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{7 e^6 (d+e x)^7}+\frac{c^2 (5 B d-A e)}{3 e^6 (d+e x)^3}-\frac{B c^2}{2 e^6 (d+e x)^2}","-\frac{c \left(a B e^2-2 A c d e+5 B c d^2\right)}{2 e^6 (d+e x)^4}+\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{5 e^6 (d+e x)^5}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{6 e^6 (d+e x)^6}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{7 e^6 (d+e x)^7}+\frac{c^2 (5 B d-A e)}{3 e^6 (d+e x)^3}-\frac{B c^2}{2 e^6 (d+e x)^2}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^2)/(7*e^6*(d + e*x)^7) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(6*e^6*(d + e*x)^6) + (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(5*e^6*(d + e*x)^5) - (c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(2*e^6*(d + e*x)^4) + (c^2*(5*B*d - A*e))/(3*e^6*(d + e*x)^3) - (B*c^2)/(2*e^6*(d + e*x)^2)","A",2,1,22,0.04545,1,"{772}"
1311,1,206,0,0.1371377,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^9} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^9,x]","-\frac{2 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{5 e^6 (d+e x)^5}+\frac{c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6 (d+e x)^6}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{7 e^6 (d+e x)^7}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{8 e^6 (d+e x)^8}+\frac{c^2 (5 B d-A e)}{4 e^6 (d+e x)^4}-\frac{B c^2}{3 e^6 (d+e x)^3}","-\frac{2 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{5 e^6 (d+e x)^5}+\frac{c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6 (d+e x)^6}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{7 e^6 (d+e x)^7}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{8 e^6 (d+e x)^8}+\frac{c^2 (5 B d-A e)}{4 e^6 (d+e x)^4}-\frac{B c^2}{3 e^6 (d+e x)^3}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^2)/(8*e^6*(d + e*x)^8) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(7*e^6*(d + e*x)^7) + (c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(3*e^6*(d + e*x)^6) - (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(5*e^6*(d + e*x)^5) + (c^2*(5*B*d - A*e))/(4*e^6*(d + e*x)^4) - (B*c^2)/(3*e^6*(d + e*x)^3)","A",2,1,22,0.04545,1,"{772}"
1312,1,206,0,0.136584,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{10}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^10,x]","-\frac{c \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^6}+\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{7 e^6 (d+e x)^7}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{8 e^6 (d+e x)^8}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{9 e^6 (d+e x)^9}+\frac{c^2 (5 B d-A e)}{5 e^6 (d+e x)^5}-\frac{B c^2}{4 e^6 (d+e x)^4}","-\frac{c \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^6}+\frac{2 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{7 e^6 (d+e x)^7}-\frac{\left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{8 e^6 (d+e x)^8}+\frac{\left(a e^2+c d^2\right)^2 (B d-A e)}{9 e^6 (d+e x)^9}+\frac{c^2 (5 B d-A e)}{5 e^6 (d+e x)^5}-\frac{B c^2}{4 e^6 (d+e x)^4}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^2)/(9*e^6*(d + e*x)^9) - ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(8*e^6*(d + e*x)^8) + (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(7*e^6*(d + e*x)^7) - (c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(3*e^6*(d + e*x)^6) + (c^2*(5*B*d - A*e))/(5*e^6*(d + e*x)^5) - (B*c^2)/(4*e^6*(d + e*x)^4)","A",2,1,22,0.04545,1,"{772}"
1313,1,334,0,0.6027292,"\int (A+B x) (d+e x)^5 \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^5*(a + c*x^2)^3,x]","-\frac{c (d+e x)^9 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{9 e^8}+\frac{3 c^2 (d+e x)^{11} \left(a B e^2-2 A c d e+7 B c d^2\right)}{11 e^8}-\frac{c^2 (d+e x)^{10} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{10 e^8}-\frac{3 c (d+e x)^8 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{8 e^8}+\frac{(d+e x)^7 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{7 e^8}-\frac{(d+e x)^6 \left(a e^2+c d^2\right)^3 (B d-A e)}{6 e^8}-\frac{c^3 (d+e x)^{12} (7 B d-A e)}{12 e^8}+\frac{B c^3 (d+e x)^{13}}{13 e^8}","-\frac{c (d+e x)^9 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{9 e^8}+\frac{3 c^2 (d+e x)^{11} \left(a B e^2-2 A c d e+7 B c d^2\right)}{11 e^8}-\frac{c^2 (d+e x)^{10} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{10 e^8}-\frac{3 c (d+e x)^8 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{8 e^8}+\frac{(d+e x)^7 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{7 e^8}-\frac{(d+e x)^6 \left(a e^2+c d^2\right)^3 (B d-A e)}{6 e^8}-\frac{c^3 (d+e x)^{12} (7 B d-A e)}{12 e^8}+\frac{B c^3 (d+e x)^{13}}{13 e^8}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^3*(d + e*x)^6)/(6*e^8) + ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)^7)/(7*e^8) - (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^8)/(8*e^8) - (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^9)/(9*e^8) - (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^10)/(10*e^8) + (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^11)/(11*e^8) - (c^3*(7*B*d - A*e)*(d + e*x)^12)/(12*e^8) + (B*c^3*(d + e*x)^13)/(13*e^8)","A",2,1,22,0.04545,1,"{772}"
1314,1,334,0,0.4485435,"\int (A+B x) (d+e x)^4 \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^4*(a + c*x^2)^3,x]","-\frac{c (d+e x)^8 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{8 e^8}+\frac{3 c^2 (d+e x)^{10} \left(a B e^2-2 A c d e+7 B c d^2\right)}{10 e^8}-\frac{c^2 (d+e x)^9 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{9 e^8}-\frac{3 c (d+e x)^7 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{7 e^8}+\frac{(d+e x)^6 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{6 e^8}-\frac{(d+e x)^5 \left(a e^2+c d^2\right)^3 (B d-A e)}{5 e^8}-\frac{c^3 (d+e x)^{11} (7 B d-A e)}{11 e^8}+\frac{B c^3 (d+e x)^{12}}{12 e^8}","-\frac{c (d+e x)^8 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{8 e^8}+\frac{3 c^2 (d+e x)^{10} \left(a B e^2-2 A c d e+7 B c d^2\right)}{10 e^8}-\frac{c^2 (d+e x)^9 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{9 e^8}-\frac{3 c (d+e x)^7 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{7 e^8}+\frac{(d+e x)^6 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{6 e^8}-\frac{(d+e x)^5 \left(a e^2+c d^2\right)^3 (B d-A e)}{5 e^8}-\frac{c^3 (d+e x)^{11} (7 B d-A e)}{11 e^8}+\frac{B c^3 (d+e x)^{12}}{12 e^8}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^3*(d + e*x)^5)/(5*e^8) + ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)^6)/(6*e^8) - (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^7)/(7*e^8) - (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^8)/(8*e^8) - (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^9)/(9*e^8) + (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^10)/(10*e^8) - (c^3*(7*B*d - A*e)*(d + e*x)^11)/(11*e^8) + (B*c^3*(d + e*x)^12)/(12*e^8)","A",2,1,22,0.04545,1,"{772}"
1315,1,334,0,0.3747612,"\int (A+B x) (d+e x)^3 \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^3*(a + c*x^2)^3,x]","-\frac{c (d+e x)^7 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{7 e^8}+\frac{c^2 (d+e x)^9 \left(a B e^2-2 A c d e+7 B c d^2\right)}{3 e^8}-\frac{c^2 (d+e x)^8 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{8 e^8}-\frac{c (d+e x)^6 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{2 e^8}+\frac{(d+e x)^5 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{5 e^8}-\frac{(d+e x)^4 \left(a e^2+c d^2\right)^3 (B d-A e)}{4 e^8}-\frac{c^3 (d+e x)^{10} (7 B d-A e)}{10 e^8}+\frac{B c^3 (d+e x)^{11}}{11 e^8}","-\frac{c (d+e x)^7 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{7 e^8}+\frac{c^2 (d+e x)^9 \left(a B e^2-2 A c d e+7 B c d^2\right)}{3 e^8}-\frac{c^2 (d+e x)^8 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{8 e^8}-\frac{c (d+e x)^6 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{2 e^8}+\frac{(d+e x)^5 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{5 e^8}-\frac{(d+e x)^4 \left(a e^2+c d^2\right)^3 (B d-A e)}{4 e^8}-\frac{c^3 (d+e x)^{10} (7 B d-A e)}{10 e^8}+\frac{B c^3 (d+e x)^{11}}{11 e^8}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^3*(d + e*x)^4)/(4*e^8) + ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)^5)/(5*e^8) - (c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^6)/(2*e^8) - (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^7)/(7*e^8) - (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^8)/(8*e^8) + (c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^9)/(3*e^8) - (c^3*(7*B*d - A*e)*(d + e*x)^10)/(10*e^8) + (B*c^3*(d + e*x)^11)/(11*e^8)","A",2,1,22,0.04545,1,"{772}"
1316,1,334,0,0.3074452,"\int (A+B x) (d+e x)^2 \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^2*(a + c*x^2)^3,x]","-\frac{c (d+e x)^6 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{6 e^8}+\frac{3 c^2 (d+e x)^8 \left(a B e^2-2 A c d e+7 B c d^2\right)}{8 e^8}-\frac{c^2 (d+e x)^7 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{7 e^8}-\frac{3 c (d+e x)^5 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8}+\frac{(d+e x)^4 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{4 e^8}-\frac{(d+e x)^3 \left(a e^2+c d^2\right)^3 (B d-A e)}{3 e^8}-\frac{c^3 (d+e x)^9 (7 B d-A e)}{9 e^8}+\frac{B c^3 (d+e x)^{10}}{10 e^8}","-\frac{c (d+e x)^6 \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{6 e^8}+\frac{3 c^2 (d+e x)^8 \left(a B e^2-2 A c d e+7 B c d^2\right)}{8 e^8}-\frac{c^2 (d+e x)^7 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{7 e^8}-\frac{3 c (d+e x)^5 \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8}+\frac{(d+e x)^4 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{4 e^8}-\frac{(d+e x)^3 \left(a e^2+c d^2\right)^3 (B d-A e)}{3 e^8}-\frac{c^3 (d+e x)^9 (7 B d-A e)}{9 e^8}+\frac{B c^3 (d+e x)^{10}}{10 e^8}",1,"-((B*d - A*e)*(c*d^2 + a*e^2)^3*(d + e*x)^3)/(3*e^8) + ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)^4)/(4*e^8) - (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^5)/(5*e^8) - (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^6)/(6*e^8) - (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^7)/(7*e^8) + (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^8)/(8*e^8) - (c^3*(7*B*d - A*e)*(d + e*x)^9)/(9*e^8) + (B*c^3*(d + e*x)^10)/(10*e^8)","A",2,1,22,0.04545,1,"{772}"
1317,1,148,0,0.2105067,"\int (A+B x) (d+e x) \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)*(a + c*x^2)^3,x]","\frac{3}{4} a^2 c x^4 (A e+B d)+\frac{1}{3} a^2 x^3 (a B e+3 A c d)+\frac{1}{2} a^3 x^2 (A e+B d)+a^3 A d x+\frac{1}{7} c^2 x^7 (3 a B e+A c d)+\frac{1}{2} a c^2 x^6 (A e+B d)+\frac{3}{5} a c x^5 (a B e+A c d)+\frac{1}{8} c^3 x^8 (A e+B d)+\frac{1}{9} B c^3 e x^9","\frac{3}{4} a^2 c x^4 (A e+B d)+\frac{1}{3} a^2 x^3 (a B e+3 A c d)+\frac{1}{2} a^3 x^2 (A e+B d)+a^3 A d x+\frac{1}{7} c^2 x^7 (3 a B e+A c d)+\frac{1}{2} a c^2 x^6 (A e+B d)+\frac{3}{5} a c x^5 (a B e+A c d)+\frac{1}{8} c^3 x^8 (A e+B d)+\frac{1}{9} B c^3 e x^9",1,"a^3*A*d*x + (a^3*(B*d + A*e)*x^2)/2 + (a^2*(3*A*c*d + a*B*e)*x^3)/3 + (3*a^2*c*(B*d + A*e)*x^4)/4 + (3*a*c*(A*c*d + a*B*e)*x^5)/5 + (a*c^2*(B*d + A*e)*x^6)/2 + (c^2*(A*c*d + 3*a*B*e)*x^7)/7 + (c^3*(B*d + A*e)*x^8)/8 + (B*c^3*e*x^9)/9","A",2,1,20,0.05000,1,"{772}"
1318,1,56,0,0.0221575,"\int (A+B x) \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(a + c*x^2)^3,x]","a^2 A c x^3+a^3 A x+\frac{3}{5} a A c^2 x^5+\frac{B \left(a+c x^2\right)^4}{8 c}+\frac{1}{7} A c^3 x^7","a^2 A c x^3+a^3 A x+\frac{3}{5} a A c^2 x^5+\frac{B \left(a+c x^2\right)^4}{8 c}+\frac{1}{7} A c^3 x^7",1,"a^3*A*x + a^2*A*c*x^3 + (3*a*A*c^2*x^5)/5 + (A*c^3*x^7)/7 + (B*(a + c*x^2)^4)/(8*c)","A",3,2,15,0.1333,1,"{641, 194}"
1319,1,290,0,0.4002086,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{d+e x} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x),x]","-\frac{c x^3 \left(A c d e \left(3 a e^2+c d^2\right)-B \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)\right)}{3 e^5}-\frac{c x^2 \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right) (B d-A e)}{2 e^6}+\frac{x \left(B \left(a e^2+c d^2\right)^3-A c d e \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)\right)}{e^7}+\frac{c^2 x^5 \left(3 a B e^2-A c d e+B c d^2\right)}{5 e^3}-\frac{c^2 x^4 \left(3 a e^2+c d^2\right) (B d-A e)}{4 e^4}-\frac{\left(a e^2+c d^2\right)^3 (B d-A e) \log (d+e x)}{e^8}-\frac{c^3 x^6 (B d-A e)}{6 e^2}+\frac{B c^3 x^7}{7 e}","-\frac{c x^3 \left(A c d e \left(3 a e^2+c d^2\right)-B \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)\right)}{3 e^5}-\frac{c x^2 \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right) (B d-A e)}{2 e^6}+\frac{x \left(B \left(a e^2+c d^2\right)^3-A c d e \left(3 a^2 e^4+3 a c d^2 e^2+c^2 d^4\right)\right)}{e^7}+\frac{c^2 x^5 \left(3 a B e^2-A c d e+B c d^2\right)}{5 e^3}-\frac{c^2 x^4 \left(3 a e^2+c d^2\right) (B d-A e)}{4 e^4}-\frac{\left(a e^2+c d^2\right)^3 (B d-A e) \log (d+e x)}{e^8}-\frac{c^3 x^6 (B d-A e)}{6 e^2}+\frac{B c^3 x^7}{7 e}",1,"((B*(c*d^2 + a*e^2)^3 - A*c*d*e*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4))*x)/e^7 - (c*(B*d - A*e)*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4)*x^2)/(2*e^6) - (c*(A*c*d*e*(c*d^2 + 3*a*e^2) - B*(c^2*d^4 + 3*a*c*d^2*e^2 + 3*a^2*e^4))*x^3)/(3*e^5) - (c^2*(B*d - A*e)*(c*d^2 + 3*a*e^2)*x^4)/(4*e^4) + (c^2*(B*c*d^2 - A*c*d*e + 3*a*B*e^2)*x^5)/(5*e^3) - (c^3*(B*d - A*e)*x^6)/(6*e^2) + (B*c^3*x^7)/(7*e) - ((B*d - A*e)*(c*d^2 + a*e^2)^3*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1320,1,309,0,0.4354601,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^2} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^2,x]","-\frac{c x^2 \left(2 A c d e \left(3 a e^2+2 c d^2\right)-B \left(3 a^2 e^4+9 a c d^2 e^2+5 c^2 d^4\right)\right)}{2 e^6}-\frac{c x \left(6 B d \left(a e^2+c d^2\right)^2-A e \left(3 a^2 e^4+9 a c d^2 e^2+5 c^2 d^4\right)\right)}{e^7}-\frac{c^2 x^4 \left(2 A c d e-3 B \left(a e^2+c d^2\right)\right)}{4 e^4}+\frac{c^2 x^3 \left(3 A e \left(a e^2+c d^2\right)-B \left(6 a d e^2+4 c d^3\right)\right)}{3 e^5}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{e^8 (d+e x)}+\frac{\left(a e^2+c d^2\right)^2 \log (d+e x) \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8}-\frac{c^3 x^5 (2 B d-A e)}{5 e^3}+\frac{B c^3 x^6}{6 e^2}","-\frac{c x^2 \left(2 A c d e \left(3 a e^2+2 c d^2\right)-B \left(3 a^2 e^4+9 a c d^2 e^2+5 c^2 d^4\right)\right)}{2 e^6}-\frac{c x \left(6 B d \left(a e^2+c d^2\right)^2-A e \left(3 a^2 e^4+9 a c d^2 e^2+5 c^2 d^4\right)\right)}{e^7}-\frac{c^2 x^4 \left(2 A c d e-3 B \left(a e^2+c d^2\right)\right)}{4 e^4}+\frac{c^2 x^3 \left(3 A e \left(a e^2+c d^2\right)-B \left(6 a d e^2+4 c d^3\right)\right)}{3 e^5}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{e^8 (d+e x)}+\frac{\left(a e^2+c d^2\right)^2 \log (d+e x) \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8}-\frac{c^3 x^5 (2 B d-A e)}{5 e^3}+\frac{B c^3 x^6}{6 e^2}",1,"-((c*(6*B*d*(c*d^2 + a*e^2)^2 - A*e*(5*c^2*d^4 + 9*a*c*d^2*e^2 + 3*a^2*e^4))*x)/e^7) - (c*(2*A*c*d*e*(2*c*d^2 + 3*a*e^2) - B*(5*c^2*d^4 + 9*a*c*d^2*e^2 + 3*a^2*e^4))*x^2)/(2*e^6) + (c^2*(3*A*e*(c*d^2 + a*e^2) - B*(4*c*d^3 + 6*a*d*e^2))*x^3)/(3*e^5) - (c^2*(2*A*c*d*e - 3*B*(c*d^2 + a*e^2))*x^4)/(4*e^4) - (c^3*(2*B*d - A*e)*x^5)/(5*e^3) + (B*c^3*x^6)/(6*e^2) + ((B*d - A*e)*(c*d^2 + a*e^2)^3)/(e^8*(d + e*x)) + ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1321,1,300,0,0.4165286,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^3} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^3,x]","-\frac{c x \left(A c d e \left(9 a e^2+10 c d^2\right)-3 B \left(a^2 e^4+6 a c d^2 e^2+5 c^2 d^4\right)\right)}{e^7}+\frac{c^2 x^3 \left(a B e^2-A c d e+2 B c d^2\right)}{e^5}-\frac{c^2 x^2 \left(-3 a A e^3+9 a B d e^2-6 A c d^2 e+10 B c d^3\right)}{2 e^6}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8 (d+e x)}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{2 e^8 (d+e x)^2}-\frac{3 c \left(a e^2+c d^2\right) \log (d+e x) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8}-\frac{c^3 x^4 (3 B d-A e)}{4 e^4}+\frac{B c^3 x^5}{5 e^3}","-\frac{c x \left(A c d e \left(9 a e^2+10 c d^2\right)-3 B \left(a^2 e^4+6 a c d^2 e^2+5 c^2 d^4\right)\right)}{e^7}+\frac{c^2 x^3 \left(a B e^2-A c d e+2 B c d^2\right)}{e^5}-\frac{c^2 x^2 \left(-3 a A e^3+9 a B d e^2-6 A c d^2 e+10 B c d^3\right)}{2 e^6}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8 (d+e x)}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{2 e^8 (d+e x)^2}-\frac{3 c \left(a e^2+c d^2\right) \log (d+e x) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8}-\frac{c^3 x^4 (3 B d-A e)}{4 e^4}+\frac{B c^3 x^5}{5 e^3}",1,"-((c*(A*c*d*e*(10*c*d^2 + 9*a*e^2) - 3*B*(5*c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4))*x)/e^7) - (c^2*(10*B*c*d^3 - 6*A*c*d^2*e + 9*a*B*d*e^2 - 3*a*A*e^3)*x^2)/(2*e^6) + (c^2*(2*B*c*d^2 - A*c*d*e + a*B*e^2)*x^3)/e^5 - (c^3*(3*B*d - A*e)*x^4)/(4*e^4) + (B*c^3*x^5)/(5*e^3) + ((B*d - A*e)*(c*d^2 + a*e^2)^3)/(2*e^8*(d + e*x)^2) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(e^8*(d + e*x)) - (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1322,1,310,0,0.3957925,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^4} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^4,x]","-\frac{c \log (d+e x) \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8}+\frac{c^2 x^2 \left(3 a B e^2-4 A c d e+10 B c d^2\right)}{2 e^6}-\frac{c^2 x \left(-3 a A e^3+12 a B d e^2-10 A c d^2 e+20 B c d^3\right)}{e^7}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{2 e^8 (d+e x)^2}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{3 e^8 (d+e x)^3}-\frac{c^3 x^3 (4 B d-A e)}{3 e^5}+\frac{B c^3 x^4}{4 e^4}","-\frac{c \log (d+e x) \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8}+\frac{c^2 x^2 \left(3 a B e^2-4 A c d e+10 B c d^2\right)}{2 e^6}-\frac{c^2 x \left(-3 a A e^3+12 a B d e^2-10 A c d^2 e+20 B c d^3\right)}{e^7}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (d+e x)}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{2 e^8 (d+e x)^2}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{3 e^8 (d+e x)^3}-\frac{c^3 x^3 (4 B d-A e)}{3 e^5}+\frac{B c^3 x^4}{4 e^4}",1,"-((c^2*(20*B*c*d^3 - 10*A*c*d^2*e + 12*a*B*d*e^2 - 3*a*A*e^3)*x)/e^7) + (c^2*(10*B*c*d^2 - 4*A*c*d*e + 3*a*B*e^2)*x^2)/(2*e^6) - (c^3*(4*B*d - A*e)*x^3)/(3*e^5) + (B*c^3*x^4)/(4*e^4) + ((B*d - A*e)*(c*d^2 + a*e^2)^3)/(3*e^8*(d + e*x)^3) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(2*e^8*(d + e*x)^2) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^8*(d + e*x)) - (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1323,1,314,0,0.3819261,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^5} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^5,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8 (d+e x)}-\frac{c^2 x \left(5 A c d e-3 B \left(a e^2+5 c d^2\right)\right)}{e^7}-\frac{c^2 \log (d+e x) \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{2 e^8 (d+e x)^2}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{3 e^8 (d+e x)^3}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{4 e^8 (d+e x)^4}-\frac{c^3 x^2 (5 B d-A e)}{2 e^6}+\frac{B c^3 x^3}{3 e^5}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8 (d+e x)}-\frac{c^2 x \left(5 A c d e-3 B \left(a e^2+5 c d^2\right)\right)}{e^7}-\frac{c^2 \log (d+e x) \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{2 e^8 (d+e x)^2}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{3 e^8 (d+e x)^3}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{4 e^8 (d+e x)^4}-\frac{c^3 x^2 (5 B d-A e)}{2 e^6}+\frac{B c^3 x^3}{3 e^5}",1,"-((c^2*(5*A*c*d*e - 3*B*(5*c*d^2 + a*e^2))*x)/e^7) - (c^3*(5*B*d - A*e)*x^2)/(2*e^6) + (B*c^3*x^3)/(3*e^5) + ((B*d - A*e)*(c*d^2 + a*e^2)^3)/(4*e^8*(d + e*x)^4) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(3*e^8*(d + e*x)^3) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(2*e^8*(d + e*x)^2) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(e^8*(d + e*x)) - (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1324,1,313,0,0.3448748,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^6} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^6,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{2 e^8 (d+e x)^2}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8 (d+e x)}+\frac{3 c^2 \log (d+e x) \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8}+\frac{c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (d+e x)^3}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{4 e^8 (d+e x)^4}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{5 e^8 (d+e x)^5}-\frac{c^3 x (6 B d-A e)}{e^7}+\frac{B c^3 x^2}{2 e^6}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{2 e^8 (d+e x)^2}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8 (d+e x)}+\frac{3 c^2 \log (d+e x) \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8}+\frac{c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (d+e x)^3}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{4 e^8 (d+e x)^4}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{5 e^8 (d+e x)^5}-\frac{c^3 x (6 B d-A e)}{e^7}+\frac{B c^3 x^2}{2 e^6}",1,"-((c^3*(6*B*d - A*e)*x)/e^7) + (B*c^3*x^2)/(2*e^6) + ((B*d - A*e)*(c*d^2 + a*e^2)^3)/(5*e^8*(d + e*x)^5) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(4*e^8*(d + e*x)^4) + (c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^8*(d + e*x)^3) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(2*e^8*(d + e*x)^2) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(e^8*(d + e*x)) + (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1325,1,320,0,0.3195661,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^7} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^7,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{3 e^8 (d+e x)^3}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8 (d+e x)}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{2 e^8 (d+e x)^2}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{4 e^8 (d+e x)^4}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{5 e^8 (d+e x)^5}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{6 e^8 (d+e x)^6}-\frac{c^3 (7 B d-A e) \log (d+e x)}{e^8}+\frac{B c^3 x}{e^7}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{3 e^8 (d+e x)^3}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8 (d+e x)}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{2 e^8 (d+e x)^2}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{4 e^8 (d+e x)^4}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{5 e^8 (d+e x)^5}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{6 e^8 (d+e x)^6}-\frac{c^3 (7 B d-A e) \log (d+e x)}{e^8}+\frac{B c^3 x}{e^7}",1,"(B*c^3*x)/e^7 + ((B*d - A*e)*(c*d^2 + a*e^2)^3)/(6*e^8*(d + e*x)^6) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(5*e^8*(d + e*x)^5) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(4*e^8*(d + e*x)^4) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(3*e^8*(d + e*x)^3) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(2*e^8*(d + e*x)^2) - (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(e^8*(d + e*x)) - (c^3*(7*B*d - A*e)*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1326,1,327,0,0.2970882,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^8} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^8,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{4 e^8 (d+e x)^4}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{2 e^8 (d+e x)^2}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{3 e^8 (d+e x)^3}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8 (d+e x)^5}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{6 e^8 (d+e x)^6}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{7 e^8 (d+e x)^7}+\frac{c^3 (7 B d-A e)}{e^8 (d+e x)}+\frac{B c^3 \log (d+e x)}{e^8}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{4 e^8 (d+e x)^4}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{2 e^8 (d+e x)^2}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{3 e^8 (d+e x)^3}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8 (d+e x)^5}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{6 e^8 (d+e x)^6}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{7 e^8 (d+e x)^7}+\frac{c^3 (7 B d-A e)}{e^8 (d+e x)}+\frac{B c^3 \log (d+e x)}{e^8}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^3)/(7*e^8*(d + e*x)^7) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(6*e^8*(d + e*x)^6) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(5*e^8*(d + e*x)^5) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(4*e^8*(d + e*x)^4) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(3*e^8*(d + e*x)^3) - (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(2*e^8*(d + e*x)^2) + (c^3*(7*B*d - A*e))/(e^8*(d + e*x)) + (B*c^3*Log[d + e*x])/e^8","A",2,1,22,0.04545,1,"{772}"
1327,1,330,0,0.2736757,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^9} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^9,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{5 e^8 (d+e x)^5}-\frac{c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8 (d+e x)^3}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{4 e^8 (d+e x)^4}+\frac{c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{2 e^8 (d+e x)^6}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{7 e^8 (d+e x)^7}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{8 e^8 (d+e x)^8}+\frac{c^3 (7 B d-A e)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{5 e^8 (d+e x)^5}-\frac{c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8 (d+e x)^3}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{4 e^8 (d+e x)^4}+\frac{c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{2 e^8 (d+e x)^6}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{7 e^8 (d+e x)^7}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{8 e^8 (d+e x)^8}+\frac{c^3 (7 B d-A e)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^3)/(8*e^8*(d + e*x)^8) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(7*e^8*(d + e*x)^7) + (c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(2*e^8*(d + e*x)^6) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(5*e^8*(d + e*x)^5) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(4*e^8*(d + e*x)^4) - (c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(e^8*(d + e*x)^3) + (c^3*(7*B*d - A*e))/(2*e^8*(d + e*x)^2) - (B*c^3)/(e^8*(d + e*x))","A",2,1,22,0.04545,1,"{772}"
1328,1,334,0,0.2643304,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{10}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^10,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{6 e^8 (d+e x)^6}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{4 e^8 (d+e x)^4}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{5 e^8 (d+e x)^5}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{7 e^8 (d+e x)^7}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{8 e^8 (d+e x)^8}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{9 e^8 (d+e x)^9}+\frac{c^3 (7 B d-A e)}{3 e^8 (d+e x)^3}-\frac{B c^3}{2 e^8 (d+e x)^2}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{6 e^8 (d+e x)^6}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{4 e^8 (d+e x)^4}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{5 e^8 (d+e x)^5}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{7 e^8 (d+e x)^7}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{8 e^8 (d+e x)^8}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{9 e^8 (d+e x)^9}+\frac{c^3 (7 B d-A e)}{3 e^8 (d+e x)^3}-\frac{B c^3}{2 e^8 (d+e x)^2}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^3)/(9*e^8*(d + e*x)^9) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(8*e^8*(d + e*x)^8) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(7*e^8*(d + e*x)^7) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(6*e^8*(d + e*x)^6) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(5*e^8*(d + e*x)^5) - (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(4*e^8*(d + e*x)^4) + (c^3*(7*B*d - A*e))/(3*e^8*(d + e*x)^3) - (B*c^3)/(2*e^8*(d + e*x)^2)","A",2,1,22,0.04545,1,"{772}"
1329,1,334,0,0.2612161,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{11}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^11,x]","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{7 e^8 (d+e x)^7}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{5 e^8 (d+e x)^5}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{6 e^8 (d+e x)^6}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{8 e^8 (d+e x)^8}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{9 e^8 (d+e x)^9}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{10 e^8 (d+e x)^{10}}+\frac{c^3 (7 B d-A e)}{4 e^8 (d+e x)^4}-\frac{B c^3}{3 e^8 (d+e x)^3}","\frac{c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{7 e^8 (d+e x)^7}-\frac{3 c^2 \left(a B e^2-2 A c d e+7 B c d^2\right)}{5 e^8 (d+e x)^5}+\frac{c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{6 e^8 (d+e x)^6}+\frac{3 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{8 e^8 (d+e x)^8}-\frac{\left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{9 e^8 (d+e x)^9}+\frac{\left(a e^2+c d^2\right)^3 (B d-A e)}{10 e^8 (d+e x)^{10}}+\frac{c^3 (7 B d-A e)}{4 e^8 (d+e x)^4}-\frac{B c^3}{3 e^8 (d+e x)^3}",1,"((B*d - A*e)*(c*d^2 + a*e^2)^3)/(10*e^8*(d + e*x)^10) - ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(9*e^8*(d + e*x)^9) + (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(8*e^8*(d + e*x)^8) + (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(7*e^8*(d + e*x)^7) + (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(6*e^8*(d + e*x)^6) - (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(5*e^8*(d + e*x)^5) + (c^3*(7*B*d - A*e))/(4*e^8*(d + e*x)^4) - (B*c^3)/(3*e^8*(d + e*x)^3)","A",2,1,22,0.04545,1,"{772}"
1330,1,240,0,0.2612571,"\int \frac{(A+B x) (d+e x)^4}{a+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a + c*x^2),x]","\frac{\log \left(a+c x^2\right) \left(B \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)+4 A c d e \left(c d^2-a e^2\right)\right)}{2 c^3}-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(4 a B d e \left(c d^2-a e^2\right)-A \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e^2 x^2 \left(-a B e^2+4 A c d e+6 B c d^2\right)}{2 c^2}+\frac{e x \left(-a A e^3-4 a B d e^2+6 A c d^2 e+4 B c d^3\right)}{c^2}+\frac{e^3 x^3 (A e+4 B d)}{3 c}+\frac{B e^4 x^4}{4 c}","\frac{\log \left(a+c x^2\right) \left(B \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)+4 A c d e \left(c d^2-a e^2\right)\right)}{2 c^3}-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(4 a B d e \left(c d^2-a e^2\right)-A \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e^2 x^2 \left(-a B e^2+4 A c d e+6 B c d^2\right)}{2 c^2}+\frac{e x \left(-a A e^3-4 a B d e^2+6 A c d^2 e+4 B c d^3\right)}{c^2}+\frac{e^3 x^3 (A e+4 B d)}{3 c}+\frac{B e^4 x^4}{4 c}",1,"(e*(4*B*c*d^3 + 6*A*c*d^2*e - 4*a*B*d*e^2 - a*A*e^3)*x)/c^2 + (e^2*(6*B*c*d^2 + 4*A*c*d*e - a*B*e^2)*x^2)/(2*c^2) + (e^3*(4*B*d + A*e)*x^3)/(3*c) + (B*e^4*x^4)/(4*c) - ((4*a*B*d*e*(c*d^2 - a*e^2) - A*(c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(5/2)) + ((4*A*c*d*e*(c*d^2 - a*e^2) + B*(c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4))*Log[a + c*x^2])/(2*c^3)","A",5,4,22,0.1818,1,"{801, 635, 205, 260}"
1331,1,167,0,0.1793652,"\int \frac{(A+B x) (d+e x)^3}{a+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + c*x^2),x]","\frac{\log \left(a+c x^2\right) \left(-a A e^3-3 a B d e^2+3 A c d^2 e+B c d^3\right)}{2 c^2}+\frac{e x \left(-a B e^2+3 A c d e+3 B c d^2\right)}{c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)-a B e \left(3 c d^2-a e^2\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e^2 x^2 (A e+3 B d)}{2 c}+\frac{B e^3 x^3}{3 c}","\frac{\log \left(a+c x^2\right) \left(-a A e^3-3 a B d e^2+3 A c d^2 e+B c d^3\right)}{2 c^2}+\frac{e x \left(-a B e^2+3 A c d e+3 B c d^2\right)}{c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)-a B e \left(3 c d^2-a e^2\right)\right)}{\sqrt{a} c^{5/2}}+\frac{e^2 x^2 (A e+3 B d)}{2 c}+\frac{B e^3 x^3}{3 c}",1,"(e*(3*B*c*d^2 + 3*A*c*d*e - a*B*e^2)*x)/c^2 + (e^2*(3*B*d + A*e)*x^2)/(2*c) + (B*e^3*x^3)/(3*c) + ((A*c*d*(c*d^2 - 3*a*e^2) - a*B*e*(3*c*d^2 - a*e^2))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(5/2)) + ((B*c*d^3 + 3*A*c*d^2*e - 3*a*B*d*e^2 - a*A*e^3)*Log[a + c*x^2])/(2*c^2)","A",5,4,22,0.1818,1,"{801, 635, 205, 260}"
1332,1,108,0,0.0946352,"\int \frac{(A+B x) (d+e x)^2}{a+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + c*x^2),x]","\frac{\log \left(a+c x^2\right) \left(-a B e^2+2 A c d e+B c d^2\right)}{2 c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(-a A e^2-2 a B d e+A c d^2\right)}{\sqrt{a} c^{3/2}}+\frac{e x (A e+2 B d)}{c}+\frac{B e^2 x^2}{2 c}","\frac{\log \left(a+c x^2\right) \left(-a B e^2+2 A c d e+B c d^2\right)}{2 c^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(-a A e^2-2 a B d e+A c d^2\right)}{\sqrt{a} c^{3/2}}+\frac{e x (A e+2 B d)}{c}+\frac{B e^2 x^2}{2 c}",1,"(e*(2*B*d + A*e)*x)/c + (B*e^2*x^2)/(2*c) + ((A*c*d^2 - 2*a*B*d*e - a*A*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(3/2)) + ((B*c*d^2 + 2*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/(2*c^2)","A",5,4,22,0.1818,1,"{801, 635, 205, 260}"
1333,1,64,0,0.0429654,"\int \frac{(A+B x) (d+e x)}{a+c x^2} \, dx","Int[((A + B*x)*(d + e*x))/(a + c*x^2),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (A c d-a B e)}{\sqrt{a} c^{3/2}}+\frac{\log \left(a+c x^2\right) (A e+B d)}{2 c}+\frac{B e x}{c}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (A c d-a B e)}{\sqrt{a} c^{3/2}}+\frac{\log \left(a+c x^2\right) (A e+B d)}{2 c}+\frac{B e x}{c}",1,"(B*e*x)/c + ((A*c*d - a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*c^(3/2)) + ((B*d + A*e)*Log[a + c*x^2])/(2*c)","A",4,4,20,0.2000,1,"{774, 635, 205, 260}"
1334,1,42,0,0.0153787,"\int \frac{A+B x}{a+c x^2} \, dx","Int[(A + B*x)/(a + c*x^2),x]","\frac{A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{B \log \left(a+c x^2\right)}{2 c}","\frac{A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{\sqrt{a} \sqrt{c}}+\frac{B \log \left(a+c x^2\right)}{2 c}",1,"(A*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]) + (B*Log[a + c*x^2])/(2*c)","A",3,3,15,0.2000,1,"{635, 205, 260}"
1335,1,109,0,0.1061801,"\int \frac{A+B x}{(d+e x) \left(a+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)*(a + c*x^2)),x]","\frac{\log \left(a+c x^2\right) (B d-A e)}{2 \left(a e^2+c d^2\right)}-\frac{(B d-A e) \log (d+e x)}{a e^2+c d^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)}{\sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)}","\frac{\log \left(a+c x^2\right) (B d-A e)}{2 \left(a e^2+c d^2\right)}-\frac{(B d-A e) \log (d+e x)}{a e^2+c d^2}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)}{\sqrt{a} \sqrt{c} \left(a e^2+c d^2\right)}",1,"((A*c*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*Sqrt[c]*(c*d^2 + a*e^2)) - ((B*d - A*e)*Log[d + e*x])/(c*d^2 + a*e^2) + ((B*d - A*e)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2))","A",5,4,22,0.1818,1,"{801, 635, 205, 260}"
1336,1,173,0,0.169804,"\int \frac{A+B x}{(d+e x)^2 \left(a+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^2*(a + c*x^2)),x]","\frac{\log \left(a+c x^2\right) \left(-a B e^2-2 A c d e+B c d^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{B d-A e}{(d+e x) \left(a e^2+c d^2\right)}-\frac{\log (d+e x) \left(-a B e^2-2 A c d e+B c d^2\right)}{\left(a e^2+c d^2\right)^2}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(-a A e^2+2 a B d e+A c d^2\right)}{\sqrt{a} \left(a e^2+c d^2\right)^2}","\frac{\log \left(a+c x^2\right) \left(-a B e^2-2 A c d e+B c d^2\right)}{2 \left(a e^2+c d^2\right)^2}+\frac{B d-A e}{(d+e x) \left(a e^2+c d^2\right)}-\frac{\log (d+e x) \left(-a B e^2-2 A c d e+B c d^2\right)}{\left(a e^2+c d^2\right)^2}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(-a A e^2+2 a B d e+A c d^2\right)}{\sqrt{a} \left(a e^2+c d^2\right)^2}",1,"(B*d - A*e)/((c*d^2 + a*e^2)*(d + e*x)) + (Sqrt[c]*(A*c*d^2 + 2*a*B*d*e - a*A*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*(c*d^2 + a*e^2)^2) - ((B*c*d^2 - 2*A*c*d*e - a*B*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^2 + ((B*c*d^2 - 2*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^2)","A",5,4,22,0.1818,1,"{801, 635, 205, 260}"
1337,1,251,0,0.322575,"\int \frac{A+B x}{(d+e x)^3 \left(a+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^3*(a + c*x^2)),x]","\frac{c \log \left(a+c x^2\right) \left(a A e^3-3 a B d e^2-3 A c d^2 e+B c d^3\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{B d-A e}{2 (d+e x)^2 \left(a e^2+c d^2\right)}+\frac{-a B e^2-2 A c d e+B c d^2}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{c \log (d+e x) \left(a A e^3-3 a B d e^2-3 A c d^2 e+B c d^3\right)}{\left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)+a B e \left(3 c d^2-a e^2\right)\right)}{\sqrt{a} \left(a e^2+c d^2\right)^3}","\frac{c \log \left(a+c x^2\right) \left(a A e^3-3 a B d e^2-3 A c d^2 e+B c d^3\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{B d-A e}{2 (d+e x)^2 \left(a e^2+c d^2\right)}+\frac{-a B e^2-2 A c d e+B c d^2}{(d+e x) \left(a e^2+c d^2\right)^2}-\frac{c \log (d+e x) \left(a A e^3-3 a B d e^2-3 A c d^2 e+B c d^3\right)}{\left(a e^2+c d^2\right)^3}+\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(c d^2-3 a e^2\right)+a B e \left(3 c d^2-a e^2\right)\right)}{\sqrt{a} \left(a e^2+c d^2\right)^3}",1,"(B*d - A*e)/(2*(c*d^2 + a*e^2)*(d + e*x)^2) + (B*c*d^2 - 2*A*c*d*e - a*B*e^2)/((c*d^2 + a*e^2)^2*(d + e*x)) + (Sqrt[c]*(A*c*d*(c*d^2 - 3*a*e^2) + a*B*e*(3*c*d^2 - a*e^2))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(Sqrt[a]*(c*d^2 + a*e^2)^3) - (c*(B*c*d^3 - 3*A*c*d^2*e - 3*a*B*d*e^2 + a*A*e^3)*Log[d + e*x])/(c*d^2 + a*e^2)^3 + (c*(B*c*d^3 - 3*A*c*d^2*e - 3*a*B*d*e^2 + a*A*e^3)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",5,4,22,0.1818,1,"{801, 635, 205, 260}"
1338,1,297,0,0.3389224,"\int \frac{(A+B x) (d+e x)^5}{\left(a+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^5)/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right)+5 a B e \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)\right)}{2 a^{3/2} c^{7/2}}-\frac{e^3 x^2 \left(-a A e^2-5 a B d e+2 A c d^2\right)}{a c^2}+\frac{e^2 \log \left(a+c x^2\right) \left(-a A e^3-5 a B d e^2+5 A c d^2 e+5 B c d^3\right)}{c^3}-\frac{e^2 x \left(3 A c d \left(2 c d^2-5 a e^2\right)-5 a B e \left(6 c d^2-a e^2\right)\right)}{2 a c^3}-\frac{e^4 x^3 (3 A c d-5 a B e)}{6 a c^2}-\frac{(d+e x)^4 (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right)+5 a B e \left(a^2 e^4-6 a c d^2 e^2+c^2 d^4\right)\right)}{2 a^{3/2} c^{7/2}}-\frac{e^3 x^2 \left(-a A e^2-5 a B d e+2 A c d^2\right)}{a c^2}+\frac{e^2 \log \left(a+c x^2\right) \left(-a A e^3-5 a B d e^2+5 A c d^2 e+5 B c d^3\right)}{c^3}-\frac{e^2 x \left(3 A c d \left(2 c d^2-5 a e^2\right)-5 a B e \left(6 c d^2-a e^2\right)\right)}{2 a c^3}-\frac{e^4 x^3 (3 A c d-5 a B e)}{6 a c^2}-\frac{(d+e x)^4 (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}",1,"-(e^2*(3*A*c*d*(2*c*d^2 - 5*a*e^2) - 5*a*B*e*(6*c*d^2 - a*e^2))*x)/(2*a*c^3) - (e^3*(2*A*c*d^2 - 5*a*B*d*e - a*A*e^2)*x^2)/(a*c^2) - (e^4*(3*A*c*d - 5*a*B*e)*x^3)/(6*a*c^2) - ((d + e*x)^4*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(2*a*c*(a + c*x^2)) + ((A*c*d*(c^2*d^4 + 10*a*c*d^2*e^2 - 15*a^2*e^4) + 5*a*B*e*(c^2*d^4 - 6*a*c*d^2*e^2 + a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(7/2)) + (e^2*(5*B*c*d^3 + 5*A*c*d^2*e - 5*a*B*d*e^2 - a*A*e^3)*Log[a + c*x^2])/c^3","A",6,5,22,0.2273,1,"{819, 801, 635, 205, 260}"
1339,1,220,0,0.2754788,"\int \frac{(A+B x) (d+e x)^4}{\left(a+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)+4 a B d e \left(c d^2-3 a e^2\right)\right)}{2 a^{3/2} c^{5/2}}+\frac{e^2 \log \left(a+c x^2\right) \left(-a B e^2+2 A c d e+3 B c d^2\right)}{c^3}-\frac{3 e^2 x \left(-a A e^2-4 a B d e+A c d^2\right)}{2 a c^2}-\frac{e^3 x^2 (A c d-2 a B e)}{2 a c^2}-\frac{(d+e x)^3 (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)+4 a B d e \left(c d^2-3 a e^2\right)\right)}{2 a^{3/2} c^{5/2}}+\frac{e^2 \log \left(a+c x^2\right) \left(-a B e^2+2 A c d e+3 B c d^2\right)}{c^3}-\frac{3 e^2 x \left(-a A e^2-4 a B d e+A c d^2\right)}{2 a c^2}-\frac{e^3 x^2 (A c d-2 a B e)}{2 a c^2}-\frac{(d+e x)^3 (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}",1,"(-3*e^2*(A*c*d^2 - 4*a*B*d*e - a*A*e^2)*x)/(2*a*c^2) - (e^3*(A*c*d - 2*a*B*e)*x^2)/(2*a*c^2) - ((d + e*x)^3*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(2*a*c*(a + c*x^2)) + ((4*a*B*d*e*(c*d^2 - 3*a*e^2) + A*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(5/2)) + (e^2*(3*B*c*d^2 + 2*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/c^3","A",6,5,22,0.2273,1,"{819, 801, 635, 205, 260}"
1340,1,161,0,0.2081612,"\int \frac{(A+B x) (d+e x)^3}{\left(a+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)+3 a B e \left(c d^2-a e^2\right)\right)}{2 a^{3/2} c^{5/2}}+\frac{e^2 \log \left(a+c x^2\right) (A e+3 B d)}{2 c^2}-\frac{e^2 x (A c d-3 a B e)}{2 a c^2}-\frac{(d+e x)^2 (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(3 a e^2+c d^2\right)+3 a B e \left(c d^2-a e^2\right)\right)}{2 a^{3/2} c^{5/2}}+\frac{e^2 \log \left(a+c x^2\right) (A e+3 B d)}{2 c^2}-\frac{e^2 x (A c d-3 a B e)}{2 a c^2}-\frac{(d+e x)^2 (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}",1,"-(e^2*(A*c*d - 3*a*B*e)*x)/(2*a*c^2) - ((d + e*x)^2*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(2*a*c*(a + c*x^2)) + ((3*a*B*e*(c*d^2 - a*e^2) + A*c*d*(c*d^2 + 3*a*e^2))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(5/2)) + (e^2*(3*B*d + A*e)*Log[a + c*x^2])/(2*c^2)","A",5,5,22,0.2273,1,"{819, 774, 635, 205, 260}"
1341,1,112,0,0.0726357,"\int \frac{(A+B x) (d+e x)^2}{\left(a+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a e (A e+2 B d)+A c d^2\right)}{2 a^{3/2} c^{3/2}}-\frac{(d+e x) (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}+\frac{B e^2 \log \left(a+c x^2\right)}{2 c^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a e (A e+2 B d)+A c d^2\right)}{2 a^{3/2} c^{3/2}}-\frac{(d+e x) (a (A e+B d)-x (A c d-a B e))}{2 a c \left(a+c x^2\right)}+\frac{B e^2 \log \left(a+c x^2\right)}{2 c^2}",1,"-((d + e*x)*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(2*a*c*(a + c*x^2)) + ((A*c*d^2 + a*e*(2*B*d + A*e))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(3/2)) + (B*e^2*Log[a + c*x^2])/(2*c^2)","A",4,4,22,0.1818,1,"{819, 635, 205, 260}"
1342,1,79,0,0.0320804,"\int \frac{(A+B x) (d+e x)}{\left(a+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x))/(a + c*x^2)^2,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)}{2 a^{3/2} c^{3/2}}-\frac{a (A e+B d)-x (A c d-a B e)}{2 a c \left(a+c x^2\right)}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)}{2 a^{3/2} c^{3/2}}-\frac{a (A e+B d)-x (A c d-a B e)}{2 a c \left(a+c x^2\right)}",1,"-(a*(B*d + A*e) - (A*c*d - a*B*e)*x)/(2*a*c*(a + c*x^2)) + ((A*c*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*c^(3/2))","A",2,2,20,0.1000,1,"{778, 205}"
1343,1,57,0,0.0166179,"\int \frac{A+B x}{\left(a+c x^2\right)^2} \, dx","Int[(A + B*x)/(a + c*x^2)^2,x]","\frac{A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{a B-A c x}{2 a c \left(a+c x^2\right)}","\frac{A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{2 a^{3/2} \sqrt{c}}-\frac{a B-A c x}{2 a c \left(a+c x^2\right)}",1,"-(a*B - A*c*x)/(2*a*c*(a + c*x^2)) + (A*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c])","A",2,2,15,0.1333,1,"{639, 205}"
1344,1,195,0,0.2808768,"\int \frac{A+B x}{(d+e x) \left(a+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)*(a + c*x^2)^2),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a B e \left(c d^2-a e^2\right)-A c d \left(3 a e^2+c d^2\right)\right)}{2 a^{3/2} \sqrt{c} \left(a e^2+c d^2\right)^2}-\frac{a (B d-A e)-x (a B e+A c d)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}+\frac{e^2 \log \left(a+c x^2\right) (B d-A e)}{2 \left(a e^2+c d^2\right)^2}-\frac{e^2 (B d-A e) \log (d+e x)}{\left(a e^2+c d^2\right)^2}","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a B e \left(c d^2-a e^2\right)-A c d \left(3 a e^2+c d^2\right)\right)}{2 a^{3/2} \sqrt{c} \left(a e^2+c d^2\right)^2}-\frac{a (B d-A e)-x (a B e+A c d)}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}+\frac{e^2 \log \left(a+c x^2\right) (B d-A e)}{2 \left(a e^2+c d^2\right)^2}-\frac{e^2 (B d-A e) \log (d+e x)}{\left(a e^2+c d^2\right)^2}",1,"-(a*(B*d - A*e) - (A*c*d + a*B*e)*x)/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) - ((a*B*e*(c*d^2 - a*e^2) - A*c*d*(c*d^2 + 3*a*e^2))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*Sqrt[c]*(c*d^2 + a*e^2)^2) - (e^2*(B*d - A*e)*Log[d + e*x])/(c*d^2 + a*e^2)^2 + (e^2*(B*d - A*e)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^2)","A",6,5,22,0.2273,1,"{823, 801, 635, 205, 260}"
1345,1,290,0,0.4107018,"\int \frac{A+B x}{(d+e x)^2 \left(a+c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^2*(a + c*x^2)^2),x]","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(2 a B d e \left(c d^2-3 a e^2\right)-A \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^3}-\frac{a (B d-A e)-x (a B e+A c d)}{2 a \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)}+\frac{e^2 \log \left(a+c x^2\right) \left(-a B e^2-4 A c d e+3 B c d^2\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{e \left(-3 a A e^2+4 a B d e+A c d^2\right)}{2 a (d+e x) \left(a e^2+c d^2\right)^2}-\frac{e^2 \log (d+e x) \left(-a B e^2-4 A c d e+3 B c d^2\right)}{\left(a e^2+c d^2\right)^3}","-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(2 a B d e \left(c d^2-3 a e^2\right)-A \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)\right)}{2 a^{3/2} \left(a e^2+c d^2\right)^3}-\frac{a (B d-A e)-x (a B e+A c d)}{2 a \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)}+\frac{e^2 \log \left(a+c x^2\right) \left(-a B e^2-4 A c d e+3 B c d^2\right)}{2 \left(a e^2+c d^2\right)^3}+\frac{e \left(-3 a A e^2+4 a B d e+A c d^2\right)}{2 a (d+e x) \left(a e^2+c d^2\right)^2}-\frac{e^2 \log (d+e x) \left(-a B e^2-4 A c d e+3 B c d^2\right)}{\left(a e^2+c d^2\right)^3}",1,"(e*(A*c*d^2 + 4*a*B*d*e - 3*a*A*e^2))/(2*a*(c*d^2 + a*e^2)^2*(d + e*x)) - (a*(B*d - A*e) - (A*c*d + a*B*e)*x)/(2*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)) - (Sqrt[c]*(2*a*B*d*e*(c*d^2 - 3*a*e^2) - A*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(2*a^(3/2)*(c*d^2 + a*e^2)^3) - (e^2*(3*B*c*d^2 - 4*A*c*d*e - a*B*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^3 + (e^2*(3*B*c*d^2 - 4*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",6,5,22,0.2273,1,"{823, 801, 635, 205, 260}"
1346,1,304,0,0.4216862,"\int \frac{(A+B x) (d+e x)^5}{\left(a+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^5)/(a + c*x^2)^3,x]","-\frac{(d+e x)^2 \left(2 a e \left(2 a A e^2+5 a B d e+A c d^2\right)-x \left(A c d \left(5 a e^2+3 c d^2\right)+5 a B e \left(c d^2-a e^2\right)\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{e^2 x \left(A c d \left(7 a e^2+3 c d^2\right)+5 a B e \left(c d^2-3 a e^2\right)\right)}{8 a^2 c^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)+5 a B e \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)\right)}{8 a^{5/2} c^{7/2}}+\frac{e^4 \log \left(a+c x^2\right) (A e+5 B d)}{2 c^3}-\frac{(d+e x)^4 (a (A e+B d)-x (A c d-a B e))}{4 a c \left(a+c x^2\right)^2}","-\frac{(d+e x)^2 \left(2 a e \left(2 a A e^2+5 a B d e+A c d^2\right)-x \left(A c d \left(5 a e^2+3 c d^2\right)+5 a B e \left(c d^2-a e^2\right)\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{e^2 x \left(A c d \left(7 a e^2+3 c d^2\right)+5 a B e \left(c d^2-3 a e^2\right)\right)}{8 a^2 c^3}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(A c d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)+5 a B e \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)\right)}{8 a^{5/2} c^{7/2}}+\frac{e^4 \log \left(a+c x^2\right) (A e+5 B d)}{2 c^3}-\frac{(d+e x)^4 (a (A e+B d)-x (A c d-a B e))}{4 a c \left(a+c x^2\right)^2}",1,"-(e^2*(5*a*B*e*(c*d^2 - 3*a*e^2) + A*c*d*(3*c*d^2 + 7*a*e^2))*x)/(8*a^2*c^3) - ((d + e*x)^4*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(4*a*c*(a + c*x^2)^2) - ((d + e*x)^2*(2*a*e*(A*c*d^2 + 5*a*B*d*e + 2*a*A*e^2) - (5*a*B*e*(c*d^2 - a*e^2) + A*c*d*(3*c*d^2 + 5*a*e^2))*x))/(8*a^2*c^2*(a + c*x^2)) + ((5*a*B*e*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4) + A*c*d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(7/2)) + (e^4*(5*B*d + A*e)*Log[a + c*x^2])/(2*c^3)","A",6,5,22,0.2273,1,"{819, 774, 635, 205, 260}"
1347,1,216,0,0.2094126,"\int \frac{(A+B x) (d+e x)^4}{\left(a+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a + c*x^2)^3,x]","-\frac{(d+e x) \left(x \left(4 a^2 B e^3-c d \left(a e (3 A e+4 B d)+3 A c d^2\right)\right)+a e \left(3 A \left(a e^2+c d^2\right)+8 a B d e\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(3 A \left(a e^2+c d^2\right)^2+4 a B d e \left(3 a e^2+c d^2\right)\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^3 (a (A e+B d)-x (A c d-a B e))}{4 a c \left(a+c x^2\right)^2}+\frac{B e^4 \log \left(a+c x^2\right)}{2 c^3}","-\frac{(d+e x) \left(x \left(4 a^2 B e^3-c d \left(a e (3 A e+4 B d)+3 A c d^2\right)\right)+a e \left(3 A \left(a e^2+c d^2\right)+8 a B d e\right)\right)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(3 A \left(a e^2+c d^2\right)^2+4 a B d e \left(3 a e^2+c d^2\right)\right)}{8 a^{5/2} c^{5/2}}-\frac{(d+e x)^3 (a (A e+B d)-x (A c d-a B e))}{4 a c \left(a+c x^2\right)^2}+\frac{B e^4 \log \left(a+c x^2\right)}{2 c^3}",1,"-((d + e*x)^3*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(4*a*c*(a + c*x^2)^2) - ((d + e*x)*(a*e*(8*a*B*d*e + 3*A*(c*d^2 + a*e^2)) + (4*a^2*B*e^3 - c*d*(3*A*c*d^2 + a*e*(4*B*d + 3*A*e)))*x))/(8*a^2*c^2*(a + c*x^2)) + ((3*A*(c*d^2 + a*e^2)^2 + 4*a*B*d*e*(c*d^2 + 3*a*e^2))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(5/2)) + (B*e^4*Log[a + c*x^2])/(2*c^3)","A",5,4,22,0.1818,1,"{819, 635, 205, 260}"
1348,1,125,0,0.0582483,"\int \frac{(A+B x) (d+e x)^3}{\left(a+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + c*x^2)^3,x]","\frac{3 \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)}{8 a^{5/2} c^{5/2}}-\frac{3 (d+e x) (a e-c d x) (a B e+A c d)}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{(d+e x)^3 (a B-A c x)}{4 a c \left(a+c x^2\right)^2}","\frac{3 \left(a e^2+c d^2\right) \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+A c d)}{8 a^{5/2} c^{5/2}}-\frac{3 (d+e x) (a e-c d x) (a B e+A c d)}{8 a^2 c^2 \left(a+c x^2\right)}-\frac{(d+e x)^3 (a B-A c x)}{4 a c \left(a+c x^2\right)^2}",1,"-((a*B - A*c*x)*(d + e*x)^3)/(4*a*c*(a + c*x^2)^2) - (3*(A*c*d + a*B*e)*(a*e - c*d*x)*(d + e*x))/(8*a^2*c^2*(a + c*x^2)) + (3*(A*c*d + a*B*e)*(c*d^2 + a*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(5/2))","A",3,3,22,0.1364,1,"{805, 723, 205}"
1349,1,142,0,0.1250661,"\int \frac{(A+B x) (d+e x)^2}{\left(a+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + c*x^2)^3,x]","-\frac{2 a e (a B e+2 A c d)-c x \left(-a A e^2+2 a B d e+3 A c d^2\right)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a A e^2+2 a B d e+3 A c d^2\right)}{8 a^{5/2} c^{3/2}}-\frac{(d+e x)^2 (a B-A c x)}{4 a c \left(a+c x^2\right)^2}","-\frac{2 a e (a B e+2 A c d)-c x \left(-a A e^2+2 a B d e+3 A c d^2\right)}{8 a^2 c^2 \left(a+c x^2\right)}+\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a A e^2+2 a B d e+3 A c d^2\right)}{8 a^{5/2} c^{3/2}}-\frac{(d+e x)^2 (a B-A c x)}{4 a c \left(a+c x^2\right)^2}",1,"-((a*B - A*c*x)*(d + e*x)^2)/(4*a*c*(a + c*x^2)^2) - (2*a*e*(2*A*c*d + a*B*e) - c*(3*A*c*d^2 + 2*a*B*d*e - a*A*e^2)*x)/(8*a^2*c^2*(a + c*x^2)) + ((3*A*c*d^2 + 2*a*B*d*e + a*A*e^2)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",3,3,22,0.1364,1,"{821, 778, 205}"
1350,1,110,0,0.0442802,"\int \frac{(A+B x) (d+e x)}{\left(a+c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x))/(a + c*x^2)^3,x]","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+3 A c d)}{8 a^{5/2} c^{3/2}}+\frac{x (a B e+3 A c d)}{8 a^2 c \left(a+c x^2\right)}-\frac{a (A e+B d)-x (A c d-a B e)}{4 a c \left(a+c x^2\right)^2}","\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) (a B e+3 A c d)}{8 a^{5/2} c^{3/2}}+\frac{x (a B e+3 A c d)}{8 a^2 c \left(a+c x^2\right)}-\frac{a (A e+B d)-x (A c d-a B e)}{4 a c \left(a+c x^2\right)^2}",1,"-(a*(B*d + A*e) - (A*c*d - a*B*e)*x)/(4*a*c*(a + c*x^2)^2) + ((3*A*c*d + a*B*e)*x)/(8*a^2*c*(a + c*x^2)) + ((3*A*c*d + a*B*e)*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*c^(3/2))","A",3,3,20,0.1500,1,"{778, 199, 205}"
1351,1,75,0,0.0209181,"\int \frac{A+B x}{\left(a+c x^2\right)^3} \, dx","Int[(A + B*x)/(a + c*x^2)^3,x]","\frac{3 A x}{8 a^2 \left(a+c x^2\right)}+\frac{3 A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}-\frac{a B-A c x}{4 a c \left(a+c x^2\right)^2}","\frac{3 A x}{8 a^2 \left(a+c x^2\right)}+\frac{3 A \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right)}{8 a^{5/2} \sqrt{c}}-\frac{a B-A c x}{4 a c \left(a+c x^2\right)^2}",1,"-(a*B - A*c*x)/(4*a*c*(a + c*x^2)^2) + (3*A*x)/(8*a^2*(a + c*x^2)) + (3*A*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c])","A",3,3,15,0.2000,1,"{639, 199, 205}"
1352,1,307,0,0.5050592,"\int \frac{A+B x}{(d+e x) \left(a+c x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)*(a + c*x^2)^3),x]","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a B e \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)-A c d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)\right)}{8 a^{5/2} \sqrt{c} \left(a e^2+c d^2\right)^3}-\frac{4 a^2 e^2 (B d-A e)+x \left(a B e \left(c d^2-3 a e^2\right)-A c d \left(7 a e^2+3 c d^2\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}-\frac{a (B d-A e)-x (a B e+A c d)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}+\frac{e^4 \log \left(a+c x^2\right) (B d-A e)}{2 \left(a e^2+c d^2\right)^3}-\frac{e^4 (B d-A e) \log (d+e x)}{\left(a e^2+c d^2\right)^3}","-\frac{\tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(a B e \left(-3 a^2 e^4+6 a c d^2 e^2+c^2 d^4\right)-A c d \left(15 a^2 e^4+10 a c d^2 e^2+3 c^2 d^4\right)\right)}{8 a^{5/2} \sqrt{c} \left(a e^2+c d^2\right)^3}-\frac{4 a^2 e^2 (B d-A e)+x \left(a B e \left(c d^2-3 a e^2\right)-A c d \left(7 a e^2+3 c d^2\right)\right)}{8 a^2 \left(a+c x^2\right) \left(a e^2+c d^2\right)^2}-\frac{a (B d-A e)-x (a B e+A c d)}{4 a \left(a+c x^2\right)^2 \left(a e^2+c d^2\right)}+\frac{e^4 \log \left(a+c x^2\right) (B d-A e)}{2 \left(a e^2+c d^2\right)^3}-\frac{e^4 (B d-A e) \log (d+e x)}{\left(a e^2+c d^2\right)^3}",1,"-(a*(B*d - A*e) - (A*c*d + a*B*e)*x)/(4*a*(c*d^2 + a*e^2)*(a + c*x^2)^2) - (4*a^2*e^2*(B*d - A*e) + (a*B*e*(c*d^2 - 3*a*e^2) - A*c*d*(3*c*d^2 + 7*a*e^2))*x)/(8*a^2*(c*d^2 + a*e^2)^2*(a + c*x^2)) - ((a*B*e*(c^2*d^4 + 6*a*c*d^2*e^2 - 3*a^2*e^4) - A*c*d*(3*c^2*d^4 + 10*a*c*d^2*e^2 + 15*a^2*e^4))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*Sqrt[c]*(c*d^2 + a*e^2)^3) - (e^4*(B*d - A*e)*Log[d + e*x])/(c*d^2 + a*e^2)^3 + (e^4*(B*d - A*e)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^3)","A",7,5,22,0.2273,1,"{823, 801, 635, 205, 260}"
1353,1,443,0,0.7244919,"\int \frac{A+B x}{(d+e x)^2 \left(a+c x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^2*(a + c*x^2)^3),x]","-\frac{e \left(2 a B d e \left(c d^2-11 a e^2\right)-3 A \left(-5 a^2 e^4+4 a c d^2 e^2+c^2 d^4\right)\right)}{8 a^2 (d+e x) \left(a e^2+c d^2\right)^3}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(2 a B d e \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right)-3 A \left(15 a^2 c d^2 e^4-5 a^3 e^6+5 a c^2 d^4 e^2+c^3 d^6\right)\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^4}-\frac{x \left(2 a B e \left(c d^2-2 a e^2\right)-3 A c d \left(3 a e^2+c d^2\right)\right)+a e \left(-5 a A e^2+6 a B d e+A c d^2\right)}{8 a^2 \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)^2}-\frac{a (B d-A e)-x (a B e+A c d)}{4 a \left(a+c x^2\right)^2 (d+e x) \left(a e^2+c d^2\right)}+\frac{e^4 \log \left(a+c x^2\right) \left(-a B e^2-6 A c d e+5 B c d^2\right)}{2 \left(a e^2+c d^2\right)^4}-\frac{e^4 \log (d+e x) \left(-a B e^2-6 A c d e+5 B c d^2\right)}{\left(a e^2+c d^2\right)^4}","-\frac{e \left(2 a B d e \left(c d^2-11 a e^2\right)-3 A \left(-5 a^2 e^4+4 a c d^2 e^2+c^2 d^4\right)\right)}{8 a^2 (d+e x) \left(a e^2+c d^2\right)^3}-\frac{\sqrt{c} \tan ^{-1}\left(\frac{\sqrt{c} x}{\sqrt{a}}\right) \left(2 a B d e \left(-15 a^2 e^4+10 a c d^2 e^2+c^2 d^4\right)-3 A \left(15 a^2 c d^2 e^4-5 a^3 e^6+5 a c^2 d^4 e^2+c^3 d^6\right)\right)}{8 a^{5/2} \left(a e^2+c d^2\right)^4}-\frac{x \left(2 a B e \left(c d^2-2 a e^2\right)-3 A c d \left(3 a e^2+c d^2\right)\right)+a e \left(-5 a A e^2+6 a B d e+A c d^2\right)}{8 a^2 \left(a+c x^2\right) (d+e x) \left(a e^2+c d^2\right)^2}-\frac{a (B d-A e)-x (a B e+A c d)}{4 a \left(a+c x^2\right)^2 (d+e x) \left(a e^2+c d^2\right)}+\frac{e^4 \log \left(a+c x^2\right) \left(-a B e^2-6 A c d e+5 B c d^2\right)}{2 \left(a e^2+c d^2\right)^4}-\frac{e^4 \log (d+e x) \left(-a B e^2-6 A c d e+5 B c d^2\right)}{\left(a e^2+c d^2\right)^4}",1,"-(e*(2*a*B*d*e*(c*d^2 - 11*a*e^2) - 3*A*(c^2*d^4 + 4*a*c*d^2*e^2 - 5*a^2*e^4)))/(8*a^2*(c*d^2 + a*e^2)^3*(d + e*x)) - (a*(B*d - A*e) - (A*c*d + a*B*e)*x)/(4*a*(c*d^2 + a*e^2)*(d + e*x)*(a + c*x^2)^2) - (a*e*(A*c*d^2 + 6*a*B*d*e - 5*a*A*e^2) + (2*a*B*e*(c*d^2 - 2*a*e^2) - 3*A*c*d*(c*d^2 + 3*a*e^2))*x)/(8*a^2*(c*d^2 + a*e^2)^2*(d + e*x)*(a + c*x^2)) - (Sqrt[c]*(2*a*B*d*e*(c^2*d^4 + 10*a*c*d^2*e^2 - 15*a^2*e^4) - 3*A*(c^3*d^6 + 5*a*c^2*d^4*e^2 + 15*a^2*c*d^2*e^4 - 5*a^3*e^6))*ArcTan[(Sqrt[c]*x)/Sqrt[a]])/(8*a^(5/2)*(c*d^2 + a*e^2)^4) - (e^4*(5*B*c*d^2 - 6*A*c*d*e - a*B*e^2)*Log[d + e*x])/(c*d^2 + a*e^2)^4 + (e^4*(5*B*c*d^2 - 6*A*c*d*e - a*B*e^2)*Log[a + c*x^2])/(2*(c*d^2 + a*e^2)^4)","A",7,5,22,0.2273,1,"{823, 801, 635, 205, 260}"
1354,1,29,0,0.0225441,"\int \frac{-11+6 x}{(-1+2 x) \left(-1+x^2\right)} \, dx","Int[(-11 + 6*x)/((-1 + 2*x)*(-1 + x^2)),x]","\frac{16}{3} \log (1-2 x)-\frac{5}{2} \log (1-x)-\frac{17}{6} \log (x+1)","\frac{16}{3} \log (1-2 x)-\frac{5}{2} \log (1-x)-\frac{17}{6} \log (x+1)",1,"(16*Log[1 - 2*x])/3 - (5*Log[1 - x])/2 - (17*Log[1 + x])/6","A",2,1,20,0.05000,1,"{801}"
1355,1,39,0,0.0151613,"\int \frac{x (1+x)^2}{\left(1+x^2\right)^3} \, dx","Int[(x*(1 + x)^2)/(1 + x^2)^3,x]","-\frac{(x+1)^2}{4 \left(x^2+1\right)^2}-\frac{1-x}{4 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)","-\frac{(x+1)^2}{4 \left(x^2+1\right)^2}-\frac{1-x}{4 \left(x^2+1\right)}+\frac{1}{4} \tan ^{-1}(x)",1,"-(1 + x)^2/(4*(1 + x^2)^2) - (1 - x)/(4*(1 + x^2)) + ArcTan[x]/4","A",3,3,14,0.2143,1,"{819, 639, 203}"
1356,1,122,0,0.0693347,"\int (5-x) (3+2 x)^4 \sqrt{2+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^4*Sqrt[2 + 3*x^2],x]","-\frac{1}{21} \left(3 x^2+2\right)^{3/2} (2 x+3)^4+\frac{29}{63} \left(3 x^2+2\right)^{3/2} (2 x+3)^3+\frac{923}{315} \left(3 x^2+2\right)^{3/2} (2 x+3)^2+\frac{2}{405} (4599 x+13781) \left(3 x^2+2\right)^{3/2}+\frac{2341}{18} x \sqrt{3 x^2+2}+\frac{2341 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}","-\frac{1}{21} \left(3 x^2+2\right)^{3/2} (2 x+3)^4+\frac{29}{63} \left(3 x^2+2\right)^{3/2} (2 x+3)^3+\frac{923}{315} \left(3 x^2+2\right)^{3/2} (2 x+3)^2+\frac{2}{405} (4599 x+13781) \left(3 x^2+2\right)^{3/2}+\frac{2341}{18} x \sqrt{3 x^2+2}+\frac{2341 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}",1,"(2341*x*Sqrt[2 + 3*x^2])/18 + (923*(3 + 2*x)^2*(2 + 3*x^2)^(3/2))/315 + (29*(3 + 2*x)^3*(2 + 3*x^2)^(3/2))/63 - ((3 + 2*x)^4*(2 + 3*x^2)^(3/2))/21 + (2*(13781 + 4599*x)*(2 + 3*x^2)^(3/2))/405 + (2341*ArcSinh[Sqrt[3/2]*x])/(9*Sqrt[3])","A",6,4,24,0.1667,1,"{833, 780, 195, 215}"
1357,1,100,0,0.0466594,"\int (5-x) (3+2 x)^3 \sqrt{2+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^3*Sqrt[2 + 3*x^2],x]","-\frac{1}{18} \left(3 x^2+2\right)^{3/2} (2 x+3)^3+\frac{17}{30} \left(3 x^2+2\right)^{3/2} (2 x+3)^2+\frac{7}{270} (267 x+898) \left(3 x^2+2\right)^{3/2}+\frac{511}{9} x \sqrt{3 x^2+2}+\frac{1022 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}","-\frac{1}{18} \left(3 x^2+2\right)^{3/2} (2 x+3)^3+\frac{17}{30} \left(3 x^2+2\right)^{3/2} (2 x+3)^2+\frac{7}{270} (267 x+898) \left(3 x^2+2\right)^{3/2}+\frac{511}{9} x \sqrt{3 x^2+2}+\frac{1022 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}",1,"(511*x*Sqrt[2 + 3*x^2])/9 + (17*(3 + 2*x)^2*(2 + 3*x^2)^(3/2))/30 - ((3 + 2*x)^3*(2 + 3*x^2)^(3/2))/18 + (7*(898 + 267*x)*(2 + 3*x^2)^(3/2))/270 + (1022*ArcSinh[Sqrt[3/2]*x])/(9*Sqrt[3])","A",5,4,24,0.1667,1,"{833, 780, 195, 215}"
1358,1,78,0,0.0302865,"\int (5-x) (3+2 x)^2 \sqrt{2+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^2*Sqrt[2 + 3*x^2],x]","-\frac{1}{15} \left(3 x^2+2\right)^{3/2} (2 x+3)^2+\frac{2}{135} (99 x+431) \left(3 x^2+2\right)^{3/2}+\frac{131}{6} x \sqrt{3 x^2+2}+\frac{131 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{1}{15} \left(3 x^2+2\right)^{3/2} (2 x+3)^2+\frac{2}{135} (99 x+431) \left(3 x^2+2\right)^{3/2}+\frac{131}{6} x \sqrt{3 x^2+2}+\frac{131 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(131*x*Sqrt[2 + 3*x^2])/6 - ((3 + 2*x)^2*(2 + 3*x^2)^(3/2))/15 + (2*(431 + 99*x)*(2 + 3*x^2)^(3/2))/135 + (131*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",4,4,24,0.1667,1,"{833, 780, 195, 215}"
1359,1,56,0,0.0141275,"\int (5-x) (3+2 x) \sqrt{2+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)*Sqrt[2 + 3*x^2],x]","\frac{1}{18} (14-3 x) \left(3 x^2+2\right)^{3/2}+\frac{23}{3} x \sqrt{3 x^2+2}+\frac{46 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{1}{18} (14-3 x) \left(3 x^2+2\right)^{3/2}+\frac{23}{3} x \sqrt{3 x^2+2}+\frac{46 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(23*x*Sqrt[2 + 3*x^2])/3 + ((14 - 3*x)*(2 + 3*x^2)^(3/2))/18 + (46*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",3,3,22,0.1364,1,"{780, 195, 215}"
1360,1,49,0,0.0104546,"\int (5-x) \sqrt{2+3 x^2} \, dx","Int[(5 - x)*Sqrt[2 + 3*x^2],x]","-\frac{1}{9} \left(3 x^2+2\right)^{3/2}+\frac{5}{2} x \sqrt{3 x^2+2}+\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}","-\frac{1}{9} \left(3 x^2+2\right)^{3/2}+\frac{5}{2} x \sqrt{3 x^2+2}+\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}",1,"(5*x*Sqrt[2 + 3*x^2])/2 - (2 + 3*x^2)^(3/2)/9 + (5*ArcSinh[Sqrt[3/2]*x])/Sqrt[3]","A",3,3,17,0.1765,1,"{641, 195, 215}"
1361,1,72,0,0.0434245,"\int \frac{(5-x) \sqrt{2+3 x^2}}{3+2 x} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x),x]","\frac{1}{4} \sqrt{3 x^2+2} (13-x)-\frac{13}{8} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{121 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{8 \sqrt{3}}","\frac{1}{4} \sqrt{3 x^2+2} (13-x)-\frac{13}{8} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{121 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{8 \sqrt{3}}",1,"((13 - x)*Sqrt[2 + 3*x^2])/4 - (121*ArcSinh[Sqrt[3/2]*x])/(8*Sqrt[3]) - (13*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/8","A",5,5,24,0.2083,1,"{815, 844, 215, 725, 206}"
1362,1,73,0,0.0430619,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^2} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^2,x]","-\frac{\sqrt{3 x^2+2} (x+8)}{2 (2 x+3)}+\frac{19 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{\sqrt{35}}+2 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{\sqrt{3 x^2+2} (x+8)}{2 (2 x+3)}+\frac{19 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{\sqrt{35}}+2 \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"-((8 + x)*Sqrt[2 + 3*x^2])/(2*(3 + 2*x)) + 2*Sqrt[3]*ArcSinh[Sqrt[3/2]*x] + (19*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/Sqrt[35]","A",5,5,24,0.2083,1,"{813, 844, 215, 725, 206}"
1363,1,79,0,0.0421219,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^3} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^3,x]","\frac{\sqrt{3 x^2+2} (187 x+53)}{140 (2 x+3)^2}-\frac{471 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{280 \sqrt{35}}-\frac{1}{8} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{\sqrt{3 x^2+2} (187 x+53)}{140 (2 x+3)^2}-\frac{471 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{280 \sqrt{35}}-\frac{1}{8} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"((53 + 187*x)*Sqrt[2 + 3*x^2])/(140*(3 + 2*x)^2) - (Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/8 - (471*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(280*Sqrt[35])","A",5,5,24,0.2083,1,"{811, 844, 215, 725, 206}"
1364,1,82,0,0.0339467,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^4} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^4,x]","-\frac{13 \left(3 x^2+2\right)^{3/2}}{105 (2 x+3)^3}-\frac{41 (4-9 x) \sqrt{3 x^2+2}}{2450 (2 x+3)^2}-\frac{123 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}","-\frac{13 \left(3 x^2+2\right)^{3/2}}{105 (2 x+3)^3}-\frac{41 (4-9 x) \sqrt{3 x^2+2}}{2450 (2 x+3)^2}-\frac{123 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}",1,"(-41*(4 - 9*x)*Sqrt[2 + 3*x^2])/(2450*(3 + 2*x)^2) - (13*(2 + 3*x^2)^(3/2))/(105*(3 + 2*x)^3) - (123*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1225*Sqrt[35])","A",4,4,24,0.1667,1,"{807, 721, 725, 206}"
1365,1,104,0,0.0523357,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^5} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^5,x]","-\frac{89 \left(3 x^2+2\right)^{3/2}}{2940 (2 x+3)^3}-\frac{13 \left(3 x^2+2\right)^{3/2}}{140 (2 x+3)^4}-\frac{33 (4-9 x) \sqrt{3 x^2+2}}{8575 (2 x+3)^2}-\frac{198 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8575 \sqrt{35}}","-\frac{89 \left(3 x^2+2\right)^{3/2}}{2940 (2 x+3)^3}-\frac{13 \left(3 x^2+2\right)^{3/2}}{140 (2 x+3)^4}-\frac{33 (4-9 x) \sqrt{3 x^2+2}}{8575 (2 x+3)^2}-\frac{198 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8575 \sqrt{35}}",1,"(-33*(4 - 9*x)*Sqrt[2 + 3*x^2])/(8575*(3 + 2*x)^2) - (13*(2 + 3*x^2)^(3/2))/(140*(3 + 2*x)^4) - (89*(2 + 3*x^2)^(3/2))/(2940*(3 + 2*x)^3) - (198*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(8575*Sqrt[35])","A",5,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1366,1,126,0,0.0713158,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^6} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^6,x]","-\frac{43 \left(3 x^2+2\right)^{3/2}}{6125 (2 x+3)^3}-\frac{23 \left(3 x^2+2\right)^{3/2}}{875 (2 x+3)^4}-\frac{13 \left(3 x^2+2\right)^{3/2}}{175 (2 x+3)^5}-\frac{339 (4-9 x) \sqrt{3 x^2+2}}{428750 (2 x+3)^2}-\frac{1017 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{214375 \sqrt{35}}","-\frac{43 \left(3 x^2+2\right)^{3/2}}{6125 (2 x+3)^3}-\frac{23 \left(3 x^2+2\right)^{3/2}}{875 (2 x+3)^4}-\frac{13 \left(3 x^2+2\right)^{3/2}}{175 (2 x+3)^5}-\frac{339 (4-9 x) \sqrt{3 x^2+2}}{428750 (2 x+3)^2}-\frac{1017 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{214375 \sqrt{35}}",1,"(-339*(4 - 9*x)*Sqrt[2 + 3*x^2])/(428750*(3 + 2*x)^2) - (13*(2 + 3*x^2)^(3/2))/(175*(3 + 2*x)^5) - (23*(2 + 3*x^2)^(3/2))/(875*(3 + 2*x)^4) - (43*(2 + 3*x^2)^(3/2))/(6125*(3 + 2*x)^3) - (1017*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(214375*Sqrt[35])","A",6,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1367,1,148,0,0.0919153,"\int \frac{(5-x) \sqrt{2+3 x^2}}{(3+2 x)^7} \, dx","Int[((5 - x)*Sqrt[2 + 3*x^2])/(3 + 2*x)^7,x]","-\frac{1207 \left(3 x^2+2\right)^{3/2}}{857500 (2 x+3)^3}-\frac{111 \left(3 x^2+2\right)^{3/2}}{17500 (2 x+3)^4}-\frac{281 \left(3 x^2+2\right)^{3/2}}{12250 (2 x+3)^5}-\frac{13 \left(3 x^2+2\right)^{3/2}}{210 (2 x+3)^6}-\frac{1017 (4-9 x) \sqrt{3 x^2+2}}{7503125 (2 x+3)^2}-\frac{6102 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{7503125 \sqrt{35}}","-\frac{1207 \left(3 x^2+2\right)^{3/2}}{857500 (2 x+3)^3}-\frac{111 \left(3 x^2+2\right)^{3/2}}{17500 (2 x+3)^4}-\frac{281 \left(3 x^2+2\right)^{3/2}}{12250 (2 x+3)^5}-\frac{13 \left(3 x^2+2\right)^{3/2}}{210 (2 x+3)^6}-\frac{1017 (4-9 x) \sqrt{3 x^2+2}}{7503125 (2 x+3)^2}-\frac{6102 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{7503125 \sqrt{35}}",1,"(-1017*(4 - 9*x)*Sqrt[2 + 3*x^2])/(7503125*(3 + 2*x)^2) - (13*(2 + 3*x^2)^(3/2))/(210*(3 + 2*x)^6) - (281*(2 + 3*x^2)^(3/2))/(12250*(3 + 2*x)^5) - (111*(2 + 3*x^2)^(3/2))/(17500*(3 + 2*x)^4) - (1207*(2 + 3*x^2)^(3/2))/(857500*(3 + 2*x)^3) - (6102*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(7503125*Sqrt[35])","A",7,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1368,1,138,0,0.0734341,"\int (5-x) (3+2 x)^4 \left(2+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^4*(2 + 3*x^2)^(3/2),x]","-\frac{1}{27} \left(3 x^2+2\right)^{5/2} (2 x+3)^4+\frac{13}{36} \left(3 x^2+2\right)^{5/2} (2 x+3)^3+\frac{4421 \left(3 x^2+2\right)^{5/2} (2 x+3)^2}{2268}+\frac{(226755 x+661583) \left(3 x^2+2\right)^{5/2}}{17010}+\frac{2777}{36} x \left(3 x^2+2\right)^{3/2}+\frac{2777}{12} x \sqrt{3 x^2+2}+\frac{2777 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}","-\frac{1}{27} \left(3 x^2+2\right)^{5/2} (2 x+3)^4+\frac{13}{36} \left(3 x^2+2\right)^{5/2} (2 x+3)^3+\frac{4421 \left(3 x^2+2\right)^{5/2} (2 x+3)^2}{2268}+\frac{(226755 x+661583) \left(3 x^2+2\right)^{5/2}}{17010}+\frac{2777}{36} x \left(3 x^2+2\right)^{3/2}+\frac{2777}{12} x \sqrt{3 x^2+2}+\frac{2777 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}",1,"(2777*x*Sqrt[2 + 3*x^2])/12 + (2777*x*(2 + 3*x^2)^(3/2))/36 + (4421*(3 + 2*x)^2*(2 + 3*x^2)^(5/2))/2268 + (13*(3 + 2*x)^3*(2 + 3*x^2)^(5/2))/36 - ((3 + 2*x)^4*(2 + 3*x^2)^(5/2))/27 + ((661583 + 226755*x)*(2 + 3*x^2)^(5/2))/17010 + (2777*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",7,4,24,0.1667,1,"{833, 780, 195, 215}"
1369,1,116,0,0.0535518,"\int (5-x) (3+2 x)^3 \left(2+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^3*(2 + 3*x^2)^(3/2),x]","-\frac{1}{24} \left(3 x^2+2\right)^{5/2} (2 x+3)^3+\frac{71}{168} \left(3 x^2+2\right)^{5/2} (2 x+3)^2+\frac{(5405 x+16973) \left(3 x^2+2\right)^{5/2}}{1260}+\frac{1087}{36} x \left(3 x^2+2\right)^{3/2}+\frac{1087}{12} x \sqrt{3 x^2+2}+\frac{1087 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}","-\frac{1}{24} \left(3 x^2+2\right)^{5/2} (2 x+3)^3+\frac{71}{168} \left(3 x^2+2\right)^{5/2} (2 x+3)^2+\frac{(5405 x+16973) \left(3 x^2+2\right)^{5/2}}{1260}+\frac{1087}{36} x \left(3 x^2+2\right)^{3/2}+\frac{1087}{12} x \sqrt{3 x^2+2}+\frac{1087 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}",1,"(1087*x*Sqrt[2 + 3*x^2])/12 + (1087*x*(2 + 3*x^2)^(3/2))/36 + (71*(3 + 2*x)^2*(2 + 3*x^2)^(5/2))/168 - ((3 + 2*x)^3*(2 + 3*x^2)^(5/2))/24 + ((16973 + 5405*x)*(2 + 3*x^2)^(5/2))/1260 + (1087*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",6,4,24,0.1667,1,"{833, 780, 195, 215}"
1370,1,94,0,0.0364657,"\int (5-x) (3+2 x)^2 \left(2+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^2*(2 + 3*x^2)^(3/2),x]","-\frac{1}{21} (2 x+3)^2 \left(3 x^2+2\right)^{5/2}+\frac{2}{315} (160 x+611) \left(3 x^2+2\right)^{5/2}+\frac{397}{36} x \left(3 x^2+2\right)^{3/2}+\frac{397}{12} x \sqrt{3 x^2+2}+\frac{397 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}","-\frac{1}{21} (2 x+3)^2 \left(3 x^2+2\right)^{5/2}+\frac{2}{315} (160 x+611) \left(3 x^2+2\right)^{5/2}+\frac{397}{36} x \left(3 x^2+2\right)^{3/2}+\frac{397}{12} x \sqrt{3 x^2+2}+\frac{397 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}",1,"(397*x*Sqrt[2 + 3*x^2])/12 + (397*x*(2 + 3*x^2)^(3/2))/36 - ((3 + 2*x)^2*(2 + 3*x^2)^(5/2))/21 + (2*(611 + 160*x)*(2 + 3*x^2)^(5/2))/315 + (397*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",5,4,24,0.1667,1,"{833, 780, 195, 215}"
1371,1,72,0,0.0190066,"\int (5-x) (3+2 x) \left(2+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)*(2 + 3*x^2)^(3/2),x]","\frac{1}{45} (21-5 x) \left(3 x^2+2\right)^{5/2}+\frac{137}{36} x \left(3 x^2+2\right)^{3/2}+\frac{137}{12} x \sqrt{3 x^2+2}+\frac{137 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}","\frac{1}{45} (21-5 x) \left(3 x^2+2\right)^{5/2}+\frac{137}{36} x \left(3 x^2+2\right)^{3/2}+\frac{137}{12} x \sqrt{3 x^2+2}+\frac{137 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}",1,"(137*x*Sqrt[2 + 3*x^2])/12 + (137*x*(2 + 3*x^2)^(3/2))/36 + ((21 - 5*x)*(2 + 3*x^2)^(5/2))/45 + (137*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",4,3,22,0.1364,1,"{780, 195, 215}"
1372,1,67,0,0.014464,"\int (5-x) \left(2+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(2 + 3*x^2)^(3/2),x]","-\frac{1}{15} \left(3 x^2+2\right)^{5/2}+\frac{5}{4} x \left(3 x^2+2\right)^{3/2}+\frac{15}{4} x \sqrt{3 x^2+2}+\frac{5}{2} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{1}{15} \left(3 x^2+2\right)^{5/2}+\frac{5}{4} x \left(3 x^2+2\right)^{3/2}+\frac{15}{4} x \sqrt{3 x^2+2}+\frac{5}{2} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(15*x*Sqrt[2 + 3*x^2])/4 + (5*x*(2 + 3*x^2)^(3/2))/4 - (2 + 3*x^2)^(5/2)/15 + (5*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/2","A",4,3,17,0.1765,1,"{641, 195, 215}"
1373,1,92,0,0.0570738,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{3+2 x} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x),x]","\frac{1}{24} (26-3 x) \left(3 x^2+2\right)^{3/2}+\frac{1}{16} (455-123 x) \sqrt{3 x^2+2}-\frac{455}{32} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{1529}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{1}{24} (26-3 x) \left(3 x^2+2\right)^{3/2}+\frac{1}{16} (455-123 x) \sqrt{3 x^2+2}-\frac{455}{32} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{1529}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"((455 - 123*x)*Sqrt[2 + 3*x^2])/16 + ((26 - 3*x)*(2 + 3*x^2)^(3/2))/24 - (1529*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/32 - (455*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/32","A",6,5,24,0.2083,1,"{815, 844, 215, 725, 206}"
1374,1,97,0,0.0606799,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^2} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^2,x]","-\frac{(x+21) \left(3 x^2+2\right)^{3/2}}{6 (2 x+3)}-\frac{1}{8} (193-63 x) \sqrt{3 x^2+2}+\frac{193}{16} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)+\frac{663}{16} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{(x+21) \left(3 x^2+2\right)^{3/2}}{6 (2 x+3)}-\frac{1}{8} (193-63 x) \sqrt{3 x^2+2}+\frac{193}{16} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)+\frac{663}{16} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"-((193 - 63*x)*Sqrt[2 + 3*x^2])/8 - ((21 + x)*(2 + 3*x^2)^(3/2))/(6*(3 + 2*x)) + (663*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/16 + (193*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/16","A",6,6,24,0.2500,1,"{813, 815, 844, 215, 725, 206}"
1375,1,104,0,0.0608168,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^3} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^3,x]","-\frac{(x+8) \left(3 x^2+2\right)^{3/2}}{4 (2 x+3)^2}+\frac{3 (12 x+37) \sqrt{3 x^2+2}}{4 (2 x+3)}-\frac{1143 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8 \sqrt{35}}-\frac{111}{8} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{(x+8) \left(3 x^2+2\right)^{3/2}}{4 (2 x+3)^2}+\frac{3 (12 x+37) \sqrt{3 x^2+2}}{4 (2 x+3)}-\frac{1143 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8 \sqrt{35}}-\frac{111}{8} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(3*(37 + 12*x)*Sqrt[2 + 3*x^2])/(4*(3 + 2*x)) - ((8 + x)*(2 + 3*x^2)^(3/2))/(4*(3 + 2*x)^2) - (111*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/8 - (1143*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(8*Sqrt[35])","A",6,5,24,0.2083,1,"{813, 844, 215, 725, 206}"
1376,1,106,0,0.058458,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^4} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^4,x]","\frac{(456 x+229) \left(3 x^2+2\right)^{3/2}}{420 (2 x+3)^3}-\frac{3 (111 x+385) \sqrt{3 x^2+2}}{280 (2 x+3)}+\frac{11727 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{560 \sqrt{35}}+\frac{33}{16} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{(456 x+229) \left(3 x^2+2\right)^{3/2}}{420 (2 x+3)^3}-\frac{3 (111 x+385) \sqrt{3 x^2+2}}{280 (2 x+3)}+\frac{11727 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{560 \sqrt{35}}+\frac{33}{16} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(-3*(385 + 111*x)*Sqrt[2 + 3*x^2])/(280*(3 + 2*x)) + ((229 + 456*x)*(2 + 3*x^2)^(3/2))/(420*(3 + 2*x)^3) + (33*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/16 + (11727*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(560*Sqrt[35])","A",6,6,24,0.2500,1,"{811, 813, 844, 215, 725, 206}"
1377,1,106,0,0.0618945,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^5} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^5,x]","\frac{(491 x+54) \left(3 x^2+2\right)^{3/2}}{840 (2 x+3)^4}+\frac{3 (4097 x+2943) \sqrt{3 x^2+2}}{19600 (2 x+3)^2}-\frac{39663 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{39200 \sqrt{35}}-\frac{3}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{(491 x+54) \left(3 x^2+2\right)^{3/2}}{840 (2 x+3)^4}+\frac{3 (4097 x+2943) \sqrt{3 x^2+2}}{19600 (2 x+3)^2}-\frac{39663 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{39200 \sqrt{35}}-\frac{3}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(3*(2943 + 4097*x)*Sqrt[2 + 3*x^2])/(19600*(3 + 2*x)^2) + ((54 + 491*x)*(2 + 3*x^2)^(3/2))/(840*(3 + 2*x)^4) - (3*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/32 - (39663*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(39200*Sqrt[35])","A",6,5,24,0.2083,1,"{811, 844, 215, 725, 206}"
1378,1,109,0,0.048901,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^6} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^6,x]","-\frac{13 \left(3 x^2+2\right)^{5/2}}{175 (2 x+3)^5}-\frac{41 (4-9 x) \left(3 x^2+2\right)^{3/2}}{4900 (2 x+3)^4}-\frac{369 (4-9 x) \sqrt{3 x^2+2}}{171500 (2 x+3)^2}-\frac{1107 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{85750 \sqrt{35}}","-\frac{13 \left(3 x^2+2\right)^{5/2}}{175 (2 x+3)^5}-\frac{41 (4-9 x) \left(3 x^2+2\right)^{3/2}}{4900 (2 x+3)^4}-\frac{369 (4-9 x) \sqrt{3 x^2+2}}{171500 (2 x+3)^2}-\frac{1107 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{85750 \sqrt{35}}",1,"(-369*(4 - 9*x)*Sqrt[2 + 3*x^2])/(171500*(3 + 2*x)^2) - (41*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(4900*(3 + 2*x)^4) - (13*(2 + 3*x^2)^(5/2))/(175*(3 + 2*x)^5) - (1107*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(85750*Sqrt[35])","A",5,4,24,0.1667,1,"{807, 721, 725, 206}"
1379,1,131,0,0.0691624,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^7} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^7,x]","-\frac{29 \left(3 x^2+2\right)^{5/2}}{1750 (2 x+3)^5}-\frac{13 \left(3 x^2+2\right)^{5/2}}{210 (2 x+3)^6}-\frac{(4-9 x) \left(3 x^2+2\right)^{3/2}}{500 (2 x+3)^4}-\frac{9 (4-9 x) \sqrt{3 x^2+2}}{17500 (2 x+3)^2}-\frac{27 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8750 \sqrt{35}}","-\frac{29 \left(3 x^2+2\right)^{5/2}}{1750 (2 x+3)^5}-\frac{13 \left(3 x^2+2\right)^{5/2}}{210 (2 x+3)^6}-\frac{(4-9 x) \left(3 x^2+2\right)^{3/2}}{500 (2 x+3)^4}-\frac{9 (4-9 x) \sqrt{3 x^2+2}}{17500 (2 x+3)^2}-\frac{27 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8750 \sqrt{35}}",1,"(-9*(4 - 9*x)*Sqrt[2 + 3*x^2])/(17500*(3 + 2*x)^2) - ((4 - 9*x)*(2 + 3*x^2)^(3/2))/(500*(3 + 2*x)^4) - (13*(2 + 3*x^2)^(5/2))/(210*(3 + 2*x)^6) - (29*(2 + 3*x^2)^(5/2))/(1750*(3 + 2*x)^5) - (27*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(8750*Sqrt[35])","A",6,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1380,1,153,0,0.100191,"\int \frac{(5-x) \left(2+3 x^2\right)^{3/2}}{(3+2 x)^8} \, dx","Int[((5 - x)*(2 + 3*x^2)^(3/2))/(3 + 2*x)^8,x]","-\frac{822 \left(3 x^2+2\right)^{5/2}}{214375 (2 x+3)^5}-\frac{404 \left(3 x^2+2\right)^{5/2}}{25725 (2 x+3)^6}-\frac{13 \left(3 x^2+2\right)^{5/2}}{245 (2 x+3)^7}-\frac{2689 (4-9 x) \left(3 x^2+2\right)^{3/2}}{6002500 (2 x+3)^4}-\frac{24201 (4-9 x) \sqrt{3 x^2+2}}{210087500 (2 x+3)^2}-\frac{72603 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{105043750 \sqrt{35}}","-\frac{822 \left(3 x^2+2\right)^{5/2}}{214375 (2 x+3)^5}-\frac{404 \left(3 x^2+2\right)^{5/2}}{25725 (2 x+3)^6}-\frac{13 \left(3 x^2+2\right)^{5/2}}{245 (2 x+3)^7}-\frac{2689 (4-9 x) \left(3 x^2+2\right)^{3/2}}{6002500 (2 x+3)^4}-\frac{24201 (4-9 x) \sqrt{3 x^2+2}}{210087500 (2 x+3)^2}-\frac{72603 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{105043750 \sqrt{35}}",1,"(-24201*(4 - 9*x)*Sqrt[2 + 3*x^2])/(210087500*(3 + 2*x)^2) - (2689*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(6002500*(3 + 2*x)^4) - (13*(2 + 3*x^2)^(5/2))/(245*(3 + 2*x)^7) - (404*(2 + 3*x^2)^(5/2))/(25725*(3 + 2*x)^6) - (822*(2 + 3*x^2)^(5/2))/(214375*(3 + 2*x)^5) - (72603*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(105043750*Sqrt[35])","A",7,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1381,1,154,0,0.0824702,"\int (5-x) (3+2 x)^4 \left(2+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^4*(2 + 3*x^2)^(5/2),x]","-\frac{1}{33} \left(3 x^2+2\right)^{7/2} (2 x+3)^4+\frac{49}{165} \left(3 x^2+2\right)^{7/2} (2 x+3)^3+\frac{6433 \left(3 x^2+2\right)^{7/2} (2 x+3)^2}{4455}+\frac{2 (62244 x+181243) \left(3 x^2+2\right)^{7/2}}{13365}+\frac{4991}{90} x \left(3 x^2+2\right)^{5/2}+\frac{4991}{36} x \left(3 x^2+2\right)^{3/2}+\frac{4991}{12} x \sqrt{3 x^2+2}+\frac{4991 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}","-\frac{1}{33} \left(3 x^2+2\right)^{7/2} (2 x+3)^4+\frac{49}{165} \left(3 x^2+2\right)^{7/2} (2 x+3)^3+\frac{6433 \left(3 x^2+2\right)^{7/2} (2 x+3)^2}{4455}+\frac{2 (62244 x+181243) \left(3 x^2+2\right)^{7/2}}{13365}+\frac{4991}{90} x \left(3 x^2+2\right)^{5/2}+\frac{4991}{36} x \left(3 x^2+2\right)^{3/2}+\frac{4991}{12} x \sqrt{3 x^2+2}+\frac{4991 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}",1,"(4991*x*Sqrt[2 + 3*x^2])/12 + (4991*x*(2 + 3*x^2)^(3/2))/36 + (4991*x*(2 + 3*x^2)^(5/2))/90 + (6433*(3 + 2*x)^2*(2 + 3*x^2)^(7/2))/4455 + (49*(3 + 2*x)^3*(2 + 3*x^2)^(7/2))/165 - ((3 + 2*x)^4*(2 + 3*x^2)^(7/2))/33 + (2*(181243 + 62244*x)*(2 + 3*x^2)^(7/2))/13365 + (4991*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",8,4,24,0.1667,1,"{833, 780, 195, 215}"
1382,1,132,0,0.0622385,"\int (5-x) (3+2 x)^3 \left(2+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^3*(2 + 3*x^2)^(5/2),x]","-\frac{1}{30} (2 x+3)^3 \left(3 x^2+2\right)^{7/2}+\frac{91}{270} (2 x+3)^2 \left(3 x^2+2\right)^{7/2}+\frac{(4977 x+15244) \left(3 x^2+2\right)^{7/2}}{1620}+\frac{3731}{180} x \left(3 x^2+2\right)^{5/2}+\frac{3731}{72} x \left(3 x^2+2\right)^{3/2}+\frac{3731}{24} x \sqrt{3 x^2+2}+\frac{3731 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{12 \sqrt{3}}","-\frac{1}{30} (2 x+3)^3 \left(3 x^2+2\right)^{7/2}+\frac{91}{270} (2 x+3)^2 \left(3 x^2+2\right)^{7/2}+\frac{(4977 x+15244) \left(3 x^2+2\right)^{7/2}}{1620}+\frac{3731}{180} x \left(3 x^2+2\right)^{5/2}+\frac{3731}{72} x \left(3 x^2+2\right)^{3/2}+\frac{3731}{24} x \sqrt{3 x^2+2}+\frac{3731 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{12 \sqrt{3}}",1,"(3731*x*Sqrt[2 + 3*x^2])/24 + (3731*x*(2 + 3*x^2)^(3/2))/72 + (3731*x*(2 + 3*x^2)^(5/2))/180 + (91*(3 + 2*x)^2*(2 + 3*x^2)^(7/2))/270 - ((3 + 2*x)^3*(2 + 3*x^2)^(7/2))/30 + ((15244 + 4977*x)*(2 + 3*x^2)^(7/2))/1620 + (3731*ArcSinh[Sqrt[3/2]*x])/(12*Sqrt[3])","A",7,4,24,0.1667,1,"{833, 780, 195, 215}"
1383,1,110,0,0.0431451,"\int (5-x) (3+2 x)^2 \left(2+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^2*(2 + 3*x^2)^(5/2),x]","-\frac{1}{27} (2 x+3)^2 \left(3 x^2+2\right)^{7/2}+\frac{1}{81} (63 x+226) \left(3 x^2+2\right)^{7/2}+\frac{133}{18} x \left(3 x^2+2\right)^{5/2}+\frac{665}{36} x \left(3 x^2+2\right)^{3/2}+\frac{665}{12} x \sqrt{3 x^2+2}+\frac{665 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}","-\frac{1}{27} (2 x+3)^2 \left(3 x^2+2\right)^{7/2}+\frac{1}{81} (63 x+226) \left(3 x^2+2\right)^{7/2}+\frac{133}{18} x \left(3 x^2+2\right)^{5/2}+\frac{665}{36} x \left(3 x^2+2\right)^{3/2}+\frac{665}{12} x \sqrt{3 x^2+2}+\frac{665 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{6 \sqrt{3}}",1,"(665*x*Sqrt[2 + 3*x^2])/12 + (665*x*(2 + 3*x^2)^(3/2))/36 + (133*x*(2 + 3*x^2)^(5/2))/18 - ((3 + 2*x)^2*(2 + 3*x^2)^(7/2))/27 + ((226 + 63*x)*(2 + 3*x^2)^(7/2))/81 + (665*ArcSinh[Sqrt[3/2]*x])/(6*Sqrt[3])","A",6,4,24,0.1667,1,"{833, 780, 195, 215}"
1384,1,88,0,0.0250976,"\int (5-x) (3+2 x) \left(2+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)*(2 + 3*x^2)^(5/2),x]","\frac{1}{12} (4-x) \left(3 x^2+2\right)^{7/2}+\frac{91}{36} x \left(3 x^2+2\right)^{5/2}+\frac{455}{72} x \left(3 x^2+2\right)^{3/2}+\frac{455}{24} x \sqrt{3 x^2+2}+\frac{455 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{12 \sqrt{3}}","\frac{1}{12} (4-x) \left(3 x^2+2\right)^{7/2}+\frac{91}{36} x \left(3 x^2+2\right)^{5/2}+\frac{455}{72} x \left(3 x^2+2\right)^{3/2}+\frac{455}{24} x \sqrt{3 x^2+2}+\frac{455 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{12 \sqrt{3}}",1,"(455*x*Sqrt[2 + 3*x^2])/24 + (455*x*(2 + 3*x^2)^(3/2))/72 + (91*x*(2 + 3*x^2)^(5/2))/36 + ((4 - x)*(2 + 3*x^2)^(7/2))/12 + (455*ArcSinh[Sqrt[3/2]*x])/(12*Sqrt[3])","A",5,3,22,0.1364,1,"{780, 195, 215}"
1385,1,83,0,0.019657,"\int (5-x) \left(2+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(2 + 3*x^2)^(5/2),x]","-\frac{1}{21} \left(3 x^2+2\right)^{7/2}+\frac{5}{6} x \left(3 x^2+2\right)^{5/2}+\frac{25}{12} x \left(3 x^2+2\right)^{3/2}+\frac{25}{4} x \sqrt{3 x^2+2}+\frac{25 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{2 \sqrt{3}}","-\frac{1}{21} \left(3 x^2+2\right)^{7/2}+\frac{5}{6} x \left(3 x^2+2\right)^{5/2}+\frac{25}{12} x \left(3 x^2+2\right)^{3/2}+\frac{25}{4} x \sqrt{3 x^2+2}+\frac{25 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{2 \sqrt{3}}",1,"(25*x*Sqrt[2 + 3*x^2])/4 + (25*x*(2 + 3*x^2)^(3/2))/12 + (5*x*(2 + 3*x^2)^(5/2))/6 - (2 + 3*x^2)^(7/2)/21 + (25*ArcSinh[Sqrt[3/2]*x])/(2*Sqrt[3])","A",5,3,17,0.1765,1,"{641, 195, 215}"
1386,1,112,0,0.0761678,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{3+2 x} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x),x]","\frac{1}{60} (39-5 x) \left(3 x^2+2\right)^{5/2}+\frac{7}{96} (130-53 x) \left(3 x^2+2\right)^{3/2}+\frac{7}{64} (2275-691 x) \sqrt{3 x^2+2}-\frac{15925}{128} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{162673 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{128 \sqrt{3}}","\frac{1}{60} (39-5 x) \left(3 x^2+2\right)^{5/2}+\frac{7}{96} (130-53 x) \left(3 x^2+2\right)^{3/2}+\frac{7}{64} (2275-691 x) \sqrt{3 x^2+2}-\frac{15925}{128} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{162673 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{128 \sqrt{3}}",1,"(7*(2275 - 691*x)*Sqrt[2 + 3*x^2])/64 + (7*(130 - 53*x)*(2 + 3*x^2)^(3/2))/96 + ((39 - 5*x)*(2 + 3*x^2)^(5/2))/60 - (162673*ArcSinh[Sqrt[3/2]*x])/(128*Sqrt[3]) - (15925*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/128","A",7,5,24,0.2083,1,"{815, 844, 215, 725, 206}"
1387,1,117,0,0.0783686,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^2} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^2,x]","-\frac{(x+34) \left(3 x^2+2\right)^{5/2}}{10 (2 x+3)}-\frac{1}{24} (310-153 x) \left(3 x^2+2\right)^{3/2}-\frac{7}{16} (775-243 x) \sqrt{3 x^2+2}+\frac{5425}{32} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)+\frac{18543}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{(x+34) \left(3 x^2+2\right)^{5/2}}{10 (2 x+3)}-\frac{1}{24} (310-153 x) \left(3 x^2+2\right)^{3/2}-\frac{7}{16} (775-243 x) \sqrt{3 x^2+2}+\frac{5425}{32} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)+\frac{18543}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(-7*(775 - 243*x)*Sqrt[2 + 3*x^2])/16 - ((310 - 153*x)*(2 + 3*x^2)^(3/2))/24 - ((34 + x)*(2 + 3*x^2)^(5/2))/(10*(3 + 2*x)) + (18543*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/32 + (5425*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/32","A",7,6,24,0.2500,1,"{813, 815, 844, 215, 725, 206}"
1388,1,126,0,0.0790293,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^3} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^3,x]","-\frac{(2 x+29) \left(3 x^2+2\right)^{5/2}}{16 (2 x+3)^2}+\frac{5 (29 x+178) \left(3 x^2+2\right)^{3/2}}{32 (2 x+3)}+\frac{15}{64} (859-267 x) \sqrt{3 x^2+2}-\frac{12885}{128} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{43995}{128} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{(2 x+29) \left(3 x^2+2\right)^{5/2}}{16 (2 x+3)^2}+\frac{5 (29 x+178) \left(3 x^2+2\right)^{3/2}}{32 (2 x+3)}+\frac{15}{64} (859-267 x) \sqrt{3 x^2+2}-\frac{12885}{128} \sqrt{35} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)-\frac{43995}{128} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(15*(859 - 267*x)*Sqrt[2 + 3*x^2])/64 + (5*(178 + 29*x)*(2 + 3*x^2)^(3/2))/(32*(3 + 2*x)) - ((29 + 2*x)*(2 + 3*x^2)^(5/2))/(16*(3 + 2*x)^2) - (43995*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/128 - (12885*Sqrt[35]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/128","A",7,6,24,0.2500,1,"{813, 815, 844, 215, 725, 206}"
1389,1,133,0,0.0792698,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^4} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^4,x]","-\frac{(x+8) \left(3 x^2+2\right)^{5/2}}{6 (2 x+3)^3}+\frac{5 (12 x+37) \left(3 x^2+2\right)^{3/2}}{12 (2 x+3)^2}-\frac{15 (37 x+119) \sqrt{3 x^2+2}}{8 (2 x+3)}+\frac{3657}{16} \sqrt{\frac{5}{7}} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)+\frac{1785}{16} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{(x+8) \left(3 x^2+2\right)^{5/2}}{6 (2 x+3)^3}+\frac{5 (12 x+37) \left(3 x^2+2\right)^{3/2}}{12 (2 x+3)^2}-\frac{15 (37 x+119) \sqrt{3 x^2+2}}{8 (2 x+3)}+\frac{3657}{16} \sqrt{\frac{5}{7}} \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)+\frac{1785}{16} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(-15*(119 + 37*x)*Sqrt[2 + 3*x^2])/(8*(3 + 2*x)) + (5*(37 + 12*x)*(2 + 3*x^2)^(3/2))/(12*(3 + 2*x)^2) - ((8 + x)*(2 + 3*x^2)^(5/2))/(6*(3 + 2*x)^3) + (1785*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/16 + (3657*Sqrt[5/7]*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/16","A",7,5,24,0.2083,1,"{813, 844, 215, 725, 206}"
1390,1,133,0,0.0803883,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^5} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^5,x]","-\frac{(4 x+19) \left(3 x^2+2\right)^{5/2}}{16 (2 x+3)^4}-\frac{(5517 x+5003) \left(3 x^2+2\right)^{3/2}}{672 (2 x+3)^3}+\frac{3 (1917 x+6125) \sqrt{3 x^2+2}}{448 (2 x+3)}-\frac{188379 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{896 \sqrt{35}}-\frac{2625}{128} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","-\frac{(4 x+19) \left(3 x^2+2\right)^{5/2}}{16 (2 x+3)^4}-\frac{(5517 x+5003) \left(3 x^2+2\right)^{3/2}}{672 (2 x+3)^3}+\frac{3 (1917 x+6125) \sqrt{3 x^2+2}}{448 (2 x+3)}-\frac{188379 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{896 \sqrt{35}}-\frac{2625}{128} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(3*(6125 + 1917*x)*Sqrt[2 + 3*x^2])/(448*(3 + 2*x)) - ((5003 + 5517*x)*(2 + 3*x^2)^(3/2))/(672*(3 + 2*x)^3) - ((19 + 4*x)*(2 + 3*x^2)^(5/2))/(16*(3 + 2*x)^4) - (2625*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/128 - (188379*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(896*Sqrt[35])","A",7,6,24,0.2500,1,"{813, 811, 844, 215, 725, 206}"
1391,1,133,0,0.0806538,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^6} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^6,x]","\frac{(76 x+23) \left(3 x^2+2\right)^{5/2}}{140 (2 x+3)^5}+\frac{(8193 x+6637) \left(3 x^2+2\right)^{3/2}}{9800 (2 x+3)^3}-\frac{9 (2643 x+8575) \sqrt{3 x^2+2}}{19600 (2 x+3)}+\frac{789723 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{39200 \sqrt{35}}+\frac{63}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{(76 x+23) \left(3 x^2+2\right)^{5/2}}{140 (2 x+3)^5}+\frac{(8193 x+6637) \left(3 x^2+2\right)^{3/2}}{9800 (2 x+3)^3}-\frac{9 (2643 x+8575) \sqrt{3 x^2+2}}{19600 (2 x+3)}+\frac{789723 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{39200 \sqrt{35}}+\frac{63}{32} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(-9*(8575 + 2643*x)*Sqrt[2 + 3*x^2])/(19600*(3 + 2*x)) + ((6637 + 8193*x)*(2 + 3*x^2)^(3/2))/(9800*(3 + 2*x)^3) + ((23 + 76*x)*(2 + 3*x^2)^(5/2))/(140*(3 + 2*x)^5) + (63*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/32 + (789723*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(39200*Sqrt[35])","A",7,6,24,0.2500,1,"{811, 813, 844, 215, 725, 206}"
1392,1,133,0,0.0778891,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^7} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^7,x]","\frac{(159 x+11) \left(3 x^2+2\right)^{5/2}}{420 (2 x+3)^6}+\frac{(403 x+202) \left(3 x^2+2\right)^{3/2}}{1568 (2 x+3)^4}+\frac{9 (5167 x+4373) \sqrt{3 x^2+2}}{109760 (2 x+3)^2}-\frac{159759 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{219520 \sqrt{35}}-\frac{9}{128} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)","\frac{(159 x+11) \left(3 x^2+2\right)^{5/2}}{420 (2 x+3)^6}+\frac{(403 x+202) \left(3 x^2+2\right)^{3/2}}{1568 (2 x+3)^4}+\frac{9 (5167 x+4373) \sqrt{3 x^2+2}}{109760 (2 x+3)^2}-\frac{159759 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{219520 \sqrt{35}}-\frac{9}{128} \sqrt{3} \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)",1,"(9*(4373 + 5167*x)*Sqrt[2 + 3*x^2])/(109760*(3 + 2*x)^2) + ((202 + 403*x)*(2 + 3*x^2)^(3/2))/(1568*(3 + 2*x)^4) + ((11 + 159*x)*(2 + 3*x^2)^(5/2))/(420*(3 + 2*x)^6) - (9*Sqrt[3]*ArcSinh[Sqrt[3/2]*x])/128 - (159759*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(219520*Sqrt[35])","A",7,5,24,0.2083,1,"{811, 844, 215, 725, 206}"
1393,1,136,0,0.0653373,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^8} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^8,x]","-\frac{13 \left(3 x^2+2\right)^{7/2}}{245 (2 x+3)^7}-\frac{41 (4-9 x) \left(3 x^2+2\right)^{5/2}}{7350 (2 x+3)^6}-\frac{41 (4-9 x) \left(3 x^2+2\right)^{3/2}}{34300 (2 x+3)^4}-\frac{369 (4-9 x) \sqrt{3 x^2+2}}{1200500 (2 x+3)^2}-\frac{1107 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{600250 \sqrt{35}}","-\frac{13 \left(3 x^2+2\right)^{7/2}}{245 (2 x+3)^7}-\frac{41 (4-9 x) \left(3 x^2+2\right)^{5/2}}{7350 (2 x+3)^6}-\frac{41 (4-9 x) \left(3 x^2+2\right)^{3/2}}{34300 (2 x+3)^4}-\frac{369 (4-9 x) \sqrt{3 x^2+2}}{1200500 (2 x+3)^2}-\frac{1107 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{600250 \sqrt{35}}",1,"(-369*(4 - 9*x)*Sqrt[2 + 3*x^2])/(1200500*(3 + 2*x)^2) - (41*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(34300*(3 + 2*x)^4) - (41*(4 - 9*x)*(2 + 3*x^2)^(5/2))/(7350*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(245*(3 + 2*x)^7) - (1107*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(600250*Sqrt[35])","A",6,4,24,0.1667,1,"{807, 721, 725, 206}"
1394,1,158,0,0.0829256,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^9} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^9,x]","-\frac{773 \left(3 x^2+2\right)^{7/2}}{68600 (2 x+3)^7}-\frac{13 \left(3 x^2+2\right)^{7/2}}{280 (2 x+3)^8}-\frac{233 (4-9 x) \left(3 x^2+2\right)^{5/2}}{171500 (2 x+3)^6}-\frac{699 (4-9 x) \left(3 x^2+2\right)^{3/2}}{2401000 (2 x+3)^4}-\frac{6291 (4-9 x) \sqrt{3 x^2+2}}{84035000 (2 x+3)^2}-\frac{18873 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42017500 \sqrt{35}}","-\frac{773 \left(3 x^2+2\right)^{7/2}}{68600 (2 x+3)^7}-\frac{13 \left(3 x^2+2\right)^{7/2}}{280 (2 x+3)^8}-\frac{233 (4-9 x) \left(3 x^2+2\right)^{5/2}}{171500 (2 x+3)^6}-\frac{699 (4-9 x) \left(3 x^2+2\right)^{3/2}}{2401000 (2 x+3)^4}-\frac{6291 (4-9 x) \sqrt{3 x^2+2}}{84035000 (2 x+3)^2}-\frac{18873 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42017500 \sqrt{35}}",1,"(-6291*(4 - 9*x)*Sqrt[2 + 3*x^2])/(84035000*(3 + 2*x)^2) - (699*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(2401000*(3 + 2*x)^4) - (233*(4 - 9*x)*(2 + 3*x^2)^(5/2))/(171500*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(280*(3 + 2*x)^8) - (773*(2 + 3*x^2)^(7/2))/(68600*(3 + 2*x)^7) - (18873*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(42017500*Sqrt[35])","A",7,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1395,1,180,0,0.1085102,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^{10}} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^10,x]","-\frac{4741 \left(3 x^2+2\right)^{7/2}}{1800750 (2 x+3)^7}-\frac{27 \left(3 x^2+2\right)^{7/2}}{2450 (2 x+3)^8}-\frac{13 \left(3 x^2+2\right)^{7/2}}{315 (2 x+3)^9}-\frac{949 (4-9 x) \left(3 x^2+2\right)^{5/2}}{3001250 (2 x+3)^6}-\frac{2847 (4-9 x) \left(3 x^2+2\right)^{3/2}}{42017500 (2 x+3)^4}-\frac{25623 (4-9 x) \sqrt{3 x^2+2}}{1470612500 (2 x+3)^2}-\frac{76869 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{735306250 \sqrt{35}}","-\frac{4741 \left(3 x^2+2\right)^{7/2}}{1800750 (2 x+3)^7}-\frac{27 \left(3 x^2+2\right)^{7/2}}{2450 (2 x+3)^8}-\frac{13 \left(3 x^2+2\right)^{7/2}}{315 (2 x+3)^9}-\frac{949 (4-9 x) \left(3 x^2+2\right)^{5/2}}{3001250 (2 x+3)^6}-\frac{2847 (4-9 x) \left(3 x^2+2\right)^{3/2}}{42017500 (2 x+3)^4}-\frac{25623 (4-9 x) \sqrt{3 x^2+2}}{1470612500 (2 x+3)^2}-\frac{76869 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{735306250 \sqrt{35}}",1,"(-25623*(4 - 9*x)*Sqrt[2 + 3*x^2])/(1470612500*(3 + 2*x)^2) - (2847*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(42017500*(3 + 2*x)^4) - (949*(4 - 9*x)*(2 + 3*x^2)^(5/2))/(3001250*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(315*(3 + 2*x)^9) - (27*(2 + 3*x^2)^(7/2))/(2450*(3 + 2*x)^8) - (4741*(2 + 3*x^2)^(7/2))/(1800750*(3 + 2*x)^7) - (76869*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(735306250*Sqrt[35])","A",8,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1396,1,202,0,0.1342027,"\int \frac{(5-x) \left(2+3 x^2\right)^{5/2}}{(3+2 x)^{11}} \, dx","Int[((5 - x)*(2 + 3*x^2)^(5/2))/(3 + 2*x)^11,x]","-\frac{739619 \left(3 x^2+2\right)^{7/2}}{1260525000 (2 x+3)^7}-\frac{4393 \left(3 x^2+2\right)^{7/2}}{1715000 (2 x+3)^8}-\frac{1171 \left(3 x^2+2\right)^{7/2}}{110250 (2 x+3)^9}-\frac{13 \left(3 x^2+2\right)^{7/2}}{350 (2 x+3)^{10}}-\frac{73233 (4-9 x) \left(3 x^2+2\right)^{5/2}}{1050437500 (2 x+3)^6}-\frac{219699 (4-9 x) \left(3 x^2+2\right)^{3/2}}{14706125000 (2 x+3)^4}-\frac{1977291 (4-9 x) \sqrt{3 x^2+2}}{514714375000 (2 x+3)^2}-\frac{5931873 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{257357187500 \sqrt{35}}","-\frac{739619 \left(3 x^2+2\right)^{7/2}}{1260525000 (2 x+3)^7}-\frac{4393 \left(3 x^2+2\right)^{7/2}}{1715000 (2 x+3)^8}-\frac{1171 \left(3 x^2+2\right)^{7/2}}{110250 (2 x+3)^9}-\frac{13 \left(3 x^2+2\right)^{7/2}}{350 (2 x+3)^{10}}-\frac{73233 (4-9 x) \left(3 x^2+2\right)^{5/2}}{1050437500 (2 x+3)^6}-\frac{219699 (4-9 x) \left(3 x^2+2\right)^{3/2}}{14706125000 (2 x+3)^4}-\frac{1977291 (4-9 x) \sqrt{3 x^2+2}}{514714375000 (2 x+3)^2}-\frac{5931873 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{257357187500 \sqrt{35}}",1,"(-1977291*(4 - 9*x)*Sqrt[2 + 3*x^2])/(514714375000*(3 + 2*x)^2) - (219699*(4 - 9*x)*(2 + 3*x^2)^(3/2))/(14706125000*(3 + 2*x)^4) - (73233*(4 - 9*x)*(2 + 3*x^2)^(5/2))/(1050437500*(3 + 2*x)^6) - (13*(2 + 3*x^2)^(7/2))/(350*(3 + 2*x)^10) - (1171*(2 + 3*x^2)^(7/2))/(110250*(3 + 2*x)^9) - (4393*(2 + 3*x^2)^(7/2))/(1715000*(3 + 2*x)^8) - (739619*(2 + 3*x^2)^(7/2))/(1260525000*(3 + 2*x)^7) - (5931873*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(257357187500*Sqrt[35])","A",9,5,24,0.2083,1,"{835, 807, 721, 725, 206}"
1397,1,106,0,0.0576403,"\int \frac{(5-x) (3+2 x)^4}{\sqrt{2+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^4)/Sqrt[2 + 3*x^2],x]","-\frac{1}{15} \sqrt{3 x^2+2} (2 x+3)^4+\frac{19}{30} \sqrt{3 x^2+2} (2 x+3)^3+\frac{1477}{270} \sqrt{3 x^2+2} (2 x+3)^2+\frac{49}{81} (99 x+383) \sqrt{3 x^2+2}+\frac{343 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{1}{15} \sqrt{3 x^2+2} (2 x+3)^4+\frac{19}{30} \sqrt{3 x^2+2} (2 x+3)^3+\frac{1477}{270} \sqrt{3 x^2+2} (2 x+3)^2+\frac{49}{81} (99 x+383) \sqrt{3 x^2+2}+\frac{343 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(1477*(3 + 2*x)^2*Sqrt[2 + 3*x^2])/270 + (19*(3 + 2*x)^3*Sqrt[2 + 3*x^2])/30 - ((3 + 2*x)^4*Sqrt[2 + 3*x^2])/15 + (49*(383 + 99*x)*Sqrt[2 + 3*x^2])/81 + (343*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",5,3,24,0.1250,1,"{833, 780, 215}"
1398,1,84,0,0.0428908,"\int \frac{(5-x) (3+2 x)^3}{\sqrt{2+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^3)/Sqrt[2 + 3*x^2],x]","-\frac{1}{12} \sqrt{3 x^2+2} (2 x+3)^3+\frac{31}{36} \sqrt{3 x^2+2} (2 x+3)^2+\frac{5}{54} (171 x+809) \sqrt{3 x^2+2}+\frac{275 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{1}{12} \sqrt{3 x^2+2} (2 x+3)^3+\frac{31}{36} \sqrt{3 x^2+2} (2 x+3)^2+\frac{5}{54} (171 x+809) \sqrt{3 x^2+2}+\frac{275 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(31*(3 + 2*x)^2*Sqrt[2 + 3*x^2])/36 - ((3 + 2*x)^3*Sqrt[2 + 3*x^2])/12 + (5*(809 + 171*x)*Sqrt[2 + 3*x^2])/54 + (275*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",4,3,24,0.1250,1,"{833, 780, 215}"
1399,1,62,0,0.0247848,"\int \frac{(5-x) (3+2 x)^2}{\sqrt{2+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^2)/Sqrt[2 + 3*x^2],x]","-\frac{1}{9} \sqrt{3 x^2+2} (2 x+3)^2+\frac{2}{27} (36 x+251) \sqrt{3 x^2+2}+\frac{127 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{1}{9} \sqrt{3 x^2+2} (2 x+3)^2+\frac{2}{27} (36 x+251) \sqrt{3 x^2+2}+\frac{127 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"-((3 + 2*x)^2*Sqrt[2 + 3*x^2])/9 + (2*(251 + 36*x)*Sqrt[2 + 3*x^2])/27 + (127*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",3,3,24,0.1250,1,"{833, 780, 215}"
1400,1,40,0,0.0122139,"\int \frac{(5-x) (3+2 x)}{\sqrt{2+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x))/Sqrt[2 + 3*x^2],x]","\frac{1}{3} \sqrt{3 x^2+2} (7-x)+\frac{47 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","\frac{1}{3} \sqrt{3 x^2+2} (7-x)+\frac{47 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"((7 - x)*Sqrt[2 + 3*x^2])/3 + (47*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",2,2,22,0.09091,1,"{780, 215}"
1401,1,33,0,0.0071272,"\int \frac{5-x}{\sqrt{2+3 x^2}} \, dx","Int[(5 - x)/Sqrt[2 + 3*x^2],x]","\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}-\frac{1}{3} \sqrt{3 x^2+2}","\frac{5 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{\sqrt{3}}-\frac{1}{3} \sqrt{3 x^2+2}",1,"-Sqrt[2 + 3*x^2]/3 + (5*ArcSinh[Sqrt[3/2]*x])/Sqrt[3]","A",2,2,17,0.1176,1,"{641, 215}"
1402,1,52,0,0.0274531,"\int \frac{5-x}{(3+2 x) \sqrt{2+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)*Sqrt[2 + 3*x^2]),x]","-\frac{13 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{2 \sqrt{35}}-\frac{\sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{2 \sqrt{3}}","-\frac{13 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{2 \sqrt{35}}-\frac{\sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{2 \sqrt{3}}",1,"-ArcSinh[Sqrt[3/2]*x]/(2*Sqrt[3]) - (13*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(2*Sqrt[35])","A",4,4,24,0.1667,1,"{844, 215, 725, 206}"
1403,1,55,0,0.0249547,"\int \frac{5-x}{(3+2 x)^2 \sqrt{2+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^2*Sqrt[2 + 3*x^2]),x]","-\frac{13 \sqrt{3 x^2+2}}{35 (2 x+3)}-\frac{41 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{35 \sqrt{35}}","-\frac{13 \sqrt{3 x^2+2}}{35 (2 x+3)}-\frac{41 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{35 \sqrt{35}}",1,"(-13*Sqrt[2 + 3*x^2])/(35*(3 + 2*x)) - (41*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(35*Sqrt[35])","A",3,3,24,0.1250,1,"{807, 725, 206}"
1404,1,77,0,0.0387895,"\int \frac{5-x}{(3+2 x)^3 \sqrt{2+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^3*Sqrt[2 + 3*x^2]),x]","-\frac{281 \sqrt{3 x^2+2}}{2450 (2 x+3)}-\frac{13 \sqrt{3 x^2+2}}{70 (2 x+3)^2}-\frac{291 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}","-\frac{281 \sqrt{3 x^2+2}}{2450 (2 x+3)}-\frac{13 \sqrt{3 x^2+2}}{70 (2 x+3)^2}-\frac{291 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}",1,"(-13*Sqrt[2 + 3*x^2])/(70*(3 + 2*x)^2) - (281*Sqrt[2 + 3*x^2])/(2450*(3 + 2*x)) - (291*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1225*Sqrt[35])","A",4,4,24,0.1667,1,"{835, 807, 725, 206}"
1405,1,99,0,0.0572682,"\int \frac{5-x}{(3+2 x)^4 \sqrt{2+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^4*Sqrt[2 + 3*x^2]),x]","-\frac{10 \sqrt{3 x^2+2}}{343 (2 x+3)}-\frac{16 \sqrt{3 x^2+2}}{245 (2 x+3)^2}-\frac{13 \sqrt{3 x^2+2}}{105 (2 x+3)^3}-\frac{57 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1715 \sqrt{35}}","-\frac{10 \sqrt{3 x^2+2}}{343 (2 x+3)}-\frac{16 \sqrt{3 x^2+2}}{245 (2 x+3)^2}-\frac{13 \sqrt{3 x^2+2}}{105 (2 x+3)^3}-\frac{57 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1715 \sqrt{35}}",1,"(-13*Sqrt[2 + 3*x^2])/(105*(3 + 2*x)^3) - (16*Sqrt[2 + 3*x^2])/(245*(3 + 2*x)^2) - (10*Sqrt[2 + 3*x^2])/(343*(3 + 2*x)) - (57*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1715*Sqrt[35])","A",5,4,24,0.1667,1,"{835, 807, 725, 206}"
1406,1,121,0,0.075237,"\int \frac{5-x}{(3+2 x)^5 \sqrt{2+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^5*Sqrt[2 + 3*x^2]),x]","-\frac{991 \sqrt{3 x^2+2}}{171500 (2 x+3)}-\frac{87 \sqrt{3 x^2+2}}{4900 (2 x+3)^2}-\frac{97 \sqrt{3 x^2+2}}{2100 (2 x+3)^3}-\frac{13 \sqrt{3 x^2+2}}{140 (2 x+3)^4}+\frac{27 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875 \sqrt{35}}","-\frac{991 \sqrt{3 x^2+2}}{171500 (2 x+3)}-\frac{87 \sqrt{3 x^2+2}}{4900 (2 x+3)^2}-\frac{97 \sqrt{3 x^2+2}}{2100 (2 x+3)^3}-\frac{13 \sqrt{3 x^2+2}}{140 (2 x+3)^4}+\frac{27 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875 \sqrt{35}}",1,"(-13*Sqrt[2 + 3*x^2])/(140*(3 + 2*x)^4) - (97*Sqrt[2 + 3*x^2])/(2100*(3 + 2*x)^3) - (87*Sqrt[2 + 3*x^2])/(4900*(3 + 2*x)^2) - (991*Sqrt[2 + 3*x^2])/(171500*(3 + 2*x)) + (27*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(42875*Sqrt[35])","A",6,4,24,0.1667,1,"{835, 807, 725, 206}"
1407,1,143,0,0.095708,"\int \frac{5-x}{(3+2 x)^6 \sqrt{2+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^6*Sqrt[2 + 3*x^2]),x]","-\frac{10023 \sqrt{3 x^2+2}}{15006250 (2 x+3)}-\frac{1611 \sqrt{3 x^2+2}}{428750 (2 x+3)^2}-\frac{797 \sqrt{3 x^2+2}}{61250 (2 x+3)^3}-\frac{439 \sqrt{3 x^2+2}}{12250 (2 x+3)^4}-\frac{13 \sqrt{3 x^2+2}}{175 (2 x+3)^5}+\frac{19737 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{7503125 \sqrt{35}}","-\frac{10023 \sqrt{3 x^2+2}}{15006250 (2 x+3)}-\frac{1611 \sqrt{3 x^2+2}}{428750 (2 x+3)^2}-\frac{797 \sqrt{3 x^2+2}}{61250 (2 x+3)^3}-\frac{439 \sqrt{3 x^2+2}}{12250 (2 x+3)^4}-\frac{13 \sqrt{3 x^2+2}}{175 (2 x+3)^5}+\frac{19737 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{7503125 \sqrt{35}}",1,"(-13*Sqrt[2 + 3*x^2])/(175*(3 + 2*x)^5) - (439*Sqrt[2 + 3*x^2])/(12250*(3 + 2*x)^4) - (797*Sqrt[2 + 3*x^2])/(61250*(3 + 2*x)^3) - (1611*Sqrt[2 + 3*x^2])/(428750*(3 + 2*x)^2) - (10023*Sqrt[2 + 3*x^2])/(15006250*(3 + 2*x)) + (19737*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(7503125*Sqrt[35])","A",7,4,24,0.1667,1,"{835, 807, 725, 206}"
1408,1,89,0,0.0427574,"\int \frac{(5-x) (3+2 x)^4}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 3*x^2)^(3/2),x]","-\frac{7 (2-7 x) (2 x+3)^3}{6 \sqrt{3 x^2+2}}-\frac{151}{27} \sqrt{3 x^2+2} (2 x+3)^2-\frac{10}{81} (207 x+185) \sqrt{3 x^2+2}+\frac{880 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)^3}{6 \sqrt{3 x^2+2}}-\frac{151}{27} \sqrt{3 x^2+2} (2 x+3)^2-\frac{10}{81} (207 x+185) \sqrt{3 x^2+2}+\frac{880 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x)^3)/(6*Sqrt[2 + 3*x^2]) - (151*(3 + 2*x)^2*Sqrt[2 + 3*x^2])/27 - (10*(185 + 207*x)*Sqrt[2 + 3*x^2])/81 + (880*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",4,4,24,0.1667,1,"{819, 833, 780, 215}"
1409,1,67,0,0.0270143,"\int \frac{(5-x) (3+2 x)^3}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 3*x^2)^(3/2),x]","-\frac{7 (2-7 x) (2 x+3)^2}{6 \sqrt{3 x^2+2}}-\frac{2}{9} (51 x+131) \sqrt{3 x^2+2}+\frac{134 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)^2}{6 \sqrt{3 x^2+2}}-\frac{2}{9} (51 x+131) \sqrt{3 x^2+2}+\frac{134 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x)^2)/(6*Sqrt[2 + 3*x^2]) - (2*(131 + 51*x)*Sqrt[2 + 3*x^2])/9 + (134*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",3,3,24,0.1250,1,"{819, 780, 215}"
1410,1,60,0,0.0222036,"\int \frac{(5-x) (3+2 x)^2}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 3*x^2)^(3/2),x]","-\frac{7 (2-7 x) (2 x+3)}{6 \sqrt{3 x^2+2}}-\frac{53}{9} \sqrt{3 x^2+2}+\frac{8 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)}{6 \sqrt{3 x^2+2}}-\frac{53}{9} \sqrt{3 x^2+2}+\frac{8 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x))/(6*Sqrt[2 + 3*x^2]) - (53*Sqrt[2 + 3*x^2])/9 + (8*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",3,3,24,0.1250,1,"{819, 641, 215}"
1411,1,40,0,0.01125,"\int \frac{(5-x) (3+2 x)}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 3*x^2)^(3/2),x]","-\frac{7 (2-7 x)}{6 \sqrt{3 x^2+2}}-\frac{2 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}","-\frac{7 (2-7 x)}{6 \sqrt{3 x^2+2}}-\frac{2 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{3 \sqrt{3}}",1,"(-7*(2 - 7*x))/(6*Sqrt[2 + 3*x^2]) - (2*ArcSinh[Sqrt[3/2]*x])/(3*Sqrt[3])","A",2,2,22,0.09091,1,"{778, 215}"
1412,1,20,0,0.0041599,"\int \frac{5-x}{\left(2+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/(2 + 3*x^2)^(3/2),x]","\frac{15 x+2}{6 \sqrt{3 x^2+2}}","\frac{15 x+2}{6 \sqrt{3 x^2+2}}",1,"(2 + 15*x)/(6*Sqrt[2 + 3*x^2])","A",1,1,17,0.05882,1,"{637}"
1413,1,53,0,0.0267461,"\int \frac{5-x}{(3+2 x) \left(2+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 3*x^2)^(3/2)),x]","\frac{41 x+26}{70 \sqrt{3 x^2+2}}-\frac{26 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{35 \sqrt{35}}","\frac{41 x+26}{70 \sqrt{3 x^2+2}}-\frac{26 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{35 \sqrt{35}}",1,"(26 + 41*x)/(70*Sqrt[2 + 3*x^2]) - (26*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(35*Sqrt[35])","A",4,4,24,0.1667,1,"{823, 12, 725, 206}"
1414,1,82,0,0.0420368,"\int \frac{5-x}{(3+2 x)^2 \left(2+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 3*x^2)^(3/2)),x]","\frac{41 x+26}{70 (2 x+3) \sqrt{3 x^2+2}}+\frac{19 \sqrt{3 x^2+2}}{1225 (2 x+3)}-\frac{632 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}","\frac{41 x+26}{70 (2 x+3) \sqrt{3 x^2+2}}+\frac{19 \sqrt{3 x^2+2}}{1225 (2 x+3)}-\frac{632 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}",1,"(26 + 41*x)/(70*(3 + 2*x)*Sqrt[2 + 3*x^2]) + (19*Sqrt[2 + 3*x^2])/(1225*(3 + 2*x)) - (632*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1225*Sqrt[35])","A",4,4,24,0.1667,1,"{823, 807, 725, 206}"
1415,1,104,0,0.0566041,"\int \frac{5-x}{(3+2 x)^3 \left(2+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 3*x^2)^(3/2)),x]","\frac{41 x+26}{70 (2 x+3)^2 \sqrt{3 x^2+2}}-\frac{331 \sqrt{3 x^2+2}}{8575 (2 x+3)}+\frac{9 \sqrt{3 x^2+2}}{245 (2 x+3)^2}-\frac{1962 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8575 \sqrt{35}}","\frac{41 x+26}{70 (2 x+3)^2 \sqrt{3 x^2+2}}-\frac{331 \sqrt{3 x^2+2}}{8575 (2 x+3)}+\frac{9 \sqrt{3 x^2+2}}{245 (2 x+3)^2}-\frac{1962 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{8575 \sqrt{35}}",1,"(26 + 41*x)/(70*(3 + 2*x)^2*Sqrt[2 + 3*x^2]) + (9*Sqrt[2 + 3*x^2])/(245*(3 + 2*x)^2) - (331*Sqrt[2 + 3*x^2])/(8575*(3 + 2*x)) - (1962*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(8575*Sqrt[35])","A",5,5,24,0.2083,1,"{823, 835, 807, 725, 206}"
1416,1,126,0,0.075735,"\int \frac{5-x}{(3+2 x)^4 \left(2+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^4*(2 + 3*x^2)^(3/2)),x]","\frac{41 x+26}{70 (2 x+3)^3 \sqrt{3 x^2+2}}-\frac{1051 \sqrt{3 x^2+2}}{42875 (2 x+3)}-\frac{27 \sqrt{3 x^2+2}}{1225 (2 x+3)^2}+\frac{23 \sqrt{3 x^2+2}}{525 (2 x+3)^3}-\frac{3312 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875 \sqrt{35}}","\frac{41 x+26}{70 (2 x+3)^3 \sqrt{3 x^2+2}}-\frac{1051 \sqrt{3 x^2+2}}{42875 (2 x+3)}-\frac{27 \sqrt{3 x^2+2}}{1225 (2 x+3)^2}+\frac{23 \sqrt{3 x^2+2}}{525 (2 x+3)^3}-\frac{3312 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875 \sqrt{35}}",1,"(26 + 41*x)/(70*(3 + 2*x)^3*Sqrt[2 + 3*x^2]) + (23*Sqrt[2 + 3*x^2])/(525*(3 + 2*x)^3) - (27*Sqrt[2 + 3*x^2])/(1225*(3 + 2*x)^2) - (1051*Sqrt[2 + 3*x^2])/(42875*(3 + 2*x)) - (3312*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(42875*Sqrt[35])","A",6,5,24,0.2083,1,"{823, 835, 807, 725, 206}"
1417,1,148,0,0.0943078,"\int \frac{5-x}{(3+2 x)^5 \left(2+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^5*(2 + 3*x^2)^(3/2)),x]","\frac{41 x+26}{70 (2 x+3)^4 \sqrt{3 x^2+2}}-\frac{14944 \sqrt{3 x^2+2}}{1500625 (2 x+3)}-\frac{708 \sqrt{3 x^2+2}}{42875 (2 x+3)^2}-\frac{298 \sqrt{3 x^2+2}}{18375 (2 x+3)^3}+\frac{58 \sqrt{3 x^2+2}}{1225 (2 x+3)^4}-\frac{30078 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1500625 \sqrt{35}}","\frac{41 x+26}{70 (2 x+3)^4 \sqrt{3 x^2+2}}-\frac{14944 \sqrt{3 x^2+2}}{1500625 (2 x+3)}-\frac{708 \sqrt{3 x^2+2}}{42875 (2 x+3)^2}-\frac{298 \sqrt{3 x^2+2}}{18375 (2 x+3)^3}+\frac{58 \sqrt{3 x^2+2}}{1225 (2 x+3)^4}-\frac{30078 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1500625 \sqrt{35}}",1,"(26 + 41*x)/(70*(3 + 2*x)^4*Sqrt[2 + 3*x^2]) + (58*Sqrt[2 + 3*x^2])/(1225*(3 + 2*x)^4) - (298*Sqrt[2 + 3*x^2])/(18375*(3 + 2*x)^3) - (708*Sqrt[2 + 3*x^2])/(42875*(3 + 2*x)^2) - (14944*Sqrt[2 + 3*x^2])/(1500625*(3 + 2*x)) - (30078*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1500625*Sqrt[35])","A",7,5,24,0.2083,1,"{823, 835, 807, 725, 206}"
1418,1,116,0,0.060576,"\int \frac{(5-x) (3+2 x)^6}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^6)/(2 + 3*x^2)^(5/2),x]","-\frac{7 (2-7 x) (2 x+3)^5}{18 \left(3 x^2+2\right)^{3/2}}+\frac{(2427 x+158) (2 x+3)^3}{54 \sqrt{3 x^2+2}}-\frac{2639}{81} \sqrt{3 x^2+2} (2 x+3)^2-\frac{70}{243} (801 x+2167) \sqrt{3 x^2+2}+\frac{20720 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{27 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)^5}{18 \left(3 x^2+2\right)^{3/2}}+\frac{(2427 x+158) (2 x+3)^3}{54 \sqrt{3 x^2+2}}-\frac{2639}{81} \sqrt{3 x^2+2} (2 x+3)^2-\frac{70}{243} (801 x+2167) \sqrt{3 x^2+2}+\frac{20720 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{27 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x)^5)/(18*(2 + 3*x^2)^(3/2)) + ((3 + 2*x)^3*(158 + 2427*x))/(54*Sqrt[2 + 3*x^2]) - (2639*(3 + 2*x)^2*Sqrt[2 + 3*x^2])/81 - (70*(2167 + 801*x)*Sqrt[2 + 3*x^2])/243 + (20720*ArcSinh[Sqrt[3/2]*x])/(27*Sqrt[3])","A",5,4,24,0.1667,1,"{819, 833, 780, 215}"
1419,1,94,0,0.0437378,"\int \frac{(5-x) (3+2 x)^5}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^5)/(2 + 3*x^2)^(5/2),x]","-\frac{7 (2-7 x) (2 x+3)^4}{18 \left(3 x^2+2\right)^{3/2}}-\frac{5 (16-421 x) (2 x+3)^2}{54 \sqrt{3 x^2+2}}-\frac{50}{81} (93 x+299) \sqrt{3 x^2+2}+\frac{1600 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{27 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)^4}{18 \left(3 x^2+2\right)^{3/2}}-\frac{5 (16-421 x) (2 x+3)^2}{54 \sqrt{3 x^2+2}}-\frac{50}{81} (93 x+299) \sqrt{3 x^2+2}+\frac{1600 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{27 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x)^4)/(18*(2 + 3*x^2)^(3/2)) - (5*(16 - 421*x)*(3 + 2*x)^2)/(54*Sqrt[2 + 3*x^2]) - (50*(299 + 93*x)*Sqrt[2 + 3*x^2])/81 + (1600*ArcSinh[Sqrt[3/2]*x])/(27*Sqrt[3])","A",4,3,24,0.1250,1,"{819, 780, 215}"
1420,1,87,0,0.0386323,"\int \frac{(5-x) (3+2 x)^4}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 3*x^2)^(5/2),x]","-\frac{7 (2-7 x) (2 x+3)^3}{18 \left(3 x^2+2\right)^{3/2}}-\frac{(318-1783 x) (2 x+3)}{54 \sqrt{3 x^2+2}}-\frac{2027}{81} \sqrt{3 x^2+2}-\frac{16 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)^3}{18 \left(3 x^2+2\right)^{3/2}}-\frac{(318-1783 x) (2 x+3)}{54 \sqrt{3 x^2+2}}-\frac{2027}{81} \sqrt{3 x^2+2}-\frac{16 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x)^3)/(18*(2 + 3*x^2)^(3/2)) - ((318 - 1783*x)*(3 + 2*x))/(54*Sqrt[2 + 3*x^2]) - (2027*Sqrt[2 + 3*x^2])/81 - (16*ArcSinh[Sqrt[3/2]*x])/(9*Sqrt[3])","A",4,3,24,0.1250,1,"{819, 641, 215}"
1421,1,67,0,0.0270609,"\int \frac{(5-x) (3+2 x)^3}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 3*x^2)^(5/2),x]","-\frac{7 (2-7 x) (2 x+3)^2}{18 \left(3 x^2+2\right)^{3/2}}-\frac{556-1461 x}{54 \sqrt{3 x^2+2}}-\frac{8 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}","-\frac{7 (2-7 x) (2 x+3)^2}{18 \left(3 x^2+2\right)^{3/2}}-\frac{556-1461 x}{54 \sqrt{3 x^2+2}}-\frac{8 \sinh ^{-1}\left(\sqrt{\frac{3}{2}} x\right)}{9 \sqrt{3}}",1,"(-7*(2 - 7*x)*(3 + 2*x)^2)/(18*(2 + 3*x^2)^(3/2)) - (556 - 1461*x)/(54*Sqrt[2 + 3*x^2]) - (8*ArcSinh[Sqrt[3/2]*x])/(9*Sqrt[3])","A",3,3,24,0.1250,1,"{819, 778, 215}"
1422,1,48,0,0.0181029,"\int \frac{(5-x) (3+2 x)^2}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 3*x^2)^(5/2),x]","\frac{(2 x+3)^2 (15 x+2)}{18 \left(3 x^2+2\right)^{3/2}}-\frac{41 (4-9 x)}{54 \sqrt{3 x^2+2}}","\frac{(2 x+3)^2 (15 x+2)}{18 \left(3 x^2+2\right)^{3/2}}-\frac{41 (4-9 x)}{54 \sqrt{3 x^2+2}}",1,"((3 + 2*x)^2*(2 + 15*x))/(18*(2 + 3*x^2)^(3/2)) - (41*(4 - 9*x))/(54*Sqrt[2 + 3*x^2])","A",2,2,24,0.08333,1,"{805, 637}"
1423,1,37,0,0.0099111,"\int \frac{(5-x) (3+2 x)}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 3*x^2)^(5/2),x]","\frac{43 x}{18 \sqrt{3 x^2+2}}-\frac{7 (2-7 x)}{18 \left(3 x^2+2\right)^{3/2}}","\frac{43 x}{18 \sqrt{3 x^2+2}}-\frac{7 (2-7 x)}{18 \left(3 x^2+2\right)^{3/2}}",1,"(-7*(2 - 7*x))/(18*(2 + 3*x^2)^(3/2)) + (43*x)/(18*Sqrt[2 + 3*x^2])","A",2,2,22,0.09091,1,"{778, 191}"
1424,1,37,0,0.0065831,"\int \frac{5-x}{\left(2+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/(2 + 3*x^2)^(5/2),x]","\frac{5 x}{6 \sqrt{3 x^2+2}}+\frac{15 x+2}{18 \left(3 x^2+2\right)^{3/2}}","\frac{5 x}{6 \sqrt{3 x^2+2}}+\frac{15 x+2}{18 \left(3 x^2+2\right)^{3/2}}",1,"(2 + 15*x)/(18*(2 + 3*x^2)^(3/2)) + (5*x)/(6*Sqrt[2 + 3*x^2])","A",2,2,17,0.1176,1,"{639, 191}"
1425,1,73,0,0.0425624,"\int \frac{5-x}{(3+2 x) \left(2+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 3*x^2)^(5/2)),x]","\frac{41 x+26}{210 \left(3 x^2+2\right)^{3/2}}+\frac{2137 x+312}{7350 \sqrt{3 x^2+2}}-\frac{104 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}","\frac{41 x+26}{210 \left(3 x^2+2\right)^{3/2}}+\frac{2137 x+312}{7350 \sqrt{3 x^2+2}}-\frac{104 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1225 \sqrt{35}}",1,"(26 + 41*x)/(210*(2 + 3*x^2)^(3/2)) + (312 + 2137*x)/(7350*Sqrt[2 + 3*x^2]) - (104*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1225*Sqrt[35])","A",5,4,24,0.1667,1,"{823, 12, 725, 206}"
1426,1,109,0,0.0587916,"\int \frac{5-x}{(3+2 x)^2 \left(2+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 3*x^2)^(5/2)),x]","\frac{41 x+26}{210 (2 x+3) \left(3 x^2+2\right)^{3/2}}+\frac{277 \sqrt{3 x^2+2}}{5145 (2 x+3)}+\frac{507 x+34}{1470 (2 x+3) \sqrt{3 x^2+2}}-\frac{176 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1715 \sqrt{35}}","\frac{41 x+26}{210 (2 x+3) \left(3 x^2+2\right)^{3/2}}+\frac{277 \sqrt{3 x^2+2}}{5145 (2 x+3)}+\frac{507 x+34}{1470 (2 x+3) \sqrt{3 x^2+2}}-\frac{176 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1715 \sqrt{35}}",1,"(26 + 41*x)/(210*(3 + 2*x)*(2 + 3*x^2)^(3/2)) + (34 + 507*x)/(1470*(3 + 2*x)*Sqrt[2 + 3*x^2]) + (277*Sqrt[2 + 3*x^2])/(5145*(3 + 2*x)) - (176*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1715*Sqrt[35])","A",5,4,24,0.1667,1,"{823, 807, 725, 206}"
1427,1,131,0,0.0767948,"\int \frac{5-x}{(3+2 x)^3 \left(2+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 3*x^2)^(5/2)),x]","\frac{41 x+26}{210 (2 x+3)^2 \left(3 x^2+2\right)^{3/2}}+\frac{857 \sqrt{3 x^2+2}}{128625 (2 x+3)}+\frac{83 \sqrt{3 x^2+2}}{1225 (2 x+3)^2}+\frac{419 x+4}{1050 (2 x+3)^2 \sqrt{3 x^2+2}}-\frac{3072 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875 \sqrt{35}}","\frac{41 x+26}{210 (2 x+3)^2 \left(3 x^2+2\right)^{3/2}}+\frac{857 \sqrt{3 x^2+2}}{128625 (2 x+3)}+\frac{83 \sqrt{3 x^2+2}}{1225 (2 x+3)^2}+\frac{419 x+4}{1050 (2 x+3)^2 \sqrt{3 x^2+2}}-\frac{3072 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{42875 \sqrt{35}}",1,"(26 + 41*x)/(210*(3 + 2*x)^2*(2 + 3*x^2)^(3/2)) + (4 + 419*x)/(1050*(3 + 2*x)^2*Sqrt[2 + 3*x^2]) + (83*Sqrt[2 + 3*x^2])/(1225*(3 + 2*x)^2) + (857*Sqrt[2 + 3*x^2])/(128625*(3 + 2*x)) - (3072*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(42875*Sqrt[35])","A",6,5,24,0.2083,1,"{823, 835, 807, 725, 206}"
1428,1,153,0,0.0981771,"\int \frac{5-x}{(3+2 x)^4 \left(2+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^4*(2 + 3*x^2)^(5/2)),x]","-\frac{114-3331 x}{7350 (2 x+3)^3 \sqrt{3 x^2+2}}-\frac{5987 \sqrt{3 x^2+2}}{1500625 (2 x+3)}+\frac{541 \sqrt{3 x^2+2}}{42875 (2 x+3)^2}+\frac{1471 \sqrt{3 x^2+2}}{18375 (2 x+3)^3}+\frac{41 x+26}{210 (2 x+3)^3 \left(3 x^2+2\right)^{3/2}}-\frac{55344 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1500625 \sqrt{35}}","-\frac{114-3331 x}{7350 (2 x+3)^3 \sqrt{3 x^2+2}}-\frac{5987 \sqrt{3 x^2+2}}{1500625 (2 x+3)}+\frac{541 \sqrt{3 x^2+2}}{42875 (2 x+3)^2}+\frac{1471 \sqrt{3 x^2+2}}{18375 (2 x+3)^3}+\frac{41 x+26}{210 (2 x+3)^3 \left(3 x^2+2\right)^{3/2}}-\frac{55344 \tanh ^{-1}\left(\frac{4-9 x}{\sqrt{35} \sqrt{3 x^2+2}}\right)}{1500625 \sqrt{35}}",1,"(26 + 41*x)/(210*(3 + 2*x)^3*(2 + 3*x^2)^(3/2)) - (114 - 3331*x)/(7350*(3 + 2*x)^3*Sqrt[2 + 3*x^2]) + (1471*Sqrt[2 + 3*x^2])/(18375*(3 + 2*x)^3) + (541*Sqrt[2 + 3*x^2])/(42875*(3 + 2*x)^2) - (5987*Sqrt[2 + 3*x^2])/(1500625*(3 + 2*x)) - (55344*ArcTanh[(4 - 9*x)/(Sqrt[35]*Sqrt[2 + 3*x^2])])/(1500625*Sqrt[35])","A",7,5,24,0.2083,1,"{823, 835, 807, 725, 206}"
1429,1,116,0,0.0616693,"\int (A+B x) (d+e x)^{3/2} \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(a + c*x^2),x]","\frac{2 (d+e x)^{7/2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{7 e^4}-\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right) (B d-A e)}{5 e^4}-\frac{2 c (d+e x)^{9/2} (3 B d-A e)}{9 e^4}+\frac{2 B c (d+e x)^{11/2}}{11 e^4}","\frac{2 (d+e x)^{7/2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{7 e^4}-\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right) (B d-A e)}{5 e^4}-\frac{2 c (d+e x)^{9/2} (3 B d-A e)}{9 e^4}+\frac{2 B c (d+e x)^{11/2}}{11 e^4}",1,"(-2*(B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^(5/2))/(5*e^4) + (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(7/2))/(7*e^4) - (2*c*(3*B*d - A*e)*(d + e*x)^(9/2))/(9*e^4) + (2*B*c*(d + e*x)^(11/2))/(11*e^4)","A",2,1,22,0.04545,1,"{772}"
1430,1,116,0,0.0511429,"\int (A+B x) \sqrt{d+e x} \left(a+c x^2\right) \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{5 e^4}-\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right) (B d-A e)}{3 e^4}-\frac{2 c (d+e x)^{7/2} (3 B d-A e)}{7 e^4}+\frac{2 B c (d+e x)^{9/2}}{9 e^4}","\frac{2 (d+e x)^{5/2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{5 e^4}-\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right) (B d-A e)}{3 e^4}-\frac{2 c (d+e x)^{7/2} (3 B d-A e)}{7 e^4}+\frac{2 B c (d+e x)^{9/2}}{9 e^4}",1,"(-2*(B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^(3/2))/(3*e^4) + (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(5/2))/(5*e^4) - (2*c*(3*B*d - A*e)*(d + e*x)^(7/2))/(7*e^4) + (2*B*c*(d + e*x)^(9/2))/(9*e^4)","A",2,1,22,0.04545,1,"{772}"
1431,1,114,0,0.0487892,"\int \frac{(A+B x) \left(a+c x^2\right)}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a + c*x^2))/Sqrt[d + e*x],x]","\frac{2 (d+e x)^{3/2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{3 e^4}-\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right) (B d-A e)}{e^4}-\frac{2 c (d+e x)^{5/2} (3 B d-A e)}{5 e^4}+\frac{2 B c (d+e x)^{7/2}}{7 e^4}","\frac{2 (d+e x)^{3/2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{3 e^4}-\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right) (B d-A e)}{e^4}-\frac{2 c (d+e x)^{5/2} (3 B d-A e)}{5 e^4}+\frac{2 B c (d+e x)^{7/2}}{7 e^4}",1,"(-2*(B*d - A*e)*(c*d^2 + a*e^2)*Sqrt[d + e*x])/e^4 + (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(3/2))/(3*e^4) - (2*c*(3*B*d - A*e)*(d + e*x)^(5/2))/(5*e^4) + (2*B*c*(d + e*x)^(7/2))/(7*e^4)","A",2,1,22,0.04545,1,"{772}"
1432,1,112,0,0.0501356,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4}+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{e^4 \sqrt{d+e x}}-\frac{2 c (d+e x)^{3/2} (3 B d-A e)}{3 e^4}+\frac{2 B c (d+e x)^{5/2}}{5 e^4}","\frac{2 \sqrt{d+e x} \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4}+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{e^4 \sqrt{d+e x}}-\frac{2 c (d+e x)^{3/2} (3 B d-A e)}{3 e^4}+\frac{2 B c (d+e x)^{5/2}}{5 e^4}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2))/(e^4*Sqrt[d + e*x]) + (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Sqrt[d + e*x])/e^4 - (2*c*(3*B*d - A*e)*(d + e*x)^(3/2))/(3*e^4) + (2*B*c*(d + e*x)^(5/2))/(5*e^4)","A",2,1,22,0.04545,1,"{772}"
1433,1,112,0,0.0496668,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^(5/2),x]","-\frac{2 \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4 \sqrt{d+e x}}+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{3 e^4 (d+e x)^{3/2}}-\frac{2 c \sqrt{d+e x} (3 B d-A e)}{e^4}+\frac{2 B c (d+e x)^{3/2}}{3 e^4}","-\frac{2 \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4 \sqrt{d+e x}}+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{3 e^4 (d+e x)^{3/2}}-\frac{2 c \sqrt{d+e x} (3 B d-A e)}{e^4}+\frac{2 B c (d+e x)^{3/2}}{3 e^4}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2))/(3*e^4*(d + e*x)^(3/2)) - (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(e^4*Sqrt[d + e*x]) - (2*c*(3*B*d - A*e)*Sqrt[d + e*x])/e^4 + (2*B*c*(d + e*x)^(3/2))/(3*e^4)","A",2,1,22,0.04545,1,"{772}"
1434,1,112,0,0.05017,"\int \frac{(A+B x) \left(a+c x^2\right)}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2))/(d + e*x)^(7/2),x]","-\frac{2 \left(a B e^2-2 A c d e+3 B c d^2\right)}{3 e^4 (d+e x)^{3/2}}+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 c (3 B d-A e)}{e^4 \sqrt{d+e x}}+\frac{2 B c \sqrt{d+e x}}{e^4}","-\frac{2 \left(a B e^2-2 A c d e+3 B c d^2\right)}{3 e^4 (d+e x)^{3/2}}+\frac{2 \left(a e^2+c d^2\right) (B d-A e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 c (3 B d-A e)}{e^4 \sqrt{d+e x}}+\frac{2 B c \sqrt{d+e x}}{e^4}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2))/(5*e^4*(d + e*x)^(5/2)) - (2*(3*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(3*e^4*(d + e*x)^(3/2)) + (2*c*(3*B*d - A*e))/(e^4*Sqrt[d + e*x]) + (2*B*c*Sqrt[d + e*x])/e^4","A",2,1,22,0.04545,1,"{772}"
1435,1,218,0,0.1270171,"\int (A+B x) \sqrt{d+e x} \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a + c*x^2)^2,x]","\frac{4 c (d+e x)^{9/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{9 e^6}-\frac{4 c (d+e x)^{7/2} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{7 e^6}+\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6}-\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6}-\frac{2 c^2 (d+e x)^{11/2} (5 B d-A e)}{11 e^6}+\frac{2 B c^2 (d+e x)^{13/2}}{13 e^6}","\frac{4 c (d+e x)^{9/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{9 e^6}-\frac{4 c (d+e x)^{7/2} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{7 e^6}+\frac{2 (d+e x)^{5/2} \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6}-\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6}-\frac{2 c^2 (d+e x)^{11/2} (5 B d-A e)}{11 e^6}+\frac{2 B c^2 (d+e x)^{13/2}}{13 e^6}",1,"(-2*(B*d - A*e)*(c*d^2 + a*e^2)^2*(d + e*x)^(3/2))/(3*e^6) + (2*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^(5/2))/(5*e^6) - (4*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(7/2))/(7*e^6) + (4*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(9/2))/(9*e^6) - (2*c^2*(5*B*d - A*e)*(d + e*x)^(11/2))/(11*e^6) + (2*B*c^2*(d + e*x)^(13/2))/(13*e^6)","A",2,1,24,0.04167,1,"{772}"
1436,1,216,0,0.0948489,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/Sqrt[d + e*x],x]","\frac{4 c (d+e x)^{7/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{7 e^6}-\frac{4 c (d+e x)^{5/2} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{5 e^6}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{3 e^6}-\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^2 (B d-A e)}{e^6}-\frac{2 c^2 (d+e x)^{9/2} (5 B d-A e)}{9 e^6}+\frac{2 B c^2 (d+e x)^{11/2}}{11 e^6}","\frac{4 c (d+e x)^{7/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{7 e^6}-\frac{4 c (d+e x)^{5/2} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{5 e^6}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{3 e^6}-\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^2 (B d-A e)}{e^6}-\frac{2 c^2 (d+e x)^{9/2} (5 B d-A e)}{9 e^6}+\frac{2 B c^2 (d+e x)^{11/2}}{11 e^6}",1,"(-2*(B*d - A*e)*(c*d^2 + a*e^2)^2*Sqrt[d + e*x])/e^6 + (2*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^(3/2))/(3*e^6) - (4*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(5/2))/(5*e^6) + (4*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(7/2))/(7*e^6) - (2*c^2*(5*B*d - A*e)*(d + e*x)^(9/2))/(9*e^6) + (2*B*c^2*(d + e*x)^(11/2))/(11*e^6)","A",2,1,24,0.04167,1,"{772}"
1437,1,214,0,0.0934932,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(3/2),x]","\frac{4 c (d+e x)^{5/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{5 e^6}-\frac{4 c (d+e x)^{3/2} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{e^6 \sqrt{d+e x}}-\frac{2 c^2 (d+e x)^{7/2} (5 B d-A e)}{7 e^6}+\frac{2 B c^2 (d+e x)^{9/2}}{9 e^6}","\frac{4 c (d+e x)^{5/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{5 e^6}-\frac{4 c (d+e x)^{3/2} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{e^6 \sqrt{d+e x}}-\frac{2 c^2 (d+e x)^{7/2} (5 B d-A e)}{7 e^6}+\frac{2 B c^2 (d+e x)^{9/2}}{9 e^6}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^2)/(e^6*Sqrt[d + e*x]) + (2*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*Sqrt[d + e*x])/e^6 - (4*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(3/2))/(3*e^6) + (4*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(5/2))/(5*e^6) - (2*c^2*(5*B*d - A*e)*(d + e*x)^(7/2))/(7*e^6) + (2*B*c^2*(d + e*x)^(9/2))/(9*e^6)","A",2,1,24,0.04167,1,"{772}"
1438,1,214,0,0.0917347,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(5/2),x]","\frac{4 c (d+e x)^{3/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6}-\frac{4 c \sqrt{d+e x} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6}-\frac{2 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6 \sqrt{d+e x}}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6 (d+e x)^{3/2}}-\frac{2 c^2 (d+e x)^{5/2} (5 B d-A e)}{5 e^6}+\frac{2 B c^2 (d+e x)^{7/2}}{7 e^6}","\frac{4 c (d+e x)^{3/2} \left(a B e^2-2 A c d e+5 B c d^2\right)}{3 e^6}-\frac{4 c \sqrt{d+e x} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6}-\frac{2 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6 \sqrt{d+e x}}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{3 e^6 (d+e x)^{3/2}}-\frac{2 c^2 (d+e x)^{5/2} (5 B d-A e)}{5 e^6}+\frac{2 B c^2 (d+e x)^{7/2}}{7 e^6}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^2)/(3*e^6*(d + e*x)^(3/2)) - (2*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(e^6*Sqrt[d + e*x]) - (4*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*Sqrt[d + e*x])/e^6 + (4*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(3/2))/(3*e^6) - (2*c^2*(5*B*d - A*e)*(d + e*x)^(5/2))/(5*e^6) + (2*B*c^2*(d + e*x)^(7/2))/(7*e^6)","A",2,1,24,0.04167,1,"{772}"
1439,1,214,0,0.0916629,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(7/2),x]","\frac{4 c \sqrt{d+e x} \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6}+\frac{4 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^{3/2}}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{5 e^6 (d+e x)^{5/2}}-\frac{2 c^2 (d+e x)^{3/2} (5 B d-A e)}{3 e^6}+\frac{2 B c^2 (d+e x)^{5/2}}{5 e^6}","\frac{4 c \sqrt{d+e x} \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6}+\frac{4 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{3 e^6 (d+e x)^{3/2}}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{5 e^6 (d+e x)^{5/2}}-\frac{2 c^2 (d+e x)^{3/2} (5 B d-A e)}{3 e^6}+\frac{2 B c^2 (d+e x)^{5/2}}{5 e^6}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^2)/(5*e^6*(d + e*x)^(5/2)) - (2*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(3*e^6*(d + e*x)^(3/2)) + (4*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^6*Sqrt[d + e*x]) + (4*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Sqrt[d + e*x])/e^6 - (2*c^2*(5*B*d - A*e)*(d + e*x)^(3/2))/(3*e^6) + (2*B*c^2*(d + e*x)^(5/2))/(5*e^6)","A",2,1,24,0.04167,1,"{772}"
1440,1,214,0,0.0968576,"\int \frac{(A+B x) \left(a+c x^2\right)^2}{(d+e x)^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^2)/(d + e*x)^(9/2),x]","-\frac{4 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 \sqrt{d+e x}}+\frac{4 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6 (d+e x)^{5/2}}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{7 e^6 (d+e x)^{7/2}}-\frac{2 c^2 \sqrt{d+e x} (5 B d-A e)}{e^6}+\frac{2 B c^2 (d+e x)^{3/2}}{3 e^6}","-\frac{4 c \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 \sqrt{d+e x}}+\frac{4 c \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{3 e^6 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right) \left(a B e^2-4 A c d e+5 B c d^2\right)}{5 e^6 (d+e x)^{5/2}}+\frac{2 \left(a e^2+c d^2\right)^2 (B d-A e)}{7 e^6 (d+e x)^{7/2}}-\frac{2 c^2 \sqrt{d+e x} (5 B d-A e)}{e^6}+\frac{2 B c^2 (d+e x)^{3/2}}{3 e^6}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^2)/(7*e^6*(d + e*x)^(7/2)) - (2*(c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2))/(5*e^6*(d + e*x)^(5/2)) + (4*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(3*e^6*(d + e*x)^(3/2)) - (4*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2))/(e^6*Sqrt[d + e*x]) - (2*c^2*(5*B*d - A*e)*Sqrt[d + e*x])/e^6 + (2*B*c^2*(d + e*x)^(3/2))/(3*e^6)","A",2,1,24,0.04167,1,"{772}"
1441,1,348,0,0.205371,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/Sqrt[d + e*x],x]","-\frac{2 c (d+e x)^{7/2} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{7 e^8}+\frac{6 c^2 (d+e x)^{11/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{11 e^8}-\frac{2 c^2 (d+e x)^{9/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{9 e^8}-\frac{6 c (d+e x)^{5/2} \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{3 e^8}-\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^3 (B d-A e)}{e^8}-\frac{2 c^3 (d+e x)^{13/2} (7 B d-A e)}{13 e^8}+\frac{2 B c^3 (d+e x)^{15/2}}{15 e^8}","-\frac{2 c (d+e x)^{7/2} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{7 e^8}+\frac{6 c^2 (d+e x)^{11/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{11 e^8}-\frac{2 c^2 (d+e x)^{9/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{9 e^8}-\frac{6 c (d+e x)^{5/2} \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8}+\frac{2 (d+e x)^{3/2} \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{3 e^8}-\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^3 (B d-A e)}{e^8}-\frac{2 c^3 (d+e x)^{13/2} (7 B d-A e)}{13 e^8}+\frac{2 B c^3 (d+e x)^{15/2}}{15 e^8}",1,"(-2*(B*d - A*e)*(c*d^2 + a*e^2)^3*Sqrt[d + e*x])/e^8 + (2*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)^(3/2))/(3*e^8) - (6*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(5/2))/(5*e^8) - (2*c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^(7/2))/(7*e^8) - (2*c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^(9/2))/(9*e^8) + (6*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(11/2))/(11*e^8) - (2*c^3*(7*B*d - A*e)*(d + e*x)^(13/2))/(13*e^8) + (2*B*c^3*(d + e*x)^(15/2))/(15*e^8)","A",2,1,24,0.04167,1,"{772}"
1442,1,344,0,0.1631175,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(3/2),x]","-\frac{2 c (d+e x)^{5/2} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{5 e^8}+\frac{2 c^2 (d+e x)^{9/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{3 e^8}-\frac{2 c^2 (d+e x)^{7/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{7 e^8}-\frac{2 c (d+e x)^{3/2} \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{e^8 \sqrt{d+e x}}-\frac{2 c^3 (d+e x)^{11/2} (7 B d-A e)}{11 e^8}+\frac{2 B c^3 (d+e x)^{13/2}}{13 e^8}","-\frac{2 c (d+e x)^{5/2} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{5 e^8}+\frac{2 c^2 (d+e x)^{9/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{3 e^8}-\frac{2 c^2 (d+e x)^{7/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{7 e^8}-\frac{2 c (d+e x)^{3/2} \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8}+\frac{2 \sqrt{d+e x} \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{e^8 \sqrt{d+e x}}-\frac{2 c^3 (d+e x)^{11/2} (7 B d-A e)}{11 e^8}+\frac{2 B c^3 (d+e x)^{13/2}}{13 e^8}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^3)/(e^8*Sqrt[d + e*x]) + (2*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*Sqrt[d + e*x])/e^8 - (2*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(3/2))/e^8 - (2*c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^(5/2))/(5*e^8) - (2*c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^(7/2))/(7*e^8) + (2*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(9/2))/(3*e^8) - (2*c^3*(7*B*d - A*e)*(d + e*x)^(11/2))/(11*e^8) + (2*B*c^3*(d + e*x)^(13/2))/(13*e^8)","A",2,1,24,0.04167,1,"{772}"
1443,1,346,0,0.1618794,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(5/2),x]","-\frac{2 c (d+e x)^{3/2} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{3 e^8}+\frac{6 c^2 (d+e x)^{7/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{7 e^8}-\frac{2 c^2 (d+e x)^{5/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{5 e^8}-\frac{6 c \sqrt{d+e x} \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8 \sqrt{d+e x}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{3 e^8 (d+e x)^{3/2}}-\frac{2 c^3 (d+e x)^{9/2} (7 B d-A e)}{9 e^8}+\frac{2 B c^3 (d+e x)^{11/2}}{11 e^8}","-\frac{2 c (d+e x)^{3/2} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{3 e^8}+\frac{6 c^2 (d+e x)^{7/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{7 e^8}-\frac{2 c^2 (d+e x)^{5/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{5 e^8}-\frac{6 c \sqrt{d+e x} \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8 \sqrt{d+e x}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{3 e^8 (d+e x)^{3/2}}-\frac{2 c^3 (d+e x)^{9/2} (7 B d-A e)}{9 e^8}+\frac{2 B c^3 (d+e x)^{11/2}}{11 e^8}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^3)/(3*e^8*(d + e*x)^(3/2)) - (2*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(e^8*Sqrt[d + e*x]) - (6*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*Sqrt[d + e*x])/e^8 - (2*c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^(3/2))/(3*e^8) - (2*c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^(5/2))/(5*e^8) + (6*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(7/2))/(7*e^8) - (2*c^3*(7*B*d - A*e)*(d + e*x)^(9/2))/(9*e^8) + (2*B*c^3*(d + e*x)^(11/2))/(11*e^8)","A",2,1,24,0.04167,1,"{772}"
1444,1,346,0,0.1616391,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(7/2),x]","-\frac{2 c \sqrt{d+e x} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8}+\frac{6 c^2 (d+e x)^{5/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{5 e^8}-\frac{2 c^2 (d+e x)^{3/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{3 e^8}+\frac{6 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{3 e^8 (d+e x)^{3/2}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{5 e^8 (d+e x)^{5/2}}-\frac{2 c^3 (d+e x)^{7/2} (7 B d-A e)}{7 e^8}+\frac{2 B c^3 (d+e x)^{9/2}}{9 e^8}","-\frac{2 c \sqrt{d+e x} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8}+\frac{6 c^2 (d+e x)^{5/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{5 e^8}-\frac{2 c^2 (d+e x)^{3/2} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{3 e^8}+\frac{6 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 \sqrt{d+e x}}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{3 e^8 (d+e x)^{3/2}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{5 e^8 (d+e x)^{5/2}}-\frac{2 c^3 (d+e x)^{7/2} (7 B d-A e)}{7 e^8}+\frac{2 B c^3 (d+e x)^{9/2}}{9 e^8}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^3)/(5*e^8*(d + e*x)^(5/2)) - (2*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(3*e^8*(d + e*x)^(3/2)) + (6*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^8*Sqrt[d + e*x]) - (2*c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*Sqrt[d + e*x])/e^8 - (2*c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^(3/2))/(3*e^8) + (6*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(5/2))/(5*e^8) - (2*c^3*(7*B*d - A*e)*(d + e*x)^(7/2))/(7*e^8) + (2*B*c^3*(d + e*x)^(9/2))/(9*e^8)","A",2,1,24,0.04167,1,"{772}"
1445,1,342,0,0.1561226,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{9/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(9/2),x]","\frac{2 c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8 \sqrt{d+e x}}+\frac{2 c^2 (d+e x)^{3/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8}-\frac{2 c^2 \sqrt{d+e x} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8}+\frac{2 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{5 e^8 (d+e x)^{5/2}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{7 e^8 (d+e x)^{7/2}}-\frac{2 c^3 (d+e x)^{5/2} (7 B d-A e)}{5 e^8}+\frac{2 B c^3 (d+e x)^{7/2}}{7 e^8}","\frac{2 c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8 \sqrt{d+e x}}+\frac{2 c^2 (d+e x)^{3/2} \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8}-\frac{2 c^2 \sqrt{d+e x} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8}+\frac{2 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (d+e x)^{3/2}}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{5 e^8 (d+e x)^{5/2}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{7 e^8 (d+e x)^{7/2}}-\frac{2 c^3 (d+e x)^{5/2} (7 B d-A e)}{5 e^8}+\frac{2 B c^3 (d+e x)^{7/2}}{7 e^8}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^3)/(7*e^8*(d + e*x)^(7/2)) - (2*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(5*e^8*(d + e*x)^(5/2)) + (2*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(e^8*(d + e*x)^(3/2)) + (2*c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(e^8*Sqrt[d + e*x]) - (2*c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*Sqrt[d + e*x])/e^8 + (2*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(3/2))/e^8 - (2*c^3*(7*B*d - A*e)*(d + e*x)^(5/2))/(5*e^8) + (2*B*c^3*(d + e*x)^(7/2))/(7*e^8)","A",2,1,24,0.04167,1,"{772}"
1446,1,346,0,0.1619998,"\int \frac{(A+B x) \left(a+c x^2\right)^3}{(d+e x)^{11/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^3)/(d + e*x)^(11/2),x]","\frac{2 c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{3 e^8 (d+e x)^{3/2}}+\frac{6 c^2 \sqrt{d+e x} \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8}+\frac{2 c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8 \sqrt{d+e x}}+\frac{6 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8 (d+e x)^{5/2}}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{7 e^8 (d+e x)^{7/2}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{9 e^8 (d+e x)^{9/2}}-\frac{2 c^3 (d+e x)^{3/2} (7 B d-A e)}{3 e^8}+\frac{2 B c^3 (d+e x)^{5/2}}{5 e^8}","\frac{2 c \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{3 e^8 (d+e x)^{3/2}}+\frac{6 c^2 \sqrt{d+e x} \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8}+\frac{2 c^2 \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8 \sqrt{d+e x}}+\frac{6 c \left(a e^2+c d^2\right) \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{5 e^8 (d+e x)^{5/2}}-\frac{2 \left(a e^2+c d^2\right)^2 \left(a B e^2-6 A c d e+7 B c d^2\right)}{7 e^8 (d+e x)^{7/2}}+\frac{2 \left(a e^2+c d^2\right)^3 (B d-A e)}{9 e^8 (d+e x)^{9/2}}-\frac{2 c^3 (d+e x)^{3/2} (7 B d-A e)}{3 e^8}+\frac{2 B c^3 (d+e x)^{5/2}}{5 e^8}",1,"(2*(B*d - A*e)*(c*d^2 + a*e^2)^3)/(9*e^8*(d + e*x)^(9/2)) - (2*(c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2))/(7*e^8*(d + e*x)^(7/2)) + (6*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3))/(5*e^8*(d + e*x)^(5/2)) + (2*c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4)))/(3*e^8*(d + e*x)^(3/2)) + (2*c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3))/(e^8*Sqrt[d + e*x]) + (6*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*Sqrt[d + e*x])/e^8 - (2*c^3*(7*B*d - A*e)*(d + e*x)^(3/2))/(3*e^8) + (2*B*c^3*(d + e*x)^(5/2))/(5*e^8)","A",2,1,24,0.04167,1,"{772}"
1447,1,237,0,0.6418332,"\int \frac{(A+B x) (d+e x)^{5/2}}{a-c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a - c*x^2),x]","-\frac{2 \sqrt{d+e x} \left(a B e^2+2 A c d e+B c d^2\right)}{c^2}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{9/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{9/4}}-\frac{2 (d+e x)^{3/2} (A e+B d)}{3 c}-\frac{2 B (d+e x)^{5/2}}{5 c}","-\frac{2 \sqrt{d+e x} \left(a B e^2+2 A c d e+B c d^2\right)}{c^2}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{9/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{9/4}}-\frac{2 (d+e x)^{3/2} (A e+B d)}{3 c}-\frac{2 B (d+e x)^{5/2}}{5 c}",1,"(-2*(B*c*d^2 + 2*A*c*d*e + a*B*e^2)*Sqrt[d + e*x])/c^2 - (2*(B*d + A*e)*(d + e*x)^(3/2))/(3*c) - (2*B*(d + e*x)^(5/2))/(5*c) + ((Sqrt[a]*B - A*Sqrt[c])*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(9/4)) + ((Sqrt[a]*B + A*Sqrt[c])*(Sqrt[c]*d + Sqrt[a]*e)^(5/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(9/4))","A",7,4,25,0.1600,1,"{825, 827, 1166, 208}"
1448,1,202,0,0.4365246,"\int \frac{(A+B x) (d+e x)^{3/2}}{a-c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a - c*x^2),x]","\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{7/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{7/4}}-\frac{2 \sqrt{d+e x} (A e+B d)}{c}-\frac{2 B (d+e x)^{3/2}}{3 c}","\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{7/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{7/4}}-\frac{2 \sqrt{d+e x} (A e+B d)}{c}-\frac{2 B (d+e x)^{3/2}}{3 c}",1,"(-2*(B*d + A*e)*Sqrt[d + e*x])/c - (2*B*(d + e*x)^(3/2))/(3*c) + ((Sqrt[a]*B - A*Sqrt[c])*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(7/4)) + ((Sqrt[a]*B + A*Sqrt[c])*(Sqrt[c]*d + Sqrt[a]*e)^(3/2)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(7/4))","A",6,4,25,0.1600,1,"{825, 827, 1166, 208}"
1449,1,179,0,0.3169029,"\int \frac{(A+B x) \sqrt{d+e x}}{a-c x^2} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a - c*x^2),x]","\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \sqrt{\sqrt{c} d-\sqrt{a} e} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{5/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{5/4}}-\frac{2 B \sqrt{d+e x}}{c}","\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \sqrt{\sqrt{c} d-\sqrt{a} e} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} c^{5/4}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \sqrt{\sqrt{a} e+\sqrt{c} d} \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} c^{5/4}}-\frac{2 B \sqrt{d+e x}}{c}",1,"(-2*B*Sqrt[d + e*x])/c + ((Sqrt[a]*B - A*Sqrt[c])*Sqrt[Sqrt[c]*d - Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(5/4)) + ((Sqrt[a]*B + A*Sqrt[c])*Sqrt[Sqrt[c]*d + Sqrt[a]*e]*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(5/4))","A",5,4,25,0.1600,1,"{825, 827, 1166, 208}"
1450,1,152,0,0.163171,"\int \frac{A+B x}{\sqrt{d+e x} \left(a-c x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a - c*x^2)),x]","\frac{\left(B-\frac{A \sqrt{c}}{\sqrt{a}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{\left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{c^{3/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}","\frac{\left(B-\frac{A \sqrt{c}}{\sqrt{a}}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{c^{3/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{\left(\frac{A \sqrt{c}}{\sqrt{a}}+B\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{c^{3/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}",1,"((B - (A*Sqrt[c])/Sqrt[a])*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(c^(3/4)*Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + ((B + (A*Sqrt[c])/Sqrt[a])*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(c^(3/4)*Sqrt[Sqrt[c]*d + Sqrt[a]*e])","A",4,3,25,0.1200,1,"{827, 1166, 208}"
1451,1,197,0,0.4024058,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a-c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a - c*x^2)),x]","-\frac{2 (B d-A e)}{\sqrt{d+e x} \left(c d^2-a e^2\right)}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}","-\frac{2 (B d-A e)}{\sqrt{d+e x} \left(c d^2-a e^2\right)}+\frac{\left(\sqrt{a} B-A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(\sqrt{a} B+A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}",1,"(-2*(B*d - A*e))/((c*d^2 - a*e^2)*Sqrt[d + e*x]) + ((Sqrt[a]*B - A*Sqrt[c])*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*c^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + ((Sqrt[a]*B + A*Sqrt[c])*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*c^(1/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))","A",5,4,25,0.1600,1,"{829, 827, 1166, 208}"
1452,1,243,0,0.5356497,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a-c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(a - c*x^2)),x]","-\frac{2 (B d-A e)}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}-\frac{2 \left(a B e^2-2 A c d e+B c d^2\right)}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}+\frac{\sqrt[4]{c} \left(\sqrt{a} B-A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\sqrt[4]{c} \left(\sqrt{a} B+A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}","-\frac{2 (B d-A e)}{3 (d+e x)^{3/2} \left(c d^2-a e^2\right)}-\frac{2 \left(a B e^2-2 A c d e+B c d^2\right)}{\sqrt{d+e x} \left(c d^2-a e^2\right)^2}+\frac{\sqrt[4]{c} \left(\sqrt{a} B-A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{\sqrt{a} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\sqrt[4]{c} \left(\sqrt{a} B+A \sqrt{c}\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{\sqrt{a} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}",1,"(-2*(B*d - A*e))/(3*(c*d^2 - a*e^2)*(d + e*x)^(3/2)) - (2*(B*c*d^2 - 2*A*c*d*e + a*B*e^2))/((c*d^2 - a*e^2)^2*Sqrt[d + e*x]) + ((Sqrt[a]*B - A*Sqrt[c])*c^(1/4)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(Sqrt[a]*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)) + ((Sqrt[a]*B + A*Sqrt[c])*c^(1/4)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(Sqrt[a]*(Sqrt[c]*d + Sqrt[a]*e)^(5/2))","A",6,4,25,0.1600,1,"{829, 827, 1166, 208}"
1453,1,269,0,0.5414561,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a-c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a - c*x^2)^2,x]","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \left(3 \sqrt{a} A \sqrt{c} e-5 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{9/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \left(-3 \sqrt{a} A \sqrt{c} e-5 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{9/4}}+\frac{e \sqrt{d+e x} (5 a B e+A c d)}{2 a c^2}+\frac{(d+e x)^{3/2} (x (a B e+A c d)+a (A e+B d))}{2 a c \left(a-c x^2\right)}","-\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \left(3 \sqrt{a} A \sqrt{c} e-5 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{9/4}}+\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \left(-3 \sqrt{a} A \sqrt{c} e-5 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{9/4}}+\frac{e \sqrt{d+e x} (5 a B e+A c d)}{2 a c^2}+\frac{(d+e x)^{3/2} (x (a B e+A c d)+a (A e+B d))}{2 a c \left(a-c x^2\right)}",1,"(e*(A*c*d + 5*a*B*e)*Sqrt[d + e*x])/(2*a*c^2) + ((d + e*x)^(3/2)*(a*(B*d + A*e) + (A*c*d + a*B*e)*x))/(2*a*c*(a - c*x^2)) - ((Sqrt[c]*d - Sqrt[a]*e)^(3/2)*(2*A*c*d - 5*a*B*e + 3*Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(9/4)) + ((Sqrt[c]*d + Sqrt[a]*e)^(3/2)*(2*A*c*d - 5*a*B*e - 3*Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(9/4))","A",6,5,25,0.2000,1,"{819, 825, 827, 1166, 208}"
1454,1,238,0,0.391526,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a-c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a - c*x^2)^2,x]","-\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \left(\sqrt{a} A \sqrt{c} e-3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{7/4}}+\frac{\sqrt{\sqrt{a} e+\sqrt{c} d} \left(-\sqrt{a} A \sqrt{c} e-3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{7/4}}+\frac{\sqrt{d+e x} (x (a B e+A c d)+a (A e+B d))}{2 a c \left(a-c x^2\right)}","-\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \left(\sqrt{a} A \sqrt{c} e-3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{7/4}}+\frac{\sqrt{\sqrt{a} e+\sqrt{c} d} \left(-\sqrt{a} A \sqrt{c} e-3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{7/4}}+\frac{\sqrt{d+e x} (x (a B e+A c d)+a (A e+B d))}{2 a c \left(a-c x^2\right)}",1,"(Sqrt[d + e*x]*(a*(B*d + A*e) + (A*c*d + a*B*e)*x))/(2*a*c*(a - c*x^2)) - (Sqrt[Sqrt[c]*d - Sqrt[a]*e]*(2*A*c*d - 3*a*B*e + Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(7/4)) + (Sqrt[Sqrt[c]*d + Sqrt[a]*e]*(2*A*c*d - 3*a*B*e - Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(7/4))","A",5,4,25,0.1600,1,"{819, 827, 1166, 208}"
1455,1,225,0,0.3973992,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a-c x^2\right)^2} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a - c*x^2)^2,x]","-\frac{\left(-\sqrt{a} A \sqrt{c} e-a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{5/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{\left(\sqrt{a} A \sqrt{c} e-a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{5/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}+\frac{\sqrt{d+e x} (a B+A c x)}{2 a c \left(a-c x^2\right)}","-\frac{\left(-\sqrt{a} A \sqrt{c} e-a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{5/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}+\frac{\left(\sqrt{a} A \sqrt{c} e-a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{5/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}+\frac{\sqrt{d+e x} (a B+A c x)}{2 a c \left(a-c x^2\right)}",1,"((a*B + A*c*x)*Sqrt[d + e*x])/(2*a*c*(a - c*x^2)) - ((2*A*c*d - a*B*e - Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(5/4)*Sqrt[Sqrt[c]*d - Sqrt[a]*e]) + ((2*A*c*d - a*B*e + Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(5/4)*Sqrt[Sqrt[c]*d + Sqrt[a]*e])","A",5,4,25,0.1600,1,"{821, 827, 1166, 208}"
1456,1,250,0,0.4980612,"\int \frac{A+B x}{\sqrt{d+e x} \left(a-c x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a - c*x^2)^2),x]","-\frac{\left(-3 \sqrt{a} A \sqrt{c} e+a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{3/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(3 \sqrt{a} A \sqrt{c} e+a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{3/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}+\frac{\sqrt{d+e x} (x (A c d-a B e)+a (B d-A e))}{2 a \left(a-c x^2\right) \left(c d^2-a e^2\right)}","-\frac{\left(-3 \sqrt{a} A \sqrt{c} e+a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} c^{3/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}+\frac{\left(3 \sqrt{a} A \sqrt{c} e+a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} c^{3/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}+\frac{\sqrt{d+e x} (x (A c d-a B e)+a (B d-A e))}{2 a \left(a-c x^2\right) \left(c d^2-a e^2\right)}",1,"(Sqrt[d + e*x]*(a*(B*d - A*e) + (A*c*d - a*B*e)*x))/(2*a*(c*d^2 - a*e^2)*(a - c*x^2)) - ((2*A*c*d + a*B*e - 3*Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(3/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) + ((2*A*c*d + a*B*e + 3*Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))","A",5,4,25,0.1600,1,"{823, 827, 1166, 208}"
1457,1,303,0,0.6857954,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a-c x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a - c*x^2)^2),x]","-\frac{\left(-5 \sqrt{a} A \sqrt{c} e+3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\left(5 \sqrt{a} A \sqrt{c} e+3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}+\frac{x (A c d-a B e)+a (B d-A e)}{2 a \left(a-c x^2\right) \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{e \left(5 a A e^2-6 a B d e+A c d^2\right)}{2 a \sqrt{d+e x} \left(c d^2-a e^2\right)^2}","-\frac{\left(-5 \sqrt{a} A \sqrt{c} e+3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\left(5 \sqrt{a} A \sqrt{c} e+3 a B e+2 A c d\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{4 a^{3/2} \sqrt[4]{c} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}+\frac{x (A c d-a B e)+a (B d-A e)}{2 a \left(a-c x^2\right) \sqrt{d+e x} \left(c d^2-a e^2\right)}-\frac{e \left(5 a A e^2-6 a B d e+A c d^2\right)}{2 a \sqrt{d+e x} \left(c d^2-a e^2\right)^2}",1,"-(e*(A*c*d^2 - 6*a*B*d*e + 5*a*A*e^2))/(2*a*(c*d^2 - a*e^2)^2*Sqrt[d + e*x]) + (a*(B*d - A*e) + (A*c*d - a*B*e)*x)/(2*a*(c*d^2 - a*e^2)*Sqrt[d + e*x]*(a - c*x^2)) - ((2*A*c*d + 3*a*B*e - 5*Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(4*a^(3/2)*c^(1/4)*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)) + ((2*A*c*d + 3*a*B*e + 5*Sqrt[a]*A*Sqrt[c]*e)*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(4*a^(3/2)*c^(1/4)*(Sqrt[c]*d + Sqrt[a]*e)^(5/2))","A",6,5,25,0.2000,1,"{823, 829, 827, 1166, 208}"
1458,1,396,0,0.8773936,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a-c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(a - c*x^2)^3,x]","\frac{\sqrt{d+e x} \left(x \left(2 A c d \left(3 c d^2-2 a e^2\right)-7 a B e \left(a e^2+c d^2\right)\right)+a e \left(-5 a A e^2-14 a B d e+7 A c d^2\right)\right)}{16 a^2 c^2 \left(a-c x^2\right)}+\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \left(7 a B e \left(3 \sqrt{a} e+2 \sqrt{c} d\right)-A \left(18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{11/4}}-\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \left(7 a B e \left(2 \sqrt{c} d-3 \sqrt{a} e\right)-A \left(-18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{11/4}}+\frac{(d+e x)^{5/2} (x (a B e+A c d)+a (A e+B d))}{4 a c \left(a-c x^2\right)^2}","\frac{\sqrt{d+e x} \left(x \left(2 A c d \left(3 c d^2-2 a e^2\right)-7 a B e \left(a e^2+c d^2\right)\right)+a e \left(-5 a A e^2-14 a B d e+7 A c d^2\right)\right)}{16 a^2 c^2 \left(a-c x^2\right)}+\frac{\left(\sqrt{c} d-\sqrt{a} e\right)^{3/2} \left(7 a B e \left(3 \sqrt{a} e+2 \sqrt{c} d\right)-A \left(18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{11/4}}-\frac{\left(\sqrt{a} e+\sqrt{c} d\right)^{3/2} \left(7 a B e \left(2 \sqrt{c} d-3 \sqrt{a} e\right)-A \left(-18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{11/4}}+\frac{(d+e x)^{5/2} (x (a B e+A c d)+a (A e+B d))}{4 a c \left(a-c x^2\right)^2}",1,"((d + e*x)^(5/2)*(a*(B*d + A*e) + (A*c*d + a*B*e)*x))/(4*a*c*(a - c*x^2)^2) + (Sqrt[d + e*x]*(a*e*(7*A*c*d^2 - 14*a*B*d*e - 5*a*A*e^2) + (2*A*c*d*(3*c*d^2 - 2*a*e^2) - 7*a*B*e*(c*d^2 + a*e^2))*x))/(16*a^2*c^2*(a - c*x^2)) + ((Sqrt[c]*d - Sqrt[a]*e)^(3/2)*(7*a*B*e*(2*Sqrt[c]*d + 3*Sqrt[a]*e) - A*(12*c^(3/2)*d^2 + 18*Sqrt[a]*c*d*e + 5*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(11/4)) - ((Sqrt[c]*d + Sqrt[a]*e)^(3/2)*(7*a*B*e*(2*Sqrt[c]*d - 3*Sqrt[a]*e) - A*(12*c^(3/2)*d^2 - 18*Sqrt[a]*c*d*e + 5*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(11/4))","A",6,4,25,0.1600,1,"{819, 827, 1166, 208}"
1459,1,372,0,0.6861174,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a-c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a - c*x^2)^3,x]","\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \left(5 a B e \left(\sqrt{a} e+2 \sqrt{c} d\right)-3 A \left(2 \sqrt{a} c d e-a \sqrt{c} e^2+4 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{9/4}}-\frac{\sqrt{\sqrt{a} e+\sqrt{c} d} \left(5 a B e \left(2 \sqrt{c} d-\sqrt{a} e\right)-A \left(-6 \sqrt{a} c d e-3 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{9/4}}+\frac{\sqrt{d+e x} \left(c x \left(6 A c d^2-a e (3 A e+5 B d)\right)+a e (3 A c d-5 a B e)\right)}{16 a^2 c^2 \left(a-c x^2\right)}+\frac{(d+e x)^{3/2} (x (a B e+A c d)+a (A e+B d))}{4 a c \left(a-c x^2\right)^2}","\frac{\sqrt{\sqrt{c} d-\sqrt{a} e} \left(5 a B e \left(\sqrt{a} e+2 \sqrt{c} d\right)-3 A \left(2 \sqrt{a} c d e-a \sqrt{c} e^2+4 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{9/4}}-\frac{\sqrt{\sqrt{a} e+\sqrt{c} d} \left(5 a B e \left(2 \sqrt{c} d-\sqrt{a} e\right)-A \left(-6 \sqrt{a} c d e-3 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{9/4}}+\frac{\sqrt{d+e x} \left(c x \left(6 A c d^2-a e (3 A e+5 B d)\right)+a e (3 A c d-5 a B e)\right)}{16 a^2 c^2 \left(a-c x^2\right)}+\frac{(d+e x)^{3/2} (x (a B e+A c d)+a (A e+B d))}{4 a c \left(a-c x^2\right)^2}",1,"((d + e*x)^(3/2)*(a*(B*d + A*e) + (A*c*d + a*B*e)*x))/(4*a*c*(a - c*x^2)^2) + (Sqrt[d + e*x]*(a*e*(3*A*c*d - 5*a*B*e) + c*(6*A*c*d^2 - a*e*(5*B*d + 3*A*e))*x))/(16*a^2*c^2*(a - c*x^2)) + (Sqrt[Sqrt[c]*d - Sqrt[a]*e]*(5*a*B*e*(2*Sqrt[c]*d + Sqrt[a]*e) - 3*A*(4*c^(3/2)*d^2 + 2*Sqrt[a]*c*d*e - a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(9/4)) - (Sqrt[Sqrt[c]*d + Sqrt[a]*e]*(5*a*B*e*(2*Sqrt[c]*d - Sqrt[a]*e) - A*(12*c^(3/2)*d^2 - 6*Sqrt[a]*c*d*e - 3*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(9/4))","A",6,5,25,0.2000,1,"{819, 821, 827, 1166, 208}"
1460,1,350,0,0.8012767,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a-c x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a - c*x^2)^3,x]","\frac{3 \left(a B e \left(2 \sqrt{c} d-\sqrt{a} e\right)-A \left(-2 \sqrt{a} c d e-a \sqrt{c} e^2+4 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{7/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}-\frac{3 \left(a B e \left(\sqrt{a} e+2 \sqrt{c} d\right)-A \left(2 \sqrt{a} c d e-a \sqrt{c} e^2+4 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{7/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\sqrt{d+e x} (a A e-3 x (2 A c d-a B e))}{16 a^2 c \left(a-c x^2\right)}+\frac{\sqrt{d+e x} (x (a B e+A c d)+a (A e+B d))}{4 a c \left(a-c x^2\right)^2}","\frac{3 \left(a B e \left(2 \sqrt{c} d-\sqrt{a} e\right)-A \left(-2 \sqrt{a} c d e-a \sqrt{c} e^2+4 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{7/4} \sqrt{\sqrt{c} d-\sqrt{a} e}}-\frac{3 \left(a B e \left(\sqrt{a} e+2 \sqrt{c} d\right)-A \left(2 \sqrt{a} c d e-a \sqrt{c} e^2+4 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{7/4} \sqrt{\sqrt{a} e+\sqrt{c} d}}-\frac{\sqrt{d+e x} (a A e-3 x (2 A c d-a B e))}{16 a^2 c \left(a-c x^2\right)}+\frac{\sqrt{d+e x} (x (a B e+A c d)+a (A e+B d))}{4 a c \left(a-c x^2\right)^2}",1,"(Sqrt[d + e*x]*(a*(B*d + A*e) + (A*c*d + a*B*e)*x))/(4*a*c*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*A*e - 3*(2*A*c*d - a*B*e)*x))/(16*a^2*c*(a - c*x^2)) + (3*(a*B*e*(2*Sqrt[c]*d - Sqrt[a]*e) - A*(4*c^(3/2)*d^2 - 2*Sqrt[a]*c*d*e - a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(7/4)*Sqrt[Sqrt[c]*d - Sqrt[a]*e]) - (3*(a*B*e*(2*Sqrt[c]*d + Sqrt[a]*e) - A*(4*c^(3/2)*d^2 + 2*Sqrt[a]*c*d*e - a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(7/4)*Sqrt[Sqrt[c]*d + Sqrt[a]*e])","A",6,5,25,0.2000,1,"{819, 823, 827, 1166, 208}"
1461,1,372,0,0.7605267,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a-c x^2\right)^3} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a - c*x^2)^3,x]","\frac{\left(a B e \left(2 \sqrt{c} d-3 \sqrt{a} e\right)-A \left(-18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{5/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}-\frac{\left(a B e \left(3 \sqrt{a} e+2 \sqrt{c} d\right)-A \left(18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{5/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}-\frac{\sqrt{d+e x} \left(a e (A c d-a B e)-c x \left(-5 a A e^2-a B d e+6 A c d^2\right)\right)}{16 a^2 c \left(a-c x^2\right) \left(c d^2-a e^2\right)}+\frac{\sqrt{d+e x} (a B+A c x)}{4 a c \left(a-c x^2\right)^2}","\frac{\left(a B e \left(2 \sqrt{c} d-3 \sqrt{a} e\right)-A \left(-18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{5/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{3/2}}-\frac{\left(a B e \left(3 \sqrt{a} e+2 \sqrt{c} d\right)-A \left(18 \sqrt{a} c d e+5 a \sqrt{c} e^2+12 c^{3/2} d^2\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{5/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{3/2}}-\frac{\sqrt{d+e x} \left(a e (A c d-a B e)-c x \left(-5 a A e^2-a B d e+6 A c d^2\right)\right)}{16 a^2 c \left(a-c x^2\right) \left(c d^2-a e^2\right)}+\frac{\sqrt{d+e x} (a B+A c x)}{4 a c \left(a-c x^2\right)^2}",1,"((a*B + A*c*x)*Sqrt[d + e*x])/(4*a*c*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*e*(A*c*d - a*B*e) - c*(6*A*c*d^2 - a*B*d*e - 5*a*A*e^2)*x))/(16*a^2*c*(c*d^2 - a*e^2)*(a - c*x^2)) + ((a*B*e*(2*Sqrt[c]*d - 3*Sqrt[a]*e) - A*(12*c^(3/2)*d^2 - 18*Sqrt[a]*c*d*e + 5*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(5/4)*(Sqrt[c]*d - Sqrt[a]*e)^(3/2)) - ((a*B*e*(2*Sqrt[c]*d + 3*Sqrt[a]*e) - A*(12*c^(3/2)*d^2 + 18*Sqrt[a]*c*d*e + 5*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(5/4)*(Sqrt[c]*d + Sqrt[a]*e)^(3/2))","A",6,5,25,0.2000,1,"{821, 823, 827, 1166, 208}"
1462,1,417,0,0.9256662,"\int \frac{A+B x}{\sqrt{d+e x} \left(a-c x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a - c*x^2)^3),x]","-\frac{\left(3 A \left(-10 \sqrt{a} c d e+7 a \sqrt{c} e^2+4 c^{3/2} d^2\right)+a B e \left(2 \sqrt{c} d-5 \sqrt{a} e\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\left(3 A \left(10 \sqrt{a} c d e+7 a \sqrt{c} e^2+4 c^{3/2} d^2\right)+a B e \left(5 \sqrt{a} e+2 \sqrt{c} d\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}-\frac{\sqrt{d+e x} \left(a e \left(-7 a A e^2+6 a B d e+A c d^2\right)-x \left(6 A c d \left(c d^2-2 a e^2\right)+a B e \left(5 a e^2+c d^2\right)\right)\right)}{16 a^2 \left(a-c x^2\right) \left(c d^2-a e^2\right)^2}+\frac{\sqrt{d+e x} (x (A c d-a B e)+a (B d-A e))}{4 a \left(a-c x^2\right)^2 \left(c d^2-a e^2\right)}","-\frac{\left(3 A \left(-10 \sqrt{a} c d e+7 a \sqrt{c} e^2+4 c^{3/2} d^2\right)+a B e \left(2 \sqrt{c} d-5 \sqrt{a} e\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{c} d-\sqrt{a} e}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{c} d-\sqrt{a} e\right)^{5/2}}+\frac{\left(3 A \left(10 \sqrt{a} c d e+7 a \sqrt{c} e^2+4 c^{3/2} d^2\right)+a B e \left(5 \sqrt{a} e+2 \sqrt{c} d\right)\right) \tanh ^{-1}\left(\frac{\sqrt[4]{c} \sqrt{d+e x}}{\sqrt{\sqrt{a} e+\sqrt{c} d}}\right)}{32 a^{5/2} c^{3/4} \left(\sqrt{a} e+\sqrt{c} d\right)^{5/2}}-\frac{\sqrt{d+e x} \left(a e \left(-7 a A e^2+6 a B d e+A c d^2\right)-x \left(6 A c d \left(c d^2-2 a e^2\right)+a B e \left(5 a e^2+c d^2\right)\right)\right)}{16 a^2 \left(a-c x^2\right) \left(c d^2-a e^2\right)^2}+\frac{\sqrt{d+e x} (x (A c d-a B e)+a (B d-A e))}{4 a \left(a-c x^2\right)^2 \left(c d^2-a e^2\right)}",1,"(Sqrt[d + e*x]*(a*(B*d - A*e) + (A*c*d - a*B*e)*x))/(4*a*(c*d^2 - a*e^2)*(a - c*x^2)^2) - (Sqrt[d + e*x]*(a*e*(A*c*d^2 + 6*a*B*d*e - 7*a*A*e^2) - (6*A*c*d*(c*d^2 - 2*a*e^2) + a*B*e*(c*d^2 + 5*a*e^2))*x))/(16*a^2*(c*d^2 - a*e^2)^2*(a - c*x^2)) - ((a*B*e*(2*Sqrt[c]*d - 5*Sqrt[a]*e) + 3*A*(4*c^(3/2)*d^2 - 10*Sqrt[a]*c*d*e + 7*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d - Sqrt[a]*e]])/(32*a^(5/2)*c^(3/4)*(Sqrt[c]*d - Sqrt[a]*e)^(5/2)) + ((a*B*e*(2*Sqrt[c]*d + 5*Sqrt[a]*e) + 3*A*(4*c^(3/2)*d^2 + 10*Sqrt[a]*c*d*e + 7*a*Sqrt[c]*e^2))*ArcTanh[(c^(1/4)*Sqrt[d + e*x])/Sqrt[Sqrt[c]*d + Sqrt[a]*e]])/(32*a^(5/2)*c^(3/4)*(Sqrt[c]*d + Sqrt[a]*e)^(5/2))","A",6,4,25,0.1600,1,"{823, 827, 1166, 208}"
1463,1,155,0,0.2114785,"\int \frac{A+B x}{\sqrt{d+e x} \left(2 A B d-A^2 e-B^2 e x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(2*A*B*d - A^2*e - B^2*e*x^2)),x]","\frac{\log \left(\sqrt{2} \sqrt{B} \sqrt{d+e x} \sqrt{2 B d-A e}-A e+B (d+e x)+B d\right)}{\sqrt{2} \sqrt{B} e \sqrt{2 B d-A e}}-\frac{\log \left(-\sqrt{2} \sqrt{B} \sqrt{d+e x} \sqrt{2 B d-A e}-A e+B (d+e x)+B d\right)}{\sqrt{2} \sqrt{B} e \sqrt{2 B d-A e}}","\frac{\log \left(\sqrt{2} \sqrt{B} \sqrt{d+e x} \sqrt{2 B d-A e}-A e+B (d+e x)+B d\right)}{\sqrt{2} \sqrt{B} e \sqrt{2 B d-A e}}-\frac{\log \left(-\sqrt{2} \sqrt{B} \sqrt{d+e x} \sqrt{2 B d-A e}-A e+B (d+e x)+B d\right)}{\sqrt{2} \sqrt{B} e \sqrt{2 B d-A e}}",1,"-(Log[B*d - A*e - Sqrt[2]*Sqrt[B]*Sqrt[2*B*d - A*e]*Sqrt[d + e*x] + B*(d + e*x)]/(Sqrt[2]*Sqrt[B]*e*Sqrt[2*B*d - A*e])) + Log[B*d - A*e + Sqrt[2]*Sqrt[B]*Sqrt[2*B*d - A*e]*Sqrt[d + e*x] + B*(d + e*x)]/(Sqrt[2]*Sqrt[B]*e*Sqrt[2*B*d - A*e])","A",4,3,38,0.07895,1,"{827, 1164, 628}"
1464,1,133,0,0.4303113,"\int \frac{A+B x}{\sqrt{\frac{A^2 e-B^2 e}{2 A B}+e x} \left(1+x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[(A^2*e - B^2*e)/(2*A*B) + e*x]*(1 + x^2)),x]","\frac{\sqrt{2} \sqrt{A} \sqrt{B} \tan ^{-1}\left(\frac{\sqrt{A} \sqrt{e \left(\frac{A}{B}-\frac{B}{A}+2 x\right)}}{\sqrt{B} \sqrt{e}}+\frac{A}{B}\right)}{\sqrt{e}}-\frac{\sqrt{2} \sqrt{A} \sqrt{B} \tan ^{-1}\left(\frac{A}{B}-\frac{\sqrt{A} \sqrt{e \left(\frac{A}{B}-\frac{B}{A}+2 x\right)}}{\sqrt{B} \sqrt{e}}\right)}{\sqrt{e}}","\frac{\sqrt{2} \sqrt{A} \sqrt{B} \tan ^{-1}\left(\frac{\sqrt{A} \sqrt{e \left(\frac{A}{B}-\frac{B}{A}+2 x\right)}}{\sqrt{B} \sqrt{e}}+\frac{A}{B}\right)}{\sqrt{e}}-\frac{\sqrt{2} \sqrt{A} \sqrt{B} \tan ^{-1}\left(\frac{A}{B}-\frac{\sqrt{A} \sqrt{e \left(\frac{A}{B}-\frac{B}{A}+2 x\right)}}{\sqrt{B} \sqrt{e}}\right)}{\sqrt{e}}",1,"-((Sqrt[2]*Sqrt[A]*Sqrt[B]*ArcTan[A/B - (Sqrt[A]*Sqrt[e*(A/B - B/A + 2*x)])/(Sqrt[B]*Sqrt[e])])/Sqrt[e]) + (Sqrt[2]*Sqrt[A]*Sqrt[B]*ArcTan[A/B + (Sqrt[A]*Sqrt[e*(A/B - B/A + 2*x)])/(Sqrt[B]*Sqrt[e])])/Sqrt[e]","A",6,4,43,0.09302,1,"{827, 1161, 618, 204}"
1465,1,66,0,0.1024991,"\int \frac{A+B x}{\sqrt{d+e x} \left(1-x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(1 - x^2)),x]","\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d+e}}\right)}{\sqrt{d+e}}-\frac{(A-B) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d-e}}\right)}{\sqrt{d-e}}","\frac{(A+B) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d+e}}\right)}{\sqrt{d+e}}-\frac{(A-B) \tanh ^{-1}\left(\frac{\sqrt{d+e x}}{\sqrt{d-e}}\right)}{\sqrt{d-e}}",1,"-(((A - B)*ArcTanh[Sqrt[d + e*x]/Sqrt[d - e]])/Sqrt[d - e]) + ((A + B)*ArcTanh[Sqrt[d + e*x]/Sqrt[d + e]])/Sqrt[d + e]","A",4,3,24,0.1250,1,"{827, 1166, 206}"
1466,1,440,0,0.6557126,"\int \frac{A+B x}{\sqrt{d+e x} \left(1+x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(1 + x^2)),x]","-\frac{\left(A e-B \left(\sqrt{d^2+e^2}+d\right)\right) \log \left(-\sqrt{2} \sqrt{\sqrt{d^2+e^2}+d} \sqrt{d+e x}+\sqrt{d^2+e^2}+d+e x\right)}{2 \sqrt{2} \sqrt{d^2+e^2} \sqrt{\sqrt{d^2+e^2}+d}}+\frac{\left(A e-B \left(\sqrt{d^2+e^2}+d\right)\right) \log \left(\sqrt{2} \sqrt{\sqrt{d^2+e^2}+d} \sqrt{d+e x}+\sqrt{d^2+e^2}+d+e x\right)}{2 \sqrt{2} \sqrt{d^2+e^2} \sqrt{\sqrt{d^2+e^2}+d}}+\frac{\left(A e-B \left(d-\sqrt{d^2+e^2}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{d^2+e^2}+d}-\sqrt{2} \sqrt{d+e x}}{\sqrt{d-\sqrt{d^2+e^2}}}\right)}{\sqrt{2} \sqrt{d^2+e^2} \sqrt{d-\sqrt{d^2+e^2}}}-\frac{\left(A e-B \left(d-\sqrt{d^2+e^2}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{d^2+e^2}+d}+\sqrt{2} \sqrt{d+e x}}{\sqrt{d-\sqrt{d^2+e^2}}}\right)}{\sqrt{2} \sqrt{d^2+e^2} \sqrt{d-\sqrt{d^2+e^2}}}","-\frac{\left(A e-B \left(\sqrt{d^2+e^2}+d\right)\right) \log \left(-\sqrt{2} \sqrt{\sqrt{d^2+e^2}+d} \sqrt{d+e x}+\sqrt{d^2+e^2}+d+e x\right)}{2 \sqrt{2} \sqrt{d^2+e^2} \sqrt{\sqrt{d^2+e^2}+d}}+\frac{\left(A e-B \left(\sqrt{d^2+e^2}+d\right)\right) \log \left(\sqrt{2} \sqrt{\sqrt{d^2+e^2}+d} \sqrt{d+e x}+\sqrt{d^2+e^2}+d+e x\right)}{2 \sqrt{2} \sqrt{d^2+e^2} \sqrt{\sqrt{d^2+e^2}+d}}+\frac{\left(A e-B \left(d-\sqrt{d^2+e^2}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{d^2+e^2}+d}-\sqrt{2} \sqrt{d+e x}}{\sqrt{d-\sqrt{d^2+e^2}}}\right)}{\sqrt{2} \sqrt{d^2+e^2} \sqrt{d-\sqrt{d^2+e^2}}}-\frac{\left(A e-B \left(d-\sqrt{d^2+e^2}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{\sqrt{d^2+e^2}+d}+\sqrt{2} \sqrt{d+e x}}{\sqrt{d-\sqrt{d^2+e^2}}}\right)}{\sqrt{2} \sqrt{d^2+e^2} \sqrt{d-\sqrt{d^2+e^2}}}",1,"((A*e - B*(d - Sqrt[d^2 + e^2]))*ArcTanh[(Sqrt[d + Sqrt[d^2 + e^2]] - Sqrt[2]*Sqrt[d + e*x])/Sqrt[d - Sqrt[d^2 + e^2]]])/(Sqrt[2]*Sqrt[d^2 + e^2]*Sqrt[d - Sqrt[d^2 + e^2]]) - ((A*e - B*(d - Sqrt[d^2 + e^2]))*ArcTanh[(Sqrt[d + Sqrt[d^2 + e^2]] + Sqrt[2]*Sqrt[d + e*x])/Sqrt[d - Sqrt[d^2 + e^2]]])/(Sqrt[2]*Sqrt[d^2 + e^2]*Sqrt[d - Sqrt[d^2 + e^2]]) - ((A*e - B*(d + Sqrt[d^2 + e^2]))*Log[d + Sqrt[d^2 + e^2] + e*x - Sqrt[2]*Sqrt[d + Sqrt[d^2 + e^2]]*Sqrt[d + e*x]])/(2*Sqrt[2]*Sqrt[d^2 + e^2]*Sqrt[d + Sqrt[d^2 + e^2]]) + ((A*e - B*(d + Sqrt[d^2 + e^2]))*Log[d + Sqrt[d^2 + e^2] + e*x + Sqrt[2]*Sqrt[d + Sqrt[d^2 + e^2]]*Sqrt[d + e*x]])/(2*Sqrt[2]*Sqrt[d^2 + e^2]*Sqrt[d + Sqrt[d^2 + e^2]])","A",10,6,22,0.2727,1,"{827, 1169, 634, 618, 206, 628}"
1467,1,202,0,0.2339498,"\int \frac{(1-x) \sqrt{1+x}}{1+x^2} \, dx","Int[((1 - x)*Sqrt[1 + x])/(1 + x^2),x]","-2 \sqrt{x+1}-\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}}}-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)","-2 \sqrt{x+1}-\frac{\log \left(x-\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}}}+\frac{\log \left(x+\sqrt{2 \left(1+\sqrt{2}\right)} \sqrt{x+1}+\sqrt{2}+1\right)}{2 \sqrt{1+\sqrt{2}}}-\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{\sqrt{2 \left(1+\sqrt{2}\right)}-2 \sqrt{x+1}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)+\sqrt{1+\sqrt{2}} \tan ^{-1}\left(\frac{2 \sqrt{x+1}+\sqrt{2 \left(1+\sqrt{2}\right)}}{\sqrt{2 \left(\sqrt{2}-1\right)}}\right)",1,"-2*Sqrt[1 + x] - Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] - 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]] + Sqrt[1 + Sqrt[2]]*ArcTan[(Sqrt[2*(1 + Sqrt[2])] + 2*Sqrt[1 + x])/Sqrt[2*(-1 + Sqrt[2])]] - Log[1 + Sqrt[2] + x - Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(2*Sqrt[1 + Sqrt[2]]) + Log[1 + Sqrt[2] + x + Sqrt[2*(1 + Sqrt[2])]*Sqrt[1 + x]]/(2*Sqrt[1 + Sqrt[2]])","A",12,8,20,0.4000,1,"{825, 12, 708, 1094, 634, 618, 204, 628}"
1468,1,45,0,0.0542021,"\int \frac{3+x}{\sqrt{4+3 x} \left(1+x^2\right)} \, dx","Int[(3 + x)/(Sqrt[4 + 3*x]*(1 + x^2)),x]","\sqrt{2} \tan ^{-1}\left(\sqrt{6 x+8}+3\right)-\sqrt{2} \tan ^{-1}\left(3-\sqrt{2} \sqrt{3 x+4}\right)","\sqrt{2} \tan ^{-1}\left(\sqrt{6 x+8}+3\right)-\sqrt{2} \tan ^{-1}\left(3-\sqrt{2} \sqrt{3 x+4}\right)",1,"-(Sqrt[2]*ArcTan[3 - Sqrt[2]*Sqrt[4 + 3*x]]) + Sqrt[2]*ArcTan[3 + Sqrt[8 + 6*x]]","A",6,4,20,0.2000,1,"{827, 1161, 618, 204}"
1469,1,53,0,0.0535199,"\int \frac{1-3 x}{\sqrt{4+3 x} \left(1+x^2\right)} \, dx","Int[(1 - 3*x)/(Sqrt[4 + 3*x]*(1 + x^2)),x]","\frac{\log \left(x+\sqrt{2} \sqrt{3 x+4}+3\right)}{\sqrt{2}}-\frac{\log \left(x-\sqrt{2} \sqrt{3 x+4}+3\right)}{\sqrt{2}}","\frac{\log \left(x+\sqrt{2} \sqrt{3 x+4}+3\right)}{\sqrt{2}}-\frac{\log \left(x-\sqrt{2} \sqrt{3 x+4}+3\right)}{\sqrt{2}}",1,"-(Log[3 + x - Sqrt[2]*Sqrt[4 + 3*x]]/Sqrt[2]) + Log[3 + x + Sqrt[2]*Sqrt[4 + 3*x]]/Sqrt[2]","A",4,3,22,0.1364,1,"{827, 1164, 628}"
1470,1,29,0,0.0331659,"\int \frac{2+x}{\sqrt{3+4 x} \left(1+x^2\right)} \, dx","Int[(2 + x)/(Sqrt[3 + 4*x]*(1 + x^2)),x]","\tan ^{-1}\left(\sqrt{4 x+3}+2\right)-\tan ^{-1}\left(2-\sqrt{4 x+3}\right)","\tan ^{-1}\left(\sqrt{4 x+3}+2\right)-\tan ^{-1}\left(2-\sqrt{4 x+3}\right)",1,"-ArcTan[2 - Sqrt[3 + 4*x]] + ArcTan[2 + Sqrt[3 + 4*x]]","A",6,4,20,0.2000,1,"{827, 1161, 618, 204}"
1471,1,57,0,0.0751797,"\int \frac{-2+x}{\sqrt{-3+x} \left(-8+x^2\right)} \, dx","Int[(-2 + x)/(Sqrt[-3 + x]*(-8 + x^2)),x]","\frac{\tan ^{-1}\left(\frac{\sqrt{x-3}}{\sqrt{3-2 \sqrt{2}}}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\frac{\sqrt{x-3}}{\sqrt{3+2 \sqrt{2}}}\right)}{\sqrt{2}}","\frac{\tan ^{-1}\left(\left(\sqrt{2}-1\right) \sqrt{x-3}\right)}{\sqrt{2}}+\frac{\tan ^{-1}\left(\left(1+\sqrt{2}\right) \sqrt{x-3}\right)}{\sqrt{2}}",1,"ArcTan[Sqrt[-3 + x]/Sqrt[3 - 2*Sqrt[2]]]/Sqrt[2] + ArcTan[Sqrt[-3 + x]/Sqrt[3 + 2*Sqrt[2]]]/Sqrt[2]","A",4,3,18,0.1667,0,"{827, 1163, 203}"
1472,1,438,0,0.4611727,"\int (A+B x) \sqrt{d+e x} \sqrt{a+c x^2} \, dx","Int[(A + B*x)*Sqrt[d + e*x]*Sqrt[a + c*x^2],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(5 a B e^2-7 A c d e+4 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{3/2} e^3 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a B e^2-3 c e x (7 A e+B d)-7 A c d e+4 B c d^2\right)}{105 c e^2}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(21 a A e^3+8 a B d e^2-7 A c d^2 e+4 B c d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 B \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(5 a B e^2-7 A c d e+4 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 c^{3/2} e^3 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a B e^2-3 c e x (7 A e+B d)-7 A c d e+4 B c d^2\right)}{105 c e^2}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(21 a A e^3+8 a B d e^2-7 A c d^2 e+4 B c d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{105 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 B \left(a+c x^2\right)^{3/2} \sqrt{d+e x}}{7 c}",1,"(-2*Sqrt[d + e*x]*(4*B*c*d^2 - 7*A*c*d*e + 5*a*B*e^2 - 3*c*e*(B*d + 7*A*e)*x)*Sqrt[a + c*x^2])/(105*c*e^2) + (2*B*Sqrt[d + e*x]*(a + c*x^2)^(3/2))/(7*c) - (4*Sqrt[-a]*(4*B*c*d^3 - 7*A*c*d^2*e + 8*a*B*d*e^2 + 21*a*A*e^3)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(105*Sqrt[c]*e^3*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*(c*d^2 + a*e^2)*(4*B*c*d^2 - 7*A*c*d*e + 5*a*B*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(105*c^(3/2)*e^3*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,26,0.2308,1,"{833, 815, 844, 719, 424, 419}"
1473,1,365,0,0.3367353,"\int \frac{(A+B x) \sqrt{a+c x^2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/Sqrt[d + e*x],x]","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) (4 B d-5 A e) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a B e^2-5 A c d e+4 B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} (-5 A e+4 B d-3 B e x)}{15 e^2}","\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) (4 B d-5 A e) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a B e^2-5 A c d e+4 B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} (-5 A e+4 B d-3 B e x)}{15 e^2}",1,"(-2*Sqrt[d + e*x]*(4*B*d - 5*A*e - 3*B*e*x)*Sqrt[a + c*x^2])/(15*e^2) - (4*Sqrt[-a]*(4*B*c*d^2 - 5*A*c*d*e + 3*a*B*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*Sqrt[c]*e^3*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*(4*B*d - 5*A*e)*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*Sqrt[c]*e^3*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{815, 844, 719, 424, 419}"
1474,1,352,0,0.2520542,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/(d + e*x)^(3/2),x]","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(a B e^2-3 A c d e+4 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{a+c x^2} (-3 A e+4 B d+B e x)}{3 e^2 \sqrt{d+e x}}+\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (4 B d-3 A e) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","-\frac{4 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(a B e^2-3 A c d e+4 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} e^3 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \sqrt{a+c x^2} (-3 A e+4 B d+B e x)}{3 e^2 \sqrt{d+e x}}+\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (4 B d-3 A e) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^3 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(2*(4*B*d - 3*A*e + B*e*x)*Sqrt[a + c*x^2])/(3*e^2*Sqrt[d + e*x]) + (4*Sqrt[-a]*Sqrt[c]*(4*B*d - 3*A*e)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^3*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (4*Sqrt[-a]*(4*B*c*d^2 - 3*A*c*d*e + a*B*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[c]*e^3*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{813, 844, 719, 424, 419}"
1475,1,420,0,0.3415724,"\int \frac{(A+B x) \sqrt{a+c x^2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*Sqrt[a + c*x^2])/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{a+c x^2} \left(e x \left(3 a B e^2-2 A c d e+5 B c d^2\right)+a A e^3+2 a B d e^2-A c d^2 e+4 B c d^3\right)}{3 e^2 (d+e x)^{3/2} \left(a e^2+c d^2\right)}-\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a B e^2-A c d e+4 B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^3 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (4 B d-A e) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^3 \sqrt{a+c x^2} \sqrt{d+e x}}","-\frac{2 \sqrt{a+c x^2} \left(e x \left(3 a B e^2-2 A c d e+5 B c d^2\right)+a A e^3+2 a B d e^2-A c d^2 e+4 B c d^3\right)}{3 e^2 (d+e x)^{3/2} \left(a e^2+c d^2\right)}-\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(3 a B e^2-A c d e+4 B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^3 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} (4 B d-A e) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 e^3 \sqrt{a+c x^2} \sqrt{d+e x}}",1,"(-2*(4*B*c*d^3 - A*c*d^2*e + 2*a*B*d*e^2 + a*A*e^3 + e*(5*B*c*d^2 - 2*A*c*d*e + 3*a*B*e^2)*x)*Sqrt[a + c*x^2])/(3*e^2*(c*d^2 + a*e^2)*(d + e*x)^(3/2)) - (4*Sqrt[-a]*Sqrt[c]*(4*B*c*d^2 - A*c*d*e + 3*a*B*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^3*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (4*Sqrt[-a]*Sqrt[c]*(4*B*d - A*e)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*e^3*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{811, 844, 719, 424, 419}"
1476,1,498,0,0.5536774,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(36 A c d e \left(2 a e^2+c d^2\right)-B \left(21 a^2 e^4+57 a c d^2 e^2+32 c^2 d^4\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(-3 e x \left(7 a B e^2-9 A c d e+8 B c d^2\right)-45 a A e^3+33 a B d e^2-36 A c d^2 e+32 B c d^3\right)}{315 e^4}+\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(-45 a A e^3+33 a B d e^2-36 A c d^2 e+32 B c d^3\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^5 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} (-9 A e+8 B d-7 B e x)}{63 e^2}","\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(36 A c d e \left(2 a e^2+c d^2\right)-B \left(21 a^2 e^4+57 a c d^2 e^2+32 c^2 d^4\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(-3 e x \left(7 a B e^2-9 A c d e+8 B c d^2\right)-45 a A e^3+33 a B d e^2-36 A c d^2 e+32 B c d^3\right)}{315 e^4}+\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(-45 a A e^3+33 a B d e^2-36 A c d^2 e+32 B c d^3\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{315 \sqrt{c} e^5 \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \left(a+c x^2\right)^{3/2} \sqrt{d+e x} (-9 A e+8 B d-7 B e x)}{63 e^2}",1,"(-4*Sqrt[d + e*x]*(32*B*c*d^3 - 36*A*c*d^2*e + 33*a*B*d*e^2 - 45*a*A*e^3 - 3*e*(8*B*c*d^2 - 9*A*c*d*e + 7*a*B*e^2)*x)*Sqrt[a + c*x^2])/(315*e^4) - (2*Sqrt[d + e*x]*(8*B*d - 9*A*e - 7*B*e*x)*(a + c*x^2)^(3/2))/(63*e^2) + (8*Sqrt[-a]*(36*A*c*d*e*(c*d^2 + 2*a*e^2) - B*(32*c^2*d^4 + 57*a*c*d^2*e^2 + 21*a^2*e^4))*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(315*Sqrt[c]*e^5*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (8*Sqrt[-a]*(c*d^2 + a*e^2)*(32*B*c*d^3 - 36*A*c*d^2*e + 33*a*B*d*e^2 - 45*a*A*e^3)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(315*Sqrt[c]*e^5*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,5,26,0.1923,1,"{815, 844, 719, 424, 419}"
1477,1,448,0,0.4444388,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(d + e*x)^(3/2),x]","-\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(5 a B e^2-28 A c d e+32 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 \sqrt{c} e^5 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a A e^3+29 a B d e^2-28 A c d^2 e+32 B c d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \left(a+c x^2\right)^{3/2} (-7 A e+8 B d+B e x)}{7 e^2 \sqrt{d+e x}}+\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a B e^2-3 c e x (8 B d-7 A e)+4 c d (8 B d-7 A e)\right)}{35 e^4}","-\frac{8 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(5 a B e^2-28 A c d e+32 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 \sqrt{c} e^5 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-21 a A e^3+29 a B d e^2-28 A c d^2 e+32 B c d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{35 e^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \left(a+c x^2\right)^{3/2} (-7 A e+8 B d+B e x)}{7 e^2 \sqrt{d+e x}}+\frac{4 \sqrt{a+c x^2} \sqrt{d+e x} \left(5 a B e^2-3 c e x (8 B d-7 A e)+4 c d (8 B d-7 A e)\right)}{35 e^4}",1,"(4*Sqrt[d + e*x]*(5*a*B*e^2 + 4*c*d*(8*B*d - 7*A*e) - 3*c*e*(8*B*d - 7*A*e)*x)*Sqrt[a + c*x^2])/(35*e^4) + (2*(8*B*d - 7*A*e + B*e*x)*(a + c*x^2)^(3/2))/(7*e^2*Sqrt[d + e*x]) + (8*Sqrt[-a]*Sqrt[c]*(32*B*c*d^3 - 28*A*c*d^2*e + 29*a*B*d*e^2 - 21*a*A*e^3)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(35*e^5*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (8*Sqrt[-a]*(c*d^2 + a*e^2)*(32*B*c*d^2 - 28*A*c*d*e + 5*a*B*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(35*Sqrt[c]*e^5*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,26,0.2308,1,"{813, 815, 844, 719, 424, 419}"
1478,1,437,0,0.460759,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(-5 a A e^3+17 a B d e^2-20 A c d^2 e+32 B c d^3\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \left(a+c x^2\right)^{3/2} (-5 A e+8 B d+3 B e x)}{15 e^2 (d+e x)^{3/2}}-\frac{4 \sqrt{a+c x^2} \left(9 a B e^2+c e x (8 B d-5 A e)+4 c d (8 B d-5 A e)\right)}{15 e^4 \sqrt{d+e x}}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(9 a B e^2+4 c d (8 B d-5 A e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(-5 a A e^3+17 a B d e^2-20 A c d^2 e+32 B c d^3\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 \left(a+c x^2\right)^{3/2} (-5 A e+8 B d+3 B e x)}{15 e^2 (d+e x)^{3/2}}-\frac{4 \sqrt{a+c x^2} \left(9 a B e^2+c e x (8 B d-5 A e)+4 c d (8 B d-5 A e)\right)}{15 e^4 \sqrt{d+e x}}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(9 a B e^2+4 c d (8 B d-5 A e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(-4*(9*a*B*e^2 + 4*c*d*(8*B*d - 5*A*e) + c*e*(8*B*d - 5*A*e)*x)*Sqrt[a + c*x^2])/(15*e^4*Sqrt[d + e*x]) + (2*(8*B*d - 5*A*e + 3*B*e*x)*(a + c*x^2)^(3/2))/(15*e^2*(d + e*x)^(3/2)) - (8*Sqrt[-a]*Sqrt[c]*(9*a*B*e^2 + 4*c*d*(8*B*d - 5*A*e))*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^5*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (8*Sqrt[-a]*Sqrt[c]*(32*B*c*d^3 - 20*A*c*d^2*e + 17*a*B*d*e^2 - 5*a*A*e^3)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^5*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,5,26,0.1923,1,"{813, 844, 719, 424, 419}"
1479,1,541,0,0.4714427,"\int \frac{(A+B x) \left(a+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a + c*x^2)^(3/2))/(d + e*x)^(7/2),x]","\frac{8 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-9 a A e^3+29 a B d e^2-12 A c d^2 e+32 B c d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 c \sqrt{a+c x^2} \left(e x \left(5 a B e^2-3 A c d e+8 B c d^2\right)-9 a A e^3+29 a B d e^2-12 A c d^2 e+32 B c d^3\right)}{15 e^4 \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{3/2} \left(e x \left(5 a B e^2-6 A c d e+11 B c d^2\right)-3 A \left(c d^2 e-a e^3\right)+2 B \left(a d e^2+4 c d^3\right)\right)}{15 e^2 (d+e x)^{5/2} \left(a e^2+c d^2\right)}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(5 a B e^2-12 A c d e+32 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \sqrt{d+e x}}","\frac{8 \sqrt{-a} c^{3/2} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-9 a A e^3+29 a B d e^2-12 A c d^2 e+32 B c d^3\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{4 c \sqrt{a+c x^2} \left(e x \left(5 a B e^2-3 A c d e+8 B c d^2\right)-9 a A e^3+29 a B d e^2-12 A c d^2 e+32 B c d^3\right)}{15 e^4 \sqrt{d+e x} \left(a e^2+c d^2\right)}-\frac{2 \left(a+c x^2\right)^{3/2} \left(e x \left(5 a B e^2-6 A c d e+11 B c d^2\right)-3 A \left(c d^2 e-a e^3\right)+2 B \left(a d e^2+4 c d^3\right)\right)}{15 e^2 (d+e x)^{5/2} \left(a e^2+c d^2\right)}-\frac{8 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} \left(5 a B e^2-12 A c d e+32 B c d^2\right) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 e^5 \sqrt{a+c x^2} \sqrt{d+e x}}",1,"(4*c*(32*B*c*d^3 - 12*A*c*d^2*e + 29*a*B*d*e^2 - 9*a*A*e^3 + e*(8*B*c*d^2 - 3*A*c*d*e + 5*a*B*e^2)*x)*Sqrt[a + c*x^2])/(15*e^4*(c*d^2 + a*e^2)*Sqrt[d + e*x]) - (2*(2*B*(4*c*d^3 + a*d*e^2) - 3*A*(c*d^2*e - a*e^3) + e*(11*B*c*d^2 - 6*A*c*d*e + 5*a*B*e^2)*x)*(a + c*x^2)^(3/2))/(15*e^2*(c*d^2 + a*e^2)*(d + e*x)^(5/2)) + (8*Sqrt[-a]*c^(3/2)*(32*B*c*d^3 - 12*A*c*d^2*e + 29*a*B*d*e^2 - 9*a*A*e^3)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^5*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (8*Sqrt[-a]*Sqrt[c]*(32*B*c*d^2 - 12*A*c*d*e + 5*a*B*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*e^5*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,6,26,0.2308,1,"{811, 813, 844, 719, 424, 419}"
1480,1,388,0,0.4079385,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a + c*x^2],x]","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) (5 A e+3 B d) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} e \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-9 a B e^2+20 A c d e+3 B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} (5 A e+3 B d)}{15 c}+\frac{2 B \sqrt{a+c x^2} (d+e x)^{3/2}}{5 c}","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) (5 A e+3 B d) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} e \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} \left(-9 a B e^2+20 A c d e+3 B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{15 c^{3/2} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{a+c x^2} \sqrt{d+e x} (5 A e+3 B d)}{15 c}+\frac{2 B \sqrt{a+c x^2} (d+e x)^{3/2}}{5 c}",1,"(2*(3*B*d + 5*A*e)*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(15*c) + (2*B*(d + e*x)^(3/2)*Sqrt[a + c*x^2])/(5*c) - (2*Sqrt[-a]*(3*B*c*d^2 + 20*A*c*d*e - 9*a*B*e^2)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*c^(3/2)*e*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*(3*B*d + 5*A*e)*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(15*c^(3/2)*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",7,5,26,0.1923,1,"{833, 844, 719, 424, 419}"
1481,1,331,0,0.2598869,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a+c x^2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/Sqrt[a + c*x^2],x]","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (3 A e+B d) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{-a} B \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 c^{3/2} e \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 B \sqrt{a+c x^2} \sqrt{d+e x}}{3 c}","-\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (3 A e+B d) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 \sqrt{c} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{2 \sqrt{-a} B \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{3 c^{3/2} e \sqrt{a+c x^2} \sqrt{d+e x}}+\frac{2 B \sqrt{a+c x^2} \sqrt{d+e x}}{3 c}",1,"(2*B*Sqrt[d + e*x]*Sqrt[a + c*x^2])/(3*c) - (2*Sqrt[-a]*(B*d + 3*A*e)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*Sqrt[c]*e*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*B*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(3*c^(3/2)*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{833, 844, 719, 424, 419}"
1482,1,288,0,0.1650751,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*Sqrt[a + c*x^2]),x]","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} (B d-A e) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-a} B \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{2 \sqrt{-a} \sqrt{\frac{c x^2}{a}+1} (B d-A e) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{2 \sqrt{-a} B \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"(-2*Sqrt[-a]*B*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[c]*e*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (2*Sqrt[-a]*(B*d - A*e)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[c]*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",5,4,26,0.1538,1,"{844, 719, 424, 419}"
1483,1,344,0,0.2613591,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{a+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*Sqrt[a + c*x^2]),x]","\frac{2 \sqrt{a+c x^2} (B d-A e)}{\sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (B d-A e) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{e \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 \sqrt{-a} B \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{d+e x}}","\frac{2 \sqrt{a+c x^2} (B d-A e)}{\sqrt{d+e x} \left(a e^2+c d^2\right)}+\frac{2 \sqrt{-a} \sqrt{c} \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (B d-A e) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{e \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{2 \sqrt{-a} B \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{c} e \sqrt{a+c x^2} \sqrt{d+e x}}",1,"(2*(B*d - A*e)*Sqrt[a + c*x^2])/((c*d^2 + a*e^2)*Sqrt[d + e*x]) + (2*Sqrt[-a]*Sqrt[c]*(B*d - A*e)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(e*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) - (2*Sqrt[-a]*B*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[c]*e*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{835, 844, 719, 424, 419}"
1484,1,345,0,0.2855665,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a + c*x^2)^(3/2),x]","-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (A c d-3 a B e) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{\sqrt{d+e x} (a (A e+B d)-x (A c d-a B e))}{a c \sqrt{a+c x^2}}+\frac{A \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}","-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (A c d-3 a B e) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}-\frac{\sqrt{d+e x} (a (A e+B d)-x (A c d-a B e))}{a c \sqrt{a+c x^2}}+\frac{A \sqrt{\frac{c x^2}{a}+1} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}",1,"-((Sqrt[d + e*x]*(a*(B*d + A*e) - (A*c*d - a*B*e)*x))/(a*c*Sqrt[a + c*x^2])) - ((A*c*d - 3*a*B*e)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*c^(3/2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (A*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{819, 844, 719, 424, 419}"
1485,1,319,0,0.2288645,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a + c*x^2)^(3/2),x]","\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} (a B e+A c d) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{d+e x} (a B-A c x)}{a c \sqrt{a+c x^2}}-\frac{A \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}","\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} (a B e+A c d) F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} c^{3/2} \sqrt{a+c x^2} \sqrt{d+e x}}-\frac{\sqrt{d+e x} (a B-A c x)}{a c \sqrt{a+c x^2}}-\frac{A \sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}",1,"-(((a*B - A*c*x)*Sqrt[d + e*x])/(a*c*Sqrt[a + c*x^2])) - (A*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + ((A*c*d + a*B*e)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*c^(3/2)*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{821, 844, 719, 424, 419}"
1486,1,356,0,0.281557,"\int \frac{A+B x}{\sqrt{d+e x} \left(a+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a + c*x^2)^(3/2)),x]","-\frac{\sqrt{d+e x} (a (B d-A e)-x (a B e+A c d))}{a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (a B e+A c d) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{A \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}","-\frac{\sqrt{d+e x} (a (B d-A e)-x (a B e+A c d))}{a \sqrt{a+c x^2} \left(a e^2+c d^2\right)}-\frac{\sqrt{\frac{c x^2}{a}+1} \sqrt{d+e x} (a B e+A c d) E\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \left(a e^2+c d^2\right) \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}}}+\frac{A \sqrt{\frac{c x^2}{a}+1} \sqrt{\frac{\sqrt{c} (d+e x)}{\sqrt{-a} e+\sqrt{c} d}} F\left(\sin ^{-1}\left(\frac{\sqrt{1-\frac{\sqrt{c} x}{\sqrt{-a}}}}{\sqrt{2}}\right)|-\frac{2 a e}{\sqrt{-a} \sqrt{c} d-a e}\right)}{\sqrt{-a} \sqrt{c} \sqrt{a+c x^2} \sqrt{d+e x}}",1,"-((Sqrt[d + e*x]*(a*(B*d - A*e) - (A*c*d + a*B*e)*x))/(a*(c*d^2 + a*e^2)*Sqrt[a + c*x^2])) - ((A*c*d + a*B*e)*Sqrt[d + e*x]*Sqrt[1 + (c*x^2)/a]*EllipticE[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*(c*d^2 + a*e^2)*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[a + c*x^2]) + (A*Sqrt[(Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)]*Sqrt[1 + (c*x^2)/a]*EllipticF[ArcSin[Sqrt[1 - (Sqrt[c]*x)/Sqrt[-a]]/Sqrt[2]], (-2*a*e)/(Sqrt[-a]*Sqrt[c]*d - a*e)])/(Sqrt[-a]*Sqrt[c]*Sqrt[d + e*x]*Sqrt[a + c*x^2])","A",6,5,26,0.1923,1,"{823, 844, 719, 424, 419}"
1487,1,372,0,0.250634,"\int (A+B x) (d+e x)^m \left(a+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^m*(a + c*x^2)^3,x]","-\frac{c (d+e x)^{m+4} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8 (m+4)}-\frac{c^2 (d+e x)^{m+5} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8 (m+5)}+\frac{3 c^2 (d+e x)^{m+6} \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8 (m+6)}-\frac{\left(a e^2+c d^2\right)^3 (B d-A e) (d+e x)^{m+1}}{e^8 (m+1)}+\frac{\left(a e^2+c d^2\right)^2 (d+e x)^{m+2} \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8 (m+2)}-\frac{3 c \left(a e^2+c d^2\right) (d+e x)^{m+3} \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (m+3)}-\frac{c^3 (7 B d-A e) (d+e x)^{m+7}}{e^8 (m+7)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)}","-\frac{c (d+e x)^{m+4} \left(4 A c d e \left(3 a e^2+5 c d^2\right)-B \left(3 a^2 e^4+30 a c d^2 e^2+35 c^2 d^4\right)\right)}{e^8 (m+4)}-\frac{c^2 (d+e x)^{m+5} \left(-3 a A e^3+15 a B d e^2-15 A c d^2 e+35 B c d^3\right)}{e^8 (m+5)}+\frac{3 c^2 (d+e x)^{m+6} \left(a B e^2-2 A c d e+7 B c d^2\right)}{e^8 (m+6)}-\frac{\left(a e^2+c d^2\right)^3 (B d-A e) (d+e x)^{m+1}}{e^8 (m+1)}+\frac{\left(a e^2+c d^2\right)^2 (d+e x)^{m+2} \left(a B e^2-6 A c d e+7 B c d^2\right)}{e^8 (m+2)}-\frac{3 c \left(a e^2+c d^2\right) (d+e x)^{m+3} \left(-a A e^3+3 a B d e^2-5 A c d^2 e+7 B c d^3\right)}{e^8 (m+3)}-\frac{c^3 (7 B d-A e) (d+e x)^{m+7}}{e^8 (m+7)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)}",1,"-(((B*d - A*e)*(c*d^2 + a*e^2)^3*(d + e*x)^(1 + m))/(e^8*(1 + m))) + ((c*d^2 + a*e^2)^2*(7*B*c*d^2 - 6*A*c*d*e + a*B*e^2)*(d + e*x)^(2 + m))/(e^8*(2 + m)) - (3*c*(c*d^2 + a*e^2)*(7*B*c*d^3 - 5*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(3 + m))/(e^8*(3 + m)) - (c*(4*A*c*d*e*(5*c*d^2 + 3*a*e^2) - B*(35*c^2*d^4 + 30*a*c*d^2*e^2 + 3*a^2*e^4))*(d + e*x)^(4 + m))/(e^8*(4 + m)) - (c^2*(35*B*c*d^3 - 15*A*c*d^2*e + 15*a*B*d*e^2 - 3*a*A*e^3)*(d + e*x)^(5 + m))/(e^8*(5 + m)) + (3*c^2*(7*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (c^3*(7*B*d - A*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (B*c^3*(d + e*x)^(8 + m))/(e^8*(8 + m))","A",2,1,22,0.04545,1,"{772}"
1488,1,234,0,0.1364683,"\int (A+B x) (d+e x)^m \left(a+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^m*(a + c*x^2)^2,x]","-\frac{\left(a e^2+c d^2\right)^2 (B d-A e) (d+e x)^{m+1}}{e^6 (m+1)}+\frac{\left(a e^2+c d^2\right) (d+e x)^{m+2} \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6 (m+2)}-\frac{2 c (d+e x)^{m+3} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 (m+3)}+\frac{2 c (d+e x)^{m+4} \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (m+4)}-\frac{c^2 (5 B d-A e) (d+e x)^{m+5}}{e^6 (m+5)}+\frac{B c^2 (d+e x)^{m+6}}{e^6 (m+6)}","-\frac{\left(a e^2+c d^2\right)^2 (B d-A e) (d+e x)^{m+1}}{e^6 (m+1)}+\frac{\left(a e^2+c d^2\right) (d+e x)^{m+2} \left(a B e^2-4 A c d e+5 B c d^2\right)}{e^6 (m+2)}-\frac{2 c (d+e x)^{m+3} \left(-a A e^3+3 a B d e^2-3 A c d^2 e+5 B c d^3\right)}{e^6 (m+3)}+\frac{2 c (d+e x)^{m+4} \left(a B e^2-2 A c d e+5 B c d^2\right)}{e^6 (m+4)}-\frac{c^2 (5 B d-A e) (d+e x)^{m+5}}{e^6 (m+5)}+\frac{B c^2 (d+e x)^{m+6}}{e^6 (m+6)}",1,"-(((B*d - A*e)*(c*d^2 + a*e^2)^2*(d + e*x)^(1 + m))/(e^6*(1 + m))) + ((c*d^2 + a*e^2)*(5*B*c*d^2 - 4*A*c*d*e + a*B*e^2)*(d + e*x)^(2 + m))/(e^6*(2 + m)) - (2*c*(5*B*c*d^3 - 3*A*c*d^2*e + 3*a*B*d*e^2 - a*A*e^3)*(d + e*x)^(3 + m))/(e^6*(3 + m)) + (2*c*(5*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (c^2*(5*B*d - A*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (B*c^2*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,22,0.04545,1,"{772}"
1489,1,126,0,0.0691842,"\int (A+B x) (d+e x)^m \left(a+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^m*(a + c*x^2),x]","-\frac{\left(a e^2+c d^2\right) (B d-A e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(d+e x)^{m+2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4 (m+2)}-\frac{c (3 B d-A e) (d+e x)^{m+3}}{e^4 (m+3)}+\frac{B c (d+e x)^{m+4}}{e^4 (m+4)}","-\frac{\left(a e^2+c d^2\right) (B d-A e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(d+e x)^{m+2} \left(a B e^2-2 A c d e+3 B c d^2\right)}{e^4 (m+2)}-\frac{c (3 B d-A e) (d+e x)^{m+3}}{e^4 (m+3)}+\frac{B c (d+e x)^{m+4}}{e^4 (m+4)}",1,"-(((B*d - A*e)*(c*d^2 + a*e^2)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((3*B*c*d^2 - 2*A*c*d*e + a*B*e^2)*(d + e*x)^(2 + m))/(e^4*(2 + m)) - (c*(3*B*d - A*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (B*c*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,20,0.05000,1,"{772}"
1490,1,202,0,0.2744797,"\int \frac{(A+B x) (d+e x)^m}{a+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a + c*x^2),x]","-\frac{\left(\sqrt{-a} A \sqrt{c}+a B\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a \sqrt{c} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{\left(\frac{\sqrt{-a} B}{\sqrt{c}}+A\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}","-\frac{\left(\sqrt{-a} A \sqrt{c}+a B\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a \sqrt{c} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{\left(\frac{\sqrt{-a} B}{\sqrt{c}}+A\right) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"-((a*B + Sqrt[-a]*A*Sqrt[c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*a*Sqrt[c]*(Sqrt[c]*d - Sqrt[-a]*e)*(1 + m)) - ((A + (Sqrt[-a]*B)/Sqrt[c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(1 + m))","A",4,2,22,0.09091,1,"{831, 68}"
1491,1,359,0,0.5827537,"\int \frac{(A+B x) (d+e x)^m}{\left(a+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a + c*x^2)^2,x]","\frac{(d+e x)^{m+1} \left(a e m (a B e+A c d)-\sqrt{-a} \sqrt{c} \left(a A e^2 (1-m)+a B d e m+A c d^2\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 a^2 \sqrt{c} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{m+1} \left(\sqrt{-a} \sqrt{c} \left(a A e^2 (1-m)+a B d e m+A c d^2\right)+a e m (a B e+A c d)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 a^2 \sqrt{c} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{m+1} (a (B d-A e)-x (a B e+A c d))}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}","\frac{(d+e x)^{m+1} \left(a e m (a B e+A c d)-\sqrt{-a} \sqrt{c} \left(A \left(a e^2 (1-m)+c d^2\right)+a B d e m\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{4 a^2 \sqrt{c} (m+1) \left(\sqrt{c} d-\sqrt{-a} e\right) \left(a e^2+c d^2\right)}+\frac{(d+e x)^{m+1} \left(\sqrt{-a} \sqrt{c} \left(A \left(a e^2 (1-m)+c d^2\right)+a B d e m\right)+a e m (a B e+A c d)\right) \, _2F_1\left(1,m+1;m+2;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{4 a^2 \sqrt{c} (m+1) \left(\sqrt{-a} e+\sqrt{c} d\right) \left(a e^2+c d^2\right)}-\frac{(d+e x)^{m+1} (a (B d-A e)-x (a B e+A c d))}{2 a \left(a+c x^2\right) \left(a e^2+c d^2\right)}",1,"-((d + e*x)^(1 + m)*(a*(B*d - A*e) - (A*c*d + a*B*e)*x))/(2*a*(c*d^2 + a*e^2)*(a + c*x^2)) + ((a*e*(A*c*d + a*B*e)*m - Sqrt[-a]*Sqrt[c]*(A*c*d^2 + a*A*e^2*(1 - m) + a*B*d*e*m))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(4*a^2*Sqrt[c]*(Sqrt[c]*d - Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + m)) + ((a*e*(A*c*d + a*B*e)*m + Sqrt[-a]*Sqrt[c]*(A*c*d^2 + a*A*e^2*(1 - m) + a*B*d*e*m))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(4*a^2*Sqrt[c]*(Sqrt[c]*d + Sqrt[-a]*e)*(c*d^2 + a*e^2)*(1 + m))","A",5,3,22,0.1364,1,"{823, 831, 68}"
1492,1,202,0,0.1855704,"\int \frac{(A+B x) (d+e x)^{1+m}}{a+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(1 + m))/(a + c*x^2),x]","-\frac{\left(\sqrt{-a} A \sqrt{c}+a B\right) (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a \sqrt{c} (m+2) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{\left(\frac{\sqrt{-a} B}{\sqrt{c}}+A\right) (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+2) \left(\sqrt{-a} e+\sqrt{c} d\right)}","-\frac{\left(\sqrt{-a} A \sqrt{c}+a B\right) (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d-\sqrt{-a} e}\right)}{2 a \sqrt{c} (m+2) \left(\sqrt{c} d-\sqrt{-a} e\right)}-\frac{\left(\frac{\sqrt{-a} B}{\sqrt{c}}+A\right) (d+e x)^{m+2} \, _2F_1\left(1,m+2;m+3;\frac{\sqrt{c} (d+e x)}{\sqrt{c} d+\sqrt{-a} e}\right)}{2 \sqrt{-a} (m+2) \left(\sqrt{-a} e+\sqrt{c} d\right)}",1,"-((a*B + Sqrt[-a]*A*Sqrt[c])*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d - Sqrt[-a]*e)])/(2*a*Sqrt[c]*(Sqrt[c]*d - Sqrt[-a]*e)*(2 + m)) - ((A + (Sqrt[-a]*B)/Sqrt[c])*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (Sqrt[c]*(d + e*x))/(Sqrt[c]*d + Sqrt[-a]*e)])/(2*Sqrt[-a]*(Sqrt[c]*d + Sqrt[-a]*e)*(2 + m))","A",4,2,24,0.08333,1,"{831, 68}"
1493,1,31,0,0.0188862,"\int (-a e+c d x) (d+e x)^{-3-2 p} \left(a+c x^2\right)^p \, dx","Int[(-(a*e) + c*d*x)*(d + e*x)^(-3 - 2*p)*(a + c*x^2)^p,x]","\frac{\left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1)}","\frac{\left(a+c x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1)}",1,"(a + c*x^2)^(1 + p)/(2*(1 + p)*(d + e*x)^(2*(1 + p)))","A",1,1,30,0.03333,1,"{803}"
1494,1,124,0,0.1892659,"\int (b+2 c x) (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{(d+e x)^6 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{6 e^4}-\frac{(d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{3 c (d+e x)^7 (2 c d-b e)}{7 e^4}+\frac{c^2 (d+e x)^8}{4 e^4}","\frac{(d+e x)^6 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{6 e^4}-\frac{(d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{3 c (d+e x)^7 (2 c d-b e)}{7 e^4}+\frac{c^2 (d+e x)^8}{4 e^4}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5)/(5*e^4) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^6)/(6*e^4) - (3*c*(2*c*d - b*e)*(d + e*x)^7)/(7*e^4) + (c^2*(d + e*x)^8)/(4*e^4)","A",2,1,24,0.04167,1,"{771}"
1495,1,124,0,0.1419306,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{(d+e x)^5 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^4}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{4 e^4}-\frac{c (d+e x)^6 (2 c d-b e)}{2 e^4}+\frac{2 c^2 (d+e x)^7}{7 e^4}","\frac{(d+e x)^5 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^4}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{4 e^4}-\frac{c (d+e x)^6 (2 c d-b e)}{2 e^4}+\frac{2 c^2 (d+e x)^7}{7 e^4}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4)/(4*e^4) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^5)/(5*e^4) - (c*(2*c*d - b*e)*(d + e*x)^6)/(2*e^4) + (2*c^2*(d + e*x)^7)/(7*e^4)","A",2,1,24,0.04167,1,"{771}"
1496,1,124,0,0.1091093,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{(d+e x)^4 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{4 e^4}-\frac{(d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4}-\frac{3 c (d+e x)^5 (2 c d-b e)}{5 e^4}+\frac{c^2 (d+e x)^6}{3 e^4}","\frac{(d+e x)^4 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{4 e^4}-\frac{(d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4}-\frac{3 c (d+e x)^5 (2 c d-b e)}{5 e^4}+\frac{c^2 (d+e x)^6}{3 e^4}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3)/(3*e^4) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^4)/(4*e^4) - (3*c*(2*c*d - b*e)*(d + e*x)^5)/(5*e^4) + (c^2*(d + e*x)^6)/(3*e^4)","A",2,1,24,0.04167,1,"{771}"
1497,1,79,0,0.0642936,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2),x]","\frac{1}{3} x^3 \left(2 a c e+b^2 e+3 b c d\right)+\frac{1}{2} x^2 \left(a b e+2 a c d+b^2 d\right)+a b d x+\frac{1}{4} c x^4 (3 b e+2 c d)+\frac{2}{5} c^2 e x^5","\frac{1}{3} x^3 \left(2 a c e+b^2 e+3 b c d\right)+\frac{1}{2} x^2 \left(a b e+2 a c d+b^2 d\right)+a b d x+\frac{1}{4} c x^4 (3 b e+2 c d)+\frac{2}{5} c^2 e x^5",1,"a*b*d*x + ((b^2*d + 2*a*c*d + a*b*e)*x^2)/2 + ((3*b*c*d + b^2*e + 2*a*c*e)*x^3)/3 + (c*(2*c*d + 3*b*e)*x^4)/4 + (2*c^2*e*x^5)/5","A",2,1,22,0.04545,1,"{771}"
1498,1,16,0,0.0036006,"\int (b+2 c x) \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2),x]","\frac{1}{2} \left(a+b x+c x^2\right)^2","\frac{1}{2} \left(a+b x+c x^2\right)^2",1,"(a + b*x + c*x^2)^2/2","A",1,1,17,0.05882,1,"{629}"
1499,1,104,0,0.1117068,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{d+e x} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x),x]","\frac{x \left(-c e (3 b d-2 a e)+b^2 e^2+2 c^2 d^2\right)}{e^3}-\frac{(2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{c x^2 (2 c d-3 b e)}{2 e^2}+\frac{2 c^2 x^3}{3 e}","\frac{x \left(-c e (3 b d-2 a e)+b^2 e^2+2 c^2 d^2\right)}{e^3}-\frac{(2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{c x^2 (2 c d-3 b e)}{2 e^2}+\frac{2 c^2 x^3}{3 e}",1,"((2*c^2*d^2 + b^2*e^2 - c*e*(3*b*d - 2*a*e))*x)/e^3 - (c*(2*c*d - 3*b*e)*x^2)/(2*e^2) + (2*c^2*x^3)/(3*e) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Log[d + e*x])/e^4","A",2,1,24,0.04167,1,"{771}"
1500,1,102,0,0.1025494,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^2} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^2,x]","\frac{\log (d+e x) \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}-\frac{c x (4 c d-3 b e)}{e^3}+\frac{c^2 x^2}{e^2}","\frac{\log (d+e x) \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}-\frac{c x (4 c d-3 b e)}{e^3}+\frac{c^2 x^2}{e^2}",1,"-((c*(4*c*d - 3*b*e)*x)/e^3) + (c^2*x^2)/e^2 + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(e^4*(d + e*x)) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*Log[d + e*x])/e^4","A",2,1,24,0.04167,1,"{771}"
1501,1,111,0,0.0937636,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^3} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^3,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{e^4 (d+e x)}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}-\frac{3 c (2 c d-b e) \log (d+e x)}{e^4}+\frac{2 c^2 x}{e^3}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{e^4 (d+e x)}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}-\frac{3 c (2 c d-b e) \log (d+e x)}{e^4}+\frac{2 c^2 x}{e^3}",1,"(2*c^2*x)/e^3 + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(2*e^4*(d + e*x)^2) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(e^4*(d + e*x)) - (3*c*(2*c*d - b*e)*Log[d + e*x])/e^4","A",2,1,24,0.04167,1,"{771}"
1502,1,119,0,0.0947904,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^4} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^4,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{2 e^4 (d+e x)^2}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^3}+\frac{3 c (2 c d-b e)}{e^4 (d+e x)}+\frac{2 c^2 \log (d+e x)}{e^4}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{2 e^4 (d+e x)^2}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^3}+\frac{3 c (2 c d-b e)}{e^4 (d+e x)}+\frac{2 c^2 \log (d+e x)}{e^4}",1,"((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(3*e^4*(d + e*x)^3) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(2*e^4*(d + e*x)^2) + (3*c*(2*c*d - b*e))/(e^4*(d + e*x)) + (2*c^2*Log[d + e*x])/e^4","A",2,1,24,0.04167,1,"{771}"
1503,1,122,0,0.0902768,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^5} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^5,x]","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{3 e^4 (d+e x)^3}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{4 e^4 (d+e x)^4}+\frac{3 c (2 c d-b e)}{2 e^4 (d+e x)^2}-\frac{2 c^2}{e^4 (d+e x)}","-\frac{-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2}{3 e^4 (d+e x)^3}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)}{4 e^4 (d+e x)^4}+\frac{3 c (2 c d-b e)}{2 e^4 (d+e x)^2}-\frac{2 c^2}{e^4 (d+e x)}",1,"((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(4*e^4*(d + e*x)^4) - (6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))/(3*e^4*(d + e*x)^3) + (3*c*(2*c*d - b*e))/(2*e^4*(d + e*x)^2) - (2*c^2)/(e^4*(d + e*x))","A",2,1,24,0.04167,1,"{771}"
1504,1,240,0,0.4159311,"\int (b+2 c x) (d+e x)^4 \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)^4*(a + b*x + c*x^2)^2,x]","\frac{c (d+e x)^8 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^6}-\frac{(d+e x)^7 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^6}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{(d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6}-\frac{5 c^2 (d+e x)^9 (2 c d-b e)}{9 e^6}+\frac{c^3 (d+e x)^{10}}{5 e^6}","\frac{c (d+e x)^8 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^6}-\frac{(d+e x)^7 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^6}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{(d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6}-\frac{5 c^2 (d+e x)^9 (2 c d-b e)}{9 e^6}+\frac{c^3 (d+e x)^{10}}{5 e^6}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^5)/(5*e^6) + ((c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^6)/(3*e^6) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^7)/(7*e^6) + (c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^8)/(2*e^6) - (5*c^2*(2*c*d - b*e)*(d + e*x)^9)/(9*e^6) + (c^3*(d + e*x)^10)/(5*e^6)","A",2,1,26,0.03846,1,"{771}"
1505,1,240,0,0.3163372,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^2,x]","\frac{4 c (d+e x)^7 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^6}-\frac{(d+e x)^6 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{6 e^6}+\frac{2 (d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^6}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6}-\frac{5 c^2 (d+e x)^8 (2 c d-b e)}{8 e^6}+\frac{2 c^3 (d+e x)^9}{9 e^6}","\frac{4 c (d+e x)^7 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^6}-\frac{(d+e x)^6 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{6 e^6}+\frac{2 (d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^6}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6}-\frac{5 c^2 (d+e x)^8 (2 c d-b e)}{8 e^6}+\frac{2 c^3 (d+e x)^9}{9 e^6}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4)/(4*e^6) + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^5)/(5*e^6) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^6)/(6*e^6) + (4*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^7)/(7*e^6) - (5*c^2*(2*c*d - b*e)*(d + e*x)^8)/(8*e^6) + (2*c^3*(d + e*x)^9)/(9*e^6)","A",2,1,26,0.03846,1,"{771}"
1506,1,240,0,0.2317659,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^2,x]","\frac{2 c (d+e x)^6 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{(d+e x)^5 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^6}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^6}-\frac{(d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6}-\frac{5 c^2 (d+e x)^7 (2 c d-b e)}{7 e^6}+\frac{c^3 (d+e x)^8}{4 e^6}","\frac{2 c (d+e x)^6 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{(d+e x)^5 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^6}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^6}-\frac{(d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6}-\frac{5 c^2 (d+e x)^7 (2 c d-b e)}{7 e^6}+\frac{c^3 (d+e x)^8}{4 e^6}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3)/(3*e^6) + ((c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^4)/(2*e^6) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^5)/(5*e^6) + (2*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^6)/(3*e^6) - (5*c^2*(2*c*d - b*e)*(d + e*x)^7)/(7*e^6) + (c^3*(d + e*x)^8)/(4*e^6)","A",2,1,26,0.03846,1,"{771}"
1507,1,153,0,0.1306951,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2)^2,x]","\frac{1}{3} x^3 \left(2 a^2 c e+2 a b^2 e+6 a b c d+b^3 d\right)+a^2 b d x+\frac{1}{4} x^4 \left(6 a b c e+4 a c^2 d+4 b^2 c d+b^3 e\right)+\frac{1}{5} c x^5 \left(4 a c e+4 b^2 e+5 b c d\right)+\frac{1}{2} a x^2 \left(a b e+2 a c d+2 b^2 d\right)+\frac{1}{6} c^2 x^6 (5 b e+2 c d)+\frac{2}{7} c^3 e x^7","\frac{1}{3} x^3 \left(2 a^2 c e+2 a b^2 e+6 a b c d+b^3 d\right)+a^2 b d x+\frac{1}{4} x^4 \left(6 a b c e+4 a c^2 d+4 b^2 c d+b^3 e\right)+\frac{1}{5} c x^5 \left(4 a c e+4 b^2 e+5 b c d\right)+\frac{1}{2} a x^2 \left(a b e+2 a c d+2 b^2 d\right)+\frac{1}{6} c^2 x^6 (5 b e+2 c d)+\frac{2}{7} c^3 e x^7",1,"a^2*b*d*x + (a*(2*b^2*d + 2*a*c*d + a*b*e)*x^2)/2 + ((b^3*d + 6*a*b*c*d + 2*a*b^2*e + 2*a^2*c*e)*x^3)/3 + ((4*b^2*c*d + 4*a*c^2*d + b^3*e + 6*a*b*c*e)*x^4)/4 + (c*(5*b*c*d + 4*b^2*e + 4*a*c*e)*x^5)/5 + (c^2*(2*c*d + 5*b*e)*x^6)/6 + (2*c^3*e*x^7)/7","A",2,1,24,0.04167,1,"{771}"
1508,1,16,0,0.0044276,"\int (b+2 c x) \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2)^2,x]","\frac{1}{3} \left(a+b x+c x^2\right)^3","\frac{1}{3} \left(a+b x+c x^2\right)^3",1,"(a + b*x + c*x^2)^3/3","A",1,1,19,0.05263,1,"{629}"
1509,1,229,0,0.2751872,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{d+e x} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x),x]","\frac{4 c (d+e x)^3 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{(d+e x)^2 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^6}+\frac{2 x \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^5}-\frac{(2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^6}-\frac{5 c^2 (d+e x)^4 (2 c d-b e)}{4 e^6}+\frac{2 c^3 (d+e x)^5}{5 e^6}","\frac{4 c (d+e x)^3 \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{(d+e x)^2 (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^6}+\frac{2 x \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^5}-\frac{(2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^6}-\frac{5 c^2 (d+e x)^4 (2 c d-b e)}{4 e^6}+\frac{2 c^3 (d+e x)^5}{5 e^6}",1,"(2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*x)/e^5 - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^2)/(2*e^6) + (4*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^3)/(3*e^6) - (5*c^2*(2*c*d - b*e)*(d + e*x)^4)/(4*e^6) + (2*c^3*(d + e*x)^5)/(5*e^6) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*Log[d + e*x])/e^6","A",2,1,26,0.03846,1,"{771}"
1510,1,223,0,0.2899594,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^2} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^2,x]","\frac{c x^2 \left(-c e (5 b d-2 a e)+2 b^2 e^2+3 c^2 d^2\right)}{e^4}-\frac{x \left(-c^2 d e (15 b d-8 a e)+2 b c e^2 (4 b d-3 a e)-b^3 e^3+8 c^3 d^3\right)}{e^5}+\frac{2 \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6 (d+e x)}-\frac{c^2 x^3 (4 c d-5 b e)}{3 e^3}+\frac{c^3 x^4}{2 e^2}","\frac{c x^2 \left(-c e (5 b d-2 a e)+2 b^2 e^2+3 c^2 d^2\right)}{e^4}-\frac{x \left(-c^2 d e (15 b d-8 a e)+2 b c e^2 (4 b d-3 a e)-b^3 e^3+8 c^3 d^3\right)}{e^5}+\frac{2 \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6 (d+e x)}-\frac{c^2 x^3 (4 c d-5 b e)}{3 e^3}+\frac{c^3 x^4}{2 e^2}",1,"-(((8*c^3*d^3 - b^3*e^3 - c^2*d*e*(15*b*d - 8*a*e) + 2*b*c*e^2*(4*b*d - 3*a*e))*x)/e^5) + (c*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(5*b*d - 2*a*e))*x^2)/e^4 - (c^2*(4*c*d - 5*b*e)*x^3)/(3*e^3) + (c^3*x^4)/(2*e^2) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^6*(d + e*x)) + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*Log[d + e*x])/e^6","A",2,1,26,0.03846,1,"{771}"
1511,1,219,0,0.2496521,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^3} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^3,x]","\frac{c x \left(-c e (15 b d-4 a e)+4 b^2 e^2+12 c^2 d^2\right)}{e^5}-\frac{2 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (d+e x)}-\frac{(2 c d-b e) \log (d+e x) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^6 (d+e x)^2}-\frac{c^2 x^2 (6 c d-5 b e)}{2 e^4}+\frac{2 c^3 x^3}{3 e^3}","\frac{c x \left(-c e (15 b d-4 a e)+4 b^2 e^2+12 c^2 d^2\right)}{e^5}-\frac{2 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (d+e x)}-\frac{(2 c d-b e) \log (d+e x) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{2 e^6 (d+e x)^2}-\frac{c^2 x^2 (6 c d-5 b e)}{2 e^4}+\frac{2 c^3 x^3}{3 e^3}",1,"(c*(12*c^2*d^2 + 4*b^2*e^2 - c*e*(15*b*d - 4*a*e))*x)/e^5 - (c^2*(6*c*d - 5*b*e)*x^2)/(2*e^4) + (2*c^3*x^3)/(3*e^3) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(2*e^6*(d + e*x)^2) - (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^6*(d + e*x)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*Log[d + e*x])/e^6","A",2,1,26,0.03846,1,"{771}"
1512,1,217,0,0.2258153,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^4} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^4,x]","\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (d+e x)^2}+\frac{4 c \log (d+e x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6 (d+e x)^3}-\frac{c^2 x (8 c d-5 b e)}{e^5}+\frac{c^3 x^2}{e^4}","\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (d+e x)^2}+\frac{4 c \log (d+e x) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6 (d+e x)^3}-\frac{c^2 x (8 c d-5 b e)}{e^5}+\frac{c^3 x^2}{e^4}",1,"-((c^2*(8*c*d - 5*b*e)*x)/e^5) + (c^3*x^2)/e^4 + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(3*e^6*(d + e*x)^3) - ((c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^6*(d + e*x)^2) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(e^6*(d + e*x)) + (4*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*Log[d + e*x])/e^6","A",2,1,26,0.03846,1,"{771}"
1513,1,227,0,0.2088983,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^5} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^5,x]","-\frac{4 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (d+e x)}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}-\frac{2 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6 (d+e x)^4}-\frac{5 c^2 (2 c d-b e) \log (d+e x)}{e^6}+\frac{2 c^3 x}{e^5}","-\frac{4 c \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (d+e x)}+\frac{(2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}-\frac{2 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6 (d+e x)^4}-\frac{5 c^2 (2 c d-b e) \log (d+e x)}{e^6}+\frac{2 c^3 x}{e^5}",1,"(2*c^3*x)/e^5 + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(4*e^6*(d + e*x)^4) - (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(3*e^6*(d + e*x)^3) + ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)))/(2*e^6*(d + e*x)^2) - (4*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^6*(d + e*x)) - (5*c^2*(2*c*d - b*e)*Log[d + e*x])/e^6","A",2,1,26,0.03846,1,"{771}"
1514,1,411,0,0.7232374,"\int (b+2 c x) (d+e x)^4 \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)^4*(a + b*x + c*x^2)^3,x]","\frac{(d+e x)^8 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{8 e^8}+\frac{3 c^2 (d+e x)^{10} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{10 e^8}-\frac{5 c (d+e x)^9 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{9 e^8}-\frac{3 (d+e x)^7 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{6 e^8}-\frac{(d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8}-\frac{7 c^3 (d+e x)^{11} (2 c d-b e)}{11 e^8}+\frac{c^4 (d+e x)^{12}}{6 e^8}","\frac{(d+e x)^8 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{8 e^8}+\frac{3 c^2 (d+e x)^{10} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{10 e^8}-\frac{5 c (d+e x)^9 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{9 e^8}-\frac{3 (d+e x)^7 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{6 e^8}-\frac{(d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8}-\frac{7 c^3 (d+e x)^{11} (2 c d-b e)}{11 e^8}+\frac{c^4 (d+e x)^{12}}{6 e^8}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5)/(5*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^6)/(6*e^8) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^7)/(7*e^8) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^8)/(8*e^8) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^9)/(9*e^8) + (3*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^10)/(10*e^8) - (7*c^3*(2*c*d - b*e)*(d + e*x)^11)/(11*e^8) + (c^4*(d + e*x)^12)/(6*e^8)","A",2,1,26,0.03846,1,"{771}"
1515,1,411,0,0.5875022,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^3,x]","\frac{(d+e x)^7 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{7 e^8}+\frac{c^2 (d+e x)^9 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8}-\frac{5 c (d+e x)^8 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{8 e^8}-\frac{(d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^8}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8}-\frac{7 c^3 (d+e x)^{10} (2 c d-b e)}{10 e^8}+\frac{2 c^4 (d+e x)^{11}}{11 e^8}","\frac{(d+e x)^7 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{7 e^8}+\frac{c^2 (d+e x)^9 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8}-\frac{5 c (d+e x)^8 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{8 e^8}-\frac{(d+e x)^6 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^8}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{(d+e x)^4 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8}-\frac{7 c^3 (d+e x)^{10} (2 c d-b e)}{10 e^8}+\frac{2 c^4 (d+e x)^{11}}{11 e^8}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/(4*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^5)/(5*e^8) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^6)/(2*e^8) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^7)/(7*e^8) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^8)/(8*e^8) + (c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^9)/(3*e^8) - (7*c^3*(2*c*d - b*e)*(d + e*x)^10)/(10*e^8) + (2*c^4*(d + e*x)^11)/(11*e^8)","A",2,1,26,0.03846,1,"{771}"
1516,1,411,0,0.454805,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^3,x]","\frac{(d+e x)^6 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{6 e^8}+\frac{3 c^2 (d+e x)^8 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{8 e^8}-\frac{5 c (d+e x)^7 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}-\frac{3 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^8}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{4 e^8}-\frac{(d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8}-\frac{7 c^3 (d+e x)^9 (2 c d-b e)}{9 e^8}+\frac{c^4 (d+e x)^{10}}{5 e^8}","\frac{(d+e x)^6 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{6 e^8}+\frac{3 c^2 (d+e x)^8 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{8 e^8}-\frac{5 c (d+e x)^7 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}-\frac{3 (d+e x)^5 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^8}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{4 e^8}-\frac{(d+e x)^3 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8}-\frac{7 c^3 (d+e x)^9 (2 c d-b e)}{9 e^8}+\frac{c^4 (d+e x)^{10}}{5 e^8}",1,"-((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^3)/(3*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^4)/(4*e^8) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^5)/(5*e^8) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^6)/(6*e^8) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^7)/(7*e^8) + (3*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^8)/(8*e^8) - (7*c^3*(2*c*d - b*e)*(d + e*x)^9)/(9*e^8) + (c^4*(d + e*x)^10)/(5*e^8)","A",2,1,26,0.03846,1,"{771}"
1517,1,251,0,0.2291756,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{5} x^5 \left(6 a^2 c^2 e+12 a b^2 c e+15 a b c^2 d+5 b^3 c d+b^4 e\right)+\frac{1}{4} x^4 \left(9 a^2 b c e+6 a^2 c^2 d+12 a b^2 c d+3 a b^3 e+b^4 d\right)+\frac{1}{3} a x^3 \left(2 a^2 c e+3 a b^2 e+9 a b c d+3 b^3 d\right)+\frac{1}{2} a^2 x^2 \left(a b e+2 a c d+3 b^2 d\right)+a^3 b d x+\frac{1}{7} c^2 x^7 \left(6 a c e+9 b^2 e+7 b c d\right)+\frac{1}{6} c x^6 \left(15 a b c e+6 a c^2 d+9 b^2 c d+5 b^3 e\right)+\frac{1}{8} c^3 x^8 (7 b e+2 c d)+\frac{2}{9} c^4 e x^9","\frac{1}{5} x^5 \left(6 a^2 c^2 e+12 a b^2 c e+15 a b c^2 d+5 b^3 c d+b^4 e\right)+\frac{1}{4} x^4 \left(9 a^2 b c e+6 a^2 c^2 d+12 a b^2 c d+3 a b^3 e+b^4 d\right)+\frac{1}{3} a x^3 \left(2 a^2 c e+3 a b^2 e+9 a b c d+3 b^3 d\right)+\frac{1}{2} a^2 x^2 \left(a b e+2 a c d+3 b^2 d\right)+a^3 b d x+\frac{1}{7} c^2 x^7 \left(6 a c e+9 b^2 e+7 b c d\right)+\frac{1}{6} c x^6 \left(15 a b c e+6 a c^2 d+9 b^2 c d+5 b^3 e\right)+\frac{1}{8} c^3 x^8 (7 b e+2 c d)+\frac{2}{9} c^4 e x^9",1,"a^3*b*d*x + (a^2*(3*b^2*d + 2*a*c*d + a*b*e)*x^2)/2 + (a*(3*b^3*d + 9*a*b*c*d + 3*a*b^2*e + 2*a^2*c*e)*x^3)/3 + ((b^4*d + 12*a*b^2*c*d + 6*a^2*c^2*d + 3*a*b^3*e + 9*a^2*b*c*e)*x^4)/4 + ((5*b^3*c*d + 15*a*b*c^2*d + b^4*e + 12*a*b^2*c*e + 6*a^2*c^2*e)*x^5)/5 + (c*(9*b^2*c*d + 6*a*c^2*d + 5*b^3*e + 15*a*b*c*e)*x^6)/6 + (c^2*(7*b*c*d + 9*b^2*e + 6*a*c*e)*x^7)/7 + (c^3*(2*c*d + 7*b*e)*x^8)/8 + (2*c^4*e*x^9)/9","A",2,1,24,0.04167,1,"{771}"
1518,1,16,0,0.0045857,"\int (b+2 c x) \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{4} \left(a+b x+c x^2\right)^4","\frac{1}{4} \left(a+b x+c x^2\right)^4",1,"(a + b*x + c*x^2)^4/4","A",1,1,19,0.05263,1,"{629}"
1519,1,399,0,0.5811115,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{d+e x} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x),x]","\frac{(d+e x)^3 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{3 e^8}+\frac{3 c^2 (d+e x)^5 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{5 c (d+e x)^4 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{4 e^8}-\frac{3 (d+e x)^2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^8}+\frac{x \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^7}-\frac{(2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^8}-\frac{7 c^3 (d+e x)^6 (2 c d-b e)}{6 e^8}+\frac{2 c^4 (d+e x)^7}{7 e^8}","\frac{(d+e x)^3 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{3 e^8}+\frac{3 c^2 (d+e x)^5 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{5 c (d+e x)^4 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{4 e^8}-\frac{3 (d+e x)^2 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^8}+\frac{x \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^7}-\frac{(2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^8}-\frac{7 c^3 (d+e x)^6 (2 c d-b e)}{6 e^8}+\frac{2 c^4 (d+e x)^7}{7 e^8}",1,"((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*x)/e^7 - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^2)/(2*e^8) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^3)/(3*e^8) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^4)/(4*e^8) + (3*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^5)/(5*e^8) - (7*c^3*(2*c*d - b*e)*(d + e*x)^6)/(6*e^8) + (2*c^4*(d + e*x)^7)/(7*e^8) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*Log[d + e*x])/e^8","A",2,1,26,0.03846,1,"{771}"
1520,1,396,0,0.5676498,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^2} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^2,x]","\frac{(d+e x)^2 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{2 e^8}+\frac{3 c^2 (d+e x)^4 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{4 e^8}-\frac{5 c (d+e x)^3 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^8}-\frac{3 x (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^7}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8 (d+e x)}-\frac{7 c^3 (d+e x)^5 (2 c d-b e)}{5 e^8}+\frac{c^4 (d+e x)^6}{3 e^8}","\frac{(d+e x)^2 \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{2 e^8}+\frac{3 c^2 (d+e x)^4 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{4 e^8}-\frac{5 c (d+e x)^3 (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^8}-\frac{3 x (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^7}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8 (d+e x)}-\frac{7 c^3 (d+e x)^5 (2 c d-b e)}{5 e^8}+\frac{c^4 (d+e x)^6}{3 e^8}",1,"(-3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*x)/e^7 + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^8*(d + e*x)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^2)/(2*e^8) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^3)/(3*e^8) + (3*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^4)/(4*e^8) - (7*c^3*(2*c*d - b*e)*(d + e*x)^5)/(5*e^8) + (c^4*(d + e*x)^6)/(3*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*Log[d + e*x])/e^8","A",2,1,26,0.03846,1,"{771}"
1521,1,390,0,0.5134831,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^3} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^3,x]","\frac{x \left(3 c^2 e^2 \left(2 a^2 e^2-15 a b d e+18 b^2 d^2\right)-3 b^2 c e^3 (5 b d-4 a e)-2 c^3 d^2 e (35 b d-18 a e)+b^4 e^4+30 c^4 d^4\right)}{e^7}+\frac{c^2 x^3 \left(-c e (7 b d-2 a e)+3 b^2 e^2+4 c^2 d^2\right)}{e^5}-\frac{c x^2 \left(-6 c^2 d e (7 b d-3 a e)+3 b c e^2 (9 b d-5 a e)-5 b^3 e^3+20 c^3 d^3\right)}{2 e^6}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 (d+e x)}-\frac{3 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{2 e^8 (d+e x)^2}-\frac{c^3 x^4 (6 c d-7 b e)}{4 e^4}+\frac{2 c^4 x^5}{5 e^3}","\frac{x \left(3 c^2 e^2 \left(2 a^2 e^2-15 a b d e+18 b^2 d^2\right)-3 b^2 c e^3 (5 b d-4 a e)-2 c^3 d^2 e (35 b d-18 a e)+b^4 e^4+30 c^4 d^4\right)}{e^7}+\frac{c^2 x^3 \left(-c e (7 b d-2 a e)+3 b^2 e^2+4 c^2 d^2\right)}{e^5}-\frac{c x^2 \left(-6 c^2 d e (7 b d-3 a e)+3 b c e^2 (9 b d-5 a e)-5 b^3 e^3+20 c^3 d^3\right)}{2 e^6}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 (d+e x)}-\frac{3 (2 c d-b e) \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{2 e^8 (d+e x)^2}-\frac{c^3 x^4 (6 c d-7 b e)}{4 e^4}+\frac{2 c^4 x^5}{5 e^3}",1,"((30*c^4*d^4 + b^4*e^4 - 2*c^3*d^2*e*(35*b*d - 18*a*e) - 3*b^2*c*e^3*(5*b*d - 4*a*e) + 3*c^2*e^2*(18*b^2*d^2 - 15*a*b*d*e + 2*a^2*e^2))*x)/e^7 - (c*(20*c^3*d^3 - 5*b^3*e^3 + 3*b*c*e^2*(9*b*d - 5*a*e) - 6*c^2*d*e*(7*b*d - 3*a*e))*x^2)/(2*e^6) + (c^2*(4*c^2*d^2 + 3*b^2*e^2 - c*e*(7*b*d - 2*a*e))*x^3)/e^5 - (c^3*(6*c*d - 7*b*e)*x^4)/(4*e^4) + (2*c^4*x^5)/(5*e^3) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(2*e^8*(d + e*x)^2) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^8*(d + e*x)) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*Log[d + e*x])/e^8","A",2,1,26,0.03846,1,"{771}"
1522,1,396,0,0.5124175,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^4} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^4,x]","\frac{\log (d+e x) \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^8}+\frac{c^2 x^2 \left(6 a c e^2+9 b^2 e^2-28 b c d e+20 c^2 d^2\right)}{2 e^6}-\frac{c x \left(-2 c^2 d e (35 b d-12 a e)+3 b c e^2 (12 b d-5 a e)-5 b^3 e^3+40 c^3 d^3\right)}{e^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^8 (d+e x)^2}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8 (d+e x)^3}-\frac{c^3 x^3 (8 c d-7 b e)}{3 e^5}+\frac{c^4 x^4}{2 e^4}","\frac{\log (d+e x) \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^8}+\frac{c^2 x^2 \left(6 a c e^2+9 b^2 e^2-28 b c d e+20 c^2 d^2\right)}{2 e^6}-\frac{c x \left(-2 c^2 d e (35 b d-12 a e)+3 b c e^2 (12 b d-5 a e)-5 b^3 e^3+40 c^3 d^3\right)}{e^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{2 e^8 (d+e x)^2}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8 (d+e x)^3}-\frac{c^3 x^3 (8 c d-7 b e)}{3 e^5}+\frac{c^4 x^4}{2 e^4}",1,"-((c*(40*c^3*d^3 - 5*b^3*e^3 - 2*c^2*d*e*(35*b*d - 12*a*e) + 3*b*c*e^2*(12*b*d - 5*a*e))*x)/e^7) + (c^2*(20*c^2*d^2 - 28*b*c*d*e + 9*b^2*e^2 + 6*a*c*e^2)*x^2)/(2*e^6) - (c^3*(8*c*d - 7*b*e)*x^3)/(3*e^5) + (c^4*x^4)/(2*e^4) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^8*(d + e*x)^3) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(2*e^8*(d + e*x)^2) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(e^8*(d + e*x)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*Log[d + e*x])/e^8","A",2,1,26,0.03846,1,"{771}"
1523,1,389,0,0.4825072,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^5} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^5,x]","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{e^8 (d+e x)}+\frac{c^2 x \left(-c e (35 b d-6 a e)+9 b^2 e^2+30 c^2 d^2\right)}{e^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^8 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8 (d+e x)^3}-\frac{5 c (2 c d-b e) \log (d+e x) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8 (d+e x)^4}-\frac{c^3 x^2 (10 c d-7 b e)}{2 e^6}+\frac{2 c^4 x^3}{3 e^5}","-\frac{6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4}{e^8 (d+e x)}+\frac{c^2 x \left(-c e (35 b d-6 a e)+9 b^2 e^2+30 c^2 d^2\right)}{e^7}+\frac{3 (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{2 e^8 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8 (d+e x)^3}-\frac{5 c (2 c d-b e) \log (d+e x) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8 (d+e x)^4}-\frac{c^3 x^2 (10 c d-7 b e)}{2 e^6}+\frac{2 c^4 x^3}{3 e^5}",1,"(c^2*(30*c^2*d^2 + 9*b^2*e^2 - c*e*(35*b*d - 6*a*e))*x)/e^7 - (c^3*(10*c*d - 7*b*e)*x^2)/(2*e^6) + (2*c^4*x^3)/(3*e^5) + ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(4*e^8*(d + e*x)^4) - ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(3*e^8*(d + e*x)^3) + (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e)))/(2*e^8*(d + e*x)^2) - (70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))/(e^8*(d + e*x)) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*Log[d + e*x])/e^8","A",2,1,26,0.03846,1,"{771}"
1524,1,299,0,0.3972743,"\int \frac{(b+2 c x) (d+e x)^4}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2),x]","\frac{\left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{e^2 x^2 \left(-2 c e (a e+2 b d)+b^2 e^2+12 c^2 d^2\right)}{2 c^2}+\frac{e x \left(-2 c^2 d e (4 a e+3 b d)+b c e^2 (3 a e+4 b d)-b^3 e^3+8 c^3 d^3\right)}{c^3}-\frac{e \sqrt{b^2-4 a c} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4}+\frac{e^3 x^3 (8 c d-b e)}{3 c}+\frac{e^4 x^4}{2}","\frac{\left(2 c^2 e^2 \left(a^2 e^2+6 a b d e+3 b^2 d^2\right)-4 b^2 c e^3 (a e+b d)-4 c^3 d^2 e (3 a e+b d)+b^4 e^4+2 c^4 d^4\right) \log \left(a+b x+c x^2\right)}{2 c^4}+\frac{e^2 x^2 \left(-2 c e (a e+2 b d)+b^2 e^2+12 c^2 d^2\right)}{2 c^2}+\frac{e x \left(-2 c^2 d e (4 a e+3 b d)+b c e^2 (3 a e+4 b d)-b^3 e^3+8 c^3 d^3\right)}{c^3}-\frac{e \sqrt{b^2-4 a c} (2 c d-b e) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^4}+\frac{e^3 x^3 (8 c d-b e)}{3 c}+\frac{e^4 x^4}{2}",1,"(e*(8*c^3*d^3 - b^3*e^3 + b*c*e^2*(4*b*d + 3*a*e) - 2*c^2*d*e*(3*b*d + 4*a*e))*x)/c^3 + (e^2*(12*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d + a*e))*x^2)/(2*c^2) + (e^3*(8*c*d - b*e)*x^3)/(3*c) + (e^4*x^4)/2 - (Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c^4 + ((2*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(b*d + a*e) - 4*c^3*d^2*e*(b*d + 3*a*e) + 2*c^2*e^2*(3*b^2*d^2 + 6*a*b*d*e + a^2*e^2))*Log[a + b*x + c*x^2])/(2*c^4)","A",6,5,26,0.1923,1,"{800, 634, 618, 206, 628}"
1525,1,188,0,0.2363513,"\int \frac{(b+2 c x) (d+e x)^3}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2),x]","\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^3}+\frac{e x \left(-c e (2 a e+3 b d)+b^2 e^2+6 c^2 d^2\right)}{c^2}-\frac{e \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3}+\frac{e^2 x^2 (6 c d-b e)}{2 c}+\frac{2 e^3 x^3}{3}","\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^3}+\frac{e x \left(-c e (2 a e+3 b d)+b^2 e^2+6 c^2 d^2\right)}{c^2}-\frac{e \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3}+\frac{e^2 x^2 (6 c d-b e)}{2 c}+\frac{2 e^3 x^3}{3}",1,"(e*(6*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + 2*a*e))*x)/c^2 + (e^2*(6*c*d - b*e)*x^2)/(2*c) + (2*e^3*x^3)/3 - (Sqrt[b^2 - 4*a*c]*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c^3 + ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,26,0.1923,1,"{800, 634, 618, 206, 628}"
1526,1,114,0,0.1333026,"\int \frac{(b+2 c x) (d+e x)^2}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2),x]","\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^2}-\frac{e \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2}+e x \left(4 d-\frac{b e}{c}\right)+e^2 x^2","\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 c^2}-\frac{e \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2}+e x \left(4 d-\frac{b e}{c}\right)+e^2 x^2",1,"e*(4*d - (b*e)/c)*x + e^2*x^2 - (Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c^2 + ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*Log[a + b*x + c*x^2])/(2*c^2)","A",6,5,26,0.1923,1,"{800, 634, 618, 206, 628}"
1527,1,70,0,0.0899044,"\int \frac{(b+2 c x) (d+e x)}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2),x]","-\frac{e \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+\frac{(2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c}+2 e x","-\frac{e \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c}+\frac{(2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c}+2 e x",1,"2*e*x - (Sqrt[b^2 - 4*a*c]*e*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/c + ((2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*c)","A",5,5,24,0.2083,1,"{773, 634, 618, 206, 628}"
1528,1,11,0,0.004236,"\int \frac{b+2 c x}{a+b x+c x^2} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2),x]","\log \left(a+b x+c x^2\right)","\log \left(a+b x+c x^2\right)",1,"Log[a + b*x + c*x^2]","A",1,1,19,0.05263,1,"{628}"
1529,1,130,0,0.175605,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)} \, dx","Int[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)),x]","\frac{e \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a e^2-b d e+c d^2}+\frac{(2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}-\frac{(2 c d-b e) \log (d+e x)}{a e^2-b d e+c d^2}","\frac{e \sqrt{b^2-4 a c} \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{a e^2-b d e+c d^2}+\frac{(2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}-\frac{(2 c d-b e) \log (d+e x)}{a e^2-b d e+c d^2}",1,"(Sqrt[b^2 - 4*a*c]*e*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*d^2 - b*d*e + a*e^2) - ((2*c*d - b*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2) + ((2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2))","A",6,5,26,0.1923,1,"{800, 634, 618, 206, 628}"
1530,1,210,0,0.2995419,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)} \, dx","Int[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)),x]","\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{\log (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^2}+\frac{e \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(a e^2-b d e+c d^2\right)^2}+\frac{2 c d-b e}{(d+e x) \left(a e^2-b d e+c d^2\right)}","\frac{\left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{\log (d+e x) \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^2}+\frac{e \sqrt{b^2-4 a c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(a e^2-b d e+c d^2\right)^2}+\frac{2 c d-b e}{(d+e x) \left(a e^2-b d e+c d^2\right)}",1,"(2*c*d - b*e)/((c*d^2 - b*d*e + a*e^2)*(d + e*x)) + (Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*d^2 - b*d*e + a*e^2)^2 - ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 + ((2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,26,0.1923,1,"{800, 634, 618, 206, 628}"
1531,1,303,0,0.4761159,"\int \frac{b+2 c x}{(d+e x)^3 \left(a+b x+c x^2\right)} \, dx","Int[(b + 2*c*x)/((d + e*x)^3*(a + b*x + c*x^2)),x]","\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{(2 c d-b e) \log (d+e x) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{e \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{2 c d-b e}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}","\frac{(2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{(2 c d-b e) \log (d+e x) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{e \sqrt{b^2-4 a c} \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{2 c d-b e}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}",1,"(2*c*d - b*e)/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) + (2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + (Sqrt[b^2 - 4*a*c]*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*d^2 - b*d*e + a*e^2)^3 - ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 + ((2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",6,5,26,0.1923,1,"{800, 634, 618, 206, 628}"
1532,1,172,0,0.2158103,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^2,x]","\frac{2 e^2 \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{c^3}-\frac{4 e (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}-\frac{(d+e x)^4}{a+b x+c x^2}+\frac{4 e^3 x (3 c d-b e)}{c^2}+\frac{2 e^4 x^2}{c}","\frac{2 e^2 \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{c^3}-\frac{4 e (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \sqrt{b^2-4 a c}}-\frac{(d+e x)^4}{a+b x+c x^2}+\frac{4 e^3 x (3 c d-b e)}{c^2}+\frac{2 e^4 x^2}{c}",1,"(4*e^3*(3*c*d - b*e)*x)/c^2 + (2*e^4*x^2)/c - (d + e*x)^4/(a + b*x + c*x^2) - (4*e*(2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) + (2*e^2*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[a + b*x + c*x^2])/c^3","A",7,6,26,0.2308,1,"{768, 701, 634, 618, 206, 628}"
1533,1,126,0,0.1448107,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^2,x]","-\frac{3 e \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{3 e^2 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c^2}-\frac{(d+e x)^3}{a+b x+c x^2}+\frac{3 e^3 x}{c}","-\frac{3 e \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{3 e^2 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c^2}-\frac{(d+e x)^3}{a+b x+c x^2}+\frac{3 e^3 x}{c}",1,"(3*e^3*x)/c - (d + e*x)^3/(a + b*x + c*x^2) - (3*e*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) + (3*e^2*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*c^2)","A",7,6,26,0.2308,1,"{768, 701, 634, 618, 206, 628}"
1534,1,87,0,0.0575549,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^2,x]","-\frac{2 e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}-\frac{(d+e x)^2}{a+b x+c x^2}+\frac{e^2 \log \left(a+b x+c x^2\right)}{c}","-\frac{2 e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}-\frac{(d+e x)^2}{a+b x+c x^2}+\frac{e^2 \log \left(a+b x+c x^2\right)}{c}",1,"-((d + e*x)^2/(a + b*x + c*x^2)) - (2*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]) + (e^2*Log[a + b*x + c*x^2])/c","A",5,5,26,0.1923,1,"{768, 634, 618, 206, 628}"
1535,1,55,0,0.029854,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^2,x]","-\frac{2 e \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{d+e x}{a+b x+c x^2}","-\frac{2 e \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c}}-\frac{d+e x}{a+b x+c x^2}",1,"-((d + e*x)/(a + b*x + c*x^2)) - (2*e*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/Sqrt[b^2 - 4*a*c]","A",3,3,24,0.1250,1,"{768, 618, 206}"
1536,1,14,0,0.0046043,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^2} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2)^2,x]","-\frac{1}{a+b x+c x^2}","-\frac{1}{a+b x+c x^2}",1,"-(a + b*x + c*x^2)^(-1)","A",1,1,19,0.05263,1,"{629}"
1537,1,236,0,0.3583258,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^2} \, dx","Int[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^2),x]","\frac{e \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{e^2 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e^2 (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^2}","\frac{e \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{e^2 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e^2 (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^2}",1,"-(((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) + (e*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2) - (e^2*(2*c*d - b*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 + (e^2*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",7,6,26,0.2308,1,"{822, 800, 634, 618, 206, 628}"
1538,1,327,0,0.5340248,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)^2} \, dx","Int[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)^2),x]","\frac{e^2 \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{\left(a e^2-b d e+c d^2\right)^3}-\frac{2 e^2 \log (d+e x) \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{2 e (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{\left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{2 e^2 (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}","\frac{e^2 \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right) \log \left(a+b x+c x^2\right)}{\left(a e^2-b d e+c d^2\right)^3}-\frac{2 e^2 \log (d+e x) \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{2 e (2 c d-b e) \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{\left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{2 e^2 (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}",1,"(2*e^2*(2*c*d - b*e))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - ((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)) + (2*e*(2*c*d - b*e)*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^3) - (2*e^2*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 + (e^2*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e))*Log[a + b*x + c*x^2])/(c*d^2 - b*d*e + a*e^2)^3","A",7,6,26,0.2308,1,"{822, 800, 634, 618, 206, 628}"
1539,1,293,0,0.677226,"\int \frac{(b+2 c x) (d+e x)^5}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^5)/(a + b*x + c*x^2)^3,x]","\frac{5 e^3 x \left(-c e (3 a e+2 b d)+b^2 e^2+3 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}+\frac{5 e \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{5 e^4 x^2 (2 c d-b e)}{2 c \left(b^2-4 a c\right)}-\frac{5 e (d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{5 e^4 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c^3}-\frac{(d+e x)^5}{2 \left(a+b x+c x^2\right)^2}","\frac{5 e^3 x \left(-c e (3 a e+2 b d)+b^2 e^2+3 c^2 d^2\right)}{c^2 \left(b^2-4 a c\right)}+\frac{5 e \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^3 \left(b^2-4 a c\right)^{3/2}}+\frac{5 e^4 x^2 (2 c d-b e)}{2 c \left(b^2-4 a c\right)}-\frac{5 e (d+e x)^3 (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{5 e^4 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 c^3}-\frac{(d+e x)^5}{2 \left(a+b x+c x^2\right)^2}",1,"(5*e^3*(3*c^2*d^2 + b^2*e^2 - c*e*(2*b*d + 3*a*e))*x)/(c^2*(b^2 - 4*a*c)) + (5*e^4*(2*c*d - b*e)*x^2)/(2*c*(b^2 - 4*a*c)) - (d + e*x)^5/(2*(a + b*x + c*x^2)^2) - (5*e*(d + e*x)^3*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (5*e*(2*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(b*d - 3*a*e) - 6*a*c^2*e^3*(2*b*d + a*e) + 2*b^2*c*e^3*(b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(3/2)) + (5*e^4*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*c^3)","A",8,7,26,0.2692,1,"{768, 738, 800, 634, 618, 206, 628}"
1540,1,197,0,0.3348068,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^3,x]","\frac{2 e (2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{2 e^3 x (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{2 e (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^4 \log \left(a+b x+c x^2\right)}{c^2}-\frac{(d+e x)^4}{2 \left(a+b x+c x^2\right)^2}","\frac{2 e (2 c d-b e) \left(-2 c e (b d-3 a e)-b^2 e^2+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c^2 \left(b^2-4 a c\right)^{3/2}}+\frac{2 e^3 x (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{2 e (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{e^4 \log \left(a+b x+c x^2\right)}{c^2}-\frac{(d+e x)^4}{2 \left(a+b x+c x^2\right)^2}",1,"(2*e^3*(2*c*d - b*e)*x)/(c*(b^2 - 4*a*c)) - (d + e*x)^4/(2*(a + b*x + c*x^2)^2) - (2*e*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (2*e*(2*c*d - b*e)*(2*c^2*d^2 - b^2*e^2 - 2*c*e*(b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*(b^2 - 4*a*c)^(3/2)) + (e^4*Log[a + b*x + c*x^2])/c^2","A",7,7,26,0.2692,1,"{768, 738, 773, 634, 618, 206, 628}"
1541,1,126,0,0.0834652,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^3,x]","\frac{6 e \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{3 e (d+e x) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{(d+e x)^3}{2 \left(a+b x+c x^2\right)^2}","\frac{6 e \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{3 e (d+e x) (-2 a e+x (2 c d-b e)+b d)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{(d+e x)^3}{2 \left(a+b x+c x^2\right)^2}",1,"-(d + e*x)^3/(2*(a + b*x + c*x^2)^2) - (3*e*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (6*e*(c*d^2 - b*d*e + a*e^2)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,26,0.1538,1,"{768, 722, 618, 206}"
1542,1,112,0,0.0615039,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^3,x]","-\frac{e (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{2 e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{(d+e x)^2}{2 \left(a+b x+c x^2\right)^2}","-\frac{e (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{2 e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{(d+e x)^2}{2 \left(a+b x+c x^2\right)^2}",1,"-(d + e*x)^2/(2*(a + b*x + c*x^2)^2) - (e*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*(a + b*x + c*x^2)) + (2*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,26,0.1538,1,"{768, 638, 618, 206}"
1543,1,91,0,0.0423818,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^3,x]","-\frac{e (b+2 c x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{2 c e \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{d+e x}{2 \left(a+b x+c x^2\right)^2}","-\frac{e (b+2 c x)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{2 c e \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2}}-\frac{d+e x}{2 \left(a+b x+c x^2\right)^2}",1,"-(d + e*x)/(2*(a + b*x + c*x^2)^2) - (e*(b + 2*c*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (2*c*e*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(3/2)","A",4,4,24,0.1667,1,"{768, 614, 618, 206}"
1544,1,16,0,0.0043297,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^3} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2)^3,x]","-\frac{1}{2 \left(a+b x+c x^2\right)^2}","-\frac{1}{2 \left(a+b x+c x^2\right)^2}",1,"-1/(2*(a + b*x + c*x^2)^2)","A",1,1,19,0.05263,1,"{629}"
1545,1,397,0,0.8229823,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^3} \, dx","Int[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^3),x]","-\frac{e \left(-2 c x \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)-b c \left(c d^2-7 a e^2\right)-8 a c^2 d e+3 b^2 c d e-2 b^3 e^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}+\frac{e^4 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}-\frac{e^4 (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}","-\frac{e \left(-2 c x \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)-b c \left(c d^2-7 a e^2\right)-8 a c^2 d e+3 b^2 c d e-2 b^3 e^2\right)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(2 b^2 c e^3 (3 a e+b d)-4 c^3 d^2 e (b d-3 a e)-6 a c^2 e^3 (a e+2 b d)-b^4 e^4+2 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{3/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}+\frac{e^4 (2 c d-b e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}-\frac{e^4 (2 c d-b e) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}",1,"-((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (e*(3*b^2*c*d*e - 8*a*c^2*d*e - 2*b^3*e^2 - b*c*(c*d^2 - 7*a*e^2) - 2*c*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*x))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - (e*(2*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(b*d - 3*a*e) - 6*a*c^2*e^3*(2*b*d + a*e) + 2*b^2*c*e^3*(b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(3/2)*(c*d^2 - b*d*e + a*e^2)^3) - (e^4*(2*c*d - b*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 + (e^4*(2*c*d - b*e)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",8,6,26,0.2308,1,"{822, 800, 634, 618, 206, 628}"
1546,1,431,0,0.7887158,"\int (b+2 c x) (d+e x)^4 \sqrt{a+b x+c x^2} \, dx","Int[(b + 2*c*x)*(d + e*x)^4*Sqrt[a + b*x + c*x^2],x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(8 c^2 e^2 \left(32 a^2 e^2+231 a b d e+87 b^2 d^2\right)+6 c e x (2 c d-b e) \left(-4 c e (19 a e+2 b d)+21 b^2 e^2+8 c^2 d^2\right)-14 b^2 c e^3 (34 a e+35 b d)-16 c^3 d^2 e (144 a e+13 b d)+105 b^4 e^4+128 c^4 d^4\right)}{1680 c^4}+\frac{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{35 c^2}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right)}{128 c^5}-\frac{e \left(b^2-4 a c\right)^2 (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{11/2}}+\frac{2}{7} (d+e x)^4 \left(a+b x+c x^2\right)^{3/2}+\frac{2 (d+e x)^3 \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{21 c}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(8 c^2 e^2 \left(32 a^2 e^2+231 a b d e+87 b^2 d^2\right)+6 c e x (2 c d-b e) \left(-4 c e (19 a e+2 b d)+21 b^2 e^2+8 c^2 d^2\right)-14 b^2 c e^3 (34 a e+35 b d)-16 c^3 d^2 e (144 a e+13 b d)+105 b^4 e^4+128 c^4 d^4\right)}{1680 c^4}+\frac{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{35 c^2}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right)}{128 c^5}-\frac{e \left(b^2-4 a c\right)^2 (2 c d-b e) \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{256 c^{11/2}}+\frac{2}{7} (d+e x)^4 \left(a+b x+c x^2\right)^{3/2}+\frac{2 (d+e x)^3 \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{21 c}",1,"((b^2 - 4*a*c)*e*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(128*c^5) + ((4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*(d + e*x)^2*(a + b*x + c*x^2)^(3/2))/(35*c^2) + (2*(2*c*d - b*e)*(d + e*x)^3*(a + b*x + c*x^2)^(3/2))/(21*c) + (2*(d + e*x)^4*(a + b*x + c*x^2)^(3/2))/7 + ((128*c^4*d^4 + 105*b^4*e^4 - 14*b^2*c*e^3*(35*b*d + 34*a*e) - 16*c^3*d^2*e*(13*b*d + 144*a*e) + 8*c^2*e^2*(87*b^2*d^2 + 231*a*b*d*e + 32*a^2*e^2) + 6*c*e*(2*c*d - b*e)*(8*c^2*d^2 + 21*b^2*e^2 - 4*c*e*(2*b*d + 19*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(1680*c^4) - ((b^2 - 4*a*c)^2*e*(2*c*d - b*e)*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(256*c^(11/2))","A",7,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1547,1,312,0,0.4192099,"\int (b+2 c x) (d+e x)^3 \sqrt{a+b x+c x^2} \, dx","Int[(b + 2*c*x)*(d + e*x)^3*Sqrt[a + b*x + c*x^2],x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(6 c e x \left(-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right)-24 c^2 d e (16 a e+3 b d)+12 b c e^2 (11 a e+10 b d)-35 b^3 e^3+64 c^3 d^3\right)}{480 c^3}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right)}{256 c^4}-\frac{e \left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{9/2}}+\frac{1}{3} (d+e x)^3 \left(a+b x+c x^2\right)^{3/2}+\frac{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{10 c}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(6 c e x \left(-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right)-24 c^2 d e (16 a e+3 b d)+12 b c e^2 (11 a e+10 b d)-35 b^3 e^3+64 c^3 d^3\right)}{480 c^3}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right)}{256 c^4}-\frac{e \left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{9/2}}+\frac{1}{3} (d+e x)^3 \left(a+b x+c x^2\right)^{3/2}+\frac{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{10 c}",1,"((b^2 - 4*a*c)*e*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(256*c^4) + ((2*c*d - b*e)*(d + e*x)^2*(a + b*x + c*x^2)^(3/2))/(10*c) + ((d + e*x)^3*(a + b*x + c*x^2)^(3/2))/3 + ((64*c^3*d^3 - 35*b^3*e^3 + 12*b*c*e^2*(10*b*d + 11*a*e) - 24*c^2*d*e*(3*b*d + 16*a*e) + 6*c*e*(8*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(2*b*d + 5*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(480*c^3) - ((b^2 - 4*a*c)^2*e*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(512*c^(9/2))","A",6,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1548,1,195,0,0.3282844,"\int (b+2 c x) (d+e x)^2 \sqrt{a+b x+c x^2} \, dx","Int[(b + 2*c*x)*(d + e*x)^2*Sqrt[a + b*x + c*x^2],x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c e (8 a e+5 b d)+5 b^2 e^2+6 c e x (2 c d-b e)+16 c^2 d^2\right)}{60 c^2}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{32 c^3}-\frac{e \left(b^2-4 a c\right)^2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{7/2}}+\frac{2}{5} (d+e x)^2 \left(a+b x+c x^2\right)^{3/2}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c e (8 a e+5 b d)+5 b^2 e^2+6 c e x (2 c d-b e)+16 c^2 d^2\right)}{60 c^2}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{32 c^3}-\frac{e \left(b^2-4 a c\right)^2 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{7/2}}+\frac{2}{5} (d+e x)^2 \left(a+b x+c x^2\right)^{3/2}",1,"((b^2 - 4*a*c)*e*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32*c^3) + (2*(d + e*x)^2*(a + b*x + c*x^2)^(3/2))/5 + ((16*c^2*d^2 + 5*b^2*e^2 - 2*c*e*(5*b*d + 8*a*e) + 6*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(60*c^2) - ((b^2 - 4*a*c)^2*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*c^(7/2))","A",5,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1549,1,122,0,0.0904475,"\int (b+2 c x) (d+e x) \sqrt{a+b x+c x^2} \, dx","Int[(b + 2*c*x)*(d + e*x)*Sqrt[a + b*x + c*x^2],x]","\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{32 c^2}-\frac{e \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (-b e+8 c d+6 c e x)}{12 c}","\frac{e \left(b^2-4 a c\right) (b+2 c x) \sqrt{a+b x+c x^2}}{32 c^2}-\frac{e \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (-b e+8 c d+6 c e x)}{12 c}",1,"((b^2 - 4*a*c)*e*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(32*c^2) + ((8*c*d - b*e + 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(12*c) - ((b^2 - 4*a*c)^2*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*c^(5/2))","A",4,4,26,0.1538,1,"{779, 612, 621, 206}"
1550,1,18,0,0.0058565,"\int (b+2 c x) \sqrt{a+b x+c x^2} \, dx","Int[(b + 2*c*x)*Sqrt[a + b*x + c*x^2],x]","\frac{2}{3} \left(a+b x+c x^2\right)^{3/2}","\frac{2}{3} \left(a+b x+c x^2\right)^{3/2}",1,"(2*(a + b*x + c*x^2)^(3/2))/3","A",1,1,21,0.04762,1,"{629}"
1551,1,199,0,0.2564547,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{d+e x} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x),x]","\frac{\left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 \sqrt{c} e^3}-\frac{(2 c d-b e) \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3}-\frac{\sqrt{a+b x+c x^2} (-3 b e+4 c d-2 c e x)}{2 e^2}","\frac{\left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 \sqrt{c} e^3}-\frac{(2 c d-b e) \sqrt{a e^2-b d e+c d^2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^3}-\frac{\sqrt{a+b x+c x^2} (-3 b e+4 c d-2 c e x)}{2 e^2}",1,"-((4*c*d - 3*b*e - 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(2*e^2) + ((8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4*Sqrt[c]*e^3) - ((2*c*d - b*e)*Sqrt[c*d^2 - b*d*e + a*e^2]*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^3","A",6,5,28,0.1786,1,"{814, 843, 621, 206, 724}"
1552,1,203,0,0.2093558,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^2} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^2,x]","\frac{\left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^3 \sqrt{a e^2-b d e+c d^2}}+\frac{\sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{e^2 (d+e x)}-\frac{2 \sqrt{c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^3}","\frac{\left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^3 \sqrt{a e^2-b d e+c d^2}}+\frac{\sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{e^2 (d+e x)}-\frac{2 \sqrt{c} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^3}",1,"((4*c*d - b*e + 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(e^2*(d + e*x)) - (2*Sqrt[c]*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e^3 + ((8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*e^3*Sqrt[c*d^2 - b*d*e + a*e^2])","A",6,5,28,0.1786,1,"{812, 843, 621, 206, 724}"
1553,1,280,0,0.3210953,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^3} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^3,x]","-\frac{\sqrt{a+b x+c x^2} \left(e x \left(-4 c e (3 b d-2 a e)+b^2 e^2+12 c^2 d^2\right)-2 c d e (3 b d-2 a e)-b e^2 (b d-2 a e)+8 c^2 d^3\right)}{4 e^2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 e^3 \left(a e^2-b d e+c d^2\right)^{3/2}}+\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^3}","-\frac{\sqrt{a+b x+c x^2} \left(e x \left(-4 c e (3 b d-2 a e)+b^2 e^2+12 c^2 d^2\right)-2 c d e (3 b d-2 a e)-b e^2 (b d-2 a e)+8 c^2 d^3\right)}{4 e^2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{(2 c d-b e) \left(-4 c e (2 b d-3 a e)-b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 e^3 \left(a e^2-b d e+c d^2\right)^{3/2}}+\frac{2 c^{3/2} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^3}",1,"-((8*c^2*d^3 - b*e^2*(b*d - 2*a*e) - 2*c*d*e*(3*b*d - 2*a*e) + e*(12*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - 2*a*e))*x)*Sqrt[a + b*x + c*x^2])/(4*e^2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) + (2*c^(3/2)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e^3 - ((2*c*d - b*e)*(8*c^2*d^2 - b^2*e^2 - 4*c*e*(2*b*d - 3*a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*e^3*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",6,5,28,0.1786,1,"{810, 843, 621, 206, 724}"
1554,1,217,0,0.2262684,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^4} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^4,x]","-\frac{e \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (-2 a e+x (2 c d-b e)+b d)}{8 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}","-\frac{e \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (-2 a e+x (2 c d-b e)+b d)}{8 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}+\frac{e \left(b^2-4 a c\right)^2 \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}",1,"-((b^2 - 4*a*c)*e*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(8*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) + ((2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) + ((b^2 - 4*a*c)^2*e*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,28,0.1429,1,"{806, 720, 724, 206}"
1555,1,307,0,0.458677,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^5} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^5,x]","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-4 c e (4 a e+b d)+5 b^2 e^2+4 c^2 d^2\right)}{24 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}-\frac{5 e \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{64 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}+\frac{5 e \left(b^2-4 a c\right)^2 (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{128 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{4 (d+e x)^4 \left(a e^2-b d e+c d^2\right)}","\frac{\left(a+b x+c x^2\right)^{3/2} \left(-4 c e (4 a e+b d)+5 b^2 e^2+4 c^2 d^2\right)}{24 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^2}-\frac{5 e \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} (2 c d-b e) (-2 a e+x (2 c d-b e)+b d)}{64 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^3}+\frac{5 e \left(b^2-4 a c\right)^2 (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{128 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{4 (d+e x)^4 \left(a e^2-b d e+c d^2\right)}",1,"(-5*(b^2 - 4*a*c)*e*(2*c*d - b*e)*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(64*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^2) + ((2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(4*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4) + ((4*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(b*d + 4*a*e))*(a + b*x + c*x^2)^(3/2))/(24*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3) + (5*(b^2 - 4*a*c)^2*e*(2*c*d - b*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(128*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,5,28,0.1786,1,"{834, 806, 720, 724, 206}"
1556,1,430,0,0.6450764,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^6} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^6,x]","-\frac{e \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^4}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (33 a e+2 b d)+35 b^2 e^2+8 c^2 d^2\right)}{240 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^3}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right)}{40 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}+\frac{e \left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{256 \left(a e^2-b d e+c d^2\right)^{9/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{5 (d+e x)^5 \left(a e^2-b d e+c d^2\right)}","-\frac{e \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) (-2 a e+x (2 c d-b e)+b d)}{128 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^4}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e) \left(-4 c e (33 a e+2 b d)+35 b^2 e^2+8 c^2 d^2\right)}{240 (d+e x)^3 \left(a e^2-b d e+c d^2\right)^3}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(-4 c e (5 a e+2 b d)+7 b^2 e^2+8 c^2 d^2\right)}{40 (d+e x)^4 \left(a e^2-b d e+c d^2\right)^2}+\frac{e \left(b^2-4 a c\right)^2 \left(-4 c e (a e+6 b d)+7 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{256 \left(a e^2-b d e+c d^2\right)^{9/2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{5 (d+e x)^5 \left(a e^2-b d e+c d^2\right)}",1,"-((b^2 - 4*a*c)*e*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*(b*d - 2*a*e + (2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(128*(c*d^2 - b*d*e + a*e^2)^4*(d + e*x)^2) + ((2*c*d - b*e)*(a + b*x + c*x^2)^(3/2))/(5*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5) + ((8*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(2*b*d + 5*a*e))*(a + b*x + c*x^2)^(3/2))/(40*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4) + ((2*c*d - b*e)*(8*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(2*b*d + 33*a*e))*(a + b*x + c*x^2)^(3/2))/(240*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^3) + ((b^2 - 4*a*c)^2*e*(24*c^2*d^2 + 7*b^2*e^2 - 4*c*e*(6*b*d + a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(256*(c*d^2 - b*d*e + a*e^2)^(9/2))","A",6,5,28,0.1786,1,"{834, 806, 720, 724, 206}"
1557,1,379,0,0.5139448,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^(3/2),x]","-\frac{3 e \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{8192 c^5}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{1024 c^4}+\frac{\left(a+b x+c x^2\right)^{5/2} \left(10 c e x \left(-4 c e (7 a e+2 b d)+9 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (96 a e+13 b d)+4 b c e^2 (61 a e+56 b d)-63 b^3 e^3+96 c^3 d^3\right)}{2240 c^3}+\frac{3 e \left(b^2-4 a c\right)^3 \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{1}{4} (d+e x)^3 \left(a+b x+c x^2\right)^{5/2}+\frac{3 (d+e x)^2 \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{56 c}","-\frac{3 e \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{8192 c^5}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right)}{1024 c^4}+\frac{\left(a+b x+c x^2\right)^{5/2} \left(10 c e x \left(-4 c e (7 a e+2 b d)+9 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (96 a e+13 b d)+4 b c e^2 (61 a e+56 b d)-63 b^3 e^3+96 c^3 d^3\right)}{2240 c^3}+\frac{3 e \left(b^2-4 a c\right)^3 \left(-4 c e (a e+8 b d)+9 b^2 e^2+32 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{1}{4} (d+e x)^3 \left(a+b x+c x^2\right)^{5/2}+\frac{3 (d+e x)^2 \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{56 c}",1,"(-3*(b^2 - 4*a*c)^2*e*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(8192*c^5) + ((b^2 - 4*a*c)*e*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(1024*c^4) + (3*(2*c*d - b*e)*(d + e*x)^2*(a + b*x + c*x^2)^(5/2))/(56*c) + ((d + e*x)^3*(a + b*x + c*x^2)^(5/2))/4 + ((96*c^3*d^3 - 63*b^3*e^3 + 4*b*c*e^2*(56*b*d + 61*a*e) - 8*c^2*d*e*(13*b*d + 96*a*e) + 10*c*e*(8*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(2*b*d + 7*a*e))*x)*(a + b*x + c*x^2)^(5/2))/(2240*c^3) + (3*(b^2 - 4*a*c)^3*e*(32*c^2*d^2 + 9*b^2*e^2 - 4*c*e*(8*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16384*c^(11/2))","A",7,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1558,1,242,0,0.4473472,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^(3/2),x]","\frac{\left(a+b x+c x^2\right)^{5/2} \left(-2 c e (12 a e+7 b d)+7 b^2 e^2+10 c e x (2 c d-b e)+24 c^2 d^2\right)}{210 c^2}-\frac{e \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{256 c^4}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{96 c^3}+\frac{e \left(b^2-4 a c\right)^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{9/2}}+\frac{2}{7} (d+e x)^2 \left(a+b x+c x^2\right)^{5/2}","\frac{\left(a+b x+c x^2\right)^{5/2} \left(-2 c e (12 a e+7 b d)+7 b^2 e^2+10 c e x (2 c d-b e)+24 c^2 d^2\right)}{210 c^2}-\frac{e \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{256 c^4}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{96 c^3}+\frac{e \left(b^2-4 a c\right)^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{9/2}}+\frac{2}{7} (d+e x)^2 \left(a+b x+c x^2\right)^{5/2}",1,"-((b^2 - 4*a*c)^2*e*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(256*c^4) + ((b^2 - 4*a*c)*e*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(96*c^3) + (2*(d + e*x)^2*(a + b*x + c*x^2)^(5/2))/7 + ((24*c^2*d^2 + 7*b^2*e^2 - 2*c*e*(7*b*d + 12*a*e) + 10*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(5/2))/(210*c^2) + ((b^2 - 4*a*c)^3*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(512*c^(9/2))","A",6,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1559,1,160,0,0.1230785,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2)^(3/2),x]","-\frac{e \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{256 c^3}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{96 c^2}+\frac{e \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{7/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (-b e+12 c d+10 c e x)}{30 c}","-\frac{e \left(b^2-4 a c\right)^2 (b+2 c x) \sqrt{a+b x+c x^2}}{256 c^3}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{96 c^2}+\frac{e \left(b^2-4 a c\right)^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{7/2}}+\frac{\left(a+b x+c x^2\right)^{5/2} (-b e+12 c d+10 c e x)}{30 c}",1,"-((b^2 - 4*a*c)^2*e*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(256*c^3) + ((b^2 - 4*a*c)*e*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(96*c^2) + ((12*c*d - b*e + 10*c*e*x)*(a + b*x + c*x^2)^(5/2))/(30*c) + ((b^2 - 4*a*c)^3*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(512*c^(7/2))","A",5,4,26,0.1538,1,"{779, 612, 621, 206}"
1560,1,18,0,0.0061973,"\int (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2)^(3/2),x]","\frac{2}{5} \left(a+b x+c x^2\right)^{5/2}","\frac{2}{5} \left(a+b x+c x^2\right)^{5/2}",1,"(2*(a + b*x + c*x^2)^(5/2))/5","A",1,1,21,0.04762,1,"{629}"
1561,1,360,0,0.6011573,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{d+e x} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x),x]","\frac{\left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{3/2} e^5}-\frac{\sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (7 b d-4 a e)+4 b c e^2 (12 b d-11 a e)-b^3 e^3+64 c^3 d^3\right)}{32 c e^4}-\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^5}-\frac{\left(a+b x+c x^2\right)^{3/2} (-7 b e+8 c d-6 c e x)}{12 e^2}","\frac{\left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{3/2} e^5}-\frac{\sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (7 b d-4 a e)+4 b c e^2 (12 b d-11 a e)-b^3 e^3+64 c^3 d^3\right)}{32 c e^4}-\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^{3/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^5}-\frac{\left(a+b x+c x^2\right)^{3/2} (-7 b e+8 c d-6 c e x)}{12 e^2}",1,"-((64*c^3*d^3 - b^3*e^3 + 4*b*c*e^2*(12*b*d - 11*a*e) - 16*c^2*d*e*(7*b*d - 4*a*e) - 2*c*e*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(32*c*e^4) - ((8*c*d - 7*b*e - 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(12*e^2) + ((128*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(2*b*d - 3*a*e) - 64*c^3*d^2*e*(4*b*d - 3*a*e) + 48*c^2*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*c^(3/2)*e^5) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(3/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^5","A",7,5,28,0.1786,1,"{814, 843, 621, 206, 724}"
1562,1,303,0,0.4808848,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^2,x]","\frac{\sqrt{a+b x+c x^2} \left(-4 c e (5 b d-a e)+5 b^2 e^2-4 c e x (2 c d-b e)+16 c^2 d^2\right)}{2 e^4}-\frac{(2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 \sqrt{c} e^5}+\frac{\sqrt{a e^2-b d e+c d^2} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^5}+\frac{\left(a+b x+c x^2\right)^{3/2} (-3 b e+8 c d+2 c e x)}{3 e^2 (d+e x)}","\frac{\sqrt{a+b x+c x^2} \left(-4 c e (5 b d-a e)+5 b^2 e^2-4 c e x (2 c d-b e)+16 c^2 d^2\right)}{2 e^4}-\frac{(2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 \sqrt{c} e^5}+\frac{\sqrt{a e^2-b d e+c d^2} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^5}+\frac{\left(a+b x+c x^2\right)^{3/2} (-3 b e+8 c d+2 c e x)}{3 e^2 (d+e x)}",1,"((16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(5*b*d - a*e) - 4*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(2*e^4) + ((8*c*d - 3*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(3*e^2*(d + e*x)) - ((2*c*d - b*e)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4*Sqrt[c]*e^5) + (Sqrt[c*d^2 - b*d*e + a*e^2]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*e^5)","A",7,6,28,0.2143,1,"{812, 814, 843, 621, 206, 724}"
1563,1,309,0,0.3685654,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^3,x]","-\frac{3 \sqrt{a+b x+c x^2} \left(-4 c e (3 b d-a e)+b^2 e^2+4 c e x (2 c d-b e)+16 c^2 d^2\right)}{4 e^4 (d+e x)}+\frac{3 \sqrt{c} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 e^5}-\frac{3 (2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 e^5 \sqrt{a e^2-b d e+c d^2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (-b e+4 c d+2 c e x)}{2 e^2 (d+e x)^2}","-\frac{3 \sqrt{a+b x+c x^2} \left(-4 c e (3 b d-a e)+b^2 e^2+4 c e x (2 c d-b e)+16 c^2 d^2\right)}{4 e^4 (d+e x)}+\frac{3 \sqrt{c} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 e^5}-\frac{3 (2 c d-b e) \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 e^5 \sqrt{a e^2-b d e+c d^2}}+\frac{\left(a+b x+c x^2\right)^{3/2} (-b e+4 c d+2 c e x)}{2 e^2 (d+e x)^2}",1,"(-3*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - a*e) + 4*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(4*e^4*(d + e*x)) + ((4*c*d - b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(2*e^2*(d + e*x)^2) + (3*Sqrt[c]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4*e^5) - (3*(2*c*d - b*e)*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*e^5*Sqrt[c*d^2 - b*d*e + a*e^2])","A",7,5,28,0.1786,1,"{812, 843, 621, 206, 724}"
1564,1,462,0,0.6256276,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^4,x]","\frac{\left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 e^5 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(3 e x \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)-4 c d e (3 b d-a e)-b e^2 (b d-4 a e)+16 c^2 d^3\right)}{12 e^2 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-4 a e)+4 b c e^2 (4 b d-5 a e)+b^3 e^3+64 c^3 d^3\right)}{8 e^4 (d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{4 c^{3/2} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^5}","\frac{\left(48 c^2 e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-8 b^2 c e^3 (2 b d-3 a e)-64 c^3 d^2 e (4 b d-3 a e)-b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 e^5 \left(a e^2-b d e+c d^2\right)^{3/2}}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(3 e x \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)-4 c d e (3 b d-a e)-b e^2 (b d-4 a e)+16 c^2 d^3\right)}{12 e^2 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-4 a e)+4 b c e^2 (4 b d-5 a e)+b^3 e^3+64 c^3 d^3\right)}{8 e^4 (d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{4 c^{3/2} (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e^5}",1,"((64*c^3*d^3 + b^3*e^3 + 4*b*c*e^2*(4*b*d - 5*a*e) - 16*c^2*d*e*(5*b*d - 4*a*e) + 2*c*e*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(8*e^4*(c*d^2 - b*d*e + a*e^2)*(d + e*x)) - ((16*c^2*d^3 - b*e^2*(b*d - 4*a*e) - 4*c*d*e*(3*b*d - a*e) + 3*e*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*x)*(a + b*x + c*x^2)^(3/2))/(12*e^2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) - (4*c^(3/2)*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e^5 + ((128*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(2*b*d - 3*a*e) - 64*c^3*d^2*e*(4*b*d - 3*a*e) + 48*c^2*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*e^5*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",7,6,28,0.2143,1,"{810, 812, 843, 621, 206, 724}"
1565,1,446,0,0.6237399,"\int (b+2 c x) (d+e x)^3 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b + 2*c*x)*(d + e*x)^3*(a + b*x + c*x^2)^(5/2),x]","\frac{3 e \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right)}{65536 c^6}-\frac{e \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right)}{8192 c^5}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right)}{2560 c^4}+\frac{\left(a+b x+c x^2\right)^{7/2} \left(14 c e x \left(-4 c e (9 a e+2 b d)+11 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (160 a e+17 b d)+4 b c e^2 (97 a e+90 b d)-99 b^3 e^3+128 c^3 d^3\right)}{6720 c^3}-\frac{3 e \left(b^2-4 a c\right)^4 \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{131072 c^{13/2}}+\frac{1}{5} (d+e x)^3 \left(a+b x+c x^2\right)^{7/2}+\frac{(d+e x)^2 \left(a+b x+c x^2\right)^{7/2} (2 c d-b e)}{30 c}","\frac{3 e \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2} \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right)}{65536 c^6}-\frac{e \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right)}{8192 c^5}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{5/2} \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right)}{2560 c^4}+\frac{\left(a+b x+c x^2\right)^{7/2} \left(14 c e x \left(-4 c e (9 a e+2 b d)+11 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (160 a e+17 b d)+4 b c e^2 (97 a e+90 b d)-99 b^3 e^3+128 c^3 d^3\right)}{6720 c^3}-\frac{3 e \left(b^2-4 a c\right)^4 \left(-4 c e (a e+10 b d)+11 b^2 e^2+40 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{131072 c^{13/2}}+\frac{1}{5} (d+e x)^3 \left(a+b x+c x^2\right)^{7/2}+\frac{(d+e x)^2 \left(a+b x+c x^2\right)^{7/2} (2 c d-b e)}{30 c}",1,"(3*(b^2 - 4*a*c)^3*e*(40*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(10*b*d + a*e))*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(65536*c^6) - ((b^2 - 4*a*c)^2*e*(40*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(10*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(8192*c^5) + ((b^2 - 4*a*c)*e*(40*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(10*b*d + a*e))*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(2560*c^4) + ((2*c*d - b*e)*(d + e*x)^2*(a + b*x + c*x^2)^(7/2))/(30*c) + ((d + e*x)^3*(a + b*x + c*x^2)^(7/2))/5 + ((128*c^3*d^3 - 99*b^3*e^3 + 4*b*c*e^2*(90*b*d + 97*a*e) - 8*c^2*d*e*(17*b*d + 160*a*e) + 14*c*e*(8*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(2*b*d + 9*a*e))*x)*(a + b*x + c*x^2)^(7/2))/(6720*c^3) - (3*(b^2 - 4*a*c)^4*e*(40*c^2*d^2 + 11*b^2*e^2 - 4*c*e*(10*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(131072*c^(13/2))","A",8,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1566,1,289,0,0.547529,"\int (b+2 c x) (d+e x)^2 \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b + 2*c*x)*(d + e*x)^2*(a + b*x + c*x^2)^(5/2),x]","\frac{\left(a+b x+c x^2\right)^{7/2} \left(-2 c e (16 a e+9 b d)+9 b^2 e^2+14 c e x (2 c d-b e)+32 c^2 d^2\right)}{504 c^2}+\frac{5 e \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{8192 c^5}-\frac{5 e \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{3072 c^4}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{192 c^3}-\frac{5 e \left(b^2-4 a c\right)^4 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{2}{9} (d+e x)^2 \left(a+b x+c x^2\right)^{7/2}","\frac{\left(a+b x+c x^2\right)^{7/2} \left(-2 c e (16 a e+9 b d)+9 b^2 e^2+14 c e x (2 c d-b e)+32 c^2 d^2\right)}{504 c^2}+\frac{5 e \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2} (2 c d-b e)}{8192 c^5}-\frac{5 e \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)^{3/2} (2 c d-b e)}{3072 c^4}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{5/2} (2 c d-b e)}{192 c^3}-\frac{5 e \left(b^2-4 a c\right)^4 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{11/2}}+\frac{2}{9} (d+e x)^2 \left(a+b x+c x^2\right)^{7/2}",1,"(5*(b^2 - 4*a*c)^3*e*(2*c*d - b*e)*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(8192*c^5) - (5*(b^2 - 4*a*c)^2*e*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(3072*c^4) + ((b^2 - 4*a*c)*e*(2*c*d - b*e)*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(192*c^3) + (2*(d + e*x)^2*(a + b*x + c*x^2)^(7/2))/9 + ((32*c^2*d^2 + 9*b^2*e^2 - 2*c*e*(9*b*d + 16*a*e) + 14*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(7/2))/(504*c^2) - (5*(b^2 - 4*a*c)^4*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16384*c^(11/2))","A",7,5,28,0.1786,1,"{832, 779, 612, 621, 206}"
1567,1,198,0,0.1691698,"\int (b+2 c x) (d+e x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b + 2*c*x)*(d + e*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{5 e \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2}}{8192 c^4}-\frac{5 e \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{3072 c^3}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{192 c^2}-\frac{5 e \left(b^2-4 a c\right)^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{9/2}}+\frac{\left(a+b x+c x^2\right)^{7/2} (-b e+16 c d+14 c e x)}{56 c}","\frac{5 e \left(b^2-4 a c\right)^3 (b+2 c x) \sqrt{a+b x+c x^2}}{8192 c^4}-\frac{5 e \left(b^2-4 a c\right)^2 (b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{3072 c^3}+\frac{e \left(b^2-4 a c\right) (b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{192 c^2}-\frac{5 e \left(b^2-4 a c\right)^4 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{16384 c^{9/2}}+\frac{\left(a+b x+c x^2\right)^{7/2} (-b e+16 c d+14 c e x)}{56 c}",1,"(5*(b^2 - 4*a*c)^3*e*(b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(8192*c^4) - (5*(b^2 - 4*a*c)^2*e*(b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(3072*c^3) + ((b^2 - 4*a*c)*e*(b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(192*c^2) + ((16*c*d - b*e + 14*c*e*x)*(a + b*x + c*x^2)^(7/2))/(56*c) - (5*(b^2 - 4*a*c)^4*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16384*c^(9/2))","A",6,4,26,0.1538,1,"{779, 612, 621, 206}"
1568,1,18,0,0.0061167,"\int (b+2 c x) \left(a+b x+c x^2\right)^{5/2} \, dx","Int[(b + 2*c*x)*(a + b*x + c*x^2)^(5/2),x]","\frac{2}{7} \left(a+b x+c x^2\right)^{7/2}","\frac{2}{7} \left(a+b x+c x^2\right)^{7/2}",1,"(2*(a + b*x + c*x^2)^(7/2))/7","A",1,1,21,0.04762,1,"{629}"
1569,1,627,0,1.1436431,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{d+e x} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x),x]","-\frac{\sqrt{a+b x+c x^2} \left(32 c^3 d e^2 \left(16 a^2 e^2-55 a b d e+40 b^2 d^2\right)-8 b c^2 e^3 \left(42 a^2 e^2-92 a b d e+49 b^2 d^2\right)-2 c e x \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)+8 b^3 c e^4 (b d-2 a e)-128 c^4 d^3 e (11 b d-8 a e)+b^5 e^5+512 c^5 d^5\right)}{256 c^2 e^6}+\frac{\left(640 c^4 d^2 e^2 \left(3 a^2 e^2-8 a b d e+5 b^2 d^2\right)+40 b^2 c^2 e^4 \left(6 a^2 e^2-8 a b d e+3 b^2 d^2\right)+4 b^4 c e^5 (2 b d-5 a e)-512 c^5 d^4 e (6 b d-5 a e)-320 c^3 e^3 (b d-a e)^2 (4 b d-a e)+b^6 e^6+1024 c^6 d^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{5/2} e^7}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c e x \left(-4 c e (6 b d-5 a e)+b^2 e^2+24 c^2 d^2\right)-8 c^2 d e (15 b d-8 a e)+4 b c e^2 (14 b d-13 a e)-b^3 e^3+64 c^3 d^3\right)}{96 c e^4}-\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^{5/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^7}-\frac{\left(a+b x+c x^2\right)^{5/2} (-11 b e+12 c d-10 c e x)}{30 e^2}","-\frac{\sqrt{a+b x+c x^2} \left(32 c^3 d e^2 \left(16 a^2 e^2-55 a b d e+40 b^2 d^2\right)-8 b c^2 e^3 \left(42 a^2 e^2-92 a b d e+49 b^2 d^2\right)-2 c e x \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right)+8 b^3 c e^4 (b d-2 a e)-128 c^4 d^3 e (11 b d-8 a e)+b^5 e^5+512 c^5 d^5\right)}{256 c^2 e^6}+\frac{\left(640 c^4 d^2 e^2 \left(3 a^2 e^2-8 a b d e+5 b^2 d^2\right)+40 b^2 c^2 e^4 \left(6 a^2 e^2-8 a b d e+3 b^2 d^2\right)+4 b^4 c e^5 (2 b d-5 a e)-512 c^5 d^4 e (6 b d-5 a e)-320 c^3 e^3 (b d-a e)^2 (4 b d-a e)+b^6 e^6+1024 c^6 d^6\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{512 c^{5/2} e^7}-\frac{\left(a+b x+c x^2\right)^{3/2} \left(-2 c e x \left(-4 c e (6 b d-5 a e)+b^2 e^2+24 c^2 d^2\right)-8 c^2 d e (15 b d-8 a e)+4 b c e^2 (14 b d-13 a e)-b^3 e^3+64 c^3 d^3\right)}{96 c e^4}-\frac{(2 c d-b e) \left(a e^2-b d e+c d^2\right)^{5/2} \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e^7}-\frac{\left(a+b x+c x^2\right)^{5/2} (-11 b e+12 c d-10 c e x)}{30 e^2}",1,"-((512*c^5*d^5 + b^5*e^5 - 128*c^4*d^3*e*(11*b*d - 8*a*e) + 8*b^3*c*e^4*(b*d - 2*a*e) + 32*c^3*d*e^2*(40*b^2*d^2 - 55*a*b*d*e + 16*a^2*e^2) - 8*b*c^2*e^3*(49*b^2*d^2 - 92*a*b*d*e + 42*a^2*e^2) - 2*c*e*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*x)*Sqrt[a + b*x + c*x^2])/(256*c^2*e^6) - ((64*c^3*d^3 - b^3*e^3 + 4*b*c*e^2*(14*b*d - 13*a*e) - 8*c^2*d*e*(15*b*d - 8*a*e) - 2*c*e*(24*c^2*d^2 + b^2*e^2 - 4*c*e*(6*b*d - 5*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(96*c*e^4) - ((12*c*d - 11*b*e - 10*c*e*x)*(a + b*x + c*x^2)^(5/2))/(30*e^2) + ((1024*c^6*d^6 + b^6*e^6 + 4*b^4*c*e^5*(2*b*d - 5*a*e) - 512*c^5*d^4*e*(6*b*d - 5*a*e) - 320*c^3*e^3*(b*d - a*e)^2*(4*b*d - a*e) + 640*c^4*d^2*e^2*(5*b^2*d^2 - 8*a*b*d*e + 3*a^2*e^2) + 40*b^2*c^2*e^4*(3*b^2*d^2 - 8*a*b*d*e + 6*a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(512*c^(5/2)*e^7) - ((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^(5/2)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/e^7","A",8,5,28,0.1786,1,"{814, 843, 621, 206, 724}"
1570,1,508,0,0.7492223,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^2,x]","\frac{\sqrt{a+b x+c x^2} \left(8 c^2 e^2 \left(8 a^2 e^2-67 a b d e+76 b^2 d^2\right)-2 c e x (2 c d-b e) \left(44 a c e^2+b^2 e^2-48 b c d e+48 c^2 d^2\right)-2 b^2 c e^3 (65 b d-62 a e)-32 c^3 d^2 e (27 b d-14 a e)+b^4 e^4+384 c^4 d^4\right)}{32 c e^6}-\frac{(2 c d-b e) \left(16 c^2 e^2 \left(15 a^2 e^2-40 a b d e+26 b^2 d^2\right)-8 b^2 c e^3 (4 b d-5 a e)-128 c^3 d^2 e (6 b d-5 a e)-b^4 e^4+384 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{3/2} e^7}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(8 a c e^2+19 b^2 e^2-18 c e x (2 c d-b e)-66 b c d e+48 c^2 d^2\right)}{12 e^4}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \left(-4 c e (6 b d-a e)+5 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^7}+\frac{\left(a+b x+c x^2\right)^{5/2} (-5 b e+12 c d+2 c e x)}{5 e^2 (d+e x)}","\frac{\sqrt{a+b x+c x^2} \left(8 c^2 e^2 \left(8 a^2 e^2-67 a b d e+76 b^2 d^2\right)-2 c e x (2 c d-b e) \left(44 a c e^2+b^2 e^2-48 b c d e+48 c^2 d^2\right)-2 b^2 c e^3 (65 b d-62 a e)-32 c^3 d^2 e (27 b d-14 a e)+b^4 e^4+384 c^4 d^4\right)}{32 c e^6}-\frac{(2 c d-b e) \left(16 c^2 e^2 \left(15 a^2 e^2-40 a b d e+26 b^2 d^2\right)-8 b^2 c e^3 (4 b d-5 a e)-128 c^3 d^2 e (6 b d-5 a e)-b^4 e^4+384 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{3/2} e^7}+\frac{\left(a+b x+c x^2\right)^{3/2} \left(8 a c e^2+19 b^2 e^2-18 c e x (2 c d-b e)-66 b c d e+48 c^2 d^2\right)}{12 e^4}+\frac{\left(a e^2-b d e+c d^2\right)^{3/2} \left(-4 c e (6 b d-a e)+5 b^2 e^2+24 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 e^7}+\frac{\left(a+b x+c x^2\right)^{5/2} (-5 b e+12 c d+2 c e x)}{5 e^2 (d+e x)}",1,"((384*c^4*d^4 + b^4*e^4 - 2*b^2*c*e^3*(65*b*d - 62*a*e) - 32*c^3*d^2*e*(27*b*d - 14*a*e) + 8*c^2*e^2*(76*b^2*d^2 - 67*a*b*d*e + 8*a^2*e^2) - 2*c*e*(2*c*d - b*e)*(48*c^2*d^2 - 48*b*c*d*e + b^2*e^2 + 44*a*c*e^2)*x)*Sqrt[a + b*x + c*x^2])/(32*c*e^6) + ((48*c^2*d^2 - 66*b*c*d*e + 19*b^2*e^2 + 8*a*c*e^2 - 18*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(12*e^4) + ((12*c*d - 5*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(5/2))/(5*e^2*(d + e*x)) - ((2*c*d - b*e)*(384*c^4*d^4 - b^4*e^4 - 8*b^2*c*e^3*(4*b*d - 5*a*e) - 128*c^3*d^2*e*(6*b*d - 5*a*e) + 16*c^2*e^2*(26*b^2*d^2 - 40*a*b*d*e + 15*a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*c^(3/2)*e^7) + ((c*d^2 - b*d*e + a*e^2)^(3/2)*(24*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(6*b*d - a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*e^7)","A",8,6,28,0.2143,1,"{812, 814, 843, 621, 206, 724}"
1571,1,464,0,0.8453489,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^3,x]","\frac{15 \left(16 c^2 e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-8 b^2 c e^3 (4 b d-3 a e)-128 c^3 d^2 e (2 b d-a e)+b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 \sqrt{c} e^7}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(-c e (7 b d-2 a e)+b^2 e^2+c e x (2 c d-b e)+8 c^2 d^2\right)}{4 e^4 (d+e x)}-\frac{15 \sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (7 b d-2 a e)+4 b c e^2 (14 b d-5 a e)-7 b^3 e^3+64 c^3 d^3\right)}{32 e^6}-\frac{15 (2 c d-b e) \sqrt{a e^2-b d e+c d^2} \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 e^7}+\frac{\left(a+b x+c x^2\right)^{5/2} (-b e+3 c d+c e x)}{2 e^2 (d+e x)^2}","\frac{15 \left(16 c^2 e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-8 b^2 c e^3 (4 b d-3 a e)-128 c^3 d^2 e (2 b d-a e)+b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 \sqrt{c} e^7}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(-c e (7 b d-2 a e)+b^2 e^2+c e x (2 c d-b e)+8 c^2 d^2\right)}{4 e^4 (d+e x)}-\frac{15 \sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (7 b d-2 a e)+4 b c e^2 (14 b d-5 a e)-7 b^3 e^3+64 c^3 d^3\right)}{32 e^6}-\frac{15 (2 c d-b e) \sqrt{a e^2-b d e+c d^2} \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 e^7}+\frac{\left(a+b x+c x^2\right)^{5/2} (-b e+3 c d+c e x)}{2 e^2 (d+e x)^2}",1,"(-15*(64*c^3*d^3 - 7*b^3*e^3 + 4*b*c*e^2*(14*b*d - 5*a*e) - 16*c^2*d*e*(7*b*d - 2*a*e) - 2*c*e*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*x)*Sqrt[a + b*x + c*x^2])/(32*e^6) - (5*(8*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 2*a*e) + c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(4*e^4*(d + e*x)) + ((3*c*d - b*e + c*e*x)*(a + b*x + c*x^2)^(5/2))/(2*e^2*(d + e*x)^2) + (15*(128*c^4*d^4 + b^4*e^4 - 8*b^2*c*e^3*(4*b*d - 3*a*e) - 128*c^3*d^2*e*(2*b*d - a*e) + 16*c^2*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*Sqrt[c]*e^7) - (15*(2*c*d - b*e)*Sqrt[c*d^2 - b*d*e + a*e^2]*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*e^7)","A",8,6,28,0.2143,1,"{812, 814, 843, 621, 206, 724}"
1572,1,473,0,0.7468193,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(5/2))/(d + e*x)^4,x]","\frac{5 \left(16 c^2 e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-8 b^2 c e^3 (4 b d-3 a e)-128 c^3 d^2 e (2 b d-a e)+b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 e^7 \sqrt{a e^2-b d e+c d^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (3 b d-a e)+b^2 e^2+4 c e x (2 c d-b e)+16 c^2 d^2\right)}{12 e^4 (d+e x)^2}+\frac{5 \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-2 a e)+12 b c e^2 (2 b d-a e)-b^3 e^3+64 c^3 d^3\right)}{8 e^6 (d+e x)}-\frac{5 \sqrt{c} (2 c d-b e) \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 e^7}+\frac{\left(a+b x+c x^2\right)^{5/2} (-b e+4 c d+2 c e x)}{3 e^2 (d+e x)^3}","\frac{5 \left(16 c^2 e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-8 b^2 c e^3 (4 b d-3 a e)-128 c^3 d^2 e (2 b d-a e)+b^4 e^4+128 c^4 d^4\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 e^7 \sqrt{a e^2-b d e+c d^2}}-\frac{5 \left(a+b x+c x^2\right)^{3/2} \left(-4 c e (3 b d-a e)+b^2 e^2+4 c e x (2 c d-b e)+16 c^2 d^2\right)}{12 e^4 (d+e x)^2}+\frac{5 \sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right)-16 c^2 d e (5 b d-2 a e)+12 b c e^2 (2 b d-a e)-b^3 e^3+64 c^3 d^3\right)}{8 e^6 (d+e x)}-\frac{5 \sqrt{c} (2 c d-b e) \left(-4 c e (2 b d-a e)+b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 e^7}+\frac{\left(a+b x+c x^2\right)^{5/2} (-b e+4 c d+2 c e x)}{3 e^2 (d+e x)^3}",1,"(5*(64*c^3*d^3 - b^3*e^3 - 16*c^2*d*e*(5*b*d - 2*a*e) + 12*b*c*e^2*(2*b*d - a*e) + 2*c*e*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*x)*Sqrt[a + b*x + c*x^2])/(8*e^6*(d + e*x)) - (5*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(3*b*d - a*e) + 4*c*e*(2*c*d - b*e)*x)*(a + b*x + c*x^2)^(3/2))/(12*e^4*(d + e*x)^2) + ((4*c*d - b*e + 2*c*e*x)*(a + b*x + c*x^2)^(5/2))/(3*e^2*(d + e*x)^3) - (5*Sqrt[c]*(2*c*d - b*e)*(8*c^2*d^2 + b^2*e^2 - 4*c*e*(2*b*d - a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*e^7) + (5*(128*c^4*d^4 + b^4*e^4 - 8*b^2*c*e^3*(4*b*d - 3*a*e) - 128*c^3*d^2*e*(2*b*d - a*e) + 16*c^2*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*e^7*Sqrt[c*d^2 - b*d*e + a*e^2])","A",8,5,28,0.1786,1,"{812, 843, 621, 206, 724}"
1573,1,245,0,0.3289485,"\int \frac{(b+2 c x) (d+e x)^3}{\sqrt{a+b x+c x^2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^3)/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (16 a e+5 b d)+4 b c e^2 (13 a e+12 b d)-15 b^3 e^3+32 c^3 d^3\right)}{32 c^3}+\frac{3 e \left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{7/2}}+\frac{1}{2} (d+e x)^3 \sqrt{a+b x+c x^2}+\frac{(d+e x)^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{4 c}","\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)-8 c^2 d e (16 a e+5 b d)+4 b c e^2 (13 a e+12 b d)-15 b^3 e^3+32 c^3 d^3\right)}{32 c^3}+\frac{3 e \left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{64 c^{7/2}}+\frac{1}{2} (d+e x)^3 \sqrt{a+b x+c x^2}+\frac{(d+e x)^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{4 c}",1,"((2*c*d - b*e)*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(4*c) + ((d + e*x)^3*Sqrt[a + b*x + c*x^2])/2 + ((32*c^3*d^3 - 15*b^3*e^3 + 4*b*c*e^2*(12*b*d + 13*a*e) - 8*c^2*d*e*(5*b*d + 16*a*e) + 2*c*e*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(32*c^3) + (3*(b^2 - 4*a*c)*e*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(64*c^(7/2))","A",5,4,28,0.1429,1,"{832, 779, 621, 206}"
1574,1,148,0,0.1993926,"\int \frac{(b+2 c x) (d+e x)^2}{\sqrt{a+b x+c x^2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^2)/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(-2 c e (4 a e+3 b d)+3 b^2 e^2+2 c e x (2 c d-b e)+8 c^2 d^2\right)}{6 c^2}+\frac{e \left(b^2-4 a c\right) (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{5/2}}+\frac{2}{3} (d+e x)^2 \sqrt{a+b x+c x^2}","\frac{\sqrt{a+b x+c x^2} \left(-2 c e (4 a e+3 b d)+3 b^2 e^2+2 c e x (2 c d-b e)+8 c^2 d^2\right)}{6 c^2}+\frac{e \left(b^2-4 a c\right) (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{5/2}}+\frac{2}{3} (d+e x)^2 \sqrt{a+b x+c x^2}",1,"(2*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/3 + ((8*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(3*b*d + 4*a*e) + 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(6*c^2) + ((b^2 - 4*a*c)*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4*c^(5/2))","A",4,4,28,0.1429,1,"{832, 779, 621, 206}"
1575,1,84,0,0.0527219,"\int \frac{(b+2 c x) (d+e x)}{\sqrt{a+b x+c x^2}} \, dx","Int[((b + 2*c*x)*(d + e*x))/Sqrt[a + b*x + c*x^2],x]","\frac{e \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{3/2}}+\frac{\sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{2 c}","\frac{e \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{3/2}}+\frac{\sqrt{a+b x+c x^2} (-b e+4 c d+2 c e x)}{2 c}",1,"((4*c*d - b*e + 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(2*c) + ((b^2 - 4*a*c)*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4*c^(3/2))","A",3,3,26,0.1154,1,"{779, 621, 206}"
1576,1,16,0,0.0057263,"\int \frac{b+2 c x}{\sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/Sqrt[a + b*x + c*x^2],x]","2 \sqrt{a+b x+c x^2}","2 \sqrt{a+b x+c x^2}",1,"2*Sqrt[a + b*x + c*x^2]","A",1,1,21,0.04762,1,"{629}"
1577,1,133,0,0.0907349,"\int \frac{b+2 c x}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \sqrt{a e^2-b d e+c d^2}}","\frac{2 \sqrt{c} \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{e}-\frac{(2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \sqrt{a e^2-b d e+c d^2}}",1,"(2*Sqrt[c]*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/e - ((2*c*d - b*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*Sqrt[c*d^2 - b*d*e + a*e^2])","A",5,4,28,0.1429,1,"{843, 621, 206, 724}"
1578,1,141,0,0.1150263,"\int \frac{b+2 c x}{(d+e x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{e \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{\sqrt{a+b x+c x^2} (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{e \left(b^2-4 a c\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"((2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*(d + e*x)) - ((b^2 - 4*a*c)*e*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",3,3,28,0.1071,1,"{806, 724, 206}"
1579,1,225,0,0.272195,"\int \frac{b+2 c x}{(d+e x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^3*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{4 (d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{3 e \left(b^2-4 a c\right) (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e)}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}","\frac{\sqrt{a+b x+c x^2} \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)}{4 (d+e x) \left(a e^2-b d e+c d^2\right)^2}-\frac{3 e \left(b^2-4 a c\right) (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e)}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}",1,"((2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) + ((4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - (3*(b^2 - 4*a*c)*e*(2*c*d - b*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,28,0.1429,1,"{834, 806, 724, 206}"
1580,1,328,0,0.4486623,"\int \frac{b+2 c x}{(d+e x)^4 \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^4*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (13 a e+2 b d)+15 b^2 e^2+8 c^2 d^2\right)}{24 (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{\sqrt{a+b x+c x^2} \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)}{12 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e)}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}","\frac{\sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (13 a e+2 b d)+15 b^2 e^2+8 c^2 d^2\right)}{24 (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{\sqrt{a+b x+c x^2} \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)}{12 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \left(b^2-4 a c\right) \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{\sqrt{a+b x+c x^2} (2 c d-b e)}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}",1,"((2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) + ((8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*Sqrt[a + b*x + c*x^2])/(12*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) + ((2*c*d - b*e)*(8*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(2*b*d + 13*a*e))*Sqrt[a + b*x + c*x^2])/(24*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - ((b^2 - 4*a*c)*e*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,4,28,0.1429,1,"{834, 806, 724, 206}"
1581,1,202,0,0.2062391,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(3/2),x]","\frac{e^2 \sqrt{a+b x+c x^2} \left(-2 c e (8 a e+27 b d)+15 b^2 e^2+10 c e x (2 c d-b e)+64 c^2 d^2\right)}{3 c^3}+\frac{e (2 c d-b e) \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{7/2}}+\frac{8 e^2 (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c}-\frac{2 (d+e x)^4}{\sqrt{a+b x+c x^2}}","\frac{e^2 \sqrt{a+b x+c x^2} \left(-2 c e (8 a e+27 b d)+15 b^2 e^2+10 c e x (2 c d-b e)+64 c^2 d^2\right)}{3 c^3}+\frac{e (2 c d-b e) \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{7/2}}+\frac{8 e^2 (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c}-\frac{2 (d+e x)^4}{\sqrt{a+b x+c x^2}}",1,"(-2*(d + e*x)^4)/Sqrt[a + b*x + c*x^2] + (8*e^2*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(3*c) + (e^2*(64*c^2*d^2 + 15*b^2*e^2 - 2*c*e*(27*b*d + 8*a*e) + 10*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(3*c^3) + (e*(2*c*d - b*e)*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(7/2))","A",5,5,28,0.1786,1,"{768, 742, 779, 621, 206}"
1582,1,153,0,0.1542523,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(3/2),x]","\frac{3 e \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{5/2}}+\frac{9 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{2 c^2}+\frac{3 e^2 (d+e x) \sqrt{a+b x+c x^2}}{c}-\frac{2 (d+e x)^3}{\sqrt{a+b x+c x^2}}","\frac{3 e \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{4 c^{5/2}}+\frac{9 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{2 c^2}+\frac{3 e^2 (d+e x) \sqrt{a+b x+c x^2}}{c}-\frac{2 (d+e x)^3}{\sqrt{a+b x+c x^2}}",1,"(-2*(d + e*x)^3)/Sqrt[a + b*x + c*x^2] + (9*e^2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(2*c^2) + (3*e^2*(d + e*x)*Sqrt[a + b*x + c*x^2])/c + (3*e*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(4*c^(5/2))","A",5,5,28,0.1786,1,"{768, 742, 640, 621, 206}"
1583,1,93,0,0.0518795,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{2 e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 (d+e x)^2}{\sqrt{a+b x+c x^2}}+\frac{4 e^2 \sqrt{a+b x+c x^2}}{c}","\frac{2 e (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 (d+e x)^2}{\sqrt{a+b x+c x^2}}+\frac{4 e^2 \sqrt{a+b x+c x^2}}{c}",1,"(-2*(d + e*x)^2)/Sqrt[a + b*x + c*x^2] + (4*e^2*Sqrt[a + b*x + c*x^2])/c + (2*e*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",4,4,28,0.1429,1,"{768, 640, 621, 206}"
1584,1,60,0,0.0292371,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}-\frac{2 (d+e x)}{\sqrt{a+b x+c x^2}}","\frac{2 e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c}}-\frac{2 (d+e x)}{\sqrt{a+b x+c x^2}}",1,"(-2*(d + e*x))/Sqrt[a + b*x + c*x^2] + (2*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/Sqrt[c]","A",3,3,26,0.1154,1,"{768, 621, 206}"
1585,1,16,0,0.0064971,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2}{\sqrt{a+b x+c x^2}}","-\frac{2}{\sqrt{a+b x+c x^2}}",1,"-2/Sqrt[a + b*x + c*x^2]","A",1,1,21,0.04762,1,"{629}"
1586,1,166,0,0.128964,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}","-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(-2*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) - (e*(2*c*d - b*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(3/2)","A",4,4,28,0.1429,1,"{822, 12, 724, 206}"
1587,1,248,0,0.2734996,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)),x]","-\frac{e \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{5/2}}-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{3 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}","-\frac{e \left(-4 c e (a e+2 b d)+3 b^2 e^2+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{5/2}}-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{3 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}",1,"(-2*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*Sqrt[a + b*x + c*x^2]) + (3*e^2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - (e*(8*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(2*b*d + a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,28,0.1429,1,"{822, 806, 724, 206}"
1588,1,208,0,0.225378,"\int \frac{(b+2 c x) (d+e x)^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(5/2),x]","\frac{8 e^2 \sqrt{a+b x+c x^2} \left(-2 c e (4 a e+3 b d)+3 b^2 e^2+2 c e x (2 c d-b e)+8 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)}-\frac{16 e (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{4 e^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}-\frac{2 (d+e x)^4}{3 \left(a+b x+c x^2\right)^{3/2}}","\frac{8 e^2 \sqrt{a+b x+c x^2} \left(-2 c e (4 a e+3 b d)+3 b^2 e^2+2 c e x (2 c d-b e)+8 c^2 d^2\right)}{3 c^2 \left(b^2-4 a c\right)}-\frac{16 e (d+e x)^2 (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{4 e^3 (2 c d-b e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}-\frac{2 (d+e x)^4}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^4)/(3*(a + b*x + c*x^2)^(3/2)) - (16*e*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (8*e^2*(8*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(3*b*d + 4*a*e) + 2*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(3*c^2*(b^2 - 4*a*c)) + (4*e^3*(2*c*d - b*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(5/2)","A",5,5,28,0.1786,1,"{768, 738, 779, 621, 206}"
1589,1,158,0,0.1156779,"\int \frac{(b+2 c x) (d+e x)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(5/2),x]","\frac{4 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{4 e (d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 (d+e x)^3}{3 \left(a+b x+c x^2\right)^{3/2}}","\frac{4 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{c \left(b^2-4 a c\right)}-\frac{4 e (d+e x) (-2 a e+x (2 c d-b e)+b d)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}-\frac{2 (d+e x)^3}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^3)/(3*(a + b*x + c*x^2)^(3/2)) - (4*e*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (4*e^2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(c*(b^2 - 4*a*c)) + (2*e^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",5,5,28,0.1786,1,"{768, 738, 640, 621, 206}"
1590,1,74,0,0.0391755,"\int \frac{(b+2 c x) (d+e x)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{8 e (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^2}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{8 e (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^2}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^2)/(3*(a + b*x + c*x^2)^(3/2)) - (8*e*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])","A",2,2,28,0.07143,1,"{768, 636}"
1591,1,59,0,0.0222422,"\int \frac{(b+2 c x) (d+e x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x))/(a + b*x + c*x^2)^(5/2),x]","-\frac{4 e (b+2 c x)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{4 e (b+2 c x)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x))/(3*(a + b*x + c*x^2)^(3/2)) - (4*e*(b + 2*c*x))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])","A",2,2,26,0.07692,1,"{768, 613}"
1592,1,18,0,0.006047,"\int \frac{b+2 c x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b + 2*c*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{2}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"-2/(3*(a + b*x + c*x^2)^(3/2))","A",1,1,21,0.04762,1,"{629}"
1593,1,291,0,0.2932548,"\int \frac{b+2 c x}{(d+e x) \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b + 2*c*x)/((d + e*x)*(a + b*x + c*x^2)^(5/2)),x]","-\frac{2 e \left(-c x \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)-2 b c \left(c d^2-5 a e^2\right)-12 a c^2 d e+5 b^2 c d e-3 b^3 e^2\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{e^3 (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{5/2}}","-\frac{2 e \left(-c x \left(-4 c e (2 a e+b d)+3 b^2 e^2+4 c^2 d^2\right)-2 b c \left(c d^2-5 a e^2\right)-12 a c^2 d e+5 b^2 c d e-3 b^3 e^2\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{e^3 (2 c d-b e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{5/2}}",1,"(-2*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2)) - (2*e*(5*b^2*c*d*e - 12*a*c^2*d*e - 3*b^3*e^2 - 2*b*c*(c*d^2 - 5*a*e^2) - c*(4*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(b*d + 2*a*e))*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[a + b*x + c*x^2]) - (e^3*(2*c*d - b*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(5/2)","A",5,4,28,0.1429,1,"{822, 12, 724, 206}"
1594,1,423,0,0.5716441,"\int \frac{b+2 c x}{(d+e x)^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{e^2 \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (13 a e+2 b d)+15 b^2 e^2+8 c^2 d^2\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{2 e \left(-c x \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)-4 b c \left(c d^2-4 a e^2\right)-20 a c^2 d e+9 b^2 c d e-5 b^3 e^2\right)}{3 \left(b^2-4 a c\right) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{e^3 \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}","\frac{e^2 \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (13 a e+2 b d)+15 b^2 e^2+8 c^2 d^2\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{2 e \left(-c x \left(-4 c e (3 a e+2 b d)+5 b^2 e^2+8 c^2 d^2\right)-4 b c \left(c d^2-4 a e^2\right)-20 a c^2 d e+9 b^2 c d e-5 b^3 e^2\right)}{3 \left(b^2-4 a c\right) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{e^3 \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{7/2}}-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^(3/2)) - (2*e*(9*b^2*c*d*e - 20*a*c^2*d*e - 5*b^3*e^2 - 4*b*c*(c*d^2 - 4*a*e^2) - c*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(2*b*d + 3*a*e))*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*Sqrt[a + b*x + c*x^2]) + (e^2*(2*c*d - b*e)*(8*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(2*b*d + 13*a*e))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - (e^3*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,4,28,0.1429,1,"{822, 806, 724, 206}"
1595,1,132,0,0.0822013,"\int (b+2 c x) (d+e x)^{5/2} \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)^(5/2)*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{9/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{9 e^4}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{7 e^4}-\frac{6 c (d+e x)^{11/2} (2 c d-b e)}{11 e^4}+\frac{4 c^2 (d+e x)^{13/2}}{13 e^4}","\frac{2 (d+e x)^{9/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{9 e^4}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{7 e^4}-\frac{6 c (d+e x)^{11/2} (2 c d-b e)}{11 e^4}+\frac{4 c^2 (d+e x)^{13/2}}{13 e^4}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(7/2))/(7*e^4) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(9/2))/(9*e^4) - (6*c*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^4) + (4*c^2*(d + e*x)^(13/2))/(13*e^4)","A",2,1,26,0.03846,1,"{771}"
1596,1,132,0,0.065797,"\int (b+2 c x) (d+e x)^{3/2} \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)^(3/2)*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{7/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{7 e^4}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{2 c (d+e x)^{9/2} (2 c d-b e)}{3 e^4}+\frac{4 c^2 (d+e x)^{11/2}}{11 e^4}","\frac{2 (d+e x)^{7/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{7 e^4}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{2 c (d+e x)^{9/2} (2 c d-b e)}{3 e^4}+\frac{4 c^2 (d+e x)^{11/2}}{11 e^4}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2))/(5*e^4) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(7/2))/(7*e^4) - (2*c*(2*c*d - b*e)*(d + e*x)^(9/2))/(3*e^4) + (4*c^2*(d + e*x)^(11/2))/(11*e^4)","A",2,1,26,0.03846,1,"{771}"
1597,1,132,0,0.0700871,"\int (b+2 c x) \sqrt{d+e x} \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*Sqrt[d + e*x]*(a + b*x + c*x^2),x]","\frac{2 (d+e x)^{5/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^4}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4}-\frac{6 c (d+e x)^{7/2} (2 c d-b e)}{7 e^4}+\frac{4 c^2 (d+e x)^{9/2}}{9 e^4}","\frac{2 (d+e x)^{5/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^4}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4}-\frac{6 c (d+e x)^{7/2} (2 c d-b e)}{7 e^4}+\frac{4 c^2 (d+e x)^{9/2}}{9 e^4}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2))/(3*e^4) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(5/2))/(5*e^4) - (6*c*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^4) + (4*c^2*(d + e*x)^(9/2))/(9*e^4)","A",2,1,26,0.03846,1,"{771}"
1598,1,130,0,0.0624168,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{\sqrt{d+e x}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/Sqrt[d + e*x],x]","\frac{2 (d+e x)^{3/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{3 e^4}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{6 c (d+e x)^{5/2} (2 c d-b e)}{5 e^4}+\frac{4 c^2 (d+e x)^{7/2}}{7 e^4}","\frac{2 (d+e x)^{3/2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{3 e^4}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{6 c (d+e x)^{5/2} (2 c d-b e)}{5 e^4}+\frac{4 c^2 (d+e x)^{7/2}}{7 e^4}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x])/e^4 + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(3/2))/(3*e^4) - (6*c*(2*c*d - b*e)*(d + e*x)^(5/2))/(5*e^4) + (4*c^2*(d + e*x)^(7/2))/(7*e^4)","A",2,1,26,0.03846,1,"{771}"
1599,1,126,0,0.0678039,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^{3/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^4 \sqrt{d+e x}}-\frac{2 c (d+e x)^{3/2} (2 c d-b e)}{e^4}+\frac{4 c^2 (d+e x)^{5/2}}{5 e^4}","\frac{2 \sqrt{d+e x} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{e^4 \sqrt{d+e x}}-\frac{2 c (d+e x)^{3/2} (2 c d-b e)}{e^4}+\frac{4 c^2 (d+e x)^{5/2}}{5 e^4}",1,"(2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(e^4*Sqrt[d + e*x]) + (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*Sqrt[d + e*x])/e^4 - (2*c*(2*c*d - b*e)*(d + e*x)^(3/2))/e^4 + (4*c^2*(d + e*x)^(5/2))/(5*e^4)","A",2,1,26,0.03846,1,"{771}"
1600,1,128,0,0.0642856,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)}{(d+e x)^{5/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2))/(d + e*x)^(5/2),x]","-\frac{2 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^{3/2}}-\frac{6 c \sqrt{d+e x} (2 c d-b e)}{e^4}+\frac{4 c^2 (d+e x)^{3/2}}{3 e^4}","-\frac{2 \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^{3/2}}-\frac{6 c \sqrt{d+e x} (2 c d-b e)}{e^4}+\frac{4 c^2 (d+e x)^{3/2}}{3 e^4}",1,"(2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2))/(3*e^4*(d + e*x)^(3/2)) - (2*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(e^4*Sqrt[d + e*x]) - (6*c*(2*c*d - b*e)*Sqrt[d + e*x])/e^4 + (4*c^2*(d + e*x)^(3/2))/(3*e^4)","A",2,1,26,0.03846,1,"{771}"
1601,1,252,0,0.1726379,"\int (b+2 c x) (d+e x)^{5/2} \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)^(5/2)*(a + b*x + c*x^2)^2,x]","\frac{8 c (d+e x)^{13/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{13 e^6}-\frac{2 (d+e x)^{11/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{11 e^6}+\frac{4 (d+e x)^{9/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{9 e^6}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{7 e^6}-\frac{2 c^2 (d+e x)^{15/2} (2 c d-b e)}{3 e^6}+\frac{4 c^3 (d+e x)^{17/2}}{17 e^6}","\frac{8 c (d+e x)^{13/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{13 e^6}-\frac{2 (d+e x)^{11/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{11 e^6}+\frac{4 (d+e x)^{9/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{9 e^6}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{7 e^6}-\frac{2 c^2 (d+e x)^{15/2} (2 c d-b e)}{3 e^6}+\frac{4 c^3 (d+e x)^{17/2}}{17 e^6}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(7/2))/(7*e^6) + (4*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(9/2))/(9*e^6) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(11/2))/(11*e^6) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(13/2))/(13*e^6) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(15/2))/(3*e^6) + (4*c^3*(d + e*x)^(17/2))/(17*e^6)","A",2,1,28,0.03571,1,"{771}"
1602,1,252,0,0.1286901,"\int (b+2 c x) (d+e x)^{3/2} \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)^(3/2)*(a + b*x + c*x^2)^2,x]","\frac{8 c (d+e x)^{11/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{11 e^6}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{9 e^6}+\frac{4 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^6}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6}-\frac{10 c^2 (d+e x)^{13/2} (2 c d-b e)}{13 e^6}+\frac{4 c^3 (d+e x)^{15/2}}{15 e^6}","\frac{8 c (d+e x)^{11/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{11 e^6}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{9 e^6}+\frac{4 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^6}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6}-\frac{10 c^2 (d+e x)^{13/2} (2 c d-b e)}{13 e^6}+\frac{4 c^3 (d+e x)^{15/2}}{15 e^6}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(5/2))/(5*e^6) + (4*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(7/2))/(7*e^6) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(9/2))/(9*e^6) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(11/2))/(11*e^6) - (10*c^2*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^6) + (4*c^3*(d + e*x)^(15/2))/(15*e^6)","A",2,1,28,0.03571,1,"{771}"
1603,1,252,0,0.1245356,"\int (b+2 c x) \sqrt{d+e x} \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*Sqrt[d + e*x]*(a + b*x + c*x^2)^2,x]","\frac{8 c (d+e x)^{9/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{9 e^6}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^6}+\frac{4 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^6}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6}-\frac{10 c^2 (d+e x)^{11/2} (2 c d-b e)}{11 e^6}+\frac{4 c^3 (d+e x)^{13/2}}{13 e^6}","\frac{8 c (d+e x)^{9/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{9 e^6}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{7 e^6}+\frac{4 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^6}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6}-\frac{10 c^2 (d+e x)^{11/2} (2 c d-b e)}{11 e^6}+\frac{4 c^3 (d+e x)^{13/2}}{13 e^6}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(3/2))/(3*e^6) + (4*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5/2))/(5*e^6) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(7/2))/(7*e^6) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(9/2))/(9*e^6) - (10*c^2*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^6) + (4*c^3*(d + e*x)^(13/2))/(13*e^6)","A",2,1,28,0.03571,1,"{771}"
1604,1,250,0,0.125853,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/Sqrt[d + e*x],x]","\frac{8 c (d+e x)^{7/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^6}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^6}+\frac{4 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6}-\frac{10 c^2 (d+e x)^{9/2} (2 c d-b e)}{9 e^6}+\frac{4 c^3 (d+e x)^{11/2}}{11 e^6}","\frac{8 c (d+e x)^{7/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{7 e^6}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^6}+\frac{4 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6}-\frac{10 c^2 (d+e x)^{9/2} (2 c d-b e)}{9 e^6}+\frac{4 c^3 (d+e x)^{11/2}}{11 e^6}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x])/e^6 + (4*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3/2))/(3*e^6) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(5/2))/(5*e^6) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(7/2))/(7*e^6) - (10*c^2*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^6) + (4*c^3*(d + e*x)^(11/2))/(11*e^6)","A",2,1,28,0.03571,1,"{771}"
1605,1,248,0,0.1272137,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^(3/2),x]","\frac{8 c (d+e x)^{5/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^6}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^6}+\frac{4 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6 \sqrt{d+e x}}-\frac{10 c^2 (d+e x)^{7/2} (2 c d-b e)}{7 e^6}+\frac{4 c^3 (d+e x)^{9/2}}{9 e^6}","\frac{8 c (d+e x)^{5/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^6}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^6}+\frac{4 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{e^6 \sqrt{d+e x}}-\frac{10 c^2 (d+e x)^{7/2} (2 c d-b e)}{7 e^6}+\frac{4 c^3 (d+e x)^{9/2}}{9 e^6}",1,"(2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^6*Sqrt[d + e*x]) + (4*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*Sqrt[d + e*x])/e^6 - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(3/2))/(3*e^6) + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(5/2))/(5*e^6) - (10*c^2*(2*c*d - b*e)*(d + e*x)^(7/2))/(7*e^6) + (4*c^3*(d + e*x)^(9/2))/(9*e^6)","A",2,1,28,0.03571,1,"{771}"
1606,1,246,0,0.126618,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^2)/(d + e*x)^(5/2),x]","\frac{8 c (d+e x)^{3/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6}-\frac{4 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6 (d+e x)^{3/2}}-\frac{2 c^2 (d+e x)^{5/2} (2 c d-b e)}{e^6}+\frac{4 c^3 (d+e x)^{7/2}}{7 e^6}","\frac{8 c (d+e x)^{3/2} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^6}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6}-\frac{4 \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6 (d+e x)^{3/2}}-\frac{2 c^2 (d+e x)^{5/2} (2 c d-b e)}{e^6}+\frac{4 c^3 (d+e x)^{7/2}}{7 e^6}",1,"(2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2)/(3*e^6*(d + e*x)^(3/2)) - (4*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^6*Sqrt[d + e*x]) - (2*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*Sqrt[d + e*x])/e^6 + (8*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(3/2))/(3*e^6) - (2*c^2*(2*c*d - b*e)*(d + e*x)^(5/2))/e^6 + (4*c^3*(d + e*x)^(7/2))/(7*e^6)","A",2,1,28,0.03571,1,"{771}"
1607,1,427,0,0.3033176,"\int (b+2 c x) (d+e x)^{5/2} \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)^(5/2)*(a + b*x + c*x^2)^3,x]","\frac{2 (d+e x)^{13/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{13 e^8}+\frac{6 c^2 (d+e x)^{17/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{17 e^8}-\frac{2 c (d+e x)^{15/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^8}-\frac{6 (d+e x)^{11/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{11 e^8}+\frac{2 (d+e x)^{9/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{9 e^8}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{7 e^8}-\frac{14 c^3 (d+e x)^{19/2} (2 c d-b e)}{19 e^8}+\frac{4 c^4 (d+e x)^{21/2}}{21 e^8}","\frac{2 (d+e x)^{13/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{13 e^8}+\frac{6 c^2 (d+e x)^{17/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{17 e^8}-\frac{2 c (d+e x)^{15/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^8}-\frac{6 (d+e x)^{11/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{11 e^8}+\frac{2 (d+e x)^{9/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{9 e^8}-\frac{2 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{7 e^8}-\frac{14 c^3 (d+e x)^{19/2} (2 c d-b e)}{19 e^8}+\frac{4 c^4 (d+e x)^{21/2}}{21 e^8}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(7/2))/(7*e^8) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(9/2))/(9*e^8) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(11/2))/(11*e^8) + (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(13/2))/(13*e^8) - (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(15/2))/(3*e^8) + (6*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(17/2))/(17*e^8) - (14*c^3*(2*c*d - b*e)*(d + e*x)^(19/2))/(19*e^8) + (4*c^4*(d + e*x)^(21/2))/(21*e^8)","A",2,1,28,0.03571,1,"{771}"
1608,1,427,0,0.2428375,"\int (b+2 c x) (d+e x)^{3/2} \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)^(3/2)*(a + b*x + c*x^2)^3,x]","\frac{2 (d+e x)^{11/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{11 e^8}+\frac{2 c^2 (d+e x)^{15/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{10 c (d+e x)^{13/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{13 e^8}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^8}+\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^8}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8}-\frac{14 c^3 (d+e x)^{17/2} (2 c d-b e)}{17 e^8}+\frac{4 c^4 (d+e x)^{19/2}}{19 e^8}","\frac{2 (d+e x)^{11/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{11 e^8}+\frac{2 c^2 (d+e x)^{15/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{10 c (d+e x)^{13/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{13 e^8}-\frac{2 (d+e x)^{9/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{3 e^8}+\frac{2 (d+e x)^{7/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^8}-\frac{2 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8}-\frac{14 c^3 (d+e x)^{17/2} (2 c d-b e)}{17 e^8}+\frac{4 c^4 (d+e x)^{19/2}}{19 e^8}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(5/2))/(5*e^8) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(7/2))/(7*e^8) - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(9/2))/(3*e^8) + (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(11/2))/(11*e^8) - (10*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(13/2))/(13*e^8) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(15/2))/(5*e^8) - (14*c^3*(2*c*d - b*e)*(d + e*x)^(17/2))/(17*e^8) + (4*c^4*(d + e*x)^(19/2))/(19*e^8)","A",2,1,28,0.03571,1,"{771}"
1609,1,427,0,0.2383875,"\int (b+2 c x) \sqrt{d+e x} \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*Sqrt[d + e*x]*(a + b*x + c*x^2)^3,x]","\frac{2 (d+e x)^{9/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{9 e^8}+\frac{6 c^2 (d+e x)^{13/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{13 e^8}-\frac{10 c (d+e x)^{11/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{11 e^8}-\frac{6 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}+\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8}-\frac{14 c^3 (d+e x)^{15/2} (2 c d-b e)}{15 e^8}+\frac{4 c^4 (d+e x)^{17/2}}{17 e^8}","\frac{2 (d+e x)^{9/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{9 e^8}+\frac{6 c^2 (d+e x)^{13/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{13 e^8}-\frac{10 c (d+e x)^{11/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{11 e^8}-\frac{6 (d+e x)^{7/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}+\frac{2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{5 e^8}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8}-\frac{14 c^3 (d+e x)^{15/2} (2 c d-b e)}{15 e^8}+\frac{4 c^4 (d+e x)^{17/2}}{17 e^8}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(3/2))/(3*e^8) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(5/2))/(5*e^8) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(7/2))/(7*e^8) + (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(9/2))/(9*e^8) - (10*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(11/2))/(11*e^8) + (6*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(13/2))/(13*e^8) - (14*c^3*(2*c*d - b*e)*(d + e*x)^(15/2))/(15*e^8) + (4*c^4*(d + e*x)^(17/2))/(17*e^8)","A",2,1,28,0.03571,1,"{771}"
1610,1,425,0,0.2338374,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/Sqrt[d + e*x],x]","\frac{2 (d+e x)^{7/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{7 e^8}+\frac{6 c^2 (d+e x)^{11/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{11 e^8}-\frac{10 c (d+e x)^{9/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{9 e^8}-\frac{6 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^8}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8}-\frac{14 c^3 (d+e x)^{13/2} (2 c d-b e)}{13 e^8}+\frac{4 c^4 (d+e x)^{15/2}}{15 e^8}","\frac{2 (d+e x)^{7/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{7 e^8}+\frac{6 c^2 (d+e x)^{11/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{11 e^8}-\frac{10 c (d+e x)^{9/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{9 e^8}-\frac{6 (d+e x)^{5/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{5 e^8}+\frac{2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8}-\frac{2 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8}-\frac{14 c^3 (d+e x)^{13/2} (2 c d-b e)}{13 e^8}+\frac{4 c^4 (d+e x)^{15/2}}{15 e^8}",1,"(-2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[d + e*x])/e^8 + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(3/2))/(3*e^8) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(5/2))/(5*e^8) + (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(7/2))/(7*e^8) - (10*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(9/2))/(9*e^8) + (6*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(11/2))/(11*e^8) - (14*c^3*(2*c*d - b*e)*(d + e*x)^(13/2))/(13*e^8) + (4*c^4*(d + e*x)^(15/2))/(15*e^8)","A",2,1,28,0.03571,1,"{771}"
1611,1,421,0,0.2386154,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^(3/2),x]","\frac{2 (d+e x)^{5/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{5 e^8}+\frac{2 c^2 (d+e x)^{9/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8}-\frac{10 c (d+e x)^{7/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8 \sqrt{d+e x}}-\frac{14 c^3 (d+e x)^{11/2} (2 c d-b e)}{11 e^8}+\frac{4 c^4 (d+e x)^{13/2}}{13 e^8}","\frac{2 (d+e x)^{5/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{5 e^8}+\frac{2 c^2 (d+e x)^{9/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{3 e^8}-\frac{10 c (d+e x)^{7/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{7 e^8}-\frac{2 (d+e x)^{3/2} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}+\frac{2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{e^8 \sqrt{d+e x}}-\frac{14 c^3 (d+e x)^{11/2} (2 c d-b e)}{11 e^8}+\frac{4 c^4 (d+e x)^{13/2}}{13 e^8}",1,"(2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^8*Sqrt[d + e*x]) + (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*Sqrt[d + e*x])/e^8 - (2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(3/2))/e^8 + (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(5/2))/(5*e^8) - (10*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(7/2))/(7*e^8) + (2*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(9/2))/(3*e^8) - (14*c^3*(2*c*d - b*e)*(d + e*x)^(11/2))/(11*e^8) + (4*c^4*(d + e*x)^(13/2))/(13*e^8)","A",2,1,28,0.03571,1,"{771}"
1612,1,421,0,0.2284552,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^3)/(d + e*x)^(5/2),x]","\frac{2 (d+e x)^{3/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{3 e^8}+\frac{6 c^2 (d+e x)^{7/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^8}-\frac{2 c (d+e x)^{5/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}-\frac{6 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8 (d+e x)^{3/2}}-\frac{14 c^3 (d+e x)^{9/2} (2 c d-b e)}{9 e^8}+\frac{4 c^4 (d+e x)^{11/2}}{11 e^8}","\frac{2 (d+e x)^{3/2} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{3 e^8}+\frac{6 c^2 (d+e x)^{7/2} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{7 e^8}-\frac{2 c (d+e x)^{5/2} (2 c d-b e) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}-\frac{6 \sqrt{d+e x} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8}-\frac{2 \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 \sqrt{d+e x}}+\frac{2 (2 c d-b e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8 (d+e x)^{3/2}}-\frac{14 c^3 (d+e x)^{9/2} (2 c d-b e)}{9 e^8}+\frac{4 c^4 (d+e x)^{11/2}}{11 e^8}",1,"(2*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^8*(d + e*x)^(3/2)) - (2*(c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e)))/(e^8*Sqrt[d + e*x]) - (6*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*Sqrt[d + e*x])/e^8 + (2*(70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(3/2))/(3*e^8) - (2*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(5/2))/e^8 + (6*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(7/2))/(7*e^8) - (14*c^3*(2*c*d - b*e)*(d + e*x)^(9/2))/(9*e^8) + (4*c^4*(d + e*x)^(11/2))/(11*e^8)","A",2,1,28,0.03571,1,"{771}"
1613,1,422,0,2.2288981,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2),x]","\frac{\sqrt{2} \left(-2 c^2 d \left(d \sqrt{b^2-4 a c}-4 a e\right)-2 c e \left(-b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(2 c^2 d \left(d \sqrt{b^2-4 a c}+4 a e\right)-2 c e \left(b d \sqrt{b^2-4 a c}+a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d+e x} (2 c d-b e)}{c}+\frac{4}{3} (d+e x)^{3/2}","\frac{\sqrt{2} \left(-2 c^2 d \left(d \sqrt{b^2-4 a c}-4 a e\right)-2 c e \left(-b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{\sqrt{2} \left(2 c^2 d \left(d \sqrt{b^2-4 a c}+4 a e\right)-2 c e \left(b d \sqrt{b^2-4 a c}+a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{2 \sqrt{d+e x} (2 c d-b e)}{c}+\frac{4}{3} (d+e x)^{3/2}",1,"(2*(2*c*d - b*e)*Sqrt[d + e*x])/c + (4*(d + e*x)^(3/2))/3 + (Sqrt[2]*(b^2*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c^2*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e) - 2*c*e*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e - a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (Sqrt[2]*(b^2*(b + Sqrt[b^2 - 4*a*c])*e^2 + 2*c^2*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e) - 2*c*e*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e + a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,4,28,0.1429,1,"{824, 826, 1166, 208}"
1614,1,291,0,0.8877328,"\int \frac{(b+2 c x) \sqrt{d+e x}}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2),x]","-\frac{\sqrt{2} \left(2 c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b e \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(b e \left(\sqrt{b^2-4 a c}+b\right)-2 c \left(d \sqrt{b^2-4 a c}+2 a e\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+4 \sqrt{d+e x}","-\frac{\sqrt{2} \left(2 c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b e \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \left(b e \left(\sqrt{b^2-4 a c}+b\right)-2 c \left(d \sqrt{b^2-4 a c}+2 a e\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{c} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+4 \sqrt{d+e x}",1,"4*Sqrt[d + e*x] - (Sqrt[2]*(b*(b - Sqrt[b^2 - 4*a*c])*e + 2*c*(Sqrt[b^2 - 4*a*c]*d - 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*(b*(b + Sqrt[b^2 - 4*a*c])*e - 2*c*(Sqrt[b^2 - 4*a*c]*d + 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[c]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,4,28,0.1429,1,"{824, 826, 1166, 208}"
1615,1,175,0,0.1760512,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)} \, dx","Int[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)),x]","-\frac{2 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{2 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}","-\frac{2 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{2 \sqrt{2} \sqrt{c} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}",1,"(-2*Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e] - (2*Sqrt[2]*Sqrt[c]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]","A",4,3,28,0.1071,1,"{826, 1166, 208}"
1616,1,354,0,0.7036159,"\int \frac{b+2 c x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)} \, dx","Int[(b + 2*c*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)),x]","\frac{\sqrt{2} \sqrt{c} \left(b e \left(\sqrt{b^2-4 a c}+b\right)-2 c \left(d \sqrt{b^2-4 a c}+2 a e\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{c} \left(2 c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b e \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{2 (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}","\frac{\sqrt{2} \sqrt{c} \left(b e \left(\sqrt{b^2-4 a c}+b\right)-2 c \left(d \sqrt{b^2-4 a c}+2 a e\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{c} \left(2 c \left(d \sqrt{b^2-4 a c}-2 a e\right)+b e \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}+\frac{2 (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}",1,"(2*(2*c*d - b*e))/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) + (Sqrt[2]*Sqrt[c]*(b*(b + Sqrt[b^2 - 4*a*c])*e - 2*c*(Sqrt[b^2 - 4*a*c]*d + 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - (Sqrt[2]*Sqrt[c]*(b*(b - Sqrt[b^2 - 4*a*c])*e + 2*c*(Sqrt[b^2 - 4*a*c]*d - 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",5,4,28,0.1429,1,"{828, 826, 1166, 208}"
1617,1,518,0,1.9020387,"\int \frac{b+2 c x}{(d+e x)^{5/2} \left(a+b x+c x^2\right)} \, dx","Int[(b + 2*c*x)/((d + e*x)^(5/2)*(a + b*x + c*x^2)),x]","\frac{2 \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{2} \sqrt{c} \left(2 c^2 d \left(d \sqrt{b^2-4 a c}+4 a e\right)-2 c e \left(b d \sqrt{b^2-4 a c}+a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{2} \sqrt{c} \left(-2 c^2 d \left(d \sqrt{b^2-4 a c}-4 a e\right)-2 c e \left(-b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 (2 c d-b e)}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}","\frac{2 \left(-2 c e (a e+b d)+b^2 e^2+2 c^2 d^2\right)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{2} \sqrt{c} \left(2 c^2 d \left(d \sqrt{b^2-4 a c}+4 a e\right)-2 c e \left(b d \sqrt{b^2-4 a c}+a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{2} \sqrt{c} \left(-2 c^2 d \left(d \sqrt{b^2-4 a c}-4 a e\right)-2 c e \left(-b d \sqrt{b^2-4 a c}-a e \sqrt{b^2-4 a c}+2 a b e+b^2 d\right)+b^2 e^2 \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 (2 c d-b e)}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}",1,"(2*(2*c*d - b*e))/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (2*(2*c^2*d^2 + b^2*e^2 - 2*c*e*(b*d + a*e)))/((c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[c]*(b^2*(b + Sqrt[b^2 - 4*a*c])*e^2 + 2*c^2*d*(Sqrt[b^2 - 4*a*c]*d + 4*a*e) - 2*c*e*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e + a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[2]*Sqrt[c]*(b^2*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c^2*d*(Sqrt[b^2 - 4*a*c]*d - 4*a*e) - 2*c*e*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d + 2*a*b*e - a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2)","A",6,4,28,0.1429,1,"{828, 826, 1166, 208}"
1618,1,350,0,1.2865316,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^2,x]","-\frac{5 e \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{5 e \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{5/2}}{a+b x+c x^2}+\frac{5 e^2 \sqrt{d+e x}}{c}","-\frac{5 e \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{5 e \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} c^{3/2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{5/2}}{a+b x+c x^2}+\frac{5 e^2 \sqrt{d+e x}}{c}",1,"(5*e^2*Sqrt[d + e*x])/c - (d + e*x)^(5/2)/(a + b*x + c*x^2) - (5*e*(2*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d - Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (5*e*(2*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d + Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*c^(3/2)*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,28,0.1786,1,"{768, 703, 826, 1166, 208}"
1619,1,224,0,0.3438847,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^2,x]","-\frac{3 e \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}+\frac{3 e \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{(d+e x)^{3/2}}{a+b x+c x^2}","-\frac{3 e \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}+\frac{3 e \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{c} \sqrt{b^2-4 a c}}-\frac{(d+e x)^{3/2}}{a+b x+c x^2}",1,"-((d + e*x)^(3/2)/(a + b*x + c*x^2)) - (3*e*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c]) + (3*e*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[c]*Sqrt[b^2 - 4*a*c])","A",5,4,28,0.1429,1,"{768, 699, 1130, 208}"
1620,1,223,0,0.3197426,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^2,x]","-\frac{\sqrt{2} \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x}}{a+b x+c x^2}","-\frac{\sqrt{2} \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}+\frac{\sqrt{2} \sqrt{c} e \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{\sqrt{d+e x}}{a+b x+c x^2}",1,"-(Sqrt[d + e*x]/(a + b*x + c*x^2)) - (Sqrt[2]*Sqrt[c]*e*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) + (Sqrt[2]*Sqrt[c]*e*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",5,4,28,0.1429,1,"{768, 707, 1093, 208}"
1621,1,364,0,0.7609108,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^2} \, dx","Int[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^2),x]","-\frac{\sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} e \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}","-\frac{\sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{c} e \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}",1,"-((Sqrt[d + e*x]*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) + (Sqrt[c]*e*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - (Sqrt[c]*e*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",5,4,28,0.1429,1,"{822, 826, 1166, 208}"
1622,1,469,0,1.7209049,"\int \frac{b+2 c x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^2} \, dx","Int[(b + 2*c*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)^2),x]","\frac{3 \sqrt{c} e \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{3 \sqrt{c} e \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{3 e^2 (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}","\frac{3 \sqrt{c} e \left(-2 c e \left(d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{3 \sqrt{c} e \left(-2 c e \left(-d \sqrt{b^2-4 a c}+a e+b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+2 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}+\frac{3 e^2 (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}",1,"(3*e^2*(2*c*d - b*e))/((c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - ((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x)/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*(a + b*x + c*x^2)) + (3*Sqrt[c]*e*(2*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d + Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) - (3*Sqrt[c]*e*(2*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(b*d - Sqrt[b^2 - 4*a*c]*d + a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,28,0.1786,1,"{822, 828, 826, 1166, 208}"
1623,1,543,0,5.7227942,"\int \frac{(b+2 c x) (d+e x)^{7/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^(7/2))/(a + b*x + c*x^2)^3,x]","\frac{7 e \left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(-b d \sqrt{b^2-4 a c}+3 a e \sqrt{b^2-4 a c}-4 a b e+b^2 d\right)+b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{7 e \left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(b d \sqrt{b^2-4 a c}-3 a e \sqrt{b^2-4 a c}-4 a b e+b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{7 e^2 \sqrt{d+e x} (2 c d-b e)}{4 c \left(b^2-4 a c\right)}-\frac{7 e (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{(d+e x)^{7/2}}{2 \left(a+b x+c x^2\right)^2}","\frac{7 e \left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(-b d \sqrt{b^2-4 a c}+3 a e \sqrt{b^2-4 a c}-4 a b e+b^2 d\right)+b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{7 e \left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-8 a e+6 b d\right)+2 c e^2 \left(b d \sqrt{b^2-4 a c}-3 a e \sqrt{b^2-4 a c}-4 a b e+b^2 d\right)+b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} c^{3/2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}+\frac{7 e^2 \sqrt{d+e x} (2 c d-b e)}{4 c \left(b^2-4 a c\right)}-\frac{7 e (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{(d+e x)^{7/2}}{2 \left(a+b x+c x^2\right)^2}",1,"(7*e^2*(2*c*d - b*e)*Sqrt[d + e*x])/(4*c*(b^2 - 4*a*c)) - (d + e*x)^(7/2)/(2*(a + b*x + c*x^2)^2) - (7*e*(d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (7*e*(8*c^3*d^3 + b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d - Sqrt[b^2 - 4*a*c]*d - 8*a*e) + 2*c*e^2*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d - 4*a*b*e + 3*a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (7*e*(8*c^3*d^3 + b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d + Sqrt[b^2 - 4*a*c]*d - 8*a*e) + 2*c*e^2*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d - 4*a*b*e - 3*a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*c^(3/2)*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",7,6,28,0.2143,1,"{768, 738, 824, 826, 1166, 208}"
1624,1,398,0,1.7035893,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^3,x]","\frac{5 e \left(-2 c e \left(-d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{5 e \left(-2 c e \left(d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{5 e \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{(d+e x)^{5/2}}{2 \left(a+b x+c x^2\right)^2}","\frac{5 e \left(-2 c e \left(-d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{5 e \left(-2 c e \left(d \sqrt{b^2-4 a c}-2 a e+4 b d\right)+b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} \sqrt{c} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{5 e \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}-\frac{(d+e x)^{5/2}}{2 \left(a+b x+c x^2\right)^2}",1,"-(d + e*x)^(5/2)/(2*(a + b*x + c*x^2)^2) - (5*e*Sqrt[d + e*x]*(b*d - 2*a*e + (2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (5*e*(8*c^2*d^2 + b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*b*d - Sqrt[b^2 - 4*a*c]*d - 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (5*e*(8*c^2*d^2 + b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*b*d + Sqrt[b^2 - 4*a*c]*d - 2*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*Sqrt[c]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,28,0.1786,1,"{768, 738, 826, 1166, 208}"
1625,1,322,0,0.7886748,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^3,x]","-\frac{3 e (b+2 c x) \sqrt{d+e x}}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{3 \sqrt{c} e \left(4 c d-e \left(2 b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{2 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{3 \sqrt{c} e \left(4 c d-e \left(\sqrt{b^2-4 a c}+2 b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{2 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{3/2}}{2 \left(a+b x+c x^2\right)^2}","-\frac{3 e (b+2 c x) \sqrt{d+e x}}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)}+\frac{3 \sqrt{c} e \left(4 c d-e \left(2 b-\sqrt{b^2-4 a c}\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{2 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}-\frac{3 \sqrt{c} e \left(4 c d-e \left(\sqrt{b^2-4 a c}+2 b\right)\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{2 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}-\frac{(d+e x)^{3/2}}{2 \left(a+b x+c x^2\right)^2}",1,"-(d + e*x)^(3/2)/(2*(a + b*x + c*x^2)^2) - (3*e*(b + 2*c*x)*Sqrt[d + e*x])/(4*(b^2 - 4*a*c)*(a + b*x + c*x^2)) + (3*Sqrt[c]*e*(4*c*d - (2*b - Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(2*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]) - (3*Sqrt[c]*e*(4*c*d - (2*b + Sqrt[b^2 - 4*a*c])*e)*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(2*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e])","A",6,5,28,0.1786,1,"{768, 736, 826, 1166, 208}"
1626,1,463,0,1.8902961,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^3} \, dx","Int[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^3,x]","\frac{\sqrt{c} e \left(-2 c e \left(-d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e \left(-2 c e \left(d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{e \sqrt{d+e x} \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{d+e x}}{2 \left(a+b x+c x^2\right)^2}","\frac{\sqrt{c} e \left(-2 c e \left(-d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(\sqrt{b^2-4 a c}+b\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{c} e \left(-2 c e \left(d \sqrt{b^2-4 a c}-6 a e+4 b d\right)-b e^2 \left(b-\sqrt{b^2-4 a c}\right)+8 c^2 d^2\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)}-\frac{e \sqrt{d+e x} \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{d+e x}}{2 \left(a+b x+c x^2\right)^2}",1,"-Sqrt[d + e*x]/(2*(a + b*x + c*x^2)^2) - (e*Sqrt[d + e*x]*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)) + (Sqrt[c]*e*(8*c^2*d^2 - b*(b + Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*b*d - Sqrt[b^2 - 4*a*c]*d - 6*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)) - (Sqrt[c]*e*(8*c^2*d^2 - b*(b - Sqrt[b^2 - 4*a*c])*e^2 - 2*c*e*(4*b*d + Sqrt[b^2 - 4*a*c]*d - 6*a*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2))","A",6,5,28,0.1786,1,"{768, 740, 826, 1166, 208}"
1627,1,673,0,5.2562007,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^3} \, dx","Int[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^3),x]","\frac{e \sqrt{d+e x} \left(c x \left(-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right)+(c d-3 b e) \left(2 a c e+b^2 (-e)+b c d\right)+5 a c e (2 c d-b e)\right)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} e \left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(b d \sqrt{b^2-4 a c}+5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{c} e \left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(-b d \sqrt{b^2-4 a c}-5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}","\frac{e \sqrt{d+e x} \left(c x \left(-2 c e (5 a e+b d)+3 b^2 e^2+2 c^2 d^2\right)+(c d-3 b e) \left(2 a c e+b^2 (-e)+b c d\right)+5 a c e (2 c d-b e)\right)}{4 \left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{c} e \left(-2 c^2 d e \left(-d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(b d \sqrt{b^2-4 a c}+5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(\sqrt{b^2-4 a c}+b\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(b-\sqrt{b^2-4 a c}\right)} \left(a e^2-b d e+c d^2\right)^2}+\frac{\sqrt{c} e \left(-2 c^2 d e \left(d \sqrt{b^2-4 a c}-16 a e+6 b d\right)-2 c e^2 \left(-b d \sqrt{b^2-4 a c}-5 a e \sqrt{b^2-4 a c}+8 a b e+b^2 d\right)+3 b^2 e^3 \left(b-\sqrt{b^2-4 a c}\right)+8 c^3 d^3\right) \tanh ^{-1}\left(\frac{\sqrt{2} \sqrt{c} \sqrt{d+e x}}{\sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}\right)}{4 \sqrt{2} \left(b^2-4 a c\right)^{3/2} \sqrt{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)} \left(a e^2-b d e+c d^2\right)^2}-\frac{\sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}",1,"-(Sqrt[d + e*x]*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) + (e*Sqrt[d + e*x]*(5*a*c*e*(2*c*d - b*e) + (c*d - 3*b*e)*(b*c*d - b^2*e + 2*a*c*e) + c*(2*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(b*d + 5*a*e))*x))/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - (Sqrt[c]*e*(8*c^3*d^3 + 3*b^2*(b + Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d - Sqrt[b^2 - 4*a*c]*d - 16*a*e) - 2*c*e^2*(b^2*d + b*Sqrt[b^2 - 4*a*c]*d + 8*a*b*e + 5*a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b - Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2) + (Sqrt[c]*e*(8*c^3*d^3 + 3*b^2*(b - Sqrt[b^2 - 4*a*c])*e^3 - 2*c^2*d*e*(6*b*d + Sqrt[b^2 - 4*a*c]*d - 16*a*e) - 2*c*e^2*(b^2*d - b*Sqrt[b^2 - 4*a*c]*d + 8*a*b*e - 5*a*Sqrt[b^2 - 4*a*c]*e))*ArcTanh[(Sqrt[2]*Sqrt[c]*Sqrt[d + e*x])/Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]])/(4*Sqrt[2]*(b^2 - 4*a*c)^(3/2)*Sqrt[2*c*d - (b + Sqrt[b^2 - 4*a*c])*e]*(c*d^2 - b*d*e + a*e^2)^2)","A",6,4,28,0.1429,1,"{822, 826, 1166, 208}"
1628,1,576,0,0.7914443,"\int (b+2 c x) \sqrt{d+e x} \sqrt{a+b x+c x^2} \, dx","Int[(b + 2*c*x)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2],x]","-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (11 b d-10 a e)+b^2 e^2-3 c e x (2 c d-b e)+8 c^2 d^2\right)}{105 c e^2}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^2 e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^2 e^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{7} \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}","-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (11 b d-10 a e)+b^2 e^2-3 c e x (2 c d-b e)+8 c^2 d^2\right)}{105 c e^2}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^2 e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{105 c^2 e^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{7} \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}",1,"(-2*Sqrt[d + e*x]*(8*c^2*d^2 + b^2*e^2 - c*e*(11*b*d - 10*a*e) - 3*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(105*c*e^2) + (4*Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2))/7 + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^2*e^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(105*c^2*e^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{832, 814, 843, 718, 424, 419}"
1629,1,487,0,0.4300209,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{\sqrt{d+e x}} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/Sqrt[d + e*x],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (-7 b e+8 c d-6 c e x)}{15 e^2}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (-7 b e+8 c d-6 c e x)}{15 e^2}",1,"(-2*Sqrt[d + e*x]*(8*c*d - 7*b*e - 6*c*e*x)*Sqrt[a + b*x + c*x^2])/(15*e^2) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c*e^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (16*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c*e^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,30,0.1667,1,"{814, 843, 718, 424, 419}"
1630,1,469,0,0.3784488,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^{3/2}} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(3/2),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{8 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (-3 b e+8 c d+2 c e x)}{3 e^2 \sqrt{d+e x}}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-a e)+3 b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{8 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (-3 b e+8 c d+2 c e x)}{3 e^2 \sqrt{d+e x}}",1,"(2*(8*c*d - 3*b*e + 2*c*e*x)*Sqrt[a + b*x + c*x^2])/(3*e^2*Sqrt[d + e*x]) - (8*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(4*b*d - a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,30,0.1667,1,"{812, 843, 718, 424, 419}"
1631,1,548,0,0.4258349,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^{5/2}} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-c d e (7 b d-4 a e)+a b e^3+8 c^2 d^3\right)}{3 e^2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}","-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-c d e (7 b d-4 a e)+a b e^3+8 c^2 d^3\right)}{3 e^2 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-3 a e)+b^2 e^2+16 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{16 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(-2*(8*c^2*d^3 + a*b*e^3 - c*d*e*(7*b*d - 4*a*e) + e*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*x)*Sqrt[a + b*x + c*x^2])/(3*e^2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 + b^2*e^2 - 4*c*e*(4*b*d - 3*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^3*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (16*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,30,0.1667,1,"{810, 843, 718, 424, 419}"
1632,1,691,0,0.7484052,"\int \frac{(b+2 c x) \sqrt{a+b x+c x^2}}{(d+e x)^{7/2}} \, dx","Int[((b + 2*c*x)*Sqrt[a + b*x + c*x^2])/(d + e*x)^(7/2),x]","\frac{4 \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)}{15 e^2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (7 b d-5 a e)+b^2 e^2+14 c^2 d^2\right)-c d e (5 b d-4 a e)-b e^2 (2 b d-3 a e)+8 c^2 d^3\right)}{15 e^2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{4 \sqrt{a+b x+c x^2} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right)}{15 e^2 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{a+b x+c x^2} \left(e x \left(-2 c e (7 b d-5 a e)+b^2 e^2+14 c^2 d^2\right)-c d e (5 b d-4 a e)-b e^2 (2 b d-3 a e)+8 c^2 d^3\right)}{15 e^2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (4 b d-5 a e)-b^2 e^2+16 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^3 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (b d-2 a e)-b^2 e^2+4 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^3 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(4*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[a + b*x + c*x^2])/(15*e^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (2*(8*c^2*d^3 - c*d*e*(5*b*d - 4*a*e) - b*e^2*(2*b*d - 3*a*e) + e*(14*c^2*d^2 + b^2*e^2 - 2*c*e*(7*b*d - 5*a*e))*x)*Sqrt[a + b*x + c*x^2])/(15*e^2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(4*c^2*d^2 - b^2*e^2 - 4*c*e*(b*d - 2*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^3*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(16*c^2*d^2 - b^2*e^2 - 4*c*e*(4*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^3*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{810, 834, 843, 718, 424, 419}"
1633,1,688,0,0.9810402,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 c^2 e^2 \left(28 a^2 e^2-76 a b d e+45 b^2 d^2\right)-b^2 c e^3 (7 b d-15 a e)-4 c^3 d^2 e (64 b d-57 a e)-b^4 e^4+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^2 e^5 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-3 c e x \left(-4 c e (8 b d-7 a e)+b^2 e^2+32 c^2 d^2\right)-12 c^2 d e (20 b d-11 a e)+3 b c e^2 (37 b d-36 a e)-b^3 e^3+128 c^3 d^3\right)}{315 c e^4}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-4 c e (32 b d-33 a e)-b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^2 e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} (-15 b e+16 c d-14 c e x)}{63 e^2}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(3 c^2 e^2 \left(28 a^2 e^2-76 a b d e+45 b^2 d^2\right)-b^2 c e^3 (7 b d-15 a e)-4 c^3 d^2 e (64 b d-57 a e)-b^4 e^4+128 c^4 d^4\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^2 e^5 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-3 c e x \left(-4 c e (8 b d-7 a e)+b^2 e^2+32 c^2 d^2\right)-12 c^2 d e (20 b d-11 a e)+3 b c e^2 (37 b d-36 a e)-b^3 e^3+128 c^3 d^3\right)}{315 c e^4}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \left(-4 c e (32 b d-33 a e)-b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{315 c^2 e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2} (-15 b e+16 c d-14 c e x)}{63 e^2}",1,"(-2*Sqrt[d + e*x]*(128*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(37*b*d - 36*a*e) - 12*c^2*d*e*(20*b*d - 11*a*e) - 3*c*e*(32*c^2*d^2 + b^2*e^2 - 4*c*e*(8*b*d - 7*a*e))*x)*Sqrt[a + b*x + c*x^2])/(315*c*e^4) - (2*Sqrt[d + e*x]*(16*c*d - 15*b*e - 14*c*e*x)*(a + b*x + c*x^2)^(3/2))/(63*e^2) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^4*d^4 - b^4*e^4 - 4*c^3*d^2*e*(64*b*d - 57*a*e) - b^2*c*e^3*(7*b*d - 15*a*e) + 3*c^2*e^2*(45*b^2*d^2 - 76*a*b*d*e + 28*a^2*e^2))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*c^2*e^5*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(128*c^2*d^2 - b^2*e^2 - 4*c*e*(32*b*d - 33*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(315*c^2*e^5*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,30,0.1667,1,"{814, 843, 718, 424, 419}"
1634,1,592,0,0.7127095,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-4 c e (44 b d-5 a e)+51 b^2 e^2-48 c e x (2 c d-b e)+128 c^2 d^2\right)}{35 e^4}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c e^5 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \left(a+b x+c x^2\right)^{3/2} (-7 b e+16 c d+2 c e x)}{7 e^2 \sqrt{d+e x}}","\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-4 c e (44 b d-5 a e)+51 b^2 e^2-48 c e x (2 c d-b e)+128 c^2 d^2\right)}{35 e^4}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{35 c e^5 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \left(a+b x+c x^2\right)^{3/2} (-7 b e+16 c d+2 c e x)}{7 e^2 \sqrt{d+e x}}",1,"(2*Sqrt[d + e*x]*(128*c^2*d^2 + 51*b^2*e^2 - 4*c*e*(44*b*d - 5*a*e) - 48*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(35*e^4) + (2*(16*c*d - 7*b*e + 2*c*e*x)*(a + b*x + c*x^2)^(3/2))/(7*e^2*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(32*b*d - 29*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(35*c*e^5*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(128*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(32*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(35*c*e^5*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{812, 814, 843, 718, 424, 419}"
1635,1,573,0,0.5803058,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^(5/2),x]","-\frac{2 \sqrt{a+b x+c x^2} \left(-4 c e (28 b d-9 a e)+15 b^2 e^2+16 c e x (2 c d-b e)+128 c^2 d^2\right)}{15 e^4 \sqrt{d+e x}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-17 a e)+15 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (32 b d-9 a e)+23 b^2 e^2+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^5 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \left(a+b x+c x^2\right)^{3/2} (-5 b e+16 c d+6 c e x)}{15 e^2 (d+e x)^{3/2}}","-\frac{2 \sqrt{a+b x+c x^2} \left(-4 c e (28 b d-9 a e)+15 b^2 e^2+16 c e x (2 c d-b e)+128 c^2 d^2\right)}{15 e^4 \sqrt{d+e x}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-17 a e)+15 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (32 b d-9 a e)+23 b^2 e^2+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^5 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \left(a+b x+c x^2\right)^{3/2} (-5 b e+16 c d+6 c e x)}{15 e^2 (d+e x)^{3/2}}",1,"(-2*(128*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(28*b*d - 9*a*e) + 16*c*e*(2*c*d - b*e)*x)*Sqrt[a + b*x + c*x^2])/(15*e^4*Sqrt[d + e*x]) + (2*(16*c*d - 5*b*e + 6*c*e*x)*(a + b*x + c*x^2)^(3/2))/(15*e^2*(d + e*x)^(3/2)) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^2*d^2 + 23*b^2*e^2 - 4*c*e*(32*b*d - 9*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^5*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(32*b*d - 17*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c*e^5*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,30,0.1667,1,"{812, 843, 718, 424, 419}"
1636,1,701,0,0.754707,"\int \frac{(b+2 c x) \left(a+b x+c x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[((b + 2*c*x)*(a + b*x + c*x^2)^(3/2))/(d + e*x)^(7/2),x]","-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(e x \left(-2 c e (11 b d-5 a e)+3 b^2 e^2+22 c^2 d^2\right)-c d e (13 b d-4 a e)+3 a b e^3+16 c^2 d^3\right)}{15 e^2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 c \sqrt{a+b x+c x^2} \left(e x \left(-4 c e (8 b d-5 a e)+3 b^2 e^2+32 c^2 d^2\right)-4 c d e (44 b d-29 a e)+3 b e^2 (17 b d-16 a e)+128 c^2 d^3\right)}{15 e^4 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^5 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","-\frac{2 \left(a+b x+c x^2\right)^{3/2} \left(e x \left(-2 c e (11 b d-5 a e)+3 b^2 e^2+22 c^2 d^2\right)-c d e (13 b d-4 a e)+3 a b e^3+16 c^2 d^3\right)}{15 e^2 (d+e x)^{5/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 c \sqrt{a+b x+c x^2} \left(e x \left(-4 c e (8 b d-5 a e)+3 b^2 e^2+32 c^2 d^2\right)-4 c d e (44 b d-29 a e)+3 b e^2 (17 b d-16 a e)+128 c^2 d^3\right)}{15 e^4 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-4 c e (32 b d-5 a e)+27 b^2 e^2+128 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^5 \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-4 c e (32 b d-29 a e)+3 b^2 e^2+128 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 e^5 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(2*c*(128*c^2*d^3 - 4*c*d*e*(44*b*d - 29*a*e) + 3*b*e^2*(17*b*d - 16*a*e) + e*(32*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(8*b*d - 5*a*e))*x)*Sqrt[a + b*x + c*x^2])/(15*e^4*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (2*(16*c^2*d^3 + 3*a*b*e^3 - c*d*e*(13*b*d - 4*a*e) + e*(22*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(11*b*d - 5*a*e))*x)*(a + b*x + c*x^2)^(3/2))/(15*e^2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(5/2)) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(128*c^2*d^2 + 3*b^2*e^2 - 4*c*e*(32*b*d - 29*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^5*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(128*c^2*d^2 + 27*b^2*e^2 - 4*c*e*(32*b*d - 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*e^5*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{810, 812, 843, 718, 424, 419}"
1637,1,600,0,0.892539,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(5/2))/Sqrt[a + b*x + c*x^2],x]","\frac{4 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right)}{21 c^2}-\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c^3 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c^3 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{7} (d+e x)^{5/2} \sqrt{a+b x+c x^2}+\frac{2 (d+e x)^{3/2} \sqrt{a+b x+c x^2} (2 c d-b e)}{7 c}","\frac{4 \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right)}{21 c^2}-\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \left(-c e (5 a e+3 b d)+2 b^2 e^2+3 c^2 d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c^3 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(-c e (29 a e+3 b d)+8 b^2 e^2+3 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{21 c^3 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{7} (d+e x)^{5/2} \sqrt{a+b x+c x^2}+\frac{2 (d+e x)^{3/2} \sqrt{a+b x+c x^2} (2 c d-b e)}{7 c}",1,"(4*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(21*c^2) + (2*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(7*c) + (4*(d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2])/7 + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(3*b*d + 29*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(21*c^3*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*(3*c^2*d^2 + 2*b^2*e^2 - c*e*(3*b*d + 5*a*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(21*c^3*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,5,30,0.1667,1,"{832, 843, 718, 424, 419}"
1638,1,507,0,0.510386,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(3/2))/Sqrt[a + b*x + c*x^2],x]","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c^2 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c^2 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{5} (d+e x)^{3/2} \sqrt{a+b x+c x^2}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{5 c}","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c^2 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{5 c^2 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{5} (d+e x)^{3/2} \sqrt{a+b x+c x^2}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{5 c}",1,"(2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(5*c) + (4*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/5 + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(5*c^2*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(5*c^2*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,30,0.1667,1,"{832, 843, 718, 424, 419}"
1639,1,441,0,0.3220191,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\sqrt{a+b x+c x^2}} \, dx","Int[((b + 2*c*x)*Sqrt[d + e*x])/Sqrt[a + b*x + c*x^2],x]","-\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{3} \sqrt{d+e x} \sqrt{a+b x+c x^2}","-\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4}{3} \sqrt{d+e x} \sqrt{a+b x+c x^2}",1,"(4*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/3 + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,30,0.1667,1,"{832, 843, 718, 424, 419}"
1640,1,391,0,0.2051513,"\int \frac{b+2 c x}{\sqrt{d+e x} \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/(Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",5,4,30,0.1333,1,"{843, 718, 424, 419}"
1641,1,458,0,0.3114215,"\int \frac{b+2 c x}{(d+e x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}",1,"(2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (4*Sqrt[2]*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,30,0.1667,1,"{834, 843, 718, 424, 419}"
1642,1,581,0,0.5071389,"\int \frac{b+2 c x}{(d+e x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{4 \sqrt{a+b x+c x^2} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}","\frac{4 \sqrt{a+b x+c x^2} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)}{3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} (2 c d-b e)}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}",1,"(2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (4*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,30,0.1667,1,"{834, 843, 718, 424, 419}"
1643,1,540,0,0.6341102,"\int \frac{(b+2 c x) (d+e x)^{7/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(7/2))/(a + b*x + c*x^2)^(3/2),x]","-\frac{56 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{7 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{56 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{15 c^2}+\frac{14 e^2 (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c}-\frac{2 (d+e x)^{7/2}}{\sqrt{a+b x+c x^2}}","-\frac{56 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{7 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (9 a e+23 b d)+8 b^2 e^2+23 c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{56 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{15 c^2}+\frac{14 e^2 (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c}-\frac{2 (d+e x)^{7/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*(d + e*x)^(7/2))/Sqrt[a + b*x + c*x^2] + (56*e^2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(15*c^2) + (14*e^2*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*c) + (7*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(23*c^2*d^2 + 8*b^2*e^2 - c*e*(23*b*d + 9*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (56*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,30,0.2333,1,"{768, 742, 832, 843, 718, 424, 419}"
1644,1,468,0,0.4093511,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^(3/2),x]","-\frac{10 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{10 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{10 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c}-\frac{2 (d+e x)^{5/2}}{\sqrt{a+b x+c x^2}}","-\frac{10 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{10 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{10 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c}-\frac{2 (d+e x)^{5/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*(d + e*x)^(5/2))/Sqrt[a + b*x + c*x^2] + (10*e^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c) + (10*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (10*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{768, 742, 843, 718, 424, 419}"
1645,1,216,0,0.1109564,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{3 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2}}{\sqrt{a+b x+c x^2}}","\frac{3 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2}}{\sqrt{a+b x+c x^2}}",1,"(-2*(d + e*x)^(3/2))/Sqrt[a + b*x + c*x^2] + (3*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2])","A",3,3,30,0.1000,1,"{768, 718, 424}"
1646,1,216,0,0.1099532,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x}}{\sqrt{a+b x+c x^2}}","\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x}}{\sqrt{a+b x+c x^2}}",1,"(-2*Sqrt[d + e*x])/Sqrt[a + b*x + c*x^2] + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",3,3,30,0.1000,1,"{768, 718, 419}"
1647,1,290,0,0.1806439,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","-\frac{2 \sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(-2*Sqrt[d + e*x]*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2])","A",4,4,30,0.1333,1,"{822, 21, 718, 424}"
1648,1,559,0,0.5479909,"\int \frac{b+2 c x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(b + 2*c*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x]","-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}","-\frac{2 \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{2} e \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{4 e^2 \sqrt{a+b x+c x^2} (2 c d-b e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}",1,"(-2*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]) + (4*e^2*(2*c*d - b*e)*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{822, 834, 843, 718, 424, 419}"
1649,1,573,0,0.6148333,"\int \frac{(b+2 c x) (d+e x)^{7/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(7/2))/(a + b*x + c*x^2)^(5/2),x]","-\frac{14 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{14 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{14 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{3 c \left(b^2-4 a c\right)}-\frac{14 e (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^{7/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{14 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{14 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{14 e^2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (2 c d-b e)}{3 c \left(b^2-4 a c\right)}-\frac{14 e (d+e x)^{3/2} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^{7/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(7/2))/(3*(a + b*x + c*x^2)^(3/2)) - (14*e*(d + e*x)^(3/2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (14*e^2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c*(b^2 - 4*a*c)) + (14*Sqrt[2]*e*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (14*Sqrt[2]*e*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",8,7,30,0.2333,1,"{768, 738, 832, 843, 718, 424, 419}"
1650,1,494,0,0.4149394,"\int \frac{(b+2 c x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^(5/2),x]","-\frac{20 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{10 e \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{5 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{5/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{20 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{10 e \sqrt{d+e x} (-2 a e+x (2 c d-b e)+b d)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{5 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{5/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(5/2))/(3*(a + b*x + c*x^2)^(3/2)) - (10*e*Sqrt[d + e*x]*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (5*Sqrt[2]*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (20*Sqrt[2]*e*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{768, 738, 843, 718, 424, 419}"
1651,1,456,0,0.3243611,"\int \frac{(b+2 c x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 e (b+2 c x) \sqrt{d+e x}}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{2 e (b+2 c x) \sqrt{d+e x}}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 (d+e x)^{3/2}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(d + e*x)^(3/2))/(3*(a + b*x + c*x^2)^(3/2)) - (2*e*(b + 2*c*x)*Sqrt[d + e*x])/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*e*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*e*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{768, 736, 843, 718, 424, 419}"
1652,1,517,0,0.3835249,"\int \frac{(b+2 c x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((b + 2*c*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 e \sqrt{d+e x} \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x}}{3 \left(a+b x+c x^2\right)^{3/2}}","-\frac{2 e \sqrt{d+e x} \left(2 a c e+b^2 (-e)+c x (2 c d-b e)+b c d\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{4 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{2 \sqrt{d+e x}}{3 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*Sqrt[d + e*x])/(3*(a + b*x + c*x^2)^(3/2)) - (2*e*Sqrt[d + e*x]*(b*c*d - b^2*e + 2*a*c*e + c*(2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*e*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (4*Sqrt[2]*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,30,0.2000,1,"{768, 740, 843, 718, 424, 419}"
1653,1,665,0,0.5875412,"\int \frac{b+2 c x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(b + 2*c*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(5/2)),x]","-\frac{2 e \sqrt{d+e x} \left(-2 c x \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)-b c \left(c d^2-7 a e^2\right)-8 a c^2 d e+3 b^2 c d e-2 b^3 e^2\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","-\frac{2 e \sqrt{d+e x} \left(-2 c x \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right)-b c \left(c d^2-7 a e^2\right)-8 a c^2 d e+3 b^2 c d e-2 b^3 e^2\right)}{3 \left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}-\frac{2 \sqrt{2} e \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c e (3 a e+b d)+b^2 e^2+c^2 d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{d+e x} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} e \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (2 c d-b e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}",1,"(-2*Sqrt[d + e*x]*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2)) - (2*e*Sqrt[d + e*x]*(3*b^2*c*d*e - 8*a*c^2*d*e - 2*b^3*e^2 - b*c*(c*d^2 - 7*a*e^2) - 2*c*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*e*(c^2*d^2 + b^2*e^2 - c*e*(b*d + 3*a*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*e*(2*c*d - b*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,30,0.1667,1,"{822, 843, 718, 424, 419}"
1654,1,449,0,0.3448345,"\int (b+2 c x) (d+e x)^m \left(a+b x+c x^2\right)^3 \, dx","Int[(b + 2*c*x)*(d + e*x)^m*(a + b*x + c*x^2)^3,x]","\frac{(d+e x)^{m+4} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^8 (m+4)}+\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 (m+2)}-\frac{3 (2 c d-b e) (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8 (m+3)}-\frac{5 c (2 c d-b e) (d+e x)^{m+5} \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8 (m+5)}+\frac{3 c^2 (d+e x)^{m+6} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 (m+6)}-\frac{(2 c d-b e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^3}{e^8 (m+1)}-\frac{7 c^3 (2 c d-b e) (d+e x)^{m+7}}{e^8 (m+7)}+\frac{2 c^4 (d+e x)^{m+8}}{e^8 (m+8)}","\frac{(d+e x)^{m+4} \left(6 c^2 e^2 \left(a^2 e^2-10 a b d e+15 b^2 d^2\right)-4 b^2 c e^3 (5 b d-3 a e)-20 c^3 d^2 e (7 b d-3 a e)+b^4 e^4+70 c^4 d^4\right)}{e^8 (m+4)}+\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^2 \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 (m+2)}-\frac{3 (2 c d-b e) (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right) \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8 (m+3)}-\frac{5 c (2 c d-b e) (d+e x)^{m+5} \left(-c e (7 b d-3 a e)+b^2 e^2+7 c^2 d^2\right)}{e^8 (m+5)}+\frac{3 c^2 (d+e x)^{m+6} \left(-2 c e (7 b d-a e)+3 b^2 e^2+14 c^2 d^2\right)}{e^8 (m+6)}-\frac{(2 c d-b e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^3}{e^8 (m+1)}-\frac{7 c^3 (2 c d-b e) (d+e x)^{m+7}}{e^8 (m+7)}+\frac{2 c^4 (d+e x)^{m+8}}{e^8 (m+8)}",1,"-(((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^8*(1 + m))) + ((c*d^2 - b*d*e + a*e^2)^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(2 + m))/(e^8*(2 + m)) - (3*(2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(3 + m))/(e^8*(3 + m)) + ((70*c^4*d^4 + b^4*e^4 - 4*b^2*c*e^3*(5*b*d - 3*a*e) - 20*c^3*d^2*e*(7*b*d - 3*a*e) + 6*c^2*e^2*(15*b^2*d^2 - 10*a*b*d*e + a^2*e^2))*(d + e*x)^(4 + m))/(e^8*(4 + m)) - (5*c*(2*c*d - b*e)*(7*c^2*d^2 + b^2*e^2 - c*e*(7*b*d - 3*a*e))*(d + e*x)^(5 + m))/(e^8*(5 + m)) + (3*c^2*(14*c^2*d^2 + 3*b^2*e^2 - 2*c*e*(7*b*d - a*e))*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (7*c^3*(2*c*d - b*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (2*c^4*(d + e*x)^(8 + m))/(e^8*(8 + m))","A",2,1,26,0.03846,1,"{771}"
1655,1,270,0,0.1891513,"\int (b+2 c x) (d+e x)^m \left(a+b x+c x^2\right)^2 \, dx","Int[(b + 2*c*x)*(d + e*x)^m*(a + b*x + c*x^2)^2,x]","\frac{2 (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (m+2)}-\frac{(2 c d-b e) (d+e x)^{m+3} \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6 (m+3)}+\frac{4 c (d+e x)^{m+4} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (m+4)}-\frac{(2 c d-b e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^6 (m+1)}-\frac{5 c^2 (2 c d-b e) (d+e x)^{m+5}}{e^6 (m+5)}+\frac{2 c^3 (d+e x)^{m+6}}{e^6 (m+6)}","\frac{2 (d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (m+2)}-\frac{(2 c d-b e) (d+e x)^{m+3} \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)}{e^6 (m+3)}+\frac{4 c (d+e x)^{m+4} \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^6 (m+4)}-\frac{(2 c d-b e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^6 (m+1)}-\frac{5 c^2 (2 c d-b e) (d+e x)^{m+5}}{e^6 (m+5)}+\frac{2 c^3 (d+e x)^{m+6}}{e^6 (m+6)}",1,"-(((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(1 + m))/(e^6*(1 + m))) + (2*(c*d^2 - b*d*e + a*e^2)*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(2 + m))/(e^6*(2 + m)) - ((2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e))*(d + e*x)^(3 + m))/(e^6*(3 + m)) + (4*c*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (5*c^2*(2*c*d - b*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (2*c^3*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,26,0.03846,1,"{771}"
1656,1,143,0,0.0918753,"\int (b+2 c x) (d+e x)^m \left(a+b x+c x^2\right) \, dx","Int[(b + 2*c*x)*(d + e*x)^m*(a + b*x + c*x^2),x]","\frac{(d+e x)^{m+2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4 (m+2)}-\frac{(2 c d-b e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}-\frac{3 c (2 c d-b e) (d+e x)^{m+3}}{e^4 (m+3)}+\frac{2 c^2 (d+e x)^{m+4}}{e^4 (m+4)}","\frac{(d+e x)^{m+2} \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^4 (m+2)}-\frac{(2 c d-b e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}-\frac{3 c (2 c d-b e) (d+e x)^{m+3}}{e^4 (m+3)}+\frac{2 c^2 (d+e x)^{m+4}}{e^4 (m+4)}",1,"-(((2*c*d - b*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e))*(d + e*x)^(2 + m))/(e^4*(2 + m)) - (3*c*(2*c*d - b*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (2*c^2*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,24,0.04167,1,"{771}"
1657,1,167,0,0.299823,"\int \frac{(b+2 c x) (d+e x)^m}{a+b x+c x^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^m)/(a + b*x + c*x^2),x]","-\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}","-\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{2 c (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}",1,"(-2*c*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + m)) - (2*c*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + m))","A",4,2,26,0.07692,1,"{830, 68}"
1658,1,358,0,0.5712302,"\int \frac{(b+2 c x) (d+e x)^m}{\left(a+b x+c x^2\right)^2} \, dx","Int[((b + 2*c*x)*(d + e*x)^m)/(a + b*x + c*x^2)^2,x]","-\frac{c e m (d+e x)^{m+1} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}+\frac{c e m (d+e x)^{m+1} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{(d+e x)^{m+1} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}","-\frac{c e m (d+e x)^{m+1} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}+\frac{c e m (d+e x)^{m+1} \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \sqrt{b^2-4 a c} \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \left(a e^2-b d e+c d^2\right)}-\frac{(d+e x)^{m+1} \left(\left(b^2-4 a c\right) (c d-b e)-c e x \left(b^2-4 a c\right)\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}",1,"-(((d + e*x)^(1 + m)*((b^2 - 4*a*c)*(c*d - b*e) - c*(b^2 - 4*a*c)*e*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2))) - (c*e*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*m*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m)) + (c*e*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*m*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m))","A",5,3,26,0.1154,1,"{822, 830, 68}"
1659,1,120,0,0.2855576,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{b (d+e x)^8 (-2 a B e-A b e+3 b B d)}{8 e^4}+\frac{(d+e x)^7 (b d-a e) (-a B e-2 A b e+3 b B d)}{7 e^4}-\frac{(d+e x)^6 (b d-a e)^2 (B d-A e)}{6 e^4}+\frac{b^2 B (d+e x)^9}{9 e^4}","-\frac{b (d+e x)^8 (-2 a B e-A b e+3 b B d)}{8 e^4}+\frac{(d+e x)^7 (b d-a e) (-a B e-2 A b e+3 b B d)}{7 e^4}-\frac{(d+e x)^6 (b d-a e)^2 (B d-A e)}{6 e^4}+\frac{b^2 B (d+e x)^9}{9 e^4}",1,"-((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^6)/(6*e^4) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^7)/(7*e^4) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^8)/(8*e^4) + (b^2*B*(d + e*x)^9)/(9*e^4)","A",3,2,29,0.06897,1,"{27, 77}"
1660,1,120,0,0.2138994,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{b (d+e x)^7 (-2 a B e-A b e+3 b B d)}{7 e^4}+\frac{(d+e x)^6 (b d-a e) (-a B e-2 A b e+3 b B d)}{6 e^4}-\frac{(d+e x)^5 (b d-a e)^2 (B d-A e)}{5 e^4}+\frac{b^2 B (d+e x)^8}{8 e^4}","-\frac{b (d+e x)^7 (-2 a B e-A b e+3 b B d)}{7 e^4}+\frac{(d+e x)^6 (b d-a e) (-a B e-2 A b e+3 b B d)}{6 e^4}-\frac{(d+e x)^5 (b d-a e)^2 (B d-A e)}{5 e^4}+\frac{b^2 B (d+e x)^8}{8 e^4}",1,"-((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^5)/(5*e^4) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^6)/(6*e^4) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^7)/(7*e^4) + (b^2*B*(d + e*x)^8)/(8*e^4)","A",3,2,29,0.06897,1,"{27, 77}"
1661,1,120,0,0.162877,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{b (d+e x)^6 (-2 a B e-A b e+3 b B d)}{6 e^4}+\frac{(d+e x)^5 (b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4}-\frac{(d+e x)^4 (b d-a e)^2 (B d-A e)}{4 e^4}+\frac{b^2 B (d+e x)^7}{7 e^4}","-\frac{b (d+e x)^6 (-2 a B e-A b e+3 b B d)}{6 e^4}+\frac{(d+e x)^5 (b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4}-\frac{(d+e x)^4 (b d-a e)^2 (B d-A e)}{4 e^4}+\frac{b^2 B (d+e x)^7}{7 e^4}",1,"-((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^4)/(4*e^4) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^5)/(5*e^4) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^6)/(6*e^4) + (b^2*B*(d + e*x)^7)/(7*e^4)","A",3,2,29,0.06897,1,"{27, 77}"
1662,1,118,0,0.1292418,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e (a+b x)^5 (-3 a B e+A b e+2 b B d)}{5 b^4}+\frac{(a+b x)^4 (b d-a e) (-3 a B e+2 A b e+b B d)}{4 b^4}+\frac{(a+b x)^3 (A b-a B) (b d-a e)^2}{3 b^4}+\frac{B e^2 (a+b x)^6}{6 b^4}","\frac{e (a+b x)^5 (-3 a B e+A b e+2 b B d)}{5 b^4}+\frac{(a+b x)^4 (b d-a e) (-3 a B e+2 A b e+b B d)}{4 b^4}+\frac{(a+b x)^3 (A b-a B) (b d-a e)^2}{3 b^4}+\frac{B e^2 (a+b x)^6}{6 b^4}",1,"((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^3)/(3*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^4)/(4*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^5)/(5*b^4) + (B*e^2*(a + b*x)^6)/(6*b^4)","A",3,2,29,0.06897,1,"{27, 77}"
1663,1,75,0,0.0759608,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(a+b x)^4 (-2 a B e+A b e+b B d)}{4 b^3}+\frac{(a+b x)^3 (A b-a B) (b d-a e)}{3 b^3}+\frac{B e (a+b x)^5}{5 b^3}","\frac{(a+b x)^4 (-2 a B e+A b e+b B d)}{4 b^3}+\frac{(a+b x)^3 (A b-a B) (b d-a e)}{3 b^3}+\frac{B e (a+b x)^5}{5 b^3}",1,"((A*b - a*B)*(b*d - a*e)*(a + b*x)^3)/(3*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^4)/(4*b^3) + (B*e*(a + b*x)^5)/(5*b^3)","A",3,2,27,0.07407,1,"{27, 77}"
1664,1,38,0,0.0282879,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}","\frac{(a+b x)^3 (A b-a B)}{3 b^2}+\frac{B (a+b x)^4}{4 b^2}",1,"((A*b - a*B)*(a + b*x)^3)/(3*b^2) + (B*(a + b*x)^4)/(4*b^2)","A",3,2,22,0.09091,1,"{27, 43}"
1665,1,92,0,0.0628983,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{d+e x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x),x]","-\frac{(a+b x)^2 (B d-A e)}{2 e^2}+\frac{b x (b d-a e) (B d-A e)}{e^3}-\frac{(b d-a e)^2 (B d-A e) \log (d+e x)}{e^4}+\frac{B (a+b x)^3}{3 b e}","-\frac{(a+b x)^2 (B d-A e)}{2 e^2}+\frac{b x (b d-a e) (B d-A e)}{e^3}-\frac{(b d-a e)^2 (B d-A e) \log (d+e x)}{e^4}+\frac{B (a+b x)^3}{3 b e}",1,"(b*(b*d - a*e)*(B*d - A*e)*x)/e^3 - ((B*d - A*e)*(a + b*x)^2)/(2*e^2) + (B*(a + b*x)^3)/(3*b*e) - ((b*d - a*e)^2*(B*d - A*e)*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 77}"
1666,1,101,0,0.1027205,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^2,x]","\frac{(b d-a e)^2 (B d-A e)}{e^4 (d+e x)}-\frac{b x (-2 a B e-A b e+2 b B d)}{e^3}+\frac{(b d-a e) \log (d+e x) (-a B e-2 A b e+3 b B d)}{e^4}+\frac{b^2 B x^2}{2 e^2}","\frac{(b d-a e)^2 (B d-A e)}{e^4 (d+e x)}-\frac{b x (-2 a B e-A b e+2 b B d)}{e^3}+\frac{(b d-a e) \log (d+e x) (-a B e-2 A b e+3 b B d)}{e^4}+\frac{b^2 B x^2}{2 e^2}",1,"-((b*(2*b*B*d - A*b*e - 2*a*B*e)*x)/e^3) + (b^2*B*x^2)/(2*e^2) + ((b*d - a*e)^2*(B*d - A*e))/(e^4*(d + e*x)) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 77}"
1667,1,106,0,0.0915613,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^3,x]","-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{e^4 (d+e x)}+\frac{(b d-a e)^2 (B d-A e)}{2 e^4 (d+e x)^2}-\frac{b \log (d+e x) (-2 a B e-A b e+3 b B d)}{e^4}+\frac{b^2 B x}{e^3}","-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{e^4 (d+e x)}+\frac{(b d-a e)^2 (B d-A e)}{2 e^4 (d+e x)^2}-\frac{b \log (d+e x) (-2 a B e-A b e+3 b B d)}{e^4}+\frac{b^2 B x}{e^3}",1,"(b^2*B*x)/e^3 + ((b*d - a*e)^2*(B*d - A*e))/(2*e^4*(d + e*x)^2) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(e^4*(d + e*x)) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 77}"
1668,1,101,0,0.0796056,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^4,x]","-\frac{(a+b x)^3 (B d-A e)}{3 e (d+e x)^3 (b d-a e)}+\frac{2 b B (b d-a e)}{e^4 (d+e x)}-\frac{B (b d-a e)^2}{2 e^4 (d+e x)^2}+\frac{b^2 B \log (d+e x)}{e^4}","-\frac{(a+b x)^3 (B d-A e)}{3 e (d+e x)^3 (b d-a e)}+\frac{2 b B (b d-a e)}{e^4 (d+e x)}-\frac{B (b d-a e)^2}{2 e^4 (d+e x)^2}+\frac{b^2 B \log (d+e x)}{e^4}",1,"-((B*d - A*e)*(a + b*x)^3)/(3*e*(b*d - a*e)*(d + e*x)^3) - (B*(b*d - a*e)^2)/(2*e^4*(d + e*x)^2) + (2*b*B*(b*d - a*e))/(e^4*(d + e*x)) + (b^2*B*Log[d + e*x])/e^4","A",4,3,29,0.1034,1,"{27, 78, 43}"
1669,1,86,0,0.0345901,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^5,x]","\frac{(a+b x)^3 (-4 a B e+A b e+3 b B d)}{12 e (d+e x)^3 (b d-a e)^2}-\frac{(a+b x)^3 (B d-A e)}{4 e (d+e x)^4 (b d-a e)}","\frac{(a+b x)^3 (-4 a B e+A b e+3 b B d)}{12 e (d+e x)^3 (b d-a e)^2}-\frac{(a+b x)^3 (B d-A e)}{4 e (d+e x)^4 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^3)/(4*e*(b*d - a*e)*(d + e*x)^4) + ((3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^3)/(12*e*(b*d - a*e)^2*(d + e*x)^3)","A",3,3,29,0.1034,1,"{27, 78, 37}"
1670,1,120,0,0.0973412,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^6,x]","\frac{b (-2 a B e-A b e+3 b B d)}{3 e^4 (d+e x)^3}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{4 e^4 (d+e x)^4}+\frac{(b d-a e)^2 (B d-A e)}{5 e^4 (d+e x)^5}-\frac{b^2 B}{2 e^4 (d+e x)^2}","\frac{b (-2 a B e-A b e+3 b B d)}{3 e^4 (d+e x)^3}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{4 e^4 (d+e x)^4}+\frac{(b d-a e)^2 (B d-A e)}{5 e^4 (d+e x)^5}-\frac{b^2 B}{2 e^4 (d+e x)^2}",1,"((b*d - a*e)^2*(B*d - A*e))/(5*e^4*(d + e*x)^5) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(4*e^4*(d + e*x)^4) + (b*(3*b*B*d - A*b*e - 2*a*B*e))/(3*e^4*(d + e*x)^3) - (b^2*B)/(2*e^4*(d + e*x)^2)","A",3,2,29,0.06897,1,"{27, 77}"
1671,1,120,0,0.083556,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^7,x]","\frac{b (-2 a B e-A b e+3 b B d)}{4 e^4 (d+e x)^4}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4 (d+e x)^5}+\frac{(b d-a e)^2 (B d-A e)}{6 e^4 (d+e x)^6}-\frac{b^2 B}{3 e^4 (d+e x)^3}","\frac{b (-2 a B e-A b e+3 b B d)}{4 e^4 (d+e x)^4}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4 (d+e x)^5}+\frac{(b d-a e)^2 (B d-A e)}{6 e^4 (d+e x)^6}-\frac{b^2 B}{3 e^4 (d+e x)^3}",1,"((b*d - a*e)^2*(B*d - A*e))/(6*e^4*(d + e*x)^6) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(5*e^4*(d + e*x)^5) + (b*(3*b*B*d - A*b*e - 2*a*B*e))/(4*e^4*(d + e*x)^4) - (b^2*B)/(3*e^4*(d + e*x)^3)","A",3,2,29,0.06897,1,"{27, 77}"
1672,1,120,0,0.0806258,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^8,x]","\frac{b (-2 a B e-A b e+3 b B d)}{5 e^4 (d+e x)^5}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{6 e^4 (d+e x)^6}+\frac{(b d-a e)^2 (B d-A e)}{7 e^4 (d+e x)^7}-\frac{b^2 B}{4 e^4 (d+e x)^4}","\frac{b (-2 a B e-A b e+3 b B d)}{5 e^4 (d+e x)^5}-\frac{(b d-a e) (-a B e-2 A b e+3 b B d)}{6 e^4 (d+e x)^6}+\frac{(b d-a e)^2 (B d-A e)}{7 e^4 (d+e x)^7}-\frac{b^2 B}{4 e^4 (d+e x)^4}",1,"((b*d - a*e)^2*(B*d - A*e))/(7*e^4*(d + e*x)^7) - ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(6*e^4*(d + e*x)^6) + (b*(3*b*B*d - A*b*e - 2*a*B*e))/(5*e^4*(d + e*x)^5) - (b^2*B)/(4*e^4*(d + e*x)^4)","A",3,2,29,0.06897,1,"{27, 77}"
1673,1,206,0,0.8036032,"\int (A+B x) (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{b^3 (d+e x)^{12} (-4 a B e-A b e+5 b B d)}{12 e^6}+\frac{2 b^2 (d+e x)^{11} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{11 e^6}-\frac{b (d+e x)^{10} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{5 e^6}+\frac{(d+e x)^9 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6}-\frac{(d+e x)^8 (b d-a e)^4 (B d-A e)}{8 e^6}+\frac{b^4 B (d+e x)^{13}}{13 e^6}","-\frac{b^3 (d+e x)^{12} (-4 a B e-A b e+5 b B d)}{12 e^6}+\frac{2 b^2 (d+e x)^{11} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{11 e^6}-\frac{b (d+e x)^{10} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{5 e^6}+\frac{(d+e x)^9 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6}-\frac{(d+e x)^8 (b d-a e)^4 (B d-A e)}{8 e^6}+\frac{b^4 B (d+e x)^{13}}{13 e^6}",1,"-((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^8)/(8*e^6) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^9)/(9*e^6) - (b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^10)/(5*e^6) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^11)/(11*e^6) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^12)/(12*e^6) + (b^4*B*(d + e*x)^13)/(13*e^6)","A",3,2,31,0.06452,1,"{27, 77}"
1674,1,206,0,0.661421,"\int (A+B x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{b^3 (d+e x)^{11} (-4 a B e-A b e+5 b B d)}{11 e^6}+\frac{b^2 (d+e x)^{10} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{5 e^6}-\frac{2 b (d+e x)^9 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6}+\frac{(d+e x)^8 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{8 e^6}-\frac{(d+e x)^7 (b d-a e)^4 (B d-A e)}{7 e^6}+\frac{b^4 B (d+e x)^{12}}{12 e^6}","-\frac{b^3 (d+e x)^{11} (-4 a B e-A b e+5 b B d)}{11 e^6}+\frac{b^2 (d+e x)^{10} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{5 e^6}-\frac{2 b (d+e x)^9 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6}+\frac{(d+e x)^8 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{8 e^6}-\frac{(d+e x)^7 (b d-a e)^4 (B d-A e)}{7 e^6}+\frac{b^4 B (d+e x)^{12}}{12 e^6}",1,"-((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^7)/(7*e^6) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^8)/(8*e^6) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^9)/(9*e^6) + (b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^10)/(5*e^6) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^11)/(11*e^6) + (b^4*B*(d + e*x)^12)/(12*e^6)","A",3,2,31,0.06452,1,"{27, 77}"
1675,1,206,0,0.5390082,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{b^3 (d+e x)^{10} (-4 a B e-A b e+5 b B d)}{10 e^6}+\frac{2 b^2 (d+e x)^9 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{9 e^6}-\frac{b (d+e x)^8 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{4 e^6}+\frac{(d+e x)^7 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{7 e^6}-\frac{(d+e x)^6 (b d-a e)^4 (B d-A e)}{6 e^6}+\frac{b^4 B (d+e x)^{11}}{11 e^6}","-\frac{b^3 (d+e x)^{10} (-4 a B e-A b e+5 b B d)}{10 e^6}+\frac{2 b^2 (d+e x)^9 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{9 e^6}-\frac{b (d+e x)^8 (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{4 e^6}+\frac{(d+e x)^7 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{7 e^6}-\frac{(d+e x)^6 (b d-a e)^4 (B d-A e)}{6 e^6}+\frac{b^4 B (d+e x)^{11}}{11 e^6}",1,"-((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^6)/(6*e^6) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^7)/(7*e^6) - (b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^8)/(4*e^6) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^9)/(9*e^6) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^10)/(10*e^6) + (b^4*B*(d + e*x)^11)/(11*e^6)","A",3,2,31,0.06452,1,"{27, 77}"
1676,1,204,0,0.4594008,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^3 (a+b x)^9 (-5 a B e+A b e+4 b B d)}{9 b^6}+\frac{e^2 (a+b x)^8 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{4 b^6}+\frac{2 e (a+b x)^7 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{7 b^6}+\frac{(a+b x)^6 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{6 b^6}+\frac{(a+b x)^5 (A b-a B) (b d-a e)^4}{5 b^6}+\frac{B e^4 (a+b x)^{10}}{10 b^6}","\frac{e^3 (a+b x)^9 (-5 a B e+A b e+4 b B d)}{9 b^6}+\frac{e^2 (a+b x)^8 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{4 b^6}+\frac{2 e (a+b x)^7 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{7 b^6}+\frac{(a+b x)^6 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{6 b^6}+\frac{(a+b x)^5 (A b-a B) (b d-a e)^4}{5 b^6}+\frac{B e^4 (a+b x)^{10}}{10 b^6}",1,"((A*b - a*B)*(b*d - a*e)^4*(a + b*x)^5)/(5*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)^6)/(6*b^6) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)^7)/(7*b^6) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^8)/(4*b^6) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^9)/(9*b^6) + (B*e^4*(a + b*x)^10)/(10*b^6)","A",3,2,31,0.06452,1,"{27, 77}"
1677,1,159,0,0.3128556,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^2 (a+b x)^8 (-4 a B e+A b e+3 b B d)}{8 b^5}+\frac{3 e (a+b x)^7 (b d-a e) (-2 a B e+A b e+b B d)}{7 b^5}+\frac{(a+b x)^6 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{6 b^5}+\frac{(a+b x)^5 (A b-a B) (b d-a e)^3}{5 b^5}+\frac{B e^3 (a+b x)^9}{9 b^5}","\frac{e^2 (a+b x)^8 (-4 a B e+A b e+3 b B d)}{8 b^5}+\frac{3 e (a+b x)^7 (b d-a e) (-2 a B e+A b e+b B d)}{7 b^5}+\frac{(a+b x)^6 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{6 b^5}+\frac{(a+b x)^5 (A b-a B) (b d-a e)^3}{5 b^5}+\frac{B e^3 (a+b x)^9}{9 b^5}",1,"((A*b - a*B)*(b*d - a*e)^3*(a + b*x)^5)/(5*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^6)/(6*b^5) + (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^7)/(7*b^5) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^8)/(8*b^5) + (B*e^3*(a + b*x)^9)/(9*b^5)","A",3,2,31,0.06452,1,"{27, 77}"
1678,1,118,0,0.2215025,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e (a+b x)^7 (-3 a B e+A b e+2 b B d)}{7 b^4}+\frac{(a+b x)^6 (b d-a e) (-3 a B e+2 A b e+b B d)}{6 b^4}+\frac{(a+b x)^5 (A b-a B) (b d-a e)^2}{5 b^4}+\frac{B e^2 (a+b x)^8}{8 b^4}","\frac{e (a+b x)^7 (-3 a B e+A b e+2 b B d)}{7 b^4}+\frac{(a+b x)^6 (b d-a e) (-3 a B e+2 A b e+b B d)}{6 b^4}+\frac{(a+b x)^5 (A b-a B) (b d-a e)^2}{5 b^4}+\frac{B e^2 (a+b x)^8}{8 b^4}",1,"((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^5)/(5*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^6)/(6*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^7)/(7*b^4) + (B*e^2*(a + b*x)^8)/(8*b^4)","A",3,2,31,0.06452,1,"{27, 77}"
1679,1,75,0,0.1375087,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^6 (-2 a B e+A b e+b B d)}{6 b^3}+\frac{(a+b x)^5 (A b-a B) (b d-a e)}{5 b^3}+\frac{B e (a+b x)^7}{7 b^3}","\frac{(a+b x)^6 (-2 a B e+A b e+b B d)}{6 b^3}+\frac{(a+b x)^5 (A b-a B) (b d-a e)}{5 b^3}+\frac{B e (a+b x)^7}{7 b^3}",1,"((A*b - a*B)*(b*d - a*e)*(a + b*x)^5)/(5*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^6)/(6*b^3) + (B*e*(a + b*x)^7)/(7*b^3)","A",3,2,29,0.06897,1,"{27, 77}"
1680,1,38,0,0.0162216,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2}","\frac{(a+b x)^5 (A b-a B)}{5 b^2}+\frac{B (a+b x)^6}{6 b^2}",1,"((A*b - a*B)*(a + b*x)^5)/(5*b^2) + (B*(a + b*x)^6)/(6*b^2)","A",3,2,24,0.08333,1,"{27, 43}"
1681,1,156,0,0.1189976,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{d+e x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x),x]","-\frac{(a+b x)^4 (B d-A e)}{4 e^2}+\frac{(a+b x)^3 (b d-a e) (B d-A e)}{3 e^3}-\frac{(a+b x)^2 (b d-a e)^2 (B d-A e)}{2 e^4}+\frac{b x (b d-a e)^3 (B d-A e)}{e^5}-\frac{(b d-a e)^4 (B d-A e) \log (d+e x)}{e^6}+\frac{B (a+b x)^5}{5 b e}","-\frac{(a+b x)^4 (B d-A e)}{4 e^2}+\frac{(a+b x)^3 (b d-a e) (B d-A e)}{3 e^3}-\frac{(a+b x)^2 (b d-a e)^2 (B d-A e)}{2 e^4}+\frac{b x (b d-a e)^3 (B d-A e)}{e^5}-\frac{(b d-a e)^4 (B d-A e) \log (d+e x)}{e^6}+\frac{B (a+b x)^5}{5 b e}",1,"(b*(b*d - a*e)^3*(B*d - A*e)*x)/e^5 - ((b*d - a*e)^2*(B*d - A*e)*(a + b*x)^2)/(2*e^4) + ((b*d - a*e)*(B*d - A*e)*(a + b*x)^3)/(3*e^3) - ((B*d - A*e)*(a + b*x)^4)/(4*e^2) + (B*(a + b*x)^5)/(5*b*e) - ((b*d - a*e)^4*(B*d - A*e)*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 77}"
1682,1,188,0,0.3164683,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^2,x]","\frac{b^2 (d+e x)^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^6}-\frac{b^3 (d+e x)^3 (-4 a B e-A b e+5 b B d)}{3 e^6}+\frac{(b d-a e)^4 (B d-A e)}{e^6 (d+e x)}-\frac{2 b x (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^5}+\frac{(b d-a e)^3 \log (d+e x) (-a B e-4 A b e+5 b B d)}{e^6}+\frac{b^4 B (d+e x)^4}{4 e^6}","\frac{b^2 (d+e x)^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^6}-\frac{b^3 (d+e x)^3 (-4 a B e-A b e+5 b B d)}{3 e^6}+\frac{(b d-a e)^4 (B d-A e)}{e^6 (d+e x)}-\frac{2 b x (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^5}+\frac{(b d-a e)^3 \log (d+e x) (-a B e-4 A b e+5 b B d)}{e^6}+\frac{b^4 B (d+e x)^4}{4 e^6}",1,"(-2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*x)/e^5 + ((b*d - a*e)^4*(B*d - A*e))/(e^6*(d + e*x)) + (b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^2)/e^6 - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^3)/(3*e^6) + (b^4*B*(d + e*x)^4)/(4*e^6) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 77}"
1683,1,193,0,0.2456682,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^3,x]","-\frac{b^3 (d+e x)^2 (-4 a B e-A b e+5 b B d)}{2 e^6}+\frac{2 b^2 x (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^5}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{e^6 (d+e x)}+\frac{(b d-a e)^4 (B d-A e)}{2 e^6 (d+e x)^2}-\frac{2 b (b d-a e)^2 \log (d+e x) (-2 a B e-3 A b e+5 b B d)}{e^6}+\frac{b^4 B (d+e x)^3}{3 e^6}","-\frac{b^3 (d+e x)^2 (-4 a B e-A b e+5 b B d)}{2 e^6}+\frac{2 b^2 x (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^5}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{e^6 (d+e x)}+\frac{(b d-a e)^4 (B d-A e)}{2 e^6 (d+e x)^2}-\frac{2 b (b d-a e)^2 \log (d+e x) (-2 a B e-3 A b e+5 b B d)}{e^6}+\frac{b^4 B (d+e x)^3}{3 e^6}",1,"(2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*x)/e^5 + ((b*d - a*e)^4*(B*d - A*e))/(2*e^6*(d + e*x)^2) - ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(e^6*(d + e*x)) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^2)/(2*e^6) + (b^4*B*(d + e*x)^3)/(3*e^6) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 77}"
1684,1,189,0,0.2240808,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^4,x]","-\frac{b^3 x (-4 a B e-A b e+4 b B d)}{e^5}+\frac{2 b^2 (b d-a e) \log (d+e x) (-3 a B e-2 A b e+5 b B d)}{e^6}+\frac{2 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6 (d+e x)}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{2 e^6 (d+e x)^2}+\frac{(b d-a e)^4 (B d-A e)}{3 e^6 (d+e x)^3}+\frac{b^4 B x^2}{2 e^4}","-\frac{b^3 x (-4 a B e-A b e+4 b B d)}{e^5}+\frac{2 b^2 (b d-a e) \log (d+e x) (-3 a B e-2 A b e+5 b B d)}{e^6}+\frac{2 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6 (d+e x)}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{2 e^6 (d+e x)^2}+\frac{(b d-a e)^4 (B d-A e)}{3 e^6 (d+e x)^3}+\frac{b^4 B x^2}{2 e^4}",1,"-((b^3*(4*b*B*d - A*b*e - 4*a*B*e)*x)/e^5) + (b^4*B*x^2)/(2*e^4) + ((b*d - a*e)^4*(B*d - A*e))/(3*e^6*(d + e*x)^3) - ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(2*e^6*(d + e*x)^2) + (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e))/(e^6*(d + e*x)) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 77}"
1685,1,189,0,0.1977281,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^5,x]","-\frac{2 b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^6 (d+e x)}-\frac{b^3 \log (d+e x) (-4 a B e-A b e+5 b B d)}{e^6}+\frac{b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6 (d+e x)^2}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{3 e^6 (d+e x)^3}+\frac{(b d-a e)^4 (B d-A e)}{4 e^6 (d+e x)^4}+\frac{b^4 B x}{e^5}","-\frac{2 b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^6 (d+e x)}-\frac{b^3 \log (d+e x) (-4 a B e-A b e+5 b B d)}{e^6}+\frac{b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6 (d+e x)^2}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{3 e^6 (d+e x)^3}+\frac{(b d-a e)^4 (B d-A e)}{4 e^6 (d+e x)^4}+\frac{b^4 B x}{e^5}",1,"(b^4*B*x)/e^5 + ((b*d - a*e)^4*(B*d - A*e))/(4*e^6*(d + e*x)^4) - ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(3*e^6*(d + e*x)^3) + (b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e))/(e^6*(d + e*x)^2) - (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e))/(e^6*(d + e*x)) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 77}"
1686,1,155,0,0.1549161,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^6,x]","-\frac{(a+b x)^5 (B d-A e)}{5 e (d+e x)^5 (b d-a e)}+\frac{4 b^3 B (b d-a e)}{e^6 (d+e x)}-\frac{3 b^2 B (b d-a e)^2}{e^6 (d+e x)^2}+\frac{4 b B (b d-a e)^3}{3 e^6 (d+e x)^3}-\frac{B (b d-a e)^4}{4 e^6 (d+e x)^4}+\frac{b^4 B \log (d+e x)}{e^6}","-\frac{(a+b x)^5 (B d-A e)}{5 e (d+e x)^5 (b d-a e)}+\frac{4 b^3 B (b d-a e)}{e^6 (d+e x)}-\frac{3 b^2 B (b d-a e)^2}{e^6 (d+e x)^2}+\frac{4 b B (b d-a e)^3}{3 e^6 (d+e x)^3}-\frac{B (b d-a e)^4}{4 e^6 (d+e x)^4}+\frac{b^4 B \log (d+e x)}{e^6}",1,"-((B*d - A*e)*(a + b*x)^5)/(5*e*(b*d - a*e)*(d + e*x)^5) - (B*(b*d - a*e)^4)/(4*e^6*(d + e*x)^4) + (4*b*B*(b*d - a*e)^3)/(3*e^6*(d + e*x)^3) - (3*b^2*B*(b*d - a*e)^2)/(e^6*(d + e*x)^2) + (4*b^3*B*(b*d - a*e))/(e^6*(d + e*x)) + (b^4*B*Log[d + e*x])/e^6","A",4,3,31,0.09677,1,"{27, 78, 43}"
1687,1,86,0,0.0336874,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^7,x]","\frac{(a+b x)^5 (-6 a B e+A b e+5 b B d)}{30 e (d+e x)^5 (b d-a e)^2}-\frac{(a+b x)^5 (B d-A e)}{6 e (d+e x)^6 (b d-a e)}","\frac{(a+b x)^5 (-6 a B e+A b e+5 b B d)}{30 e (d+e x)^5 (b d-a e)^2}-\frac{(a+b x)^5 (B d-A e)}{6 e (d+e x)^6 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^5)/(6*e*(b*d - a*e)*(d + e*x)^6) + ((5*b*B*d + A*b*e - 6*a*B*e)*(a + b*x)^5)/(30*e*(b*d - a*e)^2*(d + e*x)^5)","A",3,3,31,0.09677,1,"{27, 78, 37}"
1688,1,135,0,0.0587619,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^8,x]","\frac{b (a+b x)^5 (-7 a B e+2 A b e+5 b B d)}{210 e (d+e x)^5 (b d-a e)^3}+\frac{(a+b x)^5 (-7 a B e+2 A b e+5 b B d)}{42 e (d+e x)^6 (b d-a e)^2}-\frac{(a+b x)^5 (B d-A e)}{7 e (d+e x)^7 (b d-a e)}","\frac{b (a+b x)^5 (-7 a B e+2 A b e+5 b B d)}{210 e (d+e x)^5 (b d-a e)^3}+\frac{(a+b x)^5 (-7 a B e+2 A b e+5 b B d)}{42 e (d+e x)^6 (b d-a e)^2}-\frac{(a+b x)^5 (B d-A e)}{7 e (d+e x)^7 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^5)/(7*e*(b*d - a*e)*(d + e*x)^7) + ((5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^5)/(42*e*(b*d - a*e)^2*(d + e*x)^6) + (b*(5*b*B*d + 2*A*b*e - 7*a*B*e)*(a + b*x)^5)/(210*e*(b*d - a*e)^3*(d + e*x)^5)","A",4,4,31,0.1290,1,"{27, 78, 45, 37}"
1689,1,185,0,0.0895438,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^9,x]","\frac{b^2 (a+b x)^5 (-8 a B e+3 A b e+5 b B d)}{840 e (d+e x)^5 (b d-a e)^4}+\frac{b (a+b x)^5 (-8 a B e+3 A b e+5 b B d)}{168 e (d+e x)^6 (b d-a e)^3}+\frac{(a+b x)^5 (-8 a B e+3 A b e+5 b B d)}{56 e (d+e x)^7 (b d-a e)^2}-\frac{(a+b x)^5 (B d-A e)}{8 e (d+e x)^8 (b d-a e)}","\frac{b^2 (a+b x)^5 (-8 a B e+3 A b e+5 b B d)}{840 e (d+e x)^5 (b d-a e)^4}+\frac{b (a+b x)^5 (-8 a B e+3 A b e+5 b B d)}{168 e (d+e x)^6 (b d-a e)^3}+\frac{(a+b x)^5 (-8 a B e+3 A b e+5 b B d)}{56 e (d+e x)^7 (b d-a e)^2}-\frac{(a+b x)^5 (B d-A e)}{8 e (d+e x)^8 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^5)/(8*e*(b*d - a*e)*(d + e*x)^8) + ((5*b*B*d + 3*A*b*e - 8*a*B*e)*(a + b*x)^5)/(56*e*(b*d - a*e)^2*(d + e*x)^7) + (b*(5*b*B*d + 3*A*b*e - 8*a*B*e)*(a + b*x)^5)/(168*e*(b*d - a*e)^3*(d + e*x)^6) + (b^2*(5*b*B*d + 3*A*b*e - 8*a*B*e)*(a + b*x)^5)/(840*e*(b*d - a*e)^4*(d + e*x)^5)","A",5,4,31,0.1290,1,"{27, 78, 45, 37}"
1690,1,206,0,0.1950929,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^10,x]","\frac{b^3 (-4 a B e-A b e+5 b B d)}{5 e^6 (d+e x)^5}-\frac{b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{3 e^6 (d+e x)^6}+\frac{2 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{7 e^6 (d+e x)^7}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{8 e^6 (d+e x)^8}+\frac{(b d-a e)^4 (B d-A e)}{9 e^6 (d+e x)^9}-\frac{b^4 B}{4 e^6 (d+e x)^4}","\frac{b^3 (-4 a B e-A b e+5 b B d)}{5 e^6 (d+e x)^5}-\frac{b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{3 e^6 (d+e x)^6}+\frac{2 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{7 e^6 (d+e x)^7}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{8 e^6 (d+e x)^8}+\frac{(b d-a e)^4 (B d-A e)}{9 e^6 (d+e x)^9}-\frac{b^4 B}{4 e^6 (d+e x)^4}",1,"((b*d - a*e)^4*(B*d - A*e))/(9*e^6*(d + e*x)^9) - ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(8*e^6*(d + e*x)^8) + (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e))/(7*e^6*(d + e*x)^7) - (b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e))/(3*e^6*(d + e*x)^6) + (b^3*(5*b*B*d - A*b*e - 4*a*B*e))/(5*e^6*(d + e*x)^5) - (b^4*B)/(4*e^6*(d + e*x)^4)","A",3,2,31,0.06452,1,"{27, 77}"
1691,1,206,0,0.1600357,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^11,x]","\frac{b^3 (-4 a B e-A b e+5 b B d)}{6 e^6 (d+e x)^6}-\frac{2 b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{7 e^6 (d+e x)^7}+\frac{b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{4 e^6 (d+e x)^8}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6 (d+e x)^9}+\frac{(b d-a e)^4 (B d-A e)}{10 e^6 (d+e x)^{10}}-\frac{b^4 B}{5 e^6 (d+e x)^5}","\frac{b^3 (-4 a B e-A b e+5 b B d)}{6 e^6 (d+e x)^6}-\frac{2 b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{7 e^6 (d+e x)^7}+\frac{b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{4 e^6 (d+e x)^8}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6 (d+e x)^9}+\frac{(b d-a e)^4 (B d-A e)}{10 e^6 (d+e x)^{10}}-\frac{b^4 B}{5 e^6 (d+e x)^5}",1,"((b*d - a*e)^4*(B*d - A*e))/(10*e^6*(d + e*x)^10) - ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(9*e^6*(d + e*x)^9) + (b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e))/(4*e^6*(d + e*x)^8) - (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e))/(7*e^6*(d + e*x)^7) + (b^3*(5*b*B*d - A*b*e - 4*a*B*e))/(6*e^6*(d + e*x)^6) - (b^4*B)/(5*e^6*(d + e*x)^5)","A",3,2,31,0.06452,1,"{27, 77}"
1692,1,206,0,0.1675449,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{12}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^12,x]","\frac{b^3 (-4 a B e-A b e+5 b B d)}{7 e^6 (d+e x)^7}-\frac{b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{4 e^6 (d+e x)^8}+\frac{2 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6 (d+e x)^9}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{10 e^6 (d+e x)^{10}}+\frac{(b d-a e)^4 (B d-A e)}{11 e^6 (d+e x)^{11}}-\frac{b^4 B}{6 e^6 (d+e x)^6}","\frac{b^3 (-4 a B e-A b e+5 b B d)}{7 e^6 (d+e x)^7}-\frac{b^2 (b d-a e) (-3 a B e-2 A b e+5 b B d)}{4 e^6 (d+e x)^8}+\frac{2 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6 (d+e x)^9}-\frac{(b d-a e)^3 (-a B e-4 A b e+5 b B d)}{10 e^6 (d+e x)^{10}}+\frac{(b d-a e)^4 (B d-A e)}{11 e^6 (d+e x)^{11}}-\frac{b^4 B}{6 e^6 (d+e x)^6}",1,"((b*d - a*e)^4*(B*d - A*e))/(11*e^6*(d + e*x)^11) - ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(10*e^6*(d + e*x)^10) + (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e))/(9*e^6*(d + e*x)^9) - (b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e))/(4*e^6*(d + e*x)^8) + (b^3*(5*b*B*d - A*b*e - 4*a*B*e))/(7*e^6*(d + e*x)^7) - (b^4*B)/(6*e^6*(d + e*x)^6)","A",3,2,31,0.06452,1,"{27, 77}"
1693,1,187,0,0.2651485,"\int \frac{(A+B x) (d+e x)^4}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e^2 (a+b x)^2 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{b^6}+\frac{e^3 (a+b x)^3 (-5 a B e+A b e+4 b B d)}{3 b^6}-\frac{(A b-a B) (b d-a e)^4}{b^6 (a+b x)}+\frac{2 e x (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^5}+\frac{(b d-a e)^3 \log (a+b x) (-5 a B e+4 A b e+b B d)}{b^6}+\frac{B e^4 (a+b x)^4}{4 b^6}","\frac{e^2 (a+b x)^2 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{b^6}+\frac{e^3 (a+b x)^3 (-5 a B e+A b e+4 b B d)}{3 b^6}-\frac{(A b-a B) (b d-a e)^4}{b^6 (a+b x)}+\frac{2 e x (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^5}+\frac{(b d-a e)^3 \log (a+b x) (-5 a B e+4 A b e+b B d)}{b^6}+\frac{B e^4 (a+b x)^4}{4 b^6}",1,"(2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*x)/b^5 - ((A*b - a*B)*(b*d - a*e)^4)/(b^6*(a + b*x)) + (e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^2)/b^6 + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^3)/(3*b^6) + (B*e^4*(a + b*x)^4)/(4*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*Log[a + b*x])/b^6","A",3,2,31,0.06452,1,"{27, 77}"
1694,1,145,0,0.1760256,"\int \frac{(A+B x) (d+e x)^3}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e^2 (a+b x)^2 (-4 a B e+A b e+3 b B d)}{2 b^5}-\frac{(A b-a B) (b d-a e)^3}{b^5 (a+b x)}+\frac{3 e x (b d-a e) (-2 a B e+A b e+b B d)}{b^4}+\frac{(b d-a e)^2 \log (a+b x) (-4 a B e+3 A b e+b B d)}{b^5}+\frac{B e^3 (a+b x)^3}{3 b^5}","\frac{e^2 (a+b x)^2 (-4 a B e+A b e+3 b B d)}{2 b^5}-\frac{(A b-a B) (b d-a e)^3}{b^5 (a+b x)}+\frac{3 e x (b d-a e) (-2 a B e+A b e+b B d)}{b^4}+\frac{(b d-a e)^2 \log (a+b x) (-4 a B e+3 A b e+b B d)}{b^5}+\frac{B e^3 (a+b x)^3}{3 b^5}",1,"(3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*x)/b^4 - ((A*b - a*B)*(b*d - a*e)^3)/(b^5*(a + b*x)) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^2)/(2*b^5) + (B*e^3*(a + b*x)^3)/(3*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*Log[a + b*x])/b^5","A",3,2,31,0.06452,1,"{27, 77}"
1695,1,99,0,0.0980695,"\int \frac{(A+B x) (d+e x)^2}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{(A b-a B) (b d-a e)^2}{b^4 (a+b x)}+\frac{e x (-2 a B e+A b e+2 b B d)}{b^3}+\frac{(b d-a e) \log (a+b x) (-3 a B e+2 A b e+b B d)}{b^4}+\frac{B e^2 x^2}{2 b^2}","-\frac{(A b-a B) (b d-a e)^2}{b^4 (a+b x)}+\frac{e x (-2 a B e+A b e+2 b B d)}{b^3}+\frac{(b d-a e) \log (a+b x) (-3 a B e+2 A b e+b B d)}{b^4}+\frac{B e^2 x^2}{2 b^2}",1,"(e*(2*b*B*d + A*b*e - 2*a*B*e)*x)/b^3 + (B*e^2*x^2)/(2*b^2) - ((A*b - a*B)*(b*d - a*e)^2)/(b^4*(a + b*x)) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*Log[a + b*x])/b^4","A",3,2,31,0.06452,1,"{27, 77}"
1696,1,60,0,0.0560364,"\int \frac{(A+B x) (d+e x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{(A b-a B) (b d-a e)}{b^3 (a+b x)}+\frac{\log (a+b x) (-2 a B e+A b e+b B d)}{b^3}+\frac{B e x}{b^2}","-\frac{(A b-a B) (b d-a e)}{b^3 (a+b x)}+\frac{\log (a+b x) (-2 a B e+A b e+b B d)}{b^3}+\frac{B e x}{b^2}",1,"(B*e*x)/b^2 - ((A*b - a*B)*(b*d - a*e))/(b^3*(a + b*x)) + ((b*B*d + A*b*e - 2*a*B*e)*Log[a + b*x])/b^3","A",3,2,29,0.06897,1,"{27, 77}"
1697,1,32,0,0.02191,"\int \frac{A+B x}{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)}","\frac{B \log (a+b x)}{b^2}-\frac{A b-a B}{b^2 (a+b x)}",1,"-((A*b - a*B)/(b^2*(a + b*x))) + (B*Log[a + b*x])/b^2","A",3,2,24,0.08333,1,"{27, 43}"
1698,1,82,0,0.0633924,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{A b-a B}{b (a+b x) (b d-a e)}+\frac{\log (a+b x) (B d-A e)}{(b d-a e)^2}-\frac{(B d-A e) \log (d+e x)}{(b d-a e)^2}","-\frac{A b-a B}{b (a+b x) (b d-a e)}+\frac{\log (a+b x) (B d-A e)}{(b d-a e)^2}-\frac{(B d-A e) \log (d+e x)}{(b d-a e)^2}",1,"-((A*b - a*B)/(b*(b*d - a*e)*(a + b*x))) + ((B*d - A*e)*Log[a + b*x])/(b*d - a*e)^2 - ((B*d - A*e)*Log[d + e*x])/(b*d - a*e)^2","A",3,2,31,0.06452,1,"{27, 77}"
1699,1,117,0,0.1040805,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{A b-a B}{(a+b x) (b d-a e)^2}+\frac{B d-A e}{(d+e x) (b d-a e)^2}+\frac{\log (a+b x) (a B e-2 A b e+b B d)}{(b d-a e)^3}-\frac{\log (d+e x) (a B e-2 A b e+b B d)}{(b d-a e)^3}","-\frac{A b-a B}{(a+b x) (b d-a e)^2}+\frac{B d-A e}{(d+e x) (b d-a e)^2}+\frac{\log (a+b x) (a B e-2 A b e+b B d)}{(b d-a e)^3}-\frac{\log (d+e x) (a B e-2 A b e+b B d)}{(b d-a e)^3}",1,"-((A*b - a*B)/((b*d - a*e)^2*(a + b*x))) + (B*d - A*e)/((b*d - a*e)^2*(d + e*x)) + ((b*B*d - 2*A*b*e + a*B*e)*Log[a + b*x])/(b*d - a*e)^3 - ((b*B*d - 2*A*b*e + a*B*e)*Log[d + e*x])/(b*d - a*e)^3","A",3,2,31,0.06452,1,"{27, 77}"
1700,1,157,0,0.1544254,"\int \frac{A+B x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b (A b-a B)}{(a+b x) (b d-a e)^3}+\frac{a B e-2 A b e+b B d}{(d+e x) (b d-a e)^3}+\frac{B d-A e}{2 (d+e x)^2 (b d-a e)^2}+\frac{b \log (a+b x) (2 a B e-3 A b e+b B d)}{(b d-a e)^4}-\frac{b \log (d+e x) (2 a B e-3 A b e+b B d)}{(b d-a e)^4}","-\frac{b (A b-a B)}{(a+b x) (b d-a e)^3}+\frac{a B e-2 A b e+b B d}{(d+e x) (b d-a e)^3}+\frac{B d-A e}{2 (d+e x)^2 (b d-a e)^2}+\frac{b \log (a+b x) (2 a B e-3 A b e+b B d)}{(b d-a e)^4}-\frac{b \log (d+e x) (2 a B e-3 A b e+b B d)}{(b d-a e)^4}",1,"-((b*(A*b - a*B))/((b*d - a*e)^3*(a + b*x))) + (B*d - A*e)/(2*(b*d - a*e)^2*(d + e*x)^2) + (b*B*d - 2*A*b*e + a*B*e)/((b*d - a*e)^3*(d + e*x)) + (b*(b*B*d - 3*A*b*e + 2*a*B*e)*Log[a + b*x])/(b*d - a*e)^4 - (b*(b*B*d - 3*A*b*e + 2*a*B*e)*Log[d + e*x])/(b*d - a*e)^4","A",3,2,31,0.06452,1,"{27, 77}"
1701,1,186,0,0.2276625,"\int \frac{(A+B x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^3 x (-4 a B e+A b e+4 b B d)}{b^5}+\frac{2 e^2 (b d-a e) \log (a+b x) (-5 a B e+2 A b e+3 b B d)}{b^6}-\frac{2 e (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^6 (a+b x)}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{2 b^6 (a+b x)^2}-\frac{(A b-a B) (b d-a e)^4}{3 b^6 (a+b x)^3}+\frac{B e^4 x^2}{2 b^4}","\frac{e^3 x (-4 a B e+A b e+4 b B d)}{b^5}+\frac{2 e^2 (b d-a e) \log (a+b x) (-5 a B e+2 A b e+3 b B d)}{b^6}-\frac{2 e (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^6 (a+b x)}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{2 b^6 (a+b x)^2}-\frac{(A b-a B) (b d-a e)^4}{3 b^6 (a+b x)^3}+\frac{B e^4 x^2}{2 b^4}",1,"(e^3*(4*b*B*d + A*b*e - 4*a*B*e)*x)/b^5 + (B*e^4*x^2)/(2*b^4) - ((A*b - a*B)*(b*d - a*e)^4)/(3*b^6*(a + b*x)^3) - ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e))/(2*b^6*(a + b*x)^2) - (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e))/(b^6*(a + b*x)) + (2*e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*Log[a + b*x])/b^6","A",3,2,31,0.06452,1,"{27, 77}"
1702,1,144,0,0.1517786,"\int \frac{(A+B x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^2 \log (a+b x) (-4 a B e+A b e+3 b B d)}{b^5}-\frac{3 e (b d-a e) (-2 a B e+A b e+b B d)}{b^5 (a+b x)}-\frac{(b d-a e)^2 (-4 a B e+3 A b e+b B d)}{2 b^5 (a+b x)^2}-\frac{(A b-a B) (b d-a e)^3}{3 b^5 (a+b x)^3}+\frac{B e^3 x}{b^4}","\frac{e^2 \log (a+b x) (-4 a B e+A b e+3 b B d)}{b^5}-\frac{3 e (b d-a e) (-2 a B e+A b e+b B d)}{b^5 (a+b x)}-\frac{(b d-a e)^2 (-4 a B e+3 A b e+b B d)}{2 b^5 (a+b x)^2}-\frac{(A b-a B) (b d-a e)^3}{3 b^5 (a+b x)^3}+\frac{B e^3 x}{b^4}",1,"(B*e^3*x)/b^4 - ((A*b - a*B)*(b*d - a*e)^3)/(3*b^5*(a + b*x)^3) - ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e))/(2*b^5*(a + b*x)^2) - (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e))/(b^5*(a + b*x)) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*Log[a + b*x])/b^5","A",3,2,31,0.06452,1,"{27, 77}"
1703,1,101,0,0.0775451,"\int \frac{(A+B x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{(d+e x)^3 (A b-a B)}{3 b (a+b x)^3 (b d-a e)}-\frac{2 B e (b d-a e)}{b^4 (a+b x)}-\frac{B (b d-a e)^2}{2 b^4 (a+b x)^2}+\frac{B e^2 \log (a+b x)}{b^4}","-\frac{(d+e x)^3 (A b-a B)}{3 b (a+b x)^3 (b d-a e)}-\frac{2 B e (b d-a e)}{b^4 (a+b x)}-\frac{B (b d-a e)^2}{2 b^4 (a+b x)^2}+\frac{B e^2 \log (a+b x)}{b^4}",1,"-(B*(b*d - a*e)^2)/(2*b^4*(a + b*x)^2) - (2*B*e*(b*d - a*e))/(b^4*(a + b*x)) - ((A*b - a*B)*(d + e*x)^3)/(3*b*(b*d - a*e)*(a + b*x)^3) + (B*e^2*Log[a + b*x])/b^4","A",4,3,31,0.09677,1,"{27, 78, 43}"
1704,1,73,0,0.0588126,"\int \frac{(A+B x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{-2 a B e+A b e+b B d}{2 b^3 (a+b x)^2}-\frac{(A b-a B) (b d-a e)}{3 b^3 (a+b x)^3}-\frac{B e}{b^3 (a+b x)}","-\frac{-2 a B e+A b e+b B d}{2 b^3 (a+b x)^2}-\frac{(A b-a B) (b d-a e)}{3 b^3 (a+b x)^3}-\frac{B e}{b^3 (a+b x)}",1,"-((A*b - a*B)*(b*d - a*e))/(3*b^3*(a + b*x)^3) - (b*B*d + A*b*e - 2*a*B*e)/(2*b^3*(a + b*x)^2) - (B*e)/(b^3*(a + b*x))","A",3,2,29,0.06897,1,"{27, 77}"
1705,1,38,0,0.0233002,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{A b-a B}{3 b^2 (a+b x)^3}-\frac{B}{2 b^2 (a+b x)^2}","-\frac{A b-a B}{3 b^2 (a+b x)^3}-\frac{B}{2 b^2 (a+b x)^2}",1,"-(A*b - a*B)/(3*b^2*(a + b*x)^3) - B/(2*b^2*(a + b*x)^2)","A",3,2,24,0.08333,1,"{27, 43}"
1706,1,146,0,0.1277727,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{e^2 \log (a+b x) (B d-A e)}{(b d-a e)^4}-\frac{e^2 (B d-A e) \log (d+e x)}{(b d-a e)^4}+\frac{e (B d-A e)}{(a+b x) (b d-a e)^3}-\frac{B d-A e}{2 (a+b x)^2 (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 (b d-a e)}","\frac{e^2 \log (a+b x) (B d-A e)}{(b d-a e)^4}-\frac{e^2 (B d-A e) \log (d+e x)}{(b d-a e)^4}+\frac{e (B d-A e)}{(a+b x) (b d-a e)^3}-\frac{B d-A e}{2 (a+b x)^2 (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 (b d-a e)}",1,"-(A*b - a*B)/(3*b*(b*d - a*e)*(a + b*x)^3) - (B*d - A*e)/(2*(b*d - a*e)^2*(a + b*x)^2) + (e*(B*d - A*e))/((b*d - a*e)^3*(a + b*x)) + (e^2*(B*d - A*e)*Log[a + b*x])/(b*d - a*e)^4 - (e^2*(B*d - A*e)*Log[d + e*x])/(b*d - a*e)^4","A",3,2,31,0.06452,1,"{27, 77}"
1707,1,199,0,0.2501598,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{e^2 (B d-A e)}{(d+e x) (b d-a e)^4}+\frac{e^2 \log (a+b x) (a B e-4 A b e+3 b B d)}{(b d-a e)^5}-\frac{e^2 \log (d+e x) (a B e-4 A b e+3 b B d)}{(b d-a e)^5}+\frac{e (a B e-3 A b e+2 b B d)}{(a+b x) (b d-a e)^4}-\frac{a B e-2 A b e+b B d}{2 (a+b x)^2 (b d-a e)^3}-\frac{A b-a B}{3 (a+b x)^3 (b d-a e)^2}","\frac{e^2 (B d-A e)}{(d+e x) (b d-a e)^4}+\frac{e^2 \log (a+b x) (a B e-4 A b e+3 b B d)}{(b d-a e)^5}-\frac{e^2 \log (d+e x) (a B e-4 A b e+3 b B d)}{(b d-a e)^5}+\frac{e (a B e-3 A b e+2 b B d)}{(a+b x) (b d-a e)^4}-\frac{a B e-2 A b e+b B d}{2 (a+b x)^2 (b d-a e)^3}-\frac{A b-a B}{3 (a+b x)^3 (b d-a e)^2}",1,"-(A*b - a*B)/(3*(b*d - a*e)^2*(a + b*x)^3) - (b*B*d - 2*A*b*e + a*B*e)/(2*(b*d - a*e)^3*(a + b*x)^2) + (e*(2*b*B*d - 3*A*b*e + a*B*e))/((b*d - a*e)^4*(a + b*x)) + (e^2*(B*d - A*e))/((b*d - a*e)^4*(d + e*x)) + (e^2*(3*b*B*d - 4*A*b*e + a*B*e)*Log[a + b*x])/(b*d - a*e)^5 - (e^2*(3*b*B*d - 4*A*b*e + a*B*e)*Log[d + e*x])/(b*d - a*e)^5","A",3,2,31,0.06452,1,"{27, 77}"
1708,1,158,0,0.1851318,"\int (A+B x) (d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (-a B e-A b e+2 b B d)}{6 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e) (B d-A e)}{5 e^3 (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7}{7 e^3 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (-a B e-A b e+2 b B d)}{6 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e) (B d-A e)}{5 e^3 (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7}{7 e^3 (a+b x)}",1,"((b*d - a*e)*(B*d - A*e)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^3*(a + b*x)) + (b*B*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1709,1,158,0,0.1445365,"\int (A+B x) (d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (-a B e-A b e+2 b B d)}{5 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e) (B d-A e)}{4 e^3 (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6}{6 e^3 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (-a B e-A b e+2 b B d)}{5 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e) (B d-A e)}{4 e^3 (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6}{6 e^3 (a+b x)}",1,"((b*d - a*e)*(B*d - A*e)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) + (b*B*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^3*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1710,1,158,0,0.1182472,"\int (A+B x) (d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (-a B e-A b e+2 b B d)}{4 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e) (B d-A e)}{3 e^3 (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^3 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (-a B e-A b e+2 b B d)}{4 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e) (B d-A e)}{3 e^3 (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^3 (a+b x)}",1,"((b*d - a*e)*(B*d - A*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)) + (b*B*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1711,1,164,0,0.0845222,"\int (A+B x) (d+e x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{x^3 \sqrt{a^2+2 a b x+b^2 x^2} (a B e+A b e+b B d)}{3 (a+b x)}+\frac{x^2 \sqrt{a^2+2 a b x+b^2 x^2} (a A e+a B d+A b d)}{2 (a+b x)}+\frac{a A d x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b B e x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}","\frac{x^3 \sqrt{a^2+2 a b x+b^2 x^2} (a B e+A b e+b B d)}{3 (a+b x)}+\frac{x^2 \sqrt{a^2+2 a b x+b^2 x^2} (a A e+a B d+A b d)}{2 (a+b x)}+\frac{a A d x \sqrt{a^2+2 a b x+b^2 x^2}}{a+b x}+\frac{b B e x^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 (a+b x)}",1,"(a*A*d*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(a + b*x) + ((A*b*d + a*B*d + a*A*e)*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(a + b*x)) + ((b*B*d + A*b*e + a*B*e)*x^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*(a + b*x)) + (b*B*e*x^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(a + b*x))","A",3,2,31,0.06452,1,"{770, 77}"
1712,1,69,0,0.021708,"\int (A+B x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}","\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b^2}",1,"((A*b - a*B)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^2) + (B*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(3*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
1713,1,132,0,0.0858667,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{d+e x} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x),x]","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{e^2 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e) \log (d+e x)}{e^3 (a+b x)}+\frac{B (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b e}","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{e^2 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e) \log (d+e x)}{e^3 (a+b x)}+\frac{B (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 b e}",1,"-((b*(B*d - A*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x))) + (B*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b*e) + ((b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^3*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1714,1,144,0,0.1006579,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^2} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^2,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{e^3 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x) (-a B e-A b e+2 b B d)}{e^3 (a+b x)}+\frac{b B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^2 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{e^3 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x) (-a B e-A b e+2 b B d)}{e^3 (a+b x)}+\frac{b B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^2 (a+b x)}",1,"(b*B*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x)) - ((b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*(d + e*x)) - ((2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^3*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1715,1,151,0,0.097895,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^3} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^3,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{2 e^3 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{e^3 (a+b x) (d+e x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^3 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{2 e^3 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{e^3 (a+b x) (d+e x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^3 (a+b x)}",1,"-((b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)*(d + e*x)^2) + ((2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*(d + e*x)) + (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^3*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1716,1,104,0,0.0591883,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^4} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^4,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2} (B d-A e)}{3 (d+e x)^3 (b d-a e)^2}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 (d+e x)^2 (b d-a e)^2}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2} (B d-A e)}{3 (d+e x)^3 (b d-a e)^2}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (A b-a B)}{2 (d+e x)^2 (b d-a e)^2}",1,"((A*b - a*B)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*(b*d - a*e)^2*(d + e*x)^2) + ((B*d - A*e)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(3*(b*d - a*e)^2*(d + e*x)^3)","A",3,3,33,0.09091,1,"{769, 646, 37}"
1717,1,158,0,0.099405,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^5} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^5,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{3 e^3 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{4 e^3 (a+b x) (d+e x)^4}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x) (d+e x)^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{3 e^3 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{4 e^3 (a+b x) (d+e x)^4}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x) (d+e x)^2}",1,"-((b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)*(d + e*x)^4) + ((2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^3) - (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)*(d + e*x)^2)","A",3,2,33,0.06061,1,"{770, 77}"
1718,1,158,0,0.0933744,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^6} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^6,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{4 e^3 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{5 e^3 (a+b x) (d+e x)^5}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^3 (a+b x) (d+e x)^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{4 e^3 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{5 e^3 (a+b x) (d+e x)^5}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^3 (a+b x) (d+e x)^3}",1,"-((b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^5) + ((2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)*(d + e*x)^4) - (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^3)","A",3,2,33,0.06061,1,"{770, 77}"
1719,1,158,0,0.095612,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^7} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^7,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{5 e^3 (a+b x) (d+e x)^5}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{6 e^3 (a+b x) (d+e x)^6}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^3 (a+b x) (d+e x)^4}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{5 e^3 (a+b x) (d+e x)^5}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{6 e^3 (a+b x) (d+e x)^6}-\frac{b B \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^3 (a+b x) (d+e x)^4}",1,"-((b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^3*(a + b*x)*(d + e*x)^6) + ((2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^5) - (b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)*(d + e*x)^4)","A",3,2,33,0.06061,1,"{770, 77}"
1720,1,298,0,0.5082416,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (-3 a B e-A b e+4 b B d)}{9 e^5 (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e) (-a B e-A b e+2 b B d)}{8 e^5 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^3 (B d-A e)}{6 e^5 (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10}}{10 e^5 (a+b x)}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (-3 a B e-A b e+4 b B d)}{9 e^5 (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e) (-a B e-A b e+2 b B d)}{8 e^5 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^3 (B d-A e)}{6 e^5 (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10}}{10 e^5 (a+b x)}",1,"((b*d - a*e)^3*(B*d - A*e)*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (b^3*B*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^5*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1721,1,298,0,0.3989014,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (-3 a B e-A b e+4 b B d)}{8 e^5 (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{6 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)^3 (B d-A e)}{5 e^5 (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9}{9 e^5 (a+b x)}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (-3 a B e-A b e+4 b B d)}{8 e^5 (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{6 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)^3 (B d-A e)}{5 e^5 (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9}{9 e^5 (a+b x)}",1,"((b*d - a*e)^3*(B*d - A*e)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)) + (b^3*B*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1722,1,259,0,0.3222274,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (-4 a B e+A b e+3 b B d)}{7 b^5}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e) (-2 a B e+A b e+b B d)}{2 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{5 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B) (b d-a e)^3}{4 b^5}+\frac{B e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^5}","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (-4 a B e+A b e+3 b B d)}{7 b^5}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e) (-2 a B e+A b e+b B d)}{2 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{5 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B) (b d-a e)^3}{4 b^5}+\frac{B e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^5}",1,"((A*b - a*B)*(b*d - a*e)^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^5) + (e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^5) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) + (B*e^3*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^5)","A",3,2,33,0.06061,1,"{770, 77}"
1723,1,198,0,0.2357551,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{6 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e) (-3 a B e+2 A b e+b B d)}{5 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B) (b d-a e)^2}{4 b^4}+\frac{B e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^4}","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{6 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e) (-3 a B e+2 A b e+b B d)}{5 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B) (b d-a e)^2}{4 b^4}+\frac{B e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^4}",1,"((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^4) + (B*e^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4)","A",3,2,33,0.06061,1,"{770, 77}"
1724,1,135,0,0.143975,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (-2 a B e+A b e+b B d)}{5 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B) (b d-a e)}{4 b^3}+\frac{B e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (-2 a B e+A b e+b B d)}{5 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B) (b d-a e)}{4 b^3}+\frac{B e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^3}",1,"((A*b - a*B)*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^3) + (B*e*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3)","A",3,2,31,0.06452,1,"{770, 77}"
1725,1,69,0,0.0242733,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (A b-a B)}{4 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (A b-a B)}{4 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b^2}",1,"((A*b - a*B)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(4*b^2) + (B*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
1726,1,236,0,0.1681759,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{d+e x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x),x]","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (B d-A e)}{e^4 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{2 e^3}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{3 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e) \log (d+e x)}{e^5 (a+b x)}+\frac{B (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 b e}","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (B d-A e)}{e^4 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{2 e^3}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{3 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e) \log (d+e x)}{e^5 (a+b x)}+\frac{B (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 b e}",1,"-((b*(b*d - a*e)^2*(B*d - A*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x))) + ((b*d - a*e)*(B*d - A*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3) - ((B*d - A*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2) + (B*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b*e) + ((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1727,1,285,0,0.2667372,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^2,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{e^5 (a+b x) (d+e x)}+\frac{3 b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{e^4 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (-3 a B e-A b e+4 b B d)}{2 e^5 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x) (-a B e-3 A b e+4 b B d)}{e^5 (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^5 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{e^5 (a+b x) (d+e x)}+\frac{3 b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{e^4 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (-3 a B e-A b e+4 b B d)}{2 e^5 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x) (-a B e-3 A b e+4 b B d)}{e^5 (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^5 (a+b x)}",1,"(3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) - ((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)) + (b^3*B*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1728,1,280,0,0.2342225,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^3,x]","-\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+3 b B d)}{e^4 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{2 e^5 (a+b x) (d+e x)^2}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x) (-a B e-A b e+2 b B d)}{e^5 (a+b x)}+\frac{b^3 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x)}","-\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+3 b B d)}{e^4 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{2 e^5 (a+b x) (d+e x)^2}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x) (-a B e-A b e+2 b B d)}{e^5 (a+b x)}+\frac{b^3 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x)}",1,"-((b^2*(3*b*B*d - A*b*e - 3*a*B*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x))) + (b^3*B*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)) - ((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^2) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1729,1,284,0,0.2117294,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^4,x]","-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{2 e^5 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{3 e^5 (a+b x) (d+e x)^3}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x) (-3 a B e-A b e+4 b B d)}{e^5 (a+b x)}+\frac{b^3 B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x)}","-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{2 e^5 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{3 e^5 (a+b x) (d+e x)^3}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x) (-3 a B e-A b e+4 b B d)}{e^5 (a+b x)}+\frac{b^3 B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x)}",1,"(b^3*B*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) - ((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^3) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^2) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1730,1,257,0,0.1790162,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^5,x]","-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{4 e (d+e x)^4 (b d-a e)}+\frac{3 b^2 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^5 (a+b x) (d+e x)}-\frac{3 b B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^5 (a+b x) (d+e x)^2}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^5 (a+b x) (d+e x)^3}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^5 (a+b x)}","-\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{4 e (d+e x)^4 (b d-a e)}+\frac{3 b^2 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^5 (a+b x) (d+e x)}-\frac{3 b B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^5 (a+b x) (d+e x)^2}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^5 (a+b x) (d+e x)^3}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^5 (a+b x)}",1,"-((B*d - A*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e*(b*d - a*e)*(d + e*x)^4) + (B*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^3) - (3*b*B*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^2) + (3*b^2*B*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) + (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 78, 43}"
1731,1,106,0,0.0594985,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^6,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B)}{4 (d+e x)^4 (b d-a e)^2}+\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2} (B d-A e)}{5 (d+e x)^5 (b d-a e)^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (A b-a B)}{4 (d+e x)^4 (b d-a e)^2}+\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2} (B d-A e)}{5 (d+e x)^5 (b d-a e)^2}",1,"((A*b - a*B)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*(b*d - a*e)^2*(d + e*x)^4) + ((B*d - A*e)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(5*(b*d - a*e)^2*(d + e*x)^5)","A",3,3,33,0.09091,1,"{769, 646, 37}"
1732,1,193,0,0.147411,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^7,x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (-3 a B e+A b e+2 b B d)}{60 e (d+e x)^4 (b d-a e)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (-3 a B e+A b e+2 b B d)}{15 e (d+e x)^5 (b d-a e)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (B d-A e)}{6 e (d+e x)^6 (b d-a e)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (-3 a B e+A b e+2 b B d)}{60 e (d+e x)^4 (b d-a e)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (-3 a B e+A b e+2 b B d)}{15 e (d+e x)^5 (b d-a e)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (B d-A e)}{6 e (d+e x)^6 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e*(b*d - a*e)*(d + e*x)^6) + ((2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e*(b*d - a*e)^2*(d + e*x)^5) + (b*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(60*e*(b*d - a*e)^3*(d + e*x)^4)","A",4,4,33,0.1212,1,"{770, 78, 45, 37}"
1733,1,298,0,0.2183997,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^8,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{4 e^5 (a+b x) (d+e x)^4}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{5 e^5 (a+b x) (d+e x)^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{6 e^5 (a+b x) (d+e x)^6}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{7 e^5 (a+b x) (d+e x)^7}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^5 (a+b x) (d+e x)^3}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{4 e^5 (a+b x) (d+e x)^4}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{5 e^5 (a+b x) (d+e x)^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{6 e^5 (a+b x) (d+e x)^6}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{7 e^5 (a+b x) (d+e x)^7}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^5 (a+b x) (d+e x)^3}",1,"-((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)*(d + e*x)^6) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^5) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^5*(a + b*x)*(d + e*x)^4) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^3)","A",3,2,33,0.06061,1,"{770, 77}"
1734,1,298,0,0.1811994,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^9,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{5 e^5 (a+b x) (d+e x)^5}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{2 e^5 (a+b x) (d+e x)^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (a+b x) (d+e x)^7}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{8 e^5 (a+b x) (d+e x)^8}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^5 (a+b x) (d+e x)^4}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{5 e^5 (a+b x) (d+e x)^5}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{2 e^5 (a+b x) (d+e x)^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (a+b x) (d+e x)^7}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{8 e^5 (a+b x) (d+e x)^8}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^5 (a+b x) (d+e x)^4}",1,"-((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)*(d + e*x)^8) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) - (b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^6) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^5) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^5*(a + b*x)*(d + e*x)^4)","A",3,2,33,0.06061,1,"{770, 77}"
1735,1,298,0,0.1768708,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^10,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{6 e^5 (a+b x) (d+e x)^6}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (a+b x) (d+e x)^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{8 e^5 (a+b x) (d+e x)^8}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{9 e^5 (a+b x) (d+e x)^9}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^5 (a+b x) (d+e x)^5}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{6 e^5 (a+b x) (d+e x)^6}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (a+b x) (d+e x)^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{8 e^5 (a+b x) (d+e x)^8}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{9 e^5 (a+b x) (d+e x)^9}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^5 (a+b x) (d+e x)^5}",1,"-((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)*(d + e*x)^9) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)*(d + e*x)^8) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)*(d + e*x)^6) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^5)","A",3,2,33,0.06061,1,"{770, 77}"
1736,1,298,0,0.1766492,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^11,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{7 e^5 (a+b x) (d+e x)^7}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{8 e^5 (a+b x) (d+e x)^8}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{9 e^5 (a+b x) (d+e x)^9}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{10 e^5 (a+b x) (d+e x)^{10}}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^5 (a+b x) (d+e x)^6}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{7 e^5 (a+b x) (d+e x)^7}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{8 e^5 (a+b x) (d+e x)^8}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{9 e^5 (a+b x) (d+e x)^9}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{10 e^5 (a+b x) (d+e x)^{10}}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^5 (a+b x) (d+e x)^6}",1,"-((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^5*(a + b*x)*(d + e*x)^10) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)*(d + e*x)^9) - (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)*(d + e*x)^8) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)*(d + e*x)^6)","A",3,2,33,0.06061,1,"{770, 77}"
1737,1,298,0,0.1780969,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{12}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^12,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{8 e^5 (a+b x) (d+e x)^8}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{3 e^5 (a+b x) (d+e x)^9}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{10 e^5 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{11 e^5 (a+b x) (d+e x)^{11}}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^5 (a+b x) (d+e x)^7}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (-3 a B e-A b e+4 b B d)}{8 e^5 (a+b x) (d+e x)^8}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{3 e^5 (a+b x) (d+e x)^9}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{10 e^5 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{11 e^5 (a+b x) (d+e x)^{11}}-\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^5 (a+b x) (d+e x)^7}",1,"-((b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)*(d + e*x)^11) + ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^5*(a + b*x)*(d + e*x)^10) - (b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^9) + (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)*(d + e*x)^8) - (b^3*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7)","A",3,2,33,0.06061,1,"{770, 77}"
1738,1,436,0,1.0108651,"\int (A+B x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (-5 a B e-A b e+6 b B d)}{12 e^7 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e) (-2 a B e-A b e+3 b B d)}{11 e^7 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{9 e^7 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{8 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^5 (B d-A e)}{7 e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13}}{13 e^7 (a+b x)}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (-5 a B e-A b e+6 b B d)}{12 e^7 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e) (-2 a B e-A b e+3 b B d)}{11 e^7 (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{9 e^7 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{8 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^5 (B d-A e)}{7 e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13}}{13 e^7 (a+b x)}",1,"((b*d - a*e)^5*(B*d - A*e)*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)) + (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) - (b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*e^7*(a + b*x)) + (b^5*B*(d + e*x)^13*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1739,1,383,0,0.7947303,"\int (A+B x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10} (-6 a B e+A b e+5 b B d)}{11 b^7}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e) (-3 a B e+A b e+2 b B d)}{2 b^7}+\frac{10 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2 (-2 a B e+A b e+b B d)}{9 b^7}+\frac{5 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{8 b^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{7 b^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^5}{6 b^7}+\frac{B e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{11}}{12 b^7}","\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10} (-6 a B e+A b e+5 b B d)}{11 b^7}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e) (-3 a B e+A b e+2 b B d)}{2 b^7}+\frac{10 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2 (-2 a B e+A b e+b B d)}{9 b^7}+\frac{5 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{8 b^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4 (-6 a B e+5 A b e+b B d)}{7 b^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^5}{6 b^7}+\frac{B e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{11}}{12 b^7}",1,"((A*b - a*B)*(b*d - a*e)^5*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^7) + ((b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^7) + (5*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^7) + (10*e^2*(b*d - a*e)^2*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^7) + (e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^7) + (e^4*(5*b*B*d + A*b*e - 6*a*B*e)*(a + b*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*b^7) + (B*e^5*(a + b*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*b^7)","A",3,2,33,0.06061,1,"{770, 77}"
1740,1,324,0,0.6240545,"\int (A+B x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (-5 a B e+A b e+4 b B d)}{10 b^6}+\frac{2 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{9 b^6}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{4 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{7 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^4}{6 b^6}+\frac{B e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^6}","\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (-5 a B e+A b e+4 b B d)}{10 b^6}+\frac{2 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{9 b^6}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{4 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^3 (-5 a B e+4 A b e+b B d)}{7 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^4}{6 b^6}+\frac{B e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^6}",1,"((A*b - a*B)*(b*d - a*e)^4*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^6) + ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^6) + (e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^6) + (2*e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e)*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^6) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*b^6) + (B*e^4*(a + b*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*b^6)","A",3,2,33,0.06061,1,"{770, 77}"
1741,1,259,0,0.4606464,"\int (A+B x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (-4 a B e+A b e+3 b B d)}{9 b^5}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e) (-2 a B e+A b e+b B d)}{8 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{7 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^3}{6 b^5}+\frac{B e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (-4 a B e+A b e+3 b B d)}{9 b^5}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e) (-2 a B e+A b e+b B d)}{8 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2 (-4 a B e+3 A b e+b B d)}{7 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^3}{6 b^5}+\frac{B e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^5}",1,"((A*b - a*B)*(b*d - a*e)^3*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^5) + ((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) + (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^5) + (e^2*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^5) + (B*e^3*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*b^5)","A",3,2,33,0.06061,1,"{770, 77}"
1742,1,198,0,0.3391454,"\int (A+B x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (-3 a B e+A b e+2 b B d)}{8 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e) (-3 a B e+2 A b e+b B d)}{7 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^2}{6 b^4}+\frac{B e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (-3 a B e+A b e+2 b B d)}{8 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e) (-3 a B e+2 A b e+b B d)}{7 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)^2}{6 b^4}+\frac{B e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^4}",1,"((A*b - a*B)*(b*d - a*e)^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^4) + ((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^4) + (B*e^2*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^4)","A",3,2,33,0.06061,1,"{770, 77}"
1743,1,135,0,0.2039863,"\int (A+B x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (-2 a B e+A b e+b B d)}{7 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)}{6 b^3}+\frac{B e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (-2 a B e+A b e+b B d)}{7 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B) (b d-a e)}{6 b^3}+\frac{B e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^3}",1,"((A*b - a*B)*(b*d - a*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^3) + ((b*B*d + A*b*e - 2*a*B*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^3) + (B*e*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^3)","A",3,2,31,0.06452,1,"{770, 77}"
1744,1,69,0,0.0215879,"\int (A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (A b-a B)}{6 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}","\frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} (A b-a B)}{6 b^2}+\frac{B \left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b^2}",1,"((A*b - a*B)*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(6*b^2) + (B*(a^2 + 2*a*b*x + b^2*x^2)^(7/2))/(7*b^2)","A",2,2,26,0.07692,1,"{640, 609}"
1745,1,340,0,0.2535866,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x),x]","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (B d-A e)}{e^6 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{2 e^5}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (B d-A e)}{3 e^4}+\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{4 e^3}-\frac{(a+b x)^4 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{5 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e) \log (d+e x)}{e^7 (a+b x)}+\frac{B (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 b e}","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (B d-A e)}{e^6 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{2 e^5}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (B d-A e)}{3 e^4}+\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{4 e^3}-\frac{(a+b x)^4 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{5 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e) \log (d+e x)}{e^7 (a+b x)}+\frac{B (a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 b e}",1,"-((b*(b*d - a*e)^4*(B*d - A*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x))) + ((b*d - a*e)^3*(B*d - A*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5) - ((b*d - a*e)^2*(B*d - A*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4) + ((b*d - a*e)*(B*d - A*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3) - ((B*d - A*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2) + (B*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b*e) + ((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1746,1,423,0,0.5632508,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^2,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{e^7 (a+b x) (d+e x)}+\frac{5 b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^6 (a+b x)}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e) (-2 a B e-A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (-5 a B e-A b e+6 b B d)}{4 e^7 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x) (-a B e-5 A b e+6 b B d)}{e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^7 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{e^7 (a+b x) (d+e x)}+\frac{5 b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^6 (a+b x)}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e) (-2 a B e-A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (-5 a B e-A b e+6 b B d)}{4 e^7 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x) (-a B e-5 A b e+6 b B d)}{e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^7 (a+b x)}",1,"(5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) - (5*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)) + (b^5*B*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) - ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1747,1,424,0,0.4794672,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^3,x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (-5 a B e-A b e+6 b B d)}{3 e^7 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e) (-2 a B e-A b e+3 b B d)}{2 e^7 (a+b x)}-\frac{10 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^6 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{e^7 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{2 e^7 (a+b x) (d+e x)^2}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x) (-a B e-2 A b e+3 b B d)}{e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^7 (a+b x)}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (-5 a B e-A b e+6 b B d)}{3 e^7 (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e) (-2 a B e-A b e+3 b B d)}{2 e^7 (a+b x)}-\frac{10 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^6 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{e^7 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{2 e^7 (a+b x) (d+e x)^2}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x) (-a B e-2 A b e+3 b B d)}{e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^7 (a+b x)}",1,"(-10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^2) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) + (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (b^5*B*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)) + (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1748,1,425,0,0.4294134,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (-5 a B e-A b e+6 b B d)}{2 e^7 (a+b x)}+\frac{5 b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{e^6 (a+b x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{2 e^7 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{3 e^7 (a+b x) (d+e x)^3}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x) (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^7 (a+b x)}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (-5 a B e-A b e+6 b B d)}{2 e^7 (a+b x)}+\frac{5 b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{e^6 (a+b x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x) (d+e x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{2 e^7 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{3 e^7 (a+b x) (d+e x)^3}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x) (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^7 (a+b x)}",1,"(5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^3) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^2) - (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)) + (b^5*B*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1749,1,421,0,0.3926024,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^5,x]","-\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+5 b B d)}{e^6 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x) (d+e x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{2 e^7 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{3 e^7 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{4 e^7 (a+b x) (d+e x)^4}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x) (-2 a B e-A b e+3 b B d)}{e^7 (a+b x)}+\frac{b^5 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^5 (a+b x)}","-\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+5 b B d)}{e^6 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x) (d+e x)}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{2 e^7 (a+b x) (d+e x)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{3 e^7 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{4 e^7 (a+b x) (d+e x)^4}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x) (-2 a B e-A b e+3 b B d)}{e^7 (a+b x)}+\frac{b^5 B x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^5 (a+b x)}",1,"-((b^4*(5*b*B*d - A*b*e - 5*a*B*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x))) + (b^5*B*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)) - ((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^4) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^3) - (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^2) + (10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) + (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1750,1,422,0,0.3590781,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^6,x]","-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{e^7 (a+b x) (d+e x)}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x) (d+e x)^2}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{3 e^7 (a+b x) (d+e x)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{4 e^7 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{5 e^7 (a+b x) (d+e x)^5}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x) (-5 a B e-A b e+6 b B d)}{e^7 (a+b x)}+\frac{b^5 B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x)}","-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{e^7 (a+b x) (d+e x)}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x) (d+e x)^2}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{3 e^7 (a+b x) (d+e x)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{4 e^7 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{5 e^7 (a+b x) (d+e x)^5}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x) (-5 a B e-A b e+6 b B d)}{e^7 (a+b x)}+\frac{b^5 B x \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x)}",1,"(b^5*B*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^4) - (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^3) + (5*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^2) - (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1751,1,365,0,0.2853522,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^7,x]","-\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{6 e (d+e x)^6 (b d-a e)}+\frac{5 b^4 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)}-\frac{5 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)^2}+\frac{10 b^2 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^3}-\frac{5 b B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^7 (a+b x) (d+e x)^4}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^5}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^7 (a+b x)}","-\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{6 e (d+e x)^6 (b d-a e)}+\frac{5 b^4 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)}-\frac{5 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)^2}+\frac{10 b^2 B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^3}-\frac{5 b B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^7 (a+b x) (d+e x)^4}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^5}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^7 (a+b x)}",1,"-((B*d - A*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e*(b*d - a*e)*(d + e*x)^6) + (B*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5) - (5*b*B*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^4) + (10*b^2*B*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^3) - (5*b^3*B*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^2) + (5*b^4*B*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) + (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 78, 43}"
1752,1,106,0,0.0596924,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^8,x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 (d+e x)^6 (b d-a e)^2}+\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2} (B d-A e)}{7 (d+e x)^7 (b d-a e)^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (A b-a B)}{6 (d+e x)^6 (b d-a e)^2}+\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2} (B d-A e)}{7 (d+e x)^7 (b d-a e)^2}",1,"((A*b - a*B)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(b*d - a*e)^2*(d + e*x)^6) + ((B*d - A*e)*(a^2 + 2*a*b*x + b^2*x^2)^(7/2))/(7*(b*d - a*e)^2*(d + e*x)^7)","A",3,3,33,0.09091,1,"{769, 646, 37}"
1753,1,193,0,0.1421375,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^9} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^9,x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-4 a B e+A b e+3 b B d)}{168 e (d+e x)^6 (b d-a e)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-4 a B e+A b e+3 b B d)}{28 e (d+e x)^7 (b d-a e)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (B d-A e)}{8 e (d+e x)^8 (b d-a e)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-4 a B e+A b e+3 b B d)}{168 e (d+e x)^6 (b d-a e)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-4 a B e+A b e+3 b B d)}{28 e (d+e x)^7 (b d-a e)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (B d-A e)}{8 e (d+e x)^8 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e*(b*d - a*e)*(d + e*x)^8) + ((3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(28*e*(b*d - a*e)^2*(d + e*x)^7) + (b*(3*b*B*d + A*b*e - 4*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(168*e*(b*d - a*e)^3*(d + e*x)^6)","A",4,4,33,0.1212,1,"{770, 78, 45, 37}"
1754,1,262,0,0.1921689,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{10}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^10,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{504 e (d+e x)^6 (b d-a e)^4}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{84 e (d+e x)^7 (b d-a e)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{24 e (d+e x)^8 (b d-a e)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (B d-A e)}{9 e (d+e x)^9 (b d-a e)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{504 e (d+e x)^6 (b d-a e)^4}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{84 e (d+e x)^7 (b d-a e)^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (-3 a B e+A b e+2 b B d)}{24 e (d+e x)^8 (b d-a e)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (B d-A e)}{9 e (d+e x)^9 (b d-a e)}",1,"-((B*d - A*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e*(b*d - a*e)*(d + e*x)^9) + ((2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(24*e*(b*d - a*e)^2*(d + e*x)^8) + (b*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(84*e*(b*d - a*e)^3*(d + e*x)^7) + (b^2*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(504*e*(b*d - a*e)^4*(d + e*x)^6)","A",5,4,33,0.1212,1,"{770, 78, 45, 37}"
1755,1,438,0,0.38993,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^11,x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{5 e^7 (a+b x) (d+e x)^5}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{6 e^7 (a+b x) (d+e x)^6}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{7 e^7 (a+b x) (d+e x)^7}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{8 e^7 (a+b x) (d+e x)^8}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{9 e^7 (a+b x) (d+e x)^9}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{10 e^7 (a+b x) (d+e x)^{10}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^7 (a+b x) (d+e x)^4}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{5 e^7 (a+b x) (d+e x)^5}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{6 e^7 (a+b x) (d+e x)^6}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{7 e^7 (a+b x) (d+e x)^7}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{8 e^7 (a+b x) (d+e x)^8}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{9 e^7 (a+b x) (d+e x)^9}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{10 e^7 (a+b x) (d+e x)^{10}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^7 (a+b x) (d+e x)^4}",1,"-((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^7*(a + b*x)*(d + e*x)^10) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^9) - (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)*(d + e*x)^8) + (10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7) - (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^7*(a + b*x)*(d + e*x)^6) + (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^4)","A",3,2,33,0.06061,1,"{770, 77}"
1756,1,438,0,0.3234833,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{12}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^12,x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{6 e^7 (a+b x) (d+e x)^6}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{7 e^7 (a+b x) (d+e x)^7}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{4 e^7 (a+b x) (d+e x)^8}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{9 e^7 (a+b x) (d+e x)^9}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{10 e^7 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^7 (a+b x) (d+e x)^5}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{6 e^7 (a+b x) (d+e x)^6}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{7 e^7 (a+b x) (d+e x)^7}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{4 e^7 (a+b x) (d+e x)^8}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{9 e^7 (a+b x) (d+e x)^9}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{10 e^7 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^7 (a+b x) (d+e x)^5}",1,"-((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^7*(a + b*x)*(d + e*x)^10) - (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^9) + (5*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^8) - (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7) + (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^7*(a + b*x)*(d + e*x)^6) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5)","A",3,2,33,0.06061,1,"{770, 77}"
1757,1,438,0,0.2959489,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{13}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^13,x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{7 e^7 (a+b x) (d+e x)^7}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{8 e^7 (a+b x) (d+e x)^8}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{9 e^7 (a+b x) (d+e x)^9}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{2 e^7 (a+b x) (d+e x)^{10}}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{12 e^7 (a+b x) (d+e x)^{12}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^7 (a+b x) (d+e x)^6}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{7 e^7 (a+b x) (d+e x)^7}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{8 e^7 (a+b x) (d+e x)^8}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{9 e^7 (a+b x) (d+e x)^9}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{2 e^7 (a+b x) (d+e x)^{10}}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{12 e^7 (a+b x) (d+e x)^{12}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^7 (a+b x) (d+e x)^6}",1,"-((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*e^7*(a + b*x)*(d + e*x)^12) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) - (b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^10) + (10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^9) - (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)*(d + e*x)^8) + (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^7*(a + b*x)*(d + e*x)^6)","A",3,2,33,0.06061,1,"{770, 77}"
1758,1,435,0,0.2941928,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{14}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^14,x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{8 e^7 (a+b x) (d+e x)^8}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{9 e^7 (a+b x) (d+e x)^9}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x) (d+e x)^{10}}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{11 e^7 (a+b x) (d+e x)^{11}}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{12 e^7 (a+b x) (d+e x)^{12}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{13 e^7 (a+b x) (d+e x)^{13}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^7 (a+b x) (d+e x)^7}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (-5 a B e-A b e+6 b B d)}{8 e^7 (a+b x) (d+e x)^8}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-2 a B e-A b e+3 b B d)}{9 e^7 (a+b x) (d+e x)^9}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x) (d+e x)^{10}}-\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{11 e^7 (a+b x) (d+e x)^{11}}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{12 e^7 (a+b x) (d+e x)^{12}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{13 e^7 (a+b x) (d+e x)^{13}}-\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^7 (a+b x) (d+e x)^7}",1,"-((b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^13) + ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*e^7*(a + b*x)*(d + e*x)^12) - (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) + (b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^10) - (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^9) + (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)*(d + e*x)^8) - (b^5*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7)","A",3,2,33,0.06061,1,"{770, 77}"
1759,1,248,0,0.1387124,"\int \frac{(A+B x) (d+e x)^3}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (d+e x)^3 (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2 (A b-a B) (b d-a e)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e x (a+b x) (A b-a B) (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B) (b d-a e)^3 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) (d+e x)^4}{4 b e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (d+e x)^3 (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (d+e x)^2 (A b-a B) (b d-a e)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e x (a+b x) (A b-a B) (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B) (b d-a e)^3 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) (d+e x)^4}{4 b e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((A*b - a*B)*e*(b*d - a*e)^2*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(b*d - a*e)*(a + b*x)*(d + e*x)^2)/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x)*(d + e*x)^3)/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*(a + b*x)*(d + e*x)^4)/(4*b*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(b*d - a*e)^3*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1760,1,191,0,0.1079022,"\int \frac{(A+B x) (d+e x)^2}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (d+e x)^2 (A b-a B)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e x (a+b x) (A b-a B) (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B) (b d-a e)^2 \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) (d+e x)^3}{3 b e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (d+e x)^2 (A b-a B)}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e x (a+b x) (A b-a B) (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{(a+b x) (A b-a B) (b d-a e)^2 \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B (a+b x) (d+e x)^3}{3 b e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((A*b - a*B)*e*(b*d - a*e)*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x)*(d + e*x)^2)/(2*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*(a + b*x)*(d + e*x)^3)/(3*b*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1761,1,134,0,0.078713,"\int \frac{(A+B x) (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*(d + e*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (A b-a B) (b d-a e) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e (a+b x) (A+B x)^2}{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x (a+b x) (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (A b-a B) (b d-a e) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e (a+b x) (A+B x)^2}{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B x (a+b x) (b d-a e)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(B*(b*d - a*e)*x*(a + b*x))/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(a + b*x)*(A + B*x)^2)/(2*b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(b*d - a*e)*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,31,0.06452,1,"{770, 77}"
1762,1,69,0,0.0274003,"\int \frac{A+B x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (A b-a B) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2}}{b^2}","\frac{(a+b x) (A b-a B) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2}}{b^2}",1,"(B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/b^2 + ((A*b - a*B)*(a + b*x)*Log[a + b*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,26,0.1154,1,"{640, 608, 31}"
1763,1,107,0,0.0770278,"\int \frac{A+B x}{(d+e x) \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) (A b-a B) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{(a+b x) (B d-A e) \log (d+e x)}{e \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{(a+b x) (A b-a B) \log (a+b x)}{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{(a+b x) (B d-A e) \log (d+e x)}{e \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"((A*b - a*B)*(a + b*x)*Log[a + b*x])/(b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((B*d - A*e)*(a + b*x)*Log[d + e*x])/(e*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 72}"
1764,1,148,0,0.0808597,"\int \frac{A+B x}{(d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{(d+e x) (b d-a e)^2}+\frac{(a+b x) (A b-a B) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{(a+b x) (A b-a B) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (B d-A e)}{(d+e x) (b d-a e)^2}+\frac{(a+b x) (A b-a B) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{(a+b x) (A b-a B) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"((B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/((b*d - a*e)^2*(d + e*x)) + ((A*b - a*B)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,4,33,0.1212,1,"{769, 646, 36, 31}"
1765,1,212,0,0.1479166,"\int \frac{A+B x}{(d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^2}-\frac{(a+b x) (B d-A e)}{2 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}+\frac{b (a+b x) (A b-a B) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b (a+b x) (A b-a B) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","\frac{(a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^2}-\frac{(a+b x) (B d-A e)}{2 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}+\frac{b (a+b x) (A b-a B) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b (a+b x) (A b-a B) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"-((B*d - A*e)*(a + b*x))/(2*e*(b*d - a*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x))/((b*d - a*e)^2*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(A*b - a*B)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(A*b - a*B)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1766,1,271,0,0.177455,"\int \frac{A+B x}{(d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{b (a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}+\frac{(a+b x) (A b-a B)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}-\frac{(a+b x) (B d-A e)}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}+\frac{b^2 (a+b x) (A b-a B) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^2 (a+b x) (A b-a B) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}","\frac{b (a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}+\frac{(a+b x) (A b-a B)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}-\frac{(a+b x) (B d-A e)}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}+\frac{b^2 (a+b x) (A b-a B) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^2 (a+b x) (A b-a B) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}",1,"-((B*d - A*e)*(a + b*x))/(3*e*(b*d - a*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + ((A*b - a*B)*(a + b*x))/(2*(b*d - a*e)^2*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*(A*b - a*B)*(a + b*x))/((b*d - a*e)^3*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b^2*(A*b - a*B)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b^2*(A*b - a*B)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1767,1,329,0,0.3722292,"\int \frac{(A+B x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^3 x^2 (a+b x) (-3 a B e+A b e+4 b B d)}{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^2 x (a+b x) \left(6 a^2 B e^2-3 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^4}{2 b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e (a+b x) (b d-a e)^2 \log (a+b x) (-5 a B e+3 A b e+2 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^4 x^3 (a+b x)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e^3 x^2 (a+b x) (-3 a B e+A b e+4 b B d)}{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^2 x (a+b x) \left(6 a^2 B e^2-3 a b e (A e+4 B d)+2 b^2 d (2 A e+3 B d)\right)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^4}{2 b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e (a+b x) (b d-a e)^2 \log (a+b x) (-5 a B e+3 A b e+2 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^4 x^3 (a+b x)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - ((A*b - a*B)*(b*d - a*e)^4)/(2*b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(6*a^2*B*e^2 - 3*a*b*e*(4*B*d + A*e) + 2*b^2*d*(3*B*d + 2*A*e))*x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(4*b*B*d + A*b*e - 3*a*B*e)*x^2*(a + b*x))/(2*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e^4*x^3*(a + b*x))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e)*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1768,1,249,0,0.2229054,"\int \frac{(A+B x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^2 x (a+b x) (-3 a B e+A b e+3 b B d)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^2 (-4 a B e+3 A b e+b B d)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^3}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) (b d-a e) \log (a+b x) (-2 a B e+A b e+b B d)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^3 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e^2 x (a+b x) (-3 a B e+A b e+3 b B d)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^2 (-4 a B e+3 A b e+b B d)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^3}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) (b d-a e) \log (a+b x) (-2 a B e+A b e+b B d)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^3 x^2 (a+b x)}{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(((b*d - a*e)^2*(b*B*d + 3*A*b*e - 4*a*B*e))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - ((A*b - a*B)*(b*d - a*e)^3)/(2*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^2*(3*b*B*d + A*b*e - 3*a*B*e)*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e^3*x^2*(a + b*x))/(2*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e*(b*d - a*e)*(b*B*d + A*b*e - 2*a*B*e)*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1769,1,186,0,0.1496953,"\int \frac{(A+B x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(b d-a e) (-3 a B e+2 A b e+b B d)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^2}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e (a+b x) \log (a+b x) (-3 a B e+A b e+2 b B d)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^2 x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(b d-a e) (-3 a B e+2 A b e+b B d)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^2}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e (a+b x) \log (a+b x) (-3 a B e+A b e+2 b B d)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^2 x (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(((b*d - a*e)*(b*B*d + 2*A*b*e - 3*a*B*e))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - ((A*b - a*B)*(b*d - a*e)^2)/(2*b^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e^2*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1770,1,127,0,0.0988835,"\int \frac{(A+B x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(A b-a B) (b d-a e)}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{-2 a B e+A b e+b B d}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(A b-a B) (b d-a e)}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{-2 a B e+A b e+b B d}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e (a+b x) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((b*B*d + A*b*e - 2*a*B*e)/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - ((A*b - a*B)*(b*d - a*e))/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,31,0.06452,1,"{770, 77}"
1771,1,69,0,0.0225895,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{A b-a B}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{A b-a B}{2 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(B/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(2*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,26,0.07692,1,"{640, 607}"
1772,1,196,0,0.157076,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{B d-A e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e (a+b x) \log (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{e (a+b x) (B d-A e) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{B d-A e}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e (a+b x) \log (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{e (a+b x) (B d-A e) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"-((B*d - A*e)/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(B*d - A*e)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(B*d - A*e)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1773,1,266,0,0.2459596,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{A b-a B}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{a B e-2 A b e+b B d}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}-\frac{e (a+b x) \log (a+b x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{e (a+b x) \log (d+e x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}","-\frac{A b-a B}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{a B e-2 A b e+b B d}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}-\frac{e (a+b x) \log (a+b x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{e (a+b x) \log (d+e x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}",1,"-((b*B*d - 2*A*b*e + a*B*e)/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(2*(b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(B*d - A*e)*(a + b*x))/((b*d - a*e)^3*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1774,1,332,0,0.3191445,"\int \frac{A+B x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{b (A b-a B)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b (2 a B e-3 A b e+b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{e (a+b x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^4}-\frac{e (a+b x) (B d-A e)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^3}-\frac{3 b e (a+b x) \log (a+b x) (a B e-2 A b e+b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{3 b e (a+b x) \log (d+e x) (a B e-2 A b e+b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}","-\frac{b (A b-a B)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b (2 a B e-3 A b e+b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{e (a+b x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^4}-\frac{e (a+b x) (B d-A e)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^3}-\frac{3 b e (a+b x) \log (a+b x) (a B e-2 A b e+b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{3 b e (a+b x) \log (d+e x) (a B e-2 A b e+b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}",1,"-((b*(b*B*d - 3*A*b*e + 2*a*B*e))/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (b*(A*b - a*B))/(2*(b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(B*d - A*e)*(a + b*x))/(2*(b*d - a*e)^3*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x))/((b*d - a*e)^4*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b*e*(b*B*d - 2*A*b*e + a*B*e)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*e*(b*B*d - 2*A*b*e + a*B*e)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1775,1,373,0,0.4262437,"\int \frac{(A+B x) (d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^5)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^4 x (a+b x) (-5 a B e+A b e+5 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{10 e^2 (b d-a e)^2 (-2 a B e+A b e+b B d)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e^3 (a+b x) (b d-a e) \log (a+b x) (-3 a B e+A b e+2 b B d)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{2 b^7 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^4 (-6 a B e+5 A b e+b B d)}{3 b^7 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^5}{4 b^7 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^5 x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e^4 x (a+b x) (-5 a B e+A b e+5 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{10 e^2 (b d-a e)^2 (-2 a B e+A b e+b B d)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e^3 (a+b x) (b d-a e) \log (a+b x) (-3 a B e+A b e+2 b B d)}{b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (b d-a e)^3 (-3 a B e+2 A b e+b B d)}{2 b^7 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^4 (-6 a B e+5 A b e+b B d)}{3 b^7 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^5}{4 b^7 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^5 x^2 (a+b x)}{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-10*e^2*(b*d - a*e)^2*(b*B*d + A*b*e - 2*a*B*e))/(b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(b*d - a*e)^5)/(4*b^7*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((b*d - a*e)^4*(b*B*d + 5*A*b*e - 6*a*B*e))/(3*b^7*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(b*d - a*e)^3*(b*B*d + 2*A*b*e - 3*a*B*e))/(2*b^7*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^4*(5*b*B*d + A*b*e - 5*a*B*e)*x*(a + b*x))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e^5*x^2*(a + b*x))/(2*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^3*(b*d - a*e)*(2*b*B*d + A*b*e - 3*a*B*e)*(a + b*x)*Log[a + b*x])/(b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1776,1,310,0,0.3039441,"\int \frac{(A+B x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 e^2 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^3 (a+b x) \log (a+b x) (-5 a B e+A b e+4 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^4}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^4 x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{2 e^2 (b d-a e) (-5 a B e+2 A b e+3 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e^3 (a+b x) \log (a+b x) (-5 a B e+A b e+4 b B d)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e (b d-a e)^2 (-5 a B e+3 A b e+2 b B d)}{b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(b d-a e)^3 (-5 a B e+4 A b e+b B d)}{3 b^6 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)^4}{4 b^6 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^4 x (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-2*e^2*(b*d - a*e)*(3*b*B*d + 2*A*b*e - 5*a*B*e))/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(b*d - a*e)^4)/(4*b^6*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((b*d - a*e)^3*(b*B*d + 4*A*b*e - 5*a*B*e))/(3*b^6*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(b*d - a*e)^2*(2*b*B*d + 3*A*b*e - 5*a*B*e))/(b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e^4*x*(a + b*x))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1777,1,227,0,0.1744995,"\int \frac{(A+B x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{(d+e x)^4 (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 B e^2 (b d-a e)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 B e (b d-a e)^2}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B (b d-a e)^3}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^3 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(d+e x)^4 (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 B e^2 (b d-a e)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 B e (b d-a e)^2}{2 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B (b d-a e)^3}{3 b^5 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{B e^3 (a+b x) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(-3*B*e^2*(b*d - a*e))/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (B*(b*d - a*e)^3)/(3*b^5*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*B*e*(b*d - a*e)^2)/(2*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^4)/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (B*e^3*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 78, 43}"
1778,1,106,0,0.0624928,"\int \frac{(A+B x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{(d+e x)^4 (A b-a B)}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{(d+e x)^3 (B d-A e)}{3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)^2}","-\frac{(d+e x)^4 (A b-a B)}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{(d+e x)^3 (B d-A e)}{3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)^2}",1,"-((B*d - A*e)*(d + e*x)^3)/(3*(b*d - a*e)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - ((A*b - a*B)*(d + e*x)^4)/(4*(b*d - a*e)^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{769, 646, 37}"
1779,1,135,0,0.1009358,"\int \frac{(A+B x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{-2 a B e+A b e+b B d}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B e}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{-2 a B e+A b e+b B d}{3 b^3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(A b-a B) (b d-a e)}{4 b^3 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B e}{2 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((A*b - a*B)*(b*d - a*e))/(4*b^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*B*d + A*b*e - 2*a*B*e)/(3*b^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (B*e)/(2*b^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,31,0.06452,1,"{770, 77}"
1780,1,71,0,0.0210749,"\int \frac{A+B x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{A b-a B}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{B}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{A b-a B}{4 b^2 (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{B}{3 b^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-B/(3*b^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (A*b - a*B)/(4*b^2*(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",2,2,26,0.07692,1,"{640, 607}"
1781,1,302,0,0.2583528,"\int \frac{A+B x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{e^2 (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{e^3 (a+b x) \log (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{e^3 (a+b x) (B d-A e) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{e (B d-A e)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{B d-A e}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{e^2 (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{e^3 (a+b x) \log (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{e^3 (a+b x) (B d-A e) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{e (B d-A e)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{B d-A e}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-((e^2*(B*d - A*e))/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (B*d - A*e)/(3*(b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(B*d - A*e))/(2*(b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(B*d - A*e)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(B*d - A*e)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1782,1,388,0,0.4551187,"\int \frac{A+B x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{e^3 (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^5}-\frac{e^2 (a B e-4 A b e+3 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{e^3 (a+b x) \log (a+b x) (a B e-5 A b e+4 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{e^3 (a+b x) \log (d+e x) (a B e-5 A b e+4 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{e (a B e-3 A b e+2 b B d)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{a B e-2 A b e+b B d}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{A b-a B}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","-\frac{e^3 (a+b x) (B d-A e)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^5}-\frac{e^2 (a B e-4 A b e+3 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{e^3 (a+b x) \log (a+b x) (a B e-5 A b e+4 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{e^3 (a+b x) \log (d+e x) (a B e-5 A b e+4 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{e (a B e-3 A b e+2 b B d)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{a B e-2 A b e+b B d}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{A b-a B}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"-((e^2*(3*b*B*d - 4*A*b*e + a*B*e))/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (A*b - a*B)/(4*(b*d - a*e)^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*B*d - 2*A*b*e + a*B*e)/(3*(b*d - a*e)^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(2*b*B*d - 3*A*b*e + a*B*e))/(2*(b*d - a*e)^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(B*d - A*e)*(a + b*x))/((b*d - a*e)^5*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1783,1,460,0,0.5571498,"\int \frac{A+B x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{e^3 (a+b x) (a B e-5 A b e+4 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^6}-\frac{e^3 (a+b x) (B d-A e)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^5}-\frac{2 b e^2 (2 a B e-5 A b e+3 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}-\frac{5 b e^3 (a+b x) \log (a+b x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}+\frac{5 b e^3 (a+b x) \log (d+e x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}+\frac{3 b e (a B e-2 A b e+b B d)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{b (2 a B e-3 A b e+b B d)}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b (A b-a B)}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","-\frac{e^3 (a+b x) (a B e-5 A b e+4 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^6}-\frac{e^3 (a+b x) (B d-A e)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^5}-\frac{2 b e^2 (2 a B e-5 A b e+3 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}-\frac{5 b e^3 (a+b x) \log (a+b x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}+\frac{5 b e^3 (a+b x) \log (d+e x) (a B e-3 A b e+2 b B d)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^7}+\frac{3 b e (a B e-2 A b e+b B d)}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{b (2 a B e-3 A b e+b B d)}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b (A b-a B)}{4 (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"(-2*b*e^2*(3*b*B*d - 5*A*b*e + 2*a*B*e))/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(A*b - a*B))/(4*(b*d - a*e)^3*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (b*(b*B*d - 3*A*b*e + 2*a*B*e))/(3*(b*d - a*e)^4*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b*e*(b*B*d - 2*A*b*e + a*B*e))/(2*(b*d - a*e)^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(B*d - A*e)*(a + b*x))/(2*(b*d - a*e)^5*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x))/((b*d - a*e)^6*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*b*e^3*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)*Log[a + b*x])/((b*d - a*e)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*b*e^3*(2*b*B*d - 3*A*b*e + a*B*e)*(a + b*x)*Log[d + e*x])/((b*d - a*e)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,33,0.06061,1,"{770, 77}"
1784,1,128,0,0.0721401,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{2 b (d+e x)^{13/2} (-2 a B e-A b e+3 b B d)}{13 e^4}+\frac{2 (d+e x)^{11/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{11 e^4}-\frac{2 (d+e x)^{9/2} (b d-a e)^2 (B d-A e)}{9 e^4}+\frac{2 b^2 B (d+e x)^{15/2}}{15 e^4}","-\frac{2 b (d+e x)^{13/2} (-2 a B e-A b e+3 b B d)}{13 e^4}+\frac{2 (d+e x)^{11/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{11 e^4}-\frac{2 (d+e x)^{9/2} (b d-a e)^2 (B d-A e)}{9 e^4}+\frac{2 b^2 B (d+e x)^{15/2}}{15 e^4}",1,"(-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(13/2))/(13*e^4) + (2*b^2*B*(d + e*x)^(15/2))/(15*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1785,1,128,0,0.0566992,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{2 b (d+e x)^{11/2} (-2 a B e-A b e+3 b B d)}{11 e^4}+\frac{2 (d+e x)^{9/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{9 e^4}-\frac{2 (d+e x)^{7/2} (b d-a e)^2 (B d-A e)}{7 e^4}+\frac{2 b^2 B (d+e x)^{13/2}}{13 e^4}","-\frac{2 b (d+e x)^{11/2} (-2 a B e-A b e+3 b B d)}{11 e^4}+\frac{2 (d+e x)^{9/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{9 e^4}-\frac{2 (d+e x)^{7/2} (b d-a e)^2 (B d-A e)}{7 e^4}+\frac{2 b^2 B (d+e x)^{13/2}}{13 e^4}",1,"(-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(7/2))/(7*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(9/2))/(9*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(11/2))/(11*e^4) + (2*b^2*B*(d + e*x)^(13/2))/(13*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1786,1,128,0,0.057379,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{2 b (d+e x)^{9/2} (-2 a B e-A b e+3 b B d)}{9 e^4}+\frac{2 (d+e x)^{7/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{7 e^4}-\frac{2 (d+e x)^{5/2} (b d-a e)^2 (B d-A e)}{5 e^4}+\frac{2 b^2 B (d+e x)^{11/2}}{11 e^4}","-\frac{2 b (d+e x)^{9/2} (-2 a B e-A b e+3 b B d)}{9 e^4}+\frac{2 (d+e x)^{7/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{7 e^4}-\frac{2 (d+e x)^{5/2} (b d-a e)^2 (B d-A e)}{5 e^4}+\frac{2 b^2 B (d+e x)^{11/2}}{11 e^4}",1,"(-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(5/2))/(5*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(9/2))/(9*e^4) + (2*b^2*B*(d + e*x)^(11/2))/(11*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1787,1,128,0,0.0560255,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{2 b (d+e x)^{7/2} (-2 a B e-A b e+3 b B d)}{7 e^4}+\frac{2 (d+e x)^{5/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4}-\frac{2 (d+e x)^{3/2} (b d-a e)^2 (B d-A e)}{3 e^4}+\frac{2 b^2 B (d+e x)^{9/2}}{9 e^4}","-\frac{2 b (d+e x)^{7/2} (-2 a B e-A b e+3 b B d)}{7 e^4}+\frac{2 (d+e x)^{5/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{5 e^4}-\frac{2 (d+e x)^{3/2} (b d-a e)^2 (B d-A e)}{3 e^4}+\frac{2 b^2 B (d+e x)^{9/2}}{9 e^4}",1,"(-2*(b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(3/2))/(3*e^4) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(7/2))/(7*e^4) + (2*b^2*B*(d + e*x)^(9/2))/(9*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1788,1,126,0,0.0524879,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/Sqrt[d + e*x],x]","-\frac{2 b (d+e x)^{5/2} (-2 a B e-A b e+3 b B d)}{5 e^4}+\frac{2 (d+e x)^{3/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{3 e^4}-\frac{2 \sqrt{d+e x} (b d-a e)^2 (B d-A e)}{e^4}+\frac{2 b^2 B (d+e x)^{7/2}}{7 e^4}","-\frac{2 b (d+e x)^{5/2} (-2 a B e-A b e+3 b B d)}{5 e^4}+\frac{2 (d+e x)^{3/2} (b d-a e) (-a B e-2 A b e+3 b B d)}{3 e^4}-\frac{2 \sqrt{d+e x} (b d-a e)^2 (B d-A e)}{e^4}+\frac{2 b^2 B (d+e x)^{7/2}}{7 e^4}",1,"(-2*(b*d - a*e)^2*(B*d - A*e)*Sqrt[d + e*x])/e^4 + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(3/2))/(3*e^4) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(5/2))/(5*e^4) + (2*b^2*B*(d + e*x)^(7/2))/(7*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1789,1,124,0,0.0546105,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(3/2),x]","-\frac{2 b (d+e x)^{3/2} (-2 a B e-A b e+3 b B d)}{3 e^4}+\frac{2 \sqrt{d+e x} (b d-a e) (-a B e-2 A b e+3 b B d)}{e^4}+\frac{2 (b d-a e)^2 (B d-A e)}{e^4 \sqrt{d+e x}}+\frac{2 b^2 B (d+e x)^{5/2}}{5 e^4}","-\frac{2 b (d+e x)^{3/2} (-2 a B e-A b e+3 b B d)}{3 e^4}+\frac{2 \sqrt{d+e x} (b d-a e) (-a B e-2 A b e+3 b B d)}{e^4}+\frac{2 (b d-a e)^2 (B d-A e)}{e^4 \sqrt{d+e x}}+\frac{2 b^2 B (d+e x)^{5/2}}{5 e^4}",1,"(2*(b*d - a*e)^2*(B*d - A*e))/(e^4*Sqrt[d + e*x]) + (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[d + e*x])/e^4 - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(3/2))/(3*e^4) + (2*b^2*B*(d + e*x)^(5/2))/(5*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1790,1,124,0,0.053602,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(5/2),x]","-\frac{2 b \sqrt{d+e x} (-2 a B e-A b e+3 b B d)}{e^4}-\frac{2 (b d-a e) (-a B e-2 A b e+3 b B d)}{e^4 \sqrt{d+e x}}+\frac{2 (b d-a e)^2 (B d-A e)}{3 e^4 (d+e x)^{3/2}}+\frac{2 b^2 B (d+e x)^{3/2}}{3 e^4}","-\frac{2 b \sqrt{d+e x} (-2 a B e-A b e+3 b B d)}{e^4}-\frac{2 (b d-a e) (-a B e-2 A b e+3 b B d)}{e^4 \sqrt{d+e x}}+\frac{2 (b d-a e)^2 (B d-A e)}{3 e^4 (d+e x)^{3/2}}+\frac{2 b^2 B (d+e x)^{3/2}}{3 e^4}",1,"(2*(b*d - a*e)^2*(B*d - A*e))/(3*e^4*(d + e*x)^(3/2)) - (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(e^4*Sqrt[d + e*x]) - (2*b*(3*b*B*d - A*b*e - 2*a*B*e)*Sqrt[d + e*x])/e^4 + (2*b^2*B*(d + e*x)^(3/2))/(3*e^4)","A",3,2,31,0.06452,1,"{27, 77}"
1791,1,124,0,0.0554085,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(7/2),x]","\frac{2 b (-2 a B e-A b e+3 b B d)}{e^4 \sqrt{d+e x}}-\frac{2 (b d-a e) (-a B e-2 A b e+3 b B d)}{3 e^4 (d+e x)^{3/2}}+\frac{2 (b d-a e)^2 (B d-A e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 b^2 B \sqrt{d+e x}}{e^4}","\frac{2 b (-2 a B e-A b e+3 b B d)}{e^4 \sqrt{d+e x}}-\frac{2 (b d-a e) (-a B e-2 A b e+3 b B d)}{3 e^4 (d+e x)^{3/2}}+\frac{2 (b d-a e)^2 (B d-A e)}{5 e^4 (d+e x)^{5/2}}+\frac{2 b^2 B \sqrt{d+e x}}{e^4}",1,"(2*(b*d - a*e)^2*(B*d - A*e))/(5*e^4*(d + e*x)^(5/2)) - (2*(b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e))/(3*e^4*(d + e*x)^(3/2)) + (2*b*(3*b*B*d - A*b*e - 2*a*B*e))/(e^4*Sqrt[d + e*x]) + (2*b^2*B*Sqrt[d + e*x])/e^4","A",3,2,31,0.06452,1,"{27, 77}"
1792,1,218,0,0.1445781,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 b^3 (d+e x)^{17/2} (-4 a B e-A b e+5 b B d)}{17 e^6}+\frac{4 b^2 (d+e x)^{15/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{15 e^6}-\frac{4 b (d+e x)^{13/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{13 e^6}+\frac{2 (d+e x)^{11/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{11 e^6}-\frac{2 (d+e x)^{9/2} (b d-a e)^4 (B d-A e)}{9 e^6}+\frac{2 b^4 B (d+e x)^{19/2}}{19 e^6}","-\frac{2 b^3 (d+e x)^{17/2} (-4 a B e-A b e+5 b B d)}{17 e^6}+\frac{4 b^2 (d+e x)^{15/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{15 e^6}-\frac{4 b (d+e x)^{13/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{13 e^6}+\frac{2 (d+e x)^{11/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{11 e^6}-\frac{2 (d+e x)^{9/2} (b d-a e)^4 (B d-A e)}{9 e^6}+\frac{2 b^4 B (d+e x)^{19/2}}{19 e^6}",1,"(-2*(b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^6) + (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^6) - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(13/2))/(13*e^6) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(15/2))/(15*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(17/2))/(17*e^6) + (2*b^4*B*(d + e*x)^(19/2))/(19*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1793,1,218,0,0.0968407,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 b^3 (d+e x)^{15/2} (-4 a B e-A b e+5 b B d)}{15 e^6}+\frac{4 b^2 (d+e x)^{13/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{13 e^6}-\frac{4 b (d+e x)^{11/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{11 e^6}+\frac{2 (d+e x)^{9/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6}-\frac{2 (d+e x)^{7/2} (b d-a e)^4 (B d-A e)}{7 e^6}+\frac{2 b^4 B (d+e x)^{17/2}}{17 e^6}","-\frac{2 b^3 (d+e x)^{15/2} (-4 a B e-A b e+5 b B d)}{15 e^6}+\frac{4 b^2 (d+e x)^{13/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{13 e^6}-\frac{4 b (d+e x)^{11/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{11 e^6}+\frac{2 (d+e x)^{9/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{9 e^6}-\frac{2 (d+e x)^{7/2} (b d-a e)^4 (B d-A e)}{7 e^6}+\frac{2 b^4 B (d+e x)^{17/2}}{17 e^6}",1,"(-2*(b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(7/2))/(7*e^6) + (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(9/2))/(9*e^6) - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(11/2))/(11*e^6) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(13/2))/(13*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(15/2))/(15*e^6) + (2*b^4*B*(d + e*x)^(17/2))/(17*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1794,1,218,0,0.0985036,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 b^3 (d+e x)^{13/2} (-4 a B e-A b e+5 b B d)}{13 e^6}+\frac{4 b^2 (d+e x)^{11/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{11 e^6}-\frac{4 b (d+e x)^{9/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6}+\frac{2 (d+e x)^{7/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{7 e^6}-\frac{2 (d+e x)^{5/2} (b d-a e)^4 (B d-A e)}{5 e^6}+\frac{2 b^4 B (d+e x)^{15/2}}{15 e^6}","-\frac{2 b^3 (d+e x)^{13/2} (-4 a B e-A b e+5 b B d)}{13 e^6}+\frac{4 b^2 (d+e x)^{11/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{11 e^6}-\frac{4 b (d+e x)^{9/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{9 e^6}+\frac{2 (d+e x)^{7/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{7 e^6}-\frac{2 (d+e x)^{5/2} (b d-a e)^4 (B d-A e)}{5 e^6}+\frac{2 b^4 B (d+e x)^{15/2}}{15 e^6}",1,"(-2*(b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(5/2))/(5*e^6) + (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^6) - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(9/2))/(9*e^6) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(11/2))/(11*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(13/2))/(13*e^6) + (2*b^4*B*(d + e*x)^(15/2))/(15*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1795,1,218,0,0.0979345,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 b^3 (d+e x)^{11/2} (-4 a B e-A b e+5 b B d)}{11 e^6}+\frac{4 b^2 (d+e x)^{9/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{9 e^6}-\frac{4 b (d+e x)^{7/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{7 e^6}+\frac{2 (d+e x)^{5/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{5 e^6}-\frac{2 (d+e x)^{3/2} (b d-a e)^4 (B d-A e)}{3 e^6}+\frac{2 b^4 B (d+e x)^{13/2}}{13 e^6}","-\frac{2 b^3 (d+e x)^{11/2} (-4 a B e-A b e+5 b B d)}{11 e^6}+\frac{4 b^2 (d+e x)^{9/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{9 e^6}-\frac{4 b (d+e x)^{7/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{7 e^6}+\frac{2 (d+e x)^{5/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{5 e^6}-\frac{2 (d+e x)^{3/2} (b d-a e)^4 (B d-A e)}{3 e^6}+\frac{2 b^4 B (d+e x)^{13/2}}{13 e^6}",1,"(-2*(b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(3/2))/(3*e^6) + (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^6) - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(7/2))/(7*e^6) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(9/2))/(9*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(11/2))/(11*e^6) + (2*b^4*B*(d + e*x)^(13/2))/(13*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1796,1,216,0,0.0943628,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/Sqrt[d + e*x],x]","-\frac{2 b^3 (d+e x)^{9/2} (-4 a B e-A b e+5 b B d)}{9 e^6}+\frac{4 b^2 (d+e x)^{7/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{7 e^6}-\frac{4 b (d+e x)^{5/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{5 e^6}+\frac{2 (d+e x)^{3/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{3 e^6}-\frac{2 \sqrt{d+e x} (b d-a e)^4 (B d-A e)}{e^6}+\frac{2 b^4 B (d+e x)^{11/2}}{11 e^6}","-\frac{2 b^3 (d+e x)^{9/2} (-4 a B e-A b e+5 b B d)}{9 e^6}+\frac{4 b^2 (d+e x)^{7/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{7 e^6}-\frac{4 b (d+e x)^{5/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{5 e^6}+\frac{2 (d+e x)^{3/2} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{3 e^6}-\frac{2 \sqrt{d+e x} (b d-a e)^4 (B d-A e)}{e^6}+\frac{2 b^4 B (d+e x)^{11/2}}{11 e^6}",1,"(-2*(b*d - a*e)^4*(B*d - A*e)*Sqrt[d + e*x])/e^6 + (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(3/2))/(3*e^6) - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(5/2))/(5*e^6) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(7/2))/(7*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(9/2))/(9*e^6) + (2*b^4*B*(d + e*x)^(11/2))/(11*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1797,1,214,0,0.0945112,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(3/2),x]","-\frac{2 b^3 (d+e x)^{7/2} (-4 a B e-A b e+5 b B d)}{7 e^6}+\frac{4 b^2 (d+e x)^{5/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{5 e^6}-\frac{4 b (d+e x)^{3/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{3 e^6}+\frac{2 \sqrt{d+e x} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{e^6}+\frac{2 (b d-a e)^4 (B d-A e)}{e^6 \sqrt{d+e x}}+\frac{2 b^4 B (d+e x)^{9/2}}{9 e^6}","-\frac{2 b^3 (d+e x)^{7/2} (-4 a B e-A b e+5 b B d)}{7 e^6}+\frac{4 b^2 (d+e x)^{5/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{5 e^6}-\frac{4 b (d+e x)^{3/2} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{3 e^6}+\frac{2 \sqrt{d+e x} (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{e^6}+\frac{2 (b d-a e)^4 (B d-A e)}{e^6 \sqrt{d+e x}}+\frac{2 b^4 B (d+e x)^{9/2}}{9 e^6}",1,"(2*(b*d - a*e)^4*(B*d - A*e))/(e^6*Sqrt[d + e*x]) + (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*Sqrt[d + e*x])/e^6 - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(3/2))/(3*e^6) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(5/2))/(5*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(7/2))/(7*e^6) + (2*b^4*B*(d + e*x)^(9/2))/(9*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1798,1,214,0,0.0942208,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(5/2),x]","-\frac{2 b^3 (d+e x)^{5/2} (-4 a B e-A b e+5 b B d)}{5 e^6}+\frac{4 b^2 (d+e x)^{3/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{3 e^6}-\frac{4 b \sqrt{d+e x} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6}-\frac{2 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{e^6 \sqrt{d+e x}}+\frac{2 (b d-a e)^4 (B d-A e)}{3 e^6 (d+e x)^{3/2}}+\frac{2 b^4 B (d+e x)^{7/2}}{7 e^6}","-\frac{2 b^3 (d+e x)^{5/2} (-4 a B e-A b e+5 b B d)}{5 e^6}+\frac{4 b^2 (d+e x)^{3/2} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{3 e^6}-\frac{4 b \sqrt{d+e x} (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6}-\frac{2 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{e^6 \sqrt{d+e x}}+\frac{2 (b d-a e)^4 (B d-A e)}{3 e^6 (d+e x)^{3/2}}+\frac{2 b^4 B (d+e x)^{7/2}}{7 e^6}",1,"(2*(b*d - a*e)^4*(B*d - A*e))/(3*e^6*(d + e*x)^(3/2)) - (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(e^6*Sqrt[d + e*x]) - (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*Sqrt[d + e*x])/e^6 + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(3/2))/(3*e^6) - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(5/2))/(5*e^6) + (2*b^4*B*(d + e*x)^(7/2))/(7*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1799,1,214,0,0.0922326,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(7/2),x]","-\frac{2 b^3 (d+e x)^{3/2} (-4 a B e-A b e+5 b B d)}{3 e^6}+\frac{4 b^2 \sqrt{d+e x} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^6}+\frac{4 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6 \sqrt{d+e x}}-\frac{2 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{3 e^6 (d+e x)^{3/2}}+\frac{2 (b d-a e)^4 (B d-A e)}{5 e^6 (d+e x)^{5/2}}+\frac{2 b^4 B (d+e x)^{5/2}}{5 e^6}","-\frac{2 b^3 (d+e x)^{3/2} (-4 a B e-A b e+5 b B d)}{3 e^6}+\frac{4 b^2 \sqrt{d+e x} (b d-a e) (-3 a B e-2 A b e+5 b B d)}{e^6}+\frac{4 b (b d-a e)^2 (-2 a B e-3 A b e+5 b B d)}{e^6 \sqrt{d+e x}}-\frac{2 (b d-a e)^3 (-a B e-4 A b e+5 b B d)}{3 e^6 (d+e x)^{3/2}}+\frac{2 (b d-a e)^4 (B d-A e)}{5 e^6 (d+e x)^{5/2}}+\frac{2 b^4 B (d+e x)^{5/2}}{5 e^6}",1,"(2*(b*d - a*e)^4*(B*d - A*e))/(5*e^6*(d + e*x)^(5/2)) - (2*(b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e))/(3*e^6*(d + e*x)^(3/2)) + (4*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e))/(e^6*Sqrt[d + e*x]) + (4*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/e^6 - (2*b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(3/2))/(3*e^6) + (2*b^4*B*(d + e*x)^(5/2))/(5*e^6)","A",3,2,33,0.06061,1,"{27, 77}"
1800,1,308,0,0.2089368,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 b^5 (d+e x)^{21/2} (-6 a B e-A b e+7 b B d)}{21 e^8}+\frac{6 b^4 (d+e x)^{19/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{19 e^8}-\frac{10 b^3 (d+e x)^{17/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{17 e^8}+\frac{2 b^2 (d+e x)^{15/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8}-\frac{6 b (d+e x)^{13/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{13 e^8}+\frac{2 (d+e x)^{11/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{11 e^8}-\frac{2 (d+e x)^{9/2} (b d-a e)^6 (B d-A e)}{9 e^8}+\frac{2 b^6 B (d+e x)^{23/2}}{23 e^8}","-\frac{2 b^5 (d+e x)^{21/2} (-6 a B e-A b e+7 b B d)}{21 e^8}+\frac{6 b^4 (d+e x)^{19/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{19 e^8}-\frac{10 b^3 (d+e x)^{17/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{17 e^8}+\frac{2 b^2 (d+e x)^{15/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8}-\frac{6 b (d+e x)^{13/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{13 e^8}+\frac{2 (d+e x)^{11/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{11 e^8}-\frac{2 (d+e x)^{9/2} (b d-a e)^6 (B d-A e)}{9 e^8}+\frac{2 b^6 B (d+e x)^{23/2}}{23 e^8}",1,"(-2*(b*d - a*e)^6*(B*d - A*e)*(d + e*x)^(9/2))/(9*e^8) + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^(11/2))/(11*e^8) - (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(13/2))/(13*e^8) + (2*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(15/2))/(3*e^8) - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(17/2))/(17*e^8) + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(19/2))/(19*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(21/2))/(21*e^8) + (2*b^6*B*(d + e*x)^(23/2))/(23*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1801,1,308,0,0.1464383,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 b^5 (d+e x)^{19/2} (-6 a B e-A b e+7 b B d)}{19 e^8}+\frac{6 b^4 (d+e x)^{17/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{17 e^8}-\frac{2 b^3 (d+e x)^{15/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac{10 b^2 (d+e x)^{13/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{13 e^8}-\frac{6 b (d+e x)^{11/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{11 e^8}+\frac{2 (d+e x)^{9/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{9 e^8}-\frac{2 (d+e x)^{7/2} (b d-a e)^6 (B d-A e)}{7 e^8}+\frac{2 b^6 B (d+e x)^{21/2}}{21 e^8}","-\frac{2 b^5 (d+e x)^{19/2} (-6 a B e-A b e+7 b B d)}{19 e^8}+\frac{6 b^4 (d+e x)^{17/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{17 e^8}-\frac{2 b^3 (d+e x)^{15/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac{10 b^2 (d+e x)^{13/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{13 e^8}-\frac{6 b (d+e x)^{11/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{11 e^8}+\frac{2 (d+e x)^{9/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{9 e^8}-\frac{2 (d+e x)^{7/2} (b d-a e)^6 (B d-A e)}{7 e^8}+\frac{2 b^6 B (d+e x)^{21/2}}{21 e^8}",1,"(-2*(b*d - a*e)^6*(B*d - A*e)*(d + e*x)^(7/2))/(7*e^8) + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^(9/2))/(9*e^8) - (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(11/2))/(11*e^8) + (10*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(13/2))/(13*e^8) - (2*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(15/2))/(3*e^8) + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(17/2))/(17*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(19/2))/(19*e^8) + (2*b^6*B*(d + e*x)^(21/2))/(21*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1802,1,308,0,0.1414728,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 b^5 (d+e x)^{17/2} (-6 a B e-A b e+7 b B d)}{17 e^8}+\frac{2 b^4 (d+e x)^{15/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{5 e^8}-\frac{10 b^3 (d+e x)^{13/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{13 e^8}+\frac{10 b^2 (d+e x)^{11/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8}-\frac{2 b (d+e x)^{9/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{3 e^8}+\frac{2 (d+e x)^{7/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{7 e^8}-\frac{2 (d+e x)^{5/2} (b d-a e)^6 (B d-A e)}{5 e^8}+\frac{2 b^6 B (d+e x)^{19/2}}{19 e^8}","-\frac{2 b^5 (d+e x)^{17/2} (-6 a B e-A b e+7 b B d)}{17 e^8}+\frac{2 b^4 (d+e x)^{15/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{5 e^8}-\frac{10 b^3 (d+e x)^{13/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{13 e^8}+\frac{10 b^2 (d+e x)^{11/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{11 e^8}-\frac{2 b (d+e x)^{9/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{3 e^8}+\frac{2 (d+e x)^{7/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{7 e^8}-\frac{2 (d+e x)^{5/2} (b d-a e)^6 (B d-A e)}{5 e^8}+\frac{2 b^6 B (d+e x)^{19/2}}{19 e^8}",1,"(-2*(b*d - a*e)^6*(B*d - A*e)*(d + e*x)^(5/2))/(5*e^8) + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^(7/2))/(7*e^8) - (2*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(9/2))/(3*e^8) + (10*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(11/2))/(11*e^8) - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(13/2))/(13*e^8) + (2*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(15/2))/(5*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(17/2))/(17*e^8) + (2*b^6*B*(d + e*x)^(19/2))/(19*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1803,1,308,0,0.144463,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 b^5 (d+e x)^{15/2} (-6 a B e-A b e+7 b B d)}{15 e^8}+\frac{6 b^4 (d+e x)^{13/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{13 e^8}-\frac{10 b^3 (d+e x)^{11/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{11 e^8}+\frac{10 b^2 (d+e x)^{9/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{9 e^8}-\frac{6 b (d+e x)^{7/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{7 e^8}+\frac{2 (d+e x)^{5/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{5 e^8}-\frac{2 (d+e x)^{3/2} (b d-a e)^6 (B d-A e)}{3 e^8}+\frac{2 b^6 B (d+e x)^{17/2}}{17 e^8}","-\frac{2 b^5 (d+e x)^{15/2} (-6 a B e-A b e+7 b B d)}{15 e^8}+\frac{6 b^4 (d+e x)^{13/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{13 e^8}-\frac{10 b^3 (d+e x)^{11/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{11 e^8}+\frac{10 b^2 (d+e x)^{9/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{9 e^8}-\frac{6 b (d+e x)^{7/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{7 e^8}+\frac{2 (d+e x)^{5/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{5 e^8}-\frac{2 (d+e x)^{3/2} (b d-a e)^6 (B d-A e)}{3 e^8}+\frac{2 b^6 B (d+e x)^{17/2}}{17 e^8}",1,"(-2*(b*d - a*e)^6*(B*d - A*e)*(d + e*x)^(3/2))/(3*e^8) + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^(5/2))/(5*e^8) - (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(7/2))/(7*e^8) + (10*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(9/2))/(9*e^8) - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(11/2))/(11*e^8) + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(13/2))/(13*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(15/2))/(15*e^8) + (2*b^6*B*(d + e*x)^(17/2))/(17*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1804,1,306,0,0.1455147,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/Sqrt[d + e*x],x]","-\frac{2 b^5 (d+e x)^{13/2} (-6 a B e-A b e+7 b B d)}{13 e^8}+\frac{6 b^4 (d+e x)^{11/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{11 e^8}-\frac{10 b^3 (d+e x)^{9/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{9 e^8}+\frac{10 b^2 (d+e x)^{7/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{7 e^8}-\frac{6 b (d+e x)^{5/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{5 e^8}+\frac{2 (d+e x)^{3/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8}-\frac{2 \sqrt{d+e x} (b d-a e)^6 (B d-A e)}{e^8}+\frac{2 b^6 B (d+e x)^{15/2}}{15 e^8}","-\frac{2 b^5 (d+e x)^{13/2} (-6 a B e-A b e+7 b B d)}{13 e^8}+\frac{6 b^4 (d+e x)^{11/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{11 e^8}-\frac{10 b^3 (d+e x)^{9/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{9 e^8}+\frac{10 b^2 (d+e x)^{7/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{7 e^8}-\frac{6 b (d+e x)^{5/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{5 e^8}+\frac{2 (d+e x)^{3/2} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8}-\frac{2 \sqrt{d+e x} (b d-a e)^6 (B d-A e)}{e^8}+\frac{2 b^6 B (d+e x)^{15/2}}{15 e^8}",1,"(-2*(b*d - a*e)^6*(B*d - A*e)*Sqrt[d + e*x])/e^8 + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*(d + e*x)^(3/2))/(3*e^8) - (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(5/2))/(5*e^8) + (10*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(7/2))/(7*e^8) - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(9/2))/(9*e^8) + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(11/2))/(11*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(13/2))/(13*e^8) + (2*b^6*B*(d + e*x)^(15/2))/(15*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1805,1,300,0,0.1451253,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(3/2),x]","-\frac{2 b^5 (d+e x)^{11/2} (-6 a B e-A b e+7 b B d)}{11 e^8}+\frac{2 b^4 (d+e x)^{9/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{3 e^8}-\frac{10 b^3 (d+e x)^{7/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{7 e^8}+\frac{2 b^2 (d+e x)^{5/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8}-\frac{2 b (d+e x)^{3/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8}+\frac{2 \sqrt{d+e x} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{e^8}+\frac{2 (b d-a e)^6 (B d-A e)}{e^8 \sqrt{d+e x}}+\frac{2 b^6 B (d+e x)^{13/2}}{13 e^8}","-\frac{2 b^5 (d+e x)^{11/2} (-6 a B e-A b e+7 b B d)}{11 e^8}+\frac{2 b^4 (d+e x)^{9/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{3 e^8}-\frac{10 b^3 (d+e x)^{7/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{7 e^8}+\frac{2 b^2 (d+e x)^{5/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8}-\frac{2 b (d+e x)^{3/2} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8}+\frac{2 \sqrt{d+e x} (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{e^8}+\frac{2 (b d-a e)^6 (B d-A e)}{e^8 \sqrt{d+e x}}+\frac{2 b^6 B (d+e x)^{13/2}}{13 e^8}",1,"(2*(b*d - a*e)^6*(B*d - A*e))/(e^8*Sqrt[d + e*x]) + (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e)*Sqrt[d + e*x])/e^8 - (2*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*(d + e*x)^(3/2))/e^8 + (2*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(5/2))/e^8 - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(7/2))/(7*e^8) + (2*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(9/2))/(3*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(11/2))/(11*e^8) + (2*b^6*B*(d + e*x)^(13/2))/(13*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1806,1,302,0,0.1451866,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(5/2),x]","-\frac{2 b^5 (d+e x)^{9/2} (-6 a B e-A b e+7 b B d)}{9 e^8}+\frac{6 b^4 (d+e x)^{7/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{7 e^8}-\frac{2 b^3 (d+e x)^{5/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{e^8}+\frac{10 b^2 (d+e x)^{3/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8}-\frac{6 b \sqrt{d+e x} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8}-\frac{2 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{e^8 \sqrt{d+e x}}+\frac{2 (b d-a e)^6 (B d-A e)}{3 e^8 (d+e x)^{3/2}}+\frac{2 b^6 B (d+e x)^{11/2}}{11 e^8}","-\frac{2 b^5 (d+e x)^{9/2} (-6 a B e-A b e+7 b B d)}{9 e^8}+\frac{6 b^4 (d+e x)^{7/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{7 e^8}-\frac{2 b^3 (d+e x)^{5/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{e^8}+\frac{10 b^2 (d+e x)^{3/2} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{3 e^8}-\frac{6 b \sqrt{d+e x} (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8}-\frac{2 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{e^8 \sqrt{d+e x}}+\frac{2 (b d-a e)^6 (B d-A e)}{3 e^8 (d+e x)^{3/2}}+\frac{2 b^6 B (d+e x)^{11/2}}{11 e^8}",1,"(2*(b*d - a*e)^6*(B*d - A*e))/(3*e^8*(d + e*x)^(3/2)) - (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(e^8*Sqrt[d + e*x]) - (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e)*Sqrt[d + e*x])/e^8 + (10*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*(d + e*x)^(3/2))/(3*e^8) - (2*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(5/2))/e^8 + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(7/2))/(7*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(9/2))/(9*e^8) + (2*b^6*B*(d + e*x)^(11/2))/(11*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1807,1,304,0,0.146419,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(7/2),x]","-\frac{2 b^5 (d+e x)^{7/2} (-6 a B e-A b e+7 b B d)}{7 e^8}+\frac{6 b^4 (d+e x)^{5/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{5 e^8}-\frac{10 b^3 (d+e x)^{3/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac{10 b^2 \sqrt{d+e x} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8}+\frac{6 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8 \sqrt{d+e x}}-\frac{2 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8 (d+e x)^{3/2}}+\frac{2 (b d-a e)^6 (B d-A e)}{5 e^8 (d+e x)^{5/2}}+\frac{2 b^6 B (d+e x)^{9/2}}{9 e^8}","-\frac{2 b^5 (d+e x)^{7/2} (-6 a B e-A b e+7 b B d)}{7 e^8}+\frac{6 b^4 (d+e x)^{5/2} (b d-a e) (-5 a B e-2 A b e+7 b B d)}{5 e^8}-\frac{10 b^3 (d+e x)^{3/2} (b d-a e)^2 (-4 a B e-3 A b e+7 b B d)}{3 e^8}+\frac{10 b^2 \sqrt{d+e x} (b d-a e)^3 (-3 a B e-4 A b e+7 b B d)}{e^8}+\frac{6 b (b d-a e)^4 (-2 a B e-5 A b e+7 b B d)}{e^8 \sqrt{d+e x}}-\frac{2 (b d-a e)^5 (-a B e-6 A b e+7 b B d)}{3 e^8 (d+e x)^{3/2}}+\frac{2 (b d-a e)^6 (B d-A e)}{5 e^8 (d+e x)^{5/2}}+\frac{2 b^6 B (d+e x)^{9/2}}{9 e^8}",1,"(2*(b*d - a*e)^6*(B*d - A*e))/(5*e^8*(d + e*x)^(5/2)) - (2*(b*d - a*e)^5*(7*b*B*d - 6*A*b*e - a*B*e))/(3*e^8*(d + e*x)^(3/2)) + (6*b*(b*d - a*e)^4*(7*b*B*d - 5*A*b*e - 2*a*B*e))/(e^8*Sqrt[d + e*x]) + (10*b^2*(b*d - a*e)^3*(7*b*B*d - 4*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/e^8 - (10*b^3*(b*d - a*e)^2*(7*b*B*d - 3*A*b*e - 4*a*B*e)*(d + e*x)^(3/2))/(3*e^8) + (6*b^4*(b*d - a*e)*(7*b*B*d - 2*A*b*e - 5*a*B*e)*(d + e*x)^(5/2))/(5*e^8) - (2*b^5*(7*b*B*d - A*b*e - 6*a*B*e)*(d + e*x)^(7/2))/(7*e^8) + (2*b^6*B*(d + e*x)^(9/2))/(9*e^8)","A",3,2,33,0.06061,1,"{27, 77}"
1808,1,256,0,0.3235603,"\int \frac{(A+B x) (d+e x)^{7/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{7/2} (-9 a B e+7 A b e+2 b B d)}{7 b^2 (b d-a e)}+\frac{(d+e x)^{5/2} (-9 a B e+7 A b e+2 b B d)}{5 b^3}+\frac{(d+e x)^{3/2} (b d-a e) (-9 a B e+7 A b e+2 b B d)}{3 b^4}+\frac{\sqrt{d+e x} (b d-a e)^2 (-9 a B e+7 A b e+2 b B d)}{b^5}-\frac{(b d-a e)^{5/2} (-9 a B e+7 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{11/2}}-\frac{(d+e x)^{9/2} (A b-a B)}{b (a+b x) (b d-a e)}","\frac{(d+e x)^{7/2} (-9 a B e+7 A b e+2 b B d)}{7 b^2 (b d-a e)}+\frac{(d+e x)^{5/2} (-9 a B e+7 A b e+2 b B d)}{5 b^3}+\frac{(d+e x)^{3/2} (b d-a e) (-9 a B e+7 A b e+2 b B d)}{3 b^4}+\frac{\sqrt{d+e x} (b d-a e)^2 (-9 a B e+7 A b e+2 b B d)}{b^5}-\frac{(b d-a e)^{5/2} (-9 a B e+7 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{11/2}}-\frac{(d+e x)^{9/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"((b*d - a*e)^2*(2*b*B*d + 7*A*b*e - 9*a*B*e)*Sqrt[d + e*x])/b^5 + ((b*d - a*e)*(2*b*B*d + 7*A*b*e - 9*a*B*e)*(d + e*x)^(3/2))/(3*b^4) + ((2*b*B*d + 7*A*b*e - 9*a*B*e)*(d + e*x)^(5/2))/(5*b^3) + ((2*b*B*d + 7*A*b*e - 9*a*B*e)*(d + e*x)^(7/2))/(7*b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(9/2))/(b*(b*d - a*e)*(a + b*x)) - ((b*d - a*e)^(5/2)*(2*b*B*d + 7*A*b*e - 9*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(11/2)","A",8,5,33,0.1515,1,"{27, 78, 50, 63, 208}"
1809,1,214,0,0.2007323,"\int \frac{(A+B x) (d+e x)^{5/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{5/2} (-7 a B e+5 A b e+2 b B d)}{5 b^2 (b d-a e)}+\frac{(d+e x)^{3/2} (-7 a B e+5 A b e+2 b B d)}{3 b^3}+\frac{\sqrt{d+e x} (b d-a e) (-7 a B e+5 A b e+2 b B d)}{b^4}-\frac{(b d-a e)^{3/2} (-7 a B e+5 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}-\frac{(d+e x)^{7/2} (A b-a B)}{b (a+b x) (b d-a e)}","\frac{(d+e x)^{5/2} (-7 a B e+5 A b e+2 b B d)}{5 b^2 (b d-a e)}+\frac{(d+e x)^{3/2} (-7 a B e+5 A b e+2 b B d)}{3 b^3}+\frac{\sqrt{d+e x} (b d-a e) (-7 a B e+5 A b e+2 b B d)}{b^4}-\frac{(b d-a e)^{3/2} (-7 a B e+5 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}-\frac{(d+e x)^{7/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"((b*d - a*e)*(2*b*B*d + 5*A*b*e - 7*a*B*e)*Sqrt[d + e*x])/b^4 + ((2*b*B*d + 5*A*b*e - 7*a*B*e)*(d + e*x)^(3/2))/(3*b^3) + ((2*b*B*d + 5*A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(5*b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(7/2))/(b*(b*d - a*e)*(a + b*x)) - ((b*d - a*e)^(3/2)*(2*b*B*d + 5*A*b*e - 7*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(9/2)","A",7,5,33,0.1515,1,"{27, 78, 50, 63, 208}"
1810,1,174,0,0.1500633,"\int \frac{(A+B x) (d+e x)^{3/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{3/2} (-5 a B e+3 A b e+2 b B d)}{3 b^2 (b d-a e)}+\frac{\sqrt{d+e x} (-5 a B e+3 A b e+2 b B d)}{b^3}-\frac{\sqrt{b d-a e} (-5 a B e+3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}-\frac{(d+e x)^{5/2} (A b-a B)}{b (a+b x) (b d-a e)}","\frac{(d+e x)^{3/2} (-5 a B e+3 A b e+2 b B d)}{3 b^2 (b d-a e)}+\frac{\sqrt{d+e x} (-5 a B e+3 A b e+2 b B d)}{b^3}-\frac{\sqrt{b d-a e} (-5 a B e+3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}-\frac{(d+e x)^{5/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"((2*b*B*d + 3*A*b*e - 5*a*B*e)*Sqrt[d + e*x])/b^3 + ((2*b*B*d + 3*A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(3*b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(5/2))/(b*(b*d - a*e)*(a + b*x)) - (Sqrt[b*d - a*e]*(2*b*B*d + 3*A*b*e - 5*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(7/2)","A",6,5,33,0.1515,1,"{27, 78, 50, 63, 208}"
1811,1,140,0,0.1151269,"\int \frac{(A+B x) \sqrt{d+e x}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\sqrt{d+e x} (-3 a B e+A b e+2 b B d)}{b^2 (b d-a e)}-\frac{(-3 a B e+A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{b d-a e}}-\frac{(d+e x)^{3/2} (A b-a B)}{b (a+b x) (b d-a e)}","\frac{\sqrt{d+e x} (-3 a B e+A b e+2 b B d)}{b^2 (b d-a e)}-\frac{(-3 a B e+A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{b d-a e}}-\frac{(d+e x)^{3/2} (A b-a B)}{b (a+b x) (b d-a e)}",1,"((2*b*B*d + A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(b^2*(b*d - a*e)) - ((A*b - a*B)*(d + e*x)^(3/2))/(b*(b*d - a*e)*(a + b*x)) - ((2*b*B*d + A*b*e - 3*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(5/2)*Sqrt[b*d - a*e])","A",5,5,33,0.1515,1,"{27, 78, 50, 63, 208}"
1812,1,103,0,0.0953529,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{(-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x} (A b-a B)}{b (a+b x) (b d-a e)}","-\frac{(-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x} (A b-a B)}{b (a+b x) (b d-a e)}",1,"-(((A*b - a*B)*Sqrt[d + e*x])/(b*(b*d - a*e)*(a + b*x))) - ((2*b*B*d - A*b*e - a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*(b*d - a*e)^(3/2))","A",4,4,33,0.1212,1,"{27, 78, 63, 208}"
1813,1,140,0,0.145376,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{A b-a B}{b (a+b x) \sqrt{d+e x} (b d-a e)}+\frac{a B e-3 A b e+2 b B d}{b \sqrt{d+e x} (b d-a e)^2}-\frac{(a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} (b d-a e)^{5/2}}","-\frac{A b-a B}{b (a+b x) \sqrt{d+e x} (b d-a e)}+\frac{a B e-3 A b e+2 b B d}{b \sqrt{d+e x} (b d-a e)^2}-\frac{(a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} (b d-a e)^{5/2}}",1,"(2*b*B*d - 3*A*b*e + a*B*e)/(b*(b*d - a*e)^2*Sqrt[d + e*x]) - (A*b - a*B)/(b*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x]) - ((2*b*B*d - 3*A*b*e + a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*(b*d - a*e)^(5/2))","A",5,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1814,1,181,0,0.1707886,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{A b-a B}{b (a+b x) (d+e x)^{3/2} (b d-a e)}+\frac{3 a B e-5 A b e+2 b B d}{\sqrt{d+e x} (b d-a e)^3}+\frac{3 a B e-5 A b e+2 b B d}{3 b (d+e x)^{3/2} (b d-a e)^2}-\frac{\sqrt{b} (3 a B e-5 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}","-\frac{A b-a B}{b (a+b x) (d+e x)^{3/2} (b d-a e)}+\frac{3 a B e-5 A b e+2 b B d}{\sqrt{d+e x} (b d-a e)^3}+\frac{3 a B e-5 A b e+2 b B d}{3 b (d+e x)^{3/2} (b d-a e)^2}-\frac{\sqrt{b} (3 a B e-5 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}",1,"(2*b*B*d - 5*A*b*e + 3*a*B*e)/(3*b*(b*d - a*e)^2*(d + e*x)^(3/2)) - (A*b - a*B)/(b*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2)) + (2*b*B*d - 5*A*b*e + 3*a*B*e)/((b*d - a*e)^3*Sqrt[d + e*x]) - (Sqrt[b]*(2*b*B*d - 5*A*b*e + 3*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(7/2)","A",6,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1815,1,221,0,0.2289026,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{b^{3/2} (5 a B e-7 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{9/2}}+\frac{b (5 a B e-7 A b e+2 b B d)}{\sqrt{d+e x} (b d-a e)^4}+\frac{5 a B e-7 A b e+2 b B d}{3 (d+e x)^{3/2} (b d-a e)^3}+\frac{5 a B e-7 A b e+2 b B d}{5 b (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{b (a+b x) (d+e x)^{5/2} (b d-a e)}","-\frac{b^{3/2} (5 a B e-7 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{9/2}}+\frac{b (5 a B e-7 A b e+2 b B d)}{\sqrt{d+e x} (b d-a e)^4}+\frac{5 a B e-7 A b e+2 b B d}{3 (d+e x)^{3/2} (b d-a e)^3}+\frac{5 a B e-7 A b e+2 b B d}{5 b (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{b (a+b x) (d+e x)^{5/2} (b d-a e)}",1,"(2*b*B*d - 7*A*b*e + 5*a*B*e)/(5*b*(b*d - a*e)^2*(d + e*x)^(5/2)) - (A*b - a*B)/(b*(b*d - a*e)*(a + b*x)*(d + e*x)^(5/2)) + (2*b*B*d - 7*A*b*e + 5*a*B*e)/(3*(b*d - a*e)^3*(d + e*x)^(3/2)) + (b*(2*b*B*d - 7*A*b*e + 5*a*B*e))/((b*d - a*e)^4*Sqrt[d + e*x]) - (b^(3/2)*(2*b*B*d - 7*A*b*e + 5*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(9/2)","A",7,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1816,1,332,0,0.3332524,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{21 e^2 (d+e x)^{5/2} (-11 a B e+5 A b e+6 b B d)}{40 b^4 (b d-a e)}+\frac{7 e^2 (d+e x)^{3/2} (-11 a B e+5 A b e+6 b B d)}{8 b^5}+\frac{21 e^2 \sqrt{d+e x} (b d-a e) (-11 a B e+5 A b e+6 b B d)}{8 b^6}-\frac{21 e^2 (b d-a e)^{3/2} (-11 a B e+5 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{13/2}}-\frac{(d+e x)^{9/2} (-11 a B e+5 A b e+6 b B d)}{12 b^2 (a+b x)^2 (b d-a e)}-\frac{3 e (d+e x)^{7/2} (-11 a B e+5 A b e+6 b B d)}{8 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{11/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}","\frac{21 e^2 (d+e x)^{5/2} (-11 a B e+5 A b e+6 b B d)}{40 b^4 (b d-a e)}+\frac{7 e^2 (d+e x)^{3/2} (-11 a B e+5 A b e+6 b B d)}{8 b^5}+\frac{21 e^2 \sqrt{d+e x} (b d-a e) (-11 a B e+5 A b e+6 b B d)}{8 b^6}-\frac{21 e^2 (b d-a e)^{3/2} (-11 a B e+5 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{13/2}}-\frac{(d+e x)^{9/2} (-11 a B e+5 A b e+6 b B d)}{12 b^2 (a+b x)^2 (b d-a e)}-\frac{3 e (d+e x)^{7/2} (-11 a B e+5 A b e+6 b B d)}{8 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{11/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"(21*e^2*(b*d - a*e)*(6*b*B*d + 5*A*b*e - 11*a*B*e)*Sqrt[d + e*x])/(8*b^6) + (7*e^2*(6*b*B*d + 5*A*b*e - 11*a*B*e)*(d + e*x)^(3/2))/(8*b^5) + (21*e^2*(6*b*B*d + 5*A*b*e - 11*a*B*e)*(d + e*x)^(5/2))/(40*b^4*(b*d - a*e)) - (3*e*(6*b*B*d + 5*A*b*e - 11*a*B*e)*(d + e*x)^(7/2))/(8*b^3*(b*d - a*e)*(a + b*x)) - ((6*b*B*d + 5*A*b*e - 11*a*B*e)*(d + e*x)^(9/2))/(12*b^2*(b*d - a*e)*(a + b*x)^2) - ((A*b - a*B)*(d + e*x)^(11/2))/(3*b*(b*d - a*e)*(a + b*x)^3) - (21*e^2*(b*d - a*e)^(3/2)*(6*b*B*d + 5*A*b*e - 11*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(13/2))","A",9,6,33,0.1818,1,"{27, 78, 47, 50, 63, 208}"
1817,1,284,0,0.2416137,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{35 e^2 (d+e x)^{3/2} (-3 a B e+A b e+2 b B d)}{24 b^4 (b d-a e)}+\frac{35 e^2 \sqrt{d+e x} (-3 a B e+A b e+2 b B d)}{8 b^5}-\frac{35 e^2 \sqrt{b d-a e} (-3 a B e+A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{11/2}}-\frac{(d+e x)^{7/2} (-3 a B e+A b e+2 b B d)}{4 b^2 (a+b x)^2 (b d-a e)}-\frac{7 e (d+e x)^{5/2} (-3 a B e+A b e+2 b B d)}{8 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{9/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}","\frac{35 e^2 (d+e x)^{3/2} (-3 a B e+A b e+2 b B d)}{24 b^4 (b d-a e)}+\frac{35 e^2 \sqrt{d+e x} (-3 a B e+A b e+2 b B d)}{8 b^5}-\frac{35 e^2 \sqrt{b d-a e} (-3 a B e+A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{11/2}}-\frac{(d+e x)^{7/2} (-3 a B e+A b e+2 b B d)}{4 b^2 (a+b x)^2 (b d-a e)}-\frac{7 e (d+e x)^{5/2} (-3 a B e+A b e+2 b B d)}{8 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{9/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"(35*e^2*(2*b*B*d + A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(8*b^5) + (35*e^2*(2*b*B*d + A*b*e - 3*a*B*e)*(d + e*x)^(3/2))/(24*b^4*(b*d - a*e)) - (7*e*(2*b*B*d + A*b*e - 3*a*B*e)*(d + e*x)^(5/2))/(8*b^3*(b*d - a*e)*(a + b*x)) - ((2*b*B*d + A*b*e - 3*a*B*e)*(d + e*x)^(7/2))/(4*b^2*(b*d - a*e)*(a + b*x)^2) - ((A*b - a*B)*(d + e*x)^(9/2))/(3*b*(b*d - a*e)*(a + b*x)^3) - (35*e^2*Sqrt[b*d - a*e]*(2*b*B*d + A*b*e - 3*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(11/2))","A",8,6,33,0.1818,1,"{27, 78, 47, 50, 63, 208}"
1818,1,250,0,0.2010671,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{5 e^2 \sqrt{d+e x} (-7 a B e+A b e+6 b B d)}{8 b^4 (b d-a e)}-\frac{5 e^2 (-7 a B e+A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{9/2} \sqrt{b d-a e}}-\frac{(d+e x)^{5/2} (-7 a B e+A b e+6 b B d)}{12 b^2 (a+b x)^2 (b d-a e)}-\frac{5 e (d+e x)^{3/2} (-7 a B e+A b e+6 b B d)}{24 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{7/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}","\frac{5 e^2 \sqrt{d+e x} (-7 a B e+A b e+6 b B d)}{8 b^4 (b d-a e)}-\frac{5 e^2 (-7 a B e+A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{9/2} \sqrt{b d-a e}}-\frac{(d+e x)^{5/2} (-7 a B e+A b e+6 b B d)}{12 b^2 (a+b x)^2 (b d-a e)}-\frac{5 e (d+e x)^{3/2} (-7 a B e+A b e+6 b B d)}{24 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{7/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"(5*e^2*(6*b*B*d + A*b*e - 7*a*B*e)*Sqrt[d + e*x])/(8*b^4*(b*d - a*e)) - (5*e*(6*b*B*d + A*b*e - 7*a*B*e)*(d + e*x)^(3/2))/(24*b^3*(b*d - a*e)*(a + b*x)) - ((6*b*B*d + A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(12*b^2*(b*d - a*e)*(a + b*x)^2) - ((A*b - a*B)*(d + e*x)^(7/2))/(3*b*(b*d - a*e)*(a + b*x)^3) - (5*e^2*(6*b*B*d + A*b*e - 7*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(9/2)*Sqrt[b*d - a*e])","A",7,6,33,0.1818,1,"{27, 78, 47, 50, 63, 208}"
1819,1,209,0,0.1806614,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{e^2 (-5 a B e-A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{7/2} (b d-a e)^{3/2}}-\frac{(d+e x)^{3/2} (-5 a B e-A b e+6 b B d)}{12 b^2 (a+b x)^2 (b d-a e)}-\frac{e \sqrt{d+e x} (-5 a B e-A b e+6 b B d)}{8 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}","-\frac{e^2 (-5 a B e-A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{7/2} (b d-a e)^{3/2}}-\frac{(d+e x)^{3/2} (-5 a B e-A b e+6 b B d)}{12 b^2 (a+b x)^2 (b d-a e)}-\frac{e \sqrt{d+e x} (-5 a B e-A b e+6 b B d)}{8 b^3 (a+b x) (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"-(e*(6*b*B*d - A*b*e - 5*a*B*e)*Sqrt[d + e*x])/(8*b^3*(b*d - a*e)*(a + b*x)) - ((6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(12*b^2*(b*d - a*e)*(a + b*x)^2) - ((A*b - a*B)*(d + e*x)^(5/2))/(3*b*(b*d - a*e)*(a + b*x)^3) - (e^2*(6*b*B*d - A*b*e - 5*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(7/2)*(b*d - a*e)^(3/2))","A",6,5,33,0.1515,1,"{27, 78, 47, 63, 208}"
1820,1,209,0,0.1774267,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^2 (-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{5/2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x} (-a B e-A b e+2 b B d)}{8 b^2 (a+b x) (b d-a e)^2}-\frac{\sqrt{d+e x} (-a B e-A b e+2 b B d)}{4 b^2 (a+b x)^2 (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}","\frac{e^2 (-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{5/2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x} (-a B e-A b e+2 b B d)}{8 b^2 (a+b x) (b d-a e)^2}-\frac{\sqrt{d+e x} (-a B e-A b e+2 b B d)}{4 b^2 (a+b x)^2 (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"-((2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x])/(4*b^2*(b*d - a*e)*(a + b*x)^2) - (e*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x])/(8*b^2*(b*d - a*e)^2*(a + b*x)) - ((A*b - a*B)*(d + e*x)^(3/2))/(3*b*(b*d - a*e)*(a + b*x)^3) + (e^2*(2*b*B*d - A*b*e - a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(5/2)*(b*d - a*e)^(5/2))","A",6,6,33,0.1818,1,"{27, 78, 47, 51, 63, 208}"
1821,1,209,0,0.2014984,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{e^2 (-a B e-5 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{3/2} (b d-a e)^{7/2}}+\frac{e \sqrt{d+e x} (-a B e-5 A b e+6 b B d)}{8 b (a+b x) (b d-a e)^3}-\frac{\sqrt{d+e x} (-a B e-5 A b e+6 b B d)}{12 b (a+b x)^2 (b d-a e)^2}-\frac{\sqrt{d+e x} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}","-\frac{e^2 (-a B e-5 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{3/2} (b d-a e)^{7/2}}+\frac{e \sqrt{d+e x} (-a B e-5 A b e+6 b B d)}{8 b (a+b x) (b d-a e)^3}-\frac{\sqrt{d+e x} (-a B e-5 A b e+6 b B d)}{12 b (a+b x)^2 (b d-a e)^2}-\frac{\sqrt{d+e x} (A b-a B)}{3 b (a+b x)^3 (b d-a e)}",1,"-((A*b - a*B)*Sqrt[d + e*x])/(3*b*(b*d - a*e)*(a + b*x)^3) - ((6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[d + e*x])/(12*b*(b*d - a*e)^2*(a + b*x)^2) + (e*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[d + e*x])/(8*b*(b*d - a*e)^3*(a + b*x)) - (e^2*(6*b*B*d - 5*A*b*e - a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(3/2)*(b*d - a*e)^(7/2))","A",6,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1822,1,250,0,0.2416455,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{5 e^2 (a B e-7 A b e+6 b B d)}{8 b \sqrt{d+e x} (b d-a e)^4}-\frac{5 e^2 (a B e-7 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{b} (b d-a e)^{9/2}}+\frac{5 e (a B e-7 A b e+6 b B d)}{24 b (a+b x) \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-7 A b e+6 b B d}{12 b (a+b x)^2 \sqrt{d+e x} (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 \sqrt{d+e x} (b d-a e)}","\frac{5 e^2 (a B e-7 A b e+6 b B d)}{8 b \sqrt{d+e x} (b d-a e)^4}-\frac{5 e^2 (a B e-7 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{b} (b d-a e)^{9/2}}+\frac{5 e (a B e-7 A b e+6 b B d)}{24 b (a+b x) \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-7 A b e+6 b B d}{12 b (a+b x)^2 \sqrt{d+e x} (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 \sqrt{d+e x} (b d-a e)}",1,"(5*e^2*(6*b*B*d - 7*A*b*e + a*B*e))/(8*b*(b*d - a*e)^4*Sqrt[d + e*x]) - (A*b - a*B)/(3*b*(b*d - a*e)*(a + b*x)^3*Sqrt[d + e*x]) - (6*b*B*d - 7*A*b*e + a*B*e)/(12*b*(b*d - a*e)^2*(a + b*x)^2*Sqrt[d + e*x]) + (5*e*(6*b*B*d - 7*A*b*e + a*B*e))/(24*b*(b*d - a*e)^3*(a + b*x)*Sqrt[d + e*x]) - (5*e^2*(6*b*B*d - 7*A*b*e + a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*Sqrt[b]*(b*d - a*e)^(9/2))","A",7,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1823,1,291,0,0.3033904,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{35 e^2 (a B e-3 A b e+2 b B d)}{8 \sqrt{d+e x} (b d-a e)^5}+\frac{35 e^2 (a B e-3 A b e+2 b B d)}{24 b (d+e x)^{3/2} (b d-a e)^4}-\frac{35 \sqrt{b} e^2 (a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{11/2}}+\frac{7 e (a B e-3 A b e+2 b B d)}{8 b (a+b x) (d+e x)^{3/2} (b d-a e)^3}-\frac{a B e-3 A b e+2 b B d}{4 b (a+b x)^2 (d+e x)^{3/2} (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 (d+e x)^{3/2} (b d-a e)}","\frac{35 e^2 (a B e-3 A b e+2 b B d)}{8 \sqrt{d+e x} (b d-a e)^5}+\frac{35 e^2 (a B e-3 A b e+2 b B d)}{24 b (d+e x)^{3/2} (b d-a e)^4}-\frac{35 \sqrt{b} e^2 (a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{11/2}}+\frac{7 e (a B e-3 A b e+2 b B d)}{8 b (a+b x) (d+e x)^{3/2} (b d-a e)^3}-\frac{a B e-3 A b e+2 b B d}{4 b (a+b x)^2 (d+e x)^{3/2} (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 (d+e x)^{3/2} (b d-a e)}",1,"(35*e^2*(2*b*B*d - 3*A*b*e + a*B*e))/(24*b*(b*d - a*e)^4*(d + e*x)^(3/2)) - (A*b - a*B)/(3*b*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(3/2)) - (2*b*B*d - 3*A*b*e + a*B*e)/(4*b*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(3/2)) + (7*e*(2*b*B*d - 3*A*b*e + a*B*e))/(8*b*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)) + (35*e^2*(2*b*B*d - 3*A*b*e + a*B*e))/(8*(b*d - a*e)^5*Sqrt[d + e*x]) - (35*Sqrt[b]*e^2*(2*b*B*d - 3*A*b*e + a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(11/2))","A",8,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1824,1,339,0,0.3811444,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{21 b^{3/2} e^2 (5 a B e-11 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{13/2}}+\frac{21 b e^2 (5 a B e-11 A b e+6 b B d)}{8 \sqrt{d+e x} (b d-a e)^6}+\frac{7 e^2 (5 a B e-11 A b e+6 b B d)}{8 (d+e x)^{3/2} (b d-a e)^5}+\frac{21 e^2 (5 a B e-11 A b e+6 b B d)}{40 b (d+e x)^{5/2} (b d-a e)^4}+\frac{3 e (5 a B e-11 A b e+6 b B d)}{8 b (a+b x) (d+e x)^{5/2} (b d-a e)^3}-\frac{5 a B e-11 A b e+6 b B d}{12 b (a+b x)^2 (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 (d+e x)^{5/2} (b d-a e)}","-\frac{21 b^{3/2} e^2 (5 a B e-11 A b e+6 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 (b d-a e)^{13/2}}+\frac{21 b e^2 (5 a B e-11 A b e+6 b B d)}{8 \sqrt{d+e x} (b d-a e)^6}+\frac{7 e^2 (5 a B e-11 A b e+6 b B d)}{8 (d+e x)^{3/2} (b d-a e)^5}+\frac{21 e^2 (5 a B e-11 A b e+6 b B d)}{40 b (d+e x)^{5/2} (b d-a e)^4}+\frac{3 e (5 a B e-11 A b e+6 b B d)}{8 b (a+b x) (d+e x)^{5/2} (b d-a e)^3}-\frac{5 a B e-11 A b e+6 b B d}{12 b (a+b x)^2 (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{3 b (a+b x)^3 (d+e x)^{5/2} (b d-a e)}",1,"(21*e^2*(6*b*B*d - 11*A*b*e + 5*a*B*e))/(40*b*(b*d - a*e)^4*(d + e*x)^(5/2)) - (A*b - a*B)/(3*b*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(5/2)) - (6*b*B*d - 11*A*b*e + 5*a*B*e)/(12*b*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(5/2)) + (3*e*(6*b*B*d - 11*A*b*e + 5*a*B*e))/(8*b*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(5/2)) + (7*e^2*(6*b*B*d - 11*A*b*e + 5*a*B*e))/(8*(b*d - a*e)^5*(d + e*x)^(3/2)) + (21*b*e^2*(6*b*B*d - 11*A*b*e + 5*a*B*e))/(8*(b*d - a*e)^6*Sqrt[d + e*x]) - (21*b^(3/2)*e^2*(6*b*B*d - 11*A*b*e + 5*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(13/2))","A",9,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1825,1,393,0,0.3643929,"\int \frac{(A+B x) (d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(11/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{33 e^2 (d+e x)^{7/2} (-13 a B e+3 A b e+10 b B d)}{320 b^4 (a+b x)^2 (b d-a e)}-\frac{231 e^3 (d+e x)^{5/2} (-13 a B e+3 A b e+10 b B d)}{640 b^5 (a+b x) (b d-a e)}+\frac{77 e^4 (d+e x)^{3/2} (-13 a B e+3 A b e+10 b B d)}{128 b^6 (b d-a e)}+\frac{231 e^4 \sqrt{d+e x} (-13 a B e+3 A b e+10 b B d)}{128 b^7}-\frac{231 e^4 \sqrt{b d-a e} (-13 a B e+3 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{15/2}}-\frac{(d+e x)^{11/2} (-13 a B e+3 A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{11 e (d+e x)^{9/2} (-13 a B e+3 A b e+10 b B d)}{240 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{13/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","-\frac{33 e^2 (d+e x)^{7/2} (-13 a B e+3 A b e+10 b B d)}{320 b^4 (a+b x)^2 (b d-a e)}-\frac{231 e^3 (d+e x)^{5/2} (-13 a B e+3 A b e+10 b B d)}{640 b^5 (a+b x) (b d-a e)}+\frac{77 e^4 (d+e x)^{3/2} (-13 a B e+3 A b e+10 b B d)}{128 b^6 (b d-a e)}+\frac{231 e^4 \sqrt{d+e x} (-13 a B e+3 A b e+10 b B d)}{128 b^7}-\frac{231 e^4 \sqrt{b d-a e} (-13 a B e+3 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{15/2}}-\frac{(d+e x)^{11/2} (-13 a B e+3 A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{11 e (d+e x)^{9/2} (-13 a B e+3 A b e+10 b B d)}{240 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{13/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"(231*e^4*(10*b*B*d + 3*A*b*e - 13*a*B*e)*Sqrt[d + e*x])/(128*b^7) + (77*e^4*(10*b*B*d + 3*A*b*e - 13*a*B*e)*(d + e*x)^(3/2))/(128*b^6*(b*d - a*e)) - (231*e^3*(10*b*B*d + 3*A*b*e - 13*a*B*e)*(d + e*x)^(5/2))/(640*b^5*(b*d - a*e)*(a + b*x)) - (33*e^2*(10*b*B*d + 3*A*b*e - 13*a*B*e)*(d + e*x)^(7/2))/(320*b^4*(b*d - a*e)*(a + b*x)^2) - (11*e*(10*b*B*d + 3*A*b*e - 13*a*B*e)*(d + e*x)^(9/2))/(240*b^3*(b*d - a*e)*(a + b*x)^3) - ((10*b*B*d + 3*A*b*e - 13*a*B*e)*(d + e*x)^(11/2))/(40*b^2*(b*d - a*e)*(a + b*x)^4) - ((A*b - a*B)*(d + e*x)^(13/2))/(5*b*(b*d - a*e)*(a + b*x)^5) - (231*e^4*Sqrt[b*d - a*e]*(10*b*B*d + 3*A*b*e - 13*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(15/2))","A",10,6,33,0.1818,1,"{27, 78, 47, 50, 63, 208}"
1826,1,352,0,0.2957021,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{21 e^2 (d+e x)^{5/2} (-11 a B e+A b e+10 b B d)}{320 b^4 (a+b x)^2 (b d-a e)}-\frac{21 e^3 (d+e x)^{3/2} (-11 a B e+A b e+10 b B d)}{128 b^5 (a+b x) (b d-a e)}+\frac{63 e^4 \sqrt{d+e x} (-11 a B e+A b e+10 b B d)}{128 b^6 (b d-a e)}-\frac{63 e^4 (-11 a B e+A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{13/2} \sqrt{b d-a e}}-\frac{(d+e x)^{9/2} (-11 a B e+A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{3 e (d+e x)^{7/2} (-11 a B e+A b e+10 b B d)}{80 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{11/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","-\frac{21 e^2 (d+e x)^{5/2} (-11 a B e+A b e+10 b B d)}{320 b^4 (a+b x)^2 (b d-a e)}-\frac{21 e^3 (d+e x)^{3/2} (-11 a B e+A b e+10 b B d)}{128 b^5 (a+b x) (b d-a e)}+\frac{63 e^4 \sqrt{d+e x} (-11 a B e+A b e+10 b B d)}{128 b^6 (b d-a e)}-\frac{63 e^4 (-11 a B e+A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{13/2} \sqrt{b d-a e}}-\frac{(d+e x)^{9/2} (-11 a B e+A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{3 e (d+e x)^{7/2} (-11 a B e+A b e+10 b B d)}{80 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{11/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"(63*e^4*(10*b*B*d + A*b*e - 11*a*B*e)*Sqrt[d + e*x])/(128*b^6*(b*d - a*e)) - (21*e^3*(10*b*B*d + A*b*e - 11*a*B*e)*(d + e*x)^(3/2))/(128*b^5*(b*d - a*e)*(a + b*x)) - (21*e^2*(10*b*B*d + A*b*e - 11*a*B*e)*(d + e*x)^(5/2))/(320*b^4*(b*d - a*e)*(a + b*x)^2) - (3*e*(10*b*B*d + A*b*e - 11*a*B*e)*(d + e*x)^(7/2))/(80*b^3*(b*d - a*e)*(a + b*x)^3) - ((10*b*B*d + A*b*e - 11*a*B*e)*(d + e*x)^(9/2))/(40*b^2*(b*d - a*e)*(a + b*x)^4) - ((A*b - a*B)*(d + e*x)^(11/2))/(5*b*(b*d - a*e)*(a + b*x)^5) - (63*e^4*(10*b*B*d + A*b*e - 11*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(13/2)*Sqrt[b*d - a*e])","A",9,6,33,0.1818,1,"{27, 78, 47, 50, 63, 208}"
1827,1,313,0,0.2590758,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{7 e^2 (d+e x)^{3/2} (-9 a B e-A b e+10 b B d)}{192 b^4 (a+b x)^2 (b d-a e)}-\frac{7 e^3 \sqrt{d+e x} (-9 a B e-A b e+10 b B d)}{128 b^5 (a+b x) (b d-a e)}-\frac{7 e^4 (-9 a B e-A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{11/2} (b d-a e)^{3/2}}-\frac{(d+e x)^{7/2} (-9 a B e-A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{7 e (d+e x)^{5/2} (-9 a B e-A b e+10 b B d)}{240 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{9/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","-\frac{7 e^2 (d+e x)^{3/2} (-9 a B e-A b e+10 b B d)}{192 b^4 (a+b x)^2 (b d-a e)}-\frac{7 e^3 \sqrt{d+e x} (-9 a B e-A b e+10 b B d)}{128 b^5 (a+b x) (b d-a e)}-\frac{7 e^4 (-9 a B e-A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{11/2} (b d-a e)^{3/2}}-\frac{(d+e x)^{7/2} (-9 a B e-A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{7 e (d+e x)^{5/2} (-9 a B e-A b e+10 b B d)}{240 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{9/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"(-7*e^3*(10*b*B*d - A*b*e - 9*a*B*e)*Sqrt[d + e*x])/(128*b^5*(b*d - a*e)*(a + b*x)) - (7*e^2*(10*b*B*d - A*b*e - 9*a*B*e)*(d + e*x)^(3/2))/(192*b^4*(b*d - a*e)*(a + b*x)^2) - (7*e*(10*b*B*d - A*b*e - 9*a*B*e)*(d + e*x)^(5/2))/(240*b^3*(b*d - a*e)*(a + b*x)^3) - ((10*b*B*d - A*b*e - 9*a*B*e)*(d + e*x)^(7/2))/(40*b^2*(b*d - a*e)*(a + b*x)^4) - ((A*b - a*B)*(d + e*x)^(9/2))/(5*b*(b*d - a*e)*(a + b*x)^5) - (7*e^4*(10*b*B*d - A*b*e - 9*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(11/2)*(b*d - a*e)^(3/2))","A",8,5,33,0.1515,1,"{27, 78, 47, 63, 208}"
1828,1,313,0,0.2734277,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{e^3 \sqrt{d+e x} (-7 a B e-3 A b e+10 b B d)}{128 b^4 (a+b x) (b d-a e)^2}-\frac{e^2 \sqrt{d+e x} (-7 a B e-3 A b e+10 b B d)}{64 b^4 (a+b x)^2 (b d-a e)}+\frac{e^4 (-7 a B e-3 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{9/2} (b d-a e)^{5/2}}-\frac{e (d+e x)^{3/2} (-7 a B e-3 A b e+10 b B d)}{48 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e-3 A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{(d+e x)^{7/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","-\frac{e^3 \sqrt{d+e x} (-7 a B e-3 A b e+10 b B d)}{128 b^4 (a+b x) (b d-a e)^2}-\frac{e^2 \sqrt{d+e x} (-7 a B e-3 A b e+10 b B d)}{64 b^4 (a+b x)^2 (b d-a e)}+\frac{e^4 (-7 a B e-3 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{9/2} (b d-a e)^{5/2}}-\frac{e (d+e x)^{3/2} (-7 a B e-3 A b e+10 b B d)}{48 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e-3 A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{(d+e x)^{7/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"-(e^2*(10*b*B*d - 3*A*b*e - 7*a*B*e)*Sqrt[d + e*x])/(64*b^4*(b*d - a*e)*(a + b*x)^2) - (e^3*(10*b*B*d - 3*A*b*e - 7*a*B*e)*Sqrt[d + e*x])/(128*b^4*(b*d - a*e)^2*(a + b*x)) - (e*(10*b*B*d - 3*A*b*e - 7*a*B*e)*(d + e*x)^(3/2))/(48*b^3*(b*d - a*e)*(a + b*x)^3) - ((10*b*B*d - 3*A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(40*b^2*(b*d - a*e)*(a + b*x)^4) - ((A*b - a*B)*(d + e*x)^(7/2))/(5*b*(b*d - a*e)*(a + b*x)^5) + (e^4*(10*b*B*d - 3*A*b*e - 7*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(9/2)*(b*d - a*e)^(5/2))","A",8,6,33,0.1818,1,"{27, 78, 47, 51, 63, 208}"
1829,1,313,0,0.2685439,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{3 e^3 \sqrt{d+e x} (-a B e-A b e+2 b B d)}{128 b^3 (a+b x) (b d-a e)^3}-\frac{e^2 \sqrt{d+e x} (-a B e-A b e+2 b B d)}{64 b^3 (a+b x)^2 (b d-a e)^2}-\frac{3 e^4 (-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{7/2} (b d-a e)^{7/2}}-\frac{e \sqrt{d+e x} (-a B e-A b e+2 b B d)}{16 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{3/2} (-a B e-A b e+2 b B d)}{8 b^2 (a+b x)^4 (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","\frac{3 e^3 \sqrt{d+e x} (-a B e-A b e+2 b B d)}{128 b^3 (a+b x) (b d-a e)^3}-\frac{e^2 \sqrt{d+e x} (-a B e-A b e+2 b B d)}{64 b^3 (a+b x)^2 (b d-a e)^2}-\frac{3 e^4 (-a B e-A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{7/2} (b d-a e)^{7/2}}-\frac{e \sqrt{d+e x} (-a B e-A b e+2 b B d)}{16 b^3 (a+b x)^3 (b d-a e)}-\frac{(d+e x)^{3/2} (-a B e-A b e+2 b B d)}{8 b^2 (a+b x)^4 (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"-(e*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x])/(16*b^3*(b*d - a*e)*(a + b*x)^3) - (e^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x])/(64*b^3*(b*d - a*e)^2*(a + b*x)^2) + (3*e^3*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x])/(128*b^3*(b*d - a*e)^3*(a + b*x)) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3/2))/(8*b^2*(b*d - a*e)*(a + b*x)^4) - ((A*b - a*B)*(d + e*x)^(5/2))/(5*b*(b*d - a*e)*(a + b*x)^5) - (3*e^4*(2*b*B*d - A*b*e - a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(7/2)*(b*d - a*e)^(7/2))","A",8,6,33,0.1818,1,"{27, 78, 47, 51, 63, 208}"
1830,1,313,0,0.288091,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{e^3 \sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{128 b^2 (a+b x) (b d-a e)^4}+\frac{e^2 \sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{192 b^2 (a+b x)^2 (b d-a e)^3}+\frac{e^4 (-3 a B e-7 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{5/2} (b d-a e)^{9/2}}-\frac{e \sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{240 b^2 (a+b x)^3 (b d-a e)^2}-\frac{\sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","-\frac{e^3 \sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{128 b^2 (a+b x) (b d-a e)^4}+\frac{e^2 \sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{192 b^2 (a+b x)^2 (b d-a e)^3}+\frac{e^4 (-3 a B e-7 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{5/2} (b d-a e)^{9/2}}-\frac{e \sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{240 b^2 (a+b x)^3 (b d-a e)^2}-\frac{\sqrt{d+e x} (-3 a B e-7 A b e+10 b B d)}{40 b^2 (a+b x)^4 (b d-a e)}-\frac{(d+e x)^{3/2} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"-((10*b*B*d - 7*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(40*b^2*(b*d - a*e)*(a + b*x)^4) - (e*(10*b*B*d - 7*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(240*b^2*(b*d - a*e)^2*(a + b*x)^3) + (e^2*(10*b*B*d - 7*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(192*b^2*(b*d - a*e)^3*(a + b*x)^2) - (e^3*(10*b*B*d - 7*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(128*b^2*(b*d - a*e)^4*(a + b*x)) - ((A*b - a*B)*(d + e*x)^(3/2))/(5*b*(b*d - a*e)*(a + b*x)^5) + (e^4*(10*b*B*d - 7*A*b*e - 3*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(5/2)*(b*d - a*e)^(9/2))","A",8,6,33,0.1818,1,"{27, 78, 47, 51, 63, 208}"
1831,1,313,0,0.3145477,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{7 e^4 (-a B e-9 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{3/2} (b d-a e)^{11/2}}+\frac{7 e^3 \sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{128 b (a+b x) (b d-a e)^5}-\frac{7 e^2 \sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{192 b (a+b x)^2 (b d-a e)^4}+\frac{7 e \sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{240 b (a+b x)^3 (b d-a e)^3}-\frac{\sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{40 b (a+b x)^4 (b d-a e)^2}-\frac{\sqrt{d+e x} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}","-\frac{7 e^4 (-a B e-9 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 b^{3/2} (b d-a e)^{11/2}}+\frac{7 e^3 \sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{128 b (a+b x) (b d-a e)^5}-\frac{7 e^2 \sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{192 b (a+b x)^2 (b d-a e)^4}+\frac{7 e \sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{240 b (a+b x)^3 (b d-a e)^3}-\frac{\sqrt{d+e x} (-a B e-9 A b e+10 b B d)}{40 b (a+b x)^4 (b d-a e)^2}-\frac{\sqrt{d+e x} (A b-a B)}{5 b (a+b x)^5 (b d-a e)}",1,"-((A*b - a*B)*Sqrt[d + e*x])/(5*b*(b*d - a*e)*(a + b*x)^5) - ((10*b*B*d - 9*A*b*e - a*B*e)*Sqrt[d + e*x])/(40*b*(b*d - a*e)^2*(a + b*x)^4) + (7*e*(10*b*B*d - 9*A*b*e - a*B*e)*Sqrt[d + e*x])/(240*b*(b*d - a*e)^3*(a + b*x)^3) - (7*e^2*(10*b*B*d - 9*A*b*e - a*B*e)*Sqrt[d + e*x])/(192*b*(b*d - a*e)^4*(a + b*x)^2) + (7*e^3*(10*b*B*d - 9*A*b*e - a*B*e)*Sqrt[d + e*x])/(128*b*(b*d - a*e)^5*(a + b*x)) - (7*e^4*(10*b*B*d - 9*A*b*e - a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*b^(3/2)*(b*d - a*e)^(11/2))","A",8,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1832,1,352,0,0.3816289,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{63 e^4 (a B e-11 A b e+10 b B d)}{128 b \sqrt{d+e x} (b d-a e)^6}+\frac{21 e^3 (a B e-11 A b e+10 b B d)}{128 b (a+b x) \sqrt{d+e x} (b d-a e)^5}-\frac{21 e^2 (a B e-11 A b e+10 b B d)}{320 b (a+b x)^2 \sqrt{d+e x} (b d-a e)^4}-\frac{63 e^4 (a B e-11 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 \sqrt{b} (b d-a e)^{13/2}}+\frac{3 e (a B e-11 A b e+10 b B d)}{80 b (a+b x)^3 \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-11 A b e+10 b B d}{40 b (a+b x)^4 \sqrt{d+e x} (b d-a e)^2}-\frac{A b-a B}{5 b (a+b x)^5 \sqrt{d+e x} (b d-a e)}","\frac{63 e^4 (a B e-11 A b e+10 b B d)}{128 b \sqrt{d+e x} (b d-a e)^6}+\frac{21 e^3 (a B e-11 A b e+10 b B d)}{128 b (a+b x) \sqrt{d+e x} (b d-a e)^5}-\frac{21 e^2 (a B e-11 A b e+10 b B d)}{320 b (a+b x)^2 \sqrt{d+e x} (b d-a e)^4}-\frac{63 e^4 (a B e-11 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 \sqrt{b} (b d-a e)^{13/2}}+\frac{3 e (a B e-11 A b e+10 b B d)}{80 b (a+b x)^3 \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-11 A b e+10 b B d}{40 b (a+b x)^4 \sqrt{d+e x} (b d-a e)^2}-\frac{A b-a B}{5 b (a+b x)^5 \sqrt{d+e x} (b d-a e)}",1,"(63*e^4*(10*b*B*d - 11*A*b*e + a*B*e))/(128*b*(b*d - a*e)^6*Sqrt[d + e*x]) - (A*b - a*B)/(5*b*(b*d - a*e)*(a + b*x)^5*Sqrt[d + e*x]) - (10*b*B*d - 11*A*b*e + a*B*e)/(40*b*(b*d - a*e)^2*(a + b*x)^4*Sqrt[d + e*x]) + (3*e*(10*b*B*d - 11*A*b*e + a*B*e))/(80*b*(b*d - a*e)^3*(a + b*x)^3*Sqrt[d + e*x]) - (21*e^2*(10*b*B*d - 11*A*b*e + a*B*e))/(320*b*(b*d - a*e)^4*(a + b*x)^2*Sqrt[d + e*x]) + (21*e^3*(10*b*B*d - 11*A*b*e + a*B*e))/(128*b*(b*d - a*e)^5*(a + b*x)*Sqrt[d + e*x]) - (63*e^4*(10*b*B*d - 11*A*b*e + a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*Sqrt[b]*(b*d - a*e)^(13/2))","A",9,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1833,1,400,0,0.4478125,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{231 e^4 (3 a B e-13 A b e+10 b B d)}{128 \sqrt{d+e x} (b d-a e)^7}+\frac{77 e^4 (3 a B e-13 A b e+10 b B d)}{128 b (d+e x)^{3/2} (b d-a e)^6}+\frac{231 e^3 (3 a B e-13 A b e+10 b B d)}{640 b (a+b x) (d+e x)^{3/2} (b d-a e)^5}-\frac{33 e^2 (3 a B e-13 A b e+10 b B d)}{320 b (a+b x)^2 (d+e x)^{3/2} (b d-a e)^4}-\frac{231 \sqrt{b} e^4 (3 a B e-13 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{15/2}}+\frac{11 e (3 a B e-13 A b e+10 b B d)}{240 b (a+b x)^3 (d+e x)^{3/2} (b d-a e)^3}-\frac{3 a B e-13 A b e+10 b B d}{40 b (a+b x)^4 (d+e x)^{3/2} (b d-a e)^2}-\frac{A b-a B}{5 b (a+b x)^5 (d+e x)^{3/2} (b d-a e)}","\frac{231 e^4 (3 a B e-13 A b e+10 b B d)}{128 \sqrt{d+e x} (b d-a e)^7}+\frac{77 e^4 (3 a B e-13 A b e+10 b B d)}{128 b (d+e x)^{3/2} (b d-a e)^6}+\frac{231 e^3 (3 a B e-13 A b e+10 b B d)}{640 b (a+b x) (d+e x)^{3/2} (b d-a e)^5}-\frac{33 e^2 (3 a B e-13 A b e+10 b B d)}{320 b (a+b x)^2 (d+e x)^{3/2} (b d-a e)^4}-\frac{231 \sqrt{b} e^4 (3 a B e-13 A b e+10 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{15/2}}+\frac{11 e (3 a B e-13 A b e+10 b B d)}{240 b (a+b x)^3 (d+e x)^{3/2} (b d-a e)^3}-\frac{3 a B e-13 A b e+10 b B d}{40 b (a+b x)^4 (d+e x)^{3/2} (b d-a e)^2}-\frac{A b-a B}{5 b (a+b x)^5 (d+e x)^{3/2} (b d-a e)}",1,"(77*e^4*(10*b*B*d - 13*A*b*e + 3*a*B*e))/(128*b*(b*d - a*e)^6*(d + e*x)^(3/2)) - (A*b - a*B)/(5*b*(b*d - a*e)*(a + b*x)^5*(d + e*x)^(3/2)) - (10*b*B*d - 13*A*b*e + 3*a*B*e)/(40*b*(b*d - a*e)^2*(a + b*x)^4*(d + e*x)^(3/2)) + (11*e*(10*b*B*d - 13*A*b*e + 3*a*B*e))/(240*b*(b*d - a*e)^3*(a + b*x)^3*(d + e*x)^(3/2)) - (33*e^2*(10*b*B*d - 13*A*b*e + 3*a*B*e))/(320*b*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(3/2)) + (231*e^3*(10*b*B*d - 13*A*b*e + 3*a*B*e))/(640*b*(b*d - a*e)^5*(a + b*x)*(d + e*x)^(3/2)) + (231*e^4*(10*b*B*d - 13*A*b*e + 3*a*B*e))/(128*(b*d - a*e)^7*Sqrt[d + e*x]) - (231*Sqrt[b]*e^4*(10*b*B*d - 13*A*b*e + 3*a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*(b*d - a*e)^(15/2))","A",10,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1834,1,435,0,0.4895865,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{3003 b^{3/2} e^4 (a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{17/2}}+\frac{3003 b e^4 (a B e-3 A b e+2 b B d)}{128 \sqrt{d+e x} (b d-a e)^8}+\frac{1001 e^4 (a B e-3 A b e+2 b B d)}{128 (d+e x)^{3/2} (b d-a e)^7}+\frac{3003 e^4 (a B e-3 A b e+2 b B d)}{640 b (d+e x)^{5/2} (b d-a e)^6}+\frac{429 e^3 (a B e-3 A b e+2 b B d)}{128 b (a+b x) (d+e x)^{5/2} (b d-a e)^5}-\frac{143 e^2 (a B e-3 A b e+2 b B d)}{192 b (a+b x)^2 (d+e x)^{5/2} (b d-a e)^4}+\frac{13 e (a B e-3 A b e+2 b B d)}{48 b (a+b x)^3 (d+e x)^{5/2} (b d-a e)^3}-\frac{a B e-3 A b e+2 b B d}{8 b (a+b x)^4 (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{5 b (a+b x)^5 (d+e x)^{5/2} (b d-a e)}","-\frac{3003 b^{3/2} e^4 (a B e-3 A b e+2 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{128 (b d-a e)^{17/2}}+\frac{3003 b e^4 (a B e-3 A b e+2 b B d)}{128 \sqrt{d+e x} (b d-a e)^8}+\frac{1001 e^4 (a B e-3 A b e+2 b B d)}{128 (d+e x)^{3/2} (b d-a e)^7}+\frac{3003 e^4 (a B e-3 A b e+2 b B d)}{640 b (d+e x)^{5/2} (b d-a e)^6}+\frac{429 e^3 (a B e-3 A b e+2 b B d)}{128 b (a+b x) (d+e x)^{5/2} (b d-a e)^5}-\frac{143 e^2 (a B e-3 A b e+2 b B d)}{192 b (a+b x)^2 (d+e x)^{5/2} (b d-a e)^4}+\frac{13 e (a B e-3 A b e+2 b B d)}{48 b (a+b x)^3 (d+e x)^{5/2} (b d-a e)^3}-\frac{a B e-3 A b e+2 b B d}{8 b (a+b x)^4 (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{5 b (a+b x)^5 (d+e x)^{5/2} (b d-a e)}",1,"(3003*e^4*(2*b*B*d - 3*A*b*e + a*B*e))/(640*b*(b*d - a*e)^6*(d + e*x)^(5/2)) - (A*b - a*B)/(5*b*(b*d - a*e)*(a + b*x)^5*(d + e*x)^(5/2)) - (2*b*B*d - 3*A*b*e + a*B*e)/(8*b*(b*d - a*e)^2*(a + b*x)^4*(d + e*x)^(5/2)) + (13*e*(2*b*B*d - 3*A*b*e + a*B*e))/(48*b*(b*d - a*e)^3*(a + b*x)^3*(d + e*x)^(5/2)) - (143*e^2*(2*b*B*d - 3*A*b*e + a*B*e))/(192*b*(b*d - a*e)^4*(a + b*x)^2*(d + e*x)^(5/2)) + (429*e^3*(2*b*B*d - 3*A*b*e + a*B*e))/(128*b*(b*d - a*e)^5*(a + b*x)*(d + e*x)^(5/2)) + (1001*e^4*(2*b*B*d - 3*A*b*e + a*B*e))/(128*(b*d - a*e)^7*(d + e*x)^(3/2)) + (3003*b*e^4*(2*b*B*d - 3*A*b*e + a*B*e))/(128*(b*d - a*e)^8*Sqrt[d + e*x]) - (3003*b^(3/2)*e^4*(2*b*B*d - 3*A*b*e + a*B*e)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(128*(b*d - a*e)^(17/2))","A",11,5,33,0.1515,1,"{27, 78, 51, 63, 208}"
1835,1,164,0,0.0949783,"\int (A+B x) (d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (-a B e-A b e+2 b B d)}{11 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e) (B d-A e)}{9 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^3 (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (-a B e-A b e+2 b B d)}{11 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e) (B d-A e)}{9 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^3 (a+b x)}",1,"(2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^3*(a + b*x)) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^3*(a + b*x)) + (2*b*B*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1836,1,164,0,0.0821467,"\int (A+B x) (d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (-a B e-A b e+2 b B d)}{9 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e) (B d-A e)}{7 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^3 (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (-a B e-A b e+2 b B d)}{9 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e) (B d-A e)}{7 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^3 (a+b x)}",1,"(2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x)) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^3*(a + b*x)) + (2*b*B*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1837,1,164,0,0.0842699,"\int (A+B x) (d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (-a B e-A b e+2 b B d)}{7 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e) (B d-A e)}{5 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^3 (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (-a B e-A b e+2 b B d)}{7 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e) (B d-A e)}{5 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^3 (a+b x)}",1,"(2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x)) + (2*b*B*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1838,1,164,0,0.0844633,"\int (A+B x) \sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (-a B e-A b e+2 b B d)}{5 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e) (B d-A e)}{3 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^3 (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (-a B e-A b e+2 b B d)}{5 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e) (B d-A e)}{3 e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^3 (a+b x)}",1,"(2*(b*d - a*e)*(B*d - A*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) + (2*b*B*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1839,1,162,0,0.0881532,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/Sqrt[d + e*x],x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (-a B e-A b e+2 b B d)}{3 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e) (B d-A e)}{e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^3 (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (-a B e-A b e+2 b B d)}{3 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e) (B d-A e)}{e^3 (a+b x)}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^3 (a+b x)}",1,"(2*(b*d - a*e)*(B*d - A*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)) - (2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)) + (2*b*B*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1840,1,160,0,0.080696,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(3/2),x]","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (-a B e-A b e+2 b B d)}{e^3 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{e^3 (a+b x) \sqrt{d+e x}}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^3 (a+b x)}","-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (-a B e-A b e+2 b B d)}{e^3 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{e^3 (a+b x) \sqrt{d+e x}}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^3 (a+b x)}",1,"(-2*(b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*Sqrt[d + e*x]) - (2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)) + (2*b*B*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1841,1,160,0,0.0857776,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(5/2),x]","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{e^3 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{3 e^3 (a+b x) (d+e x)^{3/2}}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^3 (a+b x)}","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{e^3 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{3 e^3 (a+b x) (d+e x)^{3/2}}+\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^3 (a+b x)}",1,"(-2*(b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^(3/2)) + (2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*Sqrt[d + e*x]) + (2*b*B*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1842,1,162,0,0.0767258,"\int \frac{(A+B x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(7/2),x]","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{3 e^3 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{5 e^3 (a+b x) (d+e x)^{5/2}}-\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{e^3 (a+b x) \sqrt{d+e x}}","\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (-a B e-A b e+2 b B d)}{3 e^3 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e)}{5 e^3 (a+b x) (d+e x)^{5/2}}-\frac{2 b B \sqrt{a^2+2 a b x+b^2 x^2}}{e^3 (a+b x) \sqrt{d+e x}}",1,"(-2*(b*d - a*e)*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^(5/2)) + (2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^(3/2)) - (2*b*B*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*Sqrt[d + e*x])","A",3,2,35,0.05714,1,"{770, 77}"
1843,1,308,0,0.1853098,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (-3 a B e-A b e+4 b B d)}{15 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e) (-a B e-A b e+2 b B d)}{13 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{11 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3 (B d-A e)}{9 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (-3 a B e-A b e+4 b B d)}{15 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e) (-a B e-A b e+2 b B d)}{13 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{11 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3 (B d-A e)}{9 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^5 (a+b x)}",1,"(2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1844,1,308,0,0.1389172,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (-3 a B e-A b e+4 b B d)}{13 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e) (-a B e-A b e+2 b B d)}{11 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{9 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3 (B d-A e)}{7 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (-3 a B e-A b e+4 b B d)}{13 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e) (-a B e-A b e+2 b B d)}{11 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{9 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3 (B d-A e)}{7 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^5 (a+b x)}",1,"(2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1845,1,308,0,0.1436813,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (-3 a B e-A b e+4 b B d)}{11 e^5 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e) (-a B e-A b e+2 b B d)}{3 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3 (B d-A e)}{5 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (-3 a B e-A b e+4 b B d)}{11 e^5 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e) (-a B e-A b e+2 b B d)}{3 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{7 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3 (B d-A e)}{5 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^5 (a+b x)}",1,"(2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) + (2*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1846,1,308,0,0.1422065,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (-3 a B e-A b e+4 b B d)}{9 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{5 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3 (B d-A e)}{3 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (-3 a B e-A b e+4 b B d)}{9 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e) (-a B e-A b e+2 b B d)}{7 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{5 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3 (B d-A e)}{3 e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^5 (a+b x)}",1,"(2*(b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1847,1,306,0,0.1475182,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/Sqrt[d + e*x],x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (-3 a B e-A b e+4 b B d)}{7 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e) (-a B e-A b e+2 b B d)}{5 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{3 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3 (B d-A e)}{e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (-3 a B e-A b e+4 b B d)}{7 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e) (-a B e-A b e+2 b B d)}{5 e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{3 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3 (B d-A e)}{e^5 (a+b x)}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^5 (a+b x)}",1,"(2*(b*d - a*e)^3*(B*d - A*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1848,1,302,0,0.144891,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(3/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (-3 a B e-A b e+4 b B d)}{5 e^5 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{e^5 (a+b x) \sqrt{d+e x}}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (-3 a B e-A b e+4 b B d)}{5 e^5 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{e^5 (a+b x) \sqrt{d+e x}}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^5 (a+b x)}",1,"(-2*(b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) - (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + (2*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1849,1,304,0,0.1429613,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(5/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (-3 a B e-A b e+4 b B d)}{3 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{3 e^5 (a+b x) (d+e x)^{3/2}}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (-3 a B e-A b e+4 b B d)}{3 e^5 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{e^5 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{3 e^5 (a+b x) (d+e x)^{3/2}}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^5 (a+b x)}",1,"(-2*(b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^(3/2)) + (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) + (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1850,1,304,0,0.1374752,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(7/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (-3 a B e-A b e+4 b B d)}{e^5 (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{3 e^5 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{5 e^5 (a+b x) (d+e x)^{5/2}}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^5 (a+b x)}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (-3 a B e-A b e+4 b B d)}{e^5 (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (-a B e-A b e+2 b B d)}{e^5 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (-a B e-3 A b e+4 b B d)}{3 e^5 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e)}{5 e^5 (a+b x) (d+e x)^{5/2}}+\frac{2 b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^5 (a+b x)}",1,"(-2*(b*d - a*e)^3*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^(5/2)) + (2*(b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^(3/2)) - (6*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) - (2*b^2*(4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + (2*b^3*B*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1851,1,452,0,0.2830025,"\int (A+B x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{19/2} (-5 a B e-A b e+6 b B d)}{19 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{17 e^7 (a+b x)}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{3 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{13 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{11 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^5 (B d-A e)}{9 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{21/2}}{21 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{19/2} (-5 a B e-A b e+6 b B d)}{19 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{17 e^7 (a+b x)}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{3 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{13 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{11 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^5 (B d-A e)}{9 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{21/2}}{21 e^7 (a+b x)}",1,"(2*(b*d - a*e)^5*(B*d - A*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) - (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) - (4*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (10*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(19/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(19*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(21/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(21*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1852,1,452,0,0.2158341,"\int (A+B x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2} (-5 a B e-A b e+6 b B d)}{17 e^7 (a+b x)}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{13 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{11 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{9 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^5 (B d-A e)}{7 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{19/2}}{19 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2} (-5 a B e-A b e+6 b B d)}{17 e^7 (a+b x)}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{13 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{11 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{9 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^5 (B d-A e)}{7 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{19/2}}{19 e^7 (a+b x)}",1,"(2*(b*d - a*e)^5*(B*d - A*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) + (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) - (20*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) + (2*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(19/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(19*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1853,1,452,0,0.216829,"\int (A+B x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (-5 a B e-A b e+6 b B d)}{15 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{13 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{11 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{9 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{7 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5 (B d-A e)}{5 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (-5 a B e-A b e+6 b B d)}{15 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{13 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{11 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{9 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{7 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5 (B d-A e)}{5 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^7 (a+b x)}",1,"(2*(b*d - a*e)^5*(B*d - A*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) - (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) - (20*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (10*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1854,1,452,0,0.2058693,"\int (A+B x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (-5 a B e-A b e+6 b B d)}{13 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{11 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{9 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{7 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{5 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5 (B d-A e)}{3 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (-5 a B e-A b e+6 b B d)}{13 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{11 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{9 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{7 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{5 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5 (B d-A e)}{3 e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^7 (a+b x)}",1,"(2*(b*d - a*e)^5*(B*d - A*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - (20*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) + (10*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1855,1,448,0,0.2179306,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/Sqrt[d + e*x],x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (-5 a B e-A b e+6 b B d)}{11 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{9 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{7 e^7 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{3 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5 (B d-A e)}{e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (-5 a B e-A b e+6 b B d)}{11 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{9 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{7 e^7 (a+b x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{3 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5 (B d-A e)}{e^7 (a+b x)}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^7 (a+b x)}",1,"(2*(b*d - a*e)^5*(B*d - A*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (2*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (20*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (10*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1856,1,446,0,0.2163167,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(3/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (-5 a B e-A b e+6 b B d)}{9 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{7 e^7 (a+b x)}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{e^7 (a+b x) \sqrt{d+e x}}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (-5 a B e-A b e+6 b B d)}{9 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{7 e^7 (a+b x)}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{e^7 (a+b x) \sqrt{d+e x}}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^7 (a+b x)}",1,"(-2*(b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) - (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (4*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (10*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1857,1,446,0,0.20469,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(5/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (-5 a B e-A b e+6 b B d)}{7 e^7 (a+b x)}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{3 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{e^7 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{3 e^7 (a+b x) (d+e x)^{3/2}}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (-5 a B e-A b e+6 b B d)}{7 e^7 (a+b x)}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2 (-a B e-A b e+2 b B d)}{3 e^7 (a+b x)}+\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{e^7 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{3 e^7 (a+b x) (d+e x)^{3/2}}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^7 (a+b x)}",1,"(-2*(b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(3/2)) + (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) + (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (20*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (2*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1858,1,448,0,0.2048242,"\int \frac{(A+B x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[((A + B*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(7/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (-5 a B e-A b e+6 b B d)}{5 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{3 e^7 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{5 e^7 (a+b x) (d+e x)^{5/2}}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^7 (a+b x)}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (-5 a B e-A b e+6 b B d)}{5 e^7 (a+b x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e) (-2 a B e-A b e+3 b B d)}{3 e^7 (a+b x)}-\frac{20 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2 (-a B e-A b e+2 b B d)}{e^7 (a+b x)}-\frac{10 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (-a B e-2 A b e+3 b B d)}{e^7 (a+b x) \sqrt{d+e x}}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (-a B e-5 A b e+6 b B d)}{3 e^7 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e)}{5 e^7 (a+b x) (d+e x)^{5/2}}+\frac{2 b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^7 (a+b x)}",1,"(-2*(b*d - a*e)^5*(B*d - A*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^(5/2)) + (2*(b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(3/2)) - (10*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) - (20*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (10*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (2*b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (2*b^5*B*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x))","A",3,2,35,0.05714,1,"{770, 77}"
1859,1,289,0,0.222815,"\int \frac{(A+B x) (d+e x)^{5/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) (d+e x)^{5/2} (A b-a B)}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2} (A b-a B) (b d-a e)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) \sqrt{d+e x} (A b-a B) (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B (a+b x) (d+e x)^{7/2}}{7 b e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (d+e x)^{5/2} (A b-a B)}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) (d+e x)^{3/2} (A b-a B) (b d-a e)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) \sqrt{d+e x} (A b-a B) (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B (a+b x) (d+e x)^{7/2}}{7 b e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(A*b - a*B)*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x)*(d + e*x)^(5/2))/(5*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*(a + b*x)*(d + e*x)^(7/2))/(7*b*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(A*b - a*B)*(b*d - a*e)^(5/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{770, 80, 50, 63, 208}"
1860,1,230,0,0.1449061,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) (d+e x)^{3/2} (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) \sqrt{d+e x} (A b-a B) (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B (a+b x) (d+e x)^{5/2}}{5 b e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (d+e x)^{3/2} (A b-a B)}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 (a+b x) \sqrt{d+e x} (A b-a B) (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B (a+b x) (d+e x)^{5/2}}{5 b e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(A*b - a*B)*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x)*(d + e*x)^(3/2))/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*(a + b*x)*(d + e*x)^(5/2))/(5*b*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(A*b - a*B)*(b*d - a*e)^(3/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{770, 80, 50, 63, 208}"
1861,1,173,0,0.1021033,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) \sqrt{d+e x} (A b-a B)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B (a+b x) (d+e x)^{3/2}}{3 b e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) \sqrt{d+e x} (A b-a B)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 B (a+b x) (d+e x)^{3/2}}{3 b e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(A*b - a*B)*(a + b*x)*Sqrt[d + e*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*B*(a + b*x)*(d + e*x)^(3/2))/(3*b*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(A*b - a*B)*Sqrt[b*d - a*e]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,35,0.1429,1,"{770, 80, 50, 63, 208}"
1862,1,124,0,0.0758117,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 B (a+b x) \sqrt{d+e x}}{b e \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}","\frac{2 B (a+b x) \sqrt{d+e x}}{b e \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}",1,"(2*B*(a + b*x)*Sqrt[d + e*x])/(b*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(A*b - a*B)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,35,0.1143,1,"{770, 80, 63, 208}"
1863,1,138,0,0.1100256,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x) (B d-A e)}{e \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}-\frac{2 (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}","-\frac{2 (a+b x) (B d-A e)}{e \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}-\frac{2 (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}",1,"(-2*(B*d - A*e)*(a + b*x))/(e*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*(A*b - a*B)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,35,0.1143,1,"{770, 78, 63, 208}"
1864,1,194,0,0.1337385,"\int \frac{A+B x}{(d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{2 (a+b x) (B d-A e)}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}-\frac{2 \sqrt{b} (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}","\frac{2 (a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{2 (a+b x) (B d-A e)}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}-\frac{2 \sqrt{b} (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}",1,"(-2*(B*d - A*e)*(a + b*x))/(3*e*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x))/((b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*Sqrt[b]*(A*b - a*B)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1865,1,251,0,0.1557964,"\int \frac{A+B x}{(d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 b (a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{2 (a+b x) (A b-a B)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{2 (a+b x) (B d-A e)}{5 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}-\frac{2 b^{3/2} (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}","\frac{2 b (a+b x) (A b-a B)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{2 (a+b x) (A b-a B)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{2 (a+b x) (B d-A e)}{5 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}-\frac{2 b^{3/2} (a+b x) (A b-a B) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}",1,"(-2*(B*d - A*e)*(a + b*x))/(5*e*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*(A*b - a*B)*(a + b*x))/(3*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b*(A*b - a*B)*(a + b*x))/((b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b^(3/2)*(A*b - a*B)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1866,1,407,0,0.3765783,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{9/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{7/2} (-9 a B e+5 A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{7 e (a+b x) (d+e x)^{5/2} (-9 a B e+5 A b e+4 b B d)}{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{7 e (a+b x) (d+e x)^{3/2} (-9 a B e+5 A b e+4 b B d)}{12 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) \sqrt{d+e x} (b d-a e) (-9 a B e+5 A b e+4 b B d)}{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 e (a+b x) (b d-a e)^{3/2} (-9 a B e+5 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(d+e x)^{9/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{7/2} (-9 a B e+5 A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{7 e (a+b x) (d+e x)^{5/2} (-9 a B e+5 A b e+4 b B d)}{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{7 e (a+b x) (d+e x)^{3/2} (-9 a B e+5 A b e+4 b B d)}{12 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) \sqrt{d+e x} (b d-a e) (-9 a B e+5 A b e+4 b B d)}{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 e (a+b x) (b d-a e)^{3/2} (-9 a B e+5 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(7*e*(b*d - a*e)*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(a + b*x)*Sqrt[d + e*x])/(4*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(a + b*x)*(d + e*x)^(3/2))/(12*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(a + b*x)*(d + e*x)^(5/2))/(20*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((4*b*B*d + 5*A*b*e - 9*a*B*e)*(d + e*x)^(7/2))/(4*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(9/2))/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(b*d - a*e)^(3/2)*(4*b*B*d + 5*A*b*e - 9*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,6,35,0.1714,1,"{770, 78, 47, 50, 63, 208}"
1867,1,341,0,0.3044229,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{7/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e+3 A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{5 e (a+b x) (d+e x)^{3/2} (-7 a B e+3 A b e+4 b B d)}{12 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{5 e (a+b x) \sqrt{d+e x} (-7 a B e+3 A b e+4 b B d)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (a+b x) \sqrt{b d-a e} (-7 a B e+3 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(d+e x)^{7/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e+3 A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{5 e (a+b x) (d+e x)^{3/2} (-7 a B e+3 A b e+4 b B d)}{12 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{5 e (a+b x) \sqrt{d+e x} (-7 a B e+3 A b e+4 b B d)}{4 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (a+b x) \sqrt{b d-a e} (-7 a B e+3 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(5*e*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)*Sqrt[d + e*x])/(4*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)*(d + e*x)^(3/2))/(12*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((4*b*B*d + 3*A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(4*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(7/2))/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*Sqrt[b*d - a*e]*(4*b*B*d + 3*A*b*e - 7*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,35,0.1714,1,"{770, 78, 47, 50, 63, 208}"
1868,1,280,0,0.2291441,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{5/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{3/2} (-5 a B e+A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{3 e (a+b x) \sqrt{d+e x} (-5 a B e+A b e+4 b B d)}{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 e (a+b x) (-5 a B e+A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}","-\frac{(d+e x)^{5/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{3/2} (-5 a B e+A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{3 e (a+b x) \sqrt{d+e x} (-5 a B e+A b e+4 b B d)}{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 e (a+b x) (-5 a B e+A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}",1,"(3*e*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)*Sqrt[d + e*x])/(4*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((4*b*B*d + A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(4*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(5/2))/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e*(4*b*B*d + A*b*e - 5*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(7/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,6,35,0.1714,1,"{770, 78, 47, 50, 63, 208}"
1869,1,215,0,0.1876055,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{3/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x} (-3 a B e-A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{e (a+b x) (-3 a B e-A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}","-\frac{(d+e x)^{3/2} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x} (-3 a B e-A b e+4 b B d)}{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{e (a+b x) (-3 a B e-A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}",1,"-((4*b*B*d - A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(4*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(3/2))/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(4*b*B*d - A*b*e - 3*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(5/2)*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,35,0.1429,1,"{770, 78, 47, 63, 208}"
1870,1,215,0,0.2045772,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{\sqrt{d+e x} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x} (-a B e-3 A b e+4 b B d)}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{e (a+b x) (-a B e-3 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}","-\frac{\sqrt{d+e x} (A b-a B)}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x} (-a B e-3 A b e+4 b B d)}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{e (a+b x) (-a B e-3 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}",1,"-((4*b*B*d - 3*A*b*e - a*B*e)*Sqrt[d + e*x])/(4*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*Sqrt[d + e*x])/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(4*b*B*d - 3*A*b*e - a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(3/2)*(b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1871,1,280,0,0.2557822,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}-\frac{a B e-5 A b e+4 b B d}{4 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{3 e (a+b x) (a B e-5 A b e+4 b B d)}{4 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{3 e (a+b x) (a B e-5 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}","-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}-\frac{a B e-5 A b e+4 b B d}{4 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{3 e (a+b x) (a B e-5 A b e+4 b B d)}{4 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{3 e (a+b x) (a B e-5 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}",1,"-(4*b*B*d - 5*A*b*e + a*B*e)/(4*b*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x))/(4*b*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e*(4*b*B*d - 5*A*b*e + a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*Sqrt[b]*(b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1872,1,348,0,0.3185562,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}-\frac{5 e (a+b x) (3 a B e-7 A b e+4 b B d)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{3 a B e-7 A b e+4 b B d}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{5 e (a+b x) (3 a B e-7 A b e+4 b B d)}{12 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}+\frac{5 \sqrt{b} e (a+b x) (3 a B e-7 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}","-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}-\frac{5 e (a+b x) (3 a B e-7 A b e+4 b B d)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{3 a B e-7 A b e+4 b B d}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{5 e (a+b x) (3 a B e-7 A b e+4 b B d)}{12 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}+\frac{5 \sqrt{b} e (a+b x) (3 a B e-7 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}",1,"-(4*b*B*d - 7*A*b*e + 3*a*B*e)/(4*b*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(4*b*B*d - 7*A*b*e + 3*a*B*e)*(a + b*x))/(12*b*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(4*b*B*d - 7*A*b*e + 3*a*B*e)*(a + b*x))/(4*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*Sqrt[b]*e*(4*b*B*d - 7*A*b*e + 3*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1873,1,414,0,0.3733887,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{7 b e (a+b x) (5 a B e-9 A b e+4 b B d)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}-\frac{7 e (a+b x) (5 a B e-9 A b e+4 b B d)}{12 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}-\frac{5 a B e-9 A b e+4 b B d}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{7 e (a+b x) (5 a B e-9 A b e+4 b B d)}{20 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}+\frac{7 b^{3/2} e (a+b x) (5 a B e-9 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}","-\frac{7 b e (a+b x) (5 a B e-9 A b e+4 b B d)}{4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}-\frac{7 e (a+b x) (5 a B e-9 A b e+4 b B d)}{12 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}-\frac{5 a B e-9 A b e+4 b B d}{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{7 e (a+b x) (5 a B e-9 A b e+4 b B d)}{20 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{A b-a B}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}+\frac{7 b^{3/2} e (a+b x) (5 a B e-9 A b e+4 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}",1,"-(4*b*B*d - 9*A*b*e + 5*a*B*e)/(4*b*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - a*B)/(2*b*(b*d - a*e)*(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(4*b*B*d - 9*A*b*e + 5*a*B*e)*(a + b*x))/(20*b*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(4*b*B*d - 9*A*b*e + 5*a*B*e)*(a + b*x))/(12*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*b*e*(4*b*B*d - 9*A*b*e + 5*a*B*e)*(a + b*x))/(4*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*b^(3/2)*e*(4*b*B*d - 9*A*b*e + 5*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1874,1,557,0,0.5209182,"\int \frac{(A+B x) (d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(11/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{33 e^2 (d+e x)^{7/2} (-13 a B e+5 A b e+8 b B d)}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{231 e^3 (a+b x) (d+e x)^{5/2} (-13 a B e+5 A b e+8 b B d)}{320 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{77 e^3 (a+b x) (d+e x)^{3/2} (-13 a B e+5 A b e+8 b B d)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{231 e^3 (a+b x) \sqrt{d+e x} (b d-a e) (-13 a B e+5 A b e+8 b B d)}{64 b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 e^3 (a+b x) (b d-a e)^{3/2} (-13 a B e+5 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{13/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{11/2} (-13 a B e+5 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{11 e (d+e x)^{9/2} (-13 a B e+5 A b e+8 b B d)}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{33 e^2 (d+e x)^{7/2} (-13 a B e+5 A b e+8 b B d)}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{231 e^3 (a+b x) (d+e x)^{5/2} (-13 a B e+5 A b e+8 b B d)}{320 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{77 e^3 (a+b x) (d+e x)^{3/2} (-13 a B e+5 A b e+8 b B d)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{231 e^3 (a+b x) \sqrt{d+e x} (b d-a e) (-13 a B e+5 A b e+8 b B d)}{64 b^7 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{231 e^3 (a+b x) (b d-a e)^{3/2} (-13 a B e+5 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{15/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{13/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{11/2} (-13 a B e+5 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{11 e (d+e x)^{9/2} (-13 a B e+5 A b e+8 b B d)}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(231*e^3*(b*d - a*e)*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(a + b*x)*Sqrt[d + e*x])/(64*b^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (77*e^3*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(a + b*x)*(d + e*x)^(3/2))/(64*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (231*e^3*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(a + b*x)*(d + e*x)^(5/2))/(320*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (33*e^2*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(d + e*x)^(7/2))/(64*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (11*e*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(d + e*x)^(9/2))/(96*b^3*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d + 5*A*b*e - 13*a*B*e)*(d + e*x)^(11/2))/(24*b^2*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(13/2))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*e^3*(b*d - a*e)^(3/2)*(8*b*B*d + 5*A*b*e - 13*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,6,35,0.1714,1,"{770, 78, 47, 50, 63, 208}"
1875,1,489,0,0.4196478,"\int \frac{(A+B x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{21 e^2 (d+e x)^{5/2} (-11 a B e+3 A b e+8 b B d)}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{35 e^3 (a+b x) (d+e x)^{3/2} (-11 a B e+3 A b e+8 b B d)}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{105 e^3 (a+b x) \sqrt{d+e x} (-11 a B e+3 A b e+8 b B d)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{105 e^3 (a+b x) \sqrt{b d-a e} (-11 a B e+3 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{11/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{9/2} (-11 a B e+3 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 e (d+e x)^{7/2} (-11 a B e+3 A b e+8 b B d)}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{21 e^2 (d+e x)^{5/2} (-11 a B e+3 A b e+8 b B d)}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{35 e^3 (a+b x) (d+e x)^{3/2} (-11 a B e+3 A b e+8 b B d)}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{105 e^3 (a+b x) \sqrt{d+e x} (-11 a B e+3 A b e+8 b B d)}{64 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{105 e^3 (a+b x) \sqrt{b d-a e} (-11 a B e+3 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{13/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{11/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{9/2} (-11 a B e+3 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{3 e (d+e x)^{7/2} (-11 a B e+3 A b e+8 b B d)}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(105*e^3*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(a + b*x)*Sqrt[d + e*x])/(64*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*e^3*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(a + b*x)*(d + e*x)^(3/2))/(64*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (21*e^2*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(d + e*x)^(5/2))/(64*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(d + e*x)^(7/2))/(32*b^3*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d + 3*A*b*e - 11*a*B*e)*(d + e*x)^(9/2))/(24*b^2*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(11/2))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (105*e^3*Sqrt[b*d - a*e]*(8*b*B*d + 3*A*b*e - 11*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,6,35,0.1714,1,"{770, 78, 47, 50, 63, 208}"
1876,1,424,0,0.351419,"\int \frac{(A+B x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{35 e^2 (d+e x)^{3/2} (-9 a B e+A b e+8 b B d)}{192 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{35 e^3 (a+b x) \sqrt{d+e x} (-9 a B e+A b e+8 b B d)}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{35 e^3 (a+b x) (-9 a B e+A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{(d+e x)^{9/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{7/2} (-9 a B e+A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{7 e (d+e x)^{5/2} (-9 a B e+A b e+8 b B d)}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{35 e^2 (d+e x)^{3/2} (-9 a B e+A b e+8 b B d)}{192 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{35 e^3 (a+b x) \sqrt{d+e x} (-9 a B e+A b e+8 b B d)}{64 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{35 e^3 (a+b x) (-9 a B e+A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{11/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{(d+e x)^{9/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{7/2} (-9 a B e+A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{7 e (d+e x)^{5/2} (-9 a B e+A b e+8 b B d)}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(35*e^3*(8*b*B*d + A*b*e - 9*a*B*e)*(a + b*x)*Sqrt[d + e*x])/(64*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^2*(8*b*B*d + A*b*e - 9*a*B*e)*(d + e*x)^(3/2))/(192*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(8*b*B*d + A*b*e - 9*a*B*e)*(d + e*x)^(5/2))/(96*b^3*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d + A*b*e - 9*a*B*e)*(d + e*x)^(7/2))/(24*b^2*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(9/2))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^3*(8*b*B*d + A*b*e - 9*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(11/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,6,35,0.1714,1,"{770, 78, 47, 50, 63, 208}"
1877,1,359,0,0.3153281,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{5 e^2 \sqrt{d+e x} (-7 a B e-A b e+8 b B d)}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{5 e^3 (a+b x) (-7 a B e-A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{(d+e x)^{7/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e-A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{5 e (d+e x)^{3/2} (-7 a B e-A b e+8 b B d)}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{5 e^2 \sqrt{d+e x} (-7 a B e-A b e+8 b B d)}{64 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{5 e^3 (a+b x) (-7 a B e-A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{(d+e x)^{7/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{5/2} (-7 a B e-A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{5 e (d+e x)^{3/2} (-7 a B e-A b e+8 b B d)}{96 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(-5*e^2*(8*b*B*d - A*b*e - 7*a*B*e)*Sqrt[d + e*x])/(64*b^4*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(8*b*B*d - A*b*e - 7*a*B*e)*(d + e*x)^(3/2))/(96*b^3*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d - A*b*e - 7*a*B*e)*(d + e*x)^(5/2))/(24*b^2*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(7/2))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e^3*(8*b*B*d - A*b*e - 7*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(9/2)*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{770, 78, 47, 63, 208}"
1878,1,359,0,0.3237689,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{e^2 \sqrt{d+e x} (-5 a B e-3 A b e+8 b B d)}{64 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{e^3 (a+b x) (-5 a B e-3 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x} (-5 a B e-3 A b e+8 b B d)}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{3/2} (-5 a B e-3 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{e^2 \sqrt{d+e x} (-5 a B e-3 A b e+8 b B d)}{64 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{e^3 (a+b x) (-5 a B e-3 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x} (-5 a B e-3 A b e+8 b B d)}{32 b^3 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{5/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{(d+e x)^{3/2} (-5 a B e-3 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-(e^2*(8*b*B*d - 3*A*b*e - 5*a*B*e)*Sqrt[d + e*x])/(64*b^3*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(8*b*B*d - 3*A*b*e - 5*a*B*e)*Sqrt[d + e*x])/(32*b^3*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d - 3*A*b*e - 5*a*B*e)*(d + e*x)^(3/2))/(24*b^2*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(5/2))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(8*b*B*d - 3*A*b*e - 5*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(7/2)*(b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,35,0.1714,1,"{770, 78, 47, 51, 63, 208}"
1879,1,359,0,0.3500753,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^2 \sqrt{d+e x} (-3 a B e-5 A b e+8 b B d)}{64 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e^3 (a+b x) (-3 a B e-5 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}-\frac{e \sqrt{d+e x} (-3 a B e-5 A b e+8 b B d)}{96 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{(d+e x)^{3/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x} (-3 a B e-5 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{e^2 \sqrt{d+e x} (-3 a B e-5 A b e+8 b B d)}{64 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e^3 (a+b x) (-3 a B e-5 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}-\frac{e \sqrt{d+e x} (-3 a B e-5 A b e+8 b B d)}{96 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{(d+e x)^{3/2} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x} (-3 a B e-5 A b e+8 b B d)}{24 b^2 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(e^2*(8*b*B*d - 5*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(64*b^2*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d - 5*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(24*b^2*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(8*b*B*d - 5*A*b*e - 3*a*B*e)*Sqrt[d + e*x])/(96*b^2*(b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(d + e*x)^(3/2))/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(8*b*B*d - 5*A*b*e - 3*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(5/2)*(b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,35,0.1714,1,"{770, 78, 47, 51, 63, 208}"
1880,1,359,0,0.348191,"\int \frac{A+B x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{5 e^2 \sqrt{d+e x} (-a B e-7 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{5 e^3 (a+b x) (-a B e-7 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{5 e \sqrt{d+e x} (-a B e-7 A b e+8 b B d)}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{\sqrt{d+e x} (-a B e-7 A b e+8 b B d)}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{5 e^2 \sqrt{d+e x} (-a B e-7 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{5 e^3 (a+b x) (-a B e-7 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{5 e \sqrt{d+e x} (-a B e-7 A b e+8 b B d)}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{\sqrt{d+e x} (-a B e-7 A b e+8 b B d)}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x} (A b-a B)}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(-5*e^2*(8*b*B*d - 7*A*b*e - a*B*e)*Sqrt[d + e*x])/(64*b*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*Sqrt[d + e*x])/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((8*b*B*d - 7*A*b*e - a*B*e)*Sqrt[d + e*x])/(24*b*(b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e*(8*b*B*d - 7*A*b*e - a*B*e)*Sqrt[d + e*x])/(96*b*(b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^3*(8*b*B*d - 7*A*b*e - a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(3/2)*(b*d - a*e)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1881,1,424,0,0.4365052,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{35 e^3 (a+b x) (a B e-9 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}-\frac{35 e^2 (a B e-9 A b e+8 b B d)}{192 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}+\frac{35 e^3 (a+b x) (a B e-9 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}+\frac{7 e (a B e-9 A b e+8 b B d)}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-9 A b e+8 b B d}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}","-\frac{35 e^3 (a+b x) (a B e-9 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}-\frac{35 e^2 (a B e-9 A b e+8 b B d)}{192 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}+\frac{35 e^3 (a+b x) (a B e-9 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}+\frac{7 e (a B e-9 A b e+8 b B d)}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{a B e-9 A b e+8 b B d}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}",1,"(-35*e^2*(8*b*B*d - 9*A*b*e + a*B*e))/(192*b*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - a*B)/(4*b*(b*d - a*e)*(a + b*x)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (8*b*B*d - 9*A*b*e + a*B*e)/(24*b*(b*d - a*e)^2*(a + b*x)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e*(8*b*B*d - 9*A*b*e + a*B*e))/(96*b*(b*d - a*e)^3*(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^3*(8*b*B*d - 9*A*b*e + a*B*e)*(a + b*x))/(64*b*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*e^3*(8*b*B*d - 9*A*b*e + a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*Sqrt[b]*(b*d - a*e)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1882,1,496,0,0.5458614,"\int \frac{A+B x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{105 e^3 (a+b x) (3 a B e-11 A b e+8 b B d)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}-\frac{35 e^3 (a+b x) (3 a B e-11 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}-\frac{21 e^2 (3 a B e-11 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}+\frac{105 \sqrt{b} e^3 (a+b x) (3 a B e-11 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{13/2}}+\frac{3 e (3 a B e-11 A b e+8 b B d)}{32 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{3 a B e-11 A b e+8 b B d}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}","-\frac{105 e^3 (a+b x) (3 a B e-11 A b e+8 b B d)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}-\frac{35 e^3 (a+b x) (3 a B e-11 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}-\frac{21 e^2 (3 a B e-11 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}+\frac{105 \sqrt{b} e^3 (a+b x) (3 a B e-11 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{13/2}}+\frac{3 e (3 a B e-11 A b e+8 b B d)}{32 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{3 a B e-11 A b e+8 b B d}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}",1,"(-21*e^2*(8*b*B*d - 11*A*b*e + 3*a*B*e))/(64*b*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - a*B)/(4*b*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (8*b*B*d - 11*A*b*e + 3*a*B*e)/(24*b*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e*(8*b*B*d - 11*A*b*e + 3*a*B*e))/(32*b*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^3*(8*b*B*d - 11*A*b*e + 3*a*B*e)*(a + b*x))/(64*b*(b*d - a*e)^5*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (105*e^3*(8*b*B*d - 11*A*b*e + 3*a*B*e)*(a + b*x))/(64*(b*d - a*e)^6*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (105*Sqrt[b]*e^3*(8*b*B*d - 11*A*b*e + 3*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1883,1,564,0,0.5721976,"\int \frac{A+B x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{231 b e^3 (a+b x) (5 a B e-13 A b e+8 b B d)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^7}-\frac{77 e^3 (a+b x) (5 a B e-13 A b e+8 b B d)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^6}-\frac{231 e^3 (a+b x) (5 a B e-13 A b e+8 b B d)}{320 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}-\frac{33 e^2 (5 a B e-13 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}+\frac{231 b^{3/2} e^3 (a+b x) (5 a B e-13 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{15/2}}+\frac{11 e (5 a B e-13 A b e+8 b B d)}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{5 a B e-13 A b e+8 b B d}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}","-\frac{231 b e^3 (a+b x) (5 a B e-13 A b e+8 b B d)}{64 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^7}-\frac{77 e^3 (a+b x) (5 a B e-13 A b e+8 b B d)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^6}-\frac{231 e^3 (a+b x) (5 a B e-13 A b e+8 b B d)}{320 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}-\frac{33 e^2 (5 a B e-13 A b e+8 b B d)}{64 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}+\frac{231 b^{3/2} e^3 (a+b x) (5 a B e-13 A b e+8 b B d) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{15/2}}+\frac{11 e (5 a B e-13 A b e+8 b B d)}{96 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}-\frac{5 a B e-13 A b e+8 b B d}{24 b (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{A b-a B}{4 b (a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}",1,"(-33*e^2*(8*b*B*d - 13*A*b*e + 5*a*B*e))/(64*b*(b*d - a*e)^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (A*b - a*B)/(4*b*(b*d - a*e)*(a + b*x)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (8*b*B*d - 13*A*b*e + 5*a*B*e)/(24*b*(b*d - a*e)^2*(a + b*x)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (11*e*(8*b*B*d - 13*A*b*e + 5*a*B*e))/(96*b*(b*d - a*e)^3*(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*e^3*(8*b*B*d - 13*A*b*e + 5*a*B*e)*(a + b*x))/(320*b*(b*d - a*e)^5*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (77*e^3*(8*b*B*d - 13*A*b*e + 5*a*B*e)*(a + b*x))/(64*(b*d - a*e)^6*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*b*e^3*(8*b*B*d - 13*A*b*e + 5*a*B*e)*(a + b*x))/(64*(b*d - a*e)^7*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (231*b^(3/2)*e^3*(8*b*B*d - 13*A*b*e + 5*a*B*e)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,5,35,0.1429,1,"{770, 78, 51, 63, 208}"
1884,1,234,0,0.1665951,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 b^2 (b d-a e) (d+e x)^{m+4} (-3 a B e-2 A b e+5 b B d)}{e^6 (m+4)}-\frac{b^3 (d+e x)^{m+5} (-4 a B e-A b e+5 b B d)}{e^6 (m+5)}-\frac{(b d-a e)^4 (B d-A e) (d+e x)^{m+1}}{e^6 (m+1)}+\frac{(b d-a e)^3 (d+e x)^{m+2} (-a B e-4 A b e+5 b B d)}{e^6 (m+2)}-\frac{2 b (b d-a e)^2 (d+e x)^{m+3} (-2 a B e-3 A b e+5 b B d)}{e^6 (m+3)}+\frac{b^4 B (d+e x)^{m+6}}{e^6 (m+6)}","\frac{2 b^2 (b d-a e) (d+e x)^{m+4} (-3 a B e-2 A b e+5 b B d)}{e^6 (m+4)}-\frac{b^3 (d+e x)^{m+5} (-4 a B e-A b e+5 b B d)}{e^6 (m+5)}-\frac{(b d-a e)^4 (B d-A e) (d+e x)^{m+1}}{e^6 (m+1)}+\frac{(b d-a e)^3 (d+e x)^{m+2} (-a B e-4 A b e+5 b B d)}{e^6 (m+2)}-\frac{2 b (b d-a e)^2 (d+e x)^{m+3} (-2 a B e-3 A b e+5 b B d)}{e^6 (m+3)}+\frac{b^4 B (d+e x)^{m+6}}{e^6 (m+6)}",1,"-(((b*d - a*e)^4*(B*d - A*e)*(d + e*x)^(1 + m))/(e^6*(1 + m))) + ((b*d - a*e)^3*(5*b*B*d - 4*A*b*e - a*B*e)*(d + e*x)^(2 + m))/(e^6*(2 + m)) - (2*b*(b*d - a*e)^2*(5*b*B*d - 3*A*b*e - 2*a*B*e)*(d + e*x)^(3 + m))/(e^6*(3 + m)) + (2*b^2*(b*d - a*e)*(5*b*B*d - 2*A*b*e - 3*a*B*e)*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (b^3*(5*b*B*d - A*b*e - 4*a*B*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (b^4*B*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",3,2,31,0.06452,1,"{27, 77}"
1885,1,138,0,0.0836444,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{(b d-a e)^2 (B d-A e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(b d-a e) (d+e x)^{m+2} (-a B e-2 A b e+3 b B d)}{e^4 (m+2)}-\frac{b (d+e x)^{m+3} (-2 a B e-A b e+3 b B d)}{e^4 (m+3)}+\frac{b^2 B (d+e x)^{m+4}}{e^4 (m+4)}","-\frac{(b d-a e)^2 (B d-A e) (d+e x)^{m+1}}{e^4 (m+1)}+\frac{(b d-a e) (d+e x)^{m+2} (-a B e-2 A b e+3 b B d)}{e^4 (m+2)}-\frac{b (d+e x)^{m+3} (-2 a B e-A b e+3 b B d)}{e^4 (m+3)}+\frac{b^2 B (d+e x)^{m+4}}{e^4 (m+4)}",1,"-(((b*d - a*e)^2*(B*d - A*e)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((b*d - a*e)*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(2 + m))/(e^4*(2 + m)) - (b*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (b^2*B*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",3,2,29,0.06897,1,"{27, 77}"
1886,1,112,0,0.0678511,"\int \frac{(A+B x) (d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(d+e x)^{m+1} (a B e (m+1)-b (A e m+B d)) \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b (m+1) (b d-a e)^2}-\frac{(A b-a B) (d+e x)^{m+1}}{b (a+b x) (b d-a e)}","\frac{(d+e x)^{m+1} (a B e (m+1)-b (A e m+B d)) \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b (m+1) (b d-a e)^2}-\frac{(A b-a B) (d+e x)^{m+1}}{b (a+b x) (b d-a e)}",1,"-(((A*b - a*B)*(d + e*x)^(1 + m))/(b*(b*d - a*e)*(a + b*x))) + ((a*B*e*(1 + m) - b*(B*d + A*e*m))*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(b*(b*d - a*e)^2*(1 + m))","A",3,3,31,0.09677,1,"{27, 78, 68}"
1887,1,125,0,0.0725696,"\int \frac{(A+B x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{e^2 (d+e x)^{m+1} (-a B e (m+1)-A b e (2-m)+3 b B d) \, _2F_1\left(3,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{3 b (m+1) (b d-a e)^4}-\frac{(A b-a B) (d+e x)^{m+1}}{3 b (a+b x)^3 (b d-a e)}","-\frac{e^2 (d+e x)^{m+1} (b (3 B d-A e (2-m))-a B e (m+1)) \, _2F_1\left(3,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{3 b (m+1) (b d-a e)^4}-\frac{(A b-a B) (d+e x)^{m+1}}{3 b (a+b x)^3 (b d-a e)}",1,"-((A*b - a*B)*(d + e*x)^(1 + m))/(3*b*(b*d - a*e)*(a + b*x)^3) - (e^2*(3*b*B*d - A*b*e*(2 - m) - a*B*e*(1 + m))*(d + e*x)^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(3*b*(b*d - a*e)^4*(1 + m))","A",3,3,31,0.09677,1,"{27, 78, 68}"
1888,1,471,0,0.3323827,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e) (d+e x)^{m+1}}{e^7 (m+1) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+2} (-a B e-5 A b e+6 b B d)}{e^7 (m+2) (a+b x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+3} (-a B e-2 A b e+3 b B d)}{e^7 (m+3) (a+b x)}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+4} (-a B e-A b e+2 b B d)}{e^7 (m+4) (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+5} (-2 a B e-A b e+3 b B d)}{e^7 (m+5) (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+6} (-5 a B e-A b e+6 b B d)}{e^7 (m+6) (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+7}}{e^7 (m+7) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (B d-A e) (d+e x)^{m+1}}{e^7 (m+1) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+2} (-a B e-5 A b e+6 b B d)}{e^7 (m+2) (a+b x)}+\frac{5 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+3} (-a B e-2 A b e+3 b B d)}{e^7 (m+3) (a+b x)}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+4} (-a B e-A b e+2 b B d)}{e^7 (m+4) (a+b x)}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+5} (-2 a B e-A b e+3 b B d)}{e^7 (m+5) (a+b x)}-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+6} (-5 a B e-A b e+6 b B d)}{e^7 (m+6) (a+b x)}+\frac{b^5 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+7}}{e^7 (m+7) (a+b x)}",1,"((b*d - a*e)^5*(B*d - A*e)*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(1 + m)*(a + b*x)) - ((b*d - a*e)^4*(6*b*B*d - 5*A*b*e - a*B*e)*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(2 + m)*(a + b*x)) + (5*b*(b*d - a*e)^3*(3*b*B*d - 2*A*b*e - a*B*e)*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(3 + m)*(a + b*x)) - (10*b^2*(b*d - a*e)^2*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(4 + m)*(a + b*x)) + (5*b^3*(b*d - a*e)*(3*b*B*d - A*b*e - 2*a*B*e)*(d + e*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(5 + m)*(a + b*x)) - (b^4*(6*b*B*d - A*b*e - 5*a*B*e)*(d + e*x)^(6 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(6 + m)*(a + b*x)) + (b^5*B*(d + e*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(7 + m)*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1889,1,321,0,0.2075173,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e) (d+e x)^{m+1}}{e^5 (m+1) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+2} (-a B e-3 A b e+4 b B d)}{e^5 (m+2) (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+3} (-a B e-A b e+2 b B d)}{e^5 (m+3) (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+4} (-3 a B e-A b e+4 b B d)}{e^5 (m+4) (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+5}}{e^5 (m+5) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (B d-A e) (d+e x)^{m+1}}{e^5 (m+1) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+2} (-a B e-3 A b e+4 b B d)}{e^5 (m+2) (a+b x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+3} (-a B e-A b e+2 b B d)}{e^5 (m+3) (a+b x)}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+4} (-3 a B e-A b e+4 b B d)}{e^5 (m+4) (a+b x)}+\frac{b^3 B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+5}}{e^5 (m+5) (a+b x)}",1,"((b*d - a*e)^3*(B*d - A*e)*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(1 + m)*(a + b*x)) - ((b*d - a*e)^2*(4*b*B*d - 3*A*b*e - a*B*e)*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(2 + m)*(a + b*x)) + (3*b*(b*d - a*e)*(2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(3 + m)*(a + b*x)) - (b^2*(4*b*B*d - A*b*e - 3*a*B*e)*(d + e*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(4 + m)*(a + b*x)) + (b^3*B*(d + e*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(5 + m)*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1890,1,171,0,0.0966013,"\int (A+B x) (d+e x)^m \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(A + B*x)*(d + e*x)^m*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e) (d+e x)^{m+1}}{e^3 (m+1) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+2} (-a B e-A b e+2 b B d)}{e^3 (m+2) (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+3}}{e^3 (m+3) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (B d-A e) (d+e x)^{m+1}}{e^3 (m+1) (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+2} (-a B e-A b e+2 b B d)}{e^3 (m+2) (a+b x)}+\frac{b B \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+3}}{e^3 (m+3) (a+b x)}",1,"((b*d - a*e)*(B*d - A*e)*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(1 + m)*(a + b*x)) - ((2*b*B*d - A*b*e - a*B*e)*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(2 + m)*(a + b*x)) + (b*B*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(3 + m)*(a + b*x))","A",3,2,33,0.06061,1,"{770, 77}"
1891,1,135,0,0.0811784,"\int \frac{(A+B x) (d+e x)^m}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((A + B*x)*(d + e*x)^m)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{B (a+b x) (d+e x)^{m+1}}{b e (m+1) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) (A b-a B) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b (m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{B (a+b x) (d+e x)^{m+1}}{b e (m+1) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(a+b x) (A b-a B) (d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b (m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(B*(a + b*x)*(d + e*x)^(1 + m))/(b*e*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - ((A*b - a*B)*(a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(b*(b*d - a*e)*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 80, 68}"
1892,1,168,0,0.15628,"\int \frac{(A+B x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e (a+b x) (d+e x)^{m+1} (-a B e (m+1)-A b e (1-m)+2 b B d) \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{2 b (m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{(A b-a B) (d+e x)^{m+1}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{e (a+b x) (d+e x)^{m+1} (b (2 B d-A e (1-m))-a B e (m+1)) \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{2 b (m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{(A b-a B) (d+e x)^{m+1}}{2 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-((A*b - a*B)*(d + e*x)^(1 + m))/(2*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(2*b*B*d - A*b*e*(1 - m) - a*B*e*(1 + m))*(a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(2*b*(b*d - a*e)^3*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 78, 68}"
1893,1,174,0,0.1869492,"\int (A+B x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(A + B*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} (A b e (m+2 p+2)-B (a e (m+1)+b (2 d p+d))) \, _2F_1\left(m+1,-2 p;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b e^2 (m+1) (m+2 p+2)}+\frac{B (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1}}{b e (m+2 p+2)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1} \left(-\frac{e (a+b x)}{b d-a e}\right)^{-2 p} (A b e (m+2 p+2)-B (a e (m+1)+b (2 d p+d))) \, _2F_1\left(m+1,-2 p;m+2;\frac{b (d+e x)}{b d-a e}\right)}{b e^2 (m+1) (m+2 p+2)}+\frac{B (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{m+1}}{b e (m+2 p+2)}",1,"(B*(a + b*x)*(d + e*x)^(1 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b*e*(2 + m + 2*p)) + ((A*b*e*(2 + m + 2*p) - B*(a*e*(1 + m) + b*(d + 2*d*p)))*(d + e*x)^(1 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[1 + m, -2*p, 2 + m, (b*(d + e*x))/(b*d - a*e)])/(b*e^2*(1 + m)*(2 + m + 2*p)*(-((e*(a + b*x))/(b*d - a*e)))^(2*p))","A",4,4,31,0.1290,1,"{770, 80, 70, 69}"
1894,1,119,0,0.0688974,"\int (d+e x)^{-3-2 p} (f+g x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(d + e*x)^(-3 - 2*p)*(f + g*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{(a+b x) (b f-a g) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{-2 p-1}}{(2 p+1) (b d-a e)^2}-\frac{\left(a^2+2 a b x+b^2 x^2\right)^{p+1} (e f-d g) (d+e x)^{-2 (p+1)}}{2 (p+1) (b d-a e)^2}","\frac{(a+b x) (b f-a g) \left(a^2+2 a b x+b^2 x^2\right)^p (d+e x)^{-2 p-1}}{(2 p+1) (b d-a e)^2}-\frac{\left(a^2+2 a b x+b^2 x^2\right)^{p+1} (e f-d g) (d+e x)^{-2 (p+1)}}{2 (p+1) (b d-a e)^2}",1,"((b*f - a*g)*(a + b*x)*(d + e*x)^(-1 - 2*p)*(a^2 + 2*a*b*x + b^2*x^2)^p)/((b*d - a*e)^2*(1 + 2*p)) - ((e*f - d*g)*(a^2 + 2*a*b*x + b^2*x^2)^(1 + p))/(2*(b*d - a*e)^2*(1 + p)*(d + e*x)^(2*(1 + p)))","A",3,3,35,0.08571,1,"{769, 646, 37}"
1895,1,92,0,0.1549479,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{3 b^2 (d+e x)^8 (b d-a e)}{8 e^4}+\frac{3 b (d+e x)^7 (b d-a e)^2}{7 e^4}-\frac{(d+e x)^6 (b d-a e)^3}{6 e^4}+\frac{b^3 (d+e x)^9}{9 e^4}","-\frac{3 b^2 (d+e x)^8 (b d-a e)}{8 e^4}+\frac{3 b (d+e x)^7 (b d-a e)^2}{7 e^4}-\frac{(d+e x)^6 (b d-a e)^3}{6 e^4}+\frac{b^3 (d+e x)^9}{9 e^4}",1,"-((b*d - a*e)^3*(d + e*x)^6)/(6*e^4) + (3*b*(b*d - a*e)^2*(d + e*x)^7)/(7*e^4) - (3*b^2*(b*d - a*e)*(d + e*x)^8)/(8*e^4) + (b^3*(d + e*x)^9)/(9*e^4)","A",3,2,29,0.06897,1,"{27, 43}"
1896,1,92,0,0.1200253,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{3 b^2 (d+e x)^7 (b d-a e)}{7 e^4}+\frac{b (d+e x)^6 (b d-a e)^2}{2 e^4}-\frac{(d+e x)^5 (b d-a e)^3}{5 e^4}+\frac{b^3 (d+e x)^8}{8 e^4}","-\frac{3 b^2 (d+e x)^7 (b d-a e)}{7 e^4}+\frac{b (d+e x)^6 (b d-a e)^2}{2 e^4}-\frac{(d+e x)^5 (b d-a e)^3}{5 e^4}+\frac{b^3 (d+e x)^8}{8 e^4}",1,"-((b*d - a*e)^3*(d + e*x)^5)/(5*e^4) + (b*(b*d - a*e)^2*(d + e*x)^6)/(2*e^4) - (3*b^2*(b*d - a*e)*(d + e*x)^7)/(7*e^4) + (b^3*(d + e*x)^8)/(8*e^4)","A",3,2,29,0.06897,1,"{27, 43}"
1897,1,92,0,0.0954058,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e^2 (a+b x)^6 (b d-a e)}{2 b^4}+\frac{3 e (a+b x)^5 (b d-a e)^2}{5 b^4}+\frac{(a+b x)^4 (b d-a e)^3}{4 b^4}+\frac{e^3 (a+b x)^7}{7 b^4}","\frac{e^2 (a+b x)^6 (b d-a e)}{2 b^4}+\frac{3 e (a+b x)^5 (b d-a e)^2}{5 b^4}+\frac{(a+b x)^4 (b d-a e)^3}{4 b^4}+\frac{e^3 (a+b x)^7}{7 b^4}",1,"((b*d - a*e)^3*(a + b*x)^4)/(4*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^5)/(5*b^4) + (e^2*(b*d - a*e)*(a + b*x)^6)/(2*b^4) + (e^3*(a + b*x)^7)/(7*b^4)","A",3,2,29,0.06897,1,"{27, 43}"
1898,1,65,0,0.0666271,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 e (a+b x)^5 (b d-a e)}{5 b^3}+\frac{(a+b x)^4 (b d-a e)^2}{4 b^3}+\frac{e^2 (a+b x)^6}{6 b^3}","\frac{2 e (a+b x)^5 (b d-a e)}{5 b^3}+\frac{(a+b x)^4 (b d-a e)^2}{4 b^3}+\frac{e^2 (a+b x)^6}{6 b^3}",1,"((b*d - a*e)^2*(a + b*x)^4)/(4*b^3) + (2*e*(b*d - a*e)*(a + b*x)^5)/(5*b^3) + (e^2*(a + b*x)^6)/(6*b^3)","A",3,2,29,0.06897,1,"{27, 43}"
1899,1,38,0,0.0166393,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(a+b x)^4 (b d-a e)}{4 b^2}+\frac{e (a+b x)^5}{5 b^2}","\frac{(a+b x)^4 (b d-a e)}{4 b^2}+\frac{e (a+b x)^5}{5 b^2}",1,"((b*d - a*e)*(a + b*x)^4)/(4*b^2) + (e*(a + b*x)^5)/(5*b^2)","A",3,2,27,0.07407,1,"{27, 43}"
1900,1,14,0,0.0023068,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(a+b x)^4}{4 b}","\frac{(a+b x)^4}{4 b}",1,"(a + b*x)^4/(4*b)","A",2,2,22,0.09091,1,"{27, 32}"
1901,1,74,0,0.030184,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{d+e x} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x),x]","\frac{b x (b d-a e)^2}{e^3}-\frac{(a+b x)^2 (b d-a e)}{2 e^2}-\frac{(b d-a e)^3 \log (d+e x)}{e^4}+\frac{(a+b x)^3}{3 e}","\frac{b x (b d-a e)^2}{e^3}-\frac{(a+b x)^2 (b d-a e)}{2 e^2}-\frac{(b d-a e)^3 \log (d+e x)}{e^4}+\frac{(a+b x)^3}{3 e}",1,"(b*(b*d - a*e)^2*x)/e^3 - ((b*d - a*e)*(a + b*x)^2)/(2*e^2) + (a + b*x)^3/(3*e) - ((b*d - a*e)^3*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 43}"
1902,1,75,0,0.0617914,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^2} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^2,x]","-\frac{b^2 x (2 b d-3 a e)}{e^3}+\frac{(b d-a e)^3}{e^4 (d+e x)}+\frac{3 b (b d-a e)^2 \log (d+e x)}{e^4}+\frac{b^3 x^2}{2 e^2}","-\frac{b^2 x (2 b d-3 a e)}{e^3}+\frac{(b d-a e)^3}{e^4 (d+e x)}+\frac{3 b (b d-a e)^2 \log (d+e x)}{e^4}+\frac{b^3 x^2}{2 e^2}",1,"-((b^2*(2*b*d - 3*a*e)*x)/e^3) + (b^3*x^2)/(2*e^2) + (b*d - a*e)^3/(e^4*(d + e*x)) + (3*b*(b*d - a*e)^2*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 43}"
1903,1,78,0,0.0546046,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^3} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^3,x]","-\frac{3 b^2 (b d-a e) \log (d+e x)}{e^4}-\frac{3 b (b d-a e)^2}{e^4 (d+e x)}+\frac{(b d-a e)^3}{2 e^4 (d+e x)^2}+\frac{b^3 x}{e^3}","-\frac{3 b^2 (b d-a e) \log (d+e x)}{e^4}-\frac{3 b (b d-a e)^2}{e^4 (d+e x)}+\frac{(b d-a e)^3}{2 e^4 (d+e x)^2}+\frac{b^3 x}{e^3}",1,"(b^3*x)/e^3 + (b*d - a*e)^3/(2*e^4*(d + e*x)^2) - (3*b*(b*d - a*e)^2)/(e^4*(d + e*x)) - (3*b^2*(b*d - a*e)*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 43}"
1904,1,86,0,0.0572354,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^4} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^4,x]","\frac{3 b^2 (b d-a e)}{e^4 (d+e x)}-\frac{3 b (b d-a e)^2}{2 e^4 (d+e x)^2}+\frac{(b d-a e)^3}{3 e^4 (d+e x)^3}+\frac{b^3 \log (d+e x)}{e^4}","\frac{3 b^2 (b d-a e)}{e^4 (d+e x)}-\frac{3 b (b d-a e)^2}{2 e^4 (d+e x)^2}+\frac{(b d-a e)^3}{3 e^4 (d+e x)^3}+\frac{b^3 \log (d+e x)}{e^4}",1,"(b*d - a*e)^3/(3*e^4*(d + e*x)^3) - (3*b*(b*d - a*e)^2)/(2*e^4*(d + e*x)^2) + (3*b^2*(b*d - a*e))/(e^4*(d + e*x)) + (b^3*Log[d + e*x])/e^4","A",3,2,29,0.06897,1,"{27, 43}"
1905,1,143,0,0.3105295,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{5 b^4 (d+e x)^{11} (b d-a e)}{11 e^6}+\frac{b^3 (d+e x)^{10} (b d-a e)^2}{e^6}-\frac{10 b^2 (d+e x)^9 (b d-a e)^3}{9 e^6}+\frac{5 b (d+e x)^8 (b d-a e)^4}{8 e^6}-\frac{(d+e x)^7 (b d-a e)^5}{7 e^6}+\frac{b^5 (d+e x)^{12}}{12 e^6}","-\frac{5 b^4 (d+e x)^{11} (b d-a e)}{11 e^6}+\frac{b^3 (d+e x)^{10} (b d-a e)^2}{e^6}-\frac{10 b^2 (d+e x)^9 (b d-a e)^3}{9 e^6}+\frac{5 b (d+e x)^8 (b d-a e)^4}{8 e^6}-\frac{(d+e x)^7 (b d-a e)^5}{7 e^6}+\frac{b^5 (d+e x)^{12}}{12 e^6}",1,"-((b*d - a*e)^5*(d + e*x)^7)/(7*e^6) + (5*b*(b*d - a*e)^4*(d + e*x)^8)/(8*e^6) - (10*b^2*(b*d - a*e)^3*(d + e*x)^9)/(9*e^6) + (b^3*(b*d - a*e)^2*(d + e*x)^10)/e^6 - (5*b^4*(b*d - a*e)*(d + e*x)^11)/(11*e^6) + (b^5*(d + e*x)^12)/(12*e^6)","A",3,2,31,0.06452,1,"{27, 43}"
1906,1,146,0,0.2508527,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^4 (a+b x)^{10} (b d-a e)}{2 b^6}+\frac{10 e^3 (a+b x)^9 (b d-a e)^2}{9 b^6}+\frac{5 e^2 (a+b x)^8 (b d-a e)^3}{4 b^6}+\frac{5 e (a+b x)^7 (b d-a e)^4}{7 b^6}+\frac{(a+b x)^6 (b d-a e)^5}{6 b^6}+\frac{e^5 (a+b x)^{11}}{11 b^6}","\frac{e^4 (a+b x)^{10} (b d-a e)}{2 b^6}+\frac{10 e^3 (a+b x)^9 (b d-a e)^2}{9 b^6}+\frac{5 e^2 (a+b x)^8 (b d-a e)^3}{4 b^6}+\frac{5 e (a+b x)^7 (b d-a e)^4}{7 b^6}+\frac{(a+b x)^6 (b d-a e)^5}{6 b^6}+\frac{e^5 (a+b x)^{11}}{11 b^6}",1,"((b*d - a*e)^5*(a + b*x)^6)/(6*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^7)/(7*b^6) + (5*e^2*(b*d - a*e)^3*(a + b*x)^8)/(4*b^6) + (10*e^3*(b*d - a*e)^2*(a + b*x)^9)/(9*b^6) + (e^4*(b*d - a*e)*(a + b*x)^10)/(2*b^6) + (e^5*(a + b*x)^11)/(11*b^6)","A",3,2,31,0.06452,1,"{27, 43}"
1907,1,119,0,0.2158147,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{4 e^3 (a+b x)^9 (b d-a e)}{9 b^5}+\frac{3 e^2 (a+b x)^8 (b d-a e)^2}{4 b^5}+\frac{4 e (a+b x)^7 (b d-a e)^3}{7 b^5}+\frac{(a+b x)^6 (b d-a e)^4}{6 b^5}+\frac{e^4 (a+b x)^{10}}{10 b^5}","\frac{4 e^3 (a+b x)^9 (b d-a e)}{9 b^5}+\frac{3 e^2 (a+b x)^8 (b d-a e)^2}{4 b^5}+\frac{4 e (a+b x)^7 (b d-a e)^3}{7 b^5}+\frac{(a+b x)^6 (b d-a e)^4}{6 b^5}+\frac{e^4 (a+b x)^{10}}{10 b^5}",1,"((b*d - a*e)^4*(a + b*x)^6)/(6*b^5) + (4*e*(b*d - a*e)^3*(a + b*x)^7)/(7*b^5) + (3*e^2*(b*d - a*e)^2*(a + b*x)^8)/(4*b^5) + (4*e^3*(b*d - a*e)*(a + b*x)^9)/(9*b^5) + (e^4*(a + b*x)^10)/(10*b^5)","A",3,2,31,0.06452,1,"{27, 43}"
1908,1,92,0,0.1499655,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{3 e^2 (a+b x)^8 (b d-a e)}{8 b^4}+\frac{3 e (a+b x)^7 (b d-a e)^2}{7 b^4}+\frac{(a+b x)^6 (b d-a e)^3}{6 b^4}+\frac{e^3 (a+b x)^9}{9 b^4}","\frac{3 e^2 (a+b x)^8 (b d-a e)}{8 b^4}+\frac{3 e (a+b x)^7 (b d-a e)^2}{7 b^4}+\frac{(a+b x)^6 (b d-a e)^3}{6 b^4}+\frac{e^3 (a+b x)^9}{9 b^4}",1,"((b*d - a*e)^3*(a + b*x)^6)/(6*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^7)/(7*b^4) + (3*e^2*(b*d - a*e)*(a + b*x)^8)/(8*b^4) + (e^3*(a + b*x)^9)/(9*b^4)","A",3,2,31,0.06452,1,"{27, 43}"
1909,1,65,0,0.1052983,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{2 e (a+b x)^7 (b d-a e)}{7 b^3}+\frac{(a+b x)^6 (b d-a e)^2}{6 b^3}+\frac{e^2 (a+b x)^8}{8 b^3}","\frac{2 e (a+b x)^7 (b d-a e)}{7 b^3}+\frac{(a+b x)^6 (b d-a e)^2}{6 b^3}+\frac{e^2 (a+b x)^8}{8 b^3}",1,"((b*d - a*e)^2*(a + b*x)^6)/(6*b^3) + (2*e*(b*d - a*e)*(a + b*x)^7)/(7*b^3) + (e^2*(a + b*x)^8)/(8*b^3)","A",3,2,31,0.06452,1,"{27, 43}"
1910,1,38,0,0.0167707,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^6 (b d-a e)}{6 b^2}+\frac{e (a+b x)^7}{7 b^2}","\frac{(a+b x)^6 (b d-a e)}{6 b^2}+\frac{e (a+b x)^7}{7 b^2}",1,"((b*d - a*e)*(a + b*x)^6)/(6*b^2) + (e*(a + b*x)^7)/(7*b^2)","A",3,2,29,0.06897,1,"{27, 43}"
1911,1,14,0,0.0026455,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{(a+b x)^6}{6 b}","\frac{(a+b x)^6}{6 b}",1,"(a + b*x)^6/(6*b)","A",2,2,24,0.08333,1,"{27, 32}"
1912,1,122,0,0.055885,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{d+e x} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x),x]","\frac{b x (b d-a e)^4}{e^5}-\frac{(a+b x)^2 (b d-a e)^3}{2 e^4}+\frac{(a+b x)^3 (b d-a e)^2}{3 e^3}-\frac{(a+b x)^4 (b d-a e)}{4 e^2}-\frac{(b d-a e)^5 \log (d+e x)}{e^6}+\frac{(a+b x)^5}{5 e}","\frac{b x (b d-a e)^4}{e^5}-\frac{(a+b x)^2 (b d-a e)^3}{2 e^4}+\frac{(a+b x)^3 (b d-a e)^2}{3 e^3}-\frac{(a+b x)^4 (b d-a e)}{4 e^2}-\frac{(b d-a e)^5 \log (d+e x)}{e^6}+\frac{(a+b x)^5}{5 e}",1,"(b*(b*d - a*e)^4*x)/e^5 - ((b*d - a*e)^3*(a + b*x)^2)/(2*e^4) + ((b*d - a*e)^2*(a + b*x)^3)/(3*e^3) - ((b*d - a*e)*(a + b*x)^4)/(4*e^2) + (a + b*x)^5/(5*e) - ((b*d - a*e)^5*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 43}"
1913,1,130,0,0.1465145,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^2} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^2,x]","-\frac{5 b^4 (d+e x)^3 (b d-a e)}{3 e^6}+\frac{5 b^3 (d+e x)^2 (b d-a e)^2}{e^6}-\frac{10 b^2 x (b d-a e)^3}{e^5}+\frac{(b d-a e)^5}{e^6 (d+e x)}+\frac{5 b (b d-a e)^4 \log (d+e x)}{e^6}+\frac{b^5 (d+e x)^4}{4 e^6}","-\frac{5 b^4 (d+e x)^3 (b d-a e)}{3 e^6}+\frac{5 b^3 (d+e x)^2 (b d-a e)^2}{e^6}-\frac{10 b^2 x (b d-a e)^3}{e^5}+\frac{(b d-a e)^5}{e^6 (d+e x)}+\frac{5 b (b d-a e)^4 \log (d+e x)}{e^6}+\frac{b^5 (d+e x)^4}{4 e^6}",1,"(-10*b^2*(b*d - a*e)^3*x)/e^5 + (b*d - a*e)^5/(e^6*(d + e*x)) + (5*b^3*(b*d - a*e)^2*(d + e*x)^2)/e^6 - (5*b^4*(b*d - a*e)*(d + e*x)^3)/(3*e^6) + (b^5*(d + e*x)^4)/(4*e^6) + (5*b*(b*d - a*e)^4*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 43}"
1914,1,133,0,0.1271465,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^3} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^3,x]","-\frac{5 b^4 (d+e x)^2 (b d-a e)}{2 e^6}+\frac{10 b^3 x (b d-a e)^2}{e^5}-\frac{10 b^2 (b d-a e)^3 \log (d+e x)}{e^6}-\frac{5 b (b d-a e)^4}{e^6 (d+e x)}+\frac{(b d-a e)^5}{2 e^6 (d+e x)^2}+\frac{b^5 (d+e x)^3}{3 e^6}","-\frac{5 b^4 (d+e x)^2 (b d-a e)}{2 e^6}+\frac{10 b^3 x (b d-a e)^2}{e^5}-\frac{10 b^2 (b d-a e)^3 \log (d+e x)}{e^6}-\frac{5 b (b d-a e)^4}{e^6 (d+e x)}+\frac{(b d-a e)^5}{2 e^6 (d+e x)^2}+\frac{b^5 (d+e x)^3}{3 e^6}",1,"(10*b^3*(b*d - a*e)^2*x)/e^5 + (b*d - a*e)^5/(2*e^6*(d + e*x)^2) - (5*b*(b*d - a*e)^4)/(e^6*(d + e*x)) - (5*b^4*(b*d - a*e)*(d + e*x)^2)/(2*e^6) + (b^5*(d + e*x)^3)/(3*e^6) - (10*b^2*(b*d - a*e)^3*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 43}"
1915,1,130,0,0.1153163,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^4} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^4,x]","-\frac{b^4 x (4 b d-5 a e)}{e^5}+\frac{10 b^2 (b d-a e)^3}{e^6 (d+e x)}+\frac{10 b^3 (b d-a e)^2 \log (d+e x)}{e^6}-\frac{5 b (b d-a e)^4}{2 e^6 (d+e x)^2}+\frac{(b d-a e)^5}{3 e^6 (d+e x)^3}+\frac{b^5 x^2}{2 e^4}","-\frac{b^4 x (4 b d-5 a e)}{e^5}+\frac{10 b^2 (b d-a e)^3}{e^6 (d+e x)}+\frac{10 b^3 (b d-a e)^2 \log (d+e x)}{e^6}-\frac{5 b (b d-a e)^4}{2 e^6 (d+e x)^2}+\frac{(b d-a e)^5}{3 e^6 (d+e x)^3}+\frac{b^5 x^2}{2 e^4}",1,"-((b^4*(4*b*d - 5*a*e)*x)/e^5) + (b^5*x^2)/(2*e^4) + (b*d - a*e)^5/(3*e^6*(d + e*x)^3) - (5*b*(b*d - a*e)^4)/(2*e^6*(d + e*x)^2) + (10*b^2*(b*d - a*e)^3)/(e^6*(d + e*x)) + (10*b^3*(b*d - a*e)^2*Log[d + e*x])/e^6","A",3,2,31,0.06452,1,"{27, 43}"
1916,1,173,0,0.4411624,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{6 e^5 (a+b x)^{13} (b d-a e)}{13 b^7}+\frac{5 e^4 (a+b x)^{12} (b d-a e)^2}{4 b^7}+\frac{20 e^3 (a+b x)^{11} (b d-a e)^3}{11 b^7}+\frac{3 e^2 (a+b x)^{10} (b d-a e)^4}{2 b^7}+\frac{2 e (a+b x)^9 (b d-a e)^5}{3 b^7}+\frac{(a+b x)^8 (b d-a e)^6}{8 b^7}+\frac{e^6 (a+b x)^{14}}{14 b^7}","\frac{6 e^5 (a+b x)^{13} (b d-a e)}{13 b^7}+\frac{5 e^4 (a+b x)^{12} (b d-a e)^2}{4 b^7}+\frac{20 e^3 (a+b x)^{11} (b d-a e)^3}{11 b^7}+\frac{3 e^2 (a+b x)^{10} (b d-a e)^4}{2 b^7}+\frac{2 e (a+b x)^9 (b d-a e)^5}{3 b^7}+\frac{(a+b x)^8 (b d-a e)^6}{8 b^7}+\frac{e^6 (a+b x)^{14}}{14 b^7}",1,"((b*d - a*e)^6*(a + b*x)^8)/(8*b^7) + (2*e*(b*d - a*e)^5*(a + b*x)^9)/(3*b^7) + (3*e^2*(b*d - a*e)^4*(a + b*x)^10)/(2*b^7) + (20*e^3*(b*d - a*e)^3*(a + b*x)^11)/(11*b^7) + (5*e^4*(b*d - a*e)^2*(a + b*x)^12)/(4*b^7) + (6*e^5*(b*d - a*e)*(a + b*x)^13)/(13*b^7) + (e^6*(a + b*x)^14)/(14*b^7)","A",3,2,31,0.06452,1,"{27, 43}"
1917,1,143,0,0.3586803,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{5 e^4 (a+b x)^{12} (b d-a e)}{12 b^6}+\frac{10 e^3 (a+b x)^{11} (b d-a e)^2}{11 b^6}+\frac{e^2 (a+b x)^{10} (b d-a e)^3}{b^6}+\frac{5 e (a+b x)^9 (b d-a e)^4}{9 b^6}+\frac{(a+b x)^8 (b d-a e)^5}{8 b^6}+\frac{e^5 (a+b x)^{13}}{13 b^6}","\frac{5 e^4 (a+b x)^{12} (b d-a e)}{12 b^6}+\frac{10 e^3 (a+b x)^{11} (b d-a e)^2}{11 b^6}+\frac{e^2 (a+b x)^{10} (b d-a e)^3}{b^6}+\frac{5 e (a+b x)^9 (b d-a e)^4}{9 b^6}+\frac{(a+b x)^8 (b d-a e)^5}{8 b^6}+\frac{e^5 (a+b x)^{13}}{13 b^6}",1,"((b*d - a*e)^5*(a + b*x)^8)/(8*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^9)/(9*b^6) + (e^2*(b*d - a*e)^3*(a + b*x)^10)/b^6 + (10*e^3*(b*d - a*e)^2*(a + b*x)^11)/(11*b^6) + (5*e^4*(b*d - a*e)*(a + b*x)^12)/(12*b^6) + (e^5*(a + b*x)^13)/(13*b^6)","A",3,2,31,0.06452,1,"{27, 43}"
1918,1,119,0,0.2760494,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{4 e^3 (a+b x)^{11} (b d-a e)}{11 b^5}+\frac{3 e^2 (a+b x)^{10} (b d-a e)^2}{5 b^5}+\frac{4 e (a+b x)^9 (b d-a e)^3}{9 b^5}+\frac{(a+b x)^8 (b d-a e)^4}{8 b^5}+\frac{e^4 (a+b x)^{12}}{12 b^5}","\frac{4 e^3 (a+b x)^{11} (b d-a e)}{11 b^5}+\frac{3 e^2 (a+b x)^{10} (b d-a e)^2}{5 b^5}+\frac{4 e (a+b x)^9 (b d-a e)^3}{9 b^5}+\frac{(a+b x)^8 (b d-a e)^4}{8 b^5}+\frac{e^4 (a+b x)^{12}}{12 b^5}",1,"((b*d - a*e)^4*(a + b*x)^8)/(8*b^5) + (4*e*(b*d - a*e)^3*(a + b*x)^9)/(9*b^5) + (3*e^2*(b*d - a*e)^2*(a + b*x)^10)/(5*b^5) + (4*e^3*(b*d - a*e)*(a + b*x)^11)/(11*b^5) + (e^4*(a + b*x)^12)/(12*b^5)","A",3,2,31,0.06452,1,"{27, 43}"
1919,1,92,0,0.2200418,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{3 e^2 (a+b x)^{10} (b d-a e)}{10 b^4}+\frac{e (a+b x)^9 (b d-a e)^2}{3 b^4}+\frac{(a+b x)^8 (b d-a e)^3}{8 b^4}+\frac{e^3 (a+b x)^{11}}{11 b^4}","\frac{3 e^2 (a+b x)^{10} (b d-a e)}{10 b^4}+\frac{e (a+b x)^9 (b d-a e)^2}{3 b^4}+\frac{(a+b x)^8 (b d-a e)^3}{8 b^4}+\frac{e^3 (a+b x)^{11}}{11 b^4}",1,"((b*d - a*e)^3*(a + b*x)^8)/(8*b^4) + (e*(b*d - a*e)^2*(a + b*x)^9)/(3*b^4) + (3*e^2*(b*d - a*e)*(a + b*x)^10)/(10*b^4) + (e^3*(a + b*x)^11)/(11*b^4)","A",3,2,31,0.06452,1,"{27, 43}"
1920,1,65,0,0.1540445,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{2 e (a+b x)^9 (b d-a e)}{9 b^3}+\frac{(a+b x)^8 (b d-a e)^2}{8 b^3}+\frac{e^2 (a+b x)^{10}}{10 b^3}","\frac{2 e (a+b x)^9 (b d-a e)}{9 b^3}+\frac{(a+b x)^8 (b d-a e)^2}{8 b^3}+\frac{e^2 (a+b x)^{10}}{10 b^3}",1,"((b*d - a*e)^2*(a + b*x)^8)/(8*b^3) + (2*e*(b*d - a*e)*(a + b*x)^9)/(9*b^3) + (e^2*(a + b*x)^10)/(10*b^3)","A",3,2,31,0.06452,1,"{27, 43}"
1921,1,38,0,0.0175583,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^8 (b d-a e)}{8 b^2}+\frac{e (a+b x)^9}{9 b^2}","\frac{(a+b x)^8 (b d-a e)}{8 b^2}+\frac{e (a+b x)^9}{9 b^2}",1,"((b*d - a*e)*(a + b*x)^8)/(8*b^2) + (e*(a + b*x)^9)/(9*b^2)","A",3,2,29,0.06897,1,"{27, 43}"
1922,1,14,0,0.0025781,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a+b x)^8}{8 b}","\frac{(a+b x)^8}{8 b}",1,"(a + b*x)^8/(8*b)","A",2,2,24,0.08333,1,"{27, 32}"
1923,1,170,0,0.0826123,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{d+e x} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x),x]","\frac{b x (b d-a e)^6}{e^7}-\frac{(a+b x)^2 (b d-a e)^5}{2 e^6}+\frac{(a+b x)^3 (b d-a e)^4}{3 e^5}-\frac{(a+b x)^4 (b d-a e)^3}{4 e^4}+\frac{(a+b x)^5 (b d-a e)^2}{5 e^3}-\frac{(a+b x)^6 (b d-a e)}{6 e^2}-\frac{(b d-a e)^7 \log (d+e x)}{e^8}+\frac{(a+b x)^7}{7 e}","\frac{b x (b d-a e)^6}{e^7}-\frac{(a+b x)^2 (b d-a e)^5}{2 e^6}+\frac{(a+b x)^3 (b d-a e)^4}{3 e^5}-\frac{(a+b x)^4 (b d-a e)^3}{4 e^4}+\frac{(a+b x)^5 (b d-a e)^2}{5 e^3}-\frac{(a+b x)^6 (b d-a e)}{6 e^2}-\frac{(b d-a e)^7 \log (d+e x)}{e^8}+\frac{(a+b x)^7}{7 e}",1,"(b*(b*d - a*e)^6*x)/e^7 - ((b*d - a*e)^5*(a + b*x)^2)/(2*e^6) + ((b*d - a*e)^4*(a + b*x)^3)/(3*e^5) - ((b*d - a*e)^3*(a + b*x)^4)/(4*e^4) + ((b*d - a*e)^2*(a + b*x)^5)/(5*e^3) - ((b*d - a*e)*(a + b*x)^6)/(6*e^2) + (a + b*x)^7/(7*e) - ((b*d - a*e)^7*Log[d + e*x])/e^8","A",3,2,31,0.06452,1,"{27, 43}"
1924,1,186,0,0.2579073,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^2} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^2,x]","-\frac{7 b^6 (d+e x)^5 (b d-a e)}{5 e^8}+\frac{21 b^5 (d+e x)^4 (b d-a e)^2}{4 e^8}-\frac{35 b^4 (d+e x)^3 (b d-a e)^3}{3 e^8}+\frac{35 b^3 (d+e x)^2 (b d-a e)^4}{2 e^8}-\frac{21 b^2 x (b d-a e)^5}{e^7}+\frac{(b d-a e)^7}{e^8 (d+e x)}+\frac{7 b (b d-a e)^6 \log (d+e x)}{e^8}+\frac{b^7 (d+e x)^6}{6 e^8}","-\frac{7 b^6 (d+e x)^5 (b d-a e)}{5 e^8}+\frac{21 b^5 (d+e x)^4 (b d-a e)^2}{4 e^8}-\frac{35 b^4 (d+e x)^3 (b d-a e)^3}{3 e^8}+\frac{35 b^3 (d+e x)^2 (b d-a e)^4}{2 e^8}-\frac{21 b^2 x (b d-a e)^5}{e^7}+\frac{(b d-a e)^7}{e^8 (d+e x)}+\frac{7 b (b d-a e)^6 \log (d+e x)}{e^8}+\frac{b^7 (d+e x)^6}{6 e^8}",1,"(-21*b^2*(b*d - a*e)^5*x)/e^7 + (b*d - a*e)^7/(e^8*(d + e*x)) + (35*b^3*(b*d - a*e)^4*(d + e*x)^2)/(2*e^8) - (35*b^4*(b*d - a*e)^3*(d + e*x)^3)/(3*e^8) + (21*b^5*(b*d - a*e)^2*(d + e*x)^4)/(4*e^8) - (7*b^6*(b*d - a*e)*(d + e*x)^5)/(5*e^8) + (b^7*(d + e*x)^6)/(6*e^8) + (7*b*(b*d - a*e)^6*Log[d + e*x])/e^8","A",3,2,31,0.06452,1,"{27, 43}"
1925,1,185,0,0.2228201,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^3} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^3,x]","-\frac{7 b^6 (d+e x)^4 (b d-a e)}{4 e^8}+\frac{7 b^5 (d+e x)^3 (b d-a e)^2}{e^8}-\frac{35 b^4 (d+e x)^2 (b d-a e)^3}{2 e^8}+\frac{35 b^3 x (b d-a e)^4}{e^7}-\frac{21 b^2 (b d-a e)^5 \log (d+e x)}{e^8}-\frac{7 b (b d-a e)^6}{e^8 (d+e x)}+\frac{(b d-a e)^7}{2 e^8 (d+e x)^2}+\frac{b^7 (d+e x)^5}{5 e^8}","-\frac{7 b^6 (d+e x)^4 (b d-a e)}{4 e^8}+\frac{7 b^5 (d+e x)^3 (b d-a e)^2}{e^8}-\frac{35 b^4 (d+e x)^2 (b d-a e)^3}{2 e^8}+\frac{35 b^3 x (b d-a e)^4}{e^7}-\frac{21 b^2 (b d-a e)^5 \log (d+e x)}{e^8}-\frac{7 b (b d-a e)^6}{e^8 (d+e x)}+\frac{(b d-a e)^7}{2 e^8 (d+e x)^2}+\frac{b^7 (d+e x)^5}{5 e^8}",1,"(35*b^3*(b*d - a*e)^4*x)/e^7 + (b*d - a*e)^7/(2*e^8*(d + e*x)^2) - (7*b*(b*d - a*e)^6)/(e^8*(d + e*x)) - (35*b^4*(b*d - a*e)^3*(d + e*x)^2)/(2*e^8) + (7*b^5*(b*d - a*e)^2*(d + e*x)^3)/e^8 - (7*b^6*(b*d - a*e)*(d + e*x)^4)/(4*e^8) + (b^7*(d + e*x)^5)/(5*e^8) - (21*b^2*(b*d - a*e)^5*Log[d + e*x])/e^8","A",3,2,31,0.06452,1,"{27, 43}"
1926,1,187,0,0.2104898,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^4} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^4,x]","-\frac{7 b^6 (d+e x)^3 (b d-a e)}{3 e^8}+\frac{21 b^5 (d+e x)^2 (b d-a e)^2}{2 e^8}-\frac{35 b^4 x (b d-a e)^3}{e^7}+\frac{21 b^2 (b d-a e)^5}{e^8 (d+e x)}+\frac{35 b^3 (b d-a e)^4 \log (d+e x)}{e^8}-\frac{7 b (b d-a e)^6}{2 e^8 (d+e x)^2}+\frac{(b d-a e)^7}{3 e^8 (d+e x)^3}+\frac{b^7 (d+e x)^4}{4 e^8}","-\frac{7 b^6 (d+e x)^3 (b d-a e)}{3 e^8}+\frac{21 b^5 (d+e x)^2 (b d-a e)^2}{2 e^8}-\frac{35 b^4 x (b d-a e)^3}{e^7}+\frac{21 b^2 (b d-a e)^5}{e^8 (d+e x)}+\frac{35 b^3 (b d-a e)^4 \log (d+e x)}{e^8}-\frac{7 b (b d-a e)^6}{2 e^8 (d+e x)^2}+\frac{(b d-a e)^7}{3 e^8 (d+e x)^3}+\frac{b^7 (d+e x)^4}{4 e^8}",1,"(-35*b^4*(b*d - a*e)^3*x)/e^7 + (b*d - a*e)^7/(3*e^8*(d + e*x)^3) - (7*b*(b*d - a*e)^6)/(2*e^8*(d + e*x)^2) + (21*b^2*(b*d - a*e)^5)/(e^8*(d + e*x)) + (21*b^5*(b*d - a*e)^2*(d + e*x)^2)/(2*e^8) - (7*b^6*(b*d - a*e)*(d + e*x)^3)/(3*e^8) + (b^7*(d + e*x)^4)/(4*e^8) + (35*b^3*(b*d - a*e)^4*Log[d + e*x])/e^8","A",3,2,31,0.06452,1,"{27, 43}"
1927,1,97,0,0.041532,"\int \frac{(a+b x) (d+e x)^4}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e x (b d-a e)^3}{b^4}+\frac{(d+e x)^2 (b d-a e)^2}{2 b^3}+\frac{(d+e x)^3 (b d-a e)}{3 b^2}+\frac{(b d-a e)^4 \log (a+b x)}{b^5}+\frac{(d+e x)^4}{4 b}","\frac{e x (b d-a e)^3}{b^4}+\frac{(d+e x)^2 (b d-a e)^2}{2 b^3}+\frac{(d+e x)^3 (b d-a e)}{3 b^2}+\frac{(b d-a e)^4 \log (a+b x)}{b^5}+\frac{(d+e x)^4}{4 b}",1,"(e*(b*d - a*e)^3*x)/b^4 + ((b*d - a*e)^2*(d + e*x)^2)/(2*b^3) + ((b*d - a*e)*(d + e*x)^3)/(3*b^2) + (d + e*x)^4/(4*b) + ((b*d - a*e)^4*Log[a + b*x])/b^5","A",3,2,31,0.06452,1,"{27, 43}"
1928,1,73,0,0.0286476,"\int \frac{(a+b x) (d+e x)^3}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e x (b d-a e)^2}{b^3}+\frac{(d+e x)^2 (b d-a e)}{2 b^2}+\frac{(b d-a e)^3 \log (a+b x)}{b^4}+\frac{(d+e x)^3}{3 b}","\frac{e x (b d-a e)^2}{b^3}+\frac{(d+e x)^2 (b d-a e)}{2 b^2}+\frac{(b d-a e)^3 \log (a+b x)}{b^4}+\frac{(d+e x)^3}{3 b}",1,"(e*(b*d - a*e)^2*x)/b^3 + ((b*d - a*e)*(d + e*x)^2)/(2*b^2) + (d + e*x)^3/(3*b) + ((b*d - a*e)^3*Log[a + b*x])/b^4","A",3,2,31,0.06452,1,"{27, 43}"
1929,1,49,0,0.0201425,"\int \frac{(a+b x) (d+e x)^2}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{e x (b d-a e)}{b^2}+\frac{(b d-a e)^2 \log (a+b x)}{b^3}+\frac{(d+e x)^2}{2 b}","\frac{e x (b d-a e)}{b^2}+\frac{(b d-a e)^2 \log (a+b x)}{b^3}+\frac{(d+e x)^2}{2 b}",1,"(e*(b*d - a*e)*x)/b^2 + (d + e*x)^2/(2*b) + ((b*d - a*e)^2*Log[a + b*x])/b^3","A",3,2,31,0.06452,1,"{27, 43}"
1930,1,25,0,0.0205974,"\int \frac{(a+b x) (d+e x)}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{(b d-a e) \log (a+b x)}{b^2}+\frac{e x}{b}","\frac{(b d-a e) \log (a+b x)}{b^2}+\frac{e x}{b}",1,"(e*x)/b + ((b*d - a*e)*Log[a + b*x])/b^2","A",3,2,29,0.06897,1,"{27, 43}"
1931,1,10,0,0.0024471,"\int \frac{a+b x}{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{\log (a+b x)}{b}","\frac{\log (a+b x)}{b}",1,"Log[a + b*x]/b","A",2,2,24,0.08333,1,"{27, 31}"
1932,1,36,0,0.0078569,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{\log (a+b x)}{b d-a e}-\frac{\log (d+e x)}{b d-a e}","\frac{\log (a+b x)}{b d-a e}-\frac{\log (d+e x)}{b d-a e}",1,"Log[a + b*x]/(b*d - a*e) - Log[d + e*x]/(b*d - a*e)","A",4,3,31,0.09677,1,"{27, 36, 31}"
1933,1,56,0,0.0351825,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{1}{(d+e x) (b d-a e)}+\frac{b \log (a+b x)}{(b d-a e)^2}-\frac{b \log (d+e x)}{(b d-a e)^2}","\frac{1}{(d+e x) (b d-a e)}+\frac{b \log (a+b x)}{(b d-a e)^2}-\frac{b \log (d+e x)}{(b d-a e)^2}",1,"1/((b*d - a*e)*(d + e*x)) + (b*Log[a + b*x])/(b*d - a*e)^2 - (b*Log[d + e*x])/(b*d - a*e)^2","A",3,2,31,0.06452,1,"{27, 44}"
1934,1,82,0,0.0481985,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{b^2 \log (a+b x)}{(b d-a e)^3}-\frac{b^2 \log (d+e x)}{(b d-a e)^3}+\frac{b}{(d+e x) (b d-a e)^2}+\frac{1}{2 (d+e x)^2 (b d-a e)}","\frac{b^2 \log (a+b x)}{(b d-a e)^3}-\frac{b^2 \log (d+e x)}{(b d-a e)^3}+\frac{b}{(d+e x) (b d-a e)^2}+\frac{1}{2 (d+e x)^2 (b d-a e)}",1,"1/(2*(b*d - a*e)*(d + e*x)^2) + b/((b*d - a*e)^2*(d + e*x)) + (b^2*Log[a + b*x])/(b*d - a*e)^3 - (b^2*Log[d + e*x])/(b*d - a*e)^3","A",3,2,31,0.06452,1,"{27, 44}"
1935,1,106,0,0.0667677,"\int \frac{a+b x}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{b^2}{(d+e x) (b d-a e)^3}+\frac{b^3 \log (a+b x)}{(b d-a e)^4}-\frac{b^3 \log (d+e x)}{(b d-a e)^4}+\frac{b}{2 (d+e x)^2 (b d-a e)^2}+\frac{1}{3 (d+e x)^3 (b d-a e)}","\frac{b^2}{(d+e x) (b d-a e)^3}+\frac{b^3 \log (a+b x)}{(b d-a e)^4}-\frac{b^3 \log (d+e x)}{(b d-a e)^4}+\frac{b}{2 (d+e x)^2 (b d-a e)^2}+\frac{1}{3 (d+e x)^3 (b d-a e)}",1,"1/(3*(b*d - a*e)*(d + e*x)^3) + b/(2*(b*d - a*e)^2*(d + e*x)^2) + b^2/((b*d - a*e)^3*(d + e*x)) + (b^3*Log[a + b*x])/(b*d - a*e)^4 - (b^3*Log[d + e*x])/(b*d - a*e)^4","A",3,2,31,0.06452,1,"{27, 44}"
1936,1,102,0,0.0939681,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^3 x (4 b d-3 a e)}{b^4}+\frac{6 e^2 (b d-a e)^2 \log (a+b x)}{b^5}-\frac{4 e (b d-a e)^3}{b^5 (a+b x)}-\frac{(b d-a e)^4}{2 b^5 (a+b x)^2}+\frac{e^4 x^2}{2 b^3}","\frac{e^3 x (4 b d-3 a e)}{b^4}+\frac{6 e^2 (b d-a e)^2 \log (a+b x)}{b^5}-\frac{4 e (b d-a e)^3}{b^5 (a+b x)}-\frac{(b d-a e)^4}{2 b^5 (a+b x)^2}+\frac{e^4 x^2}{2 b^3}",1,"(e^3*(4*b*d - 3*a*e)*x)/b^4 + (e^4*x^2)/(2*b^3) - (b*d - a*e)^4/(2*b^5*(a + b*x)^2) - (4*e*(b*d - a*e)^3)/(b^5*(a + b*x)) + (6*e^2*(b*d - a*e)^2*Log[a + b*x])/b^5","A",3,2,31,0.06452,1,"{27, 43}"
1937,1,78,0,0.0639198,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{3 e^2 (b d-a e) \log (a+b x)}{b^4}-\frac{3 e (b d-a e)^2}{b^4 (a+b x)}-\frac{(b d-a e)^3}{2 b^4 (a+b x)^2}+\frac{e^3 x}{b^3}","\frac{3 e^2 (b d-a e) \log (a+b x)}{b^4}-\frac{3 e (b d-a e)^2}{b^4 (a+b x)}-\frac{(b d-a e)^3}{2 b^4 (a+b x)^2}+\frac{e^3 x}{b^3}",1,"(e^3*x)/b^3 - (b*d - a*e)^3/(2*b^4*(a + b*x)^2) - (3*e*(b*d - a*e)^2)/(b^4*(a + b*x)) + (3*e^2*(b*d - a*e)*Log[a + b*x])/b^4","A",3,2,31,0.06452,1,"{27, 43}"
1938,1,59,0,0.0442357,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 e (b d-a e)}{b^3 (a+b x)}-\frac{(b d-a e)^2}{2 b^3 (a+b x)^2}+\frac{e^2 \log (a+b x)}{b^3}","-\frac{2 e (b d-a e)}{b^3 (a+b x)}-\frac{(b d-a e)^2}{2 b^3 (a+b x)^2}+\frac{e^2 \log (a+b x)}{b^3}",1,"-(b*d - a*e)^2/(2*b^3*(a + b*x)^2) - (2*e*(b*d - a*e))/(b^3*(a + b*x)) + (e^2*Log[a + b*x])/b^3","A",3,2,31,0.06452,1,"{27, 43}"
1939,1,28,0,0.0043435,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{(d+e x)^2}{2 (a+b x)^2 (b d-a e)}","-\frac{(d+e x)^2}{2 (a+b x)^2 (b d-a e)}",1,"-(d + e*x)^2/(2*(b*d - a*e)*(a + b*x)^2)","A",2,2,29,0.06897,1,"{27, 37}"
1940,1,14,0,0.0024815,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{1}{2 b (a+b x)^2}","-\frac{1}{2 b (a+b x)^2}",1,"-1/(2*b*(a + b*x)^2)","A",2,2,24,0.08333,1,"{27, 32}"
1941,1,82,0,0.0513777,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{e^2 \log (a+b x)}{(b d-a e)^3}-\frac{e^2 \log (d+e x)}{(b d-a e)^3}+\frac{e}{(a+b x) (b d-a e)^2}-\frac{1}{2 (a+b x)^2 (b d-a e)}","\frac{e^2 \log (a+b x)}{(b d-a e)^3}-\frac{e^2 \log (d+e x)}{(b d-a e)^3}+\frac{e}{(a+b x) (b d-a e)^2}-\frac{1}{2 (a+b x)^2 (b d-a e)}",1,"-1/(2*(b*d - a*e)*(a + b*x)^2) + e/((b*d - a*e)^2*(a + b*x)) + (e^2*Log[a + b*x])/(b*d - a*e)^3 - (e^2*Log[d + e*x])/(b*d - a*e)^3","A",3,2,31,0.06452,1,"{27, 44}"
1942,1,109,0,0.0740146,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{e^2}{(d+e x) (b d-a e)^3}+\frac{3 b e^2 \log (a+b x)}{(b d-a e)^4}-\frac{3 b e^2 \log (d+e x)}{(b d-a e)^4}+\frac{2 b e}{(a+b x) (b d-a e)^3}-\frac{b}{2 (a+b x)^2 (b d-a e)^2}","\frac{e^2}{(d+e x) (b d-a e)^3}+\frac{3 b e^2 \log (a+b x)}{(b d-a e)^4}-\frac{3 b e^2 \log (d+e x)}{(b d-a e)^4}+\frac{2 b e}{(a+b x) (b d-a e)^3}-\frac{b}{2 (a+b x)^2 (b d-a e)^2}",1,"-b/(2*(b*d - a*e)^2*(a + b*x)^2) + (2*b*e)/((b*d - a*e)^3*(a + b*x)) + e^2/((b*d - a*e)^3*(d + e*x)) + (3*b*e^2*Log[a + b*x])/(b*d - a*e)^4 - (3*b*e^2*Log[d + e*x])/(b*d - a*e)^4","A",3,2,31,0.06452,1,"{27, 44}"
1943,1,143,0,0.1099097,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{6 b^2 e^2 \log (a+b x)}{(b d-a e)^5}-\frac{6 b^2 e^2 \log (d+e x)}{(b d-a e)^5}+\frac{3 b^2 e}{(a+b x) (b d-a e)^4}-\frac{b^2}{2 (a+b x)^2 (b d-a e)^3}+\frac{3 b e^2}{(d+e x) (b d-a e)^4}+\frac{e^2}{2 (d+e x)^2 (b d-a e)^3}","\frac{6 b^2 e^2 \log (a+b x)}{(b d-a e)^5}-\frac{6 b^2 e^2 \log (d+e x)}{(b d-a e)^5}+\frac{3 b^2 e}{(a+b x) (b d-a e)^4}-\frac{b^2}{2 (a+b x)^2 (b d-a e)^3}+\frac{3 b e^2}{(d+e x) (b d-a e)^4}+\frac{e^2}{2 (d+e x)^2 (b d-a e)^3}",1,"-b^2/(2*(b*d - a*e)^3*(a + b*x)^2) + (3*b^2*e)/((b*d - a*e)^4*(a + b*x)) + e^2/(2*(b*d - a*e)^3*(d + e*x)^2) + (3*b*e^2)/((b*d - a*e)^4*(d + e*x)) + (6*b^2*e^2*Log[a + b*x])/(b*d - a*e)^5 - (6*b^2*e^2*Log[d + e*x])/(b*d - a*e)^5","A",3,2,31,0.06452,1,"{27, 44}"
1944,1,170,0,0.152842,"\int \frac{a+b x}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{6 b^2 e^2}{(d+e x) (b d-a e)^5}+\frac{10 b^3 e^2 \log (a+b x)}{(b d-a e)^6}-\frac{10 b^3 e^2 \log (d+e x)}{(b d-a e)^6}+\frac{4 b^3 e}{(a+b x) (b d-a e)^5}-\frac{b^3}{2 (a+b x)^2 (b d-a e)^4}+\frac{3 b e^2}{2 (d+e x)^2 (b d-a e)^4}+\frac{e^2}{3 (d+e x)^3 (b d-a e)^3}","\frac{6 b^2 e^2}{(d+e x) (b d-a e)^5}+\frac{10 b^3 e^2 \log (a+b x)}{(b d-a e)^6}-\frac{10 b^3 e^2 \log (d+e x)}{(b d-a e)^6}+\frac{4 b^3 e}{(a+b x) (b d-a e)^5}-\frac{b^3}{2 (a+b x)^2 (b d-a e)^4}+\frac{3 b e^2}{2 (d+e x)^2 (b d-a e)^4}+\frac{e^2}{3 (d+e x)^3 (b d-a e)^3}",1,"-b^3/(2*(b*d - a*e)^4*(a + b*x)^2) + (4*b^3*e)/((b*d - a*e)^5*(a + b*x)) + e^2/(3*(b*d - a*e)^3*(d + e*x)^3) + (3*b*e^2)/(2*(b*d - a*e)^4*(d + e*x)^2) + (6*b^2*e^2)/((b*d - a*e)^5*(d + e*x)) + (10*b^3*e^2*Log[a + b*x])/(b*d - a*e)^6 - (10*b^3*e^2*Log[d + e*x])/(b*d - a*e)^6","A",3,2,31,0.06452,1,"{27, 44}"
1945,1,111,0,0.099135,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{4 e^3 (b d-a e)}{b^5 (a+b x)}-\frac{3 e^2 (b d-a e)^2}{b^5 (a+b x)^2}-\frac{4 e (b d-a e)^3}{3 b^5 (a+b x)^3}-\frac{(b d-a e)^4}{4 b^5 (a+b x)^4}+\frac{e^4 \log (a+b x)}{b^5}","-\frac{4 e^3 (b d-a e)}{b^5 (a+b x)}-\frac{3 e^2 (b d-a e)^2}{b^5 (a+b x)^2}-\frac{4 e (b d-a e)^3}{3 b^5 (a+b x)^3}-\frac{(b d-a e)^4}{4 b^5 (a+b x)^4}+\frac{e^4 \log (a+b x)}{b^5}",1,"-(b*d - a*e)^4/(4*b^5*(a + b*x)^4) - (4*e*(b*d - a*e)^3)/(3*b^5*(a + b*x)^3) - (3*e^2*(b*d - a*e)^2)/(b^5*(a + b*x)^2) - (4*e^3*(b*d - a*e))/(b^5*(a + b*x)) + (e^4*Log[a + b*x])/b^5","A",3,2,31,0.06452,1,"{27, 43}"
1946,1,28,0,0.0045802,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{(d+e x)^4}{4 (a+b x)^4 (b d-a e)}","-\frac{(d+e x)^4}{4 (a+b x)^4 (b d-a e)}",1,"-(d + e*x)^4/(4*(b*d - a*e)*(a + b*x)^4)","A",2,2,31,0.06452,1,"{27, 37}"
1947,1,65,0,0.04153,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 e (b d-a e)}{3 b^3 (a+b x)^3}-\frac{(b d-a e)^2}{4 b^3 (a+b x)^4}-\frac{e^2}{2 b^3 (a+b x)^2}","-\frac{2 e (b d-a e)}{3 b^3 (a+b x)^3}-\frac{(b d-a e)^2}{4 b^3 (a+b x)^4}-\frac{e^2}{2 b^3 (a+b x)^2}",1,"-(b*d - a*e)^2/(4*b^3*(a + b*x)^4) - (2*e*(b*d - a*e))/(3*b^3*(a + b*x)^3) - e^2/(2*b^3*(a + b*x)^2)","A",3,2,31,0.06452,1,"{27, 43}"
1948,1,38,0,0.0241647,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{b d-a e}{4 b^2 (a+b x)^4}-\frac{e}{3 b^2 (a+b x)^3}","-\frac{b d-a e}{4 b^2 (a+b x)^4}-\frac{e}{3 b^2 (a+b x)^3}",1,"-(b*d - a*e)/(4*b^2*(a + b*x)^4) - e/(3*b^2*(a + b*x)^3)","A",3,2,29,0.06897,1,"{27, 43}"
1949,1,14,0,0.002937,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{1}{4 b (a+b x)^4}","-\frac{1}{4 b (a+b x)^4}",1,"-1/(4*b*(a + b*x)^4)","A",2,2,24,0.08333,1,"{27, 32}"
1950,1,130,0,0.0850072,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{e^3}{(a+b x) (b d-a e)^4}-\frac{e^2}{2 (a+b x)^2 (b d-a e)^3}+\frac{e^4 \log (a+b x)}{(b d-a e)^5}-\frac{e^4 \log (d+e x)}{(b d-a e)^5}+\frac{e}{3 (a+b x)^3 (b d-a e)^2}-\frac{1}{4 (a+b x)^4 (b d-a e)}","\frac{e^3}{(a+b x) (b d-a e)^4}-\frac{e^2}{2 (a+b x)^2 (b d-a e)^3}+\frac{e^4 \log (a+b x)}{(b d-a e)^5}-\frac{e^4 \log (d+e x)}{(b d-a e)^5}+\frac{e}{3 (a+b x)^3 (b d-a e)^2}-\frac{1}{4 (a+b x)^4 (b d-a e)}",1,"-1/(4*(b*d - a*e)*(a + b*x)^4) + e/(3*(b*d - a*e)^2*(a + b*x)^3) - e^2/(2*(b*d - a*e)^3*(a + b*x)^2) + e^3/((b*d - a*e)^4*(a + b*x)) + (e^4*Log[a + b*x])/(b*d - a*e)^5 - (e^4*Log[d + e*x])/(b*d - a*e)^5","A",3,2,31,0.06452,1,"{27, 44}"
1951,1,159,0,0.1378117,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{e^4}{(d+e x) (b d-a e)^5}+\frac{4 b e^3}{(a+b x) (b d-a e)^5}-\frac{3 b e^2}{2 (a+b x)^2 (b d-a e)^4}+\frac{5 b e^4 \log (a+b x)}{(b d-a e)^6}-\frac{5 b e^4 \log (d+e x)}{(b d-a e)^6}+\frac{2 b e}{3 (a+b x)^3 (b d-a e)^3}-\frac{b}{4 (a+b x)^4 (b d-a e)^2}","\frac{e^4}{(d+e x) (b d-a e)^5}+\frac{4 b e^3}{(a+b x) (b d-a e)^5}-\frac{3 b e^2}{2 (a+b x)^2 (b d-a e)^4}+\frac{5 b e^4 \log (a+b x)}{(b d-a e)^6}-\frac{5 b e^4 \log (d+e x)}{(b d-a e)^6}+\frac{2 b e}{3 (a+b x)^3 (b d-a e)^3}-\frac{b}{4 (a+b x)^4 (b d-a e)^2}",1,"-b/(4*(b*d - a*e)^2*(a + b*x)^4) + (2*b*e)/(3*(b*d - a*e)^3*(a + b*x)^3) - (3*b*e^2)/(2*(b*d - a*e)^4*(a + b*x)^2) + (4*b*e^3)/((b*d - a*e)^5*(a + b*x)) + e^4/((b*d - a*e)^5*(d + e*x)) + (5*b*e^4*Log[a + b*x])/(b*d - a*e)^6 - (5*b*e^4*Log[d + e*x])/(b*d - a*e)^6","A",3,2,31,0.06452,1,"{27, 44}"
1952,1,192,0,0.1917082,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{10 b^2 e^3}{(a+b x) (b d-a e)^6}-\frac{3 b^2 e^2}{(a+b x)^2 (b d-a e)^5}+\frac{15 b^2 e^4 \log (a+b x)}{(b d-a e)^7}-\frac{15 b^2 e^4 \log (d+e x)}{(b d-a e)^7}+\frac{b^2 e}{(a+b x)^3 (b d-a e)^4}-\frac{b^2}{4 (a+b x)^4 (b d-a e)^3}+\frac{5 b e^4}{(d+e x) (b d-a e)^6}+\frac{e^4}{2 (d+e x)^2 (b d-a e)^5}","\frac{10 b^2 e^3}{(a+b x) (b d-a e)^6}-\frac{3 b^2 e^2}{(a+b x)^2 (b d-a e)^5}+\frac{15 b^2 e^4 \log (a+b x)}{(b d-a e)^7}-\frac{15 b^2 e^4 \log (d+e x)}{(b d-a e)^7}+\frac{b^2 e}{(a+b x)^3 (b d-a e)^4}-\frac{b^2}{4 (a+b x)^4 (b d-a e)^3}+\frac{5 b e^4}{(d+e x) (b d-a e)^6}+\frac{e^4}{2 (d+e x)^2 (b d-a e)^5}",1,"-b^2/(4*(b*d - a*e)^3*(a + b*x)^4) + (b^2*e)/((b*d - a*e)^4*(a + b*x)^3) - (3*b^2*e^2)/((b*d - a*e)^5*(a + b*x)^2) + (10*b^2*e^3)/((b*d - a*e)^6*(a + b*x)) + e^4/(2*(b*d - a*e)^5*(d + e*x)^2) + (5*b*e^4)/((b*d - a*e)^6*(d + e*x)) + (15*b^2*e^4*Log[a + b*x])/(b*d - a*e)^7 - (15*b^2*e^4*Log[d + e*x])/(b*d - a*e)^7","A",3,2,31,0.06452,1,"{27, 44}"
1953,1,222,0,0.2614913,"\int \frac{a+b x}{(d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/((d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{15 b^2 e^4}{(d+e x) (b d-a e)^7}+\frac{20 b^3 e^3}{(a+b x) (b d-a e)^7}-\frac{5 b^3 e^2}{(a+b x)^2 (b d-a e)^6}+\frac{35 b^3 e^4 \log (a+b x)}{(b d-a e)^8}-\frac{35 b^3 e^4 \log (d+e x)}{(b d-a e)^8}+\frac{4 b^3 e}{3 (a+b x)^3 (b d-a e)^5}-\frac{b^3}{4 (a+b x)^4 (b d-a e)^4}+\frac{5 b e^4}{2 (d+e x)^2 (b d-a e)^6}+\frac{e^4}{3 (d+e x)^3 (b d-a e)^5}","\frac{15 b^2 e^4}{(d+e x) (b d-a e)^7}+\frac{20 b^3 e^3}{(a+b x) (b d-a e)^7}-\frac{5 b^3 e^2}{(a+b x)^2 (b d-a e)^6}+\frac{35 b^3 e^4 \log (a+b x)}{(b d-a e)^8}-\frac{35 b^3 e^4 \log (d+e x)}{(b d-a e)^8}+\frac{4 b^3 e}{3 (a+b x)^3 (b d-a e)^5}-\frac{b^3}{4 (a+b x)^4 (b d-a e)^4}+\frac{5 b e^4}{2 (d+e x)^2 (b d-a e)^6}+\frac{e^4}{3 (d+e x)^3 (b d-a e)^5}",1,"-b^3/(4*(b*d - a*e)^4*(a + b*x)^4) + (4*b^3*e)/(3*(b*d - a*e)^5*(a + b*x)^3) - (5*b^3*e^2)/((b*d - a*e)^6*(a + b*x)^2) + (20*b^3*e^3)/((b*d - a*e)^7*(a + b*x)) + e^4/(3*(b*d - a*e)^5*(d + e*x)^3) + (5*b*e^4)/(2*(b*d - a*e)^6*(d + e*x)^2) + (15*b^2*e^4)/((b*d - a*e)^7*(d + e*x)) + (35*b^3*e^4*Log[a + b*x])/(b*d - a*e)^8 - (35*b^3*e^4*Log[d + e*x])/(b*d - a*e)^8","A",3,2,31,0.06452,1,"{27, 44}"
1954,1,146,0,0.1520573,"\int (a+b x) (d+e x)^5 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8}{8 e^3 (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)}{7 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^2}{6 e^3 (a+b x)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8}{8 e^3 (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)}{7 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^2}{6 e^3 (a+b x)}",1,"((b*d - a*e)^2*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^3*(a + b*x)) - (2*b*(b*d - a*e)*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x)) + (b^2*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^3*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1955,1,146,0,0.1328877,"\int (a+b x) (d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7}{7 e^3 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)}{3 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)^2}{5 e^3 (a+b x)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7}{7 e^3 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)}{3 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)^2}{5 e^3 (a+b x)}",1,"((b*d - a*e)^2*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) - (b*(b*d - a*e)*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)) + (b^2*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1956,1,146,0,0.1085167,"\int (a+b x) (d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6}{6 e^3 (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)}{5 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e)^2}{4 e^3 (a+b x)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6}{6 e^3 (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5 (b d-a e)}{5 e^3 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e)^2}{4 e^3 (a+b x)}",1,"((b*d - a*e)^2*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)) - (2*b*(b*d - a*e)*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) + (b^2*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^3*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1957,1,125,0,0.0969148,"\int (a+b x) (d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (b d-a e)}{2 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^2 (b d-a e)^2}{3 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{5 b^3}","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3 (b d-a e)}{2 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^2 (b d-a e)^2}{3 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{5 b^3}",1,"((b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^3) + (e*(b*d - a*e)*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^3) + (e^2*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^3)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1958,1,78,0,0.0578095,"\int (a+b x) (d+e x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^2 (b d-a e)}{3 b^2}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{4 b^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^2 (b d-a e)}{3 b^2}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^3}{4 b^2}",1,"((b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^2) + (e*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^2)","A",4,3,31,0.09677,1,"{770, 21, 43}"
1959,1,27,0,0.0077252,"\int (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 b}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(3*b)","A",1,1,26,0.03846,1,"{629}"
1960,1,122,0,0.0683175,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{d+e x} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x),x]","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^3 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 e}","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^2 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^3 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{2 e}",1,"-((b*(b*d - a*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x))) + ((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e) + ((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^3*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1961,1,132,0,0.0791044,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^2} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^2,x]","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^3 (a+b x) (d+e x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^3 (a+b x)}+\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^2 (a+b x)}","-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^3 (a+b x) (d+e x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^3 (a+b x)}+\frac{b^2 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^2 (a+b x)}",1,"(b^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^2*(a + b*x)) - ((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*(d + e*x)) - (2*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^3*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1962,1,140,0,0.0813509,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^3} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^3,x]","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^3 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^3 (a+b x) (d+e x)^2}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^3 (a+b x)}","\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^3 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^3 (a+b x) (d+e x)^2}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^3 (a+b x)}",1,"-((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)*(d + e*x)^2) + (2*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*(d + e*x)) + (b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^3*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1963,1,41,0,0.0226825,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^4} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^4,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 (d+e x)^3 (b d-a e)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{3 (d+e x)^3 (b d-a e)}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(3/2)/(3*(b*d - a*e)*(d + e*x)^3)","A",1,1,33,0.03030,1,"{767}"
1964,1,146,0,0.0822581,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^5} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^5,x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x) (d+e x)^2}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^3 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^3 (a+b x) (d+e x)^4}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x) (d+e x)^2}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^3 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^3 (a+b x) (d+e x)^4}",1,"-((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)*(d + e*x)^4) + (2*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^3) - (b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)*(d + e*x)^2)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1965,1,146,0,0.080889,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^6} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^6,x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^3 (a+b x) (d+e x)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^3 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^3 (a+b x) (d+e x)^5}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^3 (a+b x) (d+e x)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^3 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^3 (a+b x) (d+e x)^5}",1,"-((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^5) + (b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)*(d + e*x)^4) - (b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^3)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1966,1,146,0,0.080806,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^7} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^7,x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^3 (a+b x) (d+e x)^4}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^3 (a+b x) (d+e x)^5}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{6 e^3 (a+b x) (d+e x)^6}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^3 (a+b x) (d+e x)^4}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^3 (a+b x) (d+e x)^5}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{6 e^3 (a+b x) (d+e x)^6}",1,"-((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^3*(a + b*x)*(d + e*x)^6) + (2*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^5) - (b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3*(a + b*x)*(d + e*x)^4)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1967,1,146,0,0.0803163,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^8} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^8,x]","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^3 (a+b x) (d+e x)^5}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^3 (a+b x) (d+e x)^6}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^3 (a+b x) (d+e x)^7}","-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^3 (a+b x) (d+e x)^5}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^3 (a+b x) (d+e x)^6}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^3 (a+b x) (d+e x)^7}",1,"-((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x)*(d + e*x)^7) + (b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^6) - (b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^5)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1968,1,254,0,0.3518997,"\int (a+b x) (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12}}{12 e^5 (a+b x)}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)}{11 e^5 (a+b x)}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^2}{5 e^5 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^3}{9 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^4}{8 e^5 (a+b x)}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12}}{12 e^5 (a+b x)}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)}{11 e^5 (a+b x)}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^2}{5 e^5 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^3}{9 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^4}{8 e^5 (a+b x)}",1,"((b*d - a*e)^4*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)) - (4*b*(b*d - a*e)^3*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (3*b^2*(b*d - a*e)^2*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) - (4*b^3*(b*d - a*e)*(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)) + (b^4*(d + e*x)^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1969,1,254,0,0.3033808,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11}}{11 e^5 (a+b x)}-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)}{5 e^5 (a+b x)}+\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^2}{3 e^5 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^3}{2 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^4}{7 e^5 (a+b x)}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11}}{11 e^5 (a+b x)}-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)}{5 e^5 (a+b x)}+\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^2}{3 e^5 (a+b x)}-\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^3}{2 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^4}{7 e^5 (a+b x)}",1,"((b*d - a*e)^4*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (b*(b*d - a*e)^3*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)) + (2*b^2*(b*d - a*e)^2*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - (2*b^3*(b*d - a*e)*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) + (b^4*(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1970,1,254,0,0.270866,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10}}{10 e^5 (a+b x)}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)}{9 e^5 (a+b x)}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^2}{4 e^5 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^3}{7 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^4}{6 e^5 (a+b x)}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10}}{10 e^5 (a+b x)}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)}{9 e^5 (a+b x)}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^2}{4 e^5 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^7 (b d-a e)^3}{7 e^5 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^6 (b d-a e)^4}{6 e^5 (a+b x)}",1,"((b*d - a*e)^4*(d + e*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)) - (4*b*(b*d - a*e)^3*(d + e*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) + (3*b^2*(b*d - a*e)^2*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^5*(a + b*x)) - (4*b^3*(b*d - a*e)*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (b^4*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1971,1,219,0,0.2181027,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)}{2 b^5}+\frac{6 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2}{7 b^5}+\frac{2 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^3}{3 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^4}{5 b^5}+\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^5}","\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)}{2 b^5}+\frac{6 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2}{7 b^5}+\frac{2 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^3}{3 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^4}{5 b^5}+\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^5}",1,"((b*d - a*e)^4*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^5) + (2*e*(b*d - a*e)^3*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^5) + (6*e^2*(b*d - a*e)^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) + (e^3*(b*d - a*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^5) + (e^4*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^5)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1972,1,172,0,0.1797329,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{3 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)}{7 b^4}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^2}{2 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^3}{5 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^4}","\frac{3 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)}{7 b^4}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)^2}{2 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^3}{5 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^4}",1,"((b*d - a*e)^3*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^4) + (e*(b*d - a*e)^2*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^4) + (3*e^2*(b*d - a*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4) + (e^3*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^4)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1973,1,125,0,0.1348941,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)}{3 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^2}{5 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^3}","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5 (b d-a e)}{3 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)^2}{5 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{7 b^3}",1,"((b*d - a*e)^2*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^3) + (e*(b*d - a*e)*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^3) + (e^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^3)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1974,1,78,0,0.04521,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)}{5 b^2}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4 (b d-a e)}{5 b^2}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^5}{6 b^2}",1,"((b*d - a*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^2) + (e*(a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*b^2)","A",4,3,31,0.09677,1,"{770, 21, 43}"
1975,1,27,0,0.0076531,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 b}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(5*b)","A",1,1,26,0.03846,1,"{629}"
1976,1,210,0,0.1025287,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{d+e x} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x),x]","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^4 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^3}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x)}{e^5 (a+b x)}+\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e}","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^4 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^3}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x)}{e^5 (a+b x)}+\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e}",1,"-((b*(b*d - a*e)^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x))) + ((b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3) - ((b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^2) + ((a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e) + ((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1977,1,239,0,0.1632604,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^2,x]","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^5 (a+b x)}-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}{e^5 (a+b x)}+\frac{6 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^5 (a+b x) (d+e x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^5 (a+b x)}","\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^5 (a+b x)}-\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}{e^5 (a+b x)}+\frac{6 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^4 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^5 (a+b x) (d+e x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^5 (a+b x)}",1,"(6*b^2*(b*d - a*e)^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) - ((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) - (2*b^3*(b*d - a*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + (b^4*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - (4*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1978,1,238,0,0.1490628,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^3,x]","-\frac{b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (3 b d-4 a e)}{e^4 (a+b x)}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^5 (a+b x) (d+e x)^2}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^5 (a+b x)}+\frac{b^4 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x)}","-\frac{b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (3 b d-4 a e)}{e^4 (a+b x)}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^5 (a+b x) (d+e x)^2}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^5 (a+b x)}+\frac{b^4 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^3 (a+b x)}",1,"-((b^3*(3*b*d - 4*a*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x))) + (b^4*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^3*(a + b*x)) - ((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^2) + (4*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) + (6*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1979,1,238,0,0.1396298,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^4,x]","-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^5 (a+b x) (d+e x)^3}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^5 (a+b x)}+\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x)}","-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^5 (a+b x) (d+e x)^3}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^5 (a+b x)}+\frac{b^4 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^4 (a+b x)}",1,"(b^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^4*(a + b*x)) - ((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^3) + (2*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)^2) - (6*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) - (4*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1980,1,246,0,0.135284,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^5,x]","\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^5 (a+b x) (d+e x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)^2}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^5 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^5 (a+b x) (d+e x)^4}+\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^5 (a+b x)}","\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^5 (a+b x) (d+e x)}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)^2}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^5 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^5 (a+b x) (d+e x)^4}+\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^5 (a+b x)}",1,"-((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^5*(a + b*x)*(d + e*x)^4) + (4*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^3) - (3*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)^2) + (4*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)) + (b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^5*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1981,1,41,0,0.0232639,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^6,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 (d+e x)^5 (b d-a e)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{5 (d+e x)^5 (b d-a e)}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(5/2)/(5*(b*d - a*e)*(d + e*x)^5)","A",1,1,33,0.03030,1,"{767}"
1982,1,98,0,0.0520627,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^7,x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{30 (d+e x)^5 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{6 (d+e x)^6 (b d-a e)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{30 (d+e x)^5 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{6 (d+e x)^6 (b d-a e)}",1,"((a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*(b*d - a*e)*(d + e*x)^6) + (b*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(30*(b*d - a*e)^2*(d + e*x)^5)","A",4,4,33,0.1212,1,"{770, 21, 45, 37}"
1983,1,149,0,0.0655807,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^8} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^8,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{105 (d+e x)^5 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{21 (d+e x)^6 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{7 (d+e x)^7 (b d-a e)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{105 (d+e x)^5 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{21 (d+e x)^6 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^4}{7 (d+e x)^7 (b d-a e)}",1,"((a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*(b*d - a*e)*(d + e*x)^7) + (b*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(21*(b*d - a*e)^2*(d + e*x)^6) + (b^2*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(105*(b*d - a*e)^3*(d + e*x)^5)","A",5,4,33,0.1212,1,"{770, 21, 45, 37}"
1984,1,252,0,0.1306779,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^9} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^9,x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^5 (a+b x) (d+e x)^4}+\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^5 (a+b x) (d+e x)^5}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)^6}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^5 (a+b x) (d+e x)^7}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{8 e^5 (a+b x) (d+e x)^8}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{4 e^5 (a+b x) (d+e x)^4}+\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^5 (a+b x) (d+e x)^5}-\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)^6}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^5 (a+b x) (d+e x)^7}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{8 e^5 (a+b x) (d+e x)^8}",1,"-((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^5*(a + b*x)*(d + e*x)^8) + (4*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) - (b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)^6) + (4*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^5) - (b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^5*(a + b*x)*(d + e*x)^4)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1985,1,254,0,0.1318842,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{10}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^10,x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^5 (a+b x) (d+e x)^5}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^5 (a+b x) (d+e x)^6}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^5 (a+b x) (d+e x)^7}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^5 (a+b x) (d+e x)^8}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^5 (a+b x) (d+e x)^9}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^5 (a+b x) (d+e x)^5}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^5 (a+b x) (d+e x)^6}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^5 (a+b x) (d+e x)^7}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^5 (a+b x) (d+e x)^8}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^5 (a+b x) (d+e x)^9}",1,"-((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)*(d + e*x)^9) + (b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^8) - (6*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) + (2*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^6) - (b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^5)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1986,1,254,0,0.1364274,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{11}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^11,x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^5 (a+b x) (d+e x)^6}+\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{7 e^5 (a+b x) (d+e x)^7}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^5 (a+b x) (d+e x)^8}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^5 (a+b x) (d+e x)^9}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{10 e^5 (a+b x) (d+e x)^{10}}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^5 (a+b x) (d+e x)^6}+\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{7 e^5 (a+b x) (d+e x)^7}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^5 (a+b x) (d+e x)^8}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^5 (a+b x) (d+e x)^9}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{10 e^5 (a+b x) (d+e x)^{10}}",1,"-((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^5*(a + b*x)*(d + e*x)^10) + (4*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)*(d + e*x)^9) - (3*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^5*(a + b*x)*(d + e*x)^8) + (4*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7) - (b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^5*(a + b*x)*(d + e*x)^6)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1987,1,254,0,0.1333956,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{12}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^12,x]","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^5 (a+b x) (d+e x)^7}+\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^5 (a+b x) (d+e x)^8}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^5 (a+b x) (d+e x)^9}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{5 e^5 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^5 (a+b x) (d+e x)^{11}}","-\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^5 (a+b x) (d+e x)^7}+\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{2 e^5 (a+b x) (d+e x)^8}-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^5 (a+b x) (d+e x)^9}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{5 e^5 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^5 (a+b x) (d+e x)^{11}}",1,"-((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)*(d + e*x)^11) + (2*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^10) - (2*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^9) + (b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)*(d + e*x)^8) - (b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^7)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1988,1,362,0,0.6874994,"\int (a+b x) (d+e x)^9 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^9*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{16}}{16 e^7 (a+b x)}-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15} (b d-a e)}{5 e^7 (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{14} (b d-a e)^2}{14 e^7 (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13} (b d-a e)^3}{13 e^7 (a+b x)}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (b d-a e)^4}{4 e^7 (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)^5}{11 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^6}{10 e^7 (a+b x)}","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{16}}{16 e^7 (a+b x)}-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15} (b d-a e)}{5 e^7 (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{14} (b d-a e)^2}{14 e^7 (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13} (b d-a e)^3}{13 e^7 (a+b x)}+\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (b d-a e)^4}{4 e^7 (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)^5}{11 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^6}{10 e^7 (a+b x)}",1,"((b*d - a*e)^6*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^7*(a + b*x)) - (6*b*(b*d - a*e)^5*(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (5*b^2*(b*d - a*e)^4*(d + e*x)^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)) - (20*b^3*(b*d - a*e)^3*(d + e*x)^13*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^14*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(14*e^7*(a + b*x)) - (2*b^5*(b*d - a*e)*(d + e*x)^15*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (b^6*(d + e*x)^16*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(16*e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1989,1,362,0,0.5938573,"\int (a+b x) (d+e x)^8 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^8*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15}}{15 e^7 (a+b x)}-\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{14} (b d-a e)}{7 e^7 (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13} (b d-a e)^2}{13 e^7 (a+b x)}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (b d-a e)^3}{3 e^7 (a+b x)}+\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)^4}{11 e^7 (a+b x)}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^5}{5 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^6}{9 e^7 (a+b x)}","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15}}{15 e^7 (a+b x)}-\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{14} (b d-a e)}{7 e^7 (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13} (b d-a e)^2}{13 e^7 (a+b x)}-\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (b d-a e)^3}{3 e^7 (a+b x)}+\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)^4}{11 e^7 (a+b x)}-\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^5}{5 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^6}{9 e^7 (a+b x)}",1,"((b*d - a*e)^6*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) - (3*b*(b*d - a*e)^5*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (15*b^2*(b*d - a*e)^4*(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) - (5*b^3*(b*d - a*e)^3*(d + e*x)^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^13*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) - (3*b^5*(b*d - a*e)*(d + e*x)^14*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (b^6*(d + e*x)^15*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1990,1,362,0,0.5248124,"\int (a+b x) (d+e x)^7 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^7*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{14}}{14 e^7 (a+b x)}-\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13} (b d-a e)}{13 e^7 (a+b x)}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (b d-a e)^2}{4 e^7 (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)^3}{11 e^7 (a+b x)}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^4}{2 e^7 (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^5}{3 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^6}{8 e^7 (a+b x)}","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{14}}{14 e^7 (a+b x)}-\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13} (b d-a e)}{13 e^7 (a+b x)}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{12} (b d-a e)^2}{4 e^7 (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11} (b d-a e)^3}{11 e^7 (a+b x)}+\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{10} (b d-a e)^4}{2 e^7 (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^9 (b d-a e)^5}{3 e^7 (a+b x)}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^8 (b d-a e)^6}{8 e^7 (a+b x)}",1,"((b*d - a*e)^6*(d + e*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)) - (2*b*(b*d - a*e)^5*(d + e*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (3*b^2*(b*d - a*e)^4*(d + e*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)) - (20*b^3*(b*d - a*e)^3*(d + e*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (5*b^4*(b*d - a*e)^2*(d + e*x)^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)) - (6*b^5*(b*d - a*e)*(d + e*x)^13*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) + (b^6*(d + e*x)^14*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(14*e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1991,1,311,0,0.4467198,"\int (a+b x) (d+e x)^6 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^6*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{11} (b d-a e)}{2 b^7}+\frac{15 e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10} (b d-a e)^2}{11 b^7}+\frac{2 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)^3}{b^7}+\frac{5 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^4}{3 b^7}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^5}{4 b^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^6}{7 b^7}+\frac{e^6 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{12}}{13 b^7}","\frac{e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{11} (b d-a e)}{2 b^7}+\frac{15 e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10} (b d-a e)^2}{11 b^7}+\frac{2 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)^3}{b^7}+\frac{5 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^4}{3 b^7}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^5}{4 b^7}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^6}{7 b^7}+\frac{e^6 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{12}}{13 b^7}",1,"((b*d - a*e)^6*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^7) + (3*e*(b*d - a*e)^5*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^7) + (5*e^2*(b*d - a*e)^4*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^7) + (2*e^3*(b*d - a*e)^3*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/b^7 + (15*e^4*(b*d - a*e)^2*(a + b*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*b^7) + (e^5*(b*d - a*e)*(a + b*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^7) + (e^6*(a + b*x)^12*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*b^7)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1992,1,263,0,0.3765333,"\int (a+b x) (d+e x)^5 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{5 e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10} (b d-a e)}{11 b^6}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)^2}{b^6}+\frac{10 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^3}{9 b^6}+\frac{5 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^4}{8 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^5}{7 b^6}+\frac{e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{11}}{12 b^6}","\frac{5 e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10} (b d-a e)}{11 b^6}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)^2}{b^6}+\frac{10 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^3}{9 b^6}+\frac{5 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^4}{8 b^6}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^5}{7 b^6}+\frac{e^5 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{11}}{12 b^6}",1,"((b*d - a*e)^5*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^6) + (5*e*(b*d - a*e)^4*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^6) + (10*e^2*(b*d - a*e)^3*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^6) + (e^3*(b*d - a*e)^2*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/b^6 + (5*e^4*(b*d - a*e)*(a + b*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*b^6) + (e^5*(a + b*x)^11*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*b^6)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1993,1,219,0,0.3043154,"\int (a+b x) (d+e x)^4 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)}{5 b^5}+\frac{2 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2}{3 b^5}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3}{2 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4}{7 b^5}+\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^5}","\frac{2 e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9 (b d-a e)}{5 b^5}+\frac{2 e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)^2}{3 b^5}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^3}{2 b^5}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^4}{7 b^5}+\frac{e^4 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^{10}}{11 b^5}",1,"((b*d - a*e)^4*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^5) + (e*(b*d - a*e)^3*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*b^5) + (2*e^2*(b*d - a*e)^2*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^5) + (2*e^3*(b*d - a*e)*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*b^5) + (e^4*(a + b*x)^10*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*b^5)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1994,1,172,0,0.2442602,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)}{3 b^4}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^2}{8 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^3}{7 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^4}","\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8 (b d-a e)}{3 b^4}+\frac{3 e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)^2}{8 b^4}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^3}{7 b^4}+\frac{e^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^9}{10 b^4}",1,"((b*d - a*e)^3*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^4) + (3*e*(b*d - a*e)^2*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^4) + (e^2*(b*d - a*e)*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*b^4) + (e^3*(a + b*x)^9*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*b^4)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1995,1,125,0,0.1797144,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)}{4 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2}{7 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^3}","\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7 (b d-a e)}{4 b^3}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)^2}{7 b^3}+\frac{e^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^8}{9 b^3}",1,"((b*d - a*e)^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^3) + (e*(b*d - a*e)*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*b^3) + (e^2*(a + b*x)^8*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*b^3)","A",4,3,33,0.09091,1,"{770, 21, 43}"
1996,1,78,0,0.0492313,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)}{7 b^2}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^2}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6 (b d-a e)}{7 b^2}+\frac{e \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^7}{8 b^2}",1,"((b*d - a*e)*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*b^2) + (e*(a + b*x)^7*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*b^2)","A",4,3,31,0.09677,1,"{770, 21, 43}"
1997,1,27,0,0.008406,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 b}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(7/2)/(7*b)","A",1,1,26,0.03846,1,"{629}"
1998,1,298,0,0.1631529,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x),x]","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^6 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^5}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^4}+\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^3}-\frac{(a+b x)^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6 \log (d+e x)}{e^7 (a+b x)}+\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e}","-\frac{b x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^6 (a+b x)}+\frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^5}-\frac{(a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^4}+\frac{(a+b x)^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^3}-\frac{(a+b x)^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6 \log (d+e x)}{e^7 (a+b x)}+\frac{(a+b x)^5 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e}",1,"-((b*(b*d - a*e)^5*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x))) + ((b*d - a*e)^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5) - ((b*d - a*e)^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^4) + ((b*d - a*e)^2*(a + b*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^3) - ((b*d - a*e)*(a + b*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^2) + ((a + b*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e) + ((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
1999,1,345,0,0.2993672,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^2,x]","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^7 (a+b x)}-\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e)}{2 e^7 (a+b x)}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)^2}{e^7 (a+b x)}-\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^3}{e^7 (a+b x)}+\frac{15 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{e^7 (a+b x) (d+e x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 \log (d+e x)}{e^7 (a+b x)}","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^5}{5 e^7 (a+b x)}-\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4 (b d-a e)}{2 e^7 (a+b x)}+\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)^2}{e^7 (a+b x)}-\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^3}{e^7 (a+b x)}+\frac{15 b^2 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^6 (a+b x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{e^7 (a+b x) (d+e x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 \log (d+e x)}{e^7 (a+b x)}",1,"(15*b^2*(b*d - a*e)^4*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) - (10*b^3*(b*d - a*e)^3*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (5*b^4*(b*d - a*e)^2*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (3*b^5*(b*d - a*e)*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)) + (b^6*(d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) - (6*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2000,1,347,0,0.2585943,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^3,x]","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^7 (a+b x)}-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}{e^7 (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}{2 e^7 (a+b x)}-\frac{20 b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{2 e^7 (a+b x) (d+e x)^2}+\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x)}{e^7 (a+b x)}","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}{4 e^7 (a+b x)}-\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3 (b d-a e)}{e^7 (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}{2 e^7 (a+b x)}-\frac{20 b^3 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^6 (a+b x)}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{2 e^7 (a+b x) (d+e x)^2}+\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 \log (d+e x)}{e^7 (a+b x)}",1,"(-20*b^3*(b*d - a*e)^3*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^2) + (6*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)) - (2*b^5*(b*d - a*e)*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (b^6*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)) + (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2001,1,345,0,0.2502806,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^4,x]","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^7 (a+b x)}-\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}{e^7 (a+b x)}+\frac{15 b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x)}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{3 e^7 (a+b x) (d+e x)^3}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^7 (a+b x)}","\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}{3 e^7 (a+b x)}-\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)}{e^7 (a+b x)}+\frac{15 b^4 x \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^6 (a+b x)}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)^2}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{3 e^7 (a+b x) (d+e x)^3}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 \log (d+e x)}{e^7 (a+b x)}",1,"(15*b^4*(b*d - a*e)^2*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^3) + (3*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^2) - (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) - (3*b^5*(b*d - a*e)*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (b^6*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (20*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2002,1,344,0,0.2419794,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^5,x]","-\frac{b^5 x \sqrt{a^2+2 a b x+b^2 x^2} (5 b d-6 a e)}{e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^7 (a+b x) (d+e x)^2}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{4 e^7 (a+b x) (d+e x)^4}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^7 (a+b x)}+\frac{b^6 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^5 (a+b x)}","-\frac{b^5 x \sqrt{a^2+2 a b x+b^2 x^2} (5 b d-6 a e)}{e^6 (a+b x)}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^7 (a+b x) (d+e x)^2}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)^3}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{4 e^7 (a+b x) (d+e x)^4}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 \log (d+e x)}{e^7 (a+b x)}+\frac{b^6 x^2 \sqrt{a^2+2 a b x+b^2 x^2}}{2 e^5 (a+b x)}",1,"-((b^5*(5*b*d - 6*a*e)*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x))) + (b^6*x^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^5*(a + b*x)) - ((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^4) + (2*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^3) - (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^2) + (20*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) + (15*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2003,1,344,0,0.2271991,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^6,x]","-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)^2}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)^3}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{2 e^7 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{5 e^7 (a+b x) (d+e x)^5}-\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^7 (a+b x)}+\frac{b^6 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x)}","-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)}+\frac{10 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)^2}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)^3}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{2 e^7 (a+b x) (d+e x)^4}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{5 e^7 (a+b x) (d+e x)^5}-\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) \log (d+e x)}{e^7 (a+b x)}+\frac{b^6 x \sqrt{a^2+2 a b x+b^2 x^2}}{e^6 (a+b x)}",1,"(b^6*x*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^6*(a + b*x)) - ((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5) + (3*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^4) - (5*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^3) + (10*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^2) - (15*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) - (6*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2004,1,356,0,0.210466,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^7,x]","\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^7 (a+b x) (d+e x)^2}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^3}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^7 (a+b x) (d+e x)^4}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^5}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{6 e^7 (a+b x) (d+e x)^6}+\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^7 (a+b x)}","\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^7 (a+b x) (d+e x)^2}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^3}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^7 (a+b x) (d+e x)^4}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^5}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{6 e^7 (a+b x) (d+e x)^6}+\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} \log (d+e x)}{e^7 (a+b x)}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^7*(a + b*x)*(d + e*x)^6) + (6*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5) - (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^4) + (20*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^3) - (15*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^2) + (6*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)) + (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]*Log[d + e*x])/(e^7*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2005,1,41,0,0.024597,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^8,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 (d+e x)^7 (b d-a e)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{7/2}}{7 (d+e x)^7 (b d-a e)}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(7/2)/(7*(b*d - a*e)*(d + e*x)^7)","A",1,1,33,0.03030,1,"{767}"
2006,1,98,0,0.0526529,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^9} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^9,x]","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{56 (d+e x)^7 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{8 (d+e x)^8 (b d-a e)}","\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{56 (d+e x)^7 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{8 (d+e x)^8 (b d-a e)}",1,"((a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*(b*d - a*e)*(d + e*x)^8) + (b*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(56*(b*d - a*e)^2*(d + e*x)^7)","A",4,4,33,0.1212,1,"{770, 21, 45, 37}"
2007,1,149,0,0.0646765,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{10}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^10,x]","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{252 (d+e x)^7 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{36 (d+e x)^8 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{9 (d+e x)^9 (b d-a e)}","\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{252 (d+e x)^7 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{36 (d+e x)^8 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{9 (d+e x)^9 (b d-a e)}",1,"((a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*(b*d - a*e)*(d + e*x)^9) + (b*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(36*(b*d - a*e)^2*(d + e*x)^8) + (b^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(252*(b*d - a*e)^3*(d + e*x)^7)","A",5,4,33,0.1212,1,"{770, 21, 45, 37}"
2008,1,200,0,0.085155,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^11,x]","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{840 (d+e x)^7 (b d-a e)^4}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{120 (d+e x)^8 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{30 (d+e x)^9 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{10 (d+e x)^{10} (b d-a e)}","\frac{b^3 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{840 (d+e x)^7 (b d-a e)^4}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{120 (d+e x)^8 (b d-a e)^3}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{30 (d+e x)^9 (b d-a e)^2}+\frac{\sqrt{a^2+2 a b x+b^2 x^2} (a+b x)^6}{10 (d+e x)^{10} (b d-a e)}",1,"((a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*(b*d - a*e)*(d + e*x)^10) + (b*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(30*(b*d - a*e)^2*(d + e*x)^9) + (b^2*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(120*(b*d - a*e)^3*(d + e*x)^8) + (b^3*(a + b*x)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(840*(b*d - a*e)^4*(d + e*x)^7)","A",6,4,33,0.1212,1,"{770, 21, 45, 37}"
2009,1,359,0,0.1982342,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{12}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^12,x]","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^7 (a+b x) (d+e x)^5}+\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)^6}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^7 (a+b x) (d+e x)^7}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^7 (a+b x) (d+e x)^8}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^7 (a+b x) (d+e x)^9}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{11 e^7 (a+b x) (d+e x)^{11}}","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{5 e^7 (a+b x) (d+e x)^5}+\frac{b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)^6}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^7 (a+b x) (d+e x)^7}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{2 e^7 (a+b x) (d+e x)^8}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^7 (a+b x) (d+e x)^9}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^{10}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{11 e^7 (a+b x) (d+e x)^{11}}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) + (3*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^10) - (5*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^9) + (5*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^8) - (15*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7) + (b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^6) - (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^5)","A",4,3,33,0.09091,1,"{770, 21, 43}"
2010,1,362,0,0.1980795,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{13}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^13,x]","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^7 (a+b x) (d+e x)^6}+\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{7 e^7 (a+b x) (d+e x)^7}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{8 e^7 (a+b x) (d+e x)^8}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^7 (a+b x) (d+e x)^9}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^7 (a+b x) (d+e x)^{10}}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{12 e^7 (a+b x) (d+e x)^{12}}","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{6 e^7 (a+b x) (d+e x)^6}+\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{7 e^7 (a+b x) (d+e x)^7}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{8 e^7 (a+b x) (d+e x)^8}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^7 (a+b x) (d+e x)^9}-\frac{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{2 e^7 (a+b x) (d+e x)^{10}}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{12 e^7 (a+b x) (d+e x)^{12}}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(12*e^7*(a + b*x)*(d + e*x)^12) + (6*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) - (3*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^10) + (20*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^9) - (15*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)*(d + e*x)^8) + (6*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7) - (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(6*e^7*(a + b*x)*(d + e*x)^6)","A",4,3,33,0.09091,1,"{770, 21, 43}"
2011,1,360,0,0.1925992,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{14}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^14,x]","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^7 (a+b x) (d+e x)^7}+\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^7 (a+b x) (d+e x)^8}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^7 (a+b x) (d+e x)^9}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)^{10}}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^7 (a+b x) (d+e x)^{11}}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{2 e^7 (a+b x) (d+e x)^{12}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{13 e^7 (a+b x) (d+e x)^{13}}","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{7 e^7 (a+b x) (d+e x)^7}+\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{4 e^7 (a+b x) (d+e x)^8}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^7 (a+b x) (d+e x)^9}+\frac{2 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)^{10}}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^7 (a+b x) (d+e x)^{11}}+\frac{b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{2 e^7 (a+b x) (d+e x)^{12}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{13 e^7 (a+b x) (d+e x)^{13}}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^13) + (b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^12) - (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) + (2*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^10) - (5*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^9) + (3*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^8) - (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^7)","A",4,3,33,0.09091,1,"{770, 21, 43}"
2012,1,362,0,0.1979288,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{15}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^15,x]","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{8 e^7 (a+b x) (d+e x)^8}+\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^7 (a+b x) (d+e x)^9}-\frac{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^7 (a+b x) (d+e x)^{10}}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^7 (a+b x) (d+e x)^{12}}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{13 e^7 (a+b x) (d+e x)^{13}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{14 e^7 (a+b x) (d+e x)^{14}}","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{8 e^7 (a+b x) (d+e x)^8}+\frac{2 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^7 (a+b x) (d+e x)^9}-\frac{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{2 e^7 (a+b x) (d+e x)^{10}}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{4 e^7 (a+b x) (d+e x)^{12}}+\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{13 e^7 (a+b x) (d+e x)^{13}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{14 e^7 (a+b x) (d+e x)^{14}}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(14*e^7*(a + b*x)*(d + e*x)^14) + (6*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^13) - (5*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^12) + (20*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) - (3*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(2*e^7*(a + b*x)*(d + e*x)^10) + (2*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^9) - (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(8*e^7*(a + b*x)*(d + e*x)^8)","A",4,3,33,0.09091,1,"{770, 21, 43}"
2013,1,362,0,0.1968032,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{16}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^16,x]","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{9 e^7 (a+b x) (d+e x)^9}+\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^7 (a+b x) (d+e x)^{10}}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{11 e^7 (a+b x) (d+e x)^{11}}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^{12}}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{13 e^7 (a+b x) (d+e x)^{13}}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{7 e^7 (a+b x) (d+e x)^{14}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{15 e^7 (a+b x) (d+e x)^{15}}","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{9 e^7 (a+b x) (d+e x)^9}+\frac{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^7 (a+b x) (d+e x)^{10}}-\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{11 e^7 (a+b x) (d+e x)^{11}}+\frac{5 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^{12}}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{13 e^7 (a+b x) (d+e x)^{13}}+\frac{3 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{7 e^7 (a+b x) (d+e x)^{14}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{15 e^7 (a+b x) (d+e x)^{15}}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^7*(a + b*x)*(d + e*x)^15) + (3*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^14) - (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^13) + (5*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^12) - (15*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) + (3*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^10) - (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^9)","A",4,3,33,0.09091,1,"{770, 21, 43}"
2014,1,362,0,0.2006912,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{17}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^17,x]","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{10 e^7 (a+b x) (d+e x)^{10}}+\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^7 (a+b x) (d+e x)^{12}}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{13 e^7 (a+b x) (d+e x)^{13}}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{14 e^7 (a+b x) (d+e x)^{14}}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^{15}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{16 e^7 (a+b x) (d+e x)^{16}}","-\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{10 e^7 (a+b x) (d+e x)^{10}}+\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{11 e^7 (a+b x) (d+e x)^{11}}-\frac{5 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{4 e^7 (a+b x) (d+e x)^{12}}+\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{13 e^7 (a+b x) (d+e x)^{13}}-\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{14 e^7 (a+b x) (d+e x)^{14}}+\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^{15}}-\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{16 e^7 (a+b x) (d+e x)^{16}}",1,"-((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(16*e^7*(a + b*x)*(d + e*x)^16) + (2*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^15) - (15*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(14*e^7*(a + b*x)*(d + e*x)^14) + (20*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^13) - (5*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(4*e^7*(a + b*x)*(d + e*x)^12) + (6*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^11) - (b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(10*e^7*(a + b*x)*(d + e*x)^10)","A",4,3,33,0.09091,1,"{770, 21, 43}"
2015,1,39,0,0.0289572,"\int \frac{(a+b x) (d+e x)^4}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^4)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (d+e x)^5}{5 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (d+e x)^5}{5 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*(d + e*x)^5)/(5*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2016,1,39,0,0.0299404,"\int \frac{(a+b x) (d+e x)^3}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^3)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (d+e x)^4}{4 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (d+e x)^4}{4 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*(d + e*x)^4)/(4*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2017,1,39,0,0.0298452,"\int \frac{(a+b x) (d+e x)^2}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^2)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (d+e x)^3}{3 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (d+e x)^3}{3 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*(d + e*x)^3)/(3*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2018,1,62,0,0.0301969,"\int \frac{(a+b x) (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{d x (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e x^2 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{d x (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2}}+\frac{e x^2 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(d*x*(a + b*x))/Sqrt[a^2 + 2*a*b*x + b^2*x^2] + (e*x^2*(a + b*x))/(2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,2,31,0.06452,1,"{770, 21}"
2019,1,24,0,0.0071298,"\int \frac{a+b x}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b}","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{b}",1,"Sqrt[a^2 + 2*a*b*x + b^2*x^2]/b","A",1,1,26,0.03846,1,"{629}"
2020,1,35,0,0.0276059,"\int \frac{a+b x}{(d+e x) \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{(a+b x) \log (d+e x)}{e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) \log (d+e x)}{e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*Log[d + e*x])/(e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 31}"
2021,1,38,0,0.0228127,"\int \frac{a+b x}{(d+e x)^2 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x) (b d-a e)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x) (b d-a e)}",1,"Sqrt[a^2 + 2*a*b*x + b^2*x^2]/((b*d - a*e)*(d + e*x))","A",1,1,33,0.03030,1,"{767}"
2022,1,39,0,0.028474,"\int \frac{a+b x}{(d+e x)^3 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{a+b x}{2 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2}","-\frac{a+b x}{2 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2}",1,"-(a + b*x)/(2*e*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2023,1,39,0,0.0283149,"\int \frac{a+b x}{(d+e x)^4 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{a+b x}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}","-\frac{a+b x}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^3}",1,"-(a + b*x)/(3*e*(d + e*x)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2024,1,39,0,0.0278428,"\int \frac{a+b x}{(d+e x)^5 \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{a+b x}{4 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}","-\frac{a+b x}{4 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^4}",1,"-(a + b*x)/(4*e*(d + e*x)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2025,1,210,0,0.1069587,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{4 e^2 x (a+b x) (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^4}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 e (a+b x) (d+e x)^3}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e (a+b x) (d+e x)^2 (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 e (a+b x) (b d-a e)^3 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{4 e^2 x (a+b x) (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^4}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 e (a+b x) (d+e x)^3}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e (a+b x) (d+e x)^2 (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 e (a+b x) (b d-a e)^3 \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(4*e^2*(b*d - a*e)^2*x*(a + b*x))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*e*(b*d - a*e)*(a + b*x)*(d + e*x)^2)/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (4*e*(a + b*x)*(d + e*x)^3)/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^4/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (4*e*(b*d - a*e)^3*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{768, 646, 43}"
2026,1,162,0,0.0872255,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{3 e^2 x (a+b x) (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^3}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) (d+e x)^2}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) (b d-a e)^2 \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{3 e^2 x (a+b x) (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^3}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) (d+e x)^2}{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) (b d-a e)^2 \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(3*e^2*(b*d - a*e)*x*(a + b*x))/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e*(a + b*x)*(d + e*x)^2)/(2*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^3/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e*(b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{768, 646, 43}"
2027,1,106,0,0.0570713,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^2}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e (a+b x) (b d-a e) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e^2 \sqrt{a^2+2 a b x+b^2 x^2}}{b^3}","-\frac{(d+e x)^2}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e (a+b x) (b d-a e) \log (a+b x)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{2 e^2 \sqrt{a^2+2 a b x+b^2 x^2}}{b^3}",1,"-((d + e*x)^2/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (2*e^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/b^3 + (2*e*(b*d - a*e)*(a + b*x)*Log[a + b*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,33,0.1212,1,"{768, 640, 608, 31}"
2028,1,67,0,0.0293024,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e (a+b x) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{d+e x}{b \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{e (a+b x) \log (a+b x)}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{d+e x}{b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-((d + e*x)/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (e*(a + b*x)*Log[a + b*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,31,0.09677,1,"{768, 608, 31}"
2029,1,25,0,0.0080638,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{1}{b \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{1}{b \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(1/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]))","A",1,1,26,0.03846,1,"{629}"
2030,1,120,0,0.0839477,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{e (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{e (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{e (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}+\frac{e (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"-(1/((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (e*(a + b*x)*Log[a + b*x])/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e*(a + b*x)*Log[d + e*x])/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 21, 44}"
2031,1,169,0,0.1117612,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{b}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^2}-\frac{2 b e (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{2 b e (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","-\frac{b}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^2}-\frac{2 b e (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{2 b e (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"-(b/((b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (e*(a + b*x))/((b*d - a*e)^2*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b*e*(a + b*x)*Log[a + b*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (2*b*e*(a + b*x)*Log[d + e*x])/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 21, 44}"
2032,1,223,0,0.1471812,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{b^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{2 b e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}-\frac{e (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}-\frac{3 b^2 e (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{3 b^2 e (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}","-\frac{b^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{2 b e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^3}-\frac{e (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^2}-\frac{3 b^2 e (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{3 b^2 e (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}",1,"-(b^2/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (e*(a + b*x))/(2*(b*d - a*e)^2*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*b*e*(a + b*x))/((b*d - a*e)^3*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*b^2*e*(a + b*x)*Log[a + b*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b^2*e*(a + b*x)*Log[d + e*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 21, 44}"
2033,1,252,0,0.1925736,"\int \frac{(a+b x) (d+e x)^5}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^5)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{5 e^4 x (a+b x) (4 b d-3 a e)}{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{20 e^2 (b d-a e)^3}{3 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{10 e^3 (a+b x) (b d-a e)^2 \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (b d-a e)^4}{6 b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^5}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{5 e^5 x^2 (a+b x)}{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{5 e^4 x (a+b x) (4 b d-3 a e)}{3 b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{20 e^2 (b d-a e)^3}{3 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{10 e^3 (a+b x) (b d-a e)^2 \log (a+b x)}{b^6 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (b d-a e)^4}{6 b^6 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^5}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{5 e^5 x^2 (a+b x)}{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(d + e*x)^5/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (20*e^2*(b*d - a*e)^3)/(3*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(b*d - a*e)^4)/(6*b^6*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^4*(4*b*d - 3*a*e)*x*(a + b*x))/(3*b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^5*x^2*(a + b*x))/(6*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (10*e^3*(b*d - a*e)^2*(a + b*x)*Log[a + b*x])/(b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{768, 646, 43}"
2034,1,201,0,0.1443147,"\int \frac{(a+b x) (d+e x)^4}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^4)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{4 e^2 (b d-a e)^2}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 e^3 (a+b x) (b d-a e) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 e (b d-a e)^3}{3 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^4}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{4 e^4 x (a+b x)}{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{4 e^2 (b d-a e)^2}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{4 e^3 (a+b x) (b d-a e) \log (a+b x)}{b^5 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{2 e (b d-a e)^3}{3 b^5 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^4}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{4 e^4 x (a+b x)}{3 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(d + e*x)^4/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (4*e^2*(b*d - a*e)^2)/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (2*e*(b*d - a*e)^3)/(3*b^5*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (4*e^4*x*(a + b*x))/(3*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (4*e^3*(b*d - a*e)*(a + b*x)*Log[a + b*x])/(b^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{768, 646, 43}"
2035,1,154,0,0.1089304,"\int \frac{(a+b x) (d+e x)^3}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^3)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{2 e^2 (b d-a e)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e (b d-a e)^2}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^3}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{e^3 (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{2 e^2 (b d-a e)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e (b d-a e)^2}{2 b^4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^3}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}+\frac{e^3 (a+b x) \log (a+b x)}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(d + e*x)^3/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (2*e^2*(b*d - a*e))/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*(b*d - a*e)^2)/(2*b^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(a + b*x)*Log[a + b*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{768, 646, 43}"
2036,1,41,0,0.0236631,"\int \frac{(a+b x) (d+e x)^2}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^2)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{(d+e x)^3}{3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)}","-\frac{(d+e x)^3}{3 \left(a^2+2 a b x+b^2 x^2\right)^{3/2} (b d-a e)}",1,"-(d + e*x)^3/(3*(b*d - a*e)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",1,1,33,0.03030,1,"{767}"
2037,1,68,0,0.0276638,"\int \frac{(a+b x) (d+e x)}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{d+e x}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{e}{6 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{d+e x}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{e}{6 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(d + e*x)/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - e/(6*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",2,2,31,0.06452,1,"{768, 607}"
2038,1,27,0,0.0079978,"\int \frac{a+b x}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{1}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{1}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-1/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))","A",1,1,26,0.03846,1,"{629}"
2039,1,210,0,0.1401289,"\int \frac{a+b x}{(d+e x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{e^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{e}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{e^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{e^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}+\frac{e}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-(e^2/((b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - 1/(3*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + e/(2*(b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(a + b*x)*Log[a + b*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(a + b*x)*Log[d + e*x])/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 21, 44}"
2040,1,260,0,0.1857675,"\int \frac{a+b x}{(d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{e^3 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^4}-\frac{3 b e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{4 b e^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{4 b e^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{b e}{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","-\frac{e^3 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^4}-\frac{3 b e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{4 b e^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{4 b e^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}+\frac{b e}{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}-\frac{b}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"(-3*b*e^2)/((b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b/(3*(b*d - a*e)^2*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (b*e)/((b*d - a*e)^3*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(a + b*x))/((b*d - a*e)^4*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (4*b*e^3*(a + b*x)*Log[a + b*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (4*b*e^3*(a + b*x)*Log[d + e*x])/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 21, 44}"
2041,1,323,0,0.2376233,"\int \frac{a+b x}{(d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{4 b e^3 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^5}-\frac{e^3 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^4}-\frac{6 b^2 e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{10 b^2 e^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{10 b^2 e^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{3 b^2 e}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^2}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}","-\frac{4 b e^3 (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x) (b d-a e)^5}-\frac{e^3 (a+b x)}{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^2 (b d-a e)^4}-\frac{6 b^2 e^2}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}-\frac{10 b^2 e^3 (a+b x) \log (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{10 b^2 e^3 (a+b x) \log (d+e x)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}+\frac{3 b^2 e}{2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}-\frac{b^2}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}",1,"(-6*b^2*e^2)/((b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - b^2/(3*(b*d - a*e)^3*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*b^2*e)/(2*(b*d - a*e)^4*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(a + b*x))/(2*(b*d - a*e)^4*(d + e*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (4*b*e^3*(a + b*x))/((b*d - a*e)^5*(d + e*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (10*b^2*e^3*(a + b*x)*Log[a + b*x])/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (10*b^2*e^3*(a + b*x)*Log[d + e*x])/((b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,33,0.09091,1,"{770, 21, 44}"
2042,1,100,0,0.0440653,"\int (a+b x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{6 b^2 (d+e x)^{13/2} (b d-a e)}{13 e^4}+\frac{6 b (d+e x)^{11/2} (b d-a e)^2}{11 e^4}-\frac{2 (d+e x)^{9/2} (b d-a e)^3}{9 e^4}+\frac{2 b^3 (d+e x)^{15/2}}{15 e^4}","-\frac{6 b^2 (d+e x)^{13/2} (b d-a e)}{13 e^4}+\frac{6 b (d+e x)^{11/2} (b d-a e)^2}{11 e^4}-\frac{2 (d+e x)^{9/2} (b d-a e)^3}{9 e^4}+\frac{2 b^3 (d+e x)^{15/2}}{15 e^4}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^4) + (6*b*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^4) - (6*b^2*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^4) + (2*b^3*(d + e*x)^(15/2))/(15*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2043,1,100,0,0.0365831,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{6 b^2 (d+e x)^{11/2} (b d-a e)}{11 e^4}+\frac{2 b (d+e x)^{9/2} (b d-a e)^2}{3 e^4}-\frac{2 (d+e x)^{7/2} (b d-a e)^3}{7 e^4}+\frac{2 b^3 (d+e x)^{13/2}}{13 e^4}","-\frac{6 b^2 (d+e x)^{11/2} (b d-a e)}{11 e^4}+\frac{2 b (d+e x)^{9/2} (b d-a e)^2}{3 e^4}-\frac{2 (d+e x)^{7/2} (b d-a e)^3}{7 e^4}+\frac{2 b^3 (d+e x)^{13/2}}{13 e^4}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(7/2))/(7*e^4) + (2*b*(b*d - a*e)^2*(d + e*x)^(9/2))/(3*e^4) - (6*b^2*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^4) + (2*b^3*(d + e*x)^(13/2))/(13*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2044,1,100,0,0.033601,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{2 b^2 (d+e x)^{9/2} (b d-a e)}{3 e^4}+\frac{6 b (d+e x)^{7/2} (b d-a e)^2}{7 e^4}-\frac{2 (d+e x)^{5/2} (b d-a e)^3}{5 e^4}+\frac{2 b^3 (d+e x)^{11/2}}{11 e^4}","-\frac{2 b^2 (d+e x)^{9/2} (b d-a e)}{3 e^4}+\frac{6 b (d+e x)^{7/2} (b d-a e)^2}{7 e^4}-\frac{2 (d+e x)^{5/2} (b d-a e)^3}{5 e^4}+\frac{2 b^3 (d+e x)^{11/2}}{11 e^4}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(5/2))/(5*e^4) + (6*b*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^4) - (2*b^2*(b*d - a*e)*(d + e*x)^(9/2))/(3*e^4) + (2*b^3*(d + e*x)^(11/2))/(11*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2045,1,100,0,0.032099,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{6 b^2 (d+e x)^{7/2} (b d-a e)}{7 e^4}+\frac{6 b (d+e x)^{5/2} (b d-a e)^2}{5 e^4}-\frac{2 (d+e x)^{3/2} (b d-a e)^3}{3 e^4}+\frac{2 b^3 (d+e x)^{9/2}}{9 e^4}","-\frac{6 b^2 (d+e x)^{7/2} (b d-a e)}{7 e^4}+\frac{6 b (d+e x)^{5/2} (b d-a e)^2}{5 e^4}-\frac{2 (d+e x)^{3/2} (b d-a e)^3}{3 e^4}+\frac{2 b^3 (d+e x)^{9/2}}{9 e^4}",1,"(-2*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^4) + (6*b*(b*d - a*e)^2*(d + e*x)^(5/2))/(5*e^4) - (6*b^2*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^4) + (2*b^3*(d + e*x)^(9/2))/(9*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2046,1,96,0,0.0341398,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{\sqrt{d+e x}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/Sqrt[d + e*x],x]","-\frac{6 b^2 (d+e x)^{5/2} (b d-a e)}{5 e^4}+\frac{2 b (d+e x)^{3/2} (b d-a e)^2}{e^4}-\frac{2 \sqrt{d+e x} (b d-a e)^3}{e^4}+\frac{2 b^3 (d+e x)^{7/2}}{7 e^4}","-\frac{6 b^2 (d+e x)^{5/2} (b d-a e)}{5 e^4}+\frac{2 b (d+e x)^{3/2} (b d-a e)^2}{e^4}-\frac{2 \sqrt{d+e x} (b d-a e)^3}{e^4}+\frac{2 b^3 (d+e x)^{7/2}}{7 e^4}",1,"(-2*(b*d - a*e)^3*Sqrt[d + e*x])/e^4 + (2*b*(b*d - a*e)^2*(d + e*x)^(3/2))/e^4 - (6*b^2*(b*d - a*e)*(d + e*x)^(5/2))/(5*e^4) + (2*b^3*(d + e*x)^(7/2))/(7*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2047,1,94,0,0.0331072,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{3/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(3/2),x]","-\frac{2 b^2 (d+e x)^{3/2} (b d-a e)}{e^4}+\frac{6 b \sqrt{d+e x} (b d-a e)^2}{e^4}+\frac{2 (b d-a e)^3}{e^4 \sqrt{d+e x}}+\frac{2 b^3 (d+e x)^{5/2}}{5 e^4}","-\frac{2 b^2 (d+e x)^{3/2} (b d-a e)}{e^4}+\frac{6 b \sqrt{d+e x} (b d-a e)^2}{e^4}+\frac{2 (b d-a e)^3}{e^4 \sqrt{d+e x}}+\frac{2 b^3 (d+e x)^{5/2}}{5 e^4}",1,"(2*(b*d - a*e)^3)/(e^4*Sqrt[d + e*x]) + (6*b*(b*d - a*e)^2*Sqrt[d + e*x])/e^4 - (2*b^2*(b*d - a*e)*(d + e*x)^(3/2))/e^4 + (2*b^3*(d + e*x)^(5/2))/(5*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2048,1,96,0,0.0332519,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{5/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(5/2),x]","-\frac{6 b^2 \sqrt{d+e x} (b d-a e)}{e^4}-\frac{6 b (b d-a e)^2}{e^4 \sqrt{d+e x}}+\frac{2 (b d-a e)^3}{3 e^4 (d+e x)^{3/2}}+\frac{2 b^3 (d+e x)^{3/2}}{3 e^4}","-\frac{6 b^2 \sqrt{d+e x} (b d-a e)}{e^4}-\frac{6 b (b d-a e)^2}{e^4 \sqrt{d+e x}}+\frac{2 (b d-a e)^3}{3 e^4 (d+e x)^{3/2}}+\frac{2 b^3 (d+e x)^{3/2}}{3 e^4}",1,"(2*(b*d - a*e)^3)/(3*e^4*(d + e*x)^(3/2)) - (6*b*(b*d - a*e)^2)/(e^4*Sqrt[d + e*x]) - (6*b^2*(b*d - a*e)*Sqrt[d + e*x])/e^4 + (2*b^3*(d + e*x)^(3/2))/(3*e^4)","A",3,2,31,0.06452,1,"{27, 43}"
2049,1,94,0,0.0324152,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)}{(d+e x)^{7/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2))/(d + e*x)^(7/2),x]","\frac{6 b^2 (b d-a e)}{e^4 \sqrt{d+e x}}-\frac{2 b (b d-a e)^2}{e^4 (d+e x)^{3/2}}+\frac{2 (b d-a e)^3}{5 e^4 (d+e x)^{5/2}}+\frac{2 b^3 \sqrt{d+e x}}{e^4}","\frac{6 b^2 (b d-a e)}{e^4 \sqrt{d+e x}}-\frac{2 b (b d-a e)^2}{e^4 (d+e x)^{3/2}}+\frac{2 (b d-a e)^3}{5 e^4 (d+e x)^{5/2}}+\frac{2 b^3 \sqrt{d+e x}}{e^4}",1,"(2*(b*d - a*e)^3)/(5*e^4*(d + e*x)^(5/2)) - (2*b*(b*d - a*e)^2)/(e^4*(d + e*x)^(3/2)) + (6*b^2*(b*d - a*e))/(e^4*Sqrt[d + e*x]) + (2*b^3*Sqrt[d + e*x])/e^4","A",3,2,31,0.06452,1,"{27, 43}"
2050,1,158,0,0.0738924,"\int (a+b x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{10 b^4 (d+e x)^{17/2} (b d-a e)}{17 e^6}+\frac{4 b^3 (d+e x)^{15/2} (b d-a e)^2}{3 e^6}-\frac{20 b^2 (d+e x)^{13/2} (b d-a e)^3}{13 e^6}+\frac{10 b (d+e x)^{11/2} (b d-a e)^4}{11 e^6}-\frac{2 (d+e x)^{9/2} (b d-a e)^5}{9 e^6}+\frac{2 b^5 (d+e x)^{19/2}}{19 e^6}","-\frac{10 b^4 (d+e x)^{17/2} (b d-a e)}{17 e^6}+\frac{4 b^3 (d+e x)^{15/2} (b d-a e)^2}{3 e^6}-\frac{20 b^2 (d+e x)^{13/2} (b d-a e)^3}{13 e^6}+\frac{10 b (d+e x)^{11/2} (b d-a e)^4}{11 e^6}-\frac{2 (d+e x)^{9/2} (b d-a e)^5}{9 e^6}+\frac{2 b^5 (d+e x)^{19/2}}{19 e^6}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(9/2))/(9*e^6) + (10*b*(b*d - a*e)^4*(d + e*x)^(11/2))/(11*e^6) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(13/2))/(13*e^6) + (4*b^3*(b*d - a*e)^2*(d + e*x)^(15/2))/(3*e^6) - (10*b^4*(b*d - a*e)*(d + e*x)^(17/2))/(17*e^6) + (2*b^5*(d + e*x)^(19/2))/(19*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2051,1,158,0,0.0570405,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{2 b^4 (d+e x)^{15/2} (b d-a e)}{3 e^6}+\frac{20 b^3 (d+e x)^{13/2} (b d-a e)^2}{13 e^6}-\frac{20 b^2 (d+e x)^{11/2} (b d-a e)^3}{11 e^6}+\frac{10 b (d+e x)^{9/2} (b d-a e)^4}{9 e^6}-\frac{2 (d+e x)^{7/2} (b d-a e)^5}{7 e^6}+\frac{2 b^5 (d+e x)^{17/2}}{17 e^6}","-\frac{2 b^4 (d+e x)^{15/2} (b d-a e)}{3 e^6}+\frac{20 b^3 (d+e x)^{13/2} (b d-a e)^2}{13 e^6}-\frac{20 b^2 (d+e x)^{11/2} (b d-a e)^3}{11 e^6}+\frac{10 b (d+e x)^{9/2} (b d-a e)^4}{9 e^6}-\frac{2 (d+e x)^{7/2} (b d-a e)^5}{7 e^6}+\frac{2 b^5 (d+e x)^{17/2}}{17 e^6}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(7/2))/(7*e^6) + (10*b*(b*d - a*e)^4*(d + e*x)^(9/2))/(9*e^6) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(11/2))/(11*e^6) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(13/2))/(13*e^6) - (2*b^4*(b*d - a*e)*(d + e*x)^(15/2))/(3*e^6) + (2*b^5*(d + e*x)^(17/2))/(17*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2052,1,158,0,0.0574865,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{10 b^4 (d+e x)^{13/2} (b d-a e)}{13 e^6}+\frac{20 b^3 (d+e x)^{11/2} (b d-a e)^2}{11 e^6}-\frac{20 b^2 (d+e x)^{9/2} (b d-a e)^3}{9 e^6}+\frac{10 b (d+e x)^{7/2} (b d-a e)^4}{7 e^6}-\frac{2 (d+e x)^{5/2} (b d-a e)^5}{5 e^6}+\frac{2 b^5 (d+e x)^{15/2}}{15 e^6}","-\frac{10 b^4 (d+e x)^{13/2} (b d-a e)}{13 e^6}+\frac{20 b^3 (d+e x)^{11/2} (b d-a e)^2}{11 e^6}-\frac{20 b^2 (d+e x)^{9/2} (b d-a e)^3}{9 e^6}+\frac{10 b (d+e x)^{7/2} (b d-a e)^4}{7 e^6}-\frac{2 (d+e x)^{5/2} (b d-a e)^5}{5 e^6}+\frac{2 b^5 (d+e x)^{15/2}}{15 e^6}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(5/2))/(5*e^6) + (10*b*(b*d - a*e)^4*(d + e*x)^(7/2))/(7*e^6) - (20*b^2*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^6) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^6) - (10*b^4*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^6) + (2*b^5*(d + e*x)^(15/2))/(15*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2053,1,156,0,0.0538012,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{10 b^4 (d+e x)^{11/2} (b d-a e)}{11 e^6}+\frac{20 b^3 (d+e x)^{9/2} (b d-a e)^2}{9 e^6}-\frac{20 b^2 (d+e x)^{7/2} (b d-a e)^3}{7 e^6}+\frac{2 b (d+e x)^{5/2} (b d-a e)^4}{e^6}-\frac{2 (d+e x)^{3/2} (b d-a e)^5}{3 e^6}+\frac{2 b^5 (d+e x)^{13/2}}{13 e^6}","-\frac{10 b^4 (d+e x)^{11/2} (b d-a e)}{11 e^6}+\frac{20 b^3 (d+e x)^{9/2} (b d-a e)^2}{9 e^6}-\frac{20 b^2 (d+e x)^{7/2} (b d-a e)^3}{7 e^6}+\frac{2 b (d+e x)^{5/2} (b d-a e)^4}{e^6}-\frac{2 (d+e x)^{3/2} (b d-a e)^5}{3 e^6}+\frac{2 b^5 (d+e x)^{13/2}}{13 e^6}",1,"(-2*(b*d - a*e)^5*(d + e*x)^(3/2))/(3*e^6) + (2*b*(b*d - a*e)^4*(d + e*x)^(5/2))/e^6 - (20*b^2*(b*d - a*e)^3*(d + e*x)^(7/2))/(7*e^6) + (20*b^3*(b*d - a*e)^2*(d + e*x)^(9/2))/(9*e^6) - (10*b^4*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^6) + (2*b^5*(d + e*x)^(13/2))/(13*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2054,1,154,0,0.0571058,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{\sqrt{d+e x}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/Sqrt[d + e*x],x]","-\frac{10 b^4 (d+e x)^{9/2} (b d-a e)}{9 e^6}+\frac{20 b^3 (d+e x)^{7/2} (b d-a e)^2}{7 e^6}-\frac{4 b^2 (d+e x)^{5/2} (b d-a e)^3}{e^6}+\frac{10 b (d+e x)^{3/2} (b d-a e)^4}{3 e^6}-\frac{2 \sqrt{d+e x} (b d-a e)^5}{e^6}+\frac{2 b^5 (d+e x)^{11/2}}{11 e^6}","-\frac{10 b^4 (d+e x)^{9/2} (b d-a e)}{9 e^6}+\frac{20 b^3 (d+e x)^{7/2} (b d-a e)^2}{7 e^6}-\frac{4 b^2 (d+e x)^{5/2} (b d-a e)^3}{e^6}+\frac{10 b (d+e x)^{3/2} (b d-a e)^4}{3 e^6}-\frac{2 \sqrt{d+e x} (b d-a e)^5}{e^6}+\frac{2 b^5 (d+e x)^{11/2}}{11 e^6}",1,"(-2*(b*d - a*e)^5*Sqrt[d + e*x])/e^6 + (10*b*(b*d - a*e)^4*(d + e*x)^(3/2))/(3*e^6) - (4*b^2*(b*d - a*e)^3*(d + e*x)^(5/2))/e^6 + (20*b^3*(b*d - a*e)^2*(d + e*x)^(7/2))/(7*e^6) - (10*b^4*(b*d - a*e)*(d + e*x)^(9/2))/(9*e^6) + (2*b^5*(d + e*x)^(11/2))/(11*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2055,1,152,0,0.0581177,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{3/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(3/2),x]","-\frac{10 b^4 (d+e x)^{7/2} (b d-a e)}{7 e^6}+\frac{4 b^3 (d+e x)^{5/2} (b d-a e)^2}{e^6}-\frac{20 b^2 (d+e x)^{3/2} (b d-a e)^3}{3 e^6}+\frac{10 b \sqrt{d+e x} (b d-a e)^4}{e^6}+\frac{2 (b d-a e)^5}{e^6 \sqrt{d+e x}}+\frac{2 b^5 (d+e x)^{9/2}}{9 e^6}","-\frac{10 b^4 (d+e x)^{7/2} (b d-a e)}{7 e^6}+\frac{4 b^3 (d+e x)^{5/2} (b d-a e)^2}{e^6}-\frac{20 b^2 (d+e x)^{3/2} (b d-a e)^3}{3 e^6}+\frac{10 b \sqrt{d+e x} (b d-a e)^4}{e^6}+\frac{2 (b d-a e)^5}{e^6 \sqrt{d+e x}}+\frac{2 b^5 (d+e x)^{9/2}}{9 e^6}",1,"(2*(b*d - a*e)^5)/(e^6*Sqrt[d + e*x]) + (10*b*(b*d - a*e)^4*Sqrt[d + e*x])/e^6 - (20*b^2*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^6) + (4*b^3*(b*d - a*e)^2*(d + e*x)^(5/2))/e^6 - (10*b^4*(b*d - a*e)*(d + e*x)^(7/2))/(7*e^6) + (2*b^5*(d + e*x)^(9/2))/(9*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2056,1,152,0,0.0553517,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{5/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(5/2),x]","-\frac{2 b^4 (d+e x)^{5/2} (b d-a e)}{e^6}+\frac{20 b^3 (d+e x)^{3/2} (b d-a e)^2}{3 e^6}-\frac{20 b^2 \sqrt{d+e x} (b d-a e)^3}{e^6}-\frac{10 b (b d-a e)^4}{e^6 \sqrt{d+e x}}+\frac{2 (b d-a e)^5}{3 e^6 (d+e x)^{3/2}}+\frac{2 b^5 (d+e x)^{7/2}}{7 e^6}","-\frac{2 b^4 (d+e x)^{5/2} (b d-a e)}{e^6}+\frac{20 b^3 (d+e x)^{3/2} (b d-a e)^2}{3 e^6}-\frac{20 b^2 \sqrt{d+e x} (b d-a e)^3}{e^6}-\frac{10 b (b d-a e)^4}{e^6 \sqrt{d+e x}}+\frac{2 (b d-a e)^5}{3 e^6 (d+e x)^{3/2}}+\frac{2 b^5 (d+e x)^{7/2}}{7 e^6}",1,"(2*(b*d - a*e)^5)/(3*e^6*(d + e*x)^(3/2)) - (10*b*(b*d - a*e)^4)/(e^6*Sqrt[d + e*x]) - (20*b^2*(b*d - a*e)^3*Sqrt[d + e*x])/e^6 + (20*b^3*(b*d - a*e)^2*(d + e*x)^(3/2))/(3*e^6) - (2*b^4*(b*d - a*e)*(d + e*x)^(5/2))/e^6 + (2*b^5*(d + e*x)^(7/2))/(7*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2057,1,154,0,0.0548832,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^2}{(d+e x)^{7/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^2)/(d + e*x)^(7/2),x]","-\frac{10 b^4 (d+e x)^{3/2} (b d-a e)}{3 e^6}+\frac{20 b^3 \sqrt{d+e x} (b d-a e)^2}{e^6}+\frac{20 b^2 (b d-a e)^3}{e^6 \sqrt{d+e x}}-\frac{10 b (b d-a e)^4}{3 e^6 (d+e x)^{3/2}}+\frac{2 (b d-a e)^5}{5 e^6 (d+e x)^{5/2}}+\frac{2 b^5 (d+e x)^{5/2}}{5 e^6}","-\frac{10 b^4 (d+e x)^{3/2} (b d-a e)}{3 e^6}+\frac{20 b^3 \sqrt{d+e x} (b d-a e)^2}{e^6}+\frac{20 b^2 (b d-a e)^3}{e^6 \sqrt{d+e x}}-\frac{10 b (b d-a e)^4}{3 e^6 (d+e x)^{3/2}}+\frac{2 (b d-a e)^5}{5 e^6 (d+e x)^{5/2}}+\frac{2 b^5 (d+e x)^{5/2}}{5 e^6}",1,"(2*(b*d - a*e)^5)/(5*e^6*(d + e*x)^(5/2)) - (10*b*(b*d - a*e)^4)/(3*e^6*(d + e*x)^(3/2)) + (20*b^2*(b*d - a*e)^3)/(e^6*Sqrt[d + e*x]) + (20*b^3*(b*d - a*e)^2*Sqrt[d + e*x])/e^6 - (10*b^4*(b*d - a*e)*(d + e*x)^(3/2))/(3*e^6) + (2*b^5*(d + e*x)^(5/2))/(5*e^6)","A",3,2,33,0.06061,1,"{27, 43}"
2058,1,216,0,0.1084846,"\int (a+b x) (d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{2 b^6 (d+e x)^{21/2} (b d-a e)}{3 e^8}+\frac{42 b^5 (d+e x)^{19/2} (b d-a e)^2}{19 e^8}-\frac{70 b^4 (d+e x)^{17/2} (b d-a e)^3}{17 e^8}+\frac{14 b^3 (d+e x)^{15/2} (b d-a e)^4}{3 e^8}-\frac{42 b^2 (d+e x)^{13/2} (b d-a e)^5}{13 e^8}+\frac{14 b (d+e x)^{11/2} (b d-a e)^6}{11 e^8}-\frac{2 (d+e x)^{9/2} (b d-a e)^7}{9 e^8}+\frac{2 b^7 (d+e x)^{23/2}}{23 e^8}","-\frac{2 b^6 (d+e x)^{21/2} (b d-a e)}{3 e^8}+\frac{42 b^5 (d+e x)^{19/2} (b d-a e)^2}{19 e^8}-\frac{70 b^4 (d+e x)^{17/2} (b d-a e)^3}{17 e^8}+\frac{14 b^3 (d+e x)^{15/2} (b d-a e)^4}{3 e^8}-\frac{42 b^2 (d+e x)^{13/2} (b d-a e)^5}{13 e^8}+\frac{14 b (d+e x)^{11/2} (b d-a e)^6}{11 e^8}-\frac{2 (d+e x)^{9/2} (b d-a e)^7}{9 e^8}+\frac{2 b^7 (d+e x)^{23/2}}{23 e^8}",1,"(-2*(b*d - a*e)^7*(d + e*x)^(9/2))/(9*e^8) + (14*b*(b*d - a*e)^6*(d + e*x)^(11/2))/(11*e^8) - (42*b^2*(b*d - a*e)^5*(d + e*x)^(13/2))/(13*e^8) + (14*b^3*(b*d - a*e)^4*(d + e*x)^(15/2))/(3*e^8) - (70*b^4*(b*d - a*e)^3*(d + e*x)^(17/2))/(17*e^8) + (42*b^5*(b*d - a*e)^2*(d + e*x)^(19/2))/(19*e^8) - (2*b^6*(b*d - a*e)*(d + e*x)^(21/2))/(3*e^8) + (2*b^7*(d + e*x)^(23/2))/(23*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2059,1,216,0,0.0758327,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{14 b^6 (d+e x)^{19/2} (b d-a e)}{19 e^8}+\frac{42 b^5 (d+e x)^{17/2} (b d-a e)^2}{17 e^8}-\frac{14 b^4 (d+e x)^{15/2} (b d-a e)^3}{3 e^8}+\frac{70 b^3 (d+e x)^{13/2} (b d-a e)^4}{13 e^8}-\frac{42 b^2 (d+e x)^{11/2} (b d-a e)^5}{11 e^8}+\frac{14 b (d+e x)^{9/2} (b d-a e)^6}{9 e^8}-\frac{2 (d+e x)^{7/2} (b d-a e)^7}{7 e^8}+\frac{2 b^7 (d+e x)^{21/2}}{21 e^8}","-\frac{14 b^6 (d+e x)^{19/2} (b d-a e)}{19 e^8}+\frac{42 b^5 (d+e x)^{17/2} (b d-a e)^2}{17 e^8}-\frac{14 b^4 (d+e x)^{15/2} (b d-a e)^3}{3 e^8}+\frac{70 b^3 (d+e x)^{13/2} (b d-a e)^4}{13 e^8}-\frac{42 b^2 (d+e x)^{11/2} (b d-a e)^5}{11 e^8}+\frac{14 b (d+e x)^{9/2} (b d-a e)^6}{9 e^8}-\frac{2 (d+e x)^{7/2} (b d-a e)^7}{7 e^8}+\frac{2 b^7 (d+e x)^{21/2}}{21 e^8}",1,"(-2*(b*d - a*e)^7*(d + e*x)^(7/2))/(7*e^8) + (14*b*(b*d - a*e)^6*(d + e*x)^(9/2))/(9*e^8) - (42*b^2*(b*d - a*e)^5*(d + e*x)^(11/2))/(11*e^8) + (70*b^3*(b*d - a*e)^4*(d + e*x)^(13/2))/(13*e^8) - (14*b^4*(b*d - a*e)^3*(d + e*x)^(15/2))/(3*e^8) + (42*b^5*(b*d - a*e)^2*(d + e*x)^(17/2))/(17*e^8) - (14*b^6*(b*d - a*e)*(d + e*x)^(19/2))/(19*e^8) + (2*b^7*(d + e*x)^(21/2))/(21*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2060,1,214,0,0.0745669,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{14 b^6 (d+e x)^{17/2} (b d-a e)}{17 e^8}+\frac{14 b^5 (d+e x)^{15/2} (b d-a e)^2}{5 e^8}-\frac{70 b^4 (d+e x)^{13/2} (b d-a e)^3}{13 e^8}+\frac{70 b^3 (d+e x)^{11/2} (b d-a e)^4}{11 e^8}-\frac{14 b^2 (d+e x)^{9/2} (b d-a e)^5}{3 e^8}+\frac{2 b (d+e x)^{7/2} (b d-a e)^6}{e^8}-\frac{2 (d+e x)^{5/2} (b d-a e)^7}{5 e^8}+\frac{2 b^7 (d+e x)^{19/2}}{19 e^8}","-\frac{14 b^6 (d+e x)^{17/2} (b d-a e)}{17 e^8}+\frac{14 b^5 (d+e x)^{15/2} (b d-a e)^2}{5 e^8}-\frac{70 b^4 (d+e x)^{13/2} (b d-a e)^3}{13 e^8}+\frac{70 b^3 (d+e x)^{11/2} (b d-a e)^4}{11 e^8}-\frac{14 b^2 (d+e x)^{9/2} (b d-a e)^5}{3 e^8}+\frac{2 b (d+e x)^{7/2} (b d-a e)^6}{e^8}-\frac{2 (d+e x)^{5/2} (b d-a e)^7}{5 e^8}+\frac{2 b^7 (d+e x)^{19/2}}{19 e^8}",1,"(-2*(b*d - a*e)^7*(d + e*x)^(5/2))/(5*e^8) + (2*b*(b*d - a*e)^6*(d + e*x)^(7/2))/e^8 - (14*b^2*(b*d - a*e)^5*(d + e*x)^(9/2))/(3*e^8) + (70*b^3*(b*d - a*e)^4*(d + e*x)^(11/2))/(11*e^8) - (70*b^4*(b*d - a*e)^3*(d + e*x)^(13/2))/(13*e^8) + (14*b^5*(b*d - a*e)^2*(d + e*x)^(15/2))/(5*e^8) - (14*b^6*(b*d - a*e)*(d + e*x)^(17/2))/(17*e^8) + (2*b^7*(d + e*x)^(19/2))/(19*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2061,1,214,0,0.0727237,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{14 b^6 (d+e x)^{15/2} (b d-a e)}{15 e^8}+\frac{42 b^5 (d+e x)^{13/2} (b d-a e)^2}{13 e^8}-\frac{70 b^4 (d+e x)^{11/2} (b d-a e)^3}{11 e^8}+\frac{70 b^3 (d+e x)^{9/2} (b d-a e)^4}{9 e^8}-\frac{6 b^2 (d+e x)^{7/2} (b d-a e)^5}{e^8}+\frac{14 b (d+e x)^{5/2} (b d-a e)^6}{5 e^8}-\frac{2 (d+e x)^{3/2} (b d-a e)^7}{3 e^8}+\frac{2 b^7 (d+e x)^{17/2}}{17 e^8}","-\frac{14 b^6 (d+e x)^{15/2} (b d-a e)}{15 e^8}+\frac{42 b^5 (d+e x)^{13/2} (b d-a e)^2}{13 e^8}-\frac{70 b^4 (d+e x)^{11/2} (b d-a e)^3}{11 e^8}+\frac{70 b^3 (d+e x)^{9/2} (b d-a e)^4}{9 e^8}-\frac{6 b^2 (d+e x)^{7/2} (b d-a e)^5}{e^8}+\frac{14 b (d+e x)^{5/2} (b d-a e)^6}{5 e^8}-\frac{2 (d+e x)^{3/2} (b d-a e)^7}{3 e^8}+\frac{2 b^7 (d+e x)^{17/2}}{17 e^8}",1,"(-2*(b*d - a*e)^7*(d + e*x)^(3/2))/(3*e^8) + (14*b*(b*d - a*e)^6*(d + e*x)^(5/2))/(5*e^8) - (6*b^2*(b*d - a*e)^5*(d + e*x)^(7/2))/e^8 + (70*b^3*(b*d - a*e)^4*(d + e*x)^(9/2))/(9*e^8) - (70*b^4*(b*d - a*e)^3*(d + e*x)^(11/2))/(11*e^8) + (42*b^5*(b*d - a*e)^2*(d + e*x)^(13/2))/(13*e^8) - (14*b^6*(b*d - a*e)*(d + e*x)^(15/2))/(15*e^8) + (2*b^7*(d + e*x)^(17/2))/(17*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2062,1,212,0,0.0736667,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{\sqrt{d+e x}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/Sqrt[d + e*x],x]","-\frac{14 b^6 (d+e x)^{13/2} (b d-a e)}{13 e^8}+\frac{42 b^5 (d+e x)^{11/2} (b d-a e)^2}{11 e^8}-\frac{70 b^4 (d+e x)^{9/2} (b d-a e)^3}{9 e^8}+\frac{10 b^3 (d+e x)^{7/2} (b d-a e)^4}{e^8}-\frac{42 b^2 (d+e x)^{5/2} (b d-a e)^5}{5 e^8}+\frac{14 b (d+e x)^{3/2} (b d-a e)^6}{3 e^8}-\frac{2 \sqrt{d+e x} (b d-a e)^7}{e^8}+\frac{2 b^7 (d+e x)^{15/2}}{15 e^8}","-\frac{14 b^6 (d+e x)^{13/2} (b d-a e)}{13 e^8}+\frac{42 b^5 (d+e x)^{11/2} (b d-a e)^2}{11 e^8}-\frac{70 b^4 (d+e x)^{9/2} (b d-a e)^3}{9 e^8}+\frac{10 b^3 (d+e x)^{7/2} (b d-a e)^4}{e^8}-\frac{42 b^2 (d+e x)^{5/2} (b d-a e)^5}{5 e^8}+\frac{14 b (d+e x)^{3/2} (b d-a e)^6}{3 e^8}-\frac{2 \sqrt{d+e x} (b d-a e)^7}{e^8}+\frac{2 b^7 (d+e x)^{15/2}}{15 e^8}",1,"(-2*(b*d - a*e)^7*Sqrt[d + e*x])/e^8 + (14*b*(b*d - a*e)^6*(d + e*x)^(3/2))/(3*e^8) - (42*b^2*(b*d - a*e)^5*(d + e*x)^(5/2))/(5*e^8) + (10*b^3*(b*d - a*e)^4*(d + e*x)^(7/2))/e^8 - (70*b^4*(b*d - a*e)^3*(d + e*x)^(9/2))/(9*e^8) + (42*b^5*(b*d - a*e)^2*(d + e*x)^(11/2))/(11*e^8) - (14*b^6*(b*d - a*e)*(d + e*x)^(13/2))/(13*e^8) + (2*b^7*(d + e*x)^(15/2))/(15*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2063,1,206,0,0.0788397,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{3/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(3/2),x]","-\frac{14 b^6 (d+e x)^{11/2} (b d-a e)}{11 e^8}+\frac{14 b^5 (d+e x)^{9/2} (b d-a e)^2}{3 e^8}-\frac{10 b^4 (d+e x)^{7/2} (b d-a e)^3}{e^8}+\frac{14 b^3 (d+e x)^{5/2} (b d-a e)^4}{e^8}-\frac{14 b^2 (d+e x)^{3/2} (b d-a e)^5}{e^8}+\frac{14 b \sqrt{d+e x} (b d-a e)^6}{e^8}+\frac{2 (b d-a e)^7}{e^8 \sqrt{d+e x}}+\frac{2 b^7 (d+e x)^{13/2}}{13 e^8}","-\frac{14 b^6 (d+e x)^{11/2} (b d-a e)}{11 e^8}+\frac{14 b^5 (d+e x)^{9/2} (b d-a e)^2}{3 e^8}-\frac{10 b^4 (d+e x)^{7/2} (b d-a e)^3}{e^8}+\frac{14 b^3 (d+e x)^{5/2} (b d-a e)^4}{e^8}-\frac{14 b^2 (d+e x)^{3/2} (b d-a e)^5}{e^8}+\frac{14 b \sqrt{d+e x} (b d-a e)^6}{e^8}+\frac{2 (b d-a e)^7}{e^8 \sqrt{d+e x}}+\frac{2 b^7 (d+e x)^{13/2}}{13 e^8}",1,"(2*(b*d - a*e)^7)/(e^8*Sqrt[d + e*x]) + (14*b*(b*d - a*e)^6*Sqrt[d + e*x])/e^8 - (14*b^2*(b*d - a*e)^5*(d + e*x)^(3/2))/e^8 + (14*b^3*(b*d - a*e)^4*(d + e*x)^(5/2))/e^8 - (10*b^4*(b*d - a*e)^3*(d + e*x)^(7/2))/e^8 + (14*b^5*(b*d - a*e)^2*(d + e*x)^(9/2))/(3*e^8) - (14*b^6*(b*d - a*e)*(d + e*x)^(11/2))/(11*e^8) + (2*b^7*(d + e*x)^(13/2))/(13*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2064,1,208,0,0.0755252,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{5/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(5/2),x]","-\frac{14 b^6 (d+e x)^{9/2} (b d-a e)}{9 e^8}+\frac{6 b^5 (d+e x)^{7/2} (b d-a e)^2}{e^8}-\frac{14 b^4 (d+e x)^{5/2} (b d-a e)^3}{e^8}+\frac{70 b^3 (d+e x)^{3/2} (b d-a e)^4}{3 e^8}-\frac{42 b^2 \sqrt{d+e x} (b d-a e)^5}{e^8}-\frac{14 b (b d-a e)^6}{e^8 \sqrt{d+e x}}+\frac{2 (b d-a e)^7}{3 e^8 (d+e x)^{3/2}}+\frac{2 b^7 (d+e x)^{11/2}}{11 e^8}","-\frac{14 b^6 (d+e x)^{9/2} (b d-a e)}{9 e^8}+\frac{6 b^5 (d+e x)^{7/2} (b d-a e)^2}{e^8}-\frac{14 b^4 (d+e x)^{5/2} (b d-a e)^3}{e^8}+\frac{70 b^3 (d+e x)^{3/2} (b d-a e)^4}{3 e^8}-\frac{42 b^2 \sqrt{d+e x} (b d-a e)^5}{e^8}-\frac{14 b (b d-a e)^6}{e^8 \sqrt{d+e x}}+\frac{2 (b d-a e)^7}{3 e^8 (d+e x)^{3/2}}+\frac{2 b^7 (d+e x)^{11/2}}{11 e^8}",1,"(2*(b*d - a*e)^7)/(3*e^8*(d + e*x)^(3/2)) - (14*b*(b*d - a*e)^6)/(e^8*Sqrt[d + e*x]) - (42*b^2*(b*d - a*e)^5*Sqrt[d + e*x])/e^8 + (70*b^3*(b*d - a*e)^4*(d + e*x)^(3/2))/(3*e^8) - (14*b^4*(b*d - a*e)^3*(d + e*x)^(5/2))/e^8 + (6*b^5*(b*d - a*e)^2*(d + e*x)^(7/2))/e^8 - (14*b^6*(b*d - a*e)*(d + e*x)^(9/2))/(9*e^8) + (2*b^7*(d + e*x)^(11/2))/(11*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2065,1,210,0,0.0790765,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^3}{(d+e x)^{7/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^3)/(d + e*x)^(7/2),x]","-\frac{2 b^6 (d+e x)^{7/2} (b d-a e)}{e^8}+\frac{42 b^5 (d+e x)^{5/2} (b d-a e)^2}{5 e^8}-\frac{70 b^4 (d+e x)^{3/2} (b d-a e)^3}{3 e^8}+\frac{70 b^3 \sqrt{d+e x} (b d-a e)^4}{e^8}+\frac{42 b^2 (b d-a e)^5}{e^8 \sqrt{d+e x}}-\frac{14 b (b d-a e)^6}{3 e^8 (d+e x)^{3/2}}+\frac{2 (b d-a e)^7}{5 e^8 (d+e x)^{5/2}}+\frac{2 b^7 (d+e x)^{9/2}}{9 e^8}","-\frac{2 b^6 (d+e x)^{7/2} (b d-a e)}{e^8}+\frac{42 b^5 (d+e x)^{5/2} (b d-a e)^2}{5 e^8}-\frac{70 b^4 (d+e x)^{3/2} (b d-a e)^3}{3 e^8}+\frac{70 b^3 \sqrt{d+e x} (b d-a e)^4}{e^8}+\frac{42 b^2 (b d-a e)^5}{e^8 \sqrt{d+e x}}-\frac{14 b (b d-a e)^6}{3 e^8 (d+e x)^{3/2}}+\frac{2 (b d-a e)^7}{5 e^8 (d+e x)^{5/2}}+\frac{2 b^7 (d+e x)^{9/2}}{9 e^8}",1,"(2*(b*d - a*e)^7)/(5*e^8*(d + e*x)^(5/2)) - (14*b*(b*d - a*e)^6)/(3*e^8*(d + e*x)^(3/2)) + (42*b^2*(b*d - a*e)^5)/(e^8*Sqrt[d + e*x]) + (70*b^3*(b*d - a*e)^4*Sqrt[d + e*x])/e^8 - (70*b^4*(b*d - a*e)^3*(d + e*x)^(3/2))/(3*e^8) + (42*b^5*(b*d - a*e)^2*(d + e*x)^(5/2))/(5*e^8) - (2*b^6*(b*d - a*e)*(d + e*x)^(7/2))/e^8 + (2*b^7*(d + e*x)^(9/2))/(9*e^8)","A",3,2,33,0.06061,1,"{27, 43}"
2066,1,138,0,0.1247592,"\int \frac{(a+b x) (d+e x)^{7/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 \sqrt{d+e x} (b d-a e)^3}{b^4}+\frac{2 (d+e x)^{3/2} (b d-a e)^2}{3 b^3}+\frac{2 (d+e x)^{5/2} (b d-a e)}{5 b^2}-\frac{2 (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}+\frac{2 (d+e x)^{7/2}}{7 b}","\frac{2 \sqrt{d+e x} (b d-a e)^3}{b^4}+\frac{2 (d+e x)^{3/2} (b d-a e)^2}{3 b^3}+\frac{2 (d+e x)^{5/2} (b d-a e)}{5 b^2}-\frac{2 (b d-a e)^{7/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2}}+\frac{2 (d+e x)^{7/2}}{7 b}",1,"(2*(b*d - a*e)^3*Sqrt[d + e*x])/b^4 + (2*(b*d - a*e)^2*(d + e*x)^(3/2))/(3*b^3) + (2*(b*d - a*e)*(d + e*x)^(5/2))/(5*b^2) + (2*(d + e*x)^(7/2))/(7*b) - (2*(b*d - a*e)^(7/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(9/2)","A",7,4,33,0.1212,1,"{27, 50, 63, 208}"
2067,1,112,0,0.0585831,"\int \frac{(a+b x) (d+e x)^{5/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 \sqrt{d+e x} (b d-a e)^2}{b^3}+\frac{2 (d+e x)^{3/2} (b d-a e)}{3 b^2}-\frac{2 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}+\frac{2 (d+e x)^{5/2}}{5 b}","\frac{2 \sqrt{d+e x} (b d-a e)^2}{b^3}+\frac{2 (d+e x)^{3/2} (b d-a e)}{3 b^2}-\frac{2 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2}}+\frac{2 (d+e x)^{5/2}}{5 b}",1,"(2*(b*d - a*e)^2*Sqrt[d + e*x])/b^3 + (2*(b*d - a*e)*(d + e*x)^(3/2))/(3*b^2) + (2*(d + e*x)^(5/2))/(5*b) - (2*(b*d - a*e)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(7/2)","A",6,4,33,0.1212,1,"{27, 50, 63, 208}"
2068,1,86,0,0.0431648,"\int \frac{(a+b x) (d+e x)^{3/2}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 \sqrt{d+e x} (b d-a e)}{b^2}-\frac{2 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}+\frac{2 (d+e x)^{3/2}}{3 b}","\frac{2 \sqrt{d+e x} (b d-a e)}{b^2}-\frac{2 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2}}+\frac{2 (d+e x)^{3/2}}{3 b}",1,"(2*(b*d - a*e)*Sqrt[d + e*x])/b^2 + (2*(d + e*x)^(3/2))/(3*b) - (2*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(5/2)","A",5,4,33,0.1212,1,"{27, 50, 63, 208}"
2069,1,62,0,0.0292775,"\int \frac{(a+b x) \sqrt{d+e x}}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2),x]","\frac{2 \sqrt{d+e x}}{b}-\frac{2 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}","\frac{2 \sqrt{d+e x}}{b}-\frac{2 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2}}",1,"(2*Sqrt[d + e*x])/b - (2*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/b^(3/2)","A",4,4,33,0.1212,1,"{27, 50, 63, 208}"
2070,1,47,0,0.0221954,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{b d-a e}}","-\frac{2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{b d-a e}}",1,"(-2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*Sqrt[b*d - a*e])","A",3,3,33,0.09091,1,"{27, 63, 208}"
2071,1,69,0,0.0406016,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{2}{\sqrt{d+e x} (b d-a e)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}","\frac{2}{\sqrt{d+e x} (b d-a e)}-\frac{2 \sqrt{b} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{3/2}}",1,"2/((b*d - a*e)*Sqrt[d + e*x]) - (2*Sqrt[b]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(3/2)","A",4,4,33,0.1212,1,"{27, 51, 63, 208}"
2072,1,93,0,0.0463477,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}+\frac{2 b}{\sqrt{d+e x} (b d-a e)^2}+\frac{2}{3 (d+e x)^{3/2} (b d-a e)}","-\frac{2 b^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{5/2}}+\frac{2 b}{\sqrt{d+e x} (b d-a e)^2}+\frac{2}{3 (d+e x)^{3/2} (b d-a e)}",1,"2/(3*(b*d - a*e)*(d + e*x)^(3/2)) + (2*b)/((b*d - a*e)^2*Sqrt[d + e*x]) - (2*b^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(5/2)","A",5,4,33,0.1212,1,"{27, 51, 63, 208}"
2073,1,119,0,0.0594882,"\int \frac{a+b x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)} \, dx","Int[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)),x]","\frac{2 b^2}{\sqrt{d+e x} (b d-a e)^3}-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}+\frac{2 b}{3 (d+e x)^{3/2} (b d-a e)^2}+\frac{2}{5 (d+e x)^{5/2} (b d-a e)}","\frac{2 b^2}{\sqrt{d+e x} (b d-a e)^3}-\frac{2 b^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{(b d-a e)^{7/2}}+\frac{2 b}{3 (d+e x)^{3/2} (b d-a e)^2}+\frac{2}{5 (d+e x)^{5/2} (b d-a e)}",1,"2/(5*(b*d - a*e)*(d + e*x)^(5/2)) + (2*b)/(3*(b*d - a*e)^2*(d + e*x)^(3/2)) + (2*b^2)/((b*d - a*e)^3*Sqrt[d + e*x]) - (2*b^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b*d - a*e)^(7/2)","A",6,4,33,0.1212,1,"{27, 51, 63, 208}"
2074,1,175,0,0.106475,"\int \frac{(a+b x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{21 e^2 (d+e x)^{3/2} (b d-a e)}{4 b^4}+\frac{63 e^2 \sqrt{d+e x} (b d-a e)^2}{4 b^5}-\frac{63 e^2 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2}}-\frac{9 e (d+e x)^{7/2}}{4 b^2 (a+b x)}-\frac{(d+e x)^{9/2}}{2 b (a+b x)^2}+\frac{63 e^2 (d+e x)^{5/2}}{20 b^3}","\frac{21 e^2 (d+e x)^{3/2} (b d-a e)}{4 b^4}+\frac{63 e^2 \sqrt{d+e x} (b d-a e)^2}{4 b^5}-\frac{63 e^2 (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{11/2}}-\frac{9 e (d+e x)^{7/2}}{4 b^2 (a+b x)}-\frac{(d+e x)^{9/2}}{2 b (a+b x)^2}+\frac{63 e^2 (d+e x)^{5/2}}{20 b^3}",1,"(63*e^2*(b*d - a*e)^2*Sqrt[d + e*x])/(4*b^5) + (21*e^2*(b*d - a*e)*(d + e*x)^(3/2))/(4*b^4) + (63*e^2*(d + e*x)^(5/2))/(20*b^3) - (9*e*(d + e*x)^(7/2))/(4*b^2*(a + b*x)) - (d + e*x)^(9/2)/(2*b*(a + b*x)^2) - (63*e^2*(b*d - a*e)^(5/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(11/2))","A",8,5,33,0.1515,1,"{27, 47, 50, 63, 208}"
2075,1,146,0,0.0759457,"\int \frac{(a+b x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{35 e^2 \sqrt{d+e x} (b d-a e)}{4 b^4}-\frac{35 e^2 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2}}-\frac{7 e (d+e x)^{5/2}}{4 b^2 (a+b x)}-\frac{(d+e x)^{7/2}}{2 b (a+b x)^2}+\frac{35 e^2 (d+e x)^{3/2}}{12 b^3}","\frac{35 e^2 \sqrt{d+e x} (b d-a e)}{4 b^4}-\frac{35 e^2 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{9/2}}-\frac{7 e (d+e x)^{5/2}}{4 b^2 (a+b x)}-\frac{(d+e x)^{7/2}}{2 b (a+b x)^2}+\frac{35 e^2 (d+e x)^{3/2}}{12 b^3}",1,"(35*e^2*(b*d - a*e)*Sqrt[d + e*x])/(4*b^4) + (35*e^2*(d + e*x)^(3/2))/(12*b^3) - (7*e*(d + e*x)^(5/2))/(4*b^2*(a + b*x)) - (d + e*x)^(7/2)/(2*b*(a + b*x)^2) - (35*e^2*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(9/2))","A",7,5,33,0.1515,1,"{27, 47, 50, 63, 208}"
2076,1,119,0,0.0555334,"\int \frac{(a+b x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{15 e^2 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2}}-\frac{5 e (d+e x)^{3/2}}{4 b^2 (a+b x)}-\frac{(d+e x)^{5/2}}{2 b (a+b x)^2}+\frac{15 e^2 \sqrt{d+e x}}{4 b^3}","-\frac{15 e^2 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{7/2}}-\frac{5 e (d+e x)^{3/2}}{4 b^2 (a+b x)}-\frac{(d+e x)^{5/2}}{2 b (a+b x)^2}+\frac{15 e^2 \sqrt{d+e x}}{4 b^3}",1,"(15*e^2*Sqrt[d + e*x])/(4*b^3) - (5*e*(d + e*x)^(3/2))/(4*b^2*(a + b*x)) - (d + e*x)^(5/2)/(2*b*(a + b*x)^2) - (15*e^2*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(7/2))","A",6,5,33,0.1515,1,"{27, 47, 50, 63, 208}"
2077,1,100,0,0.0489792,"\int \frac{(a+b x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} \sqrt{b d-a e}}-\frac{3 e \sqrt{d+e x}}{4 b^2 (a+b x)}-\frac{(d+e x)^{3/2}}{2 b (a+b x)^2}","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{5/2} \sqrt{b d-a e}}-\frac{3 e \sqrt{d+e x}}{4 b^2 (a+b x)}-\frac{(d+e x)^{3/2}}{2 b (a+b x)^2}",1,"(-3*e*Sqrt[d + e*x])/(4*b^2*(a + b*x)) - (d + e*x)^(3/2)/(2*b*(a + b*x)^2) - (3*e^2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(5/2)*Sqrt[b*d - a*e])","A",5,4,33,0.1212,1,"{27, 47, 63, 208}"
2078,1,110,0,0.0550826,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b (a+b x) (b d-a e)}-\frac{\sqrt{d+e x}}{2 b (a+b x)^2}","\frac{e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 b^{3/2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b (a+b x) (b d-a e)}-\frac{\sqrt{d+e x}}{2 b (a+b x)^2}",1,"-Sqrt[d + e*x]/(2*b*(a + b*x)^2) - (e*Sqrt[d + e*x])/(4*b*(b*d - a*e)*(a + b*x)) + (e^2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*b^(3/2)*(b*d - a*e)^(3/2))","A",5,5,33,0.1515,1,"{27, 47, 51, 63, 208}"
2079,1,114,0,0.0493291,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} (b d-a e)^{5/2}}+\frac{3 e \sqrt{d+e x}}{4 (a+b x) (b d-a e)^2}-\frac{\sqrt{d+e x}}{2 (a+b x)^2 (b d-a e)}","-\frac{3 e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 \sqrt{b} (b d-a e)^{5/2}}+\frac{3 e \sqrt{d+e x}}{4 (a+b x) (b d-a e)^2}-\frac{\sqrt{d+e x}}{2 (a+b x)^2 (b d-a e)}",1,"-Sqrt[d + e*x]/(2*(b*d - a*e)*(a + b*x)^2) + (3*e*Sqrt[d + e*x])/(4*(b*d - a*e)^2*(a + b*x)) - (3*e^2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*Sqrt[b]*(b*d - a*e)^(5/2))","A",5,4,33,0.1212,1,"{27, 51, 63, 208}"
2080,1,140,0,0.0631258,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{15 e^2}{4 \sqrt{d+e x} (b d-a e)^3}-\frac{15 \sqrt{b} e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{7/2}}+\frac{5 e}{4 (a+b x) \sqrt{d+e x} (b d-a e)^2}-\frac{1}{2 (a+b x)^2 \sqrt{d+e x} (b d-a e)}","\frac{15 e^2}{4 \sqrt{d+e x} (b d-a e)^3}-\frac{15 \sqrt{b} e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{7/2}}+\frac{5 e}{4 (a+b x) \sqrt{d+e x} (b d-a e)^2}-\frac{1}{2 (a+b x)^2 \sqrt{d+e x} (b d-a e)}",1,"(15*e^2)/(4*(b*d - a*e)^3*Sqrt[d + e*x]) - 1/(2*(b*d - a*e)*(a + b*x)^2*Sqrt[d + e*x]) + (5*e)/(4*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x]) - (15*Sqrt[b]*e^2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(7/2))","A",6,4,33,0.1212,1,"{27, 51, 63, 208}"
2081,1,167,0,0.0827507,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","-\frac{35 b^{3/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{9/2}}+\frac{35 b e^2}{4 \sqrt{d+e x} (b d-a e)^4}+\frac{35 e^2}{12 (d+e x)^{3/2} (b d-a e)^3}+\frac{7 e}{4 (a+b x) (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{2 (a+b x)^2 (d+e x)^{3/2} (b d-a e)}","-\frac{35 b^{3/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{9/2}}+\frac{35 b e^2}{4 \sqrt{d+e x} (b d-a e)^4}+\frac{35 e^2}{12 (d+e x)^{3/2} (b d-a e)^3}+\frac{7 e}{4 (a+b x) (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{2 (a+b x)^2 (d+e x)^{3/2} (b d-a e)}",1,"(35*e^2)/(12*(b*d - a*e)^3*(d + e*x)^(3/2)) - 1/(2*(b*d - a*e)*(a + b*x)^2*(d + e*x)^(3/2)) + (7*e)/(4*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(3/2)) + (35*b*e^2)/(4*(b*d - a*e)^4*Sqrt[d + e*x]) - (35*b^(3/2)*e^2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(9/2))","A",7,4,33,0.1212,1,"{27, 51, 63, 208}"
2082,1,196,0,0.1391658,"\int \frac{a+b x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^2),x]","\frac{63 b^2 e^2}{4 \sqrt{d+e x} (b d-a e)^5}-\frac{63 b^{5/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{11/2}}+\frac{21 b e^2}{4 (d+e x)^{3/2} (b d-a e)^4}+\frac{63 e^2}{20 (d+e x)^{5/2} (b d-a e)^3}+\frac{9 e}{4 (a+b x) (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{2 (a+b x)^2 (d+e x)^{5/2} (b d-a e)}","\frac{63 b^2 e^2}{4 \sqrt{d+e x} (b d-a e)^5}-\frac{63 b^{5/2} e^2 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{4 (b d-a e)^{11/2}}+\frac{21 b e^2}{4 (d+e x)^{3/2} (b d-a e)^4}+\frac{63 e^2}{20 (d+e x)^{5/2} (b d-a e)^3}+\frac{9 e}{4 (a+b x) (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{2 (a+b x)^2 (d+e x)^{5/2} (b d-a e)}",1,"(63*e^2)/(20*(b*d - a*e)^3*(d + e*x)^(5/2)) - 1/(2*(b*d - a*e)*(a + b*x)^2*(d + e*x)^(5/2)) + (9*e)/(4*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(5/2)) + (21*b*e^2)/(4*(b*d - a*e)^4*(d + e*x)^(3/2)) + (63*b^2*e^2)/(4*(b*d - a*e)^5*Sqrt[d + e*x]) - (63*b^(5/2)*e^2*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(4*(b*d - a*e)^(11/2))","A",8,4,33,0.1212,1,"{27, 51, 63, 208}"
2083,1,198,0,0.1226211,"\int \frac{(a+b x) (d+e x)^{11/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^(11/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{33 e^2 (d+e x)^{7/2}}{32 b^3 (a+b x)^2}-\frac{231 e^3 (d+e x)^{5/2}}{64 b^4 (a+b x)}+\frac{1155 e^4 \sqrt{d+e x} (b d-a e)}{64 b^6}-\frac{1155 e^4 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{13/2}}-\frac{11 e (d+e x)^{9/2}}{24 b^2 (a+b x)^3}-\frac{(d+e x)^{11/2}}{4 b (a+b x)^4}+\frac{385 e^4 (d+e x)^{3/2}}{64 b^5}","-\frac{33 e^2 (d+e x)^{7/2}}{32 b^3 (a+b x)^2}-\frac{231 e^3 (d+e x)^{5/2}}{64 b^4 (a+b x)}+\frac{1155 e^4 \sqrt{d+e x} (b d-a e)}{64 b^6}-\frac{1155 e^4 (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{13/2}}-\frac{11 e (d+e x)^{9/2}}{24 b^2 (a+b x)^3}-\frac{(d+e x)^{11/2}}{4 b (a+b x)^4}+\frac{385 e^4 (d+e x)^{3/2}}{64 b^5}",1,"(1155*e^4*(b*d - a*e)*Sqrt[d + e*x])/(64*b^6) + (385*e^4*(d + e*x)^(3/2))/(64*b^5) - (231*e^3*(d + e*x)^(5/2))/(64*b^4*(a + b*x)) - (33*e^2*(d + e*x)^(7/2))/(32*b^3*(a + b*x)^2) - (11*e*(d + e*x)^(9/2))/(24*b^2*(a + b*x)^3) - (d + e*x)^(11/2)/(4*b*(a + b*x)^4) - (1155*e^4*(b*d - a*e)^(3/2)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(13/2))","A",9,5,33,0.1515,1,"{27, 47, 50, 63, 208}"
2084,1,171,0,0.0814466,"\int \frac{(a+b x) (d+e x)^{9/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^(9/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{21 e^2 (d+e x)^{5/2}}{32 b^3 (a+b x)^2}-\frac{105 e^3 (d+e x)^{3/2}}{64 b^4 (a+b x)}-\frac{315 e^4 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{11/2}}-\frac{3 e (d+e x)^{7/2}}{8 b^2 (a+b x)^3}-\frac{(d+e x)^{9/2}}{4 b (a+b x)^4}+\frac{315 e^4 \sqrt{d+e x}}{64 b^5}","-\frac{21 e^2 (d+e x)^{5/2}}{32 b^3 (a+b x)^2}-\frac{105 e^3 (d+e x)^{3/2}}{64 b^4 (a+b x)}-\frac{315 e^4 \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{11/2}}-\frac{3 e (d+e x)^{7/2}}{8 b^2 (a+b x)^3}-\frac{(d+e x)^{9/2}}{4 b (a+b x)^4}+\frac{315 e^4 \sqrt{d+e x}}{64 b^5}",1,"(315*e^4*Sqrt[d + e*x])/(64*b^5) - (105*e^3*(d + e*x)^(3/2))/(64*b^4*(a + b*x)) - (21*e^2*(d + e*x)^(5/2))/(32*b^3*(a + b*x)^2) - (3*e*(d + e*x)^(7/2))/(8*b^2*(a + b*x)^3) - (d + e*x)^(9/2)/(4*b*(a + b*x)^4) - (315*e^4*Sqrt[b*d - a*e]*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(11/2))","A",8,5,33,0.1515,1,"{27, 47, 50, 63, 208}"
2085,1,152,0,0.0731864,"\int \frac{(a+b x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{35 e^3 \sqrt{d+e x}}{64 b^4 (a+b x)}-\frac{35 e^2 (d+e x)^{3/2}}{96 b^3 (a+b x)^2}-\frac{35 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{9/2} \sqrt{b d-a e}}-\frac{7 e (d+e x)^{5/2}}{24 b^2 (a+b x)^3}-\frac{(d+e x)^{7/2}}{4 b (a+b x)^4}","-\frac{35 e^3 \sqrt{d+e x}}{64 b^4 (a+b x)}-\frac{35 e^2 (d+e x)^{3/2}}{96 b^3 (a+b x)^2}-\frac{35 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{9/2} \sqrt{b d-a e}}-\frac{7 e (d+e x)^{5/2}}{24 b^2 (a+b x)^3}-\frac{(d+e x)^{7/2}}{4 b (a+b x)^4}",1,"(-35*e^3*Sqrt[d + e*x])/(64*b^4*(a + b*x)) - (35*e^2*(d + e*x)^(3/2))/(96*b^3*(a + b*x)^2) - (7*e*(d + e*x)^(5/2))/(24*b^2*(a + b*x)^3) - (d + e*x)^(7/2)/(4*b*(a + b*x)^4) - (35*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(9/2)*Sqrt[b*d - a*e])","A",7,4,33,0.1212,1,"{27, 47, 63, 208}"
2086,1,162,0,0.0892755,"\int \frac{(a+b x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{5 e^3 \sqrt{d+e x}}{64 b^3 (a+b x) (b d-a e)}-\frac{5 e^2 \sqrt{d+e x}}{32 b^3 (a+b x)^2}+\frac{5 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{7/2} (b d-a e)^{3/2}}-\frac{5 e (d+e x)^{3/2}}{24 b^2 (a+b x)^3}-\frac{(d+e x)^{5/2}}{4 b (a+b x)^4}","-\frac{5 e^3 \sqrt{d+e x}}{64 b^3 (a+b x) (b d-a e)}-\frac{5 e^2 \sqrt{d+e x}}{32 b^3 (a+b x)^2}+\frac{5 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{7/2} (b d-a e)^{3/2}}-\frac{5 e (d+e x)^{3/2}}{24 b^2 (a+b x)^3}-\frac{(d+e x)^{5/2}}{4 b (a+b x)^4}",1,"(-5*e^2*Sqrt[d + e*x])/(32*b^3*(a + b*x)^2) - (5*e^3*Sqrt[d + e*x])/(64*b^3*(b*d - a*e)*(a + b*x)) - (5*e*(d + e*x)^(3/2))/(24*b^2*(a + b*x)^3) - (d + e*x)^(5/2)/(4*b*(a + b*x)^4) + (5*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(7/2)*(b*d - a*e)^(3/2))","A",7,5,33,0.1515,1,"{27, 47, 51, 63, 208}"
2087,1,172,0,0.0908595,"\int \frac{(a+b x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{3 e^3 \sqrt{d+e x}}{64 b^2 (a+b x) (b d-a e)^2}-\frac{e^2 \sqrt{d+e x}}{32 b^2 (a+b x)^2 (b d-a e)}-\frac{3 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{5/2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x}}{8 b^2 (a+b x)^3}-\frac{(d+e x)^{3/2}}{4 b (a+b x)^4}","\frac{3 e^3 \sqrt{d+e x}}{64 b^2 (a+b x) (b d-a e)^2}-\frac{e^2 \sqrt{d+e x}}{32 b^2 (a+b x)^2 (b d-a e)}-\frac{3 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{5/2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x}}{8 b^2 (a+b x)^3}-\frac{(d+e x)^{3/2}}{4 b (a+b x)^4}",1,"-(e*Sqrt[d + e*x])/(8*b^2*(a + b*x)^3) - (e^2*Sqrt[d + e*x])/(32*b^2*(b*d - a*e)*(a + b*x)^2) + (3*e^3*Sqrt[d + e*x])/(64*b^2*(b*d - a*e)^2*(a + b*x)) - (d + e*x)^(3/2)/(4*b*(a + b*x)^4) - (3*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(5/2)*(b*d - a*e)^(5/2))","A",7,5,33,0.1515,1,"{27, 47, 51, 63, 208}"
2088,1,182,0,0.0949738,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{5 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{3/2} (b d-a e)^{7/2}}-\frac{5 e^3 \sqrt{d+e x}}{64 b (a+b x) (b d-a e)^3}+\frac{5 e^2 \sqrt{d+e x}}{96 b (a+b x)^2 (b d-a e)^2}-\frac{e \sqrt{d+e x}}{24 b (a+b x)^3 (b d-a e)}-\frac{\sqrt{d+e x}}{4 b (a+b x)^4}","\frac{5 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 b^{3/2} (b d-a e)^{7/2}}-\frac{5 e^3 \sqrt{d+e x}}{64 b (a+b x) (b d-a e)^3}+\frac{5 e^2 \sqrt{d+e x}}{96 b (a+b x)^2 (b d-a e)^2}-\frac{e \sqrt{d+e x}}{24 b (a+b x)^3 (b d-a e)}-\frac{\sqrt{d+e x}}{4 b (a+b x)^4}",1,"-Sqrt[d + e*x]/(4*b*(a + b*x)^4) - (e*Sqrt[d + e*x])/(24*b*(b*d - a*e)*(a + b*x)^3) + (5*e^2*Sqrt[d + e*x])/(96*b*(b*d - a*e)^2*(a + b*x)^2) - (5*e^3*Sqrt[d + e*x])/(64*b*(b*d - a*e)^3*(a + b*x)) + (5*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*b^(3/2)*(b*d - a*e)^(7/2))","A",7,5,33,0.1515,1,"{27, 47, 51, 63, 208}"
2089,1,180,0,0.0949907,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{35 e^3 \sqrt{d+e x}}{64 (a+b x) (b d-a e)^4}-\frac{35 e^2 \sqrt{d+e x}}{96 (a+b x)^2 (b d-a e)^3}-\frac{35 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{b} (b d-a e)^{9/2}}+\frac{7 e \sqrt{d+e x}}{24 (a+b x)^3 (b d-a e)^2}-\frac{\sqrt{d+e x}}{4 (a+b x)^4 (b d-a e)}","\frac{35 e^3 \sqrt{d+e x}}{64 (a+b x) (b d-a e)^4}-\frac{35 e^2 \sqrt{d+e x}}{96 (a+b x)^2 (b d-a e)^3}-\frac{35 e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 \sqrt{b} (b d-a e)^{9/2}}+\frac{7 e \sqrt{d+e x}}{24 (a+b x)^3 (b d-a e)^2}-\frac{\sqrt{d+e x}}{4 (a+b x)^4 (b d-a e)}",1,"-Sqrt[d + e*x]/(4*(b*d - a*e)*(a + b*x)^4) + (7*e*Sqrt[d + e*x])/(24*(b*d - a*e)^2*(a + b*x)^3) - (35*e^2*Sqrt[d + e*x])/(96*(b*d - a*e)^3*(a + b*x)^2) + (35*e^3*Sqrt[d + e*x])/(64*(b*d - a*e)^4*(a + b*x)) - (35*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*Sqrt[b]*(b*d - a*e)^(9/2))","A",7,4,33,0.1212,1,"{27, 51, 63, 208}"
2090,1,206,0,0.1239596,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","\frac{315 e^4}{64 \sqrt{d+e x} (b d-a e)^5}+\frac{105 e^3}{64 (a+b x) \sqrt{d+e x} (b d-a e)^4}-\frac{21 e^2}{32 (a+b x)^2 \sqrt{d+e x} (b d-a e)^3}-\frac{315 \sqrt{b} e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 (b d-a e)^{11/2}}+\frac{3 e}{8 (a+b x)^3 \sqrt{d+e x} (b d-a e)^2}-\frac{1}{4 (a+b x)^4 \sqrt{d+e x} (b d-a e)}","\frac{315 e^4}{64 \sqrt{d+e x} (b d-a e)^5}+\frac{105 e^3}{64 (a+b x) \sqrt{d+e x} (b d-a e)^4}-\frac{21 e^2}{32 (a+b x)^2 \sqrt{d+e x} (b d-a e)^3}-\frac{315 \sqrt{b} e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 (b d-a e)^{11/2}}+\frac{3 e}{8 (a+b x)^3 \sqrt{d+e x} (b d-a e)^2}-\frac{1}{4 (a+b x)^4 \sqrt{d+e x} (b d-a e)}",1,"(315*e^4)/(64*(b*d - a*e)^5*Sqrt[d + e*x]) - 1/(4*(b*d - a*e)*(a + b*x)^4*Sqrt[d + e*x]) + (3*e)/(8*(b*d - a*e)^2*(a + b*x)^3*Sqrt[d + e*x]) - (21*e^2)/(32*(b*d - a*e)^3*(a + b*x)^2*Sqrt[d + e*x]) + (105*e^3)/(64*(b*d - a*e)^4*(a + b*x)*Sqrt[d + e*x]) - (315*Sqrt[b]*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(11/2))","A",8,4,33,0.1212,1,"{27, 51, 63, 208}"
2091,1,233,0,0.2048595,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^3),x]","-\frac{1155 b^{3/2} e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 (b d-a e)^{13/2}}+\frac{1155 b e^4}{64 \sqrt{d+e x} (b d-a e)^6}+\frac{385 e^4}{64 (d+e x)^{3/2} (b d-a e)^5}+\frac{231 e^3}{64 (a+b x) (d+e x)^{3/2} (b d-a e)^4}-\frac{33 e^2}{32 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^3}+\frac{11 e}{24 (a+b x)^3 (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{4 (a+b x)^4 (d+e x)^{3/2} (b d-a e)}","-\frac{1155 b^{3/2} e^4 \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{64 (b d-a e)^{13/2}}+\frac{1155 b e^4}{64 \sqrt{d+e x} (b d-a e)^6}+\frac{385 e^4}{64 (d+e x)^{3/2} (b d-a e)^5}+\frac{231 e^3}{64 (a+b x) (d+e x)^{3/2} (b d-a e)^4}-\frac{33 e^2}{32 (a+b x)^2 (d+e x)^{3/2} (b d-a e)^3}+\frac{11 e}{24 (a+b x)^3 (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{4 (a+b x)^4 (d+e x)^{3/2} (b d-a e)}",1,"(385*e^4)/(64*(b*d - a*e)^5*(d + e*x)^(3/2)) - 1/(4*(b*d - a*e)*(a + b*x)^4*(d + e*x)^(3/2)) + (11*e)/(24*(b*d - a*e)^2*(a + b*x)^3*(d + e*x)^(3/2)) - (33*e^2)/(32*(b*d - a*e)^3*(a + b*x)^2*(d + e*x)^(3/2)) + (231*e^3)/(64*(b*d - a*e)^4*(a + b*x)*(d + e*x)^(3/2)) + (1155*b*e^4)/(64*(b*d - a*e)^6*Sqrt[d + e*x]) - (1155*b^(3/2)*e^4*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(64*(b*d - a*e)^(13/2))","A",9,4,33,0.1212,1,"{27, 51, 63, 208}"
2092,1,152,0,0.0736086,"\int (a+b x) (d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{9 e^3 (a+b x)}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{9 e^3 (a+b x)}",1,"(2*(b*d - a*e)^2*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^3*(a + b*x)) - (4*b*(b*d - a*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^3*(a + b*x)) + (2*b^2*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2093,1,152,0,0.0703875,"\int (a+b x) (d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{9 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^3 (a+b x)}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{9 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^3 (a+b x)}",1,"(2*(b*d - a*e)^2*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x)) - (4*b*(b*d - a*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^3*(a + b*x)) + (2*b^2*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2094,1,152,0,0.067063,"\int (a+b x) (d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{5 e^3 (a+b x)}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{5 e^3 (a+b x)}",1,"(2*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) - (4*b*(b*d - a*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x)) + (2*b^2*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2095,1,152,0,0.0655219,"\int (a+b x) \sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{3 e^3 (a+b x)}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{3 e^3 (a+b x)}",1,"(2*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)) - (4*b*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)) + (2*b^2*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2096,1,150,0,0.0694768,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{\sqrt{d+e x}} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/Sqrt[d + e*x],x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^3 (a+b x)}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^3 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^3 (a+b x)}",1,"(2*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)) - (4*b*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)) + (2*b^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2097,1,148,0,0.0659191,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{3/2}} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(3/2),x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^3 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^3 (a+b x) \sqrt{d+e x}}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^3 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^3 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^3 (a+b x) \sqrt{d+e x}}",1,"(-2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*Sqrt[d + e*x]) - (4*b*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)) + (2*b^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2098,1,148,0,0.0667385,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{5/2}} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(5/2),x]","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^3 (a+b x)}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^3 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^3 (a+b x) (d+e x)^{3/2}}","\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^3 (a+b x)}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^3 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{3 e^3 (a+b x) (d+e x)^{3/2}}",1,"(-2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^(3/2)) + (4*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*Sqrt[d + e*x]) + (2*b^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2099,1,150,0,0.0694797,"\int \frac{(a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}{(d+e x)^{7/2}} \, dx","Int[((a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(d + e*x)^(7/2),x]","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{e^3 (a+b x) \sqrt{d+e x}}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^3 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^3 (a+b x) (d+e x)^{5/2}}","-\frac{2 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}{e^3 (a+b x) \sqrt{d+e x}}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^3 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^3 (a+b x) (d+e x)^{5/2}}",1,"(-2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^3*(a + b*x)*(d + e*x)^(5/2)) + (4*b*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^3*(a + b*x)*(d + e*x)^(3/2)) - (2*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(a + b*x)*Sqrt[d + e*x])","A",4,3,35,0.08571,1,"{770, 21, 43}"
2100,1,264,0,0.1279184,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)}{13 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2}{11 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3}{9 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4}{7 e^5 (a+b x)}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)}{13 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2}{11 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3}{9 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4}{7 e^5 (a+b x)}",1,"(2*(b*d - a*e)^4*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (8*b*(b*d - a*e)^3*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)) - (8*b^3*(b*d - a*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^5*(a + b*x)) + (2*b^4*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2101,1,264,0,0.1027751,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^5 (a+b x)}+\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{3 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}{5 e^5 (a+b x)}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^5 (a+b x)}+\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{3 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}{5 e^5 (a+b x)}",1,"(2*(b*d - a*e)^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) - (8*b*(b*d - a*e)^3*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) + (4*b^2*(b*d - a*e)^2*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - (8*b^3*(b*d - a*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)) + (2*b^4*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2102,1,264,0,0.104945,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{9 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{5 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}{3 e^5 (a+b x)}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{9 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{5 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}{3 e^5 (a+b x)}",1,"(2*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) - (8*b*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) - (8*b^3*(b*d - a*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)) + (2*b^4*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2103,1,262,0,0.1011478,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/Sqrt[d + e*x],x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{5 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}{e^5 (a+b x)}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{5 e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^5 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}{e^5 (a+b x)}",1,"(2*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - (8*b*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) + (12*b^2*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) - (8*b^3*(b*d - a*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)) + (2*b^4*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2104,1,258,0,0.1056935,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(3/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^5 (a+b x)}+\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^5 (a+b x) \sqrt{d+e x}}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^5 (a+b x)}+\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{e^5 (a+b x)}-\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^5 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^5 (a+b x) \sqrt{d+e x}}",1,"(-2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) - (8*b*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + (4*b^2*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - (8*b^3*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)) + (2*b^4*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2105,1,260,0,0.1035781,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^5 (a+b x)}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^5 (a+b x) (d+e x)^{3/2}}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{3 e^5 (a+b x)}+\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^5 (a+b x)}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^5 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^5 (a+b x) (d+e x)^{3/2}}",1,"(-2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^(3/2)) + (8*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) + (12*b^2*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) - (8*b^3*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)) + (2*b^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2106,1,260,0,0.0997419,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(7/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^5 (a+b x)}-\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) \sqrt{d+e x}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^5 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{5 e^5 (a+b x) (d+e x)^{5/2}}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^5 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^5 (a+b x)}-\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) \sqrt{d+e x}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^5 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{5 e^5 (a+b x) (d+e x)^{5/2}}",1,"(-2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^(5/2)) + (8*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^(3/2)) - (12*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) - (8*b^3*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)) + (2*b^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2107,1,258,0,0.1039879,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(9/2),x]","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^5 (a+b x)}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^5 (a+b x) \sqrt{d+e x}}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)^{3/2}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{5 e^5 (a+b x) (d+e x)^{5/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{7 e^5 (a+b x) (d+e x)^{7/2}}","\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^5 (a+b x)}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^5 (a+b x) \sqrt{d+e x}}-\frac{4 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^5 (a+b x) (d+e x)^{3/2}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{5 e^5 (a+b x) (d+e x)^{5/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{7 e^5 (a+b x) (d+e x)^{7/2}}",1,"(-2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^(7/2)) + (8*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^(5/2)) - (4*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*(d + e*x)^(3/2)) + (8*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x]) + (2*b^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2108,1,262,0,0.1006326,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{11/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(11/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{e^5 (a+b x) \sqrt{d+e x}}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^5 (a+b x) (d+e x)^{3/2}}-\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^5 (a+b x) (d+e x)^{5/2}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^5 (a+b x) (d+e x)^{7/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^5 (a+b x) (d+e x)^{9/2}}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{e^5 (a+b x) \sqrt{d+e x}}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{3 e^5 (a+b x) (d+e x)^{3/2}}-\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{5 e^5 (a+b x) (d+e x)^{5/2}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^5 (a+b x) (d+e x)^{7/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{9 e^5 (a+b x) (d+e x)^{9/2}}",1,"(-2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)*(d + e*x)^(9/2)) + (8*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^(7/2)) - (12*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^(5/2)) + (8*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^(3/2)) - (2*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(a + b*x)*Sqrt[d + e*x])","A",4,3,35,0.08571,1,"{770, 21, 43}"
2109,1,264,0,0.1038805,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}{(d+e x)^{13/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2))/(d + e*x)^(13/2),x]","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^5 (a+b x) (d+e x)^{3/2}}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^5 (a+b x) (d+e x)^{5/2}}-\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^5 (a+b x) (d+e x)^{7/2}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^5 (a+b x) (d+e x)^{9/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^5 (a+b x) (d+e x)^{11/2}}","-\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^5 (a+b x) (d+e x)^{3/2}}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^5 (a+b x) (d+e x)^{5/2}}-\frac{12 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^5 (a+b x) (d+e x)^{7/2}}+\frac{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^5 (a+b x) (d+e x)^{9/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^5 (a+b x) (d+e x)^{11/2}}",1,"(-2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^5*(a + b*x)*(d + e*x)^(11/2)) + (8*b*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^5*(a + b*x)*(d + e*x)^(9/2)) - (12*b^2*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^5*(a + b*x)*(d + e*x)^(7/2)) + (8*b^3*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^5*(a + b*x)*(d + e*x)^(5/2)) - (2*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^5*(a + b*x)*(d + e*x)^(3/2))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2110,1,374,0,0.16749,"\int (a+b x) (d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{19/2}}{19 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2} (b d-a e)}{17 e^7 (a+b x)}+\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)^2}{e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^3}{13 e^7 (a+b x)}+\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^4}{11 e^7 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^5}{3 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^6}{7 e^7 (a+b x)}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{19/2}}{19 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2} (b d-a e)}{17 e^7 (a+b x)}+\frac{2 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)^2}{e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^3}{13 e^7 (a+b x)}+\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^4}{11 e^7 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^5}{3 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^6}{7 e^7 (a+b x)}",1,"(2*(b*d - a*e)^6*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - (4*b*(b*d - a*e)^5*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) + (2*b^4*(b*d - a*e)^2*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (12*b^5*(b*d - a*e)*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(19/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(19*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2111,1,376,0,0.1366287,"\int (a+b x) (d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^7 (a+b x)}-\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)}{5 e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^2}{13 e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^3}{11 e^7 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^4}{3 e^7 (a+b x)}-\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^5}{7 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^6}{5 e^7 (a+b x)}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{17/2}}{17 e^7 (a+b x)}-\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2} (b d-a e)}{5 e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)^2}{13 e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^3}{11 e^7 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^4}{3 e^7 (a+b x)}-\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^5}{7 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^6}{5 e^7 (a+b x)}",1,"(2*(b*d - a*e)^6*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) - (12*b*(b*d - a*e)^5*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (10*b^2*(b*d - a*e)^4*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) - (4*b^5*(b*d - a*e)*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(17/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(17*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2112,1,376,0,0.1430521,"\int (a+b x) \sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)}{13 e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2}{11 e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3}{9 e^7 (a+b x)}+\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4}{7 e^7 (a+b x)}-\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}{5 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^6}{3 e^7 (a+b x)}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{15/2}}{15 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2} (b d-a e)}{13 e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)^2}{11 e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^3}{9 e^7 (a+b x)}+\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^4}{7 e^7 (a+b x)}-\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^5}{5 e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^6}{3 e^7 (a+b x)}",1,"(2*(b*d - a*e)^6*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (12*b*(b*d - a*e)^5*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (30*b^2*(b*d - a*e)^4*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) - (12*b^5*(b*d - a*e)*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(15/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2113,1,370,0,0.1400299,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/Sqrt[d + e*x],x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^7 (a+b x)}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{3 e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^7 (a+b x)}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}{e^7 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}{e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}{e^7 (a+b x)}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{13/2}}{13 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2} (b d-a e)}{11 e^7 (a+b x)}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)^2}{3 e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^3}{7 e^7 (a+b x)}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}{e^7 (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}{e^7 (a+b x)}+\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}{e^7 (a+b x)}",1,"(2*(b*d - a*e)^6*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (4*b*(b*d - a*e)^5*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (6*b^2*(b*d - a*e)^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (10*b^4*(b*d - a*e)^2*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) - (12*b^5*(b*d - a*e)*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2114,1,368,0,0.1387272,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(3/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^7 (a+b x)}-\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{3 e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^7 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{e^7 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}{e^7 (a+b x)}-\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}{e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{e^7 (a+b x) \sqrt{d+e x}}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{11/2}}{11 e^7 (a+b x)}-\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2} (b d-a e)}{3 e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)^2}{7 e^7 (a+b x)}-\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}{e^7 (a+b x)}+\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}{e^7 (a+b x)}-\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}{e^7 (a+b x)}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{e^7 (a+b x) \sqrt{d+e x}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) - (12*b*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (10*b^2*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (8*b^3*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (30*b^4*(b*d - a*e)^2*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) - (4*b^5*(b*d - a*e)*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2115,1,370,0,0.1443151,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(5/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^7 (a+b x)}+\frac{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^7 (a+b x)}+\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}{e^7 (a+b x)}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{3 e^7 (a+b x) (d+e x)^{3/2}}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{9/2}}{9 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2} (b d-a e)}{7 e^7 (a+b x)}+\frac{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}{e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}{3 e^7 (a+b x)}+\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}{e^7 (a+b x)}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) \sqrt{d+e x}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{3 e^7 (a+b x) (d+e x)^{3/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(3/2)) + (12*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) + (30*b^2*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (40*b^3*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)) + (6*b^4*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (12*b^5*(b*d - a*e)*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2116,1,368,0,0.1431455,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(7/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^7 (a+b x)}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^7 (a+b x)}-\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) \sqrt{d+e x}}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{5 e^7 (a+b x) (d+e x)^{5/2}}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{7/2}}{7 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}{5 e^7 (a+b x)}+\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}{e^7 (a+b x)}-\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}{e^7 (a+b x)}-\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) \sqrt{d+e x}}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{e^7 (a+b x) (d+e x)^{3/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{5 e^7 (a+b x) (d+e x)^{5/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^(5/2)) + (4*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(3/2)) - (30*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) - (40*b^3*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (10*b^4*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (12*b^5*(b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)) + (2*b^6*(d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2117,1,368,0,0.1412675,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{9/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(9/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^7 (a+b x)}-\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^7 (a+b x)}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) \sqrt{d+e x}}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)^{3/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^{5/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{7 e^7 (a+b x) (d+e x)^{7/2}}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}{5 e^7 (a+b x)}-\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}{e^7 (a+b x)}+\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}{e^7 (a+b x)}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) \sqrt{d+e x}}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)^{3/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{5 e^7 (a+b x) (d+e x)^{5/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{7 e^7 (a+b x) (d+e x)^{7/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^(7/2)) + (12*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^(5/2)) - (10*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(3/2)) + (40*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) + (30*b^4*(b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) - (4*b^5*(b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (2*b^6*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2118,1,370,0,0.1455095,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{11/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(11/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^7 (a+b x)}-\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) \sqrt{d+e x}}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^{3/2}}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)^{5/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{7 e^7 (a+b x) (d+e x)^{7/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{9 e^7 (a+b x) (d+e x)^{9/2}}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}{3 e^7 (a+b x)}-\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}{e^7 (a+b x)}-\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) \sqrt{d+e x}}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{3 e^7 (a+b x) (d+e x)^{3/2}}-\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{e^7 (a+b x) (d+e x)^{5/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{7 e^7 (a+b x) (d+e x)^{7/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{9 e^7 (a+b x) (d+e x)^{9/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^(9/2)) + (12*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^(7/2)) - (6*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(5/2)) + (40*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(3/2)) - (30*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) - (12*b^5*(b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)) + (2*b^6*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2119,1,368,0,0.1425293,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{13/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(13/2),x]","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^7 (a+b x)}+\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) \sqrt{d+e x}}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)^{3/2}}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)^{5/2}}-\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{7 e^7 (a+b x) (d+e x)^{7/2}}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{3 e^7 (a+b x) (d+e x)^{9/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{11 e^7 (a+b x) (d+e x)^{11/2}}","\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}{e^7 (a+b x)}+\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) \sqrt{d+e x}}-\frac{10 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)^{3/2}}+\frac{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{e^7 (a+b x) (d+e x)^{5/2}}-\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{7 e^7 (a+b x) (d+e x)^{7/2}}+\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{3 e^7 (a+b x) (d+e x)^{9/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{11 e^7 (a+b x) (d+e x)^{11/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^(11/2)) + (4*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(9/2)) - (30*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^(7/2)) + (8*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(5/2)) - (10*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(3/2)) + (12*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x]) + (2*b^6*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2120,1,370,0,0.141162,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{15/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(15/2),x]","-\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{e^7 (a+b x) \sqrt{d+e x}}+\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)^{3/2}}-\frac{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)^{5/2}}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^7 (a+b x) (d+e x)^{7/2}}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^7 (a+b x) (d+e x)^{9/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^7 (a+b x) (d+e x)^{11/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{13 e^7 (a+b x) (d+e x)^{13/2}}","-\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{e^7 (a+b x) \sqrt{d+e x}}+\frac{4 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{e^7 (a+b x) (d+e x)^{3/2}}-\frac{6 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{e^7 (a+b x) (d+e x)^{5/2}}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{7 e^7 (a+b x) (d+e x)^{7/2}}-\frac{10 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{3 e^7 (a+b x) (d+e x)^{9/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{11 e^7 (a+b x) (d+e x)^{11/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{13 e^7 (a+b x) (d+e x)^{13/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^(13/2)) + (12*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^(11/2)) - (10*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(9/2)) + (40*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^(7/2)) - (6*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(5/2)) + (4*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*(d + e*x)^(3/2)) - (2*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(a + b*x)*Sqrt[d + e*x])","A",4,3,35,0.08571,1,"{770, 21, 43}"
2121,1,376,0,0.1421332,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^{5/2}}{(d+e x)^{17/2}} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2))/(d + e*x)^(17/2),x]","-\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^7 (a+b x) (d+e x)^{3/2}}+\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^7 (a+b x) (d+e x)^{5/2}}-\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^7 (a+b x) (d+e x)^{7/2}}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^7 (a+b x) (d+e x)^{9/2}}-\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^7 (a+b x) (d+e x)^{11/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{13 e^7 (a+b x) (d+e x)^{13/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{15 e^7 (a+b x) (d+e x)^{15/2}}","-\frac{2 b^6 \sqrt{a^2+2 a b x+b^2 x^2}}{3 e^7 (a+b x) (d+e x)^{3/2}}+\frac{12 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}{5 e^7 (a+b x) (d+e x)^{5/2}}-\frac{30 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}{7 e^7 (a+b x) (d+e x)^{7/2}}+\frac{40 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}{9 e^7 (a+b x) (d+e x)^{9/2}}-\frac{30 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}{11 e^7 (a+b x) (d+e x)^{11/2}}+\frac{12 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5}{13 e^7 (a+b x) (d+e x)^{13/2}}-\frac{2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6}{15 e^7 (a+b x) (d+e x)^{15/2}}",1,"(-2*(b*d - a*e)^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(15*e^7*(a + b*x)*(d + e*x)^(15/2)) + (12*b*(b*d - a*e)^5*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(13*e^7*(a + b*x)*(d + e*x)^(13/2)) - (30*b^2*(b*d - a*e)^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(11*e^7*(a + b*x)*(d + e*x)^(11/2)) + (40*b^3*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(9*e^7*(a + b*x)*(d + e*x)^(9/2)) - (30*b^4*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(7*e^7*(a + b*x)*(d + e*x)^(7/2)) + (12*b^5*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(5*e^7*(a + b*x)*(d + e*x)^(5/2)) - (2*b^6*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(3*e^7*(a + b*x)*(d + e*x)^(3/2))","A",4,3,35,0.08571,1,"{770, 21, 43}"
2122,1,41,0,0.0299556,"\int \frac{(a+b x) (d+e x)^{7/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^(7/2))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) (d+e x)^{9/2}}{9 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (d+e x)^{9/2}}{9 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*(d + e*x)^(9/2))/(9*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2123,1,41,0,0.0304239,"\int \frac{(a+b x) (d+e x)^{5/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^(5/2))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) (d+e x)^{7/2}}{7 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (d+e x)^{7/2}}{7 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*(d + e*x)^(7/2))/(7*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2124,1,41,0,0.0294393,"\int \frac{(a+b x) (d+e x)^{3/2}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^(3/2))/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) (d+e x)^{5/2}}{5 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (d+e x)^{5/2}}{5 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*(d + e*x)^(5/2))/(5*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2125,1,41,0,0.0289997,"\int \frac{(a+b x) \sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*Sqrt[d + e*x])/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{2 (a+b x) (d+e x)^{3/2}}{3 e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) (d+e x)^{3/2}}{3 e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*(d + e*x)^(3/2))/(3*e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2126,1,39,0,0.0299117,"\int \frac{a+b x}{\sqrt{d+e x} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/(Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","\frac{2 (a+b x) \sqrt{d+e x}}{e \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{2 (a+b x) \sqrt{d+e x}}{e \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(2*(a + b*x)*Sqrt[d + e*x])/(e*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2127,1,39,0,0.0294353,"\int \frac{a+b x}{(d+e x)^{3/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x)}{e \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}","-\frac{2 (a+b x)}{e \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x}}",1,"(-2*(a + b*x))/(e*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2128,1,41,0,0.0292245,"\int \frac{a+b x}{(d+e x)^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x)}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}","-\frac{2 (a+b x)}{3 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2}}",1,"(-2*(a + b*x))/(3*e*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2129,1,41,0,0.0285665,"\int \frac{a+b x}{(d+e x)^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[(a + b*x)/((d + e*x)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]),x]","-\frac{2 (a+b x)}{5 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}","-\frac{2 (a+b x)}{5 e \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2}}",1,"(-2*(a + b*x))/(5*e*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,35,0.08571,1,"{770, 21, 32}"
2130,1,250,0,0.172754,"\int \frac{(a+b x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{7/2}}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) (d+e x)^{5/2}}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) (d+e x)^{3/2} (b d-a e)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) \sqrt{d+e x} (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 e (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(d+e x)^{7/2}}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) (d+e x)^{5/2}}{5 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) (d+e x)^{3/2} (b d-a e)}{3 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{7 e (a+b x) \sqrt{d+e x} (b d-a e)^2}{b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{7 e (a+b x) (b d-a e)^{5/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(7*e*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x])/(b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e*(b*d - a*e)*(a + b*x)*(d + e*x)^(3/2))/(3*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e*(a + b*x)*(d + e*x)^(5/2))/(5*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(7/2)/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(b*d - a*e)^(5/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{768, 646, 50, 63, 208}"
2131,1,198,0,0.1219719,"\int \frac{(a+b x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{5/2}}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e (a+b x) (d+e x)^{3/2}}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e (a+b x) \sqrt{d+e x} (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(d+e x)^{5/2}}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e (a+b x) (d+e x)^{3/2}}{3 b^2 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{5 e (a+b x) \sqrt{d+e x} (b d-a e)}{b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e (a+b x) (b d-a e)^{3/2} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(5*e*(b*d - a*e)*(a + b*x)*Sqrt[d + e*x])/(b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e*(a + b*x)*(d + e*x)^(3/2))/(3*b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(5/2)/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(b*d - a*e)^(3/2)*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{768, 646, 50, 63, 208}"
2132,1,148,0,0.0921657,"\int \frac{(a+b x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{(d+e x)^{3/2}}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) \sqrt{d+e x}}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{(d+e x)^{3/2}}{b \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{3 e (a+b x) \sqrt{d+e x}}{b^2 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{3 e (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2}}",1,"(3*e*(a + b*x)*Sqrt[d + e*x])/(b^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (d + e*x)^(3/2)/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (3*e*Sqrt[b*d - a*e]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,35,0.1429,1,"{768, 646, 50, 63, 208}"
2133,1,108,0,0.0697587,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{\sqrt{d+e x}}{b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}","-\frac{\sqrt{d+e x}}{b \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}",1,"-(Sqrt[d + e*x]/(b*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (e*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(b^(3/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,4,35,0.1143,1,"{768, 646, 63, 208}"
2134,1,114,0,0.0885706,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","\frac{e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","\frac{e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{\sqrt{d+e x}}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"-(Sqrt[d + e*x]/((b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) + (e*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(Sqrt[b]*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",5,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2135,1,162,0,0.1011131,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{3 e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}+\frac{3 \sqrt{b} e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}","-\frac{3 e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}+\frac{3 \sqrt{b} e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}",1,"-(1/((b*d - a*e)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (3*e*(a + b*x))/((b*d - a*e)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*Sqrt[b]*e*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2136,1,212,0,0.1100919,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{5 b e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{5 e (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}+\frac{5 b^{3/2} e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}","-\frac{5 b e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}-\frac{5 e (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}+\frac{5 b^{3/2} e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}",1,"-(1/((b*d - a*e)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (5*e*(a + b*x))/(3*(b*d - a*e)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*b*e*(a + b*x))/((b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*b^(3/2)*e*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2137,1,264,0,0.1330633,"\int \frac{a+b x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)),x]","-\frac{7 b^2 e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{7 b e (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{7 e (a+b x)}{5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}+\frac{7 b^{5/2} e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}","-\frac{7 b^2 e (a+b x)}{\sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{7 b e (a+b x)}{3 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}-\frac{7 e (a+b x)}{5 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{\sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}+\frac{7 b^{5/2} e (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}",1,"-(1/((b*d - a*e)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (7*e*(a + b*x))/(5*(b*d - a*e)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*b*e*(a + b*x))/(3*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*b^2*e*(a + b*x))/((b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*b^(5/2)*e*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/((b*d - a*e)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2138,1,241,0,0.1370935,"\int \frac{(a+b x) (d+e x)^{7/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^(7/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{35 e^2 (d+e x)^{3/2}}{24 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 e^3 (a+b x) \sqrt{d+e x}}{8 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^3 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{7/2}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{7 e (d+e x)^{5/2}}{12 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{35 e^2 (d+e x)^{3/2}}{24 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}+\frac{35 e^3 (a+b x) \sqrt{d+e x}}{8 b^4 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{35 e^3 (a+b x) \sqrt{b d-a e} \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{9/2} \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{7/2}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}-\frac{7 e (d+e x)^{5/2}}{12 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(d + e*x)^(7/2)/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) + (35*e^3*(a + b*x)*Sqrt[d + e*x])/(8*b^4*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^2*(d + e*x)^(3/2))/(24*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (7*e*(d + e*x)^(5/2))/(12*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^3*Sqrt[b*d - a*e]*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,6,35,0.1714,1,"{768, 646, 47, 50, 63, 208}"
2139,1,197,0,0.113454,"\int \frac{(a+b x) (d+e x)^{5/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^(5/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{5 e^2 \sqrt{d+e x}}{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{5 e (d+e x)^{3/2}}{12 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{5/2}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{5 e^2 \sqrt{d+e x}}{8 b^3 \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{5 e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{7/2} \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{b d-a e}}-\frac{5 e (d+e x)^{3/2}}{12 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{5/2}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-(d + e*x)^(5/2)/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (5*e^2*Sqrt[d + e*x])/(8*b^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e*(d + e*x)^(3/2))/(12*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (5*e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(7/2)*Sqrt[b*d - a*e]*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{768, 646, 47, 63, 208}"
2140,1,207,0,0.1381677,"\int \frac{(a+b x) (d+e x)^{3/2}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^(3/2))/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","-\frac{e^2 \sqrt{d+e x}}{8 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{3/2}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","-\frac{e^2 \sqrt{d+e x}}{8 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}+\frac{e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{5/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{3/2}}-\frac{e \sqrt{d+e x}}{4 b^2 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{(d+e x)^{3/2}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-(d + e*x)^(3/2)/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) - (e^2*Sqrt[d + e*x])/(8*b^2*(b*d - a*e)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*Sqrt[d + e*x])/(4*b^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(5/2)*(b*d - a*e)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,6,35,0.1714,1,"{768, 646, 47, 51, 63, 208}"
2141,1,217,0,0.1483596,"\int \frac{(a+b x) \sqrt{d+e x}}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*Sqrt[d + e*x])/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^2 \sqrt{d+e x}}{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x}}{12 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}","\frac{e^2 \sqrt{d+e x}}{8 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 b^{3/2} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{5/2}}-\frac{e \sqrt{d+e x}}{12 b (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}-\frac{\sqrt{d+e x}}{3 b \left(a^2+2 a b x+b^2 x^2\right)^{3/2}}",1,"-Sqrt[d + e*x]/(3*b*(a^2 + 2*a*b*x + b^2*x^2)^(3/2)) + (e^2*Sqrt[d + e*x])/(8*b*(b*d - a*e)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e*Sqrt[d + e*x])/(12*b*(b*d - a*e)*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*b^(3/2)*(b*d - a*e)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",6,5,35,0.1429,1,"{768, 646, 51, 63, 208}"
2142,1,225,0,0.1413332,"\int \frac{a+b x}{\sqrt{d+e x} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/(Sqrt[d + e*x]*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{5 e^2 \sqrt{d+e x}}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{5 e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}+\frac{5 e \sqrt{d+e x}}{12 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x}}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}","-\frac{5 e^2 \sqrt{d+e x}}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3}+\frac{5 e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{b} \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{7/2}}+\frac{5 e \sqrt{d+e x}}{12 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}-\frac{\sqrt{d+e x}}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)}",1,"(-5*e^2*Sqrt[d + e*x])/(8*(b*d - a*e)^3*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - Sqrt[d + e*x]/(3*(b*d - a*e)*(a + b*x)^2*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e*Sqrt[d + e*x])/(12*(b*d - a*e)^2*(a + b*x)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (5*e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*Sqrt[b]*(b*d - a*e)^(7/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",7,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2143,1,276,0,0.1795475,"\int \frac{a+b x}{(d+e x)^{3/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((d + e*x)^(3/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{35 e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{35 e^2}{24 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{35 \sqrt{b} e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{7 e}{12 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}","-\frac{35 e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^4}-\frac{35 e^2}{24 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^3}+\frac{35 \sqrt{b} e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{9/2}}+\frac{7 e}{12 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)}",1,"(-35*e^2)/(24*(b*d - a*e)^3*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(3*(b*d - a*e)*(a + b*x)^2*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (7*e)/(12*(b*d - a*e)^2*(a + b*x)*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^3*(a + b*x))/(8*(b*d - a*e)^4*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (35*Sqrt[b]*e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(9/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",8,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2144,1,328,0,0.2439925,"\int \frac{a+b x}{(d+e x)^{5/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((d + e*x)^(5/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{105 b e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}-\frac{35 e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}-\frac{21 e^2}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}+\frac{105 b^{3/2} e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}+\frac{3 e}{4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}","-\frac{105 b e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^5}-\frac{35 e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^4}-\frac{21 e^2}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^3}+\frac{105 b^{3/2} e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{11/2}}+\frac{3 e}{4 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)}",1,"(-21*e^2)/(8*(b*d - a*e)^3*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(3*(b*d - a*e)*(a + b*x)^2*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (3*e)/(4*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (35*e^3*(a + b*x))/(8*(b*d - a*e)^4*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (105*b*e^3*(a + b*x))/(8*(b*d - a*e)^5*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (105*b^(3/2)*e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(11/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",9,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2145,1,382,0,0.2496818,"\int \frac{a+b x}{(d+e x)^{7/2} \left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((d + e*x)^(7/2)*(a^2 + 2*a*b*x + b^2*x^2)^(5/2)),x]","-\frac{231 b^2 e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}-\frac{77 b e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}-\frac{231 e^3 (a+b x)}{40 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}-\frac{33 e^2}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}+\frac{231 b^{5/2} e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{13/2}}+\frac{11 e}{12 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}","-\frac{231 b^2 e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} \sqrt{d+e x} (b d-a e)^6}-\frac{77 b e^3 (a+b x)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{3/2} (b d-a e)^5}-\frac{231 e^3 (a+b x)}{40 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^4}-\frac{33 e^2}{8 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^3}+\frac{231 b^{5/2} e^3 (a+b x) \tanh ^{-1}\left(\frac{\sqrt{b} \sqrt{d+e x}}{\sqrt{b d-a e}}\right)}{8 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^{13/2}}+\frac{11 e}{12 (a+b x) \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)^2}-\frac{1}{3 (a+b x)^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{5/2} (b d-a e)}",1,"(-33*e^2)/(8*(b*d - a*e)^3*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - 1/(3*(b*d - a*e)*(a + b*x)^2*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (11*e)/(12*(b*d - a*e)^2*(a + b*x)*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*e^3*(a + b*x))/(40*(b*d - a*e)^4*(d + e*x)^(5/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (77*b*e^3*(a + b*x))/(8*(b*d - a*e)^5*(d + e*x)^(3/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) - (231*b^2*e^3*(a + b*x))/(8*(b*d - a*e)^6*Sqrt[d + e*x]*Sqrt[a^2 + 2*a*b*x + b^2*x^2]) + (231*b^(5/2)*e^3*(a + b*x)*ArcTanh[(Sqrt[b]*Sqrt[d + e*x])/Sqrt[b*d - a*e]])/(8*(b*d - a*e)^(13/2)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",10,5,35,0.1429,1,"{770, 21, 51, 63, 208}"
2146,1,239,0,0.1394682,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{21 b^2 (b d-a e)^5 (d+e x)^{m+3}}{e^8 (m+3)}+\frac{35 b^3 (b d-a e)^4 (d+e x)^{m+4}}{e^8 (m+4)}-\frac{35 b^4 (b d-a e)^3 (d+e x)^{m+5}}{e^8 (m+5)}+\frac{21 b^5 (b d-a e)^2 (d+e x)^{m+6}}{e^8 (m+6)}-\frac{7 b^6 (b d-a e) (d+e x)^{m+7}}{e^8 (m+7)}-\frac{(b d-a e)^7 (d+e x)^{m+1}}{e^8 (m+1)}+\frac{7 b (b d-a e)^6 (d+e x)^{m+2}}{e^8 (m+2)}+\frac{b^7 (d+e x)^{m+8}}{e^8 (m+8)}","-\frac{21 b^2 (b d-a e)^5 (d+e x)^{m+3}}{e^8 (m+3)}+\frac{35 b^3 (b d-a e)^4 (d+e x)^{m+4}}{e^8 (m+4)}-\frac{35 b^4 (b d-a e)^3 (d+e x)^{m+5}}{e^8 (m+5)}+\frac{21 b^5 (b d-a e)^2 (d+e x)^{m+6}}{e^8 (m+6)}-\frac{7 b^6 (b d-a e) (d+e x)^{m+7}}{e^8 (m+7)}-\frac{(b d-a e)^7 (d+e x)^{m+1}}{e^8 (m+1)}+\frac{7 b (b d-a e)^6 (d+e x)^{m+2}}{e^8 (m+2)}+\frac{b^7 (d+e x)^{m+8}}{e^8 (m+8)}",1,"-(((b*d - a*e)^7*(d + e*x)^(1 + m))/(e^8*(1 + m))) + (7*b*(b*d - a*e)^6*(d + e*x)^(2 + m))/(e^8*(2 + m)) - (21*b^2*(b*d - a*e)^5*(d + e*x)^(3 + m))/(e^8*(3 + m)) + (35*b^3*(b*d - a*e)^4*(d + e*x)^(4 + m))/(e^8*(4 + m)) - (35*b^4*(b*d - a*e)^3*(d + e*x)^(5 + m))/(e^8*(5 + m)) + (21*b^5*(b*d - a*e)^2*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (7*b^6*(b*d - a*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (b^7*(d + e*x)^(8 + m))/(e^8*(8 + m))","A",3,2,31,0.06452,1,"{27, 43}"
2147,1,175,0,0.085458,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^2 \, dx","Int[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{10 b^2 (b d-a e)^3 (d+e x)^{m+3}}{e^6 (m+3)}+\frac{10 b^3 (b d-a e)^2 (d+e x)^{m+4}}{e^6 (m+4)}-\frac{5 b^4 (b d-a e) (d+e x)^{m+5}}{e^6 (m+5)}-\frac{(b d-a e)^5 (d+e x)^{m+1}}{e^6 (m+1)}+\frac{5 b (b d-a e)^4 (d+e x)^{m+2}}{e^6 (m+2)}+\frac{b^5 (d+e x)^{m+6}}{e^6 (m+6)}","-\frac{10 b^2 (b d-a e)^3 (d+e x)^{m+3}}{e^6 (m+3)}+\frac{10 b^3 (b d-a e)^2 (d+e x)^{m+4}}{e^6 (m+4)}-\frac{5 b^4 (b d-a e) (d+e x)^{m+5}}{e^6 (m+5)}-\frac{(b d-a e)^5 (d+e x)^{m+1}}{e^6 (m+1)}+\frac{5 b (b d-a e)^4 (d+e x)^{m+2}}{e^6 (m+2)}+\frac{b^5 (d+e x)^{m+6}}{e^6 (m+6)}",1,"-(((b*d - a*e)^5*(d + e*x)^(1 + m))/(e^6*(1 + m))) + (5*b*(b*d - a*e)^4*(d + e*x)^(2 + m))/(e^6*(2 + m)) - (10*b^2*(b*d - a*e)^3*(d + e*x)^(3 + m))/(e^6*(3 + m)) + (10*b^3*(b*d - a*e)^2*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (5*b^4*(b*d - a*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (b^5*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",3,2,31,0.06452,1,"{27, 43}"
2148,1,111,0,0.0509776,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right) \, dx","Int[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{3 b^2 (b d-a e) (d+e x)^{m+3}}{e^4 (m+3)}-\frac{(b d-a e)^3 (d+e x)^{m+1}}{e^4 (m+1)}+\frac{3 b (b d-a e)^2 (d+e x)^{m+2}}{e^4 (m+2)}+\frac{b^3 (d+e x)^{m+4}}{e^4 (m+4)}","-\frac{3 b^2 (b d-a e) (d+e x)^{m+3}}{e^4 (m+3)}-\frac{(b d-a e)^3 (d+e x)^{m+1}}{e^4 (m+1)}+\frac{3 b (b d-a e)^2 (d+e x)^{m+2}}{e^4 (m+2)}+\frac{b^3 (d+e x)^{m+4}}{e^4 (m+4)}",1,"-(((b*d - a*e)^3*(d + e*x)^(1 + m))/(e^4*(1 + m))) + (3*b*(b*d - a*e)^2*(d + e*x)^(2 + m))/(e^4*(2 + m)) - (3*b^2*(b*d - a*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (b^3*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",3,2,29,0.06897,1,"{27, 43}"
2149,1,51,0,0.0145051,"\int \frac{(a+b x) (d+e x)^m}{a^2+2 a b x+b^2 x^2} \, dx","Int[((a + b*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2),x]","-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)}","-\frac{(d+e x)^{m+1} \, _2F_1\left(1,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)}",1,"-(((d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)*(1 + m)))","A",2,2,31,0.06452,1,"{27, 68}"
2150,1,54,0,0.0146187,"\int \frac{(a+b x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^2} \, dx","Int[((a + b*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^2,x]","-\frac{e^2 (d+e x)^{m+1} \, _2F_1\left(3,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^3}","-\frac{e^2 (d+e x)^{m+1} \, _2F_1\left(3,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) (b d-a e)^3}",1,"-((e^2*(d + e*x)^(1 + m)*Hypergeometric2F1[3, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^3*(1 + m)))","A",2,2,31,0.06452,1,"{27, 68}"
2151,1,395,0,0.2198679,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{5/2} \, dx","Int[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6 (d+e x)^{m+1}}{e^7 (m+1) (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (d+e x)^{m+2}}{e^7 (m+2) (a+b x)}+\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+3}}{e^7 (m+3) (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+4}}{e^7 (m+4) (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+5}}{e^7 (m+5) (a+b x)}-\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+6}}{e^7 (m+6) (a+b x)}+\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+7}}{e^7 (m+7) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^6 (d+e x)^{m+1}}{e^7 (m+1) (a+b x)}-\frac{6 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^5 (d+e x)^{m+2}}{e^7 (m+2) (a+b x)}+\frac{15 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+3}}{e^7 (m+3) (a+b x)}-\frac{20 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+4}}{e^7 (m+4) (a+b x)}+\frac{15 b^4 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+5}}{e^7 (m+5) (a+b x)}-\frac{6 b^5 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+6}}{e^7 (m+6) (a+b x)}+\frac{b^6 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+7}}{e^7 (m+7) (a+b x)}",1,"((b*d - a*e)^6*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(1 + m)*(a + b*x)) - (6*b*(b*d - a*e)^5*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(2 + m)*(a + b*x)) + (15*b^2*(b*d - a*e)^4*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(3 + m)*(a + b*x)) - (20*b^3*(b*d - a*e)^3*(d + e*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(4 + m)*(a + b*x)) + (15*b^4*(b*d - a*e)^2*(d + e*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(5 + m)*(a + b*x)) - (6*b^5*(b*d - a*e)*(d + e*x)^(6 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(6 + m)*(a + b*x)) + (b^6*(d + e*x)^(7 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^7*(7 + m)*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2152,1,277,0,0.1498059,"\int (a+b x) (d+e x)^m \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(a + b*x)*(d + e*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+1}}{e^5 (m+1) (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+2}}{e^5 (m+2) (a+b x)}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+3}}{e^5 (m+3) (a+b x)}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+4}}{e^5 (m+4) (a+b x)}+\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+5}}{e^5 (m+5) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4 (d+e x)^{m+1}}{e^5 (m+1) (a+b x)}-\frac{4 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^3 (d+e x)^{m+2}}{e^5 (m+2) (a+b x)}+\frac{6 b^2 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+3}}{e^5 (m+3) (a+b x)}-\frac{4 b^3 \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+4}}{e^5 (m+4) (a+b x)}+\frac{b^4 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+5}}{e^5 (m+5) (a+b x)}",1,"((b*d - a*e)^4*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(1 + m)*(a + b*x)) - (4*b*(b*d - a*e)^3*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(2 + m)*(a + b*x)) + (6*b^2*(b*d - a*e)^2*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(3 + m)*(a + b*x)) - (4*b^3*(b*d - a*e)*(d + e*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(4 + m)*(a + b*x)) + (b^4*(d + e*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^5*(5 + m)*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2153,1,159,0,0.0838629,"\int (a+b x) (d+e x)^m \sqrt{a^2+2 a b x+b^2 x^2} \, dx","Int[(a + b*x)*(d + e*x)^m*Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+1}}{e^3 (m+1) (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+2}}{e^3 (m+2) (a+b x)}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+3}}{e^3 (m+3) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2 (d+e x)^{m+1}}{e^3 (m+1) (a+b x)}-\frac{2 b \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e) (d+e x)^{m+2}}{e^3 (m+2) (a+b x)}+\frac{b^2 \sqrt{a^2+2 a b x+b^2 x^2} (d+e x)^{m+3}}{e^3 (m+3) (a+b x)}",1,"((b*d - a*e)^2*(d + e*x)^(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(1 + m)*(a + b*x)) - (2*b*(b*d - a*e)*(d + e*x)^(2 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(2 + m)*(a + b*x)) + (b^2*(d + e*x)^(3 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(e^3*(3 + m)*(a + b*x))","A",4,3,33,0.09091,1,"{770, 21, 43}"
2154,1,43,0,0.0339207,"\int \frac{(a+b x) (d+e x)^m}{\sqrt{a^2+2 a b x+b^2 x^2}} \, dx","Int[((a + b*x)*(d + e*x)^m)/Sqrt[a^2 + 2*a*b*x + b^2*x^2],x]","\frac{(a+b x) (d+e x)^{m+1}}{e (m+1) \sqrt{a^2+2 a b x+b^2 x^2}}","\frac{(a+b x) (d+e x)^{m+1}}{e (m+1) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"((a + b*x)*(d + e*x)^(1 + m))/(e*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 32}"
2155,1,76,0,0.0550903,"\int \frac{(a+b x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((a + b*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{e (a+b x) (d+e x)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}","\frac{e (a+b x) (d+e x)^{m+1} \, _2F_1\left(2,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^2}",1,"(e*(a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[2, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^2*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 68}"
2156,1,78,0,0.0596757,"\int \frac{(a+b x) (d+e x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{5/2}} \, dx","Int[((a + b*x)*(d + e*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^(5/2),x]","\frac{e^3 (a+b x) (d+e x)^{m+1} \, _2F_1\left(4,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}","\frac{e^3 (a+b x) (d+e x)^{m+1} \, _2F_1\left(4,m+1;m+2;\frac{b (d+e x)}{b d-a e}\right)}{(m+1) \sqrt{a^2+2 a b x+b^2 x^2} (b d-a e)^4}",1,"(e^3*(a + b*x)*(d + e*x)^(1 + m)*Hypergeometric2F1[4, 1 + m, 2 + m, (b*(d + e*x))/(b*d - a*e)])/((b*d - a*e)^4*(1 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",3,3,33,0.09091,1,"{770, 21, 68}"
2157,1,51,0,0.0262107,"\int (a c+b c x) (d+e x)^{-3-2 p} \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a*c + b*c*x)*(d + e*x)^(-3 - 2*p)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{c \left(a^2+2 a b x+b^2 x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1) (b d-a e)}","\frac{c \left(a^2+2 a b x+b^2 x^2\right)^{p+1} (d+e x)^{-2 (p+1)}}{2 (p+1) (b d-a e)}",1,"(c*(a^2 + 2*a*b*x + b^2*x^2)^(1 + p))/(2*(b*d - a*e)*(1 + p)*(d + e*x)^(2*(1 + p)))","A",1,1,38,0.02632,1,"{767}"
2158,1,183,0,0.1192486,"\int (a+b x) (d+e x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a + b*x)*(d + e*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{3 e^2 (a+b x)^4 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+2)}+\frac{3 e (a+b x)^3 (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+3)}+\frac{(a+b x)^2 (b d-a e)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+1)}+\frac{e^3 (a+b x)^5 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+5)}","\frac{3 e^2 (a+b x)^4 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+2)}+\frac{3 e (a+b x)^3 (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+3)}+\frac{(a+b x)^2 (b d-a e)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^4 (p+1)}+\frac{e^3 (a+b x)^5 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^4 (2 p+5)}",1,"((b*d - a*e)^3*(a + b*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^4*(1 + p)) + (3*e*(b*d - a*e)^2*(a + b*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^4*(3 + 2*p)) + (3*e^2*(b*d - a*e)*(a + b*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^4*(2 + p)) + (e^3*(a + b*x)^5*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^4*(5 + 2*p))","A",4,3,31,0.09677,1,"{770, 21, 43}"
2159,1,134,0,0.0858001,"\int (a+b x) (d+e x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a + b*x)*(d + e*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{2 e (a+b x)^3 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (2 p+3)}+\frac{(a+b x)^2 (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^3 (p+1)}+\frac{e^2 (a+b x)^4 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^3 (p+2)}","\frac{2 e (a+b x)^3 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{b^3 (2 p+3)}+\frac{(a+b x)^2 (b d-a e)^2 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^3 (p+1)}+\frac{e^2 (a+b x)^4 \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^3 (p+2)}",1,"((b*d - a*e)^2*(a + b*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^3*(1 + p)) + (2*e*(b*d - a*e)*(a + b*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^3*(3 + 2*p)) + (e^2*(a + b*x)^4*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^3*(2 + p))","A",4,3,31,0.09677,1,"{770, 21, 43}"
2160,1,83,0,0.054496,"\int (a+b x) (d+e x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a + b*x)*(d + e*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{(a+b x)^2 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^2 (p+1)}+\frac{e (a+b x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^2 (2 p+3)}","\frac{(a+b x)^2 (b d-a e) \left(a^2+2 a b x+b^2 x^2\right)^p}{2 b^2 (p+1)}+\frac{e (a+b x)^3 \left(a^2+2 a b x+b^2 x^2\right)^p}{b^2 (2 p+3)}",1,"((b*d - a*e)*(a + b*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*b^2*(1 + p)) + (e*(a + b*x)^3*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^2*(3 + 2*p))","A",4,3,29,0.1034,1,"{770, 21, 43}"
2161,1,32,0,0.0081101,"\int (a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{p+1}}{2 b (p+1)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^{p+1}}{2 b (p+1)}",1,"(a^2 + 2*a*b*x + b^2*x^2)^(1 + p)/(2*b*(1 + p))","A",1,1,24,0.04167,1,"{629}"
2162,1,74,0,0.0509769,"\int \frac{(a+b x) \left(a^2+2 a b x+b^2 x^2\right)^p}{d+e x} \, dx","Int[((a + b*x)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(d + e*x),x]","\frac{(a+b x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(1,2 (p+1);2 p+3;-\frac{e (a+b x)}{b d-a e}\right)}{2 (p+1) (b d-a e)}","\frac{(a+b x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p \, _2F_1\left(1,2 (p+1);2 p+3;-\frac{e (a+b x)}{b d-a e}\right)}{2 (p+1) (b d-a e)}",1,"((a + b*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p*Hypergeometric2F1[1, 2*(1 + p), 3 + 2*p, -((e*(a + b*x))/(b*d - a*e))])/(2*(b*d - a*e)*(1 + p))","A",3,3,31,0.09677,1,"{770, 21, 68}"
2163,1,58,0,0.0416603,"\int (A+B x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(A + B*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(A b-a B) (a c+b c x)^{m+7}}{b^2 c^7 (m+7)}+\frac{B (a c+b c x)^{m+8}}{b^2 c^8 (m+8)}","\frac{(A b-a B) (a c+b c x)^{m+7}}{b^2 c^7 (m+7)}+\frac{B (a c+b c x)^{m+8}}{b^2 c^8 (m+8)}",1,"((A*b - a*B)*(a*c + b*c*x)^(7 + m))/(b^2*c^7*(7 + m)) + (B*(a*c + b*c*x)^(8 + m))/(b^2*c^8*(8 + m))","A",4,3,34,0.08824,1,"{27, 21, 43}"
2164,1,64,0,0.0489636,"\int \frac{(A+B x) (a c+b c x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((A + B*x)*(a*c + b*c*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{c^5 (A b-a B) (a c+b c x)^{m-5}}{b^2 (5-m)}-\frac{B c^4 (a c+b c x)^{m-4}}{b^2 (4-m)}","-\frac{c^5 (A b-a B) (a c+b c x)^{m-5}}{b^2 (5-m)}-\frac{B c^4 (a c+b c x)^{m-4}}{b^2 (4-m)}",1,"-(((A*b - a*B)*c^5*(a*c + b*c*x)^(-5 + m))/(b^2*(5 - m))) - (B*c^4*(a*c + b*c*x)^(-4 + m))/(b^2*(4 - m))","A",4,3,34,0.08824,1,"{27, 21, 43}"
2165,1,112,0,0.0759646,"\int (A+B x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^{3/2} \, dx","Int[(A + B*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (A b-a B) (a c+b c x)^{m+4}}{b^2 c^4 (m+4) (a+b x)}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a c+b c x)^{m+5}}{b^2 c^5 (m+5) (a+b x)}","\frac{\sqrt{a^2+2 a b x+b^2 x^2} (A b-a B) (a c+b c x)^{m+4}}{b^2 c^4 (m+4) (a+b x)}+\frac{B \sqrt{a^2+2 a b x+b^2 x^2} (a c+b c x)^{m+5}}{b^2 c^5 (m+5) (a+b x)}",1,"((A*b - a*B)*(a*c + b*c*x)^(4 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(b^2*c^4*(4 + m)*(a + b*x)) + (B*(a*c + b*c*x)^(5 + m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])/(b^2*c^5*(5 + m)*(a + b*x))","A",4,3,36,0.08333,1,"{770, 21, 43}"
2166,1,112,0,0.0850823,"\int \frac{(A+B x) (a c+b c x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(a*c + b*c*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^(3/2),x]","-\frac{c^2 (a+b x) (A b-a B) (a c+b c x)^{m-2}}{b^2 (2-m) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B c (a+b x) (a c+b c x)^{m-1}}{b^2 (1-m) \sqrt{a^2+2 a b x+b^2 x^2}}","-\frac{c^2 (a+b x) (A b-a B) (a c+b c x)^{m-2}}{b^2 (2-m) \sqrt{a^2+2 a b x+b^2 x^2}}-\frac{B c (a+b x) (a c+b c x)^{m-1}}{b^2 (1-m) \sqrt{a^2+2 a b x+b^2 x^2}}",1,"-(((A*b - a*B)*c^2*(a + b*x)*(a*c + b*c*x)^(-2 + m))/(b^2*(2 - m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])) - (B*c*(a + b*x)*(a*c + b*c*x)^(-1 + m))/(b^2*(1 - m)*Sqrt[a^2 + 2*a*b*x + b^2*x^2])","A",4,3,36,0.08333,1,"{770, 21, 43}"
2167,1,100,0,0.0779676,"\int (a c+b c x)^m (f+g x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a*c + b*c*x)^m*(f + g*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{g \left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{m+2}}{b^2 c^2 (m+2 p+2)}+\frac{(b f-a g) \left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{m+1}}{b^2 c (m+2 p+1)}","\frac{g \left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{m+2}}{b^2 c^2 (m+2 p+2)}+\frac{(b f-a g) \left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{m+1}}{b^2 c (m+2 p+1)}",1,"((b*f - a*g)*(a*c + b*c*x)^(1 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^2*c*(1 + m + 2*p)) + (g*(a*c + b*c*x)^(2 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b^2*c^2*(2 + m + 2*p))","A",4,3,34,0.08824,1,"{770, 23, 43}"
2168,1,61,0,0.0426444,"\int (a c+b c x)^{-3-2 p} (f+g x) \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a*c + b*c*x)^(-3 - 2*p)*(f + g*x)*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","-\frac{(f+g x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{-2 p}}{2 c^3 (a+b x)^2 (b f-a g)}","-\frac{(f+g x)^2 \left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{-2 p}}{2 c^3 (a+b x)^2 (b f-a g)}",1,"-((f + g*x)^2*(a^2 + 2*a*b*x + b^2*x^2)^p)/(2*c^3*(b*f - a*g)*(a + b*x)^2*(a*c + b*c*x)^(2*p))","A",3,3,38,0.07895,1,"{770, 23, 37}"
2169,1,45,0,0.0278098,"\int (a+b x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^p \, dx","Int[(a + b*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^p,x]","\frac{\left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{m+2}}{b c^2 (m+2 p+2)}","\frac{\left(a^2+2 a b x+b^2 x^2\right)^p (a c+b c x)^{m+2}}{b c^2 (m+2 p+2)}",1,"((a*c + b*c*x)^(2 + m)*(a^2 + 2*a*b*x + b^2*x^2)^p)/(b*c^2*(2 + m + 2*p))","A",3,3,34,0.08824,1,"{21, 644, 32}"
2170,1,24,0,0.016604,"\int (a+b x) (a c+b c x)^m \left(a^2+2 a b x+b^2 x^2\right)^3 \, dx","Int[(a + b*x)*(a*c + b*c*x)^m*(a^2 + 2*a*b*x + b^2*x^2)^3,x]","\frac{(a c+b c x)^{m+8}}{b c^8 (m+8)}","\frac{(a c+b c x)^{m+8}}{b c^8 (m+8)}",1,"(a*c + b*c*x)^(8 + m)/(b*c^8*(8 + m))","A",4,3,34,0.08824,1,"{21, 27, 32}"
2171,1,27,0,0.0175843,"\int \frac{(a+b x) (a c+b c x)^m}{\left(a^2+2 a b x+b^2 x^2\right)^3} \, dx","Int[((a + b*x)*(a*c + b*c*x)^m)/(a^2 + 2*a*b*x + b^2*x^2)^3,x]","-\frac{c^4 (a c+b c x)^{m-4}}{b (4-m)}","-\frac{c^4 (a c+b c x)^{m-4}}{b (4-m)}",1,"-((c^4*(a*c + b*c*x)^(-4 + m))/(b*(4 - m)))","A",4,3,34,0.08824,1,"{21, 27, 32}"
2172,1,414,0,0.8302525,"\int (d+e x)^3 (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[(d + e*x)^3*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{7 (b+2 c x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g+2 c d g+4 c e f)}{512 c^5 e}-\frac{7 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+2 c d g+4 c e f)}{192 c^4 e^2}-\frac{7 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+2 c d g+4 c e f)}{160 c^3 e^2}-\frac{(d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+2 c d g+4 c e f)}{20 c^2 e^2}+\frac{7 (2 c d-b e)^5 (-3 b e g+2 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{1024 c^{11/2} e^2}-\frac{g (d+e x)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{6 c e^2}","\frac{7 (b+2 c x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g+2 c d g+4 c e f)}{512 c^5 e}-\frac{7 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+2 c d g+4 c e f)}{192 c^4 e^2}-\frac{7 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+2 c d g+4 c e f)}{160 c^3 e^2}-\frac{(d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+2 c d g+4 c e f)}{20 c^2 e^2}+\frac{7 (2 c d-b e)^5 (-3 b e g+2 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{1024 c^{11/2} e^2}-\frac{g (d+e x)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{6 c e^2}",1,"(7*(2*c*d - b*e)^3*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(512*c^5*e) - (7*(2*c*d - b*e)^2*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(192*c^4*e^2) - (7*(2*c*d - b*e)*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(160*c^3*e^2) - ((4*c*e*f + 2*c*d*g - 3*b*e*g)*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(20*c^2*e^2) - (g*(d + e*x)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(6*c*e^2) + (7*(2*c*d - b*e)^5*(4*c*e*f + 2*c*d*g - 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(1024*c^(11/2)*e^2)","A",7,6,44,0.1364,1,"{794, 670, 640, 612, 621, 204}"
2173,1,339,0,0.4629472,"\int (d+e x)^2 (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[(d + e*x)^2*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{(b+2 c x) (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+4 c d g+10 c e f)}{128 c^4 e}-\frac{(2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+4 c d g+10 c e f)}{48 c^3 e^2}-\frac{(d+e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+4 c d g+10 c e f)}{40 c^2 e^2}+\frac{(2 c d-b e)^4 (-7 b e g+4 c d g+10 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{256 c^{9/2} e^2}-\frac{g (d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{5 c e^2}","\frac{(b+2 c x) (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+4 c d g+10 c e f)}{128 c^4 e}-\frac{(2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+4 c d g+10 c e f)}{48 c^3 e^2}-\frac{(d+e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+4 c d g+10 c e f)}{40 c^2 e^2}+\frac{(2 c d-b e)^4 (-7 b e g+4 c d g+10 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{256 c^{9/2} e^2}-\frac{g (d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{5 c e^2}",1,"((2*c*d - b*e)^2*(10*c*e*f + 4*c*d*g - 7*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(128*c^4*e) - ((2*c*d - b*e)*(10*c*e*f + 4*c*d*g - 7*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(48*c^3*e^2) - ((10*c*e*f + 4*c*d*g - 7*b*e*g)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(40*c^2*e^2) - (g*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(5*c*e^2) + ((2*c*d - b*e)^4*(10*c*e*f + 4*c*d*g - 7*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(256*c^(9/2)*e^2)","A",7,7,44,0.1591,1,"{1638, 12, 670, 640, 612, 621, 204}"
2174,1,223,0,0.281498,"\int (d+e x) (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[(d + e*x)*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{(b+2 c x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+2 c d g+8 c e f)}{64 c^3 e}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (5 b e g-8 c (d g+e f)-6 c e g x)}{24 c^2 e^2}+\frac{(2 c d-b e)^3 (-5 b e g+2 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{7/2} e^2}","\frac{(b+2 c x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+2 c d g+8 c e f)}{64 c^3 e}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (5 b e g-8 c (d g+e f)-6 c e g x)}{24 c^2 e^2}+\frac{(2 c d-b e)^3 (-5 b e g+2 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{7/2} e^2}",1,"((2*c*d - b*e)*(8*c*e*f + 2*c*d*g - 5*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*c^3*e) + ((5*b*e*g - 8*c*(e*f + d*g) - 6*c*e*g*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(24*c^2*e^2) + ((2*c*d - b*e)^3*(8*c*e*f + 2*c*d*g - 5*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(128*c^(7/2)*e^2)","A",4,4,42,0.09524,1,"{779, 612, 621, 204}"
2175,1,192,0,0.2199091,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{d+e x} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x),x]","\frac{(2 c d-b e) (-b e g-2 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{3/2} e^2}+\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-b e g-2 c d g+4 c e f)}{4 c e^2}-\frac{g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{2 c e^2 (d+e x)}","\frac{(2 c d-b e) (-b e g-2 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{3/2} e^2}+\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-b e g-2 c d g+4 c e f)}{4 c e^2}-\frac{g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{2 c e^2 (d+e x)}",1,"((4*c*e*f - 2*c*d*g - b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*c*e^2) - (g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(2*c*e^2*(d + e*x)) + ((2*c*d - b*e)*(4*c*e*f - 2*c*d*g - b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(8*c^(3/2)*e^2)","A",4,4,44,0.09091,1,"{794, 664, 621, 204}"
2176,1,200,0,0.3389623,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^2} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^2,x]","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{e^2 (d+e x)^2 (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (b e g-4 c d g+2 c e f)}{e^2 (2 c d-b e)}-\frac{(b e g-4 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 \sqrt{c} e^2}","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{e^2 (d+e x)^2 (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (b e g-4 c d g+2 c e f)}{e^2 (2 c d-b e)}-\frac{(b e g-4 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 \sqrt{c} e^2}",1,"-(((2*c*e*f - 4*c*d*g + b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(2*c*d - b*e))) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(e^2*(2*c*d - b*e)*(d + e*x)^2) - ((2*c*e*f - 4*c*d*g + b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(2*Sqrt[c]*e^2)","A",4,4,44,0.09091,1,"{792, 664, 621, 204}"
2177,1,168,0,0.3190464,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^3} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^3,x]","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^3 (2 c d-b e)}-\frac{2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)}-\frac{\sqrt{c} g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{e^2}","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^3 (2 c d-b e)}-\frac{2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)}-\frac{\sqrt{c} g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{e^2}",1,"(-2*g*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(d + e*x)) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^3) - (Sqrt[c]*g*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/e^2","A",4,4,44,0.09091,1,"{792, 662, 621, 204}"
2178,1,137,0,0.2065976,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^4} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^4,x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-5 b e g+8 c d g+2 c e f)}{15 e^2 (d+e x)^3 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{5 e^2 (d+e x)^4 (2 c d-b e)}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-5 b e g+8 c d g+2 c e f)}{15 e^2 (d+e x)^3 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{5 e^2 (d+e x)^4 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^4) - (2*(2*c*e*f + 8*c*d*g - 5*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(15*e^2*(2*c*d - b*e)^2*(d + e*x)^3)","A",2,2,44,0.04545,1,"{792, 650}"
2179,1,210,0,0.3394175,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^5} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^5,x]","-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+10 c d g+4 c e f)}{105 e^2 (d+e x)^3 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+10 c d g+4 c e f)}{35 e^2 (d+e x)^4 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{7 e^2 (d+e x)^5 (2 c d-b e)}","-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+10 c d g+4 c e f)}{105 e^2 (d+e x)^3 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+10 c d g+4 c e f)}{35 e^2 (d+e x)^4 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{7 e^2 (d+e x)^5 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(7*e^2*(2*c*d - b*e)*(d + e*x)^5) - (2*(4*c*e*f + 10*c*d*g - 7*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(35*e^2*(2*c*d - b*e)^2*(d + e*x)^4) - (4*c*(4*c*e*f + 10*c*d*g - 7*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(105*e^2*(2*c*d - b*e)^3*(d + e*x)^3)","A",3,3,44,0.06818,1,"{792, 658, 650}"
2180,1,285,0,0.4566553,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^6} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^6,x]","-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+4 c d g+2 c e f)}{315 e^2 (d+e x)^3 (2 c d-b e)^4}-\frac{8 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+4 c d g+2 c e f)}{105 e^2 (d+e x)^4 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+4 c d g+2 c e f)}{21 e^2 (d+e x)^5 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{9 e^2 (d+e x)^6 (2 c d-b e)}","-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+4 c d g+2 c e f)}{315 e^2 (d+e x)^3 (2 c d-b e)^4}-\frac{8 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+4 c d g+2 c e f)}{105 e^2 (d+e x)^4 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g+4 c d g+2 c e f)}{21 e^2 (d+e x)^5 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{9 e^2 (d+e x)^6 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(9*e^2*(2*c*d - b*e)*(d + e*x)^6) - (2*(2*c*e*f + 4*c*d*g - 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(21*e^2*(2*c*d - b*e)^2*(d + e*x)^5) - (8*c*(2*c*e*f + 4*c*d*g - 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(105*e^2*(2*c*d - b*e)^3*(d + e*x)^4) - (16*c^2*(2*c*e*f + 4*c*d*g - 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(315*e^2*(2*c*d - b*e)^4*(d + e*x)^3)","A",4,3,44,0.06818,1,"{792, 658, 650}"
2181,1,360,0,0.5758107,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^7} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^7,x]","-\frac{32 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{3465 e^2 (d+e x)^3 (2 c d-b e)^5}-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{1155 e^2 (d+e x)^4 (2 c d-b e)^4}-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{231 e^2 (d+e x)^5 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{99 e^2 (d+e x)^6 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{11 e^2 (d+e x)^7 (2 c d-b e)}","-\frac{32 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{3465 e^2 (d+e x)^3 (2 c d-b e)^5}-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{1155 e^2 (d+e x)^4 (2 c d-b e)^4}-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{231 e^2 (d+e x)^5 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+14 c d g+8 c e f)}{99 e^2 (d+e x)^6 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{11 e^2 (d+e x)^7 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(11*e^2*(2*c*d - b*e)*(d + e*x)^7) - (2*(8*c*e*f + 14*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(99*e^2*(2*c*d - b*e)^2*(d + e*x)^6) - (4*c*(8*c*e*f + 14*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(231*e^2*(2*c*d - b*e)^3*(d + e*x)^5) - (16*c^2*(8*c*e*f + 14*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(1155*e^2*(2*c*d - b*e)^4*(d + e*x)^4) - (32*c^3*(8*c*e*f + 14*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3465*e^2*(2*c*d - b*e)^5*(d + e*x)^3)","A",5,3,44,0.06818,1,"{792, 658, 650}"
2182,1,439,0,0.7181841,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^8} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^8,x]","-\frac{256 c^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+16 c d g+10 c e f)}{45045 e^2 (d+e x)^3 (2 c d-b e)^6}+\frac{128 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (13 b e g-2 c (8 d g+5 e f))}{15015 e^2 (d+e x)^4 (2 c d-b e)^5}-\frac{32 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+16 c d g+10 c e f)}{3003 e^2 (d+e x)^5 (2 c d-b e)^4}+\frac{16 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (13 b e g-2 c (8 d g+5 e f))}{1287 e^2 (d+e x)^6 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+16 c d g+10 c e f)}{143 e^2 (d+e x)^7 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{13 e^2 (d+e x)^8 (2 c d-b e)}","-\frac{256 c^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+16 c d g+10 c e f)}{45045 e^2 (d+e x)^3 (2 c d-b e)^6}+\frac{128 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (13 b e g-2 c (8 d g+5 e f))}{15015 e^2 (d+e x)^4 (2 c d-b e)^5}-\frac{32 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+16 c d g+10 c e f)}{3003 e^2 (d+e x)^5 (2 c d-b e)^4}+\frac{16 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (13 b e g-2 c (8 d g+5 e f))}{1287 e^2 (d+e x)^6 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+16 c d g+10 c e f)}{143 e^2 (d+e x)^7 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{13 e^2 (d+e x)^8 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(13*e^2*(2*c*d - b*e)*(d + e*x)^8) - (2*(10*c*e*f + 16*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(143*e^2*(2*c*d - b*e)^2*(d + e*x)^7) + (16*c*(13*b*e*g - 2*c*(5*e*f + 8*d*g))*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(1287*e^2*(2*c*d - b*e)^3*(d + e*x)^6) - (32*c^2*(10*c*e*f + 16*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3003*e^2*(2*c*d - b*e)^4*(d + e*x)^5) + (128*c^3*(13*b*e*g - 2*c*(5*e*f + 8*d*g))*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(15015*e^2*(2*c*d - b*e)^5*(d + e*x)^4) - (256*c^4*(10*c*e*f + 16*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(45045*e^2*(2*c*d - b*e)^6*(d + e*x)^3)","A",6,3,44,0.06818,1,"{792, 658, 650}"
2183,1,488,0,1.0656755,"\int (d+e x)^3 (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^3*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{9 (b+2 c x) (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-11 b e g+6 c d g+16 c e f)}{16384 c^6 e}+\frac{3 (b+2 c x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+6 c d g+16 c e f)}{2048 c^5 e}-\frac{3 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+6 c d g+16 c e f)}{640 c^4 e^2}-\frac{3 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+6 c d g+16 c e f)}{448 c^3 e^2}-\frac{(d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+6 c d g+16 c e f)}{112 c^2 e^2}+\frac{9 (2 c d-b e)^7 (-11 b e g+6 c d g+16 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{32768 c^{13/2} e^2}-\frac{g (d+e x)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{8 c e^2}","\frac{9 (b+2 c x) (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-11 b e g+6 c d g+16 c e f)}{16384 c^6 e}+\frac{3 (b+2 c x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+6 c d g+16 c e f)}{2048 c^5 e}-\frac{3 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+6 c d g+16 c e f)}{640 c^4 e^2}-\frac{3 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+6 c d g+16 c e f)}{448 c^3 e^2}-\frac{(d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+6 c d g+16 c e f)}{112 c^2 e^2}+\frac{9 (2 c d-b e)^7 (-11 b e g+6 c d g+16 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{32768 c^{13/2} e^2}-\frac{g (d+e x)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{8 c e^2}",1,"(9*(2*c*d - b*e)^5*(16*c*e*f + 6*c*d*g - 11*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(16384*c^6*e) + (3*(2*c*d - b*e)^3*(16*c*e*f + 6*c*d*g - 11*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(2048*c^5*e) - (3*(2*c*d - b*e)^2*(16*c*e*f + 6*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(640*c^4*e^2) - (3*(2*c*d - b*e)*(16*c*e*f + 6*c*d*g - 11*b*e*g)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(448*c^3*e^2) - ((16*c*e*f + 6*c*d*g - 11*b*e*g)*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(112*c^2*e^2) - (g*(d + e*x)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(8*c*e^2) + (9*(2*c*d - b*e)^7*(16*c*e*f + 6*c*d*g - 11*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(32768*c^(13/2)*e^2)","A",8,6,44,0.1364,1,"{794, 670, 640, 612, 621, 204}"
2184,1,413,0,0.6027397,"\int (d+e x)^2 (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^2*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{(b+2 c x) (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+4 c d g+14 c e f)}{1024 c^5 e}+\frac{(b+2 c x) (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-9 b e g+4 c d g+14 c e f)}{384 c^4 e}-\frac{(2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+4 c d g+14 c e f)}{120 c^3 e^2}-\frac{(d+e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+4 c d g+14 c e f)}{84 c^2 e^2}+\frac{(2 c d-b e)^6 (-9 b e g+4 c d g+14 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2048 c^{11/2} e^2}-\frac{g (d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{7 c e^2}","\frac{(b+2 c x) (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+4 c d g+14 c e f)}{1024 c^5 e}+\frac{(b+2 c x) (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-9 b e g+4 c d g+14 c e f)}{384 c^4 e}-\frac{(2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+4 c d g+14 c e f)}{120 c^3 e^2}-\frac{(d+e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+4 c d g+14 c e f)}{84 c^2 e^2}+\frac{(2 c d-b e)^6 (-9 b e g+4 c d g+14 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2048 c^{11/2} e^2}-\frac{g (d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{7 c e^2}",1,"((2*c*d - b*e)^4*(14*c*e*f + 4*c*d*g - 9*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(1024*c^5*e) + ((2*c*d - b*e)^2*(14*c*e*f + 4*c*d*g - 9*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(384*c^4*e) - ((2*c*d - b*e)*(14*c*e*f + 4*c*d*g - 9*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(120*c^3*e^2) - ((14*c*e*f + 4*c*d*g - 9*b*e*g)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(84*c^2*e^2) - (g*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(7*c*e^2) + ((2*c*d - b*e)^6*(14*c*e*f + 4*c*d*g - 9*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(2048*c^(11/2)*e^2)","A",8,7,44,0.1591,1,"{1638, 12, 670, 640, 612, 621, 204}"
2185,1,297,0,0.4398878,"\int (d+e x) (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{(b+2 c x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+2 c d g+12 c e f)}{512 c^4 e}+\frac{(b+2 c x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+2 c d g+12 c e f)}{192 c^3 e}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (7 b e g-12 c (d g+e f)-10 c e g x)}{60 c^2 e^2}+\frac{(2 c d-b e)^5 (-7 b e g+2 c d g+12 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{1024 c^{9/2} e^2}","\frac{(b+2 c x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+2 c d g+12 c e f)}{512 c^4 e}+\frac{(b+2 c x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-7 b e g+2 c d g+12 c e f)}{192 c^3 e}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (7 b e g-12 c (d g+e f)-10 c e g x)}{60 c^2 e^2}+\frac{(2 c d-b e)^5 (-7 b e g+2 c d g+12 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{1024 c^{9/2} e^2}",1,"((2*c*d - b*e)^3*(12*c*e*f + 2*c*d*g - 7*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(512*c^4*e) + ((2*c*d - b*e)*(12*c*e*f + 2*c*d*g - 7*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(192*c^3*e) + ((7*b*e*g - 12*c*(e*f + d*g) - 10*c*e*g*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(60*c^2*e^2) + ((2*c*d - b*e)^5*(12*c*e*f + 2*c*d*g - 7*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(1024*c^(9/2)*e^2)","A",5,4,42,0.09524,1,"{779, 612, 621, 204}"
2186,1,266,0,0.3326706,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{d+e x} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x),x]","\frac{(b+2 c x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g-2 c d g+8 c e f)}{64 c^2 e}+\frac{(2 c d-b e)^3 (-3 b e g-2 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{5/2} e^2}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g-2 c d g+8 c e f)}{24 c e^2}-\frac{g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{4 c e^2 (d+e x)}","\frac{(b+2 c x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g-2 c d g+8 c e f)}{64 c^2 e}+\frac{(2 c d-b e)^3 (-3 b e g-2 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{5/2} e^2}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g-2 c d g+8 c e f)}{24 c e^2}-\frac{g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{4 c e^2 (d+e x)}",1,"((2*c*d - b*e)*(8*c*e*f - 2*c*d*g - 3*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*c^2*e) + ((8*c*e*f - 2*c*d*g - 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(24*c*e^2) - (g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(4*c*e^2*(d + e*x)) + ((2*c*d - b*e)^3*(8*c*e*f - 2*c*d*g - 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(128*c^(5/2)*e^2)","A",5,5,44,0.1136,1,"{794, 664, 612, 621, 204}"
2187,1,278,0,0.4201403,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^2} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^2,x]","\frac{(2 c d-b e)^2 (-b e g-4 c d g+6 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{16 c^{3/2} e^2}+\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{e^2 (d+e x)^2 (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-b e g-4 c d g+6 c e f)}{3 e^2 (2 c d-b e)}+\frac{(b+2 c x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-b e g-4 c d g+6 c e f)}{8 c e}","\frac{(2 c d-b e)^2 (-b e g-4 c d g+6 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{16 c^{3/2} e^2}+\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{e^2 (d+e x)^2 (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-b e g-4 c d g+6 c e f)}{3 e^2 (2 c d-b e)}+\frac{(b+2 c x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-b e g-4 c d g+6 c e f)}{8 c e}",1,"((6*c*e*f - 4*c*d*g - b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(8*c*e) + ((6*c*e*f - 4*c*d*g - b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)) + (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(e^2*(2*c*d - b*e)*(d + e*x)^2) + ((2*c*d - b*e)^2*(6*c*e*f - 4*c*d*g - b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(16*c^(3/2)*e^2)","A",5,5,44,0.1136,1,"{792, 664, 612, 621, 204}"
2188,1,271,0,0.4671339,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^3} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^3,x]","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{e^2 (d+e x)^3 (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (b e g-6 c d g+4 c e f)}{2 e^2 (d+e x) (2 c d-b e)}-\frac{3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (b e g-6 c d g+4 c e f)}{4 e^2}-\frac{3 (2 c d-b e) (b e g-6 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 \sqrt{c} e^2}","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{e^2 (d+e x)^3 (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (b e g-6 c d g+4 c e f)}{2 e^2 (d+e x) (2 c d-b e)}-\frac{3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (b e g-6 c d g+4 c e f)}{4 e^2}-\frac{3 (2 c d-b e) (b e g-6 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 \sqrt{c} e^2}",1,"(-3*(4*c*e*f - 6*c*d*g + b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2) - ((4*c*e*f - 6*c*d*g + b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(2*e^2*(2*c*d - b*e)*(d + e*x)) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(e^2*(2*c*d - b*e)*(d + e*x)^3) - (3*(2*c*d - b*e)*(4*c*e*f - 6*c*d*g + b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(8*Sqrt[c]*e^2)","A",5,4,44,0.09091,1,"{792, 664, 621, 204}"
2189,1,276,0,0.4542723,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^4} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^4,x]","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{3 e^2 (d+e x)^4 (2 c d-b e)}+\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (3 b e g-8 c d g+2 c e f)}{3 e^2 (d+e x)^2 (2 c d-b e)}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (3 b e g-8 c d g+2 c e f)}{e^2 (2 c d-b e)}+\frac{\sqrt{c} (3 b e g-8 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 e^2}","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{3 e^2 (d+e x)^4 (2 c d-b e)}+\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (3 b e g-8 c d g+2 c e f)}{3 e^2 (d+e x)^2 (2 c d-b e)}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (3 b e g-8 c d g+2 c e f)}{e^2 (2 c d-b e)}+\frac{\sqrt{c} (3 b e g-8 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 e^2}",1,"(c*(2*c*e*f - 8*c*d*g + 3*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(2*c*d - b*e)) + (2*(2*c*e*f - 8*c*d*g + 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^2) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^4) + (Sqrt[c]*(2*c*e*f - 8*c*d*g + 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(2*e^2)","A",5,5,44,0.1136,1,"{792, 662, 664, 621, 204}"
2190,1,214,0,0.4434026,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^5} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^5,x]","\frac{c^{3/2} g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{e^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 e^2 (d+e x)^5 (2 c d-b e)}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^3}+\frac{2 c g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)}","\frac{c^{3/2} g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{e^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 e^2 (d+e x)^5 (2 c d-b e)}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^3}+\frac{2 c g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)}",1,"(2*c*g*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(d + e*x)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^3) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^5) + (c^(3/2)*g*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/e^2","A",5,4,44,0.09091,1,"{792, 662, 621, 204}"
2191,1,138,0,0.2265426,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^6} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^6,x]","\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (7 b e g-2 c (6 d g+e f))}{35 e^2 (d+e x)^5 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{7 e^2 (d+e x)^6 (2 c d-b e)}","\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (7 b e g-2 c (6 d g+e f))}{35 e^2 (d+e x)^5 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{7 e^2 (d+e x)^6 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(7*e^2*(2*c*d - b*e)*(d + e*x)^6) + (2*(7*b*e*g - 2*c*(e*f + 6*d*g))*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(35*e^2*(2*c*d - b*e)^2*(d + e*x)^5)","A",2,2,44,0.04545,1,"{792, 650}"
2192,1,210,0,0.3462613,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^7} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^7,x]","-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+14 c d g+4 c e f)}{315 e^2 (d+e x)^5 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+14 c d g+4 c e f)}{63 e^2 (d+e x)^6 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{9 e^2 (d+e x)^7 (2 c d-b e)}","-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+14 c d g+4 c e f)}{315 e^2 (d+e x)^5 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+14 c d g+4 c e f)}{63 e^2 (d+e x)^6 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{9 e^2 (d+e x)^7 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(9*e^2*(2*c*d - b*e)*(d + e*x)^7) - (2*(4*c*e*f + 14*c*d*g - 9*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(63*e^2*(2*c*d - b*e)^2*(d + e*x)^6) - (4*c*(4*c*e*f + 14*c*d*g - 9*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(315*e^2*(2*c*d - b*e)^3*(d + e*x)^5)","A",3,3,44,0.06818,1,"{792, 658, 650}"
2193,1,285,0,0.4479093,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^8} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^8,x]","-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+16 c d g+6 c e f)}{3465 e^2 (d+e x)^5 (2 c d-b e)^4}-\frac{8 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+16 c d g+6 c e f)}{693 e^2 (d+e x)^6 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+16 c d g+6 c e f)}{99 e^2 (d+e x)^7 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{11 e^2 (d+e x)^8 (2 c d-b e)}","-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+16 c d g+6 c e f)}{3465 e^2 (d+e x)^5 (2 c d-b e)^4}-\frac{8 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+16 c d g+6 c e f)}{693 e^2 (d+e x)^6 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+16 c d g+6 c e f)}{99 e^2 (d+e x)^7 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{11 e^2 (d+e x)^8 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(11*e^2*(2*c*d - b*e)*(d + e*x)^8) - (2*(6*c*e*f + 16*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(99*e^2*(2*c*d - b*e)^2*(d + e*x)^7) - (8*c*(6*c*e*f + 16*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(693*e^2*(2*c*d - b*e)^3*(d + e*x)^6) - (16*c^2*(6*c*e*f + 16*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3465*e^2*(2*c*d - b*e)^4*(d + e*x)^5)","A",4,3,44,0.06818,1,"{792, 658, 650}"
2194,1,360,0,0.5724346,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^9} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^9,x]","-\frac{32 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{15015 e^2 (d+e x)^5 (2 c d-b e)^5}-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{3003 e^2 (d+e x)^6 (2 c d-b e)^4}-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{429 e^2 (d+e x)^7 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{143 e^2 (d+e x)^8 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{13 e^2 (d+e x)^9 (2 c d-b e)}","-\frac{32 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{15015 e^2 (d+e x)^5 (2 c d-b e)^5}-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{3003 e^2 (d+e x)^6 (2 c d-b e)^4}-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{429 e^2 (d+e x)^7 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+18 c d g+8 c e f)}{143 e^2 (d+e x)^8 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{13 e^2 (d+e x)^9 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(13*e^2*(2*c*d - b*e)*(d + e*x)^9) - (2*(8*c*e*f + 18*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(143*e^2*(2*c*d - b*e)^2*(d + e*x)^8) - (4*c*(8*c*e*f + 18*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(429*e^2*(2*c*d - b*e)^3*(d + e*x)^7) - (16*c^2*(8*c*e*f + 18*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3003*e^2*(2*c*d - b*e)^4*(d + e*x)^6) - (32*c^3*(8*c*e*f + 18*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(15015*e^2*(2*c*d - b*e)^5*(d + e*x)^5)","A",5,3,44,0.06818,1,"{792, 658, 650}"
2195,1,562,0,1.214628,"\int (d+e x)^3 (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^3*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{11 (b+2 c x) (2 c d-b e)^7 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-13 b e g+6 c d g+20 c e f)}{131072 c^7 e}+\frac{11 (b+2 c x) (2 c d-b e)^5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+6 c d g+20 c e f)}{49152 c^6 e}+\frac{11 (b+2 c x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+6 c d g+20 c e f)}{15360 c^5 e}-\frac{11 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+6 c d g+20 c e f)}{4480 c^4 e^2}-\frac{11 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+6 c d g+20 c e f)}{2880 c^3 e^2}-\frac{(d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+6 c d g+20 c e f)}{180 c^2 e^2}+\frac{11 (2 c d-b e)^9 (-13 b e g+6 c d g+20 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{262144 c^{15/2} e^2}-\frac{g (d+e x)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{10 c e^2}","\frac{11 (b+2 c x) (2 c d-b e)^7 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-13 b e g+6 c d g+20 c e f)}{131072 c^7 e}+\frac{11 (b+2 c x) (2 c d-b e)^5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-13 b e g+6 c d g+20 c e f)}{49152 c^6 e}+\frac{11 (b+2 c x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-13 b e g+6 c d g+20 c e f)}{15360 c^5 e}-\frac{11 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+6 c d g+20 c e f)}{4480 c^4 e^2}-\frac{11 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+6 c d g+20 c e f)}{2880 c^3 e^2}-\frac{(d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+6 c d g+20 c e f)}{180 c^2 e^2}+\frac{11 (2 c d-b e)^9 (-13 b e g+6 c d g+20 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{262144 c^{15/2} e^2}-\frac{g (d+e x)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{10 c e^2}",1,"(11*(2*c*d - b*e)^7*(20*c*e*f + 6*c*d*g - 13*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(131072*c^7*e) + (11*(2*c*d - b*e)^5*(20*c*e*f + 6*c*d*g - 13*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(49152*c^6*e) + (11*(2*c*d - b*e)^3*(20*c*e*f + 6*c*d*g - 13*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(15360*c^5*e) - (11*(2*c*d - b*e)^2*(20*c*e*f + 6*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(4480*c^4*e^2) - (11*(2*c*d - b*e)*(20*c*e*f + 6*c*d*g - 13*b*e*g)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(2880*c^3*e^2) - ((20*c*e*f + 6*c*d*g - 13*b*e*g)*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(180*c^2*e^2) - (g*(d + e*x)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(10*c*e^2) + (11*(2*c*d - b*e)^9*(20*c*e*f + 6*c*d*g - 13*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(262144*c^(15/2)*e^2)","A",9,6,44,0.1364,1,"{794, 670, 640, 612, 621, 204}"
2196,1,487,0,0.8113491,"\int (d+e x)^2 (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^2*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{5 (b+2 c x) (2 c d-b e)^6 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-11 b e g+4 c d g+18 c e f)}{32768 c^6 e}+\frac{5 (b+2 c x) (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+4 c d g+18 c e f)}{12288 c^5 e}+\frac{(b+2 c x) (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+4 c d g+18 c e f)}{768 c^4 e}-\frac{(2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+4 c d g+18 c e f)}{224 c^3 e^2}-\frac{(d+e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+4 c d g+18 c e f)}{144 c^2 e^2}+\frac{5 (2 c d-b e)^8 (-11 b e g+4 c d g+18 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{65536 c^{13/2} e^2}-\frac{g (d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{9 c e^2}","\frac{5 (b+2 c x) (2 c d-b e)^6 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-11 b e g+4 c d g+18 c e f)}{32768 c^6 e}+\frac{5 (b+2 c x) (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-11 b e g+4 c d g+18 c e f)}{12288 c^5 e}+\frac{(b+2 c x) (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-11 b e g+4 c d g+18 c e f)}{768 c^4 e}-\frac{(2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+4 c d g+18 c e f)}{224 c^3 e^2}-\frac{(d+e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+4 c d g+18 c e f)}{144 c^2 e^2}+\frac{5 (2 c d-b e)^8 (-11 b e g+4 c d g+18 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{65536 c^{13/2} e^2}-\frac{g (d+e x)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{9 c e^2}",1,"(5*(2*c*d - b*e)^6*(18*c*e*f + 4*c*d*g - 11*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(32768*c^6*e) + (5*(2*c*d - b*e)^4*(18*c*e*f + 4*c*d*g - 11*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(12288*c^5*e) + ((2*c*d - b*e)^2*(18*c*e*f + 4*c*d*g - 11*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(768*c^4*e) - ((2*c*d - b*e)*(18*c*e*f + 4*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(224*c^3*e^2) - ((18*c*e*f + 4*c*d*g - 11*b*e*g)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(144*c^2*e^2) - (g*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(9*c*e^2) + (5*(2*c*d - b*e)^8*(18*c*e*f + 4*c*d*g - 11*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(65536*c^(13/2)*e^2)","A",9,7,44,0.1591,1,"{1638, 12, 670, 640, 612, 621, 204}"
2197,1,371,0,0.6186323,"\int (d+e x) (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{5 (b+2 c x) (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+2 c d g+16 c e f)}{16384 c^5 e}+\frac{5 (b+2 c x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-9 b e g+2 c d g+16 c e f)}{6144 c^4 e}+\frac{(b+2 c x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+2 c d g+16 c e f)}{384 c^3 e}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (9 b e g-16 c (d g+e f)-14 c e g x)}{112 c^2 e^2}+\frac{5 (2 c d-b e)^7 (-9 b e g+2 c d g+16 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{32768 c^{11/2} e^2}","\frac{5 (b+2 c x) (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+2 c d g+16 c e f)}{16384 c^5 e}+\frac{5 (b+2 c x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-9 b e g+2 c d g+16 c e f)}{6144 c^4 e}+\frac{(b+2 c x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-9 b e g+2 c d g+16 c e f)}{384 c^3 e}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (9 b e g-16 c (d g+e f)-14 c e g x)}{112 c^2 e^2}+\frac{5 (2 c d-b e)^7 (-9 b e g+2 c d g+16 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{32768 c^{11/2} e^2}",1,"(5*(2*c*d - b*e)^5*(16*c*e*f + 2*c*d*g - 9*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(16384*c^5*e) + (5*(2*c*d - b*e)^3*(16*c*e*f + 2*c*d*g - 9*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(6144*c^4*e) + ((2*c*d - b*e)*(16*c*e*f + 2*c*d*g - 9*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(384*c^3*e) + ((9*b*e*g - 16*c*(e*f + d*g) - 14*c*e*g*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(112*c^2*e^2) + (5*(2*c*d - b*e)^7*(16*c*e*f + 2*c*d*g - 9*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(32768*c^(11/2)*e^2)","A",6,4,42,0.09524,1,"{779, 612, 621, 204}"
2198,1,346,0,0.5275414,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{d+e x} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x),x]","-\frac{(b+2 c x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (5 b e g-2 c (6 e f-d g))}{512 c^3 e}-\frac{(b+2 c x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (5 b e g-2 c (6 e f-d g))}{192 c^2 e}-\frac{(2 c d-b e)^5 (5 b e g-2 c (6 e f-d g)) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{1024 c^{7/2} e^2}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-5 b e g-2 c d g+12 c e f)}{60 c e^2}-\frac{g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{6 c e^2 (d+e x)}","-\frac{(b+2 c x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (5 b e g-2 c (6 e f-d g))}{512 c^3 e}-\frac{(b+2 c x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (5 b e g-2 c (6 e f-d g))}{192 c^2 e}-\frac{(2 c d-b e)^5 (5 b e g-2 c (6 e f-d g)) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{1024 c^{7/2} e^2}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-5 b e g-2 c d g+12 c e f)}{60 c e^2}-\frac{g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{6 c e^2 (d+e x)}",1,"-((2*c*d - b*e)^3*(5*b*e*g - 2*c*(6*e*f - d*g))*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(512*c^3*e) - ((2*c*d - b*e)*(5*b*e*g - 2*c*(6*e*f - d*g))*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(192*c^2*e) + ((12*c*e*f - 2*c*d*g - 5*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(60*c*e^2) - (g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(6*c*e^2*(d + e*x)) - ((2*c*d - b*e)^5*(5*b*e*g - 2*c*(6*e*f - d*g))*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(1024*c^(7/2)*e^2)","A",6,5,44,0.1136,1,"{794, 664, 612, 621, 204}"
2199,1,354,0,0.6087562,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^2} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^2,x]","\frac{(b+2 c x) (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g-4 c d g+10 c e f)}{128 c^2 e}+\frac{(2 c d-b e)^4 (-3 b e g-4 c d g+10 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{256 c^{5/2} e^2}+\frac{(b+2 c x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g-4 c d g+10 c e f)}{48 c e}+\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^2 (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-3 b e g-4 c d g+10 c e f)}{15 e^2 (2 c d-b e)}","\frac{(b+2 c x) (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g-4 c d g+10 c e f)}{128 c^2 e}+\frac{(2 c d-b e)^4 (-3 b e g-4 c d g+10 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{256 c^{5/2} e^2}+\frac{(b+2 c x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-3 b e g-4 c d g+10 c e f)}{48 c e}+\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^2 (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-3 b e g-4 c d g+10 c e f)}{15 e^2 (2 c d-b e)}",1,"((2*c*d - b*e)^2*(10*c*e*f - 4*c*d*g - 3*b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(128*c^2*e) + ((10*c*e*f - 4*c*d*g - 3*b*e*g)*(b + 2*c*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(48*c*e) + ((10*c*e*f - 4*c*d*g - 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(15*e^2*(2*c*d - b*e)) + (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^2) + ((2*c*d - b*e)^4*(10*c*e*f - 4*c*d*g - 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(256*c^(5/2)*e^2)","A",6,5,44,0.1136,1,"{792, 664, 612, 621, 204}"
2200,1,354,0,0.7505817,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^3} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^3,x]","\frac{5 (2 c d-b e)^3 (-b e g-6 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{3/2} e^2}+\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{e^2 (d+e x)^3 (2 c d-b e)}+\frac{5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-b e g-6 c d g+8 c e f)}{24 e^2}+\frac{(-b e+c d-c e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-b e g-6 c d g+8 c e f)}{4 e^2 (2 c d-b e)}+\frac{5 (b+2 c x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-b e g-6 c d g+8 c e f)}{64 c e}","\frac{5 (2 c d-b e)^3 (-b e g-6 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{3/2} e^2}+\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{e^2 (d+e x)^3 (2 c d-b e)}+\frac{5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-b e g-6 c d g+8 c e f)}{24 e^2}+\frac{(-b e+c d-c e x) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-b e g-6 c d g+8 c e f)}{4 e^2 (2 c d-b e)}+\frac{5 (b+2 c x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-b e g-6 c d g+8 c e f)}{64 c e}",1,"(5*(2*c*d - b*e)*(8*c*e*f - 6*c*d*g - b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*c*e) + (5*(8*c*e*f - 6*c*d*g - b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(24*e^2) + ((8*c*e*f - 6*c*d*g - b*e*g)*(c*d - b*e - c*e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(4*e^2*(2*c*d - b*e)) + (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(e^2*(2*c*d - b*e)*(d + e*x)^3) + (5*(2*c*d - b*e)^3*(8*c*e*f - 6*c*d*g - b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(128*c^(3/2)*e^2)","A",7,7,44,0.1591,1,"{792, 654, 670, 640, 612, 621, 204}"
2201,1,342,0,0.5978066,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^4} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^4,x]","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{e^2 (d+e x)^4 (2 c d-b e)}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (b e g-8 c d g+6 c e f)}{e^2 (d+e x)^2 (2 c d-b e)}-\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (b e g-8 c d g+6 c e f)}{3 e^2 (2 c d-b e)}-\frac{5 (b+2 c x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (b e g-8 c d g+6 c e f)}{8 e}-\frac{5 (2 c d-b e)^2 (b e g-8 c d g+6 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{16 \sqrt{c} e^2}","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{e^2 (d+e x)^4 (2 c d-b e)}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (b e g-8 c d g+6 c e f)}{e^2 (d+e x)^2 (2 c d-b e)}-\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (b e g-8 c d g+6 c e f)}{3 e^2 (2 c d-b e)}-\frac{5 (b+2 c x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (b e g-8 c d g+6 c e f)}{8 e}-\frac{5 (2 c d-b e)^2 (b e g-8 c d g+6 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{16 \sqrt{c} e^2}",1,"(-5*(6*c*e*f - 8*c*d*g + b*e*g)*(b + 2*c*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(8*e) - (5*c*(6*c*e*f - 8*c*d*g + b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)) - (2*(6*c*e*f - 8*c*d*g + b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(e^2*(2*c*d - b*e)*(d + e*x)^2) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(e^2*(2*c*d - b*e)*(d + e*x)^4) - (5*(2*c*d - b*e)^2*(6*c*e*f - 8*c*d*g + b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(16*Sqrt[c]*e^2)","A",6,6,44,0.1364,1,"{792, 662, 664, 612, 621, 204}"
2202,1,350,0,0.6273466,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^5} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^5,x]","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^5 (2 c d-b e)}+\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (3 b e g-10 c d g+4 c e f)}{3 e^2 (d+e x)^3 (2 c d-b e)}+\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (3 b e g-10 c d g+4 c e f)}{6 e^2 (d+e x) (2 c d-b e)}+\frac{5 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (3 b e g-10 c d g+4 c e f)}{4 e^2}+\frac{5 \sqrt{c} (2 c d-b e) (3 b e g-10 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 e^2}","-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^5 (2 c d-b e)}+\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (3 b e g-10 c d g+4 c e f)}{3 e^2 (d+e x)^3 (2 c d-b e)}+\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (3 b e g-10 c d g+4 c e f)}{6 e^2 (d+e x) (2 c d-b e)}+\frac{5 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (3 b e g-10 c d g+4 c e f)}{4 e^2}+\frac{5 \sqrt{c} (2 c d-b e) (3 b e g-10 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 e^2}",1,"(5*c*(4*c*e*f - 10*c*d*g + 3*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2) + (5*c*(4*c*e*f - 10*c*d*g + 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(6*e^2*(2*c*d - b*e)*(d + e*x)) + (2*(4*c*e*f - 10*c*d*g + 3*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^3) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^5) + (5*Sqrt[c]*(2*c*d - b*e)*(4*c*e*f - 10*c*d*g + 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(8*e^2)","A",6,5,44,0.1136,1,"{792, 662, 664, 621, 204}"
2203,1,352,0,0.5711165,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^6} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^6,x]","-\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (5 b e g-12 c d g+2 c e f)}{e^2 (2 c d-b e)}-\frac{c^{3/2} (5 b e g-12 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 e^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{5 e^2 (d+e x)^6 (2 c d-b e)}+\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (5 b e g-12 c d g+2 c e f)}{15 e^2 (d+e x)^4 (2 c d-b e)}-\frac{2 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (5 b e g-12 c d g+2 c e f)}{3 e^2 (d+e x)^2 (2 c d-b e)}","-\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (5 b e g-12 c d g+2 c e f)}{e^2 (2 c d-b e)}-\frac{c^{3/2} (5 b e g-12 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 e^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{5 e^2 (d+e x)^6 (2 c d-b e)}+\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (5 b e g-12 c d g+2 c e f)}{15 e^2 (d+e x)^4 (2 c d-b e)}-\frac{2 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (5 b e g-12 c d g+2 c e f)}{3 e^2 (d+e x)^2 (2 c d-b e)}",1,"-((c^2*(2*c*e*f - 12*c*d*g + 5*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(2*c*d - b*e))) - (2*c*(2*c*e*f - 12*c*d*g + 5*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^2) + (2*(2*c*e*f - 12*c*d*g + 5*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(15*e^2*(2*c*d - b*e)*(d + e*x)^4) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^6) - (c^(3/2)*(2*c*e*f - 12*c*d*g + 5*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(2*e^2)","A",6,5,44,0.1136,1,"{792, 662, 664, 621, 204}"
2204,1,264,0,0.5675916,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^7} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^7,x]","-\frac{2 c^2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)}-\frac{c^{5/2} g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{e^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{7 e^2 (d+e x)^7 (2 c d-b e)}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 e^2 (d+e x)^5}+\frac{2 c g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^3}","-\frac{2 c^2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)}-\frac{c^{5/2} g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{e^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{7 e^2 (d+e x)^7 (2 c d-b e)}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 e^2 (d+e x)^5}+\frac{2 c g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^3}",1,"(-2*c^2*g*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(d + e*x)) + (2*c*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^3) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*e^2*(d + e*x)^5) - (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(7*e^2*(2*c*d - b*e)*(d + e*x)^7) - (c^(5/2)*g*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/e^2","A",6,4,44,0.09091,1,"{792, 662, 621, 204}"
2205,1,138,0,0.2210607,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^8} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^8,x]","\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (9 b e g-2 c (8 d g+e f))}{63 e^2 (d+e x)^7 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{9 e^2 (d+e x)^8 (2 c d-b e)}","\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (9 b e g-2 c (8 d g+e f))}{63 e^2 (d+e x)^7 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{9 e^2 (d+e x)^8 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(9*e^2*(2*c*d - b*e)*(d + e*x)^8) + (2*(9*b*e*g - 2*c*(e*f + 8*d*g))*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(63*e^2*(2*c*d - b*e)^2*(d + e*x)^7)","A",2,2,44,0.04545,1,"{792, 650}"
2206,1,210,0,0.3271709,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^9} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^9,x]","-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+18 c d g+4 c e f)}{693 e^2 (d+e x)^7 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+18 c d g+4 c e f)}{99 e^2 (d+e x)^8 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{11 e^2 (d+e x)^9 (2 c d-b e)}","-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+18 c d g+4 c e f)}{693 e^2 (d+e x)^7 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-11 b e g+18 c d g+4 c e f)}{99 e^2 (d+e x)^8 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{11 e^2 (d+e x)^9 (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(11*e^2*(2*c*d - b*e)*(d + e*x)^9) - (2*(4*c*e*f + 18*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(99*e^2*(2*c*d - b*e)^2*(d + e*x)^8) - (4*c*(4*c*e*f + 18*c*d*g - 11*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(693*e^2*(2*c*d - b*e)^3*(d + e*x)^7)","A",3,3,44,0.06818,1,"{792, 658, 650}"
2207,1,285,0,0.4369463,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{10}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^10,x]","-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+20 c d g+6 c e f)}{9009 e^2 (d+e x)^7 (2 c d-b e)^4}-\frac{8 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+20 c d g+6 c e f)}{1287 e^2 (d+e x)^8 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+20 c d g+6 c e f)}{143 e^2 (d+e x)^9 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{13 e^2 (d+e x)^{10} (2 c d-b e)}","-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+20 c d g+6 c e f)}{9009 e^2 (d+e x)^7 (2 c d-b e)^4}-\frac{8 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+20 c d g+6 c e f)}{1287 e^2 (d+e x)^8 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-13 b e g+20 c d g+6 c e f)}{143 e^2 (d+e x)^9 (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{13 e^2 (d+e x)^{10} (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(13*e^2*(2*c*d - b*e)*(d + e*x)^10) - (2*(6*c*e*f + 20*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(143*e^2*(2*c*d - b*e)^2*(d + e*x)^9) - (8*c*(6*c*e*f + 20*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(1287*e^2*(2*c*d - b*e)^3*(d + e*x)^8) - (16*c^2*(6*c*e*f + 20*c*d*g - 13*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(9009*e^2*(2*c*d - b*e)^4*(d + e*x)^7)","A",4,3,44,0.06818,1,"{792, 658, 650}"
2208,1,360,0,0.5806176,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{11}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^11,x]","-\frac{32 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{45045 e^2 (d+e x)^7 (2 c d-b e)^5}-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{6435 e^2 (d+e x)^8 (2 c d-b e)^4}-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{715 e^2 (d+e x)^9 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{195 e^2 (d+e x)^{10} (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{15 e^2 (d+e x)^{11} (2 c d-b e)}","-\frac{32 c^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{45045 e^2 (d+e x)^7 (2 c d-b e)^5}-\frac{16 c^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{6435 e^2 (d+e x)^8 (2 c d-b e)^4}-\frac{4 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{715 e^2 (d+e x)^9 (2 c d-b e)^3}-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-15 b e g+22 c d g+8 c e f)}{195 e^2 (d+e x)^{10} (2 c d-b e)^2}-\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{15 e^2 (d+e x)^{11} (2 c d-b e)}",1,"(-2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(15*e^2*(2*c*d - b*e)*(d + e*x)^11) - (2*(8*c*e*f + 22*c*d*g - 15*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(195*e^2*(2*c*d - b*e)^2*(d + e*x)^10) - (4*c*(8*c*e*f + 22*c*d*g - 15*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(715*e^2*(2*c*d - b*e)^3*(d + e*x)^9) - (16*c^2*(8*c*e*f + 22*c*d*g - 15*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(6435*e^2*(2*c*d - b*e)^4*(d + e*x)^8) - (32*c^3*(8*c*e*f + 22*c*d*g - 15*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(45045*e^2*(2*c*d - b*e)^5*(d + e*x)^7)","A",5,3,44,0.06818,1,"{792, 658, 650}"
2209,1,340,0,0.6093601,"\int \frac{(d+e x)^3 (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[((d + e*x)^3*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{5 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+6 c d g+8 c e f)}{64 c^4 e^2}-\frac{5 (d+e x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+6 c d g+8 c e f)}{96 c^3 e^2}-\frac{(d+e x)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+6 c d g+8 c e f)}{24 c^2 e^2}+\frac{5 (2 c d-b e)^3 (-7 b e g+6 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{9/2} e^2}-\frac{g (d+e x)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{4 c e^2}","-\frac{5 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+6 c d g+8 c e f)}{64 c^4 e^2}-\frac{5 (d+e x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+6 c d g+8 c e f)}{96 c^3 e^2}-\frac{(d+e x)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+6 c d g+8 c e f)}{24 c^2 e^2}+\frac{5 (2 c d-b e)^3 (-7 b e g+6 c d g+8 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{128 c^{9/2} e^2}-\frac{g (d+e x)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{4 c e^2}",1,"(-5*(2*c*d - b*e)^2*(8*c*e*f + 6*c*d*g - 7*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*c^4*e^2) - (5*(2*c*d - b*e)*(8*c*e*f + 6*c*d*g - 7*b*e*g)*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(96*c^3*e^2) - ((8*c*e*f + 6*c*d*g - 7*b*e*g)*(d + e*x)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(24*c^2*e^2) - (g*(d + e*x)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*c*e^2) + (5*(2*c*d - b*e)^3*(8*c*e*f + 6*c*d*g - 7*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(128*c^(9/2)*e^2)","A",6,5,44,0.1136,1,"{794, 670, 640, 621, 204}"
2210,1,265,0,0.3539075,"\int \frac{(d+e x)^2 (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[((d + e*x)^2*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{(2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+4 c d g+6 c e f)}{8 c^3 e^2}-\frac{(d+e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+4 c d g+6 c e f)}{12 c^2 e^2}+\frac{(2 c d-b e)^2 (-5 b e g+4 c d g+6 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{16 c^{7/2} e^2}-\frac{g (d+e x)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{3 c e^2}","-\frac{(2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+4 c d g+6 c e f)}{8 c^3 e^2}-\frac{(d+e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+4 c d g+6 c e f)}{12 c^2 e^2}+\frac{(2 c d-b e)^2 (-5 b e g+4 c d g+6 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{16 c^{7/2} e^2}-\frac{g (d+e x)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{3 c e^2}",1,"-((2*c*d - b*e)*(6*c*e*f + 4*c*d*g - 5*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(8*c^3*e^2) - ((6*c*e*f + 4*c*d*g - 5*b*e*g)*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(12*c^2*e^2) - (g*(d + e*x)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*c*e^2) + ((2*c*d - b*e)^2*(6*c*e*f + 4*c*d*g - 5*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(16*c^(7/2)*e^2)","A",6,6,44,0.1364,1,"{1638, 12, 670, 640, 621, 204}"
2211,1,149,0,0.1569488,"\int \frac{(d+e x) (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[((d + e*x)*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (3 b e g-4 c (d g+e f)-2 c e g x)}{4 c^2 e^2}+\frac{(2 c d-b e) (-3 b e g+2 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{5/2} e^2}","\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (3 b e g-4 c (d g+e f)-2 c e g x)}{4 c^2 e^2}+\frac{(2 c d-b e) (-3 b e g+2 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{5/2} e^2}",1,"((3*b*e*g - 4*c*(e*f + d*g) - 2*c*e*g*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*c^2*e^2) + ((2*c*d - b*e)*(4*c*e*f + 2*c*d*g - 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(8*c^(5/2)*e^2)","A",3,3,42,0.07143,1,"{779, 621, 204}"
2212,1,121,0,0.1559986,"\int \frac{f+g x}{(d+e x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","\frac{g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{\sqrt{c} e^2}-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x) (2 c d-b e)}","\frac{g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{\sqrt{c} e^2}-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x) (2 c d-b e)}",1,"(-2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(2*c*d - b*e)*(d + e*x)) + (g*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(Sqrt[c]*e^2)","A",3,3,44,0.06818,1,"{792, 621, 204}"
2213,1,137,0,0.196665,"\int \frac{f+g x}{(d+e x)^2 \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)^2*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{3 e^2 (d+e x)^2 (2 c d-b e)}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g+4 c d g+2 c e f)}{3 e^2 (d+e x) (2 c d-b e)^2}","-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{3 e^2 (d+e x)^2 (2 c d-b e)}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g+4 c d g+2 c e f)}{3 e^2 (d+e x) (2 c d-b e)^2}",1,"(-2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*e^2*(2*c*d - b*e)*(d + e*x)^2) - (2*(2*c*e*f + 4*c*d*g - 3*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*e^2*(2*c*d - b*e)^2*(d + e*x))","A",2,2,44,0.04545,1,"{792, 650}"
2214,1,210,0,0.3297795,"\int \frac{f+g x}{(d+e x)^3 \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)^3*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{5 e^2 (d+e x)^3 (2 c d-b e)}-\frac{4 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{15 e^2 (d+e x) (2 c d-b e)^3}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{15 e^2 (d+e x)^2 (2 c d-b e)^2}","-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{5 e^2 (d+e x)^3 (2 c d-b e)}-\frac{4 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{15 e^2 (d+e x) (2 c d-b e)^3}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{15 e^2 (d+e x)^2 (2 c d-b e)^2}",1,"(-2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(5*e^2*(2*c*d - b*e)*(d + e*x)^3) - (2*(4*c*e*f + 6*c*d*g - 5*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(15*e^2*(2*c*d - b*e)^2*(d + e*x)^2) - (4*c*(4*c*e*f + 6*c*d*g - 5*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(15*e^2*(2*c*d - b*e)^3*(d + e*x))","A",3,3,44,0.06818,1,"{792, 658, 650}"
2215,1,285,0,0.4417941,"\int \frac{f+g x}{(d+e x)^4 \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)^4*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{16 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+8 c d g+6 c e f)}{105 e^2 (d+e x) (2 c d-b e)^4}-\frac{8 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+8 c d g+6 c e f)}{105 e^2 (d+e x)^2 (2 c d-b e)^3}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+8 c d g+6 c e f)}{35 e^2 (d+e x)^3 (2 c d-b e)^2}-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{7 e^2 (d+e x)^4 (2 c d-b e)}","-\frac{16 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+8 c d g+6 c e f)}{105 e^2 (d+e x) (2 c d-b e)^4}-\frac{8 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+8 c d g+6 c e f)}{105 e^2 (d+e x)^2 (2 c d-b e)^3}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+8 c d g+6 c e f)}{35 e^2 (d+e x)^3 (2 c d-b e)^2}-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{7 e^2 (d+e x)^4 (2 c d-b e)}",1,"(-2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(7*e^2*(2*c*d - b*e)*(d + e*x)^4) - (2*(6*c*e*f + 8*c*d*g - 7*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(35*e^2*(2*c*d - b*e)^2*(d + e*x)^3) - (8*c*(6*c*e*f + 8*c*d*g - 7*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(105*e^2*(2*c*d - b*e)^3*(d + e*x)^2) - (16*c^2*(6*c*e*f + 8*c*d*g - 7*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(105*e^2*(2*c*d - b*e)^4*(d + e*x))","A",4,3,44,0.06818,1,"{792, 658, 650}"
2216,1,360,0,0.558267,"\int \frac{f+g x}{(d+e x)^5 \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)^5*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{32 c^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{315 e^2 (d+e x) (2 c d-b e)^5}-\frac{16 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{315 e^2 (d+e x)^2 (2 c d-b e)^4}-\frac{4 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{105 e^2 (d+e x)^3 (2 c d-b e)^3}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{63 e^2 (d+e x)^4 (2 c d-b e)^2}-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{9 e^2 (d+e x)^5 (2 c d-b e)}","-\frac{32 c^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{315 e^2 (d+e x) (2 c d-b e)^5}-\frac{16 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{315 e^2 (d+e x)^2 (2 c d-b e)^4}-\frac{4 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{105 e^2 (d+e x)^3 (2 c d-b e)^3}-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-9 b e g+10 c d g+8 c e f)}{63 e^2 (d+e x)^4 (2 c d-b e)^2}-\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{9 e^2 (d+e x)^5 (2 c d-b e)}",1,"(-2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(9*e^2*(2*c*d - b*e)*(d + e*x)^5) - (2*(8*c*e*f + 10*c*d*g - 9*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(63*e^2*(2*c*d - b*e)^2*(d + e*x)^4) - (4*c*(8*c*e*f + 10*c*d*g - 9*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(105*e^2*(2*c*d - b*e)^3*(d + e*x)^3) - (16*c^2*(8*c*e*f + 10*c*d*g - 9*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(315*e^2*(2*c*d - b*e)^4*(d + e*x)^2) - (32*c^3*(8*c*e*f + 10*c*d*g - 9*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(315*e^2*(2*c*d - b*e)^5*(d + e*x))","A",5,3,44,0.06818,1,"{792, 658, 650}"
2217,1,287,0,0.4425559,"\int \frac{(d+e x)^3 (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^3*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{(d+e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{2 c^2 e^2 (2 c d-b e)}+\frac{3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{4 c^3 e^2}-\frac{3 (2 c d-b e) (-5 b e g+6 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{7/2} e^2}+\frac{2 (d+e x)^3 (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{(d+e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{2 c^2 e^2 (2 c d-b e)}+\frac{3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+6 c d g+4 c e f)}{4 c^3 e^2}-\frac{3 (2 c d-b e) (-5 b e g+6 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{7/2} e^2}+\frac{2 (d+e x)^3 (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^3)/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (3*(4*c*e*f + 6*c*d*g - 5*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*c^3*e^2) + ((4*c*e*f + 6*c*d*g - 5*b*e*g)*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(2*c^2*e^2*(2*c*d - b*e)) - (3*(2*c*d - b*e)*(4*c*e*f + 6*c*d*g - 5*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(8*c^(7/2)*e^2)","A",5,5,44,0.1136,1,"{788, 670, 640, 621, 204}"
2218,1,213,0,0.2840454,"\int \frac{(d+e x)^2 (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^2*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g+4 c d g+2 c e f)}{c^2 e^2 (2 c d-b e)}-\frac{(-3 b e g+4 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 c^{5/2} e^2}+\frac{2 (d+e x)^2 (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-3 b e g+4 c d g+2 c e f)}{c^2 e^2 (2 c d-b e)}-\frac{(-3 b e g+4 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 c^{5/2} e^2}+\frac{2 (d+e x)^2 (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^2)/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + ((2*c*e*f + 4*c*d*g - 3*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(c^2*e^2*(2*c*d - b*e)) - ((2*c*e*f + 4*c*d*g - 3*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(2*c^(5/2)*e^2)","A",4,4,44,0.09091,1,"{788, 640, 621, 204}"
2219,1,148,0,0.1727809,"\int \frac{(d+e x) (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{2 (e x (2 c d-b e)+d (2 c d-b e)) (-b e g+c d g+c e f)}{c e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{c^{3/2} e^2}","\frac{2 (d+e x) (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{c^{3/2} e^2}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d*(2*c*d - b*e) + e*(2*c*d - b*e)*x))/(c*e^2*(2*c*d - b*e)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (g*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(c^(3/2)*e^2)","A",3,3,42,0.07143,1,"{777, 621, 204}"
2220,1,136,0,0.1449474,"\int \frac{f+g x}{(d+e x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(f + g*x)/((d + e*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2)),x]","\frac{2 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{3 e (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g)}{3 e^2 (d+e x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{2 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{3 e (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g)}{3 e^2 (d+e x) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(b + 2*c*x))/(3*e*(2*c*d - b*e)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(e*f - d*g))/(3*e^2*(2*c*d - b*e)*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",2,2,44,0.04545,1,"{792, 613}"
2221,1,209,0,0.2849278,"\int \frac{f+g x}{(d+e x)^2 \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(f + g*x)/((d + e*x)^2*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2)),x]","-\frac{2 (e f-d g)}{5 e^2 (d+e x)^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{8 c (b+2 c x) (-5 b e g+4 c d g+6 c e f)}{15 e (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (-5 b e g+4 c d g+6 c e f)}{15 e^2 (d+e x) (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","-\frac{2 (e f-d g)}{5 e^2 (d+e x)^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{8 c (b+2 c x) (-5 b e g+4 c d g+6 c e f)}{15 e (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (-5 b e g+4 c d g+6 c e f)}{15 e^2 (d+e x) (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(8*c*(6*c*e*f + 4*c*d*g - 5*b*e*g)*(b + 2*c*x))/(15*e*(2*c*d - b*e)^4*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(e*f - d*g))/(5*e^2*(2*c*d - b*e)*(d + e*x)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(6*c*e*f + 4*c*d*g - 5*b*e*g))/(15*e^2*(2*c*d - b*e)^2*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",3,3,44,0.06818,1,"{792, 658, 613}"
2222,1,284,0,0.3899143,"\int \frac{f+g x}{(d+e x)^3 \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(f + g*x)/((d + e*x)^3*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2)),x]","\frac{16 c^2 (b+2 c x) (-7 b e g+6 c d g+8 c e f)}{35 e (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{4 c (-7 b e g+6 c d g+8 c e f)}{35 e^2 (d+e x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (-7 b e g+6 c d g+8 c e f)}{35 e^2 (d+e x)^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g)}{7 e^2 (d+e x)^3 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{16 c^2 (b+2 c x) (-7 b e g+6 c d g+8 c e f)}{35 e (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{4 c (-7 b e g+6 c d g+8 c e f)}{35 e^2 (d+e x) (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (-7 b e g+6 c d g+8 c e f)}{35 e^2 (d+e x)^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g)}{7 e^2 (d+e x)^3 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(16*c^2*(8*c*e*f + 6*c*d*g - 7*b*e*g)*(b + 2*c*x))/(35*e*(2*c*d - b*e)^5*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(e*f - d*g))/(7*e^2*(2*c*d - b*e)*(d + e*x)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(8*c*e*f + 6*c*d*g - 7*b*e*g))/(35*e^2*(2*c*d - b*e)^2*(d + e*x)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (4*c*(8*c*e*f + 6*c*d*g - 7*b*e*g))/(35*e^2*(2*c*d - b*e)^3*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",4,3,44,0.06818,1,"{792, 658, 613}"
2223,1,364,0,0.5554181,"\int \frac{(d+e x)^5 (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^5*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","-\frac{2 (d+e x)^3 (-7 b e g+10 c d g+4 c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{5 (d+e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+10 c d g+4 c e f)}{6 c^3 e^2 (2 c d-b e)}-\frac{5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+10 c d g+4 c e f)}{4 c^4 e^2}+\frac{5 (2 c d-b e) (-7 b e g+10 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{9/2} e^2}+\frac{2 (d+e x)^5 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","-\frac{2 (d+e x)^3 (-7 b e g+10 c d g+4 c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{5 (d+e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+10 c d g+4 c e f)}{6 c^3 e^2 (2 c d-b e)}-\frac{5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-7 b e g+10 c d g+4 c e f)}{4 c^4 e^2}+\frac{5 (2 c d-b e) (-7 b e g+10 c d g+4 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{8 c^{9/2} e^2}+\frac{2 (d+e x)^5 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^5)/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(4*c*e*f + 10*c*d*g - 7*b*e*g)*(d + e*x)^3)/(3*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (5*(4*c*e*f + 10*c*d*g - 7*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*c^4*e^2) - (5*(4*c*e*f + 10*c*d*g - 7*b*e*g)*(d + e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(6*c^3*e^2*(2*c*d - b*e)) + (5*(2*c*d - b*e)*(4*c*e*f + 10*c*d*g - 7*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(8*c^(9/2)*e^2)","A",6,6,44,0.1364,1,"{788, 668, 670, 640, 621, 204}"
2224,1,291,0,0.4282888,"\int \frac{(d+e x)^4 (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^4*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","-\frac{2 (d+e x)^2 (-5 b e g+8 c d g+2 c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+8 c d g+2 c e f)}{c^3 e^2 (2 c d-b e)}+\frac{(-5 b e g+8 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 c^{7/2} e^2}+\frac{2 (d+e x)^4 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","-\frac{2 (d+e x)^2 (-5 b e g+8 c d g+2 c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-5 b e g+8 c d g+2 c e f)}{c^3 e^2 (2 c d-b e)}+\frac{(-5 b e g+8 c d g+2 c e f) \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{2 c^{7/2} e^2}+\frac{2 (d+e x)^4 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^4)/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(2*c*e*f + 8*c*d*g - 5*b*e*g)*(d + e*x)^2)/(3*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - ((2*c*e*f + 8*c*d*g - 5*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(c^3*e^2*(2*c*d - b*e)) + ((2*c*e*f + 8*c*d*g - 5*b*e*g)*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(2*c^(7/2)*e^2)","A",5,5,44,0.1136,1,"{788, 668, 640, 621, 204}"
2225,1,177,0,0.3019741,"\int \frac{(d+e x)^3 (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^3*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","-\frac{2 g (d+e x)}{c^2 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{c^{5/2} e^2}+\frac{2 (d+e x)^3 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","-\frac{2 g (d+e x)}{c^2 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{g \tan ^{-1}\left(\frac{e (b+2 c x)}{2 \sqrt{c} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}\right)}{c^{5/2} e^2}+\frac{2 (d+e x)^3 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^3)/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*g*(d + e*x))/(c^2*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (g*ArcTan[(e*(b + 2*c*x))/(2*Sqrt[c]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])])/(c^(5/2)*e^2)","A",4,4,44,0.09091,1,"{788, 652, 621, 204}"
2226,1,146,0,0.1719881,"\int \frac{(d+e x)^2 (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^2*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^2 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{2 (d+e x) (b e g-4 c d g+2 c e f)}{3 c e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{2 (d+e x)^2 (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{2 (d+e x) (b e g-4 c d g+2 c e f)}{3 c e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^2)/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (2*(2*c*e*f - 4*c*d*g + b*e*g)*(d + e*x))/(3*c*e^2*(2*c*d - b*e)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",2,2,44,0.04545,1,"{788, 636}"
2227,1,165,0,0.1792592,"\int \frac{(d+e x) (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (b+2 c x) (-b e g-2 c d g+4 c e f)}{3 c e (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (e x (2 c d-b e)+d (2 c d-b e)) (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{2 (b+2 c x) (-b e g-2 c d g+4 c e f)}{3 c e (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (e x (2 c d-b e)+d (2 c d-b e)) (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d*(2*c*d - b*e) + e*(2*c*d - b*e)*x))/(3*c*e^2*(2*c*d - b*e)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (2*(4*c*e*f - 2*c*d*g - b*e*g)*(b + 2*c*x))/(3*c*e*(2*c*d - b*e)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",2,2,42,0.04762,1,"{777, 613}"
2228,1,208,0,0.1994522,"\int \frac{f+g x}{(d+e x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[(f + g*x)/((d + e*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]","-\frac{2 (e f-d g)}{5 e^2 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{16 c (b+2 c x) (-5 b e g+2 c d g+8 c e f)}{15 e (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (b+2 c x) (-5 b e g+2 c d g+8 c e f)}{15 e (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","-\frac{2 (e f-d g)}{5 e^2 (d+e x) (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{16 c (b+2 c x) (-5 b e g+2 c d g+8 c e f)}{15 e (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (b+2 c x) (-5 b e g+2 c d g+8 c e f)}{15 e (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(8*c*e*f + 2*c*d*g - 5*b*e*g)*(b + 2*c*x))/(15*e*(2*c*d - b*e)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(e*f - d*g))/(5*e^2*(2*c*d - b*e)*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (16*c*(8*c*e*f + 2*c*d*g - 5*b*e*g)*(b + 2*c*x))/(15*e*(2*c*d - b*e)^5*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",3,3,44,0.06818,1,"{792, 614, 613}"
2229,1,283,0,0.3951332,"\int \frac{f+g x}{(d+e x)^2 \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[(f + g*x)/((d + e*x)^2*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]","\frac{128 c^2 (b+2 c x) (-7 b e g+4 c d g+10 c e f)}{105 e (2 c d-b e)^6 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{16 c (b+2 c x) (-7 b e g+4 c d g+10 c e f)}{105 e (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (-7 b e g+4 c d g+10 c e f)}{35 e^2 (d+e x) (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (e f-d g)}{7 e^2 (d+e x)^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{128 c^2 (b+2 c x) (-7 b e g+4 c d g+10 c e f)}{105 e (2 c d-b e)^6 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{16 c (b+2 c x) (-7 b e g+4 c d g+10 c e f)}{105 e (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (-7 b e g+4 c d g+10 c e f)}{35 e^2 (d+e x) (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (e f-d g)}{7 e^2 (d+e x)^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(16*c*(10*c*e*f + 4*c*d*g - 7*b*e*g)*(b + 2*c*x))/(105*e*(2*c*d - b*e)^4*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(e*f - d*g))/(7*e^2*(2*c*d - b*e)*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(10*c*e*f + 4*c*d*g - 7*b*e*g))/(35*e^2*(2*c*d - b*e)^2*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (128*c^2*(10*c*e*f + 4*c*d*g - 7*b*e*g)*(b + 2*c*x))/(105*e*(2*c*d - b*e)^6*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",4,4,44,0.09091,1,"{792, 658, 614, 613}"
2230,1,358,0,0.5114224,"\int \frac{f+g x}{(d+e x)^3 \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[(f + g*x)/((d + e*x)^3*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]","\frac{256 c^3 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^7 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{32 c^2 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{4 c (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x)^2 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{256 c^3 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^7 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{32 c^2 (b+2 c x) (-3 b e g+2 c d g+4 c e f)}{63 e (2 c d-b e)^5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{4 c (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x) (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (-3 b e g+2 c d g+4 c e f)}{21 e^2 (d+e x)^2 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{2 (e f-d g)}{9 e^2 (d+e x)^3 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(32*c^2*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(b + 2*c*x))/(63*e*(2*c*d - b*e)^5*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(e*f - d*g))/(9*e^2*(2*c*d - b*e)*(d + e*x)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (2*(4*c*e*f + 2*c*d*g - 3*b*e*g))/(21*e^2*(2*c*d - b*e)^2*(d + e*x)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (4*c*(4*c*e*f + 2*c*d*g - 3*b*e*g))/(21*e^2*(2*c*d - b*e)^3*(d + e*x)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (256*c^3*(4*c*e*f + 2*c*d*g - 3*b*e*g)*(b + 2*c*x))/(63*e*(2*c*d - b*e)^7*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",5,4,44,0.09091,1,"{792, 658, 614, 613}"
2231,1,347,0,0.6244549,"\int (d+e x)^{5/2} (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[(d + e*x)^(5/2)*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{32 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{3465 c^5 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{1155 c^4 e^2 \sqrt{d+e x}}-\frac{4 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{231 c^3 e^2}-\frac{2 (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{99 c^2 e^2}-\frac{2 g (d+e x)^{5/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{11 c e^2}","-\frac{32 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{3465 c^5 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{1155 c^4 e^2 \sqrt{d+e x}}-\frac{4 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{231 c^3 e^2}-\frac{2 (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+5 c d g+11 c e f)}{99 c^2 e^2}-\frac{2 g (d+e x)^{5/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{11 c e^2}",1,"(-32*(2*c*d - b*e)^3*(11*c*e*f + 5*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3465*c^5*e^2*(d + e*x)^(3/2)) - (16*(2*c*d - b*e)^2*(11*c*e*f + 5*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(1155*c^4*e^2*Sqrt[d + e*x]) - (4*(2*c*d - b*e)*(11*c*e*f + 5*c*d*g - 8*b*e*g)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(231*c^3*e^2) - (2*(11*c*e*f + 5*c*d*g - 8*b*e*g)*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(99*c^2*e^2) - (2*g*(d + e*x)^(5/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(11*c*e^2)","A",5,3,46,0.06522,1,"{794, 656, 648}"
2232,1,267,0,0.4353495,"\int (d+e x)^{3/2} (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[(d + e*x)^(3/2)*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g+c d g+3 c e f)}{315 c^4 e^2 (d+e x)^{3/2}}-\frac{8 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g+c d g+3 c e f)}{105 c^3 e^2 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g+c d g+3 c e f)}{21 c^2 e^2}-\frac{2 g (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{9 c e^2}","-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g+c d g+3 c e f)}{315 c^4 e^2 (d+e x)^{3/2}}-\frac{8 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g+c d g+3 c e f)}{105 c^3 e^2 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g+c d g+3 c e f)}{21 c^2 e^2}-\frac{2 g (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{9 c e^2}",1,"(-16*(2*c*d - b*e)^2*(3*c*e*f + c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(315*c^4*e^2*(d + e*x)^(3/2)) - (8*(2*c*d - b*e)*(3*c*e*f + c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(105*c^3*e^2*Sqrt[d + e*x]) - (2*(3*c*e*f + c*d*g - 2*b*e*g)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(21*c^2*e^2) - (2*g*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(9*c*e^2)","A",4,3,46,0.06522,1,"{794, 656, 648}"
2233,1,191,0,0.3017263,"\int \sqrt{d+e x} (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[Sqrt[d + e*x]*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-4 b e g+c d g+7 c e f)}{35 c^2 e^2 \sqrt{d+e x}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-4 b e g+c d g+7 c e f)}{105 c^3 e^2 (d+e x)^{3/2}}-\frac{2 g \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{7 c e^2}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-4 b e g+c d g+7 c e f)}{35 c^2 e^2 \sqrt{d+e x}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-4 b e g+c d g+7 c e f)}{105 c^3 e^2 (d+e x)^{3/2}}-\frac{2 g \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{7 c e^2}",1,"(-4*(2*c*d - b*e)*(7*c*e*f + c*d*g - 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(105*c^3*e^2*(d + e*x)^(3/2)) - (2*(7*c*e*f + c*d*g - 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(35*c^2*e^2*Sqrt[d + e*x]) - (2*g*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(7*c*e^2)","A",3,3,46,0.06522,1,"{794, 656, 648}"
2234,1,118,0,0.174452,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/Sqrt[d + e*x],x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g-c d g+5 c e f)}{15 c^2 e^2 (d+e x)^{3/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{5 c e^2 \sqrt{d+e x}}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-2 b e g-c d g+5 c e f)}{15 c^2 e^2 (d+e x)^{3/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{5 c e^2 \sqrt{d+e x}}",1,"(-2*(5*c*e*f - c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(15*c^2*e^2*(d + e*x)^(3/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(5*c*e^2*Sqrt[d + e*x])","A",2,2,46,0.04348,1,"{794, 648}"
2235,1,186,0,0.3516635,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^(3/2),x]","\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{2 \sqrt{2 c d-b e} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 c e^2 (d+e x)^{3/2}}","\frac{2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{2 \sqrt{2 c d-b e} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 c e^2 (d+e x)^{3/2}}",1,"(2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x]) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*c*e^2*(d + e*x)^(3/2)) - (2*Sqrt[2*c*d - b*e]*(e*f - d*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/e^2","A",4,4,46,0.08696,1,"{794, 664, 660, 208}"
2236,1,223,0,0.3584712,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^(5/2),x]","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-5 c d g+c e f)}{e^2 \sqrt{d+e x} (2 c d-b e)}+\frac{(2 b e g-5 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 \sqrt{2 c d-b e}}","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-5 c d g+c e f)}{e^2 \sqrt{d+e x} (2 c d-b e)}+\frac{(2 b e g-5 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 \sqrt{2 c d-b e}}",1,"-(((c*e*f - 5*c*d*g + 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(2*c*d - b*e)*Sqrt[d + e*x])) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) + ((c*e*f - 5*c*d*g + 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*Sqrt[2*c*d - b*e])","A",4,4,46,0.08696,1,"{792, 664, 660, 208}"
2237,1,231,0,0.3684086,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^{7/2}} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^(7/2),x]","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{2 e^2 (d+e x)^{7/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+7 c d g+c e f)}{4 e^2 (d+e x)^{3/2} (2 c d-b e)}+\frac{c (-4 b e g+7 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{3/2}}","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{2 e^2 (d+e x)^{7/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+7 c d g+c e f)}{4 e^2 (d+e x)^{3/2} (2 c d-b e)}+\frac{c (-4 b e g+7 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{3/2}}",1,"-((c*e*f + 7*c*d*g - 4*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(2*e^2*(2*c*d - b*e)*(d + e*x)^(7/2)) + (c*(c*e*f + 7*c*d*g - 4*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(4*e^2*(2*c*d - b*e)^(3/2))","A",4,4,46,0.08696,1,"{792, 662, 660, 208}"
2238,1,307,0,0.5322661,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^{9/2}} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^(9/2),x]","\frac{c^2 (-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{5/2}}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+3 c d g+c e f)}{8 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+3 c d g+c e f)}{4 e^2 (d+e x)^{5/2} (2 c d-b e)}","\frac{c^2 (-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{5/2}}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+3 c d g+c e f)}{8 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+3 c d g+c e f)}{4 e^2 (d+e x)^{5/2} (2 c d-b e)}",1,"-((c*e*f + 3*c*d*g - 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) + (c*(c*e*f + 3*c*d*g - 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(8*e^2*(2*c*d - b*e)^2*(d + e*x)^(3/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) + (c^2*(c*e*f + 3*c*d*g - 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(8*e^2*(2*c*d - b*e)^(5/2))","A",5,5,46,0.1087,1,"{792, 662, 672, 660, 208}"
2239,1,387,0,0.7601058,"\int \frac{(f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}}{(d+e x)^{11/2}} \, dx","Int[((f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2])/(d + e*x)^(11/2),x]","\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+11 c d g+5 c e f)}{64 e^2 (d+e x)^{3/2} (2 c d-b e)^3}+\frac{c^3 (-8 b e g+11 c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{64 e^2 (2 c d-b e)^{7/2}}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+11 c d g+5 c e f)}{96 e^2 (d+e x)^{5/2} (2 c d-b e)^2}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{4 e^2 (d+e x)^{11/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+11 c d g+5 c e f)}{24 e^2 (d+e x)^{7/2} (2 c d-b e)}","\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+11 c d g+5 c e f)}{64 e^2 (d+e x)^{3/2} (2 c d-b e)^3}+\frac{c^3 (-8 b e g+11 c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{64 e^2 (2 c d-b e)^{7/2}}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+11 c d g+5 c e f)}{96 e^2 (d+e x)^{5/2} (2 c d-b e)^2}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{4 e^2 (d+e x)^{11/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+11 c d g+5 c e f)}{24 e^2 (d+e x)^{7/2} (2 c d-b e)}",1,"-((5*c*e*f + 11*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(24*e^2*(2*c*d - b*e)*(d + e*x)^(7/2)) + (c*(5*c*e*f + 11*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(96*e^2*(2*c*d - b*e)^2*(d + e*x)^(5/2)) + (c^2*(5*c*e*f + 11*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*e^2*(2*c*d - b*e)^3*(d + e*x)^(3/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(4*e^2*(2*c*d - b*e)*(d + e*x)^(11/2)) + (c^3*(5*c*e*f + 11*c*d*g - 8*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(64*e^2*(2*c*d - b*e)^(7/2))","A",6,5,46,0.1087,1,"{792, 662, 672, 660, 208}"
2240,1,419,0,0.7260698,"\int (d+e x)^{5/2} (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^(5/2)*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","-\frac{256 (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{45045 c^6 e^2 (d+e x)^{5/2}}-\frac{128 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{9009 c^5 e^2 (d+e x)^{3/2}}-\frac{32 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{1287 c^4 e^2 \sqrt{d+e x}}-\frac{16 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{429 c^3 e^2}-\frac{2 (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{39 c^2 e^2}-\frac{2 g (d+e x)^{5/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{15 c e^2}","-\frac{256 (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{45045 c^6 e^2 (d+e x)^{5/2}}-\frac{128 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{9009 c^5 e^2 (d+e x)^{3/2}}-\frac{32 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{1287 c^4 e^2 \sqrt{d+e x}}-\frac{16 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{429 c^3 e^2}-\frac{2 (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g+c d g+3 c e f)}{39 c^2 e^2}-\frac{2 g (d+e x)^{5/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{15 c e^2}",1,"(-256*(2*c*d - b*e)^4*(3*c*e*f + c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(45045*c^6*e^2*(d + e*x)^(5/2)) - (128*(2*c*d - b*e)^3*(3*c*e*f + c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(9009*c^5*e^2*(d + e*x)^(3/2)) - (32*(2*c*d - b*e)^2*(3*c*e*f + c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(1287*c^4*e^2*Sqrt[d + e*x]) - (16*(2*c*d - b*e)*(3*c*e*f + c*d*g - 2*b*e*g)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(429*c^3*e^2) - (2*(3*c*e*f + c*d*g - 2*b*e*g)*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(39*c^2*e^2) - (2*g*(d + e*x)^(5/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(15*c*e^2)","A",6,3,46,0.06522,1,"{794, 656, 648}"
2241,1,347,0,0.600538,"\int (d+e x)^{3/2} (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^(3/2)*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","-\frac{32 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{15015 c^5 e^2 (d+e x)^{5/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{3003 c^4 e^2 (d+e x)^{3/2}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{429 c^3 e^2 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{143 c^2 e^2}-\frac{2 g (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{13 c e^2}","-\frac{32 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{15015 c^5 e^2 (d+e x)^{5/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{3003 c^4 e^2 (d+e x)^{3/2}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{429 c^3 e^2 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+3 c d g+13 c e f)}{143 c^2 e^2}-\frac{2 g (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{13 c e^2}",1,"(-32*(2*c*d - b*e)^3*(13*c*e*f + 3*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(15015*c^5*e^2*(d + e*x)^(5/2)) - (16*(2*c*d - b*e)^2*(13*c*e*f + 3*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3003*c^4*e^2*(d + e*x)^(3/2)) - (4*(2*c*d - b*e)*(13*c*e*f + 3*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(429*c^3*e^2*Sqrt[d + e*x]) - (2*(13*c*e*f + 3*c*d*g - 8*b*e*g)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(143*c^2*e^2) - (2*g*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(13*c*e^2)","A",5,3,46,0.06522,1,"{794, 656, 648}"
2242,1,267,0,0.4278031,"\int \sqrt{d+e x} (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[Sqrt[d + e*x]*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-6 b e g+c d g+11 c e f)}{99 c^2 e^2 \sqrt{d+e x}}-\frac{8 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-6 b e g+c d g+11 c e f)}{693 c^3 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-6 b e g+c d g+11 c e f)}{3465 c^4 e^2 (d+e x)^{5/2}}-\frac{2 g \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{11 c e^2}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-6 b e g+c d g+11 c e f)}{99 c^2 e^2 \sqrt{d+e x}}-\frac{8 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-6 b e g+c d g+11 c e f)}{693 c^3 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-6 b e g+c d g+11 c e f)}{3465 c^4 e^2 (d+e x)^{5/2}}-\frac{2 g \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{11 c e^2}",1,"(-16*(2*c*d - b*e)^2*(11*c*e*f + c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3465*c^4*e^2*(d + e*x)^(5/2)) - (8*(2*c*d - b*e)*(11*c*e*f + c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(693*c^3*e^2*(d + e*x)^(3/2)) - (2*(11*c*e*f + c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(99*c^2*e^2*Sqrt[d + e*x]) - (2*g*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(11*c*e^2)","A",4,3,46,0.06522,1,"{794, 656, 648}"
2243,1,193,0,0.3076814,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/Sqrt[d + e*x],x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-4 b e g-c d g+9 c e f)}{63 c^2 e^2 (d+e x)^{3/2}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-4 b e g-c d g+9 c e f)}{315 c^3 e^2 (d+e x)^{5/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{9 c e^2 \sqrt{d+e x}}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-4 b e g-c d g+9 c e f)}{63 c^2 e^2 (d+e x)^{3/2}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-4 b e g-c d g+9 c e f)}{315 c^3 e^2 (d+e x)^{5/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{9 c e^2 \sqrt{d+e x}}",1,"(-4*(2*c*d - b*e)*(9*c*e*f - c*d*g - 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(315*c^3*e^2*(d + e*x)^(5/2)) - (2*(9*c*e*f - c*d*g - 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(63*c^2*e^2*(d + e*x)^(3/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(9*c*e^2*Sqrt[d + e*x])","A",3,3,46,0.06522,1,"{794, 656, 648}"
2244,1,118,0,0.1911223,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^(3/2),x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g-3 c d g+7 c e f)}{35 c^2 e^2 (d+e x)^{5/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{7 c e^2 (d+e x)^{3/2}}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-2 b e g-3 c d g+7 c e f)}{35 c^2 e^2 (d+e x)^{5/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{7 c e^2 (d+e x)^{3/2}}",1,"(-2*(7*c*e*f - 3*c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(35*c^2*e^2*(d + e*x)^(5/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(7*c*e^2*(d + e*x)^(3/2))","A",2,2,46,0.04348,1,"{794, 648}"
2245,1,250,0,0.4488099,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^(5/2),x]","\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^{3/2}}+\frac{2 (2 c d-b e) (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{2 (2 c d-b e)^{3/2} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 c e^2 (d+e x)^{5/2}}","\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^{3/2}}+\frac{2 (2 c d-b e) (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{2 (2 c d-b e)^{3/2} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 c e^2 (d+e x)^{5/2}}",1,"(2*(2*c*d - b*e)*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x]) + (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^(3/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*c*e^2*(d + e*x)^(5/2)) - (2*(2*c*d - b*e)^(3/2)*(e*f - d*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/e^2","A",5,4,46,0.08696,1,"{794, 664, 660, 208}"
2246,1,288,0,0.4815871,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^{7/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^(7/2),x]","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{e^2 (d+e x)^{7/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (2 b e g-7 c d g+3 c e f)}{3 e^2 (d+e x)^{3/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-7 c d g+3 c e f)}{e^2 \sqrt{d+e x}}+\frac{\sqrt{2 c d-b e} (2 b e g-7 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{e^2 (d+e x)^{7/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (2 b e g-7 c d g+3 c e f)}{3 e^2 (d+e x)^{3/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-7 c d g+3 c e f)}{e^2 \sqrt{d+e x}}+\frac{\sqrt{2 c d-b e} (2 b e g-7 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}",1,"-(((3*c*e*f - 7*c*d*g + 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x])) - ((3*c*e*f - 7*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(e^2*(2*c*d - b*e)*(d + e*x)^(7/2)) + (Sqrt[2*c*d - b*e]*(3*c*e*f - 7*c*d*g + 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/e^2","A",5,4,46,0.08696,1,"{792, 664, 660, 208}"
2247,1,305,0,0.4831246,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^{9/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^(9/2),x]","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{2 e^2 (d+e x)^{9/2} (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (4 b e g-9 c d g+c e f)}{4 e^2 (d+e x)^{5/2} (2 c d-b e)}+\frac{3 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (4 b e g-9 c d g+c e f)}{4 e^2 \sqrt{d+e x} (2 c d-b e)}-\frac{3 c (4 b e g-9 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 \sqrt{2 c d-b e}}","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{2 e^2 (d+e x)^{9/2} (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (4 b e g-9 c d g+c e f)}{4 e^2 (d+e x)^{5/2} (2 c d-b e)}+\frac{3 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (4 b e g-9 c d g+c e f)}{4 e^2 \sqrt{d+e x} (2 c d-b e)}-\frac{3 c (4 b e g-9 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 \sqrt{2 c d-b e}}",1,"(3*c*(c*e*f - 9*c*d*g + 4*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2*(2*c*d - b*e)*Sqrt[d + e*x]) + ((c*e*f - 9*c*d*g + 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(4*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(2*e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) - (3*c*(c*e*f - 9*c*d*g + 4*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(4*e^2*Sqrt[2*c*d - b*e])","A",5,5,46,0.1087,1,"{792, 662, 664, 660, 208}"
2248,1,307,0,0.4820113,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^{11/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^(11/2),x]","-\frac{c^2 (-6 b e g+11 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{3/2}}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{3 e^2 (d+e x)^{11/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-6 b e g+11 c d g+c e f)}{12 e^2 (d+e x)^{7/2} (2 c d-b e)}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+11 c d g+c e f)}{8 e^2 (d+e x)^{3/2} (2 c d-b e)}","-\frac{c^2 (-6 b e g+11 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{3/2}}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{3 e^2 (d+e x)^{11/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-6 b e g+11 c d g+c e f)}{12 e^2 (d+e x)^{7/2} (2 c d-b e)}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+11 c d g+c e f)}{8 e^2 (d+e x)^{3/2} (2 c d-b e)}",1,"(c*(c*e*f + 11*c*d*g - 6*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(8*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)) - ((c*e*f + 11*c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(12*e^2*(2*c*d - b*e)*(d + e*x)^(7/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^(11/2)) - (c^2*(c*e*f + 11*c*d*g - 6*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(8*e^2*(2*c*d - b*e)^(3/2))","A",5,4,46,0.08696,1,"{792, 662, 660, 208}"
2249,1,387,0,0.6518101,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}}{(d+e x)^{13/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2))/(d + e*x)^(13/2),x]","-\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+13 c d g+3 c e f)}{64 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{c^3 (-8 b e g+13 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{64 e^2 (2 c d-b e)^{5/2}}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+13 c d g+3 c e f)}{32 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{4 e^2 (d+e x)^{13/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+13 c d g+3 c e f)}{24 e^2 (d+e x)^{9/2} (2 c d-b e)}","-\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+13 c d g+3 c e f)}{64 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{c^3 (-8 b e g+13 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{64 e^2 (2 c d-b e)^{5/2}}+\frac{c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+13 c d g+3 c e f)}{32 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{4 e^2 (d+e x)^{13/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+13 c d g+3 c e f)}{24 e^2 (d+e x)^{9/2} (2 c d-b e)}",1,"(c*(3*c*e*f + 13*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(32*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) - (c^2*(3*c*e*f + 13*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*e^2*(2*c*d - b*e)^2*(d + e*x)^(3/2)) - ((3*c*e*f + 13*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(24*e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(4*e^2*(2*c*d - b*e)*(d + e*x)^(13/2)) - (c^3*(3*c*e*f + 13*c*d*g - 8*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(64*e^2*(2*c*d - b*e)^(5/2))","A",6,5,46,0.1087,1,"{792, 662, 672, 660, 208}"
2250,1,501,0,0.9601188,"\int (d+e x)^{5/2} (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^(5/2)*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","-\frac{512 (2 c d-b e)^5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{2909907 c^7 e^2 (d+e x)^{7/2}}-\frac{256 (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{415701 c^6 e^2 (d+e x)^{5/2}}-\frac{64 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac{32 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{12597 c^4 e^2 \sqrt{d+e x}}-\frac{4 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{969 c^3 e^2}-\frac{2 (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{323 c^2 e^2}-\frac{2 g (d+e x)^{5/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{19 c e^2}","-\frac{512 (2 c d-b e)^5 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{2909907 c^7 e^2 (d+e x)^{7/2}}-\frac{256 (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{415701 c^6 e^2 (d+e x)^{5/2}}-\frac{64 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{46189 c^5 e^2 (d+e x)^{3/2}}-\frac{32 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{12597 c^4 e^2 \sqrt{d+e x}}-\frac{4 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{969 c^3 e^2}-\frac{2 (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-12 b e g+5 c d g+19 c e f)}{323 c^2 e^2}-\frac{2 g (d+e x)^{5/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{19 c e^2}",1,"(-512*(2*c*d - b*e)^5*(19*c*e*f + 5*c*d*g - 12*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(2909907*c^7*e^2*(d + e*x)^(7/2)) - (256*(2*c*d - b*e)^4*(19*c*e*f + 5*c*d*g - 12*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(415701*c^6*e^2*(d + e*x)^(5/2)) - (64*(2*c*d - b*e)^3*(19*c*e*f + 5*c*d*g - 12*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(46189*c^5*e^2*(d + e*x)^(3/2)) - (32*(2*c*d - b*e)^2*(19*c*e*f + 5*c*d*g - 12*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(12597*c^4*e^2*Sqrt[d + e*x]) - (4*(2*c*d - b*e)*(19*c*e*f + 5*c*d*g - 12*b*e*g)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(969*c^3*e^2) - (2*(19*c*e*f + 5*c*d*g - 12*b*e*g)*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(323*c^2*e^2) - (2*g*(d + e*x)^(5/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(19*c*e^2)","A",7,3,46,0.06522,1,"{794, 656, 648}"
2251,1,424,0,0.7640895,"\int (d+e x)^{3/2} (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^(3/2)*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","-\frac{256 (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{765765 c^6 e^2 (d+e x)^{7/2}}-\frac{128 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{109395 c^5 e^2 (d+e x)^{5/2}}-\frac{32 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{3315 c^3 e^2 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{255 c^2 e^2}-\frac{2 g (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{17 c e^2}","-\frac{256 (2 c d-b e)^4 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{765765 c^6 e^2 (d+e x)^{7/2}}-\frac{128 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{109395 c^5 e^2 (d+e x)^{5/2}}-\frac{32 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{12155 c^4 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{3315 c^3 e^2 \sqrt{d+e x}}-\frac{2 \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-10 b e g+3 c d g+17 c e f)}{255 c^2 e^2}-\frac{2 g (d+e x)^{3/2} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{17 c e^2}",1,"(-256*(2*c*d - b*e)^4*(17*c*e*f + 3*c*d*g - 10*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(765765*c^6*e^2*(d + e*x)^(7/2)) - (128*(2*c*d - b*e)^3*(17*c*e*f + 3*c*d*g - 10*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(109395*c^5*e^2*(d + e*x)^(5/2)) - (32*(2*c*d - b*e)^2*(17*c*e*f + 3*c*d*g - 10*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(12155*c^4*e^2*(d + e*x)^(3/2)) - (16*(2*c*d - b*e)*(17*c*e*f + 3*c*d*g - 10*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(3315*c^3*e^2*Sqrt[d + e*x]) - (2*(17*c*e*f + 3*c*d*g - 10*b*e*g)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(255*c^2*e^2) - (2*g*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(17*c*e^2)","A",6,3,46,0.06522,1,"{794, 656, 648}"
2252,1,343,0,0.5749287,"\int \sqrt{d+e x} (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[Sqrt[d + e*x]*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{195 c^2 e^2 \sqrt{d+e x}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{715 c^3 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{6435 c^4 e^2 (d+e x)^{5/2}}-\frac{32 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{45045 c^5 e^2 (d+e x)^{7/2}}-\frac{2 g \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{15 c e^2}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{195 c^2 e^2 \sqrt{d+e x}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{715 c^3 e^2 (d+e x)^{3/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{6435 c^4 e^2 (d+e x)^{5/2}}-\frac{32 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-8 b e g+c d g+15 c e f)}{45045 c^5 e^2 (d+e x)^{7/2}}-\frac{2 g \sqrt{d+e x} \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{15 c e^2}",1,"(-32*(2*c*d - b*e)^3*(15*c*e*f + c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(45045*c^5*e^2*(d + e*x)^(7/2)) - (16*(2*c*d - b*e)^2*(15*c*e*f + c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(6435*c^4*e^2*(d + e*x)^(5/2)) - (4*(2*c*d - b*e)*(15*c*e*f + c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(715*c^3*e^2*(d + e*x)^(3/2)) - (2*(15*c*e*f + c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(195*c^2*e^2*Sqrt[d + e*x]) - (2*g*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(15*c*e^2)","A",5,3,46,0.06522,1,"{794, 656, 648}"
2253,1,270,0,0.4394268,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{\sqrt{d+e x}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/Sqrt[d + e*x],x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-6 b e g-c d g+13 c e f)}{143 c^2 e^2 (d+e x)^{3/2}}-\frac{8 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-6 b e g-c d g+13 c e f)}{1287 c^3 e^2 (d+e x)^{5/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-6 b e g-c d g+13 c e f)}{9009 c^4 e^2 (d+e x)^{7/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{13 c e^2 \sqrt{d+e x}}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-6 b e g-c d g+13 c e f)}{143 c^2 e^2 (d+e x)^{3/2}}-\frac{8 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-6 b e g-c d g+13 c e f)}{1287 c^3 e^2 (d+e x)^{5/2}}-\frac{16 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-6 b e g-c d g+13 c e f)}{9009 c^4 e^2 (d+e x)^{7/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{13 c e^2 \sqrt{d+e x}}",1,"(-16*(2*c*d - b*e)^2*(13*c*e*f - c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(9009*c^4*e^2*(d + e*x)^(7/2)) - (8*(2*c*d - b*e)*(13*c*e*f - c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(1287*c^3*e^2*(d + e*x)^(5/2)) - (2*(13*c*e*f - c*d*g - 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(143*c^2*e^2*(d + e*x)^(3/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(13*c*e^2*Sqrt[d + e*x])","A",4,3,46,0.06522,1,"{794, 656, 648}"
2254,1,193,0,0.3395729,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{3/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(3/2),x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-4 b e g-3 c d g+11 c e f)}{99 c^2 e^2 (d+e x)^{5/2}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-4 b e g-3 c d g+11 c e f)}{693 c^3 e^2 (d+e x)^{7/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{11 c e^2 (d+e x)^{3/2}}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-4 b e g-3 c d g+11 c e f)}{99 c^2 e^2 (d+e x)^{5/2}}-\frac{4 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-4 b e g-3 c d g+11 c e f)}{693 c^3 e^2 (d+e x)^{7/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{11 c e^2 (d+e x)^{3/2}}",1,"(-4*(2*c*d - b*e)*(11*c*e*f - 3*c*d*g - 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(693*c^3*e^2*(d + e*x)^(7/2)) - (2*(11*c*e*f - 3*c*d*g - 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(99*c^2*e^2*(d + e*x)^(5/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(11*c*e^2*(d + e*x)^(3/2))","A",3,3,46,0.06522,1,"{794, 656, 648}"
2255,1,118,0,0.1905358,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{5/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(5/2),x]","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-2 b e g-5 c d g+9 c e f)}{63 c^2 e^2 (d+e x)^{7/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{9 c e^2 (d+e x)^{5/2}}","-\frac{2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2} (-2 b e g-5 c d g+9 c e f)}{63 c^2 e^2 (d+e x)^{7/2}}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{9 c e^2 (d+e x)^{5/2}}",1,"(-2*(9*c*e*f - 5*c*d*g - 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(63*c^2*e^2*(d + e*x)^(7/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(9*c*e^2*(d + e*x)^(5/2))","A",2,2,46,0.04348,1,"{794, 648}"
2256,1,316,0,0.5884618,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{7/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(7/2),x]","\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 e^2 (d+e x)^{5/2}}+\frac{2 (2 c d-b e) (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^{3/2}}+\frac{2 (2 c d-b e)^2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{2 (2 c d-b e)^{5/2} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{7 c e^2 (d+e x)^{7/2}}","\frac{2 (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{5 e^2 (d+e x)^{5/2}}+\frac{2 (2 c d-b e) (e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{3 e^2 (d+e x)^{3/2}}+\frac{2 (2 c d-b e)^2 (e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 \sqrt{d+e x}}-\frac{2 (2 c d-b e)^{5/2} (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}-\frac{2 g \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{7 c e^2 (d+e x)^{7/2}}",1,"(2*(2*c*d - b*e)^2*(e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x]) + (2*(2*c*d - b*e)*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^(3/2)) + (2*(e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*e^2*(d + e*x)^(5/2)) - (2*g*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(7*c*e^2*(d + e*x)^(7/2)) - (2*(2*c*d - b*e)^(5/2)*(e*f - d*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/e^2","A",6,4,46,0.08696,1,"{794, 664, 660, 208}"
2257,1,360,0,0.6098127,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{9/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(9/2),x]","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (2 b e g-9 c d g+5 c e f)}{5 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (2 b e g-9 c d g+5 c e f)}{3 e^2 (d+e x)^{3/2}}-\frac{(2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-9 c d g+5 c e f)}{e^2 \sqrt{d+e x}}+\frac{(2 c d-b e)^{3/2} (2 b e g-9 c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (2 b e g-9 c d g+5 c e f)}{5 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (2 b e g-9 c d g+5 c e f)}{3 e^2 (d+e x)^{3/2}}-\frac{(2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (2 b e g-9 c d g+5 c e f)}{e^2 \sqrt{d+e x}}+\frac{(2 c d-b e)^{3/2} (2 b e g-9 c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2}",1,"-(((2*c*d - b*e)*(5*c*e*f - 9*c*d*g + 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*Sqrt[d + e*x])) - ((5*c*e*f - 9*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(3*e^2*(d + e*x)^(3/2)) - ((5*c*e*f - 9*c*d*g + 2*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) + ((2*c*d - b*e)^(3/2)*(5*c*e*f - 9*c*d*g + 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/e^2","A",6,4,46,0.08696,1,"{792, 664, 660, 208}"
2258,1,372,0,0.6036196,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{11/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(11/2),x]","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{2 e^2 (d+e x)^{11/2} (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (4 b e g-11 c d g+3 c e f)}{4 e^2 (d+e x)^{7/2} (2 c d-b e)}+\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (4 b e g-11 c d g+3 c e f)}{12 e^2 (d+e x)^{3/2} (2 c d-b e)}+\frac{5 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (4 b e g-11 c d g+3 c e f)}{4 e^2 \sqrt{d+e x}}-\frac{5 c \sqrt{2 c d-b e} (4 b e g-11 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2}","-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{2 e^2 (d+e x)^{11/2} (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (4 b e g-11 c d g+3 c e f)}{4 e^2 (d+e x)^{7/2} (2 c d-b e)}+\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (4 b e g-11 c d g+3 c e f)}{12 e^2 (d+e x)^{3/2} (2 c d-b e)}+\frac{5 c \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (4 b e g-11 c d g+3 c e f)}{4 e^2 \sqrt{d+e x}}-\frac{5 c \sqrt{2 c d-b e} (4 b e g-11 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2}",1,"(5*c*(3*c*e*f - 11*c*d*g + 4*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2*Sqrt[d + e*x]) + (5*c*(3*c*e*f - 11*c*d*g + 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(12*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)) + ((3*c*e*f - 11*c*d*g + 4*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(4*e^2*(2*c*d - b*e)*(d + e*x)^(7/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(2*e^2*(2*c*d - b*e)*(d + e*x)^(11/2)) - (5*c*Sqrt[2*c*d - b*e]*(3*c*e*f - 11*c*d*g + 4*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(4*e^2)","A",6,5,46,0.1087,1,"{792, 662, 664, 660, 208}"
2259,1,383,0,0.5896292,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{13/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(13/2),x]","-\frac{5 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (6 b e g-13 c d g+c e f)}{8 e^2 \sqrt{d+e x} (2 c d-b e)}+\frac{5 c^2 (6 b e g-13 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 \sqrt{2 c d-b e}}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^{13/2} (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (6 b e g-13 c d g+c e f)}{12 e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (6 b e g-13 c d g+c e f)}{24 e^2 (d+e x)^{5/2} (2 c d-b e)}","-\frac{5 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (6 b e g-13 c d g+c e f)}{8 e^2 \sqrt{d+e x} (2 c d-b e)}+\frac{5 c^2 (6 b e g-13 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 \sqrt{2 c d-b e}}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{3 e^2 (d+e x)^{13/2} (2 c d-b e)}+\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (6 b e g-13 c d g+c e f)}{12 e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (6 b e g-13 c d g+c e f)}{24 e^2 (d+e x)^{5/2} (2 c d-b e)}",1,"(-5*c^2*(c*e*f - 13*c*d*g + 6*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(8*e^2*(2*c*d - b*e)*Sqrt[d + e*x]) - (5*c*(c*e*f - 13*c*d*g + 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(24*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) + ((c*e*f - 13*c*d*g + 6*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(12*e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(3*e^2*(2*c*d - b*e)*(d + e*x)^(13/2)) + (5*c^2*(c*e*f - 13*c*d*g + 6*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(8*e^2*Sqrt[2*c*d - b*e])","A",6,5,46,0.1087,1,"{792, 662, 664, 660, 208}"
2260,1,383,0,0.5940487,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{15/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(15/2),x]","-\frac{5 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+15 c d g+c e f)}{64 e^2 (d+e x)^{3/2} (2 c d-b e)}+\frac{5 c^3 (-8 b e g+15 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{64 e^2 (2 c d-b e)^{3/2}}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{4 e^2 (d+e x)^{15/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+15 c d g+c e f)}{24 e^2 (d+e x)^{11/2} (2 c d-b e)}+\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+15 c d g+c e f)}{96 e^2 (d+e x)^{7/2} (2 c d-b e)}","-\frac{5 c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+15 c d g+c e f)}{64 e^2 (d+e x)^{3/2} (2 c d-b e)}+\frac{5 c^3 (-8 b e g+15 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{64 e^2 (2 c d-b e)^{3/2}}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{4 e^2 (d+e x)^{15/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-8 b e g+15 c d g+c e f)}{24 e^2 (d+e x)^{11/2} (2 c d-b e)}+\frac{5 c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-8 b e g+15 c d g+c e f)}{96 e^2 (d+e x)^{7/2} (2 c d-b e)}",1,"(-5*c^2*(c*e*f + 15*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)) + (5*c*(c*e*f + 15*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(96*e^2*(2*c*d - b*e)*(d + e*x)^(7/2)) - ((c*e*f + 15*c*d*g - 8*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(24*e^2*(2*c*d - b*e)*(d + e*x)^(11/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(4*e^2*(2*c*d - b*e)*(d + e*x)^(15/2)) + (5*c^3*(c*e*f + 15*c*d*g - 8*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(64*e^2*(2*c*d - b*e)^(3/2))","A",6,4,46,0.08696,1,"{792, 662, 660, 208}"
2261,1,464,0,0.7512393,"\int \frac{(f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}}{(d+e x)^{17/2}} \, dx","Int[((f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2))/(d + e*x)^(17/2),x]","\frac{c^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-10 b e g+17 c d g+3 c e f)}{128 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-10 b e g+17 c d g+3 c e f)}{64 e^2 (d+e x)^{5/2} (2 c d-b e)}+\frac{c^4 (-10 b e g+17 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{128 e^2 (2 c d-b e)^{5/2}}+\frac{c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-10 b e g+17 c d g+3 c e f)}{48 e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{5 e^2 (d+e x)^{17/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-10 b e g+17 c d g+3 c e f)}{40 e^2 (d+e x)^{13/2} (2 c d-b e)}","\frac{c^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-10 b e g+17 c d g+3 c e f)}{128 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{c^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-10 b e g+17 c d g+3 c e f)}{64 e^2 (d+e x)^{5/2} (2 c d-b e)}+\frac{c^4 (-10 b e g+17 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{128 e^2 (2 c d-b e)^{5/2}}+\frac{c \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2} (-10 b e g+17 c d g+3 c e f)}{48 e^2 (d+e x)^{9/2} (2 c d-b e)}-\frac{(e f-d g) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{5 e^2 (d+e x)^{17/2} (2 c d-b e)}-\frac{\left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2} (-10 b e g+17 c d g+3 c e f)}{40 e^2 (d+e x)^{13/2} (2 c d-b e)}",1,"-(c^2*(3*c*e*f + 17*c*d*g - 10*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(64*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) + (c^3*(3*c*e*f + 17*c*d*g - 10*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(128*e^2*(2*c*d - b*e)^2*(d + e*x)^(3/2)) + (c*(3*c*e*f + 17*c*d*g - 10*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(48*e^2*(2*c*d - b*e)*(d + e*x)^(9/2)) - ((3*c*e*f + 17*c*d*g - 10*b*e*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(40*e^2*(2*c*d - b*e)*(d + e*x)^(13/2)) - ((e*f - d*g)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(5*e^2*(2*c*d - b*e)*(d + e*x)^(17/2)) + (c^4*(3*c*e*f + 17*c*d*g - 10*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(128*e^2*(2*c*d - b*e)^(5/2))","A",7,5,46,0.1087,1,"{792, 662, 672, 660, 208}"
2262,1,270,0,0.4552826,"\int \frac{(d+e x)^{5/2} (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{2 (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+5 c d g+7 c e f)}{35 c^2 e^2}-\frac{8 \sqrt{d+e x} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+5 c d g+7 c e f)}{105 c^3 e^2}-\frac{16 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+5 c d g+7 c e f)}{105 c^4 e^2 \sqrt{d+e x}}-\frac{2 g (d+e x)^{5/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{7 c e^2}","-\frac{2 (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+5 c d g+7 c e f)}{35 c^2 e^2}-\frac{8 \sqrt{d+e x} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+5 c d g+7 c e f)}{105 c^3 e^2}-\frac{16 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+5 c d g+7 c e f)}{105 c^4 e^2 \sqrt{d+e x}}-\frac{2 g (d+e x)^{5/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{7 c e^2}",1,"(-16*(2*c*d - b*e)^2*(7*c*e*f + 5*c*d*g - 6*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(105*c^4*e^2*Sqrt[d + e*x]) - (8*(2*c*d - b*e)*(7*c*e*f + 5*c*d*g - 6*b*e*g)*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(105*c^3*e^2) - (2*(7*c*e*f + 5*c*d*g - 6*b*e*g)*(d + e*x)^(3/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(35*c^2*e^2) - (2*g*(d + e*x)^(5/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(7*c*e^2)","A",4,3,46,0.06522,1,"{794, 656, 648}"
2263,1,193,0,0.3244144,"\int \frac{(d+e x)^{3/2} (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{2 \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+3 c d g+5 c e f)}{15 c^2 e^2}-\frac{4 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+3 c d g+5 c e f)}{15 c^3 e^2 \sqrt{d+e x}}-\frac{2 g (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{5 c e^2}","-\frac{2 \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+3 c d g+5 c e f)}{15 c^2 e^2}-\frac{4 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+3 c d g+5 c e f)}{15 c^3 e^2 \sqrt{d+e x}}-\frac{2 g (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{5 c e^2}",1,"(-4*(2*c*d - b*e)*(5*c*e*f + 3*c*d*g - 4*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(15*c^3*e^2*Sqrt[d + e*x]) - (2*(5*c*e*f + 3*c*d*g - 4*b*e*g)*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(15*c^2*e^2) - (2*g*(d + e*x)^(3/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(5*c*e^2)","A",3,3,46,0.06522,1,"{794, 656, 648}"
2264,1,117,0,0.1797817,"\int \frac{\sqrt{d+e x} (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+c d g+3 c e f)}{3 c^2 e^2 \sqrt{d+e x}}-\frac{2 g \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{3 c e^2}","-\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+c d g+3 c e f)}{3 c^2 e^2 \sqrt{d+e x}}-\frac{2 g \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{3 c e^2}",1,"(-2*(3*c*e*f + c*d*g - 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*c^2*e^2*Sqrt[d + e*x]) - (2*g*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*c*e^2)","A",2,2,46,0.04348,1,"{794, 648}"
2265,1,131,0,0.196237,"\int \frac{f+g x}{\sqrt{d+e x} \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/(Sqrt[d + e*x]*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{2 (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 \sqrt{2 c d-b e}}-\frac{2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{c e^2 \sqrt{d+e x}}","-\frac{2 (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 \sqrt{2 c d-b e}}-\frac{2 g \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{c e^2 \sqrt{d+e x}}",1,"(-2*g*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(c*e^2*Sqrt[d + e*x]) - (2*(e*f - d*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*Sqrt[2*c*d - b*e])","A",3,3,46,0.06522,1,"{794, 660, 208}"
2266,1,153,0,0.2285305,"\int \frac{f+g x}{(d+e x)^{3/2} \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)^(3/2)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{(e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)^{3/2} (2 c d-b e)}-\frac{(-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{3/2}}","-\frac{(e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{e^2 (d+e x)^{3/2} (2 c d-b e)}-\frac{(-2 b e g+3 c d g+c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{3/2}}",1,"-(((e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(e^2*(2*c*d - b*e)*(d + e*x)^(3/2))) - ((c*e*f + 3*c*d*g - 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*(2*c*d - b*e)^(3/2))","A",3,3,46,0.06522,1,"{792, 660, 208}"
2267,1,233,0,0.3739666,"\int \frac{f+g x}{(d+e x)^{5/2} \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[(f + g*x)/((d + e*x)^(5/2)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2]),x]","-\frac{(e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{2 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+5 c d g+3 c e f)}{4 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{c (-4 b e g+5 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{5/2}}","-\frac{(e f-d g) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{2 e^2 (d+e x)^{5/2} (2 c d-b e)}-\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+5 c d g+3 c e f)}{4 e^2 (d+e x)^{3/2} (2 c d-b e)^2}-\frac{c (-4 b e g+5 c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{5/2}}",1,"-((e*f - d*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(2*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)) - ((3*c*e*f + 5*c*d*g - 4*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(4*e^2*(2*c*d - b*e)^2*(d + e*x)^(3/2)) - (c*(3*c*e*f + 5*c*d*g - 4*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(4*e^2*(2*c*d - b*e)^(5/2))","A",4,4,46,0.08696,1,"{792, 672, 660, 208}"
2268,1,369,0,0.5545286,"\int \frac{(d+e x)^{9/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(9/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{2 (d+e x)^{5/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{7 c^2 e^2 (2 c d-b e)}+\frac{12 (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{35 c^3 e^2}+\frac{16 \sqrt{d+e x} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{35 c^4 e^2}+\frac{32 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{35 c^5 e^2 \sqrt{d+e x}}+\frac{2 (d+e x)^{9/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{2 (d+e x)^{5/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{7 c^2 e^2 (2 c d-b e)}+\frac{12 (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{35 c^3 e^2}+\frac{16 \sqrt{d+e x} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{35 c^4 e^2}+\frac{32 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-8 b e g+9 c d g+7 c e f)}{35 c^5 e^2 \sqrt{d+e x}}+\frac{2 (d+e x)^{9/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(9/2))/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (32*(2*c*d - b*e)^2*(7*c*e*f + 9*c*d*g - 8*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(35*c^5*e^2*Sqrt[d + e*x]) + (16*(2*c*d - b*e)*(7*c*e*f + 9*c*d*g - 8*b*e*g)*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(35*c^4*e^2) + (12*(7*c*e*f + 9*c*d*g - 8*b*e*g)*(d + e*x)^(3/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(35*c^3*e^2) + (2*(7*c*e*f + 9*c*d*g - 8*b*e*g)*(d + e*x)^(5/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(7*c^2*e^2*(2*c*d - b*e))","A",5,3,46,0.06522,1,"{788, 656, 648}"
2269,1,292,0,0.4142528,"\int \frac{(d+e x)^{7/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(7/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{2 (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+7 c d g+5 c e f)}{5 c^2 e^2 (2 c d-b e)}+\frac{8 \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+7 c d g+5 c e f)}{15 c^3 e^2}+\frac{16 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+7 c d g+5 c e f)}{15 c^4 e^2 \sqrt{d+e x}}+\frac{2 (d+e x)^{7/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{2 (d+e x)^{3/2} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+7 c d g+5 c e f)}{5 c^2 e^2 (2 c d-b e)}+\frac{8 \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+7 c d g+5 c e f)}{15 c^3 e^2}+\frac{16 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-6 b e g+7 c d g+5 c e f)}{15 c^4 e^2 \sqrt{d+e x}}+\frac{2 (d+e x)^{7/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(7/2))/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (16*(2*c*d - b*e)*(5*c*e*f + 7*c*d*g - 6*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(15*c^4*e^2*Sqrt[d + e*x]) + (8*(5*c*e*f + 7*c*d*g - 6*b*e*g)*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(15*c^3*e^2) + (2*(5*c*e*f + 7*c*d*g - 6*b*e*g)*(d + e*x)^(3/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(5*c^2*e^2*(2*c*d - b*e))","A",4,3,46,0.06522,1,"{788, 656, 648}"
2270,1,217,0,0.2884309,"\int \frac{(d+e x)^{5/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{2 \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+5 c d g+3 c e f)}{3 c^2 e^2 (2 c d-b e)}+\frac{4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+5 c d g+3 c e f)}{3 c^3 e^2 \sqrt{d+e x}}+\frac{2 (d+e x)^{5/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{2 \sqrt{d+e x} \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+5 c d g+3 c e f)}{3 c^2 e^2 (2 c d-b e)}+\frac{4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-4 b e g+5 c d g+3 c e f)}{3 c^3 e^2 \sqrt{d+e x}}+\frac{2 (d+e x)^{5/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(5/2))/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (4*(3*c*e*f + 5*c*d*g - 4*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*c^3*e^2*Sqrt[d + e*x]) + (2*(3*c*e*f + 5*c*d*g - 4*b*e*g)*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(3*c^2*e^2*(2*c*d - b*e))","A",3,3,46,0.06522,1,"{788, 656, 648}"
2271,1,148,0,0.1562861,"\int \frac{(d+e x)^{3/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+3 c d g+c e f)}{c^2 e^2 \sqrt{d+e x} (2 c d-b e)}+\frac{2 (d+e x)^{3/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} (-2 b e g+3 c d g+c e f)}{c^2 e^2 \sqrt{d+e x} (2 c d-b e)}+\frac{2 (d+e x)^{3/2} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(3/2))/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (2*(c*e*f + 3*c*d*g - 2*b*e*g)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(c^2*e^2*(2*c*d - b*e)*Sqrt[d + e*x])","A",2,2,46,0.04348,1,"{788, 648}"
2272,1,155,0,0.1707349,"\int \frac{\sqrt{d+e x} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{2 \sqrt{d+e x} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{3/2}}","\frac{2 \sqrt{d+e x} (-b e g+c d g+c e f)}{c e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*Sqrt[d + e*x])/(c*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(e*f - d*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*(2*c*d - b*e)^(3/2))","A",3,3,46,0.06522,1,"{788, 660, 208}"
2273,1,223,0,0.3540691,"\int \frac{f+g x}{\sqrt{d+e x} \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(f + g*x)/(Sqrt[d + e*x]*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2)),x]","-\frac{e f-d g}{e^2 \sqrt{d+e x} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{\sqrt{d+e x} (-2 b e g+c d g+3 c e f)}{e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{(-2 b e g+c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{5/2}}","-\frac{e f-d g}{e^2 \sqrt{d+e x} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{\sqrt{d+e x} (-2 b e g+c d g+3 c e f)}{e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{(-2 b e g+c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{5/2}}",1,"-((e*f - d*g)/(e^2*(2*c*d - b*e)*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])) + ((3*c*e*f + c*d*g - 2*b*e*g)*Sqrt[d + e*x])/(e^2*(2*c*d - b*e)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - ((3*c*e*f + c*d*g - 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*(2*c*d - b*e)^(5/2))","A",4,4,46,0.08696,1,"{792, 666, 660, 208}"
2274,1,308,0,0.4667178,"\int \frac{f+g x}{(d+e x)^{3/2} \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(f + g*x)/((d + e*x)^(3/2)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2)),x]","-\frac{e f-d g}{2 e^2 (d+e x)^{3/2} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{3 c \sqrt{d+e x} (-4 b e g+3 c d g+5 c e f)}{4 e^2 (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{-4 b e g+3 c d g+5 c e f}{4 e^2 \sqrt{d+e x} (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{3 c (-4 b e g+3 c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{7/2}}","-\frac{e f-d g}{2 e^2 (d+e x)^{3/2} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{3 c \sqrt{d+e x} (-4 b e g+3 c d g+5 c e f)}{4 e^2 (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{-4 b e g+3 c d g+5 c e f}{4 e^2 \sqrt{d+e x} (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{3 c (-4 b e g+3 c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{7/2}}",1,"-(e*f - d*g)/(2*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (5*c*e*f + 3*c*d*g - 4*b*e*g)/(4*e^2*(2*c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (3*c*(5*c*e*f + 3*c*d*g - 4*b*e*g)*Sqrt[d + e*x])/(4*e^2*(2*c*d - b*e)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (3*c*(5*c*e*f + 3*c*d*g - 4*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(4*e^2*(2*c*d - b*e)^(7/2))","A",5,5,46,0.1087,1,"{792, 672, 666, 660, 208}"
2275,1,387,0,0.6285223,"\int \frac{f+g x}{(d+e x)^{5/2} \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[(f + g*x)/((d + e*x)^(5/2)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2)),x]","\frac{5 c^2 \sqrt{d+e x} (-6 b e g+5 c d g+7 c e f)}{8 e^2 (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{5 c^2 (-6 b e g+5 c d g+7 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{9/2}}-\frac{5 c (-6 b e g+5 c d g+7 c e f)}{24 e^2 \sqrt{d+e x} (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{-6 b e g+5 c d g+7 c e f}{12 e^2 (d+e x)^{3/2} (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{e f-d g}{3 e^2 (d+e x)^{5/2} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{5 c^2 \sqrt{d+e x} (-6 b e g+5 c d g+7 c e f)}{8 e^2 (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{5 c^2 (-6 b e g+5 c d g+7 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{9/2}}-\frac{5 c (-6 b e g+5 c d g+7 c e f)}{24 e^2 \sqrt{d+e x} (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{-6 b e g+5 c d g+7 c e f}{12 e^2 (d+e x)^{3/2} (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{e f-d g}{3 e^2 (d+e x)^{5/2} (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"-(e*f - d*g)/(3*e^2*(2*c*d - b*e)*(d + e*x)^(5/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (7*c*e*f + 5*c*d*g - 6*b*e*g)/(12*e^2*(2*c*d - b*e)^2*(d + e*x)^(3/2)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (5*c*(7*c*e*f + 5*c*d*g - 6*b*e*g))/(24*e^2*(2*c*d - b*e)^3*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (5*c^2*(7*c*e*f + 5*c*d*g - 6*b*e*g)*Sqrt[d + e*x])/(8*e^2*(2*c*d - b*e)^4*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (5*c^2*(7*c*e*f + 5*c*d*g - 6*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(8*e^2*(2*c*d - b*e)^(9/2))","A",6,5,46,0.1087,1,"{792, 672, 666, 660, 208}"
2276,1,448,0,0.7050722,"\int \frac{(d+e x)^{13/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(13/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^{9/2} (-10 b e g+13 c d g+7 c e f)}{21 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{16 (d+e x)^{7/2} (-10 b e g+13 c d g+7 c e f)}{105 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{32 (d+e x)^{5/2} (2 c d-b e) (-10 b e g+13 c d g+7 c e f)}{105 c^4 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{128 (d+e x)^{3/2} (2 c d-b e)^2 (-10 b e g+13 c d g+7 c e f)}{105 c^5 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{256 \sqrt{d+e x} (2 c d-b e)^3 (-10 b e g+13 c d g+7 c e f)}{105 c^6 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{13/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{2 (d+e x)^{9/2} (-10 b e g+13 c d g+7 c e f)}{21 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{16 (d+e x)^{7/2} (-10 b e g+13 c d g+7 c e f)}{105 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{32 (d+e x)^{5/2} (2 c d-b e) (-10 b e g+13 c d g+7 c e f)}{105 c^4 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{128 (d+e x)^{3/2} (2 c d-b e)^2 (-10 b e g+13 c d g+7 c e f)}{105 c^5 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{256 \sqrt{d+e x} (2 c d-b e)^3 (-10 b e g+13 c d g+7 c e f)}{105 c^6 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{13/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(13/2))/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (256*(2*c*d - b*e)^3*(7*c*e*f + 13*c*d*g - 10*b*e*g)*Sqrt[d + e*x])/(105*c^6*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (128*(2*c*d - b*e)^2*(7*c*e*f + 13*c*d*g - 10*b*e*g)*(d + e*x)^(3/2))/(105*c^5*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (32*(2*c*d - b*e)*(7*c*e*f + 13*c*d*g - 10*b*e*g)*(d + e*x)^(5/2))/(105*c^4*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (16*(7*c*e*f + 13*c*d*g - 10*b*e*g)*(d + e*x)^(7/2))/(105*c^3*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (2*(7*c*e*f + 13*c*d*g - 10*b*e*g)*(d + e*x)^(9/2))/(21*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",6,3,46,0.06522,1,"{788, 656, 648}"
2277,1,371,0,0.5460336,"\int \frac{(d+e x)^{11/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(11/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^{7/2} (-8 b e g+11 c d g+5 c e f)}{15 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{4 (d+e x)^{5/2} (-8 b e g+11 c d g+5 c e f)}{15 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{16 (d+e x)^{3/2} (2 c d-b e) (-8 b e g+11 c d g+5 c e f)}{15 c^4 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{32 \sqrt{d+e x} (2 c d-b e)^2 (-8 b e g+11 c d g+5 c e f)}{15 c^5 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{11/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{2 (d+e x)^{7/2} (-8 b e g+11 c d g+5 c e f)}{15 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{4 (d+e x)^{5/2} (-8 b e g+11 c d g+5 c e f)}{15 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{16 (d+e x)^{3/2} (2 c d-b e) (-8 b e g+11 c d g+5 c e f)}{15 c^4 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{32 \sqrt{d+e x} (2 c d-b e)^2 (-8 b e g+11 c d g+5 c e f)}{15 c^5 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{11/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(11/2))/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (32*(2*c*d - b*e)^2*(5*c*e*f + 11*c*d*g - 8*b*e*g)*Sqrt[d + e*x])/(15*c^5*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (16*(2*c*d - b*e)*(5*c*e*f + 11*c*d*g - 8*b*e*g)*(d + e*x)^(3/2))/(15*c^4*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (4*(5*c*e*f + 11*c*d*g - 8*b*e*g)*(d + e*x)^(5/2))/(15*c^3*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (2*(5*c*e*f + 11*c*d*g - 8*b*e*g)*(d + e*x)^(7/2))/(15*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",5,3,46,0.06522,1,"{788, 656, 648}"
2278,1,291,0,0.412777,"\int \frac{(d+e x)^{9/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(9/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^{5/2} (-2 b e g+3 c d g+c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{8 (d+e x)^{3/2} (-2 b e g+3 c d g+c e f)}{3 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{16 \sqrt{d+e x} (2 c d-b e) (-2 b e g+3 c d g+c e f)}{3 c^4 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{9/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{2 (d+e x)^{5/2} (-2 b e g+3 c d g+c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{8 (d+e x)^{3/2} (-2 b e g+3 c d g+c e f)}{3 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{16 \sqrt{d+e x} (2 c d-b e) (-2 b e g+3 c d g+c e f)}{3 c^4 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{9/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(9/2))/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (16*(2*c*d - b*e)*(c*e*f + 3*c*d*g - 2*b*e*g)*Sqrt[d + e*x])/(3*c^4*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (8*(c*e*f + 3*c*d*g - 2*b*e*g)*(d + e*x)^(3/2))/(3*c^3*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (2*(c*e*f + 3*c*d*g - 2*b*e*g)*(d + e*x)^(5/2))/(3*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",4,3,46,0.06522,1,"{788, 656, 648}"
2279,1,217,0,0.2866858,"\int \frac{(d+e x)^{7/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(7/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^{3/2} (-4 b e g+7 c d g+c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{4 \sqrt{d+e x} (-4 b e g+7 c d g+c e f)}{3 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{7/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{2 (d+e x)^{3/2} (-4 b e g+7 c d g+c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{4 \sqrt{d+e x} (-4 b e g+7 c d g+c e f)}{3 c^3 e^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{7/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(7/2))/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (4*(c*e*f + 7*c*d*g - 4*b*e*g)*Sqrt[d + e*x])/(3*c^3*e^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (2*(c*e*f + 7*c*d*g - 4*b*e*g)*(d + e*x)^(3/2))/(3*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",3,3,46,0.06522,1,"{788, 656, 648}"
2280,1,152,0,0.160173,"\int \frac{(d+e x)^{5/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(5/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 \sqrt{d+e x} (2 b e g-5 c d g+c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{5/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{2 \sqrt{d+e x} (2 b e g-5 c d g+c e f)}{3 c^2 e^2 (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 (d+e x)^{5/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(5/2))/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (2*(c*e*f - 5*c*d*g + 2*b*e*g)*Sqrt[d + e*x])/(3*c^2*e^2*(2*c*d - b*e)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",2,2,46,0.04348,1,"{788, 648}"
2281,1,221,0,0.3035388,"\int \frac{(d+e x)^{3/2} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^(3/2)*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{2 (d+e x)^{3/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{2 \sqrt{d+e x} (e f-d g)}{e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{5/2}}","\frac{2 (d+e x)^{3/2} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{2 \sqrt{d+e x} (e f-d g)}{e^2 (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{2 (e f-d g) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{5/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*(d + e*x)^(3/2))/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (2*(e*f - d*g)*Sqrt[d + e*x])/(e^2*(2*c*d - b*e)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (2*(e*f - d*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*(2*c*d - b*e)^(5/2))","A",4,4,46,0.08696,1,"{788, 666, 660, 208}"
2282,1,313,0,0.4351216,"\int \frac{\sqrt{d+e x} (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[(Sqrt[d + e*x]*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{\sqrt{d+e x} (-2 b e g-c d g+5 c e f)}{e^2 (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{-2 b e g-c d g+5 c e f}{3 c e^2 \sqrt{d+e x} (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 \sqrt{d+e x} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{(-2 b e g-c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{7/2}}","\frac{\sqrt{d+e x} (-2 b e g-c d g+5 c e f)}{e^2 (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{-2 b e g-c d g+5 c e f}{3 c e^2 \sqrt{d+e x} (2 c d-b e)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{2 \sqrt{d+e x} (-b e g+c d g+c e f)}{3 c e^2 (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{(-2 b e g-c d g+5 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{e^2 (2 c d-b e)^{7/2}}",1,"(2*(c*e*f + c*d*g - b*e*g)*Sqrt[d + e*x])/(3*c*e^2*(2*c*d - b*e)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (5*c*e*f - c*d*g - 2*b*e*g)/(3*c*e^2*(2*c*d - b*e)^2*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + ((5*c*e*f - c*d*g - 2*b*e*g)*Sqrt[d + e*x])/(e^2*(2*c*d - b*e)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - ((5*c*e*f - c*d*g - 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(e^2*(2*c*d - b*e)^(7/2))","A",5,5,46,0.1087,1,"{788, 672, 666, 660, 208}"
2283,1,378,0,0.5899848,"\int \frac{f+g x}{\sqrt{d+e x} \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[(f + g*x)/(Sqrt[d + e*x]*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]","-\frac{e f-d g}{2 e^2 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{5 c \sqrt{d+e x} (-4 b e g+c d g+7 c e f)}{4 e^2 (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{5 (-4 b e g+c d g+7 c e f)}{12 e^2 \sqrt{d+e x} (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{\sqrt{d+e x} (-4 b e g+c d g+7 c e f)}{6 e^2 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{5 c (-4 b e g+c d g+7 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{9/2}}","-\frac{e f-d g}{2 e^2 \sqrt{d+e x} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}+\frac{5 c \sqrt{d+e x} (-4 b e g+c d g+7 c e f)}{4 e^2 (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{5 (-4 b e g+c d g+7 c e f)}{12 e^2 \sqrt{d+e x} (2 c d-b e)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{\sqrt{d+e x} (-4 b e g+c d g+7 c e f)}{6 e^2 (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{5 c (-4 b e g+c d g+7 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{4 e^2 (2 c d-b e)^{9/2}}",1,"-(e*f - d*g)/(2*e^2*(2*c*d - b*e)*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + ((7*c*e*f + c*d*g - 4*b*e*g)*Sqrt[d + e*x])/(6*e^2*(2*c*d - b*e)^2*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (5*(7*c*e*f + c*d*g - 4*b*e*g))/(12*e^2*(2*c*d - b*e)^3*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (5*c*(7*c*e*f + c*d*g - 4*b*e*g)*Sqrt[d + e*x])/(4*e^2*(2*c*d - b*e)^4*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (5*c*(7*c*e*f + c*d*g - 4*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(4*e^2*(2*c*d - b*e)^(9/2))","A",6,5,46,0.1087,1,"{792, 666, 672, 660, 208}"
2284,1,457,0,0.7529252,"\int \frac{f+g x}{(d+e x)^{3/2} \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[(f + g*x)/((d + e*x)^(3/2)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2)),x]","\frac{35 c^2 \sqrt{d+e x} (-2 b e g+c d g+3 c e f)}{8 e^2 (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{35 c^2 (-2 b e g+c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{11/2}}-\frac{35 c (-2 b e g+c d g+3 c e f)}{24 e^2 \sqrt{d+e x} (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{7 c \sqrt{d+e x} (-2 b e g+c d g+3 c e f)}{12 e^2 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{-2 b e g+c d g+3 c e f}{4 e^2 \sqrt{d+e x} (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{e f-d g}{3 e^2 (d+e x)^{3/2} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}","\frac{35 c^2 \sqrt{d+e x} (-2 b e g+c d g+3 c e f)}{8 e^2 (2 c d-b e)^5 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{35 c^2 (-2 b e g+c d g+3 c e f) \tanh ^{-1}\left(\frac{\sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{\sqrt{d+e x} \sqrt{2 c d-b e}}\right)}{8 e^2 (2 c d-b e)^{11/2}}-\frac{35 c (-2 b e g+c d g+3 c e f)}{24 e^2 \sqrt{d+e x} (2 c d-b e)^4 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}+\frac{7 c \sqrt{d+e x} (-2 b e g+c d g+3 c e f)}{12 e^2 (2 c d-b e)^3 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{-2 b e g+c d g+3 c e f}{4 e^2 \sqrt{d+e x} (2 c d-b e)^2 \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{e f-d g}{3 e^2 (d+e x)^{3/2} (2 c d-b e) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}",1,"-(e*f - d*g)/(3*e^2*(2*c*d - b*e)*(d + e*x)^(3/2)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (3*c*e*f + c*d*g - 2*b*e*g)/(4*e^2*(2*c*d - b*e)^2*Sqrt[d + e*x]*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) + (7*c*(3*c*e*f + c*d*g - 2*b*e*g)*Sqrt[d + e*x])/(12*e^2*(2*c*d - b*e)^3*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - (35*c*(3*c*e*f + c*d*g - 2*b*e*g))/(24*e^2*(2*c*d - b*e)^4*Sqrt[d + e*x]*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) + (35*c^2*(3*c*e*f + c*d*g - 2*b*e*g)*Sqrt[d + e*x])/(8*e^2*(2*c*d - b*e)^5*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - (35*c^2*(3*c*e*f + c*d*g - 2*b*e*g)*ArcTanh[Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]/(Sqrt[2*c*d - b*e]*Sqrt[d + e*x])])/(8*e^2*(2*c*d - b*e)^(11/2))","A",7,5,46,0.1087,1,"{792, 672, 666, 660, 208}"
2285,1,221,0,0.3529324,"\int (d+e x)^m (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2} \, dx","Int[(d + e*x)^m*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{(2 c d-b e)^2 (d+e x)^m (-b e+c d-c e x)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+7)-2 c (d g m+e f (m+7))) \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{7 c^4 e^2 (m+7)}-\frac{g (d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{c e^2 (m+7)}","\frac{(2 c d-b e)^2 (d+e x)^m (-b e+c d-c e x)^3 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+7)-2 c (d g m+e f (m+7))) \, _2F_1\left(\frac{7}{2},-m-\frac{5}{2};\frac{9}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{7 c^4 e^2 (m+7)}-\frac{g (d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{7/2}}{c e^2 (m+7)}",1,"-((g*(d + e*x)^m*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(7/2))/(c*e^2*(7 + m))) + ((2*c*d - b*e)^2*(b*e*g*(7 + 2*m) - 2*c*(d*g*m + e*f*(7 + m)))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*(c*d - b*e - c*e*x)^3*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]*Hypergeometric2F1[7/2, -5/2 - m, 9/2, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(7*c^4*e^2*(7 + m))","A",5,5,44,0.1136,1,"{794, 679, 677, 70, 69}"
2286,1,219,0,0.3404764,"\int (d+e x)^m (f+g x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2} \, dx","Int[(d + e*x)^m*(f + g*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{(2 c d-b e) (d+e x)^m (-b e+c d-c e x)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+5)-2 c (d g m+e f (m+5))) \, _2F_1\left(\frac{5}{2},-m-\frac{3}{2};\frac{7}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{5 c^3 e^2 (m+5)}-\frac{g (d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{c e^2 (m+5)}","\frac{(2 c d-b e) (d+e x)^m (-b e+c d-c e x)^2 \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+5)-2 c (d g m+e f (m+5))) \, _2F_1\left(\frac{5}{2},-m-\frac{3}{2};\frac{7}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{5 c^3 e^2 (m+5)}-\frac{g (d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{5/2}}{c e^2 (m+5)}",1,"-((g*(d + e*x)^m*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(5/2))/(c*e^2*(5 + m))) + ((2*c*d - b*e)*(b*e*g*(5 + 2*m) - 2*c*(d*g*m + e*f*(5 + m)))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*(c*d - b*e - c*e*x)^2*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]*Hypergeometric2F1[5/2, -3/2 - m, 7/2, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(5*c^3*e^2*(5 + m))","A",5,5,44,0.1136,1,"{794, 679, 677, 70, 69}"
2287,1,208,0,0.3095327,"\int (d+e x)^m (f+g x) \sqrt{c d^2-b d e-b e^2 x-c e^2 x^2} \, dx","Int[(d + e*x)^m*(f + g*x)*Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{(d+e x)^m (-b e+c d-c e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+3)-2 c (d g m+e f (m+3))) \, _2F_1\left(\frac{3}{2},-m-\frac{1}{2};\frac{5}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{3 c^2 e^2 (m+3)}-\frac{g (d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{c e^2 (m+3)}","\frac{(d+e x)^m (-b e+c d-c e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2} \left(\frac{c (d+e x)}{2 c d-b e}\right)^{-m-\frac{1}{2}} (b e g (2 m+3)-2 c (d g m+e f (m+3))) \, _2F_1\left(\frac{3}{2},-m-\frac{1}{2};\frac{5}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{3 c^2 e^2 (m+3)}-\frac{g (d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}{c e^2 (m+3)}",1,"-((g*(d + e*x)^m*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2))/(c*e^2*(3 + m))) + ((b*e*g*(3 + 2*m) - 2*c*(d*g*m + e*f*(3 + m)))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(-1/2 - m)*(c*d - b*e - c*e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]*Hypergeometric2F1[3/2, -1/2 - m, 5/2, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(3*c^2*e^2*(3 + m))","A",5,5,44,0.1136,1,"{794, 679, 677, 70, 69}"
2288,1,205,0,0.312948,"\int \frac{(d+e x)^m (f+g x)}{\sqrt{c d^2-b d e-b e^2 x-c e^2 x^2}} \, dx","Int[((d + e*x)^m*(f + g*x))/Sqrt[c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2],x]","\frac{(d+e x)^m (-b e+c d-c e x) \left(\frac{c (d+e x)}{2 c d-b e}\right)^{\frac{1}{2}-m} (b e g (2 m+1)-2 c (d g m+e f (m+1))) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{c^2 e^2 (m+1) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{g (d+e x)^m \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{c e^2 (m+1)}","\frac{(d+e x)^m (-b e+c d-c e x) \left(\frac{c (d+e x)}{2 c d-b e}\right)^{\frac{1}{2}-m} (b e g (2 m+1)-2 c (d g m+e f (m+1))) \, _2F_1\left(\frac{1}{2},\frac{1}{2}-m;\frac{3}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{c^2 e^2 (m+1) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{g (d+e x)^m \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}{c e^2 (m+1)}",1,"-((g*(d + e*x)^m*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])/(c*e^2*(1 + m))) + ((b*e*g*(1 + 2*m) - 2*c*(d*g*m + e*f*(1 + m)))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(1/2 - m)*(c*d - b*e - c*e*x)*Hypergeometric2F1[1/2, 1/2 - m, 3/2, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(c^2*e^2*(1 + m)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",5,5,44,0.1136,1,"{794, 679, 677, 70, 69}"
2289,1,210,0,0.3299507,"\int \frac{(d+e x)^m (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{3/2}} \, dx","Int[((d + e*x)^m*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(3/2),x]","\frac{g (d+e x)^m}{c e^2 (1-m) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{(d+e x)^m \left(\frac{c (d+e x)}{2 c d-b e}\right)^{\frac{1}{2}-m} (b e g (1-2 m)-2 c (e f (1-m)-d g m)) \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-m;\frac{1}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{c e^2 (1-m) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{g (d+e x)^m}{c e^2 (1-m) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}-\frac{(d+e x)^m \left(\frac{c (d+e x)}{2 c d-b e}\right)^{\frac{1}{2}-m} (b e g (1-2 m)-2 c (e f (1-m)-d g m)) \, _2F_1\left(-\frac{1}{2},\frac{3}{2}-m;\frac{1}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{c e^2 (1-m) (2 c d-b e) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(g*(d + e*x)^m)/(c*e^2*(1 - m)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2]) - ((b*e*g*(1 - 2*m) - 2*c*(e*f*(1 - m) - d*g*m))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(1/2 - m)*Hypergeometric2F1[-1/2, 3/2 - m, 1/2, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(c*e^2*(2*c*d - b*e)*(1 - m)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",5,5,44,0.1136,1,"{794, 679, 677, 70, 69}"
2290,1,224,0,0.3275167,"\int \frac{(d+e x)^m (f+g x)}{\left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^{5/2}} \, dx","Int[((d + e*x)^m*(f + g*x))/(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^(5/2),x]","\frac{g (d+e x)^m}{c e^2 (3-m) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{(d+e x)^m \left(\frac{c (d+e x)}{2 c d-b e}\right)^{\frac{1}{2}-m} (b e g (3-2 m)-2 c (e f (3-m)-d g m)) \, _2F_1\left(-\frac{3}{2},\frac{5}{2}-m;-\frac{1}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{3 e^2 (3-m) (2 c d-b e)^2 (-b e+c d-c e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}","\frac{g (d+e x)^m}{c e^2 (3-m) \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{3/2}}-\frac{(d+e x)^m \left(\frac{c (d+e x)}{2 c d-b e}\right)^{\frac{1}{2}-m} (b e g (3-2 m)-2 c (e f (3-m)-d g m)) \, _2F_1\left(-\frac{3}{2},\frac{5}{2}-m;-\frac{1}{2};\frac{c d-b e-c e x}{2 c d-b e}\right)}{3 e^2 (3-m) (2 c d-b e)^2 (-b e+c d-c e x) \sqrt{d (c d-b e)-b e^2 x-c e^2 x^2}}",1,"(g*(d + e*x)^m)/(c*e^2*(3 - m)*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(3/2)) - ((b*e*g*(3 - 2*m) - 2*c*(e*f*(3 - m) - d*g*m))*(d + e*x)^m*((c*(d + e*x))/(2*c*d - b*e))^(1/2 - m)*Hypergeometric2F1[-3/2, 5/2 - m, -1/2, (c*d - b*e - c*e*x)/(2*c*d - b*e)])/(3*e^2*(2*c*d - b*e)^2*(3 - m)*(c*d - b*e - c*e*x)*Sqrt[d*(c*d - b*e) - b*e^2*x - c*e^2*x^2])","A",5,5,44,0.1136,1,"{794, 679, 677, 70, 69}"
2291,1,42,0,0.0534318,"\int (d+e x)^m (c d m-b e (1+m+p)-c e (2+m+2 p) x) \left(c d^2-b d e-b e^2 x-c e^2 x^2\right)^p \, dx","Int[(d + e*x)^m*(c*d*m - b*e*(1 + m + p) - c*e*(2 + m + 2*p)*x)*(c*d^2 - b*d*e - b*e^2*x - c*e^2*x^2)^p,x]","\frac{(d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{p+1}}{e}","\frac{(d+e x)^m \left(d (c d-b e)-b e^2 x-c e^2 x^2\right)^{p+1}}{e}",1,"((d + e*x)^m*(d*(c*d - b*e) - b*e^2*x - c*e^2*x^2)^(1 + p))/e","A",1,1,61,0.01639,1,"{786}"
2292,1,64,0,0.035016,"\int (d+e x)^{-3-2 p} (f+g x) \left(d (e f+d g+d g p)+e (e f+3 d g+2 d g p) x+e^2 g (2+p) x^2\right)^p \, dx","Int[(d + e*x)^(-3 - 2*p)*(f + g*x)*(d*(e*f + d*g + d*g*p) + e*(e*f + 3*d*g + 2*d*g*p)*x + e^2*g*(2 + p)*x^2)^p,x]","-\frac{(d+e x)^{-2 p-3} \left(e x (d g (2 p+3)+e f)+d (d g (p+1)+e f)+e^2 g (p+2) x^2\right)^{p+1}}{e^2 (p+2)}","-\frac{(d+e x)^{-2 p-3} \left(e x (d g (2 p+3)+e f)+d (d g (p+1)+e f)+e^2 g (p+2) x^2\right)^{p+1}}{e^2 (p+2)}",1,"-(((d + e*x)^(-3 - 2*p)*(d*(e*f + d*g*(1 + p)) + e*(e*f + d*g*(3 + 2*p))*x + e^2*g*(2 + p)*x^2)^(1 + p))/(e^2*(2 + p)))","A",1,1,60,0.01667,1,"{786}"
2293,1,143,0,0.20921,"\int \frac{(d+e x)^2 (f+g x)}{\left(c f^2-b f g-b g^2 x-c g^2 x^2\right)^2} \, dx","Int[((d + e*x)^2*(f + g*x))/(c*f^2 - b*f*g - b*g^2*x - c*g^2*x^2)^2,x]","\frac{(-b e g+c d g+c e f)^2}{c^2 g^3 (2 c f-b g) (-b g+c f-c g x)}+\frac{(-b e g-c d g+3 c e f) (-b e g+c d g+c e f) \log (-b g+c f-c g x)}{c^2 g^3 (2 c f-b g)^2}+\frac{(e f-d g)^2 \log (f+g x)}{g^3 (2 c f-b g)^2}","\frac{(-b e g+c d g+c e f)^2}{c^2 g^3 (2 c f-b g) (-b g+c f-c g x)}+\frac{(-b e g-c d g+3 c e f) (-b e g+c d g+c e f) \log (-b g+c f-c g x)}{c^2 g^3 (2 c f-b g)^2}+\frac{(e f-d g)^2 \log (f+g x)}{g^3 (2 c f-b g)^2}",1,"(c*e*f + c*d*g - b*e*g)^2/(c^2*g^3*(2*c*f - b*g)*(c*f - b*g - c*g*x)) + ((e*f - d*g)^2*Log[f + g*x])/(g^3*(2*c*f - b*g)^2) + ((3*c*e*f - c*d*g - b*e*g)*(c*e*f + c*d*g - b*e*g)*Log[c*f - b*g - c*g*x])/(c^2*g^3*(2*c*f - b*g)^2)","A",3,2,42,0.04762,1,"{798, 88}"
2294,1,73,0,0.0529385,"\int (1+x)^4 (a+b x) \left(1-x+x^2\right)^4 \, dx","Int[(1 + x)^4*(a + b*x)*(1 - x + x^2)^4,x]","\frac{a x^{13}}{13}+\frac{2 a x^{10}}{5}+\frac{6 a x^7}{7}+a x^4+a x+\frac{b x^{14}}{14}+\frac{4 b x^{11}}{11}+\frac{3 b x^8}{4}+\frac{4 b x^5}{5}+\frac{b x^2}{2}","\frac{a x^{13}}{13}+\frac{2 a x^{10}}{5}+\frac{6 a x^7}{7}+a x^4+a x+\frac{b x^{14}}{14}+\frac{4 b x^{11}}{11}+\frac{3 b x^8}{4}+\frac{4 b x^5}{5}+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + a*x^4 + (4*b*x^5)/5 + (6*a*x^7)/7 + (3*b*x^8)/4 + (2*a*x^10)/5 + (4*b*x^11)/11 + (a*x^13)/13 + (b*x^14)/14","A",2,1,21,0.04762,1,"{771}"
2295,1,60,0,0.037747,"\int (1+x)^3 (a+b x) \left(1-x+x^2\right)^3 \, dx","Int[(1 + x)^3*(a + b*x)*(1 - x + x^2)^3,x]","\frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2}","\frac{a x^{10}}{10}+\frac{3 a x^7}{7}+\frac{3 a x^4}{4}+a x+\frac{b x^{11}}{11}+\frac{3 b x^8}{8}+\frac{3 b x^5}{5}+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (3*a*x^4)/4 + (3*b*x^5)/5 + (3*a*x^7)/7 + (3*b*x^8)/8 + (a*x^10)/10 + (b*x^11)/11","A",2,1,21,0.04762,1,"{771}"
2296,1,44,0,0.0283479,"\int (1+x)^2 (a+b x) \left(1-x+x^2\right)^2 \, dx","Int[(1 + x)^2*(a + b*x)*(1 - x + x^2)^2,x]","\frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2}","\frac{a x^7}{7}+\frac{a x^4}{2}+a x+\frac{b x^8}{8}+\frac{2 b x^5}{5}+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (a*x^4)/2 + (2*b*x^5)/5 + (a*x^7)/7 + (b*x^8)/8","A",2,1,21,0.04762,1,"{771}"
2297,1,28,0,0.0165361,"\int (1+x) (a+b x) \left(1-x+x^2\right) \, dx","Int[(1 + x)*(a + b*x)*(1 - x + x^2),x]","\frac{a x^4}{4}+a x+\frac{b x^5}{5}+\frac{b x^2}{2}","\frac{a x^4}{4}+a x+\frac{b x^5}{5}+\frac{b x^2}{2}",1,"a*x + (b*x^2)/2 + (a*x^4)/4 + (b*x^5)/5","A",2,1,17,0.05882,1,"{771}"
2298,1,54,0,0.0662246,"\int \frac{a+b x}{(1+x) \left(1-x+x^2\right)} \, dx","Int[(a + b*x)/((1 + x)*(1 - x + x^2)),x]","-\frac{1}{6} (a-b) \log \left(x^2-x+1\right)+\frac{1}{3} (a-b) \log (x+1)-\frac{(a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}","-\frac{1}{6} (a-b) \log \left(x^2-x+1\right)+\frac{1}{3} (a-b) \log (x+1)-\frac{(a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{\sqrt{3}}",1,"-(((a + b)*ArcTan[(1 - 2*x)/Sqrt[3]])/Sqrt[3]) + ((a - b)*Log[1 + x])/3 - ((a - b)*Log[1 - x + x^2])/6","A",6,5,21,0.2381,1,"{800, 634, 618, 204, 628}"
2299,1,79,0,0.067177,"\int \frac{a+b x}{(1+x)^2 \left(1-x+x^2\right)^2} \, dx","Int[(a + b*x)/((1 + x)^2*(1 - x + x^2)^2),x]","\frac{x (a+b x)}{3 \left(x^3+1\right)}-\frac{1}{18} (2 a-b) \log \left(x^2-x+1\right)+\frac{1}{9} (2 a-b) \log (x+1)-\frac{(2 a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}","\frac{x (a+b x)}{3 \left(x^3+1\right)}-\frac{1}{18} (2 a-b) \log \left(x^2-x+1\right)+\frac{1}{9} (2 a-b) \log (x+1)-\frac{(2 a+b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{3 \sqrt{3}}",1,"(x*(a + b*x))/(3*(1 + x^3)) - ((2*a + b)*ArcTan[(1 - 2*x)/Sqrt[3]])/(3*Sqrt[3]) + ((2*a - b)*Log[1 + x])/9 - ((2*a - b)*Log[1 - x + x^2])/18","A",8,8,21,0.3810,1,"{809, 1855, 1860, 31, 634, 618, 204, 628}"
2300,1,101,0,0.097348,"\int \frac{a+b x}{(1+x)^3 \left(1-x+x^2\right)^3} \, dx","Int[(a + b*x)/((1 + x)^3*(1 - x + x^2)^3),x]","\frac{x (a+b x)}{6 \left(x^3+1\right)^2}+\frac{x (5 a+4 b x)}{18 \left(x^3+1\right)}-\frac{1}{54} (5 a-2 b) \log \left(x^2-x+1\right)+\frac{1}{27} (5 a-2 b) \log (x+1)-\frac{(5 a+2 b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{9 \sqrt{3}}","\frac{x (a+b x)}{6 \left(x^3+1\right)^2}+\frac{x (5 a+4 b x)}{18 \left(x^3+1\right)}-\frac{1}{54} (5 a-2 b) \log \left(x^2-x+1\right)+\frac{1}{27} (5 a-2 b) \log (x+1)-\frac{(5 a+2 b) \tan ^{-1}\left(\frac{1-2 x}{\sqrt{3}}\right)}{9 \sqrt{3}}",1,"(x*(a + b*x))/(6*(1 + x^3)^2) + (x*(5*a + 4*b*x))/(18*(1 + x^3)) - ((5*a + 2*b)*ArcTan[(1 - 2*x)/Sqrt[3]])/(9*Sqrt[3]) + ((5*a - 2*b)*Log[1 + x])/27 - ((5*a - 2*b)*Log[1 - x + x^2])/54","A",9,8,21,0.3810,1,"{809, 1855, 1860, 31, 634, 618, 204, 628}"
2301,1,365,0,0.2052961,"\int (1+x)^{3/2} (a+b x) \left(1-x+x^2\right)^{3/2} \, dx","Int[(1 + x)^(3/2)*(a + b*x)*(1 - x + x^2)^(3/2),x]","\frac{18 \sqrt{x^2-x+1} \sqrt{x+1} \left(91 a x+55 b x^2\right)}{5005}+\frac{2}{143} \sqrt{x^2-x+1} \left(x^3+1\right) \sqrt{x+1} \left(13 a x+11 b x^2\right)+\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} \left(91 a-55 \left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5005 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}+\frac{54 b \sqrt{x^2-x+1} \sqrt{x+1}}{91 \left(x+\sqrt{3}+1\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{18 \sqrt{x^2-x+1} \sqrt{x+1} \left(91 a x+55 b x^2\right)}{5005}+\frac{2}{143} \sqrt{x^2-x+1} \left(x^3+1\right) \sqrt{x+1} \left(13 a x+11 b x^2\right)+\frac{18\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} \left(91 a-55 \left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{5005 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}+\frac{54 b \sqrt{x^2-x+1} \sqrt{x+1}}{91 \left(x+\sqrt{3}+1\right)}-\frac{27 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{91 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(54*b*Sqrt[1 + x]*Sqrt[1 - x + x^2])/(91*(1 + Sqrt[3] + x)) + (18*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(91*a*x + 55*b*x^2))/5005 + (2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(13*a*x + 11*b*x^2)*(1 + x^3))/143 - (27*3^(1/4)*Sqrt[2 - Sqrt[3]]*b*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(91*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3)) + (18*3^(3/4)*Sqrt[2 + Sqrt[3]]*(91*a - 55*(1 - Sqrt[3])*b)*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(5005*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",6,5,25,0.2000,1,"{809, 1853, 1878, 218, 1877}"
2302,1,326,0,0.1434419,"\int \sqrt{1+x} (a+b x) \sqrt{1-x+x^2} \, dx","Int[Sqrt[1 + x]*(a + b*x)*Sqrt[1 - x + x^2],x]","\frac{2}{35} \sqrt{x^2-x+1} \sqrt{x+1} \left(7 a x+5 b x^2\right)+\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} \left(7 a-5 \left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{35 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}+\frac{6 b \sqrt{x^2-x+1} \sqrt{x+1}}{7 \left(x+\sqrt{3}+1\right)}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}","\frac{2}{35} \sqrt{x^2-x+1} \sqrt{x+1} \left(7 a x+5 b x^2\right)+\frac{2\ 3^{3/4} \sqrt{2+\sqrt{3}} \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} \left(7 a-5 \left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{35 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}+\frac{6 b \sqrt{x^2-x+1} \sqrt{x+1}}{7 \left(x+\sqrt{3}+1\right)}-\frac{3 \sqrt[4]{3} \sqrt{2-\sqrt{3}} b \sqrt{x^2-x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} (x+1)^{3/2} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{7 \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(x^3+1\right)}",1,"(6*b*Sqrt[1 + x]*Sqrt[1 - x + x^2])/(7*(1 + Sqrt[3] + x)) + (2*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(7*a*x + 5*b*x^2))/35 - (3*3^(1/4)*Sqrt[2 - Sqrt[3]]*b*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(7*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3)) + (2*3^(3/4)*Sqrt[2 + Sqrt[3]]*(7*a - 5*(1 - Sqrt[3])*b)*(1 + x)^(3/2)*Sqrt[1 - x + x^2]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(35*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*(1 + x^3))","A",5,5,25,0.2000,1,"{809, 1853, 1878, 218, 1877}"
2303,1,275,0,0.1038875,"\int \frac{a+b x}{\sqrt{1+x} \sqrt{1-x+x^2}} \, dx","Int[(a + b*x)/(Sqrt[1 + x]*Sqrt[1 - x + x^2]),x]","\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(a-\left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}+\frac{2 b \left(x^3+1\right)}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} b \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(a-\left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}+\frac{2 b \left(x^3+1\right)}{\sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}-\frac{\sqrt[4]{3} \sqrt{2-\sqrt{3}} b \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{\sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*b*(1 + x^3))/(Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) - (3^(1/4)*Sqrt[2 - Sqrt[3]]*b*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (2*Sqrt[2 + Sqrt[3]]*(a - (1 - Sqrt[3])*b)*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",4,4,25,0.1600,1,"{809, 1878, 218, 1877}"
2304,1,304,0,0.1604417,"\int \frac{a+b x}{(1+x)^{3/2} \left(1-x+x^2\right)^{3/2}} \, dx","Int[(a + b*x)/((1 + x)^(3/2)*(1 - x + x^2)^(3/2)),x]","\frac{2 x (a+b x)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(a-\sqrt{3} b+b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{2 b \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{\sqrt{2-\sqrt{3}} b \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 x (a+b x)}{3 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(a-\sqrt{3} b+b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{2 b \left(x^3+1\right)}{3 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{\sqrt{2-\sqrt{3}} b \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*x*(a + b*x))/(3*Sqrt[1 + x]*Sqrt[1 - x + x^2]) - (2*b*(1 + x^3))/(3*Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) + (Sqrt[2 - Sqrt[3]]*b*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (2*Sqrt[2 + Sqrt[3]]*(a + b - Sqrt[3]*b)*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(3*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",5,5,25,0.2000,1,"{809, 1855, 1878, 218, 1877}"
2305,1,351,0,0.1901582,"\int \frac{a+b x}{(1+x)^{5/2} \left(1-x+x^2\right)^{5/2}} \, dx","Int[(a + b*x)/((1 + x)^(5/2)*(1 - x + x^2)^(5/2)),x]","\frac{2 x (a+b x)}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{2 x (7 a+5 b x)}{27 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(7 a+5 \left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{10 b \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{5 \sqrt{2-\sqrt{3}} b \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}","\frac{2 x (a+b x)}{9 \sqrt{x+1} \sqrt{x^2-x+1} \left(x^3+1\right)}+\frac{2 x (7 a+5 b x)}{27 \sqrt{x+1} \sqrt{x^2-x+1}}+\frac{2 \sqrt{2+\sqrt{3}} \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} \left(7 a+5 \left(1-\sqrt{3}\right) b\right) F\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{27 \sqrt[4]{3} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}-\frac{10 b \left(x^3+1\right)}{27 \sqrt{x+1} \left(x+\sqrt{3}+1\right) \sqrt{x^2-x+1}}+\frac{5 \sqrt{2-\sqrt{3}} b \sqrt{x+1} \sqrt{\frac{x^2-x+1}{\left(x+\sqrt{3}+1\right)^2}} E\left(\sin ^{-1}\left(\frac{x-\sqrt{3}+1}{x+\sqrt{3}+1}\right)|-7-4 \sqrt{3}\right)}{9\ 3^{3/4} \sqrt{\frac{x+1}{\left(x+\sqrt{3}+1\right)^2}} \sqrt{x^2-x+1}}",1,"(2*x*(7*a + 5*b*x))/(27*Sqrt[1 + x]*Sqrt[1 - x + x^2]) + (2*x*(a + b*x))/(9*Sqrt[1 + x]*Sqrt[1 - x + x^2]*(1 + x^3)) - (10*b*(1 + x^3))/(27*Sqrt[1 + x]*(1 + Sqrt[3] + x)*Sqrt[1 - x + x^2]) + (5*Sqrt[2 - Sqrt[3]]*b*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticE[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(9*3^(3/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2]) + (2*Sqrt[2 + Sqrt[3]]*(7*a + 5*(1 - Sqrt[3])*b)*Sqrt[1 + x]*Sqrt[(1 - x + x^2)/(1 + Sqrt[3] + x)^2]*EllipticF[ArcSin[(1 - Sqrt[3] + x)/(1 + Sqrt[3] + x)], -7 - 4*Sqrt[3]])/(27*3^(1/4)*Sqrt[(1 + x)/(1 + Sqrt[3] + x)^2]*Sqrt[1 - x + x^2])","A",6,5,25,0.2000,1,"{809, 1855, 1878, 218, 1877}"
2306,1,133,0,0.2625098,"\int (A+B x) (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{(d+e x)^6 \left(-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2\right)}{6 e^4}-\frac{(d+e x)^5 (B d-A e) \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{(d+e x)^7 (-A c e-b B e+3 B c d)}{7 e^4}+\frac{B c (d+e x)^8}{8 e^4}","-\frac{(d+e x)^6 \left(A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)\right)}{6 e^4}-\frac{(d+e x)^5 (B d-A e) \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{(d+e x)^7 (-A c e-b B e+3 B c d)}{7 e^4}+\frac{B c (d+e x)^8}{8 e^4}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5)/(5*e^4) + ((3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))*(d + e*x)^6)/(6*e^4) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^7)/(7*e^4) + (B*c*(d + e*x)^8)/(8*e^4)","A",2,1,23,0.04348,1,"{771}"
2307,1,133,0,0.1852632,"\int (A+B x) (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{(d+e x)^5 \left(-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2\right)}{5 e^4}-\frac{(d+e x)^4 (B d-A e) \left(a e^2-b d e+c d^2\right)}{4 e^4}-\frac{(d+e x)^6 (-A c e-b B e+3 B c d)}{6 e^4}+\frac{B c (d+e x)^7}{7 e^4}","-\frac{(d+e x)^5 \left(A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)\right)}{5 e^4}-\frac{(d+e x)^4 (B d-A e) \left(a e^2-b d e+c d^2\right)}{4 e^4}-\frac{(d+e x)^6 (-A c e-b B e+3 B c d)}{6 e^4}+\frac{B c (d+e x)^7}{7 e^4}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4)/(4*e^4) + ((3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))*(d + e*x)^5)/(5*e^4) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^6)/(6*e^4) + (B*c*(d + e*x)^7)/(7*e^4)","A",2,1,23,0.04348,1,"{771}"
2308,1,133,0,0.1352908,"\int (A+B x) (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{(d+e x)^4 \left(-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2\right)}{4 e^4}-\frac{(d+e x)^3 (B d-A e) \left(a e^2-b d e+c d^2\right)}{3 e^4}-\frac{(d+e x)^5 (-A c e-b B e+3 B c d)}{5 e^4}+\frac{B c (d+e x)^6}{6 e^4}","-\frac{(d+e x)^4 \left(A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)\right)}{4 e^4}-\frac{(d+e x)^3 (B d-A e) \left(a e^2-b d e+c d^2\right)}{3 e^4}-\frac{(d+e x)^5 (-A c e-b B e+3 B c d)}{5 e^4}+\frac{B c (d+e x)^6}{6 e^4}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3)/(3*e^4) + ((3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))*(d + e*x)^4)/(4*e^4) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^5)/(5*e^4) + (B*c*(d + e*x)^6)/(6*e^4)","A",2,1,23,0.04348,1,"{771}"
2309,1,80,0,0.0814684,"\int (A+B x) (d+e x) \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)*(a + b*x + c*x^2),x]","\frac{1}{3} x^3 (a B e+A b e+A c d+b B d)+\frac{1}{2} x^2 (a A e+a B d+A b d)+a A d x+\frac{1}{4} x^4 (A c e+b B e+B c d)+\frac{1}{5} B c e x^5","\frac{1}{3} x^3 (a B e+A b e+A c d+b B d)+\frac{1}{2} x^2 (a A e+a B d+A b d)+a A d x+\frac{1}{4} x^4 (A c e+b B e+B c d)+\frac{1}{5} B c e x^5",1,"a*A*d*x + ((A*b*d + a*B*d + a*A*e)*x^2)/2 + ((b*B*d + A*c*d + A*b*e + a*B*e)*x^3)/3 + ((B*c*d + b*B*e + A*c*e)*x^4)/4 + (B*c*e*x^5)/5","A",2,1,21,0.04762,1,"{771}"
2310,1,42,0,0.0361817,"\int (A+B x) \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(a + b*x + c*x^2),x]","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4","\frac{1}{2} x^2 (a B+A b)+a A x+\frac{1}{3} x^3 (A c+b B)+\frac{1}{4} B c x^4",1,"a*A*x + ((A*b + a*B)*x^2)/2 + ((b*B + A*c)*x^3)/3 + (B*c*x^4)/4","A",2,1,16,0.06250,1,"{631}"
2311,1,109,0,0.1328879,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{d+e x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x),x]","\frac{x \left(-B e (b d-a e)-A e (c d-b e)+B c d^2\right)}{e^3}-\frac{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{x^2 (-A c e-b B e+B c d)}{2 e^2}+\frac{B c x^3}{3 e}","-\frac{x \left(A e (c d-b e)-B \left(c d^2-e (b d-a e)\right)\right)}{e^3}-\frac{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{x^2 (-A c e-b B e+B c d)}{2 e^2}+\frac{B c x^3}{3 e}",1,"((B*c*d^2 - B*e*(b*d - a*e) - A*e*(c*d - b*e))*x)/e^3 - ((B*c*d - b*B*e - A*c*e)*x^2)/(2*e^2) + (B*c*x^3)/(3*e) - ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)*Log[d + e*x])/e^4","A",2,1,23,0.04348,1,"{771}"
2312,1,114,0,0.1344119,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^2,x]","\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2\right)}{e^4}-\frac{x (-A c e-b B e+2 B c d)}{e^3}+\frac{B c x^2}{2 e^2}","\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}-\frac{\log (d+e x) \left(A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)\right)}{e^4}-\frac{x (-A c e-b B e+2 B c d)}{e^3}+\frac{B c x^2}{2 e^2}",1,"-(((2*B*c*d - b*B*e - A*c*e)*x)/e^3) + (B*c*x^2)/(2*e^2) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2))/(e^4*(d + e*x)) + ((3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))*Log[d + e*x])/e^4","A",2,1,23,0.04348,1,"{771}"
2313,1,119,0,0.132751,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^3,x]","\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}-\frac{-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2}{e^4 (d+e x)}-\frac{\log (d+e x) (-A c e-b B e+3 B c d)}{e^4}+\frac{B c x}{e^3}","\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}+\frac{A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)}{e^4 (d+e x)}-\frac{\log (d+e x) (-A c e-b B e+3 B c d)}{e^4}+\frac{B c x}{e^3}",1,"(B*c*x)/e^3 + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2))/(2*e^4*(d + e*x)^2) - (3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))/(e^4*(d + e*x)) - ((3*B*c*d - b*B*e - A*c*e)*Log[d + e*x])/e^4","A",2,1,23,0.04348,1,"{771}"
2314,1,126,0,0.1201703,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^4,x]","-\frac{-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2}{2 e^4 (d+e x)^2}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^3}+\frac{-A c e-b B e+3 B c d}{e^4 (d+e x)}+\frac{B c \log (d+e x)}{e^4}","\frac{A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)}{2 e^4 (d+e x)^2}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^3}+\frac{-A c e-b B e+3 B c d}{e^4 (d+e x)}+\frac{B c \log (d+e x)}{e^4}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2))/(3*e^4*(d + e*x)^3) - (3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))/(2*e^4*(d + e*x)^2) + (3*B*c*d - b*B*e - A*c*e)/(e^4*(d + e*x)) + (B*c*Log[d + e*x])/e^4","A",2,1,23,0.04348,1,"{771}"
2315,1,131,0,0.1209425,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^5,x]","-\frac{-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2}{3 e^4 (d+e x)^3}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{4 e^4 (d+e x)^4}+\frac{-A c e-b B e+3 B c d}{2 e^4 (d+e x)^2}-\frac{B c}{e^4 (d+e x)}","\frac{A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)}{3 e^4 (d+e x)^3}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{4 e^4 (d+e x)^4}+\frac{-A c e-b B e+3 B c d}{2 e^4 (d+e x)^2}-\frac{B c}{e^4 (d+e x)}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2))/(4*e^4*(d + e*x)^4) - (3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))/(3*e^4*(d + e*x)^3) + (3*B*c*d - b*B*e - A*c*e)/(2*e^4*(d + e*x)^2) - (B*c)/(e^4*(d + e*x))","A",2,1,23,0.04348,1,"{771}"
2316,1,133,0,0.1077434,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^6,x]","-\frac{-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2}{4 e^4 (d+e x)^4}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{5 e^4 (d+e x)^5}+\frac{-A c e-b B e+3 B c d}{3 e^4 (d+e x)^3}-\frac{B c}{2 e^4 (d+e x)^2}","\frac{A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)}{4 e^4 (d+e x)^4}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{5 e^4 (d+e x)^5}+\frac{-A c e-b B e+3 B c d}{3 e^4 (d+e x)^3}-\frac{B c}{2 e^4 (d+e x)^2}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2))/(5*e^4*(d + e*x)^5) - (3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))/(4*e^4*(d + e*x)^4) + (3*B*c*d - b*B*e - A*c*e)/(3*e^4*(d + e*x)^3) - (B*c)/(2*e^4*(d + e*x)^2)","A",2,1,23,0.04348,1,"{771}"
2317,1,133,0,0.1024883,"\int \frac{(A+B x) \left(a+b x+c x^2\right)}{(d+e x)^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2))/(d + e*x)^7,x]","-\frac{-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2}{5 e^4 (d+e x)^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{6 e^4 (d+e x)^6}+\frac{-A c e-b B e+3 B c d}{4 e^4 (d+e x)^4}-\frac{B c}{3 e^4 (d+e x)^3}","\frac{A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)}{5 e^4 (d+e x)^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)}{6 e^4 (d+e x)^6}+\frac{-A c e-b B e+3 B c d}{4 e^4 (d+e x)^4}-\frac{B c}{3 e^4 (d+e x)^3}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2))/(6*e^4*(d + e*x)^6) - (3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))/(5*e^4*(d + e*x)^5) + (3*B*c*d - b*B*e - A*c*e)/(4*e^4*(d + e*x)^4) - (B*c)/(3*e^4*(d + e*x)^3)","A",2,1,23,0.04348,1,"{771}"
2318,1,302,0,0.8218579,"\int (A+B x) (d+e x)^5 \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^5*(a + b*x + c*x^2)^2,x]","-\frac{(d+e x)^9 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{9 e^6}-\frac{(d+e x)^8 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{8 e^6}+\frac{(d+e x)^7 \left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{7 e^6}-\frac{(d+e x)^6 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{6 e^6}-\frac{c (d+e x)^{10} (-A c e-2 b B e+5 B c d)}{10 e^6}+\frac{B c^2 (d+e x)^{11}}{11 e^6}","-\frac{(d+e x)^9 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{9 e^6}-\frac{(d+e x)^8 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{8 e^6}-\frac{(d+e x)^7 \left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{7 e^6}-\frac{(d+e x)^6 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{6 e^6}-\frac{c (d+e x)^{10} (-A c e-2 b B e+5 B c d)}{10 e^6}+\frac{B c^2 (d+e x)^{11}}{11 e^6}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^6)/(6*e^6) + ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^7)/(7*e^6) - ((B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*(d + e*x)^8)/(8*e^6) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))*(d + e*x)^9)/(9*e^6) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^10)/(10*e^6) + (B*c^2*(d + e*x)^11)/(11*e^6)","A",2,1,25,0.04000,1,"{771}"
2319,1,302,0,0.6286018,"\int (A+B x) (d+e x)^4 \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^4*(a + b*x + c*x^2)^2,x]","-\frac{(d+e x)^8 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{8 e^6}-\frac{(d+e x)^7 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{7 e^6}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{6 e^6}-\frac{(d+e x)^5 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6}-\frac{c (d+e x)^9 (-A c e-2 b B e+5 B c d)}{9 e^6}+\frac{B c^2 (d+e x)^{10}}{10 e^6}","-\frac{(d+e x)^8 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{8 e^6}-\frac{(d+e x)^7 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{7 e^6}-\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{6 e^6}-\frac{(d+e x)^5 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6}-\frac{c (d+e x)^9 (-A c e-2 b B e+5 B c d)}{9 e^6}+\frac{B c^2 (d+e x)^{10}}{10 e^6}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^5)/(5*e^6) + ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^6)/(6*e^6) - ((B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*(d + e*x)^7)/(7*e^6) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))*(d + e*x)^8)/(8*e^6) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^9)/(9*e^6) + (B*c^2*(d + e*x)^10)/(10*e^6)","A",2,1,25,0.04000,1,"{771}"
2320,1,302,0,0.4940123,"\int (A+B x) (d+e x)^3 \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2)^2,x]","-\frac{(d+e x)^7 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{7 e^6}-\frac{(d+e x)^6 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{6 e^6}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{5 e^6}-\frac{(d+e x)^4 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6}-\frac{c (d+e x)^8 (-A c e-2 b B e+5 B c d)}{8 e^6}+\frac{B c^2 (d+e x)^9}{9 e^6}","-\frac{(d+e x)^7 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{7 e^6}-\frac{(d+e x)^6 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{6 e^6}-\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{5 e^6}-\frac{(d+e x)^4 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6}-\frac{c (d+e x)^8 (-A c e-2 b B e+5 B c d)}{8 e^6}+\frac{B c^2 (d+e x)^9}{9 e^6}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^4)/(4*e^6) + ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^5)/(5*e^6) - ((B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*(d + e*x)^6)/(6*e^6) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))*(d + e*x)^7)/(7*e^6) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^8)/(8*e^6) + (B*c^2*(d + e*x)^9)/(9*e^6)","A",2,1,25,0.04000,1,"{771}"
2321,1,302,0,0.4426802,"\int (A+B x) (d+e x)^2 \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^2*(a + b*x + c*x^2)^2,x]","-\frac{(d+e x)^6 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{6 e^6}-\frac{(d+e x)^5 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{5 e^6}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{4 e^6}-\frac{(d+e x)^3 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6}-\frac{c (d+e x)^7 (-A c e-2 b B e+5 B c d)}{7 e^6}+\frac{B c^2 (d+e x)^8}{8 e^6}","-\frac{(d+e x)^6 \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{6 e^6}-\frac{(d+e x)^5 \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{5 e^6}-\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{4 e^6}-\frac{(d+e x)^3 (B d-A e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6}-\frac{c (d+e x)^7 (-A c e-2 b B e+5 B c d)}{7 e^6}+\frac{B c^2 (d+e x)^8}{8 e^6}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^3)/(3*e^6) + ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^4)/(4*e^6) - ((B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*(d + e*x)^5)/(5*e^6) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))*(d + e*x)^6)/(6*e^6) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^7)/(7*e^6) + (B*c^2*(d + e*x)^8)/(8*e^6)","A",2,1,25,0.04000,1,"{771}"
2322,1,180,0,0.2973868,"\int (A+B x) (d+e x) \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)*(a + b*x + c*x^2)^2,x]","a^2 A d x+\frac{1}{5} x^5 \left(c (2 a B e+A c d)+2 b c (A e+B d)+b^2 B e\right)+\frac{1}{4} x^4 \left(2 b (a B e+A c d)+2 a c (A e+B d)+b^2 (A e+B d)\right)+\frac{1}{3} x^3 \left(A \left(2 a b e+2 a c d+b^2 d\right)+a B (a e+2 b d)\right)+\frac{1}{2} a x^2 (a A e+a B d+2 A b d)+\frac{1}{6} c x^6 (A c e+2 b B e+B c d)+\frac{1}{7} B c^2 e x^7","a^2 A d x+\frac{1}{5} x^5 \left(c (2 a B e+A c d)+2 b c (A e+B d)+b^2 B e\right)+\frac{1}{4} x^4 \left(2 b (a B e+A c d)+2 a c (A e+B d)+b^2 (A e+B d)\right)+\frac{1}{3} x^3 \left(A \left(2 a b e+2 a c d+b^2 d\right)+a B (a e+2 b d)\right)+\frac{1}{2} a x^2 (a A e+a B d+2 A b d)+\frac{1}{6} c x^6 (A c e+2 b B e+B c d)+\frac{1}{7} B c^2 e x^7",1,"a^2*A*d*x + (a*(2*A*b*d + a*B*d + a*A*e)*x^2)/2 + ((a*B*(2*b*d + a*e) + A*(b^2*d + 2*a*c*d + 2*a*b*e))*x^3)/3 + ((b^2*(B*d + A*e) + 2*a*c*(B*d + A*e) + 2*b*(A*c*d + a*B*e))*x^4)/4 + ((b^2*B*e + 2*b*c*(B*d + A*e) + c*(A*c*d + 2*a*B*e))*x^5)/5 + (c*(B*c*d + 2*b*B*e + A*c*e)*x^6)/6 + (B*c^2*e*x^7)/7","A",2,1,23,0.04348,1,"{771}"
2323,1,96,0,0.0928615,"\int (A+B x) \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^2,x]","a^2 A x+\frac{1}{4} x^4 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{3} x^3 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{6} B c^2 x^6","a^2 A x+\frac{1}{4} x^4 \left(2 a B c+2 A b c+b^2 B\right)+\frac{1}{3} x^3 \left(A \left(2 a c+b^2\right)+2 a b B\right)+\frac{1}{2} a x^2 (a B+2 A b)+\frac{1}{5} c x^5 (A c+2 b B)+\frac{1}{6} B c^2 x^6",1,"a^2*A*x + (a*(2*A*b + a*B)*x^2)/2 + ((2*a*b*B + A*(b^2 + 2*a*c))*x^3)/3 + ((b^2*B + 2*A*b*c + 2*a*B*c)*x^4)/4 + (c*(2*b*B + A*c)*x^5)/5 + (B*c^2*x^6)/6","A",2,1,18,0.05556,1,"{631}"
2324,1,257,0,0.5378281,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{d+e x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x),x]","-\frac{x^3 \left(A c e (c d-2 b e)-B \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{3 e^3}-\frac{x^2 \left(B (c d-b e) \left(c d^2-e (b d-2 a e)\right)-A e \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{2 e^4}-\frac{x \left(A e (c d-b e) \left(c d^2-e (b d-2 a e)\right)-B \left(c d^2-e (b d-a e)\right)^2\right)}{e^5}-\frac{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^6}-\frac{c x^4 (-A c e-2 b B e+B c d)}{4 e^2}+\frac{B c^2 x^5}{5 e}","-\frac{x^3 \left(A c e (c d-2 b e)-B \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{3 e^3}-\frac{x^2 \left(B (c d-b e) \left(c d^2-e (b d-2 a e)\right)-A e \left(-2 c e (b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{2 e^4}-\frac{x \left(A e (c d-b e) \left(c d^2-e (b d-2 a e)\right)-B \left(c d^2-e (b d-a e)\right)^2\right)}{e^5}-\frac{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^2}{e^6}-\frac{c x^4 (-A c e-2 b B e+B c d)}{4 e^2}+\frac{B c^2 x^5}{5 e}",1,"-(((A*e*(c*d - b*e)*(c*d^2 - e*(b*d - 2*a*e)) - B*(c*d^2 - e*(b*d - a*e))^2)*x)/e^5) - ((B*(c*d - b*e)*(c*d^2 - e*(b*d - 2*a*e)) - A*e*(c^2*d^2 + b^2*e^2 - 2*c*e*(b*d - a*e)))*x^2)/(2*e^4) - ((A*c*e*(c*d - 2*b*e) - B*(c^2*d^2 + b^2*e^2 - 2*c*e*(b*d - a*e)))*x^3)/(3*e^3) - (c*(B*c*d - 2*b*B*e - A*c*e)*x^4)/(4*e^2) + (B*c^2*x^5)/(5*e) - ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2*Log[d + e*x])/e^6","A",2,1,25,0.04000,1,"{771}"
2325,1,264,0,0.4904386,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^2,x]","-\frac{x^2 \left(2 A c e (c d-b e)-B \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)\right)}{2 e^4}-\frac{x \left(2 B (2 c d-b e) \left(c d^2-e (b d-a e)\right)-A e \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)\right)}{e^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{e^6 (d+e x)}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{e^6}-\frac{c x^3 (-A c e-2 b B e+2 B c d)}{3 e^3}+\frac{B c^2 x^4}{4 e^2}","-\frac{x^2 \left(2 A c e (c d-b e)-B \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)\right)}{2 e^4}-\frac{x \left(2 B (2 c d-b e) \left(c d^2-e (b d-a e)\right)-A e \left(-2 c e (2 b d-a e)+b^2 e^2+3 c^2 d^2\right)\right)}{e^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{e^6 (d+e x)}-\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{e^6}-\frac{c x^3 (-A c e-2 b B e+2 B c d)}{3 e^3}+\frac{B c^2 x^4}{4 e^2}",1,"-(((2*B*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e)) - A*e*(3*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d - a*e)))*x)/e^5) - ((2*A*c*e*(c*d - b*e) - B*(3*c^2*d^2 + b^2*e^2 - 2*c*e*(2*b*d - a*e)))*x^2)/(2*e^4) - (c*(2*B*c*d - 2*b*B*e - A*c*e)*x^3)/(3*e^3) + (B*c^2*x^4)/(4*e^2) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(e^6*(d + e*x)) + ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e))*Log[d + e*x])/e^6","A",2,1,25,0.04000,1,"{771}"
2326,1,280,0,0.4395046,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^3,x]","-\frac{x \left(A c e (3 c d-2 b e)-B \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{e^5}-\frac{\log (d+e x) \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{e^6}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{e^6 (d+e x)}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{2 e^6 (d+e x)^2}-\frac{c x^2 (-A c e-2 b B e+3 B c d)}{2 e^4}+\frac{B c^2 x^3}{3 e^3}","-\frac{x \left(A c e (3 c d-2 b e)-B \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{e^5}-\frac{\log (d+e x) \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{e^6}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{e^6 (d+e x)}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{2 e^6 (d+e x)^2}-\frac{c x^2 (-A c e-2 b B e+3 B c d)}{2 e^4}+\frac{B c^2 x^3}{3 e^3}",1,"-(((A*c*e*(3*c*d - 2*b*e) - B*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*x)/e^5) - (c*(3*B*c*d - 2*b*B*e - A*c*e)*x^2)/(2*e^4) + (B*c^2*x^3)/(3*e^3) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(2*e^6*(d + e*x)^2) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(e^6*(d + e*x)) - ((B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*Log[d + e*x])/e^6","A",2,1,25,0.04000,1,"{771}"
2327,1,284,0,0.4092314,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^4,x]","\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^6 (d+e x)}-\frac{\log (d+e x) \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{e^6}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{2 e^6 (d+e x)^2}-\frac{c x (-A c e-2 b B e+4 B c d)}{e^5}+\frac{B c^2 x^2}{2 e^4}","\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{e^6 (d+e x)}-\frac{\log (d+e x) \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{e^6}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{3 e^6 (d+e x)^3}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{2 e^6 (d+e x)^2}-\frac{c x (-A c e-2 b B e+4 B c d)}{e^5}+\frac{B c^2 x^2}{2 e^4}",1,"-((c*(4*B*c*d - 2*b*B*e - A*c*e)*x)/e^5) + (B*c^2*x^2)/(2*e^4) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(3*e^6*(d + e*x)^3) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(2*e^6*(d + e*x)^2) + (B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(e^6*(d + e*x)) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))*Log[d + e*x])/e^6","A",2,1,25,0.04000,1,"{771}"
2328,1,287,0,0.361698,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^5,x]","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{e^6 (d+e x)}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{2 e^6 (d+e x)^2}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{3 e^6 (d+e x)^3}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6 (d+e x)^4}-\frac{c \log (d+e x) (-A c e-2 b B e+5 B c d)}{e^6}+\frac{B c^2 x}{e^5}","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{e^6 (d+e x)}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{2 e^6 (d+e x)^2}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{3 e^6 (d+e x)^3}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{4 e^6 (d+e x)^4}-\frac{c \log (d+e x) (-A c e-2 b B e+5 B c d)}{e^6}+\frac{B c^2 x}{e^5}",1,"(B*c^2*x)/e^5 + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(4*e^6*(d + e*x)^4) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(3*e^6*(d + e*x)^3) + (B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(2*e^6*(d + e*x)^2) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))/(e^6*(d + e*x)) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*Log[d + e*x])/e^6","A",2,1,25,0.04000,1,"{771}"
2329,1,295,0,0.3442829,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^6,x]","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{3 e^6 (d+e x)^3}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{4 e^6 (d+e x)^4}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6 (d+e x)^5}+\frac{c (-A c e-2 b B e+5 B c d)}{e^6 (d+e x)}+\frac{B c^2 \log (d+e x)}{e^6}","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{2 e^6 (d+e x)^2}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{4 e^6 (d+e x)^4}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{5 e^6 (d+e x)^5}+\frac{c (-A c e-2 b B e+5 B c d)}{e^6 (d+e x)}+\frac{B c^2 \log (d+e x)}{e^6}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(5*e^6*(d + e*x)^5) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(4*e^6*(d + e*x)^4) + (B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(3*e^6*(d + e*x)^3) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))/(2*e^6*(d + e*x)^2) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(e^6*(d + e*x)) + (B*c^2*Log[d + e*x])/e^6","A",2,1,25,0.04000,1,"{771}"
2330,1,300,0,0.322769,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^7,x]","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{4 e^6 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{5 e^6 (d+e x)^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{6 e^6 (d+e x)^6}+\frac{c (-A c e-2 b B e+5 B c d)}{2 e^6 (d+e x)^2}-\frac{B c^2}{e^6 (d+e x)}","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{3 e^6 (d+e x)^3}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{4 e^6 (d+e x)^4}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{5 e^6 (d+e x)^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{6 e^6 (d+e x)^6}+\frac{c (-A c e-2 b B e+5 B c d)}{2 e^6 (d+e x)^2}-\frac{B c^2}{e^6 (d+e x)}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(6*e^6*(d + e*x)^6) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(5*e^6*(d + e*x)^5) + (B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(4*e^6*(d + e*x)^4) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))/(3*e^6*(d + e*x)^3) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(2*e^6*(d + e*x)^2) - (B*c^2)/(e^6*(d + e*x))","A",2,1,25,0.04000,1,"{771}"
2331,1,302,0,0.31928,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^8,x]","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{4 e^6 (d+e x)^4}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^6 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{6 e^6 (d+e x)^6}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{7 e^6 (d+e x)^7}+\frac{c (-A c e-2 b B e+5 B c d)}{3 e^6 (d+e x)^3}-\frac{B c^2}{2 e^6 (d+e x)^2}","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{4 e^6 (d+e x)^4}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{5 e^6 (d+e x)^5}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{6 e^6 (d+e x)^6}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{7 e^6 (d+e x)^7}+\frac{c (-A c e-2 b B e+5 B c d)}{3 e^6 (d+e x)^3}-\frac{B c^2}{2 e^6 (d+e x)^2}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(7*e^6*(d + e*x)^7) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(6*e^6*(d + e*x)^6) + (B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(5*e^6*(d + e*x)^5) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))/(4*e^6*(d + e*x)^4) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(3*e^6*(d + e*x)^3) - (B*c^2)/(2*e^6*(d + e*x)^2)","A",2,1,25,0.04000,1,"{771}"
2332,1,302,0,0.3167391,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^2}{(d+e x)^9} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^2)/(d + e*x)^9,x]","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^6 (d+e x)^5}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{6 e^6 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{7 e^6 (d+e x)^7}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{8 e^6 (d+e x)^8}+\frac{c (-A c e-2 b B e+5 B c d)}{4 e^6 (d+e x)^4}-\frac{B c^2}{3 e^6 (d+e x)^3}","\frac{2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)}{5 e^6 (d+e x)^5}+\frac{B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)}{6 e^6 (d+e x)^6}+\frac{\left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{7 e^6 (d+e x)^7}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^2}{8 e^6 (d+e x)^8}+\frac{c (-A c e-2 b B e+5 B c d)}{4 e^6 (d+e x)^4}-\frac{B c^2}{3 e^6 (d+e x)^3}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2)/(8*e^6*(d + e*x)^8) - ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e)))/(7*e^6*(d + e*x)^7) + (B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))/(6*e^6*(d + e*x)^6) + (2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))/(5*e^6*(d + e*x)^5) + (c*(5*B*c*d - 2*b*B*e - A*c*e))/(4*e^6*(d + e*x)^4) - (B*c^2)/(3*e^6*(d + e*x)^3)","A",2,1,25,0.04000,1,"{771}"
2333,1,553,0,1.7465863,"\int (A+B x) (d+e x)^5 \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^5*(a + b*x + c*x^2)^3,x]","-\frac{(d+e x)^9 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{9 e^8}-\frac{3 c (d+e x)^{11} \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{11 e^8}-\frac{(d+e x)^{10} \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{10 e^8}-\frac{3 (d+e x)^8 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{8 e^8}+\frac{(d+e x)^7 \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{7 e^8}-\frac{(d+e x)^6 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{6 e^8}-\frac{c^2 (d+e x)^{12} (-A c e-3 b B e+7 B c d)}{12 e^8}+\frac{B c^3 (d+e x)^{13}}{13 e^8}","-\frac{(d+e x)^9 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{9 e^8}-\frac{3 c (d+e x)^{11} \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{11 e^8}-\frac{(d+e x)^{10} \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{10 e^8}-\frac{3 (d+e x)^8 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{8 e^8}-\frac{(d+e x)^7 \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{7 e^8}-\frac{(d+e x)^6 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{6 e^8}-\frac{c^2 (d+e x)^{12} (-A c e-3 b B e+7 B c d)}{12 e^8}+\frac{B c^3 (d+e x)^{13}}{13 e^8}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^6)/(6*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^7)/(7*e^8) - (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^8)/(8*e^8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^9)/(9*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^10)/(10*e^8) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^11)/(11*e^8) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^12)/(12*e^8) + (B*c^3*(d + e*x)^13)/(13*e^8)","A",2,1,25,0.04000,1,"{771}"
2334,1,553,0,1.3781458,"\int (A+B x) (d+e x)^4 \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^4*(a + b*x + c*x^2)^3,x]","-\frac{(d+e x)^8 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{8 e^8}-\frac{3 c (d+e x)^{10} \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{10 e^8}-\frac{(d+e x)^9 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{9 e^8}-\frac{3 (d+e x)^7 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{7 e^8}+\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{6 e^8}-\frac{(d+e x)^5 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8}-\frac{c^2 (d+e x)^{11} (-A c e-3 b B e+7 B c d)}{11 e^8}+\frac{B c^3 (d+e x)^{12}}{12 e^8}","-\frac{(d+e x)^8 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{8 e^8}-\frac{3 c (d+e x)^{10} \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{10 e^8}-\frac{(d+e x)^9 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{9 e^8}-\frac{3 (d+e x)^7 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{7 e^8}-\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{6 e^8}-\frac{(d+e x)^5 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8}-\frac{c^2 (d+e x)^{11} (-A c e-3 b B e+7 B c d)}{11 e^8}+\frac{B c^3 (d+e x)^{12}}{12 e^8}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^5)/(5*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^6)/(6*e^8) - (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^7)/(7*e^8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^8)/(8*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^9)/(9*e^8) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^10)/(10*e^8) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^11)/(11*e^8) + (B*c^3*(d + e*x)^12)/(12*e^8)","A",2,1,25,0.04000,1,"{771}"
2335,1,553,0,1.1099707,"\int (A+B x) (d+e x)^3 \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^3*(a + b*x + c*x^2)^3,x]","-\frac{(d+e x)^7 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{7 e^8}-\frac{c (d+e x)^9 \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{3 e^8}-\frac{(d+e x)^8 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{8 e^8}-\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8}+\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{5 e^8}-\frac{(d+e x)^4 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8}-\frac{c^2 (d+e x)^{10} (-A c e-3 b B e+7 B c d)}{10 e^8}+\frac{B c^3 (d+e x)^{11}}{11 e^8}","-\frac{(d+e x)^7 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{7 e^8}-\frac{c (d+e x)^9 \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{3 e^8}-\frac{(d+e x)^8 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{8 e^8}-\frac{(d+e x)^6 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8}-\frac{(d+e x)^5 \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{5 e^8}-\frac{(d+e x)^4 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8}-\frac{c^2 (d+e x)^{10} (-A c e-3 b B e+7 B c d)}{10 e^8}+\frac{B c^3 (d+e x)^{11}}{11 e^8}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^4)/(4*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^5)/(5*e^8) - ((c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^6)/(2*e^8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^7)/(7*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^8)/(8*e^8) - (c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^9)/(3*e^8) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^10)/(10*e^8) + (B*c^3*(d + e*x)^11)/(11*e^8)","A",2,1,25,0.04000,1,"{771}"
2336,1,553,0,0.8631528,"\int (A+B x) (d+e x)^2 \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^2*(a + b*x + c*x^2)^3,x]","-\frac{(d+e x)^6 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{6 e^8}-\frac{3 c (d+e x)^8 \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{8 e^8}-\frac{(d+e x)^7 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{7 e^8}-\frac{3 (d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{5 e^8}+\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{4 e^8}-\frac{(d+e x)^3 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8}-\frac{c^2 (d+e x)^9 (-A c e-3 b B e+7 B c d)}{9 e^8}+\frac{B c^3 (d+e x)^{10}}{10 e^8}","-\frac{(d+e x)^6 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{6 e^8}-\frac{3 c (d+e x)^8 \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{8 e^8}-\frac{(d+e x)^7 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{7 e^8}-\frac{3 (d+e x)^5 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{5 e^8}-\frac{(d+e x)^4 \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{4 e^8}-\frac{(d+e x)^3 (B d-A e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8}-\frac{c^2 (d+e x)^9 (-A c e-3 b B e+7 B c d)}{9 e^8}+\frac{B c^3 (d+e x)^{10}}{10 e^8}",1,"-((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^3)/(3*e^8) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^4)/(4*e^8) - (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^5)/(5*e^8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^6)/(6*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^7)/(7*e^8) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^8)/(8*e^8) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^9)/(9*e^8) + (B*c^3*(d + e*x)^10)/(10*e^8)","A",2,1,25,0.04000,1,"{771}"
2337,1,310,0,0.63988,"\int (A+B x) (d+e x) \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{4} x^4 \left(A \left(3 a^2 c e+3 a b^2 e+6 a b c d+b^3 d\right)+3 a B \left(a b e+a c d+b^2 d\right)\right)+\frac{1}{2} a^2 x^2 (a A e+a B d+3 A b d)+a^3 A d x+\frac{1}{6} x^6 \left(3 b c (2 a B e+A c d)+3 a c^2 (A e+B d)+3 b^2 c (A e+B d)+b^3 B e\right)+\frac{1}{7} c x^7 \left(c (3 a B e+A c d)+3 b c (A e+B d)+3 b^2 B e\right)+\frac{1}{5} x^5 \left(3 b^2 (a B e+A c d)+6 a b c (A e+B d)+3 a c (a B e+A c d)+b^3 (A e+B d)\right)+\frac{1}{3} a x^3 \left(3 A \left(a b e+a c d+b^2 d\right)+a B (a e+3 b d)\right)+\frac{1}{8} c^2 x^8 (A c e+3 b B e+B c d)+\frac{1}{9} B c^3 e x^9","\frac{1}{4} x^4 \left(A \left(3 a^2 c e+3 a b^2 e+6 a b c d+b^3 d\right)+3 a B \left(a b e+a c d+b^2 d\right)\right)+\frac{1}{2} a^2 x^2 (a A e+a B d+3 A b d)+a^3 A d x+\frac{1}{6} x^6 \left(3 b c (2 a B e+A c d)+3 a c^2 (A e+B d)+3 b^2 c (A e+B d)+b^3 B e\right)+\frac{1}{7} c x^7 \left(c (3 a B e+A c d)+3 b c (A e+B d)+3 b^2 B e\right)+\frac{1}{5} x^5 \left(3 b^2 (a B e+A c d)+6 a b c (A e+B d)+3 a c (a B e+A c d)+b^3 (A e+B d)\right)+\frac{1}{3} a x^3 \left(3 A \left(a b e+a c d+b^2 d\right)+a B (a e+3 b d)\right)+\frac{1}{8} c^2 x^8 (A c e+3 b B e+B c d)+\frac{1}{9} B c^3 e x^9",1,"a^3*A*d*x + (a^2*(3*A*b*d + a*B*d + a*A*e)*x^2)/2 + (a*(a*B*(3*b*d + a*e) + 3*A*(b^2*d + a*c*d + a*b*e))*x^3)/3 + ((3*a*B*(b^2*d + a*c*d + a*b*e) + A*(b^3*d + 6*a*b*c*d + 3*a*b^2*e + 3*a^2*c*e))*x^4)/4 + ((b^3*(B*d + A*e) + 6*a*b*c*(B*d + A*e) + 3*b^2*(A*c*d + a*B*e) + 3*a*c*(A*c*d + a*B*e))*x^5)/5 + ((b^3*B*e + 3*b^2*c*(B*d + A*e) + 3*a*c^2*(B*d + A*e) + 3*b*c*(A*c*d + 2*a*B*e))*x^6)/6 + (c*(3*b^2*B*e + 3*b*c*(B*d + A*e) + c*(A*c*d + 3*a*B*e))*x^7)/7 + (c^2*(B*c*d + 3*b*B*e + A*c*e)*x^8)/8 + (B*c^3*e*x^9)/9","A",2,1,23,0.04348,1,"{771}"
2338,1,158,0,0.2062022,"\int (A+B x) \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(a + b*x + c*x^2)^3,x]","\frac{1}{2} a^2 x^2 (a B+3 A b)+a^3 A x+\frac{1}{5} x^5 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{8} B c^3 x^8","\frac{1}{2} a^2 x^2 (a B+3 A b)+a^3 A x+\frac{1}{5} x^5 \left(3 a A c^2+6 a b B c+3 A b^2 c+b^3 B\right)+\frac{1}{2} c x^6 \left(a B c+A b c+b^2 B\right)+\frac{1}{4} x^4 \left(A \left(6 a b c+b^3\right)+3 a B \left(a c+b^2\right)\right)+a x^3 \left(A \left(a c+b^2\right)+a b B\right)+\frac{1}{7} c^2 x^7 (A c+3 b B)+\frac{1}{8} B c^3 x^8",1,"a^3*A*x + (a^2*(3*A*b + a*B)*x^2)/2 + a*(a*b*B + A*(b^2 + a*c))*x^3 + ((3*a*B*(b^2 + a*c) + A*(b^3 + 6*a*b*c))*x^4)/4 + ((b^3*B + 3*A*b^2*c + 6*a*b*B*c + 3*a*A*c^2)*x^5)/5 + (c*(b^2*B + A*b*c + a*B*c)*x^6)/2 + (c^2*(3*b*B + A*c)*x^7)/7 + (B*c^3*x^8)/8","A",2,1,18,0.05556,1,"{631}"
2339,1,541,0,1.1947417,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{d+e x} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x),x]","-\frac{(d+e x)^3 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{3 e^8}-\frac{3 c (d+e x)^5 \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{5 e^8}-\frac{(d+e x)^4 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{4 e^8}-\frac{3 (d+e x)^2 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8}+\frac{x \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{e^7}-\frac{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^8}-\frac{c^2 (d+e x)^6 (-A c e-3 b B e+7 B c d)}{6 e^8}+\frac{B c^3 (d+e x)^7}{7 e^8}","-\frac{(d+e x)^3 \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{3 e^8}-\frac{3 c (d+e x)^5 \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{5 e^8}-\frac{(d+e x)^4 \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{4 e^8}-\frac{3 (d+e x)^2 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8}-\frac{x \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{e^7}-\frac{(B d-A e) \log (d+e x) \left(a e^2-b d e+c d^2\right)^3}{e^8}-\frac{c^2 (d+e x)^6 (-A c e-3 b B e+7 B c d)}{6 e^8}+\frac{B c^3 (d+e x)^7}{7 e^8}",1,"((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*x)/e^7 - (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^2)/(2*e^8) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^3)/(3*e^8) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^4)/(4*e^8) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^5)/(5*e^8) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^6)/(6*e^8) + (B*c^3*(d + e*x)^7)/(7*e^8) - ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2340,1,522,0,1.0934416,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^2} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^2,x]","-\frac{x^2 \left(A e (c d-b e) \left(-c e (5 b d-6 a e)+b^2 e^2+4 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-b^2 e^3 (2 b d-3 a e)-3 c^2 d^2 e (4 b d-3 a e)+5 c^3 d^4\right)\right)}{2 e^6}-\frac{x \left(3 B (2 c d-b e) \left(c d^2-e (b d-a e)\right)^2-A e \left(3 c e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-b^2 e^3 (2 b d-3 a e)-3 c^2 d^2 e (4 b d-3 a e)+5 c^3 d^4\right)\right)}{e^7}-\frac{c x^4 \left(A c e (2 c d-3 b e)-3 B \left(-c e (2 b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{4 e^4}-\frac{x^3 \left(B (c d-b e) \left(-c e (5 b d-6 a e)+b^2 e^2+4 c^2 d^2\right)-3 A c e \left(-c e (2 b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{3 e^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{e^8 (d+e x)}+\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{e^8}-\frac{c^2 x^5 (-A c e-3 b B e+2 B c d)}{5 e^3}+\frac{B c^3 x^6}{6 e^2}","-\frac{x^2 \left(A e (c d-b e) \left(-c e (5 b d-6 a e)+b^2 e^2+4 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-b^2 e^3 (2 b d-3 a e)-3 c^2 d^2 e (4 b d-3 a e)+5 c^3 d^4\right)\right)}{2 e^6}-\frac{x \left(3 B (2 c d-b e) \left(c d^2-e (b d-a e)\right)^2-A e \left(3 c e^2 \left(a^2 e^2-4 a b d e+3 b^2 d^2\right)-b^2 e^3 (2 b d-3 a e)-3 c^2 d^2 e (4 b d-3 a e)+5 c^3 d^4\right)\right)}{e^7}-\frac{c x^4 \left(A c e (2 c d-3 b e)-3 B \left(-c e (2 b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{4 e^4}-\frac{x^3 \left(B (c d-b e) \left(-c e (5 b d-6 a e)+b^2 e^2+4 c^2 d^2\right)-3 A c e \left(-c e (2 b d-a e)+b^2 e^2+c^2 d^2\right)\right)}{3 e^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{e^8 (d+e x)}-\frac{\log (d+e x) \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{e^8}-\frac{c^2 x^5 (-A c e-3 b B e+2 B c d)}{5 e^3}+\frac{B c^3 x^6}{6 e^2}",1,"-(((3*B*(2*c*d - b*e)*(c*d^2 - e*(b*d - a*e))^2 - A*e*(5*c^3*d^4 - b^2*e^3*(2*b*d - 3*a*e) - 3*c^2*d^2*e*(4*b*d - 3*a*e) + 3*c*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2)))*x)/e^7) - ((A*e*(c*d - b*e)*(4*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - 6*a*e)) - B*(5*c^3*d^4 - b^2*e^3*(2*b*d - 3*a*e) - 3*c^2*d^2*e*(4*b*d - 3*a*e) + 3*c*e^2*(3*b^2*d^2 - 4*a*b*d*e + a^2*e^2)))*x^2)/(2*e^6) - ((B*(c*d - b*e)*(4*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - 6*a*e)) - 3*A*c*e*(c^2*d^2 + b^2*e^2 - c*e*(2*b*d - a*e)))*x^3)/(3*e^5) - (c*(A*c*e*(2*c*d - 3*b*e) - 3*B*(c^2*d^2 + b^2*e^2 - c*e*(2*b*d - a*e)))*x^4)/(4*e^4) - (c^2*(2*B*c*d - 3*b*B*e - A*c*e)*x^5)/(5*e^3) + (B*c^3*x^6)/(6*e^2) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(e^8*(d + e*x)) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2341,1,530,0,1.0848831,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^3} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^3,x]","-\frac{x \left(A e \left(-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right)-3 B \left(c e^2 \left(a^2 e^2-6 a b d e+6 b^2 d^2\right)-b^2 e^3 (b d-a e)-2 c^2 d^2 e (5 b d-3 a e)+5 c^3 d^4\right)\right)}{e^7}-\frac{c x^3 \left(A c e (c d-b e)-B \left(-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right)\right)}{e^5}-\frac{x^2 \left(B \left(-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right)-3 A c e \left(-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right)\right)}{2 e^6}-\frac{3 \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{e^8 (d+e x)}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{2 e^8 (d+e x)^2}-\frac{c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}+\frac{B c^3 x^5}{5 e^3}","-\frac{x \left(A e \left(-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right)-3 B \left(c e^2 \left(a^2 e^2-6 a b d e+6 b^2 d^2\right)-b^2 e^3 (b d-a e)-2 c^2 d^2 e (5 b d-3 a e)+5 c^3 d^4\right)\right)}{e^7}-\frac{c x^3 \left(A c e (c d-b e)-B \left(-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right)\right)}{e^5}-\frac{x^2 \left(B \left(-9 c^2 d e (2 b d-a e)+3 b c e^2 (3 b d-2 a e)-b^3 e^3+10 c^3 d^3\right)-3 A c e \left(-c e (3 b d-a e)+b^2 e^2+2 c^2 d^2\right)\right)}{2 e^6}-\frac{3 \log (d+e x) \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{e^8 (d+e x)}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{2 e^8 (d+e x)^2}-\frac{c^2 x^4 (-A c e-3 b B e+3 B c d)}{4 e^4}+\frac{B c^3 x^5}{5 e^3}",1,"-(((A*e*(10*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(3*b*d - 2*a*e) - 9*c^2*d*e*(2*b*d - a*e)) - 3*B*(5*c^3*d^4 - 2*c^2*d^2*e*(5*b*d - 3*a*e) - b^2*e^3*(b*d - a*e) + c*e^2*(6*b^2*d^2 - 6*a*b*d*e + a^2*e^2)))*x)/e^7) - ((B*(10*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(3*b*d - 2*a*e) - 9*c^2*d*e*(2*b*d - a*e)) - 3*A*c*e*(2*c^2*d^2 + b^2*e^2 - c*e*(3*b*d - a*e)))*x^2)/(2*e^6) - (c*(A*c*e*(c*d - b*e) - B*(2*c^2*d^2 + b^2*e^2 - c*e*(3*b*d - a*e)))*x^3)/e^5 - (c^2*(3*B*c*d - 3*b*B*e - A*c*e)*x^4)/(4*e^4) + (B*c^3*x^5)/(5*e^3) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(2*e^8*(d + e*x)^2) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(e^8*(d + e*x)) - (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2342,1,519,0,0.9901819,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^4} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^4,x]","-\frac{\log (d+e x) \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{e^8}-\frac{c x^2 \left(A c e (4 c d-3 b e)-B \left(-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right)\right)}{2 e^6}-\frac{x \left(B (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-A c e \left(-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right)\right)}{e^7}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (d+e x)}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{2 e^8 (d+e x)^2}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8 (d+e x)^3}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}+\frac{B c^3 x^4}{4 e^4}","-\frac{\log (d+e x) \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{e^8}-\frac{c x^2 \left(A c e (4 c d-3 b e)-B \left(-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right)\right)}{2 e^6}-\frac{x \left(B (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-A c e \left(-3 c e (4 b d-a e)+3 b^2 e^2+10 c^2 d^2\right)\right)}{e^7}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (d+e x)}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{2 e^8 (d+e x)^2}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{3 e^8 (d+e x)^3}-\frac{c^2 x^3 (-A c e-3 b B e+4 B c d)}{3 e^5}+\frac{B c^3 x^4}{4 e^4}",1,"-(((B*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - A*c*e*(10*c^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e)))*x)/e^7) - (c*(A*c*e*(4*c*d - 3*b*e) - B*(10*c^2*d^2 + 3*b^2*e^2 - 3*c*e*(4*b*d - a*e)))*x^2)/(2*e^6) - (c^2*(4*B*c*d - 3*b*B*e - A*c*e)*x^3)/(3*e^5) + (B*c^3*x^4)/(4*e^4) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(3*e^8*(d + e*x)^3) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(2*e^8*(d + e*x)^2) + (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(e^8*(d + e*x)) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2343,1,531,0,0.943193,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^5} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^5,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{e^8 (d+e x)}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8 (d+e x)^2}-\frac{c x \left(A c e (5 c d-3 b e)-3 B \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^7}-\frac{\log (d+e x) \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{3 e^8 (d+e x)^3}-\frac{c^2 x^2 (-A c e-3 b B e+5 B c d)}{2 e^6}+\frac{B c^3 x^3}{3 e^5}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{e^8 (d+e x)}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8 (d+e x)^2}-\frac{c x \left(A c e (5 c d-3 b e)-3 B \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^7}-\frac{\log (d+e x) \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{4 e^8 (d+e x)^4}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{3 e^8 (d+e x)^3}-\frac{c^2 x^2 (-A c e-3 b B e+5 B c d)}{2 e^6}+\frac{B c^3 x^3}{3 e^5}",1,"-((c*(A*c*e*(5*c*d - 3*b*e) - 3*B*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*x)/e^7) - (c^2*(5*B*c*d - 3*b*B*e - A*c*e)*x^2)/(2*e^6) + (B*c^3*x^3)/(3*e^5) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(4*e^8*(d + e*x)^4) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(3*e^8*(d + e*x)^3) + (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(2*e^8*(d + e*x)^2) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(e^8*(d + e*x)) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2344,1,532,0,0.9014475,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^6} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^6,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{2 e^8 (d+e x)^2}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^8 (d+e x)}+\frac{\left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (d+e x)^3}-\frac{3 c \log (d+e x) \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{4 e^8 (d+e x)^4}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8 (d+e x)^5}-\frac{c^2 x (-A c e-3 b B e+6 B c d)}{e^7}+\frac{B c^3 x^2}{2 e^6}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{2 e^8 (d+e x)^2}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{e^8 (d+e x)}+\frac{\left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (d+e x)^3}-\frac{3 c \log (d+e x) \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{4 e^8 (d+e x)^4}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{5 e^8 (d+e x)^5}-\frac{c^2 x (-A c e-3 b B e+6 B c d)}{e^7}+\frac{B c^3 x^2}{2 e^6}",1,"-((c^2*(6*B*c*d - 3*b*B*e - A*c*e)*x)/e^7) + (B*c^3*x^2)/(2*e^6) + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(5*e^8*(d + e*x)^5) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(4*e^8*(d + e*x)^4) + ((c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(e^8*(d + e*x)^3) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(2*e^8*(d + e*x)^2) + (B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(e^8*(d + e*x)) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2345,1,539,0,0.8104694,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^7} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^7,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{3 e^8 (d+e x)^3}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8 (d+e x)}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^8 (d+e x)^2}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{4 e^8 (d+e x)^4}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{5 e^8 (d+e x)^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{6 e^8 (d+e x)^6}-\frac{c^2 \log (d+e x) (-A c e-3 b B e+7 B c d)}{e^8}+\frac{B c^3 x}{e^7}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{3 e^8 (d+e x)^3}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8 (d+e x)}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{2 e^8 (d+e x)^2}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{4 e^8 (d+e x)^4}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{5 e^8 (d+e x)^5}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{6 e^8 (d+e x)^6}-\frac{c^2 \log (d+e x) (-A c e-3 b B e+7 B c d)}{e^8}+\frac{B c^3 x}{e^7}",1,"(B*c^3*x)/e^7 + ((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(6*e^8*(d + e*x)^6) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(5*e^8*(d + e*x)^5) + (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(4*e^8*(d + e*x)^4) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(3*e^8*(d + e*x)^3) + (B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(2*e^8*(d + e*x)^2) + (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e))))/(e^8*(d + e*x)) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2346,1,546,0,0.767961,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^8} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^8,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{4 e^8 (d+e x)^4}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{2 e^8 (d+e x)^2}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^8 (d+e x)^3}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{5 e^8 (d+e x)^5}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{6 e^8 (d+e x)^6}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{7 e^8 (d+e x)^7}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{e^8 (d+e x)}+\frac{B c^3 \log (d+e x)}{e^8}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{4 e^8 (d+e x)^4}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{2 e^8 (d+e x)^2}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{3 e^8 (d+e x)^3}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{5 e^8 (d+e x)^5}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{6 e^8 (d+e x)^6}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{7 e^8 (d+e x)^7}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{e^8 (d+e x)}+\frac{B c^3 \log (d+e x)}{e^8}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(7*e^8*(d + e*x)^7) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(6*e^8*(d + e*x)^6) + (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(5*e^8*(d + e*x)^5) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(4*e^8*(d + e*x)^4) + (B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(3*e^8*(d + e*x)^3) + (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e))))/(2*e^8*(d + e*x)^2) + (c^2*(7*B*c*d - 3*b*B*e - A*c*e))/(e^8*(d + e*x)) + (B*c^3*Log[d + e*x])/e^8","A",2,1,25,0.04000,1,"{771}"
2347,1,548,0,0.7058407,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^9} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^9,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{5 e^8 (d+e x)^5}+\frac{c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8 (d+e x)^3}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^8 (d+e x)^4}+\frac{\left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8 (d+e x)^6}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{7 e^8 (d+e x)^7}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{8 e^8 (d+e x)^8}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{5 e^8 (d+e x)^5}+\frac{c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8 (d+e x)^3}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{4 e^8 (d+e x)^4}+\frac{\left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{2 e^8 (d+e x)^6}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{7 e^8 (d+e x)^7}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{8 e^8 (d+e x)^8}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{2 e^8 (d+e x)^2}-\frac{B c^3}{e^8 (d+e x)}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(8*e^8*(d + e*x)^8) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(7*e^8*(d + e*x)^7) + ((c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(2*e^8*(d + e*x)^6) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(5*e^8*(d + e*x)^5) + (B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(4*e^8*(d + e*x)^4) + (c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e))))/(e^8*(d + e*x)^3) + (c^2*(7*B*c*d - 3*b*B*e - A*c*e))/(2*e^8*(d + e*x)^2) - (B*c^3)/(e^8*(d + e*x))","A",2,1,25,0.04000,1,"{771}"
2348,1,553,0,0.7438397,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^{10}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^10,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{6 e^8 (d+e x)^6}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{4 e^8 (d+e x)^4}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^8 (d+e x)^5}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{7 e^8 (d+e x)^7}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{8 e^8 (d+e x)^8}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{9 e^8 (d+e x)^9}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{3 e^8 (d+e x)^3}-\frac{B c^3}{2 e^8 (d+e x)^2}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{6 e^8 (d+e x)^6}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{4 e^8 (d+e x)^4}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{5 e^8 (d+e x)^5}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{7 e^8 (d+e x)^7}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{8 e^8 (d+e x)^8}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{9 e^8 (d+e x)^9}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{3 e^8 (d+e x)^3}-\frac{B c^3}{2 e^8 (d+e x)^2}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(9*e^8*(d + e*x)^9) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(8*e^8*(d + e*x)^8) + (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(7*e^8*(d + e*x)^7) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(6*e^8*(d + e*x)^6) + (B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(5*e^8*(d + e*x)^5) + (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e))))/(4*e^8*(d + e*x)^4) + (c^2*(7*B*c*d - 3*b*B*e - A*c*e))/(3*e^8*(d + e*x)^3) - (B*c^3)/(2*e^8*(d + e*x)^2)","A",2,1,25,0.04000,1,"{771}"
2349,1,553,0,0.6725265,"\int \frac{(A+B x) \left(a+b x+c x^2\right)^3}{(d+e x)^{11}} \, dx","Int[((A + B*x)*(a + b*x + c*x^2)^3)/(d + e*x)^11,x]","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{7 e^8 (d+e x)^7}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{5 e^8 (d+e x)^5}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{6 e^8 (d+e x)^6}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{8 e^8 (d+e x)^8}-\frac{\left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{9 e^8 (d+e x)^9}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{10 e^8 (d+e x)^{10}}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{4 e^8 (d+e x)^4}-\frac{B c^3}{3 e^8 (d+e x)^3}","\frac{A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)}{7 e^8 (d+e x)^7}+\frac{3 c \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{5 e^8 (d+e x)^5}+\frac{B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)}{6 e^8 (d+e x)^6}+\frac{3 \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{8 e^8 (d+e x)^8}+\frac{\left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{9 e^8 (d+e x)^9}+\frac{(B d-A e) \left(a e^2-b d e+c d^2\right)^3}{10 e^8 (d+e x)^{10}}+\frac{c^2 (-A c e-3 b B e+7 B c d)}{4 e^8 (d+e x)^4}-\frac{B c^3}{3 e^8 (d+e x)^3}",1,"((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3)/(10*e^8*(d + e*x)^10) - ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e)))/(9*e^8*(d + e*x)^9) + (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e))))/(8*e^8*(d + e*x)^8) + (A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))/(7*e^8*(d + e*x)^7) + (B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))/(6*e^8*(d + e*x)^6) + (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e))))/(5*e^8*(d + e*x)^5) + (c^2*(7*B*c*d - 3*b*B*e - A*c*e))/(4*e^8*(d + e*x)^4) - (B*c^3)/(3*e^8*(d + e*x)^3)","A",2,1,25,0.04000,1,"{771}"
2350,1,121,0,0.0813408,"\int x (d+e x)^m \left(a+b x+c x^2\right) \, dx","Int[x*(d + e*x)^m*(a + b*x + c*x^2),x]","-\frac{d (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}+\frac{(d+e x)^{m+2} \left(3 c d^2-e (2 b d-a e)\right)}{e^4 (m+2)}-\frac{(3 c d-b e) (d+e x)^{m+3}}{e^4 (m+3)}+\frac{c (d+e x)^{m+4}}{e^4 (m+4)}","-\frac{d (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}+\frac{(d+e x)^{m+2} \left(3 c d^2-e (2 b d-a e)\right)}{e^4 (m+2)}-\frac{(3 c d-b e) (d+e x)^{m+3}}{e^4 (m+3)}+\frac{c (d+e x)^{m+4}}{e^4 (m+4)}",1,"-((d*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((3*c*d^2 - e*(2*b*d - a*e))*(d + e*x)^(2 + m))/(e^4*(2 + m)) - ((3*c*d - b*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (c*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,19,0.05263,1,"{771}"
2351,1,103,0,0.1633123,"\int x (d+e x)^5 \left(a+b x+c x^2\right) \, dx","Int[x*(d + e*x)^5*(a + b*x + c*x^2),x]","\frac{(d+e x)^7 \left(3 c d^2-e (2 b d-a e)\right)}{7 e^4}-\frac{d (d+e x)^6 \left(a e^2-b d e+c d^2\right)}{6 e^4}-\frac{(d+e x)^8 (3 c d-b e)}{8 e^4}+\frac{c (d+e x)^9}{9 e^4}","\frac{(d+e x)^7 \left(3 c d^2-e (2 b d-a e)\right)}{7 e^4}-\frac{d (d+e x)^6 \left(a e^2-b d e+c d^2\right)}{6 e^4}-\frac{(d+e x)^8 (3 c d-b e)}{8 e^4}+\frac{c (d+e x)^9}{9 e^4}",1,"-(d*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^6)/(6*e^4) + ((3*c*d^2 - e*(2*b*d - a*e))*(d + e*x)^7)/(7*e^4) - ((3*c*d - b*e)*(d + e*x)^8)/(8*e^4) + (c*(d + e*x)^9)/(9*e^4)","A",2,1,19,0.05263,1,"{771}"
2352,1,103,0,0.1258335,"\int x (d+e x)^4 \left(a+b x+c x^2\right) \, dx","Int[x*(d + e*x)^4*(a + b*x + c*x^2),x]","\frac{(d+e x)^6 \left(3 c d^2-e (2 b d-a e)\right)}{6 e^4}-\frac{d (d+e x)^5 \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{(d+e x)^7 (3 c d-b e)}{7 e^4}+\frac{c (d+e x)^8}{8 e^4}","\frac{(d+e x)^6 \left(3 c d^2-e (2 b d-a e)\right)}{6 e^4}-\frac{d (d+e x)^5 \left(a e^2-b d e+c d^2\right)}{5 e^4}-\frac{(d+e x)^7 (3 c d-b e)}{7 e^4}+\frac{c (d+e x)^8}{8 e^4}",1,"-(d*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^5)/(5*e^4) + ((3*c*d^2 - e*(2*b*d - a*e))*(d + e*x)^6)/(6*e^4) - ((3*c*d - b*e)*(d + e*x)^7)/(7*e^4) + (c*(d + e*x)^8)/(8*e^4)","A",2,1,19,0.05263,1,"{771}"
2353,1,103,0,0.1026895,"\int x (d+e x)^3 \left(a+b x+c x^2\right) \, dx","Int[x*(d + e*x)^3*(a + b*x + c*x^2),x]","\frac{(d+e x)^5 \left(3 c d^2-e (2 b d-a e)\right)}{5 e^4}-\frac{d (d+e x)^4 \left(a e^2-b d e+c d^2\right)}{4 e^4}-\frac{(d+e x)^6 (3 c d-b e)}{6 e^4}+\frac{c (d+e x)^7}{7 e^4}","\frac{(d+e x)^5 \left(3 c d^2-e (2 b d-a e)\right)}{5 e^4}-\frac{d (d+e x)^4 \left(a e^2-b d e+c d^2\right)}{4 e^4}-\frac{(d+e x)^6 (3 c d-b e)}{6 e^4}+\frac{c (d+e x)^7}{7 e^4}",1,"-(d*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^4)/(4*e^4) + ((3*c*d^2 - e*(2*b*d - a*e))*(d + e*x)^5)/(5*e^4) - ((3*c*d - b*e)*(d + e*x)^6)/(6*e^4) + (c*(d + e*x)^7)/(7*e^4)","A",2,1,19,0.05263,1,"{771}"
2354,1,78,0,0.0734819,"\int x (d+e x)^2 \left(a+b x+c x^2\right) \, dx","Int[x*(d + e*x)^2*(a + b*x + c*x^2),x]","\frac{1}{4} x^4 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{3} d x^3 (2 a e+b d)+\frac{1}{2} a d^2 x^2+\frac{1}{5} e x^5 (b e+2 c d)+\frac{1}{6} c e^2 x^6","\frac{1}{4} x^4 \left(e (a e+2 b d)+c d^2\right)+\frac{1}{3} d x^3 (2 a e+b d)+\frac{1}{2} a d^2 x^2+\frac{1}{5} e x^5 (b e+2 c d)+\frac{1}{6} c e^2 x^6",1,"(a*d^2*x^2)/2 + (d*(b*d + 2*a*e)*x^3)/3 + ((c*d^2 + e*(2*b*d + a*e))*x^4)/4 + (e*(2*c*d + b*e)*x^5)/5 + (c*e^2*x^6)/6","A",2,1,19,0.05263,1,"{771}"
2355,1,47,0,0.0373681,"\int x (d+e x) \left(a+b x+c x^2\right) \, dx","Int[x*(d + e*x)*(a + b*x + c*x^2),x]","\frac{1}{3} x^3 (a e+b d)+\frac{1}{2} a d x^2+\frac{1}{4} x^4 (b e+c d)+\frac{1}{5} c e x^5","\frac{1}{3} x^3 (a e+b d)+\frac{1}{2} a d x^2+\frac{1}{4} x^4 (b e+c d)+\frac{1}{5} c e x^5",1,"(a*d*x^2)/2 + ((b*d + a*e)*x^3)/3 + ((c*d + b*e)*x^4)/4 + (c*e*x^5)/5","A",2,1,17,0.05882,1,"{765}"
2356,1,25,0,0.0075142,"\int x \left(a+b x+c x^2\right) \, dx","Int[x*(a + b*x + c*x^2),x]","\frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4}","\frac{a x^2}{2}+\frac{b x^3}{3}+\frac{c x^4}{4}",1,"(a*x^2)/2 + (b*x^3)/3 + (c*x^4)/4","A",2,1,12,0.08333,1,"{14}"
2357,1,79,0,0.073496,"\int \frac{x \left(a+b x+c x^2\right)}{d+e x} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x),x]","\frac{x \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{d \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{x^2 (c d-b e)}{2 e^2}+\frac{c x^3}{3 e}","\frac{x \left(a e^2-b d e+c d^2\right)}{e^3}-\frac{d \log (d+e x) \left(a e^2-b d e+c d^2\right)}{e^4}-\frac{x^2 (c d-b e)}{2 e^2}+\frac{c x^3}{3 e}",1,"((c*d^2 - b*d*e + a*e^2)*x)/e^3 - ((c*d - b*e)*x^2)/(2*e^2) + (c*x^3)/(3*e) - (d*(c*d^2 - b*d*e + a*e^2)*Log[d + e*x])/e^4","A",2,1,19,0.05263,1,"{771}"
2358,1,84,0,0.0904978,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^2} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x)^2,x]","\frac{d \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(3 c d^2-e (2 b d-a e)\right)}{e^4}-\frac{x (2 c d-b e)}{e^3}+\frac{c x^2}{2 e^2}","\frac{d \left(a e^2-b d e+c d^2\right)}{e^4 (d+e x)}+\frac{\log (d+e x) \left(3 c d^2-e (2 b d-a e)\right)}{e^4}-\frac{x (2 c d-b e)}{e^3}+\frac{c x^2}{2 e^2}",1,"-(((2*c*d - b*e)*x)/e^3) + (c*x^2)/(2*e^2) + (d*(c*d^2 - b*d*e + a*e^2))/(e^4*(d + e*x)) + ((3*c*d^2 - e*(2*b*d - a*e))*Log[d + e*x])/e^4","A",2,1,19,0.05263,1,"{771}"
2359,1,89,0,0.0834127,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^3} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x)^3,x]","\frac{d \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}-\frac{3 c d^2-e (2 b d-a e)}{e^4 (d+e x)}-\frac{(3 c d-b e) \log (d+e x)}{e^4}+\frac{c x}{e^3}","\frac{d \left(a e^2-b d e+c d^2\right)}{2 e^4 (d+e x)^2}-\frac{3 c d^2-e (2 b d-a e)}{e^4 (d+e x)}-\frac{(3 c d-b e) \log (d+e x)}{e^4}+\frac{c x}{e^3}",1,"(c*x)/e^3 + (d*(c*d^2 - b*d*e + a*e^2))/(2*e^4*(d + e*x)^2) - (3*c*d^2 - e*(2*b*d - a*e))/(e^4*(d + e*x)) - ((3*c*d - b*e)*Log[d + e*x])/e^4","A",2,1,19,0.05263,1,"{771}"
2360,1,96,0,0.0778137,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^4} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x)^4,x]","-\frac{3 c d^2-e (2 b d-a e)}{2 e^4 (d+e x)^2}+\frac{d \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^3}+\frac{3 c d-b e}{e^4 (d+e x)}+\frac{c \log (d+e x)}{e^4}","-\frac{3 c d^2-e (2 b d-a e)}{2 e^4 (d+e x)^2}+\frac{d \left(a e^2-b d e+c d^2\right)}{3 e^4 (d+e x)^3}+\frac{3 c d-b e}{e^4 (d+e x)}+\frac{c \log (d+e x)}{e^4}",1,"(d*(c*d^2 - b*d*e + a*e^2))/(3*e^4*(d + e*x)^3) - (3*c*d^2 - e*(2*b*d - a*e))/(2*e^4*(d + e*x)^2) + (3*c*d - b*e)/(e^4*(d + e*x)) + (c*Log[d + e*x])/e^4","A",2,1,19,0.05263,1,"{771}"
2361,1,101,0,0.0733396,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^5} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x)^5,x]","-\frac{3 c d^2-e (2 b d-a e)}{3 e^4 (d+e x)^3}+\frac{d \left(a e^2-b d e+c d^2\right)}{4 e^4 (d+e x)^4}+\frac{3 c d-b e}{2 e^4 (d+e x)^2}-\frac{c}{e^4 (d+e x)}","-\frac{3 c d^2-e (2 b d-a e)}{3 e^4 (d+e x)^3}+\frac{d \left(a e^2-b d e+c d^2\right)}{4 e^4 (d+e x)^4}+\frac{3 c d-b e}{2 e^4 (d+e x)^2}-\frac{c}{e^4 (d+e x)}",1,"(d*(c*d^2 - b*d*e + a*e^2))/(4*e^4*(d + e*x)^4) - (3*c*d^2 - e*(2*b*d - a*e))/(3*e^4*(d + e*x)^3) + (3*c*d - b*e)/(2*e^4*(d + e*x)^2) - c/(e^4*(d + e*x))","A",2,1,19,0.05263,1,"{771}"
2362,1,103,0,0.0749924,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^6} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x)^6,x]","-\frac{3 c d^2-e (2 b d-a e)}{4 e^4 (d+e x)^4}+\frac{d \left(a e^2-b d e+c d^2\right)}{5 e^4 (d+e x)^5}+\frac{3 c d-b e}{3 e^4 (d+e x)^3}-\frac{c}{2 e^4 (d+e x)^2}","-\frac{3 c d^2-e (2 b d-a e)}{4 e^4 (d+e x)^4}+\frac{d \left(a e^2-b d e+c d^2\right)}{5 e^4 (d+e x)^5}+\frac{3 c d-b e}{3 e^4 (d+e x)^3}-\frac{c}{2 e^4 (d+e x)^2}",1,"(d*(c*d^2 - b*d*e + a*e^2))/(5*e^4*(d + e*x)^5) - (3*c*d^2 - e*(2*b*d - a*e))/(4*e^4*(d + e*x)^4) + (3*c*d - b*e)/(3*e^4*(d + e*x)^3) - c/(2*e^4*(d + e*x)^2)","A",2,1,19,0.05263,1,"{771}"
2363,1,103,0,0.0731911,"\int \frac{x \left(a+b x+c x^2\right)}{(d+e x)^7} \, dx","Int[(x*(a + b*x + c*x^2))/(d + e*x)^7,x]","-\frac{3 c d^2-e (2 b d-a e)}{5 e^4 (d+e x)^5}+\frac{d \left(a e^2-b d e+c d^2\right)}{6 e^4 (d+e x)^6}+\frac{3 c d-b e}{4 e^4 (d+e x)^4}-\frac{c}{3 e^4 (d+e x)^3}","-\frac{3 c d^2-e (2 b d-a e)}{5 e^4 (d+e x)^5}+\frac{d \left(a e^2-b d e+c d^2\right)}{6 e^4 (d+e x)^6}+\frac{3 c d-b e}{4 e^4 (d+e x)^4}-\frac{c}{3 e^4 (d+e x)^3}",1,"(d*(c*d^2 - b*d*e + a*e^2))/(6*e^4*(d + e*x)^6) - (3*c*d^2 - e*(2*b*d - a*e))/(5*e^4*(d + e*x)^5) + (3*c*d - b*e)/(4*e^4*(d + e*x)^4) - c/(3*e^4*(d + e*x)^3)","A",2,1,19,0.05263,1,"{771}"
2364,1,357,0,0.6524969,"\int \frac{(A+B x) (d+e x)^3}{a+b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2),x]","\frac{\log \left(a+b x+c x^2\right) \left(A c e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+B \left(-3 c^2 d e (a e+b d)+b c e^2 (2 a e+3 b d)-b^3 e^3+c^3 d^3\right)\right)}{2 c^4}+\frac{e x \left(B \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+A c e (3 c d-b e)\right)}{c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b^2 c e \left(-4 a B e^2+3 A c d e+3 B c d^2\right)-b c^2 \left(-3 a A e^3-9 a B d e^2+3 A c d^2 e+B c d^3\right)+2 c^2 \left(A c d \left(c d^2-3 a e^2\right)-a B e \left(3 c d^2-a e^2\right)\right)-b^3 c e^2 (A e+3 B d)+b^4 B e^3\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{e^2 x^2 (A c e-b B e+3 B c d)}{2 c^2}+\frac{B e^3 x^3}{3 c}","\frac{\log \left(a+b x+c x^2\right) \left(A c e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+B \left(-3 c^2 d e (a e+b d)+b c e^2 (2 a e+3 b d)-b^3 e^3+c^3 d^3\right)\right)}{2 c^4}+\frac{e x \left(B \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)+A c e (3 c d-b e)\right)}{c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b^2 c e \left(-4 a B e^2+3 A c d e+3 B c d^2\right)-b c^2 \left(-3 a A e^3-9 a B d e^2+3 A c d^2 e+B c d^3\right)+2 c^2 \left(A c d \left(c d^2-3 a e^2\right)-a B e \left(3 c d^2-a e^2\right)\right)-b^3 c e^2 (A e+3 B d)+b^4 B e^3\right)}{c^4 \sqrt{b^2-4 a c}}+\frac{e^2 x^2 (A c e-b B e+3 B c d)}{2 c^2}+\frac{B e^3 x^3}{3 c}",1,"(e*(A*c*e*(3*c*d - b*e) + B*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e)))*x)/c^3 + (e^2*(3*B*c*d - b*B*e + A*c*e)*x^2)/(2*c^2) + (B*e^3*x^3)/(3*c) - ((b^4*B*e^3 - b^3*c*e^2*(3*B*d + A*e) + b^2*c*e*(3*B*c*d^2 + 3*A*c*d*e - 4*a*B*e^2) - b*c^2*(B*c*d^3 + 3*A*c*d^2*e - 9*a*B*d*e^2 - 3*a*A*e^3) + 2*c^2*(A*c*d*(c*d^2 - 3*a*e^2) - a*B*e*(3*c*d^2 - a*e^2)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^4*Sqrt[b^2 - 4*a*c]) + ((A*c*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e)) + B*(c^3*d^3 - b^3*e^3 - 3*c^2*d*e*(b*d + a*e) + b*c*e^2*(3*b*d + 2*a*e)))*Log[a + b*x + c*x^2])/(2*c^4)","A",6,5,25,0.2000,1,"{800, 634, 618, 206, 628}"
2365,1,205,0,0.3709863,"\int \frac{(A+B x) (d+e x)^2}{a+b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2),x]","\frac{\log \left(a+b x+c x^2\right) \left(B \left(-c e (a e+2 b d)+b^2 e^2+c^2 d^2\right)+A c e (2 c d-b e)\right)}{2 c^3}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b c \left(-3 a B e^2+2 A c d e+B c d^2\right)-2 c^2 \left(-a A e^2-2 a B d e+A c d^2\right)-b^2 c e (A e+2 B d)+b^3 B e^2\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{e x (A c e-b B e+2 B c d)}{c^2}+\frac{B e^2 x^2}{2 c}","\frac{\log \left(a+b x+c x^2\right) \left(B \left(-c e (a e+2 b d)+b^2 e^2+c^2 d^2\right)+A c e (2 c d-b e)\right)}{2 c^3}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b c \left(-3 a B e^2+2 A c d e+B c d^2\right)-2 c^2 \left(-a A e^2-2 a B d e+A c d^2\right)-b^2 c e (A e+2 B d)+b^3 B e^2\right)}{c^3 \sqrt{b^2-4 a c}}+\frac{e x (A c e-b B e+2 B c d)}{c^2}+\frac{B e^2 x^2}{2 c}",1,"(e*(2*B*c*d - b*B*e + A*c*e)*x)/c^2 + (B*e^2*x^2)/(2*c) + ((b^3*B*e^2 - b^2*c*e*(2*B*d + A*e) - 2*c^2*(A*c*d^2 - 2*a*B*d*e - a*A*e^2) + b*c*(B*c*d^2 + 2*A*c*d*e - 3*a*B*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*Sqrt[b^2 - 4*a*c]) + ((A*c*e*(2*c*d - b*e) + B*(c^2*d^2 + b^2*e^2 - c*e*(2*b*d + a*e)))*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,25,0.2000,1,"{800, 634, 618, 206, 628}"
2366,1,108,0,0.1280478,"\int \frac{(A+B x) (d+e x)}{a+b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x))/(a + b*x + c*x^2),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right) (A c e-b B e+B c d)}{2 c^2}+\frac{B e x}{c}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)}{c^2 \sqrt{b^2-4 a c}}+\frac{\log \left(a+b x+c x^2\right) (A c e-b B e+B c d)}{2 c^2}+\frac{B e x}{c}",1,"(B*e*x)/c - ((b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^2*Sqrt[b^2 - 4*a*c]) + ((B*c*d - b*B*e + A*c*e)*Log[a + b*x + c*x^2])/(2*c^2)","A",5,5,23,0.2174,1,"{773, 634, 618, 206, 628}"
2367,1,64,0,0.0389597,"\int \frac{A+B x}{a+b x+c x^2} \, dx","Int[(A + B*x)/(a + b*x + c*x^2),x]","\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{B \log \left(a+b x+c x^2\right)}{2 c}","\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{c \sqrt{b^2-4 a c}}+\frac{B \log \left(a+b x+c x^2\right)}{2 c}",1,"((b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c*Sqrt[b^2 - 4*a*c]) + (B*Log[a + b*x + c*x^2])/(2*c)","A",4,4,18,0.2222,1,"{634, 618, 206, 628}"
2368,1,146,0,0.2244559,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)),x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) (-2 a B e+A b e-2 A c d+b B d)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{(B d-A e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}-\frac{(B d-A e) \log (d+e x)}{a e^2-b d e+c d^2}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) (-2 a B e+A b e-2 A c d+b B d)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)}+\frac{(B d-A e) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)}-\frac{(B d-A e) \log (d+e x)}{a e^2-b d e+c d^2}",1,"((b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)) - ((B*d - A*e)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2) + ((B*d - A*e)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2))","A",6,5,25,0.2000,1,"{800, 634, 618, 206, 628}"
2369,1,255,0,0.4440415,"\int \frac{A+B x}{(d+e x)^2 \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-b \left(a B e^2+2 A c d e+B c d^2\right)+2 c \left(-a A e^2+2 a B d e+A c d^2\right)+A b^2 e^2\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{\log \left(a+b x+c x^2\right) \left(A e (2 c d-b e)-B \left(c d^2-a e^2\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{B d-A e}{(d+e x) \left(a e^2-b d e+c d^2\right)}+\frac{\log (d+e x) \left(A e (2 c d-b e)-B \left(c d^2-a e^2\right)\right)}{\left(a e^2-b d e+c d^2\right)^2}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-b \left(a B e^2+2 A c d e+B c d^2\right)+2 c \left(-a A e^2+2 a B d e+A c d^2\right)+A b^2 e^2\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^2}-\frac{\log \left(a+b x+c x^2\right) \left(A e (2 c d-b e)-B \left(c d^2-a e^2\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^2}+\frac{B d-A e}{(d+e x) \left(a e^2-b d e+c d^2\right)}+\frac{\log (d+e x) \left(A e (2 c d-b e)-B \left(c d^2-a e^2\right)\right)}{\left(a e^2-b d e+c d^2\right)^2}",1,"(B*d - A*e)/((c*d^2 - b*d*e + a*e^2)*(d + e*x)) - ((A*b^2*e^2 + 2*c*(A*c*d^2 + 2*a*B*d*e - a*A*e^2) - b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2) + ((A*e*(2*c*d - b*e) - B*(c*d^2 - a*e^2))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^2 - ((A*e*(2*c*d - b*e) - B*(c*d^2 - a*e^2))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^2)","A",6,5,25,0.2000,1,"{800, 634, 618, 206, 628}"
2370,1,414,0,0.8031908,"\int \frac{A+B x}{(d+e x)^3 \left(a+b x+c x^2\right)} \, dx","Int[(A + B*x)/((d + e*x)^3*(a + b*x + c*x^2)),x]","\frac{\log \left(a+b x+c x^2\right) \left(B \left(a b e^3-3 a c d e^2+c^2 d^3\right)-A e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^3}-\frac{\log (d+e x) \left(B \left(a b e^3-3 a c d e^2+c^2 d^3\right)-A e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-b^2 e^2 (a B e+3 A c d)+b c \left(-3 a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)-2 c \left(A c d \left(c d^2-3 a e^2\right)+a B e \left(3 c d^2-a e^2\right)\right)+A b^3 e^3\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}+\frac{B d-A e}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{A e (2 c d-b e)-B \left(c d^2-a e^2\right)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}","\frac{\log \left(a+b x+c x^2\right) \left(B \left(a b e^3-3 a c d e^2+c^2 d^3\right)-A e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)\right)}{2 \left(a e^2-b d e+c d^2\right)^3}-\frac{\log (d+e x) \left(B \left(a b e^3-3 a c d e^2+c^2 d^3\right)-A e \left(-c e (a e+3 b d)+b^2 e^2+3 c^2 d^2\right)\right)}{\left(a e^2-b d e+c d^2\right)^3}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-b^2 e^2 (a B e+3 A c d)+b c \left(-3 a A e^3+3 a B d e^2+3 A c d^2 e+B c d^3\right)-2 c \left(A c d \left(c d^2-3 a e^2\right)+a B e \left(3 c d^2-a e^2\right)\right)+A b^3 e^3\right)}{\sqrt{b^2-4 a c} \left(a e^2-b d e+c d^2\right)^3}+\frac{B d-A e}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{A e (2 c d-b e)-B \left(c d^2-a e^2\right)}{(d+e x) \left(a e^2-b d e+c d^2\right)^2}",1,"(B*d - A*e)/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) - (A*e*(2*c*d - b*e) - B*(c*d^2 - a*e^2))/((c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + ((A*b^3*e^3 - b^2*e^2*(3*A*c*d + a*B*e) + b*c*(B*c*d^3 + 3*A*c*d^2*e + 3*a*B*d*e^2 - 3*a*A*e^3) - 2*c*(A*c*d*(c*d^2 - 3*a*e^2) + a*B*e*(3*c*d^2 - a*e^2)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^3) - ((B*(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3) - A*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e)))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 + ((B*(c^2*d^3 - 3*a*c*d*e^2 + a*b*e^3) - A*e*(3*c^2*d^2 + b^2*e^2 - c*e*(3*b*d + a*e)))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",6,5,25,0.2000,1,"{800, 634, 618, 206, 628}"
2371,1,543,0,1.2139072,"\int \frac{(d+e x)^4 (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[((d + e*x)^4*(f + g*x))/(a + b*x + c*x^2)^3,x]","\frac{(d+e x) \left(x \left(-c^2 e \left(16 a^2 e^2 g+2 a b e (11 d g+3 e f)+b^2 (-d) (5 d g+6 e f)\right)+b^2 c e^2 g (15 a e+b d)-2 c^3 d (3 b d (d g+3 e f)-2 a e (4 d g+3 e f))-2 b^4 e^3 g+12 c^4 d^3 f\right)+2 b c \left(7 a^2 e^3 g+a c d e (7 d g+9 e f)+3 c^2 d^3 f\right)+b^3 e g \left(c d^2-2 a e^2\right)-b^2 c d \left(a e^2 g+3 c d (d g+2 e f)\right)-4 a c^2 e \left(a e (8 d g+3 e f)+3 c d^2 f\right)\right)}{2 c^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(4 c^3 e \left(3 a^2 e^2 (4 d g+e f)-3 a b d e (3 d g+2 e f)+b^2 d^2 (2 d g+3 e f)\right)-30 a^2 b c^2 e^4 g+10 a b^3 c e^4 g-2 c^4 d^2 (3 b d (d g+4 e f)-4 a e (2 d g+3 e f))+b^5 \left(-e^4\right) g+12 c^5 d^4 f\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}+\frac{(d+e x)^3 \left(-x \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)-b (a e g+c d f)+2 a c (d g+e f)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{e^4 g \log \left(a+b x+c x^2\right)}{2 c^3}","\frac{(d+e x) \left(x \left(-c^2 e \left(16 a^2 e^2 g+2 a b e (11 d g+3 e f)+b^2 (-d) (5 d g+6 e f)\right)+b^2 c e^2 g (15 a e+b d)-2 c^3 d (3 b d (d g+3 e f)-2 a e (4 d g+3 e f))-2 b^4 e^3 g+12 c^4 d^3 f\right)+2 b c \left(7 a^2 e^3 g+a c d e (7 d g+9 e f)+3 c^2 d^3 f\right)+b^3 e g \left(c d^2-2 a e^2\right)-b^2 c d \left(a e^2 g+3 c d (d g+2 e f)\right)-4 a c^2 e \left(a e (8 d g+3 e f)+3 c d^2 f\right)\right)}{2 c^2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(4 c^3 e \left(3 a^2 e^2 (4 d g+e f)-3 a b d e (3 d g+2 e f)+b^2 d^2 (2 d g+3 e f)\right)-30 a^2 b c^2 e^4 g+10 a b^3 c e^4 g-2 c^4 d^2 (3 b d (d g+4 e f)-4 a e (2 d g+3 e f))+b^5 \left(-e^4\right) g+12 c^5 d^4 f\right)}{c^3 \left(b^2-4 a c\right)^{5/2}}+\frac{(d+e x)^3 \left(-x \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)-b (a e g+c d f)+2 a c (d g+e f)\right)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{e^4 g \log \left(a+b x+c x^2\right)}{2 c^3}",1,"((d + e*x)^3*(2*a*c*(e*f + d*g) - b*(c*d*f + a*e*g) - (2*c^2*d*f + b^2*e*g - c*(b*e*f + b*d*g + 2*a*e*g))*x))/(2*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + ((d + e*x)*(b^3*e*(c*d^2 - 2*a*e^2)*g - b^2*c*d*(a*e^2*g + 3*c*d*(2*e*f + d*g)) + 2*b*c*(3*c^2*d^3*f + 7*a^2*e^3*g + a*c*d*e*(9*e*f + 7*d*g)) - 4*a*c^2*e*(3*c*d^2*f + a*e*(3*e*f + 8*d*g)) + (12*c^4*d^3*f - 2*b^4*e^3*g + b^2*c*e^2*(b*d + 15*a*e)*g - 2*c^3*d*(3*b*d*(3*e*f + d*g) - 2*a*e*(3*e*f + 4*d*g)) - c^2*e*(16*a^2*e^2*g - b^2*d*(6*e*f + 5*d*g) + 2*a*b*e*(3*e*f + 11*d*g)))*x))/(2*c^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - ((12*c^5*d^4*f - b^5*e^4*g + 10*a*b^3*c*e^4*g - 30*a^2*b*c^2*e^4*g - 2*c^4*d^2*(3*b*d*(4*e*f + d*g) - 4*a*e*(3*e*f + 2*d*g)) + 4*c^3*e*(b^2*d^2*(3*e*f + 2*d*g) - 3*a*b*d*e*(2*e*f + 3*d*g) + 3*a^2*e^2*(e*f + 4*d*g)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(c^3*(b^2 - 4*a*c)^(5/2)) + (e^4*g*Log[a + b*x + c*x^2])/(2*c^3)","A",6,5,25,0.2000,1,"{818, 634, 618, 206, 628}"
2372,1,195,0,0.1616562,"\int \frac{(d+e x)^3 (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[((d + e*x)^3*(f + g*x))/(a + b*x + c*x^2)^3,x]","-\frac{6 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) (2 a e g-b d g-b e f+2 c d f)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^3 (-2 a g+x (2 c f-b g)+b f)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 (d+e x) (-2 a e+x (2 c d-b e)+b d) (2 a e g-b d g-b e f+2 c d f)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}","-\frac{6 \left(a e^2-b d e+c d^2\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) (2 a e g-b d g-b e f+2 c d f)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^3 (-2 a g+x (2 c f-b g)+b f)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}+\frac{3 (d+e x) (-2 a e+x (2 c d-b e)+b d) (2 a e g-b d g-b e f+2 c d f)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}",1,"-((d + e*x)^3*(b*f - 2*a*g + (2*c*f - b*g)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*(2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*(d + e*x)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (6*(c*d^2 - b*d*e + a*e^2)*(2*c*d*f - b*e*f - b*d*g + 2*a*e*g)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,25,0.1600,1,"{804, 722, 618, 206}"
2373,1,303,0,0.3797156,"\int \frac{(d+e x)^2 (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[((d + e*x)^2*(f + g*x))/(a + b*x + c*x^2)^3,x]","-\frac{-x \left(-2 c^2 (2 a e (e f-2 d g)+3 b d (d g+2 e f))-2 b c e (a e g-2 b (d g+e f))+b^3 \left(-e^2\right) g+12 c^3 d^2 f\right)+b^2 \left(a e^2 g+c d (3 d g+2 e f)\right)-6 b c \left(a e (2 d g+e f)+c d^2 f\right)+8 a c e (a e g+2 c d f)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(b e (-3 a e g+2 b d g+b e f)+2 a c e (2 d g+e f)-3 b c d (d g+2 e f)+6 c^2 d^2 f\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^2 (-2 a g+x (2 c f-b g)+b f)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}","-\frac{-x \left(-2 c^2 (2 a e (e f-2 d g)+3 b d (d g+2 e f))-2 b c e (a e g-2 b (d g+e f))+b^3 \left(-e^2\right) g+12 c^3 d^2 f\right)+b^2 \left(a e^2 g+c d (3 d g+2 e f)\right)-6 b c \left(a e (2 d g+e f)+c d^2 f\right)+8 a c e (a e g+2 c d f)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-c (3 b d (d g+2 e f)-2 a e (2 d g+e f))+b e (-3 a e g+2 b d g+b e f)+6 c^2 d^2 f\right)}{\left(b^2-4 a c\right)^{5/2}}-\frac{(d+e x)^2 (-2 a g+x (2 c f-b g)+b f)}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}",1,"-((d + e*x)^2*(b*f - 2*a*g + (2*c*f - b*g)*x))/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) - (8*a*c*e*(2*c*d*f + a*e*g) - 6*b*c*(c*d^2*f + a*e*(e*f + 2*d*g)) + b^2*(a*e^2*g + c*d*(2*e*f + 3*d*g)) - (12*c^3*d^2*f - b^3*e^2*g - 2*b*c*e*(a*e*g - 2*b*(e*f + d*g)) - 2*c^2*(2*a*e*(e*f - 2*d*g) + 3*b*d*(2*e*f + d*g)))*x)/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (2*(6*c^2*d^2*f - 3*b*c*d*(2*e*f + d*g) + 2*a*c*e*(e*f + 2*d*g) + b*e*(b*e*f + 2*b*d*g - 3*a*e*g))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,25,0.1600,1,"{820, 777, 618, 206}"
2374,1,219,0,0.2092465,"\int \frac{(d+e x) (f+g x)}{\left(a+b x+c x^2\right)^3} \, dx","Int[((d + e*x)*(f + g*x))/(a + b*x + c*x^2)^3,x]","\frac{(b+2 c x) \left(2 a c e g+b^2 e g-3 b c (d g+e f)+6 c^2 d f\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{-x \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)-b (a e g+c d f)+2 a c (d g+e f)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(2 a c e g+b^2 e g-3 b c (d g+e f)+6 c^2 d f\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{(b+2 c x) \left(c (2 a e g-3 b (d g+e f))+b^2 e g+6 c^2 d f\right)}{2 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}+\frac{-x \left(-c (2 a e g+b d g+b e f)+b^2 e g+2 c^2 d f\right)-b (a e g+c d f)+2 a c (d g+e f)}{2 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{2 \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(c (2 a e g-3 b (d g+e f))+b^2 e g+6 c^2 d f\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"(2*a*c*(e*f + d*g) - b*(c*d*f + a*e*g) - (2*c^2*d*f + b^2*e*g - c*(b*e*f + b*d*g + 2*a*e*g))*x)/(2*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + ((6*c^2*d*f + b^2*e*g + 2*a*c*e*g - 3*b*c*(e*f + d*g))*(b + 2*c*x))/(2*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (2*(6*c^2*d*f + b^2*e*g + 2*a*c*e*g - 3*b*c*(e*f + d*g))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,23,0.1739,1,"{777, 614, 618, 206}"
2375,1,131,0,0.056064,"\int \frac{f+g x}{\left(a+b x+c x^2\right)^3} \, dx","Int[(f + g*x)/(a + b*x + c*x^2)^3,x]","\frac{3 (b+2 c x) (2 c f-b g)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{-2 a g+x (2 c f-b g)+b f}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{6 c (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}","\frac{3 (b+2 c x) (2 c f-b g)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)}-\frac{-2 a g+x (2 c f-b g)+b f}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2}-\frac{6 c (2 c f-b g) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2}}",1,"-(b*f - 2*a*g + (2*c*f - b*g)*x)/(2*(b^2 - 4*a*c)*(a + b*x + c*x^2)^2) + (3*(2*c*f - b*g)*(b + 2*c*x))/(2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)) - (6*c*(2*c*f - b*g)*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/(b^2 - 4*a*c)^(5/2)","A",4,4,18,0.2222,1,"{638, 614, 618, 206}"
2376,1,664,0,2.5508631,"\int \frac{f+g x}{(d+e x) \left(a+b x+c x^2\right)^3} \, dx","Int[(f + g*x)/((d + e*x)*(a + b*x + c*x^2)^3),x]","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-6 c^2 e^2 \left(a^2 b e^2 (d g+5 e f)-2 a^3 e^3 g-6 a b^2 d^2 e g+2 b^3 d^3 g\right)+4 c^3 d e \left(3 a^2 e^2 (5 e f-2 d g)-3 a b d e (d g+5 e f)+b^2 d^2 (4 d g+5 e f)\right)+10 a b^3 c e^4 (e f-d g)+2 c^4 d^3 (2 a e (10 e f-d g)-3 b d (d g+5 e f))+b^5 \left(-e^4\right) (e f-d g)+12 c^5 d^5 f\right)}{\left(b^2-4 a c\right)^{5/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{c x \left(3 c e (b d-2 a e) (2 a e g-b (d g+e f)+2 c d f)-(2 c d-b e) \left(2 a c e (4 e f-d g)-2 b^2 e (e f-d g)-3 b c d (d g+e f)+6 c^2 d^2 f\right)\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(2 a c e (4 e f-d g)-2 b^2 e (e f-d g)-3 b c d (d g+e f)+6 c^2 d^2 f\right)+3 a c e (2 c d-b e) (2 a e g-b (d g+e f)+2 c d f)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{c x (2 a e g-b (d g+e f)+2 c d f)+a b e g-2 a c d g+2 a c e f+b^2 (-e) f+b c d f}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}-\frac{e^4 (e f-d g) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{e^4 (e f-d g) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}","-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right) \left(-6 c^2 e^2 \left(a^2 b e^2 (d g+5 e f)-2 a^3 e^3 g-6 a b^2 d^2 e g+2 b^3 d^3 g\right)+4 c^3 d e \left(3 a^2 e^2 (5 e f-2 d g)-3 a b d e (d g+5 e f)+b^2 d^2 (4 d g+5 e f)\right)+10 a b^3 c e^4 (e f-d g)+2 c^4 d^3 (2 a e (10 e f-d g)-3 b d (d g+5 e f))+b^5 \left(-e^4\right) (e f-d g)+12 c^5 d^5 f\right)}{\left(b^2-4 a c\right)^{5/2} \left(a e^2-b d e+c d^2\right)^3}-\frac{c x \left(3 c e (b d-2 a e) (2 a e g-b (d g+e f)+2 c d f)-(2 c d-b e) \left(c (2 a e (4 e f-d g)-3 b d (d g+e f))-2 b^2 e (e f-d g)+6 c^2 d^2 f\right)\right)-\left(2 a c e+b^2 (-e)+b c d\right) \left(c (2 a e (4 e f-d g)-3 b d (d g+e f))-2 b^2 e (e f-d g)+6 c^2 d^2 f\right)+3 a c e (2 c d-b e) (2 a e g-b (d g+e f)+2 c d f)}{2 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)^2}-\frac{c x (2 a e g-b (d g+e f)+2 c d f)+a b e g-2 a c d g+2 a c e f+b^2 (-e) f+b c d f}{2 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^2 \left(a e^2-b d e+c d^2\right)}-\frac{e^4 (e f-d g) \log \left(a+b x+c x^2\right)}{2 \left(a e^2-b d e+c d^2\right)^3}+\frac{e^4 (e f-d g) \log (d+e x)}{\left(a e^2-b d e+c d^2\right)^3}",1,"-(b*c*d*f - b^2*e*f + 2*a*c*e*f - 2*a*c*d*g + a*b*e*g + c*(2*c*d*f + 2*a*e*g - b*(e*f + d*g))*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^2) - (3*a*c*e*(2*c*d - b*e)*(2*c*d*f + 2*a*e*g - b*(e*f + d*g)) - (b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2*f - 2*b^2*e*(e*f - d*g) + 2*a*c*e*(4*e*f - d*g) - 3*b*c*d*(e*f + d*g)) + c*(3*c*e*(b*d - 2*a*e)*(2*c*d*f + 2*a*e*g - b*(e*f + d*g)) - (2*c*d - b*e)*(6*c^2*d^2*f - 2*b^2*e*(e*f - d*g) + 2*a*c*e*(4*e*f - d*g) - 3*b*c*d*(e*f + d*g)))*x)/(2*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)) - ((12*c^5*d^5*f - b^5*e^4*(e*f - d*g) + 10*a*b^3*c*e^4*(e*f - d*g) + 2*c^4*d^3*(2*a*e*(10*e*f - d*g) - 3*b*d*(5*e*f + d*g)) - 6*c^2*e^2*(2*b^3*d^3*g - 6*a*b^2*d^2*e*g - 2*a^3*e^3*g + a^2*b*e^2*(5*e*f + d*g)) + 4*c^3*d*e*(3*a^2*e^2*(5*e*f - 2*d*g) - 3*a*b*d*e*(5*e*f + d*g) + b^2*d^2*(5*e*f + 4*d*g)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^3) + (e^4*(e*f - d*g)*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^3 - (e^4*(e*f - d*g)*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^3)","A",8,6,25,0.2400,1,"{822, 800, 634, 618, 206, 628}"
2377,1,1043,0,6.2943552,"\int \frac{f+g x}{(d+e x)^2 \left(a+b x+c x^2\right)^3} \, dx","Int[(f + g*x)/((d + e*x)^2*(a + b*x + c*x^2)^3),x]","\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x) e^4}{\left(c d^2-b e d+a e^2\right)^4}-\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left(c x^2+b x+a\right) e^4}{2 \left(c d^2-b e d+a e^2\right)^4}+\frac{\left(6 c^4 f d^4+c^3 (4 a e (6 e f-d g)-3 b d (4 e f+d g)) d^2-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left(-3 d (e f-d g) b^2-a e (21 e f-13 d g) b+7 a^2 e^2 g\right)-c^2 e \left(-b^2 (3 e f+7 d g) d^2+6 a b e (4 e f+d g) d+2 a^2 e^2 (15 e f-22 d g)\right)\right) e}{\left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^3 (d+e x)}-\frac{\left(12 c^6 f d^6+2 c^5 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g)) d^4+10 c^4 e \left(b^2 (3 e f+2 d g) d^2-a b e (12 e f+d g) d+2 a^2 e^2 (9 e f-4 d g)\right) d^2+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left(-d (6 e f-5 d g) b^2-10 a e (3 e f-2 d g) b+10 a^2 e^2 g\right)-10 a b c^2 e^4 \left(-d (6 e f-5 d g) b^2-3 a e (3 e f-2 d g) b+3 a^2 e^2 g\right)-10 c^3 e^2 \left(2 b^3 g d^4-8 a b^2 e g d^3+3 a^2 b e^2 (6 e f-d g) d+6 a^3 e^3 (e f-2 d g)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2} \left(c d^2-b e d+a e^2\right)^4}-\frac{4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left(-e b^2+c d b+2 a c e\right) \left(6 c^2 f d^2-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right)-c \left(12 c^3 f d^3+2 c^2 (2 a e (9 e f-2 d g)-3 b d (3 e f+d g)) d+b^2 e^2 (3 b e f-2 b d g-a e g)+c e \left(11 b^2 g d^2+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right)\right) x}{2 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 (d+e x) \left(c x^2+b x+a\right)}-\frac{-e f b^2+c d f b+a e g b+2 a c e f-2 a c d g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (d+e x) \left(c x^2+b x+a\right)^2}","\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log (d+e x) e^4}{\left(c d^2-b e d+a e^2\right)^4}-\frac{(c d (6 e f-5 d g)-e (3 b e f-2 b d g-a e g)) \log \left(c x^2+b x+a\right) e^4}{2 \left(c d^2-b e d+a e^2\right)^4}+\frac{\left(6 c^4 f d^4+c^3 (4 a e (6 e f-d g)-3 b d (4 e f+d g)) d^2-b^3 e^3 (3 b e f-2 b d g-a e g)-b c e^2 \left(-3 d (e f-d g) b^2-a e (21 e f-13 d g) b+7 a^2 e^2 g\right)-c^2 e \left(-b^2 (3 e f+7 d g) d^2+6 a b e (4 e f+d g) d+2 a^2 e^2 (15 e f-22 d g)\right)\right) e}{\left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^3 (d+e x)}-\frac{\left(12 c^6 f d^6+2 c^5 (2 a e (15 e f-2 d g)-3 b d (6 e f+d g)) d^4+10 c^4 e \left(b^2 (3 e f+2 d g) d^2-a b e (12 e f+d g) d+2 a^2 e^2 (9 e f-4 d g)\right) d^2+b^5 e^5 (3 b e f-2 b d g-a e g)+b^3 c e^4 \left(-d (6 e f-5 d g) b^2-10 a e (3 e f-2 d g) b+10 a^2 e^2 g\right)-10 a b c^2 e^4 \left(-d (6 e f-5 d g) b^2-3 a e (3 e f-2 d g) b+3 a^2 e^2 g\right)-10 c^3 e^2 \left(2 b^3 g d^4-8 a b^2 e g d^3+3 a^2 b e^2 (6 e f-d g) d+6 a^3 e^3 (e f-2 d g)\right)\right) \tanh ^{-1}\left(\frac{b+2 c x}{\sqrt{b^2-4 a c}}\right)}{\left(b^2-4 a c\right)^{5/2} \left(c d^2-b e d+a e^2\right)^4}-\frac{4 a c e (2 c d-b e) (2 c d f+2 a e g-b (e f+d g))-\left(-e b^2+c d b+2 a c e\right) \left(6 c^2 f d^2-b e (3 b e f-2 b d g-a e g)+c (2 a e (5 e f-2 d g)-b d (2 e f+3 d g))\right)-c \left(12 c^3 f d^3+2 c^2 (2 a e (9 e f-2 d g)-3 b d (3 e f+d g)) d+b^2 e^2 (3 b e f-2 b d g-a e g)+c e \left(11 b^2 g d^2+16 a^2 e^2 g-2 a b e (9 e f+5 d g)\right)\right) x}{2 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 (d+e x) \left(c x^2+b x+a\right)}-\frac{-e f b^2+c d f b+a e g b+2 a c e f-2 a c d g+c (2 c d f+2 a e g-b (e f+d g)) x}{2 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) (d+e x) \left(c x^2+b x+a\right)^2}",1,"(e*(6*c^4*d^4*f - b^3*e^3*(3*b*e*f - 2*b*d*g - a*e*g) - b*c*e^2*(7*a^2*e^2*g - a*b*e*(21*e*f - 13*d*g) - 3*b^2*d*(e*f - d*g)) + c^3*d^2*(4*a*e*(6*e*f - d*g) - 3*b*d*(4*e*f + d*g)) - c^2*e*(2*a^2*e^2*(15*e*f - 22*d*g) + 6*a*b*d*e*(4*e*f + d*g) - b^2*d^2*(3*e*f + 7*d*g))))/((b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - (b*c*d*f - b^2*e*f + 2*a*c*e*f - 2*a*c*d*g + a*b*e*g + c*(2*c*d*f + 2*a*e*g - b*(e*f + d*g))*x)/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^2) - (4*a*c*e*(2*c*d - b*e)*(2*c*d*f + 2*a*e*g - b*(e*f + d*g)) - (b*c*d - b^2*e + 2*a*c*e)*(6*c^2*d^2*f - b*e*(3*b*e*f - 2*b*d*g - a*e*g) + c*(2*a*e*(5*e*f - 2*d*g) - b*d*(2*e*f + 3*d*g))) - c*(12*c^3*d^3*f + b^2*e^2*(3*b*e*f - 2*b*d*g - a*e*g) + 2*c^2*d*(2*a*e*(9*e*f - 2*d*g) - 3*b*d*(3*e*f + d*g)) + c*e*(11*b^2*d^2*g + 16*a^2*e^2*g - 2*a*b*e*(9*e*f + 5*d*g)))*x)/(2*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*(a + b*x + c*x^2)) - ((12*c^6*d^6*f + b^5*e^5*(3*b*e*f - 2*b*d*g - a*e*g) + b^3*c*e^4*(10*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g) - 10*a*b*e*(3*e*f - 2*d*g)) - 10*a*b*c^2*e^4*(3*a^2*e^2*g - b^2*d*(6*e*f - 5*d*g) - 3*a*b*e*(3*e*f - 2*d*g)) - 10*c^3*e^2*(2*b^3*d^4*g - 8*a*b^2*d^3*e*g + 6*a^3*e^3*(e*f - 2*d*g) + 3*a^2*b*d*e^2*(6*e*f - d*g)) + 2*c^5*d^4*(2*a*e*(15*e*f - 2*d*g) - 3*b*d*(6*e*f + d*g)) + 10*c^4*d^2*e*(2*a^2*e^2*(9*e*f - 4*d*g) - a*b*d*e*(12*e*f + d*g) + b^2*d^2*(3*e*f + 2*d*g)))*ArcTanh[(b + 2*c*x)/Sqrt[b^2 - 4*a*c]])/((b^2 - 4*a*c)^(5/2)*(c*d^2 - b*d*e + a*e^2)^4) + (e^4*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[d + e*x])/(c*d^2 - b*d*e + a*e^2)^4 - (e^4*(c*d*(6*e*f - 5*d*g) - e*(3*b*e*f - 2*b*d*g - a*e*g))*Log[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)^4)","A",8,6,25,0.2400,1,"{822, 800, 634, 618, 206, 628}"
2378,1,43,0,0.0244776,"\int \frac{(5-x) (3+2 x)^4}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2),x]","-\frac{4 x^4}{3}+\frac{32 x^3}{27}+\frac{1156 x^2}{27}+\frac{11576 x}{81}-6 \log (x+1)+\frac{10625}{243} \log (3 x+2)","-\frac{4 x^4}{3}+\frac{32 x^3}{27}+\frac{1156 x^2}{27}+\frac{11576 x}{81}-6 \log (x+1)+\frac{10625}{243} \log (3 x+2)",1,"(11576*x)/81 + (1156*x^2)/27 + (32*x^3)/27 - (4*x^4)/3 - 6*Log[1 + x] + (10625*Log[2 + 3*x])/243","A",5,3,25,0.1200,1,"{800, 632, 31}"
2379,1,36,0,0.0239243,"\int \frac{(5-x) (3+2 x)^3}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2),x]","-\frac{8 x^3}{9}+\frac{26 x^2}{9}+\frac{922 x}{27}-6 \log (x+1)+\frac{2125}{81} \log (3 x+2)","-\frac{8 x^3}{9}+\frac{26 x^2}{9}+\frac{922 x}{27}-6 \log (x+1)+\frac{2125}{81} \log (3 x+2)",1,"(922*x)/27 + (26*x^2)/9 - (8*x^3)/9 - 6*Log[1 + x] + (2125*Log[2 + 3*x])/81","A",5,3,25,0.1200,1,"{800, 632, 31}"
2380,1,29,0,0.0225528,"\int \frac{(5-x) (3+2 x)^2}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2),x]","-\frac{2 x^2}{3}+\frac{44 x}{9}-6 \log (x+1)+\frac{425}{27} \log (3 x+2)","-\frac{2 x^2}{3}+\frac{44 x}{9}-6 \log (x+1)+\frac{425}{27} \log (3 x+2)",1,"(44*x)/9 - (2*x^2)/3 - 6*Log[1 + x] + (425*Log[2 + 3*x])/27","A",5,3,25,0.1200,1,"{800, 632, 31}"
2381,1,22,0,0.0145041,"\int \frac{(5-x) (3+2 x)}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2),x]","-\frac{2 x}{3}-6 \log (x+1)+\frac{85}{9} \log (3 x+2)","-\frac{2 x}{3}-6 \log (x+1)+\frac{85}{9} \log (3 x+2)",1,"(-2*x)/3 - 6*Log[1 + x] + (85*Log[2 + 3*x])/9","A",4,3,23,0.1304,1,"{773, 632, 31}"
2382,1,17,0,0.0060647,"\int \frac{5-x}{2+5 x+3 x^2} \, dx","Int[(5 - x)/(2 + 5*x + 3*x^2),x]","\frac{17}{3} \log (3 x+2)-6 \log (x+1)","\frac{17}{3} \log (3 x+2)-6 \log (x+1)",1,"-6*Log[1 + x] + (17*Log[2 + 3*x])/3","A",3,2,18,0.1111,1,"{632, 31}"
2383,1,27,0,0.0257944,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)),x]","-6 \log (x+1)+\frac{13}{5} \log (2 x+3)+\frac{17}{5} \log (3 x+2)","-6 \log (x+1)+\frac{13}{5} \log (2 x+3)+\frac{17}{5} \log (3 x+2)",1,"-6*Log[1 + x] + (13*Log[3 + 2*x])/5 + (17*Log[2 + 3*x])/5","A",2,1,25,0.04000,1,"{800}"
2384,1,38,0,0.0289858,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)),x]","-\frac{13}{5 (2 x+3)}-6 \log (x+1)+\frac{99}{25} \log (2 x+3)+\frac{51}{25} \log (3 x+2)","-\frac{13}{5 (2 x+3)}-6 \log (x+1)+\frac{99}{25} \log (2 x+3)+\frac{51}{25} \log (3 x+2)",1,"-13/(5*(3 + 2*x)) - 6*Log[1 + x] + (99*Log[3 + 2*x])/25 + (51*Log[2 + 3*x])/25","A",2,1,25,0.04000,1,"{800}"
2385,1,49,0,0.0348011,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)),x]","-\frac{99}{25 (2 x+3)}-\frac{13}{10 (2 x+3)^2}-6 \log (x+1)+\frac{597}{125} \log (2 x+3)+\frac{153}{125} \log (3 x+2)","-\frac{99}{25 (2 x+3)}-\frac{13}{10 (2 x+3)^2}-6 \log (x+1)+\frac{597}{125} \log (2 x+3)+\frac{153}{125} \log (3 x+2)",1,"-13/(10*(3 + 2*x)^2) - 99/(25*(3 + 2*x)) - 6*Log[1 + x] + (597*Log[3 + 2*x])/125 + (153*Log[2 + 3*x])/125","A",2,1,25,0.04000,1,"{800}"
2386,1,60,0,0.0379009,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)),x]","-\frac{597}{125 (2 x+3)}-\frac{99}{50 (2 x+3)^2}-\frac{13}{15 (2 x+3)^3}-6 \log (x+1)+\frac{3291}{625} \log (2 x+3)+\frac{459}{625} \log (3 x+2)","-\frac{597}{125 (2 x+3)}-\frac{99}{50 (2 x+3)^2}-\frac{13}{15 (2 x+3)^3}-6 \log (x+1)+\frac{3291}{625} \log (2 x+3)+\frac{459}{625} \log (3 x+2)",1,"-13/(15*(3 + 2*x)^3) - 99/(50*(3 + 2*x)^2) - 597/(125*(3 + 2*x)) - 6*Log[1 + x] + (3291*Log[3 + 2*x])/625 + (459*Log[2 + 3*x])/625","A",2,1,25,0.04000,1,"{800}"
2387,1,50,0,0.0558867,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^2,x]","-\frac{8 x^2}{9}-\frac{12083 x+11597}{81 \left(3 x^2+5 x+2\right)}+\frac{112 x}{27}+83 \log (x+1)-\frac{1625}{27} \log (3 x+2)","-\frac{8 x^2}{9}-\frac{12083 x+11597}{81 \left(3 x^2+5 x+2\right)}+\frac{112 x}{27}+83 \log (x+1)-\frac{1625}{27} \log (3 x+2)",1,"(112*x)/27 - (8*x^2)/9 - (11597 + 12083*x)/(81*(2 + 5*x + 3*x^2)) + 83*Log[1 + x] - (1625*Log[2 + 3*x])/27","A",7,5,25,0.2000,1,"{816, 1660, 1657, 632, 31}"
2388,1,43,0,0.0470334,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^2,x]","-\frac{2611 x+2449}{27 \left(3 x^2+5 x+2\right)}-\frac{8 x}{9}+71 \log (x+1)-\frac{1825}{27} \log (3 x+2)","-\frac{2611 x+2449}{27 \left(3 x^2+5 x+2\right)}-\frac{8 x}{9}+71 \log (x+1)-\frac{1825}{27} \log (3 x+2)",1,"(-8*x)/9 - (2449 + 2611*x)/(27*(2 + 5*x + 3*x^2)) + 71*Log[1 + x] - (1825*Log[2 + 3*x])/27","A",7,5,25,0.2000,1,"{816, 1660, 1657, 632, 31}"
2389,1,38,0,0.0355339,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^2,x]","-\frac{587 x+533}{9 \left(3 x^2+5 x+2\right)}+59 \log (x+1)-\frac{535}{9} \log (3 x+2)","-\frac{587 x+533}{9 \left(3 x^2+5 x+2\right)}+59 \log (x+1)-\frac{535}{9} \log (3 x+2)",1,"-(533 + 587*x)/(9*(2 + 5*x + 3*x^2)) + 59*Log[1 + x] - (535*Log[2 + 3*x])/9","A",5,4,25,0.1600,1,"{816, 1660, 632, 31}"
2390,1,36,0,0.0145328,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^2,x]","-\frac{139 x+121}{3 \left(3 x^2+5 x+2\right)}+47 \log (x+1)-47 \log (3 x+2)","-\frac{139 x+121}{3 \left(3 x^2+5 x+2\right)}+47 \log (x+1)-47 \log (3 x+2)",1,"-(121 + 139*x)/(3*(2 + 5*x + 3*x^2)) + 47*Log[1 + x] - 47*Log[2 + 3*x]","A",4,3,23,0.1304,1,"{777, 616, 31}"
2391,1,34,0,0.0103481,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/(2 + 5*x + 3*x^2)^2,x]","-\frac{35 x+29}{3 x^2+5 x+2}+35 \log (x+1)-35 \log (3 x+2)","-\frac{35 x+29}{3 x^2+5 x+2}+35 \log (x+1)-35 \log (3 x+2)",1,"-((29 + 35*x)/(2 + 5*x + 3*x^2)) + 35*Log[1 + x] - 35*Log[2 + 3*x]","A",4,3,18,0.1667,1,"{638, 616, 31}"
2392,1,48,0,0.0380793,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 \left(3 x^2+5 x+2\right)}+23 \log (x+1)+\frac{52}{25} \log (2 x+3)-\frac{627}{25} \log (3 x+2)","-\frac{3 (47 x+37)}{5 \left(3 x^2+5 x+2\right)}+23 \log (x+1)+\frac{52}{25} \log (2 x+3)-\frac{627}{25} \log (3 x+2)",1,"(-3*(37 + 47*x))/(5*(2 + 5*x + 3*x^2)) + 23*Log[1 + x] + (52*Log[3 + 2*x])/25 - (627*Log[2 + 3*x])/25","A",3,2,25,0.08000,1,"{822, 800}"
2393,1,66,0,0.0468649,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 (2 x+3) \left(3 x^2+5 x+2\right)}-\frac{454}{25 (2 x+3)}+11 \log (x+1)+\frac{812}{125} \log (2 x+3)-\frac{2187}{125} \log (3 x+2)","-\frac{3 (47 x+37)}{5 (2 x+3) \left(3 x^2+5 x+2\right)}-\frac{454}{25 (2 x+3)}+11 \log (x+1)+\frac{812}{125} \log (2 x+3)-\frac{2187}{125} \log (3 x+2)",1,"-454/(25*(3 + 2*x)) - (3*(37 + 47*x))/(5*(3 + 2*x)*(2 + 5*x + 3*x^2)) + 11*Log[1 + x] + (812*Log[3 + 2*x])/125 - (2187*Log[2 + 3*x])/125","A",3,2,25,0.08000,1,"{822, 800}"
2394,1,77,0,0.0502562,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 (2 x+3)^2 \left(3 x^2+5 x+2\right)}-\frac{2618}{125 (2 x+3)}-\frac{428}{25 (2 x+3)^2}-\log (x+1)+\frac{8104}{625} \log (2 x+3)-\frac{7479}{625} \log (3 x+2)","-\frac{3 (47 x+37)}{5 (2 x+3)^2 \left(3 x^2+5 x+2\right)}-\frac{2618}{125 (2 x+3)}-\frac{428}{25 (2 x+3)^2}-\log (x+1)+\frac{8104}{625} \log (2 x+3)-\frac{7479}{625} \log (3 x+2)",1,"-428/(25*(3 + 2*x)^2) - 2618/(125*(3 + 2*x)) - (3*(37 + 47*x))/(5*(3 + 2*x)^2*(2 + 5*x + 3*x^2)) - Log[1 + x] + (8104*Log[3 + 2*x])/625 - (7479*Log[2 + 3*x])/625","A",3,2,25,0.08000,1,"{822, 800}"
2395,1,88,0,0.056415,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 (2 x+3)^3 \left(3 x^2+5 x+2\right)}-\frac{16522}{625 (2 x+3)}-\frac{2212}{125 (2 x+3)^2}-\frac{1258}{75 (2 x+3)^3}-13 \log (x+1)+\frac{65816 \log (2 x+3)}{3125}-\frac{25191 \log (3 x+2)}{3125}","-\frac{3 (47 x+37)}{5 (2 x+3)^3 \left(3 x^2+5 x+2\right)}-\frac{16522}{625 (2 x+3)}-\frac{2212}{125 (2 x+3)^2}-\frac{1258}{75 (2 x+3)^3}-13 \log (x+1)+\frac{65816 \log (2 x+3)}{3125}-\frac{25191 \log (3 x+2)}{3125}",1,"-1258/(75*(3 + 2*x)^3) - 2212/(125*(3 + 2*x)^2) - 16522/(625*(3 + 2*x)) - (3*(37 + 47*x))/(5*(3 + 2*x)^3*(2 + 5*x + 3*x^2)) - 13*Log[1 + x] + (65816*Log[3 + 2*x])/3125 - (25191*Log[2 + 3*x])/3125","A",3,2,25,0.08000,1,"{822, 800}"
2396,1,64,0,0.0800288,"\int \frac{(5-x) (3+2 x)^5}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^5)/(2 + 5*x + 3*x^2)^3,x]","\frac{502254 x+398585}{486 \left(3 x^2+5 x+2\right)}-\frac{57499 x+56041}{486 \left(3 x^2+5 x+2\right)^2}-\frac{32 x}{27}-1085 \log (x+1)+\frac{29375}{27} \log (3 x+2)","\frac{502254 x+398585}{486 \left(3 x^2+5 x+2\right)}-\frac{57499 x+56041}{486 \left(3 x^2+5 x+2\right)^2}-\frac{32 x}{27}-1085 \log (x+1)+\frac{29375}{27} \log (3 x+2)",1,"(-32*x)/27 - (56041 + 57499*x)/(486*(2 + 5*x + 3*x^2)^2) + (398585 + 502254*x)/(486*(2 + 5*x + 3*x^2)) - 1085*Log[1 + x] + (29375*Log[2 + 3*x])/27","A",8,5,25,0.2000,1,"{816, 1660, 1657, 632, 31}"
2397,1,59,0,0.049438,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^3,x]","-\frac{12083 x+11597}{162 \left(3 x^2+5 x+2\right)^2}+\frac{7 (20298 x+16651)}{162 \left(3 x^2+5 x+2\right)}-883 \log (x+1)+\frac{23825}{27} \log (3 x+2)","-\frac{12083 x+11597}{162 \left(3 x^2+5 x+2\right)^2}+\frac{7 (20298 x+16651)}{162 \left(3 x^2+5 x+2\right)}-883 \log (x+1)+\frac{23825}{27} \log (3 x+2)",1,"-(11597 + 12083*x)/(162*(2 + 5*x + 3*x^2)^2) + (7*(16651 + 20298*x))/(162*(2 + 5*x + 3*x^2)) - 883*Log[1 + x] + (23825*Log[2 + 3*x])/27","A",6,4,25,0.1600,1,"{816, 1660, 632, 31}"
2398,1,69,0,0.0303941,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^3,x]","-\frac{(35 x+29) (2 x+3)^3}{2 \left(3 x^2+5 x+2\right)^2}+\frac{141 (8 x+7) (2 x+3)}{2 \left(3 x^2+5 x+2\right)}-705 \log (x+1)+705 \log (3 x+2)","-\frac{(35 x+29) (2 x+3)^3}{2 \left(3 x^2+5 x+2\right)^2}+\frac{141 (8 x+7) (2 x+3)}{2 \left(3 x^2+5 x+2\right)}-705 \log (x+1)+705 \log (3 x+2)",1,"-((3 + 2*x)^3*(29 + 35*x))/(2*(2 + 5*x + 3*x^2)^2) + (141*(3 + 2*x)*(7 + 8*x))/(2*(2 + 5*x + 3*x^2)) - 705*Log[1 + x] + 705*Log[2 + 3*x]","A",5,4,25,0.1600,1,"{804, 722, 616, 31}"
2399,1,57,0,0.0428569,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^3,x]","-\frac{587 x+533}{18 \left(3 x^2+5 x+2\right)^2}+\frac{9918 x+8269}{18 \left(3 x^2+5 x+2\right)}-551 \log (x+1)+551 \log (3 x+2)","-\frac{587 x+533}{18 \left(3 x^2+5 x+2\right)^2}+\frac{9918 x+8269}{18 \left(3 x^2+5 x+2\right)}-551 \log (x+1)+551 \log (3 x+2)",1,"-(533 + 587*x)/(18*(2 + 5*x + 3*x^2)^2) + (8269 + 9918*x)/(18*(2 + 5*x + 3*x^2)) - 551*Log[1 + x] + 551*Log[2 + 3*x]","A",6,5,25,0.2000,1,"{816, 1660, 638, 616, 31}"
2400,1,57,0,0.0207376,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^3,x]","\frac{421 (6 x+5)}{6 \left(3 x^2+5 x+2\right)}-\frac{139 x+121}{6 \left(3 x^2+5 x+2\right)^2}-421 \log (x+1)+421 \log (3 x+2)","\frac{421 (6 x+5)}{6 \left(3 x^2+5 x+2\right)}-\frac{139 x+121}{6 \left(3 x^2+5 x+2\right)^2}-421 \log (x+1)+421 \log (3 x+2)",1,"-(121 + 139*x)/(6*(2 + 5*x + 3*x^2)^2) + (421*(5 + 6*x))/(6*(2 + 5*x + 3*x^2)) - 421*Log[1 + x] + 421*Log[2 + 3*x]","A",5,4,23,0.1739,1,"{777, 614, 616, 31}"
2401,1,57,0,0.015495,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/(2 + 5*x + 3*x^2)^3,x]","\frac{105 (6 x+5)}{2 \left(3 x^2+5 x+2\right)}-\frac{35 x+29}{2 \left(3 x^2+5 x+2\right)^2}-315 \log (x+1)+315 \log (3 x+2)","\frac{105 (6 x+5)}{2 \left(3 x^2+5 x+2\right)}-\frac{35 x+29}{2 \left(3 x^2+5 x+2\right)^2}-315 \log (x+1)+315 \log (3 x+2)",1,"-(29 + 35*x)/(2*(2 + 5*x + 3*x^2)^2) + (105*(5 + 6*x))/(2*(2 + 5*x + 3*x^2)) - 315*Log[1 + x] + 315*Log[2 + 3*x]","A",5,4,18,0.2222,1,"{638, 614, 616, 31}"
2402,1,69,0,0.0528511,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 (47 x+37)}{10 \left(3 x^2+5 x+2\right)^2}+\frac{11442 x+9587}{50 \left(3 x^2+5 x+2\right)}-233 \log (x+1)+\frac{208}{125} \log (2 x+3)+\frac{28917}{125} \log (3 x+2)","-\frac{3 (47 x+37)}{10 \left(3 x^2+5 x+2\right)^2}+\frac{11442 x+9587}{50 \left(3 x^2+5 x+2\right)}-233 \log (x+1)+\frac{208}{125} \log (2 x+3)+\frac{28917}{125} \log (3 x+2)",1,"(-3*(37 + 47*x))/(10*(2 + 5*x + 3*x^2)^2) + (9587 + 11442*x)/(50*(2 + 5*x + 3*x^2)) - 233*Log[1 + x] + (208*Log[3 + 2*x])/125 + (28917*Log[2 + 3*x])/125","A",4,2,25,0.08000,1,"{822, 800}"
2403,1,94,0,0.0599182,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 (47 x+37)}{10 (2 x+3) \left(3 x^2+5 x+2\right)^2}+\frac{10848 x+9293}{50 (2 x+3) \left(3 x^2+5 x+2\right)}+\frac{12946}{125 (2 x+3)}-175 \log (x+1)+\frac{4912}{625} \log (2 x+3)+\frac{104463}{625} \log (3 x+2)","-\frac{3 (47 x+37)}{10 (2 x+3) \left(3 x^2+5 x+2\right)^2}+\frac{10848 x+9293}{50 (2 x+3) \left(3 x^2+5 x+2\right)}+\frac{12946}{125 (2 x+3)}-175 \log (x+1)+\frac{4912}{625} \log (2 x+3)+\frac{104463}{625} \log (3 x+2)",1,"12946/(125*(3 + 2*x)) - (3*(37 + 47*x))/(10*(3 + 2*x)*(2 + 5*x + 3*x^2)^2) + (9293 + 10848*x)/(50*(3 + 2*x)*(2 + 5*x + 3*x^2)) - 175*Log[1 + x] + (4912*Log[3 + 2*x])/625 + (104463*Log[2 + 3*x])/625","A",4,2,25,0.08000,1,"{822, 800}"
2404,1,105,0,0.0700943,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 (47 x+37)}{10 (2 x+3)^2 \left(3 x^2+5 x+2\right)^2}+\frac{10254 x+8999}{50 (2 x+3)^2 \left(3 x^2+5 x+2\right)}+\frac{35886}{625 (2 x+3)}+\frac{11856}{125 (2 x+3)^2}-141 \log (x+1)+\frac{68592 \log (2 x+3)}{3125}+\frac{372033 \log (3 x+2)}{3125}","-\frac{3 (47 x+37)}{10 (2 x+3)^2 \left(3 x^2+5 x+2\right)^2}+\frac{10254 x+8999}{50 (2 x+3)^2 \left(3 x^2+5 x+2\right)}+\frac{35886}{625 (2 x+3)}+\frac{11856}{125 (2 x+3)^2}-141 \log (x+1)+\frac{68592 \log (2 x+3)}{3125}+\frac{372033 \log (3 x+2)}{3125}",1,"11856/(125*(3 + 2*x)^2) + 35886/(625*(3 + 2*x)) - (3*(37 + 47*x))/(10*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^2) + (8999 + 10254*x)/(50*(3 + 2*x)^2*(2 + 5*x + 3*x^2)) - 141*Log[1 + x] + (68592*Log[3 + 2*x])/3125 + (372033*Log[2 + 3*x])/3125","A",4,2,25,0.08000,1,"{822, 800}"
2405,1,33,0,0.0133338,"\int \frac{x (1+x)^2}{\left(1+x+x^2\right)^3} \, dx","Int[(x*(1 + x)^2)/(1 + x + x^2)^3,x]","-\frac{(x+1) (2 x+1)}{6 \left(x^2+x+1\right)^2}-\frac{1}{6 \left(x^2+x+1\right)}","-\frac{(x+1) (2 x+1)}{6 \left(x^2+x+1\right)^2}-\frac{1}{6 \left(x^2+x+1\right)}",1,"-((1 + x)*(1 + 2*x))/(6*(1 + x + x^2)^2) - 1/(6*(1 + x + x^2))","A",2,2,15,0.1333,1,"{818, 629}"
2406,1,160,0,0.0949389,"\int (5-x) (3+2 x)^4 \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{21} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^4+\frac{229}{378} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^3+\frac{478}{315} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^2+\frac{(378774 x+874301) \left(3 x^2+5 x+2\right)^{3/2}}{68040}+\frac{25969 (6 x+5) \sqrt{3 x^2+5 x+2}}{15552}-\frac{25969 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{31104 \sqrt{3}}","-\frac{1}{21} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^4+\frac{229}{378} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^3+\frac{478}{315} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^2+\frac{(378774 x+874301) \left(3 x^2+5 x+2\right)^{3/2}}{68040}+\frac{25969 (6 x+5) \sqrt{3 x^2+5 x+2}}{15552}-\frac{25969 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{31104 \sqrt{3}}",1,"(25969*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/15552 + (478*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2))/315 + (229*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2))/378 - ((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(3/2))/21 + ((874301 + 378774*x)*(2 + 5*x + 3*x^2)^(3/2))/68040 - (25969*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(31104*Sqrt[3])","A",7,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2407,1,135,0,0.0736717,"\int (5-x) (3+2 x)^3 \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{18} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^3+\frac{11}{15} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^2+\frac{(11538 x+27487) \left(3 x^2+5 x+2\right)^{3/2}}{3240}+\frac{6221 (6 x+5) \sqrt{3 x^2+5 x+2}}{5184}-\frac{6221 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{10368 \sqrt{3}}","-\frac{1}{18} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^3+\frac{11}{15} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^2+\frac{(11538 x+27487) \left(3 x^2+5 x+2\right)^{3/2}}{3240}+\frac{6221 (6 x+5) \sqrt{3 x^2+5 x+2}}{5184}-\frac{6221 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{10368 \sqrt{3}}",1,"(6221*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/5184 + (11*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2))/15 - ((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2))/18 + ((27487 + 11538*x)*(2 + 5*x + 3*x^2)^(3/2))/3240 - (6221*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(10368*Sqrt[3])","A",6,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2408,1,110,0,0.0488296,"\int (5-x) (3+2 x)^2 \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{15} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^2+\frac{(3006 x+7969) \left(3 x^2+5 x+2\right)^{3/2}}{1620}+\frac{2267 (6 x+5) \sqrt{3 x^2+5 x+2}}{2592}-\frac{2267 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{5184 \sqrt{3}}","-\frac{1}{15} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^2+\frac{(3006 x+7969) \left(3 x^2+5 x+2\right)^{3/2}}{1620}+\frac{2267 (6 x+5) \sqrt{3 x^2+5 x+2}}{2592}-\frac{2267 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{5184 \sqrt{3}}",1,"(2267*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/2592 - ((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2))/15 + ((7969 + 3006*x)*(2 + 5*x + 3*x^2)^(3/2))/1620 - (2267*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(5184*Sqrt[3])","A",5,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2409,1,85,0,0.0268036,"\int (5-x) (3+2 x) \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{108} (109-18 x) \left(3 x^2+5 x+2\right)^{3/2}+\frac{559}{864} (6 x+5) \sqrt{3 x^2+5 x+2}-\frac{559 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1728 \sqrt{3}}","\frac{1}{108} (109-18 x) \left(3 x^2+5 x+2\right)^{3/2}+\frac{559}{864} (6 x+5) \sqrt{3 x^2+5 x+2}-\frac{559 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1728 \sqrt{3}}",1,"(559*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/864 + ((109 - 18*x)*(2 + 5*x + 3*x^2)^(3/2))/108 - (559*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(1728*Sqrt[3])","A",4,4,25,0.1600,1,"{779, 612, 621, 206}"
2410,1,80,0,0.0226837,"\int (5-x) \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{9} \left(3 x^2+5 x+2\right)^{3/2}+\frac{35}{72} (6 x+5) \sqrt{3 x^2+5 x+2}-\frac{35 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{144 \sqrt{3}}","-\frac{1}{9} \left(3 x^2+5 x+2\right)^{3/2}+\frac{35}{72} (6 x+5) \sqrt{3 x^2+5 x+2}-\frac{35 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{144 \sqrt{3}}",1,"(35*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/72 - (2 + 5*x + 3*x^2)^(3/2)/9 - (35*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(144*Sqrt[3])","A",4,4,20,0.2000,1,"{640, 612, 621, 206}"
2411,1,100,0,0.0619984,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{3+2 x} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x),x]","\frac{1}{24} \sqrt{3 x^2+5 x+2} (73-6 x)-\frac{311 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{48 \sqrt{3}}+\frac{13}{8} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","\frac{1}{24} \sqrt{3 x^2+5 x+2} (73-6 x)-\frac{311 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{48 \sqrt{3}}+\frac{13}{8} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"((73 - 6*x)*Sqrt[2 + 5*x + 3*x^2])/24 - (311*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(48*Sqrt[3]) + (13*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/8","A",6,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
2412,1,105,0,0.0596928,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^2} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2,x]","-\frac{\sqrt{3 x^2+5 x+2} (x+8)}{2 (2 x+3)}+\frac{43 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{8 \sqrt{3}}-\frac{57 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{8 \sqrt{5}}","-\frac{\sqrt{3 x^2+5 x+2} (x+8)}{2 (2 x+3)}+\frac{43 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{8 \sqrt{3}}-\frac{57 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{8 \sqrt{5}}",1,"-((8 + x)*Sqrt[2 + 5*x + 3*x^2])/(2*(3 + 2*x)) + (43*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(8*Sqrt[3]) - (57*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(8*Sqrt[5])","A",6,5,27,0.1852,1,"{812, 843, 621, 206, 724}"
2413,1,107,0,0.060585,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^3} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^3,x]","\frac{\sqrt{3 x^2+5 x+2} (124 x+121)}{40 (2 x+3)^2}-\frac{1}{8} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{27 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{80 \sqrt{5}}","\frac{\sqrt{3 x^2+5 x+2} (124 x+121)}{40 (2 x+3)^2}-\frac{1}{8} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{27 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{80 \sqrt{5}}",1,"((121 + 124*x)*Sqrt[2 + 5*x + 3*x^2])/(40*(3 + 2*x)^2) - (Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/8 + (27*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(80*Sqrt[5])","A",6,5,27,0.1852,1,"{810, 843, 621, 206, 724}"
2414,1,94,0,0.0443192,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^4} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^4,x]","-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{15 (2 x+3)^3}+\frac{47 (8 x+7) \sqrt{3 x^2+5 x+2}}{200 (2 x+3)^2}-\frac{47 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{400 \sqrt{5}}","-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{15 (2 x+3)^3}+\frac{47 (8 x+7) \sqrt{3 x^2+5 x+2}}{200 (2 x+3)^2}-\frac{47 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{400 \sqrt{5}}",1,"(47*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(200*(3 + 2*x)^2) - (13*(2 + 5*x + 3*x^2)^(3/2))/(15*(3 + 2*x)^3) - (47*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(400*Sqrt[5])","A",4,4,27,0.1481,1,"{806, 720, 724, 206}"
2415,1,119,0,0.0642309,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^5} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^5,x]","-\frac{4 \left(3 x^2+5 x+2\right)^{3/2}}{5 (2 x+3)^3}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{20 (2 x+3)^4}+\frac{153 (8 x+7) \sqrt{3 x^2+5 x+2}}{800 (2 x+3)^2}-\frac{153 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1600 \sqrt{5}}","-\frac{4 \left(3 x^2+5 x+2\right)^{3/2}}{5 (2 x+3)^3}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{20 (2 x+3)^4}+\frac{153 (8 x+7) \sqrt{3 x^2+5 x+2}}{800 (2 x+3)^2}-\frac{153 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1600 \sqrt{5}}",1,"(153*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(800*(3 + 2*x)^2) - (13*(2 + 5*x + 3*x^2)^(3/2))/(20*(3 + 2*x)^4) - (4*(2 + 5*x + 3*x^2)^(3/2))/(5*(3 + 2*x)^3) - (153*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(1600*Sqrt[5])","A",5,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2416,1,144,0,0.0898709,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^6} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^6,x]","-\frac{87 \left(3 x^2+5 x+2\right)^{3/2}}{125 (2 x+3)^3}-\frac{339 \left(3 x^2+5 x+2\right)^{3/2}}{500 (2 x+3)^4}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{25 (2 x+3)^5}+\frac{3159 (8 x+7) \sqrt{3 x^2+5 x+2}}{20000 (2 x+3)^2}-\frac{3159 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40000 \sqrt{5}}","-\frac{87 \left(3 x^2+5 x+2\right)^{3/2}}{125 (2 x+3)^3}-\frac{339 \left(3 x^2+5 x+2\right)^{3/2}}{500 (2 x+3)^4}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{25 (2 x+3)^5}+\frac{3159 (8 x+7) \sqrt{3 x^2+5 x+2}}{20000 (2 x+3)^2}-\frac{3159 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40000 \sqrt{5}}",1,"(3159*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20000*(3 + 2*x)^2) - (13*(2 + 5*x + 3*x^2)^(3/2))/(25*(3 + 2*x)^5) - (339*(2 + 5*x + 3*x^2)^(3/2))/(500*(3 + 2*x)^4) - (87*(2 + 5*x + 3*x^2)^(3/2))/(125*(3 + 2*x)^3) - (3159*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40000*Sqrt[5])","A",6,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2417,1,169,0,0.1091713,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^7} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^7,x]","-\frac{2237 \left(3 x^2+5 x+2\right)^{3/2}}{3750 (2 x+3)^3}-\frac{3113 \left(3 x^2+5 x+2\right)^{3/2}}{5000 (2 x+3)^4}-\frac{73 \left(3 x^2+5 x+2\right)^{3/2}}{125 (2 x+3)^5}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{30 (2 x+3)^6}+\frac{26453 (8 x+7) \sqrt{3 x^2+5 x+2}}{200000 (2 x+3)^2}-\frac{26453 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{400000 \sqrt{5}}","-\frac{2237 \left(3 x^2+5 x+2\right)^{3/2}}{3750 (2 x+3)^3}-\frac{3113 \left(3 x^2+5 x+2\right)^{3/2}}{5000 (2 x+3)^4}-\frac{73 \left(3 x^2+5 x+2\right)^{3/2}}{125 (2 x+3)^5}-\frac{13 \left(3 x^2+5 x+2\right)^{3/2}}{30 (2 x+3)^6}+\frac{26453 (8 x+7) \sqrt{3 x^2+5 x+2}}{200000 (2 x+3)^2}-\frac{26453 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{400000 \sqrt{5}}",1,"(26453*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(200000*(3 + 2*x)^2) - (13*(2 + 5*x + 3*x^2)^(3/2))/(30*(3 + 2*x)^6) - (73*(2 + 5*x + 3*x^2)^(3/2))/(125*(3 + 2*x)^5) - (3113*(2 + 5*x + 3*x^2)^(3/2))/(5000*(3 + 2*x)^4) - (2237*(2 + 5*x + 3*x^2)^(3/2))/(3750*(3 + 2*x)^3) - (26453*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(400000*Sqrt[5])","A",7,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2418,1,183,0,0.1079745,"\int (5-x) (3+2 x)^4 \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{1}{27} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^4+\frac{299}{648} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^3+\frac{487}{486} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^2+\frac{(188910 x+420721) \left(3 x^2+5 x+2\right)^{5/2}}{58320}+\frac{454969 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{559872}-\frac{454969 (6 x+5) \sqrt{3 x^2+5 x+2}}{4478976}+\frac{454969 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{8957952 \sqrt{3}}","-\frac{1}{27} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^4+\frac{299}{648} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^3+\frac{487}{486} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^2+\frac{(188910 x+420721) \left(3 x^2+5 x+2\right)^{5/2}}{58320}+\frac{454969 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{559872}-\frac{454969 (6 x+5) \sqrt{3 x^2+5 x+2}}{4478976}+\frac{454969 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{8957952 \sqrt{3}}",1,"(-454969*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/4478976 + (454969*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/559872 + (487*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2))/486 + (299*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(5/2))/648 - ((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(5/2))/27 + ((420721 + 188910*x)*(2 + 5*x + 3*x^2)^(5/2))/58320 + (454969*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(8957952*Sqrt[3])","A",8,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2419,1,158,0,0.082797,"\int (5-x) (3+2 x)^3 \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{1}{24} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^3+\frac{67}{126} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^2+\frac{(33210 x+75451) \left(3 x^2+5 x+2\right)^{5/2}}{15120}+\frac{12277 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{20736}-\frac{12277 (6 x+5) \sqrt{3 x^2+5 x+2}}{165888}+\frac{12277 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{331776 \sqrt{3}}","-\frac{1}{24} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^3+\frac{67}{126} \left(3 x^2+5 x+2\right)^{5/2} (2 x+3)^2+\frac{(33210 x+75451) \left(3 x^2+5 x+2\right)^{5/2}}{15120}+\frac{12277 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{20736}-\frac{12277 (6 x+5) \sqrt{3 x^2+5 x+2}}{165888}+\frac{12277 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{331776 \sqrt{3}}",1,"(-12277*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/165888 + (12277*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/20736 + (67*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2))/126 - ((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(5/2))/24 + ((75451 + 33210*x)*(2 + 5*x + 3*x^2)^(5/2))/15120 + (12277*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(331776*Sqrt[3])","A",7,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2420,1,133,0,0.0612113,"\int (5-x) (3+2 x)^2 \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{1}{21} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{5/2}+\frac{(2370 x+5827) \left(3 x^2+5 x+2\right)^{5/2}}{1890}+\frac{1129 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{2592}-\frac{1129 (6 x+5) \sqrt{3 x^2+5 x+2}}{20736}+\frac{1129 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{41472 \sqrt{3}}","-\frac{1}{21} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{5/2}+\frac{(2370 x+5827) \left(3 x^2+5 x+2\right)^{5/2}}{1890}+\frac{1129 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{2592}-\frac{1129 (6 x+5) \sqrt{3 x^2+5 x+2}}{20736}+\frac{1129 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{41472 \sqrt{3}}",1,"(-1129*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/20736 + (1129*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/2592 - ((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2))/21 + ((5827 + 2370*x)*(2 + 5*x + 3*x^2)^(5/2))/1890 + (1129*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(41472*Sqrt[3])","A",6,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2421,1,108,0,0.0391732,"\int (5-x) (3+2 x) \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2),x]","\frac{1}{270} (161-30 x) \left(3 x^2+5 x+2\right)^{5/2}+\frac{839 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{2592}-\frac{839 (6 x+5) \sqrt{3 x^2+5 x+2}}{20736}+\frac{839 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{41472 \sqrt{3}}","\frac{1}{270} (161-30 x) \left(3 x^2+5 x+2\right)^{5/2}+\frac{839 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{2592}-\frac{839 (6 x+5) \sqrt{3 x^2+5 x+2}}{20736}+\frac{839 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{41472 \sqrt{3}}",1,"(-839*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/20736 + (839*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/2592 + ((161 - 30*x)*(2 + 5*x + 3*x^2)^(5/2))/270 + (839*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(41472*Sqrt[3])","A",5,4,25,0.1600,1,"{779, 612, 621, 206}"
2422,1,103,0,0.0288204,"\int (5-x) \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{1}{15} \left(3 x^2+5 x+2\right)^{5/2}+\frac{35}{144} (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}-\frac{35 (6 x+5) \sqrt{3 x^2+5 x+2}}{1152}+\frac{35 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{2304 \sqrt{3}}","-\frac{1}{15} \left(3 x^2+5 x+2\right)^{5/2}+\frac{35}{144} (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}-\frac{35 (6 x+5) \sqrt{3 x^2+5 x+2}}{1152}+\frac{35 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{2304 \sqrt{3}}",1,"(-35*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/1152 + (35*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/144 - (2 + 5*x + 3*x^2)^(5/2)/15 + (35*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(2304*Sqrt[3])","A",5,4,20,0.2000,1,"{640, 612, 621, 206}"
2423,1,123,0,0.0789957,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{3+2 x} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x),x]","\frac{1}{48} (47-6 x) \left(3 x^2+5 x+2\right)^{3/2}+\frac{1}{128} (175-414 x) \sqrt{3 x^2+5 x+2}-\frac{2011 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{256 \sqrt{3}}+\frac{65}{32} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","\frac{1}{48} (47-6 x) \left(3 x^2+5 x+2\right)^{3/2}+\frac{1}{128} (175-414 x) \sqrt{3 x^2+5 x+2}-\frac{2011 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{256 \sqrt{3}}+\frac{65}{32} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"((175 - 414*x)*Sqrt[2 + 5*x + 3*x^2])/128 + ((47 - 6*x)*(2 + 5*x + 3*x^2)^(3/2))/48 - (2011*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(256*Sqrt[3]) + (65*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/32","A",7,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
2424,1,128,0,0.0825067,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^2} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^2,x]","-\frac{(x+21) \left(3 x^2+5 x+2\right)^{3/2}}{6 (2 x+3)}-\frac{1}{96} (361-726 x) \sqrt{3 x^2+5 x+2}+\frac{3743 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{192 \sqrt{3}}-\frac{161}{32} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","-\frac{(x+21) \left(3 x^2+5 x+2\right)^{3/2}}{6 (2 x+3)}-\frac{1}{96} (361-726 x) \sqrt{3 x^2+5 x+2}+\frac{3743 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{192 \sqrt{3}}-\frac{161}{32} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"-((361 - 726*x)*Sqrt[2 + 5*x + 3*x^2])/96 - ((21 + x)*(2 + 5*x + 3*x^2)^(3/2))/(6*(3 + 2*x)) + (3743*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(192*Sqrt[3]) - (161*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/32","A",7,6,27,0.2222,1,"{812, 814, 843, 621, 206, 724}"
2425,1,135,0,0.0816325,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^3} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^3,x]","-\frac{(x+8) \left(3 x^2+5 x+2\right)^{3/2}}{4 (2 x+3)^2}+\frac{3 (43 x+93) \sqrt{3 x^2+5 x+2}}{16 (2 x+3)}-\frac{343}{64} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{1329 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{64 \sqrt{5}}","-\frac{(x+8) \left(3 x^2+5 x+2\right)^{3/2}}{4 (2 x+3)^2}+\frac{3 (43 x+93) \sqrt{3 x^2+5 x+2}}{16 (2 x+3)}-\frac{343}{64} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{1329 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{64 \sqrt{5}}",1,"(3*(93 + 43*x)*Sqrt[2 + 5*x + 3*x^2])/(16*(3 + 2*x)) - ((8 + x)*(2 + 5*x + 3*x^2)^(3/2))/(4*(3 + 2*x)^2) - (343*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/64 + (1329*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(64*Sqrt[5])","A",7,5,27,0.1852,1,"{812, 843, 621, 206, 724}"
2426,1,137,0,0.0810219,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^4} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^4,x]","\frac{(342 x+383) \left(3 x^2+5 x+2\right)^{3/2}}{120 (2 x+3)^3}-\frac{(402 x+845) \sqrt{3 x^2+5 x+2}}{160 (2 x+3)}+\frac{51}{32} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)-\frac{1973 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{320 \sqrt{5}}","\frac{(342 x+383) \left(3 x^2+5 x+2\right)^{3/2}}{120 (2 x+3)^3}-\frac{(402 x+845) \sqrt{3 x^2+5 x+2}}{160 (2 x+3)}+\frac{51}{32} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)-\frac{1973 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{320 \sqrt{5}}",1,"-((845 + 402*x)*Sqrt[2 + 5*x + 3*x^2])/(160*(3 + 2*x)) + ((383 + 342*x)*(2 + 5*x + 3*x^2)^(3/2))/(120*(3 + 2*x)^3) + (51*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/32 - (1973*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(320*Sqrt[5])","A",7,6,27,0.2222,1,"{810, 812, 843, 621, 206, 724}"
2427,1,137,0,0.0799698,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^5} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^5,x]","\frac{(352 x+333) \left(3 x^2+5 x+2\right)^{3/2}}{240 (2 x+3)^4}+\frac{(1528 x+2087) \sqrt{3 x^2+5 x+2}}{3200 (2 x+3)^2}-\frac{3}{32} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{2359 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{6400 \sqrt{5}}","\frac{(352 x+333) \left(3 x^2+5 x+2\right)^{3/2}}{240 (2 x+3)^4}+\frac{(1528 x+2087) \sqrt{3 x^2+5 x+2}}{3200 (2 x+3)^2}-\frac{3}{32} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{2359 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{6400 \sqrt{5}}",1,"((2087 + 1528*x)*Sqrt[2 + 5*x + 3*x^2])/(3200*(3 + 2*x)^2) + ((333 + 352*x)*(2 + 5*x + 3*x^2)^(3/2))/(240*(3 + 2*x)^4) - (3*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/32 + (2359*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(6400*Sqrt[5])","A",7,5,27,0.1852,1,"{810, 843, 621, 206, 724}"
2428,1,124,0,0.0616323,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^6} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^6,x]","-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{25 (2 x+3)^5}+\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{400 (2 x+3)^4}-\frac{141 (8 x+7) \sqrt{3 x^2+5 x+2}}{16000 (2 x+3)^2}+\frac{141 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{32000 \sqrt{5}}","-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{25 (2 x+3)^5}+\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{400 (2 x+3)^4}-\frac{141 (8 x+7) \sqrt{3 x^2+5 x+2}}{16000 (2 x+3)^2}+\frac{141 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{32000 \sqrt{5}}",1,"(-141*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(16000*(3 + 2*x)^2) + (47*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(400*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(25*(3 + 2*x)^5) + (141*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(32000*Sqrt[5])","A",5,4,27,0.1481,1,"{806, 720, 724, 206}"
2429,1,149,0,0.0819372,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^7} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^7,x]","-\frac{167 \left(3 x^2+5 x+2\right)^{5/2}}{375 (2 x+3)^5}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{30 (2 x+3)^6}+\frac{1141 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{12000 (2 x+3)^4}-\frac{1141 (8 x+7) \sqrt{3 x^2+5 x+2}}{160000 (2 x+3)^2}+\frac{1141 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{320000 \sqrt{5}}","-\frac{167 \left(3 x^2+5 x+2\right)^{5/2}}{375 (2 x+3)^5}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{30 (2 x+3)^6}+\frac{1141 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{12000 (2 x+3)^4}-\frac{1141 (8 x+7) \sqrt{3 x^2+5 x+2}}{160000 (2 x+3)^2}+\frac{1141 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{320000 \sqrt{5}}",1,"(-1141*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(160000*(3 + 2*x)^2) + (1141*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(12000*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(30*(3 + 2*x)^6) - (167*(2 + 5*x + 3*x^2)^(5/2))/(375*(3 + 2*x)^5) + (1141*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(320000*Sqrt[5])","A",6,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2430,1,174,0,0.1067459,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^8} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^8,x]","-\frac{4892 \left(3 x^2+5 x+2\right)^{5/2}}{13125 (2 x+3)^5}-\frac{433 \left(3 x^2+5 x+2\right)^{5/2}}{1050 (2 x+3)^6}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{35 (2 x+3)^7}+\frac{4663 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{60000 (2 x+3)^4}-\frac{4663 (8 x+7) \sqrt{3 x^2+5 x+2}}{800000 (2 x+3)^2}+\frac{4663 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1600000 \sqrt{5}}","-\frac{4892 \left(3 x^2+5 x+2\right)^{5/2}}{13125 (2 x+3)^5}-\frac{433 \left(3 x^2+5 x+2\right)^{5/2}}{1050 (2 x+3)^6}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{35 (2 x+3)^7}+\frac{4663 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{60000 (2 x+3)^4}-\frac{4663 (8 x+7) \sqrt{3 x^2+5 x+2}}{800000 (2 x+3)^2}+\frac{4663 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1600000 \sqrt{5}}",1,"(-4663*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(800000*(3 + 2*x)^2) + (4663*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(60000*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(35*(3 + 2*x)^7) - (433*(2 + 5*x + 3*x^2)^(5/2))/(1050*(3 + 2*x)^6) - (4892*(2 + 5*x + 3*x^2)^(5/2))/(13125*(3 + 2*x)^5) + (4663*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(1600000*Sqrt[5])","A",7,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2431,1,199,0,0.1349134,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^9} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^9,x]","-\frac{3879 \left(3 x^2+5 x+2\right)^{5/2}}{12500 (2 x+3)^5}-\frac{717 \left(3 x^2+5 x+2\right)^{5/2}}{2000 (2 x+3)^6}-\frac{19 \left(3 x^2+5 x+2\right)^{5/2}}{50 (2 x+3)^7}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{40 (2 x+3)^8}+\frac{51309 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{800000 (2 x+3)^4}-\frac{153927 (8 x+7) \sqrt{3 x^2+5 x+2}}{32000000 (2 x+3)^2}+\frac{153927 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{64000000 \sqrt{5}}","-\frac{3879 \left(3 x^2+5 x+2\right)^{5/2}}{12500 (2 x+3)^5}-\frac{717 \left(3 x^2+5 x+2\right)^{5/2}}{2000 (2 x+3)^6}-\frac{19 \left(3 x^2+5 x+2\right)^{5/2}}{50 (2 x+3)^7}-\frac{13 \left(3 x^2+5 x+2\right)^{5/2}}{40 (2 x+3)^8}+\frac{51309 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{800000 (2 x+3)^4}-\frac{153927 (8 x+7) \sqrt{3 x^2+5 x+2}}{32000000 (2 x+3)^2}+\frac{153927 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{64000000 \sqrt{5}}",1,"(-153927*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(32000000*(3 + 2*x)^2) + (51309*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(800000*(3 + 2*x)^4) - (13*(2 + 5*x + 3*x^2)^(5/2))/(40*(3 + 2*x)^8) - (19*(2 + 5*x + 3*x^2)^(5/2))/(50*(3 + 2*x)^7) - (717*(2 + 5*x + 3*x^2)^(5/2))/(2000*(3 + 2*x)^6) - (3879*(2 + 5*x + 3*x^2)^(5/2))/(12500*(3 + 2*x)^5) + (153927*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(64000000*Sqrt[5])","A",8,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2432,1,206,0,0.1183778,"\int (5-x) (3+2 x)^4 \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{1}{33} \left(3 x^2+5 x+2\right)^{7/2} (2 x+3)^4+\frac{41}{110} \left(3 x^2+5 x+2\right)^{7/2} (2 x+3)^3+\frac{3298 \left(3 x^2+5 x+2\right)^{7/2} (2 x+3)^2}{4455}+\frac{(3365726 x+7405817) \left(3 x^2+5 x+2\right)^{7/2}}{1496880}+\frac{249299 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{466560}-\frac{249299 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{4478976}+\frac{249299 (6 x+5) \sqrt{3 x^2+5 x+2}}{35831808}-\frac{249299 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{71663616 \sqrt{3}}","-\frac{1}{33} \left(3 x^2+5 x+2\right)^{7/2} (2 x+3)^4+\frac{41}{110} \left(3 x^2+5 x+2\right)^{7/2} (2 x+3)^3+\frac{3298 \left(3 x^2+5 x+2\right)^{7/2} (2 x+3)^2}{4455}+\frac{(3365726 x+7405817) \left(3 x^2+5 x+2\right)^{7/2}}{1496880}+\frac{249299 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{466560}-\frac{249299 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{4478976}+\frac{249299 (6 x+5) \sqrt{3 x^2+5 x+2}}{35831808}-\frac{249299 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{71663616 \sqrt{3}}",1,"(249299*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/35831808 - (249299*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/4478976 + (249299*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/466560 + (3298*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(7/2))/4455 + (41*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(7/2))/110 - ((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(7/2))/33 + ((7405817 + 3365726*x)*(2 + 5*x + 3*x^2)^(7/2))/1496880 - (249299*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(71663616*Sqrt[3])","A",9,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2433,1,181,0,0.0975396,"\int (5-x) (3+2 x)^3 \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{1}{30} (2 x+3)^3 \left(3 x^2+5 x+2\right)^{7/2}+\frac{169}{405} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{7/2}+\frac{(213878 x+477101) \left(3 x^2+5 x+2\right)^{7/2}}{136080}+\frac{182917 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{466560}-\frac{182917 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{4478976}+\frac{182917 (6 x+5) \sqrt{3 x^2+5 x+2}}{35831808}-\frac{182917 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{71663616 \sqrt{3}}","-\frac{1}{30} (2 x+3)^3 \left(3 x^2+5 x+2\right)^{7/2}+\frac{169}{405} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{7/2}+\frac{(213878 x+477101) \left(3 x^2+5 x+2\right)^{7/2}}{136080}+\frac{182917 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{466560}-\frac{182917 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{4478976}+\frac{182917 (6 x+5) \sqrt{3 x^2+5 x+2}}{35831808}-\frac{182917 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{71663616 \sqrt{3}}",1,"(182917*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/35831808 - (182917*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/4478976 + (182917*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/466560 + (169*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(7/2))/405 - ((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(7/2))/30 + ((477101 + 213878*x)*(2 + 5*x + 3*x^2)^(7/2))/136080 - (182917*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(71663616*Sqrt[3])","A",8,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2434,1,156,0,0.0700996,"\int (5-x) (3+2 x)^2 \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{1}{27} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{7/2}+\frac{(4298 x+10211) \left(3 x^2+5 x+2\right)^{7/2}}{4536}+\frac{4507 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{15552}-\frac{22535 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{746496}+\frac{22535 (6 x+5) \sqrt{3 x^2+5 x+2}}{5971968}-\frac{22535 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{11943936 \sqrt{3}}","-\frac{1}{27} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{7/2}+\frac{(4298 x+10211) \left(3 x^2+5 x+2\right)^{7/2}}{4536}+\frac{4507 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{15552}-\frac{22535 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{746496}+\frac{22535 (6 x+5) \sqrt{3 x^2+5 x+2}}{5971968}-\frac{22535 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{11943936 \sqrt{3}}",1,"(22535*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/5971968 - (22535*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/746496 + (4507*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/15552 - ((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(7/2))/27 + ((10211 + 4298*x)*(2 + 5*x + 3*x^2)^(7/2))/4536 - (22535*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(11943936*Sqrt[3])","A",7,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2435,1,131,0,0.0455891,"\int (5-x) (3+2 x) \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)*(2 + 5*x + 3*x^2)^(5/2),x]","\frac{1}{168} (71-14 x) \left(3 x^2+5 x+2\right)^{7/2}+\frac{373 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{1728}-\frac{1865 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{82944}+\frac{1865 (6 x+5) \sqrt{3 x^2+5 x+2}}{663552}-\frac{1865 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1327104 \sqrt{3}}","\frac{1}{168} (71-14 x) \left(3 x^2+5 x+2\right)^{7/2}+\frac{373 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{1728}-\frac{1865 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{82944}+\frac{1865 (6 x+5) \sqrt{3 x^2+5 x+2}}{663552}-\frac{1865 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1327104 \sqrt{3}}",1,"(1865*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/663552 - (1865*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/82944 + (373*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/1728 + ((71 - 14*x)*(2 + 5*x + 3*x^2)^(7/2))/168 - (1865*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(1327104*Sqrt[3])","A",6,4,25,0.1600,1,"{779, 612, 621, 206}"
2436,1,126,0,0.040626,"\int (5-x) \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{1}{21} \left(3 x^2+5 x+2\right)^{7/2}+\frac{35}{216} (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}-\frac{175 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{10368}+\frac{175 (6 x+5) \sqrt{3 x^2+5 x+2}}{82944}-\frac{175 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{165888 \sqrt{3}}","-\frac{1}{21} \left(3 x^2+5 x+2\right)^{7/2}+\frac{35}{216} (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}-\frac{175 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{10368}+\frac{175 (6 x+5) \sqrt{3 x^2+5 x+2}}{82944}-\frac{175 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{165888 \sqrt{3}}",1,"(175*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/82944 - (175*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/10368 + (35*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/216 - (2 + 5*x + 3*x^2)^(7/2)/21 - (175*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(165888*Sqrt[3])","A",6,4,20,0.2000,1,"{640, 612, 621, 206}"
2437,1,146,0,0.0999991,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{3+2 x} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x),x]","\frac{1}{360} (209-30 x) \left(3 x^2+5 x+2\right)^{5/2}+\frac{(25-5586 x) \left(3 x^2+5 x+2\right)^{3/2}}{3456}+\frac{(51455-106734 x) \sqrt{3 x^2+5 x+2}}{27648}-\frac{543811 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{55296 \sqrt{3}}+\frac{325}{128} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","\frac{1}{360} (209-30 x) \left(3 x^2+5 x+2\right)^{5/2}+\frac{(25-5586 x) \left(3 x^2+5 x+2\right)^{3/2}}{3456}+\frac{(51455-106734 x) \sqrt{3 x^2+5 x+2}}{27648}-\frac{543811 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{55296 \sqrt{3}}+\frac{325}{128} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"((51455 - 106734*x)*Sqrt[2 + 5*x + 3*x^2])/27648 + ((25 - 5586*x)*(2 + 5*x + 3*x^2)^(3/2))/3456 + ((209 - 30*x)*(2 + 5*x + 3*x^2)^(5/2))/360 - (543811*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(55296*Sqrt[3]) + (325*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/128","A",8,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
2438,1,151,0,0.1021596,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^2} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^2,x]","-\frac{(x+34) \left(3 x^2+5 x+2\right)^{5/2}}{10 (2 x+3)}-\frac{1}{192} (65-1194 x) \left(3 x^2+5 x+2\right)^{3/2}-\frac{1}{512} (3865-8082 x) \sqrt{3 x^2+5 x+2}+\frac{41053 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1024 \sqrt{3}}-\frac{1325}{128} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","-\frac{(x+34) \left(3 x^2+5 x+2\right)^{5/2}}{10 (2 x+3)}-\frac{1}{192} (65-1194 x) \left(3 x^2+5 x+2\right)^{3/2}-\frac{1}{512} (3865-8082 x) \sqrt{3 x^2+5 x+2}+\frac{41053 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1024 \sqrt{3}}-\frac{1325}{128} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"-((3865 - 8082*x)*Sqrt[2 + 5*x + 3*x^2])/512 - ((65 - 1194*x)*(2 + 5*x + 3*x^2)^(3/2))/192 - ((34 + x)*(2 + 5*x + 3*x^2)^(5/2))/(10*(3 + 2*x)) + (41053*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(1024*Sqrt[3]) - (1325*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/128","A",8,6,27,0.2222,1,"{812, 814, 843, 621, 206, 724}"
2439,1,160,0,0.1037461,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^3} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^3,x]","-\frac{(2 x+29) \left(3 x^2+5 x+2\right)^{5/2}}{16 (2 x+3)^2}+\frac{5 (164 x+573) \left(3 x^2+5 x+2\right)^{3/2}}{192 (2 x+3)}+\frac{5 (3763-7854 x) \sqrt{3 x^2+5 x+2}}{1536}-\frac{199615 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{3072 \sqrt{3}}+\frac{4295}{256} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","-\frac{(2 x+29) \left(3 x^2+5 x+2\right)^{5/2}}{16 (2 x+3)^2}+\frac{5 (164 x+573) \left(3 x^2+5 x+2\right)^{3/2}}{192 (2 x+3)}+\frac{5 (3763-7854 x) \sqrt{3 x^2+5 x+2}}{1536}-\frac{199615 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{3072 \sqrt{3}}+\frac{4295}{256} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"(5*(3763 - 7854*x)*Sqrt[2 + 5*x + 3*x^2])/1536 + (5*(573 + 164*x)*(2 + 5*x + 3*x^2)^(3/2))/(192*(3 + 2*x)) - ((29 + 2*x)*(2 + 5*x + 3*x^2)^(5/2))/(16*(3 + 2*x)^2) - (199615*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(3072*Sqrt[3]) + (4295*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/256","A",8,6,27,0.2222,1,"{812, 814, 843, 621, 206, 724}"
2440,1,165,0,0.1098661,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^4} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^4,x]","-\frac{(x+8) \left(3 x^2+5 x+2\right)^{5/2}}{6 (2 x+3)^3}+\frac{5 (43 x+93) \left(3 x^2+5 x+2\right)^{3/2}}{48 (2 x+3)^2}-\frac{5 (343 x+736) \sqrt{3 x^2+5 x+2}}{64 (2 x+3)}+\frac{13505 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{256 \sqrt{3}}-\frac{3487}{256} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","-\frac{(x+8) \left(3 x^2+5 x+2\right)^{5/2}}{6 (2 x+3)^3}+\frac{5 (43 x+93) \left(3 x^2+5 x+2\right)^{3/2}}{48 (2 x+3)^2}-\frac{5 (343 x+736) \sqrt{3 x^2+5 x+2}}{64 (2 x+3)}+\frac{13505 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{256 \sqrt{3}}-\frac{3487}{256} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"(-5*(736 + 343*x)*Sqrt[2 + 5*x + 3*x^2])/(64*(3 + 2*x)) + (5*(93 + 43*x)*(2 + 5*x + 3*x^2)^(3/2))/(48*(3 + 2*x)^2) - ((8 + x)*(2 + 5*x + 3*x^2)^(5/2))/(6*(3 + 2*x)^3) + (13505*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(256*Sqrt[3]) - (3487*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/256","A",8,5,27,0.1852,1,"{812, 843, 621, 206, 724}"
2441,1,167,0,0.1035955,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^5} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^5,x]","-\frac{(4 x+19) \left(3 x^2+5 x+2\right)^{5/2}}{16 (2 x+3)^4}-\frac{(2898 x+3727) \left(3 x^2+5 x+2\right)^{3/2}}{384 (2 x+3)^3}+\frac{(5718 x+12265) \sqrt{3 x^2+5 x+2}}{512 (2 x+3)}-\frac{1875}{256} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{29047 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1024 \sqrt{5}}","-\frac{(4 x+19) \left(3 x^2+5 x+2\right)^{5/2}}{16 (2 x+3)^4}-\frac{(2898 x+3727) \left(3 x^2+5 x+2\right)^{3/2}}{384 (2 x+3)^3}+\frac{(5718 x+12265) \sqrt{3 x^2+5 x+2}}{512 (2 x+3)}-\frac{1875}{256} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{29047 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1024 \sqrt{5}}",1,"((12265 + 5718*x)*Sqrt[2 + 5*x + 3*x^2])/(512*(3 + 2*x)) - ((3727 + 2898*x)*(2 + 5*x + 3*x^2)^(3/2))/(384*(3 + 2*x)^3) - ((19 + 4*x)*(2 + 5*x + 3*x^2)^(5/2))/(16*(3 + 2*x)^4) - (1875*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/256 + (29047*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(1024*Sqrt[5])","A",8,6,27,0.2222,1,"{812, 810, 843, 621, 206, 724}"
2442,1,167,0,0.1060515,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^6} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^6,x]","\frac{(114 x+119) \left(3 x^2+5 x+2\right)^{5/2}}{80 (2 x+3)^5}+\frac{(13074 x+17051) \left(3 x^2+5 x+2\right)^{3/2}}{9600 (2 x+3)^3}-\frac{(26934 x+57845) \sqrt{3 x^2+5 x+2}}{12800 (2 x+3)}+\frac{177}{128} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)-\frac{137111 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25600 \sqrt{5}}","\frac{(114 x+119) \left(3 x^2+5 x+2\right)^{5/2}}{80 (2 x+3)^5}+\frac{(13074 x+17051) \left(3 x^2+5 x+2\right)^{3/2}}{9600 (2 x+3)^3}-\frac{(26934 x+57845) \sqrt{3 x^2+5 x+2}}{12800 (2 x+3)}+\frac{177}{128} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)-\frac{137111 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25600 \sqrt{5}}",1,"-((57845 + 26934*x)*Sqrt[2 + 5*x + 3*x^2])/(12800*(3 + 2*x)) + ((17051 + 13074*x)*(2 + 5*x + 3*x^2)^(3/2))/(9600*(3 + 2*x)^3) + ((119 + 114*x)*(2 + 5*x + 3*x^2)^(5/2))/(80*(3 + 2*x)^5) + (177*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/128 - (137111*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(25600*Sqrt[5])","A",8,6,27,0.2222,1,"{810, 812, 843, 621, 206, 724}"
2443,1,167,0,0.1034883,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^7} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^7,x]","\frac{(116 x+109) \left(3 x^2+5 x+2\right)^{5/2}}{120 (2 x+3)^6}+\frac{(328 x+437) \left(3 x^2+5 x+2\right)^{3/2}}{1920 (2 x+3)^4}+\frac{(10952 x+14083) \sqrt{3 x^2+5 x+2}}{25600 (2 x+3)^2}-\frac{9}{128} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{13931 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{51200 \sqrt{5}}","\frac{(116 x+109) \left(3 x^2+5 x+2\right)^{5/2}}{120 (2 x+3)^6}+\frac{(328 x+437) \left(3 x^2+5 x+2\right)^{3/2}}{1920 (2 x+3)^4}+\frac{(10952 x+14083) \sqrt{3 x^2+5 x+2}}{25600 (2 x+3)^2}-\frac{9}{128} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{13931 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{51200 \sqrt{5}}",1,"((14083 + 10952*x)*Sqrt[2 + 5*x + 3*x^2])/(25600*(3 + 2*x)^2) + ((437 + 328*x)*(2 + 5*x + 3*x^2)^(3/2))/(1920*(3 + 2*x)^4) + ((109 + 116*x)*(2 + 5*x + 3*x^2)^(5/2))/(120*(3 + 2*x)^6) - (9*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/128 + (13931*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(51200*Sqrt[5])","A",8,5,27,0.1852,1,"{810, 843, 621, 206, 724}"
2444,1,154,0,0.0777246,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^8} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^8,x]","-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{35 (2 x+3)^7}+\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{600 (2 x+3)^6}-\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{9600 (2 x+3)^4}+\frac{47 (8 x+7) \sqrt{3 x^2+5 x+2}}{128000 (2 x+3)^2}-\frac{47 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{256000 \sqrt{5}}","-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{35 (2 x+3)^7}+\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{600 (2 x+3)^6}-\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{9600 (2 x+3)^4}+\frac{47 (8 x+7) \sqrt{3 x^2+5 x+2}}{128000 (2 x+3)^2}-\frac{47 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{256000 \sqrt{5}}",1,"(47*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(128000*(3 + 2*x)^2) - (47*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(9600*(3 + 2*x)^4) + (47*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(600*(3 + 2*x)^6) - (13*(2 + 5*x + 3*x^2)^(7/2))/(35*(3 + 2*x)^7) - (47*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(256000*Sqrt[5])","A",6,4,27,0.1481,1,"{806, 720, 724, 206}"
2445,1,179,0,0.1024817,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^9} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^9,x]","-\frac{107 \left(3 x^2+5 x+2\right)^{7/2}}{350 (2 x+3)^7}-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{40 (2 x+3)^8}+\frac{1517 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{24000 (2 x+3)^6}-\frac{1517 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{384000 (2 x+3)^4}+\frac{1517 (8 x+7) \sqrt{3 x^2+5 x+2}}{5120000 (2 x+3)^2}-\frac{1517 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{10240000 \sqrt{5}}","-\frac{107 \left(3 x^2+5 x+2\right)^{7/2}}{350 (2 x+3)^7}-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{40 (2 x+3)^8}+\frac{1517 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{24000 (2 x+3)^6}-\frac{1517 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{384000 (2 x+3)^4}+\frac{1517 (8 x+7) \sqrt{3 x^2+5 x+2}}{5120000 (2 x+3)^2}-\frac{1517 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{10240000 \sqrt{5}}",1,"(1517*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(5120000*(3 + 2*x)^2) - (1517*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(384000*(3 + 2*x)^4) + (1517*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(24000*(3 + 2*x)^6) - (13*(2 + 5*x + 3*x^2)^(7/2))/(40*(3 + 2*x)^8) - (107*(2 + 5*x + 3*x^2)^(7/2))/(350*(3 + 2*x)^7) - (1517*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(10240000*Sqrt[5])","A",7,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2446,1,204,0,0.1290718,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{10}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^10,x]","-\frac{1321 \left(3 x^2+5 x+2\right)^{7/2}}{5250 (2 x+3)^7}-\frac{527 \left(3 x^2+5 x+2\right)^{7/2}}{1800 (2 x+3)^8}-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{45 (2 x+3)^9}+\frac{6167 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{120000 (2 x+3)^6}-\frac{6167 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{1920000 (2 x+3)^4}+\frac{6167 (8 x+7) \sqrt{3 x^2+5 x+2}}{25600000 (2 x+3)^2}-\frac{6167 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{51200000 \sqrt{5}}","-\frac{1321 \left(3 x^2+5 x+2\right)^{7/2}}{5250 (2 x+3)^7}-\frac{527 \left(3 x^2+5 x+2\right)^{7/2}}{1800 (2 x+3)^8}-\frac{13 \left(3 x^2+5 x+2\right)^{7/2}}{45 (2 x+3)^9}+\frac{6167 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{120000 (2 x+3)^6}-\frac{6167 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{1920000 (2 x+3)^4}+\frac{6167 (8 x+7) \sqrt{3 x^2+5 x+2}}{25600000 (2 x+3)^2}-\frac{6167 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{51200000 \sqrt{5}}",1,"(6167*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(25600000*(3 + 2*x)^2) - (6167*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(1920000*(3 + 2*x)^4) + (6167*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(120000*(3 + 2*x)^6) - (13*(2 + 5*x + 3*x^2)^(7/2))/(45*(3 + 2*x)^9) - (527*(2 + 5*x + 3*x^2)^(7/2))/(1800*(3 + 2*x)^8) - (1321*(2 + 5*x + 3*x^2)^(7/2))/(5250*(3 + 2*x)^7) - (6167*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(51200000*Sqrt[5])","A",8,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2447,1,229,0,0.1407708,"\int (5-x) (3+2 x)^4 \left(2+5 x+3 x^2\right)^{7/2} \, dx","Int[(5 - x)*(3 + 2*x)^4*(2 + 5*x + 3*x^2)^(7/2),x]","-\frac{1}{39} (2 x+3)^4 \left(3 x^2+5 x+2\right)^{9/2}+\frac{439 (2 x+3)^3 \left(3 x^2+5 x+2\right)^{9/2}}{1404}+\frac{205}{351} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{(389394 x+852175) \left(3 x^2+5 x+2\right)^{9/2}}{227448}+\frac{74167 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{186624}-\frac{519169 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{13436928}+\frac{2595845 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{644972544}-\frac{2595845 (6 x+5) \sqrt{3 x^2+5 x+2}}{5159780352}+\frac{2595845 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{10319560704 \sqrt{3}}","-\frac{1}{39} (2 x+3)^4 \left(3 x^2+5 x+2\right)^{9/2}+\frac{439 (2 x+3)^3 \left(3 x^2+5 x+2\right)^{9/2}}{1404}+\frac{205}{351} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{(389394 x+852175) \left(3 x^2+5 x+2\right)^{9/2}}{227448}+\frac{74167 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{186624}-\frac{519169 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{13436928}+\frac{2595845 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{644972544}-\frac{2595845 (6 x+5) \sqrt{3 x^2+5 x+2}}{5159780352}+\frac{2595845 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{10319560704 \sqrt{3}}",1,"(-2595845*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/5159780352 + (2595845*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/644972544 - (519169*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/13436928 + (74167*(5 + 6*x)*(2 + 5*x + 3*x^2)^(7/2))/186624 + (205*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(9/2))/351 + (439*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(9/2))/1404 - ((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(9/2))/39 + ((852175 + 389394*x)*(2 + 5*x + 3*x^2)^(9/2))/227448 + (2595845*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(10319560704*Sqrt[3])","A",10,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2448,1,204,0,0.1065239,"\int (5-x) (3+2 x)^3 \left(2+5 x+3 x^2\right)^{7/2} \, dx","Int[(5 - x)*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(7/2),x]","-\frac{1}{36} (2 x+3)^3 \left(3 x^2+5 x+2\right)^{9/2}+\frac{34}{99} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{(390798 x+863825) \left(3 x^2+5 x+2\right)^{9/2}}{320760}+\frac{91087 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{311040}-\frac{637609 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{22394880}+\frac{637609 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{214990848}-\frac{637609 (6 x+5) \sqrt{3 x^2+5 x+2}}{1719926784}+\frac{637609 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{3439853568 \sqrt{3}}","-\frac{1}{36} (2 x+3)^3 \left(3 x^2+5 x+2\right)^{9/2}+\frac{34}{99} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{(390798 x+863825) \left(3 x^2+5 x+2\right)^{9/2}}{320760}+\frac{91087 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{311040}-\frac{637609 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{22394880}+\frac{637609 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{214990848}-\frac{637609 (6 x+5) \sqrt{3 x^2+5 x+2}}{1719926784}+\frac{637609 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{3439853568 \sqrt{3}}",1,"(-637609*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/1719926784 + (637609*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/214990848 - (637609*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/22394880 + (91087*(5 + 6*x)*(2 + 5*x + 3*x^2)^(7/2))/311040 + (34*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(9/2))/99 - ((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(9/2))/36 + ((863825 + 390798*x)*(2 + 5*x + 3*x^2)^(9/2))/320760 + (637609*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(3439853568*Sqrt[3])","A",9,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2449,1,179,0,0.0837517,"\int (5-x) (3+2 x)^2 \left(2+5 x+3 x^2\right)^{7/2} \, dx","Int[(5 - x)*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(7/2),x]","-\frac{1}{33} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{(20358 x+47425) \left(3 x^2+5 x+2\right)^{9/2}}{26730}+\frac{5627 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{25920}-\frac{39389 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{1866240}+\frac{39389 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{17915904}-\frac{39389 (6 x+5) \sqrt{3 x^2+5 x+2}}{143327232}+\frac{39389 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{286654464 \sqrt{3}}","-\frac{1}{33} (2 x+3)^2 \left(3 x^2+5 x+2\right)^{9/2}+\frac{(20358 x+47425) \left(3 x^2+5 x+2\right)^{9/2}}{26730}+\frac{5627 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{25920}-\frac{39389 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{1866240}+\frac{39389 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{17915904}-\frac{39389 (6 x+5) \sqrt{3 x^2+5 x+2}}{143327232}+\frac{39389 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{286654464 \sqrt{3}}",1,"(-39389*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/143327232 + (39389*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/17915904 - (39389*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/1866240 + (5627*(5 + 6*x)*(2 + 5*x + 3*x^2)^(7/2))/25920 - ((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(9/2))/33 + ((47425 + 20358*x)*(2 + 5*x + 3*x^2)^(9/2))/26730 + (39389*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(286654464*Sqrt[3])","A",8,5,27,0.1852,1,"{832, 779, 612, 621, 206}"
2450,1,154,0,0.0583206,"\int (5-x) (3+2 x) \left(2+5 x+3 x^2\right)^{7/2} \, dx","Int[(5 - x)*(3 + 2*x)*(2 + 5*x + 3*x^2)^(7/2),x]","\frac{1}{810} (265-54 x) \left(3 x^2+5 x+2\right)^{9/2}+\frac{1399 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{8640}-\frac{9793 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{622080}+\frac{9793 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{5971968}-\frac{9793 (6 x+5) \sqrt{3 x^2+5 x+2}}{47775744}+\frac{9793 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{95551488 \sqrt{3}}","\frac{1}{810} (265-54 x) \left(3 x^2+5 x+2\right)^{9/2}+\frac{1399 (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}}{8640}-\frac{9793 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{622080}+\frac{9793 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{5971968}-\frac{9793 (6 x+5) \sqrt{3 x^2+5 x+2}}{47775744}+\frac{9793 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{95551488 \sqrt{3}}",1,"(-9793*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/47775744 + (9793*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/5971968 - (9793*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/622080 + (1399*(5 + 6*x)*(2 + 5*x + 3*x^2)^(7/2))/8640 + ((265 - 54*x)*(2 + 5*x + 3*x^2)^(9/2))/810 + (9793*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(95551488*Sqrt[3])","A",7,4,25,0.1600,1,"{779, 612, 621, 206}"
2451,1,149,0,0.0502869,"\int (5-x) \left(2+5 x+3 x^2\right)^{7/2} \, dx","Int[(5 - x)*(2 + 5*x + 3*x^2)^(7/2),x]","-\frac{1}{27} \left(3 x^2+5 x+2\right)^{9/2}+\frac{35}{288} (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}-\frac{245 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{20736}+\frac{1225 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{995328}-\frac{1225 (6 x+5) \sqrt{3 x^2+5 x+2}}{7962624}+\frac{1225 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{15925248 \sqrt{3}}","-\frac{1}{27} \left(3 x^2+5 x+2\right)^{9/2}+\frac{35}{288} (6 x+5) \left(3 x^2+5 x+2\right)^{7/2}-\frac{245 (6 x+5) \left(3 x^2+5 x+2\right)^{5/2}}{20736}+\frac{1225 (6 x+5) \left(3 x^2+5 x+2\right)^{3/2}}{995328}-\frac{1225 (6 x+5) \sqrt{3 x^2+5 x+2}}{7962624}+\frac{1225 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{15925248 \sqrt{3}}",1,"(-1225*(5 + 6*x)*Sqrt[2 + 5*x + 3*x^2])/7962624 + (1225*(5 + 6*x)*(2 + 5*x + 3*x^2)^(3/2))/995328 - (245*(5 + 6*x)*(2 + 5*x + 3*x^2)^(5/2))/20736 + (35*(5 + 6*x)*(2 + 5*x + 3*x^2)^(7/2))/288 - (2 + 5*x + 3*x^2)^(9/2)/27 + (1225*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(15925248*Sqrt[3])","A",7,4,20,0.2000,1,"{640, 612, 621, 206}"
2452,1,169,0,0.128263,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{3+2 x} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x),x]","\frac{1}{672} (277-42 x) \left(3 x^2+5 x+2\right)^{7/2}-\frac{(7446 x+589) \left(3 x^2+5 x+2\right)^{5/2}}{6912}+\frac{5 (6205-127338 x) \left(3 x^2+5 x+2\right)^{3/2}}{331776}+\frac{5 (1229315-2568342 x) \sqrt{3 x^2+5 x+2}}{2654208}-\frac{65251715 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{5308416 \sqrt{3}}+\frac{1625}{512} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","\frac{1}{672} (277-42 x) \left(3 x^2+5 x+2\right)^{7/2}-\frac{(7446 x+589) \left(3 x^2+5 x+2\right)^{5/2}}{6912}+\frac{5 (6205-127338 x) \left(3 x^2+5 x+2\right)^{3/2}}{331776}+\frac{5 (1229315-2568342 x) \sqrt{3 x^2+5 x+2}}{2654208}-\frac{65251715 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{5308416 \sqrt{3}}+\frac{1625}{512} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"(5*(1229315 - 2568342*x)*Sqrt[2 + 5*x + 3*x^2])/2654208 + (5*(6205 - 127338*x)*(2 + 5*x + 3*x^2)^(3/2))/331776 - ((589 + 7446*x)*(2 + 5*x + 3*x^2)^(5/2))/6912 + ((277 - 42*x)*(2 + 5*x + 3*x^2)^(7/2))/672 - (65251715*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(5308416*Sqrt[3]) + (1625*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/512","A",9,5,27,0.1852,1,"{814, 843, 621, 206, 724}"
2453,1,174,0,0.122866,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^2} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^2,x]","-\frac{(x+47) \left(3 x^2+5 x+2\right)^{7/2}}{14 (2 x+3)}+\frac{(8310 x+283) \left(3 x^2+5 x+2\right)^{5/2}}{1440}-\frac{(6925-151098 x) \left(3 x^2+5 x+2\right)^{3/2}}{13824}-\frac{(1454315-3037062 x) \sqrt{3 x^2+5 x+2}}{110592}+\frac{15434623 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{221184 \sqrt{3}}-\frac{9225}{512} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)","-\frac{(x+47) \left(3 x^2+5 x+2\right)^{7/2}}{14 (2 x+3)}+\frac{(8310 x+283) \left(3 x^2+5 x+2\right)^{5/2}}{1440}-\frac{(6925-151098 x) \left(3 x^2+5 x+2\right)^{3/2}}{13824}-\frac{(1454315-3037062 x) \sqrt{3 x^2+5 x+2}}{110592}+\frac{15434623 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{221184 \sqrt{3}}-\frac{9225}{512} \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)",1,"-((1454315 - 3037062*x)*Sqrt[2 + 5*x + 3*x^2])/110592 - ((6925 - 151098*x)*(2 + 5*x + 3*x^2)^(3/2))/13824 + ((283 + 8310*x)*(2 + 5*x + 3*x^2)^(5/2))/1440 - ((47 + x)*(2 + 5*x + 3*x^2)^(7/2))/(14*(3 + 2*x)) + (15434623*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(221184*Sqrt[3]) - (9225*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/512","A",9,6,27,0.2222,1,"{812, 814, 843, 621, 206, 724}"
2454,1,181,0,0.1282581,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^3} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^3,x]","-\frac{(x+21) \left(3 x^2+5 x+2\right)^{7/2}}{12 (2 x+3)^2}+\frac{7 (121 x+584) \left(3 x^2+5 x+2\right)^{5/2}}{240 (2 x+3)}+\frac{7 (805-17394 x) \left(3 x^2+5 x+2\right)^{3/2}}{4608}+\frac{7 (167495-349806 x) \sqrt{3 x^2+5 x+2}}{36864}-\frac{12443893 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{73728 \sqrt{3}}+\frac{44625 \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1024}","-\frac{(x+21) \left(3 x^2+5 x+2\right)^{7/2}}{12 (2 x+3)^2}+\frac{7 (121 x+584) \left(3 x^2+5 x+2\right)^{5/2}}{240 (2 x+3)}+\frac{7 (805-17394 x) \left(3 x^2+5 x+2\right)^{3/2}}{4608}+\frac{7 (167495-349806 x) \sqrt{3 x^2+5 x+2}}{36864}-\frac{12443893 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{73728 \sqrt{3}}+\frac{44625 \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1024}",1,"(7*(167495 - 349806*x)*Sqrt[2 + 5*x + 3*x^2])/36864 + (7*(805 - 17394*x)*(2 + 5*x + 3*x^2)^(3/2))/4608 + (7*(584 + 121*x)*(2 + 5*x + 3*x^2)^(5/2))/(240*(3 + 2*x)) - ((21 + x)*(2 + 5*x + 3*x^2)^(7/2))/(12*(3 + 2*x)^2) - (12443893*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(73728*Sqrt[3]) + (44625*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/1024","A",9,6,27,0.2222,1,"{812, 814, 843, 621, 206, 724}"
2455,1,190,0,0.1294344,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^4} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^4,x]","-\frac{(3 x+37) \left(3 x^2+5 x+2\right)^{7/2}}{30 (2 x+3)^3}+\frac{7 (414 x+1171) \left(3 x^2+5 x+2\right)^{5/2}}{960 (2 x+3)^2}-\frac{7 (1652 x+5713) \left(3 x^2+5 x+2\right)^{3/2}}{768 (2 x+3)}-\frac{7 (37375-78054 x) \sqrt{3 x^2+5 x+2}}{6144}+\frac{2776697 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{12288 \sqrt{3}}-\frac{59745 \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1024}","-\frac{(3 x+37) \left(3 x^2+5 x+2\right)^{7/2}}{30 (2 x+3)^3}+\frac{7 (414 x+1171) \left(3 x^2+5 x+2\right)^{5/2}}{960 (2 x+3)^2}-\frac{7 (1652 x+5713) \left(3 x^2+5 x+2\right)^{3/2}}{768 (2 x+3)}-\frac{7 (37375-78054 x) \sqrt{3 x^2+5 x+2}}{6144}+\frac{2776697 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{12288 \sqrt{3}}-\frac{59745 \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{1024}",1,"(-7*(37375 - 78054*x)*Sqrt[2 + 5*x + 3*x^2])/6144 - (7*(5713 + 1652*x)*(2 + 5*x + 3*x^2)^(3/2))/(768*(3 + 2*x)) + (7*(1171 + 414*x)*(2 + 5*x + 3*x^2)^(5/2))/(960*(3 + 2*x)^2) - ((37 + 3*x)*(2 + 5*x + 3*x^2)^(7/2))/(30*(3 + 2*x)^3) + (2776697*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(12288*Sqrt[3]) - (59745*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/1024","A",9,6,27,0.2222,1,"{812, 814, 843, 621, 206, 724}"
2456,1,195,0,0.1301793,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^5} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^5,x]","-\frac{(x+8) \left(3 x^2+5 x+2\right)^{7/2}}{8 (2 x+3)^4}+\frac{7 (43 x+93) \left(3 x^2+5 x+2\right)^{5/2}}{96 (2 x+3)^3}-\frac{35 (343 x+736) \left(3 x^2+5 x+2\right)^{3/2}}{768 (2 x+3)^2}+\frac{35 (2701 x+5795) \sqrt{3 x^2+5 x+2}}{1024 (2 x+3)}-\frac{744275 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{4096 \sqrt{3}}+\frac{192171 \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{4096}","-\frac{(x+8) \left(3 x^2+5 x+2\right)^{7/2}}{8 (2 x+3)^4}+\frac{7 (43 x+93) \left(3 x^2+5 x+2\right)^{5/2}}{96 (2 x+3)^3}-\frac{35 (343 x+736) \left(3 x^2+5 x+2\right)^{3/2}}{768 (2 x+3)^2}+\frac{35 (2701 x+5795) \sqrt{3 x^2+5 x+2}}{1024 (2 x+3)}-\frac{744275 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{4096 \sqrt{3}}+\frac{192171 \sqrt{5} \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{4096}",1,"(35*(5795 + 2701*x)*Sqrt[2 + 5*x + 3*x^2])/(1024*(3 + 2*x)) - (35*(736 + 343*x)*(2 + 5*x + 3*x^2)^(3/2))/(768*(3 + 2*x)^2) + (7*(93 + 43*x)*(2 + 5*x + 3*x^2)^(5/2))/(96*(3 + 2*x)^3) - ((8 + x)*(2 + 5*x + 3*x^2)^(7/2))/(8*(3 + 2*x)^4) - (744275*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(4096*Sqrt[3]) + (192171*Sqrt[5]*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/4096","A",9,5,27,0.1852,1,"{812, 843, 621, 206, 724}"
2457,1,197,0,0.1264866,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^6} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^6,x]","-\frac{(5 x+27) \left(3 x^2+5 x+2\right)^{7/2}}{30 (2 x+3)^5}+\frac{7 (548 x+1003) \left(3 x^2+5 x+2\right)^{5/2}}{960 (2 x+3)^4}+\frac{7 (33142 x+42733) \left(3 x^2+5 x+2\right)^{3/2}}{7680 (2 x+3)^3}-\frac{21 (21974 x+47145) \sqrt{3 x^2+5 x+2}}{10240 (2 x+3)}+\frac{30275 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1024}-\frac{2345091 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{20480 \sqrt{5}}","-\frac{(5 x+27) \left(3 x^2+5 x+2\right)^{7/2}}{30 (2 x+3)^5}+\frac{7 (548 x+1003) \left(3 x^2+5 x+2\right)^{5/2}}{960 (2 x+3)^4}+\frac{7 (33142 x+42733) \left(3 x^2+5 x+2\right)^{3/2}}{7680 (2 x+3)^3}-\frac{21 (21974 x+47145) \sqrt{3 x^2+5 x+2}}{10240 (2 x+3)}+\frac{30275 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1024}-\frac{2345091 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{20480 \sqrt{5}}",1,"(-21*(47145 + 21974*x)*Sqrt[2 + 5*x + 3*x^2])/(10240*(3 + 2*x)) + (7*(42733 + 33142*x)*(2 + 5*x + 3*x^2)^(3/2))/(7680*(3 + 2*x)^3) + (7*(1003 + 548*x)*(2 + 5*x + 3*x^2)^(5/2))/(960*(3 + 2*x)^4) - ((27 + 5*x)*(2 + 5*x + 3*x^2)^(7/2))/(30*(3 + 2*x)^5) + (30275*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/1024 - (2345091*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(20480*Sqrt[5])","A",9,6,27,0.2222,1,"{812, 810, 843, 621, 206, 724}"
2458,1,197,0,0.1313792,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^7} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^7,x]","-\frac{(3 x+11) \left(3 x^2+5 x+2\right)^{7/2}}{12 (2 x+3)^6}-\frac{7 (1046 x+1301) \left(3 x^2+5 x+2\right)^{5/2}}{1920 (2 x+3)^5}-\frac{7 (31174 x+40201) \left(3 x^2+5 x+2\right)^{3/2}}{25600 (2 x+3)^3}+\frac{63 (20678 x+44365) \sqrt{3 x^2+5 x+2}}{102400 (2 x+3)}-\frac{8547 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1024}+\frac{6620481 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{204800 \sqrt{5}}","-\frac{(3 x+11) \left(3 x^2+5 x+2\right)^{7/2}}{12 (2 x+3)^6}-\frac{7 (1046 x+1301) \left(3 x^2+5 x+2\right)^{5/2}}{1920 (2 x+3)^5}-\frac{7 (31174 x+40201) \left(3 x^2+5 x+2\right)^{3/2}}{25600 (2 x+3)^3}+\frac{63 (20678 x+44365) \sqrt{3 x^2+5 x+2}}{102400 (2 x+3)}-\frac{8547 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1024}+\frac{6620481 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{204800 \sqrt{5}}",1,"(63*(44365 + 20678*x)*Sqrt[2 + 5*x + 3*x^2])/(102400*(3 + 2*x)) - (7*(40201 + 31174*x)*(2 + 5*x + 3*x^2)^(3/2))/(25600*(3 + 2*x)^3) - (7*(1301 + 1046*x)*(2 + 5*x + 3*x^2)^(5/2))/(1920*(3 + 2*x)^5) - ((11 + 3*x)*(2 + 5*x + 3*x^2)^(7/2))/(12*(3 + 2*x)^6) - (8547*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/1024 + (6620481*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(204800*Sqrt[5])","A",9,6,27,0.2222,1,"{812, 810, 843, 621, 206, 724}"
2459,1,197,0,0.128826,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^8} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^8,x]","\frac{(266 x+269) \left(3 x^2+5 x+2\right)^{7/2}}{280 (2 x+3)^7}+\frac{3 (106 x+135) \left(3 x^2+5 x+2\right)^{5/2}}{640 (2 x+3)^5}+\frac{(30858 x+39767) \left(3 x^2+5 x+2\right)^{3/2}}{25600 (2 x+3)^3}-\frac{3 (61278 x+131465) \sqrt{3 x^2+5 x+2}}{102400 (2 x+3)}+\frac{603}{512} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)-\frac{934161 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{204800 \sqrt{5}}","\frac{(266 x+269) \left(3 x^2+5 x+2\right)^{7/2}}{280 (2 x+3)^7}+\frac{3 (106 x+135) \left(3 x^2+5 x+2\right)^{5/2}}{640 (2 x+3)^5}+\frac{(30858 x+39767) \left(3 x^2+5 x+2\right)^{3/2}}{25600 (2 x+3)^3}-\frac{3 (61278 x+131465) \sqrt{3 x^2+5 x+2}}{102400 (2 x+3)}+\frac{603}{512} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)-\frac{934161 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{204800 \sqrt{5}}",1,"(-3*(131465 + 61278*x)*Sqrt[2 + 5*x + 3*x^2])/(102400*(3 + 2*x)) + ((39767 + 30858*x)*(2 + 5*x + 3*x^2)^(3/2))/(25600*(3 + 2*x)^3) + (3*(135 + 106*x)*(2 + 5*x + 3*x^2)^(5/2))/(640*(3 + 2*x)^5) + ((269 + 266*x)*(2 + 5*x + 3*x^2)^(7/2))/(280*(3 + 2*x)^7) + (603*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/512 - (934161*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(204800*Sqrt[5])","A",9,6,27,0.2222,1,"{810, 812, 843, 621, 206, 724}"
2460,1,197,0,0.13238,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^9} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^9,x]","\frac{(808 x+757) \left(3 x^2+5 x+2\right)^{7/2}}{1120 (2 x+3)^8}+\frac{(664 x+881) \left(3 x^2+5 x+2\right)^{5/2}}{6400 (2 x+3)^6}+\frac{(17096 x+20959) \left(3 x^2+5 x+2\right)^{3/2}}{102400 (2 x+3)^4}+\frac{3 (434104 x+559841) \sqrt{3 x^2+5 x+2}}{4096000 (2 x+3)^2}-\frac{27}{512} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{1673211 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{8192000 \sqrt{5}}","\frac{(808 x+757) \left(3 x^2+5 x+2\right)^{7/2}}{1120 (2 x+3)^8}+\frac{(664 x+881) \left(3 x^2+5 x+2\right)^{5/2}}{6400 (2 x+3)^6}+\frac{(17096 x+20959) \left(3 x^2+5 x+2\right)^{3/2}}{102400 (2 x+3)^4}+\frac{3 (434104 x+559841) \sqrt{3 x^2+5 x+2}}{4096000 (2 x+3)^2}-\frac{27}{512} \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)+\frac{1673211 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{8192000 \sqrt{5}}",1,"(3*(559841 + 434104*x)*Sqrt[2 + 5*x + 3*x^2])/(4096000*(3 + 2*x)^2) + ((20959 + 17096*x)*(2 + 5*x + 3*x^2)^(3/2))/(102400*(3 + 2*x)^4) + ((881 + 664*x)*(2 + 5*x + 3*x^2)^(5/2))/(6400*(3 + 2*x)^6) + ((757 + 808*x)*(2 + 5*x + 3*x^2)^(7/2))/(1120*(3 + 2*x)^8) - (27*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/512 + (1673211*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(8192000*Sqrt[5])","A",9,5,27,0.1852,1,"{810, 843, 621, 206, 724}"
2461,1,184,0,0.0964,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{10}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^10,x]","-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{45 (2 x+3)^9}+\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{800 (2 x+3)^8}-\frac{329 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{96000 (2 x+3)^6}+\frac{329 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{1536000 (2 x+3)^4}-\frac{329 (8 x+7) \sqrt{3 x^2+5 x+2}}{20480000 (2 x+3)^2}+\frac{329 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40960000 \sqrt{5}}","-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{45 (2 x+3)^9}+\frac{47 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{800 (2 x+3)^8}-\frac{329 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{96000 (2 x+3)^6}+\frac{329 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{1536000 (2 x+3)^4}-\frac{329 (8 x+7) \sqrt{3 x^2+5 x+2}}{20480000 (2 x+3)^2}+\frac{329 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40960000 \sqrt{5}}",1,"(-329*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20480000*(3 + 2*x)^2) + (329*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(1536000*(3 + 2*x)^4) - (329*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(96000*(3 + 2*x)^6) + (47*(7 + 8*x)*(2 + 5*x + 3*x^2)^(7/2))/(800*(3 + 2*x)^8) - (13*(2 + 5*x + 3*x^2)^(9/2))/(45*(3 + 2*x)^9) + (329*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40960000*Sqrt[5])","A",7,4,27,0.1481,1,"{806, 720, 724, 206}"
2462,1,209,0,0.1209765,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{11}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^11,x]","-\frac{29 \left(3 x^2+5 x+2\right)^{9/2}}{125 (2 x+3)^9}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{50 (2 x+3)^{10}}+\frac{1893 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{40000 (2 x+3)^8}-\frac{4417 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{1600000 (2 x+3)^6}+\frac{4417 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{25600000 (2 x+3)^4}-\frac{13251 (8 x+7) \sqrt{3 x^2+5 x+2}}{1024000000 (2 x+3)^2}+\frac{13251 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2048000000 \sqrt{5}}","-\frac{29 \left(3 x^2+5 x+2\right)^{9/2}}{125 (2 x+3)^9}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{50 (2 x+3)^{10}}+\frac{1893 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{40000 (2 x+3)^8}-\frac{4417 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{1600000 (2 x+3)^6}+\frac{4417 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{25600000 (2 x+3)^4}-\frac{13251 (8 x+7) \sqrt{3 x^2+5 x+2}}{1024000000 (2 x+3)^2}+\frac{13251 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2048000000 \sqrt{5}}",1,"(-13251*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(1024000000*(3 + 2*x)^2) + (4417*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(25600000*(3 + 2*x)^4) - (4417*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(1600000*(3 + 2*x)^6) + (1893*(7 + 8*x)*(2 + 5*x + 3*x^2)^(7/2))/(40000*(3 + 2*x)^8) - (13*(2 + 5*x + 3*x^2)^(9/2))/(50*(3 + 2*x)^10) - (29*(2 + 5*x + 3*x^2)^(9/2))/(125*(3 + 2*x)^9) + (13251*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(2048000000*Sqrt[5])","A",8,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2463,1,234,0,0.1524949,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{12}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^12,x]","-\frac{3904 \left(3 x^2+5 x+2\right)^{9/2}}{20625 (2 x+3)^9}-\frac{621 \left(3 x^2+5 x+2\right)^{9/2}}{2750 (2 x+3)^{10}}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{55 (2 x+3)^{11}}+\frac{7671 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{200000 (2 x+3)^8}-\frac{17899 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{8000000 (2 x+3)^6}+\frac{17899 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{128000000 (2 x+3)^4}-\frac{53697 (8 x+7) \sqrt{3 x^2+5 x+2}}{5120000000 (2 x+3)^2}+\frac{53697 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{10240000000 \sqrt{5}}","-\frac{3904 \left(3 x^2+5 x+2\right)^{9/2}}{20625 (2 x+3)^9}-\frac{621 \left(3 x^2+5 x+2\right)^{9/2}}{2750 (2 x+3)^{10}}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{55 (2 x+3)^{11}}+\frac{7671 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{200000 (2 x+3)^8}-\frac{17899 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{8000000 (2 x+3)^6}+\frac{17899 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{128000000 (2 x+3)^4}-\frac{53697 (8 x+7) \sqrt{3 x^2+5 x+2}}{5120000000 (2 x+3)^2}+\frac{53697 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{10240000000 \sqrt{5}}",1,"(-53697*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(5120000000*(3 + 2*x)^2) + (17899*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(128000000*(3 + 2*x)^4) - (17899*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(8000000*(3 + 2*x)^6) + (7671*(7 + 8*x)*(2 + 5*x + 3*x^2)^(7/2))/(200000*(3 + 2*x)^8) - (13*(2 + 5*x + 3*x^2)^(9/2))/(55*(3 + 2*x)^11) - (621*(2 + 5*x + 3*x^2)^(9/2))/(2750*(3 + 2*x)^10) - (3904*(2 + 5*x + 3*x^2)^(9/2))/(20625*(3 + 2*x)^9) + (53697*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(10240000000*Sqrt[5])","A",9,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2464,1,259,0,0.1821516,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{7/2}}{(3+2 x)^{13}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(7/2))/(3 + 2*x)^13,x]","-\frac{6379 \left(3 x^2+5 x+2\right)^{9/2}}{41250 (2 x+3)^9}-\frac{2067 \left(3 x^2+5 x+2\right)^{9/2}}{11000 (2 x+3)^{10}}-\frac{12 \left(3 x^2+5 x+2\right)^{9/2}}{55 (2 x+3)^{11}}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{60 (2 x+3)^{12}}+\frac{25017 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{800000 (2 x+3)^8}-\frac{58373 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{32000000 (2 x+3)^6}+\frac{58373 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{512000000 (2 x+3)^4}-\frac{175119 (8 x+7) \sqrt{3 x^2+5 x+2}}{20480000000 (2 x+3)^2}+\frac{175119 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40960000000 \sqrt{5}}","-\frac{6379 \left(3 x^2+5 x+2\right)^{9/2}}{41250 (2 x+3)^9}-\frac{2067 \left(3 x^2+5 x+2\right)^{9/2}}{11000 (2 x+3)^{10}}-\frac{12 \left(3 x^2+5 x+2\right)^{9/2}}{55 (2 x+3)^{11}}-\frac{13 \left(3 x^2+5 x+2\right)^{9/2}}{60 (2 x+3)^{12}}+\frac{25017 (8 x+7) \left(3 x^2+5 x+2\right)^{7/2}}{800000 (2 x+3)^8}-\frac{58373 (8 x+7) \left(3 x^2+5 x+2\right)^{5/2}}{32000000 (2 x+3)^6}+\frac{58373 (8 x+7) \left(3 x^2+5 x+2\right)^{3/2}}{512000000 (2 x+3)^4}-\frac{175119 (8 x+7) \sqrt{3 x^2+5 x+2}}{20480000000 (2 x+3)^2}+\frac{175119 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{40960000000 \sqrt{5}}",1,"(-175119*(7 + 8*x)*Sqrt[2 + 5*x + 3*x^2])/(20480000000*(3 + 2*x)^2) + (58373*(7 + 8*x)*(2 + 5*x + 3*x^2)^(3/2))/(512000000*(3 + 2*x)^4) - (58373*(7 + 8*x)*(2 + 5*x + 3*x^2)^(5/2))/(32000000*(3 + 2*x)^6) + (25017*(7 + 8*x)*(2 + 5*x + 3*x^2)^(7/2))/(800000*(3 + 2*x)^8) - (13*(2 + 5*x + 3*x^2)^(9/2))/(60*(3 + 2*x)^12) - (12*(2 + 5*x + 3*x^2)^(9/2))/(55*(3 + 2*x)^11) - (2067*(2 + 5*x + 3*x^2)^(9/2))/(11000*(3 + 2*x)^10) - (6379*(2 + 5*x + 3*x^2)^(9/2))/(41250*(3 + 2*x)^9) + (175119*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(40960000000*Sqrt[5])","A",10,5,27,0.1852,1,"{834, 806, 720, 724, 206}"
2465,1,407,0,0.6839482,"\int \frac{(A+B x) (d+e x)^3}{\sqrt{a+b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(B \left(-4 c e (9 a e+16 b d)+35 b^2 e^2+24 c^2 d^2\right)+40 A c e (2 c d-b e)\right)+8 A c e \left(-2 c e (8 a e+27 b d)+15 b^2 e^2+64 c^2 d^2\right)+B \left(-8 c^2 d e (48 a e+47 b d)+20 b c e^2 (11 a e+18 b d)-105 b^3 e^3+96 c^3 d^3\right)\right)}{192 c^4}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(24 b^2 c e \left(-5 a B e^2+6 A c d e+6 B c d^2\right)-32 b c^2 \left(-3 a A e^3-9 a B d e^2+6 A c d^2 e+2 B c d^3\right)+16 c^2 \left(4 A c d \left(2 c d^2-3 a e^2\right)-3 a B e \left(4 c d^2-a e^2\right)\right)-40 b^3 c e^2 (A e+3 B d)+35 b^4 B e^3\right)}{128 c^{9/2}}+\frac{(d+e x)^2 \sqrt{a+b x+c x^2} (8 A c e-7 b B e+6 B c d)}{24 c^2}+\frac{B (d+e x)^3 \sqrt{a+b x+c x^2}}{4 c}","\frac{\sqrt{a+b x+c x^2} \left(2 c e x \left(B \left(-4 c e (9 a e+16 b d)+35 b^2 e^2+24 c^2 d^2\right)+40 A c e (2 c d-b e)\right)+8 A c e \left(-2 c e (8 a e+27 b d)+15 b^2 e^2+64 c^2 d^2\right)+B \left(-8 c^2 d e (48 a e+47 b d)+20 b c e^2 (11 a e+18 b d)-105 b^3 e^3+96 c^3 d^3\right)\right)}{192 c^4}+\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(24 b^2 c e \left(-5 a B e^2+6 A c d e+6 B c d^2\right)-32 b c^2 \left(-3 a A e^3-9 a B d e^2+6 A c d^2 e+2 B c d^3\right)+16 c^2 \left(4 A c d \left(2 c d^2-3 a e^2\right)-3 a B e \left(4 c d^2-a e^2\right)\right)-40 b^3 c e^2 (A e+3 B d)+35 b^4 B e^3\right)}{128 c^{9/2}}+\frac{(d+e x)^2 \sqrt{a+b x+c x^2} (8 A c e-7 b B e+6 B c d)}{24 c^2}+\frac{B (d+e x)^3 \sqrt{a+b x+c x^2}}{4 c}",1,"((6*B*c*d - 7*b*B*e + 8*A*c*e)*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(24*c^2) + (B*(d + e*x)^3*Sqrt[a + b*x + c*x^2])/(4*c) + ((8*A*c*e*(64*c^2*d^2 + 15*b^2*e^2 - 2*c*e*(27*b*d + 8*a*e)) + B*(96*c^3*d^3 - 105*b^3*e^3 + 20*b*c*e^2*(18*b*d + 11*a*e) - 8*c^2*d*e*(47*b*d + 48*a*e)) + 2*c*e*(40*A*c*e*(2*c*d - b*e) + B*(24*c^2*d^2 + 35*b^2*e^2 - 4*c*e*(16*b*d + 9*a*e)))*x)*Sqrt[a + b*x + c*x^2])/(192*c^4) + ((35*b^4*B*e^3 - 40*b^3*c*e^2*(3*B*d + A*e) + 24*b^2*c*e*(6*B*c*d^2 + 6*A*c*d*e - 5*a*B*e^2) - 32*b*c^2*(2*B*c*d^3 + 6*A*c*d^2*e - 9*a*B*d*e^2 - 3*a*A*e^3) + 16*c^2*(4*A*c*d*(2*c*d^2 - 3*a*e^2) - 3*a*B*e*(4*c*d^2 - a*e^2)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(128*c^(9/2))","A",5,4,27,0.1481,1,"{832, 779, 621, 206}"
2466,1,234,0,0.2495016,"\int \frac{(A+B x) (d+e x)^2}{\sqrt{a+b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{a+b x+c x^2} \left(B \left(-4 c e (4 a e+9 b d)+15 b^2 e^2+16 c^2 d^2\right)+2 c e x (6 A c e-5 b B e+4 B c d)+6 A c e (8 c d-3 b e)\right)}{24 c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 b c \left(-3 a B e^2+4 A c d e+2 B c d^2\right)-8 c^2 \left(-a A e^2-2 a B d e+2 A c d^2\right)-6 b^2 c e (A e+2 B d)+5 b^3 B e^2\right)}{16 c^{7/2}}+\frac{B (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c}","\frac{\sqrt{a+b x+c x^2} \left(B \left(-4 c e (4 a e+9 b d)+15 b^2 e^2+16 c^2 d^2\right)+2 c e x (6 A c e-5 b B e+4 B c d)+6 A c e (8 c d-3 b e)\right)}{24 c^3}-\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 b c \left(-3 a B e^2+4 A c d e+2 B c d^2\right)-8 c^2 \left(-a A e^2-2 a B d e+2 A c d^2\right)-6 b^2 c e (A e+2 B d)+5 b^3 B e^2\right)}{16 c^{7/2}}+\frac{B (d+e x)^2 \sqrt{a+b x+c x^2}}{3 c}",1,"(B*(d + e*x)^2*Sqrt[a + b*x + c*x^2])/(3*c) + ((6*A*c*e*(8*c*d - 3*b*e) + B*(16*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(9*b*d + 4*a*e)) + 2*c*e*(4*B*c*d - 5*b*B*e + 6*A*c*e)*x)*Sqrt[a + b*x + c*x^2])/(24*c^3) - ((5*b^3*B*e^2 - 6*b^2*c*e*(2*B*d + A*e) - 8*c^2*(2*A*c*d^2 - 2*a*B*d*e - a*A*e^2) + 4*b*c*(2*B*c*d^2 + 4*A*c*d*e - 3*a*B*e^2))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(16*c^(7/2))","A",4,4,27,0.1481,1,"{832, 779, 621, 206}"
2467,1,115,0,0.0876261,"\int \frac{(A+B x) (d+e x)}{\sqrt{a+b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x))/Sqrt[a + b*x + c*x^2],x]","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(-4 a B c e-4 b c (A e+B d)+8 A c^2 d+3 b^2 B e\right)}{8 c^{5/2}}-\frac{\sqrt{a+b x+c x^2} (-4 c (A e+B d)+3 b B e-2 B c e x)}{4 c^2}","\frac{\tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(4 c (2 A c d-a B e)-4 b c (A e+B d)+3 b^2 B e\right)}{8 c^{5/2}}-\frac{\sqrt{a+b x+c x^2} (-4 c (A e+B d)+3 b B e-2 B c e x)}{4 c^2}",1,"-((3*b*B*e - 4*c*(B*d + A*e) - 2*B*c*e*x)*Sqrt[a + b*x + c*x^2])/(4*c^2) + ((8*A*c^2*d + 3*b^2*B*e - 4*a*B*c*e - 4*b*c*(B*d + A*e))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(5/2))","A",3,3,25,0.1200,1,"{779, 621, 206}"
2468,1,67,0,0.0235932,"\int \frac{A+B x}{\sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/Sqrt[a + b*x + c*x^2],x]","\frac{B \sqrt{a+b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2}}","\frac{B \sqrt{a+b x+c x^2}}{c}-\frac{(b B-2 A c) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{2 c^{3/2}}",1,"(B*Sqrt[a + b*x + c*x^2])/c - ((b*B - 2*A*c)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(3/2))","A",3,3,20,0.1500,1,"{640, 621, 206}"
2469,1,132,0,0.1212769,"\int \frac{A+B x}{(d+e x) \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)*Sqrt[a + b*x + c*x^2]),x]","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} e}-\frac{(B d-A e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \sqrt{a e^2-b d e+c d^2}}","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{\sqrt{c} e}-\frac{(B d-A e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{e \sqrt{a e^2-b d e+c d^2}}",1,"(B*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(Sqrt[c]*e) - ((B*d - A*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(e*Sqrt[c*d^2 - b*d*e + a*e^2])","A",5,4,27,0.1481,1,"{843, 621, 206, 724}"
2470,1,150,0,0.1379494,"\int \frac{A+B x}{(d+e x)^2 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^2*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} (B d-A e)}{(d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{(-2 a B e+A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{\sqrt{a+b x+c x^2} (B d-A e)}{(d+e x) \left(a e^2-b d e+c d^2\right)}-\frac{(-2 a B e+A b e-2 A c d+b B d) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{3/2}}",1,"((B*d - A*e)*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*(d + e*x)) - ((b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(3/2))","A",3,3,27,0.1111,1,"{806, 724, 206}"
2471,1,269,0,0.3781981,"\int \frac{A+B x}{(d+e x)^3 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^3*Sqrt[a + b*x + c*x^2]),x]","\frac{\left(-4 b \left(a B e^2+2 A c d e+B c d^2\right)+4 c \left(-a A e^2+3 a B d e+2 A c d^2\right)+b^2 e (3 A e+B d)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\sqrt{a+b x+c x^2} (B d-A e)}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(B e (b d-4 a e)-3 A e (2 c d-b e)+2 B c d^2\right)}{4 (d+e x) \left(a e^2-b d e+c d^2\right)^2}","\frac{\left(-4 b \left(a B e^2+2 A c d e+B c d^2\right)+4 c \left(-a A e^2+3 a B d e+2 A c d^2\right)+b^2 e (3 A e+B d)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 \left(a e^2-b d e+c d^2\right)^{5/2}}+\frac{\sqrt{a+b x+c x^2} (B d-A e)}{2 (d+e x)^2 \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{a+b x+c x^2} \left(3 A e (2 c d-b e)-B \left(e (b d-4 a e)+2 c d^2\right)\right)}{4 (d+e x) \left(a e^2-b d e+c d^2\right)^2}",1,"((B*d - A*e)*Sqrt[a + b*x + c*x^2])/(2*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2) + ((2*B*c*d^2 + B*e*(b*d - 4*a*e) - 3*A*e*(2*c*d - b*e))*Sqrt[a + b*x + c*x^2])/(4*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) + ((b^2*e*(B*d + 3*A*e) + 4*c*(2*A*c*d^2 + 3*a*B*d*e - a*A*e^2) - 4*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,27,0.1481,1,"{834, 806, 724, 206}"
2472,1,442,0,0.8354729,"\int \frac{A+B x}{(d+e x)^4 \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^4*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{a+b x+c x^2} \left(B \left(2 c d e (5 b d-26 a e)-3 b e^2 (b d-6 a e)+8 c^2 d^3\right)-A e \left(-4 c e (4 a e+11 b d)+15 b^2 e^2+44 c^2 d^2\right)\right)}{24 (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(-2 b^2 e \left(3 a B e^2+9 A c d e+2 B c d^2\right)+4 b c \left(-3 a A e^3+5 a B d e^2+6 A c d^2 e+2 B c d^3\right)-8 c \left(A c d \left(2 c d^2-3 a e^2\right)+a B e \left(4 c d^2-a e^2\right)\right)+b^3 e^2 (5 A e+B d)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{\sqrt{a+b x+c x^2} (B d-A e)}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{a+b x+c x^2} \left(B e (b d-6 a e)-5 A e (2 c d-b e)+4 B c d^2\right)}{12 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}","\frac{\sqrt{a+b x+c x^2} \left(B \left(2 c d e (5 b d-26 a e)-3 b e^2 (b d-6 a e)+8 c^2 d^3\right)-A e \left(-4 c e (4 a e+11 b d)+15 b^2 e^2+44 c^2 d^2\right)\right)}{24 (d+e x) \left(a e^2-b d e+c d^2\right)^3}-\frac{\left(-2 b^2 e \left(3 a B e^2+9 A c d e+2 B c d^2\right)+4 b c \left(-3 a A e^3+5 a B d e^2+6 A c d^2 e+2 B c d^3\right)-8 c \left(A c d \left(2 c d^2-3 a e^2\right)+a B e \left(4 c d^2-a e^2\right)\right)+b^3 e^2 (5 A e+B d)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{16 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{\sqrt{a+b x+c x^2} (B d-A e)}{3 (d+e x)^3 \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{a+b x+c x^2} \left(5 A e (2 c d-b e)-B \left(e (b d-6 a e)+4 c d^2\right)\right)}{12 (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}",1,"((B*d - A*e)*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^3) + ((4*B*c*d^2 + B*e*(b*d - 6*a*e) - 5*A*e*(2*c*d - b*e))*Sqrt[a + b*x + c*x^2])/(12*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) + ((B*(8*c^2*d^3 + 2*c*d*e*(5*b*d - 26*a*e) - 3*b*e^2*(b*d - 6*a*e)) - A*e*(44*c^2*d^2 + 15*b^2*e^2 - 4*c*e*(11*b*d + 4*a*e)))*Sqrt[a + b*x + c*x^2])/(24*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - ((b^3*e^2*(B*d + 5*A*e) - 2*b^2*e*(2*B*c*d^2 + 9*A*c*d*e + 3*a*B*e^2) + 4*b*c*(2*B*c*d^3 + 6*A*c*d^2*e + 5*a*B*d*e^2 - 3*a*A*e^3) - 8*c*(A*c*d*(2*c*d^2 - 3*a*e^2) + a*B*e*(4*c*d^2 - a*e^2)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(16*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,4,27,0.1481,1,"{834, 806, 724, 206}"
2473,1,325,0,0.3384761,"\int \frac{(A+B x) (d+e x)^3}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(3/2),x]","-\frac{e \sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c (3 a B e+A b e+b B d)+8 A c^2 d+5 b^2 B e\right)+4 b c \left(-13 a B e^2+6 A c d e+4 B c d^2\right)-32 c^2 \left(-a A e^2-3 a B d e+A c d^2\right)-12 b^2 c e (A e+3 B d)+15 b^3 B e^2\right)}{4 c^3 \left(b^2-4 a c\right)}+\frac{3 e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(B \left(-4 c e (a e+3 b d)+5 b^2 e^2+8 c^2 d^2\right)+4 A c e (2 c d-b e)\right)}{8 c^{7/2}}+\frac{2 (d+e x)^2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{e \sqrt{a+b x+c x^2} \left(-2 c e x \left(-4 c (3 a B e+A b e+b B d)+8 A c^2 d+5 b^2 B e\right)+4 b c \left(-13 a B e^2+6 A c d e+4 B c d^2\right)-32 c^2 \left(-a A e^2-3 a B d e+A c d^2\right)-12 b^2 c e (A e+3 B d)+15 b^3 B e^2\right)}{4 c^3 \left(b^2-4 a c\right)}+\frac{3 e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) \left(B \left(-4 c e (a e+3 b d)+5 b^2 e^2+8 c^2 d^2\right)+4 A c e (2 c d-b e)\right)}{8 c^{7/2}}+\frac{2 (d+e x)^2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(2*(d + e*x)^2*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) - (e*(15*b^3*B*e^2 - 12*b^2*c*e*(3*B*d + A*e) - 32*c^2*(A*c*d^2 - 3*a*B*d*e - a*A*e^2) + 4*b*c*(4*B*c*d^2 + 6*A*c*d*e - 13*a*B*e^2) - 2*c*e*(8*A*c^2*d + 5*b^2*B*e - 4*c*(b*B*d + A*b*e + 3*a*B*e))*x)*Sqrt[a + b*x + c*x^2])/(4*c^3*(b^2 - 4*a*c)) + (3*e*(4*A*c*e*(2*c*d - b*e) + B*(8*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(3*b*d + a*e)))*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(8*c^(7/2))","A",4,4,27,0.1481,1,"{818, 779, 621, 206}"
2474,1,210,0,0.1894661,"\int \frac{(A+B x) (d+e x)^2}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(3/2),x]","\frac{e \sqrt{a+b x+c x^2} \left(-2 c (4 a B e+A b e+b B d)+4 A c^2 d+3 b^2 B e\right)}{c^2 \left(b^2-4 a c\right)}+\frac{2 (d+e x) \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (2 A c e-3 b B e+4 B c d)}{2 c^{5/2}}","\frac{e \sqrt{a+b x+c x^2} \left(-2 c (4 a B e+A b e+b B d)+4 A c^2 d+3 b^2 B e\right)}{c^2 \left(b^2-4 a c\right)}+\frac{2 (d+e x) \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (2 A c e-3 b B e+4 B c d)}{2 c^{5/2}}",1,"(2*(d + e*x)*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (e*(4*A*c^2*d + 3*b^2*B*e - 2*c*(b*B*d + A*b*e + 4*a*B*e))*Sqrt[a + b*x + c*x^2])/(c^2*(b^2 - 4*a*c)) + (e*(4*B*c*d - 3*b*B*e + 2*A*c*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(5/2))","A",4,4,27,0.1481,1,"{818, 640, 621, 206}"
2475,1,126,0,0.0642382,"\int \frac{(A+B x) (d+e x)}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{B e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}","\frac{2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{B e \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{3/2}}",1,"(2*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (B*e*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(3/2)","A",3,3,25,0.1200,1,"{777, 621, 206}"
2476,1,45,0,0.0111191,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x))/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2])","A",1,1,20,0.05000,1,"{636}"
2477,1,188,0,0.1556306,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e (B d-A e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}","\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e (B d-A e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{3/2}}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) - (e*(B*d - A*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(3/2)","A",4,4,27,0.1481,1,"{822, 12, 724, 206}"
2478,1,332,0,0.4249407,"\int \frac{A+B x}{(d+e x)^2 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)^(3/2)),x]","\frac{e \sqrt{a+b x+c x^2} \left(2 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(-2 a A e^2+3 a B d e+A c d^2\right)+b^2 e (B d-3 A e)\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{e \left(-B e (2 a e+b d)-3 A e (2 c d-b e)+4 B c d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{5/2}}","\frac{e \sqrt{a+b x+c x^2} \left(2 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(-2 a A e^2+3 a B d e+A c d^2\right)+b^2 e (B d-3 A e)\right)}{\left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{e \left(3 A e (2 c d-b e)-B \left(4 c d^2-e (2 a e+b d)\right)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{5/2}}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*Sqrt[a + b*x + c*x^2]) + (e*(b^2*e*(B*d - 3*A*e) - 4*c*(A*c*d^2 + 3*a*B*d*e - 2*a*A*e^2) + 2*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)) - (e*(4*B*c*d^2 - B*e*(b*d + 2*a*e) - 3*A*e*(2*c*d - b*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(5/2))","A",4,4,27,0.1481,1,"{822, 806, 724, 206}"
2479,1,545,0,0.9328468,"\int \frac{A+B x}{(d+e x)^3 \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^3*(a + b*x + c*x^2)^(3/2)),x]","\frac{3 e \left(A e \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right)-B \left(-4 c d e (3 a e+b d)+b e^2 (4 a e+b d)+8 c^2 d^3\right)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{e \sqrt{a+b x+c x^2} \left(4 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(-3 a A e^2+5 a B d e+2 A c d^2\right)+b^2 e (B d-5 A e)\right)}{2 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \sqrt{a+b x+c x^2} \left(-2 b^2 e \left(-6 a B e^2-19 A c d e+5 B c d^2\right)-4 b c \left(-13 a A e^3+9 a B d e^2+6 A c d^2 e+2 B c d^3\right)+8 c \left(A c d \left(2 c d^2-13 a e^2\right)+a B e \left(11 c d^2-4 a e^2\right)\right)+3 b^3 e^2 (B d-5 A e)\right)}{4 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) (d+e x)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}","\frac{3 e \left(A e \left(-4 c e (a e+4 b d)+5 b^2 e^2+16 c^2 d^2\right)-B \left(-4 c d e (3 a e+b d)+b e^2 (4 a e+b d)+8 c^2 d^3\right)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{8 \left(a e^2-b d e+c d^2\right)^{7/2}}+\frac{e \sqrt{a+b x+c x^2} \left(4 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(-3 a A e^2+5 a B d e+2 A c d^2\right)+b^2 e (B d-5 A e)\right)}{2 \left(b^2-4 a c\right) (d+e x)^2 \left(a e^2-b d e+c d^2\right)^2}-\frac{e \sqrt{a+b x+c x^2} \left(-2 b^2 e \left(-6 a B e^2-19 A c d e+5 B c d^2\right)-4 b c \left(-13 a A e^3+9 a B d e^2+6 A c d^2 e+2 B c d^3\right)+8 c \left(A c d \left(2 c d^2-13 a e^2\right)+a B e \left(11 c d^2-4 a e^2\right)\right)+3 b^3 e^2 (B d-5 A e)\right)}{4 \left(b^2-4 a c\right) (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) (d+e x)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^2*Sqrt[a + b*x + c*x^2]) + (e*(b^2*e*(B*d - 5*A*e) - 4*c*(2*A*c*d^2 + 5*a*B*d*e - 3*a*A*e^2) + 4*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*Sqrt[a + b*x + c*x^2])/(2*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^2) - (e*(3*b^3*e^2*(B*d - 5*A*e) - 2*b^2*e*(5*B*c*d^2 - 19*A*c*d*e - 6*a*B*e^2) - 4*b*c*(2*B*c*d^3 + 6*A*c*d^2*e + 9*a*B*d*e^2 - 13*a*A*e^3) + 8*c*(A*c*d*(2*c*d^2 - 13*a*e^2) + a*B*e*(11*c*d^2 - 4*a*e^2)))*Sqrt[a + b*x + c*x^2])/(4*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) + (3*e*(A*e*(16*c^2*d^2 + 5*b^2*e^2 - 4*c*e*(4*b*d + a*e)) - B*(8*c^2*d^3 - 4*c*d*e*(b*d + 3*a*e) + b*e^2*(b*d + 4*a*e)))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(8*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,5,27,0.1852,1,"{822, 834, 806, 724, 206}"
2480,1,608,0,0.8354606,"\int \frac{(A+B x) (d+e x)^4}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(5/2),x]","\frac{e \sqrt{a+b x+c x^2} \left(-4 b^2 c e \left(25 a B e^2+A c d e+2 B c d^2\right)+8 b c^2 \left(5 a A e^3+13 a B d e^2+6 A c d^2 e+2 B c d^3\right)-16 c^2 \left(A c d \left(5 a e^2+2 c d^2\right)+4 a B e \left(c d^2-2 a e^2\right)\right)-2 b^3 c e^2 (3 A e+7 B d)+15 b^4 B e^3\right)}{3 c^3 \left(b^2-4 a c\right)^2}+\frac{2 (d+e x) \left(-x \left(-4 b^2 c e \left(8 a B e^2+A c d e+B c d^2\right)+8 b c^2 \left(2 a A e^3+6 a B d e^2+3 A c d^2 e+B c d^3\right)-16 c^2 \left(A c d \left(2 a e^2+c d^2\right)+2 a B e \left(c d^2-a e^2\right)\right)-2 b^3 c e^2 (A e+3 B d)+5 b^4 B e^3\right)-2 b^2 c \left(-a A e^3-2 a B d e^2+5 A c d^2 e+2 B c d^3\right)+4 b c \left(2 A c d \left(3 a e^2+c d^2\right)+a B e \left(7 a e^2+5 c d^2\right)\right)-8 a c^2 e \left(3 a A e^2+8 a B d e+A c d^2\right)+b^3 B e \left(c d^2-5 a e^2\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 (d+e x)^3 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (2 A c e-5 b B e+8 B c d)}{2 c^{7/2}}","\frac{e \sqrt{a+b x+c x^2} \left(-4 b^2 c e \left(25 a B e^2+A c d e+2 B c d^2\right)+8 b c^2 \left(5 a A e^3+13 a B d e^2+6 A c d^2 e+2 B c d^3\right)-16 c^2 \left(A c d \left(5 a e^2+2 c d^2\right)+4 a B e \left(c d^2-2 a e^2\right)\right)-2 b^3 c e^2 (3 A e+7 B d)+15 b^4 B e^3\right)}{3 c^3 \left(b^2-4 a c\right)^2}+\frac{2 (d+e x) \left(-x \left(-4 b^2 c e \left(8 a B e^2+A c d e+B c d^2\right)+8 b c^2 \left(2 a A e^3+6 a B d e^2+3 A c d^2 e+B c d^3\right)-16 c^2 \left(A c d \left(2 a e^2+c d^2\right)+2 a B e \left(c d^2-a e^2\right)\right)-2 b^3 c e^2 (A e+3 B d)+5 b^4 B e^3\right)-2 b^2 c \left(-a A e^3-2 a B d e^2+5 A c d^2 e+2 B c d^3\right)+4 b c \left(2 A c d \left(3 a e^2+c d^2\right)+a B e \left(7 a e^2+5 c d^2\right)\right)-8 a c^2 e \left(3 a A e^2+8 a B d e+A c d^2\right)+b^3 B e \left(c d^2-5 a e^2\right)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 (d+e x)^3 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right) (2 A c e-5 b B e+8 B c d)}{2 c^{7/2}}",1,"(2*(d + e*x)^3*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*(d + e*x)*(b^3*B*e*(c*d^2 - 5*a*e^2) - 8*a*c^2*e*(A*c*d^2 + 8*a*B*d*e + 3*a*A*e^2) - 2*b^2*c*(2*B*c*d^3 + 5*A*c*d^2*e - 2*a*B*d*e^2 - a*A*e^3) + 4*b*c*(2*A*c*d*(c*d^2 + 3*a*e^2) + a*B*e*(5*c*d^2 + 7*a*e^2)) - (5*b^4*B*e^3 - 2*b^3*c*e^2*(3*B*d + A*e) - 4*b^2*c*e*(B*c*d^2 + A*c*d*e + 8*a*B*e^2) + 8*b*c^2*(B*c*d^3 + 3*A*c*d^2*e + 6*a*B*d*e^2 + 2*a*A*e^3) - 16*c^2*(2*a*B*e*(c*d^2 - a*e^2) + A*c*d*(c*d^2 + 2*a*e^2)))*x))/(3*c^2*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + (e*(15*b^4*B*e^3 - 2*b^3*c*e^2*(7*B*d + 3*A*e) - 4*b^2*c*e*(2*B*c*d^2 + A*c*d*e + 25*a*B*e^2) + 8*b*c^2*(2*B*c*d^3 + 6*A*c*d^2*e + 13*a*B*d*e^2 + 5*a*A*e^3) - 16*c^2*(4*a*B*e*(c*d^2 - 2*a*e^2) + A*c*d*(2*c*d^2 + 5*a*e^2)))*Sqrt[a + b*x + c*x^2])/(3*c^3*(b^2 - 4*a*c)^2) + (e^3*(8*B*c*d - 5*b*B*e + 2*A*c*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(7/2))","A",5,4,27,0.1481,1,"{818, 640, 621, 206}"
2481,1,397,0,0.3411336,"\int \frac{(A+B x) (d+e x)^3}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 \left(-x \left(2 b^2 c e \left(11 a B e^2+4 A c d e+3 B c d^2\right)-8 b c^2 \left(a A e^3+4 a B d e^2+3 A c d^2 e+B c d^3\right)+8 c^2 \left(2 A c d \left(a e^2+c d^2\right)+3 a B e \left(c d^2-a e^2\right)\right)+2 b^3 B c d e^2-3 b^4 B e^3\right)-4 b c \left(2 A c d \left(3 a e^2+c d^2\right)+5 a B e \left(a e^2+c d^2\right)\right)+16 a c^2 e \left(a A e^2+3 a B d e+A c d^2\right)+b^3 (-B) \left(c d^2 e-3 a e^3\right)+4 b^2 c^2 d^2 (2 A e+B d)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 (d+e x)^2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{B e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}","-\frac{2 \left(-x \left(2 b^2 c e \left(11 a B e^2+4 A c d e+3 B c d^2\right)-8 b c^2 \left(a A e^3+4 a B d e^2+3 A c d^2 e+B c d^3\right)+8 c^2 \left(2 A c d \left(a e^2+c d^2\right)+3 a B e \left(c d^2-a e^2\right)\right)+2 b^3 B c d e^2-3 b^4 B e^3\right)-4 b c \left(2 A c d \left(3 a e^2+c d^2\right)+5 a B e \left(a e^2+c d^2\right)\right)+16 a c^2 e \left(a A e^2+3 a B d e+A c d^2\right)+b^3 (-B) \left(c d^2 e-3 a e^3\right)+4 b^2 c^2 d^2 (2 A e+B d)\right)}{3 c^2 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 (d+e x)^2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}+\frac{B e^3 \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{a+b x+c x^2}}\right)}{c^{5/2}}",1,"(2*(d + e*x)^2*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (2*(4*b^2*c^2*d^2*(B*d + 2*A*e) + 16*a*c^2*e*(A*c*d^2 + 3*a*B*d*e + a*A*e^2) - b^3*B*(c*d^2*e - 3*a*e^3) - 4*b*c*(5*a*B*e*(c*d^2 + a*e^2) + 2*A*c*d*(c*d^2 + 3*a*e^2)) - (2*b^3*B*c*d*e^2 - 3*b^4*B*e^3 + 2*b^2*c*e*(3*B*c*d^2 + 4*A*c*d*e + 11*a*B*e^2) - 8*b*c^2*(B*c*d^3 + 3*A*c*d^2*e + 4*a*B*d*e^2 + a*A*e^3) + 8*c^2*(3*a*B*e*(c*d^2 - a*e^2) + 2*A*c*d*(c*d^2 + a*e^2)))*x))/(3*c^2*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2]) + (B*e^3*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(5/2)","A",4,4,27,0.1481,1,"{818, 777, 621, 206}"
2482,1,121,0,0.067421,"\int \frac{(A+B x) (d+e x)^2}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(5/2),x]","-\frac{2 (d+e x)^2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}-\frac{8 (-2 a e+x (2 c d-b e)+b d) (-2 a B e+A b e-2 A c d+b B d)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}","-\frac{2 (d+e x)^2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}-\frac{8 (-2 a e+x (2 c d-b e)+b d) (-2 a B e+A b e-2 A c d+b B d)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x)*(d + e*x)^2)/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (8*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,27,0.07407,1,"{804, 636}"
2483,1,158,0,0.1236123,"\int \frac{(A+B x) (d+e x)}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[((A + B*x)*(d + e*x))/(a + b*x + c*x^2)^(5/2),x]","\frac{2 (b+2 c x) \left(4 c (a B e+2 A c d)-4 b c (A e+B d)+b^2 B e\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","\frac{2 (b+2 c x) \left(4 c (a B e+2 A c d)-4 b c (A e+B d)+b^2 B e\right)}{3 c \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}+\frac{2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{3 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(2*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(3*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) + (2*(b^2*B*e - 4*b*c*(B*d + A*e) + 4*c*(2*A*c*d + a*B*e))*(b + 2*c*x))/(3*c*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,25,0.08000,1,"{777, 613}"
2484,1,90,0,0.0212365,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/(a + b*x + c*x^2)^(5/2),x]","-\frac{8 (b+2 c x) (b B-2 A c)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}","-\frac{8 (b+2 c x) (b B-2 A c)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2}}-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x))/(3*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(3/2)) - (8*(b*B - 2*A*c)*(b + 2*c*x))/(3*(b^2 - 4*a*c)^2*Sqrt[a + b*x + c*x^2])","A",2,2,20,0.1000,1,"{638, 613}"
2485,1,436,0,0.5541695,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)^(5/2)),x]","\frac{2 \left(c x \left((2 c d-b e) \left(4 c \left(3 a A e^2-a B d e+2 A c d^2\right)+3 b^2 e (B d-A e)-4 b c d (A e+B d)\right)+4 c e (b d-2 a e) (-2 a B e+A b e-2 A c d+b B d)\right)+\left(2 a c e+b^2 (-e)+b c d\right) \left(4 c \left(3 a A e^2-a B d e+2 A c d^2\right)+3 b^2 e (B d-A e)-4 b c d (A e+B d)\right)+4 a c e (2 c d-b e) (-2 a B e+A b e-2 A c d+b B d)\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{e^3 (B d-A e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{5/2}}","\frac{2 \left(c x \left((2 c d-b e) \left(4 c \left(3 a A e^2-a B d e+2 A c d^2\right)+3 b^2 e (B d-A e)-4 b c d (A e+B d)\right)+4 c e (b d-2 a e) (-2 a B e+A b e-2 A c d+b B d)\right)+\left(2 a c e+b^2 (-e)+b c d\right) \left(4 c \left(3 a A e^2-a B d e+2 A c d^2\right)+3 b^2 e (B d-A e)-4 b c d (A e+B d)\right)+4 a c e (2 c d-b e) (-2 a B e+A b e-2 A c d+b B d)\right)}{3 \left(b^2-4 a c\right)^2 \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{3 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{e^3 (B d-A e) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{\left(a e^2-b d e+c d^2\right)^{5/2}}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(3/2)) + (2*(4*a*c*e*(2*c*d - b*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (b*c*d - b^2*e + 2*a*c*e)*(3*b^2*e*(B*d - A*e) - 4*b*c*d*(B*d + A*e) + 4*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2)) + c*(4*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(3*b^2*e*(B*d - A*e) - 4*b*c*d*(B*d + A*e) + 4*c*(2*A*c*d^2 - a*B*d*e + 3*a*A*e^2)))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[a + b*x + c*x^2]) - (e^3*(B*d - A*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(5/2)","A",5,4,27,0.1481,1,"{822, 12, 724, 206}"
2486,1,744,0,1.5575178,"\int \frac{A+B x}{(d+e x)^2 \left(a+b x+c x^2\right)^{5/2}} \, dx","Int[(A + B*x)/((d + e*x)^2*(a + b*x + c*x^2)^(5/2)),x]","\frac{e \sqrt{a+b x+c x^2} \left(-8 b c \left(B \left(5 a^2 e^4+3 a c d^2 e^2+2 c^2 d^4\right)+2 A c d e \left(9 a e^2+4 c d^2\right)\right)-16 c^2 \left(a B d e \left(2 c d^2-13 a e^2\right)-A \left(-8 a^2 e^4+9 a c d^2 e^2+2 c^2 d^4\right)\right)-2 b^3 e^2 \left(-3 a B e^2-10 A c d e+9 B c d^2\right)+4 b^2 c e \left(25 a A e^3-14 a B d e^2+3 A c d^2 e+10 B c d^3\right)+3 b^4 e^3 (3 B d-5 A e)\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{2 \left(c x \left((2 c d-b e) \left(-2 b \left(-a B e^2+A c d e+2 B c d^2\right)+8 c \left(2 a A e^2-a B d e+A c d^2\right)+b^2 e (3 B d-5 A e)\right)+6 c e (b d-2 a e) (-2 a B e+A b e-2 A c d+b B d)\right)+\left(2 a c e+b^2 (-e)+b c d\right) \left(-2 b \left(-a B e^2+A c d e+2 B c d^2\right)+8 c \left(2 a A e^2-a B d e+A c d^2\right)+b^2 e (3 B d-5 A e)\right)+6 a c e (2 c d-b e) (-2 a B e+A b e-2 A c d+b B d)\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{e^3 \left(-B e (2 a e+3 b d)-5 A e (2 c d-b e)+8 B c d^2\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{7/2}}","\frac{e \sqrt{a+b x+c x^2} \left(-8 b c \left(B \left(5 a^2 e^4+3 a c d^2 e^2+2 c^2 d^4\right)+2 A c d e \left(9 a e^2+4 c d^2\right)\right)-16 c^2 \left(a B d e \left(2 c d^2-13 a e^2\right)-A \left(-8 a^2 e^4+9 a c d^2 e^2+2 c^2 d^4\right)\right)-2 b^3 e^2 \left(-3 a B e^2-10 A c d e+9 B c d^2\right)+4 b^2 c e \left(25 a A e^3-14 a B d e^2+3 A c d^2 e+10 B c d^3\right)+3 b^4 e^3 (3 B d-5 A e)\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \left(a e^2-b d e+c d^2\right)^3}+\frac{2 \left(c x \left((2 c d-b e) \left(-2 b \left(-a B e^2+A c d e+2 B c d^2\right)+8 c \left(2 a A e^2-a B d e+A c d^2\right)+b^2 e (3 B d-5 A e)\right)+6 c e (b d-2 a e) (-2 a B e+A b e-2 A c d+b B d)\right)+\left(2 a c e+b^2 (-e)+b c d\right) \left(-2 b \left(-a B e^2+A c d e+2 B c d^2\right)+8 c \left(2 a A e^2-a B d e+A c d^2\right)+b^2 e (3 B d-5 A e)\right)+6 a c e (2 c d-b e) (-2 a B e+A b e-2 A c d+b B d)\right)}{3 \left(b^2-4 a c\right)^2 (d+e x) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{3 \left(b^2-4 a c\right) (d+e x) \left(a+b x+c x^2\right)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{e^3 \left(5 A e (2 c d-b e)-B \left(8 c d^2-e (2 a e+3 b d)\right)\right) \tanh ^{-1}\left(\frac{-2 a e+x (2 c d-b e)+b d}{2 \sqrt{a+b x+c x^2} \sqrt{a e^2-b d e+c d^2}}\right)}{2 \left(a e^2-b d e+c d^2\right)^{7/2}}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/(3*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)*(a + b*x + c*x^2)^(3/2)) + (2*(6*a*c*e*(2*c*d - b*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (b*c*d - b^2*e + 2*a*c*e)*(b^2*e*(3*B*d - 5*A*e) + 8*c*(A*c*d^2 - a*B*d*e + 2*a*A*e^2) - 2*b*(2*B*c*d^2 + A*c*d*e - a*B*e^2)) + c*(6*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(b^2*e*(3*B*d - 5*A*e) + 8*c*(A*c*d^2 - a*B*d*e + 2*a*A*e^2) - 2*b*(2*B*c*d^2 + A*c*d*e - a*B*e^2)))*x))/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)*Sqrt[a + b*x + c*x^2]) + (e*(3*b^4*e^3*(3*B*d - 5*A*e) - 2*b^3*e^2*(9*B*c*d^2 - 10*A*c*d*e - 3*a*B*e^2) + 4*b^2*c*e*(10*B*c*d^3 + 3*A*c*d^2*e - 14*a*B*d*e^2 + 25*a*A*e^3) - 16*c^2*(a*B*d*e*(2*c*d^2 - 13*a*e^2) - A*(2*c^2*d^4 + 9*a*c*d^2*e^2 - 8*a^2*e^4)) - 8*b*c*(2*A*c*d*e*(4*c*d^2 + 9*a*e^2) + B*(2*c^2*d^4 + 3*a*c*d^2*e^2 + 5*a^2*e^4)))*Sqrt[a + b*x + c*x^2])/(3*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)) - (e^3*(8*B*c*d^2 - B*e*(3*b*d + 2*a*e) - 5*A*e*(2*c*d - b*e))*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(2*(c*d^2 - b*d*e + a*e^2)^(7/2))","A",5,4,27,0.1481,1,"{822, 806, 724, 206}"
2487,1,1401,0,2.1951947,"\int \frac{(A+B x) (d+e x)^6}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[((A + B*x)*(d + e*x)^6)/(a + b*x + c*x^2)^(7/2),x]","\frac{(12 B c d-7 b B e+2 A c e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^5}{2 c^{9/2}}+\frac{\left(105 B e^5 b^6-10 c e^4 (11 B d+3 A e) b^5-4 c e^3 \left(5 A c d e+8 B \left(2 c d^2+35 a e^2\right)\right) b^4-16 c^2 e^2 \left(3 B c d^3+A c e d^2-78 a B e^2 d-20 a A e^3\right) b^3+16 c^2 e \left(6 A c d e \left(9 c d^2+2 a e^2\right)+7 B \left(4 c^2 d^4+6 a c e^2 d^2+33 a^2 e^4\right)\right) b^2-32 c^3 \left(A e \left(40 c^2 d^4+78 a c e^2 d^2+33 a^2 e^4\right)+B \left(8 c^2 d^5+74 a c e^2 d^3+141 a^2 e^4 d\right)\right) b+64 c^3 \left(6 a B e \left(2 c^2 d^4+9 a c e^2 d^2-8 a^2 e^4\right)+A c d \left(8 c^2 d^4+26 a c e^2 d^2+33 a^2 e^4\right)\right)\right) \sqrt{c x^2+b x+a} e}{15 c^4 \left(b^2-4 a c\right)^3}+\frac{2 (d+e x) \left(7 B e^3 \left(c d^2-5 a e^2\right) b^5-2 c e^3 \left(A c d^2-16 a B e d-5 a A e^2\right) b^4-8 c e \left(A c d e \left(21 c d^2-a e^2\right)+6 B \left(2 c^2 d^4+a c e^2 d^2-7 a^2 e^4\right)\right) b^3+16 c^2 \left(6 A e \left(3 c^2 d^4+6 a c e^2 d^2-a^2 e^4\right)+B \left(4 c^2 d^5+37 a c e^2 d^3-21 a^2 e^4 d\right)\right) b^2-16 c^2 \left(2 A c d \left(4 c^2 d^4+19 a c e^2 d^2+21 a^2 e^4\right)+a B e \left(16 c^2 d^4+75 a c e^2 d^2+57 a^2 e^4\right)\right) b+32 a c^3 e \left(6 a B d e \left(c d^2+11 a e^2\right)+A \left(4 c^2 d^4+9 a c e^2 d^2+15 a^2 e^4\right)\right)-\left(35 B e^5 b^6-2 c e^4 (23 B d+5 A e) b^5-4 c e^3 \left(5 B c d^2+A c e d+91 a B e^2\right) b^4-8 c^2 e^2 \left(5 B c d^3+7 A c e d^2-63 a B e^2 d-13 a A e^3\right) b^3+16 c^2 e \left(A c d e \left(29 c d^2+9 a e^2\right)+B \left(14 c^2 d^4+21 a c e^2 d^2+72 a^2 e^4\right)\right) b^2-32 c^3 \left(A e \left(20 c^2 d^4+33 a c e^2 d^2+12 a^2 e^4\right)+B \left(4 c^2 d^5+35 a c e^2 d^3+60 a^2 e^4 d\right)\right) b+64 c^3 \left(6 a B e \left(c^2 d^4+4 a c e^2 d^2-2 a^2 e^4\right)+A c d \left(4 c^2 d^4+11 a c e^2 d^2+12 a^2 e^4\right)\right)\right) x\right)}{15 c^3 \left(b^2-4 a c\right)^3 \sqrt{c x^2+b x+a}}+\frac{2 (d+e x)^3 \left(B e \left(3 c d^2-7 a e^2\right) b^3-2 c \left(4 B c d^3+9 A c e d^2-a A e^3\right) b^2+4 c \left(4 A c d \left(c d^2+3 a e^2\right)+a B e \left(9 c d^2+11 a e^2\right)\right) b-8 a c^2 e \left(3 A c d^2+12 a B e d+5 a A e^2\right)-\left(7 B e^3 b^4-2 c e^2 (3 B d+A e) b^3-12 c e \left(B c d^2+A c e d+4 a B e^2\right) b^2+8 c^2 \left(2 B c d^3+6 A c e d^2+9 a B e^2 d+3 a A e^3\right) b-16 c^2 \left(3 a B e \left(c d^2-a e^2\right)+A c d \left(2 c d^2+3 a e^2\right)\right)\right) x\right)}{15 c^2 \left(b^2-4 a c\right)^2 \left(c x^2+b x+a\right)^{3/2}}+\frac{2 (d+e x)^5 \left(2 a c (B d+A e)-b (A c d+a B e)-\left(B e b^2-c (B d+A e) b+2 c (A c d-a B e)\right) x\right)}{5 c \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{5/2}}","\frac{(12 B c d-7 b B e+2 A c e) \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^5}{2 c^{9/2}}+\frac{\left(105 B e^5 b^6-10 c e^4 (11 B d+3 A e) b^5-4 c e^3 \left(5 A c d e+8 B \left(2 c d^2+35 a e^2\right)\right) b^4-16 c^2 e^2 \left(3 B c d^3+A c e d^2-78 a B e^2 d-20 a A e^3\right) b^3+16 c^2 e \left(6 A c d e \left(9 c d^2+2 a e^2\right)+7 B \left(4 c^2 d^4+6 a c e^2 d^2+33 a^2 e^4\right)\right) b^2-32 c^3 \left(A e \left(40 c^2 d^4+78 a c e^2 d^2+33 a^2 e^4\right)+B \left(8 c^2 d^5+74 a c e^2 d^3+141 a^2 e^4 d\right)\right) b+64 c^3 \left(6 a B e \left(2 c^2 d^4+9 a c e^2 d^2-8 a^2 e^4\right)+A c d \left(8 c^2 d^4+26 a c e^2 d^2+33 a^2 e^4\right)\right)\right) \sqrt{c x^2+b x+a} e}{15 c^4 \left(b^2-4 a c\right)^3}+\frac{2 (d+e x) \left(7 B e^3 \left(c d^2-5 a e^2\right) b^5-2 c e^3 \left(A c d^2-16 a B e d-5 a A e^2\right) b^4-8 c e \left(A c d e \left(21 c d^2-a e^2\right)+6 B \left(2 c^2 d^4+a c e^2 d^2-7 a^2 e^4\right)\right) b^3+16 c^2 \left(6 A e \left(3 c^2 d^4+6 a c e^2 d^2-a^2 e^4\right)+B \left(4 c^2 d^5+37 a c e^2 d^3-21 a^2 e^4 d\right)\right) b^2-16 c^2 \left(2 A c d \left(4 c^2 d^4+19 a c e^2 d^2+21 a^2 e^4\right)+a B e \left(16 c^2 d^4+75 a c e^2 d^2+57 a^2 e^4\right)\right) b+32 a c^3 e \left(6 a B d e \left(c d^2+11 a e^2\right)+A \left(4 c^2 d^4+9 a c e^2 d^2+15 a^2 e^4\right)\right)-\left(35 B e^5 b^6-2 c e^4 (23 B d+5 A e) b^5-4 c e^3 \left(5 B c d^2+A c e d+91 a B e^2\right) b^4-8 c^2 e^2 \left(5 B c d^3+7 A c e d^2-63 a B e^2 d-13 a A e^3\right) b^3+16 c^2 e \left(A c d e \left(29 c d^2+9 a e^2\right)+B \left(14 c^2 d^4+21 a c e^2 d^2+72 a^2 e^4\right)\right) b^2-32 c^3 \left(A e \left(20 c^2 d^4+33 a c e^2 d^2+12 a^2 e^4\right)+B \left(4 c^2 d^5+35 a c e^2 d^3+60 a^2 e^4 d\right)\right) b+64 c^3 \left(6 a B e \left(c^2 d^4+4 a c e^2 d^2-2 a^2 e^4\right)+A c d \left(4 c^2 d^4+11 a c e^2 d^2+12 a^2 e^4\right)\right)\right) x\right)}{15 c^3 \left(b^2-4 a c\right)^3 \sqrt{c x^2+b x+a}}+\frac{2 (d+e x)^3 \left(B e \left(3 c d^2-7 a e^2\right) b^3-2 c \left(4 B c d^3+9 A c e d^2-a A e^3\right) b^2+4 c \left(4 A c d \left(c d^2+3 a e^2\right)+a B e \left(9 c d^2+11 a e^2\right)\right) b-8 a c^2 e \left(3 A c d^2+12 a B e d+5 a A e^2\right)-\left(7 B e^3 b^4-2 c e^2 (3 B d+A e) b^3-12 c e \left(B c d^2+A c e d+4 a B e^2\right) b^2+8 c^2 \left(2 B c d^3+6 A c e d^2+9 a B e^2 d+3 a A e^3\right) b-16 c^2 \left(3 a B e \left(c d^2-a e^2\right)+A c d \left(2 c d^2+3 a e^2\right)\right)\right) x\right)}{15 c^2 \left(b^2-4 a c\right)^2 \left(c x^2+b x+a\right)^{3/2}}+\frac{2 (d+e x)^5 \left(2 a c (B d+A e)-b (A c d+a B e)-\left(B e b^2-c (B d+A e) b+2 c (A c d-a B e)\right) x\right)}{5 c \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{5/2}}",1,"(2*(d + e*x)^5*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(5*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) + (2*(d + e*x)^3*(b^3*B*e*(3*c*d^2 - 7*a*e^2) - 8*a*c^2*e*(3*A*c*d^2 + 12*a*B*d*e + 5*a*A*e^2) - 2*b^2*c*(4*B*c*d^3 + 9*A*c*d^2*e - a*A*e^3) + 4*b*c*(4*A*c*d*(c*d^2 + 3*a*e^2) + a*B*e*(9*c*d^2 + 11*a*e^2)) - (7*b^4*B*e^3 - 2*b^3*c*e^2*(3*B*d + A*e) - 12*b^2*c*e*(B*c*d^2 + A*c*d*e + 4*a*B*e^2) + 8*b*c^2*(2*B*c*d^3 + 6*A*c*d^2*e + 9*a*B*d*e^2 + 3*a*A*e^3) - 16*c^2*(3*a*B*e*(c*d^2 - a*e^2) + A*c*d*(2*c*d^2 + 3*a*e^2)))*x))/(15*c^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) + (2*(d + e*x)*(7*b^5*B*e^3*(c*d^2 - 5*a*e^2) - 2*b^4*c*e^3*(A*c*d^2 - 16*a*B*d*e - 5*a*A*e^2) - 8*b^3*c*e*(A*c*d*e*(21*c*d^2 - a*e^2) + 6*B*(2*c^2*d^4 + a*c*d^2*e^2 - 7*a^2*e^4)) + 32*a*c^3*e*(6*a*B*d*e*(c*d^2 + 11*a*e^2) + A*(4*c^2*d^4 + 9*a*c*d^2*e^2 + 15*a^2*e^4)) - 16*b*c^2*(2*A*c*d*(4*c^2*d^4 + 19*a*c*d^2*e^2 + 21*a^2*e^4) + a*B*e*(16*c^2*d^4 + 75*a*c*d^2*e^2 + 57*a^2*e^4)) + 16*b^2*c^2*(6*A*e*(3*c^2*d^4 + 6*a*c*d^2*e^2 - a^2*e^4) + B*(4*c^2*d^5 + 37*a*c*d^3*e^2 - 21*a^2*d*e^4)) - (35*b^6*B*e^5 - 2*b^5*c*e^4*(23*B*d + 5*A*e) - 4*b^4*c*e^3*(5*B*c*d^2 + A*c*d*e + 91*a*B*e^2) - 8*b^3*c^2*e^2*(5*B*c*d^3 + 7*A*c*d^2*e - 63*a*B*d*e^2 - 13*a*A*e^3) + 64*c^3*(6*a*B*e*(c^2*d^4 + 4*a*c*d^2*e^2 - 2*a^2*e^4) + A*c*d*(4*c^2*d^4 + 11*a*c*d^2*e^2 + 12*a^2*e^4)) + 16*b^2*c^2*e*(A*c*d*e*(29*c*d^2 + 9*a*e^2) + B*(14*c^2*d^4 + 21*a*c*d^2*e^2 + 72*a^2*e^4)) - 32*b*c^3*(A*e*(20*c^2*d^4 + 33*a*c*d^2*e^2 + 12*a^2*e^4) + B*(4*c^2*d^5 + 35*a*c*d^3*e^2 + 60*a^2*d*e^4)))*x))/(15*c^3*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2]) + (e*(105*b^6*B*e^5 - 10*b^5*c*e^4*(11*B*d + 3*A*e) - 16*b^3*c^2*e^2*(3*B*c*d^3 + A*c*d^2*e - 78*a*B*d*e^2 - 20*a*A*e^3) - 4*b^4*c*e^3*(5*A*c*d*e + 8*B*(2*c*d^2 + 35*a*e^2)) + 16*b^2*c^2*e*(6*A*c*d*e*(9*c*d^2 + 2*a*e^2) + 7*B*(4*c^2*d^4 + 6*a*c*d^2*e^2 + 33*a^2*e^4)) + 64*c^3*(6*a*B*e*(2*c^2*d^4 + 9*a*c*d^2*e^2 - 8*a^2*e^4) + A*c*d*(8*c^2*d^4 + 26*a*c*d^2*e^2 + 33*a^2*e^4)) - 32*b*c^3*(A*e*(40*c^2*d^4 + 78*a*c*d^2*e^2 + 33*a^2*e^4) + B*(8*c^2*d^5 + 74*a*c*d^3*e^2 + 141*a^2*d*e^4)))*Sqrt[a + b*x + c*x^2])/(15*c^4*(b^2 - 4*a*c)^3) + (e^5*(12*B*c*d - 7*b*B*e + 2*A*c*e)*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/(2*c^(9/2))","A",6,4,27,0.1481,1,"{818, 640, 621, 206}"
2488,1,942,0,0.9605727,"\int \frac{(A+B x) (d+e x)^5}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[((A + B*x)*(d + e*x)^5)/(a + b*x + c*x^2)^(7/2),x]","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^5}{c^{7/2}}+\frac{2 \left(5 B e^3 \left(c d^2-3 a e^2\right) b^5+4 B c^2 d^3 e^2 b^4-8 c e \left(16 A c^2 e d^3+B \left(11 c^2 d^4+7 a c e^2 d^2-20 a^2 e^4\right)\right) b^3+32 c^3 d^2 \left(2 B c d^3+8 A c e d^2+17 a B e^2 d+16 a A e^3\right) b^2-16 c^2 \left(8 A c d \left(c^2 d^4+6 a c e^2 d^2+5 a^2 e^4\right)+a B e \left(18 c^2 d^4+71 a c e^2 d^2+33 a^2 e^4\right)\right) b+64 a c^3 e \left(4 A \left(c d^2+a e^2\right)^2+5 a B d e \left(c d^2+4 a e^2\right)\right)+\left(-15 B e^5 b^6+10 B c d e^4 b^5+2 B c e^3 \left(3 c d^2+85 a e^2\right) b^4+16 c^2 d e^2 \left(6 B c d^2+8 A c e d-7 a B e^2\right) b^3-16 c^2 e \left(16 A c d e \left(2 c d^2+a e^2\right)+B \left(15 c^2 d^4+29 a c e^2 d^2+39 a^2 e^4\right)\right) b^2+32 c^3 \left(4 A e \left(5 c^2 d^4+6 a c e^2 d^2+a^2 e^4\right)+B \left(4 c^2 d^5+28 a c e^2 d^3+29 a^2 e^4 d\right)\right) b-32 c^3 \left(8 A c d \left(c d^2+a e^2\right)^2+5 a B e \left(2 c^2 d^4+5 a c e^2 d^2-3 a^2 e^4\right)\right)\right) x\right)}{15 c^3 \left(b^2-4 a c\right)^3 \sqrt{c x^2+b x+a}}+\frac{2 (d+e x)^2 \left(B e \left(3 c d^2-5 a e^2\right) b^3-4 c d \left(2 B c d^2+4 A c e d+a B e^2\right) b^2+4 c \left(9 a B e \left(c d^2+a e^2\right)+4 A c d \left(c d^2+3 a e^2\right)\right) b-16 a c^2 e \left(5 a B d e+2 A \left(c d^2+a e^2\right)\right)+\left(-5 B e^3 b^4+2 B c d e^2 b^3+2 c e \left(7 B c d^2+8 A c e d+19 a B e^2\right) b^2-8 c^2 \left(2 B c d^3+6 A c e d^2+7 a B e^2 d+2 a A e^3\right) b+8 c^2 \left(5 a B e \left(c d^2-a e^2\right)+4 A c d \left(c d^2+a e^2\right)\right)\right) x\right)}{15 c^2 \left(b^2-4 a c\right)^2 \left(c x^2+b x+a\right)^{3/2}}+\frac{2 (d+e x)^4 \left(2 a c (B d+A e)-b (A c d+a B e)-\left(B e b^2-c (B d+A e) b+2 c (A c d-a B e)\right) x\right)}{5 c \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{5/2}}","\frac{B \tanh ^{-1}\left(\frac{b+2 c x}{2 \sqrt{c} \sqrt{c x^2+b x+a}}\right) e^5}{c^{7/2}}+\frac{2 \left(5 B e^3 \left(c d^2-3 a e^2\right) b^5+4 B c^2 d^3 e^2 b^4-8 c e \left(16 A c^2 e d^3+B \left(11 c^2 d^4+7 a c e^2 d^2-20 a^2 e^4\right)\right) b^3+32 c^3 d^2 \left(2 B c d^3+8 A c e d^2+17 a B e^2 d+16 a A e^3\right) b^2-16 c^2 \left(8 A c d \left(c^2 d^4+6 a c e^2 d^2+5 a^2 e^4\right)+a B e \left(18 c^2 d^4+71 a c e^2 d^2+33 a^2 e^4\right)\right) b+64 a c^3 e \left(4 A \left(c d^2+a e^2\right)^2+5 a B d e \left(c d^2+4 a e^2\right)\right)+\left(-15 B e^5 b^6+10 B c d e^4 b^5+2 B c e^3 \left(3 c d^2+85 a e^2\right) b^4+16 c^2 d e^2 \left(6 B c d^2+8 A c e d-7 a B e^2\right) b^3-16 c^2 e \left(16 A c d e \left(2 c d^2+a e^2\right)+B \left(15 c^2 d^4+29 a c e^2 d^2+39 a^2 e^4\right)\right) b^2+32 c^3 \left(4 A e \left(5 c^2 d^4+6 a c e^2 d^2+a^2 e^4\right)+B \left(4 c^2 d^5+28 a c e^2 d^3+29 a^2 e^4 d\right)\right) b-32 c^3 \left(8 A c d \left(c d^2+a e^2\right)^2+5 a B e \left(2 c^2 d^4+5 a c e^2 d^2-3 a^2 e^4\right)\right)\right) x\right)}{15 c^3 \left(b^2-4 a c\right)^3 \sqrt{c x^2+b x+a}}+\frac{2 (d+e x)^2 \left(B e \left(3 c d^2-5 a e^2\right) b^3-4 c d \left(2 B c d^2+4 A c e d+a B e^2\right) b^2+4 c \left(9 a B e \left(c d^2+a e^2\right)+4 A c d \left(c d^2+3 a e^2\right)\right) b-16 a c^2 e \left(5 a B d e+2 A \left(c d^2+a e^2\right)\right)+\left(-5 B e^3 b^4+2 B c d e^2 b^3+2 c e \left(7 B c d^2+8 A c e d+19 a B e^2\right) b^2-8 c^2 \left(2 B c d^3+6 A c e d^2+7 a B e^2 d+2 a A e^3\right) b+8 c^2 \left(5 a B e \left(c d^2-a e^2\right)+4 A c d \left(c d^2+a e^2\right)\right)\right) x\right)}{15 c^2 \left(b^2-4 a c\right)^2 \left(c x^2+b x+a\right)^{3/2}}+\frac{2 (d+e x)^4 \left(2 a c (B d+A e)-b (A c d+a B e)-\left(B e b^2-c (B d+A e) b+2 c (A c d-a B e)\right) x\right)}{5 c \left(b^2-4 a c\right) \left(c x^2+b x+a\right)^{5/2}}",1,"(2*(d + e*x)^4*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(5*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) + (2*(d + e*x)^2*(b^3*B*e*(3*c*d^2 - 5*a*e^2) - 4*b^2*c*d*(2*B*c*d^2 + 4*A*c*d*e + a*B*e^2) - 16*a*c^2*e*(5*a*B*d*e + 2*A*(c*d^2 + a*e^2)) + 4*b*c*(9*a*B*e*(c*d^2 + a*e^2) + 4*A*c*d*(c*d^2 + 3*a*e^2)) + (2*b^3*B*c*d*e^2 - 5*b^4*B*e^3 + 2*b^2*c*e*(7*B*c*d^2 + 8*A*c*d*e + 19*a*B*e^2) - 8*b*c^2*(2*B*c*d^3 + 6*A*c*d^2*e + 7*a*B*d*e^2 + 2*a*A*e^3) + 8*c^2*(5*a*B*e*(c*d^2 - a*e^2) + 4*A*c*d*(c*d^2 + a*e^2)))*x))/(15*c^2*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) + (2*(4*b^4*B*c^2*d^3*e^2 + 5*b^5*B*e^3*(c*d^2 - 3*a*e^2) + 32*b^2*c^3*d^2*(2*B*c*d^3 + 8*A*c*d^2*e + 17*a*B*d*e^2 + 16*a*A*e^3) + 64*a*c^3*e*(4*A*(c*d^2 + a*e^2)^2 + 5*a*B*d*e*(c*d^2 + 4*a*e^2)) - 8*b^3*c*e*(16*A*c^2*d^3*e + B*(11*c^2*d^4 + 7*a*c*d^2*e^2 - 20*a^2*e^4)) - 16*b*c^2*(8*A*c*d*(c^2*d^4 + 6*a*c*d^2*e^2 + 5*a^2*e^4) + a*B*e*(18*c^2*d^4 + 71*a*c*d^2*e^2 + 33*a^2*e^4)) + (10*b^5*B*c*d*e^4 - 15*b^6*B*e^5 + 2*b^4*B*c*e^3*(3*c*d^2 + 85*a*e^2) + 16*b^3*c^2*d*e^2*(6*B*c*d^2 + 8*A*c*d*e - 7*a*B*e^2) - 32*c^3*(8*A*c*d*(c*d^2 + a*e^2)^2 + 5*a*B*e*(2*c^2*d^4 + 5*a*c*d^2*e^2 - 3*a^2*e^4)) - 16*b^2*c^2*e*(16*A*c*d*e*(2*c*d^2 + a*e^2) + B*(15*c^2*d^4 + 29*a*c*d^2*e^2 + 39*a^2*e^4)) + 32*b*c^3*(4*A*e*(5*c^2*d^4 + 6*a*c*d^2*e^2 + a^2*e^4) + B*(4*c^2*d^5 + 28*a*c*d^3*e^2 + 29*a^2*d*e^4)))*x))/(15*c^3*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2]) + (B*e^5*ArcTanh[(b + 2*c*x)/(2*Sqrt[c]*Sqrt[a + b*x + c*x^2])])/c^(7/2)","A",5,4,27,0.1481,1,"{818, 777, 621, 206}"
2489,1,210,0,0.1351487,"\int \frac{(A+B x) (d+e x)^4}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[((A + B*x)*(d + e*x)^4)/(a + b*x + c*x^2)^(7/2),x]","\frac{128 \left(a e^2-b d e+c d^2\right) (-2 a e+x (2 c d-b e)+b d) (-2 a B e+A b e-2 A c d+b B d)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^4 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}-\frac{16 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d) (-2 a B e+A b e-2 A c d+b B d)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}","\frac{128 \left(a e^2-b d e+c d^2\right) (-2 a e+x (2 c d-b e)+b d) (-2 a B e+A b e-2 A c d+b B d)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^4 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}-\frac{16 (d+e x)^2 (-2 a e+x (2 c d-b e)+b d) (-2 a B e+A b e-2 A c d+b B d)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x)*(d + e*x)^4)/(5*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) - (16*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(d + e*x)^2*(b*d - 2*a*e + (2*c*d - b*e)*x))/(15*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) + (128*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(c*d^2 - b*d*e + a*e^2)*(b*d - 2*a*e + (2*c*d - b*e)*x))/(15*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",3,3,27,0.1111,1,"{804, 722, 636}"
2490,1,264,0,0.3616264,"\int \frac{(A+B x) (d+e x)^3}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[((A + B*x)*(d + e*x)^3)/(a + b*x + c*x^2)^(7/2),x]","-\frac{16 (-2 a e+x (2 c d-b e)+b d) \left(-8 b \left(a B e^2+2 A c d e+B c d^2\right)+4 c \left(a A e^2+3 a B d e+4 A c d^2\right)+b^2 e (3 A e+5 B d)\right)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^3 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}-\frac{4 (d+e x)^2 \left(-x \left(4 c (3 a B e+4 A c d)-8 b c (A e+B d)+b^2 B e\right)-8 b (a B e+A c d)+4 a A c e+b^2 (3 A e+4 B d)\right)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}","-\frac{16 (-2 a e+x (2 c d-b e)+b d) \left(-8 b \left(a B e^2+2 A c d e+B c d^2\right)+4 c \left(a A e^2+3 a B d e+4 A c d^2\right)+b^2 e (3 A e+5 B d)\right)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{2 (d+e x)^3 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}-\frac{4 (d+e x)^2 \left(-x \left(4 c (3 a B e+4 A c d)-8 b c (A e+B d)+b^2 B e\right)-8 b (a B e+A c d)+4 a A c e+b^2 (3 A e+4 B d)\right)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x)*(d + e*x)^3)/(5*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) - (4*(d + e*x)^2*(4*a*A*c*e + b^2*(4*B*d + 3*A*e) - 8*b*(A*c*d + a*B*e) - (b^2*B*e - 8*b*c*(B*d + A*e) + 4*c*(4*A*c*d + 3*a*B*e))*x))/(15*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) - (16*(b^2*e*(5*B*d + 3*A*e) + 4*c*(4*A*c*d^2 + 3*a*B*d*e + a*A*e^2) - 8*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*(b*d - 2*a*e + (2*c*d - b*e)*x))/(15*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",3,3,27,0.1111,1,"{820, 804, 636}"
2491,1,324,0,0.3852662,"\int \frac{(A+B x) (d+e x)^2}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[((A + B*x)*(d + e*x)^2)/(a + b*x + c*x^2)^(7/2),x]","\frac{8 (b+2 c x) \left(4 b c \left(3 a B e^2+8 A c d e+4 B c d^2\right)-8 c^2 \left(a A e^2+2 a B d e+4 A c d^2\right)-6 b^2 c e (A e+2 B d)+b^3 B e^2\right)}{15 c \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{8 \left(x \left(-4 c^2 \left(-a A e^2+a B d e+2 A c d^2\right)-3 b^2 c e (A e+B d)+4 b c^2 d (2 A e+B d)+b^3 B e^2\right)+b^2 \left(a B e^2+A c d e+2 B c d^2\right)-4 b c \left(a A e^2+2 a B d e+A c d^2\right)+4 a c e (a B e+3 A c d)\right)}{15 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 (d+e x)^2 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}","\frac{8 (b+2 c x) \left(4 b c \left(3 a B e^2+8 A c d e+4 B c d^2\right)-8 c^2 \left(a A e^2+2 a B d e+4 A c d^2\right)-6 b^2 c e (A e+2 B d)+b^3 B e^2\right)}{15 c \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{8 \left(x \left(-4 c^2 \left(-a A e^2+a B d e+2 A c d^2\right)-3 b^2 c e (A e+B d)+4 b c^2 d (2 A e+B d)+b^3 B e^2\right)+b^2 \left(a B e^2+A c d e+2 B c d^2\right)-4 b c \left(a A e^2+2 a B d e+A c d^2\right)+4 a c e (a B e+3 A c d)\right)}{15 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 (d+e x)^2 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x)*(d + e*x)^2)/(5*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) - (8*(4*a*c*e*(3*A*c*d + a*B*e) - 4*b*c*(A*c*d^2 + 2*a*B*d*e + a*A*e^2) + b^2*(2*B*c*d^2 + A*c*d*e + a*B*e^2) + (b^3*B*e^2 - 3*b^2*c*e*(B*d + A*e) + 4*b*c^2*d*(B*d + 2*A*e) - 4*c^2*(2*A*c*d^2 + a*B*d*e - a*A*e^2))*x))/(15*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) + (8*(b^3*B*e^2 - 6*b^2*c*e*(2*B*d + A*e) - 8*c^2*(4*A*c*d^2 + 2*a*B*d*e + a*A*e^2) + 4*b*c*(4*B*c*d^2 + 8*A*c*d*e + 3*a*B*e^2))*(b + 2*c*x))/(15*c*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",3,3,27,0.1111,1,"{820, 777, 613}"
2492,1,225,0,0.1835042,"\int \frac{(A+B x) (d+e x)}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[((A + B*x)*(d + e*x))/(a + b*x + c*x^2)^(7/2),x]","-\frac{16 (b+2 c x) \left(4 c (a B e+4 A c d)-8 b c (A e+B d)+3 b^2 B e\right)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}+\frac{2 (b+2 c x) \left(4 c (a B e+4 A c d)-8 b c (A e+B d)+3 b^2 B e\right)}{15 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}+\frac{2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{5 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}","-\frac{16 (b+2 c x) \left(4 c (a B e+4 A c d)-8 b c (A e+B d)+3 b^2 B e\right)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}+\frac{2 (b+2 c x) \left(4 c (a B e+4 A c d)-8 b c (A e+B d)+3 b^2 B e\right)}{15 c \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}+\frac{2 \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{5 c \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}",1,"(2*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(5*c*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) + (2*(3*b^2*B*e - 8*b*c*(B*d + A*e) + 4*c*(4*A*c*d + a*B*e))*(b + 2*c*x))/(15*c*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) - (16*(3*b^2*B*e - 8*b*c*(B*d + A*e) + 4*c*(4*A*c*d + a*B*e))*(b + 2*c*x))/(15*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",3,3,25,0.1200,1,"{777, 614, 613}"
2493,1,133,0,0.0373278,"\int \frac{A+B x}{\left(a+b x+c x^2\right)^{7/2}} \, dx","Int[(A + B*x)/(a + b*x + c*x^2)^(7/2),x]","\frac{128 c (b+2 c x) (b B-2 A c)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{16 (b+2 c x) (b B-2 A c)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}","\frac{128 c (b+2 c x) (b B-2 A c)}{15 \left(b^2-4 a c\right)^3 \sqrt{a+b x+c x^2}}-\frac{16 (b+2 c x) (b B-2 A c)}{15 \left(b^2-4 a c\right)^2 \left(a+b x+c x^2\right)^{3/2}}-\frac{2 (-2 a B-x (b B-2 A c)+A b)}{5 \left(b^2-4 a c\right) \left(a+b x+c x^2\right)^{5/2}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x))/(5*(b^2 - 4*a*c)*(a + b*x + c*x^2)^(5/2)) - (16*(b*B - 2*A*c)*(b + 2*c*x))/(15*(b^2 - 4*a*c)^2*(a + b*x + c*x^2)^(3/2)) + (128*c*(b*B - 2*A*c)*(b + 2*c*x))/(15*(b^2 - 4*a*c)^3*Sqrt[a + b*x + c*x^2])","A",3,3,20,0.1500,1,"{638, 614, 613}"
2494,1,974,0,1.7095126,"\int \frac{A+B x}{(d+e x) \left(a+b x+c x^2\right)^{7/2}} \, dx","Int[(A + B*x)/((d + e*x)*(a + b*x + c*x^2)^(7/2)),x]","-\frac{(B d-A e) \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) e^5}{\left(c d^2-b e d+a e^2\right)^{7/2}}+\frac{2 \left(4 a c e (2 c d-b e) \left(8 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+(2 c d-b e) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)-\left(-e b^2+c d b+2 a c e\right) \left(8 c d e (b B d-2 A c d+A b e-2 a B e) \left(-3 e b^2+4 c d b+4 a c e\right)+\left(8 c^2 d^2-3 b^2 e^2-4 c e (b d-3 a e)\right) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)+c \left(4 c e (b d-2 a e) \left(8 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+(2 c d-b e) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)-(2 c d-b e) \left(8 c d e (b B d-2 A c d+A b e-2 a B e) \left(-3 e b^2+4 c d b+4 a c e\right)+\left(8 c^2 d^2-3 b^2 e^2-4 c e (b d-3 a e)\right) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)\right) x\right)}{15 \left(b^2-4 a c\right)^3 \left(c d^2-b e d+a e^2\right)^3 \sqrt{c x^2+b x+a}}+\frac{2 \left(8 a c e (2 c d-b e) (b B d-2 A c d+A b e-2 a B e)+\left(-e b^2+c d b+2 a c e\right) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)+c \left(8 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+(2 c d-b e) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right) x\right)}{15 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)^{3/2}}+\frac{2 \left(a B (2 c d-b e)-A \left(-e b^2+c d b+2 a c e\right)+c (b B d-2 A c d+A b e-2 a B e) x\right)}{5 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^{5/2}}","-\frac{(B d-A e) \tanh ^{-1}\left(\frac{b d-2 a e+(2 c d-b e) x}{2 \sqrt{c d^2-b e d+a e^2} \sqrt{c x^2+b x+a}}\right) e^5}{\left(c d^2-b e d+a e^2\right)^{7/2}}+\frac{2 \left(4 a c e (2 c d-b e) \left(8 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+(2 c d-b e) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)-\left(-e b^2+c d b+2 a c e\right) \left(8 c d e (b B d-2 A c d+A b e-2 a B e) \left(-3 e b^2+4 c d b+4 a c e\right)+\left(8 c^2 d^2-3 b^2 e^2-4 c e (b d-3 a e)\right) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)+c \left(4 c e (b d-2 a e) \left(8 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+(2 c d-b e) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)-(2 c d-b e) \left(8 c d e (b B d-2 A c d+A b e-2 a B e) \left(-3 e b^2+4 c d b+4 a c e\right)+\left(8 c^2 d^2-3 b^2 e^2-4 c e (b d-3 a e)\right) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right)\right) x\right)}{15 \left(b^2-4 a c\right)^3 \left(c d^2-b e d+a e^2\right)^3 \sqrt{c x^2+b x+a}}+\frac{2 \left(8 a c e (2 c d-b e) (b B d-2 A c d+A b e-2 a B e)+\left(-e b^2+c d b+2 a c e\right) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)+c \left(8 c e (b d-2 a e) (b B d-2 A c d+A b e-2 a B e)+(2 c d-b e) \left(5 e (B d-A e) b^2-8 c d (B d+A e) b+4 c \left(4 A c d^2-a B e d+5 a A e^2\right)\right)\right) x\right)}{15 \left(b^2-4 a c\right)^2 \left(c d^2-b e d+a e^2\right)^2 \left(c x^2+b x+a\right)^{3/2}}+\frac{2 \left(a B (2 c d-b e)-A \left(-e b^2+c d b+2 a c e\right)+c (b B d-2 A c d+A b e-2 a B e) x\right)}{5 \left(b^2-4 a c\right) \left(c d^2-b e d+a e^2\right) \left(c x^2+b x+a\right)^{5/2}}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/(5*(b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)^(5/2)) + (2*(8*a*c*e*(2*c*d - b*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (b*c*d - b^2*e + 2*a*c*e)*(5*b^2*e*(B*d - A*e) - 8*b*c*d*(B*d + A*e) + 4*c*(4*A*c*d^2 - a*B*d*e + 5*a*A*e^2)) + c*(8*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(5*b^2*e*(B*d - A*e) - 8*b*c*d*(B*d + A*e) + 4*c*(4*A*c*d^2 - a*B*d*e + 5*a*A*e^2)))*x))/(15*(b^2 - 4*a*c)^2*(c*d^2 - b*d*e + a*e^2)^2*(a + b*x + c*x^2)^(3/2)) + (2*(4*a*c*e*(2*c*d - b*e)*(8*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(5*b^2*e*(B*d - A*e) - 8*b*c*d*(B*d + A*e) + 4*c*(4*A*c*d^2 - a*B*d*e + 5*a*A*e^2))) - (b*c*d - b^2*e + 2*a*c*e)*(8*c*d*e*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(4*b*c*d - 3*b^2*e + 4*a*c*e) + (8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(b*d - 3*a*e))*(5*b^2*e*(B*d - A*e) - 8*b*c*d*(B*d + A*e) + 4*c*(4*A*c*d^2 - a*B*d*e + 5*a*A*e^2))) + c*(4*c*e*(b*d - 2*a*e)*(8*c*e*(b*d - 2*a*e)*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e) + (2*c*d - b*e)*(5*b^2*e*(B*d - A*e) - 8*b*c*d*(B*d + A*e) + 4*c*(4*A*c*d^2 - a*B*d*e + 5*a*A*e^2))) - (2*c*d - b*e)*(8*c*d*e*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(4*b*c*d - 3*b^2*e + 4*a*c*e) + (8*c^2*d^2 - 3*b^2*e^2 - 4*c*e*(b*d - 3*a*e))*(5*b^2*e*(B*d - A*e) - 8*b*c*d*(B*d + A*e) + 4*c*(4*A*c*d^2 - a*B*d*e + 5*a*A*e^2))))*x))/(15*(b^2 - 4*a*c)^3*(c*d^2 - b*d*e + a*e^2)^3*Sqrt[a + b*x + c*x^2]) - (e^5*(B*d - A*e)*ArcTanh[(b*d - 2*a*e + (2*c*d - b*e)*x)/(2*Sqrt[c*d^2 - b*d*e + a*e^2]*Sqrt[a + b*x + c*x^2])])/(c*d^2 - b*d*e + a*e^2)^(7/2)","A",6,4,27,0.1481,1,"{822, 12, 724, 206}"
2495,1,137,0,0.0856792,"\int \frac{(5-x) (3+2 x)^4}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^4)/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{15} \sqrt{3 x^2+5 x+2} (2 x+3)^4+\frac{53}{60} \sqrt{3 x^2+5 x+2} (2 x+3)^3+\frac{391}{135} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{1}{648} (9650 x+27519) \sqrt{3 x^2+5 x+2}+\frac{28051 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1296 \sqrt{3}}","-\frac{1}{15} \sqrt{3 x^2+5 x+2} (2 x+3)^4+\frac{53}{60} \sqrt{3 x^2+5 x+2} (2 x+3)^3+\frac{391}{135} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{1}{648} (9650 x+27519) \sqrt{3 x^2+5 x+2}+\frac{28051 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1296 \sqrt{3}}",1,"(391*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2])/135 + (53*(3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2])/60 - ((3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2])/15 + ((27519 + 9650*x)*Sqrt[2 + 5*x + 3*x^2])/648 + (28051*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(1296*Sqrt[3])","A",6,4,27,0.1481,1,"{832, 779, 621, 206}"
2496,1,112,0,0.0639784,"\int \frac{(5-x) (3+2 x)^3}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^3)/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{12} \sqrt{3 x^2+5 x+2} (2 x+3)^3+\frac{32}{27} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{5}{648} (1078 x+3261) \sqrt{3 x^2+5 x+2}+\frac{19405 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1296 \sqrt{3}}","-\frac{1}{12} \sqrt{3 x^2+5 x+2} (2 x+3)^3+\frac{32}{27} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{5}{648} (1078 x+3261) \sqrt{3 x^2+5 x+2}+\frac{19405 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{1296 \sqrt{3}}",1,"(32*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2])/27 - ((3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2])/12 + (5*(3261 + 1078*x)*Sqrt[2 + 5*x + 3*x^2])/648 + (19405*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(1296*Sqrt[3])","A",5,4,27,0.1481,1,"{832, 779, 621, 206}"
2497,1,87,0,0.0452249,"\int \frac{(5-x) (3+2 x)^2}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^2)/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{1}{9} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{1}{54} (194 x+699) \sqrt{3 x^2+5 x+2}+\frac{1147 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{108 \sqrt{3}}","-\frac{1}{9} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{1}{54} (194 x+699) \sqrt{3 x^2+5 x+2}+\frac{1147 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{108 \sqrt{3}}",1,"-((3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2])/9 + ((699 + 194*x)*Sqrt[2 + 5*x + 3*x^2])/54 + (1147*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(108*Sqrt[3])","A",4,4,27,0.1481,1,"{832, 779, 621, 206}"
2498,1,62,0,0.0231248,"\int \frac{(5-x) (3+2 x)}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x))/Sqrt[2 + 5*x + 3*x^2],x]","\frac{1}{6} \sqrt{3 x^2+5 x+2} (19-2 x)+\frac{31 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{4 \sqrt{3}}","\frac{1}{6} \sqrt{3 x^2+5 x+2} (19-2 x)+\frac{31 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{4 \sqrt{3}}",1,"((19 - 2*x)*Sqrt[2 + 5*x + 3*x^2])/6 + (31*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(4*Sqrt[3])","A",3,3,25,0.1200,1,"{779, 621, 206}"
2499,1,57,0,0.0155406,"\int \frac{5-x}{\sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/Sqrt[2 + 5*x + 3*x^2],x]","\frac{35 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{6 \sqrt{3}}-\frac{1}{3} \sqrt{3 x^2+5 x+2}","\frac{35 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{6 \sqrt{3}}-\frac{1}{3} \sqrt{3 x^2+5 x+2}",1,"-Sqrt[2 + 5*x + 3*x^2]/3 + (35*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(6*Sqrt[3])","A",3,3,20,0.1500,1,"{640, 621, 206}"
2500,1,77,0,0.0460193,"\int \frac{5-x}{(3+2 x) \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{13 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2 \sqrt{5}}-\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{2 \sqrt{3}}","\frac{13 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2 \sqrt{5}}-\frac{\tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{2 \sqrt{3}}",1,"-ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])]/(2*Sqrt[3]) + (13*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(2*Sqrt[5])","A",5,4,27,0.1481,1,"{843, 621, 206, 724}"
2501,1,64,0,0.0414352,"\int \frac{5-x}{(3+2 x)^2 \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{47 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{10 \sqrt{5}}-\frac{13 \sqrt{3 x^2+5 x+2}}{5 (2 x+3)}","\frac{47 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{10 \sqrt{5}}-\frac{13 \sqrt{3 x^2+5 x+2}}{5 (2 x+3)}",1,"(-13*Sqrt[2 + 5*x + 3*x^2])/(5*(3 + 2*x)) + (47*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(10*Sqrt[5])","A",3,3,27,0.1111,1,"{806, 724, 206}"
2502,1,89,0,0.0608025,"\int \frac{5-x}{(3+2 x)^3 \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{73 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}-\frac{13 \sqrt{3 x^2+5 x+2}}{10 (2 x+3)^2}+\frac{389 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{100 \sqrt{5}}","-\frac{73 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}-\frac{13 \sqrt{3 x^2+5 x+2}}{10 (2 x+3)^2}+\frac{389 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{100 \sqrt{5}}",1,"(-13*Sqrt[2 + 5*x + 3*x^2])/(10*(3 + 2*x)^2) - (73*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)) + (389*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(100*Sqrt[5])","A",4,4,27,0.1481,1,"{834, 806, 724, 206}"
2503,1,114,0,0.07495,"\int \frac{5-x}{(3+2 x)^4 \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{72 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}-\frac{49 \sqrt{3 x^2+5 x+2}}{30 (2 x+3)^2}-\frac{13 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^3}+\frac{331 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{100 \sqrt{5}}","-\frac{72 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}-\frac{49 \sqrt{3 x^2+5 x+2}}{30 (2 x+3)^2}-\frac{13 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^3}+\frac{331 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{100 \sqrt{5}}",1,"(-13*Sqrt[2 + 5*x + 3*x^2])/(15*(3 + 2*x)^3) - (49*Sqrt[2 + 5*x + 3*x^2])/(30*(3 + 2*x)^2) - (72*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)) + (331*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(100*Sqrt[5])","A",5,4,27,0.1481,1,"{834, 806, 724, 206}"
2504,1,139,0,0.0972799,"\int \frac{5-x}{(3+2 x)^5 \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^5*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{681 \sqrt{3 x^2+5 x+2}}{250 (2 x+3)}-\frac{41 \sqrt{3 x^2+5 x+2}}{24 (2 x+3)^2}-\frac{86 \sqrt{3 x^2+5 x+2}}{75 (2 x+3)^3}-\frac{13 \sqrt{3 x^2+5 x+2}}{20 (2 x+3)^4}+\frac{5771 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2000 \sqrt{5}}","-\frac{681 \sqrt{3 x^2+5 x+2}}{250 (2 x+3)}-\frac{41 \sqrt{3 x^2+5 x+2}}{24 (2 x+3)^2}-\frac{86 \sqrt{3 x^2+5 x+2}}{75 (2 x+3)^3}-\frac{13 \sqrt{3 x^2+5 x+2}}{20 (2 x+3)^4}+\frac{5771 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2000 \sqrt{5}}",1,"(-13*Sqrt[2 + 5*x + 3*x^2])/(20*(3 + 2*x)^4) - (86*Sqrt[2 + 5*x + 3*x^2])/(75*(3 + 2*x)^3) - (41*Sqrt[2 + 5*x + 3*x^2])/(24*(3 + 2*x)^2) - (681*Sqrt[2 + 5*x + 3*x^2])/(250*(3 + 2*x)) + (5771*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(2000*Sqrt[5])","A",6,4,27,0.1481,1,"{834, 806, 724, 206}"
2505,1,164,0,0.1439139,"\int \frac{5-x}{(3+2 x)^6 \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^6*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{15891 \sqrt{3 x^2+5 x+2}}{6250 (2 x+3)}-\frac{1007 \sqrt{3 x^2+5 x+2}}{600 (2 x+3)^2}-\frac{2321 \sqrt{3 x^2+5 x+2}}{1875 (2 x+3)^3}-\frac{443 \sqrt{3 x^2+5 x+2}}{500 (2 x+3)^4}-\frac{13 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)^5}+\frac{128381 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{50000 \sqrt{5}}","-\frac{15891 \sqrt{3 x^2+5 x+2}}{6250 (2 x+3)}-\frac{1007 \sqrt{3 x^2+5 x+2}}{600 (2 x+3)^2}-\frac{2321 \sqrt{3 x^2+5 x+2}}{1875 (2 x+3)^3}-\frac{443 \sqrt{3 x^2+5 x+2}}{500 (2 x+3)^4}-\frac{13 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)^5}+\frac{128381 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{50000 \sqrt{5}}",1,"(-13*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)^5) - (443*Sqrt[2 + 5*x + 3*x^2])/(500*(3 + 2*x)^4) - (2321*Sqrt[2 + 5*x + 3*x^2])/(1875*(3 + 2*x)^3) - (1007*Sqrt[2 + 5*x + 3*x^2])/(600*(3 + 2*x)^2) - (15891*Sqrt[2 + 5*x + 3*x^2])/(6250*(3 + 2*x)) + (128381*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(50000*Sqrt[5])","A",7,4,27,0.1481,1,"{834, 806, 724, 206}"
2506,1,117,0,0.0742198,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (139 x+121) (2 x+3)^3}{3 \sqrt{3 x^2+5 x+2}}+\frac{1664}{27} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{10}{81} (1438 x+3369) \sqrt{3 x^2+5 x+2}+\frac{6265 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{81 \sqrt{3}}","-\frac{2 (139 x+121) (2 x+3)^3}{3 \sqrt{3 x^2+5 x+2}}+\frac{1664}{27} \sqrt{3 x^2+5 x+2} (2 x+3)^2+\frac{10}{81} (1438 x+3369) \sqrt{3 x^2+5 x+2}+\frac{6265 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{81 \sqrt{3}}",1,"(-2*(3 + 2*x)^3*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (1664*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2])/27 + (10*(3369 + 1438*x)*Sqrt[2 + 5*x + 3*x^2])/81 + (6265*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(81*Sqrt[3])","A",5,5,27,0.1852,1,"{818, 832, 779, 621, 206}"
2507,1,92,0,0.0522933,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (139 x+121) (2 x+3)^2}{3 \sqrt{3 x^2+5 x+2}}+\frac{2}{9} (554 x+1239) \sqrt{3 x^2+5 x+2}+\frac{247 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{9 \sqrt{3}}","-\frac{2 (139 x+121) (2 x+3)^2}{3 \sqrt{3 x^2+5 x+2}}+\frac{2}{9} (554 x+1239) \sqrt{3 x^2+5 x+2}+\frac{247 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{9 \sqrt{3}}",1,"(-2*(3 + 2*x)^2*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (2*(1239 + 554*x)*Sqrt[2 + 5*x + 3*x^2])/9 + (247*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(9*Sqrt[3])","A",4,4,27,0.1481,1,"{818, 779, 621, 206}"
2508,1,83,0,0.0388993,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (2 x+3) (139 x+121)}{3 \sqrt{3 x^2+5 x+2}}+\frac{184}{3} \sqrt{3 x^2+5 x+2}+2 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)","-\frac{2 (2 x+3) (139 x+121)}{3 \sqrt{3 x^2+5 x+2}}+\frac{184}{3} \sqrt{3 x^2+5 x+2}+2 \sqrt{3} \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)",1,"(-2*(3 + 2*x)*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (184*Sqrt[2 + 5*x + 3*x^2])/3 + 2*Sqrt[3]*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])]","A",4,4,27,0.1481,1,"{818, 640, 621, 206}"
2509,1,62,0,0.0236256,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (139 x+121)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{3 \sqrt{3}}","-\frac{2 (139 x+121)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{3 \sqrt{3}}",1,"(-2*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) - (2*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(3*Sqrt[3])","A",3,3,25,0.1200,1,"{777, 621, 206}"
2510,1,21,0,0.0049068,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (35 x+29)}{\sqrt{3 x^2+5 x+2}}","-\frac{2 (35 x+29)}{\sqrt{3 x^2+5 x+2}}",1,"(-2*(29 + 35*x))/Sqrt[2 + 5*x + 3*x^2]","A",1,1,20,0.05000,1,"{636}"
2511,1,62,0,0.0382234,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2)),x]","\frac{26 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{5 \sqrt{5}}-\frac{6 (47 x+37)}{5 \sqrt{3 x^2+5 x+2}}","\frac{26 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{5 \sqrt{5}}-\frac{6 (47 x+37)}{5 \sqrt{3 x^2+5 x+2}}",1,"(-6*(37 + 47*x))/(5*Sqrt[2 + 5*x + 3*x^2]) + (26*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(5*Sqrt[5])","A",4,4,27,0.1481,1,"{822, 12, 724, 206}"
2512,1,94,0,0.0531627,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 (2 x+3) \sqrt{3 x^2+5 x+2}}-\frac{856 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}+\frac{302 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}","-\frac{6 (47 x+37)}{5 (2 x+3) \sqrt{3 x^2+5 x+2}}-\frac{856 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}+\frac{302 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}",1,"(-6*(37 + 47*x))/(5*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2]) - (856*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)) + (302*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(25*Sqrt[5])","A",4,4,27,0.1481,1,"{822, 806, 724, 206}"
2513,1,119,0,0.074717,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 (2 x+3)^2 \sqrt{3 x^2+5 x+2}}-\frac{864 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}-\frac{166 \sqrt{3 x^2+5 x+2}}{5 (2 x+3)^2}+\frac{483 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}","-\frac{6 (47 x+37)}{5 (2 x+3)^2 \sqrt{3 x^2+5 x+2}}-\frac{864 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}-\frac{166 \sqrt{3 x^2+5 x+2}}{5 (2 x+3)^2}+\frac{483 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}",1,"(-6*(37 + 47*x))/(5*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2]) - (166*Sqrt[2 + 5*x + 3*x^2])/(5*(3 + 2*x)^2) - (864*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)) + (483*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(25*Sqrt[5])","A",5,5,27,0.1852,1,"{822, 834, 806, 724, 206}"
2514,1,144,0,0.1027388,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 (2 x+3)^3 \sqrt{3 x^2+5 x+2}}-\frac{4632 \sqrt{3 x^2+5 x+2}}{125 (2 x+3)}-\frac{478 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^2}-\frac{2464 \sqrt{3 x^2+5 x+2}}{75 (2 x+3)^3}+\frac{3289 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{125 \sqrt{5}}","-\frac{6 (47 x+37)}{5 (2 x+3)^3 \sqrt{3 x^2+5 x+2}}-\frac{4632 \sqrt{3 x^2+5 x+2}}{125 (2 x+3)}-\frac{478 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^2}-\frac{2464 \sqrt{3 x^2+5 x+2}}{75 (2 x+3)^3}+\frac{3289 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{125 \sqrt{5}}",1,"(-6*(37 + 47*x))/(5*(3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2]) - (2464*Sqrt[2 + 5*x + 3*x^2])/(75*(3 + 2*x)^3) - (478*Sqrt[2 + 5*x + 3*x^2])/(15*(3 + 2*x)^2) - (4632*Sqrt[2 + 5*x + 3*x^2])/(125*(3 + 2*x)) + (3289*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(125*Sqrt[5])","A",6,5,27,0.1852,1,"{822, 834, 806, 724, 206}"
2515,1,169,0,0.1173336,"\int \frac{5-x}{(3+2 x)^5 \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^5*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 (2 x+3)^4 \sqrt{3 x^2+5 x+2}}-\frac{25458 \sqrt{3 x^2+5 x+2}}{625 (2 x+3)}-\frac{973 \sqrt{3 x^2+5 x+2}}{30 (2 x+3)^2}-\frac{11596 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^3}-\frac{817 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)^4}+\frac{82039 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2500 \sqrt{5}}","-\frac{6 (47 x+37)}{5 (2 x+3)^4 \sqrt{3 x^2+5 x+2}}-\frac{25458 \sqrt{3 x^2+5 x+2}}{625 (2 x+3)}-\frac{973 \sqrt{3 x^2+5 x+2}}{30 (2 x+3)^2}-\frac{11596 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^3}-\frac{817 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)^4}+\frac{82039 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{2500 \sqrt{5}}",1,"(-6*(37 + 47*x))/(5*(3 + 2*x)^4*Sqrt[2 + 5*x + 3*x^2]) - (817*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)^4) - (11596*Sqrt[2 + 5*x + 3*x^2])/(375*(3 + 2*x)^3) - (973*Sqrt[2 + 5*x + 3*x^2])/(30*(3 + 2*x)^2) - (25458*Sqrt[2 + 5*x + 3*x^2])/(625*(3 + 2*x)) + (82039*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(2500*Sqrt[5])","A",7,5,27,0.1852,1,"{822, 834, 806, 724, 206}"
2516,1,115,0,0.0571135,"\int \frac{(5-x) (3+2 x)^4}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^4)/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 (139 x+121) (2 x+3)^3}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 (7976 x+6809) (2 x+3)}{27 \sqrt{3 x^2+5 x+2}}-\frac{6848}{9} \sqrt{3 x^2+5 x+2}+\frac{152 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{27 \sqrt{3}}","-\frac{2 (139 x+121) (2 x+3)^3}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 (7976 x+6809) (2 x+3)}{27 \sqrt{3 x^2+5 x+2}}-\frac{6848}{9} \sqrt{3 x^2+5 x+2}+\frac{152 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{27 \sqrt{3}}",1,"(-2*(3 + 2*x)^3*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (4*(3 + 2*x)*(6809 + 7976*x))/(27*Sqrt[2 + 5*x + 3*x^2]) - (6848*Sqrt[2 + 5*x + 3*x^2])/9 + (152*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(27*Sqrt[3])","A",5,4,27,0.1481,1,"{818, 640, 621, 206}"
2517,1,92,0,0.0420306,"\int \frac{(5-x) (3+2 x)^3}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^3)/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 (139 x+121) (2 x+3)^2}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 (2834 x+2481)}{9 \sqrt{3 x^2+5 x+2}}-\frac{8 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{9 \sqrt{3}}","-\frac{2 (139 x+121) (2 x+3)^2}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 (2834 x+2481)}{9 \sqrt{3 x^2+5 x+2}}-\frac{8 \tanh ^{-1}\left(\frac{6 x+5}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}\right)}{9 \sqrt{3}}",1,"(-2*(3 + 2*x)^2*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (4*(2481 + 2834*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (8*ArcTanh[(5 + 6*x)/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])])/(9*Sqrt[3])","A",4,4,27,0.1481,1,"{818, 777, 621, 206}"
2518,1,54,0,0.0216529,"\int \frac{(5-x) (3+2 x)^2}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^2)/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{376 (8 x+7)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 (2 x+3)^2 (35 x+29)}{3 \left(3 x^2+5 x+2\right)^{3/2}}","\frac{376 (8 x+7)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 (2 x+3)^2 (35 x+29)}{3 \left(3 x^2+5 x+2\right)^{3/2}}",1,"(-2*(3 + 2*x)^2*(29 + 35*x))/(3*(2 + 5*x + 3*x^2)^(3/2)) + (376*(7 + 8*x))/(3*Sqrt[2 + 5*x + 3*x^2])","A",2,2,27,0.07407,1,"{804, 636}"
2519,1,47,0,0.0156649,"\int \frac{(5-x) (3+2 x)}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x))/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{1124 (6 x+5)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 (139 x+121)}{9 \left(3 x^2+5 x+2\right)^{3/2}}","\frac{1124 (6 x+5)}{9 \sqrt{3 x^2+5 x+2}}-\frac{2 (139 x+121)}{9 \left(3 x^2+5 x+2\right)^{3/2}}",1,"(-2*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (1124*(5 + 6*x))/(9*Sqrt[2 + 5*x + 3*x^2])","A",2,2,25,0.08000,1,"{777, 613}"
2520,1,47,0,0.01041,"\int \frac{5-x}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/(2 + 5*x + 3*x^2)^(5/2),x]","\frac{280 (6 x+5)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 (35 x+29)}{3 \left(3 x^2+5 x+2\right)^{3/2}}","\frac{280 (6 x+5)}{3 \sqrt{3 x^2+5 x+2}}-\frac{2 (35 x+29)}{3 \left(3 x^2+5 x+2\right)^{3/2}}",1,"(-2*(29 + 35*x))/(3*(2 + 5*x + 3*x^2)^(3/2)) + (280*(5 + 6*x))/(3*Sqrt[2 + 5*x + 3*x^2])","A",2,2,20,0.1000,1,"{638, 613}"
2521,1,85,0,0.0545099,"\int \frac{5-x}{(3+2 x) \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{12 (836 x+701)}{25 \sqrt{3 x^2+5 x+2}}+\frac{104 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}","-\frac{2 (47 x+37)}{5 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{12 (836 x+701)}{25 \sqrt{3 x^2+5 x+2}}+\frac{104 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}",1,"(-2*(37 + 47*x))/(5*(2 + 5*x + 3*x^2)^(3/2)) + (12*(701 + 836*x))/(25*Sqrt[2 + 5*x + 3*x^2]) + (104*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(25*Sqrt[5])","A",5,4,27,0.1481,1,"{822, 12, 724, 206}"
2522,1,124,0,0.0726515,"\int \frac{5-x}{(3+2 x)^2 \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^2*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 (2 x+3) \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4416 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}+\frac{4 (462 x+401)}{5 (2 x+3) \sqrt{3 x^2+5 x+2}}+\frac{408 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}","-\frac{2 (47 x+37)}{5 (2 x+3) \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4416 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)}+\frac{4 (462 x+401)}{5 (2 x+3) \sqrt{3 x^2+5 x+2}}+\frac{408 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{25 \sqrt{5}}",1,"(-2*(37 + 47*x))/(5*(3 + 2*x)*(2 + 5*x + 3*x^2)^(3/2)) + (4*(401 + 462*x))/(5*(3 + 2*x)*Sqrt[2 + 5*x + 3*x^2]) + (4416*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)) + (408*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(25*Sqrt[5])","A",5,4,27,0.1481,1,"{822, 806, 724, 206}"
2523,1,147,0,0.094746,"\int \frac{5-x}{(3+2 x)^3 \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^3*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 (2 x+3)^2 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{11808 \sqrt{3 x^2+5 x+2}}{125 (2 x+3)}+\frac{152 \sqrt{3 x^2+5 x+2}}{(2 x+3)^2}+\frac{4 (2112 x+1907)}{25 (2 x+3)^2 \sqrt{3 x^2+5 x+2}}+\frac{4884 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{125 \sqrt{5}}","-\frac{2 (47 x+37)}{5 (2 x+3)^2 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{11808 \sqrt{3 x^2+5 x+2}}{125 (2 x+3)}+\frac{152 \sqrt{3 x^2+5 x+2}}{(2 x+3)^2}+\frac{4 (2112 x+1907)}{25 (2 x+3)^2 \sqrt{3 x^2+5 x+2}}+\frac{4884 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{125 \sqrt{5}}",1,"(-2*(37 + 47*x))/(5*(3 + 2*x)^2*(2 + 5*x + 3*x^2)^(3/2)) + (4*(1907 + 2112*x))/(25*(3 + 2*x)^2*Sqrt[2 + 5*x + 3*x^2]) + (152*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^2 + (11808*Sqrt[2 + 5*x + 3*x^2])/(125*(3 + 2*x)) + (4884*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(125*Sqrt[5])","A",6,5,27,0.1852,1,"{822, 834, 806, 724, 206}"
2524,1,174,0,0.1158792,"\int \frac{5-x}{(3+2 x)^4 \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^4*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 (2 x+3)^3 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{9696 \sqrt{3 x^2+5 x+2}}{625 (2 x+3)}+\frac{1048 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^2}+\frac{47552 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^3}+\frac{12 (638 x+603)}{25 (2 x+3)^3 \sqrt{3 x^2+5 x+2}}+\frac{46108 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{625 \sqrt{5}}","-\frac{2 (47 x+37)}{5 (2 x+3)^3 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{9696 \sqrt{3 x^2+5 x+2}}{625 (2 x+3)}+\frac{1048 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^2}+\frac{47552 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^3}+\frac{12 (638 x+603)}{25 (2 x+3)^3 \sqrt{3 x^2+5 x+2}}+\frac{46108 \tanh ^{-1}\left(\frac{8 x+7}{2 \sqrt{5} \sqrt{3 x^2+5 x+2}}\right)}{625 \sqrt{5}}",1,"(-2*(37 + 47*x))/(5*(3 + 2*x)^3*(2 + 5*x + 3*x^2)^(3/2)) + (12*(603 + 638*x))/(25*(3 + 2*x)^3*Sqrt[2 + 5*x + 3*x^2]) + (47552*Sqrt[2 + 5*x + 3*x^2])/(375*(3 + 2*x)^3) + (1048*Sqrt[2 + 5*x + 3*x^2])/(15*(3 + 2*x)^2) + (9696*Sqrt[2 + 5*x + 3*x^2])/(625*(3 + 2*x)) + (46108*ArcTanh[(7 + 8*x)/(2*Sqrt[5]*Sqrt[2 + 5*x + 3*x^2])])/(625*Sqrt[5])","A",7,5,27,0.1852,1,"{822, 834, 806, 724, 206}"
2525,1,35,0,0.0303598,"\int \frac{-1+x}{(1+x) \sqrt{1+x+x^2}} \, dx","Int[(-1 + x)/((1 + x)*Sqrt[1 + x + x^2]),x]","2 \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)+\sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)","2 \tanh ^{-1}\left(\frac{1-x}{2 \sqrt{x^2+x+1}}\right)+\sinh ^{-1}\left(\frac{2 x+1}{\sqrt{3}}\right)",1,"ArcSinh[(1 + 2*x)/Sqrt[3]] + 2*ArcTanh[(1 - x)/(2*Sqrt[1 + x + x^2])]","A",5,5,19,0.2632,1,"{843, 619, 215, 724, 206}"
2526,1,53,0,0.015605,"\int (5-x) (3+2 x)^{7/2} \left(2+5 x+3 x^2\right) \, dx","Int[(5 - x)*(3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2),x]","-\frac{1}{40} (2 x+3)^{15/2}+\frac{47}{104} (2 x+3)^{13/2}-\frac{109}{88} (2 x+3)^{11/2}+\frac{65}{72} (2 x+3)^{9/2}","-\frac{1}{40} (2 x+3)^{15/2}+\frac{47}{104} (2 x+3)^{13/2}-\frac{109}{88} (2 x+3)^{11/2}+\frac{65}{72} (2 x+3)^{9/2}",1,"(65*(3 + 2*x)^(9/2))/72 - (109*(3 + 2*x)^(11/2))/88 + (47*(3 + 2*x)^(13/2))/104 - (3 + 2*x)^(15/2)/40","A",2,1,25,0.04000,1,"{771}"
2527,1,53,0,0.0155132,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right) \, dx","Int[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2),x]","-\frac{3}{104} (2 x+3)^{13/2}+\frac{47}{88} (2 x+3)^{11/2}-\frac{109}{72} (2 x+3)^{9/2}+\frac{65}{56} (2 x+3)^{7/2}","-\frac{3}{104} (2 x+3)^{13/2}+\frac{47}{88} (2 x+3)^{11/2}-\frac{109}{72} (2 x+3)^{9/2}+\frac{65}{56} (2 x+3)^{7/2}",1,"(65*(3 + 2*x)^(7/2))/56 - (109*(3 + 2*x)^(9/2))/72 + (47*(3 + 2*x)^(11/2))/88 - (3*(3 + 2*x)^(13/2))/104","A",2,1,25,0.04000,1,"{771}"
2528,1,53,0,0.0197465,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right) \, dx","Int[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2),x]","-\frac{3}{88} (2 x+3)^{11/2}+\frac{47}{72} (2 x+3)^{9/2}-\frac{109}{56} (2 x+3)^{7/2}+\frac{13}{8} (2 x+3)^{5/2}","-\frac{3}{88} (2 x+3)^{11/2}+\frac{47}{72} (2 x+3)^{9/2}-\frac{109}{56} (2 x+3)^{7/2}+\frac{13}{8} (2 x+3)^{5/2}",1,"(13*(3 + 2*x)^(5/2))/8 - (109*(3 + 2*x)^(7/2))/56 + (47*(3 + 2*x)^(9/2))/72 - (3*(3 + 2*x)^(11/2))/88","A",2,1,25,0.04000,1,"{771}"
2529,1,53,0,0.015023,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right) \, dx","Int[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2),x]","-\frac{1}{24} (2 x+3)^{9/2}+\frac{47}{56} (2 x+3)^{7/2}-\frac{109}{40} (2 x+3)^{5/2}+\frac{65}{24} (2 x+3)^{3/2}","-\frac{1}{24} (2 x+3)^{9/2}+\frac{47}{56} (2 x+3)^{7/2}-\frac{109}{40} (2 x+3)^{5/2}+\frac{65}{24} (2 x+3)^{3/2}",1,"(65*(3 + 2*x)^(3/2))/24 - (109*(3 + 2*x)^(5/2))/40 + (47*(3 + 2*x)^(7/2))/56 - (3 + 2*x)^(9/2)/24","A",2,1,25,0.04000,1,"{771}"
2530,1,53,0,0.0161647,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{\sqrt{3+2 x}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2))/Sqrt[3 + 2*x],x]","-\frac{3}{56} (2 x+3)^{7/2}+\frac{47}{40} (2 x+3)^{5/2}-\frac{109}{24} (2 x+3)^{3/2}+\frac{65}{8} \sqrt{2 x+3}","-\frac{3}{56} (2 x+3)^{7/2}+\frac{47}{40} (2 x+3)^{5/2}-\frac{109}{24} (2 x+3)^{3/2}+\frac{65}{8} \sqrt{2 x+3}",1,"(65*Sqrt[3 + 2*x])/8 - (109*(3 + 2*x)^(3/2))/24 + (47*(3 + 2*x)^(5/2))/40 - (3*(3 + 2*x)^(7/2))/56","A",2,1,25,0.04000,1,"{771}"
2531,1,53,0,0.015937,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{(3+2 x)^{3/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2))/(3 + 2*x)^(3/2),x]","-\frac{3}{40} (2 x+3)^{5/2}+\frac{47}{24} (2 x+3)^{3/2}-\frac{109}{8} \sqrt{2 x+3}-\frac{65}{8 \sqrt{2 x+3}}","-\frac{3}{40} (2 x+3)^{5/2}+\frac{47}{24} (2 x+3)^{3/2}-\frac{109}{8} \sqrt{2 x+3}-\frac{65}{8 \sqrt{2 x+3}}",1,"-65/(8*Sqrt[3 + 2*x]) - (109*Sqrt[3 + 2*x])/8 + (47*(3 + 2*x)^(3/2))/24 - (3*(3 + 2*x)^(5/2))/40","A",2,1,25,0.04000,1,"{771}"
2532,1,53,0,0.0162295,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{(3+2 x)^{5/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2))/(3 + 2*x)^(5/2),x]","-\frac{1}{8} (2 x+3)^{3/2}+\frac{47}{8} \sqrt{2 x+3}+\frac{109}{8 \sqrt{2 x+3}}-\frac{65}{24 (2 x+3)^{3/2}}","-\frac{1}{8} (2 x+3)^{3/2}+\frac{47}{8} \sqrt{2 x+3}+\frac{109}{8 \sqrt{2 x+3}}-\frac{65}{24 (2 x+3)^{3/2}}",1,"-65/(24*(3 + 2*x)^(3/2)) + 109/(8*Sqrt[3 + 2*x]) + (47*Sqrt[3 + 2*x])/8 - (3 + 2*x)^(3/2)/8","A",2,1,25,0.04000,1,"{771}"
2533,1,53,0,0.0152661,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)}{(3+2 x)^{7/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2))/(3 + 2*x)^(7/2),x]","-\frac{3}{8} \sqrt{2 x+3}-\frac{47}{8 \sqrt{2 x+3}}+\frac{109}{24 (2 x+3)^{3/2}}-\frac{13}{8 (2 x+3)^{5/2}}","-\frac{3}{8} \sqrt{2 x+3}-\frac{47}{8 \sqrt{2 x+3}}+\frac{109}{24 (2 x+3)^{3/2}}-\frac{13}{8 (2 x+3)^{5/2}}",1,"-13/(8*(3 + 2*x)^(5/2)) + 109/(24*(3 + 2*x)^(3/2)) - 47/(8*Sqrt[3 + 2*x]) - (3*Sqrt[3 + 2*x])/8","A",2,1,25,0.04000,1,"{771}"
2534,1,79,0,0.0238475,"\int (5-x) (3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^2 \, dx","Int[(5 - x)*(3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^2,x]","-\frac{9}{608} (2 x+3)^{19/2}+\frac{165}{544} (2 x+3)^{17/2}-\frac{359}{240} (2 x+3)^{15/2}+\frac{651}{208} (2 x+3)^{13/2}-\frac{1065}{352} (2 x+3)^{11/2}+\frac{325}{288} (2 x+3)^{9/2}","-\frac{9}{608} (2 x+3)^{19/2}+\frac{165}{544} (2 x+3)^{17/2}-\frac{359}{240} (2 x+3)^{15/2}+\frac{651}{208} (2 x+3)^{13/2}-\frac{1065}{352} (2 x+3)^{11/2}+\frac{325}{288} (2 x+3)^{9/2}",1,"(325*(3 + 2*x)^(9/2))/288 - (1065*(3 + 2*x)^(11/2))/352 + (651*(3 + 2*x)^(13/2))/208 - (359*(3 + 2*x)^(15/2))/240 + (165*(3 + 2*x)^(17/2))/544 - (9*(3 + 2*x)^(19/2))/608","A",2,1,27,0.03704,1,"{771}"
2535,1,79,0,0.0232201,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^2 \, dx","Int[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2,x]","-\frac{9}{544} (2 x+3)^{17/2}+\frac{11}{32} (2 x+3)^{15/2}-\frac{359}{208} (2 x+3)^{13/2}+\frac{651}{176} (2 x+3)^{11/2}-\frac{355}{96} (2 x+3)^{9/2}+\frac{325}{224} (2 x+3)^{7/2}","-\frac{9}{544} (2 x+3)^{17/2}+\frac{11}{32} (2 x+3)^{15/2}-\frac{359}{208} (2 x+3)^{13/2}+\frac{651}{176} (2 x+3)^{11/2}-\frac{355}{96} (2 x+3)^{9/2}+\frac{325}{224} (2 x+3)^{7/2}",1,"(325*(3 + 2*x)^(7/2))/224 - (355*(3 + 2*x)^(9/2))/96 + (651*(3 + 2*x)^(11/2))/176 - (359*(3 + 2*x)^(13/2))/208 + (11*(3 + 2*x)^(15/2))/32 - (9*(3 + 2*x)^(17/2))/544","A",2,1,27,0.03704,1,"{771}"
2536,1,79,0,0.023153,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^2 \, dx","Int[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^2,x]","-\frac{3}{160} (2 x+3)^{15/2}+\frac{165}{416} (2 x+3)^{13/2}-\frac{359}{176} (2 x+3)^{11/2}+\frac{217}{48} (2 x+3)^{9/2}-\frac{1065}{224} (2 x+3)^{7/2}+\frac{65}{32} (2 x+3)^{5/2}","-\frac{3}{160} (2 x+3)^{15/2}+\frac{165}{416} (2 x+3)^{13/2}-\frac{359}{176} (2 x+3)^{11/2}+\frac{217}{48} (2 x+3)^{9/2}-\frac{1065}{224} (2 x+3)^{7/2}+\frac{65}{32} (2 x+3)^{5/2}",1,"(65*(3 + 2*x)^(5/2))/32 - (1065*(3 + 2*x)^(7/2))/224 + (217*(3 + 2*x)^(9/2))/48 - (359*(3 + 2*x)^(11/2))/176 + (165*(3 + 2*x)^(13/2))/416 - (3*(3 + 2*x)^(15/2))/160","A",2,1,27,0.03704,1,"{771}"
2537,1,79,0,0.0225127,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^2 \, dx","Int[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^2,x]","-\frac{9}{416} (2 x+3)^{13/2}+\frac{15}{32} (2 x+3)^{11/2}-\frac{359}{144} (2 x+3)^{9/2}+\frac{93}{16} (2 x+3)^{7/2}-\frac{213}{32} (2 x+3)^{5/2}+\frac{325}{96} (2 x+3)^{3/2}","-\frac{9}{416} (2 x+3)^{13/2}+\frac{15}{32} (2 x+3)^{11/2}-\frac{359}{144} (2 x+3)^{9/2}+\frac{93}{16} (2 x+3)^{7/2}-\frac{213}{32} (2 x+3)^{5/2}+\frac{325}{96} (2 x+3)^{3/2}",1,"(325*(3 + 2*x)^(3/2))/96 - (213*(3 + 2*x)^(5/2))/32 + (93*(3 + 2*x)^(7/2))/16 - (359*(3 + 2*x)^(9/2))/144 + (15*(3 + 2*x)^(11/2))/32 - (9*(3 + 2*x)^(13/2))/416","A",2,1,27,0.03704,1,"{771}"
2538,1,79,0,0.0234889,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{\sqrt{3+2 x}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^2)/Sqrt[3 + 2*x],x]","-\frac{9}{352} (2 x+3)^{11/2}+\frac{55}{96} (2 x+3)^{9/2}-\frac{359}{112} (2 x+3)^{7/2}+\frac{651}{80} (2 x+3)^{5/2}-\frac{355}{32} (2 x+3)^{3/2}+\frac{325}{32} \sqrt{2 x+3}","-\frac{9}{352} (2 x+3)^{11/2}+\frac{55}{96} (2 x+3)^{9/2}-\frac{359}{112} (2 x+3)^{7/2}+\frac{651}{80} (2 x+3)^{5/2}-\frac{355}{32} (2 x+3)^{3/2}+\frac{325}{32} \sqrt{2 x+3}",1,"(325*Sqrt[3 + 2*x])/32 - (355*(3 + 2*x)^(3/2))/32 + (651*(3 + 2*x)^(5/2))/80 - (359*(3 + 2*x)^(7/2))/112 + (55*(3 + 2*x)^(9/2))/96 - (9*(3 + 2*x)^(11/2))/352","A",2,1,27,0.03704,1,"{771}"
2539,1,79,0,0.0328533,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{(3+2 x)^{3/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^2)/(3 + 2*x)^(3/2),x]","-\frac{1}{32} (2 x+3)^{9/2}+\frac{165}{224} (2 x+3)^{7/2}-\frac{359}{80} (2 x+3)^{5/2}+\frac{217}{16} (2 x+3)^{3/2}-\frac{1065}{32} \sqrt{2 x+3}-\frac{325}{32 \sqrt{2 x+3}}","-\frac{1}{32} (2 x+3)^{9/2}+\frac{165}{224} (2 x+3)^{7/2}-\frac{359}{80} (2 x+3)^{5/2}+\frac{217}{16} (2 x+3)^{3/2}-\frac{1065}{32} \sqrt{2 x+3}-\frac{325}{32 \sqrt{2 x+3}}",1,"-325/(32*Sqrt[3 + 2*x]) - (1065*Sqrt[3 + 2*x])/32 + (217*(3 + 2*x)^(3/2))/16 - (359*(3 + 2*x)^(5/2))/80 + (165*(3 + 2*x)^(7/2))/224 - (3 + 2*x)^(9/2)/32","A",2,1,27,0.03704,1,"{771}"
2540,1,79,0,0.026224,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{(3+2 x)^{5/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^2)/(3 + 2*x)^(5/2),x]","-\frac{9}{224} (2 x+3)^{7/2}+\frac{33}{32} (2 x+3)^{5/2}-\frac{359}{48} (2 x+3)^{3/2}+\frac{651}{16} \sqrt{2 x+3}+\frac{1065}{32 \sqrt{2 x+3}}-\frac{325}{96 (2 x+3)^{3/2}}","-\frac{9}{224} (2 x+3)^{7/2}+\frac{33}{32} (2 x+3)^{5/2}-\frac{359}{48} (2 x+3)^{3/2}+\frac{651}{16} \sqrt{2 x+3}+\frac{1065}{32 \sqrt{2 x+3}}-\frac{325}{96 (2 x+3)^{3/2}}",1,"-325/(96*(3 + 2*x)^(3/2)) + 1065/(32*Sqrt[3 + 2*x]) + (651*Sqrt[3 + 2*x])/16 - (359*(3 + 2*x)^(3/2))/48 + (33*(3 + 2*x)^(5/2))/32 - (9*(3 + 2*x)^(7/2))/224","A",2,1,27,0.03704,1,"{771}"
2541,1,79,0,0.0236495,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^2}{(3+2 x)^{7/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^2)/(3 + 2*x)^(7/2),x]","-\frac{9}{160} (2 x+3)^{5/2}+\frac{55}{32} (2 x+3)^{3/2}-\frac{359}{16} \sqrt{2 x+3}-\frac{651}{16 \sqrt{2 x+3}}+\frac{355}{32 (2 x+3)^{3/2}}-\frac{65}{32 (2 x+3)^{5/2}}","-\frac{9}{160} (2 x+3)^{5/2}+\frac{55}{32} (2 x+3)^{3/2}-\frac{359}{16} \sqrt{2 x+3}-\frac{651}{16 \sqrt{2 x+3}}+\frac{355}{32 (2 x+3)^{3/2}}-\frac{65}{32 (2 x+3)^{5/2}}",1,"-65/(32*(3 + 2*x)^(5/2)) + 355/(32*(3 + 2*x)^(3/2)) - 651/(16*Sqrt[3 + 2*x]) - (359*Sqrt[3 + 2*x])/16 + (55*(3 + 2*x)^(3/2))/32 - (9*(3 + 2*x)^(5/2))/160","A",2,1,27,0.03704,1,"{771}"
2542,1,105,0,0.0352645,"\int (5-x) (3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^3 \, dx","Int[(5 - x)*(3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^3,x]","-\frac{27 (2 x+3)^{23/2}}{2944}+\frac{27}{128} (2 x+3)^{21/2}-\frac{3519 (2 x+3)^{19/2}}{2432}+\frac{10475 (2 x+3)^{17/2}}{2176}-\frac{17201 (2 x+3)^{15/2}}{1920}+\frac{16005 (2 x+3)^{13/2}}{1664}-\frac{7925 (2 x+3)^{11/2}}{1408}+\frac{1625 (2 x+3)^{9/2}}{1152}","-\frac{27 (2 x+3)^{23/2}}{2944}+\frac{27}{128} (2 x+3)^{21/2}-\frac{3519 (2 x+3)^{19/2}}{2432}+\frac{10475 (2 x+3)^{17/2}}{2176}-\frac{17201 (2 x+3)^{15/2}}{1920}+\frac{16005 (2 x+3)^{13/2}}{1664}-\frac{7925 (2 x+3)^{11/2}}{1408}+\frac{1625 (2 x+3)^{9/2}}{1152}",1,"(1625*(3 + 2*x)^(9/2))/1152 - (7925*(3 + 2*x)^(11/2))/1408 + (16005*(3 + 2*x)^(13/2))/1664 - (17201*(3 + 2*x)^(15/2))/1920 + (10475*(3 + 2*x)^(17/2))/2176 - (3519*(3 + 2*x)^(19/2))/2432 + (27*(3 + 2*x)^(21/2))/128 - (27*(3 + 2*x)^(23/2))/2944","A",2,1,27,0.03704,1,"{771}"
2543,1,105,0,0.0376753,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^3 \, dx","Int[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^3,x]","-\frac{9}{896} (2 x+3)^{21/2}+\frac{567 (2 x+3)^{19/2}}{2432}-\frac{207}{128} (2 x+3)^{17/2}+\frac{2095}{384} (2 x+3)^{15/2}-\frac{17201 (2 x+3)^{13/2}}{1664}+\frac{1455}{128} (2 x+3)^{11/2}-\frac{7925 (2 x+3)^{9/2}}{1152}+\frac{1625}{896} (2 x+3)^{7/2}","-\frac{9}{896} (2 x+3)^{21/2}+\frac{567 (2 x+3)^{19/2}}{2432}-\frac{207}{128} (2 x+3)^{17/2}+\frac{2095}{384} (2 x+3)^{15/2}-\frac{17201 (2 x+3)^{13/2}}{1664}+\frac{1455}{128} (2 x+3)^{11/2}-\frac{7925 (2 x+3)^{9/2}}{1152}+\frac{1625}{896} (2 x+3)^{7/2}",1,"(1625*(3 + 2*x)^(7/2))/896 - (7925*(3 + 2*x)^(9/2))/1152 + (1455*(3 + 2*x)^(11/2))/128 - (17201*(3 + 2*x)^(13/2))/1664 + (2095*(3 + 2*x)^(15/2))/384 - (207*(3 + 2*x)^(17/2))/128 + (567*(3 + 2*x)^(19/2))/2432 - (9*(3 + 2*x)^(21/2))/896","A",2,1,27,0.03704,1,"{771}"
2544,1,105,0,0.0325764,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^3 \, dx","Int[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^3,x]","-\frac{27 (2 x+3)^{19/2}}{2432}+\frac{567 (2 x+3)^{17/2}}{2176}-\frac{1173}{640} (2 x+3)^{15/2}+\frac{10475 (2 x+3)^{13/2}}{1664}-\frac{17201 (2 x+3)^{11/2}}{1408}+\frac{5335}{384} (2 x+3)^{9/2}-\frac{7925}{896} (2 x+3)^{7/2}+\frac{325}{128} (2 x+3)^{5/2}","-\frac{27 (2 x+3)^{19/2}}{2432}+\frac{567 (2 x+3)^{17/2}}{2176}-\frac{1173}{640} (2 x+3)^{15/2}+\frac{10475 (2 x+3)^{13/2}}{1664}-\frac{17201 (2 x+3)^{11/2}}{1408}+\frac{5335}{384} (2 x+3)^{9/2}-\frac{7925}{896} (2 x+3)^{7/2}+\frac{325}{128} (2 x+3)^{5/2}",1,"(325*(3 + 2*x)^(5/2))/128 - (7925*(3 + 2*x)^(7/2))/896 + (5335*(3 + 2*x)^(9/2))/384 - (17201*(3 + 2*x)^(11/2))/1408 + (10475*(3 + 2*x)^(13/2))/1664 - (1173*(3 + 2*x)^(15/2))/640 + (567*(3 + 2*x)^(17/2))/2176 - (27*(3 + 2*x)^(19/2))/2432","A",2,1,27,0.03704,1,"{771}"
2545,1,105,0,0.0341499,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^3 \, dx","Int[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^3,x]","-\frac{27 (2 x+3)^{17/2}}{2176}+\frac{189}{640} (2 x+3)^{15/2}-\frac{3519 (2 x+3)^{13/2}}{1664}+\frac{10475 (2 x+3)^{11/2}}{1408}-\frac{17201 (2 x+3)^{9/2}}{1152}+\frac{16005}{896} (2 x+3)^{7/2}-\frac{1585}{128} (2 x+3)^{5/2}+\frac{1625}{384} (2 x+3)^{3/2}","-\frac{27 (2 x+3)^{17/2}}{2176}+\frac{189}{640} (2 x+3)^{15/2}-\frac{3519 (2 x+3)^{13/2}}{1664}+\frac{10475 (2 x+3)^{11/2}}{1408}-\frac{17201 (2 x+3)^{9/2}}{1152}+\frac{16005}{896} (2 x+3)^{7/2}-\frac{1585}{128} (2 x+3)^{5/2}+\frac{1625}{384} (2 x+3)^{3/2}",1,"(1625*(3 + 2*x)^(3/2))/384 - (1585*(3 + 2*x)^(5/2))/128 + (16005*(3 + 2*x)^(7/2))/896 - (17201*(3 + 2*x)^(9/2))/1152 + (10475*(3 + 2*x)^(11/2))/1408 - (3519*(3 + 2*x)^(13/2))/1664 + (189*(3 + 2*x)^(15/2))/640 - (27*(3 + 2*x)^(17/2))/2176","A",2,1,27,0.03704,1,"{771}"
2546,1,105,0,0.0298382,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{\sqrt{3+2 x}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^3)/Sqrt[3 + 2*x],x]","-\frac{9}{640} (2 x+3)^{15/2}+\frac{567 (2 x+3)^{13/2}}{1664}-\frac{3519 (2 x+3)^{11/2}}{1408}+\frac{10475 (2 x+3)^{9/2}}{1152}-\frac{17201}{896} (2 x+3)^{7/2}+\frac{3201}{128} (2 x+3)^{5/2}-\frac{7925}{384} (2 x+3)^{3/2}+\frac{1625}{128} \sqrt{2 x+3}","-\frac{9}{640} (2 x+3)^{15/2}+\frac{567 (2 x+3)^{13/2}}{1664}-\frac{3519 (2 x+3)^{11/2}}{1408}+\frac{10475 (2 x+3)^{9/2}}{1152}-\frac{17201}{896} (2 x+3)^{7/2}+\frac{3201}{128} (2 x+3)^{5/2}-\frac{7925}{384} (2 x+3)^{3/2}+\frac{1625}{128} \sqrt{2 x+3}",1,"(1625*Sqrt[3 + 2*x])/128 - (7925*(3 + 2*x)^(3/2))/384 + (3201*(3 + 2*x)^(5/2))/128 - (17201*(3 + 2*x)^(7/2))/896 + (10475*(3 + 2*x)^(9/2))/1152 - (3519*(3 + 2*x)^(11/2))/1408 + (567*(3 + 2*x)^(13/2))/1664 - (9*(3 + 2*x)^(15/2))/640","A",2,1,27,0.03704,1,"{771}"
2547,1,105,0,0.0311547,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{(3+2 x)^{3/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(3/2),x]","-\frac{27 (2 x+3)^{13/2}}{1664}+\frac{567 (2 x+3)^{11/2}}{1408}-\frac{391}{128} (2 x+3)^{9/2}+\frac{10475}{896} (2 x+3)^{7/2}-\frac{17201}{640} (2 x+3)^{5/2}+\frac{5335}{128} (2 x+3)^{3/2}-\frac{7925}{128} \sqrt{2 x+3}-\frac{1625}{128 \sqrt{2 x+3}}","-\frac{27 (2 x+3)^{13/2}}{1664}+\frac{567 (2 x+3)^{11/2}}{1408}-\frac{391}{128} (2 x+3)^{9/2}+\frac{10475}{896} (2 x+3)^{7/2}-\frac{17201}{640} (2 x+3)^{5/2}+\frac{5335}{128} (2 x+3)^{3/2}-\frac{7925}{128} \sqrt{2 x+3}-\frac{1625}{128 \sqrt{2 x+3}}",1,"-1625/(128*Sqrt[3 + 2*x]) - (7925*Sqrt[3 + 2*x])/128 + (5335*(3 + 2*x)^(3/2))/128 - (17201*(3 + 2*x)^(5/2))/640 + (10475*(3 + 2*x)^(7/2))/896 - (391*(3 + 2*x)^(9/2))/128 + (567*(3 + 2*x)^(11/2))/1408 - (27*(3 + 2*x)^(13/2))/1664","A",2,1,27,0.03704,1,"{771}"
2548,1,105,0,0.0303977,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{(3+2 x)^{5/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(5/2),x]","-\frac{27 (2 x+3)^{11/2}}{1408}+\frac{63}{128} (2 x+3)^{9/2}-\frac{3519}{896} (2 x+3)^{7/2}+\frac{2095}{128} (2 x+3)^{5/2}-\frac{17201}{384} (2 x+3)^{3/2}+\frac{16005}{128} \sqrt{2 x+3}+\frac{7925}{128 \sqrt{2 x+3}}-\frac{1625}{384 (2 x+3)^{3/2}}","-\frac{27 (2 x+3)^{11/2}}{1408}+\frac{63}{128} (2 x+3)^{9/2}-\frac{3519}{896} (2 x+3)^{7/2}+\frac{2095}{128} (2 x+3)^{5/2}-\frac{17201}{384} (2 x+3)^{3/2}+\frac{16005}{128} \sqrt{2 x+3}+\frac{7925}{128 \sqrt{2 x+3}}-\frac{1625}{384 (2 x+3)^{3/2}}",1,"-1625/(384*(3 + 2*x)^(3/2)) + 7925/(128*Sqrt[3 + 2*x]) + (16005*Sqrt[3 + 2*x])/128 - (17201*(3 + 2*x)^(3/2))/384 + (2095*(3 + 2*x)^(5/2))/128 - (3519*(3 + 2*x)^(7/2))/896 + (63*(3 + 2*x)^(9/2))/128 - (27*(3 + 2*x)^(11/2))/1408","A",2,1,27,0.03704,1,"{771}"
2549,1,105,0,0.0282774,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^3}{(3+2 x)^{7/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^3)/(3 + 2*x)^(7/2),x]","-\frac{3}{128} (2 x+3)^{9/2}+\frac{81}{128} (2 x+3)^{7/2}-\frac{3519}{640} (2 x+3)^{5/2}+\frac{10475}{384} (2 x+3)^{3/2}-\frac{17201}{128} \sqrt{2 x+3}-\frac{16005}{128 \sqrt{2 x+3}}+\frac{7925}{384 (2 x+3)^{3/2}}-\frac{325}{128 (2 x+3)^{5/2}}","-\frac{3}{128} (2 x+3)^{9/2}+\frac{81}{128} (2 x+3)^{7/2}-\frac{3519}{640} (2 x+3)^{5/2}+\frac{10475}{384} (2 x+3)^{3/2}-\frac{17201}{128} \sqrt{2 x+3}-\frac{16005}{128 \sqrt{2 x+3}}+\frac{7925}{384 (2 x+3)^{3/2}}-\frac{325}{128 (2 x+3)^{5/2}}",1,"-325/(128*(3 + 2*x)^(5/2)) + 7925/(384*(3 + 2*x)^(3/2)) - 16005/(128*Sqrt[3 + 2*x]) - (17201*Sqrt[3 + 2*x])/128 + (10475*(3 + 2*x)^(3/2))/384 - (3519*(3 + 2*x)^(5/2))/640 + (81*(3 + 2*x)^(7/2))/128 - (3*(3 + 2*x)^(9/2))/128","A",2,1,27,0.03704,1,"{771}"
2550,1,94,0,0.0988257,"\int \frac{(5-x) (3+2 x)^{7/2}}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2),x]","-\frac{2}{21} (2 x+3)^{7/2}+\frac{62}{45} (2 x+3)^{5/2}+\frac{526}{81} (2 x+3)^{3/2}+\frac{3278}{81} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{4250}{81} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{2}{21} (2 x+3)^{7/2}+\frac{62}{45} (2 x+3)^{5/2}+\frac{526}{81} (2 x+3)^{3/2}+\frac{3278}{81} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{4250}{81} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(3278*Sqrt[3 + 2*x])/81 + (526*(3 + 2*x)^(3/2))/81 + (62*(3 + 2*x)^(5/2))/45 - (2*(3 + 2*x)^(7/2))/21 + 12*ArcTanh[Sqrt[3 + 2*x]] - (4250*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/81","A",8,4,27,0.1481,1,"{824, 826, 1166, 207}"
2551,1,81,0,0.0789454,"\int \frac{(5-x) (3+2 x)^{5/2}}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2),x]","-\frac{2}{15} (2 x+3)^{5/2}+\frac{62}{27} (2 x+3)^{3/2}+\frac{526}{27} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{850}{27} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{2}{15} (2 x+3)^{5/2}+\frac{62}{27} (2 x+3)^{3/2}+\frac{526}{27} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{850}{27} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(526*Sqrt[3 + 2*x])/27 + (62*(3 + 2*x)^(3/2))/27 - (2*(3 + 2*x)^(5/2))/15 + 12*ArcTanh[Sqrt[3 + 2*x]] - (850*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/27","A",7,4,27,0.1481,1,"{824, 826, 1166, 207}"
2552,1,68,0,0.0597366,"\int \frac{(5-x) (3+2 x)^{3/2}}{2+5 x+3 x^2} \, dx","Int[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2),x]","-\frac{2}{9} (2 x+3)^{3/2}+\frac{62}{9} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{170}{9} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{2}{9} (2 x+3)^{3/2}+\frac{62}{9} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{170}{9} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(62*Sqrt[3 + 2*x])/9 - (2*(3 + 2*x)^(3/2))/9 + 12*ArcTanh[Sqrt[3 + 2*x]] - (170*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/9","A",6,4,27,0.1481,1,"{824, 826, 1166, 207}"
2553,1,55,0,0.0462726,"\int \frac{(5-x) \sqrt{3+2 x}}{2+5 x+3 x^2} \, dx","Int[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2),x]","-\frac{2}{3} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{34}{3} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{2}{3} \sqrt{2 x+3}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{34}{3} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(-2*Sqrt[3 + 2*x])/3 + 12*ArcTanh[Sqrt[3 + 2*x]] - (34*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/3","A",5,4,27,0.1481,1,"{824, 826, 1166, 207}"
2554,1,38,0,0.0304311,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)),x]","12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{34 \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{\sqrt{15}}","12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{34 \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{\sqrt{15}}",1,"12*ArcTanh[Sqrt[3 + 2*x]] - (34*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/Sqrt[15]","A",4,3,27,0.1111,1,"{826, 1166, 207}"
2555,1,55,0,0.0450021,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)),x]","-\frac{26}{5 \sqrt{2 x+3}}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{34}{5} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{26}{5 \sqrt{2 x+3}}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{34}{5} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-26/(5*Sqrt[3 + 2*x]) + 12*ArcTanh[Sqrt[3 + 2*x]] - (34*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/5","A",5,4,27,0.1481,1,"{828, 826, 1166, 207}"
2556,1,68,0,0.0619013,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)),x]","-\frac{198}{25 \sqrt{2 x+3}}-\frac{26}{15 (2 x+3)^{3/2}}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{102}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{198}{25 \sqrt{2 x+3}}-\frac{26}{15 (2 x+3)^{3/2}}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{102}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-26/(15*(3 + 2*x)^(3/2)) - 198/(25*Sqrt[3 + 2*x]) + 12*ArcTanh[Sqrt[3 + 2*x]] - (102*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/25","A",6,4,27,0.1481,1,"{828, 826, 1166, 207}"
2557,1,81,0,0.0784931,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)} \, dx","Int[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)),x]","-\frac{1194}{125 \sqrt{2 x+3}}-\frac{66}{25 (2 x+3)^{3/2}}-\frac{26}{25 (2 x+3)^{5/2}}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{306}{125} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{1194}{125 \sqrt{2 x+3}}-\frac{66}{25 (2 x+3)^{3/2}}-\frac{26}{25 (2 x+3)^{5/2}}+12 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{306}{125} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-26/(25*(3 + 2*x)^(5/2)) - 66/(25*(3 + 2*x)^(3/2)) - 1194/(125*Sqrt[3 + 2*x]) + 12*ArcTanh[Sqrt[3 + 2*x]] - (306*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/125","A",7,4,27,0.1481,1,"{828, 826, 1166, 207}"
2558,1,98,0,0.0811127,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^2,x]","-\frac{(139 x+121) (2 x+3)^{5/2}}{3 \left(3 x^2+5 x+2\right)}+\frac{826}{27} (2 x+3)^{3/2}+\frac{1358}{27} \sqrt{2 x+3}-154 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{2800}{27} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{(139 x+121) (2 x+3)^{5/2}}{3 \left(3 x^2+5 x+2\right)}+\frac{826}{27} (2 x+3)^{3/2}+\frac{1358}{27} \sqrt{2 x+3}-154 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{2800}{27} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(1358*Sqrt[3 + 2*x])/27 + (826*(3 + 2*x)^(3/2))/27 - ((3 + 2*x)^(5/2)*(121 + 139*x))/(3*(2 + 5*x + 3*x^2)) - 154*ArcTanh[Sqrt[3 + 2*x]] + (2800*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/27","A",7,5,27,0.1852,1,"{818, 824, 826, 1166, 207}"
2559,1,81,0,0.0714276,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^2,x]","-\frac{(139 x+121) (2 x+3)^{3/2}}{3 \left(3 x^2+5 x+2\right)}+30 \sqrt{2 x+3}-130 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+100 \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{(139 x+121) (2 x+3)^{3/2}}{3 \left(3 x^2+5 x+2\right)}+30 \sqrt{2 x+3}-130 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+100 \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"30*Sqrt[3 + 2*x] - ((3 + 2*x)^(3/2)*(121 + 139*x))/(3*(2 + 5*x + 3*x^2)) - 130*ArcTanh[Sqrt[3 + 2*x]] + 100*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]","A",6,5,27,0.1852,1,"{818, 824, 826, 1166, 207}"
2560,1,72,0,0.0463592,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^2,x]","-\frac{\sqrt{2 x+3} (139 x+121)}{3 \left(3 x^2+5 x+2\right)}-106 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{248}{3} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{\sqrt{2 x+3} (139 x+121)}{3 \left(3 x^2+5 x+2\right)}-106 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{248}{3} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-(Sqrt[3 + 2*x]*(121 + 139*x))/(3*(2 + 5*x + 3*x^2)) - 106*ArcTanh[Sqrt[3 + 2*x]] + (248*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/3","A",5,4,27,0.1481,1,"{818, 826, 1166, 207}"
2561,1,66,0,0.0399227,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^2} \, dx","Int[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^2,x]","-\frac{\sqrt{2 x+3} (35 x+29)}{3 x^2+5 x+2}-82 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{316 \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{\sqrt{15}}","-\frac{\sqrt{2 x+3} (35 x+29)}{3 x^2+5 x+2}-82 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{316 \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{\sqrt{15}}",1,"-((Sqrt[3 + 2*x]*(29 + 35*x))/(2 + 5*x + 3*x^2)) - 82*ArcTanh[Sqrt[3 + 2*x]] + (316*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/Sqrt[15]","A",5,4,27,0.1481,1,"{820, 826, 1166, 207}"
2562,1,72,0,0.0450731,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 \sqrt{2 x+3} (47 x+37)}{5 \left(3 x^2+5 x+2\right)}-58 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{384}{5} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 \sqrt{2 x+3} (47 x+37)}{5 \left(3 x^2+5 x+2\right)}-58 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{384}{5} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(-3*Sqrt[3 + 2*x]*(37 + 47*x))/(5*(2 + 5*x + 3*x^2)) - 58*ArcTanh[Sqrt[3 + 2*x]] + (384*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/5","A",5,4,27,0.1481,1,"{822, 826, 1166, 207}"
2563,1,85,0,0.0612812,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)}-\frac{506}{25 \sqrt{2 x+3}}-34 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{1356}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 (47 x+37)}{5 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)}-\frac{506}{25 \sqrt{2 x+3}}-34 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{1356}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-506/(25*Sqrt[3 + 2*x]) - (3*(37 + 47*x))/(5*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)) - 34*ArcTanh[Sqrt[3 + 2*x]] + (1356*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/25","A",6,5,27,0.1852,1,"{822, 828, 826, 1166, 207}"
2564,1,98,0,0.0802408,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)}-\frac{686}{25 \sqrt{2 x+3}}-\frac{262}{15 (2 x+3)^{3/2}}-10 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{936}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 (47 x+37)}{5 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)}-\frac{686}{25 \sqrt{2 x+3}}-\frac{262}{15 (2 x+3)^{3/2}}-10 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{936}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-262/(15*(3 + 2*x)^(3/2)) - 686/(25*Sqrt[3 + 2*x]) - (3*(37 + 47*x))/(5*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)) - 10*ArcTanh[Sqrt[3 + 2*x]] + (936*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/25","A",7,5,27,0.1852,1,"{822, 828, 826, 1166, 207}"
2565,1,111,0,0.0979208,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^2} \, dx","Int[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^2),x]","-\frac{3 (47 x+37)}{5 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)}-\frac{24626}{625 \sqrt{2 x+3}}-\frac{7042}{375 (2 x+3)^{3/2}}-\frac{2114}{125 (2 x+3)^{5/2}}+14 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{15876}{625} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 (47 x+37)}{5 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)}-\frac{24626}{625 \sqrt{2 x+3}}-\frac{7042}{375 (2 x+3)^{3/2}}-\frac{2114}{125 (2 x+3)^{5/2}}+14 \tanh ^{-1}\left(\sqrt{2 x+3}\right)+\frac{15876}{625} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-2114/(125*(3 + 2*x)^(5/2)) - 7042/(375*(3 + 2*x)^(3/2)) - 24626/(625*Sqrt[3 + 2*x]) - (3*(37 + 47*x))/(5*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)) + 14*ArcTanh[Sqrt[3 + 2*x]] + (15876*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/625","A",8,5,27,0.1852,1,"{822, 828, 826, 1166, 207}"
2566,1,115,0,0.0820516,"\int \frac{(5-x) (3+2 x)^{9/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^(9/2))/(2 + 5*x + 3*x^2)^3,x]","-\frac{(139 x+121) (2 x+3)^{7/2}}{6 \left(3 x^2+5 x+2\right)^2}+\frac{(12473 x+10832) (2 x+3)^{3/2}}{18 \left(3 x^2+5 x+2\right)}-\frac{3983}{9} \sqrt{2 x+3}+1962 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{13675}{9} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{(139 x+121) (2 x+3)^{7/2}}{6 \left(3 x^2+5 x+2\right)^2}+\frac{(12473 x+10832) (2 x+3)^{3/2}}{18 \left(3 x^2+5 x+2\right)}-\frac{3983}{9} \sqrt{2 x+3}+1962 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{13675}{9} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(-3983*Sqrt[3 + 2*x])/9 - ((3 + 2*x)^(7/2)*(121 + 139*x))/(6*(2 + 5*x + 3*x^2)^2) + ((3 + 2*x)^(3/2)*(10832 + 12473*x))/(18*(2 + 5*x + 3*x^2)) + 1962*ArcTanh[Sqrt[3 + 2*x]] - (13675*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/9","A",7,5,27,0.1852,1,"{818, 824, 826, 1166, 207}"
2567,1,100,0,0.0632812,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^3,x]","-\frac{(139 x+121) (2 x+3)^{5/2}}{6 \left(3 x^2+5 x+2\right)^2}+\frac{7 (619 x+546) \sqrt{2 x+3}}{6 \left(3 x^2+5 x+2\right)}+1582 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-1225 \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{(139 x+121) (2 x+3)^{5/2}}{6 \left(3 x^2+5 x+2\right)^2}+\frac{7 (619 x+546) \sqrt{2 x+3}}{6 \left(3 x^2+5 x+2\right)}+1582 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-1225 \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-((3 + 2*x)^(5/2)*(121 + 139*x))/(6*(2 + 5*x + 3*x^2)^2) + (7*Sqrt[3 + 2*x]*(546 + 619*x))/(6*(2 + 5*x + 3*x^2)) + 1582*ArcTanh[Sqrt[3 + 2*x]] - 1225*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]","A",6,4,27,0.1481,1,"{818, 826, 1166, 207}"
2568,1,102,0,0.0594209,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^3,x]","-\frac{(139 x+121) (2 x+3)^{3/2}}{6 \left(3 x^2+5 x+2\right)^2}+\frac{25 (131 x+112) \sqrt{2 x+3}}{6 \left(3 x^2+5 x+2\right)}+1250 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{2905}{3} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{(139 x+121) (2 x+3)^{3/2}}{6 \left(3 x^2+5 x+2\right)^2}+\frac{25 (131 x+112) \sqrt{2 x+3}}{6 \left(3 x^2+5 x+2\right)}+1250 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{2905}{3} \sqrt{\frac{5}{3}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-((3 + 2*x)^(3/2)*(121 + 139*x))/(6*(2 + 5*x + 3*x^2)^2) + (25*Sqrt[3 + 2*x]*(112 + 131*x))/(6*(2 + 5*x + 3*x^2)) + 1250*ArcTanh[Sqrt[3 + 2*x]] - (2905*Sqrt[5/3]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/3","A",6,5,27,0.1852,1,"{818, 820, 826, 1166, 207}"
2569,1,100,0,0.0667299,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^3,x]","-\frac{\sqrt{2 x+3} (139 x+121)}{6 \left(3 x^2+5 x+2\right)^2}+\frac{\sqrt{2 x+3} (2529 x+2090)}{6 \left(3 x^2+5 x+2\right)}+966 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-1247 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{\sqrt{2 x+3} (139 x+121)}{6 \left(3 x^2+5 x+2\right)^2}+\frac{\sqrt{2 x+3} (2529 x+2090)}{6 \left(3 x^2+5 x+2\right)}+966 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-1247 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-(Sqrt[3 + 2*x]*(121 + 139*x))/(6*(2 + 5*x + 3*x^2)^2) + (Sqrt[3 + 2*x]*(2090 + 2529*x))/(6*(2 + 5*x + 3*x^2)) + 966*ArcTanh[Sqrt[3 + 2*x]] - 1247*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]]","A",6,5,27,0.1852,1,"{818, 822, 826, 1166, 207}"
2570,1,102,0,0.0623808,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^3} \, dx","Int[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^3,x]","-\frac{\sqrt{2 x+3} (35 x+29)}{2 \left(3 x^2+5 x+2\right)^2}+\frac{3 \sqrt{2 x+3} (1063 x+878)}{10 \left(3 x^2+5 x+2\right)}+730 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{4713}{5} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{\sqrt{2 x+3} (35 x+29)}{2 \left(3 x^2+5 x+2\right)^2}+\frac{3 \sqrt{2 x+3} (1063 x+878)}{10 \left(3 x^2+5 x+2\right)}+730 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{4713}{5} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"-(Sqrt[3 + 2*x]*(29 + 35*x))/(2*(2 + 5*x + 3*x^2)^2) + (3*Sqrt[3 + 2*x]*(878 + 1063*x))/(10*(2 + 5*x + 3*x^2)) + 730*ArcTanh[Sqrt[3 + 2*x]] - (4713*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/5","A",6,5,27,0.1852,1,"{820, 822, 826, 1166, 207}"
2571,1,102,0,0.063425,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 \sqrt{2 x+3} (47 x+37)}{10 \left(3 x^2+5 x+2\right)^2}+\frac{\sqrt{2 x+3} (11739 x+9734)}{50 \left(3 x^2+5 x+2\right)}+542 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{17463}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 \sqrt{2 x+3} (47 x+37)}{10 \left(3 x^2+5 x+2\right)^2}+\frac{\sqrt{2 x+3} (11739 x+9734)}{50 \left(3 x^2+5 x+2\right)}+542 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{17463}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"(-3*Sqrt[3 + 2*x]*(37 + 47*x))/(10*(2 + 5*x + 3*x^2)^2) + (Sqrt[3 + 2*x]*(9734 + 11739*x))/(50*(2 + 5*x + 3*x^2)) + 542*ArcTanh[Sqrt[3 + 2*x]] - (17463*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/25","A",6,4,27,0.1481,1,"{822, 826, 1166, 207}"
2572,1,115,0,0.084689,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 (47 x+37)}{10 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^2}+\frac{2229 x+1888}{10 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)}+\frac{2667}{25 \sqrt{2 x+3}}+402 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{12717}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 (47 x+37)}{10 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^2}+\frac{2229 x+1888}{10 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)}+\frac{2667}{25 \sqrt{2 x+3}}+402 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{12717}{25} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"2667/(25*Sqrt[3 + 2*x]) - (3*(37 + 47*x))/(10*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^2) + (1888 + 2229*x)/(10*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)) + 402*ArcTanh[Sqrt[3 + 2*x]] - (12717*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/25","A",7,5,27,0.1852,1,"{822, 828, 826, 1166, 207}"
2573,1,128,0,0.0961882,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 (47 x+37)}{10 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^2}+\frac{10551 x+9146}{50 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)}+\frac{6853}{125 \sqrt{2 x+3}}+\frac{7451}{75 (2 x+3)^{3/2}}+310 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{45603}{125} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)","-\frac{3 (47 x+37)}{10 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^2}+\frac{10551 x+9146}{50 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)}+\frac{6853}{125 \sqrt{2 x+3}}+\frac{7451}{75 (2 x+3)^{3/2}}+310 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{45603}{125} \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)",1,"7451/(75*(3 + 2*x)^(3/2)) + 6853/(125*Sqrt[3 + 2*x]) - (3*(37 + 47*x))/(10*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^2) + (9146 + 10551*x)/(50*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)) + 310*ArcTanh[Sqrt[3 + 2*x]] - (45603*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/125","A",8,5,27,0.1852,1,"{822, 828, 826, 1166, 207}"
2574,1,141,0,0.1163582,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^3} \, dx","Int[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^3),x]","-\frac{3 (47 x+37)}{10 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^2}+\frac{9957 x+8852}{50 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)}-\frac{24409}{3125 \sqrt{2 x+3}}+\frac{102697}{1875 (2 x+3)^{3/2}}+\frac{56399}{625 (2 x+3)^{5/2}}+266 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{806841 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{3125}","-\frac{3 (47 x+37)}{10 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^2}+\frac{9957 x+8852}{50 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)}-\frac{24409}{3125 \sqrt{2 x+3}}+\frac{102697}{1875 (2 x+3)^{3/2}}+\frac{56399}{625 (2 x+3)^{5/2}}+266 \tanh ^{-1}\left(\sqrt{2 x+3}\right)-\frac{806841 \sqrt{\frac{3}{5}} \tanh ^{-1}\left(\sqrt{\frac{3}{5}} \sqrt{2 x+3}\right)}{3125}",1,"56399/(625*(3 + 2*x)^(5/2)) + 102697/(1875*(3 + 2*x)^(3/2)) - 24409/(3125*Sqrt[3 + 2*x]) - (3*(37 + 47*x))/(10*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^2) + (8852 + 9957*x)/(50*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)) + 266*ArcTanh[Sqrt[3 + 2*x]] - (806841*Sqrt[3/5]*ArcTanh[Sqrt[3/5]*Sqrt[3 + 2*x]])/3125","A",9,5,27,0.1852,1,"{822, 828, 826, 1166, 207}"
2575,1,115,0,0.2432279,"\int \frac{5+\sqrt{35}+10 x}{\sqrt{1+2 x} \left(2+3 x+5 x^2\right)} \, dx","Int[(5 + Sqrt[35] + 10*x)/(Sqrt[1 + 2*x]*(2 + 3*x + 5*x^2)),x]","2 \sqrt{\frac{10}{\sqrt{35}-2}} \tan ^{-1}\left(\frac{10 \sqrt{2 x+1}+\sqrt{10 \left(2+\sqrt{35}\right)}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)-2 \sqrt{\frac{10}{\sqrt{35}-2}} \tan ^{-1}\left(\frac{\sqrt{10 \left(2+\sqrt{35}\right)}-10 \sqrt{2 x+1}}{\sqrt{10 \left(\sqrt{35}-2\right)}}\right)","2 \sqrt{\frac{10}{\sqrt{35}-2}} \tan ^{-1}\left(\frac{\sqrt{20 x+10}+\sqrt{2+\sqrt{35}}}{\sqrt{\sqrt{35}-2}}\right)-2 \sqrt{\frac{10}{\sqrt{35}-2}} \tan ^{-1}\left(\frac{\sqrt{2+\sqrt{35}}-\sqrt{20 x+10}}{\sqrt{\sqrt{35}-2}}\right)",1,"-2*Sqrt[10/(-2 + Sqrt[35])]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] - 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]] + 2*Sqrt[10/(-2 + Sqrt[35])]*ArcTan[(Sqrt[10*(2 + Sqrt[35])] + 10*Sqrt[1 + 2*x])/Sqrt[10*(-2 + Sqrt[35])]]","A",6,4,32,0.1250,1,"{826, 1161, 618, 204}"
2576,1,224,0,0.1566562,"\int (5-x) (3+2 x)^{5/2} \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{33} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^{5/2}+\frac{730}{891} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^{3/2}+\frac{12130 \left(3 x^2+5 x+2\right)^{3/2} \sqrt{2 x+3}}{6237}+\frac{(280359 x+250447) \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}}{56133}+\frac{168145 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{112266 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{32567 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{16038 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{33} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^{5/2}+\frac{730}{891} \left(3 x^2+5 x+2\right)^{3/2} (2 x+3)^{3/2}+\frac{12130 \left(3 x^2+5 x+2\right)^{3/2} \sqrt{2 x+3}}{6237}+\frac{(280359 x+250447) \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}}{56133}+\frac{168145 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{112266 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{32567 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{16038 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(Sqrt[3 + 2*x]*(250447 + 280359*x)*Sqrt[2 + 5*x + 3*x^2])/56133 + (12130*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2))/6237 + (730*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2))/891 - (2*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2))/33 - (32567*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(16038*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (168145*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(112266*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2577,1,197,0,0.1333769,"\int (5-x) (3+2 x)^{3/2} \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{27} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{3/2}+\frac{202}{189} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}+\frac{\sqrt{2 x+3} (30033 x+27914) \sqrt{3 x^2+5 x+2}}{8505}+\frac{5773 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3402 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{4729 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{2430 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{27} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{3/2}+\frac{202}{189} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}+\frac{\sqrt{2 x+3} (30033 x+27914) \sqrt{3 x^2+5 x+2}}{8505}+\frac{5773 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3402 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{4729 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{2430 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(Sqrt[3 + 2*x]*(27914 + 30033*x)*Sqrt[2 + 5*x + 3*x^2])/8505 + (202*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2))/189 - (2*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2))/27 - (4729*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(2430*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (5773*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3402*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2578,1,170,0,0.1239727,"\int (5-x) \sqrt{3+2 x} \sqrt{2+5 x+3 x^2} \, dx","Int[(5 - x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{21} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}+\frac{1}{945} \sqrt{2 x+3} (2169 x+2327) \sqrt{3 x^2+5 x+2}+\frac{1039 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{378 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{697 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{270 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{21} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}+\frac{1}{945} \sqrt{2 x+3} (2169 x+2327) \sqrt{3 x^2+5 x+2}+\frac{1039 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{378 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{697 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{270 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(Sqrt[3 + 2*x]*(2327 + 2169*x)*Sqrt[2 + 5*x + 3*x^2])/945 - (2*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2))/21 - (697*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(270*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (1039*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(378*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2579,1,143,0,0.0808324,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{\sqrt{3+2 x}} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/Sqrt[3 + 2*x],x]","\frac{1}{45} \sqrt{2 x+3} \sqrt{3 x^2+5 x+2} (88-9 x)+\frac{191 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{18 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{761 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{90 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{1}{45} \sqrt{2 x+3} \sqrt{3 x^2+5 x+2} (88-9 x)+\frac{191 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{18 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{761 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{90 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((88 - 9*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/45 - (761*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(90*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (191*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(18*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{814, 843, 718, 424, 419}"
2580,1,141,0,0.0831997,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{3/2}} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(3/2),x]","-\frac{\sqrt{3 x^2+5 x+2} (x+21)}{3 \sqrt{2 x+3}}-\frac{161 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{6 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{121 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{6 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{\sqrt{3 x^2+5 x+2} (x+21)}{3 \sqrt{2 x+3}}-\frac{161 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{6 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{121 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{6 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-((21 + x)*Sqrt[2 + 5*x + 3*x^2])/(3*Sqrt[3 + 2*x]) + (121*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(6*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (161*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(6*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{812, 843, 718, 424, 419}"
2581,1,143,0,0.0854779,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{5/2}} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(5/2),x]","\frac{\sqrt{3 x^2+5 x+2} (119 x+146)}{15 (2 x+3)^{3/2}}+\frac{17 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{67 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{10 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{\sqrt{3 x^2+5 x+2} (119 x+146)}{15 (2 x+3)^{3/2}}+\frac{17 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{2 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{67 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{10 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((146 + 119*x)*Sqrt[2 + 5*x + 3*x^2])/(15*(3 + 2*x)^(3/2)) - (67*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(10*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (17*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(2*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{810, 843, 718, 424, 419}"
2582,1,170,0,0.1079844,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{7/2}} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(7/2),x]","\frac{\sqrt{3 x^2+5 x+2} (43 x+32)}{25 (2 x+3)^{5/2}}+\frac{49 \sqrt{3 x^2+5 x+2}}{125 \sqrt{2 x+3}}+\frac{9 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{50 \sqrt{3 x^2+5 x+2}}-\frac{49 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{250 \sqrt{3 x^2+5 x+2}}","\frac{\sqrt{3 x^2+5 x+2} (43 x+32)}{25 (2 x+3)^{5/2}}+\frac{49 \sqrt{3 x^2+5 x+2}}{125 \sqrt{2 x+3}}+\frac{9 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{50 \sqrt{3 x^2+5 x+2}}-\frac{49 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{250 \sqrt{3 x^2+5 x+2}}",1,"(49*Sqrt[2 + 5*x + 3*x^2])/(125*Sqrt[3 + 2*x]) + ((32 + 43*x)*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)^(5/2)) - (49*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(250*Sqrt[2 + 5*x + 3*x^2]) + (9*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(50*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{810, 834, 843, 718, 424, 419}"
2583,1,197,0,0.1355136,"\int \frac{(5-x) \sqrt{2+5 x+3 x^2}}{(3+2 x)^{9/2}} \, dx","Int[((5 - x)*Sqrt[2 + 5*x + 3*x^2])/(3 + 2*x)^(9/2),x]","\frac{\sqrt{3 x^2+5 x+2} (139 x+46)}{175 (2 x+3)^{7/2}}+\frac{159 \sqrt{3 x^2+5 x+2}}{625 \sqrt{2 x+3}}+\frac{183 \sqrt{3 x^2+5 x+2}}{875 (2 x+3)^{3/2}}+\frac{183 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1750 \sqrt{3 x^2+5 x+2}}-\frac{159 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1250 \sqrt{3 x^2+5 x+2}}","\frac{\sqrt{3 x^2+5 x+2} (139 x+46)}{175 (2 x+3)^{7/2}}+\frac{159 \sqrt{3 x^2+5 x+2}}{625 \sqrt{2 x+3}}+\frac{183 \sqrt{3 x^2+5 x+2}}{875 (2 x+3)^{3/2}}+\frac{183 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1750 \sqrt{3 x^2+5 x+2}}-\frac{159 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1250 \sqrt{3 x^2+5 x+2}}",1,"(183*Sqrt[2 + 5*x + 3*x^2])/(875*(3 + 2*x)^(3/2)) + (159*Sqrt[2 + 5*x + 3*x^2])/(625*Sqrt[3 + 2*x]) + ((46 + 139*x)*Sqrt[2 + 5*x + 3*x^2])/(175*(3 + 2*x)^(7/2)) - (159*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(1250*Sqrt[2 + 5*x + 3*x^2]) + (183*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(1750*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{810, 834, 843, 718, 424, 419}"
2584,1,256,0,0.192898,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2}{45} (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{202}{351} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{13318 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}}{11583}+\frac{\sqrt{2 x+3} (629153 x+534271) \left(3 x^2+5 x+2\right)^{3/2}}{243243}-\frac{\sqrt{2 x+3} (7817373 x+6006884) \sqrt{3 x^2+5 x+2}}{21891870}+\frac{1015187 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{8756748 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{207851 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{6254820 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{45} (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{202}{351} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{13318 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}}{11583}+\frac{\sqrt{2 x+3} (629153 x+534271) \left(3 x^2+5 x+2\right)^{3/2}}{243243}-\frac{\sqrt{2 x+3} (7817373 x+6006884) \sqrt{3 x^2+5 x+2}}{21891870}+\frac{1015187 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{8756748 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{207851 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{6254820 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-(Sqrt[3 + 2*x]*(6006884 + 7817373*x)*Sqrt[2 + 5*x + 3*x^2])/21891870 + (Sqrt[3 + 2*x]*(534271 + 629153*x)*(2 + 5*x + 3*x^2)^(3/2))/243243 + (13318*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2))/11583 + (202*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(5/2))/351 - (2*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(5/2))/45 - (207851*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(6254820*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (1015187*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(8756748*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",10,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2585,1,229,0,0.1627766,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2}{39} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{886 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}}{1287}+\frac{\sqrt{2 x+3} (50771 x+43822) \left(3 x^2+5 x+2\right)^{3/2}}{27027}-\frac{\sqrt{2 x+3} (783711 x+486863) \sqrt{3 x^2+5 x+2}}{2432430}+\frac{332459 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{972972 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{152657 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{694980 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{39} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{5/2}+\frac{886 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}}{1287}+\frac{\sqrt{2 x+3} (50771 x+43822) \left(3 x^2+5 x+2\right)^{3/2}}{27027}-\frac{\sqrt{2 x+3} (783711 x+486863) \sqrt{3 x^2+5 x+2}}{2432430}+\frac{332459 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{972972 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{152657 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{694980 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-(Sqrt[3 + 2*x]*(486863 + 783711*x)*Sqrt[2 + 5*x + 3*x^2])/2432430 + (Sqrt[3 + 2*x]*(43822 + 50771*x)*(2 + 5*x + 3*x^2)^(3/2))/27027 + (886*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2))/1287 - (2*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(5/2))/39 - (152657*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(694980*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (332459*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(972972*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2586,1,202,0,0.1296748,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{3/2} \, dx","Int[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2}{33} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}+\frac{1}{99} \sqrt{2 x+3} (127 x+119) \left(3 x^2+5 x+2\right)^{3/2}-\frac{\sqrt{2 x+3} (3987 x+1246) \sqrt{3 x^2+5 x+2}}{8910}+\frac{4153 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3564 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{15283 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{17820 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{33} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}+\frac{1}{99} \sqrt{2 x+3} (127 x+119) \left(3 x^2+5 x+2\right)^{3/2}-\frac{\sqrt{2 x+3} (3987 x+1246) \sqrt{3 x^2+5 x+2}}{8910}+\frac{4153 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3564 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{15283 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{17820 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-(Sqrt[3 + 2*x]*(1246 + 3987*x)*Sqrt[2 + 5*x + 3*x^2])/8910 + (Sqrt[3 + 2*x]*(119 + 127*x)*(2 + 5*x + 3*x^2)^(3/2))/99 - (2*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2))/33 - (15283*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(17820*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (4153*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3564*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2587,1,175,0,0.1051648,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{\sqrt{3+2 x}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/Sqrt[3 + 2*x],x]","\frac{1}{63} (52-7 x) \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}-\frac{\sqrt{2 x+3} (12429 x+107) \sqrt{3 x^2+5 x+2}}{5670}+\frac{20501 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{2268 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{11123 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1620 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{1}{63} (52-7 x) \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}-\frac{\sqrt{2 x+3} (12429 x+107) \sqrt{3 x^2+5 x+2}}{5670}+\frac{20501 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{2268 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{11123 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1620 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-(Sqrt[3 + 2*x]*(107 + 12429*x)*Sqrt[2 + 5*x + 3*x^2])/5670 + ((52 - 7*x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2))/63 - (11123*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(1620*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (20501*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(2268*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{814, 843, 718, 424, 419}"
2588,1,173,0,0.1027977,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{3/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(3/2),x]","-\frac{(x+47) \left(3 x^2+5 x+2\right)^{3/2}}{7 \sqrt{2 x+3}}-\frac{1}{210} (136-2493 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}-\frac{4427 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{84 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{2411 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{60 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{(x+47) \left(3 x^2+5 x+2\right)^{3/2}}{7 \sqrt{2 x+3}}-\frac{1}{210} (136-2493 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}-\frac{4427 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{84 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{2411 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{60 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-((136 - 2493*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/210 - ((47 + x)*(2 + 5*x + 3*x^2)^(3/2))/(7*Sqrt[3 + 2*x]) + (2411*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(60*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (4427*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(84*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{812, 814, 843, 718, 424, 419}"
2589,1,175,0,0.1019675,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{5/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(5/2),x]","-\frac{(3 x+37) \left(3 x^2+5 x+2\right)^{3/2}}{15 (2 x+3)^{3/2}}+\frac{(69 x+241) \sqrt{3 x^2+5 x+2}}{10 \sqrt{2 x+3}}+\frac{289 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{4 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{367 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{20 \sqrt{3 x^2+5 x+2}}","-\frac{(3 x+37) \left(3 x^2+5 x+2\right)^{3/2}}{15 (2 x+3)^{3/2}}+\frac{(69 x+241) \sqrt{3 x^2+5 x+2}}{10 \sqrt{2 x+3}}+\frac{289 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{4 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{367 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{20 \sqrt{3 x^2+5 x+2}}",1,"((241 + 69*x)*Sqrt[2 + 5*x + 3*x^2])/(10*Sqrt[3 + 2*x]) - ((37 + 3*x)*(2 + 5*x + 3*x^2)^(3/2))/(15*(3 + 2*x)^(3/2)) - (367*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(20*Sqrt[2 + 5*x + 3*x^2]) + (289*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(4*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{812, 843, 718, 424, 419}"
2590,1,175,0,0.1038104,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{7/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(7/2),x]","\frac{(337 x+408) \left(3 x^2+5 x+2\right)^{3/2}}{75 (2 x+3)^{5/2}}-\frac{(181 x+614) \sqrt{3 x^2+5 x+2}}{50 \sqrt{2 x+3}}-\frac{243 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{20 \sqrt{3 x^2+5 x+2}}+\frac{2779 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{100 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(337 x+408) \left(3 x^2+5 x+2\right)^{3/2}}{75 (2 x+3)^{5/2}}-\frac{(181 x+614) \sqrt{3 x^2+5 x+2}}{50 \sqrt{2 x+3}}-\frac{243 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{20 \sqrt{3 x^2+5 x+2}}+\frac{2779 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{100 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-((614 + 181*x)*Sqrt[2 + 5*x + 3*x^2])/(50*Sqrt[3 + 2*x]) + ((408 + 337*x)*(2 + 5*x + 3*x^2)^(3/2))/(75*(3 + 2*x)^(5/2)) + (2779*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(100*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (243*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(20*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{810, 812, 843, 718, 424, 419}"
2591,1,175,0,0.099538,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{9/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(9/2),x]","\frac{(347 x+358) \left(3 x^2+5 x+2\right)^{3/2}}{175 (2 x+3)^{7/2}}+\frac{(6179 x+8561) \sqrt{3 x^2+5 x+2}}{1750 (2 x+3)^{3/2}}+\frac{1327 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{700 \sqrt{3 x^2+5 x+2}}-\frac{721 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{500 \sqrt{3 x^2+5 x+2}}","\frac{(347 x+358) \left(3 x^2+5 x+2\right)^{3/2}}{175 (2 x+3)^{7/2}}+\frac{(6179 x+8561) \sqrt{3 x^2+5 x+2}}{1750 (2 x+3)^{3/2}}+\frac{1327 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{700 \sqrt{3 x^2+5 x+2}}-\frac{721 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{500 \sqrt{3 x^2+5 x+2}}",1,"((8561 + 6179*x)*Sqrt[2 + 5*x + 3*x^2])/(1750*(3 + 2*x)^(3/2)) + ((358 + 347*x)*(2 + 5*x + 3*x^2)^(3/2))/(175*(3 + 2*x)^(7/2)) - (721*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(500*Sqrt[2 + 5*x + 3*x^2]) + (1327*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(700*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{810, 843, 718, 424, 419}"
2592,1,202,0,0.1269211,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{11/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(11/2),x]","\frac{(51 x+44) \left(3 x^2+5 x+2\right)^{3/2}}{45 (2 x+3)^{9/2}}-\frac{(211 x+189) \sqrt{3 x^2+5 x+2}}{2250 (2 x+3)^{5/2}}-\frac{23 \sqrt{3 x^2+5 x+2}}{11250 \sqrt{2 x+3}}+\frac{7 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1500 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{23 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{7500 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(51 x+44) \left(3 x^2+5 x+2\right)^{3/2}}{45 (2 x+3)^{9/2}}-\frac{(211 x+189) \sqrt{3 x^2+5 x+2}}{2250 (2 x+3)^{5/2}}-\frac{23 \sqrt{3 x^2+5 x+2}}{11250 \sqrt{2 x+3}}+\frac{7 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1500 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{23 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{7500 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-23*Sqrt[2 + 5*x + 3*x^2])/(11250*Sqrt[3 + 2*x]) - ((189 + 211*x)*Sqrt[2 + 5*x + 3*x^2])/(2250*(3 + 2*x)^(5/2)) + ((44 + 51*x)*(2 + 5*x + 3*x^2)^(3/2))/(45*(3 + 2*x)^(9/2)) + (23*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(7500*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (7*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(1500*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{810, 834, 843, 718, 424, 419}"
2593,1,229,0,0.1522242,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{3/2}}{(3+2 x)^{13/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(3/2))/(3 + 2*x)^(13/2),x]","\frac{(367 x+258) \left(3 x^2+5 x+2\right)^{3/2}}{495 (2 x+3)^{11/2}}-\frac{(14773 x+15647) \sqrt{3 x^2+5 x+2}}{57750 (2 x+3)^{7/2}}+\frac{5861 \sqrt{3 x^2+5 x+2}}{618750 \sqrt{2 x+3}}+\frac{14807 \sqrt{3 x^2+5 x+2}}{866250 (2 x+3)^{3/2}}+\frac{14807 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{577500 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{5861 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{412500 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(367 x+258) \left(3 x^2+5 x+2\right)^{3/2}}{495 (2 x+3)^{11/2}}-\frac{(14773 x+15647) \sqrt{3 x^2+5 x+2}}{57750 (2 x+3)^{7/2}}+\frac{5861 \sqrt{3 x^2+5 x+2}}{618750 \sqrt{2 x+3}}+\frac{14807 \sqrt{3 x^2+5 x+2}}{866250 (2 x+3)^{3/2}}+\frac{14807 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{577500 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{5861 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{412500 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(14807*Sqrt[2 + 5*x + 3*x^2])/(866250*(3 + 2*x)^(3/2)) + (5861*Sqrt[2 + 5*x + 3*x^2])/(618750*Sqrt[3 + 2*x]) - ((15647 + 14773*x)*Sqrt[2 + 5*x + 3*x^2])/(57750*(3 + 2*x)^(7/2)) + ((258 + 367*x)*(2 + 5*x + 3*x^2)^(3/2))/(495*(3 + 2*x)^(11/2)) - (5861*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(412500*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (14807*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(577500*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{810, 834, 843, 718, 424, 419}"
2594,1,288,0,0.2157579,"\int (5-x) (3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2}{57} (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{7/2}+\frac{430}{969} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{7/2}+\frac{2350 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{7/2}}{2907}+\frac{25 \sqrt{2 x+3} (86493 x+72737) \left(3 x^2+5 x+2\right)^{5/2}}{1247103}-\frac{125 \sqrt{2 x+3} (79583 x+64006) \left(3 x^2+5 x+2\right)^{3/2}}{52378326}+\frac{25 \sqrt{2 x+3} (216603 x+749099) \sqrt{3 x^2+5 x+2}}{942809868}+\frac{142149125 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1885619736 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{16503475 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{269374248 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{57} (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{7/2}+\frac{430}{969} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{7/2}+\frac{2350 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{7/2}}{2907}+\frac{25 \sqrt{2 x+3} (86493 x+72737) \left(3 x^2+5 x+2\right)^{5/2}}{1247103}-\frac{125 \sqrt{2 x+3} (79583 x+64006) \left(3 x^2+5 x+2\right)^{3/2}}{52378326}+\frac{25 \sqrt{2 x+3} (216603 x+749099) \sqrt{3 x^2+5 x+2}}{942809868}+\frac{142149125 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1885619736 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{16503475 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{269374248 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(25*Sqrt[3 + 2*x]*(749099 + 216603*x)*Sqrt[2 + 5*x + 3*x^2])/942809868 - (125*Sqrt[3 + 2*x]*(64006 + 79583*x)*(2 + 5*x + 3*x^2)^(3/2))/52378326 + (25*Sqrt[3 + 2*x]*(72737 + 86493*x)*(2 + 5*x + 3*x^2)^(5/2))/1247103 + (2350*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(7/2))/2907 + (430*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(7/2))/969 - (2*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(7/2))/57 - (16503475*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(269374248*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (142149125*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(1885619736*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",11,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2595,1,261,0,0.2026366,"\int (5-x) (3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2}{51} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{7/2}+\frac{1166 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{7/2}}{2295}+\frac{\sqrt{2 x+3} (1253571 x+1063774) \left(3 x^2+5 x+2\right)^{5/2}}{984555}-\frac{\sqrt{2 x+3} (1332121 x+949997) \left(3 x^2+5 x+2\right)^{3/2}}{8270262}+\frac{(12174838-22593339 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{744323580}+\frac{62005241 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{297729432 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{34355693 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{212663880 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{51} (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{7/2}+\frac{1166 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{7/2}}{2295}+\frac{\sqrt{2 x+3} (1253571 x+1063774) \left(3 x^2+5 x+2\right)^{5/2}}{984555}-\frac{\sqrt{2 x+3} (1332121 x+949997) \left(3 x^2+5 x+2\right)^{3/2}}{8270262}+\frac{(12174838-22593339 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{744323580}+\frac{62005241 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{297729432 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{34355693 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{212663880 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((12174838 - 22593339*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/744323580 - (Sqrt[3 + 2*x]*(949997 + 1332121*x)*(2 + 5*x + 3*x^2)^(3/2))/8270262 + (Sqrt[3 + 2*x]*(1063774 + 1253571*x)*(2 + 5*x + 3*x^2)^(5/2))/984555 + (1166*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(7/2))/2295 - (2*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(7/2))/51 - (34355693*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(212663880*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (62005241*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(297729432*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",10,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2596,1,234,0,0.1553427,"\int (5-x) \sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{5/2} \, dx","Int[(5 - x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2}{45} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{7/2}+\frac{\sqrt{2 x+3} (17193 x+15467) \left(3 x^2+5 x+2\right)^{5/2}}{19305}-\frac{\sqrt{2 x+3} (34643 x+15076) \left(3 x^2+5 x+2\right)^{3/2}}{162162}+\frac{(287729-2667537 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{14594580}+\frac{5021353 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5837832 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{2742319 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{4169880 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{45} \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{7/2}+\frac{\sqrt{2 x+3} (17193 x+15467) \left(3 x^2+5 x+2\right)^{5/2}}{19305}-\frac{\sqrt{2 x+3} (34643 x+15076) \left(3 x^2+5 x+2\right)^{3/2}}{162162}+\frac{(287729-2667537 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{14594580}+\frac{5021353 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5837832 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{2742319 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{4169880 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((287729 - 2667537*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/14594580 - (Sqrt[3 + 2*x]*(15076 + 34643*x)*(2 + 5*x + 3*x^2)^(3/2))/162162 + (Sqrt[3 + 2*x]*(15467 + 17193*x)*(2 + 5*x + 3*x^2)^(5/2))/19305 - (2*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(7/2))/45 - (2742319*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(4169880*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (5021353*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5837832*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{832, 814, 843, 718, 424, 419}"
2597,1,207,0,0.1271584,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{\sqrt{3+2 x}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/Sqrt[3 + 2*x],x]","\frac{1}{429} (224-33 x) \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}-\frac{5 \sqrt{2 x+3} (4669 x+563) \left(3 x^2+5 x+2\right)^{3/2}}{18018}+\frac{(34372-676791 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{324324}+\frac{5983645 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{648648 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{651617 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{92664 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{1}{429} (224-33 x) \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{5/2}-\frac{5 \sqrt{2 x+3} (4669 x+563) \left(3 x^2+5 x+2\right)^{3/2}}{18018}+\frac{(34372-676791 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{324324}+\frac{5983645 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{648648 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{651617 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{92664 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((34372 - 676791*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/324324 - (5*Sqrt[3 + 2*x]*(563 + 4669*x)*(2 + 5*x + 3*x^2)^(3/2))/18018 + ((224 - 33*x)*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2))/429 - (651617*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(92664*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (5983645*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(648648*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,5,29,0.1724,1,"{814, 843, 718, 424, 419}"
2598,1,205,0,0.1293842,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{3/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(3/2),x]","-\frac{(x+73) \left(3 x^2+5 x+2\right)^{5/2}}{11 \sqrt{2 x+3}}+\frac{5 \sqrt{2 x+3} (3031 x+218) \left(3 x^2+5 x+2\right)^{3/2}}{1386}-\frac{(21871-471213 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{24948}-\frac{4145485 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{49896 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{451331 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{7128 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{(x+73) \left(3 x^2+5 x+2\right)^{5/2}}{11 \sqrt{2 x+3}}+\frac{5 \sqrt{2 x+3} (3031 x+218) \left(3 x^2+5 x+2\right)^{3/2}}{1386}-\frac{(21871-471213 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}{24948}-\frac{4145485 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{49896 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{451331 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{7128 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-((21871 - 471213*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/24948 + (5*Sqrt[3 + 2*x]*(218 + 3031*x)*(2 + 5*x + 3*x^2)^(3/2))/1386 - ((73 + x)*(2 + 5*x + 3*x^2)^(5/2))/(11*Sqrt[3 + 2*x]) + (451331*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(7128*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (4145485*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(49896*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{812, 814, 843, 718, 424, 419}"
2599,1,205,0,0.1302164,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{5/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(5/2),x]","-\frac{(x+21) \left(3 x^2+5 x+2\right)^{5/2}}{9 (2 x+3)^{3/2}}+\frac{5 (121 x+745) \left(3 x^2+5 x+2\right)^{3/2}}{126 \sqrt{2 x+3}}+\frac{5}{756} (326-6957 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}+\frac{306175 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1512 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{33335 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{216 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{(x+21) \left(3 x^2+5 x+2\right)^{5/2}}{9 (2 x+3)^{3/2}}+\frac{5 (121 x+745) \left(3 x^2+5 x+2\right)^{3/2}}{126 \sqrt{2 x+3}}+\frac{5}{756} (326-6957 x) \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}+\frac{306175 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{1512 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{33335 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{216 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(5*(326 - 6957*x)*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/756 + (5*(745 + 121*x)*(2 + 5*x + 3*x^2)^(3/2))/(126*Sqrt[3 + 2*x]) - ((21 + x)*(2 + 5*x + 3*x^2)^(5/2))/(9*(3 + 2*x)^(3/2)) - (33335*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(216*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (306175*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(1512*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{812, 814, 843, 718, 424, 419}"
2600,1,207,0,0.132171,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{7/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(7/2),x]","-\frac{(5 x+53) \left(3 x^2+5 x+2\right)^{5/2}}{35 (2 x+3)^{5/2}}+\frac{(879 x+2291) \left(3 x^2+5 x+2\right)^{3/2}}{210 (2 x+3)^{3/2}}-\frac{(3117 x+10763) \sqrt{3 x^2+5 x+2}}{140 \sqrt{2 x+3}}-\frac{12857 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{56 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{2333 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{40 \sqrt{3 x^2+5 x+2}}","-\frac{(5 x+53) \left(3 x^2+5 x+2\right)^{5/2}}{35 (2 x+3)^{5/2}}+\frac{(879 x+2291) \left(3 x^2+5 x+2\right)^{3/2}}{210 (2 x+3)^{3/2}}-\frac{(3117 x+10763) \sqrt{3 x^2+5 x+2}}{140 \sqrt{2 x+3}}-\frac{12857 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{56 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{2333 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{40 \sqrt{3 x^2+5 x+2}}",1,"-((10763 + 3117*x)*Sqrt[2 + 5*x + 3*x^2])/(140*Sqrt[3 + 2*x]) + ((2291 + 879*x)*(2 + 5*x + 3*x^2)^(3/2))/(210*(3 + 2*x)^(3/2)) - ((53 + 5*x)*(2 + 5*x + 3*x^2)^(5/2))/(35*(3 + 2*x)^(5/2)) + (2333*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(40*Sqrt[2 + 5*x + 3*x^2]) - (12857*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(56*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,5,29,0.1724,1,"{812, 843, 718, 424, 419}"
2601,1,207,0,0.1295722,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{9/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(9/2),x]","-\frac{(7 x+43) \left(3 x^2+5 x+2\right)^{5/2}}{35 (2 x+3)^{7/2}}-\frac{(2531 x+3354) \left(3 x^2+5 x+2\right)^{3/2}}{210 (2 x+3)^{5/2}}+\frac{(1823 x+6292) \sqrt{3 x^2+5 x+2}}{140 \sqrt{2 x+3}}+\frac{2505 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{56 \sqrt{3 x^2+5 x+2}}-\frac{4091 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{40 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{(7 x+43) \left(3 x^2+5 x+2\right)^{5/2}}{35 (2 x+3)^{7/2}}-\frac{(2531 x+3354) \left(3 x^2+5 x+2\right)^{3/2}}{210 (2 x+3)^{5/2}}+\frac{(1823 x+6292) \sqrt{3 x^2+5 x+2}}{140 \sqrt{2 x+3}}+\frac{2505 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{56 \sqrt{3 x^2+5 x+2}}-\frac{4091 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{40 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((6292 + 1823*x)*Sqrt[2 + 5*x + 3*x^2])/(140*Sqrt[3 + 2*x]) - ((3354 + 2531*x)*(2 + 5*x + 3*x^2)^(3/2))/(210*(3 + 2*x)^(5/2)) - ((43 + 7*x)*(2 + 5*x + 3*x^2)^(5/2))/(35*(3 + 2*x)^(7/2)) - (4091*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(40*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (2505*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(56*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{812, 810, 843, 718, 424, 419}"
2602,1,207,0,0.1289236,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{11/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(11/2),x]","\frac{(113 x+124) \left(3 x^2+5 x+2\right)^{5/2}}{63 (2 x+3)^{9/2}}+\frac{(10729 x+14311) \left(3 x^2+5 x+2\right)^{3/2}}{3150 (2 x+3)^{5/2}}-\frac{(7877 x+27213) \sqrt{3 x^2+5 x+2}}{2100 \sqrt{2 x+3}}-\frac{32513 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{840 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{17699 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{600 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(113 x+124) \left(3 x^2+5 x+2\right)^{5/2}}{63 (2 x+3)^{9/2}}+\frac{(10729 x+14311) \left(3 x^2+5 x+2\right)^{3/2}}{3150 (2 x+3)^{5/2}}-\frac{(7877 x+27213) \sqrt{3 x^2+5 x+2}}{2100 \sqrt{2 x+3}}-\frac{32513 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{840 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{17699 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{600 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-((27213 + 7877*x)*Sqrt[2 + 5*x + 3*x^2])/(2100*Sqrt[3 + 2*x]) + ((14311 + 10729*x)*(2 + 5*x + 3*x^2)^(3/2))/(3150*(3 + 2*x)^(5/2)) + ((124 + 113*x)*(2 + 5*x + 3*x^2)^(5/2))/(63*(3 + 2*x)^(9/2)) + (17699*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(600*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (32513*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(840*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{810, 812, 843, 718, 424, 419}"
2603,1,207,0,0.133028,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{13/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(13/2),x]","\frac{(115 x+114) \left(3 x^2+5 x+2\right)^{5/2}}{99 (2 x+3)^{11/2}}+\frac{(18699 x+24161) \left(3 x^2+5 x+2\right)^{3/2}}{34650 (2 x+3)^{7/2}}+\frac{(948443 x+1301762) \sqrt{3 x^2+5 x+2}}{346500 (2 x+3)^{3/2}}+\frac{198109 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{46200 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{107857 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{33000 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(115 x+114) \left(3 x^2+5 x+2\right)^{5/2}}{99 (2 x+3)^{11/2}}+\frac{(18699 x+24161) \left(3 x^2+5 x+2\right)^{3/2}}{34650 (2 x+3)^{7/2}}+\frac{(948443 x+1301762) \sqrt{3 x^2+5 x+2}}{346500 (2 x+3)^{3/2}}+\frac{198109 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{46200 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{107857 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{33000 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"((1301762 + 948443*x)*Sqrt[2 + 5*x + 3*x^2])/(346500*(3 + 2*x)^(3/2)) + ((24161 + 18699*x)*(2 + 5*x + 3*x^2)^(3/2))/(34650*(3 + 2*x)^(7/2)) + ((114 + 115*x)*(2 + 5*x + 3*x^2)^(5/2))/(99*(3 + 2*x)^(11/2)) - (107857*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(33000*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (198109*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(46200*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,5,29,0.1724,1,"{810, 843, 718, 424, 419}"
2604,1,234,0,0.1615921,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{15/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(15/2),x]","\frac{(9 x+8) \left(3 x^2+5 x+2\right)^{5/2}}{11 (2 x+3)^{13/2}}+\frac{(73-33 x) \left(3 x^2+5 x+2\right)^{3/2}}{6930 (2 x+3)^{9/2}}+\frac{(17833 x+21492) \sqrt{3 x^2+5 x+2}}{346500 (2 x+3)^{5/2}}-\frac{5083 \sqrt{3 x^2+5 x+2}}{247500 \sqrt{2 x+3}}-\frac{9421 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{231000 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{5083 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{165000 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(9 x+8) \left(3 x^2+5 x+2\right)^{5/2}}{11 (2 x+3)^{13/2}}+\frac{(73-33 x) \left(3 x^2+5 x+2\right)^{3/2}}{6930 (2 x+3)^{9/2}}+\frac{(17833 x+21492) \sqrt{3 x^2+5 x+2}}{346500 (2 x+3)^{5/2}}-\frac{5083 \sqrt{3 x^2+5 x+2}}{247500 \sqrt{2 x+3}}-\frac{9421 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{231000 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{5083 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{165000 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-5083*Sqrt[2 + 5*x + 3*x^2])/(247500*Sqrt[3 + 2*x]) + ((21492 + 17833*x)*Sqrt[2 + 5*x + 3*x^2])/(346500*(3 + 2*x)^(5/2)) + ((73 - 33*x)*(2 + 5*x + 3*x^2)^(3/2))/(6930*(3 + 2*x)^(9/2)) + ((8 + 9*x)*(2 + 5*x + 3*x^2)^(5/2))/(11*(3 + 2*x)^(13/2)) + (5083*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(165000*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (9421*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(231000*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{810, 834, 843, 718, 424, 419}"
2605,1,261,0,0.1876978,"\int \frac{(5-x) \left(2+5 x+3 x^2\right)^{5/2}}{(3+2 x)^{17/2}} \, dx","Int[((5 - x)*(2 + 5*x + 3*x^2)^(5/2))/(3 + 2*x)^(17/2),x]","\frac{(119 x+94) \left(3 x^2+5 x+2\right)^{5/2}}{195 (2 x+3)^{15/2}}-\frac{(8399 x+8901) \left(3 x^2+5 x+2\right)^{3/2}}{64350 (2 x+3)^{11/2}}-\frac{(328339 x+386846) \sqrt{3 x^2+5 x+2}}{7507500 (2 x+3)^{7/2}}+\frac{335723 \sqrt{3 x^2+5 x+2}}{80437500 \sqrt{2 x+3}}+\frac{594851 \sqrt{3 x^2+5 x+2}}{112612500 (2 x+3)^{3/2}}+\frac{594851 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{75075000 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{335723 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{53625000 \sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{(119 x+94) \left(3 x^2+5 x+2\right)^{5/2}}{195 (2 x+3)^{15/2}}-\frac{(8399 x+8901) \left(3 x^2+5 x+2\right)^{3/2}}{64350 (2 x+3)^{11/2}}-\frac{(328339 x+386846) \sqrt{3 x^2+5 x+2}}{7507500 (2 x+3)^{7/2}}+\frac{335723 \sqrt{3 x^2+5 x+2}}{80437500 \sqrt{2 x+3}}+\frac{594851 \sqrt{3 x^2+5 x+2}}{112612500 (2 x+3)^{3/2}}+\frac{594851 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{75075000 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{335723 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{53625000 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(594851*Sqrt[2 + 5*x + 3*x^2])/(112612500*(3 + 2*x)^(3/2)) + (335723*Sqrt[2 + 5*x + 3*x^2])/(80437500*Sqrt[3 + 2*x]) - ((386846 + 328339*x)*Sqrt[2 + 5*x + 3*x^2])/(7507500*(3 + 2*x)^(7/2)) - ((8901 + 8399*x)*(2 + 5*x + 3*x^2)^(3/2))/(64350*(3 + 2*x)^(11/2)) + ((94 + 119*x)*(2 + 5*x + 3*x^2)^(5/2))/(195*(3 + 2*x)^(15/2)) - (335723*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(53625000*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (594851*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(75075000*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",10,6,29,0.2069,1,"{810, 834, 843, 718, 424, 419}"
2606,1,192,0,0.1296203,"\int \frac{(5-x) (3+2 x)^{5/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^(5/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{21} \sqrt{3 x^2+5 x+2} (2 x+3)^{5/2}+\frac{10}{7} \sqrt{3 x^2+5 x+2} (2 x+3)^{3/2}+\frac{1010}{189} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{2525 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{189 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{865 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{21} \sqrt{3 x^2+5 x+2} (2 x+3)^{5/2}+\frac{10}{7} \sqrt{3 x^2+5 x+2} (2 x+3)^{3/2}+\frac{1010}{189} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{2525 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{189 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{865 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(1010*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/189 + (10*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])/7 - (2*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2])/21 + (865*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (2525*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(189*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,5,29,0.1724,1,"{832, 843, 718, 424, 419}"
2607,1,165,0,0.1004536,"\int \frac{(5-x) (3+2 x)^{3/2}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*(3 + 2*x)^(3/2))/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{15} \sqrt{3 x^2+5 x+2} (2 x+3)^{3/2}+\frac{326}{135} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{163 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{2743 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{135 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{15} \sqrt{3 x^2+5 x+2} (2 x+3)^{3/2}+\frac{326}{135} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{163 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{2743 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{135 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(326*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/135 - (2*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])/15 + (2743*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(135*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (163*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{832, 843, 718, 424, 419}"
2608,1,138,0,0.0781303,"\int \frac{(5-x) \sqrt{3+2 x}}{\sqrt{2+5 x+3 x^2}} \, dx","Int[((5 - x)*Sqrt[3 + 2*x])/Sqrt[2 + 5*x + 3*x^2],x]","-\frac{2}{9} \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}+\frac{5 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{101 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2}{9} \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}+\frac{5 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{101 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/9 + (101*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(9*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (5*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(9*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{832, 843, 718, 424, 419}"
2609,1,107,0,0.0545174,"\int \frac{5-x}{\sqrt{3+2 x} \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/(Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2]),x]","\frac{13 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{\sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}","\frac{13 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{\sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"-((Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])) + (13*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",5,4,29,0.1379,1,"{843, 718, 424, 419}"
2610,1,136,0,0.0811321,"\int \frac{5-x}{(3+2 x)^{3/2} \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{26 \sqrt{3 x^2+5 x+2}}{5 \sqrt{2 x+3}}-\frac{\sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{13 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}","-\frac{26 \sqrt{3 x^2+5 x+2}}{5 \sqrt{2 x+3}}-\frac{\sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{13 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}",1,"(-26*Sqrt[2 + 5*x + 3*x^2])/(5*Sqrt[3 + 2*x]) + (13*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5*Sqrt[2 + 5*x + 3*x^2]) - (Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{834, 843, 718, 424, 419}"
2611,1,165,0,0.1042098,"\int \frac{5-x}{(3+2 x)^{5/2} \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{386 \sqrt{3 x^2+5 x+2}}{75 \sqrt{2 x+3}}-\frac{26 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^{3/2}}-\frac{13 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{193 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{386 \sqrt{3 x^2+5 x+2}}{75 \sqrt{2 x+3}}-\frac{26 \sqrt{3 x^2+5 x+2}}{15 (2 x+3)^{3/2}}-\frac{13 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{193 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-26*Sqrt[2 + 5*x + 3*x^2])/(15*(3 + 2*x)^(3/2)) - (386*Sqrt[2 + 5*x + 3*x^2])/(75*Sqrt[3 + 2*x]) + (193*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(25*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (13*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{834, 843, 718, 424, 419}"
2612,1,192,0,0.1324326,"\int \frac{5-x}{(3+2 x)^{7/2} \sqrt{2+5 x+3 x^2}} \, dx","Int[(5 - x)/((3 + 2*x)^(7/2)*Sqrt[2 + 5*x + 3*x^2]),x]","-\frac{9002 \sqrt{3 x^2+5 x+2}}{1875 \sqrt{2 x+3}}-\frac{782 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^{3/2}}-\frac{26 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)^{5/2}}-\frac{391 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{4501 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{625 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{9002 \sqrt{3 x^2+5 x+2}}{1875 \sqrt{2 x+3}}-\frac{782 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^{3/2}}-\frac{26 \sqrt{3 x^2+5 x+2}}{25 (2 x+3)^{5/2}}-\frac{391 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{4501 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{625 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-26*Sqrt[2 + 5*x + 3*x^2])/(25*(3 + 2*x)^(5/2)) - (782*Sqrt[2 + 5*x + 3*x^2])/(375*(3 + 2*x)^(3/2)) - (9002*Sqrt[2 + 5*x + 3*x^2])/(1875*Sqrt[3 + 2*x]) + (4501*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(625*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (391*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(125*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,5,29,0.1724,1,"{834, 843, 718, 424, 419}"
2613,1,197,0,0.1276993,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (139 x+121) (2 x+3)^{5/2}}{3 \sqrt{3 x^2+5 x+2}}+\frac{308}{5} \sqrt{3 x^2+5 x+2} (2 x+3)^{3/2}+\frac{12068}{135} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{6034 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{34174 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{135 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 (139 x+121) (2 x+3)^{5/2}}{3 \sqrt{3 x^2+5 x+2}}+\frac{308}{5} \sqrt{3 x^2+5 x+2} (2 x+3)^{3/2}+\frac{12068}{135} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{6034 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{34174 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{135 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*(3 + 2*x)^(5/2)*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (12068*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/135 + (308*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2])/5 + (34174*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(135*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (6034*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{818, 832, 843, 718, 424, 419}"
2614,1,170,0,0.1022079,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 (139 x+121) (2 x+3)^{3/2}}{3 \sqrt{3 x^2+5 x+2}}+\frac{1660}{27} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{4150 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{3830 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 (139 x+121) (2 x+3)^{3/2}}{3 \sqrt{3 x^2+5 x+2}}+\frac{1660}{27} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}-\frac{4150 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{3830 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*(3 + 2*x)^(3/2)*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (1660*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/27 + (3830*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (4150*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{818, 832, 843, 718, 424, 419}"
2615,1,143,0,0.0779076,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \sqrt{2 x+3} (139 x+121)}{3 \sqrt{3 x^2+5 x+2}}-\frac{350 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{274 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 \sqrt{2 x+3} (139 x+121)}{3 \sqrt{3 x^2+5 x+2}}-\frac{350 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{274 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[3 + 2*x]*(121 + 139*x))/(3*Sqrt[2 + 5*x + 3*x^2]) + (274*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (350*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{818, 843, 718, 424, 419}"
2616,1,137,0,0.0795167,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^(3/2),x]","-\frac{2 \sqrt{2 x+3} (35 x+29)}{\sqrt{3 x^2+5 x+2}}-\frac{94 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{70 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 \sqrt{2 x+3} (35 x+29)}{\sqrt{3 x^2+5 x+2}}-\frac{94 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{70 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[3 + 2*x]*(29 + 35*x))/Sqrt[2 + 5*x + 3*x^2] + (70*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (94*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{820, 843, 718, 424, 419}"
2617,1,141,0,0.0850018,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 \sqrt{2 x+3} (47 x+37)}{5 \sqrt{3 x^2+5 x+2}}-\frac{70 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{94 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}","-\frac{6 \sqrt{2 x+3} (47 x+37)}{5 \sqrt{3 x^2+5 x+2}}-\frac{70 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{94 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}",1,"(-6*Sqrt[3 + 2*x]*(37 + 47*x))/(5*Sqrt[2 + 5*x + 3*x^2]) + (94*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5*Sqrt[2 + 5*x + 3*x^2]) - (70*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",6,5,29,0.1724,1,"{822, 843, 718, 424, 419}"
2618,1,170,0,0.1108555,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}-\frac{908 \sqrt{3 x^2+5 x+2}}{25 \sqrt{2 x+3}}-\frac{94 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}+\frac{454 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3 x^2+5 x+2}}","-\frac{6 (47 x+37)}{5 \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}-\frac{908 \sqrt{3 x^2+5 x+2}}{25 \sqrt{2 x+3}}-\frac{94 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}+\frac{454 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3 x^2+5 x+2}}",1,"(-6*(37 + 47*x))/(5*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2]) - (908*Sqrt[2 + 5*x + 3*x^2])/(25*Sqrt[3 + 2*x]) + (454*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(25*Sqrt[2 + 5*x + 3*x^2]) - (94*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2619,1,197,0,0.1300626,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 (2 x+3)^{3/2} \sqrt{3 x^2+5 x+2}}-\frac{14876 \sqrt{3 x^2+5 x+2}}{375 \sqrt{2 x+3}}-\frac{2516 \sqrt{3 x^2+5 x+2}}{75 (2 x+3)^{3/2}}-\frac{1258 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{7438 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{6 (47 x+37)}{5 (2 x+3)^{3/2} \sqrt{3 x^2+5 x+2}}-\frac{14876 \sqrt{3 x^2+5 x+2}}{375 \sqrt{2 x+3}}-\frac{2516 \sqrt{3 x^2+5 x+2}}{75 (2 x+3)^{3/2}}-\frac{1258 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{7438 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-6*(37 + 47*x))/(5*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2]) - (2516*Sqrt[2 + 5*x + 3*x^2])/(75*(3 + 2*x)^(3/2)) - (14876*Sqrt[2 + 5*x + 3*x^2])/(375*Sqrt[3 + 2*x]) + (7438*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(125*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (1258*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(25*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2620,1,224,0,0.1547366,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^{3/2}} \, dx","Int[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^(3/2)),x]","-\frac{6 (47 x+37)}{5 (2 x+3)^{5/2} \sqrt{3 x^2+5 x+2}}-\frac{426748 \sqrt{3 x^2+5 x+2}}{9375 \sqrt{2 x+3}}-\frac{61468 \sqrt{3 x^2+5 x+2}}{1875 (2 x+3)^{3/2}}-\frac{4124 \sqrt{3 x^2+5 x+2}}{125 (2 x+3)^{5/2}}-\frac{30734 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{625 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{213374 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3125 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{6 (47 x+37)}{5 (2 x+3)^{5/2} \sqrt{3 x^2+5 x+2}}-\frac{426748 \sqrt{3 x^2+5 x+2}}{9375 \sqrt{2 x+3}}-\frac{61468 \sqrt{3 x^2+5 x+2}}{1875 (2 x+3)^{3/2}}-\frac{4124 \sqrt{3 x^2+5 x+2}}{125 (2 x+3)^{5/2}}-\frac{30734 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{625 \sqrt{3} \sqrt{3 x^2+5 x+2}}+\frac{213374 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3125 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-6*(37 + 47*x))/(5*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2]) - (4124*Sqrt[2 + 5*x + 3*x^2])/(125*(3 + 2*x)^(5/2)) - (61468*Sqrt[2 + 5*x + 3*x^2])/(1875*(3 + 2*x)^(3/2)) - (426748*Sqrt[2 + 5*x + 3*x^2])/(9375*Sqrt[3 + 2*x]) + (213374*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3125*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) - (30734*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(625*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2621,1,202,0,0.1286986,"\int \frac{(5-x) (3+2 x)^{9/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(9/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 (139 x+121) (2 x+3)^{7/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 (2571 x+2164) (2 x+3)^{3/2}}{9 \sqrt{3 x^2+5 x+2}}-\frac{59512}{81} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}+\frac{148780 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{81 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{110516 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{81 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 (139 x+121) (2 x+3)^{7/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 (2571 x+2164) (2 x+3)^{3/2}}{9 \sqrt{3 x^2+5 x+2}}-\frac{59512}{81} \sqrt{3 x^2+5 x+2} \sqrt{2 x+3}+\frac{148780 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{81 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{110516 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{81 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*(3 + 2*x)^(7/2)*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (4*(3 + 2*x)^(3/2)*(2164 + 2571*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (59512*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2])/81 - (110516*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(81*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (148780*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(81*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{818, 832, 843, 718, 424, 419}"
2622,1,175,0,0.1082218,"\int \frac{(5-x) (3+2 x)^{7/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(7/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 (139 x+121) (2 x+3)^{5/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{28 (1177 x+1018) \sqrt{2 x+3}}{27 \sqrt{3 x^2+5 x+2}}+\frac{41860 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{31892 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 (139 x+121) (2 x+3)^{5/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{28 (1177 x+1018) \sqrt{2 x+3}}{27 \sqrt{3 x^2+5 x+2}}+\frac{41860 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{31892 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{27 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*(3 + 2*x)^(5/2)*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (28*Sqrt[3 + 2*x]*(1018 + 1177*x))/(27*Sqrt[2 + 5*x + 3*x^2]) - (31892*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (41860*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(27*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{818, 843, 718, 424, 419}"
2623,1,175,0,0.103817,"\int \frac{(5-x) (3+2 x)^{5/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(5/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 (139 x+121) (2 x+3)^{3/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{20 (431 x+364) \sqrt{2 x+3}}{9 \sqrt{3 x^2+5 x+2}}+\frac{11300 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{8620 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 (139 x+121) (2 x+3)^{3/2}}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{20 (431 x+364) \sqrt{2 x+3}}{9 \sqrt{3 x^2+5 x+2}}+\frac{11300 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{8620 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{9 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*(3 + 2*x)^(3/2)*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (20*Sqrt[3 + 2*x]*(364 + 431*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (8620*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(9*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (11300*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(9*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{818, 820, 843, 718, 424, 419}"
2624,1,175,0,0.1071146,"\int \frac{(5-x) (3+2 x)^{3/2}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*(3 + 2*x)^(3/2))/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 \sqrt{2 x+3} (139 x+121)}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 \sqrt{2 x+3} (1689 x+1390)}{9 \sqrt{3 x^2+5 x+2}}+\frac{2956 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{2252 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 \sqrt{2 x+3} (139 x+121)}{9 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 \sqrt{2 x+3} (1689 x+1390)}{9 \sqrt{3 x^2+5 x+2}}+\frac{2956 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{2252 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[3 + 2*x]*(121 + 139*x))/(9*(2 + 5*x + 3*x^2)^(3/2)) + (4*Sqrt[3 + 2*x]*(1390 + 1689*x))/(9*Sqrt[2 + 5*x + 3*x^2]) - (2252*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (2956*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{818, 822, 843, 718, 424, 419}"
2625,1,173,0,0.1028187,"\int \frac{(5-x) \sqrt{3+2 x}}{\left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[((5 - x)*Sqrt[3 + 2*x])/(2 + 5*x + 3*x^2)^(5/2),x]","-\frac{2 \sqrt{2 x+3} (35 x+29)}{3 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 \sqrt{2 x+3} (2139 x+1759)}{15 \sqrt{3 x^2+5 x+2}}+\frac{748 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{2852 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 \sqrt{2 x+3} (35 x+29)}{3 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 \sqrt{2 x+3} (2139 x+1759)}{15 \sqrt{3 x^2+5 x+2}}+\frac{748 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{\sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{2852 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[3 + 2*x]*(29 + 35*x))/(3*(2 + 5*x + 3*x^2)^(3/2)) + (4*Sqrt[3 + 2*x]*(1759 + 2139*x))/(15*Sqrt[2 + 5*x + 3*x^2]) - (2852*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (748*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",7,6,29,0.2069,1,"{820, 822, 843, 718, 424, 419}"
2626,1,175,0,0.1084246,"\int \frac{5-x}{\sqrt{3+2 x} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/(Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 \sqrt{2 x+3} (47 x+37)}{5 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 \sqrt{2 x+3} (2607 x+2152)}{25 \sqrt{3 x^2+5 x+2}}+\frac{916 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}-\frac{3476 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3 x^2+5 x+2}}","-\frac{2 \sqrt{2 x+3} (47 x+37)}{5 \left(3 x^2+5 x+2\right)^{3/2}}+\frac{4 \sqrt{2 x+3} (2607 x+2152)}{25 \sqrt{3 x^2+5 x+2}}+\frac{916 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{5 \sqrt{3 x^2+5 x+2}}-\frac{3476 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3 x^2+5 x+2}}",1,"(-2*Sqrt[3 + 2*x]*(37 + 47*x))/(5*(2 + 5*x + 3*x^2)^(3/2)) + (4*Sqrt[3 + 2*x]*(2152 + 2607*x))/(25*Sqrt[2 + 5*x + 3*x^2]) - (3476*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(25*Sqrt[2 + 5*x + 3*x^2]) + (916*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(5*Sqrt[2 + 5*x + 3*x^2])","A",7,5,29,0.1724,1,"{822, 843, 718, 424, 419}"
2627,1,202,0,0.1314066,"\int \frac{5-x}{(3+2 x)^{3/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{23464 \sqrt{3 x^2+5 x+2}}{125 \sqrt{2 x+3}}+\frac{4 (2409 x+2054)}{25 \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}+\frac{3212 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3 x^2+5 x+2}}-\frac{11732 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3 x^2+5 x+2}}","-\frac{2 (47 x+37)}{5 \sqrt{2 x+3} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{23464 \sqrt{3 x^2+5 x+2}}{125 \sqrt{2 x+3}}+\frac{4 (2409 x+2054)}{25 \sqrt{2 x+3} \sqrt{3 x^2+5 x+2}}+\frac{3212 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{25 \sqrt{3 x^2+5 x+2}}-\frac{11732 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3 x^2+5 x+2}}",1,"(-2*(37 + 47*x))/(5*Sqrt[3 + 2*x]*(2 + 5*x + 3*x^2)^(3/2)) + (4*(2054 + 2409*x))/(25*Sqrt[3 + 2*x]*Sqrt[2 + 5*x + 3*x^2]) + (23464*Sqrt[2 + 5*x + 3*x^2])/(125*Sqrt[3 + 2*x]) - (11732*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(125*Sqrt[2 + 5*x + 3*x^2]) + (3212*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(25*Sqrt[2 + 5*x + 3*x^2])","A",8,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2628,1,229,0,0.157071,"\int \frac{5-x}{(3+2 x)^{5/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{190792 \sqrt{3 x^2+5 x+2}}{1875 \sqrt{2 x+3}}+\frac{61672 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^{3/2}}+\frac{12 (737 x+652)}{25 (2 x+3)^{3/2} \sqrt{3 x^2+5 x+2}}+\frac{30836 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{95396 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{625 \sqrt{3} \sqrt{3 x^2+5 x+2}}","-\frac{2 (47 x+37)}{5 (2 x+3)^{3/2} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{190792 \sqrt{3 x^2+5 x+2}}{1875 \sqrt{2 x+3}}+\frac{61672 \sqrt{3 x^2+5 x+2}}{375 (2 x+3)^{3/2}}+\frac{12 (737 x+652)}{25 (2 x+3)^{3/2} \sqrt{3 x^2+5 x+2}}+\frac{30836 \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{125 \sqrt{3} \sqrt{3 x^2+5 x+2}}-\frac{95396 \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{625 \sqrt{3} \sqrt{3 x^2+5 x+2}}",1,"(-2*(37 + 47*x))/(5*(3 + 2*x)^(3/2)*(2 + 5*x + 3*x^2)^(3/2)) + (12*(652 + 737*x))/(25*(3 + 2*x)^(3/2)*Sqrt[2 + 5*x + 3*x^2]) + (61672*Sqrt[2 + 5*x + 3*x^2])/(375*(3 + 2*x)^(3/2)) + (190792*Sqrt[2 + 5*x + 3*x^2])/(1875*Sqrt[3 + 2*x]) - (95396*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(625*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2]) + (30836*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(125*Sqrt[3]*Sqrt[2 + 5*x + 3*x^2])","A",9,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2629,1,256,0,0.1889037,"\int \frac{5-x}{(3+2 x)^{7/2} \left(2+5 x+3 x^2\right)^{5/2}} \, dx","Int[(5 - x)/((3 + 2*x)^(7/2)*(2 + 5*x + 3*x^2)^(5/2)),x]","-\frac{2 (47 x+37)}{5 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{215096 \sqrt{3 x^2+5 x+2}}{15625 \sqrt{2 x+3}}+\frac{258536 \sqrt{3 x^2+5 x+2}}{3125 (2 x+3)^{3/2}}+\frac{87144 \sqrt{3 x^2+5 x+2}}{625 (2 x+3)^{5/2}}+\frac{4 (2013 x+1858)}{25 (2 x+3)^{5/2} \sqrt{3 x^2+5 x+2}}+\frac{129268 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3125 \sqrt{3 x^2+5 x+2}}-\frac{107548 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{15625 \sqrt{3 x^2+5 x+2}}","-\frac{2 (47 x+37)}{5 (2 x+3)^{5/2} \left(3 x^2+5 x+2\right)^{3/2}}+\frac{215096 \sqrt{3 x^2+5 x+2}}{15625 \sqrt{2 x+3}}+\frac{258536 \sqrt{3 x^2+5 x+2}}{3125 (2 x+3)^{3/2}}+\frac{87144 \sqrt{3 x^2+5 x+2}}{625 (2 x+3)^{5/2}}+\frac{4 (2013 x+1858)}{25 (2 x+3)^{5/2} \sqrt{3 x^2+5 x+2}}+\frac{129268 \sqrt{3} \sqrt{-3 x^2-5 x-2} F\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{3125 \sqrt{3 x^2+5 x+2}}-\frac{107548 \sqrt{3} \sqrt{-3 x^2-5 x-2} E\left(\sin ^{-1}\left(\sqrt{3} \sqrt{x+1}\right)|-\frac{2}{3}\right)}{15625 \sqrt{3 x^2+5 x+2}}",1,"(-2*(37 + 47*x))/(5*(3 + 2*x)^(5/2)*(2 + 5*x + 3*x^2)^(3/2)) + (4*(1858 + 2013*x))/(25*(3 + 2*x)^(5/2)*Sqrt[2 + 5*x + 3*x^2]) + (87144*Sqrt[2 + 5*x + 3*x^2])/(625*(3 + 2*x)^(5/2)) + (258536*Sqrt[2 + 5*x + 3*x^2])/(3125*(3 + 2*x)^(3/2)) + (215096*Sqrt[2 + 5*x + 3*x^2])/(15625*Sqrt[3 + 2*x]) - (107548*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticE[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(15625*Sqrt[2 + 5*x + 3*x^2]) + (129268*Sqrt[3]*Sqrt[-2 - 5*x - 3*x^2]*EllipticF[ArcSin[Sqrt[3]*Sqrt[1 + x]], -2/3])/(3125*Sqrt[2 + 5*x + 3*x^2])","A",10,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2630,1,545,0,0.7840945,"\int \frac{(A+B x) (d+e x)^{3/2}}{\sqrt{a+b x+c x^2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/Sqrt[a + b*x + c*x^2],x]","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (5 A c e-4 b B e+3 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(B \left(-c e (9 a e+13 b d)+8 b^2 e^2+3 c^2 d^2\right)+10 A c e (2 c d-b e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (5 A c e-4 b B e+3 B c d)}{15 c^2}+\frac{2 B (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c}","-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (5 A c e-4 b B e+3 B c d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(B \left(-c e (9 a e+13 b d)+8 b^2 e^2+3 c^2 d^2\right)+10 A c e (2 c d-b e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{15 c^3 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \sqrt{a+b x+c x^2} (5 A c e-4 b B e+3 B c d)}{15 c^2}+\frac{2 B (d+e x)^{3/2} \sqrt{a+b x+c x^2}}{5 c}",1,"(2*(3*B*c*d - 4*b*B*e + 5*A*c*e)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(15*c^2) + (2*B*(d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2])/(5*c) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(10*A*c*e*(2*c*d - b*e) + B*(3*c^2*d^2 + 8*b^2*e^2 - c*e*(13*b*d + 9*a*e)))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(3*B*c*d - 4*b*B*e + 5*A*c*e)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(15*c^3*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,29,0.1724,1,"{832, 843, 718, 424, 419}"
2631,1,452,0,0.3950946,"\int \frac{(A+B x) \sqrt{d+e x}}{\sqrt{a+b x+c x^2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/Sqrt[a + b*x + c*x^2],x]","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (3 A c e-2 b B e+B c d) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} B \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 B \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c}","\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (3 A c e-2 b B e+B c d) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} B \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^2 e \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{2 B \sqrt{d+e x} \sqrt{a+b x+c x^2}}{3 c}",1,"(2*B*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c) + (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(B*c*d - 2*b*B*e + 3*A*c*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*B*Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^2*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{832, 843, 718, 424, 419}"
2632,1,393,0,0.2125769,"\int \frac{A+B x}{\sqrt{d+e x} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]),x]","\frac{\sqrt{2} B \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (B d-A e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}","\frac{\sqrt{2} B \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}-\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (B d-A e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(Sqrt[2]*B*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(B*d - A*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",5,4,29,0.1379,1,"{843, 718, 424, 419}"
2633,1,460,0,0.3430318,"\int \frac{A+B x}{(d+e x)^{3/2} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*Sqrt[a + b*x + c*x^2]),x]","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (B d-A e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (B d-A e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} B \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}","-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (B d-A e) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (B d-A e)}{\sqrt{d+e x} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} B \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c e \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(2*(B*d - A*e)*Sqrt[a + b*x + c*x^2])/((c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(B*d - A*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(e*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*B*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*e*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{834, 843, 718, 424, 419}"
2634,1,587,0,0.623606,"\int \frac{A+B x}{(d+e x)^{5/2} \sqrt{a+b x+c x^2}} \, dx","Int[(A + B*x)/((d + e*x)^(5/2)*Sqrt[a + b*x + c*x^2]),x]","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (B d-A e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(B e (b d-3 a e)-2 A e (2 c d-b e)+B c d^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (B d-A e)}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{a+b x+c x^2} \left(B e (b d-3 a e)-2 A e (2 c d-b e)+B c d^2\right)}{3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}","\frac{2 \sqrt{2} \sqrt{b^2-4 a c} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (B d-A e) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{\sqrt{2} \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(2 A e (2 c d-b e)-B \left(e (b d-3 a e)+c d^2\right)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 e \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{a+b x+c x^2} (B d-A e)}{3 (d+e x)^{3/2} \left(a e^2-b d e+c d^2\right)}-\frac{2 \sqrt{a+b x+c x^2} \left(2 A e (2 c d-b e)-B \left(e (b d-3 a e)+c d^2\right)\right)}{3 \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}",1,"(2*(B*d - A*e)*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(3/2)) + (2*(B*c*d^2 + B*e*(b*d - 3*a*e) - 2*A*e*(2*c*d - b*e))*Sqrt[a + b*x + c*x^2])/(3*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[2]*Sqrt[b^2 - 4*a*c]*(B*c*d^2 + B*e*(b*d - 3*a*e) - 2*A*e*(2*c*d - b*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*Sqrt[b^2 - 4*a*c]*(B*d - A*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*e*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,5,29,0.1724,1,"{834, 843, 718, 424, 419}"
2635,1,678,0,1.0313438,"\int \frac{(A+B x) (d+e x)^{5/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(5/2))/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(2 c (3 A c d-5 a B e)-3 b c (A e+B d)+4 b^2 B e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(b c \left(-29 a B e^2+6 A c d e+3 B c d^2\right)-2 c^2 \left(-9 a A e^2-20 a B d e+3 A c d^2\right)-b^2 c e (6 A e+13 B d)+8 b^3 B e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(2 c (3 A c d-5 a B e)-3 b c (A e+B d)+4 b^2 B e\right)}{3 c^2 \left(b^2-4 a c\right)}+\frac{2 (d+e x)^{3/2} \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","-\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} \left(2 c (3 A c d-5 a B e)-3 b c (A e+B d)+4 b^2 B e\right) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(b c \left(-29 a B e^2+6 A c d e+3 B c d^2\right)-2 c^2 \left(-9 a A e^2-20 a B d e+3 A c d^2\right)-b^2 c e (6 A e+13 B d)+8 b^3 B e^2\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{3 c^3 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 e \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(2 c (3 A c d-5 a B e)-3 b c (A e+B d)+4 b^2 B e\right)}{3 c^2 \left(b^2-4 a c\right)}+\frac{2 (d+e x)^{3/2} \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(2*(d + e*x)^(3/2)*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (2*e*(4*b^2*B*e - 3*b*c*(B*d + A*e) + 2*c*(3*A*c*d - 5*a*B*e))*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])/(3*c^2*(b^2 - 4*a*c)) - (Sqrt[2]*(8*b^3*B*e^2 - b^2*c*e*(13*B*d + 6*A*e) - 2*c^2*(3*A*c*d^2 - 20*a*B*d*e - 9*a*A*e^2) + b*c*(3*B*c*d^2 + 6*A*c*d*e - 29*a*B*e^2))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^3*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) - (2*Sqrt[2]*(c*d^2 - b*d*e + a*e^2)*(4*b^2*B*e - 3*b*c*(B*d + A*e) + 2*c*(3*A*c*d - 5*a*B*e))*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(3*c^3*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,29,0.2069,1,"{818, 832, 843, 718, 424, 419}"
2636,1,530,0,0.5089868,"\int \frac{(A+B x) (d+e x)^{3/2}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*(d + e*x)^(3/2))/(a + b*x + c*x^2)^(3/2),x]","\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b B-2 A c) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c (6 a B e+A b e+b B d)+2 A c^2 d+2 b^2 B e\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}","\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b B-2 A c) \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}+\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(-c (6 a B e+A b e+b B d)+2 A c^2 d+2 b^2 B e\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c^2 \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{d+e x} \left(-x \left(2 c (A c d-a B e)-b c (A e+B d)+b^2 B e\right)-b (a B e+A c d)+2 a c (A e+B d)\right)}{c \left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}",1,"(2*Sqrt[d + e*x]*(2*a*c*(B*d + A*e) - b*(A*c*d + a*B*e) - (b^2*B*e - b*c*(B*d + A*e) + 2*c*(A*c*d - a*B*e))*x))/(c*(b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) + (Sqrt[2]*(2*A*c^2*d + 2*b^2*B*e - c*(b*B*d + A*b*e + 6*a*B*e))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c^2*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(b*B - 2*A*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c^2*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{818, 843, 718, 424, 419}"
2637,1,460,0,0.3844975,"\int \frac{(A+B x) \sqrt{d+e x}}{\left(a+b x+c x^2\right)^{3/2}} \, dx","Int[((A + B*x)*Sqrt[d + e*x])/(a + b*x + c*x^2)^(3/2),x]","-\frac{2 \sqrt{d+e x} (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (-2 a B e+A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b B-2 A c) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","-\frac{2 \sqrt{d+e x} (-2 a B-x (b B-2 A c)+A b)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2}}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (-2 a B e+A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b B-2 A c) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(-2*(A*b - 2*a*B - (b*B - 2*A*c)*x)*Sqrt[d + e*x])/((b^2 - 4*a*c)*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*(b*B - 2*A*c)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{820, 843, 718, 424, 419}"
2638,1,528,0,0.397957,"\int \frac{A+B x}{\sqrt{d+e x} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/(Sqrt[d + e*x]*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 \sqrt{d+e x} \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (-2 a B e+A b e-2 A c d+b B d) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b B-2 A c) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}","\frac{2 \sqrt{d+e x} \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (-2 a B e+A b e-2 A c d+b B d) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} (b B-2 A c) \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{c \sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2}}",1,"(2*Sqrt[d + e*x]*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[a + b*x + c*x^2]) - (Sqrt[2]*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(b*B - 2*A*c)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(c*Sqrt[b^2 - 4*a*c]*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",6,5,29,0.1724,1,"{822, 843, 718, 424, 419}"
2639,1,705,0,0.8467307,"\int \frac{A+B x}{(d+e x)^{3/2} \left(a+b x+c x^2\right)^{3/2}} \, dx","Int[(A + B*x)/((d + e*x)^(3/2)*(a + b*x + c*x^2)^(3/2)),x]","\frac{2 e \sqrt{a+b x+c x^2} \left(b \left(a B e^2+2 A c d e+B c d^2\right)-2 c \left(-3 a A e^2+4 a B d e+A c d^2\right)+b^2 e (B d-2 A e)\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (-2 a B e+A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(b \left(a B e^2+2 A c d e+B c d^2\right)-2 c \left(-3 a A e^2+4 a B d e+A c d^2\right)+b^2 e (B d-2 A e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}","\frac{2 e \sqrt{a+b x+c x^2} \left(b \left(a B e^2+2 A c d e+B c d^2\right)-2 c \left(-3 a A e^2+4 a B d e+A c d^2\right)+b^2 e (B d-2 A e)\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \left(a e^2-b d e+c d^2\right)^2}+\frac{2 \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}+\frac{2 \sqrt{2} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}} (-2 a B e+A b e-2 A c d+b B d) F\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{d+e x} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)}-\frac{\sqrt{2} \sqrt{d+e x} \sqrt{-\frac{c \left(a+b x+c x^2\right)}{b^2-4 a c}} \left(b \left(a B e^2+2 A c d e+B c d^2\right)-2 c \left(-3 a A e^2+4 a B d e+A c d^2\right)+b^2 e (B d-2 A e)\right) E\left(\sin ^{-1}\left(\frac{\sqrt{\frac{b+2 c x+\sqrt{b^2-4 a c}}{\sqrt{b^2-4 a c}}}}{\sqrt{2}}\right)|-\frac{2 \sqrt{b^2-4 a c} e}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{\sqrt{b^2-4 a c} \sqrt{a+b x+c x^2} \left(a e^2-b d e+c d^2\right)^2 \sqrt{\frac{c (d+e x)}{2 c d-e \left(\sqrt{b^2-4 a c}+b\right)}}}",1,"(2*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2]) + (2*e*(b^2*e*(B*d - 2*A*e) - 2*c*(A*c*d^2 + 4*a*B*d*e - 3*a*A*e^2) + b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*Sqrt[a + b*x + c*x^2])/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[d + e*x]) - (Sqrt[2]*(b^2*e*(B*d - 2*A*e) - 2*c*(A*c*d^2 + 4*a*B*d*e - 3*a*A*e^2) + b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2))*Sqrt[d + e*x]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticE[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)^2*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[a + b*x + c*x^2]) + (2*Sqrt[2]*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*Sqrt[(c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)]*Sqrt[-((c*(a + b*x + c*x^2))/(b^2 - 4*a*c))]*EllipticF[ArcSin[Sqrt[(b + Sqrt[b^2 - 4*a*c] + 2*c*x)/Sqrt[b^2 - 4*a*c]]/Sqrt[2]], (-2*Sqrt[b^2 - 4*a*c]*e)/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/(Sqrt[b^2 - 4*a*c]*(c*d^2 - b*d*e + a*e^2)*Sqrt[d + e*x]*Sqrt[a + b*x + c*x^2])","A",7,6,29,0.2069,1,"{822, 834, 843, 718, 424, 419}"
2640,1,591,0,0.687204,"\int (A+B x) (d+e x)^m \left(a+b x+c x^2\right)^3 \, dx","Int[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2)^3,x]","-\frac{(d+e x)^{m+4} \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{e^8 (m+4)}-\frac{3 (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (m+3)}-\frac{(d+e x)^{m+5} \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (m+5)}-\frac{3 c (d+e x)^{m+6} \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8 (m+6)}-\frac{(B d-A e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^3}{e^8 (m+1)}+\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^2 \left(-B e (4 b d-a e)-3 A e (2 c d-b e)+7 B c d^2\right)}{e^8 (m+2)}-\frac{c^2 (d+e x)^{m+7} (-A c e-3 b B e+7 B c d)}{e^8 (m+7)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)}","-\frac{(d+e x)^{m+4} \left(A e (2 c d-b e) \left(-2 c e (5 b d-3 a e)+b^2 e^2+10 c^2 d^2\right)-B \left(3 c e^2 \left(a^2 e^2-8 a b d e+10 b^2 d^2\right)-b^2 e^3 (4 b d-3 a e)-30 c^2 d^2 e (2 b d-a e)+35 c^3 d^4\right)\right)}{e^8 (m+4)}-\frac{3 (d+e x)^{m+3} \left(a e^2-b d e+c d^2\right) \left(B \left(-c d e (8 b d-3 a e)+b e^2 (2 b d-a e)+7 c^2 d^3\right)-A e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (m+3)}-\frac{(d+e x)^{m+5} \left(B \left(-15 c^2 d e (3 b d-a e)+3 b c e^2 (5 b d-2 a e)-b^3 e^3+35 c^3 d^3\right)-3 A c e \left(-c e (5 b d-a e)+b^2 e^2+5 c^2 d^2\right)\right)}{e^8 (m+5)}-\frac{3 c (d+e x)^{m+6} \left(A c e (2 c d-b e)-B \left(-c e (6 b d-a e)+b^2 e^2+7 c^2 d^2\right)\right)}{e^8 (m+6)}-\frac{(B d-A e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^3}{e^8 (m+1)}-\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right)^2 \left(3 A e (2 c d-b e)-B \left(7 c d^2-e (4 b d-a e)\right)\right)}{e^8 (m+2)}-\frac{c^2 (d+e x)^{m+7} (-A c e-3 b B e+7 B c d)}{e^8 (m+7)}+\frac{B c^3 (d+e x)^{m+8}}{e^8 (m+8)}",1,"-(((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^3*(d + e*x)^(1 + m))/(e^8*(1 + m))) + ((c*d^2 - b*d*e + a*e^2)^2*(7*B*c*d^2 - B*e*(4*b*d - a*e) - 3*A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^8*(2 + m)) - (3*(c*d^2 - b*d*e + a*e^2)*(B*(7*c^2*d^3 - c*d*e*(8*b*d - 3*a*e) + b*e^2*(2*b*d - a*e)) - A*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^(3 + m))/(e^8*(3 + m)) - ((A*e*(2*c*d - b*e)*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(5*b*d - 3*a*e)) - B*(35*c^3*d^4 - b^2*e^3*(4*b*d - 3*a*e) - 30*c^2*d^2*e*(2*b*d - a*e) + 3*c*e^2*(10*b^2*d^2 - 8*a*b*d*e + a^2*e^2)))*(d + e*x)^(4 + m))/(e^8*(4 + m)) - ((B*(35*c^3*d^3 - b^3*e^3 + 3*b*c*e^2*(5*b*d - 2*a*e) - 15*c^2*d*e*(3*b*d - a*e)) - 3*A*c*e*(5*c^2*d^2 + b^2*e^2 - c*e*(5*b*d - a*e)))*(d + e*x)^(5 + m))/(e^8*(5 + m)) - (3*c*(A*c*e*(2*c*d - b*e) - B*(7*c^2*d^2 + b^2*e^2 - c*e*(6*b*d - a*e)))*(d + e*x)^(6 + m))/(e^8*(6 + m)) - (c^2*(7*B*c*d - 3*b*B*e - A*c*e)*(d + e*x)^(7 + m))/(e^8*(7 + m)) + (B*c^3*(d + e*x)^(8 + m))/(e^8*(8 + m))","A",2,1,25,0.04000,1,"{771}"
2641,1,330,0,0.3505686,"\int (A+B x) (d+e x)^m \left(a+b x+c x^2\right)^2 \, dx","Int[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2)^2,x]","-\frac{(d+e x)^{m+3} \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{e^6 (m+3)}-\frac{(d+e x)^{m+4} \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{e^6 (m+4)}-\frac{(B d-A e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^6 (m+1)}+\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) \left(-B e (3 b d-a e)-2 A e (2 c d-b e)+5 B c d^2\right)}{e^6 (m+2)}-\frac{c (d+e x)^{m+5} (-A c e-2 b B e+5 B c d)}{e^6 (m+5)}+\frac{B c^2 (d+e x)^{m+6}}{e^6 (m+6)}","-\frac{(d+e x)^{m+3} \left(B \left(-6 c d e (2 b d-a e)+b e^2 (3 b d-2 a e)+10 c^2 d^3\right)-A e \left(-2 c e (3 b d-a e)+b^2 e^2+6 c^2 d^2\right)\right)}{e^6 (m+3)}-\frac{(d+e x)^{m+4} \left(2 A c e (2 c d-b e)-B \left(-2 c e (4 b d-a e)+b^2 e^2+10 c^2 d^2\right)\right)}{e^6 (m+4)}-\frac{(B d-A e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)^2}{e^6 (m+1)}-\frac{(d+e x)^{m+2} \left(a e^2-b d e+c d^2\right) \left(2 A e (2 c d-b e)-B \left(5 c d^2-e (3 b d-a e)\right)\right)}{e^6 (m+2)}-\frac{c (d+e x)^{m+5} (-A c e-2 b B e+5 B c d)}{e^6 (m+5)}+\frac{B c^2 (d+e x)^{m+6}}{e^6 (m+6)}",1,"-(((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)^2*(d + e*x)^(1 + m))/(e^6*(1 + m))) + ((c*d^2 - b*d*e + a*e^2)*(5*B*c*d^2 - B*e*(3*b*d - a*e) - 2*A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^6*(2 + m)) - ((B*(10*c^2*d^3 + b*e^2*(3*b*d - 2*a*e) - 6*c*d*e*(2*b*d - a*e)) - A*e*(6*c^2*d^2 + b^2*e^2 - 2*c*e*(3*b*d - a*e)))*(d + e*x)^(3 + m))/(e^6*(3 + m)) - ((2*A*c*e*(2*c*d - b*e) - B*(10*c^2*d^2 + b^2*e^2 - 2*c*e*(4*b*d - a*e)))*(d + e*x)^(4 + m))/(e^6*(4 + m)) - (c*(5*B*c*d - 2*b*B*e - A*c*e)*(d + e*x)^(5 + m))/(e^6*(5 + m)) + (B*c^2*(d + e*x)^(6 + m))/(e^6*(6 + m))","A",2,1,25,0.04000,1,"{771}"
2642,1,151,0,0.1086173,"\int (A+B x) (d+e x)^m \left(a+b x+c x^2\right) \, dx","Int[(A + B*x)*(d + e*x)^m*(a + b*x + c*x^2),x]","-\frac{(B d-A e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}+\frac{(d+e x)^{m+2} \left(-B e (2 b d-a e)-A e (2 c d-b e)+3 B c d^2\right)}{e^4 (m+2)}-\frac{(d+e x)^{m+3} (-A c e-b B e+3 B c d)}{e^4 (m+3)}+\frac{B c (d+e x)^{m+4}}{e^4 (m+4)}","-\frac{(B d-A e) (d+e x)^{m+1} \left(a e^2-b d e+c d^2\right)}{e^4 (m+1)}-\frac{(d+e x)^{m+2} \left(A e (2 c d-b e)-B \left(3 c d^2-e (2 b d-a e)\right)\right)}{e^4 (m+2)}-\frac{(d+e x)^{m+3} (-A c e-b B e+3 B c d)}{e^4 (m+3)}+\frac{B c (d+e x)^{m+4}}{e^4 (m+4)}",1,"-(((B*d - A*e)*(c*d^2 - b*d*e + a*e^2)*(d + e*x)^(1 + m))/(e^4*(1 + m))) + ((3*B*c*d^2 - B*e*(2*b*d - a*e) - A*e*(2*c*d - b*e))*(d + e*x)^(2 + m))/(e^4*(2 + m)) - ((3*B*c*d - b*B*e - A*c*e)*(d + e*x)^(3 + m))/(e^4*(3 + m)) + (B*c*(d + e*x)^(4 + m))/(e^4*(4 + m))","A",2,1,23,0.04348,1,"{771}"
2643,1,212,0,0.4589733,"\int \frac{(A+B x) (d+e x)^m}{a+b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a + b*x + c*x^2),x]","-\frac{(d+e x)^{m+1} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{(d+e x)^{m+1} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}","-\frac{(d+e x)^{m+1} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{(d+e x)^{m+1} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}",1,"-(((B - (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(1 + m))) - ((B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(1 + m))","A",4,2,25,0.08000,1,"{830, 68}"
2644,1,536,0,3.4937373,"\int \frac{(A+B x) (d+e x)^m}{\left(a+b x+c x^2\right)^2} \, dx","Int[((A + B*x)*(d + e*x)^m)/(a + b*x + c*x^2)^2,x]","\frac{c (d+e x)^{m+1} \left(e m (-2 a B e+A b e-2 A c d+b B d)-\frac{2 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(a A e^2 (1-m)+a B d e m+A c d^2\right)+b^2 (-e) (A e m+B d (2-m))}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}+\frac{c (d+e x)^{m+1} \left(\frac{2 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(a A e^2 (1-m)+a B d e m+A c d^2\right)+b^2 (-e) (A e m+B d (2-m))}{\sqrt{b^2-4 a c}}+e m (-2 a B e+A b e-2 A c d+b B d)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \left(a e^2-b d e+c d^2\right)}+\frac{(d+e x)^{m+1} \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}","\frac{c (d+e x)^{m+1} \left(e m (-2 a B e+A b e-2 A c d+b B d)-\frac{2 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(A \left(a e^2 (1-m)+c d^2\right)+a B d e m\right)+b^2 (-e) (A e m+B d (2-m))}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}+\frac{c (d+e x)^{m+1} \left(\frac{2 b \left(a B e^2+2 A c d e+B c d^2\right)-4 c \left(A \left(a e^2 (1-m)+c d^2\right)+a B d e m\right)+b^2 (-e) (A e m+B d (2-m))}{\sqrt{b^2-4 a c}}+e m (-2 a B e+A b e-2 A c d+b B d)\right) \, _2F_1\left(1,m+1;m+2;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+1) \left(b^2-4 a c\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right) \left(a e^2-b d e+c d^2\right)}+\frac{(d+e x)^{m+1} \left(-A \left(2 a c e+b^2 (-e)+b c d\right)+c x (-2 a B e+A b e-2 A c d+b B d)+a B (2 c d-b e)\right)}{\left(b^2-4 a c\right) \left(a+b x+c x^2\right) \left(a e^2-b d e+c d^2\right)}",1,"((d + e*x)^(1 + m)*(a*B*(2*c*d - b*e) - A*(b*c*d - b^2*e + 2*a*c*e) + c*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*x))/((b^2 - 4*a*c)*(c*d^2 - b*d*e + a*e^2)*(a + b*x + c*x^2)) + (c*(e*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*m - (2*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2) - b^2*e*(B*d*(2 - m) + A*e*m) - 4*c*(A*c*d^2 + a*A*e^2*(1 - m) + a*B*d*e*m))/Sqrt[b^2 - 4*a*c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/((b^2 - 4*a*c)*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m)) + (c*(e*(b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*m + (2*b*(B*c*d^2 + 2*A*c*d*e + a*B*e^2) - b^2*e*(B*d*(2 - m) + A*e*m) - 4*c*(A*c*d^2 + a*A*e^2*(1 - m) + a*B*d*e*m))/Sqrt[b^2 - 4*a*c])*(d + e*x)^(1 + m)*Hypergeometric2F1[1, 1 + m, 2 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((b^2 - 4*a*c)*(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + m))","A",5,3,25,0.1200,1,"{822, 830, 68}"
2645,1,212,0,0.3094653,"\int \frac{(A+B x) (d+e x)^{1+m}}{a+b x+c x^2} \, dx","Int[((A + B*x)*(d + e*x)^(1 + m))/(a + b*x + c*x^2),x]","-\frac{(d+e x)^{m+2} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+2;m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+2) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{(d+e x)^{m+2} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \, _2F_1\left(1,m+2;m+3;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+2) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}","-\frac{(d+e x)^{m+2} \left(B-\frac{b B-2 A c}{\sqrt{b^2-4 a c}}\right) \, _2F_1\left(1,m+2;m+3;\frac{2 c (d+e x)}{2 c d-\left(b-\sqrt{b^2-4 a c}\right) e}\right)}{(m+2) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}-\frac{(d+e x)^{m+2} \left(\frac{b B-2 A c}{\sqrt{b^2-4 a c}}+B\right) \, _2F_1\left(1,m+2;m+3;\frac{2 c (d+e x)}{2 c d-\left(b+\sqrt{b^2-4 a c}\right) e}\right)}{(m+2) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}",1,"-(((B - (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (2*c*(d + e*x))/(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)])/((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(2 + m))) - ((B + (b*B - 2*A*c)/Sqrt[b^2 - 4*a*c])*(d + e*x)^(2 + m)*Hypergeometric2F1[1, 2 + m, 3 + m, (2*c*(d + e*x))/(2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)])/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(2 + m))","A",4,2,27,0.07407,1,"{830, 68}"
2646,1,349,0,0.2659785,"\int (A+B x) (d+e x)^{-3-2 p} \left(a+b x+c x^2\right)^p \, dx","Int[(A + B*x)*(d + e*x)^(-3 - 2*p)*(a + b*x + c*x^2)^p,x]","\frac{(B d-A e) (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+1) \left(a e^2-b d e+c d^2\right)}-\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p (-2 a B e+A b e-2 A c d+b B d) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 (2 p+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}","\frac{(B d-A e) (d+e x)^{-2 (p+1)} \left(a+b x+c x^2\right)^{p+1}}{2 (p+1) \left(a e^2-b d e+c d^2\right)}-\frac{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) (d+e x)^{-2 p-1} \left(a+b x+c x^2\right)^p (-2 a B e+A b e-2 A c d+b B d) \left(\frac{\left(\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right)}{\left(-\sqrt{b^2-4 a c}+b+2 c x\right) \left(2 c d-e \left(\sqrt{b^2-4 a c}+b\right)\right)}\right)^{-p} \, _2F_1\left(-2 p-1,-p;-2 p;-\frac{4 c \sqrt{b^2-4 a c} (d+e x)}{\left(2 c d-\left(b+\sqrt{b^2-4 a c}\right) e\right) \left(b+2 c x-\sqrt{b^2-4 a c}\right)}\right)}{2 (2 p+1) \left(2 c d-e \left(b-\sqrt{b^2-4 a c}\right)\right) \left(a e^2-b d e+c d^2\right)}",1,"((B*d - A*e)*(a + b*x + c*x^2)^(1 + p))/(2*(c*d^2 - b*d*e + a*e^2)*(1 + p)*(d + e*x)^(2*(1 + p))) - ((b*B*d - 2*A*c*d + A*b*e - 2*a*B*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)*(d + e*x)^(-1 - 2*p)*(a + b*x + c*x^2)^p*Hypergeometric2F1[-1 - 2*p, -p, -2*p, (-4*c*Sqrt[b^2 - 4*a*c]*(d + e*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x))])/(2*(2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(c*d^2 - b*d*e + a*e^2)*(1 + 2*p)*(((2*c*d - (b - Sqrt[b^2 - 4*a*c])*e)*(b + Sqrt[b^2 - 4*a*c] + 2*c*x))/((2*c*d - (b + Sqrt[b^2 - 4*a*c])*e)*(b - Sqrt[b^2 - 4*a*c] + 2*c*x)))^p)","A",2,2,29,0.06897,1,"{806, 726}"